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on Econometrics |
| By: | Karun Adusumilli; Taisuke Otsu; Chen Qiu |
| Abstract: | This paper is concerned with inference on finite dimensional parameters in semiparametric moment condition models, where the moment functionals are linear with respect to unknown nuisance functions. By exploiting this linearity, we reformulate the inference problem via the Riesz representer, and develop a general inference procedure based on nonparametric likelihood. For treatment effect or missing data analysis, the Riesz representer is typically associated with the inverse propensity score even though the scope of our framework is much wider. In particular, we propose a two-step procedure, where the first step computes the projection weights to approximate the Riesz representer, and the second step re-weights the moment conditions so that the likelihood increment admits an asymptotically pivotal chi-square calibration. Our re-weighting method is naturally extended to inference on treatment effects and data combination models, and other semiparametric problems. Simulation and empirical examples illustrate usefulness of the proposed method. |
| Keywords: | Nonparametric likelihood, Linear functional, Balancing weights |
| JEL: | C12 C14 |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:cep:stiecm:614&r=all |
| By: | Guannan Liu (School of Economics and WISE, Xiamen University, Xiamen, Fujian 361005, China); Wei Long (Department of Economics, Tulane University, New Orleans, LA 70118, USA); Bingduo Yang (Lingnan (University) College, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China); Zongwu Cai (Department of Economics, The University of Kansas, Lawrence, KS 66045, USA) |
| Abstract: | Conditional copula models allow the dependence structure among variables to vary with covariates, and thus can describe the evolution of the dependence structure with those factors. This paper proposes a conditional mixture copula which is a weighted average of several individual conditional copulas. We allow both the weights and copula parameters to vary with a covariate so that the conditional mixture copula offers additional flexibility and accuracy in describing the dependence structure. We propose a two-step semiparametric estimation method and develop asymptotic properties of the estimators. Moreover, we introduce model selection procedures to select the component copulas of the conditional mixture copula model. Simulation results suggest that the proposed procedures have a good performance in estimating and selecting conditional mixture copulas with different model specifications. The proposed model is then applied to investigate how the dependence structures among international equity markets evolve with the volatility in the exchange rate markets. |
| Keywords: | Conditional copula; Mixture copula; Model selection; Semiparametric estimation |
| JEL: | C14 C22 |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:kan:wpaper:202104&r=all |
| By: | Joseph Altonji; Hidehiko Ichimura; Taisuke Otsu |
| Abstract: | This paper studies nonparametric estimation of d-dimensional conditional quantile functions and their derivatives in the tails. We investigate asymptotic properties of the local and global nonparametric quantile regression estimators proposed by Chaudhuri (1991a, b), respectively, under the intermediate order quantile asymptotics: as the sample size n goes to infinity, the quantile αn and a bandwidth parameter δn satisfy αn → 0 and nδd nαn → ∞ (or αn → 1 and nδd n(1−αn) →∞). We derive the pointwise convergence rate and asymptotic distribution of the local nonparametric quantile regression estimator, and the sup-norm convergence rate of the global nonparametric quantile regression estimator. Our results complement the papers by Chaudhuri (1991a, b), where the quantile αn does not vary with n, and Chernozhukov (1998), where the quantile αn satisfies αn → 0 and nδd nαn → 0. |
| Keywords: | Quantile regression, Local polynomial regression: Extremes |
| JEL: | C14 |
| Date: | 2019–11 |
| URL: | http://d.repec.org/n?u=RePEc:cep:stiecm:608&r=all |
| By: | Zongwu Cai (Department of Economics, The University of Kansas, Lawrence, KS 66045, USA); Ying Fang (The Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, Fujian 361005, China and Department of Statistics, School of Economics, Xiamen University, Xiamen, Fujian 361005, China); Ming Lin (The Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, Fujian 361005, China and Department of Statistics, School of Economics, Xiamen University, Xiamen, Fujian 361005, China); Shengfang Tang (Department of Statistics, School of Economics, Xiamen University, Xiamen, Fujian 361005, China) |
