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Tax policy and resource allocation
C H A P T E R
3 Tax policy and resource allocation Kun-Young Yun Department of Economics, Yonsei University, Seoul, Korea
3.1 Introduction
Fullerton and Rogers (1993, 1996), and Jorgenson et al. (1997). These innovations enhanced the realism of the models and improved representation of the economy and the tax system. More importantly, the presence of heterogeneous consumers in the model made it possible to analyze distributional effects of tax policy. Jorgenson and Yun (1986a, 1986b, 1990, 2001, 2013) developed a dynamic general equilibrium model (DGEM) of the US economy, which has been used to evaluate the welfare effects of various tax policies including major tax reform proposals in the United States. Our DGEM consists of four sectors: household, business, government, and the rest of the world. The household sector is populated by identical consumers with infinite life and perfect foresight. In the business sector, labor and capital services are used to produce consumption and investment goods. The government collects taxes, issues debts, purchases goods and services, and makes transfer payments to households and the rest of the world. The rest of the world trades with the United States in consumption goods, investment goods, and labor services. In our DGEM, the cost of capital approach pioneered by Jorgenson in his celebrated paper
Since Harberger (1962), measuring efficiency cost of taxation has been an important issue in tax policy analyses. The original Harberger model was a simple two-sector static model with fixed supplies of capital and labor. However, the real world is much more complex and, in response to the rising interest in reliable estimates of the economic effects of tax policy, economic models used for the analysis of tax policy have been extended in a number of important directions. One of the most important innovations is the introduction of dynamic general equilibrium models in which consumers maximize intertemporal welfare and capital is accumulated through investment. Two types of models emerged along this line of developments. One is the overlapping generations (OLG) models introduced by Summers (1981) and Auerbach and Kotlikoff (1987). The other is the infinite time-horizon models of Chamley (1981, 1986) and Jorgenson and Yun (1986a, 1986b). Another important development is the extension of models by introducing heterogeneous consumers and/or multiple commodities/industries as in Auerbach and Kotlikoff (1987),
Measuring Economic Growth and Productivity https://doi.org/10.1016/B978-0-12-817596-5.00003-2
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3. Tax policy and resource allocation
(Jorgenson, 1963) plays a central role by providing a convenient platform for representing the complex structure of taxation of income from capital in the United States. We employ the cost of capital approach to represent corporate income tax, individual taxes on capital income (interests, dividends, and capital gains), property taxes, economic depreciation, and the private returns to capital. Modeling the income tax on labor and the sales taxes on commodities is straightforward. Section 3.2 describes the cost of capital for the corporate, noncorporate, and household sectors. The cost of capital is used to estimate the social and private rates of return on capital, tax wedges, and the corresponding effective tax rates. Section 3.3 describes the basic structure of DGEM and its parameterization. Section 3.4 describes the equilibrium and dynamics of the model and explains the solution algorithm. In Section 3.5, we measure the marginal and average efficiency costs of tax revenues from various parts of the US tax system. We also consider alternative tax reform proposals and discuss their welfare effects. Section 3.6 concludes the chapter.
3.2 Cost of capital and effective tax rates
noncorporate, and corporate sectors. Tax treatment of income from capital also depends upon the type of assets employed in the corporate and noncorporate sectors. The main differences in the tax treatment of assets in the business sectors are in investment tax credits and depreciation allowances for tax purposes. In addition, consumers and producers may treat capital services from different types of assets as less than perfect substitutes. We thus distinguish two types of assets based on durability, shortlived and long-lived assets, in each of the three sectors.1 The cost of capital approach introduced by Jorgenson (1963) provides a convenient and versatile vehicle for representing the complex details of the taxation of income from capital. It can easily handle the various tax reform proposals discussed in the tax policy circles around the world as well. The cost of capital approach starts with the assumption that equity holders maximize their wealth by appropriately choosing inputs and outputs in a given period of time and investment strategies over time. For income from corporate capital, equity holders are taxed on dividends and capital gains. The portfolio equilibrium of equity holders requires: g Divt TDt þ 1 tq ðEt Et1 Nt Þ ¼ ret Et1 (3.1)
3.2.1 Cost of capital Capital services are consumed by households and used for production in corporate and noncorporate businesses. Tax treatment of income from capital depends upon the sector in which capital is employed. In order to represent these differences, we distinguish the demands for capital services from household,
where Divt is dividends in period t, TDt is indig vidual income tax on dividends, tq is marginal tax rate on accrued capital gains, Et is the value of equity, Nt is the value of new share issues, and ret is the equilibrium nominal rate of return to equity. TDt is proportional to dividends, i.e., TDt ¼ teq Divt , where teq is marginal tax rate on dividends.
1 In the household sector, short-lived assets include consumer durables and producer durable equipment, and longlived assets include residential and nonresidential structures and land. In the corporate and noncorporate sectors, short-lived assets include producer durable equipment and long-lived assets include residential and nonresidential structures, farm and nonfarm inventories, and land.
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3.2 Cost of capital and effective tax rates
Under the transversality condition that !1 resþt 1þ Etþsþ1 approaches zero as s g 1 tq s¼1 approaches infinity, Eq. (3.1) can be solved for Et: !1 " ! N sY þ1 X 1 teq resþt 1þ Et ¼ g g1 1 tq 1 tq s¼0 s¼1 # sþ1 Y
Divtþsþ1 þ ðDivtþsþ1 Ntþþ1 Þ
The cash flow constraint of the corporation is: Divt Nt ¼ Pt Qt wt Lt ð1 kq tq zq Þqt It p
tq qt1 Kt1 bq ð1 kq tq zq Þ ½ðit pt Þqt1 Kt1 qt ðKt Kt1 Þ TCt (3.5) where investment in period t is given by: It ¼ Kt ð1 dq ÞKt1
(3.2) We assume that dividends are a constant proportion a of corporate cash flow after property and corporate income taxes: h Divt ¼ a Pt Qt ðKt1 ; Lt Þ wt Lt ð1 kq p
tq zq Þdqt Kt1 tq qt1 Kt1 bq ð1 kq i tq zq Þðit pt Þqt1 Kt1 TCt (3.3) where Pt is price of output, Qt(.) is production function, Kt1 and Lt are capital and labor inputs, respectively, and wt is wage rate. kq and zq are the rate of investment tax credit and the present value of depreciation allowances for one dollar’s worth of investment, respectively, and tq is corporate income tax rate. d is rate of economic depreciation, qt is price of investment good, tpq is property tax rate, bq is debt/capital ratio, it and pt are nominal interest rate and the rate of inflation, respectively, and TCt is corporate income tax. The subscript q refers to the corporate sector. Corporations are taxed on income from capital net of depreciation allowances, interest payments, and property taxes, and the tax liability is reduced by investment tax credits, i.e.: h TCt ¼ tq Pt Qt wt Lt ð1 kq i p tq zq Þqt1 Kt1 bq it tq qt1 Kt1 (3.4)
(3.6)
We assume that corporations keep dividends payout ratio, a, and debt/capital ratio, bq, constant. It follows that retaining is independent of investment, and the marginal sources of investment funds are debt and new share issues, with debt accounting for the fraction bq, and new share issues, 1bq. An alternative would be to assume that a is endogenous and new share issues are somehow determined independent of investment. Then retaining becomes the marginal source of equity financing. For example, if we assume that new share issues are zero, retaining depends upon investment, and marginal investment funds are financed with debt and retaining. By substituting Eqs. (3.3)e(3.6) into Eq. (3.2) and taking the derivative of Vt with respect to Ktþ1, we obtain the first-order condition for maximization of Et, which can be rearranged to give the cost of capital: 1 kq tq zq q ct p rt pt þ ð1 þ pt Þd þ tq ¼ qt1 1 tq (3.7) q rt
is the weighted average of marginal where costs of corporate debt and equity: q rt pt ¼ bq ½ð1 tq Þit pt þ 1 bq 2 3 g (3.8) ret 1 tq pt 4 5 g 1 teq a þ 1 tq ð1 aÞ
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3. Tax policy and resource allocation
The cost of capital in Eq. (3.7) is the price of capital services from one dollar’s worth of lagged capital stock, which includes compensation for depreciation adjusted for investment tax credit and depreciation allowances for tax purposes. The real social rate return for corporate capital is defined as:
in Eq. (3.9) and the corresponding real private rate of return is: h i rht pt ¼ bh 1 tdh it pt þ ð1 bh Þ ret pt : (3.14)
(3.9)
The subscripts and superscripts h refer to the household sector. For the noncorporate businesses, the cost of capital is:
Similarly, the real private rate return for corporate capital is defined as: h i q rt pt ¼ bq 1 tdq it pt þ 1 bq ret pt (3.10)
ct 1 km tem zm m p ¼ rt pt þ ð1 þ pt Þd þ tm qt1 1 tem
q
s t pt ¼
ct ð1 þ pt Þd. qt1
where tdq is the marginal tax rate on individual income from interest payments on corporate debt. Finally, the after-tax real corporate rate of return is defined as: q
rct pt ¼ rt pt þ bt tq it
(3.11)
We can proceed in a similar manner to derive the cost of capital and the corresponding social and private rates of return on capital employed in the household and noncorporate sectors. In order to avoid repetition, we simply present the results without fully describing the derivation process.2 The cost of capital for household assets is: p ct ¼ rht pt þ ð1 þ pt Þd þ 1 teh th (3.12) qt1 where
rht pt ¼ bh 1 teh it pt þ ð1 bh Þ ret pt :
(3.13)
The real social rate of return on household assets is defined as the cost of capital net of economic depreciation adjusted for inflation as 2
(3.15) where e e rm t pt ¼ bm 1 tm it pt þ ð1 bm Þ rt g 1 t m pt : ð3:16Þ The real social rate of return on noncorporate assets, smpt, is defined as in (Eq. 3.9), and the corresponding real private rate of return is: h i d rm t pt ¼ bm 1 tm it pt (3.17) þ ð1 bm Þ ret pt : In Eqs. (3.15)e(3.17), the subscripts and superscripts m refer to the noncorporate sector.
3.2.2 Tax wedges and effective tax rates Auerbach and Jorgenson (1980) introduced the concept of marginal effective tax rate, which is defined as the ratio between the tax wedge and the social rate of return. It is natural to define the tax wedge as the difference between social and private rates of return. In the case of corporate q
assets, the effective tax rate is defined as
q
st rt . q st pt
Similarly, we can define the effective corporate
Interested readers are referred to Chapter 2 of Jorgenson and Yun (2001).
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3.2 Cost of capital and effective tax rates q
s rc
income tax rate as sqt pt , and the effective individt
t
q
rc r
ual income tax rate as stq pt . The effective tax rates t
t
for assets in the household and noncorporate sectors are defined analogously. Table 3.1 shows the real social rates of return, tax wedges, and effective tax rates for short-lived and long-lived assets in the corporate, noncorporate, all business, and household sectors in the US Notice that the tax wedges in the corporate and noncorporate businesses are substantial in absolute values as well as relative to the real social rates of return. The effective tax rates are 42.7% and 33.5% in the corporate and
TABLE 3.1
Corporate
Noncorporate
Effective tax rates (2010 tax law). SROR
TW
ETR
S
0.0940
0.0341
0.3631
L
0.1088
0.0490
0.4501
A
0.1045
0.0447
0.4275
S
0.0863
0.0225
0.2612
L
0.0969
0.0332
0.3421
A
0.0959
0.0321
0.3351
noncorporate sectors, respectively. For the entire business sector, the effective tax rate is 40.0%. The substantial tax wedges and the corresponding effective tax rates suggest that taxation of income from capital in the business sector may present a significant barrier to efficient allocation of resources between present and future. Panel 1 of Table 3.2 presents the tax wedges between short-lived and long-lived assets in the corporate, noncorporate, and all businesses. The interasset tax wedges are defined as the difference between the social rates of return on short-lived and long-lived assets. Considering that the average social rates of return in the corporate and noncorporate businesses are 10.45% and 9.59%, respectively, the interasset tax wedges of 1.49% in the corporate sector and 1.06% in the noncorporate sector may not appear to be large, but they are still significant. Panel 2 of Table 3.2 shows the intersector tax wedges between the social rates of return on assets in the corporate and noncorporate sectors, corporate and household sectors, and noncorporate and household sectors, respectively. Among these intersector tax wedges, the wedges between corporate and noncorporate sectors have drawn most attention in textbooks and tax policy TABLE 3.2 Tax Wedges (2010 tax law).
