Fiscal policy and business cycle characteristics in a heterogeneous agent macro model

Journal of Economic Behavior & Organization 92 (2013) 224–240

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Journal of Economic Behavior & Organization journal homepage: www.elsevier.com/locate/jebo

Fiscal policy and business cycle characteristics in a heterogeneous agent macro model夽 Andre R. Neveu ∗ Department of Economics, James Madison University, Harrisonburg, VA 22807, United States

a r t i c l e

i n f o

Article history: Received 15 December 2010 Received in revised form 21 May 2013 Accepted 14 June 2013 Available online 26 June 2013 JEL classification: C63 E62 E37 Keywords: Agent-based computational models Fiscal policy Business cycles CATS models

a b s t r a c t This paper explores the macroeconomic implications of changing fiscal policy in a Heterogeneous Interacting Agent (“HIA”) model. The key contributions to the existing HIA complex adaptive trivial system (“CATS”) literature include the addition of a progressive income tax structure, an expanded role for redistribution, and a stylized reactive government sector. In certain specifications deficit financed tax cuts are shown to effectively shorten recessions, while deficit financed spending stimulus is able to lengthen recoveries. Alternative specifications provide ambiguous support for generalizing the effectiveness of these policy treatments. Robustness checks support the general findings that increased redistribution towards the unemployed results in higher unemployment rates, greater inequality, and shorter contractions. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Theoretical heterogeneous interacting agent (“HIA”) models are increasingly being used as an alternative to general equilibrium models to examine aggregate economic activity and macroeconomic policy questions. Previous examples of policy-based macroeconomic HIA models include Russo et al. (2007) who showed how government transfers can impact R&D and growth, as well as Delli Gatti et al. (2005b) and Giulioni (2007) who examined the role for competing monetary policy rules.1 The HIA macroeconomic modeling approach has also been used to help explain the process of collapse and contagion (Battiston et al., 2007, 2012; Delli Gatti et al., 2010b). In this context, agent-based models may provide insight regarding policies to slow contagion and reverse business cycle contractions. The recent crises in the U.S. and Europe underscore the desire of policy makers and the public for the government to react when a downturn occurs.

夽 The author would like to thank five anonymous referees for their helpful comments on previous versions of this paper. The author would like to thank James Madison University and the Battle Family, A.P. Boxley III, and W. Carlton Family Endowments for faculty support in the CoB for their generous assistance. ∗ Tel.: +1 2025560389. E-mail addresses: [email protected], [email protected] Fagiolo and Roventini (2012) discuss a variety of agent-based models (e.g., (Dosi et al., 2006, 2008, 2010)) where a government sector which redistributes income plays a role in both fostering growth and dampening cycles. Dosi et al. (2010) extends their previous work to account for an explicitly modeled government sector which results in higher growth and more stable fluctuations. 1

0167-2681/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jebo.2013.06.006

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Previously developed HIA complex adaptive trivial system (“CATS”) models demonstrated an ability to replicate realistic business cycle features (Gaffeo et al., 2008), and showed that redistribution of revenues to the unemployed reduced growth, while government spending on R&D increased growth (Russo et al., 2007). This paper explores the potential effectiveness of fiscal policy actions conducted by expanding on these previously developed policy-based models.2 The key additions include a reactive government sector, progressive income tax policy, and flexible redistribution. This paper examines how differing fiscal plans might impact the longest contractions, as well as the role fiscal policy plays in shortening business cycles in an agent-based model. A reactive government sector operates by changing fiscal policy during extended contractionary phases of the business cycle. Relative to a baseline specification without a reactive government sector, three treatments are applied: a fiscal stimulus paid for through borrowing; a tax reduction accompanied by spending cuts; and a deficit financed tax cut that holds spending fixed. Consistent application of the various treatments suggest that a policy of deficit funded tax cuts manages to shorten recessions relative to the baseline specification while substantially reducing the number of long contractions. A policy of deficit financed spending is able to lengthen expansions relative to the baseline specification. There is also evidence that increasing redistribution to the unemployed raises the average rate of unemployment but is not inherently growth reducing. The primary baseline specification is selected from a simple calibration against recent U.S. macroeconomic data. Several alternative specifications are examined and small changes to key parameters reverse or dampen many of the conclusions drawn from the baseline specification. A number of robustness checks confirm that these policy choices cannot be generalized. While this reiterates the need for further work in agent-based modeling, it is not surprising that differently specified models require different treatments. Section 2 contains a discussion about the basic HIA model employed here, and outlines the theoretical mechanisms of the baseline specification. Section 3 describes the method of calibrating the baseline specification. Section 4 examines the policy treatments applied to the baseline specification as well as robustness checks, and Section 5 concludes.

2. CATS model There are a wide variety of HIA-CATS models which each tend to have a specific focus. The model employed here is a unique variant on the HIA models used by Gaffeo et al. (2008), Delli Gatti et al. (2005b), and Russo et al. (2007) who model production as a linear function of labor.3 CATS models have been shown to exhibit self-organizing stable states as well as conditions where small idiosyncratic shocks may push an economy into instability. Delli Gatti et al. (2008) and Gaffeo et al. (2007) describe CATS as sequential economies founded on bounded rationality which result in spontaneous market order.4 CATS models are built on the foundation of individual rule-based behavior in a market environment, but lack a centralized solving mechanism that would be observed in a general equilibrium model. The CATS model is designed with sequential decision making using decentralized markets for labor and goods. Adaptive behavior is built into the model as agents use new information to update their satisficing rules in manner that is backward-looking, sequential, and path dependent (Gaffeo et al., 2007).5 This paper builds on the research of Russo et al. (2007) by adding a progressive income tax system. Progressive income tax systems are a primary source of government revenue and redistribution in many developed economies. The structure of this model is similar to that used by Russo et al. (2007) who redistribute all government revenues to either unemployed individuals or to firms for research and development (“R&D”). This model allows for redistribution to occur in a way that money can flow to both households or firms in the same simulation.6 The model adapted for use here is stock-flow consistent with respect to firm equity, transactional, and government cash flows. When firms fail due to bankruptcy, not only do households lose their source of income, but their wealth is negatively

2 As noted by Marks (2007) the HIA approach is more of an exploratory tool than a prediction tool. This paper focuses on trying to understand what the model reveals in its emergent behavior and what these revelations suggest in terms of policy action. 3 In contrast, other heterogeneous agent-based models like those proposed by Delli Gatti et al. (2008), Delli Gatti et al. (2005a), Gallegati et al. (2003a), and Battiston et al. (2007) model production as a linear function of capital only. Delli Gatti et al. (2005a) and Giulioni (2007) use capital in production, and also have endogenous entry and exit so the number of firms can grow over time. Growth in the number of firms over time is somewhat novel relative to the other articles in the HIA-CATS literature. Delli Gatti et al. (2005a) and Giulioni (2007) have no labor market, and therefore no way of capturing unemployment changes or the impact of taxes on labor income. Another CATS model with potential to extend the research presented here is by Delli Gatti et al. (2005b) who uniquely model output as a function of capital and labor, where capital is a direct reflection of total net worth. Delli Gatti et al. (2005b) designed their model to specifically explore central bank behavior and responses. 4 Delli Gatti et al. (2008) and Delli Gatti et al. (2007) describe and display numerous stylized facts that the agent-based approach can explain which representative agent general equilibrium models cannot. CATS models typically result in scale-free distributions observed in empirical data such as power laws in wealth, firm size, and income. Additionally, CATS models are able to display long periods of both high aggregate volatility and tranquility like those observed in most advanced economies before, during, and after the Great Moderation. 5 An example of satisficing behavior might be a worker looking for a job with a wage that exceeds their reservation wage. Any job offer which pays as much as or more than a worker’s reservation wage could result in matching a worker to an employer. Thus, rather than searching for the highest possible wage, satisficing behavior assumes that a worker can accept the highest wage available to them within search constraints. This behavior can be applied to product, wage, and financial markets. 6 Government redistribution of income to the unemployed has also been employed in work by Dosi et al. (2010).

