
on Econometrics 
By:  Zhan Gao; M. Hashem Pesaran 
Abstract:  This paper proposes a linear categorical random coefficient model, in which the random coefficients follow parametric categorical distributions. The distributional parameters are identified based on a linear recurrence structure of moments of the random coefficients. A Generalized Method of Moments estimator is proposed, and its finite sample properties are examined using Monte Carlo simulations. The utility of the proposed method is illustrated by estimating the distribution of returns to education in the U.S. by gender and educational levels. We find that rising heterogeneity between educational groups is mainly due to the increasing returns to education for those with postsecondary education, whereas within group heterogeneity has been rising mostly in the case of individuals with high school or less education. 
Keywords:  random coefficient models, categorical distribution, return to education 
JEL:  C01 C21 C13 C46 J30 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:ces:ceswps:_9714&r= 
By:  TaeHwy Lee (Department of Economics, University of California at Riverside, CA 92521); Shahnaz Parsaeian (Department of Economics, University of Kansas, Lawrence, KS 66045); Aman Ullah (Department of Economics, University of California at Riverside, CA 92521) 
Abstract:  In forecasting a time series containing a structural break, it is important to determine how much weight can be given to the observations prior to the time when the break occurred. In this context, Pesaran et al. (2013) (PPP) proposed a weighted least squares estimator by giving different weights to observations before and after a break point for forecasting outofsample. We revisit their approach by introducing an improved weighted generalized least squares estimator (WGLS) using a weight (kernel) function to give different weights to observations before and after a break. The kernel weight is estimated by crossvalidation rather than analytically derived from a parametric model as in PPP. Therefore, the WGLS estimator facilitates implementation of the PPP method for the optimal use of the prebreak and postbreak sample observations without having to derive the parametric weights which may be misspecified. We show that the kernel weight estimated by crossvalidation is asymptotically optimal in the sense of Li (1987). Monte Carlo simulations and an empirical application to forecasting equity premium are provided for verification and illustration. 
Keywords:  Crossvalidation; Kernel; Structural breaks; Model averaging 
JEL:  C14 C22 C53 
Date:  2022–06 
URL:  http://d.repec.org/n?u=RePEc:kan:wpaper:202212&r= 
By:  Victor Chernozhukov; Denis Chetverikov; Kengo Kato; Yuta Koike 
Abstract:  This article reviews recent progress in highdimensional bootstrap. We first review highdimensional central limit theorems for distributions of sample mean vectors over the rectangles, bootstrap consistency results in high dimensions, and key techniques used to establish those results. We then review selected applications of highdimensional bootstrap: construction of simultaneous confidence sets for highdimensional vector parameters, multiple hypothesis testing via stepdown, postselection inference, intersection bounds for partially identified parameters, and inference on best policies in policy evaluation. Finally, we also comment on a couple of future research directions. 
Date:  2022–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2205.09691&r= 
By:  Ravi Kumar; Shahin Boluki; Karl Isler; Jonas Rauch; Darius Walczak 
Abstract:  We consider the problem of dynamic pricing of a product in the presence of featuredependent price sensitivity. Based on the Poisson semiparametric approach, we construct a flexible yet interpretable demand model where the price related part is parametric while the remaining (nuisance) part of the model is nonparametric and can be modeled via sophisticated ML techniques. The estimation of pricesensitivity parameters of this model via direct onestage regression techniques may lead to biased estimates. We propose a twostage estimation methodology which makes the estimation of the pricesensitivity parameters robust to biases in the nuisance parameters of the model. In the firststage we construct the estimators of observed purchases and price given the feature vector using sophisticated ML estimators like deep neural networks. Utilizing the estimators from the firststage, in the secondstage we leverage a Bayesian dynamic generalized linear model to estimate the pricesensitivity parameters. We test the performance of the proposed estimation schemes on simulated and real sales transaction data from Airline industry. Our numerical studies demonstrate that the twostage approach provides more accurate estimates of pricesensitivity parameters as compared to direct onestage approach. 
Date:  2022–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2205.01875&r= 
By:  Luc Clair 
Abstract:  The literature on nonparametric instrumental variable (IV) methods has been growing, and while the mathematics behind these methods are highly technical, researchers believe that these methods will soon emerge as viable alternatives to parametric approaches. The diculty of these methods stems from the fact that the nonparametric instrumental variable estimator is the solution to a illposed inverse problem. The illposed inverse problem is solved by using regularization methods. Therefore there are two steps for solving the nonparametric (IV) problem: estimating conditional means and regularization. When analysis is performed using complex survey data, one must also consider the sampling design. When endogeneous sampling is present, traditional estimation methods will be inconsistent. I extend the theory of nonparametric IV models to account for sample design by estimating the conditional mean functions using a probability weighted local constant estimator. 
Date:  2022–05 
URL:  http://d.repec.org/n?u=RePEc:win:winwop:202201&r= 
By:  Haoge Chang; Yusuke Narita; Kota Saito 
Abstract:  We obtain a necessary and sufficient condition under which parametric randomcoefficient discrete choice models can approximate the choice behavior generated by nonparametric random utility models. The condition turns out to be very simple and tractable. For the case under which the condition is not satisfied (and hence, where some stochastic choice data are generated by a random utility model that cannot be approximated), we provide algorithms to measure the approximation errors. After applying our theoretical results and the algorithm to real data, we found that the approximation errors can be large in practice. 
