Knowledge that Transforms

This paper proposes a test for common conditionally heteroskedastic (CH) features in asset returns. Following Engle and Kozicki (1993), the common CH features property is expressed in terms of testable overidentifying moment restrictions. However, as we show, these moment conditions have a degenerate Jacobian matrix at the true parameter value and therefore the standard asymptotic results of Hansen (1982) do not apply. We show in this context that Hansen's (1982) J-test statistic is asymptotically distributed as the minimum of the limit of a certain random process with a markedly nonstandard distribution. If two assets are considered, this asymptotic distribution is a fifty–fifty mixture of χ2H−1 and χ2H, where H is the number of moment conditions, as opposed to a χ2H−1. With more than two assets, this distribution lies between the χ2H−p and χ2H (p denotes the number of parameters). These results show that ignoring the lack of first-order identification of the moment condition model leads to oversized tests with a possibly increasing overrejection rate with the number of assets. A Monte Carlo study illustrates these findings.

We present two examples of discounted stochastic games, each with a continuum of states, finitely many players, and actions, that possess no stationary equilibria. The first example has deterministic transitions—an assumption undertaken in most of the early applications of dynamics games in economics—and perfect information, and does not possess even stationary approximate equilibria or Markovian equilibria. The second example satisfies, in addition to stronger regularity assumptions, that all transitions are absolutely continuous with respect to a fixed measure—an assumption that has been widely used in more recent economic applications. This assumption has been undertaken in several positive results on the existence of stationary equilibria in special cases, and in particular, guarantees the existence of stationary approximate equilibria.

We study whether priors that admit full surplus extraction (FSE) are generic, an issue that becomes a gauge to evaluate the validity of the current mechanism design paradigm. We consider the space of priors on the universal type space, and thereby relax the assumption of a fixed finite number of types made by Crémer and McLean (1988). We show that FSE priors are topologically generic, contrary to the result of Heifetz and Neeman (2006) that FSE is generically impossible, both geometrically and measure-theoretically. Instead of using the BDP approach or convex combinations of priors adopted in Heifetz and Neeman (2006), we prove our genericity results by showing a robustness property of Crémer–McLean mechanisms.

A group of peers must choose one of them to receive a prize; everyone cares only about winning, not about who gets the prize if someone else. An award rule is impartial if one's message never influences whether or not one wins the prize. We explore the consequences of impartiality when each agent nominates a single (other) agent for the prize. On the positive side, we construct impartial nomination rules where both the influence of individual messages and the requirements to win the prize are not very different across agents. Partition the agents in two or more districts, each of size at least 3, and call an agent a local winner if he is nominated by a majority of members of his own district; the rule selects a local winner with the largest support from nonlocal winners, or a fixed default agent in case there is no local winner. On the negative side, impartiality implies that ballots cannot be processed anonymously as in plurality voting. Moreover, we cannot simultaneously guarantee that the winner always gets at least one nomination, and that an agent nominated by everyone else always wins.

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or, equivalently, the value of a linear programming problem with a potentially infinite constraint set. We show that many bounds characterizations in econometrics, for instance bounds on parameters under conditional moment inequalities, can be formulated as intersection bounds. Our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are nonseparable in parameters. Since analog estimators for intersection bounds can be severely biased in finite samples, routinely underestimating the size of the identified set, we also offer a median-bias-corrected estimator of such bounds as a by-product of our inferential procedures. We develop theory for large sample inference based on the strong approximation of a sequence of series or kernel-based empirical processes by a sequence of “penultimate” Gaussian processes. These penultimate processes are generally not weakly convergent, and thus are non-Donsker. Our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes. Our construction also provides new adaptive inequality/moment selection methods. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for any general series estimator admitting linearization, which may be of independent interest.

Using centuries of Nile flood data, I document that during deviant Nile floods, Egypt's highest-ranking religious authority was less likely to be replaced and relative allocations to religious structures increased. These findings are consistent with historical evidence that Nile shocks increased this authority's political influence by raising the probability he could coordinate a revolt. I find that the available data provide support for this interpretation and weigh against some of the most plausible alternatives. For example, I show that while Nile shocks increased historical references to social unrest, deviant floods did not increase a proxy for popular religiosity. Together, the results suggest an increase in the political power of religious leaders during periods of economic downturn. [PUBLICATION ABSTRACT]

This paper examines three distinct hypothesis testing problems that arise in the context of identification of some nonparametric models with endogeneity. The first hypothesis testing problem we study concerns testing necessary conditions for identification in some nonparametric models with endogeneity involving mean independence restrictions. These conditions are typically referred to as completeness conditions. The second and third hypothesis testing problems we examine concern testing for identification directly in some nonparametric models with endogeneity involving quantile independence restrictions. For each of these hypothesis testing problems, we provide conditions under which any test will have power no greater than size against any alternative. In this sense, we conclude that no nontrivial tests for these hypothesis testing problems exist.

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. 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 also study 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 as a substantial 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 of wages and hours.

We study selection rules: voting procedures used by committees to choose whether to place an issue on their agenda.At the selection stage of the model, committee members are uncertain about their final preferences.They only have some private information about these preferences.We show that voters become more conservative when the selection rule itself becomes more conservative.The decision rule has the opposite effect.We compare these voting procedures to the designation of an agenda setter among the committee, and to a utilitarian social planner with all the ex interim private information.

This paper is concerned with robust estimation under moment restrictions. A moment restriction model is semiparametric and distribution-free; therefore it imposes mild assumptions. Yet it is reasonable to expect that the probability law of observations may have some deviations from the ideal distribution being modeled, due to various factors such as measurement errors. It is then sensible to seek an estimation procedure that is robust against slight perturbation in the probability measure that generates observations. This paper considers local deviations within shrinking topological neighborhoods to develop its large sample theory, so that both bias and variance matter asymptotically. The main result shows that there exists a computationally convenient estimator that achieves optimal minimax robust properties. It is semiparametrically efficient when the model assumption holds, and, at the same time, it enjoys desirable robust properties when it does not.