مالیات، ریسک پذیری و رشد: تجزیه و تحلیل تعادل عمومی تصادفی با پیوستگی زمانی با انتخاب کار و اوقات فراغت

This paper investigates the equilibrium relationship between taxation, portfolio choice (risk-taking) and capital accumulation. Specifically, it examines how taxes affect risk-taking and capital accumulation. We extend the existing literature by relaxing two crucial assumptions in modelling risk-taking behavior: (i) that the investment opportunity set is fixed and (ii) that there is no distinction between attitudes towards risk and behavior towards intertemporal substitution. We extend the investment opportunity set of individuals through optimally determined human capital; and distinguish intertemporal substitution from attitudes towards risk via a recursive utility function. In the presence of these extensions, the paper successfully derives a closed-form solution to the stochastic growth model with stochastic wage income.

The relationship between taxation, risk-taking and economic growth has been the topic of several papers in recent years (see Sandmo, 1989; Turnovsky, 1993; Smith, 1996b; Asea and Turnovsky, 1998, inter alia). Asea and Turnovsky (1998), for example, analyze the effect of taxes on capital income on risk taking and capital accumulation to address the question of whether taxing the return on investment increases the total amount of investment and the total amount of risk undertaken. This paper builds on this literature and extends it in two important directions. First, we explore the interaction between taxation, risk-taking and capital accumulation in a model with labor supply flexibility. We allow the labor-leisure choice to be endogenously determined within the model. This allows us to examine the impact of taxation on both capital and labor income on the growth rate, the volatility of the growth rate and the shares of equity, government bonds and the safe asset in the optimal portfolio. In order to carry out this analysis the paper successfully derives a closed-form solution to the stochastic growth model with stochastic wage income. Second, we distinguish between attitudes towards risk (the desire to smooth consumption across states of nature) and attitudes towards intertemporal substitution (the desire to smooth consumption across time). To explore the interaction between taxation, risk-taking and capital accumulation in a model with labor supply flexibility and the separation of risk aversion and intertemporal substitutability, we adopt the continuous-time stochastic dynamic general equilibrium framework developed by (Eaton, 1981) and lately extended by (Grinols and Turnovsky, 1993).1 Since the analytical framework is essentially an intertemporal CAPM in general equilibrium, the model is ideally suited to the analysis of the interactions between taxation, portfolio choice and growth. This offers an advantage over the models used in the endogenous growth theory literature, which explain the mean of the growth rate, and the real business cycle literature, which explains the variability of the growth rate. Since the former literature is interested in the first moment while the latter deals with the second moment, neither is useful for analyzing portfolio choice issues. Our model does not suffer from this shortcoming. We extend the Eaton–Grinols–Turnovsky (EGT) type of the continuous-time stochastic dynamic general equilibrium model: (i) to incorporate endogenous labor supply along the lines of (Bodie et al., 1992a) and (ii) to relax the parametric restriction on risk aversion and intertemporal substitution imposed by the expected utility function by adopting ‘generalized isoelastic preferences’ along the lines of Svensson (1989), Grinols (1996) and Obstfeld (1994b). Recently, the first extension has been received a considerable attention in the literature since the optimal choice of labor-leisure generates a flexible investment opportunity set, and thereby affects the optimal portfolio choice and furthermore leads to time-varying portfolio choice as opposed to the atemporal portfolio choice that is established in the classical Merton model (see Merton, 1969). However, mostly these papers use a partial equilibrium analysis (see Elmendorf and Kimball, 2000). To our knowledge, Basak (1999), Turnovsky (2000) and Turnovsky and Chattopadhyay (2003) are the only three papers which model labor in a continuous time general equilibrium framework. Basak (1999) provides analytical comparative static analysis of the effects of labor-leisure choice on consumption, stock market, and other fluctuations without explicitly solving it. There are also other limitations in the model of Basak: there is no capital and his analysis is restricted to the expected utility case. This is not surprising since there is no general solution to the precautionary savings problem with CRRA utility. Therefore, either the focus of the EGT class of stochastic growth models is restricted to models without wage income or models assume no capital as in Basak (1999). Unlike Basak (1999), Turnovsky (2000) and Turnovsky and Chattopadhyay (2003) explicitly solve the problem and examines the growth and welfare effects of taxation and public expenditure. Our approach is close to that of Turnovsky (2000) and Turnovsky and Chattopadhyay (2003) but we use a different solution method and model labor differently both on the supply side and on the demand side. The significance of the solution method used in this paper is that it is firmly based on the contingent claims pricing idea of finance theory. More precisely, we apply the human capital valuation method developed by Bodie et al. (1992b) in order to derive a closed-form solution by exploiting the fact that in EGT models wage growth is perfectly correlated with the rate of return to the risky asset. We allow the tax rates on the deterministic components of capital income and labor income to be different from the tax rates on the stochastic components of capital income and labor income. This reflects the possibility that the tax code might include offset provisions which have the effect of taxing the stochastic components of asset returns differently from the expected component. The explicit introduction of stochastic elements brings new insights to bear on familiar questions and issues in economics. First, agents may care not only about the first moment of income or prices but also about their second moment. The first moment is usually the concern of standard deterministic models, such as representative agent and overlapping generations models, in which uncertainty is effectively assumed away. In the finance literature, however, the conditional variance of income or prices is as important as the mean and therefore needs to be considered. Second, it is likely that taxes will affect the variance as well as the mean return to an investment. Since taxes reduce the variance and encourage agents to hold risky assets in a stochastic environment, tax policy design issues arise. Furthermore, our work also shed lights into the two recent issues: (i) the relationship between growth and volatility and (ii) estimate how much current consumption society would be willing to forgo to avoid volatility. The literature on growth is challengingly ambiguous: the relationship is positive or negative depending on the theoretical model used and existing empirical evidence does not resolve the conflict.2 In the literature following Lucas (1987) there is ongoing development and refinement of his measure of the welfare costs of macroeconomic volatility.3 Now, to the extent that changes in economic welfare are determined by what happens to growth, these two literatures have a common focus. However, the methods and models utilized in these literatures are sufficiently different to have served to create something of a dichotomy between them. In this paper, we utilize a framework which allows us to consider the growth and welfare effects of volatility as jointly determined; and explore the role of preference-related deep parameters in changing the scale and direction of influence of volatility on growth and welfare. The rest of the paper is organized as follows. Section 2 outlines our continuous time stochastic dynamic general equilibrium model with recursive utility and endogenous labor income. Section 3 considers the optimal saving and portfolio choice decision. We numerically analyze the model in Section 4 while Section 5 discusses possible extensions to the model. Section 6 provides some concluding remarks.

