پویایی نابرابری و امنیت اجتماعی در تعادل عمومی

This paper analyzes the dynamic politico-economic equilibrium of a model where repeated voting on social security and the evolution of household characteristics in general equilibrium are mutually affected over time. In particular, we incorporate within-cohort heterogeneity in a two-period Overlapping-Generation model to capture the intra-generational redistributive effect of social security transfers. Political decision-making is represented by a probabilistic voting à la Lindbeck and Weibull (1987). We analytically characterize the Markov perfect equilibrium, in which social security tax rates are shown to be increasing in wealth inequality. A dynamic interaction between inequality and social security leads to larger social security programs. In a model calibrated to the U.S. economy, the dynamic interaction is shown to be quantitatively important: It accounts for more than half of the social security growth in the dynamics. We also perform some normative analysis, showing that the politico-economic equilibrium outcomes can be fundamentally different from the Ramsey allocation.

Most developed countries have large public pension programs, involving both inter-generational and intra-generational transfers. For instance, social security contributions are roughly proportional to income, while benefits have important lump- sum components. The general equilibrium effects and the welfare implications of such social security programs have been extensively studied in the literature. 1 However, the welfare state is not exogenously imposed, but endogenously determined by policy choices that reflect rich dynamic interactions between political and economic factors. For instance, the evolution of the distribution of household characteristics in general equilibrium may alter the political support for the social security system since households with different characteristics tend to have different preferences over transfers. Despite this, most of the existing literature has either assumed away politico-economic factors or, when considering them, focused on models where the size of social security is decided once and for all. As a result, the feedback of endogenous changes of household characteristics on the decision of social security transfers over time has been ignored altogether (e.g., Tabellini, 2000; Cooley and Soares, 1999; Conesa and Krueger, 1999). 2 The present paper explores the positive implications and the welfare properties of a rational-choice theory implying interactions between private intertemporal choices and repeated political decisions about social security. To this end, we construct a dynamic general equilibrium model where agents repeatedly vote on the social security system. Our analytical results show that the dynamic interaction between inequality and social security leads to larger social security programs. In a model calibrated to the U.S. economy, the dynamic interaction is shown to be quantitatively important: It accounts for more than half of the social security growth in the dynamics. We also perform some normative analysis, showing that the politico-economic equilibrium outcomes can be fundamentally different from the Ramsey allocation chosen by a benevolent planner with a commitment technology. In our model, the incumbent government cannot commit to future transfers since they are decided by future elected governments. Instead, transfers are determined in each period by the current constituency, the wealth inequality of which is a key factor. Forward-looking households adjust their private savings when rationally anticipating the equilibrium dynamics of wealth inequality and social security. A main theoretical finding is that this interaction leads to an equilibrium where social security transfers increase over time. The underlying mechanism is twofold. On the one hand, the establishment of a social security increases future wealth inequality since within-cohort transfers discourage the private savings of low-income households more than proportionally. On the other hand, larger wealth inequality makes transfers more desirable in the future. This provides the political support for an increasing size of social security in subsequent periods. Our workhorse is a standard two-period Overlapping-Generation model. To capture the intra-generational redistributive role of social security, we incorporate within-cohort heterogeneity by assuming young households to be born with different labor productivities. Old households are different in terms of wealth. In other words, there exists multi-dimensional hetero- geneity across voters. Each group of voters has its own preferences over transfers. The political decision process is modeled by a repeated probabilistic voting framework. 3 In equilibrium, policymaker candidates respond to electoral uncertainty by proposing a policy platform that maximizes a weighted-average welfare of all groups of voters. We focus on Markov perfect equilibria, where the size of social security is conditioned on payoff-relevant fundamental elements: the distribution of assets held by old households and the demographic structure. The Markov perfect equilibrium is obtained as one takes the limit of a finite horizon environment. 4 Moreover, under logarithm utility and Cobb–Douglas pro- duction technology, the equilibrium can be characterized analytically, making the underlying politico-economic mechanism highly transparent. In particular, we show that the equilibrium social security tax rate is increasing in wealth inequality, and this positive relationship generates growing social security over time. When calibrated to the U.S. economy from 1947 to 1969, the model predicts the initial and steady state social security tax rate of 3 . 5 percent and 7 . 2 percent, respectively. The growth of the tax rate is quantitatively close to the data, though the level of tax rate is higher: The average Old-Age and Survivors Insurance (OASI henceforth) contribution rate increases from 2 percent in the 1930s to 4 . 7 percent in the period from 1947 to 1969. The exercise also suggests that the dynamic interaction between inequality and social security is quanti- tatively important: It generates a 3 . 7-percentage-point increase of the tax rate in the dynamics. We then extend the model by incorporating the ageing population in the U.S. The average dependency ratio rises to 19 . 3 percent from 1970 to 2000, substantially higher than 15 . 7 percent from 1947 to 1969. Such a change will lead to a further increase in the size of social security. The extended model predicts a tax rate of 9 percent, which is roughly in line with the average OASI contribution rate of 9 . 8 percent in the 1970 to 2000 period. In addition, more social security benefits make wealth distribution more unequal. The Gini coefficient of wealth in the model economy increases by 3 . 