This paper examines the asymptotic risk of nested least-squares averaging estimators when the averaging weights are selected to minimize a penalized least-squares criterion. We find conditions under which the asymptotic risk of the averaging estimator is globally smaller than the unrestricted least-squares estimator. For the Mallows averaging estimator under homoskedastic errors, the condition takes the simple form that the regressors have been grouped into sets of four or larger. This condition is a direct extension of the classic theory of James–Stein shrinkage. This discovery suggests the practical rule that implementation of averaging estimators be restricted to models in which the regressors have been grouped in this manner. Our simulations show that this new recommendation results in substantial reduction in mean-squared error relative to averaging over all nested submodels. We illustrate the method with an application to the regression estimates of Fryer and Levitt (2013).

]]>This paper establishes conditions for nonparametric identification of dynamic optimization models in which agents make both discrete and continuous choices. We consider identification of both the payoff function and the distribution of unobservables. Models of this kind are prevalent in applied microeconomics and many of the required conditions are standard assumptions currently used in empirical work. We focus on conditions on the model that can be implied by economic theory and assumptions about the data generating process that are likely to be satisfied in a typical application. Our analysis is intended to highlight the identifying power of each assumption individually, where possible, and our proofs are constructive in nature.

]]>We consider the decomposition of shocks to a dynamic process into a persistent and a transitory component. Without additional assumptions (such as zero correlation) the decomposition of shocks into a persistent and transitory component is indeterminate. The assumption that is conventional in the earnings literature is that there is no correlation. The Beveridge–Nelson decomposition that is widely used in time series analysis assumes a perfect correlation. Without restrictions on the correlation, the persistent-transitory decomposition is only set-identified. For reasonable autoregressive moving average (ARMA) parameters the bounds for widely used objects of interest are very wide. We illustrate that these disquieting findings are of considerable practical importance, using a sample of male workers drawn from the Panel Study of Income Dynamics (PSID).

]]>Differences in college enrollment between poor and rich are striking in Latin America. Explanations such as differences in college preparedness and credit constraints have been advanced. An alternative explanation could be differences in information sets between poor and rich, for example, about career opportunities, translating into different expected returns to college. Poor people might expect low returns and thus decide not to attend or they might face high (unobserved) costs that prevent them from attending despite high expected returns. I use data on people's subjective expectations of returns to address this identification problem. I find that poor individuals require higher expected returns to be induced to attend college than individuals from rich families. Testing predictions of a model of college attendance shows that poor individuals are particularly responsive to changes in direct costs, which is consistent with them being credit constrained. Performing counterfactual policy experiments, I find that a sizeable fraction of poor individuals would change their decision in response to a reduction in direct costs and that these individuals at the margin have expected returns that are as high or higher than the individuals already attending college.

]]>Are households more likely to be homeowners when “housing risk” is higher? We show that home-ownership rates and loan-to-value (LTV) ratios at the city level are strongly negatively correlated with local house price volatility. However, causal inference is confounded by house price levels, which are systematically correlated with housing risk in an intuitive way: in cities where the land value is larger relative to the local cost of structures, house prices are higher and more volatile. We disentangle the contributions of high price levels from high volatilities by building a life-cycle model of home-ownership choices. We find that higher price levels can explain most of the lower home-ownership. Higher risk in the model leads to slightly lower home-ownership and LTV ratios in high land value cities. The relationship between LTV and risk is corroborated by LTV's negative correlation with price volatility in the data and highlights the importance of including other means of incomplete insurance in models of home-ownership.

]]>The aim of this paper is to study the relationship between the intertemporal behavior of taxes and wealth distribution. The optimal-taxation literature has often concentrated on representative-agent models, in which it is optimal to smooth distortionary taxes. When tax liabilities are unevenly spread in the population, deviations from tax smoothing lead to interest rate changes that redistribute wealth. When a “bad shock” hits the economy, the optimal policy will then call for smaller or larger deficits, depending on the political power of different groups. This effect is particularly relevant in the case of large shocks to government finances, such as wars.

]]>How do families behave dynamically? We provide a framework for studying economic problems in which family behavior is essential. Our key innovation is the inclusion of imperfectly altruistic agents in an otherwise standard consumption–savings problem with exogenous income risk. This gives rise to altruistic transfers and strategic behavior in the consumption–savings decision. We study the Markov-perfect equilibrium that arises from the limit of equilibria in a sequence of finite games. The equilibrium's transfer patterns are empirically plausible. Furthermore, agents overconsume relative to the social optimum. In contrast to two-period models, *both* the richer and the poorer players overconsume long before transfers actually occur. The poorer agent also faces incentives to engage in excessive risk-taking because losses from a gamble are absorbed by both while gains are enjoyed alone.