Many dynamic problems in economics are characterized by large state spaces which make both computing and estimating the model infeasible. We introduce a method for approximating the value function of highdimensional dynamic models based on sieves and establish results for the (a) consistency, (b) rates of convergence, and (c) bounds on the error of approximation. We embed this method for approximating the solution to the dynamic problem within an estimation routine and prove that it provides consistent estimates of the modelik's parameters. We provide Monte Carlo evidence that our method can successfully be used to approximate models that would otherwise be infeasible to compute, suggesting that these techniques may substantially broaden the class of models that can be solved and estimated. Copyright © 2013 by Emerald Group Publishing Limited.
This paper studies the behavior, under local misspecification, of several confidence sets (CSs) commonly used in the literature on inference in moment (in)equality models. We propose the amount of asymptotic confidence size distortion as a criterion to choose among competing inference methods. This criterion is then applied to compare across test statistics and critical values employed in the construction of CSs. We find two important results under weak assumptions. First, we show that CSs based on subsampling and generalized moment selection (Andrews and Soares (2010)) suffer from the same degree of asymptotic confidence size distortion, despite the fact that asymptotically the latter can lead to CSs with strictly smaller expected volume under correct model specification. Second, we show that the asymptotic confidence size of CSs based on the quasi-likelihood ratio test statistic can be an arbitrary small fraction of the asymptotic confidence size of CSs based on the modified method of moments test statistic. © 2012 The Econometric Society.
This paper explores the relationship between the state-specific child labor legislation and the decline in child labor that occurred in the US between 1880 and 1900. The existing literature that addresses this question uses a difference-in-difference estimation technique. We contribute to this literature in two ways. First, we argue that this estimation technique can produce misleading results due to (a) the possibility of multiplicity of equilibria and (b) the non-linearity of the underlying econometric model. Second, we develop an empirical strategy to identify the mechanism by which the legislation affected child labor decisions. In particular, besides establishing whether the legislation was effective or not, our analysis may determine whether the legislation constituted a benign policy or not, i. e., whether the legislation constrained the behavior of families (not benign) or whether it changed the labor market to a new equilibrium in which families voluntarily respected the law (benign). © 2011 Springer-Verlag.
Economic data are frequently generated by stochastic processes that can be modeled as realizations of random functions (functional data). This paper adapts the specification test for functional data developed by Bugni, Hall, Horowitz, and Neumann (2009, Econometrics Journal12, S1a-S18) to the presence of missing observations. By using a worst case scenario approach, our method is able to extract the information available in the observed portion of the data while being agnostic about the nature of the missing observations. The presence of missing data implies that our test will not only result in the rejection or lack of rejection of the null hypothesis, but it may also be inconclusive. Under the null hypothesis, our specification test will reject the null hypothesis with a probability that, in the limit, does not exceed the significance level of the test. Moreover, the power of the test converges to one whenever the distribution of the observations conveys that the null hypothesis is false. Monte Carlo evidence shows that the test may produce informative results (either rejection or lack of rejection of the null hypothesis) even under the presence of significant amounts of missing data. The procedure is illustrated by testing whether the Burdetta-Mortensen labor market model is the correct framework for wage paths constructed from the National Longitudinal Survery of Youth, 1979 survey. © 2012 Cambridge University Press.
This paper introduces a novel bootstrap procedure to perform inference in a wide class of partially identified econometric models. We consider econometric models defined by finitely many weak moment inequalities,2 which encompass many applications of economic interest. The objective of our inferential procedure is to cover the identified set with a prespecified probability.3 We compare our bootstrap procedure, a competing asymptotic approximation, and subsampling procedures in terms of the rate at which they achieve the desired coverage level, also known as the error in the coverage probability. Under certain conditions, we show that our bootstrap procedure and the asymptotic approximation have the same order of error in the coverage probability, which is smaller than that obtained by using subsampling. This implies that inference based on our bootstrap and asymptotic approximation should eventually be more precise than inference based on subsampling. A Monte Carlo study confirms this finding in a small sample simulation. © 2010 The Econometric Society.
Economic data are frequently generated by stochastic processes that can be modelled as occurring in continuous time. That is, the data are treated as realizations of a random function (functional data). Sometimes an economic theory model specifies the process up to a finite-dimensional parameter. This paper develops a test of the null hypothesis that a given functional data set was generated by a specified parametric model of a continuous-time process. The alternative hypothesis is non-parametric. A random function is a form of infinite-dimensional random variable, and the test presented here a generalization of the familiar Cramér-von Mises test to an infinite dimensional random variable. The test is illustrated by using it to test the hypothesis that a sample of wage paths was generated by a certain equilibrium job search model. Simulation studies show that the test has good finite-sample performance. © Journal compilation © 2009 Royal Economic Society.