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Balanced-budget rules and risk-sharing in a fiscal union
Accepted Manuscript
Balanced-Budget Rules and Risk-sharing in a Fiscal Union# Vladimir V Dashkeev , Stephen J Turnovsky PII: DOI: Reference:
S0164-0704(18)30161-7 10.1016/j.jmacro.2018.06.008 JMACRO 3040
To appear in:
Journal of Macroeconomics
Received date: Revised date: Accepted date:
17 April 2018 19 June 2018 21 June 2018
Please cite this article as: Vladimir V Dashkeev , Stephen J Turnovsky , Balanced-Budget Rules and Risk-sharing in a Fiscal Union# , Journal of Macroeconomics (2018), doi: 10.1016/j.jmacro.2018.06.008
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Balanced-Budget Rules and Risk-sharing in a Fiscal Union§ Stephen J. Turnovsky∗∗
Revised version June 2018 Abstract
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Vladimir V. Dashkeev∗
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This paper addresses the following question: What are the implications of the asymmetry of balanced-budget rules for interregional risk sharing in a fiscal union? We investigate our research question in a two-region, open economy DSGE model that is augmented with the public-sector features of a federal state. The analysis demonstrates that the asymmetry of balanced-budget rules is detrimental for the risk sharing in the union. The degree of risk sharing is a function of the public good productivity, specification of the technology process, and distribution of productivity shocks in the fiscal union.
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Keywords: balanced-budget rule, fiscal federalism, fiscal union, occasionally binding constraints, productive public expenditures, risk sharing JEL codes: E62, H60, H74, H77
§ The authors gratefully acknowledge comments they received from Alberto Bisin, Yu -chin Chen,
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Mikhail Dmitriev, Fabio Ghironi, Luca Guerrieri, Levis Kochin, Pavel Krivenko, David Lagakos, Oksana Leukhina, Federico Mandelman, B. Ravikumar, Alexander Rodivilov, Antonio Rodriguez-Lopez, MuJeung Yang, and participants of the Association of Public Economic Theory conference in Rio de Janeiro, July 2016 and MTI seminars at the University of Washington. The suggestions of a referee are also appreciated. ∗ Seattle University, Department of Economics, Albers School of Business and Economics, Pigott Building 316B, Seattle, WA 98122. Email: [email protected]. ** University of Washington, Department of Economics, Savery Hall 343, Box 353330, Seattle, WA, 98195. Email: [email protected].
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1.
Introduction
Federal states can grant varying degrees of fiscal sovereignty to their constituent members. These powers may range from delegating substantial fiscal autonomy to their member states, such as the
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United States, to unions having a powerful centralized supra-regional authority, such as Australia. Numerous important questions arise in considering the structure of governance, particularly with regard to the former scenario. This paper addresses the following issue: What are the implications of the asymmetry of balanced-budget rules for interregional risk-sharing in a fiscal union? This question is motivated by two stylized facts characterizing the U.S. as a fiscal union: (i) the asymmetric public
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borrowing limits across U.S. states and (ii) the heterogeneous structure of government expenditures across different levels of the union government.1 We view it as an important issue, since risk-sharing is one of the principal criteria that shape the choice of national governance systems and design of stabilization policies. In a union with initially identical interregional allocations, a deterioration of
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risk-sharing will likely have the undesirable effect of increasing inequality across the regions. The asymmetry of public borrowing limits adopted by state governments is institutionalized
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as state-specific, balanced-budget rules, and presents one of the salient features of the U.S. federal system.2 To render the analysis of these balanced-budget rules tractable, states have typically been
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classified into one of the following two categories: (i) states having strict balanced-budget rules and (ii) those with more flexible rules. This dichotomy is based on the Advisory Commission on
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Intergovernmental Relations index, ACIR (1987), which takes into account characteristics of the rules in each state.3 According to the accepted taxonomy in the fiscal federalism literature, states
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having an ACIR index between 7 and 10 are classified as having strict borrowing rules, while those with an index between 0 and 6 have more flexible rules. The latter group consists of 13, mostly
Henceforth, the terms “balanced-budget rules” and “borrowing limits” are used interchangeably to refer to the set of institutional constraints on the government’s ability to incur a budget deficit. 2 The ability of the federal government to borrow is taken as a given in the present study. 3 The index assumes values from 0 to 10, so that Vermont (the only state without a balanced-budget requirement) is at 0, while the states that require their budgets to be balanced at the end of the budgetary period are at 10. States receive intermediate values according to other characteristics of their balanced-budget rules, such as provisions for carrying debt over to future budget periods, and if so, then for how long, or whether the borrowing limits are constitutional or statutory. Additional details about the balanced-budget rules in the U.S. are presented in Appendix A. 1
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large, states (Figure 1). Cumulatively, these states having less stringent balanced-budget rules produced 46.2% of the U.S. GDP between 1977 and 2000.4,5 As discussed below, the states’ balanced-budget rules have real effects on the states’ fiscal policy, especially their stabilization policy over business cycles. The second inherent aspect of the U.S. fiscal federalism system incorporated in this study is
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the asymmetric provision of different types of public expenditures by the federal government and state governments, respectively. Centralization makes it possible to achieve substantial economies of scale in the provision of certain public consumption goods, such as national defense. Hence, this function is performed by the federal authorities. The provision of local, predominantly productive, public
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goods is usually delegated to regional governments, because decentralization is preferable in addressing local needs. These expenditures consist primarily of outlays for infrastructure and education-related items.6 In the U.S., more than two-thirds of public consumption goods are supplied by the federal government and over three-quarters of public productive goods are provided by state
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governments (Table 1).
Hence, the U.S. presents a natural case for the study of the asymmetry of borrowing limits in
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a fiscal union with heterogeneous public goods. To our knowledge, the economic consequences of these two important and empirically relevant forms of heterogeneity – asymmetry of the borrowing
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limits and of the public goods provision – have not been addressed within an integrated analytical framework. We investigate their economic consequences in a microbased, dynamic market-clearing
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general equilibrium model. Specifically, we augment the open economy model by Backus, Kehoe,
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Unless otherwise noted, this study uses 1977–2000 data due to the limited availability of state-level public finance and income series. Annual U.S. Census data start in 1977 and the BEA series for Gross State Product have a break in 2000 due to a transition from the SIC to NAICS. 5 Following the literature, Alaska and Hawaii are omitted from the present analysis due to their idiosyncratic characteristics. Alaska has persistent surpluses driven by its small economic size and dependence on oil production, while Hawaii has a unique public education system. Both states have strict balanced-budget rules. The re-estimated share of the cumulative output by the states with less stringent balanced-budget rules is reduced slightly to 45.7%. 6 The term “productive public goods” may assume different meanings. The seminal work of Aschauer (1989) operates with a narrow definition of productive public goods. It includes only investment in “core infrastructure,” i.e., highways, railroads, seaports, airports, utilities, etc. Such an approach remains common throughout the theoretical literature, e.g., Turnovsky and Fisher (1995) or, more recently, Leeper, Walker, and Yang (2010), and Leduc and Wilson (2013). Yet, a broad definition of productive public goods that includes expenditures that enhance the productivity of the private sector and encourage private investment suggests that Aschauer’s definition should be expanded. For example, models with human capital that treat education as an important factor of development suggest that expenditures on education should be included in the category of productive public goods. See, e.g., Lucas (1988) for a theoretical approach and Mankiw, Romer, and Weil (1992), for an empirical.
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and Kydland (1992) to include the public-sector features of a federal state, in which the provision of consumption and productive public goods receives special attention, as in Turnovsky and Fisher (1995), and more recently by Economides et. al. (2011) and Chatterjee and Ghosh (2011). The federal state we consider comprises two regions: “Rigid” and “Flexible”. The regional economies are identical (in terms of their size, technology, and preferences), with the exception of
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fiscal policy, specifically their ability to borrow or lack thereof. Each region is populated by a representative household and a representative firm. Labor mobility is prohibited between the regions, but there are no barriers to interregional capital mobility.7 We employ this framework to analyze the transmission of productivity shocks in the union, as well as to study the implications of the
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asymmetry for interregional consumption risk-sharing and welfare.
The analysis of the transmission mechanism of productivity shocks reveals the contrasting dynamic responses of the union members, highlighting how the asymmetric balanced-budget rules endogenously create heterogeneous allocations, even in response to common aggregate shocks.
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Consequently, the asymmetric public borrowing limits impair interregional risk-sharing. Following an adverse aggregate productivity shock, the region with no borrowing limit stabilizes its economy
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faster, by attracting resources from the region constrained by the balanced budget requirement. The intuition for this result is straightforward. The driving force behind the heterogeneous
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responses across union members to an aggregate productivity shock is the asymmetric dynamics of the regional public expenditures. Following the realization of the shock, the declining supply of the
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productive public good from the Rigid government, combined with the steady supply from Flexible, yields interregional differentials of marginal productivities. These interregional marginal
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productivity ratios are tilted in favor of Flexible, which leads to a shift of resources to the more productive jurisdiction in the union, thereby adversely affecting risk-sharing. The state-specific provision of productive public goods dwindles in the region with the restriction on public borrowing,
7 This treatment of regions serves to sharpen the asymmetry of interregional allocations created by heterogeneous balanced-budget rules. Labor supply is treated as fixed to contrast the effects of borrowing limits and government expenditure composition on the time paths of capital accumulation and welfare. If not shut down, the negative wealth effect channel would increase the supply of labor and, subsequently, capital stock and output, and then ultimately narrow the regional differences. Relaxing the assumption of the symmetric technology could either amplify or mitigate the interregional differences induced by the asymmetric fiscal policy. The exact outcome would depend on the direction of the technological asymmetry and the relative productivity of the regions.
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which amplifies the interregional differences. This mechanism contrasts with that of standard models, such as Backus, Kehoe, and Kydland (1992), where resources are shifted in response to idiosyncratic shocks. The nature of the regional budget balance requirements, in conjunction with the productivity of public capital, are important determinants of risk-sharing in the fiscal union, and for the relative welfare of
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the agents within its respective regions. Irrespective of its source, a sustained negative productivity shock results in lifetime welfare losses, though with markedly different impacts on the two regions. In all cases, the impact on the Flexible region is essentially independent of the productivity of public capital. This is because, by being able to borrow, Flexible has the ability to offset the negative effects of the decline in
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productivity. In contrast, the impact on welfare in the Rigid region is highly sensitive to the productivity of public capital. This is because of the balanced budget requirement which forces it to cut back on the provision of its public good, so that the more productive is government spending, the greater the decline in productivity, thereby exacerbating the adverse effects on lifetime welfare. Numerical simulations that we
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undertake suggest that in the extreme case where government capital is highly productive, the welfare loss experienced by Flexible following an aggregate (economy-wide) decline in productivity is only around
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60% of that in Rigid. However, the ratio of the Flexible region’s loss to that of the Rigid region increases as the productivity of public capital declines, and if the latter is extremely low, Flexible’s decline in
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welfare may even slightly exceed that experienced by Rigid. In the absence of spillovers, the welfare costs of regional (idiosyncratic) adverse productivity
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shocks are borne almost entirely by the region in which they occur, and vary inversely with the degree of persistence. In the case of Rigid the welfare costs increase with the productivity of public capital, while in
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Flexible they are essentially invariant with respect to this factor. While the impact on the other region is extremely weak, our simulations suggest that if the degree of persistence is sufficiently high, a productivity decline in one region may actually lead to a slight welfare gain in the other region. The existence of technological spillovers across the two regions leads to a sharing of the welfare costs between them. In the case where the adverse productivity shock occurs in Flexible, as the productivity of public capital increases, the welfare costs are increasingly shifted to Rigid, to the point where if the productivity is sufficiently high, the welfare costs are shared approximately equally. Thus to summarize: the degree 5
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of risk-sharing in the fiscal union is a function of the public good productivity, the nature of the technology process, and distribution of productivity shocks in the union. The remainder of the paper is structured as follows. Section 2 briefly relates our paper to the existing relevant literature. Sections 3 and 4 describe the economic environment and the resulting equilibrium conditions. The calibration of the key parameters is summarized in Section 5. In Section
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6, the effects of temporary, adverse productivity shocks of different types on regional performance are analyzed. Additionally, the implications of public good productivity for risk-sharing are considered. Section 7 concludes. An Appendix provides additional technical details. These include: (A) additional information regarding balanced-budget rules in the U.S; (B) derivation of the equation for
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net regional asset accumulation; (C) summary of the equilibrium conditions of the model; and (D) some simulations obtained under alternative assumptions regarding technology process specifications. 2.
Relationship to the literature
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This paper sets itself apart from the existing literature by its simultaneous focus on regional
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integration, the composition of public goods, and the nature of the fiscal rules imposed on the regions. The optimum currency area literature provides the theoretical foundation for regional integration. Seminal works, including those of Mundell (1961), McKinnon (1963), and Kenen (1969),
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motivate integration through the improved ability of the union, rather than individual states, to
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withstand different types of adverse shocks. Mundell (1961) and McKinnon (1963) argue that monetary unions are optimal in the face of aggregate shocks. However, if the union economy is
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affected by member-specific shocks, no benefit is accrued from monetary integration. Kenen (1969) points out the desirability of complementing monetary integration with fiscal unification. He supports his argument with the U.S. experience in which transfers from federal to state governments serve as interregional fiscal risk-sharing. Results of the present analysis can be interpreted as an extension of Kenen (1969), in that members of a fiscal union can benefit from their membership after a realization of aggregate shocks. Recent theoretical studies of fiscal unions continue to analyze the conditions for unification, 6
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from the standpoint of the risk-sharing improvement. See, e.g., Farhi and Werning (7) and Dmitriev and Hoddenbagh (2015). However, such analyses are undertaken in symmetric environments, in which aggregate shocks would not yield interesting dynamics and there would be no benefit of the fiscal unification in the absence of idiosyncratic shocks. Both studies abstract from public borrowing limits as well as productive public goods.
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Several empirical studies of fiscal unions focus on the channels of risk-sharing. Asdrubali, Sorensen, and Yosha (1996) find that 13% of output shocks are smoothed by the U.S. federal government through taxes, transfers, and grants, while about two-thirds of the shocks are accommodated by capital and credit markets. A similar relative importance of the consumption-
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smoothing channels is found in other federations, e.g., Hepp and von Hagen (2013) obtain close results for unified Germany. Sorensen and Yosha (1998) examine consumption smoothing in the European Union and find that the transfers among its eight oldest members smooth at most 7% of output shocks.
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The literature studying the structural forms of the composition of public expenditure is relatively sparse. To the best of our knowledge, all such studies model public expenditures on the part
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of the general government in a unitary state and without consideration of public borrowing limits. For example, Turnovsky and Fisher (1995) consider heterogeneous public goods. They introduce both
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productive and consumption public expenditures and analyze macroeconomic effects of temporary and permanent changes in the expenditures on capital accumulation and welfare.8
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Leduc and Wilson (2013) depart from the tradition of modeling the general government public expenditure in unitary states. They consider a two-region model of the U.S., with the provision of a
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productive public good, highway infrastructure. Short- to medium-run effects of the productive public good provision generated by their structural model match the empirical responses of the key macroeconomic variables. The effects of balanced-budget rules have been previously studied in the context of unitary economies. Stockman (2001) analyzes the potential welfare effects of the balanced-budget rule proposed in 1995 for the U.S. Federal Government. Aiyagari, Marcet, Sargent, and Seppala (2002) 8
For example, Agenor (2013) provides a comprehensive study of different types of public goods.
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focus on the cost of debt service in a unitary economy, in which the government is subject to a borrowing limit. They find that a decrease in the stock of public debt increases welfare and argued for the accumulation of reserves to reduce the costs of future stabilization policies. Azzimonti, Battaglini, and Coate (2010) study the political economy of balanced-budget rules, explicitly modeling the election process. They find that borrowing limits increase welfare through the
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elimination of pork-barrel spending.
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3.
Analytical framework
This section sets out a general description of the underlying economic environment, which augments Backus et al. (1992) to include the key public-sector features of a federal state. Special attention is paid to the provision of consumption and productive public goods, as in Turnovsky and Fisher (1995) and
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more recently Economides et al. (2011). The economy comprises households, firms, and two levels of government: federal and regional. Following this description of the environment, the implied equilibrium conditions for the economy are derived. 3.1
Economic environment
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As noted, we consider a federal state that comprises two regions: Rigid and Flexible. The regional economies are identical, with the exception of their respective fiscal policies. Each region is inhabited by a representative household and a representative firm. Labor is immobile between the regions, but there are no impediments to interregional capital mobility.9
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The government in the federal state consists of two levels. The first level is represented by the Federal government, which collects capital income and labor income taxes from both regions, and
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provides a public consumption good equally available to both regions. Regional governments represent the second level of governance. Each regional government provides a productive public
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good to the local representative firm financed primarily by a consumption tax collected from the residents of its own region. In addition to using the productive public good, firms employ private
regions.
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capital and labor to manufacture a consumption-investment good that is homogeneous across the
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Households in both regions have access to one-period, risk-free private and public bonds. The
public bonds can be issued by either the federal or regional authorities. However, region-specific borrowing limits are introduced to ensure the model’s consistency with the stylized facts that characterize the heterogeneous balanced-budget rules adopted by the U.S. states. Accordingly, only one of the regions, Flexible, has the authority to borrow, while the Rigid region has a zero-borrowing
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See footnote 7 for the motivation for these assumptions.
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limit. Since all types of bonds are risk-free, the asset markets are incomplete. In describing the model we shall focus on Rigid. Unless otherwise stated, the Flexible region’s environment is symmetric; variables pertaining to the Flexible region are indicated by asterisks. Firms
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3.2
The representative firm hires labor, Lt , supplied inelastically, from its region. It employs private capital, K, and uses the stock of region-specific publicly provided physical capital, KRG, to produce a homogeneous output good, Y, in accordance with the Cobb-Douglas production function (1):
0 1
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Yt Zt Kt L1 ( K RG,t )G ,
(1)
Output also depends on the total factor productivity, Z t , which is affected by the realization of a technology shock. Total factor productivities of the two regions are generated by the following
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autoregressive processes:
ZZ Zt 1 t . Z Zt*1 t* *
(2)
*
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Zt Z Z * t Z *Z
Thus, in general, the technology shocks across the two regions are interdependent, giving rise to
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regional spillovers. Section 5 below, imposes more structure on the matrix Φ in (2), drawn from
3.3
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empirical evidence.