All business (corporate D noncorporate)
Households
Interasset tax wedges (long-short)
S
0.0930
0.0319
0.3430
L
0.1045
0.0434
0.4155
Corporate
0.0149
A
0.1018
0.0408
0.4004
Noncorporate
0.0106
A
0.0700
0.0048
0.0680
All business
0.0115
Property taxes are included in the calculation and the after-corporatetax real rate of return, rcpi, real interest rate, and the corporate dividend payout ratio are set at their 1970e2010 averages, 6.628%, 4.658%, and 47.86%, respectively. For asset category A (all assets), social and private rates of return are calculated as the averages of short-lived and long-lived assets, where the values of assets are used as the weights. Similarly for the All business sector. SROR: real social rate of return TW: tax wedge. ETR: effective tax rate. S, short-lived assets. L: long-lived assets. A: all assets (short þ long).
Intersector tax wedges S
L
A
Corporateenoncorporate
0.0076
0.0119
0.0086
Corporateehouseholds
0.0240
0.0389
0.0345
Noncorporateehouseholds
0.0163
0.0269
0.0259
A: all assets (short þ long). L: long-lived assets. S: short-lived assets.
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3. Tax policy and resource allocation
analyses. Indeed the famous Harberger triangle originally represented the efficiency loss in capital allocation between corporate and noncorporate sectors caused by the double taxation of corporate income. It is interesting to note that, while corporate tax integration has been an important tax reform issue in the United States and partial integration of the corporate and individual income taxes has been implemented in many other countries, the average tax wedge (for all assets) between corporate and noncorporate sectors of 0.86% is small compared with the tax wedge between corporate and household sectors of 3.45%, or the wedge between noncorporate and household sectors of 2.59%.
3.3 Dynamic general equilibrium model of the US Economy Tax wedges and effective tax rates are useful for understanding the barriers to efficient resource allocation. However, a narrative on tax distortion is incomplete without information on the displacements of resource allocation caused by the substitution effects of tax wedges. Under the US tax system, there are numerous tax policy instruments, and practically all of them affect relative prices and hence generate substitution effects. Our dynamic general equilibrium model provides a convenient framework for representing the US tax system and measuring the welfare effects of tax distortion.
3.3.1 Consumer behavior The consumers in the household sector are identical and endowed with infinite life and perfect foresight. The representative consumer maximizes the intertemporal welfare function: N Y t 1 X 1 þ ns V ¼ (3.18) U1s t 1 s t¼1 s¼1 1 þ g
where s is the inverse of the elasticity of intertemporal substitution, ns is the rate of population growth, g is the subjective rate of time preference, and Ut is the per capita utility function: Ut ¼ Ft ð1 aT Þt ; ðt ¼ 1; 2; .Þ
(3.19)
In Eq. (3.19), Ft is per capita full consumption in period t, where population is measured in efficiency unit, and aT is the growth rate of labor productivity. The representative consumer maximizes the intertemporal welfare function subject to the budget constraint: Q N X PFt Ft ð1 aT Þt ts¼1 ð1 þ ns Þ W ¼ (3.20) Qt s¼1 ð1 þ rs Þ t¼1 where W is lifetime wealth, PFt is price of full consumption, and r is nominal private rate of return. The necessary condition for maximization of intertemporal welfare subject to the budget constraint is given by the Euler equation:
1= s Ft PFt1 1 þ rt ¼ $ ; t ¼ 1; 2; .N s Ft1 PFt ð1 þ gÞð1 aT Þ (3.21) Eq. (3.21) plays a central role in determining the optimal path of the economy over time. Specifically, it determines the optimal growth rate of full consumption per capita in efficiency unit. If the level of full consumption in any one period is known, the entire path of full consumption can be determined. Among the infinite number of paths for full consumption that satisfy the Euler equation, the one that satisfies the intertemporal budget constraint will be chosen by the welfare maximizing consumer. It is useful to note that Eq. (3.21) implies that, in a steady state with a constant rate of inflation, the real private rate of return is constant. In the steady state, full consumption per capita in efficiency unit is constant, i.e., Ft1 ¼ Ft, and the constant rate of inflation implies that PFt ¼ 1 þ pt is constant, where pt is the rate of PFt1
3.3 Dynamic general equilibrium model of the US Economy
inflation in period t. It follows that the real private rate of return consistent with the steady s state is ð1 þ gÞð1 aT Þ 1. The steady-state real private rate of return depends only upon the parameters of the intertemporal welfare function, g and s, and the growth rate of labor productivity, aT. In particular, it is independent of any government policy to the extent that government policy does not affect g, s, and aT. More generally, Eq. (3.21) implies that the growth rate of full consumption per capita is approximately proportional to the difference between real private rate of return and its steady state value. Once the path of full consumption is determined, the consumer allocates full consumption among consumption goods, capital services, and leisure in each period. In order to represent the allocation of full consumption, we employ translog form of price function for full consumption and the corresponding value share equations introduced by Christensen, Jorgenson, and Lau (1975). The demand for household capital services are further allocated to short-lived and long-lived assets. In order to represent the allocation of household capital services, we employ translog price function for household capital services and the corresponding value share equations. In the translog price function of full consumption, the price of full consumption, PFt, is expressed as a function of the consumer prices of consumption goods, capital services, and leisure. The consumer price of consumption goods includes sales taxes and the price of leisure is the wage rate net of marginal tax on labor income. In the translog price function of household capital services, the price of (aggregate) household capital services is expressed as a function of the prices of capital services from short-lived and long-lived assets.
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and investment goods. However, we do not assign separate production processes for corporate and noncorporate businesses, or for consumption and investment goods. Instead we assume that the entire business sector acts like a single producer and employs labor and capital services from corporate and noncorporate businesses to produce consumption and investment goods. Specifically, we represent the production technology of the entire business sector with a single translog price function of Christensen, Jorgenson, and Lau (1973), where the price of labor services is expressed as a function of the prices of consumption goods, investment goods, corporate and noncorporate capital services, and time. The value share equations corresponding to the price function determine the values of capital services from corporate and noncorporate sectors and the values of consumption and investment goods relative to the value of labor input. As in the household sector, the allocation of corporate and noncorporate capital services between short-lived and longlived assets is represented by translog price functions and the corresponding value share equations. The partial derivative of the translog price function for labor with respect to time represents the rate of productivity growth. We require the model to be consistent with a balanced growth equilibrium in which labor productivity grows at a constant rate and value shares and relative prices of inputs and outputs are constant when labor is measured in efficiency unit. It follows that the value shares and the growth rate of labor productivity are independent of time. These conditions constrain the parameters of the translog price function for labor.
3.3.3 Government 3.3.2 Producer behavior In the business sector, there are two types of producers, corporate and noncorporate businesses, and two types of outputs, consumption
We consolidate the federal and state and local governments into a single government sector. Similarly, we consolidate the federal and state and local government enterprises into a single
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3. Tax policy and resource allocation
government enterprise sector. The government collects taxes from the household and business sectors, issues debt to finance deficits, and spends its revenues on consumption goods, investment goods, labor services, interest payments on government debt, and transfer payments to households and the rest of the world. The deficit of the government is added to the government debt. Government enterprises employ labor and produce consumption goods, and turn over any surplus to the general government. The government collects taxes from a variety of sources. In addition to the taxes on income from capital described in Section 3.2, the government levies income tax on labor, sales taxes on consumption and investment goods, property taxes, and wealth taxes. In representing the US tax system in our model, we distinguish marginal and average tax rates. The distinction is particularly important in the taxation of individual income where graduated tax rates apply. In general, marginal tax rates affect relative prices and average tax rates are used to generate tax revenues. For example, we calculate the price of as the price of labor services times leisure 1 tm where tm L L is the marginal tax rate on labor income. In calculating tax revenue, however, we use the average tax rate, i.e., RL ¼ taL $BL, where RL is the tax revenue from labor income, taL is the average tax rate, and BL is total labor compensation. In the case of capital income taxation, the prices relevant for resource allocation are the costs of capital derived in Section 3.2. The tax revenue from individual equity income is given by RE ¼ taE $BE ITCM, where taE is the average tax rate, BE is the tax base, and ITCM is investment tax credits for noncorporate businesses. Similarly, the tax revenue from interest payments on debt is calculated as RD ¼ taD $BD, where taD is the average tax rate, and BD is the tax base. Since sales taxes and property taxes are proportional, average and marginal tax rates are the same and the calculation of tax revenues is straightforward. In the case of corporate income
tax, the rate structure is graduated. Nevertheless, since most of corporate income is taxed at the maximum rate, we calculate the tax revenue as Rq ¼ tq$BQITCQ, where tq is the corporate income tax rate, BQ is the tax base, and ITCQ is tax credit for corporate investment. We assume that the government allocates its total expenditure, net of interest payments on government debt, in constant proportions among consumption goods, investment goods, labor services, and transfer payments to households and the rest of the world. We represent the allocation of government expenditure, net of interest payments, into these five categories of spending with a CobbeDouglas price function of the aggregate government spending. This representation is useful in the simulation of alternative tax policies in which the path of real government spending need to be controlled.
3.3.4 Rest of the world The rest of the world trades with the United States in consumption goods, investment goods, and labor services, pays compensation on US claims on the rest of the world, and receives transfer payments from US government. The current account deficit of the rest of the world is added to the US claims on the rest of the world.
3.3.5 Parameter values We estimate the parameters of the model using time series data of the United States for 1970e2010. This data set, informally referred to as the US Worksheet among Jorgenson and his associates, incorporates the cost of capital into a complete system of US national accounts in accordance with Christensen and Jorgenson (1973). The parameters of the consumer and producer models are estimated by nonlinear threestage least square method (NL3SLS) developed by Jorgenson and Laffont (1974) and Amemiya (1977). Most of the other parameters are set at
3.4 Equilibrium of the model and solution algorithm
historical values. For example, in the allocation of government expenditure, net of interest payment on government debt, the shares of consumption goods, investment goods, labor services, and transfer payments to households and the rest of the world are set at their sample averages. Similarly, we set the dividend payout ratio, a, and the debt/capital ratios in the household and business sectors, bj (j ¼ h, m, q), and the real interest rate at their sample averages. In the base case simulation, we set all the tax rates at their 2010 values, similarly for investment tax credits and the present values of capital consumption allowances. In all the simulations, we assume that new tax policies are introduced in 2011 and set the total time endowment and the prices of investment goods and the six categories of assets at their 2011 values. Finally, we set the ratio of government expenditure to GDP (SGOV), the proportion of purchases of consumption goods by the rest of the world to domestic purchases (SCR), and the proportion of purchases of investment goods by the rest of the world to domestic supply (SIR) at appropriate values so that the steady-state values of government debt/GDP and the claims on the rest of the world/GDP ratios are reasonable.
government enterprises, and the rest of the world purchase labor services from households. Finally, in the capital market, the capital stock owned by households is allocated to meet the demands for capital services from the corporate, noncorporate, and household sectors. Due to Walras’ law, one of the four market equilibrium conditions is redundant.
