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Register a new userLinear programming approach to nonparametric inference under shape restrictions: with an application to regression kink designs
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We develop a novel method of constructing confidence bands for nonparametric regression functions under shape constraints. This method can be implemented via a linear programming, and it is thus computationally appealing. We illustrate a usage of our proposed method with an application to the regression kink design (RKD). Econometric analyses based on the RKD often suffer from wide confidence intervals due to slow convergence rates of nonparametric derivative estimators. We demonstrate that economic models and structures motivate shape restrictions, which in turn contribute to shrinking the confidence interval for an analysis of the causal effects of unemployment insurance benefits on unemployment durations.
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We develop a distribution regression model under endogenous sample selection. This model is a semiparametric generalization of the Heckman selection model that accommodates much richer patterns of heterogeneity in the selection process and effect of the covariates. The model applies to continuous, discrete and mixed outcomes. We study the identification of the model, and develop a computationally attractive two-step method to estimate the model parameters, where the first step is a probit regression for the selection equation and the second step consists of multiple distribution regressions with selection corrections for the outcome equation. We construct estimators of functionals of interest such as actual and counterfactual distributions of latent and observed outcomes via plug-in rule. We derive functional central limit theorems for all the estimators and show the validity of multiplier bootstrap to carry out functional inference. We apply the methods to wage decompositions in the UK using new data. Here we decompose the difference between the male and female wage distributions into four effects: composition, wage structure, selection structure and selection sorting. After controlling for endogenous employment selection, we still find substantial gender wage gap -- ranging from 21% to 40% throughout the (latent) offered wage distribution that is not explained by observable labor market characteristics. We also uncover positive sorting for single men and negative sorting for married women that accounts for a substantive fraction of the gender wage gap at the top of the distribution. These findings can be interpreted as evidence of assortative matching in the marriage market and glass-ceiling in the labor market.
Regression discontinuity (RD) design in a practical context is often contaminated by units behavior to manipulate their treatment assignment. However, we have no formal justification for point identification in such a contaminated RD design. Diagnostic tests have been proposed to detect manipulations, but they do not guarantee identification without some auxiliary assumptions, and the auxiliary assumptions have not been proposed. This study proposes a set of restrictions for possibly manipulated RD designs to validate point identification and diagnostic tests. The same restrictions simultaneously validate worst-case bounds when the diagnostic tests are validated. Therefore, our designs are manipulation robust in testing and identification. The worst-case bounds have two shorter bounds as special cases, and we apply special-case bounds to a controversy regarding the incumbency margin study of the U.S. House of Representatives elections studied in Lee (2008).
A new statistical procedure, based on a modified spline basis, is proposed to identify the linear components in the panel data model with fixed effects. Under some mild assumptions, the proposed procedure is shown to consistently estimate the underlying regression function, correctly select the linear components, and effectively conduct the statistical inference. When compared to existing methods for detection of linearity in the panel model, our approach is demonstrated to be theoretically justified as well as practically convenient. We provide a computational algorithm that implements the proposed procedure along with a path-based solution method for linearity detection, which avoids the burden of selecting the tuning parameter for the penalty term. Monte Carlo simulations are conducted to examine the finite sample performance of our proposed procedure with detailed findings that confirm our theoretical results in the paper. Applications to Aggregate Production and Environmental Kuznets Curve data also illustrate the necessity for detecting linearity in the partially linear panel model.
Dynamic model averaging (DMA) combines the forecasts of a large number of dynamic linear models (DLMs) to predict the future value of a time series. The performance of DMA critically depends on the appropriate choice of two forgetting factors. The first of these controls the speed of adaptation of the coefficient vector of each DLM, while the second enables time variation in the model averaging stage. In this paper we develop a novel, adaptive dynamic model averaging (ADMA) methodology. The proposed methodology employs a stochastic optimisation algorithm that sequentially updates the forgetting factor of each DLM, and uses a state-of-the-art non-parametric model combination algorithm from the prediction with expert advice literature, which offers finite-time performance guarantees. An empirical application to quarterly UK house price data suggests that ADMA produces more accurate forecasts than the benchmark autoregressive model, as well as competing DMA specifications.
This paper develops the asymptotic theory of a Fully Modified Generalized Least Squares estimator for multivariate cointegrating polynomial regressions. Such regressions allow for deterministic trends, stochastic trends and integer powers of stochastic trends to enter the cointegrating relations. Our fully modified estimator incorporates: (1) the direct estimation of the inverse autocovariance matrix of the multidimensional errors, and (2) second order bias corrections. The resulting estimator has the intuitive interpretation of applying a weighted least squares objective function to filtered data series. Moreover, the required second order bias corrections are convenient byproducts of our approach and lead to standard asymptotic inference. We also study several multivariate KPSS-type of tests for the null of cointegration. A comprehensive simulation study shows good performance of the FM-GLS estimator and the related tests. As a practical illustration, we reinvestigate the Environmental Kuznets Curve (EKC) hypothesis for six early industrialized countries as in Wagner et al. (2020).
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