Households
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The representative household in the Rigid region derives instantaneous utility from private and public consumption goods, C and CG, according to an isoelastic utility function (3), where 0 is the inverse of the intertemporal elasticity of substitution for the private consumption good and
G 0 pertains to the public consumption good. Ct1 CG1 G . 1 1 G 10
(3)
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3.4
Federal Government
The Federal government collects capital and labor income taxes at uniform rates, K and L , from both regions, and provides fixed amounts of the public consumption good, CG, available equally to residents of both regions. In the absence of any borrowing limits imposed on it, the Federal
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government issues one-period, risk-free bonds, BFG, that pay an interest rate RFG,t at the beginning of period t. The federal bonds are available for purchase to households of both regions. The federal 10
* authorities also impose lump-sum taxes on the residents of each region, TFG and TFG . Thus, the
budget constraint of the Federal government is expressed by the following relationship: * * BFG ,t 1 BFG ,t 1 CG (1 RFG ,t )( BFG ,t BFG ,t )
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* K ( Rt Kt Rt* Kt* ) L (Wt L Wt * L* ) TFG ,t TFG ,t
(4)
where R, R* are the returns to private capital, W ,W * are the wage rates, both determined below. 3.5
Regional Governments
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Both regional governments collect consumption taxes at a uniform rate, C , from the residents of
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their respective regions, and provide a productive public good, IRG, to the local representative firm. * They are also assumed to levy regional lump-sum taxes, TRG and TRG respectively. Although many
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U.S. states collect income taxes in addition to, or instead of, consumption taxes, we restrict the regions to collect consumption (and lump-sum) taxes only. The reason for imposing this restriction
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is to ensure that the results of our study reflect the role of the asymmetric balanced-budget rules rather than also reflecting differences in the interregional tax-systems.11
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The regional governments’ borrowing limits, and hence their budget constraints, are regionspecific. The form of these constraints is based on the findings of empirical studies that confirm the real (and asymmetric) effects of balanced-budget rules across different types of states on their fiscal policy. Using data from the early 1990s, GAO (1993) summarize the states’ responses to prospective
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The lump-sum taxes may be negative, in which case they may be interpreted as transfers, such as welfare and social security payments. 11 We acknowledge that the asymmetry of regional tax structures is important for the macroeconomic performance of the union; thus, we study its implications in a companion paper.
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deficits. In those cases in which the deficit was estimated after the budget had been passed by the legislature, only 4% of the deficit reduction was achieved via revenue increases, while 60% was achieved by sequestration. The remaining 36% of the prospective deficits were accounted for by “adjustment of budget execution,” including short-term borrowing.12 Poterba (1994, 1995) and Bohn and Inman (1996) confirm that increasing tax revenue is the
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least common response on the part of state governments to the negative shocks. States with strict balanced-budget rules are less likely to borrow, and most often resort to a reduction of their public expenditures. States with less stringent rules rely on borrowing to maintain their public spending at the pre-shock level. Bayoumi and Eichengreen (1995) show that the cyclical responsiveness of the
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states is affected negatively by the stringency of their balanced-budget rules. In this sense, the fiscal policy of the states with strict balanced-budget rules amplifies business cycle downturns, and therefore leads to destabilization, while the fiscal policy of those states with less stringent balanced-budget rules mitigates economic downturns.
In the case of windfall tax revenues, the behavior of the two types of the states differs as
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well.13 Although both groups of states change their expenditures little during expansions, their use of
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the unplanned tax revenues varies. States with strict balanced-budget rules direct the budget surplus to finance lump-sum transfers. At the same time, states with less stringent balanced-budget rules also
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use the windfall revenues to reduce their debt burdens. These facts from the data and empirical studies motivate the construction of the model in
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which the balanced-budget rules have real effects. Thus, using Poterba’s (7) terminology, the present analysis contributes to the “public choice view,” as opposed to the “institutional irrelevance”
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hypothesis. The former treats institutional constraints as important factors of fiscal policy, while the latter suggests that such limitations can be circumvented effectively and therefore do not affect policymakers’ actions. In our stylized model, the government of the Rigid region has a zero-borrowing limit and the
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Besides borrowing, “adjustment of budget execution” refers to a number of temporary measures, including the use of rainy-day funds and various accounting gimmicks, such as interfund transfers and deferrals of payments. 13 See, e.g., Poterba (1995) and Sorensen and Yosha (2001).
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public good provision is thus determined only by current tax revenues of the region and is exogenously capped at the steady-state level, I RG :
C Ct TRG ,t I RG ,t , (5)
I RG ,t min{ C Ct , I RG }.
The Flexible region’s government is unconstrained by a borrowing limit and therefore can F
, where
RG F
denotes “Flexible Regional Government”, to
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issue one-period, risk-free bonds, BRG
maintain the provision of the productive public good independently of transitory shocks to its revenues, that is at the exogenously predetermined steady-state level. The interest rate RRG F,t is paid to the bondholders at the beginning of the period. Accordingly, the budget constraint of the Flexible
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government takes the following form:
* * * * C Ct* BRG F ,t 1 BRG F ,t 1 TRG ,t I RG (1 RRG F ,t ) BRG F ,t (1 RRG F ,t ) BRG F ,t ,
(6)
* where BRG F and BRG F refer to the bond holdings of the representative households in the Rigid and
4.1
Equilibrium Conditions Firms
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4.
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Flexible regions, respectively.
The representative firm in the Rigid region maximizes its profits, which in the absence of adjustment
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costs, yields the standard optimality conditions (7a) and (7b), equating the wage and the return to
W (1 )Yt L ,
(7a)
Rt Yt Kt .
(7b)
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private capital to marginal productivities of labor and capital stock, respectively:
The rate of accumulation of the private capital stock is standard, where δ ∈ (0, 1) denotes the depreciation rate:
Kt It (1 ) Kt 1 . Analogous conditions apply to the firms in the Flexible region. 4.2
Households 13
(7c)
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The representative household in the Rigid region chooses its rates of consumption, and accumulation of private capital, and holdings of private and public (Federal and Flexible) bonds, to maximize its intertemporal utility (8), where β ∈ (0, 1) is a subjective discount factor, subject to the budget constraint (9):
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C 1 C 1 G max Ct , Kt1 , Bt1 , BFG ,t 1 , BRG F ,t 1 Et t t G t 0 1 1 G subject to
(8)
Kt 1 Bt 1 BFG ,t 1 BRG F ,t 1 (1 L )Wt L (1 C )Ct
[(1 K ) Rt (1 )]Kt (1 RPRI ,t ) Bt (1 RFG ,t ) BFG ,t (1 RRG F ,t ) BRG F ,t
(9)
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( Bt 1 ) 2 ( BFG ,t 1 ) 2 ( BRG F ,t 1 ) 2 TFG ,t TRG ,t T ,t . 2 2 2
The budget constraint asserts that the household allocates its disposable labor and capital income and returns on its bond holdings between consumption spending, the accumulation of productive private capital, and purchases of the private and public bonds. Households pay a bond-
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holding adjustment fees (brokerage fees) η to financial intermediaries. With all bonds being riskless,
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quadratic bond-holding adjustment costs, such as are being introduced here, are necessary to ensure a determinate macroeconomic equilibrium and stationary the responses of the economy to transitory
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shocks.14 These transactions fees are rebated to households via Tη. Finally, the household pays lumpsum taxes to, or receives lump-sum transfers from, both levels of government, TFG and TRG.
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The solution to the optimization problem yields the set of Euler equations (10a) – (10d) for the Rigid households. In the absence of any capital controls, these yield no-arbitrage conditions that
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equate interest rates on all types of bonds with returns on private capital, adjusted for depreciation and the tax on capital income. (Ct ) Et [(1 K ) Rt 1 1 ] Et (Ct 1 )
(10a)
14 The issue here is the familiar one of indeterminacy of equilibrium of a small open economy facing perfect world financial markets. Various approaches (offering varying degrees of sophistication) to closing such a model and thereby ensuring a determinate equilibrium have been proposed. The specification of quadratic fees, first introduced by Turnovsky (1985) and adopted subsequently by various authors (e.g. Benigno (2009), Erceg et al. (2006), Ghironi (2007), Cacciatore (2014)) suffices in the present context.
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(1 RPRI ,t 1 ) (Ct ) (1 Bt 1 ) Et (Ct 1 )
(10b)
(1 RFG ,t 1 ) (Ct ) Et (Ct 1 ) (1 BFG ,t 1 )
(10c)
(1 RRG F ,t 1 ) (Ct ) Et (Ct 1 ) (1 BRG F ,t 1 )
(10d)
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Finally, to satisfy the intertemporal budget constraint, the household is subject to the usual transversality conditions on capital and the various bonds. The former ensures that all capital is used by the end of time; the latter implies that the household cannot finance its consumption indefinitely by borrowing. Analogous conditions apply to households in Flexible. Federal Government
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4.3
In order to rule out the explosion of public debt, a fiscal feedback rule is introduced.15 We adopt the rule from Erceg, Guerrieri, and Gust’s (2006) SIGMA model, which relates the budget-deficit-to-
region takes the following form:
TFG ,t 1
B B st FG ,t 1 stst Ystst Yt
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TFG ,t
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output ratio to the debt-to-output ratio. The rule for the federal debt held by residents of the Rigid
Yt
Yt 1
BFG ,t 1 BFG ,t gr Yt 1 Yt
,
(11)
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where parameter ιgr ∈ (0, 1) determines the speed of the debt adjustment, which increases with ιgr, parameter ιst ∈ (0, 1) determines the cyclicality of the adjustment, and the variables with the stst
refer to their steady-state values. The adjustment rule for the federal debt held by
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subscript
residents of the Flexible region is symmetric. Regional Governments
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4.4
Similar to the federal government’s case, an analogous fiscal feedback rule restricts the accumulation of the regional public debt. Since only Flexible has no borrowing limit, only one regional rule is necessary. The rule applies to the bonds issued by the government of the Flexible region and held by households in both the Flexible and Rigid regions: 15
A discussion of the necessity of the fiscal feedback rule for determinacy of equilibrium and model stability can be found in Aiyagari et al. (2002).
15
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* TRG ,t
Yt *
* BRG F ,t 1 BRG BRG F stst , F ,t 1 * st * * Yt 1 Yt Ystst * * BRG F ,t 1 BRG F ,t 1 BRG F ,t BRG F ,t gr . * * Y Y t t 1 * TRG ,t 1
(12)
The rate of accumulation of public capital, KRG, is analogous to that of private capital. Parameter G
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∈ (0, 1) is the rate of depreciation of public capital stock. K RG ,t 1 I RG ,t (1 G ) K RG ,t
4.5
Aggregation and Interregional Trade
(13)
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Combining the budget constraints of the households and the governments yields the aggregate market clearing condition (14), where the aggregation is over activity in the two regions.16 * Yt Yt* Ct Ct* It It* CG I RG,t I RG ,t .
(14)
In a multi-regional economy, trade between the regions can occur and, in general, need not balance, in
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which case the balance of trade (BOT) can be expressed as:
(15)
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BOTt Yt Ct It 0.5CG I RG ,t .
In the case where one region runs a trade deficit, its representative household issues private debt obligations to finance its private expenditures. Then the equation for the Rigid net regional asset
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accumulation takes the following form:17
1 1 Rt Kt Rt* Kt* (Wt L Wt * L* ) 2 2 1 1 1 * Ct Ct* I t I t* I RG ,t I RG . 2 2 2
(16)
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Bt 1 (1 RPRI ,t ) Bt
Finally, in the two-region economy, private bonds issued by one region are necessarily purchased by the other, and hence the bonds are in zero net supply:
16 More specifically, to derive (14), substitute the taxes and bond holdings in the household budget constraints (9), together with the corresponding terms from the federal and regional budget constraints (4, 5, 6). As described above, assume that the bond-holding adjustment fees are rebated to the households. Summing up the regional household budget constraints yields the union accounting identity. 17 Being a two-region economy, the positive net regional asset position of one region corresponds to the net positive holdings of assets issued by the other region by the residents of the former region. See Appendix B for details.
16
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Bt Bt* 0.
5.
(17)
Calibration
The model’s parameters are calibrated at an annual frequency, and their values are summarized in Table 2. The discount factor, β, is set to 0.9615. Setting γ = 2 implies an intertemporal elasticity of
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substitution for private consumption goods of 0.5, well within the estimated range reported by Guvenen (2006); γG = 2 is an analogous parameter for the public consumption good.18
The share of national income that accrues to private capital, α, is 0.36, while the remainder accrues to labor. The elasticity of the output with respect to public capital, G , reflects its productivity, and its estimates are more far-ranging.19 The original estimate of this parameter
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reported by Aschauer (1989), 0.39, exceeds the productivity of private capital. Aschauer’s work spurred numerous empirical studies that generated a broad range of productivity estimates for total public expenditures and its components. The sweeping majority of the obtained estimates vary between 0.05 and 0.4, with a consensus that some categories of public expenditures increase private sector
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productivity more than others. Bom and Ligthart (2014) conduct a meta-regression analysis of 68 public good productivity studies published between 1983 and 2008. Their results range from 0.083
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for the short-run estimates to 0.122 for the long-run estimates. When attention is restricted to regional productive public goods, the productivity estimate increases to 0.193. Given the range of
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empirical estimates of the productivity of public investment, we choose G 0.2 as a baseline (medium) value and conduct robustness tests with alternative values of the productivity parameter:
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0.05 (very low), 0.1 (low), and 0.3 (high). The depreciation rate is set to 0.10 for private capital stock and 0.08 for more durable public
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capital. The capital income tax rate, K , is set to 0.305, the labor income tax rate, L , is 0.24, and the consumption tax rate, C , is 0.10.20 The speed of public debt adjustment, ιgr, is chosen following the SIGMA model and is equal to 0.1. The bond-holding adjustment cost, η, is set to the frequently
18
Our decision to calibrate at an annual frequency is dictated by the fact that regional governments typically budget on an annual basis. 19 Eicher and Turnovsky (2000) interpret low public good productivity as substantial congestion of the public goods. 20 These tax rates are generally reflective of the US tax rates over a number of years as summarized by McDaniel (2007).
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adopted value in the literature, 0.0025 (see e.g. Cacciatore (2014) and Ghironi (2007)). Next, the bivariate exogenous productivity process must be parameterized. In the absence of information at the regional level, we draw on parameterization employed at the international level. Even here, as Baxter and Farr (2005) have noted, it has proven difficult to estimate the parameters of
processes, to capture the likely range of parameter estimates:
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the productivity process with much precision. Accordingly, we allow for two types of technology
First, we adopt the parameterization suggested by Baxter and Farr (2005) on the basis of empirical evidence of extremely high persistence of shocks and no interregional spillovers, which we transform to annual frequency as:21:
ZZ 0.996 0 . Z 0 0.996 *
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Z Z *Z
(18)
*
Second, Heathcote and Perri (2002) estimate a somewhat lower degree of persistence, but with positive spillovers, which we transform to annual frequency as
ZZ 0.888 0.091 . Z 0.091 0.888 *
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Z Z *Z
(19)
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*
In order to quantify the marginal influence of the technology spillovers on interregional consumption risk-sharing and welfare resulting from the transmission of productivity shocks across regions, as a
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third alternative we omit the spillover component from the Heathcote-Perri specification, modifying it
Z Z *Z
ZZ 0.888 0.000 . Z 0.000 0.888 *
(20)
*
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to:
Finally, consumption, investment, and government expenditure shares are calibrated to 62.4%,
17.9%, and 19.7% of national output, respectively.22 We calibrate the share of the consumption public good provided by the federal government and the share of productive public goods provided by the regional governments to the corresponding shares of current and capital operations budgets in 21 Both the Baxter-Farr (2005) and the Heathcote-Perri (2002) process specifications are based on a quarterly frequency, which we have transformed to an annual frequency, since, as noted, this is a more appropriate time unit for our analysis. 22 The average values for 1977–2000 were calculated from the NIPA Table 1.1. The national output is defined as domestic absorption consistently with the market-clearing condition (21).
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the national income, 15.3% and 4.4%, respectively. This approach is adopted for a number of reasons. It is consistent with fiscal policy studies that model general government behavior. Moreover, it helps to mitigate the ambiguity regarding the attribution of different types of expenditures to publicly provided consumption and productive goods. First, not all capital expenditures are productive. For example, Aschauer (1989), Finn (1993), and others show little productive effect of national defense
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expenditures and some smaller categories of government investment. Second, some authors argue that the current expenditures can be productive; for instance, Evans and Karras (1994) emphasize the productive role of current expenditures on education. Such arguments, combined with the fact that current expenditures on education amount to 41% of state expenditures, make it worrisome to dismiss
6.
Analysis of Shocks in the Union
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the entire current expenditures category as completely unproductive.
Using the calibrated parameter values, the equilibrium conditions derived in Section 3 and summarized in Appendix C, are solved numerically for the unique symmetric steady state. Decision
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rules and dynamic responses of the endogenous variables to productivity shocks are obtained with
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the first-order perturbation technique. The choice of the linear solution method is dictated by the compatibility requirements of the Guerrieri and Iacoviello (2015) occasionally binding constraints toolkit. Having derived the numerical solutions, we then investigate how the asymmetric public
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borrowing limits affect the transmission channels of productivity shocks in the fiscal union. We also
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analyze the welfare effects of the shocks and check the sensitivity of the results to the productivity of public goods.
The productivity shock we consider is an adverse one, specified as a one-time 1% reduction
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in productivity. Initially the medium productivity ( G 0.2 ) of public goods is assumed. We begin by assuming that the productivity shock is common to both regions (Section 6.1) followed by those specific to one region only (Section 6.2). To sharpen the effects of borrowing limits on the macroeconomic dynamics, Section 6.1 begins by abstracting from possible technological spillovers between the regions. This specification is plausible for regions having different industrial structures, such as if one region specializes in services, such as IT and finance, while the other is primarily 19
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agricultural. After establishing the intuition for the transmission of shocks, in Section 3 we allow for technology spillovers between the regions. This case is more relevant for regions having similar industrial structures and correspondingly stronger technology linkages. Section 6.4 discusses the consequences of varying degrees of public good productivity for risk-sharing before turning attention
6.1
Aggregate Shock in Absence of Spillovers
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to their welfare implications (Section 6.5).
