A choice function is backwards-induction rationalizable if there exists a finite perfect-information extensive-form game such that for each subset of alternatives, the backwards-induction outcome of the restriction of the game to that subset of alternatives coincides with the choice from that subset. We prove that every choice function is backwards-induction rationalizable.
We study the asymptotic distribution of three-step estimators of a finite-dimensional parameter vector where the second step consists of one or more nonparametric regressions on a regressor that is estimated in the first step. The first-step estimator is either parametric or nonparametric. Using Newey's (1994) path-derivative method, we derive the contribution of the first-step estimator to the influence function. In this derivation, it is important to account for the dual role that the first-step estimator plays in the second-step nonparametric regression, that is, that of conditioning variable and that of argument.
In this note, we prove an equilibrium existence theorem for games with discontinuous payoffs and convex and compact strategy spaces. It generalizes the classical result of Reny (1999), as well as the recent paper of McLennan, Monteiro, and Tourky (2011). Our conditions are simple and easy to verify. Importantly, examples of spatial location models show that our conditions allow for economically meaningful payoff discontinuities, that are not covered by other conditions in the literature.
We consider the estimation of dynamic panel data models in the presence of incidental parameters in both dimensions: individual fixed-effects and time fixed-effects, as well as incidental parameters in the variances. We adopt the factor analytical approach by estimating the sample variance of individual effects rather than the effects themselves. In the presence of cross-sectional heteroskedasticity, the factor method estimates the average of the cross-sectional variances instead of the individual variances. The method thereby eliminates the incidental-parameter problem in the means and in the variances over the cross-sectional dimension. We further show that estimating the time effects and heteroskedasticities in the time dimension does not lead to the incidental-parameter bias even when T and N are comparable. Moreover, efficient and robust estimation is obtained by jointly estimating heteroskedasticities.
We develop an asymptotic theory for the pre-averaging estimator when asset price jumps are weakly identified, here modeled as local to zero. The theory unifies the conventional asymptotic theory for continuous and discontinuous semimartingales as two polar cases with a continuum of local asymptotics, and explains the breakdown of the conventional procedures under weak identification. We propose simple bias-corrected estimators for jump power variations, and construct robust confidence sets with valid asymptotic size in a uniform sense. The method is also robust to certain forms of microstructure noise.
We take cohorts of entering freshmen at the United States Air Force Academy and assign half to peer groups designed to maximize the academic performance of the lowest ability students. Our assignment algorithm uses nonlinear peer effects estimates from the historical pre-treatment data, in which students were randomly assigned to peer groups. We find a negative and significant treatment effect for the students we intended to help. We provide evidence that within our “optimally” designed peer groups, students avoided the peers with whom we intended them to interact and instead formed more homogeneous subgroups. These results illustrate how policies that manipulate peer groups for a desired social outcome can be confounded by changes in the endogenous patterns of social interactions within the group.
Across a wide set of nongroup insurance markets, applicants are rejected based on observable, often high-risk, characteristics. This paper argues that private information, held by the potential applicant pool, explains rejections. I formulate this argument by developing and testing a model in which agents may have private information about their risk. I first derive a new no-trade result that theoretically explains how private information could cause rejections. I then develop a new empirical methodology to test whether this no-trade condition can explain rejections. The methodology uses subjective probability elicitations as noisy measures of agents' beliefs. I apply this approach to three nongroup markets: long-term care, disability, and life insurance. Consistent with the predictions of the theory, in all three settings I find significant amounts of private information held by those who would be rejected; I find generally more private information for those who would be rejected relative to those who can purchase insurance, and I show it is enough private information to explain a complete absence of trade for those who would be rejected. The results suggest that private information prevents the existence of large segments of these three major insurance markets.
We investigate the role of deeply-rooted pre-colonial ethnic institutions in shaping comparative regional development within African countries. We combine information on the spatial distribution of ethnicities before colonization with regional variation in contemporary economic performance, as proxied by satellite images of light density at night. We document a strong association between pre-colonial ethnic political centralization and regional development. This pattern is not driven by differences in local geographic features or by other observable ethnic-specific cultural and economic variables. The strong positive association between pre-colonial political complexity and contemporary development obtains also within pairs of adjacent ethnic homelands with different legacies of pre-colonial political institutions.
This paper derives optimal inheritance tax formulas that capture the key equity-efficiency trade-off, are expressed in terms of estimable sufficient statistics, and are robust to the underlying structure of preferences. We consider dynamic stochastic models with general and heterogeneous bequest tastes and labor productivities. We limit ourselves to simple but realistic linear or two-bracket tax structures to obtain tractable formulas. We show that long-run optimal inheritance tax rates can always be expressed in terms of aggregate earnings and bequest elasticities with respect to tax rates, distributional parameters, and social preferences for redistribution. Those results carry over with tractable modifications to (a) the case with social discounting (instead of steady-state welfare maximization), (b) the case with partly accidental bequests, (c) the standard Barro–Becker dynastic model. The optimal tax rate is positive and quantitatively large if the elasticity of bequests to the tax rate is low, bequest concentration is high, and society cares mostly about those receiving little inheritance. We propose a calibration using micro-data for France and the United States. We find that, for realistic parameters, the optimal inheritance tax rate might be as large as 50%–60%—or even higher for top bequests, in line with historical experience.
The aim of this paper is to develop revealed preference tests for Cournot equilibrium. The tests are akin to the widely used revealed preference tests for consumption, but have to take into account the presence of strategic interaction in a game-theoretic setting. The tests take the form of linear programs, the solutions to which also allow us to recover cost information on the firms. To check that these nonparametric tests are sufficiently discriminating to reject real data, we apply them to the market for crude oil.