A reexamination of tax distortions in general equilibrium models

NBER WORKING PAPER SERIES A REEXAMINATION OF TAX DISTORTIONS IN GENERAL EQUILIERItJIvI MODELS Donald Fullerton Roger H. Gordon Working Paper No. 673 NATIONPj, BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge MA 02138 May 1981 This paper was presented at the NBER Conference on Behavioral Simulation Methods in Tax Policy Analysis on January 25—27, 1981, in Palm Beach. We would like to thank Yolanda Kodrzycki Henderson for careful assistance throughout the course of this research. We would also like to thank Tom Kronmiller, who helped with some of the programming, and Daniel Feenberg and Burton Malkiel who helped us obtain needed data. We are grateful to Charles McLure for thorough comments on a draft of this paper, as well as helpful discussion throughout the course of this project. Finally, we would like to thank the participants in the NEER preconference at Sturbridge, particularly David Bradford, for helpful comments on an earlier draft. The research reported here is part of the NBER's research program in Taxation and projects in Capital Formation and Tax Simulation. Any opinions expressed are those of the authors and not those of the National Bureau of Economic Research. KEEP CONFERENCE PAPER SERIES Available from the Conference on SIMULATiON METHODS TN TX .Jfl'' ANtLl'SlS Fapers Palm Feach, Florida Jariary Con ference Paper 25—21, 1981 No. WP 197 "Alternative Tax Treatments of the Family: Simulation and Results," by Daniel Feenberg and Harvey S. Rosen Methodolor "Stochastic Problems in the Simulation of Labor Supply," by Jerry Hausman to the "Alternatives Lawrence B. Lindsey Current Maximum Tax on Earned income," 'by "The Distribution of Gains and Losses from Changes in the Tax Treatment of Housing," by Mervyn King WP 682 "Simulating Nonlinear Tax Rules and Nonstandard Behavior: An Application to the Tax Treatment of Charitable Contributions," 'by Martin Feldstein and Lawrence B. Lindsey "Issues in the Taxation of Foreign Source Income," by Daniel Frisch WP 583 "Modeling Alternative Solutions to the Long—Run Social Security Funding Problem," by Michael Boskin, Marcy Avrin, and Kenneth Cone "Domestic Tax Policy and the Foreign Sector: The Importance of Alternative Foreign Sector Formulations to Results from a General Equilibrium Tax Analysis Model," by Lawrence Goulder, John Shoven, and John Whalley WP 673 "A Reexamination of Tax Distortions in General Equilibrium Models," 'by Don Fullerton and Roger Gordon "A General Equilibrium Model of Taxation with Endogenous Financial Behavior," 'by WP 681 Joel Slerarod "Alternative Tax Rules and Personal Savings Incentives: Microeconomic Data and Behavioral Simulations," by Martin Feldstein and Daniel Feenberg "National Savings, Economic Welfare, and the Structure of Taxation," by Alan Auerbach and Laurence Kotlikoff "Tax Reform and Corporate Investment: A Micro—Econometric Simulation Study," by Michael Salinger and Lawrence Summers It is expected that the papers resulting from this conference will be published in a volume edited 'by Martin Feldstein. Copies of these conference papers may be obtained by sending $1.50 per copy to Conference Papers, NBER, 1050 Massachusetts Avenue, Cambridge, MA 02138. Please make checks payable to National Bureau of Econonilc Research. Advance payment is required on orders totaling less than $10.00 List of Participants SIMULATION METHODS IN TAX POLICY ANALYSIS The Breakers, Palm Beach January 25—21, 1981 Affiliation Name Henry J. Aaron Alan J. Auerbach Martin J. Bailey Michael J. Fskin Daniel H. Feenberg Martin Feldstein Daniel Don Fhllerton Harvey Galper Roger H. Gordon Lawrence H. Goulder David G. Hartman Jerry A. Hausman J. Frisch James J. Heckman Patric Hendershott Thomas 0. Horst Mervyn A. King Laurence J. Kotlikoff Lawrence B. Lindsey Charles E. McLure, Jr. Peter Mieszkowski Joseph J. Minarik Richard A. Musgrave Joseph A. Pechman Michael Salinger RoLert J. Shiller John B. Shoven Joel Slemrod Joseph E. Stiglitz Lawrence H. Summers John Whalley David Wise The Brookings Institution Harvard University University of Maryland Stanford University National Harvard Bureau of Economic Research University and NBER University of Washington Princeton University U.S. Department of the Treasury Bell Lahoratories Stanford University Harvard University Massachusetts Institute of Technolor Unversity of Chicago Purdue University U.S. Department of the Treasury University of Birmingham, England Yale University Harvard University National Bureau of Economic Research University of Houston The Brookings Institution Harvard University & the University of California at Santa Cruz The Brookings Institution Massachusetts Institute of Technolo University of Pennsylvania Stanford University University of Minnesota Princeton University Massachusetts Institute of Technolor University of Western Ontario Harvard University NBER Working Paper #673 May 1981 A Reexamination of Tax Distortions in General Equilibrium Models ABSTRACT General equilibrium models have recently been used to simulate the effects of many proposed tax changes. However, in modelling the effects of the government on the economy, these models have assumed for simplicity that marginal tax rates equal the observed average tax rates, and that marginal benefit rates are zero. The main purpose of this paper is to derive improved estimates of various marginal tax and benefit rates. Most importantly, we include in the model recent theories concerning the effects of combined corporate and personal taxes on corporate financial and investment decisions. The conclusions previously derived concerning the effects of corporate tax integration are then reexamined in light of the proposed changes. Donald Fullerton Woodrow Wilson School Princeton University Princeton, N.J. 08544 (609) 452—4811/6407 Roger H. Gordon Bell Laboratories 600 Mountain Avenue Murray Hill, N.J. 07974 (201) 582—6472 A REEXAMINATION OF TAX DISTORTIONS IN GENERAL EQUILIBRIUM MODELS by Don Fullerton Princeton University and Roger H. Gordon Bell Laboratories 600 Mountain Avenue Murray Hill, New Jersey 07974 General equilibrium models of the U.S. economy have grown much more realistic in the last few years, becoming more disaggregated and using more recent and extensive data on differences in behavior among individual consumers and producers. Serious attempts have been made using these models to simulate the effects of several proposed tax changes, includ- ing integration of the corporate with the personal income tax and replacement of the income tax with a consumption tax. However, in attempting to capture the effects of the government on the economy, these models have generally assumed for simplicity that marginal tax rates equal the observed average tax rates and that marginal benefit rates are zero. The main purpose of this paper is to derive improved estimates of various marginal tax rates and to take into account certain offsetting marginal benefits. We use the general equilibrium tax model of Fullerton, Shoven, and Whalley (1978, 1980), hereafter denoted by FSW, as a starting point for this remodelling effort. Most importantly, we include in the model recent theories developed in Gordon (1980) concerning the effects of combined corporate and personal taxes on firms' financial and capital intensity decisions. We also apply the same theoretical approach to the modelling of governmental financial and capital intensity decisions. This approach takes explicit account of uncertainty, the flexibility of corporate financial policy, and inflation. In addition, we briefly reexamine the modelling of the property tax, unemployment insurance, workmen's compensation, and social security. To test the importance of the above changes in the modelling of government- -2- induced distortions, we resimulate the effects of integration of corporate with personal income taes. We find, contrary to FSW, that the welfare gains of lessening tax distortions through integration are more than offset by the welfare losses resulting from raising tax rates on labor income in order to replace lost revenue. This result is particularly strong because FSW included only intertemporal and interindustry allocation welfare gains, whereas we allow further welfare gains from eliminating the tax distortion which favors debt finance. The organization of the paper is as follows. In Section I, we reexamine some of the marginal distortions created by the various taxes on labor. In Section II, we describe our nodeIling of the effects of corporate and personal taxes on firms' financial and investmentdeci- sions. We also describe here the construction of the data needed to calculate the new industry specific marginal costs of capital. Section III describes a few other adjustments in the model made necessary by the change in the modelling of taxes on capital income. Finally, Section IV describes the simulation procedure and the results from our resimulation of corporate tax integration using our revised general equilibrium model. I. Changes in the Modelling of Tax Distortions on Labor Income While FSW carefully measure the size of the various taxes that apply to labor income, they ignore the fact that higher tax payments are often associated with larger transfer receipts. In particular, benefits are closely associated with tax payments in the Social Security program, in unemployment insurance, and in workmen's compensation. The taxes from these programs are distorting only to the degree that marginal taxes differ from marginal benefits. We discuss each of these programs in turn. We do not attempt to take into account in this paper other transfer programs, such as food stamps, public housing, and AFDC, where benefits also create an implicit tax on labor income. We model these transfers as though they are paid in a lump sum fashion, as did FSW. As a result, we may underestimate the welfare costs of increases in tax rates on labor income.1 -3- A. Social Security The effect of current labor supply on future Social Security benefits is very compli- cated, as described in Blinder, Gordon, and Wise (1980). The present value of marginal benefits arising from further work will exceed marginal taxes for older men (at least as old as 65) but will probably fall short of marginal taxes for the very elderly, for younger workers, and for most women. However, we have insufficient information to capture this diversity of net distortions. We would need to know the age, and sex composition of workers in each industry as well as individuals in each consumer group. Instead, in the simulations below, we assume that the average net distortion from Social Security is zero, on the assumption that those facing a net subsidy come close to counterbalancing those who face a net tax. Since we therefore omit from the model the diverse distortions on individual labor supply created by Social Security, we may further underestimate the welfare costs of tax increases on labor income. B. Unemployment Insurance Most state unemployment insurance programs use a reserve ratio formula to set the firm's tax rate. This formula tries to ensure that the tax payments made by the firm would just match the benefits received by its former workers. When this happens, workers anticipate future benefits equal in value to the taxes they currently pay, so the program should not distort labor supply decisions. For a discussion of the law and some remaining distortions, see Brown (1980). However, state unemployment insurance programs also set a maximum and minimum tax rate on each firm. When a firm is at such a constraint, its workers should antici- pate receiving either more or less in benefits, on average, than they currently pay in taxes, implying a net tax or subsidy. The degree to which this happens does differ systematically by industry. Becker (1972) examined the net transfers among industries in several states during the 1950's and 1960's and calculated a net tax or subsidy rate for many industries.2 The appen- dix describes how we obtain labor tax rates for our industry classification from Becker's classification. Table I, column 1, reports the resulting net unemployment insurance tax rates -4- by industry. C. Workmen's Compensation The final change we made was to assume that workmen's compensation programs are nondistorting. While such programs are normally mandated by the government, the cost of the program to each firm is typically negotiated with a private insurance company. Competition among insurance companies implies that expected taxes and benefits ought to be equal for each firm. There are a few public programs, but these correspond closely in form to the private programs, and should therefore be nearly nondistorting as well. II. Tax Distortions Affecting Firms' Financial and Investment Decisions In the FSW model, corporate financial policy is exogenous, while capital intensity decisions are distorted by a marginal tax rate set equal to the observed average tax rate on capi- tal income, calculated separately by industry. The average tax rate in each industry is set equal to the ratio of corporate, personal, and property tax payments in 1973 to capital income in that year. Capital is then allocated such that the rate of return to capital net of taxes and depreciation is equated in all industries. This approach conveniently abstracts from the many detailed provisions of the U. S. tax law. However, it has many problems. Most immediately, the measured average tax rate depends critically on the measure for true earnings to capital. This latter number is difficult to calculate appropriately in any year, and varies greatly from year to year. This variation implies that there is substantial measurement error in the calculated tax rates. In this paper, we instead model the tax law directly and calculate the cost of capital implied by the prevailing market interest rate and the existing tax law. While this procedure requires much new data in order to characterize the tax law by industry, it does not require capital income and tax payment figures, which can fluctuate sharply from year to year. A more important reason for our remodelling, however, is that the explicit model of the effect of taxes on capital intensity decisions implies that marginal tax distortions differ -5- dramatically from average tax rates, even if all figures can be measured without error. In this model, the government shares in the risk in the return to capital since its tax revenue is sto- chastic. The benefits to the firm of transferring to the government some of the risk in the return to its capital is not taken into account when calculating an average tax rate. This offsetting benefit turns out to be very important. In addition to explicitly modelling a firm's capital intensity decisions, we model simultaneously how taxes affect the firm's optimal financial policy.3 We assume that firms cho.9se a debt-equity ratio which minimizes their cost of capital, trading off the tax advantages of debt against bankruptcy or other leverage related costs. These leverage related costs are real costs which profit maximizing firms will choose to bear in order to save taxes, and are part of the distortion costs created by the existing taxes on capital income. In our model of both financial and capital intensity decisions, we explicitly model both uncertainty and inflation. The basic model, a generalization of the capital asset pricing model, is developed in Gordon-Bradford (l980). It is further analyzed in Gordon-Malkiel (1980) and in Gordon (1980). In the next two sections, we briefly describe how in this model corporate financial and capital intensity decisions depend on the tax law. A. Modelling of Corporate Financial Decisions The tax law treats differently the returns to bonds and equity. First, only payments to bond holders are deductible from the corporate tax base. Counterbalancing this, however, the personal income tax is generally higher on income from bonds, since much of the income from equity is in the form of capital gains, which are taxed more lightly. Let (1—a) represent the effective personal tax rate on nominal income earned from stocks, (l—ab) the effective per- sonal tax rate on interest income from bonds, r the corporate tax rate, and r the nominal interest rate paid on bonds. Then if the firm were to issue another dollar of debt and use the proceeds to repurchase a dollar of equity (holding the capital stock unchanged), the change in after tax income to investors would be abr—ar(l—r). The new bond holder receives abr after tax while the remaining equity holders lose only ar(l—r) after both corporate and personal -6- income taxes (when they pay the interest on the extra debt). Gordon-Malkiel (1980) showthat for plausible values of a and as,, the expression r(ab—a(l—1)) is positive, which implies that investors as a group can save on taxes by any and all increases in the firm's debt-capital ratio. While replacing equity with debt is advantageous for tax reasons, a higher debtcapital ratio also implies a higher probability of default. Bankruptcy and the threat of bankruptcy create real costs.5 The firm's debt-capital ratio is in equilibrium when the increase in expected leverage related costs resulting from replacing a dollar of equity with a dollar of debt just offsets the tax savings from using a dollar of debt instead of equity. Let y represent the firm's debt-capital