In this paper, we have developed a stochastic dynamic general equilibrium model of the relationship between taxation, risk-taking and capital accumulation. This model extends the current literature in two ways. First, we extend the model to include the supply of labor. This allows us to analyze the effects of labor income on capital accumulation and the effects of taxation on labor income on economic growth. We allow the supply of labor to be endogenously determined and find that the flexibility and uncertainty this generates for labor income significantly affect risk-taking and capital accumulation. Even allowing the supply of labor to be exogenously fixed significantly influences the results. Second, we allow the representative household to maximize a stochastic differential utility function that breaks the relationship between the coefficient of relative risk aversion and the elasticity of intertemporal substitution. Using this specification of utility, we are able to show that the optimal consumption and portfolio choice is driven not only by attitudes towards risk but also by the intertemporal elasticity of substitution. We analyze the model numerically and find that increasing tax rate on the deterministic component of capital income reduces the mean growth rate while increasing its variance. This reduction in the growth rate and increase in the variance of the growth rate is far more pronounced when labor is introduced into the model. Increasing the tax rate on the deterministic component of capital income leads to a reduction in investment in the productive asset (equity) and an increase in investment in the unproductive risky asset (government bonds). These findings support those of Asea and Turnovsky (1998). Increasing the tax rate on the stochastic component of capital income has the opposite effect to an increase in the tax rate on the deterministic component, encouraging investment in equity and increasing the growth rate. Increasing the tax rate on labor income has the same effect as increasing the tax rate on capital income, although the magnitude of the effects is far less pronounced. We identify two extensions to the model developed in this paper are worth pursuing. First, the model could be extended to incorporate undiversifiable labor income risk. Second, the model could be extended to consider the effect of shocks to the distribution of factor incomes. Both will change the correlation between wage income and capital income and since human capital is a risky asset, it is likely that the proportion of financial wealth invested in this asset will alter. Finally, it should be noted that the model we develop is relevant for the analysis of international finance issues and monetary issues. It is possible to open up the economy by allowing for international trade and/or international capital mobility. Money can be introduced into the model either through a cash-in-advance constraint or through the structure of utility. With these extensions, this framework is suitable for calibrated analyzes of issues such as the Feldstein–Horioka puzzle, the optimality of interest rate smoothing and the welfare cost of volatility.