3.4.2 Dynamics of the model When a new economic policy is introduced, the economy jumps on a new transition path which eventually converges to the steady state. Along the transition path, the economy must be in equilibrium in each period and the entire path must be optimal in the sense that it maximizes intertemporal welfare of the consumer subject to the lifetime budget constraint. The transition of the economy from one period to the next is described by the transition of full consumption and the accumulation of capital stock, government debt, and the claims on the rest of the world. The transition of full consumption is described by the Euler Eq. (3.21). The accumulation of capital stock is represented by: VK ¼ VKL þ PI$ID Dep þ Rev
3.4 Equilibrium of the model and solution algorithm 3.4.1 Market equilibrium In a given period, there are four markets that need to be in equilibrium simultaneously. They are the markets for consumption goods, investment goods, labor services, and capital services. In the consumption goods market, households, government, and the rest of the world purchase goods from private businesses and government enterprises. In the investment goods market, households, government, and the rest of the world purchase goods from businesses. In the labor market, businesses, government,
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(3.22)
where VK is the value of capital stock at the end of the period, VKL is its lagged value, ID is private domestic investment, PI is the price of investment goods inclusive of sales tax, Dep is economic depreciation, and Rev is revaluation of domestic capital. The accumulation of government debt is described by: VG ¼ DG þ VGL
(3.23)
where VG and VGL are the current and lagged values of government debt, respectively, and DG is government budget deficit. Finally, the claims on the rest of the world evolve according to: VR ¼ DR þ ð1 þ pÞVRL
(3.24)
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3. Tax policy and resource allocation
where VR and VRL are the current and lagged values of the claims on the rest of the world, respectively, and DR is current account deficit of the rest of the world. Obviously the economy as a whole cannot run deficit or surplus, and the sum of the deficits of the household, business, government, and the rest of the world sectors must be zero. In other words, private savings net of investment are used to finance the deficits of government and the rest of the world: S ¼ PI$ID þ DG þ DR
(3.25)
where S is private saving. At the beginning of a period on the transition path, the quantities of capital stock, government debt, and claims on the rest of the world are predetermined. However, full consumption is free to jump in the first period of the transition, although it is constrained by the Euler equation thereafter. If we know the value of FS0 ¼ F0 $ 1 PFs0 in the Euler Eq. (3.21), we can solve for FS1, and the entire transition path of the economy can be calculated. We thus pretend that new policy is introduced in period 0 and start with a guess of FS0 and solve the model forward. Finding the correct value of FS0 is the essence of the solution algorithm.
3.4.3 Solution algorithm In order to evaluate the economic impacts of a new tax policy, we need to establish a reference with which to compare the performance of the economy under an alternative tax policy. We take the US economy under the tax laws of 2011 as the reference. For the year 2011, the lagged values of capital stock, government debt, and the claims on the rest of the world and the amount of total time endowment are
set at their historical values. Since there is no guarantee that the US economy is in a steady state in 2011, we proceed under the assumption that the economy is on a transition path toward a steady state. We refer to the US economy under the 2011 tax law as the base case. In any period on the transition path, once the lagged values of FS (FSL), capital stock (KL), government debt (GL), and the claims on the rest of the world (RL) are known, the equilibrium of the economy can be solved from the market clearing conditions for consumption goods, investment goods, capital stock, and labor services.3 Since one of the four market clearing conditions is redundant, we drop the labor market clearing condition. Since our dynamic general equilibrium model of the US economy converges to the steady state, it is convenient to solve for the steady state first. The transition path can then be found by solving for FS0, or FSL for period 1, that leads the economy to the steady state. Solving for the steady state is similar to solving for the equilibrium for a period on the transition path. However there are two differences. First, in the steady state of the base case, FSL and the lagged values of the three stock variables (KL, GL, RL) are not known. We need to solve for their steady-state values along with three endogenous variables that clear the four markets. Second, the Euler equation for full consumption implies that the real private rate of return on wealth is constant and known. In our model, total time endowment, rate of inflation in the price investment good, interest rate on debt, and the relative prices of investment good and the six categories of assets are fixed. In order to solve for the steady state of the base case, we start with seven unknowns (FSL, KL, GL, RL, re, PC, LD), where PC is the
In our model, the relative prices of investment good and the six categories of assets are fixed at their 2011 values and the rate of inflation in the price of investment goods is exogenous. The path of total time endowment is also exogenous. 3
3.4 Equilibrium of the model and solution algorithm
consumer price of consumption goods and LD is labor demand of the business sector. We make use of the Euler equation for full consumption, three market clearing conditions, and the steady state conditions of the three accumulation Eqs. (3.22)e(3.24), and apply Newton’s method to solve for the seven unknowns.4 The intertemporal welfare function of the consumer does not reflect the welfare effects of government expenditure, net of interest payments on government debts. We thus control the path of real government expenditure, net of interest payments. Similarly, in order to focus on the differential effects of alternative tax policies, we control the paths of government debt and the claims on the rest of the world. In order to constrain government debt and the claims on the rest of the world on reasonable paths, we set SGOV ¼ 0.20168, SCR ¼ 0.0007, and SIR ¼ 0.0022 so that, in the steady state of the base case, government debt/GDP ratio and the claims on the rest of the world/GDP ratio become 0.40 and 0.05, respectively. Once the steady state values of government debt and the claims on the rest of the world are determined, we construct complete paths of these two variables by connecting their historical values in 2010 and their steady state values. In our model, the economy comes very close to the steady state in less than thirty years after the introduction of a new tax policy. We thus constrain the government debt and the claims on the rest of the world to reach their steady state values in 40 years after the start of the transition. For all practical purposes, it is sufficient to assume that the economy converges to the steady state in 100 years. With these preparations, we solve for the transition path of the economy with an initial guess of FS0. Along the transition path, government debt and the claims on the rest of the world are
4
47
constrained to the paths described above. To control the path of government debt in the base case, we adjust total government expenditure including interest payments on government debt. To control the path of the claims on the rest of the world, we adjust the absolute value of the net exports of consumption goods, investment goods, and labor services. In a given period on the transition path, FSL, KL, GL, and RL are predetermined and the equilibrium of the base case economy can be determined by solving for the three unknowns (re, PC, LD) with the three market clearing conditions. However, to cut through the complex interdependence of F, PF, and re, we add full consumption (F) to the list of the unknowns and add the Euler equation to the simultaneous equation system. Once the equilibrium of one period is found, we move on to the next. If we solve the entire path of transition starting with an initial guess of FSL ¼ FS0 for period 1, the process is likely to be explosive. To control the explosiveness and make the iteration process manageable, we use the multiple-shooting technique. For example, we divide the 100-year transition path into ten 10-year intervals and solve for the transition path for each of the intervals. In this process, we need to provide each interval with an initial guess for the pair (FSL, KL), except for the first interval for which KL for the first period is set at the historical value. We use Newton’s method to solve for FS0 and the nine pairs of (FSL, KL) that satisfy the Euler equation for full consumption (3.21) and the capital accumulation Eq. (3.22). We solve for the equilibrium of the economy under an alternative tax policy in a similar manner. The paths of government debt and the claims on the rest of the world are constrained at their paths in the base case. In the base case, the path of real government spending is
Steady state condition of a stock variable requires that its real value per capita in efficiency unit remain constant as the economy proceeds from one period to the next.
48
3. Tax policy and resource allocation
determined endogenously so that government budget constraint is satisfied. Under an alternative tax policy, however, real government spending and budget deficits are constrained at their base case values. We thus need to adjust total tax revenue in each period to meet the government budget constraint. We consider the adjustment of lump-sum tax, labor income tax, sales tax, and individual income tax.
3.5 Welfare effects of tax reform 3.5.1 Intertemporal expenditure function Once a transition path of the economy is found, we can evaluate the corresponding level of the intertemporal welfare. Making use of the Euler equation for full consumption, we can express Ft in terms of F0 and the real private rates of return from period 1 through t, i.e.: 1 t
Y s 1 þ rs Ft ¼ F0 s ; ðt ¼ 1; 2; .Þ ð1 þ gÞð1 aT Þ s¼1 (3.26) where rs ¼ ð1 þ rs Þ 1 is the real private rate of return on wealth. Substituting Eq. (3.26) into Eq. (3.19) and then the result into Eq. (3.18), we obtain PFs1 PFs
F1s 0 D; (3.27) 1s " #t t N Y P 1s 1 D ¼ ð1 þns Þð1 þ rs Þ s . 1 V ¼
where
t¼1
ð1þgÞs
s¼1
Substituting Eq. (3.26) into the intertemporal budget constraint Eq. (3.20), we can express F0 in terms of full wealth and the future real private W 1 . Substituting this rates of return, i.e., F0 ¼ PF 0 D expression in Eq. (3.27) and solving for W, we obtain the intertemporal expenditure function:
1 ð1 sÞV 1s WðPF0 ; D; VÞ ¼ PF0 (3.28) Ds
Eq. (3.28) gives the minimum value of lifetime wealth that is required to achieve the intertemporal welfare level of V, where the effects of future real private rates of return are summarized by D. With the intertemporal expenditure function in our hand, it is straightforward to calculate the welfare effects of an alternative tax policy. Suppose D ¼ D0, V ¼ V0, and W ¼ W0 in the base case. If the economy attains a welfare level of V1 under an alternative policy, the equivalent variation measure of the welfare effects of the new policy is: EV ¼ WðPF0 ; D0 ; V1 Þ WðPF0 ; D0 ; V0 Þ (3.29) ¼ WðPF0 ; D0 ; V1 Þ W0
3.5.2 Efficiency cost of taxation in the United States In order to estimate the efficiency cost of taxation, we simulate the economy under the alternative tax policy in which the tax rates in part or all of the tax system are reduced and a hypothetical lump-sum tax is collected to keep government debt and government spending on the same trajectories as in the base case. Let the level of intertemporal welfare attainable under the alternative tax policy be V1. Then Eq. (3.29) gives the equivalent variation measure of the efficiency cost of the part of the tax system that has been replaced by the lump-sum tax. Jorgenson and Yun (2001) define the average efficiency cost, say AEC, as the efficiency cost per dollar of tax revenue: AEC ¼
EV TLUMP
(3.30)
where TLUMP is the present value of the tax revenue that has been replaced by the lump-sum tax. In order to calculate TLUMP, we convert the path of lump-sum tax into the path of full consumption and add it to the time path of the full consumption in the base case. Making use of
3.5 Welfare effects of tax reform
the intertemporal welfare function, we can evaluate the welfare level that can be attained with this composite path of full consumption in the base case and the lump-sum tax under the alternative policy. We use Eq. (3.29) and calculate the present value of lump-sum tax under the alternative tax policy. In this process, we in effect discount the lump-sum tax with the marginal rates of substitution between full consumptions in different time periods in the base case. We can also measure the marginal efficiency cost of tax revenue by considering a sequence of small changes in the tax policy. Suppose we reduce the tax rates in part of the tax system by 10% interval. In the first simulation, we cut the tax rates by 10%, and evaluate the efficiency cost and call it EV1. In the second simulation, cut the tax rates by 20% and let the corresponding efficiency cost be EV2, and so on. The 10th simulation will be the one that sets all the relevant tax rates at zero and measures the total efficiency cost of the taxes under consideration. The marginal efficiency cost of the tax revenue is defined as: MEC ¼
DEV DTLUMP
(3.31)
where DEV and DTLUMP are the changes in EV and TLUMP due to the incremental changes in the tax rates. In order to evaluate the efficiency cost of taxation in the United States, we consider 10 overlapping parts of the US tax system and simulate the economy with the corresponding tax rates reduced by 10% intervals until the tax rates are reduced to zero. However, since the efficiency cost of taxation tends to increase more than proportionally with tax rates, we divide the first interval into two and run an additional simulation with the tax rates reduced by 5%.5 We select 10
5
49
sets of taxes in the US tax system: (1) corporate income tax, (2) individual capital income tax, (3) property tax, (4) capital income tax (1 þ 2), (5) labor income tax, (6) capital and labor income tax (1 þ 2 þ 5 ¼ 4 þ 5), (7) individual income tax (2 þ 5), (8) sales tax, (9) all taxes except for property tax (1 þ 2 þ 5 þ 8), (10) all taxes (1 þ 2 þ 3 þ 5 þ 8). The results are presented in Table 3.3. Since we start with the base case, when the tax rates are first reduced by 5%, MEC and AEC are the same. As the tax rates are further reduced, MEC declines faster than AEC until the tax rates are eventually reduced to zero. These results are consistent with the economic theory that excess burden increases more than proportionally with the marginal tax rates. Table 3.3 indicates that corporate and individual capital income taxes are most inefficient per dollar of tax revenue. In particular, capital income taxes are substantially more inefficient than labor income taxes. Compared to the taxes on capital and labor income, the revenues from property tax and sales taxes are small and so are the associated tax distortions. For the entire US tax system of 2010, MEC and AEC are 20 cents and 10 cents per dollar of tax revenue, respectively. As noted above, MECs decline faster than the corresponding AECs. In the cases of “all taxes” and “all taxes except for property tax,” MECs converges to zero as the tax rates are reduced to zero. However, in all the other cases, MECs do not appear to approach zero even when the relevant tax rates are reduced to zero. The reason is that, when the scope of the tax reduction is limited, there remain substantial nonzero taxes that interact with the taxes being reduced. Capturing the effects of the interaction between taxes is one advantage of general equilibrium analysis.