Figure 2 illustrates the dynamic response of the economy without technology spillovers in the scenario of an aggregate adverse productivity shock with a high degree of persistence.23 We begin with the
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analysis of the public sector dynamics, which are the underlying driving force. On impact of the shock, all types of tax revenues (consumption, capital income, and labor income) decline in both regions, as their corresponding tax base contracts (consumption expenditures, investment expenditures, and wages, respectively). However, the response of public investment differs between
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the regions. The Rigid government, constrained by the zero-borrowing limit, finances its expenditures with tax revenues only, which fall during the downturn. The Flexible government has
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the authority to borrow and thereby maintain the provision of the productive public good at the preshock level. These dynamics are reflected in the time paths of the public investment and public capital
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stock.
The reduced supply of the productive public good from the Rigid government leads to
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interregional differentials of marginal productivities. Since the productive public good augments the productivity of both private factors, the marginal productivity of capital as well as the marginal
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productivity of labor are affected.24 Their interregional productivity ratios move in favor of Flexible, which leads to the shift of resources to the more productive region in the union and, in turn, thereby reducing the amount of risk-sharing. Although the reduction of the public expenditures in the Rigid region increases availability of
23
The transmission of aggregate shocks in an economy with technology spillovers is qualitatively identical. The corresponding impulse responses are presented in Figure D.1. 24 The decline of the marginal products of labor is due to the dynamics of the total factor productivity and, with an inelastic labor supply, changes at the private and public capital margins rather than the labor margin.
20
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the resources for private absorption, these resources are not used for private investment locally, but instead are loaned to private and public borrowers in the rest of the union. Moreover, the Rigid region’s consumption, as well as private and public investments, fall faster than does its output due to the interregional shift of resources. The undersupply of both public and private investments in the Rigid region has a negative influence on its post-shock recovery.
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Productive public good provision in the Flexible region is financed in part by its own residents, while the rest of the funding comes from the residents of Rigid. Contrary to the Rigid region, the interregional shift of resources dampens the contraction of private consumption and investment in Flexible. Additionally, the allocations in the Flexible region return to their respective
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steady-state levels more rapidly.
The Federal government is unconstrained by a borrowing limit and provides the public consumption good at a steady rate. The debt-financed portion of its provision is financed by the Rigid representative household. Because marginal productivity is lower in the Rigid region, its household has an incentive to invest in public bonds, instead of local private capital. Thus, the Federal
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government’s borrowing increases the asymmetry of allocations in the union. On the other hand, the
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steady provision of the consumption public good by the Federal government improves interregional risk-sharing.
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The Rigid representative household holds a net positive asset position in all types of bonds on impact and during the early periods after the shock. Over time, once the effect of the productivity
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shock weakens sufficiently and the decumulation of private capital increases the return on capital, the marginal productivity ratios reverse and the shift of resources changes its direction.
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The demand for loanable funds grows as the indebtedness of both the Federal and Flexible governments and of the Flexible representative household increases. Hence, the returns on all types of bonds grow, which is consistent with the no-arbitrage condition implied by the Euler equations (10a) – (10d). The uninterrupted flow of the productivity-augmenting public good provided by the Flexible government allows that region to utilize the shift of resources, stabilize its economy, and improve its relative performance. From the union’s standpoint, the drawback of this policy is the deterioration of the interregional risk-sharing. 21
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6.2
Idiosyncratic Shocks in Absence of Spillovers
In the scenarios of idiosyncratic shocks, the region in which the shock is realized is hurt due to both the decreased marginal productivity of private factors and the consequential outward shift of resources. The other region is affected positively by the inward shift of resources, correspondingly.
improves the relative performance of the region that adopts it. 6.2.1 Shock to Rigid Region
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Similar to the scenario of aggregate shocks, the Flexible fiscal policy acts as a shock absorber and
The adjustment of the macroeconomic variables after a negative asymmetric shock to the Rigid
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region’s economy is illustrated in Panel A of Figure 3. Since the adverse disturbance directly affects the Rigid region, in the absence of spillovers, the Flexible region is affected positively via the shift of resources from Rigid. Interregional trade is no longer balanced in response to the marginal productivity differential between the regions. The balance of trade captures the corresponding shift
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of resources to the more productive region. On impact and immediately after the shock, the Rigid region runs a trade deficit, and the Flexible region holds a positive net regional asset position in
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private bonds against the Rigid region. The inward shift of resources increases Flexible’s transitional allocations of investment, consumption, and output above their respective steady-state levels.
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The behavior of the other endogenous variables follows the pattern established in the analysis of the aggregate shock scenario. The allocations of the variables diverge across the regions. The
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impulse responses of consumption demonstrate that the interregional risk-sharing deteriorates. This deterioration is more pronounced than that in the previously discussed scenario of aggregate shocks
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and as compared with the scenario of an idiosyncratic shock to Flexible, as discussed next. 6.2.2 Shock to Flexible Region Following an adverse productivity shock to the Flexible region, marginal productivity differentials are tilted in favor of the Rigid region, as illustrated by Panel A of Figure 4. Hence, the latter region receives the inflow of resources from the former. This shift of resources is smaller as compared to the previous scenario, and so is the overaccumulation of capital by the Rigid region, unaffected by 22
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the shock directly. As before, the dynamics of the regional public good supply are responsible for this outcome. However, contrary to the previous scenario, the government of the region directly affected by the negative shock does not allow the provision of the local productive public good to contract. This enables a faster recovery of that region’s marginal productivities. Hence, the interregional ratio of
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the marginal products of capital flips, and reverses the shift of resources substantially faster than in the scenario of an idiosyncratic shock to the Rigid region. Intuition for the dynamics of other variables is as discussed in the preceding section.
Note that in the scenario of an idiosyncratic shock to Flexible, the asymmetric borrowing
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limits adopted by the regions have beneficial implications for risk-sharing. In such an arrangement, the absence of a borrowing limit allows the Flexible region affected by the adverse disturbance to stabilize its economy and to recover from the shock’s effects faster. One can arrive at this conclusion by visually examining the allocations of consumption on Panel A of Figure 4. Numerical support for
Shocks in Presence of Spillovers
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6.3
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this statement is presented in Section 6.5 below.
Having identified the shock transmission mechanism in the absence of technology spillovers, it is
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natural to consider an economy with interregional spillovers. Such a specification is arguably more realistic for the U.S., as a union with numerous interregional and interindustry links. On one hand,
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the choice of the technology process specification is immaterial for the dynamic response of the model economy in the scenario of aggregate shocks. Figures 2 and D.1 show that the time paths of
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macroeconomic variables are virtually identical. On the other hand, the spillovers start playing a role in the idiosyncratic shock scenarios. A
comparison of Panels A with Panels B of Figures 3 and 4 points out that the technology spillovers ensure comovement of the endogenous variables, speed up the transition, and hence affect quantitative outcomes of the model. For example, output expansions in the regions unaffected by adverse idiosyncratic shocks directly are short-lived in the framework with spillovers. Additionally, a recession in one region leads to a downturn instead of an expansion in another, albeit a smaller one 23
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and with a lag. Also, in the region affected by the shocks indirectly, through spillovers, consumption never increases (although output does), due to the forward-looking, consumption-smoothing behavior of rational households. The main finding from the comparison of the economy responses in the presence and in the absence of technology spillovers is as follows. By inducing comovement of the macroeconomic
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variables, and by reducing the range of fluctuations, spillovers mitigate the effects of the asymmetric balanced-budget rules in the idiosyncratic shock scenarios. Hence, the interregional technology linkages improve interregional risk-sharing, conditional on the realization of idiosyncratic shocks, though not in the scenario of aggregate disturbances. This finding is numerically supported by the
6.4
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analysis presented in Section 6.5 below. Effects of Public Good Productivity
To assess the consequences of the variations in the degrees of public good productivity, we investigate the model’s behavior under alternative parameterization of the productivity of public
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goods, G . Besides the baseline medium productivity value of 0.2, we consider high, low, and very
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low values of public good productivity ( G 0.30, 0.10, 0.05 ). The highest considered value of 0.30 is closer to Aschauer’s original estimate of public infrastructure productivity of 0.39, but still below
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the private capital productivity. The lowest value, 0.05, reflects the diminished productivity of significantly congested productive public goods.
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The risk-sharing implications of public borrowing limits in this model are robust with respect to G , ranging from low to high levels. The higher productivity of public goods is associated with
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worse interregional risk-sharing, as it leads to: greater differences between the two types of regions in output, wages, consumption, private and public investment, and private and public capital stock; larger fluctuations in interregional trade and all types of bond holdings; and smaller fluctuations in interest rates. Panel A of Figure 5 illustrates this point with the time paths for consumption, output, and interregional balance of trade after an aggregate shock in the economy with spillovers. The analysis of the transition after idiosyncratic shocks (Panels B and C of Figure 5) supports that observation. When the productivity of public goods is higher, the undersupply of the public 24
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goods becomes costlier as measured by levels of macroeconomic variables or interregional differentials. The scenario of an idiosyncratic shock to the Rigid region sharpens strongly the difference between alternative fiscal policies (Panel C of Figure 5). The relative loss, measured as a percentage deviation from the steady-state levels, is quite steady in the Flexible region regardless of the public
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good productivity. This is in contrast to the dynamics in the Rigid region as represented in Panel B of Figure 5. The shift of resources from the Rigid to the Flexible region becomes costlier for the former region when public good productivity is higher. The undersupply of public goods negatively affects the marginal productivity of private factors and therefore brings about a larger shift of resources and
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greater losses of consumption and output. These results obtained for the technology process specification with spillovers qualitatively hold in the absence of spillovers (Figure D.2). As public good productivity falls to being very low (G 0.05) , not only does the interregional consumption differential become smaller, but the relative performance of the two regions is reversed as well. At first glance, this result might appear surprising, as it seems to
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contradict Barro’s (1979) tax-smoothing hypothesis, which implies the optimality of public
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borrowing.25 However, there is no contradiction. Barro’s analysis does not consider productive government expenditures. Once productive public goods are introduced, as in the present study, the
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optimality of public borrowing is determined by two counteracting forces associated with the provision of productive public goods: an enhanced private-factor productivity due to productive
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public expenditures, on one hand, and, on the other, decreased private investment and consumption due to the resource-withdrawal effect. Hence, in the case of sufficiently low productivity of public
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goods, debt financing of public expenditures is not justified, since the cost of public investment is greater than its benefit, and refraining from public borrowing improves welfare of the local representative household. 6.5
Welfare
25 In Barro’s model, public borrowing helps to maintain a constant tax rate after a realization of adverse shocks. The government debt eliminates wedges associated with the adjustment of distortionary tax rates. Hence, public debt that is brought about by a budget deficit can be viewed as a byproduct of optimal fiscal policy.
25
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We begin by analyzing lifetime welfare in the model economy following the realization of a one-time aggregate productivity shock. Then, idiosyncratic shocks are considered. 6.5.1 Aggregate Shock Consider two technology process specifications: one with high persistence and without technology
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spillovers (eq. 18), and another with lower persistence and with technology spillovers (eq. 19). Conditional on the medium productivity of the public goods, the Flexible region is better insulated against aggregate adverse shocks than the Rigid region (Panel A of Table 3). The welfare loss amounts to 1.57 to 2.12% (1.19 to 1.61%) of the Rigid (Flexible) region’s lifetime welfare,
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depending on the technology process specification.
Due to the difference in regional fiscal policies, the Rigid representative household enjoys a 0.38 to 0.51 percentage point lower lifetime consumption relative to the Flexible household in the aftermath of the shock. Panel A of Table 3 shows that, as the public good productivity increases, the under-provision of public goods becomes costlier for the region, as measured by its representative
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household’s loss of welfare. Consequently, as G decreases, the benefit of public borrowing
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vanishes. Both the absolute welfare loss and the consumption differential between two regions decreases.
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If the public good productivity is too low, or if the goods are substantially congested, the adoption of the Flexible fiscal policy is no longer welfare improving, as compared with the Rigid
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policy. The intuition for this outcome was presented in Subsection 6.4 above. Finally, to assess the marginal effect of the technology spillovers, results of the model with
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lower persistence of the shocks and without spillovers (eq. 20) are presented in the remaining columns of Table 3. Our analysis shows that the spillovers are responsible for approximately one half of the welfare loss in the specification with lower persistence of the productivity shocks. 6.5.2 Idiosyncratic Shocks Panels B and C of Table 3 document the welfare consequences of idiosyncratic shocks to the union, conditional on the strength of technology spillovers and persistence of the shocks. 26
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In the specification with high persistence and without technology spillovers, the shift of resources is more pronounced. An idiosyncratic shock to Rigid leads to welfare improvement in Flexible, and vice versa, as a shock to Flexible improves the welfare of Rigid. However, due to the adoption of the Flexible fiscal policy, the corresponding regional welfare gain is larger (and the loss is smaller), conditional on the realization of idiosyncratic shocks. The exception is represented by a
Rigid household for the reasons discussed in Subsection 6.4.
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case with very low public good productivity. The consumption differential is tilted in favor of the
In the presence of spillovers and with lower persistence of the technology process, when the adverse shock is realized in one region only, both regions are affected negatively through the
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interregional technology linkages, which mitigate the shift of resources. The welfare loss is increasing (decreasing) in the productivity of public goods in the Rigid (Flexible) region, regardless of the destination of the idiosyncratic shock. The zero-borrowing limit of the Rigid region hinders its post-shock recovery, which becomes more apparent as the public good productivity increases from
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low to high.
The welfare and consumption differential between the union members is increasing in public
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good productivity, conditional on an idiosyncratic shock to the Rigid region (Panel B of Table 3), but is decreasing if the shock hits the Flexible region (Panel C). The asymmetry of public borrowing
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limits generates the shift of resources, which allows Flexible to recover faster, especially if the productivity of public goods is higher. This explains the finding that the consumption differential
shock.
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between the regions closes faster (slower) when only the Flexible (Rigid) region is affected by the
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Therefore, such asymmetric fiscal union design improves interregional risk-sharing only after the realization of productivity shocks in the Flexible region and deteriorates the risk-sharing if the shocks are realized in the Rigid region or in both regions simultaneously. The last columns of Panels B and C of Table 3 confirm the observation that the marginal effect of the spillovers is substantial. Without the interregional linkages, welfare losses of both regions decrease (as the shocks dissipate faster in the absence of the spillovers), but the interregional differential widens (as the shocks are contained within the region in which they realized). 27
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7.
Conclusions
This paper has employed a microfounded, dynamic market-clearing general equilibrium framework to study the question: What are the implications of the asymmetry of balanced-budget rules for the interregional risk-sharing in a fiscal union? This question was motivated by two stylized facts about
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the U.S. as a fiscal union: (i) the presence of asymmetric public borrowing limits across the U.S. states, and (ii) the heterogeneous structure of government expenditures across different levels of the union government. We found that the asymmetry of balanced-budget rules creates welfare losses in the union. The exact magnitude of the risk-sharing deterioration in the fiscal union is a function of the productivity of the public good, specification of the technology processes, and distribution of the
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productivity shocks across the union. Overall, for productive government expenditure consistent with the empirical evidence, our numerical simulations tend to favor a flexible budget balance regime in terms of reducing the welfare losses in response to adverse productivity shocks. Our analysis can be extended to show that it is possible to increase efficiency and improve
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interregional risk-sharing in the fiscal union by adopting symmetric borrowing limits, thereby minimizing the shift of resources between the regions.26 The choice of the specific form of public
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borrowing limits then hinges on the productivity of public goods. If the productivity of the public good is sufficiently high, welfare is maximized by lifting any restrictions on public borrowing. But
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when the productivity is sufficiently low, imposing borrowing limits improves welfare. As a caveat to our analysis we should recall two special assumptions on which it is based. These
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pertain to (i) the abstraction of intergovernmental transfers that are typically present in fiscal unions and (ii) the prohibition of labor mobility across the regions. Both of these assumptions are introduced in
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order to sharpen the contrast in the effects of the borrowing limits and government expenditure composition on the time paths of capital accumulation and welfare. In either case, we acknowledge that the differential effects of the balanced-budget rules would be mitigated in the absence of these assumptions. Transfers from the federal authorities to regional governments would serve to reduce directly the differential economic performances of the two regions. The migration of households from 26
The shift of resources is minimized, conditional on the realization of asymmetric shocks, and eliminated if aggregate disturbances are realized.
28
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the less productive to more productive regions in response to the negative wealth effect would narrow the regional differences by affecting the interregional marginal productivity differential. These are clearly interesting and relevant aspects that merit further consideration. In addition, our framework opens up several more avenues for future research. These include the analysis of the policy interactions between the union members, as well as the exploration of the
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need for policy intervention by the federal government in the design of regional borrowing limits. Moreover, the setup we have developed can be utilized for the analysis of other important aspects of fiscal policy in a fiscal union, such as the heterogeneity of tax systems across the union members and
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the interregional transfer-mechanism design.
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Appendix A.