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impacted. Furthermore, when households lose their jobs and turn to their savings in order to consume, firm equity falls pushing more firms to the credit markets.7 Firm-level borrowing is incorporated such that the role for the banking system is limited to supplying funding to firms, setting interest rates, and paying interest on deposits. The focus of study is limited to reactive fiscal policy changes rather than monetary policy to avoid the additional layer of complexity regarding the issue of coordination between a central bank and the government sector. A related paper by Gaffeo et al. (2008) incorporates more refined behavior for banks and borrowing which yields firm-specific interest rates and a version of the financial accelerator. Reactive monetary policy in this context is certainly worth exploring, but these questions are left for future study to focus on fiscal policy. 2.1. Production Using a linear production function (Eq. (1)), a fixed number of heterogeneous firms (Fi,t ) (i = 1, . . ., I; time index t = 0, . . ., p e ) and a firm-specific labor-augmenting technology T) produce a homogeneous non-storable good (Yi,t ) using hired labor (Li,t (˛i,t ). At t = 0, firms are randomly endowed with technology (˛i,0 ) from a uniform distribution.8 All workers inelastically provide a single unit of labor, are presumed to have the same ability, and are only as productive as a firm’s technology. p

e Yi,t = ˛i,t Li,t

(1)

2.2. Technology and firm equity evolution f

All firms are initially solvent and endowed with a positive random amount of initial equity Ai,0 > 0 using a uniform distribution. Net worth evolves with R&D investment being accumulated along with retained profits or losses. f

f

Ai,t = Ai,t−1 + i,t−1

(2)

A fixed portion   of any positive profits (i,t ) from each period is invested in R&D. This model diverges from Gaffeo et al. (2008) and Russo et al. (2007) by not removing R&D expenditures from overall equity. To prevent equity from being destroyed due to investment at this step, it is assumed that expenditures on R&D are returned to equity balances later in the round. For example, if a firm with $100 in profit spends $10 on investment, both the $90 in retained earnings and the $10 in investment spending is returned to the bottom line. This assumes that new technology is valued at cost as an intangible asset, but that money spent on investment is not able to be used as collateral until future periods. f f At the beginning of each period firms check their net worth (Ai,t ) to determine if they are solvent. If Ai,t > 0 firm i continues to the production stage, while those that are insolvent face bankruptcy and are replaced by copying a surviving firm based on the level of technology. As a proxy for startup costs and technology implementation, newly entering firms are limited to replicating technology from those in the lowest decile of surviving firms.9 Firm replication from the lowest technology firms draws on the most labor intensive firms without explicitly having individual households seek out larger firms in terms of employment. Previous HIA models including Gaffeo et al. (2008) and Delli Gatti et al. (2010a) keep unemployment at reasonable levels by modeling consumers as preferentially attached to the largest firms in terms of production. Delli Gatti et al. (2010a) showed that using consumers who are preferentially attached to large firms allowed their model to exhibit crashes and cycles instead of smooth growth in output. Similar results are achieved here by using both consumers that are preferentially attached to firms that have lower prices and firm entry that copies the least technologically advanced firms.10 Previous values of technology, labor demand, expected output, and prices are retained from the existing firm for the purpose of setting labor demand for the new firm. Newly entering firms begin with an amount of equity replicated from a surviving firm. In order to maintain a fixed equity stock during a time period while accounting for bankruptices, it is assumed that households rebalance the remainder of their equity portfolio away from surviving firms and towards newly

7 Cincotti et al. (2010) provide a deeper discussion of stock-flow consistency in an agent-based model, describing the balance sheets of households, firms, and banks. A similar approach is taken here, but out of concern for space balance sheets were not laid out in detail. 8 Using uniformly distributed, normally distributed, or identical values as initial conditions yields similar results. A uniform initial distribution was chosen for the reason that a greater degree of dispersion at the outset leads to pseudo-steady states more rapidly than when using identical or normally distributed values. Unreported tests show that the final distribution of variables such as equity is dependent on the dynamics of the model rather than the initial distribution of equity. The following initial conditions are set using a uniform distribution: ˛ (technology) between a lower (˛0,lb ) and upper bound f

f

(˛0,ub ), Af (firm equity) between a lower (A0,lb ) and upper bound (A0,ub ), Ah (household equity) between a lower (An0,lb ) and upper bound (An0,ub ), P (prices) d between a lower (Plb ) and upper bound (Pub ), w (wages) between a lower (w0,lb ) and upper bound (w0,ub ), and Ld (labor demand) between a lower (L0,lb ) d and upper bound (L0,ub ). 9 When considering stock-flow consistency any replication costs borne by new firms would still be fed back into the equity of pre-existing firms and households. Further justification for entering firms to have lower productivity than surviving firms is empirical evidence suggesting that newly entering firms are significantly less productive than surviving firms in both the manufacturing and service industries (Foster et al., 2001). 10 See Section 2.3 for further description of the preferential attachment model used here. Other preferential attachment methods were explored in Section 4.3 including price, labor demand, and output. Without preferential attachment this model tends to converge to a state where each firm demands a single worker and the economy experiences persistent deflation and negative growth.

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entering firms. Surviving firms lose a portion of their equity in proportion to their share of total equity after accounting for firm bankruptcies so that newly entering firms neither immediately go bankrupt nor enter the market with previously non-existent capital. The process of rebalancing forces households and firms to absorb the equity losses of system-wide bankruptcy and preserves the stock of equity in the system.   ) the government funds R&D ( ) based upon tax revenues. Government funded In addition to self-funded R&D (i,t i,t i,t R&D is distributed to firms based on their proportion of positive profits at time t (Eq. (8)). Thus, total R&D investment for a  single firm with positive profits is RDi,t = i,t i,t−1 + i,t−1 . Technological growth is subject to a random component zi,t−1 which ensures investments in R&D have uncertain payoffs (Eq. (3)). The value zi,t−1 is a random variable drawn from an exponential distribution with mean i,t−1 =

RDi,t pi,t−1 Y s

i,t−1

s where Yi,t−1 represents the amount of goods actually sold by the firm

during period t − 1. Using an exponential distribution leads to slow technology growth for most firms, but occasionally large increases for a few firms.11 ˛i,t = ˛i,t−1 + zi,t−1

(3)