ratio, and let c('y) represent the increase in expected leverage related costs borne by investors as a group from having an extra dollar of debt when the initial debt-capital ratio is y.6 Then in equilibrium is chosen such that: r(ab—a(l—r)) = c(y). One would expect that c(0)0 and — > 0. If there were no tax distortion favoring debt, this formula implies that the firm would use only equity finance and thus avoid all bankruptcy risk. Leverage related costs include more than just direct litigation costs in bankruptcy. As Warner (1977) and Gordon-Malkiel (1980) show, litigation costs themselves are very small. When the firm faces the possibility of bankruptcy, however, it also faces distorted investment incentives, as described in Myers (1977). When considering a risky investment, equity holders ignore the higher probability of losses to existing debt holders. Since equity holders receive any gains, but pass large enough loses onto bond holders, they face distorted investment decisions. Though debt holders would presumably charge for these costs ex-ante, distorted investment incentives would remain and equity holders would bear the costs of this inefficiency. In addition, labor costs can rise, since employees would be reluctant to remain in a jobwith an uncertain future. The function c(y) is intended to capture all such leverage related costs. Let represent the amount of debt chosen to finance the capital stock K, and let = D/K. Then, since c (y) measures the marginal leverage costs of using a dollar more debt, 5 c(D/K)dD measures the total leverage cost borne by the firm's investors. If we -7- assume that c(_y) has the functional form c(y) = a_ye, then in equilibrium the total costs from having D* of debt would be a_yD* — rD*(ab_a(l_r)) e+l (1) e+l This expression provides a measure of the privately borne costs resulting from the tax distortion favoring debt finance.7 However, any extra expenses arising from a higher debt-capital ratio, e.g. resources spent negotiating and monitoring an agreement, would be deductible from the corporate tax base. These net of corporate tax costs would then also reduce the individual's personal tax base. Therefore, the expression for private leverage costs c(-y) represents only a(l—r) percent of the total (social) extra leverage related costs resulting from replacing a dollar of equity with a dollar of debt. Total before tax leverage related costs can then be approximated by rD * (ab —a (1 —r)) a(l—r)(e+l) In the simulations of proposed tax changes, we will calculate the change in this esti- mate of leverage related costs. This change represents an efficiency gain (or loss) resulting from changing the tax distortion which presently favors debt finance. B. Modelling of Capital Intensity Decisions Corporate capital intensity decisions will depend on the cost of finance when the firm is using this optimal debt-capital ratio. We assume that the capital stock of a corporation is in equilibrium when investors are willing to pay just a dollar for the returns from an additional dollar of capital. Consider a type of investment where the returns are nonstochastic. Then the investment would be pursued using debt finance (with the capital as security), since there would be no leverage related costs offsetting the tax advantage of debt. When the return to an investment is risky, however, the optimal percent of debt, used in financing it will be lower because the firm will trade off the tax advantages of debt against the costs arising from the higher risk of default. If the return from new investment is just as risky as the return from -8- existing capital, we would expect that the appropriate y'' for the new capital would equal the existing y for the firm as a whole. We will assume that these conditions hold, so that the marginal y equals the average y. To be willing to finance a project, equity and debt holders must receive at least the risk free return after tax, plus enough to compensate them for the risk that they bear. Define as the total after tax risk premium required by corporate equity and debt holders together on the return from each dollar they invest in the project. By definition, t5 includes any leverage related costs. Also, let r the before tax risk free interest rate, and let Pc be the project's be expected rate of return gross of both tax and depreciation. Then, in equilibrium, the marginal investment ought to earn a p such that a(1—r)(p—yr) + abyr = abrZ+t5C. (2) The first term on the left hand side measures the return to equity holders after tax, and the second term measures the after tax return to debt holders. This implies that ab a(l—r) The )—yr( ab—a(lr) a(1—r) . )+ ________ a(l—r) (3) right hand side of this equation in effect measures the before tax rate of return to the investment required by the market. Note that, at the optimal debt-capital ratio, this expression is minimized.8 This derivation ignores many complications, however. Suppose that, for each indus- try, d is the geometric rate of economic depreciation of capital, and d is the constant geometric rate of depreciation for tax purposes that implies the same discounted present value of tax deductions as the more complicated tax law. Suppose that k is the effective rate of the investment tax credit, and 1,, is the effective rate of state and local property tax (net of benefits) on the capital stock. Suppose also that ir is the expected inflation rate. When all these additional factors are introduced, the equilibrium value of Pc will satisfy:9 -9- ab )+ pd+t+(l—k)r( a(1—T) —yr aba(1r) + o(1—k) a(1—r) r(d—dX) — ______ a(1—r) (1—r) (l—r) (4) . Here, Pc is a real rate of return, while r and r are nominal risky and risk-free interest rates, respectively. This formula is basically a generalization of the well known formula for the cost of capital in Hall-Jorgenson (1967). If uncertainty is ignored (so ö,'=O and r=r), if personal and property taxes are ignored (so aab—l and :=O), if inflation is ignored (so r=O), and finally, if the possibility of debt finance is ignored (so yO), the above formula simplifies to Pc d+r(1—k)—rd l—r (5) . This formula now differs from that in Hall-Jorgenson only because the decision under consideration here is to invest a dollar now and then maintain a dollar of capital in place through later investments to offset depreciation. Hall-Jorgenson, in contrast, consider only whether to invest a dollar now.10 Each of the generalizations included here changes the degree to which taxes affect the equilibrium marginal product of capital. In some cases they change it greatly. Now consider the capital stock of a non-corporate firm in the same setting. It will +l .1 t...., +, ,l ....naknLJnl aink. +n.a,\ 1# nil ...juzzi EJLI.4nhn V. nl.1l Lu,., l,,JjjJ,nnan I s#l.an An aLL..,n LLS,I kan..,oJ kjtaala +1 LII return on a risk-free asset plus enough to compensate for the risk. Define A LS#I La/k as the after tax risk premium required by non-corporate proprietors in each industry on the return from each dollar they invest, and define m as the proprietor's personal marginal tax rate. Then, will satisfy (1—k) (p,+1r—t — d) — -j-- (p,—d—t) = r(1—m) + ô (6) Solving for p,, we find p,.nd+tp+(lk)r+ (±;;k) + lm (d—d)— l-m (7) -10- In these equations, we have assumed that the proprietor finances the capital himself. If he obtains extra funds from another party with the same marginal tax rate, then the equation con- tinues to hold, whether the proprietor borrows from the other individual or makes him a partner in the business. Since there is no tax advantage to debt finance here, debt will only be used when it creates no leverage related costs. Also, since the proprietor's personal assets, as well as the business's assets, can be put up as collateral, debt can be kept riskless, and presumably free of leverage costs, much more easily here than in the corporate sector. We modified equation (6) slightly for the real estate industry, which includes both rental and owner occupied housing. For owner occupied housing, there is basically no personal income tax on the returns to the investment, though t continues to be deductible, implying that in equilibrium (1—k) (p+ dt,,(1m)) = r(1—in) + ô,, . (8) The above analysis of non-corporate investment is also not quite appropriate for ren- tal housing. We ignore any taxation of inflationary capital gains in other noncorporate business on the presumption that the gains would be realized sufficiently rarely, except at death when they would be tax free. In rental housing, however, gains are realized much more frequently. If g equals the effective capital gains tax rate, then the equilibrium condition becomes (p,+irdt) (1k) (p,.—di) — — (1—k) r(1—m)+ô, (9) To obtain p,.,, for the real estate industry as a whole, we took a weighted average ofthe equilibrium values for rental and owner occupied housing. For weights, we used the sizes of the capital stock in each sector.11 In order to apply the above theory to the FSW general equilibrium model, several further assumptions must be made. Each industry will be characterized by its own values for d, d, k, and , the risk premium when there are no leverage costs. In effect, the inherent riskiness and durability of capital assets used by each industry will be taken to be exogenous. The corporate sector in each industry will also be characterized by its observed values for 'y and —11— ô. However, corporate financial policy (-y) will be endogenous in the model, as will be the size of the leverage cost component of ö. A later section derives expressions for the inherent risk component of ô, which will remain constant, and the leverage cost component of .5, which varies with 'y. When tax changes are simulated, these parameters and ö, will vary systematically from their observed values. The values for these industry specific parameters, together with the market parame- ters r, r, r, r, a, and ab determine a value of p, for each industry. The same industry and market parameters are used along with a proprietor's tax rate m to determine a value of p in each industry. We then take a weighted average of PC and P,. using as weights the relative sizes of the corporate and non-corporate capital stocks in that industry. The percent of capital in each industry used by incorporated firms is assumed to be exogenous)2 The resulting industry wide value for the marginal product of capital we denote by p. Given the market interest rates r and r2, we have a separate value of p for each industry. Given the rest of the model, these values for p imply a desired capital stock for each industry. The sum over all industries of these desired capital stocks equals the total demand for capital. In each equilibrium simulation, the solution algorithm finds an r such that this total demand for capital just equals the available supply of capital.'3 The supply of capital in each period is fixed, but the endogenous savings response of one period is used to appropriately aug- ment the capital stock for the next equilibrium in the sequence. This process is described in more detail below. C. Derivation of Data Required to Calculate p In order to use the above procedure to calculate the equilibrium marginal product in each industry, much new data are needed. In this section, we describe how we calculate each of the needed variables. We calculate data values for 1973 in order to be comparable with the FSW model. -12- 1. Property Tax Rates (tn) In FSW, the property tax is modelled as a distorting proportional income tax on cap- ital. The benchmark tax rate on any industry is set equal to the observed property tax payments relative to net capital income in that industry. Since owner-occupied housing is included in the housing industry, this modelling applies to household as well as commercial and industrial payers of property taxes. In the above derivation, the property tax was modelled instead as a proportional tax on the value of the capital stock. However, the appropriate value of t, is not clear. The average tax rate can readily be calculated by taking the ratio of property tax payments to the value of the capital stock in each industry. However, local public expenditures financed by the pro- perty tax provide some offsetting benefits. Tiebout (1956), McGuire (1974), and Hamilton (1976) take both benefits and taxes into account, and develop a set of assumptions under which the property tax on residential property is nondistorting. It is just a price at which households can purchase local public goods. The assumptions underlying this conclusion are strong. For example, they rule out any spillover of benefits across community lines. They also require a large number of communities, yet the population of each community must be sufficiently large that further expansion entails congestion costs which just offset the gains from sharing the costs of public expenditures with more people. In this paper, however, we wili accept the Tiebout hypothesis for households as a first approximation. Specifically, we assume that the effective property tax rate in the housing industry is zero.'4 However, we do report briefly below on a simulation where half of property taxes on housing are treated as distorting. Application of the Tiebout hypothesis to commercial and industrial property seems less convincing. A defense of this application is developed in Fischel (1975) and White (1975). The essence of the argument is that if communities compete to obtain commercial and industrial property, then the property tax payments and the benefits will, in equilibrium, be set such that the community is indifferent to whether or not a new firm enters. As a result, a profit maximizing firm will choose the most efficient location. Its tax payments may go not only to -13- finance the benefits it receives but also to compensate the community for the noise, pollution, or congestion that it creates. In this setting it seems plausible to assume that the tax is nondistorting. However, once a firm has located and is considering additional investment, it has lost its bargaining position with the community. To relocate, the firm would incur large fixed Costs. The community may have some inhibition about exploiting captive firms. Some firms may indeed leave and certainly new firms would as a result be more reluctant to enter. Yet in this context there is certainly less competitive pressure to equate additional taxes with additional benefits. Because of the ambiguity of the theory, we ran two sets of simulations. In one simulation, all property tax payments were exactly offset by benefits. In the other simulation, half of nonresidential tax payments were assumed to be offset by benefits, while all ofresiden- tial tax payments continued to be offset by benefits. Together the two simulations provide a sensitivity test of the importance of the treatment of the property tax. The effective tax rates used in the second case are reported in column 2 of Table 1. These parameters equal half of the observed property tax divided by the capital stock in that industry. 