Some Additional Characteristics of Balanced-Budget Rules
Federal Government
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Although the U.S. federal government has faced a debt ceiling since 1917, when the Second Liberty Bond Act was passed, the ceiling serves primarily as a tool for partisan negotiations in the U.S. Congress and does not effectively constrain borrowing by the federal government. During the period this paper considers, 1977–2000, the debt limit was lifted 32 times.53 The debt ceiling was not raised in a timely manner only once, in 1995, due to a conflict between President Clinton and the Republican–controlled Congress, which ultimately led to a government shutdown. Between 2001 and 2015, the debt ceiling was increased 14 times, and in the three instances when the debt limit was not increased in a timely manner, it was suspended. State Governments
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Unlike the federal government, which has never defaulted on its debt obligations, subnational governments have not always avoided bankruptcies. Nine of 25 U.S. state governments and several cities delayed or ceased interest and principal payments on their bonds during and in the aftermath of the 1837 recession.54 This resulted in the loss of investor confidence, lengthy periods of debt repayment by the bankrupt states, and the imposition of unpopular excise and property taxes for that purpose. As a result, some states imposed constitutional and statutory requirements to balance budgets and limitations on issuance of municipal bonds in order to improve fiscal discipline.55 Nonetheless, the measures taken after the 1837 recession did not prevent another municipal debt crisis, which was brought about by the 65-month-long Great Depression of 1873. However, states joining the Union, as well as existing members, chose to adopt some form of borrowing limitations. Presently, only one state, Vermont, does not have a legal requirement to balance its budget. One of the characteristics of balanced-budget rules is the types of funds or budgets that are considered subject to the rule. Forty-nine states impose borrowing restrictions on their current operations budgets (also called general funds). Technically, 25 states do require that their capital budgets are balanced, but all of these states allow long-term revenue bond proceeds to be included in the budget revenue (U.S. General Accounting Office GAO (1993)). Such treatment of the capital budget balance is likely an artifact of the early attempts to circumvent borrowing limits, when revenue bonds (guaranteed by the revenue flow from the operation of an erected capital structure but not by the full faith and credit of the state) were first introduced by the State of Washington in 1897. The attempt was successful because such bonds were exempted from the borrowing limits by the courts, which ruled that the limits did not apply to obligations that are not guaranteed by the state taxpayers. Note that this separation of current and capital operation budgets is consistent with Bassetto and Sargent (2006), who make a case for it from an intergenerational point of view. They employ an overlapping generations model with productive and consumption public goods to show that exempting the capital operations budget from the balanced-budget requirement increases efficiency. In their model, once a balanced-budget rule is imposed, public goods would be underprovided. Due to the availability of public borrowing, older generations are able to shift the 53
The rationale for focusing on the 1977–2000 period is data driven and presented in Footnote 4. The list of insolvent states in Kiewiet and Szakaly (1996) includes the 10th bankrupt state, Florida, which joined the Union in 1845. 55Restrictions were imposed on the only type of bonds available at the time – guaranteed – also referred to as full-faith and credit or general obligation bonds that are secured with all available to the government means to repay the principal and interest. 54
27
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B.
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The balanced-budget rules adopted are state-specific and vary in terms of their stringency. The stringency of the regulations is determined by the stage of the budget process at which the budget must be balanced and by the legal provision for debt carry-over from one budget period to the next. Some states require budgets to be balanced at the beginning of the budget period, while others require them to be balanced at the end. In the former case, the governor must submit a balanced budget and/or the state legislature has to pass it. Hence, the start-of-the-period balanced-budget requirement does not rule out deficits occurring after the enactment of the budget. Those states having budgets that must be balanced at the end of the budget period have to take measures to balance their budgets if expenditures increase, or revenues decline unexpectedly, or both. Such unforeseen deficits typically occur during recessions. Net Regional Asset Accumulation
This appendix derives the expression for net regional asset accumulation for the Rigid region. Aggregate accounting implies the following laws of motion for net regional assets in the Rigid and Flexible regions:
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1 Bt 1 (1 RPRI ,t ) Bt Rt Kt Wt L Ct I t I RG ,t CG , 2
1 * Bt*1 (1 RPRI ,t ) Bt* Rt* Kt* Wt* L* Ct* I t* I RG CG . 2
(B.1) (B.2)
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The last term in each equation is due to the Federal government apportioning procurement of the consumption public good equally between the regions. The right-hand side of each of the laws of motion is a regional equivalent of the System of National Accounts’ definition of national savings for a sovereign state: national income less domestic absorption. If the regional savings are positive (negative), the region runs a trade surplus (deficit) and holds a positive (negative) net regional asset position. Subtracting (B.2) from (B.1) and using the fact that private bonds are in zero net supply, Bt + Bt∗ = 0, yields:
1 1 Rt Kt Rt* Kt* (Wt L Wt * L* ) 2 2 1 1 1 * Ct Ct* I t I t* I RG ,t I RG . 2 2 2
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Bt 1 (1 RPRI ,t ) Bt
(B.3)
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Equation (B.3) relates the Rigid region’s net regional asset accumulation to the interest income and differentials between the regions’ capital income, labor income, private absorption, and public absorption.
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C: Summary of the Model Equilibrium Conditions
Wt (1 )Yt / L
Rate of return on labor
Wt* (1 )Yt* / L* Rt Yt / Kt
Rate of return on capital
Rt* Yt* / Kt*
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Yt Zt Kt L1 ( K RG ,t )G
Production function
G * Yt* Zt* Kt* L*1 ( K RG ,t )
Kt It (1 ) Kt 1
Law of motion for private capital
Kt* It* (1 ) Kt*1
(Ct ) Et [(1 K ) Rt 1 1 ] Et (Ct 1 )
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Consumption-Euler equation
(Ct* ) Et [(1 K ) Rt*1 1 ] Et (Ct*1 )
(1 RPRI ,t 1 ) (Ct ) (1 Bt 1 ) Et (Ct 1 )
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Euler equation (private bonds)
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Euler equation (federal bonds)
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Euler equation (Flexible bonds)
Federal government budget constraint
* (1 RPRI (Ct* ) ,t 1 ) * * (1 Bt 1 ) Et (Ct 1 )
(1 RFG ,t 1 ) (Ct ) Et (Ct 1 ) (1 BFG ,t 1 ) * (1 RFG (Ct* ) ,t 1 ) * Et (Ct*1 ) (1 BFG ,t 1 )
(1 RRG F ,t 1 ) (Ct ) Et (Ct 1 ) (1 BRG F ,t 1 ) * (1 RRG (Ct* ) F ,t 1 ) * * Et (Ct 1 ) (1 BRG F ,t 1 ) * * BFG ,t 1 BFG ,t 1 CG (1 RFG ,t )( BFG ,t BFG ,t ) * K ( Rt Kt Rt* Kt* ) L (Wt L Wt * L* ) TFG ,t TFG ,t
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Federal government fiscal feedback rule
TFG ,t Yt * TFG ,t
Yt
*
TFG ,t 1 Yt 1 * TFG ,t 1
* t 1
Y
B B B B st FG ,t 1 stst gr FG ,t 1 FG ,t Ystst Yt 1 Yt Yt * BFG B* st *,t 1 stst * Ystst Yt
Rigid regional government budget constraint
C Ct TRG ,t I RG ,t ,
Flexible regional government budget constraint
* * C Ct* BRG F ,t 1 BRG F ,t 1 TRG ,t
Flexible regional government fiscal feedback rule
* TRG ,t
Law of motion for public capital
K RG,t I RG,t (1 G ) KRG ,t 1
* * BFG BFG ,t 1 ,t gr * * Yt 1 Yt
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I RG ,t min{ C Ct , I RG }
* * I RG (1 RRG F ,t ) BRG F ,t (1 RRG F ,t ) BRG F ,t * TRG ,t 1
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Yt *
* BRG F ,t 1 BRG BRG F stst , F ,t 1 st * * * Yt 1 Yt Ystst * * BRG F ,t 1 BRG F ,t 1 BRG F ,t BRG F ,t gr Yt * Yt *1
* * * K RG ,t I RG ,t (1 G ) K RG ,t 1
* Yt Yt* Ct Ct* It It* CG I RG ,t I RG ,t
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Union resource constraint
BOTt Yt Ct It 0.5CG I RG ,t
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Balance of trade
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Rigid net regional asset accumulation
* BOTt* Yt* Ct* It* 0.5CG I RG ,t
1 1 Rt Kt Rt* Kt* (Wt L Wt * L* ) 2 2 1 1 1 * Ct Ct* I t I t* I RG ,t I RG 2 2 2
Bt 1 (1 RPRI ,t ) Bt
Bt Bt* 0
Bivariate productivity process
Zt Z Z * t Z *Z
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Bonds are in zero net supply
ZZ Zt 1 t Z Zt*1 t* *
*
Note: The equations in the table constitute a system of 31 equations in 31 endogenous variables.
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Appendix D: Some Results Conditional on Alternative Technology Process Specification
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Figure D.1: Responses of the endogenous variables to the aggregate -1% productivity shock
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Notes: The fiscal union consists of the Rigid and Flexible regions. The technology process with lower persistence and with spillovers is adopted. The vertical axis measures percentage deviations of the endogenous variables from their respective steady states with the exception of the balance of trade and bonds measured relative to the steady-state output as well as the interest rates measured as percentages. The horizontal axis measures periods after the shock.
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Panel B: Idiosyncratic shock to Rigid
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Figure D.2: Responses of output, consumption, and investment to the -1% productivity shocks under alternative assumptions about the productivity of public goods. Panel A: Aggregate shock
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Panel C: Idiosyncratic shock to Flexible
Notes: The fiscal union consists of the Rigid and Flexible regions. The vertical axis measures percentage deviations of the variables from their respective steady states with the exception of the balance of trade measured relative to the steady-state output. The technology process with high persistence and without spillovers is adopted. The horizontal axis measures periods after the shock.
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References ACIR, 1987. Fiscal Discipline in the Federal System: National Reform and the Experience of the States. Agenor, P-R., 2013. Public Capital, Growth, and Welfare, Princeton University Press, Princeton NJ.
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Aiyagari, S.R., Marcet, A., Sargent, T.J. Seppala, J., 2002. Optimal taxation without state- contingent debt. Journal of Political Economy 110, 1220–1254. Aschauer, D.A., 1989. Is public expenditure productive? Journal of Monetary Economics 23: 177–200. Asdrubali, P., Sorensen, B.E., Yosha, O., 1996. Channels of interstate risk-sharing: United States 1963-1990. Quarterly Journal of Economics 111, 1081–1110. Azzimonti, M., Battaglini, M., Coate, S., 2010. On the case for a balanced budget amendment to the U.S. Constitution. MPRA Paper 25935, University Library of Munich, Germany.
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Backus, D.K., Kehoe, P.J., Kydland, F.E., 1992. International real business cycles. Journal of Political Economy 100, 745–75. Barro, R.J., 1979. On the determination of the public debt. Journal of Political Economy 87, 940–971. Bassetto, M., Sargent, T.J., 2006. Politics and efficiency of separating capital and ordinary government budgets. Quarterly Journal of Economics 121, 1167–1210.
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Baxter, M., Farr, D.D., 2005. Variable capital utilization and international business cycles. Journal of International Economics 65, 335–347.
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Bayoumi, T., Eichengreen, B., 1995. Restraining yourself: The implications of fiscal rules for economic stabilization. IMF Staff Papers 42, 32–48.
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Benigno, P., 2009. Price stability with imperfect financial integration. Journal of Money, Credit and Banking 41, 121–149. Bohn, H., Inman, R.P., 1996. Balanced budget rules and public deficits: Evidence from the U.S. states. Carnegie-Rochester Conference Series on Public Policy 45, 13–76.
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Bom, P., Ligthart, J., 2014. What have we learned from three decades of research on the productivity of public capital? Journal of Economic Surveys 28, 889–916.
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Cacciatore, M., 2014. International trade and macroeconomic dynamics with labor market frictions. Journal of International Economics 93, 17–30. Chatterjee, S., Ghosh,S., 2011. The dual nature of public goods and congestion: The role of fiscal policy revisited. Canadian Journal of Economics 44, 1471–1496. Dmitriev, M., Hoddenbagh, J., 2015. The Optimal Design of a Fiscal Union. Manuscript. Economides, G., Park, H., Philippopoulos, A., 2011. How should the government allocate its tax revenues between productivity-enhancing and utility-enhancing public goods? Macroeconomic Dynamics 15, 336– 64.
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Eicher, T., Turnovsky, S.J., 2000. Scale, congestion and growth. Economica 67, 325–46. Erceg, C.J., Guerrieri, L., Gust, C., 2006. SIGMA: A new open economy model for policy analysis. International Journal of Central Banking 2, 1–50. Evans, P., Karras, G., 1994. Are government activities productive? Evidence from a panel of U.S. states. Review of Economics and Statistics 76, 1–11.
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Farhi, E., Werning, I., 2017. Fiscal unions. American Economic Review 107, 3788–3834. Finn, M., 1993. Is all government capital productive? Federal Reserve Bank of Richmond Economic Quarterly, (Fall), 53–80. GAO, 1993. Balanced Budget Requirements: State Experiences and Implications for the Federal Government.
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Ghironi, F., 2006, Macroeconomic interdependence under incomplete markets. Journal of International Economics 70, 428–450. Guerrieri, L., Iacoviello, M., 2015. OccBin: A toolkit for solving dynamic models with occasionally binding constraints easily. Journal of Monetary Economics 70, 22–38. Guvenen, F., 2006. Reconciling conflicting evidence on the elasticity of intertemporal substitution: A macroeconomic perspective. Journal of Monetary Economics 53, 1451–1472.
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Heathcote, J., Perri, F., 2002. Financial autarky and international business cycles. Journal of Monetary Economics 49, 601–627.
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Hepp, R., von Hagen, J., 2013. Interstate risk-sharing in Germany: 1970–2006. Oxford Economic Papers 65, 1–24. Kenen, P., 1969. The theory of optimum currency areas: An eclectic view. In R. Mundell and A. Swoboda (eds.) Monetary Problems of the International Economy. University of Chicago Press.
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Kiewiet, D.R., Szakaly, K., 1996. Constitutional limitations on borrowing: An analysis of state bonded indebtedness. Journal of Law, Economics and Organization 12, 62–97.
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Leduc, S., Wilson, D., 2013. Roads to prosperity or bridges to nowhere? Theory and evidence on impact of public infrastructure investment. NBER Macroeconomics Annual 27, 89–142.
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Leeper, E., Walker, T., Yang, S.-C., 2010. Government investment and fiscal stimulus. Journal of Monetary Economics 57, 1000–1012. Lucas, R., Jr., 1988. On the mechanics of economic development. Journal of Monetary Economics 22, 3–42. Mankiw, N.G., Romer, D., Weil, D.N., 1992. A contribution to the empirics of economic growth. Quarterly Journal of Economics 107, 407–37. McDaniel, C., 2007. Average tax rates on consumption, investment, labor and capital in the OECD 19502003, unpublished ms. Arizona State University. McKinnon, R.I., 1963. Optimum currency areas. American Economic Review 53, 717–725. Mundell, R.A., 1961. A theory of optimum currency areas. American Economic Review 51, 657–665.
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Poterba, J.M., 1994. State responses to fiscal crises: The effects of budgetary institutions and politics. Journal of Political Economy 102, 799–821. Poterba, J.M., 1995. Balanced budget rules and fiscal policy: Evidence from the States. National Tax Journal 48, 329–336. Poterba, J.M., 1997. Do budget rules work? In A. Auerbach (ed.) Fiscal Policy: Lessons from Empirical Research, MIT Press, Cambridge MA.
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Sorensen, B.E., Yosha, O., 1998. International risk-sharing and European monetary unification. Journal of International Economics 45, 211–238. Sorensen, B.E., Yosha, O., 2001. Is state fiscal policy asymmetric over the business cycle? Federal Reserve Bank of Kansas Economic Review 8,: 43–64.
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Stockman, D.R., 2001. Balanced-budget rules: Welfare loss and optimal policies. Review of Economic Dynamics, 4, 438–459. Turnovsky, S.J., 1985. Domestic and foreign disturbances in an optimizing model of exchange-rate determination. Journal of International Money and Finance 4, 151–171.
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Turnovsky, S.J., Fisher, W.H., 1995. The composition of government expenditure and its consequences for macroeconomic performance. Journal of Economic Dynamics and Control 19, 747–786.
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Table 1: Functional composition of the federal and state government expenditures, 1977– 2000,% of general government expenditures Federal expenditures 47.8 37.8 29.9 2.1 3.2 0.9 0.5 1.0 0.2 10.0 0.7 9.3
State expenditures 52.2 20.9 0.0 6.0 2.6 1.2 2.3 7.7 1.1 31.3 23.8 7.5
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Total expenditures Consumption public goods National defense General public service Health Housing and community services Income security Public order and safety Recreation and culture Productive public goods Education Economic affairs
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Source: U.S. National Income and Product Accounts, Section 3. Note: The data in the table are consistent with the NIPA expenditures approach. Namely, transfers from the federal government to state governments are included in the expenditures of the federal government and transfers from governments to individuals are not reported as a part of government expenditures.
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Table 2: Calibrated parameters Parameter
α G
δ
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G
Preferences discount factor inverse of intertemporal elasticity of substitution for private consumption inverse of intertemporal elasticity of substitution for public consumption Technology capital income share elasticity of output with respect to public capital rate of depreciation of private capital rate of depreciation of public capital
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β γ
K
L
C
ιst ιgr η
Value
capital income tax labor income tax consumption tax cyclicality of public debt adjustment speed of public debt adjustment bond-holding adjustment cost
0.9615 2 2 0.36 0.05, 0.1, 0.2, 0.3 0.10 0.08
Policy 0.305 0.24 0.10 0.1 0.001 0.0025
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Table 3: Lifetime welfare dynamics under alternative assumptions about the productivity of public goods and technology spillovers in the fiscal union. Panel A. Aggregate shock High persistence, without spillovers V low Low Med High 0.05 0.1 0.2 0.3 1.61 1.75 2.12 2.70 1.63 1.62 1.61 1.58 1.01 0.93 0.76 0.59
Lower persistence, with spillovers V low Low Med High 0.05 0.1 0.2 0.3 1.19 1.30 1.57 2.00 1.21 1.20 1.19 1.17 1.01 0.93 0.76 0.58
Lower persistence, without spillovers V low Low Med High 0.05 0.1 0.2 0.3 0.52 0.57 0.69 0.88 0.53 0.53 0.52 0.51 1.02 0.93 0.75 0.58
Panel B. Idiosyncratic shock to Rigid High persistence, Lower persistence, without spillovers with spillovers V low Low Med High V low Low Med High Elasticity of output with respect to public capital, G 0.05 0.1 0.2 0.3 0.05 0.1 0.2 0.3 Loss of lifetime welfare in Rigid, % 1.64 1.78 2.16 2.75 0.75 0.82 0.99 1.26 Loss of lifetime welfare in Flexible, % -0.03 -0.04 -0.06 -0.08 0.45 0.44 0.44 0.42
Lower persistence, without spillovers V low Low Med High 0.05 0.1 0.2 0.3 0.51 0.55 0.67 0.85 0.01 0.01 0.00 0.00
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Elasticity of output with respect to public capital, G
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Loss of lifetime welfare in Rigid, % Loss of lifetime welfare in Flexible, % Ratio of Flexible-Rigid welfare loss
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Panel C. Idiosyncratic shock to Flexible High persistence, Lower persistence, without spillovers with spillovers V low Low Med High V low Low Med High Elasticity of output with respect to public capital, G 0.05 0.1 0.2 0.3 0.05 0.1 0.2 0.3 Loss of lifetime welfare in Rigid, % -0.03 -0.03 -0.03 -0.02 0.44 0.48 0.58 0.74 Loss of lifetime welfare in Flexible, % 1.66 1.66 1.66 1.66 0.76 0.76 0.75 0.75
Lower persistence, without spillovers V low Low Med High 0.05 0.1 0.2 0.3 0.01 0.01 0.02 0.03 0.52 0.52 0.52 0.51
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Notes: The fiscal union consists of the Rigid and Flexible regions. The table entries are calculated using consumption scale factors and have the interpretation of compensating variation measured in terms of private lifetime consumption.