2.3. Consumption price & expected demand evolution Households Nj,t (j = 1, . . ., J) shop for both jobs and goods in decentralized markets. Consumers purchase goods at variable prices (Pi,t ) owing to consumers limited capacity to search markets for the lowest price.12 Prices are determined in a decentralized market where consumers shop at a number of firms (Z) based on search costs that remain fixed throughout a simulation. Higher search costs—lower Z—are represented by fewer firm prices being visible to consumers in each time period. In the baseline model Z is set to equal 50% of the total number of firms.13 In every period households are randomly assigned to view 50% of firms using a preferential attachment rule that guides consumers to shop at lower priced firms with greater probability.14 Finally, households sort their personal subset of firms by price, and use their after-tax income to purchase consumption at the lowest available price.15 Consumers can be locked out of consuming and forced to save if the firms they shop at run out of goods. Using rules borrowed from Gaffeo et al. (2008) expected demand and prices are set using functions of previous sales relative to previous production and adapt based upon boundedly rational decision rules.16 Each period a firm is randomly assigned using a 50/50 draw to adjust either prices or output, but not both. e ) to set their desired level of output (Y d ). Managers would Firms chosen to adjust output calculate expected demand (Di,t i,t p

s expect increased demand and therefore desire to increase production if all goods were sold in t − 1 (Yi,t−1 = Yi,t−1 ), but

decrease expected demand and production if previous sales did not meet output

 e Di,t

=

s (Yi,t−1

<

p Yi,t−1 ).17

p

e s Di,t−1 (1 + i,t ) if Yi,t−1 = Yi,t−1

(4)

p

e s Di,t−1 (1 − i,t ) if Yi,t−1 < Yi,t−1

Firms chosen to adjust prices would increase prices if they had no remaining inventory in t − 1 and reduce prices otherwise.

 s Pi,t

=

p

min , P s max[Pi,t i,t−1 (1 + i,t )] if Yi,t−1 = Yi,t−1 p

min , P s max[Pi,t i,t−1 (1 − i,t )] if Yi,t−1 < Yi,t−1

(5)

11 The exponential distribution was chosen to be consistent with Gaffeo et al. (2008) and Russo et al. (2007). Gaffeo et al. (2008) choose to use an exponential function for technology growth based on theoretical and empirical support provided by Reynard (1979) and Fazzari and Athey (1987). 12 In the presence of search costs the conditions for perfect competition do not apply and therefore the law of one price does not necessarily apply (Stiglitz, 1989). 13 Search costs are set through calibration as a percentage of the total number of firms. Robustness checks discussed later in Section 4.3 also examine how baseline specification predictions hold up under varying levels of search costs. 14 Wilson and Price (2010) provide survey evidence that consumers do not necessarily seek out the best price, and may suffer from inattention or decision error. In the calibration phase two size-based preferential attachment variables are tested—firm labor demand and previous output. Previous studies used size-based measures for preferential attachment arguing that larger firms in terms of production are more visible and thus more likely to be found (Delli Gatti et al. (2010a), Gaffeo et al. (2008)). Previously posted prices act in a similar way. Firms with lower prices are assumed to be easier to find than those that have higher prices without guaranteeing an individual finds the lowest price available. Variations on preferential attachment are discussed in more detail in Section 4.3. 15 For example, if a consumer would like to purchase 20 units of consumption, and a firm only has 15 units available for sale, the consumer would purchase the remaining goods from this firm and then move on to the next firm they selected to shop at to see if they can purchase the remaining 5 units. 16 Gaffeo et al. (2008) provide a brief discussion of research by Kawasaki et al. (1982) and Bhaskar et al. (1993) which provides survey support for this method of firm price and quantity adjustment. e 17 The additional notation for Di,t is employed since firm production at t − 1 may not equal desired production. New expectations are set by adjusting

previous expected demand and not previous actual production.

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Random adjustments to prices and output are selected from positive uniform distributions over the ranges [0, h ] [0, min = W /Y p each period such that the entire wage bill could h ].18 Prices are subject to a firm-specific minimum price Pi,t i,t i,t be recouped if all goods are sold.

2.4. Labor market, wages, and contracts Search costs play a key role in the ability for firms to meet their labor demands. If firms completely meet their hiring needs, workers can be shut out of the labor market. Alternatively, firms might not fill all their openings since there are a limited number of applicants who apply to each firm. Firms produce less than their desired level of output if the amount of e ≤ Ld ). labor hired is less than desired (Li,t i,t

d Li,t =

d Yi,t

(6)

˛i,t

Labor demand after t ≥ 1 is backed out from the desired level of output using Eq. (6). Since labor must be an integer, demand for employment is rounded down so firms do not hire more than necessary. Firms are randomly assigned to sequentially hire each period. Households inelastically supply a single unit of labor each period and submit applications for employment to a number of firms (M). Higher search costs are represented by fewer applications—lower M—in a single period. Applications from potential workers are sorted into blocks such that previously hired employees are retained ahead of d < Ld ), then the firm fires workers randomly until new applicants. If a firm’s labor demand falls from a previous period (Li,t i,t−1 d > Ld employment is equal to demand. When labor demand rises (Li,t ) managers turn to their personal pool of applicants i,t−1 and hire applicants with the lowest wages first. New workers enter into individual contracts of a random length on the uniform interval [1, CUB ]. Once an employee agrees to a contract they are removed from the pool of available workers for all other firms. Workers are then paid their wage prior to production.19 The wage setting mechanism is designed to reflect empirical evidence that there is downward nominal wage rigidity, and that contracted workers are often compensated for increases in price levels. Wages are modeled in a manner similar to that in Gaffeo et al. (2008) and Russo et al. (2007), but limits inflation-related nominal wage increases to contracted workers.20 Bewley (1999) provides survey evidence that nominal wages rarely fall for individual workers even in recessions, and shows nominal wage rigidity is especially true for those who are currently employed versus new hires. Firms hire workers at their individual reservation wages each period. Reservation wages are slowly revised downward in the absence of work, or rise as workers remain employed. The general rate of inflation is used in wage setting, and is determined as the rate of change in a price index (Pttw ) that weights firm prices by the number of goods sold each time period. Employees whose contracts are not set to expire (contract >1) have nominal wages that increase at the rate of tw ) when  > 0, plus an additional amount ϕ for any worker employed at t − 1.21 Nominal wages inflation (t = Pttw − Pt−1 t j,t are not indexed to inflation for those workers whose contracts are expiring (contract = 1). For workers unemployed at t − 1, reservation wages fall by an amount ϕj,t , a uniformly distributed random variable on the interval [0, hϕ ]. A binding minimum ˆ t ) is set at 45% of the median reservation wage from time t − 1.22 reservation wage (w

wj,t =

⎧ ˆ t , wj,t−1 (1 + ϕj,t )) max(w ⎪ ⎨ ⎪ ⎩

if employed in t − 1, and contract = 1 at t

ˆ t , wj,t−1 (1 + ϕj,t )max(1, 1 + t )) max(w

if employed in t − 1, and contract > 1 at t

ˆ t , wj,t−1 (1 − ϕj,t )) max(w

if unemployed during t − 1

Firms are allowed to borrow (Borrowingi,t ) in order to meet their wage bills if they do not have sufficient equity to pay their wages. Loans must be repaid at the end of t or the firm declares bankruptcy. Interest on loans is paid at a rate i,t determined by the banking system (Section 2.7). Revenues are collected from sales, while wages and outstanding loans

18

Uniform distributions were used here to be consistent with Russo et al. (2007) and Gaffeo et al. (2008). The method of randomly contracting workers differs from Russo et al. (2007) where contracts are endogenously determined based on search costs and Gaffeo et al. (2008) where contracts are fixed at 8 periods. 20 Gaffeo et al. (2008) provides a brief discussion of the theoretical and empirical work of Campbell and Kamlani (1997) and Baker et al. (1994) to justify this modeling choice. 21 Inflation is limited to have only positive impacts on wage demands to prevent nominal wages from falling for contracted workers. 22 The median hourly wage reported by the Bureau of Labor Statistics for 2012 was $16.57 (http://www.bls.gov/oes/current/oes nat.htm#00-0000), with a minimum wage of $7.25, or about 45%. This value varies with changes to minimum wage laws, but is held fixed for the duration of this study. Without a floor on wages, unemployed workers continually offer lower nominal wages over time, adding additional downward pressure to prices which makes it rare to observe positive rates of inflation in the overall economy. 19