| Abstract: | This paper proposes a new model, termed as the partially conditional quantile treatment effect model, to characterize the heterogeneity of treatment effect conditional on some predetermined variable(s). We show that this partially conditional quantile treatment effect is identified under the assumption of selection on observables, which leads to a semiparametric estimation procedure in two steps: first, parametric estimation of the propensity score function and then, nonparametric estimation of conditional quantile treatment effects. Under some regularity conditions, the consistency and asymptotic normality of the proposed semiparametric estimator are derived. Furthermore, the finite sample performance of the proposed method is illustrated through Monte Carlo experiments. Finally, we apply our methods to estimate the quantile treatment effects of a first-time motherÕs smoking during the pregnancy on the babyÕs weight as a function of the motherÕs age, and our empirical results show substantial heterogeneity across different motherÕs ages with a significant negative effect of smoking on infant birth weight across all motherÕs ages and quantiles considered. |
| Keywords: | Conditional quantile treatment effect; Heterogeneity; Propensity score; Semiparametric estimation; Treatment effect on treated |
| JEL: | C21 C13 C14 C54 |
| Date: | 2021–01 |
| URL: | http://d.repec.org/n?u=RePEc:kan:wpaper:202103&r=all |
| By: | Yukitoshi Matsushita; Taisuke Otsu |
| Abstract: | This paper studies second-order properties of the many instruments robust t-ratios based on the limited information maximum likelihood and Fuller estimators for instrumental variable regression models under the many instruments asymptotics, where the number of instruments may increase proportionally with the sample size n, and proposes second-order refinements to the t-ratios to improve the size and power properties. Based on asymptotic expansions of the null and non-null distributions of the t-ratios derived under the many instruments asymptotics, we show that the second order terms of those expansions may have non-trivial impacts on the size as well as the power properties. Furthermore, we propose adjusted t-ratios whose approximation errors for the null rejection probabilities are of order O(n^{-1}) in contrast to the ones for the unadjusted t-ratios of order O(n^{-1/2}), and show that these adjustments induce some desirable power properties in terms of the local maximinity. |
| Keywords: | simultaneous equation, many instrumental variables, higher order expansion |
| JEL: | C12 C26 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:cep:stiecm:612&r=all |
| By: | Yukitoshi Matsushita; Taisuke Otsu |
| Abstract: | This paper proposes a jackknife Lagrange multiplier (JLM) test for instrumental variable regression models, which is robust to (i) many instruments, where the number of instruments may increase proportionally with the sample size, (ii) arbitrarily weak instruments, and (iii) heteroskedastic errors. To the best of our knowledge, currently there is no asymptotically size correct test in this setting. Our idea is to modify the score statistic by jackknifing and to construct its heteroskedasticity robust variance estimator. Compared to Hansen, Hausman and Newey's (2008) modification for many instruments on the LM test by Kleibergen (2002) and Moreira (2001), our JLM test is robust for heteroskedastic errors and may circumvent possible decrease in the power function. Simulation results illustrate the desirable size robustness and power properties of the proposed method. |
| Keywords: | many instruments, weak instruments, Lagrange multiplier test, jackknife |
| JEL: | C12 C26 |
| Date: | 2020–08 |
| URL: | http://d.repec.org/n?u=RePEc:cep:stiecm:613&r=all |
| By: | Knorre, Fabian (TU Dortmund University, Germany and Ruhr Graduate School in Economics Essen, Germany); Wagner, Martin (University of Klagenfurt, Austria, and Bank of Slovenia, Ljubljana, Slovenia, and Institute for Advanced Studies, Vienna, Austria); Grupe, Maximilian (TU Dortmund University, Germany) |
| Abstract: | This paper develops residual-based monitoring procedures for cointegrating polynomial regressions, i. e., regression models including deterministic variables, integrated processes as well as integer powers of integrated processes as regressors. The regressors are allowed to be endogenous and the stationary errors are allowed to be serially correlated. We consider five variants of monitoring statistics and develop the results for three modified least squares estimators for the parameters of the CPRs. The simulations show that using the combination of self-normalization and a moving window leads to the best performance. We use the developed monitoring statistics to assess the structural stability of environmental Kuznets curves (EKCs) for both CO2and SO2 emissions for twelve industrialized country since the first oil price shock. |
