Anthony A. Smith

Income and Wealth Heterogeneity in the Macroeconomy

How do movements in the distribution of income and wealth affect the macroeconomy? We analyze this question using a calibrated version of the stochastic growth model with partially uninsurable idiosyncratic risk and movements in aggregate productivity. Our main finding is that, in the stationary stochastic equilibrium, the behavior of the macroeconomic aggregates can be almost perfectly described using only the mean of the wealth distribution. This result is robust to substantial changes in both parameter values and model specification. Our benchmark model, whose only difference from the representative‐agent framework is the existence of uninsurable idiosyncratic risk, displays far less cross‐sectional dispersion and skewness in wealth than U.S. data. However, an extension that relies on a small amount of heterogeneity in thrift does succeed in replicating the key features of the wealth data. Furthermore, this extension features aggregate time series that depart significantly from permanent income behavior.

CONSUMPTION-SAVINGS DECISIONS WITH QUASI-GEOMETRIC DISCOUNTING

How do individuals with time-inconsistent preferences make consumption-savings decisions? We try to answer this question by considering the simplest possible form of consumption-savings problem, assuming that discounting is quasi-geometric. A solution to the decision problem is then a subgame-perfect equilibrium of a dynamic game between the individuals ‘successive selves’. When the time horizon is finite, our question has a well-defined answer in terms of primitives. When the time horizon is infinite, we are left without a sharp answer: we cannot rule out the possibility that two identical individuals in the exact same situation make different decisions! In particular, there is a continuum of dynamic equilibria even if we restrict attention to equilibria where current consumption decisions depend only on current wealth.

INCOME AND WEALTH HETEROGENEITY, PORTFOLIO CHOICE, AND EQUILIBRIUM ASSET RETURNS

We derive asset-pricing and portfolio-choice implications of a dynamic incomplete-markets model in which consumers are heterogeneous in several respects: labor income, asset wealth, and preferences. In contrast to earlier papers, we insist on at least roughly matching the models implications for heterogeneity — notably, the equilibrium distributions of income and wealth — with those in U.S. data. This approach seems natural: Models that rely critically on heterogeneity for explaining asset prices are not convincing unless the heterogeneity is quantitatively reasonable. We find that the class of models we consider here is very far from success in explaining the equity premium when parameters are restricted to produce reasonable equilibrium heterogeneity. We express the equity premium as a product of two factors: the standard deviation of the excess return and the market price of risk. The first factor, as expected, is much too low in the model. The size of the market price of risk depends crucially on the constraints on borrowing. If substantial borrowing is allowed, the market price of risk is about one one-hundredth of what it is in the data (and about 15% higher than in the representative-agent model). However, under the most severe borrowing constraints that we consider, the market price of risk is quite close to the observed value.

Equilibrium Welfare and Government Policy with Quasi-Geometric Discounting

We consider a representative-agent equilibrium model where the consumer has quasi geometric discounting and cannot commit to future actions. We restrict attention to a parametric class for preferences and technology and solve for time-consistent competitive equilibria globally and explicitly. We then characterize the welfare properties of competitive equilibria and compare them to that of a planning problem. The planner is a consumer representative who, without commitment but in a time-consistent way, maximizes his presentvalue utility subject to resource constraints. The competitive equilibrium results in strictly higher welfare than does the planning problem whenever the discounting is not geometric.

MODELING EARNINGS DYNAMICS

In this paper we use indirect inference to estimate a joint model of earnings, employment, job changes, wage rates, and work hours over a career. Our model incorporates duration dependence in several variables, multiple sources of unobserved heterogeneity, job-specific error components in both wages and hours, and measurement error. We use the model to address a number of important questions in labor economics, including the source of the experience profile of wages, the response of job changes to outside wage offers, and the effects of seniority on job changes. We provide estimates of the dynamic response of wage rates, hours, and earnings to various shocks and measure the relative contributions of the shocks to the variance of earnings in a given year and over a lifetime. We find that human capital accounts for most of the growth of earnings over a career although job seniority and job mobility also play significant roles. Unemployment shocks have a large impact on earnings in the short run as well a substantial long long-term effect that operates through the wage rate. Shocks associated with job changes and unemployment make a large contribution to the variance of career earnings and operate mostly through the job-specific error components in wages and hours.