When the taxes are not proportional, both average and marginal tax rates are reduced by the same proportion. In the case of capital income taxes on businesses, investment tax credits are reduced by the same proportion as the tax rates.
50 TABLE 3.3
3. Tax policy and resource allocation
Efficiency cost of taxation in the United States: 2010 tax law. Reduction in tax rates (%)
Taxes 1. Corporate income tax
5
50
60
70
80
90
100
0.311 0.307 0.299 0.291 0.285 0.278 0.273 0.267 0.262 0.258 0.253
0.331 0.327 0.318 0.310 0.302 0.294 0.286 0.279 0.272 0.265 0.258
0.123 0.123 0.121 0.120 0.119 0.117 0.116 0.114 0.113 0.111 0.110
MEC 0.318 0.302 0.280 0.253 0.228 0.204 0.182 0.161 0.141 0.122 0.105 AEC
5. Labor income tax
40
MEC 0.123 0.122 0.120 0.117 0.115 0.112 0.109 0.106 0.103 0.100 0.097 AEC
4. Capital income tax (1 þ 2)
30
MEC 0.331 0.322 0.309 0.293 0.277 0.261 0.247 0.233 0.219 0.206 0.193 AEC
3. Property tax
20
MEC 0.311 0.302 0.290 0.275 0.261 0.248 0.236 0.225 0.215 0.206 0.197 AEC
2. Individual capital income tax
10
0.318 0.310 0.296 0.282 0.269 0.257 0.246 0.235 0.225 0.215 0.206
MEC 0.172 0.165 0.156 0.144 0.134 0.125 0.118 0.112 0.107 0.104 0.102 AEC
0.172 0.169 0.162 0.156 0.151 0.146 0.142 0.138 0.135 0.132 0.129
6. Capital and labor income tax (1 þ 2þ5 ¼ 4 þ 5)
MEC 0.249 0.235 0.216 0.191 0.167 0.145 0.125 0.106 0.088 0.071 0.056
7. Individual income tax
MEC 0.229 0.220 0.207 0.190 0.174 0.159 0.144 0.131 0.119 0.107 0.097
AEC
AEC 8. Sales tax
0.249 0.243 0.229 0.217 0.206 0.195 0.184 0.175 0.166 0.157 0.149
0.229 0.225 0.216 0.207 0.199 0.192 0.184 0.178 0.171 0.165 0.159
MEC 0.115 0.114 0.113 0.111 0.109 0.107 0.105 0.103 0.101 0.100 0.098 AEC
0.115 0.115 0.114 0.113 0.112 0.111 0.110 0.109 0.108 0.107 0.106
9. All taxes (except for property tax) MEC 0.214 0.201 0.182 0.158 0.135 0.115 0.095 0.078 0.061 0.047 0.033 AEC 10. All taxes
0.214 0.208 0.195 0.183 0.172 0.161 0.151 0.142 0.133 0.125 0.118
MEC 0.198 0.185 0.165 0.140 0.116 0.094 0.073 0.053 0.034 0.017 0.001 AEC
0.198 0.192 0.178 0.166 0.154 0.142 0.131 0.121 0.111 0.101 0.092
3.5.3 Welfare effects of tax reform Table 3.3 suggests some useful directions for tax reform. First of all, the declining MECs in all of the simulations support the widely accepted notion that efficient taxation requires low marginal tax rates applied to broadly defined bases. This classical wisdom is valid for the entire tax system as well as for parts of it. In the first and second sets of simulations in Table 3.3, we find that the MECs for 5% reduction of the tax rates and AECs for 100% reduction
are substantially higher than in other simulations. In particular, in terms of excess burden, taxation of income from capital is much more expensive than taxation of labor income. It follows that reducing the distortion caused by taxation of income from capital need to be an important objective of tax reform in the United States. We may think of two basic approaches. One is to maintain the general framework of the current tax system and pursue incremental changes in the tax policies. The corporate tax cut of 2018 is a good example.
51
3.5 Welfare effects of tax reform
The other approach is to overhaul the entire tax system as in the case of the consumption tax of Hall and Rabushka (1995). Jorgenson and Yun (2013) consider various alternative tax reform proposals for the United States and evaluate their performance in terms of the improvement in the welfare of the economy. Table 3.4 reproduces some of the simulation results. In the first set of simulations, interasset and intersector tax wedges are eliminated by setting the social rates of return on short-lived and long-lived assets in the corporate and noncorporate sectors to be equal to their capital-weighted average in the steady state of the base case. In the second set of simulations, we extend the analysis to the household sector and eliminate all TABLE 3.4
the tax wedges for capital allocation in the entire private sector. This change in tax policy improves the efficiency of the US economy dramatically and produces huge welfare gains. These results are consistent with Table 3.2 which shows that the major tax distortion in the allocation of capital is between the business and household sectors. Since the elimination of the tax wedges in the first two sets of simulation are roughly revenue neutral, the necessary revenue adjustments are small and the welfare effects are not sensitive to the choice of revenue adjustment. The third set of simulations is for corporate tax integration. We implement corporate tax integration by setting the steady state social rates of return on short-lived and long-lived assets in the corporate sector to be equal to their values
Welfare effects of tax distortion: 2010 tax law (billions of 2011 US dollars). Additivea
Eliminated wedges and method of revenue adjustment
Proportionalb
Interasset and intersector distortion: Corporate and noncorporate sectors, all assets Lump-sum tax adjustment
303.9
303.9
Labor income tax adjustment
253.9
248.1
Sales tax adjustment
223.0
223.0
227.6
226.9
Lump-sum tax adjustment
5567.0
5567.0
(6963.6)
Labor income tax adjustment
5558.1
5619.4
(6961.1)
Sales tax adjustment
5550.3
5550.3
(6988.2)
Individual income tax adjustment
5545.4
5612.6
(6980.7)
Lump-sum tax adjustment
2320.2
2320.2
Labor income tax adjustment
1715.4
398.3
Sales tax adjustment
1237.6
1237.6
Individual income tax adjustment
1422.4
100.0
Individual income tax adjustment c
Interasset and intersector distortion: All sectors, all assets
Corporate tax integration
a
Under the additive tax adjustment, the average and marginal tax rates of labor income and the average tax rates of individual capital income are adjusted in the same percentage points. The marginal tax rates of individual capital income are adjusted in the same proportion as the marginal tax rate of labor income. b Under the proportional tax adjustment, average and marginal tax rates are adjusted in the same proportion. c The figures in the parentheses represent the welfare effects under the revenue neutral proportional labor income tax.
52
3. Tax policy and resource allocation
in the noncorporate sector in the steady state of the base case, i.e., sq ¼ sm. Since corporate tax integration shifts tax burden from corporate capital to elsewhere in the tax system, it is not revenue neutral and the welfare effect is sensitive to the method of tax adjustment. Under the hypothetical lump-sum tax adjustment, the welfare effect is as large as 2320.2 billion US dollars. However, it becomes much smaller when realistic tax adjustments are used to offset the revenue shortfall caused by the reduction of corporate income tax. It is useful to compare the welfare gain from corporate tax integration with lump-sum tax adjustment, 2320.2 billion dollars, with the corresponding welfare gain from the first set of simulations, 303.9 billion dollars. Under corporate tax integration, although intersector tax wedges are eliminated between corporate and noncorporate sectors, interasset tax wedges still remain in both sectors. In contrast, in the first set of simulations, both interasset and intersectoral tax wedges are eliminated. Nevertheless, the welfare gain from corporate tax integration is much larger. This may appear strange from the viewpoint of static Harberger model. The key lies in the fact that corporate tax integration reduces the tax burden on corporate capital, and intertemporal resource allocation is affected. We finally consider the welfare cost of progressive labor income taxation in the context of the second set of simulations where capital is efficiently allocated across the private sector. In order to evaluate the welfare cost of the progressivity of labor income tax, we set the marginal tax rate of labor income at its average tax rate. This procedure reduces the marginal tax rate of labor income from 25.1% to 9.5%. The welfare effects are presented in the parentheses of Table 3.4. We find that the additional welfare gains from flattening labor income tax are substantial. Since the tax change is roughly revenue neutral, the results are not sensitive to the method of tax adjustment.
3.6 Concluding remarks In this chapter, we presented the DGEM that Dale Jorgenson and I developed to evaluate the welfare effects of tax policy and government spending. Important features of the DGEM include the cost of capital, translog price functions, NL3SLS estimation of the consumer and producer models, and two-stage allocation of lifetime wealth. The intertemporal expenditure function based on the DGEM plays a central role in the welfare analysis of alternative tax policies. The cost of capital approach provides an excellent framework for modeling taxation of income from capital. All of the current instruments of capital income taxation in the United States are represented in the cost of capital formulas. Indeed, the cost of capital can accommodate practically any reasonable proposals for taxation of income from capital. The cost of capital approach allows us to measure tax wedges and effective tax rates of income from capital. Although tax wedges and effective tax rates alone do not determine the efficiency costs of tax distortion, they provide useful information about the major sources of tax distortion in the allocation of capital. Our analyses of the efficiency costs of tax revenues from various parts of the US tax system allow us to gain a general view of the structure of efficiency cost of taxation. We found that taxation of income from capital is most expensive in terms of the efficiency cost per dollar of tax revenue. It seems reasonable to conclude that the first priority of tax reform in the United States is to reduce the distortions caused by taxation of income from capital. In view of our analysis, the corporate tax cut of 2018 in the United States seems to be a step in the right direction. To evaluate the welfare effects of tax reform proposals in a more realistic setting, we simulated the economy with four alternative tax
References
adjustments. We obtain the largest welfare gain when all the tax wedges for capital allocation are removed and capital is efficiently allocated across the entire private sector. The welfare gain further increases as labor income tax is flattened. One important message from these simulations is that we do not have to reduce the effective tax rate of capital to zero to attain a high level of welfare. One may be reasonably confident that we can design a number of tax reform proposals that attain high levels of welfare for the economy. However, efficiency is not the only virtue that makes a good tax policy. Equity, however it is defined, is another important virtue a good tax policy must support. In a democratic society, equitable taxation is not only an important virtue in itself, it is also essential for securing political support for tax policy. In reality, we need to be prepared to sacrifice some efficiency for the equity of tax burden. Indeed it is possible to evaluate distributional effects of efficiency enhancing tax reform proposals. OLG models with multiple consumers distinguished by age and level of income can be used to analyze distributional effects of tax policy across age cohorts and income groups. Jorgenson et al. (1997) and Jorgenson et al. (2013) provide even more flexible framework in which distributional effects of tax policy can be analyzed with consumers distinguished by wage rate and many other attributes. The critical issue is to put together an efficient and equitable tax reform proposal that is attractive to majority of politicians and voters.
References Amemiya T: The maximum likelihood and the nonlinear three-stage least squares estimator in the general nonlinear simultaneous model, Econometrica 89(3): 548e560, 1977. Auerbach AJ, Jorgenson DW: Inflation-proof depreciation of assets, Harvard Business Review 58(5):113e118, 1980.