Andre R. Neveu / Journal of Economic Behavior & Organization 92 (2013) 224–240 s P − are repaid. Pre-tax profits are calculated as i,t = Yi,t i,t

 j

229

i − Borrowing .23 Remaining profits are taxed at the wj,t i,t i,t

corporate tax rate  c = 22.5%.24 Labor earnings are taxed at rates  1 = 7.5% ,  2 = 15 %, and  3 = 22.5% in order to fund government spending.25 A portion ı of taxes are redistributed and doled out to unemployed individuals in the amount of j,t (Eq. (9)). Thus, when ı > 0 individuals add Depositsj,t equal to wj,t if employed or j,t if unemployed. When ı = 0 unemployed workers have no available new deposits for consumption.

2.5. Household equity and consumption Household equity is rebalanced each period in order to maintain stock-flow consistency of overall equity and to ensure government bonds are fully paid for. Net equity is endowed to individual households such that the sum is equal to five times the sum of firm equity.26 The stock of consumer net wealth (Anj,t ) at any given point in time, is the sum of previous wealth (Anj,t−1 ) and the flow of any unspent deposits (i.e., savings) (Savingsj,t−1 = Depositsj,t−1 − Expendituresj,t−1 ). Household wealth is invested across three assets: cash, government bonds, and an equity asset which is a diversified portfolio of firm equity. Each period household portfolios are rebalanced between the three assets to maintain the fixed ratio of 4:1 between total cash holdings and other assets. When the government issues debt, households pay for newly issued bonds using available cash, and then resort to their equity holdings if necessary. Households again rebalance their portfolios by raising their cash holdings and reducing their equity. Individual firm equity is reduced in proportion to the firm’s share of equity in the system.27 In effect, government borrowing crowds out equity available to firms by reducing the outstanding amount, increasing both their interest rates and need to borrow. Desired consumption is modeled in the spirit of Duesenberry’s relative income hypothesis in two steps.28 In the first step individuals set aside 90% of their after-tax nominal income for consumption, creating a “soft” nominal ceiling on consumption d ) that for a household, with the remaining 10% saved. In the second step a floor is set for minimum real consumption (cj,t adjusts in an adaptive manner based on previous consumption and overall economic growth (Eq. (7)). Households that have little or no income still attempt to consume the same real amount they did in the previous period by drawing on their savings or equity balances. Savings rates are therefore independent of nominal income as theorized by Duesenberry. When households either cannot afford their desired minimum consumption out of their after-tax wages, or they are locked out of consuming they adjust desired real consumption downward by the amount 1 in t + 1 after accounting for real economic growth. The parameter 0 ≤ 2 ≤ 1 acts to adjust the rate real consumption can fall. The values for 1 and 2 are set in calibration (see Section 3.2 for detail).

 d cj,t

=

p

p

d d cj,t−1 Yt /Yt−1 + 1 (cj,t−1 − cj,t−1 )

if consumption > desired in t − 1

p p d cj,t−1 Yt /Yt−1

if consumption < desired in t − 1

d − 2 (1 − 1 )(cj,t−1

− cj,t−1 )

(7)

2.6. Government The primary role of the government in this model is to collect and redistribute taxes for the purposes of (i) maintaining a standard of living during unemployment, (ii) funding R&D at the firm level, and (iii) setting fiscal policy in reaction to f changing economic conditions. Income tax (Rtn ) and corporate tax revenues (Rt−1 ) are redistributed during time t among consumers and firms. The dole rate (0 < ı < 1) is the percentage of tax revenue that goes towards unemployed workers, and

23 The implication here is that firms with positive net worth, but insufficient revenues to cover costs can suffer periodic negative profits without going bankrupt. For example, a firm with A1 = 100, revenues of $90, wages of $110, and a 5% interest rate, would have to borrow $10 from the banking system to cover their wage bill. They would accordingly suffer a loss of 90 − 110 − 0.05(10) = −20.5 reducing net worth at t = 2 to A2 = 79.5. 24 U.S. corporate tax rates are currently near a statutory rate of 40% of profits, but firms generally pay much lower rates in practice. Corporate tax rates in practice averaged 25.6% between 1987 and 2007, and recently fell to around 13% (Congressional Budget Office, 2012). For simplicity, the top corporate tax rate is fixed at 22.5% to match the highest income tax rate. Other policies are explored in Section 4.3. 25 Tax rates apply to all income and should not be interpreted as marginal tax rates. These rates are chosen to approximate practical rather than statutory U.S. average income and payroll tax rates as reported by the Congressional Budget Office (2010) for 2007. In 2007 the bottom two deciles paid average tax rates of approximately 2% and 9% respectively, and the top decile paid slightly more than 20%. We simplified the structure by setting the three tax categories equidistant from the middle rate of 15% 26 The 2011 Flow of Funds report estimates total assets held as credit market instruments, corporate equity, and equity in non-corporate business total around 20-25% of total assets (Board of Governors of the Federal Reserve System, 2011). 27 It is assumed that there is no cost to move between cash holdings, equity, or bonds, and that equity is recoverable on a dollar for dollar basis. If costs are imposed shifting between deposits and equity those fees would be paid to the banking system and ultimately recovered by households to retain stock-flow consistency. 28 Holländer (2001) provides a thorough discussion of both standard theory and the relative income hypothesis.

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the percentage 1 − ı goes towards firm R&D. Government spending per firm on R&D ( i,t ) and individual unemployment benefits ( j,t ) are calculated as: i,t =

i,t−1 f (1 − ı)(Rt−1 + Rtn + Gt ) t−1

(8)

f

ˆ lb , j,t = min(w

n + Gt ) ı(Rt−1 + Rt−1

Ut

)

(9)