2. Corporate Debt-Capital Ratios (rny) Gordon-Malkjel (1980) used data from the COMPUSTAT'5 tape to estimate the ratio of the market value of debt to the market value of debt plus equity. This calculation included firms with securities traded on the New York Stock Exchange, on the American Stock Exchange, and over the counter. Only economy wide figures were reported in that paper. Here, we used the same procedure to calculate the ratio separately for each of our eighteen private industries.'6 The resulting figures for 1973 are reported in column 3 of Table l.' 3. Risk Premiums, (o and ö,,) Consider a particular security s, with an expected after tax return ,, where the bar indicates expectations. The capital asset pricing model implies that the risk premium — a, r ought to equal (i — a, ri), where F,, is the expected after tax return on the market -14- is the covariance of r and rm, divided by the variance of Tm. The risk prem- portfolio, and ium can be measured either directly, by using i — a, r, or it can be measured indirectly by estimating for that security and multiplying by the expected risk premium on the market portfolio. Here, in estimating &, we have chosen the indirect method to measure the risk premium on equity in each industry, and the direct method to measure the risk premium on bonds. The risk premium &, appropriate for a dollar invested in corporate capital in each indus- try is then the sum of the risk premium on dollars of debt and the risk premium on (1—7) dollars of equity. To calculate each industry's risk premium on equity, we proceeded by first estimating the fi for a value weighted portfolio of the equity from all firms in the industry which were traded publicly on the New York Stock Exchange. The estimation was done over the period 1969-1973 using the Center for Research in Securities Prices monthly returns data. The market portfolio was taken to be a value weighted portfolio of the equity from all firms traded on the New York Stock Exchange. The risk premium on the equity in each industry is then this estimate of fi times the expected excess return on the market portfolio, which Merton (1980) estimates to be .1075 18 Lacking information about how the risk premium on bonds varied by industry, we assumed a common risk premium of ab(r—r2), which equals .0246 using the parameter values discussed below. The value of ô, was then set equal to .1075(l—y)/3-+.02467 in each industry. Implicitly we assume here that the potential new capital in an industry is equally as risky as the existing capital. The resulting values for &, by industry are reported in column 4 of Table 1. The value of ô,.,. ought to differ from that for &. for two major reasons. First, given present tax law, investment will be riskier in the corporate sector where tax incentives favor debt. For non-corporate investment, no taxes are saved through debt rather than "equity" finance, so there is no tax incentive to accept real leverage related costs.'9 Therefore, the risk premium on a non-corporate investment ought to be smaller than that on an otherwise -15- equivalent corporate investment since it ought to be free of leverage related costs. To estimate the additional leverage cost arising from investment in one more dollar of corporate capital, assume that leverage costs are proportional to the size of the capital stock for any firm, holding -y constant. The marginal leverage costs would then equal the expression for privately borne leverage costs derived earlier, divided by the size of the capital stock, or e+l . Without the tax distortion favoring debt, the corporate risk premium would be smaller by this amount. A second reason for to differ from 5 is that the government absorbs a different percent of the risk from investment in each sector. The risk borne by investors on a dollar investment would differ between the sectors, even if the inherent20 riskiness of the investment were the same, because the tax rates differ. Because of taxes, the risk borne by corporate investors is only a(1—r) percent of the total risk in the return to corporate capital. Similarly, non-corporate investors bear only (1—rn) percent of the total risk in the return on their capital. We assume that these are the only two reasons why ô,,, differs from &. In particu- lar, we assume that non-corporate capital is just as risky as corporate capital, leverage costs aside, and that non-corporate investors charge the same risk premium per unit risk that they bear as do corporate investors.2i We then conclude that: = (1—rn) a(1—r) — yr(aba(1T)) b+1 j. (10) In the simulations, we will assign to the investment in each industry a constant o inherent risk premium, 5, equal to l-m (This measure corrects for the fact that only (1—rn) percent of non-corporate risk is borne privately and does not include any leverage costs.) The risk premium appropriate for privately borne risk in the non-corporate sector will then be sim- ply (1—rn). Only if the proprietor's tax rate changes in a simulation would the non-corporate risk premium change. Similarly, the corporate risk premium for privately borne risk will be set equal to: -16- C a(lr) 5+ -yr(ab—a(l—T)) b+1 (11) Thus, if the tax incentive favoring debt is reduced, the leverage cost component of 5 will decline. 4. Investment Tax Credit Rates (k) After an April 1969 repeal, the investment tax credit (ITC) was reintroduced in 1971. It allowed any corporate or non-corporate business to subtract from its tax bill 7% (4% for public utilities) of its eligible investment expenditures, defined as equipment with at least a seven year useful life. One-third credit was allowed for assets with 3 to 5 year lives and twothirds credit for 5 to 7 year lives. The 7% statutory rate was increased to 10% in 1975 and sub- sequently made permanent. The parameter k in above formulae, however, refers to an effective ITC rate on all investment (including inventories and plant as well as equipment). It ought to take into account all limitations, carry-forward, and carry-back provisions. Because the proportion of investments which are eligible for the credit, or for different fractions of the credit, will vary by industry, the effective ITC rate, k, will also vary by industry. In order to estimate this effective ITC rate in each industry, we looked at the dollar value of credit taken in a particular year relative to that year's total investment. Because the credit taken in 1973 may not reflect the credit which eventually accrued to 1973 investments, we took the average of the effective rates in 1973 and 1974.22 We thus tried to obtain a "steady state" rate which accounts for carry-forwards and carry-backs. The appendix provides details concerning how the data were obtained. The resulting figures for the effective ITC rates appear for each industry in Table I, column 5. 5. Economic Depreciation Rates (d) The above formulae require eighteen annualized rates of depreciation for the indus- tries defined in this model. Several other studies23 have estimated rates of depreciation using various assumptions and various investment disaggregates, but none is immediately applicable for our purposes. Some studies, however, provide dollar values of economic depreciation for -17- industry definitions similar to ours. Using time-series on investment by industry, we can estimate geometric annual rates of depreciation for use in this model. Looking at a particular industry, suppose that ED, is the dollar figure for economic depreciation in the ith year during the period 1972 to 1974. The sources for data on ED are described in the appendix. We then tried to find that geometric depreciation rate on all prior investments in that industry which would be most consistent with the observed values ED1. Let j,R represent gross real investment undertaken in year t, in year i dollars. Then if there were geometric depreciation at rate d, economic depreciation in year i would equal: ED1 = d (1 —d )t J,. Here, ED, represents the predicted value, in contrast to the actual value of ED1. One problem, of course, is that investment data by industry were not available prior to 1947. The small effect of pre-1947 investment can be approximated by assuming that invest- ment in all years before 1947 grew at the same rate, . We estimated to be .027 for all non- residential investment and .021 for residential investment from aggregate data available over the period 1929 to 1947. If these two categories of real investments did grow at these rates before 1947, and if the same depreciation rate applied in all years before 1947, then the depreciation on pre-1947 investments in 1972 would be df26 11947 e'e di = aAIR —26d (12) where 26 is the number of years between 1946 and 1972. In general, then, we approximated ED1 by - ED1 = We dIR —d(i—1947+1) +d + 1—1947 t=O dIfL1 (1 —d)' . (13) then chose that value of d for each industry which minimized the sum of squared differences between the observed ED, and our predicted ED1 during the period 1972- 1974. The appendix provides information about the sources of the data and further details -18- about the procedure. The eighteen resulting economic depreciation rates, d, are reported in Table 1, column 6. 6. Tax Depreciation Rates (di) Above formulae used d as the effective constant nominal depreciation allowance for tax purposes per dollar of maintained capital. We estimated this concept by starting with the assumption that the tax law allows exponential depreciation at an annual rate d' based on his- torical cost. (Derivation of the value of d' which best approximates the actual tax code is described below.) In the situation of equation (4), we consider an additional dollar of investment which is maintained in nominal terms through subsequent replacement investment at the rate (d—ir). Exponential depreciation for tax purposes at rate d' on this maintained investment will generally not result in a constant stream of allowances. Though d' may remain constant, the remaining basis for tax purposes does not. In particular, the basis in the first year is one dollar, while the basis in the second year is (l—d') + (d—ir). The second year basis will not equal one d'+ ir. The inflation rate enters here since tax depreciation is based on historical dollar if d cost. Since the basis is nonconstant, depreciation allowances of d' times the basis are also nonconstant. As shown in Gordon (1980), the value of d, which is constant over time and which implies the same present value of deductions for corporations as the nonconstant d' stream, would satisfy: d = d' (d—ir) + r(l—r) d +r(l—r) (14) (For non-corporate firms, the same expression applies, except that r is replaced by m.) We therefore can solve for d based on figures for d' and other data.24 Analogous to the economic depreciation rates d, the tax depreciation rates d' are estimated from IRS depreciation data and time-series on investment. Looking at a particular industry, suppose that TD, is the dollar figure for tax depreciation in the ith year between 1972 -19- and 1976. We then solved for the geometric depreciation rate d' that best approximates the observed tax depreciation allowances TD1, using a procedure similar to that used in solving for d. If!, measures the nominal investment in a given industry which occurred in year!, then d' was chosen so as to minimize: 1976 (TD1 — TD1)2 (15) 1972 where / TD1 = —1947 iO / c., J-_, (1—d_,)' + d1947!1947e —d1947(i—1947+1) / + d197 Here, d, is a function of time since the relevant tax law changed several times during the period. Also, u here refers to the growth rate for nominal investment prior to 1947, estimated to be .057 for nonresidential investment and .059 for residential investment. In the appendix, we describe how I, and d, were obtained. The eighteen resulting effective constant tax depreci- ation rates d for 1973 appear in column 7 of Table 1. 7. Proprietors' Marginal Tax Rates, (m ,g) The parameter m represents the average personal marginal tax rate paid by proprie- tors in the non-corporate sector. In principle, this marginal tax rate should vary by industry, but we found no data capable of providing such information. Instead, we used the NBERTAXSIM programs to calculate economy-wide average marginal tax rates for business income, supplemental schedule income, partnership income, and small business corporation profits. We then set m equal to .365, the weighted average of the average marginal tax rates for each category of income.25 The parameter g represents the effective capital gains tax rate on rental housing. By 1973 tax law, only half of capital gains is taxable. We assumed in addition that the postpone- ment of the tax payment until realization halves the effective tax rate. We therefore assumed that g = .25m = .091. -20- 8. Other Parameter Values (re, e, a, ab, r, r, r) There remain several economy wide parameters that need to be estimated for 1973. For r2, the nominal before tax risk free interest rate, many economists have used the Treasury bill rate, which equaled .07 in 1973. While Treasury bills are not risky in nominal terms, they are risky in real terms. Lacking any better estimate, we assumed the risk premium in the Treasury bill interest rate was .02, implying a risk free interest rate of .05. As a sensitivity test, we also report results for a .07 risk free rate. We estimated e using time series data for y and the market interest rate. According to the theory developed in Section I, the debt-capital ratio will be in equilibrium when c(y) = aye = r(ab—a(l—r)). This implies that 1 log('y) =—log( i ab—a(lr) +—log(r) a (16) If a,e,a,,a, and r are all constant across time, e can be estimated by regressing log(') on log(r) and a constant term using time series data, and taking the inverse of the estimated coefficient of log(r). Gordon-Malkiel (1980) provide yearly data on y for the period 19581978. For r, we used a yearly commercial paper rate. When we regressed log('y) on log(r), we obtained log(y) = —2.44 (0.19) + .557 log(r) (.116) where standard errors are in parentheses under the coefficient estimates.26 We therefore used _____ = 1.79 as .557 an estimate fore. Next consider a and a, the personal tax parameters for equity and bonds. There is no need to estimate each parameter separately since it is only their ratio ab/a which matters in any of the computations.27 Let us consider then the problem of measuring the ratio ab/a. The first problem faced is that the tax treatment of the returns to equity depends on whether the returns take the form of dividends or capital gains. It is not clear how to proceed since economists do not yet -21- have a good explanation for why dividends are paid, given their unfavorable tax treatment (see Black (1976)). By repurchasing shares, a firm can create a dollar in capital gains in lieu of paying a dollar in dividends, and presumably would do so if capital gains were valued more highly by the market. Since firms do pay dividends, we assume that the market does value dividends and capital gains equally. In fact, Gordon-Bradford (1980) estimate the value in the market of dividends vs. capital gains, and find that the market value of a dollar of dividends does not differ systematically from the market value of a dollar of capital gains. That is, dividends must provide some other advantage which offsets their tax disadvantage. We therefore assume that the effective tax rate on equity is the capital gains tax rate. The ratio ab/a thus measures the value in the market of a dollar of interest pay- ments relative to a dollar in either dividends or capital gains. According to the derivation in Gordon-Bradford (1980), this ratio is a weighted average of the valuation each investor gives to interest relative to capital gains.28 The weights are proportional to the investor's wealth and inversely proportional to a measure of his risk aversion. We therefore calculated an estimate for ab/a directly from the twelve consumer groups of the FSW model by taking a weighted average of their relative valuations of interest and capital gains. In doing so, we made the following assumptions: 1) risk preferences do not vary across consumers, 2) the effective tax rate on capital gains is one-eighth of the tax rate on interest,29 and 3) only 70% of an individual's investments are taxable. According to 1973 Flow of Funds data, approximately 30% of savings were in pensions, IRA accounts, or other tax free vehicles. The implied value of cxb/a was .82. The remaining parameters r, , and r were directly observable. We set r=.08 and T=.05,30 based on the data for 1973 appearing in the Economic Report of the President. We set r=.48, the statutory tax rate in 1973. III. Other Changes to the Fullerton, Shoven, Whalley Model A. Modelling of Government Enterprises and General Government The FSW model includes not only the eighteen private sectors described above but two government sectors as well. One, government enterprises, includes government run -22- business activities, mainly the post office and TVA. This sector was modelled like the other private industries except that it received a large output subsidy from general government. The other sector, general government, captures the remaining activities of government. We need to calculate equilibrium values for p for these two "industries" comparable to those which charac- terize the other eighteen industries to help determine the demand for capital. Unfortunately, we do not have available the same quality of information for these two sectors. We assume that government enterprises are cost minimizing industries which meet all demand at the output prices dictated to them by higher levels of government. We assume therefore that they invest until the real marginal product of their capital is just high enough to cover depreciation, the real risk free interest rate, and a suitable risk premium, ÔG. Formally, we assume that p = r — r + d + bG Lacking any independent information about d in this industry, we assume that it equals the weighted average of the values in the eighteen private industries, where the weights are the sizes of the capital stock in each industry. To construct an estimate for ÔG, we first calculate for each private industry the value of the risk premium on a dollar of capital that would prevail if there were no leverage costs (as with noncorporate invest- ments), and if all risk were borne by the private sector. This risk premium would equal U') •32 (1—rn) We then took the weighted average of these values over the eighteen private industries. General government includes all remaining activities of government. It receives revenue from the various taxes and from selling its endowment of capital on the market. Part of the total revenue is earmarked for lump sum transfers to each consumer group. The benchmark transfers are based on data for welfare, government retirement, food stamps, and similar programs.33 As prices change in a simulation, government maintains the same real payments in transfers to each group. General government also purchases each of the nineteen producer goods (18 private industry outputs and government enterprises output), plus capital and labor. In doing so, it is assumed to maximize a Cobb-Douglas utility function whose arguments are these nineteen -23- producer goods plus capital and labor. The question here is the appropriate measure for the cost of capital to government. Since most of the capital used in general government is used in state and local governments,34 we model capital intensity decisions in this sector as if they were entirely local public decisions. The capital intensity of a community's public sector is in equilibrium when the (assumed) homogeneous residents in that community are indifferent to adding an extra dollar of capital. The community must also decide whether it is cheaper to