Temptation and Taxation

In this paper we attempt to (i) extend the competitive equilibrium neoclassical growth model to incorporate consumer preferences that are of the Gul-Pesendorfer variety; (ii) use the model to analyze taxation and welfare; and (iii) extend and specialize the Gul-Pesendorfer temptation formulation to be dynamic and, in particular, quasi-geometric, thus providing a link to, and possibly an interpretation of, the Laibson model.

Is Piketty's "Second Law of Capitalism" Fundamental?

In Capital in the Twenty-First Century , Thomas Piketty uses what he calls “the second fundamental law of capitalism” to predict that capital-to-income ratios are poised to increase dramatically as economies’ growth rates fall during the twenty-first century. This law states that in the long run the capital-to-income ratio equals s=g, where s is the economy’s saving rate and g its growth rate. We argue that this law rests on a theory of saving that is hard to justify. First, it holds the net saving rate constant as growth falls, driving the gross savings rate to one as growth goes to zero. Second, it is inconsistent with both the textbook growth model and the theory of optimal saving: in both of these theories the net saving rate goes to zero as growth goes to zero. Third, both of these theories provide a reasonable fit to observed data on gross and net saving rates and growth rates in cross-country panel data, whereas Piketty’s does not. Finally, contrary to Piketty’s second law, both of these theories predict that capital-to-income ratios increase only modestly as growth falls.

Rules of thumb in macroeconomic equilibrium A quantitative analysis

Abstract We investigate the robustness of the general equilibrium stochastic growth model to the introduction of small costs of behavioral sophistication. Consumers choose amongst savings rules which vary in sophistication and effort cost. In our model, a given consumers gain from using a sophisticated rule is higher when other consumers use simple rules. Thus, decentralization makes it harder for simple rules to survive than in similar decision-theoretic models. Nevertheless, we find: 1. (i) that sophisticated behavior, which we model as fully unrestricted, occurs in equilibrium only if its relative effort cost is extremely low; and 2. (ii) that rule-of-thumb economies can generate aggregate time series that differ substantially from those of the standard model.

A Sequential Game Model of Sports Championship Series: Theory and Estimation

Using data from professional baseball, basketball, and hockey, we estimate the parameters of a sequential game model of best-of-n championship series controlling for measured and unmeasured differences in team strength and bootstrapping the maximum-likelihood estimates to improve their small sample properties. We find negligible strategic effects in all three sports: teams play as well as possible in each game regardless of the games importance in the series. We also estimate negligible unobserved heterogeneity after controlling for regular season records and past appearance in the championship series: Teams are estimated to be exactly as strong as they appear on paper.

Inferring Labor Income Risk and Partial Insurance From Economic Choices

This paper uses the information contained in the joint dynamics of individuals labor earnings and consumption‐choice decisions to quantify both the amount of income risk that individuals face and the extent to which they have access to informal insurance against this risk. We accomplish this task by using indirect inference to estimate a structural consumption–savings model, in which individuals both learn about the nature of their income process and partly insure shocks via informal mechanisms. In this framework, we estimate (i) the degree of partial insurance, (ii) the extent of systematic differences in income growth rates, (iii) the precision with which individuals know their own income growth rates when they begin their working lives, (iv) the persistence of typical labor income shocks, (v) the tightness of borrowing constraints, and (vi) the amount of measurement error in the data. In implementing indirect inference, we find that an auxiliary model that approximates the true structural equations of the model (which are not estimable) works very well, with negligible small sample bias. The main substantive findings are that income shocks are moderately persistent, systematic differences in income growth rates are large, individuals have substantial amounts of information about their income growth rates, and about one‐half of income shocks are smoothed via partial insurance. Putting these findings together, the amount of uninsurable lifetime income risk that individuals perceive is substantially smaller than what is typically assumed in calibrated macroeconomic models with incomplete markets.