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Figure 1: Balanced-budget rules in the continental U.S. states
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Source: ACIR (1987). Note: The yellow (lighter) color represents states with less stringent balanced-budget rules and corresponds to the ACIR index value of 6 and below. The green (darker) color represents states with strict balanced-budget rules and corresponds to the ACIR index value of 7 and above. The breakpoint value between the two types of the states is borrowed from the fiscal federalism literature.
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Figure 2: Responses of the endogenous variables to the aggregate -1% productivity shock
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Notes: The fiscal union consists of the Rigid and Flexible regions. The technology process with high persistence and without spillovers is adopted. The vertical axis measures percentage deviations of the endogenous variables from their respective steady states with the exception of the balance of trade and bonds measured relative to the steady-state output as well as the interest rates measured as percentages. The horizontal axis measures periods after the shock.
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Figure 3: Responses of the endogenous variables to the idiosyncratic -1% productivity shock to the Rigid region Panel B. Lower persistence, with spillovers.
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Panel A. High persistence, without spillovers.
Notes: The fiscal union consists of the Rigid and Flexible regions. The vertical axis measures percentage deviations of the endogenous variables from their respective steady states with the exception of the balance of trade and bonds measured relative to the steady-state output as well as the interest rates measured as percentages. The horizontal axis measures periods after the shock.
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Panel A. High persistence, without spillovers.
Notes: The fiscal union consists of the Rigid and Flexible regions. The vertical axis measures percentage deviations of the endogenous variables from their respective steady states with the exception of the balance of trade and bonds measured relative to the steady-state output as well as the interest rates measured as percentages. The horizontal axis measures periods after the shock.
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Figure 5: Responses of output, consumption, and investment to the -1% productivity shocks under alternative assumptions about the productivity of public goods
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Panel A: Aggregate shock
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Panel B: Idiosyncratic shock to Rigid
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Panel C: Idiosyncratic shock to Flexible
Notes: The fiscal union consists of the Rigid and Flexible regions. The vertical axis measures percentage deviations of the variables from their respective steady states with the exception of the balance of trade measured relative to the steady-state output. The technology process with lower persistence and with spillovers is adopted. The horizontal axis measures periods after the shock.
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Balanced-Budget Rules and Risk-sharing in a Fiscal Union# Vladimir V Dashkeev , Stephen J Turnovsky PII: DOI: Reference:
S0164-0704(18)30161-7 10.1016/j.jmacro.2018.06.008 JMACRO 3040
To appear in:
Journal of Macroeconomics
Received date: Revised date: Accepted date:
17 April 2018 19 June 2018 21 June 2018
Please cite this article as: Vladimir V Dashkeev , Stephen J Turnovsky , Balanced-Budget Rules and Risk-sharing in a Fiscal Union# , Journal of Macroeconomics (2018), doi: 10.1016/j.jmacro.2018.06.008
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Balanced-Budget Rules and Risk-sharing in a Fiscal Union§ Stephen J. Turnovsky∗∗
Revised version June 2018 Abstract
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Vladimir V. Dashkeev∗
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This paper addresses the following question: What are the implications of the asymmetry of balanced-budget rules for interregional risk sharing in a fiscal union? We investigate our research question in a two-region, open economy DSGE model that is augmented with the public-sector features of a federal state. The analysis demonstrates that the asymmetry of balanced-budget rules is detrimental for the risk sharing in the union. The degree of risk sharing is a function of the public good productivity, specification of the technology process, and distribution of productivity shocks in the fiscal union.
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Keywords: balanced-budget rule, fiscal federalism, fiscal union, occasionally binding constraints, productive public expenditures, risk sharing JEL codes: E62, H60, H74, H77
§ The authors gratefully acknowledge comments they received from Alberto Bisin, Yu -chin Chen,
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Mikhail Dmitriev, Fabio Ghironi, Luca Guerrieri, Levis Kochin, Pavel Krivenko, David Lagakos, Oksana Leukhina, Federico Mandelman, B. Ravikumar, Alexander Rodivilov, Antonio Rodriguez-Lopez, MuJeung Yang, and participants of the Association of Public Economic Theory conference in Rio de Janeiro, July 2016 and MTI seminars at the University of Washington. The suggestions of a referee are also appreciated. ∗ Seattle University, Department of Economics, Albers School of Business and Economics, Pigott Building 316B, Seattle, WA 98122. Email: [email protected]. ** University of Washington, Department of Economics, Savery Hall 343, Box 353330, Seattle, WA, 98195. Email: [email protected].
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1.
Introduction
Federal states can grant varying degrees of fiscal sovereignty to their constituent members. These powers may range from delegating substantial fiscal autonomy to their member states, such as the
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United States, to unions having a powerful centralized supra-regional authority, such as Australia. Numerous important questions arise in considering the structure of governance, particularly with regard to the former scenario. This paper addresses the following issue: What are the implications of the asymmetry of balanced-budget rules for interregional risk-sharing in a fiscal union? This question is motivated by two stylized facts characterizing the U.S. as a fiscal union: (i) the asymmetric public
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borrowing limits across U.S. states and (ii) the heterogeneous structure of government expenditures across different levels of the union government.1 We view it as an important issue, since risk-sharing is one of the principal criteria that shape the choice of national governance systems and design of stabilization policies. In a union with initially identical interregional allocations, a deterioration of
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risk-sharing will likely have the undesirable effect of increasing inequality across the regions. The asymmetry of public borrowing limits adopted by state governments is institutionalized
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as state-specific, balanced-budget rules, and presents one of the salient features of the U.S. federal system.2 To render the analysis of these balanced-budget rules tractable, states have typically been
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classified into one of the following two categories: (i) states having strict balanced-budget rules and (ii) those with more flexible rules. This dichotomy is based on the Advisory Commission on
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Intergovernmental Relations index, ACIR (1987), which takes into account characteristics of the rules in each state.3 According to the accepted taxonomy in the fiscal federalism literature, states
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having an ACIR index between 7 and 10 are classified as having strict borrowing rules, while those with an index between 0 and 6 have more flexible rules. The latter group consists of 13, mostly
Henceforth, the terms “balanced-budget rules” and “borrowing limits” are used interchangeably to refer to the set of institutional constraints on the government’s ability to incur a budget deficit. 2 The ability of the federal government to borrow is taken as a given in the present study. 3 The index assumes values from 0 to 10, so that Vermont (the only state without a balanced-budget requirement) is at 0, while the states that require their budgets to be balanced at the end of the budgetary period are at 10. States receive intermediate values according to other characteristics of their balanced-budget rules, such as provisions for carrying debt over to future budget periods, and if so, then for how long, or whether the borrowing limits are constitutional or statutory. Additional details about the balanced-budget rules in the U.S. are presented in Appendix A. 1
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large, states (Figure 1). Cumulatively, these states having less stringent balanced-budget rules produced 46.2% of the U.S. GDP between 1977 and 2000.4,5 As discussed below, the states’ balanced-budget rules have real effects on the states’ fiscal policy, especially their stabilization policy over business cycles. The second inherent aspect of the U.S. fiscal federalism system incorporated in this study is
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the asymmetric provision of different types of public expenditures by the federal government and state governments, respectively. Centralization makes it possible to achieve substantial economies of scale in the provision of certain public consumption goods, such as national defense. Hence, this function is performed by the federal authorities. The provision of local, predominantly productive, public
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goods is usually delegated to regional governments, because decentralization is preferable in addressing local needs. These expenditures consist primarily of outlays for infrastructure and education-related items.6 In the U.S., more than two-thirds of public consumption goods are supplied by the federal government and over three-quarters of public productive goods are provided by state
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governments (Table 1).
Hence, the U.S. presents a natural case for the study of the asymmetry of borrowing limits in
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a fiscal union with heterogeneous public goods. To our knowledge, the economic consequences of these two important and empirically relevant forms of heterogeneity – asymmetry of the borrowing
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limits and of the public goods provision – have not been addressed within an integrated analytical framework. We investigate their economic consequences in a microbased, dynamic market-clearing
4
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general equilibrium model. Specifically, we augment the open economy model by Backus, Kehoe,
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Unless otherwise noted, this study uses 1977–2000 data due to the limited availability of state-level public finance and income series. Annual U.S. Census data start in 1977 and the BEA series for Gross State Product have a break in 2000 due to a transition from the SIC to NAICS. 5 Following the literature, Alaska and Hawaii are omitted from the present analysis due to their idiosyncratic characteristics. Alaska has persistent surpluses driven by its small economic size and dependence on oil production, while Hawaii has a unique public education system. Both states have strict balanced-budget rules. The re-estimated share of the cumulative output by the states with less stringent balanced-budget rules is reduced slightly to 45.7%. 6 The term “productive public goods” may assume different meanings. The seminal work of Aschauer (1989) operates with a narrow definition of productive public goods. It includes only investment in “core infrastructure,” i.e., highways, railroads, seaports, airports, utilities, etc. Such an approach remains common throughout the theoretical literature, e.g., Turnovsky and Fisher (1995) or, more recently, Leeper, Walker, and Yang (2010), and Leduc and Wilson (2013). Yet, a broad definition of productive public goods that includes expenditures that enhance the productivity of the private sector and encourage private investment suggests that Aschauer’s definition should be expanded. For example, models with human capital that treat education as an important factor of development suggest that expenditures on education should be included in the category of productive public goods. See, e.g., Lucas (1988) for a theoretical approach and Mankiw, Romer, and Weil (1992), for an empirical.
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and Kydland (1992) to include the public-sector features of a federal state, in which the provision of consumption and productive public goods receives special attention, as in Turnovsky and Fisher (1995), and more recently by Economides et. al. (2011) and Chatterjee and Ghosh (2011). The federal state we consider comprises two regions: “Rigid” and “Flexible”. The regional economies are identical (in terms of their size, technology, and preferences), with the exception of
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fiscal policy, specifically their ability to borrow or lack thereof. Each region is populated by a representative household and a representative firm. Labor mobility is prohibited between the regions, but there are no barriers to interregional capital mobility.7 We employ this framework to analyze the transmission of productivity shocks in the union, as well as to study the implications of the
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asymmetry for interregional consumption risk-sharing and welfare.
The analysis of the transmission mechanism of productivity shocks reveals the contrasting dynamic responses of the union members, highlighting how the asymmetric balanced-budget rules endogenously create heterogeneous allocations, even in response to common aggregate shocks.
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Consequently, the asymmetric public borrowing limits impair interregional risk-sharing. Following an adverse aggregate productivity shock, the region with no borrowing limit stabilizes its economy
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faster, by attracting resources from the region constrained by the balanced budget requirement. The intuition for this result is straightforward. The driving force behind the heterogeneous
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responses across union members to an aggregate productivity shock is the asymmetric dynamics of the regional public expenditures. Following the realization of the shock, the declining supply of the
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productive public good from the Rigid government, combined with the steady supply from Flexible, yields interregional differentials of marginal productivities. These interregional marginal
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productivity ratios are tilted in favor of Flexible, which leads to a shift of resources to the more productive jurisdiction in the union, thereby adversely affecting risk-sharing. The state-specific provision of productive public goods dwindles in the region with the restriction on public borrowing,
7 This treatment of regions serves to sharpen the asymmetry of interregional allocations created by heterogeneous balanced-budget rules. Labor supply is treated as fixed to contrast the effects of borrowing limits and government expenditure composition on the time paths of capital accumulation and welfare. If not shut down, the negative wealth effect channel would increase the supply of labor and, subsequently, capital stock and output, and then ultimately narrow the regional differences. Relaxing the assumption of the symmetric technology could either amplify or mitigate the interregional differences induced by the asymmetric fiscal policy. The exact outcome would depend on the direction of the technological asymmetry and the relative productivity of the regions.
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which amplifies the interregional differences. This mechanism contrasts with that of standard models, such as Backus, Kehoe, and Kydland (1992), where resources are shifted in response to idiosyncratic shocks. The nature of the regional budget balance requirements, in conjunction with the productivity of public capital, are important determinants of risk-sharing in the fiscal union, and for the relative welfare of
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the agents within its respective regions. Irrespective of its source, a sustained negative productivity shock results in lifetime welfare losses, though with markedly different impacts on the two regions. In all cases, the impact on the Flexible region is essentially independent of the productivity of public capital. This is because, by being able to borrow, Flexible has the ability to offset the negative effects of the decline in
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productivity. In contrast, the impact on welfare in the Rigid region is highly sensitive to the productivity of public capital. This is because of the balanced budget requirement which forces it to cut back on the provision of its public good, so that the more productive is government spending, the greater the decline in productivity, thereby exacerbating the adverse effects on lifetime welfare. Numerical simulations that we
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undertake suggest that in the extreme case where government capital is highly productive, the welfare loss experienced by Flexible following an aggregate (economy-wide) decline in productivity is only around
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60% of that in Rigid. However, the ratio of the Flexible region’s loss to that of the Rigid region increases as the productivity of public capital declines, and if the latter is extremely low, Flexible’s decline in
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welfare may even slightly exceed that experienced by Rigid. In the absence of spillovers, the welfare costs of regional (idiosyncratic) adverse productivity
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shocks are borne almost entirely by the region in which they occur, and vary inversely with the degree of persistence. In the case of Rigid the welfare costs increase with the productivity of public capital, while in
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Flexible they are essentially invariant with respect to this factor. While the impact on the other region is extremely weak, our simulations suggest that if the degree of persistence is sufficiently high, a productivity decline in one region may actually lead to a slight welfare gain in the other region. The existence of technological spillovers across the two regions leads to a sharing of the welfare costs between them. In the case where the adverse productivity shock occurs in Flexible, as the productivity of public capital increases, the welfare costs are increasingly shifted to Rigid, to the point where if the productivity is sufficiently high, the welfare costs are shared approximately equally. Thus to summarize: the degree 5
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of risk-sharing in the fiscal union is a function of the public good productivity, the nature of the technology process, and distribution of productivity shocks in the union. The remainder of the paper is structured as follows. Section 2 briefly relates our paper to the existing relevant literature. Sections 3 and 4 describe the economic environment and the resulting equilibrium conditions. The calibration of the key parameters is summarized in Section 5. In Section
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6, the effects of temporary, adverse productivity shocks of different types on regional performance are analyzed. Additionally, the implications of public good productivity for risk-sharing are considered. Section 7 concludes. An Appendix provides additional technical details. These include: (A) additional information regarding balanced-budget rules in the U.S; (B) derivation of the equation for
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net regional asset accumulation; (C) summary of the equilibrium conditions of the model; and (D) some simulations obtained under alternative assumptions regarding technology process specifications. 2.
Relationship to the literature
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This paper sets itself apart from the existing literature by its simultaneous focus on regional
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integration, the composition of public goods, and the nature of the fiscal rules imposed on the regions. The optimum currency area literature provides the theoretical foundation for regional integration. Seminal works, including those of Mundell (1961), McKinnon (1963), and Kenen (1969),
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motivate integration through the improved ability of the union, rather than individual states, to
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withstand different types of adverse shocks. Mundell (1961) and McKinnon (1963) argue that monetary unions are optimal in the face of aggregate shocks. However, if the union economy is
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affected by member-specific shocks, no benefit is accrued from monetary integration. Kenen (1969) points out the desirability of complementing monetary integration with fiscal unification. He supports his argument with the U.S. experience in which transfers from federal to state governments serve as interregional fiscal risk-sharing. Results of the present analysis can be interpreted as an extension of Kenen (1969), in that members of a fiscal union can benefit from their membership after a realization of aggregate shocks. Recent theoretical studies of fiscal unions continue to analyze the conditions for unification, 6
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from the standpoint of the risk-sharing improvement. See, e.g., Farhi and Werning (7) and Dmitriev and Hoddenbagh (2015). However, such analyses are undertaken in symmetric environments, in which aggregate shocks would not yield interesting dynamics and there would be no benefit of the fiscal unification in the absence of idiosyncratic shocks. Both studies abstract from public borrowing limits as well as productive public goods.
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Several empirical studies of fiscal unions focus on the channels of risk-sharing. Asdrubali, Sorensen, and Yosha (1996) find that 13% of output shocks are smoothed by the U.S. federal government through taxes, transfers, and grants, while about two-thirds of the shocks are accommodated by capital and credit markets. A similar relative importance of the consumption-
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smoothing channels is found in other federations, e.g., Hepp and von Hagen (2013) obtain close results for unified Germany. Sorensen and Yosha (1998) examine consumption smoothing in the European Union and find that the transfers among its eight oldest members smooth at most 7% of output shocks.