finance its capital stock directly through property taxes or indirectly through the municipal bond market. The key tax factors in determining the equilibrium p here are: 1) property tax payments are deductible from taxable personal income if the residents itemize, 2) the interest rate paid on debt is the municipal bond rate, and 3) there is no tax on the "profits" of the sector. In calculating the equilibrium marginal product of capital in the local public sector, let us assume that 'y percent of an additional dollar of capital investment under consideration would be financed by debt. Let n equal the effective personal marginal tax rate at which residents deduct property taxes.35 Then the community must put up l—y through taxes to finance the nondebt part of the one dollar investment, at an after tax cost of (l—n)(1—-y). Let p represent the dollar value in each period to residents in the community of the marginal product of this dollar investment. Also, let rf be the nominal (tax free) municipal bond interest rate at which the community borrows. Then, as a result of this investment, residents receive an implicit net nominal return equal to p — 'yrj(l—n) — (d—ir)rj/r.36 Bond holders receive yrj before and after tax. Together the community and the bondholders have invested (I—n) (l—-y) + y dol- lars and must absorb together the risk in the return from the investment. Because of this risk, they demand a suitable risk premium, öG, which we assume equals the risk premium for government enterprises. Bondholders would require a risk free return of r12, the risk free municipal bond rate, while members of the community would require an after tax risk free return of abr2. Together they therefore would require a return on their investment of -24(1—n) (1—y) abrZ + -yr12 + ÔG. Therefore in equilibrium p—'r1 (1—n)—(d—T)rf/r+-,rf(1—n)(1—7)abrZ+-yrfZ+öG (17) We find solving for p that p = (d—7r)rf/r + (1—n) abr2 — yUln)abr2 + nr1—r12) + 5G (18) The required value for p is lower when y is larger. Therefore the community would use only debt finance unless marginal leverage costs are sufficiently large. We will assume that y=l, implying that p = (d—ir)rj/r + rf2—nrf +ÔG. The equilibrium p here is lower than that for government enterprises because of both the income tax deductibility of property tax payments and the availability of municipal bond interest rates. Similarly, property taxes paid to cover other local government expenses are deducti- ble from the Federal personal income tax. In particular, the after tax cost of hiring one more dollar of labor services is only (1—n) dollars. We therefore include an n percent factor subsidy to labor in this industry. Current expenditures on any of the nineteen commodities also cost (1—n) percent of the market price.37 In order to calculate values for p and the labor factor subsidy in this industry, we need values for d, 6G' r1, r12, and n. We set d and 6G equal to the same weighted averages used for government enterprises. We also assumed that municipal bond interest rates are a given fraction 8 of the interest rates on taxable bonds, so that rj=8r and r12=0r2. Gordon-Malkiel (1980) measure 8 to be .75. In calculating a value for n, several steps were involved. First, according to the NBER-TAXSIM file, the weighted average marginal tax rate in 1975 for those who itemized and deducted property tax payments was .260. In making this calculation, an individual's tax rate was weighted by the size of his property tax payments.38 We assume that the same rate applied in 1973. However, not all property owners itemize. Using unpublished data from the -25- National Income Division of the Commerce Department along with the figures from the TAX- SIM file, we infer that only 44.8 percent of property taxes paid on residential property was in fact deducted from taxable income. This implies that the average marginal value of n equals (.448)(.260) = .117. This calculation, however, ignores the possibility that industrial and commercial pro- perty may pay part of the costs of additional local public services. In fact, only two-thirds of property tax receipts come from residential property. When considering the effective property tax rate on business investment in earlier sections, we decided to explore the two alternative assumptions that: 1) benefits completely offset taxes at the margin, and 2) firms (except in real estate) receive benefits which offset half of their property taxes. In the first scenario, we set n = .11 7 because households are subsidized in their local public good "purchases" by the deductibility of their property taxes. Households receive no further subsidy or benefits from taxing businesses, because competitive pressure prevents communities from collecting any tax from firms without paying for commensurate benefits to them. In the second scenario, however, half of industrial property taxes are left for services to residential property. (The other half of the revenues from business property are used to provide services to the firms.) Consider, for the moment, $1.20 of local property 'tax reve- nue. One-third or $40 on average would be paid by businesses. They would receive $.20 in benefits, which leaves exactly $1.00 for residential benefits. Residents then would pay only $80 for a dollar of benefits, at a cost of $.80 (1-.l17)$.707 after taxes. We therefore use (l-.707).293 for n when simulating the second scenario. B. Measurement of Initial Capital Stocks In the FSW model, net corporate earnings (NCE) after tax and after depreciation were assumed to be proportional to the true capital stock (i.e. to equal rK, where r is the same for all industries). Therefore, NCE/r provided a measure of the capital stock in each industry.39 -26- According to the model in this paper, the size of corporate earnings relative to the underlying capital stock will depend on many factors such as the risk premium, tax vs. true depreciation rates, etc. However, expected gross corporate earnings (GCE), before tax and before depreciation ought to equal pK. Pc was defined in Section II,B as the cost of capital gross of tax and depreciation, and varies by industry. We therefore used GCE/p as a measure of the corporate capital stock in each industry. Here, GCE was defined to equal the sum of: I) corporate profits, from the Survey of Current Business (SCB) corrected for the Inventory Valuation Adjustment 2) corporate capital consumption allowances, from the SCB 3) corporate interest payments, from unpublished data of the Commerce Department's National Income Division (NID), and 4) corporate rental payments. Rents paid by industry were available from NID, and we divided these into corporate and non-corporate payments in the same proportions that the sum of other earnings were divided in each industry. The same procedure will not work for the non-corporate sector since earnings there are also in part labor income of the proprietors. Instead we assumed that within any industry, capital consumption allowances are proportional to the capital stock. We then multiplied our estimate of the corporate capital stock in each industry by the ratio of non-corporate to cor- porate capital consumption allowances in that industry to produce an estimate of the noncorporate capital stock. This logic also helps provide estimates of initial (1973) labor income in the non-corporate sector. If K p,. is equal to before tax earnings of capital, and GPE is gross proprietor's earnings, then GPE — K p,. equals imputed labor income. Here, GPE is defined to equal the sum of non-corporate profits (from the SCB), non-corporate capital consumption allowances (from NID), interest paid (from NID), and rents paid. Non-corporate rents were imputed by the above procedure. if this residual for labor in 1973 turned out to be negative, we assumed there was measurement error and used zero for the initial non-corporate labor in -27- that industry. For the two government sectors, we used estimates from Musgrave (1980) for the size of the 1973 capital stocks. C. Measurement of Capital Income, Before and After Tax The FSW model defined total capital income net of tax and depreciation to equal the sum of corporate profits, capital consumption adjustment, net interest paid, net rents paid, and non-corporate returns to capital. In the new model, we set total capital income equal to K(p—d). The major differences from the old procedure are: 1) depreciation is measured by the calculated dK rather than by reported capital consumption allowances with capital consumption adjustment, and 2) non-corporate capital income is in effect measured by K(p,—d) rather than by the reported data for non-corporate capital income.40 Let tk equal the average capital tax rate. We initially set tk equal to the ratio of observed 1973 capital taxes to before tax capital income, K(p—d). In simulations, net capital income then equals K(p—d)(1—tk) and capital tax revenue equals K(p—d)tk. Calculation of the benchmark equilibrium replicates observed capital taxes in 1973, while appropriate changes Ifl tk (together with changes in r,k,d', etc.) allow simulation of counterfactual equilibria. D. Savings Incentives While the procedure described above provides estimates for the capital stock in the initial equilibrium, the capital stock in the next period will equal this initial capital stock, plus net savings undertaken during the initial period by the twelve separate consumer groups. The capital stock in later periods will follow in a similar fashion. While we made much effort in this paper to improve the modelling of investment decisions (by taking account of uncertainty and the optimal form of finance), we made few changes to the assumptions about individual savings decisions found in the earlier model. In the FSW model, individuals in each consumer group j1,12 choose to save some income to finance future consumption Cj. They allocate the rest to a subutility function, H, -28- which is defined over fifteen consumption goods X, and leisure . The fifteen X1 consumption goods enter a Cobb-Douglas function with preference parameters X. as exponents. Specifically, each of the twelve consumer groups will be characterized by a nested CES utility function = XIX', QJ Cf]. (19) As in the FSW model, we use .15 for the uncornpensated labor supply elasticity of each group with respect to its net of tax wage. This parameter is used to set the elasticity of substitution for the inner nest, between consumption goods and leisure. Unlike the FSW model, however, we cannot use a savings elasticity with respect to the real after tax interest rate. In our model, this rate will normally be negative. Instead, we use 12.3 as the uncompen- sated savings elasticity with respect to one plus the real after tax interest rate. This parameter is used to set the elasticity of substitution for the outer nest, between present and future con- sumption. The 12.3 figure was derived from Boskin's (1978) equation (2). Boskin estimated that log C =A—l.07R, where C is consumption, R is the real net of tax interest rate, and A represents other variables in his equation. But therefore, log C A—1.07 log(1+R). It then follows that 1±R 35 = 1.07 (--). In 1973, the ratio of total consumption to net sav- ings was 11.5, from the Economic Report of the President. We then used (1.07)(11.5) 12.3 for the elasticity of S with respect to l+R in all periods for all consumer groups. In spite of many objections to Boskin's estimation procedure, we felt there was no good alternative. Saving is then converted immediately into investment demand for producer goods. A remaining issue is the determination of the net of tax real market interest rate faced by each group. As in the FSW model, we assume that individuals put a fixed fraction of their (marginal) savings into pensions, Keogh and IRA accounts, and life insurance. We assume that such savings earn the market rate of return free of tax. Based on Flow ofFunds data for 1973, we set this fraction equal to .3. The remaining seventy percent of their savings is then invested either in taxable bonds or in tax free municipal bonds. The return on taxable bonds is taxed at a constant personal tax rate m which ranges from .01 to .40 across the twelve -29- consumer groups. Each individual can therefore earn a real net of tax risk free4' rate of return on his savings equal to .3r + .7 max (rj, (l—m)r) — ir. In this expression rj represents the risk free municipal bond rate. In the initial simulations, we set rj = .75 r, based on the results in Gordon-Malkiel (1980). E. The Benchmark Equilibrium The FSW model, as used here, consists of eighteen producer industries, fifteen consumer goods, twelve consumer groups, plus the two government sectors. Before the model can be simulated, production and utility functions and their parameters must be specified. The overall strategy is to choose remaining parameters such that the model will calculate an equilibrium that exactly replicates the consistent benchmark data set. Each industry in the FSW model is characterized by either a constant elasticity of substitution or a Cobb-Douglas production function. Substitution elasticities are chosen from the best estimates in the available literature. The size of each industry's capital stock is calcu- lated as described in Section III.B. The size of the benchmark demand for labor in the corporate sector is measured by the size of the labor payments in that industry in 1973, as reported in the Survey of Current Business. The demand for labor in the non-corporate sector is measured as gross income of the industry minus our estimate for the gross return to capital, As in the FSW model, the parameters in the production function were then selected such that the optimal capital-labor ratio would equal the ratio which was in fact chosen, and such that the output produced using these factors would equal the observed 1973 output. In doing so, the rental cost of capital was set equal to the calculated equilibrium rate p—d for that industry. The cost of a standardized unit of labor was set equal to one plus the effective unemployment compensation tax rate reported in column 1 of Table 1. Various Federal excise taxes and indirect business taxes were modelled as output taxes for each of the eighteen industries. As in equation (19) above, each consumer group has a nested utility function over future consumption, leisure, and fifteen commodities. The inner-most nest is a Cobb-Douglas utility function over the fifteen consumer goods. The X, coefficients were chosen so as to -30- replicate observed relative expenditures on these commodities. In doing so, expenditures were measured gross of state and local sales taxes. In the next nest, there is a CES function by which the consumer chooses between these commodities and leisure. Weights were chosen such that individuals will choose to work forty hours out of a potential seventy hours at their net of tax wage rate. In the outer nest of equation (19), individuals choose between current and future consumption. Similarly, general government has a Cobb-Douglas utility function over the nineteen producer goods plus capital and labor.42 The parameters in this function were selected such that optimal demands for goods, given market prices, would equal actual demands in 1973. Finally, the foreign sector is modelled by the assumption that the net value of exports less imports for each producer good is constant. This simple treatment closes the model, maintains zero trade balance, and allows easy calculation of trade quantities given prices.43 Because the data set for this model comes from many different sources, the figures are often inconsistent. For example, Treasury data on various forms of capital income of con- sumers differs from Commerce Department data on industry payments for capital. In such cases, the data on one side of the account were judged to be of superior quality and the other data were adjusted to match. All reported industry and government uses of factors were accepted, so consumers' factor incomes and expenditures were scaled to match. Reported tax receipts and transfers were accepted, so government expenditures were scaled to balance the budget. The nearly balanced actual budget of 1973 luckily makes this treatment more reasonable. Similar adjustments ensure that supply equals demand for all goods and factors. The above assumptions guarantee that the model simulation in the initial period will replicate the 1973 figures. The dynamic model is derived assuming that the 1973 benchmark equilibrium lies on a steady state growth path. Observed saving behavior and the capital endowment are translated into an annual growth rate for capital, and this growth rate is also attributed to effective labor units. The benchmark sequence of equilibria is then calculated by -31maintaining all tax rates and preferences fixed, increasing labor exogenously, and allowing sav- ing to augment capital endowments over time. By construction, this sequence will have constant factor ratios and constant prices. In simulations of revised tax policies, labor growth is exogenous while capital growth depends on the savings response to new tax rates and interest rates. IV. Model Simulations A. simulation Procedure A variant of Scarf's (1973) algorithm is used to solve for each equilibrium. A new dynamic sequence of the economy results from a change in initial conditions, such as a change in the tax law. In each