In Section 4 the model is extended to allow for deficit spending or repayment of Gt which impacts the amount spent on unemployment or R&D (Gt > 0 during stimulus and Gt < 0 during repayment). All workers that are unemployed (Ut ) during t ˆ lb ). If more receive an equal share of benefits limited to not exceed the lowest wage received by an employed household (w tax revenue is collected than is needed to provide for the total amount of redistributive spending, then all excess funds are returned to working households in proportion to their share of the overall tax bill. At all times government borrowing is limited so that it would not exceed outstanding equity and savings. Government debts are repaid with interest as described in Section 2.7. 2.7. Banks The model contains a single bank with a couple of key roles. The bank provides credit to firms for paying wages when internal net worth is insufficient to fund production. If a firm does not sell enough goods to repay their debt, they will declare bankruptcy at time t + 1. The total amount of credit is not limited, nor is it specifically offered to firms with better financial positions. However, higher interest rates make it more difficult for firms to repay their debt. Nominal interest rates on government debt are set equal to the U.S. 1985–2012 average quarterly interest rate of 1.5%, plus the average weighted rate of inflation and rate of growth in real production.29 The interest rate paid on savings is equal to the rate paid on government bonds, minus a historical average spread of 0.35%.30 Firms pay a minimum interest rate ( i,t ) of 0.31% over the government bond rate, plus 0.25% multiplied by the value of ((Borrowingi,t /Equityi,t ) − 1) when Borrowingi,t > Equityi,t . Thus firms do not start paying a penalty rate until their borrowing exceeds equity.31 All interest rates are nominal, and are limited to have a zero floor. Money is the sum of all household deposits and savings that can be used for purchases. Households have access to additional funds if they choose to sell bonds and equity in order to raise cash. It is further assumed that every dollar of firm equity can be used to costlessly borrow one dollar in cash per period to pay wages.32 Interest earned on government bond holdings, and interest earned by banks on firm borrowing is repaid to households. The quantity of money in the economy rises at the rate of savings growth and interest paid on bonds, but falls when firms declare bankruptcy. Thus households bear the burden of bankruptcy and job loss in a similar manner to Gaffeo et al. (2008).33 3. Baseline specification selection and calibration The four-step indirect calibration method suggested by Fagiolo et al. (2007) is used to calibrate and study the model. First, post-war U.S. macroeconomic aggregates were selected as the stylized facts for reference and fitting. Second, as described above, the model has been developed in a way that keeps the microeconomic components as close to empirical evidence as possible. Third, empirical evidence and the ability to fit stylized facts were used to restrict the parameter space for the model. Finally, after calibration a number of robustness tests are conducted in Section 4.3 to examine the generality of these findings as well as the causal mechanisms underlying emergent behavior. In searching for a baseline specification, the choice was made to try and find the closest match to a real economy in terms of growth rates, unemployment rates, inflation rates, and business cycle contraction and expansion length. Any number of features could be fit, but fitting the most basic features of a real economy takes primary importance. Previous research by Canning et al. (1998), Gaffeo et al. (2003), Di Guilmi et al. (2004), Gallegati et al. (2003a), Gallegati et al. (2003), and Delli Gatti et al. (2008) each use filtering techniques that define cycles as departures from a permanent trend component. One reason to depart from that custom here is that it is doubtful a reactive government sector would set policy based on

29

Data available from the St. Louis Federal Reserve, http://research.stlouisfed.org/fred2/series/GS10/downloaddata?cid=115. Calculated as the interest rate spread on 3m deposits to government debt from 1985 to 2012. Data is available from the St. Louis Federal Reserve, http://research.stlouisfed.org/fred2/series/CD3M/downloaddata?cid=121. 31 If equity is zero, then the firm pays the 0.25% penalty rate. These rates are estimated by using the 1985–2012 historical AAA Rate spread of 0.31% over government bonds, and the historical spread of 0.25% on Baa debt over AAA debt http://research.stlouisfed.org/fred2/series/AAA/downloaddata?cid=119 and http://research.stlouisfed.org/fred2/series/BAA/downloaddata?cid=119. 32 In order to avoid creating free-standing equity and bond markets it was assumed that households “sell” their equity stake back to firms who then have reduced access to free cash. All corporate borrowing is held by the banking system, and all interest flows back to households. Assuming bank profits flow back to households would yield the same result. 33 Alternatively, one could create a fully specified credit market for consumers, however this was avoided to focus on fiscal rather than monetary policy. Without an increase in the supply of money over time, the prices of all goods would fall in a nominal economy as output rises. 30

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Table 1 Primary baseline specification. T Firms (F) Population (N) M: labor search Z: product search ı h

600 30 150 15 15 100% 0.25

h hϕ

1

2 Pref. att Cmax ˘

0.05 0.05 0.75 0 Pi,t 14 0.1

departures from trend growth as implied in decomposed data. A benefit to using HIA models is their ability for the economy to settle into various states of stability rather than reverting to some statistically filtered natural rate of unemployment. Thus it was instead decided that the model should try to fit classical cycle measurements advanced by Harding and Pagan (2002). Classical cycles do not measure cycles in filtered data, but instead focus on the levels of data in defining turning points.34 3.1. The classical cycle algorithm Harding and Pagan (2002) created a method to detect turning points in a data series based on a modification to the “two consecutive quarters of negative growth signals a recession” rule of thumb. The algorithm searches for phases lasting at least k = 2 periods, and full cycles which last at least m = 5 periods. The requirement that m = 5 serves as a censor limiting detected peaks and troughs to be a certain minimum distance apart. The values of minimum phase length and full cycle requirements are intended to match the description of a recession by Burns and Mitchell (1946) that recessions should last six months and full cycles should last at least 15 months. Also, the turning points are censored such that peaks and troughs must alternate so that continuous cycles can be measured. Peaks are found when Yts , exceeds the level of the neighboring two periods before and after t (i.e., 2 yt > 0, yt > 0, yt+1 < 0, 2 yt+2 < 0). Troughs are located when Yts is lower than the neighboring two periods before and after t (i.e., 2 yt < 0, yt < 0, yt+1 > 0, 2 yt+2 > 0).35 3.2. Calibration The baseline specification was selected by narrowing down the collective set of parameter values through performing a very coarse grid search across all combinations of ı ∈ {0, 0.25, 0.5, 0.75, 1}, M = Z ∈ {1, 15, 30}, 1 ∈ {0.1, 0.25, 0.5, 0.75, 0.9}, 2 ∈ {0, 0.5, 1},  = ϕ ∈ {0.05, 0.1, 0.15, 0.20}, with preferential attachment ∈{Ld , Yp , P}. Individual simulations use an identical random variable seed, and any that collapse are excluded from future consideration.36 Each simulation is scored using the sum of squared deviations of average simulation values from quarterly empirical measures for the U.S. between 1948 and 2011 (Table 2). Deviations are normalized using the empirical means for each of five macroeconomic variables: unemployment rates; inflation rates; growth rates (log difference of sales); contraction length; and expansion length.37 The ten sets of parameters with the lowest sum of squared deviations were each further refined for values , ı, and Cmax . Each set of parameters are individually and sequentially tested for the following values: 

∈ {0.5, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5}

ı ∈ {0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1} Cmax

∈ {1, 2, 4, 6, 8, 10, 12, 14, 16}.

The ten sets of parameters that most closely fit after this second exercise are each run 100 times, and the set of parameters with the lowest average score is used as the preferred baseline specification (parameters listed in Table 1). The primary baseline specification is used to examine the policy treatments addressed below.38 Table 2 displays the macroeconomic reference values and the average of 100 replications using the primary baseline specification. The reference value is inside of the center 90 percent of the simulated empirical distribution for three of the five variables (Fig. 1). The preferred baseline specification exhibits higher average unemployment and inflation and slower average growth than the reference values, but simulated values are within reason. Also, observed cycles are

34 While filtering has its place in macroeconomics, it is not clear if one is actually studying trends or cycles when examining filtered data (Harding and Pagan, 2005). 35 2 yt = yt − yt−2 . 36 Collapsing entails that enough firms in the simulation fail that the economy ceases to produce. While these simulations might be interesting to analyze, further analysis is beyond the scope of this paper. 37 Alternative methods of calibrating the model to fit these stylized facts or those determined from a structural model include those suggested by Franke (2009) and Franke and Westerhoff (2012) who use a method of simulated moments to fit their model to data. Alternative calibration methods may enable the model to fit certain stylized facts such as growth better, but it also might detract from the current focus on cyclical features. Further research on competing calibration methods would be a worthwhile pursuit in the agent-based literature. 38 This calibration method does not fully capture the possible interactions over the finer parameter ranges. The goal is not to find a perfect real world model, but simply one that can reasonably replicate the macroeconomic data the model is aiming to fit. This also provides a set of comparably parameterized specifications to determine the sensitivity of results to the preferred parameter specification.