4 percent. This might explain a significant part of the 10-percent increase in the Gini coefficient of household financial wealth in the Survey of the Financial Characteristics of Consumers (SFCC henceforth) and the Survey of Consumer Finances (SCF henceforth) from the 1960s to the 1980s. The tractable model allows a comparison between the politico-economic equilibrium outcome and the Ramsey allocation, in which a benevolent planner with a commitment technology maximizes the discounted sum of the welfare of all current and future generations. Under logarithm utility and Cobb–Douglas production technology, the Ramsey solution can also be characterized analytically. We find that the Ramsey solution may feature a decreasing size of social security if the social discount factor is not too small. This sharply contrasts growing transfers in the political equilibrium. The basic intuition is straightforward. The initial inelastic capital stock provides the incentive for the Ramsey planner to impose high taxes for redistributive reasons. 5 However, since she can commit to future policies, low taxation will be adopted for encouraging capital accumulation in periods other than the initial one It is worth emphasizing that in Markov equilibria, voters not only hold rational expectations on future equilibrium outcomes, but may also strategically affect future policies via the impact of current policies on private intertemporal choices. Under logarithm utility, the current tax rate does not affect household saving rates due to a cancellation of the income and substitution effects. Thus, it cannot affect future states of the economy (wealth distribution) or future policy outcomes. In other words, strategic effects are mute in the particular case of logarithm utility. Strategic effects appear when the intertemporal elasticity of substitution is different from unity. In these cases, analytical results cannot be obtained, but we can numerically study the qualitative and quantitative impact of strategic effects. We show that if the intertemporal elasticity of substitution is smaller than unity, as many empirical studies suggest, the strategic effect is positive. A higher tax rate today widens wealth inequality tomorrow and, hence, leads to larger transfers tomorrow. Due to the positive strategic effect, current voters have the incentive to strategically raise the current social security tax rate in order to harvest larger future transfers. The calibrated economy indicates that the strategic effect in Markovian equilibria is quantitatively unimportant: The relative increase in transfers due to the strategic effect is less than 5 percent. Although the sustainability of the social security system has been widely discussed in the literature, 6 its dynamic pat- terns have been much less investigated. Some pioneering studies abstracting repeated voting include Verbon (1987) and Boadway and Wildasin (1989). More recently, Forni (2005) shows that in a repeated political decision process, self-fulfilled expectations on the positive relationship between current and future social security transfers can lead to a growing pension scheme. The present paper extends the literature by linking the evolution of the system to some economic fundamentals – i.e., wealth distribution. Our model suggests that, though the inter-generational redistributive effect is key to sustain the system, the intra-generational redistributive effect plays a central role in the evolution of social security in general equi- librium. In particular, the interaction between transfers and wealth inequality can generate the growth of social security. Hassler et al. (2003) investigate the political sustainability of a welfare system with both inter- and intra-generational redis- tribution. In their model, the size of the rich and of the poor is determined by human capital investment. The endogenous political constituency implies strong strategic effects that may even result in multiple equilibria. With a focus on wealth accumulation, our paper shuts down the channel through which private intertemporal choices affect political constituency at the extensive margin. This results in a much weaker strategic effect. Our work is part of a growing literature on dynamic politico-economic equilibrium, where current voting may change fundamentals in the future political environment and, hence, affect future policy outcomes. Because of the complexity of dynamic interaction between individual intertemporal choice and voting strategy, analytical results are usually unattainable, except in some small open economies (e.g., Hassler et al., 2003; Azzimonti Renzo, forthcoming). An exception is Gonzalez- Eiras and Niepelt (2008), which shows that a closed-form solution of social security transfers can be obtained in a growth model with logarithm utility and Cobb–Douglas production technology. However, the equilibrium policy rule degenerates into a constant in their model with constant population growth. The present paper generalizes Gonzalez-Eiras and Niepelt’s work by incorporating within-cohort heterogeneity, keeping all results analytical. 7 The generalization gives an equilibrium policy rule which is non-trivially dependent of fundamental elements in the politico-economic environment and, hence, provides much richer implications for the dynamics of policies. This also contrasts the literature that resorts to numerical characterizations for non-trivial equilibrium policy rules in general equilibrium (e.g., Krusell et al., 1997; Krusell and Rios- Rull, 1999). The rest of the paper is organized as follows. Section 2 presents the model. In Section 3, the dynamic politico-economic equilibrium is defined and solved under logarithm utility. Quantitative exercises are conducted in Section 4. Section 5 characterizes the Ramsey allocation. In Section 6, we solve numerically the political equilibrium under a more general CRRA utility form. Section 7 concludes.

Redistributive transfers in the pay-as-you-go social security system create conflicts of interest among various groups of households. The evolution of household characteristics may change the political support for the system over time. Despite extensive studies of the aggregate and distributive effects of social security, most of the existing literature is silent on how the public decision on social security responds to time-varying political supports in dynamic general equilibrium. In this paper, we analytically characterize the Markov perfect political equilibrium, in which private intertemporal choices and the repeated political decision on social security are mutually affected over time. The main finding is that the dynamic interaction between social security and wealth inequality leads to the growing size of social security. This result may shed light on the increasing generosity of social security in OECD countries during the post-war period (Breyer and Craig, 1997). In addition, the dynamic interaction is shown to be quantitatively important: It accounts for more than half of the social security growth in the dynamics. Our analysis is subject to a number of caveats. For instance, the theory is completely silent on the structure of so- cial security. An interesting extension is to analyze the determination of the size of social security and the degree of its redistributiveness simultaneously. 34 For analytical convenience, we impose a balanced budget on social security transfers. A natural extension of the model would be to relax this assumption. In a related work, Song et al. (2007) analyze the determination of public debt in a small open economy without social security. It will be interesting for future research to incorporate government borrowing into the current setup, to see how public debt interacts with social security.