equilibrium period of the sequence, demand will equal supply for all producer goods and factors, and each industry will have zero profits. Both capital and labor are assumed to be homogeneous and freely mobile across industries. In addition, as described below, we adjust personal income tax rates so as to produce a government revenue at each date which provides the same utility to government given the new market prices as it had in the same period of the benchmark equilibrium sequence. We make this assumption so that in the simulations we can focus on the changes in utility that individuals derive from private activities, holding constant the utility that individuals implicitly derive from public activities. Simplex dimensions are required only for w, r, and the additive surtax rate on the personal income tax. Knowledge of these values is sufficient to evaluate the behavior of all agents. Producer good prices are based on factor prices and zero profits, while consumer good prices are based on producer good prices. A complete set of prices, quantities, incomes, and allocations are calculated for every equilibrium. A revised tax equilibrium can be compared to the benchmark equilibrium to provide a direct examination of the effects of the proposed tax changes. In describing the effects of any proposed tax change, we also calculate the equivalent variation in each period. This is the lump sum dollar amount that would have to be transferred -32- to individuals in the benchmark equilibrium so as to give each consumer group the utility that they would have in the revised tax equilibrium. One complication in calculating this equivalent variation is that tax changes cause a change in the amount of risk and leverage costs, yet these costs do not appear explicitly in the model:45 our individual utility functions implicitly include the utility provided from spending the risk premiums, but do not explicitly subtract for the disutility of bearing risk. However, by assumption, the risk premiums i3 or ô,., measure the cost to the indi- viduals of bearing what risk is left after taxes from their investments. In addition, the government bears risk since its tax revenue is uncertain, yet costs of risk bearing do not appear in the government utility function either. We assume in this paper that individuals ultimately bear this risk in proportion to their wealth, and find it just as costly to bear as risk they receive directly.46 In each simulation, we then measure the time pattern of consumption that each con- sumer group would have had, everything else equal, if it did not receive the risk premium appropriate for all the risk in the return on its capital (including that borne by the government), but also bore no risk. Since we have then standardized utility at the point where there is no risk, we can directly compare utilities across simulations. The reported values for the equivalent variation refer to this standardized measure for utility.47 B. Tax Distortions on Capital in the Initial Equilibrium In our initial simulations with the model, we left all tax rates at their observed values in 1973, thereby replicating the historical equilibrium. The results from this simulation provide us with a benchmark ftom which we can examine the welfare effects of several proposed tax changes. The key element that characterizes each of the simulations that we undertake is the function relating the market interest rate r to the equilibrium marginal product of capital p in each industry. The formula used in calculating p in the initial equilibrium was derived in Sec- tion II. The equilibrium p is a weighted average of the values p and p,.,, characterizing corporate and non-corporate investment. -33- In the first three columns of Table 2, we report the equilibrium values by industry for i+ -—d — o(l—k) a(I—r) Sp p + —d — (l—k) (I—rn) (20) and their weighted average by industry, defined as s. Here we assume that the property tax is nondistorting. Each of these figures represents the nominal return required by investors in that industry before any taxes but after depreciation. These returns are measured net of compensa- tion for the riskness in the return and net of any leverage costs. As such, they also represent the nominal social marginal product of the investment, net of the social costs from depreciation, risk, and leverage costs.48 Were there no corporation tax, the risk free nominal return on corporate capital s ought to equal the risk free nominal market interest rate r = .05. This equivalence would hold even if there were a (comprehensive) personal income tax on the nominal return from all forms of saving. Had we just used the simplified modelling of the corporate tax as a flat tax rate on the nominal return to corporate capital, as did Harberger (1962), then S would equal 1—i- or .096 with our parameters. In sharp contrast, the equihbnum values of s reported in Table 2 are not only well below .096 but are also mostly below .05. In fact, the weighted aver- ,ti.. V t&* SJS can ii .Jv.1 ant .. Lii .. flJiiiJ •VJ.JJ. fl2 Ili.;..., C........1.. Sj01fl5•k LIIi... ti_fl UJItW f,.. nit i_&a.,Ltii_O £0 ''tjtnOLIUII (A\ Wi.. re-express s (without the property tax) as: = r1(y + (1—k-—-y) — 1—i- + ab a(1—r) ) — 'y(r—r2) ab a(1—r) — (21) 1 1—i- The following factors, identifiable in this formula, account for the surprisingly low value for s: 1) Equity holders require an after-corporate-tax return of only a, T2 a , not r1, since the personal income tax rate on the alternative risk free asset earning r exceeds the personal tax rate on corporate equity. This lowers s from to a(1—r) , which equals .079. -34- 2) The use of debt finance has multiple effects. First, the required nominal risk free rate of return on debt before corporate taxes is only r = .05. Since on average 40 percent of capital is financed by debt, s iS thereby lowered to (.079)(.6) -I- (.05)(.4) = Second, ab percent of the risk premium on bonds is received by bondholders after tax, while only a(l—r) percent of the risk remains on the investment after taxes. This exchange is favorable to investors, lowering .c by another .007. 3) The inflationary capital gains component of the nominal return .r, is not subject to the corporate tax. This lowers the equilibrium value of 5 by ni. I —i .055. 4) Partially offsetting this, the effective tax depreciation rate d is below the economic depreciation rate d due to depreciation at historical cost in the tax law. This raises s on average by .033. 5) Finally the availability of the investment tax credit lowers the equilibrium s, by .002. The equilibrium values of the non-corporate s,.. are also normally below r because of the above explanations #3 and #5, more than offsetting explanation #4. The nominal equilibrium return to all capital s is on average only .034 (in column 3 of Table 2). The equilibrium marginal time preference rate of individuals will also be well below r because of the personal income tax. The weighted average marginal time preference rate5° for our twelve consumer groups turns out to be .043. Therefore, while individuals require a return of .043 on their savings, the resulting investment produces a net return of only .034. An implicit government subsidy of .009 makes up the difference. Tax distortions therefore result in an inefficiently large amount of savings and investment. (When we assume that the property tax is half distorting in industries other than real estate, there will still be a small net subsidy to savings and investment.) If this distortion is negative, though small, why is so much tax revenue collected on the return to capital, from both the corporate and personal income taxes? The explanation for -35- this apparent puzzle is that most (in fact more than all, according to our figures) of the taxable expected return is the risk premium. Yet while a significant per cent of the risk premium is taxed away, the same percent of the risk (standard deviation) is absorbed by the government through risky tax revenues. According to the capital asset pricing model, investors demand a risk premium proportional to the amount of risk that they bear. Investors are therefore indifferent when they lose to the government a given per cent of both the risk premium and the risk, so their behavior is undistorted. The government is just charging the market price for the risk that it absorbs. Since the risk premium is positive, however, expected tax revenues will be positive. Even if the saving-investment distortion is small, however, other tax distortions remain. First, the variation of the numbers in column 3 of Table 2 implies an intersectoral misallocation of capital across industries, as emphasized in Harberger (1962). In addition, savings is misallocated across individuals because of the variation in after-tax rates of return across investors. (Efficiency requires the same marginal time preference rate for each investor, and thus the same available after tax rate of return.) Also, as always, labor supply decisions are dis- torted because of the personal tax. Finally, in our initial simulation, yearly leverage related costs are estimated to equal .7 per cent of the value of the corporate capital stock, or .6 per cent of GNP. This is hardly an insigniflcant figure. C. Modelling of the Proposed Tax Revision The model in this paper is used to evaluate the general equilibrium effects of integrating corporate and personal taxes. Detailed descriptions of such proposals can be found in McLure (1975, 1979). Under the full integration proposal, as modelled in Fullerton, King, Shoven and Whalley (1980, 1981), the corporate tax would be eliminated. Instead, corporate earnings would be included in the personal income tax base of each of the shareholders in proportion to their holdings, and would be taxed at ordinary personal income tax rates.51 Several changes must be made in the model to capture the effects of this tax change. First, equation (4) relating Pc and r changes substantially. Corporate profits would now be -36- taxed at each investor's ordinary tax rate, regardless of corporate financial decisions. Since the tax distortion favoring debt finance is thereby eliminated, y goes to zero. There is now no offsetting advantage to counterbalance the leverage costs arising from debt finance. As a result, leverage related costs go to zero as well. After integration, the corporation would be treated for tax purposes as if it were a partnership. The only reason why p now differs from is that the average marginal tax rates of corporate and non-corporate investors differ.52 We previously estimated that the marginal tax rate of non-corporate investors equaled .365. Let m corporate investors after integration. We set mC equal equal the average marginal tax rate of to .7 12 i—I w1m, which equals .1948. are the marginal tax rates of the twelve consumer groups, and the w are the pro- Here, the portions of consumer wealth held by each group.53 We continue to assume that only 70% of capital income is taxable. The s after corporate tax integration can therefore be obtained from the s formula in equation (20), with m = .365 replaced by mC .l948. The resulting figures, reported in column 4 of Table 2, are calculated under the assumption that r2 remains unchanged at .05, to ensure comparability with the other figures in Table 2. (In the simulations, as r2 changes, all the s will change in response.) Note that tax integration will not affect the equilibrium value of s,., holding r constant. We find that the new values for s. exceed the (new and old) values for s,.. Investing in real capital is advantageous during inflation since inflationary capital gains escape full taxation. This advantage is greater in the non-corporate sector where the marginal tax rate is greater. (Use of historical cost depreciation is more of a disadvantage when marginal tax rates are greater, but this effect is not as important.) The relation between the values for s before and after integration is more complicated. The advantage to investing in real capital, where inflationary capital gains escape full tax- ation, declines with integration since the ordinary marginal tax rate on the return to capital declines. Offsetting this, however, the required before tax risk free nominal return on equity financed capital was abr a(1—r) before integration, while the required return declines to r after -37- integration, regardless of the form of finance. When we assume that property taxes are half distorting in all industries except hous- ing, then the equilibrium values for s, s,, and s, with or without integration, all go up by the values for t,, reported in column 2 of Table I. In columns 5 and 6 of Table 2 we report expli- citly the resulting values for s before and after corporate tax integration. In addition to recalculating the values for s, we need to calculate how government revenues change each period as a result of corporate tax integration. Clearly, corporate tax revenues go to zero. However, corporate earnings, whether retained or paid out as dividends, become fully taxable under the personal income tax. The new average tax rate on capital income, zj,, is set equal to the ratio of these revised capital taxes to the capital income, K(p—d), in the benchmark equilibrium. These new taxes include only property tax payments (when relevant) and personal income tax payments, as they would be with no corporate tax but with full personal taxation of all corporate earnings. (These personal income tax payments will be referred to as the personal factor tax.) Tax revenue from taxation of capital income in the revised equilibrium will then equal t,, K'(p'—d), where primes denote the values in the revised equilibrium. We simulated corporate tax integration under several sets of assumptions in order to test the sensitivity of the results to the different specifications. Table 3 summarizes the param- eter values assumed in each of the simulations. The basic simulation, summarized under Case I", assumes that half of the property tax was distorting in all industries except real estate, where it was assumed to be nondistorting. In order to make up for lost tax revenue in this simulation, we assumed that all per- sonal tax rates would be raised by a uniform scalar amount. This scalar increase in tax rates was chosen in each period so that government had just enough revenue to attain the utility level that it had in the same period of the benchmark sequence. In particular, we added the same scalar to the following tax rates: -38- the personal tax rates of the twelve consumer groups (j=l,12) in the personal tax rate of proprietors , the personal tax rate of corporate owners with integration n the implicit rate of subsidy for purchase 02 local public goods , — rj2/r the implicit tax rate on municipal bonds. , Each of the other simulations represents a slight variation from this central case simulation. In the second simulation, we assumed that the property tax was nondistorting in all industries. In this case property tax revenues are deleted from government revenues in both base and revised simulations. Property taxes are implicitly treated as benefit payments for public 'consumer goods" or intermediate inputs in production. In the third simulation, we set the risk free rate to .07, the treasury bill rate in 1973. This change affected the parameterization of the benchmark equilibrium, which was carried through to the new revised equilibrium. Finally, in the fourth simulation, we assumed that any extra tax revenue needed to maintain government utility is raised through a lump sum tax on individuals. The amount of extra tax paid by each group is proportional to their original after-tax incomes, but the extra tax has no price effects. While this case is unrealistic, it allows us to isolate the effects of changing the tax distortions on capital income. (With additions to personal income tax rates, there are further distortions in labor-leisure choices.) D. Simulation Results Tables 4-6 present some of the information from our simulations of corporate and personal tax integration. As a basis of comparison, we extended the consistent 1973 benchmark economy to a sequence of seven equilibria spaced five years apart. Each equilibria is pro- portionately larger than the previous one, with all values growing at the steady state rate. For a revised case, the first period has the same total capital as in the benchmark. The endogenous savings response determines capital stock in the six subsequent periods, again spaced five years -39- apart. With disproportionate growth, however, we need to interpolate values for intervening years. For each variable, we calculate the annual growth rate implied by its values from two successive periods. This rate is applied to the value from the first of those periods to obtain values for each year between them. Table 4 presents equivalent variations for all 31 years, each measured relative to national income in the corresponding year of the benchmark simulation. The seven actual equilibrium calculations are reflected in years 1, 6, 11, 16, 21, 26, and 31. while other years' values are obtained using interpolated data. Table 5 summarizes results by looking at just a few key variables in each of the seven periods. Each entry is the ratio of the revise-case value to the base-case value of the same period. A capital stock ratio less than one, for example, does not imply reduced