وضع مالیات تصادفی و قیمت گذاری دارایی در تعادل عمومی پویا

Tax rates have fluctuated considerably since federal income taxes were introduced in the U.S. in 1913. This paper analyzes the effects of stochastic taxation on asset prices in a dynamic general equilibrium model. Stochastic taxation affects the after-tax returns of both risky and safe assets. Whenever taxes change, bond and equity prices adjust to clear the asset markets. These price adjustments affect assets with long durations, such as equities and long-term bonds, more than short-term assets. Under plausible conditions, investors require higher term and equity premia as compensation for the risk introduced by tax changes.

One of the few certain forecasts about the tax system is that it will change. Since federal income taxes were introduced in 1913, the tax system of the U.S. has been reformed several times. Tax rates have fluctuated considerably over this period, as depicted in Fig. 1, which shows the federal marginal income tax rates for individuals in five different tax brackets.1 Besides marginal tax rate changes, other provisions of the tax code also changed, adding to the overall uncertainty of tax law. This paper investigates how stochastic tax policies affect asset prices and whether they introduce an additional risk factor in the economy, which changes equity and term premia. Full-size image (34 K) Fig. 1. Marginal income tax rates at different real income levels. The marginal income tax rates over the period from 1913 to 1999 are depicted for families with real income levels of 50, 100, 250, and 500 thousand U.S. dollars (with 1999 consumer prices), and the marginal tax rate for the highest tax bracket. Figure options This paper analyzes the effects of stochastic taxation on asset prices in a dynamic general equilibrium model. The theoretical model generalizes the Lucas (1978) asset pricing model by introducing a flat consumption tax that follows a two-state Markov chain. Whenever taxes change unexpectedly, stock and bond prices adjust instantaneously to clear the asset markets. The price adjustments are larger for assets with long durations, such as equities and long-term bonds, than for assets with shorter durations. This paper demonstrates that individuals require higher expected returns for holding the assets with larger price changes. Hence, long-term bonds and equities tend to pay on average higher returns than short-term bonds. Stochastic taxes affect asset prices in three ways. First, they change the level of disposable income over time (income effect). Frequent tax changes increase the variability of consumption for a given production process. A higher variability of consumption significantly affects asset prices and leads to a higher equity premium, as previously shown in the asset pricing literature. Second, time-varying tax rates distort the relative price of consumption over time and affect the incentives to save and invest (substitution effect). Even if all the tax revenues were to be rebated to taxpayers and the consumption process remained completely unaffected by tax changes, stochastic taxes would still affect asset prices and equity and term premia. Third, taxes can influence the rate of growth of the economy and thereby affect asset prices (growth effect). Some tax regimes might be more conducive to economic growth than others. This paper is related to the literature in finance that addresses the high equity premium and to the literature in public economics that analyzes the effects of taxes on savings decisions and portfolio choice. The papers in the finance literature show that conventional asset pricing models cannot generate equity premia, as observed in the U.S. during the last century. The literature has focused on three related puzzles. Mehra and Prescott (1985) show that extremely high levels of risk aversion are necessary to explain the large equity premium (equity premium puzzle). Weil (1989) demonstrates that the risk-free rate increases dramatically at higher levels of risk aversion (risk-free rate puzzle). And Shiller (1981) argues that stock prices tend to be more volatile than the underlying uncertainty in the economy (excess volatility puzzle). Many alternative explanations have been identified as potential explanations for these puzzles. 2 These generalizations of conventional asset pricing models contribute to a resolution of the equity premium puzzle but the puzzle can still not be resolved completely. This paper sheds light on the effects of stochastic taxes on asset prices and equity and term premia. Many papers in public economics analyze the effects of taxes on saving decisions and portfolio choice.3 However, the literature in public economics has only peripherally dealt with random taxes. Stiglitz (1982) discusses the welfare effects of random taxation. Bizer and Judd (1989) present a dynamic general equilibrium model where taxpayers understand the uncertainty in tax policy when making their portfolio decisions. On the other hand, Auerbach and Hines (1988) and Hassett and Metcalf (1999) analyze the pattern of U.S. corporate investment incentives and study the impact of tax policy uncertainty on firm-level and aggregate investment. This paper does not discuss the efficiency and the welfare implications of random taxation. Instead, this paper studies the effects of uncertain taxes on the distribution of asset prices and on term and equity premia, which have not been previously studied. An important insight into the role of the tax system on the equity premium puzzle has recently been provided by McGrattan and Prescott, 2003 and McGrattan and Prescott, 2004. They find that changes in the tax and legal environment in the U.S., especially the introduction of tax-qualified retirement saving vehicles and the decrease in the top marginal income tax rate, account for the high return on corporate equity between 1960 and 2000 relative to long-term debt.4 They compare the return on equities relative to the return on long-term debt, because short-term debt provides important liquidity services and has therefore relatively low rates of return. My paper shows that uncertain taxes have the largest impact for long-duration assets, such as equity and long-term bonds. Thus, uncertain taxes increase the equity and the term premium even if there is no differential taxation between different asset classes. The remainder of the paper is divided into six sections. Section 2 describes the representative agent model. Section 3 derives closed-form solutions for equity prices. The pricing of zero-coupon bonds with different maturities is explored in Section 4. Section 5 summarizes the necessary conditions for an increasing term structure of interest rates and Section 6 proves that, if certain conditions are satisfied, the equity premium increases in an environment with tax reforms. Sections 7 and 8 check the sensitivity of the results using a numerical example.

This paper generalizes the Lucas (1978) asset pricing model by introducing a flat consumption tax, which follows a two-state Markov chain. This tax does not merely affect equity securities: it affects all assets symmetrically. Whenever taxes change, asset prices need to adjust instantaneously to clear asset markets. These price changes increase the variability of expected and actual asset returns. The price adjustments are more severe for assets with long durations, such as equity and long-term bonds, than for assets with shorter durations. Individuals require higher expected returns for holding the assets with more severe price changes under plausible conditions. Tax rate changes affect asset prices even if all the tax revenues are rebated to the representative individual and the consumption process remains completely unaffected by tax changes. Stochastic taxes remain important in this case because tax changes distort the price of consumption over time and affect investment incentives. This paper makes several simplifying assumptions which could be relaxed in future work. First, the model uses a simple exchange economy without real investment opportunities to illustrate the effects of tax changes. Endogenizing real investment choices will result in a more realistic model of the economy. Second, the current tax system in the U.S. is not a flat consumption tax system. It is a progressive income tax system where some income sources are exempt from taxes (e.g., tax-deferred accounts, municipal bonds). In particular, stocks and bonds face different effective tax rates. The effects of tax reforms will differ if the effective tax on stock returns is smaller than the tax on bond returns and if the variability of the tax rates of the two assets differs. The analysis under a more realistic tax system would be interesting.