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Table 2 Empirical and simulation business cycle characteristics

Unemployment Inflation Growth Expansions Contractions

U.S. 1947–2011 (Quarterly)

Baseline (Periods)

5.8% 0.9% 0.83% 19.5 3.7

11.9%* 1.6%* 0.22% 11.4 4.4*

Note: Inflation rates and growth rates are log-differences, but reported as the approximate percentage change. * Indicates the U.S. quarterly value is included in the central 90% of the 100 simulation empirical probability distribution.

significantly shorter in average than the reference data. Only one of the 100 simulations yielded an average expansion length equal to the U.S. average of 19.5 periods. The average contraction is slightly longer than the U.S. average, but contraction lengths are within the central 90% of the simulation empirical distribution. Aggregated cyclical data shows the primary specification is reasonable as approximately 50% of individual contractions are longer than the reference value, and about 13% of expansions are longer than the reference value of 19.5 periods. It is also worth noting that the cyclical data the model is calibrated to match is based on stylized facts that themselves rely on fewer than 300 data points. Such a short historical record on cycles implies the average length of real world recessions and expansions can change quite dramatically with one “unusually” long or short cycle. The NBER has recorded 33 complete cycles between 1854 and 2009 (620 quarters) with average recession lengths of 5.3 quarters and average expansions of 14 quarters. While the primary baseline specification fits better according to these metrics, more recent post-war statistics are used as the basis for comparison.

Unemployment Rates

Inflation Rates

Growth Rates

0.6

0.4

0.3

0.3

0.4

0.2

0.2 0.2

0.1

0.1 0

0

0 −1

50

0

Percent

1

2

0 −1

3

0

Percent

1

Percent

Expansions

Contractions

0.4

0.5

0.3

0.4 0.3

0.2 0.2 0.1 0

0.1 0

5

10

15

20

0

0

2

Periods Fig. 1. Distribution of simulation averages for calibration.

4 Periods

6

8

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The rate of change in output using the primary baseline specification exhibits excess kurtosis over individual iterations as seen in U.S. data.39 In contrast to previous literature, Russo et al. (2007) exhibited growth rates that were approximately normally distributed, while Gaffeo et al. (2008) exhibited fat tails in growth rates. The primary specification exhibits very large occasional declines in output, and has a positive trend growth rate over the full 300 periods in over 90% of simulations. 4. Fiscal policy treatments Computational policy experiments are performed using a rule that triggers a reaction after contractions measure at least four periods. Considering the typical lag time between the start of a real-world contraction and confirmation of a contraction is often between six months and a year, it is reasonable to trigger a government reaction only after four full contractionary periods have passed. The Harding and Pagan (2002) algorithm can only detect turning points two periods from the endpoint; therefore the policy is not implemented until six periods have passed from the last turning point. Comparisons are made across specifications and treatments using Monte Carlo simulation methods to create 100 unique time paths each with 600 time periods. The first 300 periods are discarded for all simulations in order to compare semi-stable states across specifications. To maintain some measure of comparability across treatments each uses the same 100 unique random number seeds. Policy treatments are only instituted after t = 300 so that all treatment paths begin at the same state. Even though the simulations are seeded, path dependence causes divergence in specifications as soon as a single change occurs in any random variable. Three highly stylized government policy treatments are applied to the primary baseline specification in Table 1. Treatment 1: Deficit financed fiscal stimulus. Fiscal spending stimulus is enacted by increasing benefits by 7.5% of t − 1 consumer expenditure while keeping tax rates fixed.40 Government stimulus continues to accumulate until the authorities witness the end of the recession in real-time. Since the authorities do not have knowledge of the real-time economic state stimulus continues for a two-period lag after the end of a contraction. Bonds are sold to the public, and interest is paid to households on all outstanding government debt. The government runs deficits each period accumulating a quantity of debt up to 100% of total expenditures in t − 1.41 In order to prevent runaway debts and non-convergent simulations debt repayment is strictly enforced. As soon as the following trough in the business cycle is detected and two additional periods have passed (t + 6 after the trough), the government reverses course and begins paying off the debt at a rate of 10% per period relative to the original aggregate debt. Debt repayment occurs every period as long as the economy continues to expand for up to ten periods to complete repayment. If the economy begins contracting again, then repayment pauses until the next expansion takes hold. Should a new extended contraction be identified a new round of stimulus begins as described above. In this treatment, debt repayment occurs through reduced unemployment benefits and reduced R&D funding from the government. Treatment 2: Tax cut and spending cuts. Taxes and spending are simultaneously cut when the trigger mechanism indicates a sufficiently long recession. All tax rates are reduced by 25% during this time. Benefits to the unemployed and R&D are immediately cut reflecting reductions in tax revenue and maintenance of a balanced budget. After the end of the recession, tax and spending rates are returned to their original level.42 Treatment 3: Deficit financed tax cut. The third treatment cuts taxes while keeping spending fixed. Using the same trigger mechanism and algorithms as above, taxes are reduced by 25% during recessions so that they would be the same as under the second treatment. However, this treatment keeps government spending and benefits fixed at previous levels during the period that taxes are cut. The government treats deficits and debts the same as in treatment one by accumulating debt up to 100% of t − 1 expenditures. Repayment begins after four periods of expansion have passed from the end of the previous contraction. 4.1. Comparing a single baseline and treatment specifications Fig. 2 displays a single representative log output path using the primary baseline specification along with log output paths for each of the three treatments. Output fluctuates dramatically in the baseline simulation, counting 13 contractions at an average length of 5.1 periods. The longest contraction lasts 14 periods, and is visible near t = 250 when the simulated economy experiences a mild contraction and does not return to steady growth for some time. Expansions in this baseline simulation last on average 16.8 periods, and there are two expansions which last 34 periods each.

39 U.S. quarterly growth rates in GDP from 1947 to 2011 exhibit a kurtosis around 5 and a slightly positive skewed distribution. The kurtosis of the iteration shown here is around 24, with a skewness of approximately −2.0. 40 A 7.5% stimulus is large in historical context, amounting to about $1 of stimulus for $13 of previous expenditures. This amount is approximately on par with recent U.S. budget deficits as a percent of GDP. 41 Changes to the debt ceiling and interest on the debt can be accommodated but have been left out intentionally in these simulations. Also, debt may exceed 100% of expenditures if output contracts following a large accrual of debt. 42 A 25% tax cut compares to the 7.5% increase in spending but cannot be held at a constant comparative level since each simulation is different. Roughly speaking, taxes amount to around 30% of all expenditures in the baseline specification. A 7.5% increase in spending if expenditures were $1000 would be $75, with taxes being around $300. A 25% cut in taxes would be approximately equal to the $75 in increased spending.

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8.0 7.0 6.0

Log(Output)

9.0

Treatment 1

0

50

100

150

200

250

300

200

250

300

200

250

300

8.0 7.0 6.0

Log(Output)

9.0

Treatment 2

0

50

100

150

8.0 7.0 6.0

Log(Output)

9.0

Treatment 3

0

50

100

150

Fig. 2. Comparison of total output for baseline and treatments.