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The literature studying the structural forms of the composition of public expenditure is relatively sparse. To the best of our knowledge, all such studies model public expenditures on the part
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of the general government in a unitary state and without consideration of public borrowing limits. For example, Turnovsky and Fisher (1995) consider heterogeneous public goods. They introduce both
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productive and consumption public expenditures and analyze macroeconomic effects of temporary and permanent changes in the expenditures on capital accumulation and welfare.8
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Leduc and Wilson (2013) depart from the tradition of modeling the general government public expenditure in unitary states. They consider a two-region model of the U.S., with the provision of a
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productive public good, highway infrastructure. Short- to medium-run effects of the productive public good provision generated by their structural model match the empirical responses of the key macroeconomic variables. The effects of balanced-budget rules have been previously studied in the context of unitary economies. Stockman (2001) analyzes the potential welfare effects of the balanced-budget rule proposed in 1995 for the U.S. Federal Government. Aiyagari, Marcet, Sargent, and Seppala (2002) 8
For example, Agenor (2013) provides a comprehensive study of different types of public goods.
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focus on the cost of debt service in a unitary economy, in which the government is subject to a borrowing limit. They find that a decrease in the stock of public debt increases welfare and argued for the accumulation of reserves to reduce the costs of future stabilization policies. Azzimonti, Battaglini, and Coate (2010) study the political economy of balanced-budget rules, explicitly modeling the election process. They find that borrowing limits increase welfare through the
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elimination of pork-barrel spending.
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3.
Analytical framework
This section sets out a general description of the underlying economic environment, which augments Backus et al. (1992) to include the key public-sector features of a federal state. Special attention is paid to the provision of consumption and productive public goods, as in Turnovsky and Fisher (1995) and
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more recently Economides et al. (2011). The economy comprises households, firms, and two levels of government: federal and regional. Following this description of the environment, the implied equilibrium conditions for the economy are derived. 3.1
Economic environment
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As noted, we consider a federal state that comprises two regions: Rigid and Flexible. The regional economies are identical, with the exception of their respective fiscal policies. Each region is inhabited by a representative household and a representative firm. Labor is immobile between the regions, but there are no impediments to interregional capital mobility.9
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The government in the federal state consists of two levels. The first level is represented by the Federal government, which collects capital income and labor income taxes from both regions, and
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provides a public consumption good equally available to both regions. Regional governments represent the second level of governance. Each regional government provides a productive public
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good to the local representative firm financed primarily by a consumption tax collected from the residents of its own region. In addition to using the productive public good, firms employ private
regions.
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capital and labor to manufacture a consumption-investment good that is homogeneous across the
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Households in both regions have access to one-period, risk-free private and public bonds. The
public bonds can be issued by either the federal or regional authorities. However, region-specific borrowing limits are introduced to ensure the model’s consistency with the stylized facts that characterize the heterogeneous balanced-budget rules adopted by the U.S. states. Accordingly, only one of the regions, Flexible, has the authority to borrow, while the Rigid region has a zero-borrowing
9
See footnote 7 for the motivation for these assumptions.
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limit. Since all types of bonds are risk-free, the asset markets are incomplete. In describing the model we shall focus on Rigid. Unless otherwise stated, the Flexible region’s environment is symmetric; variables pertaining to the Flexible region are indicated by asterisks. Firms
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3.2
The representative firm hires labor, Lt , supplied inelastically, from its region. It employs private capital, K, and uses the stock of region-specific publicly provided physical capital, KRG, to produce a homogeneous output good, Y, in accordance with the Cobb-Douglas production function (1):
0 1
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Yt Zt Kt L1 ( K RG,t )G ,
(1)
Output also depends on the total factor productivity, Z t , which is affected by the realization of a technology shock. Total factor productivities of the two regions are generated by the following
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autoregressive processes:
ZZ Zt 1 t . Z Zt*1 t* *
(2)
*
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Zt Z Z * t Z *Z
Thus, in general, the technology shocks across the two regions are interdependent, giving rise to
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regional spillovers. Section 5 below, imposes more structure on the matrix Φ in (2), drawn from
3.3
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empirical evidence.
Households
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The representative household in the Rigid region derives instantaneous utility from private and public consumption goods, C and CG, according to an isoelastic utility function (3), where 0 is the inverse of the intertemporal elasticity of substitution for the private consumption good and
G 0 pertains to the public consumption good. Ct1 CG1 G . 1 1 G 10
(3)
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3.4
Federal Government
The Federal government collects capital and labor income taxes at uniform rates, K and L , from both regions, and provides fixed amounts of the public consumption good, CG, available equally to residents of both regions. In the absence of any borrowing limits imposed on it, the Federal
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government issues one-period, risk-free bonds, BFG, that pay an interest rate RFG,t at the beginning of period t. The federal bonds are available for purchase to households of both regions. The federal 10
* authorities also impose lump-sum taxes on the residents of each region, TFG and TFG . Thus, the
budget constraint of the Federal government is expressed by the following relationship: * * BFG ,t 1 BFG ,t 1 CG (1 RFG ,t )( BFG ,t BFG ,t )
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* K ( Rt Kt Rt* Kt* ) L (Wt L Wt * L* ) TFG ,t TFG ,t
(4)
where R, R* are the returns to private capital, W ,W * are the wage rates, both determined below. 3.5
Regional Governments
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Both regional governments collect consumption taxes at a uniform rate, C , from the residents of
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their respective regions, and provide a productive public good, IRG, to the local representative firm. * They are also assumed to levy regional lump-sum taxes, TRG and TRG respectively. Although many
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U.S. states collect income taxes in addition to, or instead of, consumption taxes, we restrict the regions to collect consumption (and lump-sum) taxes only. The reason for imposing this restriction
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is to ensure that the results of our study reflect the role of the asymmetric balanced-budget rules rather than also reflecting differences in the interregional tax-systems.11
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The regional governments’ borrowing limits, and hence their budget constraints, are regionspecific. The form of these constraints is based on the findings of empirical studies that confirm the real (and asymmetric) effects of balanced-budget rules across different types of states on their fiscal policy. Using data from the early 1990s, GAO (1993) summarize the states’ responses to prospective
10
The lump-sum taxes may be negative, in which case they may be interpreted as transfers, such as welfare and social security payments. 11 We acknowledge that the asymmetry of regional tax structures is important for the macroeconomic performance of the union; thus, we study its implications in a companion paper.
11
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deficits. In those cases in which the deficit was estimated after the budget had been passed by the legislature, only 4% of the deficit reduction was achieved via revenue increases, while 60% was achieved by sequestration. The remaining 36% of the prospective deficits were accounted for by “adjustment of budget execution,” including short-term borrowing.12 Poterba (1994, 1995) and Bohn and Inman (1996) confirm that increasing tax revenue is the
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least common response on the part of state governments to the negative shocks. States with strict balanced-budget rules are less likely to borrow, and most often resort to a reduction of their public expenditures. States with less stringent rules rely on borrowing to maintain their public spending at the pre-shock level. Bayoumi and Eichengreen (1995) show that the cyclical responsiveness of the
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states is affected negatively by the stringency of their balanced-budget rules. In this sense, the fiscal policy of the states with strict balanced-budget rules amplifies business cycle downturns, and therefore leads to destabilization, while the fiscal policy of those states with less stringent balanced-budget rules mitigates economic downturns.
In the case of windfall tax revenues, the behavior of the two types of the states differs as
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well.13 Although both groups of states change their expenditures little during expansions, their use of
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the unplanned tax revenues varies. States with strict balanced-budget rules direct the budget surplus to finance lump-sum transfers. At the same time, states with less stringent balanced-budget rules also
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use the windfall revenues to reduce their debt burdens. These facts from the data and empirical studies motivate the construction of the model in
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which the balanced-budget rules have real effects. Thus, using Poterba’s (7) terminology, the present analysis contributes to the “public choice view,” as opposed to the “institutional irrelevance”
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hypothesis. The former treats institutional constraints as important factors of fiscal policy, while the latter suggests that such limitations can be circumvented effectively and therefore do not affect policymakers’ actions. In our stylized model, the government of the Rigid region has a zero-borrowing limit and the
12
Besides borrowing, “adjustment of budget execution” refers to a number of temporary measures, including the use of rainy-day funds and various accounting gimmicks, such as interfund transfers and deferrals of payments. 13 See, e.g., Poterba (1995) and Sorensen and Yosha (2001).
12
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public good provision is thus determined only by current tax revenues of the region and is exogenously capped at the steady-state level, I RG :
C Ct TRG ,t I RG ,t , (5)
I RG ,t min{ C Ct , I RG }.
The Flexible region’s government is unconstrained by a borrowing limit and therefore can F
, where
RG F
denotes “Flexible Regional Government”, to
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issue one-period, risk-free bonds, BRG
maintain the provision of the productive public good independently of transitory shocks to its revenues, that is at the exogenously predetermined steady-state level. The interest rate RRG F,t is paid to the bondholders at the beginning of the period. Accordingly, the budget constraint of the Flexible
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government takes the following form:
* * * * C Ct* BRG F ,t 1 BRG F ,t 1 TRG ,t I RG (1 RRG F ,t ) BRG F ,t (1 RRG F ,t ) BRG F ,t ,
(6)
* where BRG F and BRG F refer to the bond holdings of the representative households in the Rigid and
4.1
Equilibrium Conditions Firms
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4.
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Flexible regions, respectively.
The representative firm in the Rigid region maximizes its profits, which in the absence of adjustment
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costs, yields the standard optimality conditions (7a) and (7b), equating the wage and the return to
W (1 )Yt L ,
(7a)
Rt Yt Kt .
(7b)
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private capital to marginal productivities of labor and capital stock, respectively:
The rate of accumulation of the private capital stock is standard, where δ ∈ (0, 1) denotes the depreciation rate:
Kt It (1 ) Kt 1 . Analogous conditions apply to the firms in the Flexible region. 4.2
Households 13
(7c)
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The representative household in the Rigid region chooses its rates of consumption, and accumulation of private capital, and holdings of private and public (Federal and Flexible) bonds, to maximize its intertemporal utility (8), where β ∈ (0, 1) is a subjective discount factor, subject to the budget constraint (9):
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C 1 C 1 G max Ct , Kt1 , Bt1 , BFG ,t 1 , BRG F ,t 1 Et t t G t 0 1 1 G subject to
(8)
Kt 1 Bt 1 BFG ,t 1 BRG F ,t 1 (1 L )Wt L (1 C )Ct
[(1 K ) Rt (1 )]Kt (1 RPRI ,t ) Bt (1 RFG ,t ) BFG ,t (1 RRG F ,t ) BRG F ,t
(9)
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( Bt 1 ) 2 ( BFG ,t 1 ) 2 ( BRG F ,t 1 ) 2 TFG ,t TRG ,t T ,t . 2 2 2
The budget constraint asserts that the household allocates its disposable labor and capital income and returns on its bond holdings between consumption spending, the accumulation of productive private capital, and purchases of the private and public bonds. Households pay a bond-
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holding adjustment fees (brokerage fees) η to financial intermediaries. With all bonds being riskless,
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quadratic bond-holding adjustment costs, such as are being introduced here, are necessary to ensure a determinate macroeconomic equilibrium and stationary the responses of the economy to transitory
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shocks.14 These transactions fees are rebated to households via Tη. Finally, the household pays lumpsum taxes to, or receives lump-sum transfers from, both levels of government, TFG and TRG.
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The solution to the optimization problem yields the set of Euler equations (10a) – (10d) for the Rigid households. In the absence of any capital controls, these yield no-arbitrage conditions that
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equate interest rates on all types of bonds with returns on private capital, adjusted for depreciation and the tax on capital income. (Ct ) Et [(1 K ) Rt 1 1 ] Et (Ct 1 )
(10a)
14 The issue here is the familiar one of indeterminacy of equilibrium of a small open economy facing perfect world financial markets. Various approaches (offering varying degrees of sophistication) to closing such a model and thereby ensuring a determinate equilibrium have been proposed. The specification of quadratic fees, first introduced by Turnovsky (1985) and adopted subsequently by various authors (e.g. Benigno (2009), Erceg et al. (2006), Ghironi (2007), Cacciatore (2014)) suffices in the present context.
14
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(1 RPRI ,t 1 ) (Ct ) (1 Bt 1 ) Et (Ct 1 )
(10b)
(1 RFG ,t 1 ) (Ct ) Et (Ct 1 ) (1 BFG ,t 1 )
(10c)
(1 RRG F ,t 1 ) (Ct ) Et (Ct 1 ) (1 BRG F ,t 1 )
(10d)
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Finally, to satisfy the intertemporal budget constraint, the household is subject to the usual transversality conditions on capital and the various bonds. The former ensures that all capital is used by the end of time; the latter implies that the household cannot finance its consumption indefinitely by borrowing. Analogous conditions apply to households in Flexible. Federal Government
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4.3
In order to rule out the explosion of public debt, a fiscal feedback rule is introduced.15 We adopt the rule from Erceg, Guerrieri, and Gust’s (2006) SIGMA model, which relates the budget-deficit-to-
region takes the following form:
TFG ,t 1
B B st FG ,t 1 stst Ystst Yt
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TFG ,t
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output ratio to the debt-to-output ratio. The rule for the federal debt held by residents of the Rigid
Yt
Yt 1
BFG ,t 1 BFG ,t gr Yt 1 Yt
,
(11)
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where parameter ιgr ∈ (0, 1) determines the speed of the debt adjustment, which increases with ιgr, parameter ιst ∈ (0, 1) determines the cyclicality of the adjustment, and the variables with the stst
refer to their steady-state values. The adjustment rule for the federal debt held by
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subscript
residents of the Flexible region is symmetric. Regional Governments
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4.4
Similar to the federal government’s case, an analogous fiscal feedback rule restricts the accumulation of the regional public debt. Since only Flexible has no borrowing limit, only one regional rule is necessary. The rule applies to the bonds issued by the government of the Flexible region and held by households in both the Flexible and Rigid regions: 15
A discussion of the necessity of the fiscal feedback rule for determinacy of equilibrium and model stability can be found in Aiyagari et al. (2002).
15
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* TRG ,t
Yt *
* BRG F ,t 1 BRG BRG F stst , F ,t 1 * st * * Yt 1 Yt Ystst * * BRG F ,t 1 BRG F ,t 1 BRG F ,t BRG F ,t gr . * * Y Y t t 1 * TRG ,t 1
(12)
The rate of accumulation of public capital, KRG, is analogous to that of private capital. Parameter G
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∈ (0, 1) is the rate of depreciation of public capital stock. K RG ,t 1 I RG ,t (1 G ) K RG ,t
4.5
Aggregation and Interregional Trade
(13)
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Combining the budget constraints of the households and the governments yields the aggregate market clearing condition (14), where the aggregation is over activity in the two regions.16 * Yt Yt* Ct Ct* It It* CG I RG,t I RG ,t .
(14)
In a multi-regional economy, trade between the regions can occur and, in general, need not balance, in
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which case the balance of trade (BOT) can be expressed as:
(15)
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BOTt Yt Ct It 0.5CG I RG ,t .
In the case where one region runs a trade deficit, its representative household issues private debt obligations to finance its private expenditures. Then the equation for the Rigid net regional asset
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accumulation takes the following form:17
1 1 Rt Kt Rt* Kt* (Wt L Wt * L* ) 2 2 1 1 1 * Ct Ct* I t I t* I RG ,t I RG . 2 2 2
(16)
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Bt 1 (1 RPRI ,t ) Bt
Finally, in the two-region economy, private bonds issued by one region are necessarily purchased by the other, and hence the bonds are in zero net supply:
16 More specifically, to derive (14), substitute the taxes and bond holdings in the household budget constraints (9), together with the corresponding terms from the federal and regional budget constraints (4, 5, 6). As described above, assume that the bond-holding adjustment fees are rebated to the households. Summing up the regional household budget constraints yields the union accounting identity. 17 Being a two-region economy, the positive net regional asset position of one region corresponds to the net positive holdings of assets issued by the other region by the residents of the former region. See Appendix B for details.
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Bt Bt* 0.
5.
(17)
Calibration
The model’s parameters are calibrated at an annual frequency, and their values are summarized in Table 2. The discount factor, β, is set to 0.9615. Setting γ = 2 implies an intertemporal elasticity of
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substitution for private consumption goods of 0.5, well within the estimated range reported by Guvenen (2006); γG = 2 is an analogous parameter for the public consumption good.18
The share of national income that accrues to private capital, α, is 0.36, while the remainder accrues to labor. The elasticity of the output with respect to public capital, G , reflects its productivity, and its estimates are more far-ranging.19 The original estimate of this parameter
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reported by Aschauer (1989), 0.39, exceeds the productivity of private capital. Aschauer’s work spurred numerous empirical studies that generated a broad range of productivity estimates for total public expenditures and its components. The sweeping majority of the obtained estimates vary between 0.05 and 0.4, with a consensus that some categories of public expenditures increase private sector
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productivity more than others. Bom and Ligthart (2014) conduct a meta-regression analysis of 68 public good productivity studies published between 1983 and 2008. Their results range from 0.083
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for the short-run estimates to 0.122 for the long-run estimates. When attention is restricted to regional productive public goods, the productivity estimate increases to 0.193. Given the range of
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empirical estimates of the productivity of public investment, we choose G 0.2 as a baseline (medium) value and conduct robustness tests with alternative values of the productivity parameter:
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0.05 (very low), 0.1 (low), and 0.3 (high). The depreciation rate is set to 0.10 for private capital stock and 0.08 for more durable public
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capital. The capital income tax rate, K , is set to 0.305, the labor income tax rate, L , is 0.24, and the consumption tax rate, C , is 0.10.20 The speed of public debt adjustment, ιgr, is chosen following the SIGMA model and is equal to 0.1. The bond-holding adjustment cost, η, is set to the frequently
18
Our decision to calibrate at an annual frequency is dictated by the fact that regional governments typically budget on an annual basis. 19 Eicher and Turnovsky (2000) interpret low public good productivity as substantial congestion of the public goods. 20 These tax rates are generally reflective of the US tax rates over a number of years as summarized by McDaniel (2007).
