Jian Hong |
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Placement Director: Vijay Krishna
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Graduate Secretary & Placement Assistant: Lynn Sebulsky (814)865-1458 lms50@psu.edu |
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THESIS ABSTRACT Essay 1: Nonparametric Identification and Estimation of Production Functions Using Control Function Approaches to Endogeneity (Job Market Paper) Using control function approaches to endogeneity, nonparametric identification is established for production functions under the given conditions. The distribution of productivity is also recovered nonparametrically. Instead of "inverting out" the productivity shock, control functions "expect out" unobserved shocks. Multiple shocks are typically allowed, which provide sources of exogenous variations. Uncertainty and adjustment costs make input decisions respond differently to the evolution of shocks. The collinearity among input decisions is then avoided by appropriate timing assumptions. Exogenous variations may come from instruments as well. This paper extends the methods of Olley and Pakes (1996) and Levinsohn and Petrin (2003), and answers the identification questions raised by Ackerberg, Caves and Frazer (2006) and Bond and Söderbom (2005). Nonparametric estimation of production functions then closely follows the identification strategy without imposing extra modeling assumptions. When intermediate inputs are observed, they can serve as controls; controls can also be estimated from instruments. Accordingly, two kernel estimators are proposed for nonparametric regressions with endogeneity. The estimator with estimated controls achieves the optimal uniform convergence rate if the preliminary estimators of controls converge sufficiently fast. This paper provides a kernel-based alternative to the series estimators proposed by Newey, Powell, and Vella (1999). The finite sample performance of the proposed kernel estimators is illustrated by Monte-Carlo experiments. An application to a Chilean panel demonstrates its empirical relevance.
Essay 2: Semiparametric Identification and Estimation of Production Functions The identification strategy using control function approaches to endogeneity proposed in Essay 1 is adapted to the Cobb-Douglas production function. A partial linear model arises naturally where the parametric part represents the production function and the nonparametric part is the control function to "expect out" unobserved shocks. With appropriate choices of controls, both capital and labor coefficients can be identified and estimated simultaneously under reasonable timing assumptions. In this case, the estimators achieve Root-N-Consistency and the computation is simple in that there is no iterative optimization algorithm involved. When only cross-sectional data is available, the labor coefficient can be identified and estimated by Robinson's method. A moment condition based on the non-transmitted error is proposed to estimate the capital coefficient. The empirical distribution of productivity can also be recovered. The performance of semiparametric estimation procedures in finite samples is demonstrated by Monte-Carlo experiments. The procedures are applied again to the Chilean panel data and result in reasonable estimates of capital and labor coefficients. Essay 3: A Nonparametric Hausman Test of Exogeneity When exogeneity is assumed in nonparametric regression models, it is natural to test whether this assumption is valid. Many parametric tests are inconsistent as they only have power against certain alternatives. A nonparametric Hausman test of exogeneity is proposed, which is consistent and has power in every direction. Following the idea of the original Hausman test, this test compares the nonparametric estimator of the conditional mean to a consistent estimator that takes the potential endogeneity into account. For the latter, a kernel estimator derived by control function approaches is used. These two estimators converge to each other when the regressors are exogenous, and diverge otherwise. Thus, the weighted integrated square difference between the two estimators can serve as a test statistic. The asymptotical normality of the normalized test statistic is established using U-statistics. The performance of the test statistic is examined by a Monte-Carlo study, in which the test is able to detect sequences of local alternatives.
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