capital stock over time; it only implies less capital than in the growing benchmark sequence. Table 6 shows the reallocation of the fixed total capital stock in the first period. The entry for each industry is the percent change in capital used in the first period of the revised sequence from the first period of the base sequence. Integration of the corporate income tax with the personal income tax may seem like a dramatic change in the tax law. indeed, Fullerton, King, Shoven, and Whailey (1980, 1981) find significant welfare gains from integration. However, the results here indicate that the effects on the economy would be very modest. Except when revenues are replaced by a lump sum tax, Table 4 shows that the tax change results in a very slight drop in the utility from current consumption of commodities and leisure during at least the first thirty years after the tax change. Net welfare losses occur with integration when the revenue is replaced by raising personal tax rates, because the labor-leisure distortion is exacerbated.56 This over-all loss occurs in spite of welfare improvements on three other margins. First, integration eliminates the distortion favoring debt finance, removing the leverage costs that were .6% of benchmark national income. -40- Second, inter-industry welfare gains follow along the lines of previous Harberger- type analyses, as indicated in the last two columns of Table 2. The generally high required rates of return in manufacturing are lowered, while the low required rates of return in real estate and petroleum refining are raised. Third, there are welfare effects on the intertemporal allocation of consumption. Table 2 shows that the average s iS a bit higher with integration, whether or not the property tax was modelled as distorting. Integration reduces the small net subsidy to the risk free return on savings, discussed in an earlier section. These three welfare effects are summarized in the fourth simulation of Table 4, where revenue losses with integration are recovered through lump-sum taxes. Together they imply a slight welfare gain from integration alone. Without changing personal tax rates, labor supply remains basically unchanged. If personal tax rates have to rise, however, the first three columns of Table 4 indicate a net welfare loss from integration. We find hat the resulting drop in labor supply creates the largest welfare effect. We probably underestimate the welfare cost of this drop in labor supply because we ignore some existing distortions to labor supply created by various transfer programs such as food stamps and AFDC. In the first period of the central case, labor supply drops by 1.4% in response to the .026 rise in marginal tax rates. The figures for the second and third cases are very similar. In the third case, where r = .07 in the benchmark equilibrium, the equivalent variation figures are even less favorable. It turns out that the benchmark intersectoral misallocation of capital and the intertemporal savings-investment distortion are slightly smaller in this case. The smaller gains from integration on those margins are offset by the same size loss from raising personal tax rates, for a larger net loss over-all. Because of the drop in labor supply with a fixed initial supply of capital, capital-labor ratios rise in the first period in all sectors except general government. In order to encourage this increase in capital-labor ratios, the cost of capital must fall. The last two columns of Table 2 show that with no change in interest rates, integration would imply a higher cost of capital on -41- average. Therefore, the market interest rate must fall initially, as seen in Table 5. The lower interest rate causes a fall in savings. The resulting reduction in the growth rate of the capital stock allows r to rise back up slightly above .05. When r = .07, however, the tax change tends to increase the Cost of capital relatively less (since lowering ab r a(l—r) to r2 becomes more important). In this simulation, interest rates have to rise to offset the stronger investment incentive resulting from the tax change. Note also that when labor supply does not fall, as when lump sum taxes are used to replace lost tax revenue, the story is reversed. Interest rates initially rise in order to maintain an unchanged capital-labor ratio. The resulting savings rate is sufficiently high, however, that interest rates must fall later to create demand for all the resulting capital. Capital-labor ratios do not rise uniformly, however. Capital is reallocated slightly across sectors in response to the tax change, as shown for the first period in Table 6. Capital tends to leave the industries that are little affected by the tax changes: government57, the pri- marily non-corporate industries (#'s 1 and 17), and, to a lesser degree, industries which are heavily debt financed initially (#'s 16, 17, and 18). The major impetus for this reallocation of capital is the change in s, resulting from the tax change, but many other factors are also nunIuea-l lnrliirled nrnnno thece nther fQrtnrc re the rplot.,ie 017P nf the Pnrnnrnte certar the relative size of the drop in leverage costs, and varying factor substitution elasticities in each industry. We also see from Table 5 that current consumption (of both commodities and leisure) falls eventually except when lump sum taxes are used to replace lost revenue. In cases I and 2, this fall in consumption results mainly from the fall in potential output caused by the fall in the capital stock. In case 3 it results from the rise in interest rates which shifts income into savings. These current consumption figures are less interesting than the equivalent variation figures, however, since they do not control for the amount of risk bearing. Note that risk bearing increases initially (in spite of the elimination of leverage costs) because of the reallocation of capital towards riskier industries. -42- In addition to these four simulations, we ran several others, not reported here, which produced very similar results. In particular, the assumption that property taxes on hous- ing are also half distorting made almost no difference to the results. Also, raising extra tax revenues through a proportional rather than an additive increase in all personal tax rates made little difference. V. Conclusions Previous versions of the FSW model have assumed that marginal tax rates equal average tax rates and that government expenditures are nondistoring. In this paper we have reexamined the modelling of many of these marginal tax and benefit distortions. Particular attention was paid to the modelling of the effect of taxes on financial and investment decisions of corporations and local public governments. We found that average tax rates provide a poor characterization of government created distortions. In the cases of the Social Security, Unemployment Insurance, and Workmen's Compensation programs, we have argued that individuals receive extra government benefits which would come close to offsetting any extra taxes they pay on the margin, as well as on average. We also argued that recipients of capital income receive benefits which largely compensate them for the taxes they pay and often more than compensate them. However, this compensation comes in a subtle form: these recipients are able to reduce some of the risk in the return on their investments by transferring it to the government through risky tax revenue. We also found that the tax distortion favoring corporate use of debt rather than equity finance is quite costly from a social point of view. Our results also emphasize the importance of using a general equilibrium model to evaluate welfare effects in a second best world. The current model simultaneously accounts for tax distortions in corporate financial decisions, in the interindustry (and private vs. government) allocations of labor and capital, in the intertemporal allocation of consumption, and in the labor/leisure choice of individuals. Concentration on only some of these distortions can give a very misleading view of the effects of integrating the corporate income tax with the -43- personal income tax. In particular, we find that the extra distortion costs caused by raising per- sonal income tax rates to restore government revenue more than offset the efficiency gains from changing the method of taxing income from corporate capital through corporate tax integration. Table 1: Data Used in Calculating Tax Rates Labor Tax Rate ALL INDUSTRIES (1) (2) (3) 14) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) 116) (17) (13) AGRICuLTURE. FORESTRY AND FISHERIES MINING CRUDE PETROLEjM AND GAS CONSTRUCTION FOOD AND TORACCO TEXTILE, APPAREL AND LEATHER PAPER AND PRINTING PETROLEUM REFINING CHEMICALS AND RU63ER LUM8ER, FURNITURE, STONE, CLAY AND GLASS METALS AND MACHINERY TRANSPORTATION EQUIPMENT MOTOR VEHICLES TANSPORTATI0N. COMMUNICATION AND UTiLITiES TRADE FINANCE AND INSURANCE REAL ESTATE SERVICES t/ p I 6 C k d 0.002 0.005 0.399 0.079 0.021 0.036 0.004 —0.035 —0.006 —0.006 —0.023 —0.004 —0.008 0.009 O.00i 0.007 —0.005 0.008 0.020 0.010 0.021 0.009 0.008 0.015 0.010 0.002 0.006 0.007 0.009 0.159 0.039 0.058 0.054 0.013 0.094 0.057 0.213 0.106 0.005 0.020 0.016 —0.010 0.056 0.020 0.167 0.011 0.0O 0.006 0.0o6 0.007 0.003 0.010 0.012 0.005 0.0 0.013 0.168 0,096 0.107 0.110 0.073 0.092 0.096 0.oei 0.079 0.111 0.095 0.108 0.092 0.058 0.098 0.067 0.057 0.102 0.012 0.004 0.003 0.25 0.435 0.268 0.194 0.160 0.433 0.255 0.497 0.313 0.605 0.787 0.503 0.021 0.012 0.020 0.061 0.005 0.043 0.037 0.038 0.094 0.035 0.057 0.046 0.035 0.025 0.049 0.001 0.011 0.081 0.081 0.064 0.117 0.039 0.051 0.053 0.079 0.009 0.042 0.059—0.019 0.040 0.042 0.026 0.078 'xj 0.005 0.013 0.015 0.041 —0.016 9 0.006 o 1 1 'Note that t is half of the average property tax payment rate in each industry except real estate. Table 2: Nominal Risk—Free Returns to Capital Net of Depreciation No Property Tax Base S ALL INDUSTRIES!! I— 1)) A(HICULTURE, FORESTRYAND FISHERIES (4) (5) 16) (7) (8) (9) *0) (II) (12) (13) 114) (Is) (16) (17) (16) (19) (20) CRUDE PETROLEUM AND GAS CONSTRUCTION FOOD AND TOBACCO TEXTILE. APPAREL AND LEATPSR ?APEp AND PRINTIN%, PETROLEUM REFINING CM1CALS AMD RU83ER LUMbER. FUR'IITURE. STONE. CLAY ANt) GLASS METALS ANt) MACH1NRY TRANSPORTATION EQUIPMENT MOTOR VEHICLES TRANSPORTATIQN. COMMUNICATION AND UTILITIES S S C S C 0.034 0.040 0.044 0.049 0.033 0.034 0.026 0.034 0,035 0.041 0.041 o.oi O.0ó9 0.055 0.057 0.062 0.050 0.053 0.04 0.046 o.osi 0.035 0.051 0.041 0.049 0.036 0.040 0.033 0.042 TRADE flC 0.032 0.036 FINANCE AND INSURANCE REAL ESTATE SERVICES hI G(NERNMEMT EP4TER?RISES— GtNEHAL GOVERNMENT S Base 0.036 0.045 (2) MINING (3) C With Property Tax Revise 0.028 0.010 0.033 0.050 0.037 0.035 0.04? 0.031 0.042 0.040 0.039 0.025 0.036 0.031 0.033 0.033 0.030 0.033 0.046 0.051 0.035 0.034 0.032 0.032 0.034 0.050 0.037 0.051 0.040 0.048 0.036 0.040 0.033 0.040 0.028 0.030 0.033 0.050 0.037 0.039 0.041 0.039 0.045 0.043 0.037 0.042 0.038 0.040 0.040 0.038 0.041 0.041 0.040 0.039 0.042 0.050 0.037 Revise S C 0.048 0.Ool 0.051 0.060 0.049 0.047 0.061 0.060 0.061 0.053 0.039 0.04d 0.045 0.049 0.089 0.037 0.05? 0.048 0.058 0.086 0.043 0.043 O.54 0.033 0.010 0.046 0.050 0.026 0.041 0.051 0.053 0.044 0.039 0.055 0.050 0.026 !!Averages are calculated over eighteen private industries. All use benchmark corporate capital as weights. The s column uses benchmark noncorporate capital as weights, and S uses benchmark total nc capital as weights. sectors are neither corporate nor noncorporate. We show their S values for purposes of comparison. a Table 3: Summary Information for the Different Cases Considered Case 3 Case 4 Case 1 Case 2 central no property tax .8222 .8052 .8052 .8052 .8052 .48 .1948 .1948 .1948 .1948 CIT+PFT(+PT) capital income PFT' + PT capital income PFT' capital income PFT' + PT capital income Pfl' + PT capital income Benchmark — Identifier r = .07 Z lump—sum equal yield TAX CHANGES: ab r a! — tk SENSITIVITY ANALYSIS: as real estate: all real estate: real estate: nondistorting nondistorting nondistorting nondistorting others: half others: half others: half appropriate for P comparison as. appropriate for comparison r extra tax for equalb, — yield !'CIT = PT = .05 .07 .05 add scalar to personal rates add scalar to personal rates add scalar to personal rates lump—sum tax on individuals — .05 Corporate Income Tax, PFT = Personal Factor Tax (explained in the text), Property Tax. Only the distorting part of observed 1973 property tax revenues are added to the numerator. For case 2, no PT is in the numerator of either base a revised average tax rates. PFT' indicates a changed PFT (see text). text for descriptions. Table 4: Equivalent Variations Relative to National Income for Each Year, Integration of Corporate and Personal Taxes (E.V./N.I.) 1 2 Year I 3 4 5 () 7 9 10 11 12 13 116 14 17 19 20 21 22 23 2272 28 29 30 31 4 3 No r .07 Lump— sum Central Case Property Tax Case —o .oooi —o • 0002 —0. 'JOJi —0 • 000.) —J • 0025 —o • 03 5 0.0041 0004 —0.0024 0. J31 0 • 0042 —C. 3003 —Li. 30)3 —0 • 0004 —0 • —0 • 0035 —0. 0005 —0 • 00J5 —Ci • 003b —0 • 0006 —o • 0007 —o .ooo 7 —0 0007 —o • 0037 —0.0007 —0.0007 —0.000? —0.0007 • 3007 • 000? —0 .0007 —0 • 000? —0.0007 —0 • 0007 r.,sr7 —o .0007 —0 p0007 — —0.0004 —0 • 000•.) —0.0005 • 0035 —0. 0035 —0 • —0. 0005 —0. 0005 —0 • —i) • oo5 0005 —0 • 0005 —0.0005 —0 • 00)5 —0 • 0005 —0. 0005 —0.0006 —0.0006 —00006 —0. OOub _n_ nnri- —0,0006 —00307 —0.0306 —0 • 0006 —o • 0006 —0. 0030 —o • 0006 —Ø • —0 • 0006 —0.0037 —0.0007 —0 • 300•r 0007 z Case —0 • 00 ? —0 • 0024 —0.0024 —0. 0024 —0.0023 —0.0023 —o • 0023 —0.0023 —0.0023 —0.0023 —0.0023 —0.0023 —0 • 0023 —0.0023 —0 .0023 —0. 0023 —0.0023 —0.0023 —0.0023 —0 • 0023 _n —0. 0022 —0.0022 —0.0022 —0.0022 —0.0023 —0 • 0023 —0.0023 Equal Yield Case 0 • 0040 0.0043 0.0043 0. 0044 0 • 0044 0 • 0044 0.0344 0 • 0044 0.0044 0. oO4 0.0044 0.0044 0 • 0044 0.0044 o. 0044 0.0044 0. OA4 0.0044 0.0044 0• ( r.fi1. 0 • 0044 3 • 0044 0. 0044 0 • 0044 0 • 0044 0.0044 O • 0044 Table 5: Key Variables Relative to the Benchmark, Over Five Year Periods for Integration of Corporate and Personal Taxes (Revise Value/Base Value) Time Period 1. Central Case 1 Case Interest Rate 1.0016 0.9b57 0.9798 1.0000 0.99i.4 0.9906 0.9745 1.0039 1.0110 o.994 0.931 4 0.9972 0.9972 0.9912 0.9972 0.9639 1 • 1.0009 2 09985 3 4 5 0.9980 0.997d 0.9978 6 0.9978 7 0.997t3 1 2 3 4 5 6 7 4. Lump—sum Equal Yield Case Stock 3 6 7 3. r = .07 Saving 0,9982 2 2. No Property Tax Case Consumption 1 2 3 4 5 6 7 0.93j 0.941 0.9341 0.9341 0.9901 0.9750 0.9847 0.9•71 0.9877 0.9878 0.9879 O.9b79 1.0000 0.9945 0.9931 0.9993 0.9993 0.9993 0.9994 0.9994 1.0078 1.0050 1.0043 1.0041 1.0039 1.0044 1.0039 0.9994 1.0013 1.00)7 1.00)8 1.0018 1.0018 1.0018 1.0189 1.0110 1.0092 1.00o6 1.0087 1.0087 1.0087 0.9933 0.9991 0.9J 0.991 0.9923 0.9927 0.9927 0.9927 1.0000 1.0013 ],003 1.0024 1.0025 1.0025 1.0026 - 1.0033 1.0042 1,00t2 1.00,4 ).004 1.004 1.0054 1.016 1.0130 1.0131 1.0131 0.9870 3.0071 1.0121 1.0133 1.0135 1.0136 1.0136 1.0320 1.0275 1.02ó3 1.0259 1.0259 1.02b1 1.0256 1.0111 ----- 0.9952 0.9917 0,9909 09907 0.9907 Table 6: Reallocation of Capital with and Personal Tax Integration: Corporate Percent Change From the Benchmark Use of Capital for Each Sector Industry GICULTU. FORSY (I) (2) MININ., (3) C4u PEIkULiUM Ai'ID ANI) FJSHERFS GAS (4) C.JN1UCL1DN (5) FuOD ANE TiACC0 (6) T:XTILE. APAREL AND LEATHER (7) PAPER AND PRINTINi (8) P_TRQLEUM REFINING (9) CHEMICALS ANJ RUBrER (10) (11) (12) (13) (14) (15) LUMbL, FUN1TJE. TuNE, CLAY AND GLASS METALS ANt) MACHINERY TANSP0RTATIUN ELJIPMCNT ijTO VEHICLES TNANSPORTATJUN, COMMUt41CATIOM A4L) UTiLITIES TRADE (16) FINANCE AND iNSURANCE (17) SEAL ESTATE (i3) S-.RV1CES (19) G:3vEkNM.NT (20) G.:NAL G0VRNME'1T NTISES 1 2 Central Case No Property Tax Case —0.282 1.492 —0.844 3.551 3.747 3.955 5.169 —0.538 6.889 1.752 3.173 1.316 2.217 1.249 2.526 —1.075 --0.934 0.156 —Q.453 —1.009 '3 '-0.311 1.710 —0.814 3.928 3.833 4,151 5.348 —0.579 7.027 1.946 3.511 1.681 2.270 1.055 2.577 -4.573 —1.298 —0.078 —0.700 —0.537 4 3 r .07 Lump—sum Case Equal Yield Case —0.549 3.479 0.445 6.610 4.712 0.364 2.648 0.314 5.390 3.439 4.009 5.446 0.343 6.854 3.162 4.573 z 6.151 7.105 0.210 8.687 4.265 5.635 3.b4B 4.246 4.537 3.981 2.012 —2.206 1.228 —1.5d1 ..j.87 1.683 3.167 0.336 ----2.610 -.Zl2 —1.763 -—0.178 —0.104 —0.2.71 F-I Footnotes 1. This underestimation of welfare losses from the replacement tax serves to strengthen our result that this welfare loss more than offsets welfare gains from integration, as discussed below. 2. For a discussion of the interindustry labor misallocations and general equilibrium incidence effects caused by this tax/subsidy system, see McLure (1977). 3. For an earlier introduction of an endogenous debt-equity decision into a Harberger (1962) style general equilibrium model, see Ballentine and McLure (1981). 4. This version of the capital asset pricing model allows for an arbitrary variation in tax rates across investors and across types of return (e.g. interest payments vs. capital gains). The key assumptions underlying the mode! are: 1) investors care only about the mean and the variance in the return on their portfolio, 2) only returns taxed at capital gains rates are stochastic, 3) capital gains are taxed at accrual, 4) there are no short sales constraints, and 5) the tax law allows for full loss offset. The latter assumption, as stated, is clearly false. A firm with tax hc th Qh1itJ huivr ...