17
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adopted value in the literature, 0.0025 (see e.g. Cacciatore (2014) and Ghironi (2007)). Next, the bivariate exogenous productivity process must be parameterized. In the absence of information at the regional level, we draw on parameterization employed at the international level. Even here, as Baxter and Farr (2005) have noted, it has proven difficult to estimate the parameters of
processes, to capture the likely range of parameter estimates:
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the productivity process with much precision. Accordingly, we allow for two types of technology
First, we adopt the parameterization suggested by Baxter and Farr (2005) on the basis of empirical evidence of extremely high persistence of shocks and no interregional spillovers, which we transform to annual frequency as:21:
ZZ 0.996 0 . Z 0 0.996 *
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Z Z *Z
(18)
*
Second, Heathcote and Perri (2002) estimate a somewhat lower degree of persistence, but with positive spillovers, which we transform to annual frequency as
ZZ 0.888 0.091 . Z 0.091 0.888 *
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Z Z *Z
(19)
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*
In order to quantify the marginal influence of the technology spillovers on interregional consumption risk-sharing and welfare resulting from the transmission of productivity shocks across regions, as a
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third alternative we omit the spillover component from the Heathcote-Perri specification, modifying it
Z Z *Z
ZZ 0.888 0.000 . Z 0.000 0.888 *
(20)
*
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to:
Finally, consumption, investment, and government expenditure shares are calibrated to 62.4%,
17.9%, and 19.7% of national output, respectively.22 We calibrate the share of the consumption public good provided by the federal government and the share of productive public goods provided by the regional governments to the corresponding shares of current and capital operations budgets in 21 Both the Baxter-Farr (2005) and the Heathcote-Perri (2002) process specifications are based on a quarterly frequency, which we have transformed to an annual frequency, since, as noted, this is a more appropriate time unit for our analysis. 22 The average values for 1977–2000 were calculated from the NIPA Table 1.1. The national output is defined as domestic absorption consistently with the market-clearing condition (21).
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the national income, 15.3% and 4.4%, respectively. This approach is adopted for a number of reasons. It is consistent with fiscal policy studies that model general government behavior. Moreover, it helps to mitigate the ambiguity regarding the attribution of different types of expenditures to publicly provided consumption and productive goods. First, not all capital expenditures are productive. For example, Aschauer (1989), Finn (1993), and others show little productive effect of national defense
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expenditures and some smaller categories of government investment. Second, some authors argue that the current expenditures can be productive; for instance, Evans and Karras (1994) emphasize the productive role of current expenditures on education. Such arguments, combined with the fact that current expenditures on education amount to 41% of state expenditures, make it worrisome to dismiss
6.
Analysis of Shocks in the Union
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the entire current expenditures category as completely unproductive.
Using the calibrated parameter values, the equilibrium conditions derived in Section 3 and summarized in Appendix C, are solved numerically for the unique symmetric steady state. Decision
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rules and dynamic responses of the endogenous variables to productivity shocks are obtained with
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the first-order perturbation technique. The choice of the linear solution method is dictated by the compatibility requirements of the Guerrieri and Iacoviello (2015) occasionally binding constraints toolkit. Having derived the numerical solutions, we then investigate how the asymmetric public
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borrowing limits affect the transmission channels of productivity shocks in the fiscal union. We also
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analyze the welfare effects of the shocks and check the sensitivity of the results to the productivity of public goods.
The productivity shock we consider is an adverse one, specified as a one-time 1% reduction
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in productivity. Initially the medium productivity ( G 0.2 ) of public goods is assumed. We begin by assuming that the productivity shock is common to both regions (Section 6.1) followed by those specific to one region only (Section 6.2). To sharpen the effects of borrowing limits on the macroeconomic dynamics, Section 6.1 begins by abstracting from possible technological spillovers between the regions. This specification is plausible for regions having different industrial structures, such as if one region specializes in services, such as IT and finance, while the other is primarily 19
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agricultural. After establishing the intuition for the transmission of shocks, in Section 3 we allow for technology spillovers between the regions. This case is more relevant for regions having similar industrial structures and correspondingly stronger technology linkages. Section 6.4 discusses the consequences of varying degrees of public good productivity for risk-sharing before turning attention
6.1
Aggregate Shock in Absence of Spillovers
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to their welfare implications (Section 6.5).
Figure 2 illustrates the dynamic response of the economy without technology spillovers in the scenario of an aggregate adverse productivity shock with a high degree of persistence.23 We begin with the
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analysis of the public sector dynamics, which are the underlying driving force. On impact of the shock, all types of tax revenues (consumption, capital income, and labor income) decline in both regions, as their corresponding tax base contracts (consumption expenditures, investment expenditures, and wages, respectively). However, the response of public investment differs between
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the regions. The Rigid government, constrained by the zero-borrowing limit, finances its expenditures with tax revenues only, which fall during the downturn. The Flexible government has
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the authority to borrow and thereby maintain the provision of the productive public good at the preshock level. These dynamics are reflected in the time paths of the public investment and public capital
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stock.
The reduced supply of the productive public good from the Rigid government leads to
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interregional differentials of marginal productivities. Since the productive public good augments the productivity of both private factors, the marginal productivity of capital as well as the marginal
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productivity of labor are affected.24 Their interregional productivity ratios move in favor of Flexible, which leads to the shift of resources to the more productive region in the union and, in turn, thereby reducing the amount of risk-sharing. Although the reduction of the public expenditures in the Rigid region increases availability of
23
The transmission of aggregate shocks in an economy with technology spillovers is qualitatively identical. The corresponding impulse responses are presented in Figure D.1. 24 The decline of the marginal products of labor is due to the dynamics of the total factor productivity and, with an inelastic labor supply, changes at the private and public capital margins rather than the labor margin.
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the resources for private absorption, these resources are not used for private investment locally, but instead are loaned to private and public borrowers in the rest of the union. Moreover, the Rigid region’s consumption, as well as private and public investments, fall faster than does its output due to the interregional shift of resources. The undersupply of both public and private investments in the Rigid region has a negative influence on its post-shock recovery.
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Productive public good provision in the Flexible region is financed in part by its own residents, while the rest of the funding comes from the residents of Rigid. Contrary to the Rigid region, the interregional shift of resources dampens the contraction of private consumption and investment in Flexible. Additionally, the allocations in the Flexible region return to their respective
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steady-state levels more rapidly.
The Federal government is unconstrained by a borrowing limit and provides the public consumption good at a steady rate. The debt-financed portion of its provision is financed by the Rigid representative household. Because marginal productivity is lower in the Rigid region, its household has an incentive to invest in public bonds, instead of local private capital. Thus, the Federal
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government’s borrowing increases the asymmetry of allocations in the union. On the other hand, the
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steady provision of the consumption public good by the Federal government improves interregional risk-sharing.
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The Rigid representative household holds a net positive asset position in all types of bonds on impact and during the early periods after the shock. Over time, once the effect of the productivity
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shock weakens sufficiently and the decumulation of private capital increases the return on capital, the marginal productivity ratios reverse and the shift of resources changes its direction.
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The demand for loanable funds grows as the indebtedness of both the Federal and Flexible governments and of the Flexible representative household increases. Hence, the returns on all types of bonds grow, which is consistent with the no-arbitrage condition implied by the Euler equations (10a) – (10d). The uninterrupted flow of the productivity-augmenting public good provided by the Flexible government allows that region to utilize the shift of resources, stabilize its economy, and improve its relative performance. From the union’s standpoint, the drawback of this policy is the deterioration of the interregional risk-sharing. 21
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6.2
Idiosyncratic Shocks in Absence of Spillovers
In the scenarios of idiosyncratic shocks, the region in which the shock is realized is hurt due to both the decreased marginal productivity of private factors and the consequential outward shift of resources. The other region is affected positively by the inward shift of resources, correspondingly.
improves the relative performance of the region that adopts it. 6.2.1 Shock to Rigid Region
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Similar to the scenario of aggregate shocks, the Flexible fiscal policy acts as a shock absorber and
The adjustment of the macroeconomic variables after a negative asymmetric shock to the Rigid
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region’s economy is illustrated in Panel A of Figure 3. Since the adverse disturbance directly affects the Rigid region, in the absence of spillovers, the Flexible region is affected positively via the shift of resources from Rigid. Interregional trade is no longer balanced in response to the marginal productivity differential between the regions. The balance of trade captures the corresponding shift
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of resources to the more productive region. On impact and immediately after the shock, the Rigid region runs a trade deficit, and the Flexible region holds a positive net regional asset position in
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private bonds against the Rigid region. The inward shift of resources increases Flexible’s transitional allocations of investment, consumption, and output above their respective steady-state levels.
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The behavior of the other endogenous variables follows the pattern established in the analysis of the aggregate shock scenario. The allocations of the variables diverge across the regions. The
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impulse responses of consumption demonstrate that the interregional risk-sharing deteriorates. This deterioration is more pronounced than that in the previously discussed scenario of aggregate shocks
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and as compared with the scenario of an idiosyncratic shock to Flexible, as discussed next. 6.2.2 Shock to Flexible Region Following an adverse productivity shock to the Flexible region, marginal productivity differentials are tilted in favor of the Rigid region, as illustrated by Panel A of Figure 4. Hence, the latter region receives the inflow of resources from the former. This shift of resources is smaller as compared to the previous scenario, and so is the overaccumulation of capital by the Rigid region, unaffected by 22
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the shock directly. As before, the dynamics of the regional public good supply are responsible for this outcome. However, contrary to the previous scenario, the government of the region directly affected by the negative shock does not allow the provision of the local productive public good to contract. This enables a faster recovery of that region’s marginal productivities. Hence, the interregional ratio of
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the marginal products of capital flips, and reverses the shift of resources substantially faster than in the scenario of an idiosyncratic shock to the Rigid region. Intuition for the dynamics of other variables is as discussed in the preceding section.
Note that in the scenario of an idiosyncratic shock to Flexible, the asymmetric borrowing
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limits adopted by the regions have beneficial implications for risk-sharing. In such an arrangement, the absence of a borrowing limit allows the Flexible region affected by the adverse disturbance to stabilize its economy and to recover from the shock’s effects faster. One can arrive at this conclusion by visually examining the allocations of consumption on Panel A of Figure 4. Numerical support for
Shocks in Presence of Spillovers
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6.3
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this statement is presented in Section 6.5 below.
Having identified the shock transmission mechanism in the absence of technology spillovers, it is
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natural to consider an economy with interregional spillovers. Such a specification is arguably more realistic for the U.S., as a union with numerous interregional and interindustry links. On one hand,
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the choice of the technology process specification is immaterial for the dynamic response of the model economy in the scenario of aggregate shocks. Figures 2 and D.1 show that the time paths of
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macroeconomic variables are virtually identical. On the other hand, the spillovers start playing a role in the idiosyncratic shock scenarios. A
comparison of Panels A with Panels B of Figures 3 and 4 points out that the technology spillovers ensure comovement of the endogenous variables, speed up the transition, and hence affect quantitative outcomes of the model. For example, output expansions in the regions unaffected by adverse idiosyncratic shocks directly are short-lived in the framework with spillovers. Additionally, a recession in one region leads to a downturn instead of an expansion in another, albeit a smaller one 23
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and with a lag. Also, in the region affected by the shocks indirectly, through spillovers, consumption never increases (although output does), due to the forward-looking, consumption-smoothing behavior of rational households. The main finding from the comparison of the economy responses in the presence and in the absence of technology spillovers is as follows. By inducing comovement of the macroeconomic
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variables, and by reducing the range of fluctuations, spillovers mitigate the effects of the asymmetric balanced-budget rules in the idiosyncratic shock scenarios. Hence, the interregional technology linkages improve interregional risk-sharing, conditional on the realization of idiosyncratic shocks, though not in the scenario of aggregate disturbances. This finding is numerically supported by the
6.4
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analysis presented in Section 6.5 below. Effects of Public Good Productivity
To assess the consequences of the variations in the degrees of public good productivity, we investigate the model’s behavior under alternative parameterization of the productivity of public
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goods, G . Besides the baseline medium productivity value of 0.2, we consider high, low, and very
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low values of public good productivity ( G 0.30, 0.10, 0.05 ). The highest considered value of 0.30 is closer to Aschauer’s original estimate of public infrastructure productivity of 0.39, but still below
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the private capital productivity. The lowest value, 0.05, reflects the diminished productivity of significantly congested productive public goods.
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The risk-sharing implications of public borrowing limits in this model are robust with respect to G , ranging from low to high levels. The higher productivity of public goods is associated with
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worse interregional risk-sharing, as it leads to: greater differences between the two types of regions in output, wages, consumption, private and public investment, and private and public capital stock; larger fluctuations in interregional trade and all types of bond holdings; and smaller fluctuations in interest rates. Panel A of Figure 5 illustrates this point with the time paths for consumption, output, and interregional balance of trade after an aggregate shock in the economy with spillovers. The analysis of the transition after idiosyncratic shocks (Panels B and C of Figure 5) supports that observation. When the productivity of public goods is higher, the undersupply of the public 24
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goods becomes costlier as measured by levels of macroeconomic variables or interregional differentials. The scenario of an idiosyncratic shock to the Rigid region sharpens strongly the difference between alternative fiscal policies (Panel C of Figure 5). The relative loss, measured as a percentage deviation from the steady-state levels, is quite steady in the Flexible region regardless of the public
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good productivity. This is in contrast to the dynamics in the Rigid region as represented in Panel B of Figure 5. The shift of resources from the Rigid to the Flexible region becomes costlier for the former region when public good productivity is higher. The undersupply of public goods negatively affects the marginal productivity of private factors and therefore brings about a larger shift of resources and
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greater losses of consumption and output. These results obtained for the technology process specification with spillovers qualitatively hold in the absence of spillovers (Figure D.2). As public good productivity falls to being very low (G 0.05) , not only does the interregional consumption differential become smaller, but the relative performance of the two regions is reversed as well. At first glance, this result might appear surprising, as it seems to
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contradict Barro’s (1979) tax-smoothing hypothesis, which implies the optimality of public
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borrowing.25 However, there is no contradiction. Barro’s analysis does not consider productive government expenditures. Once productive public goods are introduced, as in the present study, the
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optimality of public borrowing is determined by two counteracting forces associated with the provision of productive public goods: an enhanced private-factor productivity due to productive
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public expenditures, on one hand, and, on the other, decreased private investment and consumption due to the resource-withdrawal effect. Hence, in the case of sufficiently low productivity of public
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goods, debt financing of public expenditures is not justified, since the cost of public investment is greater than its benefit, and refraining from public borrowing improves welfare of the local representative household. 6.5
Welfare
25 In Barro’s model, public borrowing helps to maintain a constant tax rate after a realization of adverse shocks. The government debt eliminates wedges associated with the adjustment of distortionary tax rates. Hence, public debt that is brought about by a budget deficit can be viewed as a byproduct of optimal fiscal policy.
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We begin by analyzing lifetime welfare in the model economy following the realization of a one-time aggregate productivity shock. Then, idiosyncratic shocks are considered. 6.5.1 Aggregate Shock Consider two technology process specifications: one with high persistence and without technology
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spillovers (eq. 18), and another with lower persistence and with technology spillovers (eq. 19). Conditional on the medium productivity of the public goods, the Flexible region is better insulated against aggregate adverse shocks than the Rigid region (Panel A of Table 3). The welfare loss amounts to 1.57 to 2.12% (1.19 to 1.61%) of the Rigid (Flexible) region’s lifetime welfare,
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depending on the technology process specification.
Due to the difference in regional fiscal policies, the Rigid representative household enjoys a 0.38 to 0.51 percentage point lower lifetime consumption relative to the Flexible household in the aftermath of the shock. Panel A of Table 3 shows that, as the public good productivity increases, the under-provision of public goods becomes costlier for the region, as measured by its representative
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household’s loss of welfare. Consequently, as G decreases, the benefit of public borrowing
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vanishes. Both the absolute welfare loss and the consumption differential between two regions decreases.
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If the public good productivity is too low, or if the goods are substantially congested, the adoption of the Flexible fiscal policy is no longer welfare improving, as compared with the Rigid
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policy. The intuition for this outcome was presented in Subsection 6.4 above. Finally, to assess the marginal effect of the technology spillovers, results of the model with
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lower persistence of the shocks and without spillovers (eq. 20) are presented in the remaining columns of Table 3. Our analysis shows that the spillovers are responsible for approximately one half of the welfare loss in the specification with lower persistence of the productivity shocks. 6.5.2 Idiosyncratic Shocks Panels B and C of Table 3 document the welfare consequences of idiosyncratic shocks to the union, conditional on the strength of technology spillovers and persistence of the shocks. 26
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In the specification with high persistence and without technology spillovers, the shift of resources is more pronounced. An idiosyncratic shock to Rigid leads to welfare improvement in Flexible, and vice versa, as a shock to Flexible improves the welfare of Rigid. However, due to the adoption of the Flexible fiscal policy, the corresponding regional welfare gain is larger (and the loss is smaller), conditional on the realization of idiosyncratic shocks. The exception is represented by a
Rigid household for the reasons discussed in Subsection 6.4.
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case with very low public good productivity. The consumption differential is tilted in favor of the
In the presence of spillovers and with lower persistence of the technology process, when the adverse shock is realized in one region only, both regions are affected negatively through the
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interregional technology linkages, which mitigate the shift of resources. The welfare loss is increasing (decreasing) in the productivity of public goods in the Rigid (Flexible) region, regardless of the destination of the idiosyncratic shock. The zero-borrowing limit of the Rigid region hinders its post-shock recovery, which becomes more apparent as the public good productivity increases from
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low to high.
The welfare and consumption differential between the union members is increasing in public
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good productivity, conditional on an idiosyncratic shock to the Rigid region (Panel B of Table 3), but is decreasing if the shock hits the Flexible region (Panel C). The asymmetry of public borrowing
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limits generates the shift of resources, which allows Flexible to recover faster, especially if the productivity of public goods is higher. This explains the finding that the consumption differential
shock.
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between the regions closes faster (slower) when only the Flexible (Rigid) region is affected by the
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Therefore, such asymmetric fiscal union design improves interregional risk-sharing only after the realization of productivity shocks in the Flexible region and deteriorates the risk-sharing if the shocks are realized in the Rigid region or in both regions simultaneously. The last columns of Panels B and C of Table 3 confirm the observation that the marginal effect of the spillovers is substantial. Without the interregional linkages, welfare losses of both regions decrease (as the shocks dissipate faster in the absence of the spillovers), but the interregional differential widens (as the shocks are contained within the region in which they realized). 27
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7.