The first treatment for the representative simulation produces 21 contractions that last on average 4 periods, with a maximum of 7. Expansions are shorter and contractions are more frequent, lasting only 10 periods on average. The longest expansion in the first treatment lasts 28 periods. The second and third treatments have 14 and 11 contractions respectively, and an average length of 4.5 and 4.4 periods. Thus, for this single simulation, each of the treatments results in shorter and shallower contractions. However, it is generally not the case that these treatments are effective at reducing contraction length.

4.2. General comparison of baseline and treatment specifications A number of tests were conducted to compare the shape and centrality of the different treatments including both Wilcoxon rank-sum and Kolmogorov–Smirnov (K–S tests) tests.43 Treatment three appears to be the only generally successful treatment as it significantly shortens contractions relative to the primary baseline specification. In treatment three, output recovers significantly faster than in other treatments partially due to the fact that the amplitude of contractions is significantly smaller. Averaging across all 100 simulations, unemployment rates are lower by an insignificant amount for treatment three, with no significant change to average growth (Table 3). While tests show the third treatment results in inflation rates that are statistically higher, they are not practically different from baseline. Additionally, the average and distribution of contraction length are statistically shorter in treatment three relative to the baseline. The differences may seem small, but in context a 0.22 period reduction of average recession length represents just over one fewer year, or 5% less time spent in recession over the course of 75 years.

43 There is no significant difference in the average value of the fitting scores for any of the treatments relative to the baseline. This provides some assurance that the results presented here are not due to the lack of similarity across specifications.

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Table 3 Average of simulation means over 100 simulations.

Baseline Treatment 1 Treatment 2 Treatment 3

Unemployment (%)

Inflation (%)

Growth (%)

Expansions (Periods)

Contractions (Periods)

11.9 11.8 12.0 11.8

1.6 1.7 1.6 1.7*, †

0.22 0.22 0.23 0.24

11.4 11.7 11.5 12.1

4.37 4.33 4.37 4.15**, †

Note: Averages across simulation means may not match Table 4 which uses accumulated data. * Wilcoxon test is significantly different from baseline at the 5% level. ** Wilcoxon test is significantly different from baseline at the 10% level. † K–S test is significantly different from baseline at the 5% level.

Table 4 Number (average length) of accumulated contractions across 100 simulations

Baseline Treatment 1 Treatment 2 Treatment 3

All

>4 periods

>6 periods

>8 periods

>10 periods

>12 periods

1883 (4.3) 1846 (4.3) 1865 (4.4) 1859 (4.1)

586 (7.6) 628 (7.3) 613 (7.4) 618 (6.9)*, †

289 (9.8) 298 (9.3)* 305 (9.5) 249 (9.0)*, †

150 (12.0) 130 (11.9) 142 (11.8) 94 (11.7)

81 (14.2) 70 (14.1) 74 (14.0) 45 (14.1)

45 (16.5) 35 (16.7) 41 (16.0) 23 (16.4)

Statistical tests confirm differences in mean and distribution of average values. * Wilcoxon test is significantly different from baseline at the 5% level. † K–S test is significantly different from baseline at the 5% level.

Debt financed stimulus spending apparently does little to stop contractions from continuing, but does help modestly increase the length of the recovery even in the face of debt repayment. Treatment one also does not result in any significant change in growth rates, unemployment rates, or inflation. Without any means of stimulus but a cut in tax rates, treatment two does little to shorten the length of contractions or lengthen expansions. Generally, treatment two does little to impact the average or distribution of any of the variables tracked here. Aggregating the information from all 100 simulations yields between 1800 and 1900 complete cycles for the baseline and each treatment. Approximately 66–69% of all contractions are for four periods or less, and there are about 19 cycles per iteration on average. Tests fail to reject significant differences in all but one of the distributions of aggregated contractions and expansions, with the lone exception that the average length of expansions is larger in treatment one relative to the baseline. Since over 66% of all contractions are shorter than five periods, it is not surprising that the complete distributions are statistically similar. These results essentially rule out the possibility that augmenting fiscal policy for severe contractions has any impact on more moderate downturns. Closer examination of extreme values is warranted considering the treatments are designed to shorten contractions lasting longer than four periods and only take effect after six periods. While the full distributions are not statistically different, the average length and occurrence of longer contractions often significantly differs relative to the baseline (Table 4). Under treatment three, the average length of contractions longer than six periods is 9.0 periods, significantly shorter than the baseline by 0.8 periods. It is even more notable that the third treatment nearly cuts in half the number of contractions lasting longer than 12 periods when compared to the baseline. Treatment one significantly shortens contraction length for those lasting more than six periods, reducing the average to 9.3 periods, and reduces the number of contractions longer than 12 periods by over 20%. Additionally, treatment one significantly lengthens the average expansion.44 Density plots display another comparison of contractions for each of the treatments compared against the baseline (Fig. 3).45 Treatment three exhibits a visible shift in the tail, with fewer extended contractions (Fig. 3, panel 3). In combination with the results in Table 4, treatment three appears to be a strong candidate for shortening the severest of recessions.

4.3. Robustness checks and alternative baseline specifications The same baseline and treatment experiments are conducted using a number of parameter variations to determine what generalities can be drawn from this model. Fifty iterations are conducted for each of the alternative baseline scenarios along with each policy treatment. Evidence from these robustness checks often conflicts with the results from the primary baseline specification.

44 Unreported K-S and Wilcoxon tests show the distribution of aggregated expansions from treatment one are significantly longer than in the primary baseline specification at the 10% level. Tests of treatment one average expansion length in Table 3 are close to, but not significant at the 10% level. 45 Fig. 3 displays density plots for contractions longer than eight periods to visualize the difference in the right-hand tail that is not clearly visible when all data is presented.

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0.10 0.00

Density

(1)

10

15

20

25

30

25

30

25

30

0.10 0.00

Density

(2)

10

15

20

0.10 0.00

Density

0.20

(3)

10

15

20

Fig. 3. Density of contraction length exceeding eight periods.

4.3.1. Preferential attachment Alternative specifications are examined for the consumer preferential attachment variable, including both labor demand and previous output. The third and fourth best fitting specifications from calibration used previous output and labor demand variables for consumer preferential attachment respectively.46 Consistent with previous research these alternative preferential attachment variables emphasize that consumers will shop at the largest firms in terms of size (Gaffeo et al., 2008; Russo et al., 2007). Using the aforementioned parameter specification for previous output as the preferential attachment variable reversed many of the findings of the primary specification. Treatment three in this secondary baseline specification resulted in an insignificant lengthening of contractions relative to the baseline, with few other notable significant differences. Using labor demand as the preferential attachment variable resulted in findings that were very similar to the primary baseline specification. Treatment three experienced significantly shorter contraction lengths, but growth did not significantly differ. The finding that treatment one lengthened expansions did not hold up under this alternative baseline scenario. However, contraction lengths were reduced by an insignificant amount under treatment one. Treatment two was again nearly identical to the baseline for all measures we considered. 4.3.2. Dole percentage When ı = 0, compared to the primary specification ı = 1, unemployment rates fall very close to zero, and growth rates are nearly identical (Fig. 4, panels (a) and (b)).47 However, as ı is increased the average rate of growth declines, until becoming negative at ı = 0.8 and ı = 0.9. When ı = 0.9 unemployment hovers around 70% on average. Real output declines steadily as employers have low labor demand and households receive low wages. Contractions get longer and expansions get shorter on average as ı increases towards 0.9. However, when ı = 1.0 under the primary baseline, growth rates rise above the value when

46 The “previous output” specification that best fit the data also differed by ı = 0, h = 0.2, hϕ = 0.2, 1 = 0.5, 2 = 0.5, Cmax = 16. The only difference between the “labor demand” specification and the primary baseline specification is the value of Cmax = 12 rather than 14. 47 Only variations to the primary baseline specification are shown in Fig. 4. Treatment effects are not shown since they very closely track the baseline.