| Keywords: | Cointegrating Polynomial Regression, Environmental Kuznets Curve, Monitoring, Structural Change |
| JEL: | C22 C52 Q56 |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:ihs:ihswps:27&r=all |
| By: | Paul Ho; Thomas A. Lubik; Christian Matthes |
| Abstract: | This paper estimates a panel model with endogenously time-varying parameters for COVID-19 cases and deaths in U.S. states. The functional form for infections incorporates important features of epidemiological models but is flexibly parameterized to capture different trajectories of the pandemic. Daily deaths are modeled as a spike-and-slab regression on lagged cases. The paper's Bayesian estimation reveals that social distancing and testing have significant effects on the parameters. For example, a 10 percentage point increase in the positive test rate is associated with a 2 percentage point increase in the death rate among reported cases. The model forecasts perform well, even relative to models from epidemiology and statistics. |
| Keywords: | Bayesian Estimation; Panel; Time-Varying Parameters |
| JEL: | C32 C51 |
| Date: | 2020–08–21 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedrwp:88807&r=all |
| By: | Kohtaro Hitomi (Kyoto Institute of Technology); Masamune Iwasawa (Otaru University of Commerce); Yoshihiko Nishiyama (Institute of Economic Research, Kyoto University) |
| Abstract: | This study investigates optimal minimax rates for specification testing when the alternative hypothesis is built on a set of non-smooth functions. The set consists of bounded functions that are not necessarily differentiable with no smoothness constraints imposed on their derivatives. In the instrumental variable regression set up with an unknown error variance structure, we find that the optimal minimax rate is n−1/4, where n is the sample size. The rate is achieved by a simple test based on the difference between non-parametric and parametric variance estimators. |
| Keywords: | optimal minimax rate; specification test; instrumental variable regression model; nearest neighbor method |
| JEL: | C12 C14 |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:1051&r=all |
| By: | V A Hajivassiliou |
| Keywords: | Switching regressions models, Measurement Errors, Trigger-price mechanisms, Price- ,xing |
| JEL: | C72 L12 C51 C52 C15 |
| Date: | 2019–11 |
| URL: | http://d.repec.org/n?u=RePEc:cep:stiecm:610&r=all |
| By: | Malo, Pekka; Eskelinen, Juha; Zhou, Xun; Kuosmanen, Timo |
| Abstract: | The synthetic control method (SCM) is a major innovation in the estimation of causal effects of policy interventions and programs in a comparative case study setting. In this paper, we demonstrate that the data-driven approach to SCM requires solving a bilevel optimization problem. We show how the SCM problem can be solved using iterative algorithms based on Tykhonov descent or KKT approximations. |
| Keywords: | Causal effects; Comparative case studies; Policy impact assessment |
| JEL: | C54 C63 |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:104085&r=all |
| By: | Andrew B. Martinez (Office of Macroeconomic Analysis, US Department of the Treasury); Jennifer L. Castle (Magdalen College, Climate Econometrics, and Institute for New Economic Thinking at the Oxford Martin School, University of Oxford); David F. Hendry (Nuffield College, Climate Econometrics, and Institute for New Economic Thinking at the Oxford Martin School, University of Oxford) |
| Abstract: | We investigate whether smooth robust methods for forecasting can help mitigate pronounced and persistent failure across multiple forecast horizons. We demonstrate that naive predictors are interpretable as local estimators of the long-run relationship with the advantage of adapting quickly after a break, but at a cost of additional forecast error variance. Smoothing over naive estimates helps retain these advantages while reducing the costs, especially for longer forecast horizons. We derive the performance of these predictors after a location shift, and confirm the results using simulations. We apply smooth methods to forecasts of U.K. productivity and U.S. 10-year Treasury yields and show that they can dramatically reduce persistent forecast failure exhibited by forecasts from macroeconomic models and professional forecasters. |
| Keywords: | Location Shifts; Long differencing; Productivity forecasts; Robust forecasts |
| JEL: | C51 C53 |
| Date: | 2020–12 |
| URL: | http://d.repec.org/n?u=RePEc:gwc:wpaper:2020-009&r=all |