ESTIMATION AND INFERENCE FOR MOMENTS OF RATIOS WITH ROBUSTNESS AGAINST LARGE TRIMMING BIAS

Researchers often trim observations with small values of the denominator A when they estimate moments of the form $\mathbb {E}[B/A]$ . Large trimming is common in practice to reduce variance, but it incurs a large bias. This paper provides a novel method of correcting the large trimming bias. If a researcher is willing to assume that the joint distribution between A and B is smooth, then the trimming bias may be estimated well. Along with the proposed bias correction method, we also develop an inference method. Practical advantages of the proposed method are demonstrated through simulation studies, where the data generating process entails a heavy-tailed distribution of $B/A$ . Applying the proposed method to the Compustat database, we analyze the history of external financial dependence of U.S. manufacturing firms for years 2000–2010.

[1]  D. Horvitz,et al.  A Generalization of Sampling Without Replacement from a Finite Universe , 1952 .

[2]  C. Mallows,et al.  Limit Distributions of Self-normalized Sums , 1973 .

[3]  D. Rubin,et al.  The central role of the propensity score in observational studies for causal effects , 1983 .

[4]  The central limit problem for trimmed sums , 1987 .

[5]  S. Geer.  Estimating a Regression Function , 1990 .

[6]  D. Mason,et al.  The Asymptotic Distribution of Trimmed Sums , 1988 .

[7]  Asymptotic Normality and Subsequential Limits of Trimmed Sums , 1989 .

[8]  Brian J. Eastwood,et al.  Adaptive Rules for Seminonparametric Estimators That Achieve Asymptotic Normality , 1991, Econometric Theory.

[9]  A. Ronald Gallant,et al.  On the asymptotic normality of Fourier flexible form estimates , 1991 .

[10]  D. Andrews.  Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models , 1991 .

[11]  Luigi Zingales,et al.  Financial Dependence and Growth , 1996 .

[12]  Arthur Lewbel,et al.  Semiparametric Estimation of Location and Other Discrete Choice Moments , 1997, Econometric Theory.

[13]  W. Newey,et al.  Convergence rates and asymptotic normality for series estimators , 1997 .

[14]  Arthur Lewbel,et al.  Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors , 1998 .

[15]  Joseph P. Romano,et al.  Subsampling inference for the mean in the heavy-tailed case , 1999 .

[16]  Donald W. K. Andrews,et al.  Semiparametric Estimation of the Intercept of a Sample Selection Model , 1998 .

[17]  A. Lewbel,et al.  Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables , 2000 .

[18]  L. Peng.  Estimating the mean of a heavy tailed distribution , 2001 .

[19]  R. Jong.  A note on "Convergence rates and asymptotic normality for series estimators": uniform convergence rates , 2002 .

[20]  S. Geer.  M-estimation using penalties or sieves , 2002 .

[21]  Jianhua Z. Huang.  Local asymptotics for polynomial spline regression , 2003 .

[22]  Liang Peng,et al.  EMPIRICAL-LIKELIHOOD-BASED CONFIDENCE INTERVAL FOR THE MEAN WITH A HEAVY-TAILED DISTRIBUTION , 2004, math/0406523.

[23]  Xiaohong Chen.  Chapter 76 Large Sample Sieve Estimation of Semi-Nonparametric Models , 2007 .

[24]  Jonathan B. Hill,et al.  Generalized Method of Moments with Tail Trimming , 2009 .

[25]  É. Renault,et al.  Efficient Gmm with Nearly-Weak Instruments , 2009 .

[26]  Richard K. Crump,et al.  Dealing with limited overlap in estimation of average treatment effects , 2009 .

[27]  Alastair R. Hall,et al.  Generalized Method of Moments (GMM) , 2010 .

[28]  Peter C. B. Phillips,et al.  Bimodal T-Ratios: The Impact of Thick Tails on Inference , 2010 .

[29]  Shakeeb Khan,et al.  Irregular Identification, Support Conditions, and Inverse Weight Estimation , 2010 .

[30]  É. Renault,et al.  Efficient Minimum Distance Estimation with Multiple Rates of Convergence , 2012 .

[31]  Kengo Kato,et al.  Gaussian approximation of suprema of empirical processes , 2012, 1212.6885.

[32]  Kengo Kato,et al.  Some new asymptotic theory for least squares series: Pointwise and uniform results , 2012, 1212.0442.

[33]  A. Lewbel,et al.  An Overview of the Special Regressor Method , 2012 .

[34]  J. Powell,et al.  Identification and Estimation of Average Partial Effects in “Irregular” Correlated Random Coefficient Panel Data Models , 2012 .

[35]  Denis Nekipelov,et al.  On Uniform Inference in Nonlinear Models with Endogeneity , 2013, Journal of Econometrics.

[36]  Max H. Farrell,et al.  Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators☆ , 2013 .

[37]  David T. Jacho-Chávez,et al.  Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing , 2014 .

[38]  Xiaohong Chen,et al.  Optimal Uniform Convergence Rates and Asymptotic Normality for Series Estimators Under Weak Dependence and Weak Conditions , 2014, 1412.6020.

[39]  Zhipeng Liao,et al.  Sieve M inference on irregular parameters , 2014 .

[40]  Sebastian Calonico,et al.  Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs , 2014 .

[41]  Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models: Sieve Wald and QLR Inference , 2015 .

[42]  C. Rothe.  Robust Confidence Intervals for Average Treatment Effects Under Limited Overlap , 2017, SSRN Electronic Journal.

[43]  Saraswata Chaudhuri,et al.  Heavy Tail Robust Estimation and Inference for Average Treatment Eects , 2015 .

[44]  B. Hansen.  A Unified Asymptotic Distribution Theory for Parametric and Non-Parametric Least Squares , 2015 .

[45]  J. Escanciano.  SEMIPARAMETRIC IDENTIFICATION AND FISHER INFORMATION , 2016, Econometric Theory.

[46]  David T. Jacho-Chávez,et al.  Identification and estimation of semiparametric two‐step models , 2016 .

[47]  Liang Peng,et al.  Inference for Heavy-Tailed Data: Applications in Insurance and Finance , 2017 .

[48]  P. Ding,et al.  Asymptotic inference of causal effects with observational studies trimmed by the estimated propensity scores , 2018 .

[49]  A. Lewbel,et al.  Identification of Random Resource Shares in Collective Households Without Preference Similarity Restrictions , 2019, Journal of Business & Economic Statistics.

[50]  Michael P. Leung,et al.  Inference on finite-population treatment effects under limited overlap , 2019, The Econometrics Journal.

[51]  Xinwei Ma,et al.  Robust Inference Using Inverse Probability Weighting , 2018, Journal of the American Statistical Association.

[52]  Ekaterina Kazak,et al.  Valid inference for treatment effect parameters under irregular identification and many extreme propensity scores , 2020, Journal of Econometrics.