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Auerbach AJ, Kotlikoff LJ: Dynamic fiscal policy, Cambridge, 1987, Cambridge University Press. Chamley C: The welfare cost of capital income taxation in a growing economy, Journal of Political Economy 89(3): 468e496, 1981. Chamley C: Optimal taxation of capital income in general equilibrium with infinite lives, Econometrica 54:607e622, 1986. Christensen LR, Jorgenson DW: Measuring economic performance in the private sector. In Moss M, editor: The measurement of economic and social performance, New York, NY, 1973, Columbia University Press, pp 233e251. Christensen LR, Jorgenson DW, Lau LJ: Transcendental logarithmic production frontiers, The Review of Economics and Statistics 55(1):28e45, 1973. Christensen LR, Jorgenson DW, Lau LJ: Transcendental logarithmic utility functions, The American Economic Review 65(3):367e383, 1975. Fullerton D, Rogers DL: Who bears the lifetime tax burden?, Washington, DC, 1993, Brookings Institution. Fullerton D, Rogers DL: Lifetime effects of fundamental tax reform. In Aaron H, Gale WB, editors: Economic effects of fundamental tax reform, Brookings Institution, pp 321e352. Hall RE, Rabushka A: The flat tax, second ed., Stanford, CA, 1995, Hoover Institution Press. Harberger AC: The incidence of corporate income tax, Journal of Political Economy 70:215e240, 1962. Jorgenson DW: Capital theory and investment behavior, The American Economic Review 53(2):247e259, 1963. Jorgenson DW, Goettle RJ, Ho MS, Wilcoxen PJ: Energy, the environment and US economic growth. In , Waltham MA, 2013, North-Holland, pp 477e552. Dixon PB, Jorgenson DW, editors: Handbook of computable general equilibrium modeling, vol. 1A. Waltham MA, 2013, North-Holland, pp 477e552. Jorgenson DW, Laffont J-J: Efficient estimation of nonlinear simultaneous equations with additive disturbances, Annals of Economic and Social Measurement 3(1):615e640, 1974. Jorgenson DW, Slesnick DT, Wilcoxen PJ: Carbon taxes and economic welfare. In Jorgenson DW, editor: Measuring social welfare, Cambridge, MA, 1997, MIT Press, pp 361e400. Jorgenson DW, Yun KY: The efficiency of capital allocation, The Scandinavian Journal of Economics 88(1):85e107, 1986a. Jorgenson DW, Yun KY: Tax policy and capital allocation, The Scandinavian Journal of Economics 88(2):355e377, 1986b. Jorgenson DW, Yun KY: Tax reform and U.S. economic growth, Journal of Political Economy 98(5):S151eS193, 1990. part 2. Jorgenson DW, Yun KY: Lifting the burden: tax reform, the cost of capital, and U.S. economic growth, Cambridge, MA, 2001, MIT Press.
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Jorgenson DW, Yun KY: Taxation, efficiency and economic growth. In Dixon PB, Jorgenson DW, editors: Handbook of computable general equilibrium modeling vol. 1A, pp 659e741. Waltham MA, North-Holland.
Summers LH: Capital taxation and accumulation in a lifecycle growth model, The American Economic Review 71(4):533e544, 1981.
3 Tax policy and resource allocation Kun-Young Yun Department of Economics, Yonsei University, Seoul, Korea
3.1 Introduction
Fullerton and Rogers (1993, 1996), and Jorgenson et al. (1997). These innovations enhanced the realism of the models and improved representation of the economy and the tax system. More importantly, the presence of heterogeneous consumers in the model made it possible to analyze distributional effects of tax policy. Jorgenson and Yun (1986a, 1986b, 1990, 2001, 2013) developed a dynamic general equilibrium model (DGEM) of the US economy, which has been used to evaluate the welfare effects of various tax policies including major tax reform proposals in the United States. Our DGEM consists of four sectors: household, business, government, and the rest of the world. The household sector is populated by identical consumers with infinite life and perfect foresight. In the business sector, labor and capital services are used to produce consumption and investment goods. The government collects taxes, issues debts, purchases goods and services, and makes transfer payments to households and the rest of the world. The rest of the world trades with the United States in consumption goods, investment goods, and labor services. In our DGEM, the cost of capital approach pioneered by Jorgenson in his celebrated paper
Since Harberger (1962), measuring efficiency cost of taxation has been an important issue in tax policy analyses. The original Harberger model was a simple two-sector static model with fixed supplies of capital and labor. However, the real world is much more complex and, in response to the rising interest in reliable estimates of the economic effects of tax policy, economic models used for the analysis of tax policy have been extended in a number of important directions. One of the most important innovations is the introduction of dynamic general equilibrium models in which consumers maximize intertemporal welfare and capital is accumulated through investment. Two types of models emerged along this line of developments. One is the overlapping generations (OLG) models introduced by Summers (1981) and Auerbach and Kotlikoff (1987). The other is the infinite time-horizon models of Chamley (1981, 1986) and Jorgenson and Yun (1986a, 1986b). Another important development is the extension of models by introducing heterogeneous consumers and/or multiple commodities/industries as in Auerbach and Kotlikoff (1987),
Measuring Economic Growth and Productivity https://doi.org/10.1016/B978-0-12-817596-5.00003-2
37
Copyright © 2020 Elsevier Inc. All rights reserved.
38
3. Tax policy and resource allocation
(Jorgenson, 1963) plays a central role by providing a convenient platform for representing the complex structure of taxation of income from capital in the United States. We employ the cost of capital approach to represent corporate income tax, individual taxes on capital income (interests, dividends, and capital gains), property taxes, economic depreciation, and the private returns to capital. Modeling the income tax on labor and the sales taxes on commodities is straightforward. Section 3.2 describes the cost of capital for the corporate, noncorporate, and household sectors. The cost of capital is used to estimate the social and private rates of return on capital, tax wedges, and the corresponding effective tax rates. Section 3.3 describes the basic structure of DGEM and its parameterization. Section 3.4 describes the equilibrium and dynamics of the model and explains the solution algorithm. In Section 3.5, we measure the marginal and average efficiency costs of tax revenues from various parts of the US tax system. We also consider alternative tax reform proposals and discuss their welfare effects. Section 3.6 concludes the chapter.
3.2 Cost of capital and effective tax rates
noncorporate, and corporate sectors. Tax treatment of income from capital also depends upon the type of assets employed in the corporate and noncorporate sectors. The main differences in the tax treatment of assets in the business sectors are in investment tax credits and depreciation allowances for tax purposes. In addition, consumers and producers may treat capital services from different types of assets as less than perfect substitutes. We thus distinguish two types of assets based on durability, shortlived and long-lived assets, in each of the three sectors.1 The cost of capital approach introduced by Jorgenson (1963) provides a convenient and versatile vehicle for representing the complex details of the taxation of income from capital. It can easily handle the various tax reform proposals discussed in the tax policy circles around the world as well. The cost of capital approach starts with the assumption that equity holders maximize their wealth by appropriately choosing inputs and outputs in a given period of time and investment strategies over time. For income from corporate capital, equity holders are taxed on dividends and capital gains. The portfolio equilibrium of equity holders requires: g Divt TDt þ 1 tq ðEt Et1 Nt Þ ¼ ret Et1 (3.1)
3.2.1 Cost of capital Capital services are consumed by households and used for production in corporate and noncorporate businesses. Tax treatment of income from capital depends upon the sector in which capital is employed. In order to represent these differences, we distinguish the demands for capital services from household,
where Divt is dividends in period t, TDt is indig vidual income tax on dividends, tq is marginal tax rate on accrued capital gains, Et is the value of equity, Nt is the value of new share issues, and ret is the equilibrium nominal rate of return to equity. TDt is proportional to dividends, i.e., TDt ¼ teq Divt , where teq is marginal tax rate on dividends.
1 In the household sector, short-lived assets include consumer durables and producer durable equipment, and longlived assets include residential and nonresidential structures and land. In the corporate and noncorporate sectors, short-lived assets include producer durable equipment and long-lived assets include residential and nonresidential structures, farm and nonfarm inventories, and land.
39
3.2 Cost of capital and effective tax rates
Under the transversality condition that !1 resþt 1þ Etþsþ1 approaches zero as s g 1 tq s¼1 approaches infinity, Eq. (3.1) can be solved for Et: !1 " ! N sY þ1 X 1 teq resþt 1þ Et ¼ g g1 1 tq 1 tq s¼0 s¼1 # sþ1 Y
Divtþsþ1 þ ðDivtþsþ1 Ntþþ1 Þ
The cash flow constraint of the corporation is: Divt Nt ¼ Pt Qt wt Lt ð1 kq tq zq Þqt It p
tq qt1 Kt1 bq ð1 kq tq zq Þ ½ðit pt Þqt1 Kt1 qt ðKt Kt1 Þ TCt (3.5) where investment in period t is given by: It ¼ Kt ð1 dq ÞKt1
(3.2) We assume that dividends are a constant proportion a of corporate cash flow after property and corporate income taxes: h Divt ¼ a Pt Qt ðKt1 ; Lt Þ wt Lt ð1 kq p
tq zq Þdqt Kt1 tq qt1 Kt1 bq ð1 kq i tq zq Þðit pt Þqt1 Kt1 TCt (3.3) where Pt is price of output, Qt(.) is production function, Kt1 and Lt are capital and labor inputs, respectively, and wt is wage rate. kq and zq are the rate of investment tax credit and the present value of depreciation allowances for one dollar’s worth of investment, respectively, and tq is corporate income tax rate. d is rate of economic depreciation, qt is price of investment good, tpq is property tax rate, bq is debt/capital ratio, it and pt are nominal interest rate and the rate of inflation, respectively, and TCt is corporate income tax. The subscript q refers to the corporate sector. Corporations are taxed on income from capital net of depreciation allowances, interest payments, and property taxes, and the tax liability is reduced by investment tax credits, i.e.: h TCt ¼ tq Pt Qt wt Lt ð1 kq i p tq zq Þqt1 Kt1 bq it tq qt1 Kt1 (3.4)
(3.6)
We assume that corporations keep dividends payout ratio, a, and debt/capital ratio, bq, constant. It follows that retaining is independent of investment, and the marginal sources of investment funds are debt and new share issues, with debt accounting for the fraction bq, and new share issues, 1bq. An alternative would be to assume that a is endogenous and new share issues are somehow determined independent of investment. Then retaining becomes the marginal source of equity financing. For example, if we assume that new share issues are zero, retaining depends upon investment, and marginal investment funds are financed with debt and retaining. By substituting Eqs. (3.3)e(3.6) into Eq. (3.2) and taking the derivative of Vt with respect to Ktþ1, we obtain the first-order condition for maximization of Et, which can be rearranged to give the cost of capital: 1 kq tq zq q ct p rt pt þ ð1 þ pt Þd þ tq ¼ qt1 1 tq (3.7) q rt
is the weighted average of marginal where costs of corporate debt and equity: q rt pt ¼ bq ½ð1 tq Þit pt þ 1 bq 2 3 g (3.8) ret 1 tq pt 4 5 g 1 teq a þ 1 tq ð1 aÞ
40
3. Tax policy and resource allocation
The cost of capital in Eq. (3.7) is the price of capital services from one dollar’s worth of lagged capital stock, which includes compensation for depreciation adjusted for investment tax credit and depreciation allowances for tax purposes. The real social rate return for corporate capital is defined as:
in Eq. (3.9) and the corresponding real private rate of return is: h i rht pt ¼ bh 1 tdh it pt þ ð1 bh Þ ret pt : (3.14)
(3.9)
The subscripts and superscripts h refer to the household sector. For the noncorporate businesses, the cost of capital is:
Similarly, the real private rate return for corporate capital is defined as: h i q rt pt ¼ bq 1 tdq it pt þ 1 bq ret pt (3.10)
ct 1 km tem zm m p ¼ rt pt þ ð1 þ pt Þd þ tm qt1 1 tem
q
s t pt ¼
ct ð1 þ pt Þd. qt1
where tdq is the marginal tax rate on individual income from interest payments on corporate debt. Finally, the after-tax real corporate rate of return is defined as: q
rct pt ¼ rt pt þ bt tq it
(3.11)
We can proceed in a similar manner to derive the cost of capital and the corresponding social and private rates of return on capital employed in the household and noncorporate sectors. In order to avoid repetition, we simply present the results without fully describing the derivation process.2 The cost of capital for household assets is: p ct ¼ rht pt þ ð1 þ pt Þd þ 1 teh th (3.12) qt1 where
rht pt ¼ bh 1 teh it pt þ ð1 bh Þ ret pt :
(3.13)
The real social rate of return on household assets is defined as the cost of capital net of economic depreciation adjusted for inflation as 2
(3.15) where e e rm t pt ¼ bm 1 tm it pt þ ð1 bm Þ rt g 1 t m pt : ð3:16Þ The real social rate of return on noncorporate assets, smpt, is defined as in (Eq. 3.9), and the corresponding real private rate of return is: h i d rm t pt ¼ bm 1 tm it pt (3.17) þ ð1 bm Þ ret pt : In Eqs. (3.15)e(3.17), the subscripts and superscripts m refer to the noncorporate sector.