-_..--.J tr Irrv has h kwrt nd frwrd tr—.-.— nthr ty vr nd it the option to merge with a firm with taxable profits. Moreover, we are concerned with the marginal investment and not necessarily the marginal firm. Most of these marginal investments will be undertaken by pre-existing firms that are, on average, profitable. Any loss on such a marginal investment would only serve to reduce the taxable profits of such a firm. We assume that, given these possibilities, full loss offset is a reasonable first approximation. 5. If there were no bankruptcy costs, but merely a transfer of risk to bondholders, then the firm still has the incentive to move to all debt finance, as shown in Modigliani-Miller (1963). 6. The form of the function c(-y), and so the optimal value of 'y, will vary by firm. 7. To the extent that others are hurt but cannot charge the firm for their costs, even ex-ante, F-2 then this measure is an underestimate of the private costs of leverage. 8. Differentiating the right hand side with respect to y and equating to zero implies that d r(ab—a(l—r)) = —i---—. This equation is just the equilibrium condition for an optimal debtcapital ratio derived above, where 9. See d —i—-— corresponds to c(y). Gordon (1980) for a derivation. 10. Hall-Jorgenson also describe tax depreciation allowances in terms of their present value Z rather than the equivalent constant flow d. 11. There are no explicit estimates for the proportion of housing capital that is owner occu- pied. Using numbers from the Statistical Abstract, we multiplied the number of homeowners by the median value of owner-occupied homes, and then divided by the value of the total housing stock. These figures reveal that although approximately 65% of households own their own homes, 85% of the value of housing stock is owner-occupied. 12. Too little is known about the responsiveness to tax parameters of the decision to incorporate to model this decision explicitly. 13. We assume that the bond risk premium r—r2 equals a given pre-set value in all contexts. It would have been preferable to allow it to vary by industry and across simulations. Lacking the information necessary to do this seriously, we did not attempt to do it at all. Fortunately, sensitivity analysis indicates that the value of the risk premium r—r has very little effect on the value of p. 14. The application of the Tiebout model to the property tax depends critically on the availa- bility of zoning regulations (see Hamilton (1976)). The argument does not apply to state and local income (wage) taxes, where zoning is not available to enforce the creation of communities with homogeneous income as well as homogeneous tastes for public services. We therefore continue to treat state and local income taxes as distorting taxes. F- 3 15. COMPUSTAT is a data set complied by Standard and Poors Corporation, containing balance sheet information on many publicly traded corporations. 16. Only the book value of debt is reported on the COMPUSTAT tape. We used figures from von Furstenburg, Malkiel, and Watson (1980) on each industry's average ratio of market value to book value of debt to construct figures for the market value of debt for each firm on the tape. When the ratio of the market value of debt to the book value of debt was not available for a specific industry, we applied the economy wide ratio to the firms of that industry. 17. The debt-value ratio, as calculated here, will differ slightly from the debt-capital ratio used in the theory, however. In particular, a dollar raised in the market is sufficient to purchase (1k) dollars of capital yet is valued in the market at a dollar. Therefore the calculated debt- value ratio would equal (I—k) , where -y is the debt-capital ratio. 18. We used the estimates from Merton's Model 3, estimated over the time period 19621978. 19. There may be other reasons besides taxes to prefer debt finance, however. 20. By inherent risk, we refer to risk associated with the capital asset, regardless of financing, and regardless of taxes. 21. Noncorporate investors may not have the same ability to spread risk, however, since their securities are not publicly traded so they may require a larger risk premium. The tax system may discourage incorporation where risk bearing is more efficient, but we ignore this tax distor- tion and assume that the risk premium required per unit risk is indeed the same. 22. These are the two years for which the best data were available. The same 7% credit rate applied from 1971 to 1975. 23. See, for example, Christenson - Jorgenson (1969) and Hulten-Wykoff (1980). F-4 24. In the simulations, d' is kept constant, while d varies due to changes in r, r, or m 25. In calculating capital income in each category to use as weights, we followed the Treasury Department procedure of assuming that only 30% of business income, partnership income, and small business corporation income is really return to capital, the rest being return to labor. We would like to thank Daniel Feenberg for performing these calculations for us. 26. Of course, if any of the terms assumed to be constant had varied significantly over time, then the estimate of e could be biased. Probably the most important problem is that any increase in the riskiness in the economy during the period would have caused the function c(-y) to shift upwards, raising the parameter a. If this had occurred, our estimate of e should be too high, implying that our estimate of leverage costs may be too small. 27. The only place where a appears alone is in the term a(l—r) . However, , while defined to be the after tax risk premium, is estimated in this paper as in others by using before personal tax data. The resulting estimate therefore equals directly, avoiding any need for a separate estimate of a. 28. Some authors, e.g. Miller (1977), have constructed models with sharp clientele effects. where ab/a would equal the marginal tax rate of the marginal individual investing in bonds rather than stocks. All other individuals specialize in either bonds or stocks. However, in a model with uncertainty and no short sales constraints, as in Gordon-Bradford (1980), all investors will hold some amount (positive or negative) of both types of investment, so that everyone is a marginal investor. 29. Only one half of capital gains was taxable in 1973. In addition, the effective tax rate is approximately halved due to the postponement of tax payments until realization. We assume it is about halved again due to the mark up of the basis at death, and due to the selective realization of capital losses sooner than capital gains. F- 5 30. While r represents the expected inflation rate, we set it equal to the observed rate on the assumption of myopic expectations. 31. This equation can be derived from equation (7) by setting (1) equal to 0G' one and set- ting k, t,! and rn, equal to zero. 32. The extra term (1—k) enters because one (1-rn) measures the risk premium required for all the risk resulting from a dollar invested in a firm. But this investment buys (1—k) dollars of new capital. 33. While the former (FSW) model includes social security and unemployment compensation payments as part of the government's lump sum transfers, our model assumes these net out at the industry level. 34. According to the figures in Musgrave (1980), 72% of the capital stock in this sector is owned by state and local governments. 35. This rate n is equal to the personal marginal tax rate, if (homogeneous) residents in the community itemize, and is equal to zero if they do not itemize. In the calculations, we use a weighted average value for n, as described below. 36. This expression captures the annual flows to community residents when they make a municipal investment, maintained in nominal terms through the reinvestment of (d—ir) each year. This subsequent capital loss and reinvestment is also assumed to be financed by issuing municipal bonds, generating an after-tax interest expense in each future year of (d—ir)rj(l—n). We then need the present value of these costs in the year the capital loss takes place. Because individuals could have made non-municipal investments with an after tax return r(l—n), their relevant discount rate is r(l—n). The present value of the stream of interest payments (d—r)rj(1--n), in the year of the capital loss itself, is (d—ir)rj/r. F-6 37. One might argue, however, that these implicit subsidies to local public expenditures are to a degree Pigovian subsidies which correct for the spillover of benefits to other communities. To that degree, they are nondistorting. In this paper, however, we assume that these subsidies are distorting. 38. We would like to thank Daniel Feenberg for performing these calculations for us. 39. Interest payments and rental payments are included in NCE so as to capture the return to bond and land owners as well as equity owners. 40. Data are available only for total non-corporate income I and for the number of noncorporate workers L. FSW set the non-corporate wage rate w equal to the observed average wage rate from the corporate part of that industry, then set initial (1973) non-corporate capital income equal to I—wL. In this paper, we instead calculate a net rate of return to capital p,,—d, then set initial non-corporate labor income equal to I—K,.(p—d). 41. We assume that savers respond to the real net of tax risk free rate of return. Although they can obtain a higher real after tax return by accepting risk, this premium is not inherently part of the return to savings, It is a return to accepting risk. 42. We use this aggregate function to capture the utility created by government expenditures, rather than having government expenditures enter directly into production functions or each consumer group's utility function. Because we always hold government utility constant in the simulations described below, this treatment will not affect our estimates of changes in consumer welfare attributable to tax policy changes. 43. Goulder, Shoven, and Whalley (1981) suggest that the results may be sensitive to this assumption. 44. We assume that the relative wealth of the twelve consumer groups remains unchanged over time. While the groups save different proportions of income, the unmodelled movement of individuals across our twelve groups over time ought to maintain the initial wealth F- 7 distribution. 45. Corporations take account of leverage costs when making investment decisions at the margin, but these costs are never actually subtracted from firms' profits. 46. Diamond (1967) provides a formal argument for this assumption. Also, we assume that individuals view the risk they bear indirectly as a lump sum tax, even though we apply this tax' in proportion to their (initial) wealth. We could have distributed the lump-sum tax in proportion to (initial) income, but the results would be very similar. The difference between these two procedures is only a lump-sum redistribution, which has general equilibrium effects only to the degree that individual preferences for commodities differ. 47. The FSW model calculated the discounted sum of this stream of equivalent variations to obtain a present value of welfare gains. The proper discount rate, however, is the real after tax interest rate, which in our model is negative. The present value of any stream of gains or losses would then be infinite. Instead, we report the stream directly. 48. We assume that risk borne by the government has the same social Cost as risk remaining in the private sector, as would be implied by efficient risk spreading. The risk terms in equation (20) then do indeed correct for the social costs of the risk created by the marginal invest- ment. We also assume that the measure of leverage costs included in t5 captures the social costs of leverage. If the government bears risk more cheaply, then there is a social benefit from taxes on capital income due to the resulting redistribution of risk. 49. Also, leverage costs per unit capital are raised to .007, as implied by equation (11), though this does not show up in equation (21) since s is net of leverage costs. 50. The marginal time preference rate for consumer group j was assumed to equal (.3r + .7 max (rj, (I—m)r2)), the risk free after tax return to savings. Thirty per cent of (marginal or average) savings are assumed here to be untaxed. 51. The major purpose of this paper is to investigate, for integration of corporate and personal F-8 taxes, the sensitivity of estimates to different model specifications. Rather than look at several types of integration (including partial plans or dividend relief) under one model specification, we find it more useful to look at one type of integration under several model specifications. For more discussion of partial integration plans, see McLure (1979) or Fullerton, King, Shoyen, and Whalley (1981). 52. These marginal tax rates differ if individuals who choose to form their own businesses differ systematically from those who invest in financial securities. 53. This formula for m follows from the derivation of the Gordon-Bradford (1980) model on the assumption that individuals are equally risk averse at the margin. 54. An equivalent procedure, actually used in our calculations, uses equation (4) for p, sets r to .1948, and sets ab to l.-.1948 = .8052. Together, these changes imply that -y=O and that leverage costs go to zero. 55. For income effects of taxation in this model, we use features from the FSW model. In the benchmark equilibrium, only 96% of dividends are taxable, to account for the $100 dividend exclusion in 1973. Retained earnings were assumed to generate equivalent accrued capital gains, but these are taxed on a deferred basis at preferential rates. Accounting for taxation of purely nominal capital gains, however, FSW use 73% as the proportion of retained earnings subject to full personal rates. Integration changes both of these latter proportions to one. Also in the benchmark, individuals reduce their personal tax base by 30% of savings, the amount contributed to pensions, Keogh, and IRA accounts. This remained unchanged under integration. 56. When personal income tax rates are raised, the interpersonal allocation of savings is further distorted, as are local public goods decisions. 57. Capital tends to leave general government in part because as personal income tax rates rise, its relative prices for labor and commodities (which are proportional to (1—n)) fall more F-9 than does the cost of capital. Appendix Footnotes 58. Both Tables 5.8 and 6.16 of the SCB provide data on the inventory valuation adjustment, but are taken from different sources. Table 5.8 estimates are used in the product side of the GNP accounts, while Table 6.16 estimates are used for the income side. See the Survey of Current Business for further detail on the concepts. 59. Note that .l62/.205 equals .789, while .123/.205 equals .600. R- 1 References Ballentine, J. Gregory and McLure, Charles E., Jr. Taxation and corporate financial policy. Quarterly Journal of Economics 94: 35 1-372. Becker, Joseph M. 1972. Experience Rating in Unemployment Insurance. Baltimore: The Johns Hopkins University Press. Black, Fisher 1976. The dividend puzzle. Journal of Portfolio Management 2: 5-8. Blinder, Alan S., Gordon, Roger H., and Wise, Donald E. 1980. Reconsidering the work disincentive effects of social security, National Tax Journal. Forthcoming. Boskin, Michael J. 1978. Taxation, saving, and the rate of interest. Journal of Political Economy 86: S3-S27. Brown, Eleanor. 1980. Experience rating for unemployment insurance taxes. Princeton University Ph.D dissertation. Coen, Robert M. 1980. Alternative measures of capital and its rate of return in U.S. manufac- turing. In Usher, Daniel, ed., The Measurement of Capital. Chicago: The University of Chicago Press. Christensen Laurits and Jorgenson, Dale W. 1969. The measurement of U.S. real capital input, 1929-1967. Review of Income and Wealth 15: 293-320. Diamond, Peter A. 1967. The role of a stock market in a general equilibrium model with technological uncertainty. American Economic Review 57: 759-76. Feldstein, Martin S. and Summers, Lawrence 1979. Inflation and the taxation of capital income in the corporate sector. National Tax Journal 32: 445-470. Fishel, William A. 1975. Fiscal and environmental considerations in the location of firms in R-2 suburban communities. In Mills, Edwin S. and Oates, Wallance E., eds., Fiscal Zoning and Land Use Controls. Lexington, Mass.: Lexington Books. Fullerton, Don, King, A. Thomas, Shoven, John B., and Whalley, John. 1980. Corporate and personal tax integration in the United States: some preliminary findings. In Haveman, R. H. and Hollenbeck, K. eds., Microeconomic Simulation Models for Public Policy Analysis. New York: Academic Press, Inc. ______________ 1981. Corporate Tax Integration in the United States: a general equilibrium approach. American Economic Review. Forthcoming. Fullerton, Don, Shoven, John B., and Whalley, John. 1978. General equilibrium analysis of U.S. taxation policy. In United States Office of Tax Analysis, Department of Treasury, 1978 Compendium of Tax Research. Washington, D.C.: Government Printing Office. ______________ 1980. Dynamic general equilibrium impacts of replacing the U.S. income tax with a progressive consumption tax. NBER conference paper no. 55. Gordon, Roger H. 1980. Inflation, taxation, and corporate behavior. NBER working paper no. 588. Gordon, Roger H. and Bradford, David F. 1980. Taxation and the stock market valuation of capital gains and dividends. Journal of Public Economics 14: 277-308. Gordon, Roger H. and Malkiel, Burton G. 1980. Taxation and corporation finance. NBER working paper no. 576. Goulder, Lawrence H., Shoven, John B., and Whalley, John. 1981. Domestic tax policy and the foreign sector. This volume. Hall, Robert E. and Jorgenson, Dale W. 1967. Tax policy and investment behavior. American Economic Review 57: 391-414. R-3 Hamilton, Bruce W. 1976. Capitalization of intrajurisdictional differences in local tax prices. American Economic Review 66: 743-753. Harberger, Arnold 1962. The incidence of the corporation income tax. Journal of Political Economy 70: 2 15-240. Hulten, Charles R. and Wykoff, Frank C. 1980. The estimation of economic depreciation using vintage asset prices. Urban Institute working paper # 1390-01. Kendrick, John W. 1976. The National Wealth of the United States. New York: The Conference Board, Inc. King, Mervyn A. 1974. Taxation and the cost of capital. Review of Economic Studies 41: 21-36. McGuire, Martin. 