Conclusions
This paper has employed a microfounded, dynamic market-clearing general equilibrium framework to study the question: What are the implications of the asymmetry of balanced-budget rules for the interregional risk-sharing in a fiscal union? This question was motivated by two stylized facts about
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the U.S. as a fiscal union: (i) the presence of asymmetric public borrowing limits across the U.S. states, and (ii) the heterogeneous structure of government expenditures across different levels of the union government. We found that the asymmetry of balanced-budget rules creates welfare losses in the union. The exact magnitude of the risk-sharing deterioration in the fiscal union is a function of the productivity of the public good, specification of the technology processes, and distribution of the
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productivity shocks across the union. Overall, for productive government expenditure consistent with the empirical evidence, our numerical simulations tend to favor a flexible budget balance regime in terms of reducing the welfare losses in response to adverse productivity shocks. Our analysis can be extended to show that it is possible to increase efficiency and improve
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interregional risk-sharing in the fiscal union by adopting symmetric borrowing limits, thereby minimizing the shift of resources between the regions.26 The choice of the specific form of public
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borrowing limits then hinges on the productivity of public goods. If the productivity of the public good is sufficiently high, welfare is maximized by lifting any restrictions on public borrowing. But
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when the productivity is sufficiently low, imposing borrowing limits improves welfare. As a caveat to our analysis we should recall two special assumptions on which it is based. These
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pertain to (i) the abstraction of intergovernmental transfers that are typically present in fiscal unions and (ii) the prohibition of labor mobility across the regions. Both of these assumptions are introduced in
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order to sharpen the contrast in the effects of the borrowing limits and government expenditure composition on the time paths of capital accumulation and welfare. In either case, we acknowledge that the differential effects of the balanced-budget rules would be mitigated in the absence of these assumptions. Transfers from the federal authorities to regional governments would serve to reduce directly the differential economic performances of the two regions. The migration of households from 26
The shift of resources is minimized, conditional on the realization of asymmetric shocks, and eliminated if aggregate disturbances are realized.
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the less productive to more productive regions in response to the negative wealth effect would narrow the regional differences by affecting the interregional marginal productivity differential. These are clearly interesting and relevant aspects that merit further consideration. In addition, our framework opens up several more avenues for future research. These include the analysis of the policy interactions between the union members, as well as the exploration of the
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need for policy intervention by the federal government in the design of regional borrowing limits. Moreover, the setup we have developed can be utilized for the analysis of other important aspects of fiscal policy in a fiscal union, such as the heterogeneity of tax systems across the union members and
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the interregional transfer-mechanism design.
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Appendix A.
Some Additional Characteristics of Balanced-Budget Rules
Federal Government
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Although the U.S. federal government has faced a debt ceiling since 1917, when the Second Liberty Bond Act was passed, the ceiling serves primarily as a tool for partisan negotiations in the U.S. Congress and does not effectively constrain borrowing by the federal government. During the period this paper considers, 1977–2000, the debt limit was lifted 32 times.53 The debt ceiling was not raised in a timely manner only once, in 1995, due to a conflict between President Clinton and the Republican–controlled Congress, which ultimately led to a government shutdown. Between 2001 and 2015, the debt ceiling was increased 14 times, and in the three instances when the debt limit was not increased in a timely manner, it was suspended. State Governments
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Unlike the federal government, which has never defaulted on its debt obligations, subnational governments have not always avoided bankruptcies. Nine of 25 U.S. state governments and several cities delayed or ceased interest and principal payments on their bonds during and in the aftermath of the 1837 recession.54 This resulted in the loss of investor confidence, lengthy periods of debt repayment by the bankrupt states, and the imposition of unpopular excise and property taxes for that purpose. As a result, some states imposed constitutional and statutory requirements to balance budgets and limitations on issuance of municipal bonds in order to improve fiscal discipline.55 Nonetheless, the measures taken after the 1837 recession did not prevent another municipal debt crisis, which was brought about by the 65-month-long Great Depression of 1873. However, states joining the Union, as well as existing members, chose to adopt some form of borrowing limitations. Presently, only one state, Vermont, does not have a legal requirement to balance its budget. One of the characteristics of balanced-budget rules is the types of funds or budgets that are considered subject to the rule. Forty-nine states impose borrowing restrictions on their current operations budgets (also called general funds). Technically, 25 states do require that their capital budgets are balanced, but all of these states allow long-term revenue bond proceeds to be included in the budget revenue (U.S. General Accounting Office GAO (1993)). Such treatment of the capital budget balance is likely an artifact of the early attempts to circumvent borrowing limits, when revenue bonds (guaranteed by the revenue flow from the operation of an erected capital structure but not by the full faith and credit of the state) were first introduced by the State of Washington in 1897. The attempt was successful because such bonds were exempted from the borrowing limits by the courts, which ruled that the limits did not apply to obligations that are not guaranteed by the state taxpayers. Note that this separation of current and capital operation budgets is consistent with Bassetto and Sargent (2006), who make a case for it from an intergenerational point of view. They employ an overlapping generations model with productive and consumption public goods to show that exempting the capital operations budget from the balanced-budget requirement increases efficiency. In their model, once a balanced-budget rule is imposed, public goods would be underprovided. Due to the availability of public borrowing, older generations are able to shift the 53
The rationale for focusing on the 1977–2000 period is data driven and presented in Footnote 4. The list of insolvent states in Kiewiet and Szakaly (1996) includes the 10th bankrupt state, Florida, which joined the Union in 1845. 55Restrictions were imposed on the only type of bonds available at the time – guaranteed – also referred to as full-faith and credit or general obligation bonds that are secured with all available to the government means to repay the principal and interest. 54
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B.
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The balanced-budget rules adopted are state-specific and vary in terms of their stringency. The stringency of the regulations is determined by the stage of the budget process at which the budget must be balanced and by the legal provision for debt carry-over from one budget period to the next. Some states require budgets to be balanced at the beginning of the budget period, while others require them to be balanced at the end. In the former case, the governor must submit a balanced budget and/or the state legislature has to pass it. Hence, the start-of-the-period balanced-budget requirement does not rule out deficits occurring after the enactment of the budget. Those states having budgets that must be balanced at the end of the budget period have to take measures to balance their budgets if expenditures increase, or revenues decline unexpectedly, or both. Such unforeseen deficits typically occur during recessions. Net Regional Asset Accumulation
This appendix derives the expression for net regional asset accumulation for the Rigid region. Aggregate accounting implies the following laws of motion for net regional assets in the Rigid and Flexible regions:
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1 Bt 1 (1 RPRI ,t ) Bt Rt Kt Wt L Ct I t I RG ,t CG , 2
1 * Bt*1 (1 RPRI ,t ) Bt* Rt* Kt* Wt* L* Ct* I t* I RG CG . 2
(B.1) (B.2)
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The last term in each equation is due to the Federal government apportioning procurement of the consumption public good equally between the regions. The right-hand side of each of the laws of motion is a regional equivalent of the System of National Accounts’ definition of national savings for a sovereign state: national income less domestic absorption. If the regional savings are positive (negative), the region runs a trade surplus (deficit) and holds a positive (negative) net regional asset position. Subtracting (B.2) from (B.1) and using the fact that private bonds are in zero net supply, Bt + Bt∗ = 0, yields:
1 1 Rt Kt Rt* Kt* (Wt L Wt * L* ) 2 2 1 1 1 * Ct Ct* I t I t* I RG ,t I RG . 2 2 2
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Bt 1 (1 RPRI ,t ) Bt
(B.3)
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Equation (B.3) relates the Rigid region’s net regional asset accumulation to the interest income and differentials between the regions’ capital income, labor income, private absorption, and public absorption.
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C: Summary of the Model Equilibrium Conditions
Wt (1 )Yt / L
Rate of return on labor
Wt* (1 )Yt* / L* Rt Yt / Kt
Rate of return on capital
Rt* Yt* / Kt*
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Yt Zt Kt L1 ( K RG ,t )G
Production function
G * Yt* Zt* Kt* L*1 ( K RG ,t )
Kt It (1 ) Kt 1
Law of motion for private capital
Kt* It* (1 ) Kt*1
(Ct ) Et [(1 K ) Rt 1 1 ] Et (Ct 1 )
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Consumption-Euler equation
(Ct* ) Et [(1 K ) Rt*1 1 ] Et (Ct*1 )
(1 RPRI ,t 1 ) (Ct ) (1 Bt 1 ) Et (Ct 1 )
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Euler equation (private bonds)
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Euler equation (federal bonds)
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Euler equation (Flexible bonds)
Federal government budget constraint
* (1 RPRI (Ct* ) ,t 1 ) * * (1 Bt 1 ) Et (Ct 1 )
(1 RFG ,t 1 ) (Ct ) Et (Ct 1 ) (1 BFG ,t 1 ) * (1 RFG (Ct* ) ,t 1 ) * Et (Ct*1 ) (1 BFG ,t 1 )
(1 RRG F ,t 1 ) (Ct ) Et (Ct 1 ) (1 BRG F ,t 1 ) * (1 RRG (Ct* ) F ,t 1 ) * * Et (Ct 1 ) (1 BRG F ,t 1 ) * * BFG ,t 1 BFG ,t 1 CG (1 RFG ,t )( BFG ,t BFG ,t ) * K ( Rt Kt Rt* Kt* ) L (Wt L Wt * L* ) TFG ,t TFG ,t
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Federal government fiscal feedback rule
TFG ,t Yt * TFG ,t
Yt
*
TFG ,t 1 Yt 1 * TFG ,t 1
* t 1
Y
B B B B st FG ,t 1 stst gr FG ,t 1 FG ,t Ystst Yt 1 Yt Yt * BFG B* st *,t 1 stst * Ystst Yt
Rigid regional government budget constraint
C Ct TRG ,t I RG ,t ,
Flexible regional government budget constraint
* * C Ct* BRG F ,t 1 BRG F ,t 1 TRG ,t
Flexible regional government fiscal feedback rule
* TRG ,t
Law of motion for public capital
K RG,t I RG,t (1 G ) KRG ,t 1
* * BFG BFG ,t 1 ,t gr * * Yt 1 Yt
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I RG ,t min{ C Ct , I RG }
* * I RG (1 RRG F ,t ) BRG F ,t (1 RRG F ,t ) BRG F ,t * TRG ,t 1
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Yt *
* BRG F ,t 1 BRG BRG F stst , F ,t 1 st * * * Yt 1 Yt Ystst * * BRG F ,t 1 BRG F ,t 1 BRG F ,t BRG F ,t gr Yt * Yt *1
* * * K RG ,t I RG ,t (1 G ) K RG ,t 1
* Yt Yt* Ct Ct* It It* CG I RG ,t I RG ,t
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Union resource constraint
BOTt Yt Ct It 0.5CG I RG ,t
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Balance of trade
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Rigid net regional asset accumulation
* BOTt* Yt* Ct* It* 0.5CG I RG ,t
1 1 Rt Kt Rt* Kt* (Wt L Wt * L* ) 2 2 1 1 1 * Ct Ct* I t I t* I RG ,t I RG 2 2 2
Bt 1 (1 RPRI ,t ) Bt
Bt Bt* 0
Bivariate productivity process
Zt Z Z * t Z *Z
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Bonds are in zero net supply
ZZ Zt 1 t Z Zt*1 t* *
*
Note: The equations in the table constitute a system of 31 equations in 31 endogenous variables.
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Appendix D: Some Results Conditional on Alternative Technology Process Specification
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Figure D.1: Responses of the endogenous variables to the aggregate -1% productivity shock
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Notes: The fiscal union consists of the Rigid and Flexible regions. The technology process with lower persistence and with spillovers is adopted. The vertical axis measures percentage deviations of the endogenous variables from their respective steady states with the exception of the balance of trade and bonds measured relative to the steady-state output as well as the interest rates measured as percentages. The horizontal axis measures periods after the shock.
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Panel B: Idiosyncratic shock to Rigid
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Figure D.2: Responses of output, consumption, and investment to the -1% productivity shocks under alternative assumptions about the productivity of public goods. Panel A: Aggregate shock
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Panel C: Idiosyncratic shock to Flexible
Notes: The fiscal union consists of the Rigid and Flexible regions. The vertical axis measures percentage deviations of the variables from their respective steady states with the exception of the balance of trade measured relative to the steady-state output. The technology process with high persistence and without spillovers is adopted. The horizontal axis measures periods after the shock.
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Table 1: Functional composition of the federal and state government expenditures, 1977– 2000,% of general government expenditures Federal expenditures 47.8 37.8 29.9 2.1 3.2 0.9 0.5 1.0 0.2 10.0 0.7 9.3
State expenditures 52.2 20.9 0.0 6.0 2.6 1.2 2.3 7.7 1.1 31.3 23.8 7.5
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Total expenditures Consumption public goods National defense General public service Health Housing and community services Income security Public order and safety Recreation and culture Productive public goods Education Economic affairs
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Source: U.S. National Income and Product Accounts, Section 3. Note: The data in the table are consistent with the NIPA expenditures approach. Namely, transfers from the federal government to state governments are included in the expenditures of the federal government and transfers from governments to individuals are not reported as a part of government expenditures.
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Table 2: Calibrated parameters Parameter
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Preferences discount factor inverse of intertemporal elasticity of substitution for private consumption inverse of intertemporal elasticity of substitution for public consumption Technology capital income share elasticity of output with respect to public capital rate of depreciation of private capital rate of depreciation of public capital
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ιst ιgr η
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capital income tax labor income tax consumption tax cyclicality of public debt adjustment speed of public debt adjustment bond-holding adjustment cost
0.9615 2 2 0.36 0.05, 0.1, 0.2, 0.3 0.10 0.08
Policy 0.305 0.24 0.10 0.1 0.001 0.0025
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Table 3: Lifetime welfare dynamics under alternative assumptions about the productivity of public goods and technology spillovers in the fiscal union. Panel A. Aggregate shock High persistence, without spillovers V low Low Med High 0.05 0.1 0.2 0.3 1.61 1.75 2.12 2.70 1.63 1.62 1.61 1.58 1.01 0.93 0.76 0.59
Lower persistence, with spillovers V low Low Med High 0.05 0.1 0.2 0.3 1.19 1.30 1.57 2.00 1.21 1.20 1.19 1.17 1.01 0.93 0.76 0.58
Lower persistence, without spillovers V low Low Med High 0.05 0.1 0.2 0.3 0.52 0.57 0.69 0.88 0.53 0.53 0.52 0.51 1.02 0.93 0.75 0.58
Panel B. Idiosyncratic shock to Rigid High persistence, Lower persistence, without spillovers with spillovers V low Low Med High V low Low Med High Elasticity of output with respect to public capital, G 0.05 0.1 0.2 0.3 0.05 0.1 0.2 0.3 Loss of lifetime welfare in Rigid, % 1.64 1.78 2.16 2.75 0.75 0.82 0.99 1.26 Loss of lifetime welfare in Flexible, % -0.03 -0.04 -0.06 -0.08 0.45 0.44 0.44 0.42
Lower persistence, without spillovers V low Low Med High 0.05 0.1 0.2 0.3 0.51 0.55 0.67 0.85 0.01 0.01 0.00 0.00
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Elasticity of output with respect to public capital, G
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Loss of lifetime welfare in Rigid, % Loss of lifetime welfare in Flexible, % Ratio of Flexible-Rigid welfare loss
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Panel C. Idiosyncratic shock to Flexible High persistence, Lower persistence, without spillovers with spillovers V low Low Med High V low Low Med High Elasticity of output with respect to public capital, G 0.05 0.1 0.2 0.3 0.05 0.1 0.2 0.3 Loss of lifetime welfare in Rigid, % -0.03 -0.03 -0.03 -0.02 0.44 0.48 0.58 0.74 Loss of lifetime welfare in Flexible, % 1.66 1.66 1.66 1.66 0.76 0.76 0.75 0.75
Lower persistence, without spillovers V low Low Med High 0.05 0.1 0.2 0.3 0.01 0.01 0.02 0.03 0.52 0.52 0.52 0.51
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Notes: The fiscal union consists of the Rigid and Flexible regions. The table entries are calculated using consumption scale factors and have the interpretation of compensating variation measured in terms of private lifetime consumption.
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Figure 1: Balanced-budget rules in the continental U.S. states
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Source: ACIR (1987). Note: The yellow (lighter) color represents states with less stringent balanced-budget rules and corresponds to the ACIR index value of 6 and below. The green (darker) color represents states with strict balanced-budget rules and corresponds to the ACIR index value of 7 and above. The breakpoint value between the two types of the states is borrowed from the fiscal federalism literature.
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Figure 2: Responses of the endogenous variables to the aggregate -1% productivity shock
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Notes: The fiscal union consists of the Rigid and Flexible regions. The technology process with high persistence and without spillovers is adopted. The vertical axis measures percentage deviations of the endogenous variables from their respective steady states with the exception of the balance of trade and bonds measured relative to the steady-state output as well as the interest rates measured as percentages. The horizontal axis measures periods after the shock.
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Figure 3: Responses of the endogenous variables to the idiosyncratic -1% productivity shock to the Rigid region Panel B. Lower persistence, with spillovers.
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Panel A. High persistence, without spillovers.
Notes: The fiscal union consists of the Rigid and Flexible regions. The vertical axis measures percentage deviations of the endogenous variables from their respective steady states with the exception of the balance of trade and bonds measured relative to the steady-state output as well as the interest rates measured as percentages. The horizontal axis measures periods after the shock.
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Panel A. High persistence, without spillovers.
Notes: The fiscal union consists of the Rigid and Flexible regions. The vertical axis measures percentage deviations of the endogenous variables from their respective steady states with the exception of the balance of trade and bonds measured relative to the steady-state output as well as the interest rates measured as percentages. The horizontal axis measures periods after the shock.
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Figure 5: Responses of output, consumption, and investment to the -1% productivity shocks under alternative assumptions about the productivity of public goods
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Panel A: Aggregate shock
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Panel B: Idiosyncratic shock to Rigid
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Panel C: Idiosyncratic shock to Flexible
Notes: The fiscal union consists of the Rigid and Flexible regions. The vertical axis measures percentage deviations of the variables from their respective steady states with the exception of the balance of trade measured relative to the steady-state output. The technology process with lower persistence and with spillovers is adopted. The horizontal axis measures periods after the shock.
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