3.2.2 Tax wedges and effective tax rates Auerbach and Jorgenson (1980) introduced the concept of marginal effective tax rate, which is defined as the ratio between the tax wedge and the social rate of return. It is natural to define the tax wedge as the difference between social and private rates of return. In the case of corporate q
assets, the effective tax rate is defined as
q
st rt . q st pt
Similarly, we can define the effective corporate
Interested readers are referred to Chapter 2 of Jorgenson and Yun (2001).
41
3.2 Cost of capital and effective tax rates q
s rc
income tax rate as sqt pt , and the effective individt
t
q
rc r
ual income tax rate as stq pt . The effective tax rates t
t
for assets in the household and noncorporate sectors are defined analogously. Table 3.1 shows the real social rates of return, tax wedges, and effective tax rates for short-lived and long-lived assets in the corporate, noncorporate, all business, and household sectors in the US Notice that the tax wedges in the corporate and noncorporate businesses are substantial in absolute values as well as relative to the real social rates of return. The effective tax rates are 42.7% and 33.5% in the corporate and
TABLE 3.1
Corporate
Noncorporate
Effective tax rates (2010 tax law). SROR
TW
ETR
S
0.0940
0.0341
0.3631
L
0.1088
0.0490
0.4501
A
0.1045
0.0447
0.4275
S
0.0863
0.0225
0.2612
L
0.0969
0.0332
0.3421
A
0.0959
0.0321
0.3351
noncorporate sectors, respectively. For the entire business sector, the effective tax rate is 40.0%. The substantial tax wedges and the corresponding effective tax rates suggest that taxation of income from capital in the business sector may present a significant barrier to efficient allocation of resources between present and future. Panel 1 of Table 3.2 presents the tax wedges between short-lived and long-lived assets in the corporate, noncorporate, and all businesses. The interasset tax wedges are defined as the difference between the social rates of return on short-lived and long-lived assets. Considering that the average social rates of return in the corporate and noncorporate businesses are 10.45% and 9.59%, respectively, the interasset tax wedges of 1.49% in the corporate sector and 1.06% in the noncorporate sector may not appear to be large, but they are still significant. Panel 2 of Table 3.2 shows the intersector tax wedges between the social rates of return on assets in the corporate and noncorporate sectors, corporate and household sectors, and noncorporate and household sectors, respectively. Among these intersector tax wedges, the wedges between corporate and noncorporate sectors have drawn most attention in textbooks and tax policy TABLE 3.2 Tax Wedges (2010 tax law).
All business (corporate D noncorporate)
Households
Interasset tax wedges (long-short)
S
0.0930
0.0319
0.3430
L
0.1045
0.0434
0.4155
Corporate
0.0149
A
0.1018
0.0408
0.4004
Noncorporate
0.0106
A
0.0700
0.0048
0.0680
All business
0.0115
Property taxes are included in the calculation and the after-corporatetax real rate of return, rcpi, real interest rate, and the corporate dividend payout ratio are set at their 1970e2010 averages, 6.628%, 4.658%, and 47.86%, respectively. For asset category A (all assets), social and private rates of return are calculated as the averages of short-lived and long-lived assets, where the values of assets are used as the weights. Similarly for the All business sector. SROR: real social rate of return TW: tax wedge. ETR: effective tax rate. S, short-lived assets. L: long-lived assets. A: all assets (short þ long).
Intersector tax wedges S
L
A
Corporateenoncorporate
0.0076
0.0119
0.0086
Corporateehouseholds
0.0240
0.0389
0.0345
Noncorporateehouseholds
0.0163
0.0269
0.0259
A: all assets (short þ long). L: long-lived assets. S: short-lived assets.
42
3. Tax policy and resource allocation
analyses. Indeed the famous Harberger triangle originally represented the efficiency loss in capital allocation between corporate and noncorporate sectors caused by the double taxation of corporate income. It is interesting to note that, while corporate tax integration has been an important tax reform issue in the United States and partial integration of the corporate and individual income taxes has been implemented in many other countries, the average tax wedge (for all assets) between corporate and noncorporate sectors of 0.86% is small compared with the tax wedge between corporate and household sectors of 3.45%, or the wedge between noncorporate and household sectors of 2.59%.
3.3 Dynamic general equilibrium model of the US Economy Tax wedges and effective tax rates are useful for understanding the barriers to efficient resource allocation. However, a narrative on tax distortion is incomplete without information on the displacements of resource allocation caused by the substitution effects of tax wedges. Under the US tax system, there are numerous tax policy instruments, and practically all of them affect relative prices and hence generate substitution effects. Our dynamic general equilibrium model provides a convenient framework for representing the US tax system and measuring the welfare effects of tax distortion.
3.3.1 Consumer behavior The consumers in the household sector are identical and endowed with infinite life and perfect foresight. The representative consumer maximizes the intertemporal welfare function: N Y t 1 X 1 þ ns V ¼ (3.18) U1s t 1 s t¼1 s¼1 1 þ g
where s is the inverse of the elasticity of intertemporal substitution, ns is the rate of population growth, g is the subjective rate of time preference, and Ut is the per capita utility function: Ut ¼ Ft ð1 aT Þt ; ðt ¼ 1; 2; .Þ
(3.19)
In Eq. (3.19), Ft is per capita full consumption in period t, where population is measured in efficiency unit, and aT is the growth rate of labor productivity. The representative consumer maximizes the intertemporal welfare function subject to the budget constraint: Q N X PFt Ft ð1 aT Þt ts¼1 ð1 þ ns Þ W ¼ (3.20) Qt s¼1 ð1 þ rs Þ t¼1 where W is lifetime wealth, PFt is price of full consumption, and r is nominal private rate of return. The necessary condition for maximization of intertemporal welfare subject to the budget constraint is given by the Euler equation:
1= s Ft PFt1 1 þ rt ¼ $ ; t ¼ 1; 2; .N s Ft1 PFt ð1 þ gÞð1 aT Þ (3.21) Eq. (3.21) plays a central role in determining the optimal path of the economy over time. Specifically, it determines the optimal growth rate of full consumption per capita in efficiency unit. If the level of full consumption in any one period is known, the entire path of full consumption can be determined. Among the infinite number of paths for full consumption that satisfy the Euler equation, the one that satisfies the intertemporal budget constraint will be chosen by the welfare maximizing consumer. It is useful to note that Eq. (3.21) implies that, in a steady state with a constant rate of inflation, the real private rate of return is constant. In the steady state, full consumption per capita in efficiency unit is constant, i.e., Ft1 ¼ Ft, and the constant rate of inflation implies that PFt ¼ 1 þ pt is constant, where pt is the rate of PFt1
3.3 Dynamic general equilibrium model of the US Economy
inflation in period t. It follows that the real private rate of return consistent with the steady s state is ð1 þ gÞð1 aT Þ 1. The steady-state real private rate of return depends only upon the parameters of the intertemporal welfare function, g and s, and the growth rate of labor productivity, aT. In particular, it is independent of any government policy to the extent that government policy does not affect g, s, and aT. More generally, Eq. (3.21) implies that the growth rate of full consumption per capita is approximately proportional to the difference between real private rate of return and its steady state value. Once the path of full consumption is determined, the consumer allocates full consumption among consumption goods, capital services, and leisure in each period. In order to represent the allocation of full consumption, we employ translog form of price function for full consumption and the corresponding value share equations introduced by Christensen, Jorgenson, and Lau (1975). The demand for household capital services are further allocated to short-lived and long-lived assets. In order to represent the allocation of household capital services, we employ translog price function for household capital services and the corresponding value share equations. In the translog price function of full consumption, the price of full consumption, PFt, is expressed as a function of the consumer prices of consumption goods, capital services, and leisure. The consumer price of consumption goods includes sales taxes and the price of leisure is the wage rate net of marginal tax on labor income. In the translog price function of household capital services, the price of (aggregate) household capital services is expressed as a function of the prices of capital services from short-lived and long-lived assets.
43
and investment goods. However, we do not assign separate production processes for corporate and noncorporate businesses, or for consumption and investment goods. Instead we assume that the entire business sector acts like a single producer and employs labor and capital services from corporate and noncorporate businesses to produce consumption and investment goods. Specifically, we represent the production technology of the entire business sector with a single translog price function of Christensen, Jorgenson, and Lau (1973), where the price of labor services is expressed as a function of the prices of consumption goods, investment goods, corporate and noncorporate capital services, and time. The value share equations corresponding to the price function determine the values of capital services from corporate and noncorporate sectors and the values of consumption and investment goods relative to the value of labor input. As in the household sector, the allocation of corporate and noncorporate capital services between short-lived and longlived assets is represented by translog price functions and the corresponding value share equations. The partial derivative of the translog price function for labor with respect to time represents the rate of productivity growth. We require the model to be consistent with a balanced growth equilibrium in which labor productivity grows at a constant rate and value shares and relative prices of inputs and outputs are constant when labor is measured in efficiency unit. It follows that the value shares and the growth rate of labor productivity are independent of time. These conditions constrain the parameters of the translog price function for labor.
3.3.3 Government 3.3.2 Producer behavior In the business sector, there are two types of producers, corporate and noncorporate businesses, and two types of outputs, consumption
We consolidate the federal and state and local governments into a single government sector. Similarly, we consolidate the federal and state and local government enterprises into a single
44
3. Tax policy and resource allocation
government enterprise sector. The government collects taxes from the household and business sectors, issues debt to finance deficits, and spends its revenues on consumption goods, investment goods, labor services, interest payments on government debt, and transfer payments to households and the rest of the world. The deficit of the government is added to the government debt. Government enterprises employ labor and produce consumption goods, and turn over any surplus to the general government. The government collects taxes from a variety of sources. In addition to the taxes on income from capital described in Section 3.2, the government levies income tax on labor, sales taxes on consumption and investment goods, property taxes, and wealth taxes. In representing the US tax system in our model, we distinguish marginal and average tax rates. The distinction is particularly important in the taxation of individual income where graduated tax rates apply. In general, marginal tax rates affect relative prices and average tax rates are used to generate tax revenues. For example, we calculate the price of as the price of labor services times leisure 1 tm where tm L L is the marginal tax rate on labor income. In calculating tax revenue, however, we use the average tax rate, i.e., RL ¼ taL $BL, where RL is the tax revenue from labor income, taL is the average tax rate, and BL is total labor compensation. In the case of capital income taxation, the prices relevant for resource allocation are the costs of capital derived in Section 3.2. The tax revenue from individual equity income is given by RE ¼ taE $BE ITCM, where taE is the average tax rate, BE is the tax base, and ITCM is investment tax credits for noncorporate businesses. Similarly, the tax revenue from interest payments on debt is calculated as RD ¼ taD $BD, where taD is the average tax rate, and BD is the tax base. Since sales taxes and property taxes are proportional, average and marginal tax rates are the same and the calculation of tax revenues is straightforward. In the case of corporate income
tax, the rate structure is graduated. Nevertheless, since most of corporate income is taxed at the maximum rate, we calculate the tax revenue as Rq ¼ tq$BQITCQ, where tq is the corporate income tax rate, BQ is the tax base, and ITCQ is tax credit for corporate investment. We assume that the government allocates its total expenditure, net of interest payments on government debt, in constant proportions among consumption goods, investment goods, labor services, and transfer payments to households and the rest of the world. We represent the allocation of government expenditure, net of interest payments, into these five categories of spending with a CobbeDouglas price function of the aggregate government spending. This representation is useful in the simulation of alternative tax policies in which the path of real government spending need to be controlled.
3.3.4 Rest of the world The rest of the world trades with the United States in consumption goods, investment goods, and labor services, pays compensation on US claims on the rest of the world, and receives transfer payments from US government. The current account deficit of the rest of the world is added to the US claims on the rest of the world.