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Fig. 4. (a) Primary specification with adjusted parameters; (b) primary specification with adjusted parameters; (c) primary specification with adjusted parameters; (d) primary specification with adjusted parameters; (e): primary specification with adjusted parameters; and (f): primary specification with adjusted parameters.

ı = 0. These results somewhat disagree with the findings of Russo et al. (2007) who showed that changing the redistribution of tax revenue from solely R&D (ı = 0) to only unemployment benefits (ı = 1) reduced growth rates. In agreement with Russo et al. (2007) it appears there are drawbacks to redistribution. When all tax revenue is redistributed to households rather than R&D unemployment rates are higher, inflation rates are higher, and business cycle contractions are shorter. The treatment effects discussed under the primary baseline specification are also not as promising as ı changes. Contraction lengths are often the same or slightly longer under treatment three as ı rises from 0 to 0.9. While unemployment benefits act as an automatic stabilizer and keep the economy growing, complete allocation towards R&D increases technology growth and employment. At the point ı = 1.0 however, the model reverts back to the primary specification. The value of ı also has an effect on the level of inequality for wealth and consumption. In the primary baseline specification wealth is very equally distributed with a Gini coefficient measuring around 0.2, while consumption is very unequal around 0.9 implying a few people do almost all of the consumption. Gini coefficients when ı = 0 are near 0.4 and 0.6 for income and wealth respectively. These values are far closer to those seen in the U.S. where estimated Gini coefficients for income are approximately 0.4 to 0.5 and those for wealth range between 0.6 and 0.8. Somewhat counterintuitively, greater benefits to the unemployed result in an increase in inequality. This can be explained by the fact that by supporting the unemployed, household wages either fall or stagnate resulting in a limited capacity to save. Households that retain employment continue to gain shares of wealth and overall consumption. Before concluding that unemployment benefits are destabilizing the economy through longer contractions, recall that ı = 0 does not entail there is no redistribution, but that all tax revenue is

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directed to firms for improving efficiency. These results imply a policy of directing most—if not all—tax revenue towards R&D would lead to an economy with less inequality, lower unemployment, and more frequent but shorter recessions. A deeper examination of the secondary baseline specification which uses previous output as a preferential attachment variable provides additional conflicting evidence. Unemployment rates rise as ı increases, and growth rates remain essentially constant. On average, contractions and expansions become shorter as more revenue flows to the unemployed. Contrary to the primary baseline specification, treatment three appears to be more effective at reducing unemployment and contraction length as the value of ı increases from 0 to 0.9. 4.3.3. Search costs When search costs are increased (M and Z decrease) using the primary specification expansions lengthen and contractions shorten until leveling off near the values seen in Table 4 (Fig. 4, panels (c) and (d)). When search costs are highest at 10% of firms, the average unemployment rate across all simulations is near 40%, and growth is negative. As households gain access to more firms, growth and inflation rates rise and unemployment rates fall. Additionally, when search costs are highest there is evidence that wealth inequality suffers. Wealth accrues in a more unequal manner when search costs increase, steadily doubling the Gini coefficient from 0.25 to 0.5. 4.3.4. Tax rates Using the primary baseline specification, holding income tax rates fixed, and varying the corporate tax rate between 10 and 50% shows average growth and unemployment rates do not monotonically fall as rates increase (Fig. 4, panels (e) and (f)). Growth rates do have a general downward trend as corporate tax rates increase which supports the work of Russo et al. (2007). Average contraction length declines at first when corporate tax rates are low, but then increases as tax rates rise to 50%. Firms burdened by higher taxes have slower technological growth and the economies tend to take more time to recover from contractions. As in the primary baseline specification, treatment three often is able to significantly reduce the length of contractions as tax rates increase. Additionally, each treatment is tested against a baseline specification where all tax rates are set to a flat 15%. With flat tax rates, treatments one and three do not appear effective in reducing contraction length. This evidence suggests that the progressivity in the tax code is essential for the treatments to be effective in altering business cycle dynamics. Progressivity is likely an important feature here since it acts to temporarily augment the automatic stabilizers in the first and third treatments, while the second treatment merely dampens their effect. These findings are supported by recent empirical evidence showing progressive taxation is associated with less output volatility (Attinasi et al., 2011). Recent calls for increased use of automatic stabilizers are based on the fact that progressive stabilization policies direct money to those with higher marginal propensities to consume and the liquidity constrained.48 5. Conclusions The HIA approach to macroeconomics shows promise as an alternative to the general equilibrium approach, but there is still progress to be made. The HIA model developed here furthers the CATS approach to examining an agent-based macroeconomy by including taxation at both the individual and firm level, as well as allowing for a flexible redistributive policy that can be used to study a variety of policy choices. The primary specification found through a calibration exercise reveals some insights on the business cycle and macroeconomic effects of three different types of fiscal responses intended to stem the damage from severe contractions. Under the calibrated model a policy of deficit-financed stimulus spending is able to increase the length of recovery periods. A second policy which cuts tax rates and simultaneously reduces spending to maintain balanced budgets does not do anything to significantly alter the distribution of business cycle contractions, unemployment, growth, or inequality. A third policy of deficit-fianced tax cuts which reduce income and corporate taxes by 25% leads to shorter average recessions and vastly reduces the number of lengthy contractions. Under the primary baseline specification these policy experiments suggest that deficit-financed tax cuts and spending increases can significantly impact the ability for an economy to recover from recession. These results are likely due to the fact that these policies act to strengthen automatic stabilizers and redistribution mechanisms that were already in place. However, testing reveals that many of these results cannot be widely generalized. A secondary baseline specification that changes the preferential attachment variable from price to previous output reveals no significant impact from the policy treatments on measured contractions or growth rates. These robustness checks reveal a few general findings where the secondary and primary specifications agree. Increases in redistribution towards the unemployed results in higher unemployment rates, more inequality in consumption and wealth, and shorter contractions without impacting growth. However, increasing unemployment benefits in the secondary specification results in shorter expansions with almost no impact on growth rates. These experiments suggest that the HIA-CATS model can reveal some generalities while other conclusions are very sensitive to parameter specifications. These findings match reality in the sense that we probably should not expect a “onesize-fits-all” approach to reduce the severity of business cycles. Varying institutional arrangements and behavioral patterns

48

While not utilized in the model presented here, differential marginal propensities to consume have been used elsewhere in the agent-based literature.

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might require different solutions. The exploratory nature of these models begs one to be careful of making general predictions as suggested by Marks (2007). With that in mind, the approach taken here can be expanded in a number of ways to incorporate more policy choices as well as a financially fragile banking sector. However, we caution others that careful and timeconsuming calibration measures and robustness checks may still prove policy changes inconclusive. Another potential avenue for research would examine the speed that fiscal authorities could react to downturns through stimulus spending or automatic stabilizers. If fiscal authorities could react immediately by providing additional stimulus then all contractions could be potentially shortened. However, it took approximately 4 quarters before the 2007 recession was even declared in the U.S., and 5 quarters following the conclusion before the end date was recognized. 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