1974. Group segregation and optimal jurisdictions. Journal of Political Econamy 82: 112-132. McLure, Charles E., Jr. 1975. Integration of the personal and corporate taxes: The missing element in recent tax reform proposals. Harvard Law Review 88: 532-582. ______________ 1977. The incidence of the financing of unemployment insurance. Industrial and Labor Relations Review 30: 469-479. _____________ 1979. Must Corporate Income Be Taxed Twice. Washington, D.C.: Brookings Institution. Merton, Robert C. 1980. On estimating the expected return on the market. N.B.E.R. working paper no. 444. Miller, Merton H. 1977. Debt and taxes. Journal of Finance 32: 26 1-275. Modigliani, Franco and Miller, Merton H. 1963. Corporate income taxes and the cost of capital: A correction. American Economic Review 53: 433-43. / R-4 Musgrave, John C. 1980. Government owned fixed capital in the United States, 1925-79. Survey of Current Business. Washington, D.C.: Government Printing Office. Myers, Stewart C. 1977. Determinants of corporate borrowing. Journal of Financial Economics 5: 147-175. Scarf, Herbert E., with the collaboration of Terje Hansen. 1973. The Computation of Economic Equilibria. New Haven: Yale University Press. Shoven, John B. 1976. Incidence and efficiency effects of taxes on income from capital. Journalof Political Economy 84: 1261-1283. Stiglitz, Joseph E. 1973. Taxation, corporate financial policy, and the cost of capital. Journal of Public Economics 2: 1-34. Tiebout, Charles. 1956. A pure theory of local expenditures. Journal of Political Economy 64: 4 16-424. United States, Bureau of Economic Analysis, Department of Commerce. Survey of Current Busi- ness. Washington, D.C.: Government Printing Office. United States, Internal Revenue Service, Department of Treasury. Statistics of income. Washington, D.C.: Government Printing Office. Vasquez, Thomas. 1974. The effects of the asset depreciation range system on depreciation practices. U.S. Treasury Department Office of Tax Analysis, paper no. 1. Von Furstenburg, George M., Malkiel, Burton G., and Watson, H. S. 1980. The distribution of investment between industries. In Furstenburg, George M., ed., Capital, Efficiency, and Growth. Washington, D.C.: American Council of Life Insurance. Warner, Jerold. 1977. Bankruptcy costs, absolute priority, and the pricing of risky debt claims. Journal of Financial Economics 4: 239-276. R-5 White, Michelle. 1975. Firm location in a zoned metropolitan area. In Mills, Edwin S. and Oates, Wallace E., eds., Fiscal Zoning and Land Use Controls. Lexington, Mass: Lexington Books. A-i Appendix Construction of Industry-Specific Data by Yolanda Kodrzycki Henderson This appendix describes the procedures for obtaining four data series: unemploy- ment insurance tax rates, investment tax credit rates, economic depreciation rates, and tax depreciation rates. I. Unemployment Insurance Tax Rates In the above simulations, we required the net (of benefit) unemployment insurance tax rates for 1973, for eighteen private industries. These industries are for the most part aggre- gations of two to three SIC two-digit industries in manufacturing, and broader classifications (e.g., wholesale and retail trade) outside of manufacturing. Becker's (1972) data for unemploy- ment insurance benefit and tax rates, on the other hand, came from sixteen state employment security agencies for various combinations of years and industries (see his tables A.5 to A.9). He has provided information for 1961, 1967, and the 1957-67 average. Industry detail included broad classifications such as "manufacturing" and "wholesale and retail trade", selected two-digit industries, and selected three-digit industries. Typically, data for a particular industry were available for only a few states, and not all time periods. In view of the discrepancies between required and available data, we computed the net tax rate for each industry from the 1957-67 sample and the 1967 sample. The unweighted average from the two samples was taken as the estimate for the industry. If the FSW industry consisted of several two-digit industries, this procedure was applied to each two-digit industry, and the average of these tax rates was used as the FSW industry tax rate. There were two exceptions to this general procedure caused by lack of industry information. For the two mining industries, petroleum and natural gas and other mining, we used the same estimate, the one A-2 available for their total. For petroleum refining, we averaged estimates for two other nondurable industries, chemicals and rubber and paper and printing. II. Effective Investment Tax Credit Rates To compute the investment tax credit rates, we divided the dollar amount of the credit taken in each industry by the level of investment in that industry. Because we were calculating effective rates, investment included purchases of structures and the change in inven- tories, even though these types of investment are not eligible for the ITC. We were forced to aggregate corporate and non-corporate data because there was no separate information about investment in these two sectors. This procedure is appropriate in that the same statutory rates apply to both sectors, but may be inaccurate if the type of investment differs between the corporate and non-corporate sectors of an industry. Tables on the investment tax credit by industry appear in the Internal Revenue Service Statistics of Income, Corporation Income Tax Returns, but the ITC for sole proprietors and partners does not appear in the Statistics of Income publications for these returns. Unpublished data on the 1973 non-corporate ITC were made available by the Treasury Department, and we used the assumption of a constant ratio of non-corporate to corporate ITC in each industry to estimate the non-corporate ITC for 1974. These data were then aggregated to our industry definitions for each of the two years. Our principle source for data on fixed investment by industry was the Commerce Department's survey of expenditures for new plant and equipment by U.S. business, as reported in the Survey of Current Business (SCB). Supplementary unpublished data were pro- vided by the Bureau of Economic Analysis (BEA) of the Commerce Department. The coverage of this survey was satisfactory for our manufacturing industries and for transportation, corn- munications, and utilities. Information on other industries was inadequate for various reasons: agricultural business and housing are excluded entirely from the survey, some service industries are omitted, and investment in mining is underreported because capital expenditures for unsuccessful mineral explorations are expensed rather than being included as an investment on corn- A-3 pany books. As a result, we used several different procedures for obtaining investment in these remaining industries. For real estate, we used the National Income and Product Accounts (NIPA) figures for residential investment. This omits the relatively small nonresidential invest- ment by this industry (brokers' offices), but we were not able to find information on this com- ponent. For agriculture, we used NIPA data on investment in agricultural machinery and nonresidential farm structures. Agricultural machinery is only part of the equipment purchased by farmers, and the rest (tractors, trucks, automobiles, etc.) is not broken down between agricul- tural and nonagricultural uses on an annual basis. We scaled up our estimate of equipment spending to total agricultural equipment in both years using information from the 1972 capital flow table (CFT) of BEA. For the remaining industries, we used the CFT data for 1972, multiplied by growth rates for the closest corresponding category from the 1973 and 1974 investment surveys. Inventory investment estimates for agriculture and trade came directly from the Sur- vey of Current Business (Tables 1.1 and 5.8, respectively). For other industries, we added together the book value change in inventories and the inventory valuation adjustment (IVA). BEA provided unpublished data for the IVA (consistent with Table 6.16 of the SCB) for each of our industries for 1973. The 1974 IVA's were estimated using growth rates in the IVA for broad industry classifications (such as "durable manufacturing') from Table 5.8 of the SCB.58 The change in the book value of inventories came from the Census Bureau's monthly report on Manufacturers' Shipments, Inventories, and Orders, available from Data Resources, Inc. (DRI). In some cases, it was necessary to impute data for two-digit manufacturing industries and non-manufacturing industries. This was done using information on the size of the industry as measured by investment in the 1972 CFT, as well as information on inventory change in Table 5.8 of the SCB. III. Economic Depreciation Rates As described in Section II.C.5 above, economic depreciation rates were found for each industry by calculating the rate that was most consistent with the dollar value of economic A-4 depreciation for the period 1972 to 1974 and the stream of investment through 1974. For economic depreciation in twelve two-digit and three-digit manufacturing indus- tries, we used the "variant C" estimates of Coen (1980), which are provided through 1974. For agriculture and real estate we used the Commerce Department's capital consumption allowances with capital consumption adjustment from the SCB, Tables 1.13, 6.15, and 6.24. Estimates of economic depreciation rates were not available for more than these fourteen industries, but a procedure to extend depreciation rates to other industries is described below. The data for nominal fixed investment described in the previous section on invest- ment tax credit rates were extended back to 1947, and the price deflator for fixed investment from the National Income Accounts was used to convert those figures to constant dollars for the appropriate year (i1972, 1973, 1974). This was not possible for all industries, however. The investment survey data described in the previous section were available from DRI for six- teen two-digit industries since 1947 (including the twelve manufacturing industries). For the real estate industry, we were able to use the NIPA data discussed in the previous section. For agriculture, we had investment in agricultural machinery since 1947, but information on non- farm structures was available only back to 1958. We extended the latter to 1947 by assuming that it was .77 of the former, a figure based on the ratios for 1958, 1959, and 1960. We still had to account for the (small) amount of the capital stock in 1972 to 1974 that was the result of investment prior to 1947. Using NIPA data, we estimated that real nonresidential fixed investment increased at a 2.7% rate between 1929 and 1947, and real residential investment at a 2.1% rate, and applied these aggregate growth rates as described in the text. Using the above information, we computed economic depreciation rates for fourteen industries. Some of the eighteen FSW industries correspond exactly to these industries. Some are aggregates of these available industries, and we computed economic depreciation rates for these aggregates. For industries for which we had no depreciation data, we inferred information on the durability of their capital stock from data on their relative purchases of structures and A-5 equipment, as reported in the 1972 BEA CFT, which was available for all of our disaggregated industries. We used our estimated depreciation rates for available two-digit and three-digit industries, agriculture, and real estate in a regression on the ratios of equipment to total plant and equipment (and the square of that ratio). This regression gave us a predictive equation for depreciation rates of other two-digit industries based on their ratios of equipment to total plant and equipment. If one of the model's industries was entirely unrepresented in the available depreciation rate estimates, we used the predicted rate based on its 1972 CFT data. If part of an industry was represented in the available depreciation rate estimates, we used that estimate in combination with a prediction for the other part, weighting by the value of the capital stock in 1972 in each section of the industry. Since a published estimate of the capital stock was not available for each two-digit industry, we estimated each capital stock ourselves. In particular, if d is our estimate for the economic depreciation rate in a particular industry, if is the estimated growth rate in real investment in that industry during the period 1947 to 1972, and if 1R is the real gross fixed investment in the industry in 1972, then we approximated the capital stock in the industry in 1972 by: K= 1R e e -di dt Where an industry's growth rate of investment was unavailable, we used a growth rate based on more aggregated data (e.g. manufacturing). IV. Tax Depreciation Rates The methodology for computing tax depreciation rates was similar to the methodol- ogy for economic depreciation: we searched for the rate in each industry that was consistent with observed depreciation allowances and investment streams. The data for depreciation allowances came from the IRS Statistics of Income for both corporate and non-corporate enter- prises, by industry. For real estate and agriculture, we used SCB tables 6.15 and 6.24. The rates for industries for which investment data were missing were derived in a manner similar to A-6 the economic depreciation rates, by regressions using the ratio of equipment to total investmen t. The main difference in the methodology from that for economic depreciation rates was that we accounted for major changes in tax laws regarding depreciation allowances. In par- ticular. prior to 1954, firms could use straight line depreciation based on Bulletin F lifetimes. In 1954, double declining balance or sum of the years' digits methods of tax depreciation were introduced, and in 1971, tax lifetimes were reduced by twenty percent through the Asset Depreciation Range (ADR) system. In each of these periods, therefore, the tax depreciation rate was different. We proceeded by calculating how the effective geometric depreciation rates would differ among these periods for a representative asset with a 14 year tax lifetime prior to ADR. Suppose investment in this asset had been growing continuously at the nominal rate #.07 (calculated by regressing the log of the NIPA total fixed nonresidential investment from 1947 to 1976 on time). Then under the double declining balance formula, tax depreciation deductions in year i would be: TD = f 0 e' di + T/2 T I, fT/2T -- I, e_2 e_Mtdi T where I is nominal investment in year i. The equivalent geometric depreciation rate would be that rate d' which would have implied the same size of tax deductions. With geometric depreciation, tax deductions would have been: TD d'J, ed'tet When we equate these two formulas and use T = 14 di and L = .07, the only remaining unknown is d'. We therefore conclude that the effective depreciation rate for this representative asset would have been .162 for the period 1954-1970. After 1971, when T was reduced by 20%, the effective rate implied by the above formulas increased to .205. In contrast, with straight line depreciation, tax deductions would have been: '° T e'dt TD1 = I T A-7 Therefore, the effective geometric depreciation rate for this representative asset prior to 1954 would have been .123. Based on these results, we assumed in our calculations that if the effective geometric depreciation rate d' was available on investments made since 1971, then the rate .789 d' was available during the period 1954-70, and the rate .600 d' during the period prior to l954. We recognize that our procedure omits the effects of many other revisions during the period both in Treasury Department rulings and in the degree to which firms took advantage of the avail- able rulings. A more thorough procedure, for example, might use information from Vasquez (1974) on the proportion of investment that was depreciated by the faster methods allowed fol- lowing the 1954 and 1971 changes in the law. Our procedure should effectively capture the basic differences in the tax treatment of depreciation among the various industries, which is what we needed.