3.3.5 Parameter values We estimate the parameters of the model using time series data of the United States for 1970e2010. This data set, informally referred to as the US Worksheet among Jorgenson and his associates, incorporates the cost of capital into a complete system of US national accounts in accordance with Christensen and Jorgenson (1973). The parameters of the consumer and producer models are estimated by nonlinear threestage least square method (NL3SLS) developed by Jorgenson and Laffont (1974) and Amemiya (1977). Most of the other parameters are set at
3.4 Equilibrium of the model and solution algorithm
historical values. For example, in the allocation of government expenditure, net of interest payment on government debt, the shares of consumption goods, investment goods, labor services, and transfer payments to households and the rest of the world are set at their sample averages. Similarly, we set the dividend payout ratio, a, and the debt/capital ratios in the household and business sectors, bj (j ¼ h, m, q), and the real interest rate at their sample averages. In the base case simulation, we set all the tax rates at their 2010 values, similarly for investment tax credits and the present values of capital consumption allowances. In all the simulations, we assume that new tax policies are introduced in 2011 and set the total time endowment and the prices of investment goods and the six categories of assets at their 2011 values. Finally, we set the ratio of government expenditure to GDP (SGOV), the proportion of purchases of consumption goods by the rest of the world to domestic purchases (SCR), and the proportion of purchases of investment goods by the rest of the world to domestic supply (SIR) at appropriate values so that the steady-state values of government debt/GDP and the claims on the rest of the world/GDP ratios are reasonable.
government enterprises, and the rest of the world purchase labor services from households. Finally, in the capital market, the capital stock owned by households is allocated to meet the demands for capital services from the corporate, noncorporate, and household sectors. Due to Walras’ law, one of the four market equilibrium conditions is redundant.
3.4.2 Dynamics of the model When a new economic policy is introduced, the economy jumps on a new transition path which eventually converges to the steady state. Along the transition path, the economy must be in equilibrium in each period and the entire path must be optimal in the sense that it maximizes intertemporal welfare of the consumer subject to the lifetime budget constraint. The transition of the economy from one period to the next is described by the transition of full consumption and the accumulation of capital stock, government debt, and the claims on the rest of the world. The transition of full consumption is described by the Euler Eq. (3.21). The accumulation of capital stock is represented by: VK ¼ VKL þ PI$ID Dep þ Rev
3.4 Equilibrium of the model and solution algorithm 3.4.1 Market equilibrium In a given period, there are four markets that need to be in equilibrium simultaneously. They are the markets for consumption goods, investment goods, labor services, and capital services. In the consumption goods market, households, government, and the rest of the world purchase goods from private businesses and government enterprises. In the investment goods market, households, government, and the rest of the world purchase goods from businesses. In the labor market, businesses, government,
45
(3.22)
where VK is the value of capital stock at the end of the period, VKL is its lagged value, ID is private domestic investment, PI is the price of investment goods inclusive of sales tax, Dep is economic depreciation, and Rev is revaluation of domestic capital. The accumulation of government debt is described by: VG ¼ DG þ VGL
(3.23)
where VG and VGL are the current and lagged values of government debt, respectively, and DG is government budget deficit. Finally, the claims on the rest of the world evolve according to: VR ¼ DR þ ð1 þ pÞVRL
(3.24)
46
3. Tax policy and resource allocation
where VR and VRL are the current and lagged values of the claims on the rest of the world, respectively, and DR is current account deficit of the rest of the world. Obviously the economy as a whole cannot run deficit or surplus, and the sum of the deficits of the household, business, government, and the rest of the world sectors must be zero. In other words, private savings net of investment are used to finance the deficits of government and the rest of the world: S ¼ PI$ID þ DG þ DR
(3.25)
where S is private saving. At the beginning of a period on the transition path, the quantities of capital stock, government debt, and claims on the rest of the world are predetermined. However, full consumption is free to jump in the first period of the transition, although it is constrained by the Euler equation thereafter. If we know the value of FS0 ¼ F0 $ 1 PFs0 in the Euler Eq. (3.21), we can solve for FS1, and the entire transition path of the economy can be calculated. We thus pretend that new policy is introduced in period 0 and start with a guess of FS0 and solve the model forward. Finding the correct value of FS0 is the essence of the solution algorithm.
3.4.3 Solution algorithm In order to evaluate the economic impacts of a new tax policy, we need to establish a reference with which to compare the performance of the economy under an alternative tax policy. We take the US economy under the tax laws of 2011 as the reference. For the year 2011, the lagged values of capital stock, government debt, and the claims on the rest of the world and the amount of total time endowment are
set at their historical values. Since there is no guarantee that the US economy is in a steady state in 2011, we proceed under the assumption that the economy is on a transition path toward a steady state. We refer to the US economy under the 2011 tax law as the base case. In any period on the transition path, once the lagged values of FS (FSL), capital stock (KL), government debt (GL), and the claims on the rest of the world (RL) are known, the equilibrium of the economy can be solved from the market clearing conditions for consumption goods, investment goods, capital stock, and labor services.3 Since one of the four market clearing conditions is redundant, we drop the labor market clearing condition. Since our dynamic general equilibrium model of the US economy converges to the steady state, it is convenient to solve for the steady state first. The transition path can then be found by solving for FS0, or FSL for period 1, that leads the economy to the steady state. Solving for the steady state is similar to solving for the equilibrium for a period on the transition path. However there are two differences. First, in the steady state of the base case, FSL and the lagged values of the three stock variables (KL, GL, RL) are not known. We need to solve for their steady-state values along with three endogenous variables that clear the four markets. Second, the Euler equation for full consumption implies that the real private rate of return on wealth is constant and known. In our model, total time endowment, rate of inflation in the price investment good, interest rate on debt, and the relative prices of investment good and the six categories of assets are fixed. In order to solve for the steady state of the base case, we start with seven unknowns (FSL, KL, GL, RL, re, PC, LD), where PC is the
In our model, the relative prices of investment good and the six categories of assets are fixed at their 2011 values and the rate of inflation in the price of investment goods is exogenous. The path of total time endowment is also exogenous. 3
3.4 Equilibrium of the model and solution algorithm
consumer price of consumption goods and LD is labor demand of the business sector. We make use of the Euler equation for full consumption, three market clearing conditions, and the steady state conditions of the three accumulation Eqs. (3.22)e(3.24), and apply Newton’s method to solve for the seven unknowns.4 The intertemporal welfare function of the consumer does not reflect the welfare effects of government expenditure, net of interest payments on government debts. We thus control the path of real government expenditure, net of interest payments. Similarly, in order to focus on the differential effects of alternative tax policies, we control the paths of government debt and the claims on the rest of the world. In order to constrain government debt and the claims on the rest of the world on reasonable paths, we set SGOV ¼ 0.20168, SCR ¼ 0.0007, and SIR ¼ 0.0022 so that, in the steady state of the base case, government debt/GDP ratio and the claims on the rest of the world/GDP ratio become 0.40 and 0.05, respectively. Once the steady state values of government debt and the claims on the rest of the world are determined, we construct complete paths of these two variables by connecting their historical values in 2010 and their steady state values. In our model, the economy comes very close to the steady state in less than thirty years after the introduction of a new tax policy. We thus constrain the government debt and the claims on the rest of the world to reach their steady state values in 40 years after the start of the transition. For all practical purposes, it is sufficient to assume that the economy converges to the steady state in 100 years. With these preparations, we solve for the transition path of the economy with an initial guess of FS0. Along the transition path, government debt and the claims on the rest of the world are
4
47
constrained to the paths described above. To control the path of government debt in the base case, we adjust total government expenditure including interest payments on government debt. To control the path of the claims on the rest of the world, we adjust the absolute value of the net exports of consumption goods, investment goods, and labor services. In a given period on the transition path, FSL, KL, GL, and RL are predetermined and the equilibrium of the base case economy can be determined by solving for the three unknowns (re, PC, LD) with the three market clearing conditions. However, to cut through the complex interdependence of F, PF, and re, we add full consumption (F) to the list of the unknowns and add the Euler equation to the simultaneous equation system. Once the equilibrium of one period is found, we move on to the next. If we solve the entire path of transition starting with an initial guess of FSL ¼ FS0 for period 1, the process is likely to be explosive. To control the explosiveness and make the iteration process manageable, we use the multiple-shooting technique. For example, we divide the 100-year transition path into ten 10-year intervals and solve for the transition path for each of the intervals. In this process, we need to provide each interval with an initial guess for the pair (FSL, KL), except for the first interval for which KL for the first period is set at the historical value. We use Newton’s method to solve for FS0 and the nine pairs of (FSL, KL) that satisfy the Euler equation for full consumption (3.21) and the capital accumulation Eq. (3.22). We solve for the equilibrium of the economy under an alternative tax policy in a similar manner. The paths of government debt and the claims on the rest of the world are constrained at their paths in the base case. In the base case, the path of real government spending is
Steady state condition of a stock variable requires that its real value per capita in efficiency unit remain constant as the economy proceeds from one period to the next.
48
3. Tax policy and resource allocation
determined endogenously so that government budget constraint is satisfied. Under an alternative tax policy, however, real government spending and budget deficits are constrained at their base case values. We thus need to adjust total tax revenue in each period to meet the government budget constraint. We consider the adjustment of lump-sum tax, labor income tax, sales tax, and individual income tax.
3.5 Welfare effects of tax reform 3.5.1 Intertemporal expenditure function Once a transition path of the economy is found, we can evaluate the corresponding level of the intertemporal welfare. Making use of the Euler equation for full consumption, we can express Ft in terms of F0 and the real private rates of return from period 1 through t, i.e.: 1 t
Y s 1 þ rs Ft ¼ F0 s ; ðt ¼ 1; 2; .Þ ð1 þ gÞð1 aT Þ s¼1 (3.26) where rs ¼ ð1 þ rs Þ 1 is the real private rate of return on wealth. Substituting Eq. (3.26) into Eq. (3.19) and then the result into Eq. (3.18), we obtain PFs1 PFs
F1s 0 D; (3.27) 1s " #t t N Y P 1s 1 D ¼ ð1 þns Þð1 þ rs Þ s . 1 V ¼
where
t¼1
ð1þgÞs
s¼1
Substituting Eq. (3.26) into the intertemporal budget constraint Eq. (3.20), we can express F0 in terms of full wealth and the future real private W 1 . Substituting this rates of return, i.e., F0 ¼ PF 0 D expression in Eq. (3.27) and solving for W, we obtain the intertemporal expenditure function:
1 ð1 sÞV 1s WðPF0 ; D; VÞ ¼ PF0 (3.28) Ds
Eq. (3.28) gives the minimum value of lifetime wealth that is required to achieve the intertemporal welfare level of V, where the effects of future real private rates of return are summarized by D. With the intertemporal expenditure function in our hand, it is straightforward to calculate the welfare effects of an alternative tax policy. Suppose D ¼ D0, V ¼ V0, and W ¼ W0 in the base case. If the economy attains a welfare level of V1 under an alternative policy, the equivalent variation measure of the welfare effects of the new policy is: EV ¼ WðPF0 ; D0 ; V1 Þ WðPF0 ; D0 ; V0 Þ (3.29) ¼ WðPF0 ; D0 ; V1 Þ W0
3.5.2 Efficiency cost of taxation in the United States In order to estimate the efficiency cost of taxation, we simulate the economy under the alternative tax policy in which the tax rates in part or all of the tax system are reduced and a hypothetical lump-sum tax is collected to keep government debt and government spending on the same trajectories as in the base case. Let the level of intertemporal welfare attainable under the alternative tax policy be V1. Then Eq. (3.29) gives the equivalent variation measure of the efficiency cost of the part of the tax system that has been replaced by the lump-sum tax. Jorgenson and Yun (2001) define the average efficiency cost, say AEC, as the efficiency cost per dollar of tax revenue: AEC ¼
EV TLUMP
(3.30)
where TLUMP is the present value of the tax revenue that has been replaced by the lump-sum tax. In order to calculate TLUMP, we convert the path of lump-sum tax into the path of full consumption and add it to the time path of the full consumption in the base case. Making use of
3.5 Welfare effects of tax reform
the intertemporal welfare function, we can evaluate the welfare level that can be attained with this composite path of full consumption in the base case and the lump-sum tax under the alternative policy. We use Eq. (3.29) and calculate the present value of lump-sum tax under the alternative tax policy. In this process, we in effect discount the lump-sum tax with the marginal rates of substitution between full consumptions in different time periods in the base case. We can also measure the marginal efficiency cost of tax revenue by considering a sequence of small changes in the tax policy. Suppose we reduce the tax rates in part of the tax system by 10% interval. In the first simulation, we cut the tax rates by 10%, and evaluate the efficiency cost and call it EV1. In the second simulation, cut the tax rates by 20% and let the corresponding efficiency cost be EV2, and so on. The 10th simulation will be the one that sets all the relevant tax rates at zero and measures the total efficiency cost of the taxes under consideration. The marginal efficiency cost of the tax revenue is defined as: MEC ¼
DEV DTLUMP
(3.31)
where DEV and DTLUMP are the changes in EV and TLUMP due to the incremental changes in the tax rates. In order to evaluate the efficiency cost of taxation in the United States, we consider 10 overlapping parts of the US tax system and simulate the economy with the corresponding tax rates reduced by 10% intervals until the tax rates are reduced to zero. However, since the efficiency cost of taxation tends to increase more than proportionally with tax rates, we divide the first interval into two and run an additional simulation with the tax rates reduced by 5%.5 We select 10
5
49
sets of taxes in the US tax system: (1) corporate income tax, (2) individual capital income tax, (3) property tax, (4) capital income tax (1 þ 2), (5) labor income tax, (6) capital and labor income tax (1 þ 2 þ 5 ¼ 4 þ 5), (7) individual income tax (2 þ 5), (8) sales tax, (9) all taxes except for property tax (1 þ 2 þ 5 þ 8), (10) all taxes (1 þ 2 þ 3 þ 5 þ 8). The results are presented in Table 3.3. Since we start with the base case, when the tax rates are first reduced by 5%, MEC and AEC are the same. As the tax rates are further reduced, MEC declines faster than AEC until the tax rates are eventually reduced to zero. These results are consistent with the economic theory that excess burden increases more than proportionally with the marginal tax rates. Table 3.3 indicates that corporate and individual capital income taxes are most inefficient per dollar of tax revenue. In particular, capital income taxes are substantially more inefficient than labor income taxes. Compared to the taxes on capital and labor income, the revenues from property tax and sales taxes are small and so are the associated tax distortions. For the entire US tax system of 2010, MEC and AEC are 20 cents and 10 cents per dollar of tax revenue, respectively. As noted above, MECs decline faster than the corresponding AECs. In the cases of “all taxes” and “all taxes except for property tax,” MECs converges to zero as the tax rates are reduced to zero. However, in all the other cases, MECs do not appear to approach zero even when the relevant tax rates are reduced to zero. The reason is that, when the scope of the tax reduction is limited, there remain substantial nonzero taxes that interact with the taxes being reduced. Capturing the effects of the interaction between taxes is one advantage of general equilibrium analysis.