Date:  2022–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2205.01882&r= 
By:  Yuefeng Han; Rong Chen; CunHui Zhang 
Abstract:  Factor model is an appealing and effective analytic tool for highdimensional time series, with a wide range of applications in economics, finance and statistics. This paper develops two criteria for the determination of the number of factors for tensor factor models where the signal part of an observed tensor time series assumes a Tucker decomposition with the core tensor as the factor tensor. The task is to determine the dimensions of the core tensor. One of the proposed criteria is similar to information based criteria of model selection, and the other is an extension of the approaches based on the ratios of consecutive eigenvalues often used in factor analysis for panel time series. Theoretically results, including sufficient conditions and convergence rates, are established. The results include the vector factor models as special cases, with an additional convergence rates. Simulation studies provide promising finite sample performance for the two criteria. 
Date:  2020–11 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2011.07131&r= 
By:  Matthew A. Masten; Alexandre Poirier 
Abstract:  There are many kinds of exogeneity assumptions. How should researchers choose among them? When exogeneity is imposed on an unobservable like a potential outcome, we argue that the form of exogeneity should be chosen based on the kind of selection on unobservables it allows. Consequently, researchers can assess the plausibility of any exogeneity assumption by studying the distributions of treatment given the unobservables that are consistent with that assumption. We use this approach to study two common exogeneity assumptions: quantile and mean independence. We show that both assumptions require a kind of nonmonotonic relationship between treatment and the potential outcomes. We discuss how to assess the plausibility of this kind of treatment selection. We also show how to define a new and weaker version of quantile independence that allows for monotonic treatment selection. We then show the implications of the choice of exogeneity assumption for identification. We apply these results in an empirical illustration of the effect of child soldiering on wages. 
Date:  2022–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2205.02288&r= 
By:  Edward C. Norton 
Abstract:  This paper shows how to calculate consistent marginal effects on the original scale of the outcome variable in Stata after estimating a linear regression with a dependent variable that has been transformed by the inverse hyperbolic sine function. The method uses a nonparametric retransformation of the error term and accounts for any scaling of the dependent variable. The inverse hyperbolic sine function is not invariant to scaling, which is known to shift marginal effects between those from an untransformed dependent variable to those of a logtransformed dependent variable. 
JEL:  C16 I1 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:29998&r= 
By:  Erkin Diyarbakirlioglu (IRG  Institut de Recherche en Gestion  UPEC UP12  Université ParisEst Créteil ValdeMarne  Paris 12  Université Gustave Eiffel); Marc Desban (IRG  Institut de Recherche en Gestion  UPEC UP12  Université ParisEst Créteil ValdeMarne  Paris 12  Université Gustave Eiffel); Souad Lajili Jarjir (IRG  Institut de Recherche en Gestion  UPEC UP12  Université ParisEst Créteil ValdeMarne  Paris 12  Université Gustave Eiffel) 
Abstract:  We implement a new framework to mitigate the errorsinvariables (EIV) problem in the estimation of asset pricing models. Considering an international data of portfolio stock returns from 1990 to 2021 widely used in empirical studies, we highlight the importance of the estimation method in timeseries regressions. We compare the traditional OrdinaryLeast Squares (OLS) method to an alternative estimator based on a Compact Genetic Algorithm (CGA) in the case of the CAPM, three, and fivefactor models. Based on intercepts, betas, adjusted R2 , and the Gibbons, Ross and Shanken (1989) test, we find that the CGAbased method outperforms overall the OLS for the three asset pricing models. In particular, we obtain less statistically significant intercepts, smoother R2 across different portfolios and lower GRS test statistics. Specifically, in line with Roll's critique (1977) on the unobservability of the market portfolio, we reduce the attenuation bias in market risk premium estimates. Moreover, our results are robust to alternative methods such as Instrumental Variables estimated with GeneralizedMethod of Moments (GMM). Our findings have several empirical and managerial implications related to the estimation of asset pricing models as well as their interpretation as a popular tool in terms of corporate financial decisionmaking. 
Keywords:  Asset pricing,CAPM,FamaFrench threeand fivefactor models,Market Portfolio,Timeseries regressions,OrdinaryLeast Squares (OLS),Errorsinvariables (EIV),GMM with Instrumental Variables,Compact Genetic Algorithms (CGA) 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03643083&r= 
By:  Nikhil Agarwal; Paulo J. Somaini 
Abstract:  Consumer choices are constrained in many markets due to either supplyside rationing or information frictions. Examples include matching markets for schools and colleges; entrylevel labor markets; limited brand awareness and inattention in consumer markets; and selective admissions to healthcare services. Accounting for these choice constraints is essential for estimating consumer demand. We use a general random utility model for consumer preferences that allows for endogenous characteristics and a reducedform choiceset formation rule that can be derived from models of the examples described above. The choicesets can be arbitrarily correlated with preferences. We study nonparametric identification of this model, propose an estimator, and apply these methods to study admissions in the market for kidney dialysis in California. Our results establish identification of the model using two sets of instruments, one that only affects consumer preferences and the other that only affects choice sets. Moreover, these instruments are necessary for identification. We find that dialysis facilities are less likely to admit new patients when they have higher than normal caseload and that patients are more likely to travel further when nearby facilities have high caseloads. Finally, we estimate consumers' preferences and facilities' rationing rules using a Gibbs sampler. 
JEL:  C50 I11 L0 
Date:  2022–04 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:29993&r= 