When the taxes are not proportional, both average and marginal tax rates are reduced by the same proportion. In the case of capital income taxes on businesses, investment tax credits are reduced by the same proportion as the tax rates.
50 TABLE 3.3
3. Tax policy and resource allocation
Efficiency cost of taxation in the United States: 2010 tax law. Reduction in tax rates (%)
Taxes 1. Corporate income tax
5
50
60
70
80
90
100
0.311 0.307 0.299 0.291 0.285 0.278 0.273 0.267 0.262 0.258 0.253
0.331 0.327 0.318 0.310 0.302 0.294 0.286 0.279 0.272 0.265 0.258
0.123 0.123 0.121 0.120 0.119 0.117 0.116 0.114 0.113 0.111 0.110
MEC 0.318 0.302 0.280 0.253 0.228 0.204 0.182 0.161 0.141 0.122 0.105 AEC
5. Labor income tax
40
MEC 0.123 0.122 0.120 0.117 0.115 0.112 0.109 0.106 0.103 0.100 0.097 AEC
4. Capital income tax (1 þ 2)
30
MEC 0.331 0.322 0.309 0.293 0.277 0.261 0.247 0.233 0.219 0.206 0.193 AEC
3. Property tax
20
MEC 0.311 0.302 0.290 0.275 0.261 0.248 0.236 0.225 0.215 0.206 0.197 AEC
2. Individual capital income tax
10
0.318 0.310 0.296 0.282 0.269 0.257 0.246 0.235 0.225 0.215 0.206
MEC 0.172 0.165 0.156 0.144 0.134 0.125 0.118 0.112 0.107 0.104 0.102 AEC
0.172 0.169 0.162 0.156 0.151 0.146 0.142 0.138 0.135 0.132 0.129
6. Capital and labor income tax (1 þ 2þ5 ¼ 4 þ 5)
MEC 0.249 0.235 0.216 0.191 0.167 0.145 0.125 0.106 0.088 0.071 0.056
7. Individual income tax
MEC 0.229 0.220 0.207 0.190 0.174 0.159 0.144 0.131 0.119 0.107 0.097
AEC
AEC 8. Sales tax
0.249 0.243 0.229 0.217 0.206 0.195 0.184 0.175 0.166 0.157 0.149
0.229 0.225 0.216 0.207 0.199 0.192 0.184 0.178 0.171 0.165 0.159
MEC 0.115 0.114 0.113 0.111 0.109 0.107 0.105 0.103 0.101 0.100 0.098 AEC
0.115 0.115 0.114 0.113 0.112 0.111 0.110 0.109 0.108 0.107 0.106
9. All taxes (except for property tax) MEC 0.214 0.201 0.182 0.158 0.135 0.115 0.095 0.078 0.061 0.047 0.033 AEC 10. All taxes
0.214 0.208 0.195 0.183 0.172 0.161 0.151 0.142 0.133 0.125 0.118
MEC 0.198 0.185 0.165 0.140 0.116 0.094 0.073 0.053 0.034 0.017 0.001 AEC
0.198 0.192 0.178 0.166 0.154 0.142 0.131 0.121 0.111 0.101 0.092
3.5.3 Welfare effects of tax reform Table 3.3 suggests some useful directions for tax reform. First of all, the declining MECs in all of the simulations support the widely accepted notion that efficient taxation requires low marginal tax rates applied to broadly defined bases. This classical wisdom is valid for the entire tax system as well as for parts of it. In the first and second sets of simulations in Table 3.3, we find that the MECs for 5% reduction of the tax rates and AECs for 100% reduction
are substantially higher than in other simulations. In particular, in terms of excess burden, taxation of income from capital is much more expensive than taxation of labor income. It follows that reducing the distortion caused by taxation of income from capital need to be an important objective of tax reform in the United States. We may think of two basic approaches. One is to maintain the general framework of the current tax system and pursue incremental changes in the tax policies. The corporate tax cut of 2018 is a good example.
51
3.5 Welfare effects of tax reform
The other approach is to overhaul the entire tax system as in the case of the consumption tax of Hall and Rabushka (1995). Jorgenson and Yun (2013) consider various alternative tax reform proposals for the United States and evaluate their performance in terms of the improvement in the welfare of the economy. Table 3.4 reproduces some of the simulation results. In the first set of simulations, interasset and intersector tax wedges are eliminated by setting the social rates of return on short-lived and long-lived assets in the corporate and noncorporate sectors to be equal to their capital-weighted average in the steady state of the base case. In the second set of simulations, we extend the analysis to the household sector and eliminate all TABLE 3.4
the tax wedges for capital allocation in the entire private sector. This change in tax policy improves the efficiency of the US economy dramatically and produces huge welfare gains. These results are consistent with Table 3.2 which shows that the major tax distortion in the allocation of capital is between the business and household sectors. Since the elimination of the tax wedges in the first two sets of simulation are roughly revenue neutral, the necessary revenue adjustments are small and the welfare effects are not sensitive to the choice of revenue adjustment. The third set of simulations is for corporate tax integration. We implement corporate tax integration by setting the steady state social rates of return on short-lived and long-lived assets in the corporate sector to be equal to their values
Welfare effects of tax distortion: 2010 tax law (billions of 2011 US dollars). Additivea
Eliminated wedges and method of revenue adjustment
Proportionalb
Interasset and intersector distortion: Corporate and noncorporate sectors, all assets Lump-sum tax adjustment
303.9
303.9
Labor income tax adjustment
253.9
248.1
Sales tax adjustment
223.0
223.0
227.6
226.9
Lump-sum tax adjustment
5567.0
5567.0
(6963.6)
Labor income tax adjustment
5558.1
5619.4
(6961.1)
Sales tax adjustment
5550.3
5550.3
(6988.2)
Individual income tax adjustment
5545.4
5612.6
(6980.7)
Lump-sum tax adjustment
2320.2
2320.2
Labor income tax adjustment
1715.4
398.3
Sales tax adjustment
1237.6
1237.6
Individual income tax adjustment
1422.4
100.0
Individual income tax adjustment c
Interasset and intersector distortion: All sectors, all assets
Corporate tax integration
a
Under the additive tax adjustment, the average and marginal tax rates of labor income and the average tax rates of individual capital income are adjusted in the same percentage points. The marginal tax rates of individual capital income are adjusted in the same proportion as the marginal tax rate of labor income. b Under the proportional tax adjustment, average and marginal tax rates are adjusted in the same proportion. c The figures in the parentheses represent the welfare effects under the revenue neutral proportional labor income tax.
52
3. Tax policy and resource allocation
in the noncorporate sector in the steady state of the base case, i.e., sq ¼ sm. Since corporate tax integration shifts tax burden from corporate capital to elsewhere in the tax system, it is not revenue neutral and the welfare effect is sensitive to the method of tax adjustment. Under the hypothetical lump-sum tax adjustment, the welfare effect is as large as 2320.2 billion US dollars. However, it becomes much smaller when realistic tax adjustments are used to offset the revenue shortfall caused by the reduction of corporate income tax. It is useful to compare the welfare gain from corporate tax integration with lump-sum tax adjustment, 2320.2 billion dollars, with the corresponding welfare gain from the first set of simulations, 303.9 billion dollars. Under corporate tax integration, although intersector tax wedges are eliminated between corporate and noncorporate sectors, interasset tax wedges still remain in both sectors. In contrast, in the first set of simulations, both interasset and intersectoral tax wedges are eliminated. Nevertheless, the welfare gain from corporate tax integration is much larger. This may appear strange from the viewpoint of static Harberger model. The key lies in the fact that corporate tax integration reduces the tax burden on corporate capital, and intertemporal resource allocation is affected. We finally consider the welfare cost of progressive labor income taxation in the context of the second set of simulations where capital is efficiently allocated across the private sector. In order to evaluate the welfare cost of the progressivity of labor income tax, we set the marginal tax rate of labor income at its average tax rate. This procedure reduces the marginal tax rate of labor income from 25.1% to 9.5%. The welfare effects are presented in the parentheses of Table 3.4. We find that the additional welfare gains from flattening labor income tax are substantial. Since the tax change is roughly revenue neutral, the results are not sensitive to the method of tax adjustment.
3.6 Concluding remarks In this chapter, we presented the DGEM that Dale Jorgenson and I developed to evaluate the welfare effects of tax policy and government spending. Important features of the DGEM include the cost of capital, translog price functions, NL3SLS estimation of the consumer and producer models, and two-stage allocation of lifetime wealth. The intertemporal expenditure function based on the DGEM plays a central role in the welfare analysis of alternative tax policies. The cost of capital approach provides an excellent framework for modeling taxation of income from capital. All of the current instruments of capital income taxation in the United States are represented in the cost of capital formulas. Indeed, the cost of capital can accommodate practically any reasonable proposals for taxation of income from capital. The cost of capital approach allows us to measure tax wedges and effective tax rates of income from capital. Although tax wedges and effective tax rates alone do not determine the efficiency costs of tax distortion, they provide useful information about the major sources of tax distortion in the allocation of capital. Our analyses of the efficiency costs of tax revenues from various parts of the US tax system allow us to gain a general view of the structure of efficiency cost of taxation. We found that taxation of income from capital is most expensive in terms of the efficiency cost per dollar of tax revenue. It seems reasonable to conclude that the first priority of tax reform in the United States is to reduce the distortions caused by taxation of income from capital. In view of our analysis, the corporate tax cut of 2018 in the United States seems to be a step in the right direction. To evaluate the welfare effects of tax reform proposals in a more realistic setting, we simulated the economy with four alternative tax
References
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