
on Econometrics 
By:  Ya Chen (Hefei University of Technology, China); Mike Tsionas (Lancaster University, United Kingdom); Valentin Zelenyuk (School of Economics and Centre for Efficiency and Productivity Analysis (CEPA) at The University of Queensland, Australia) 
Abstract:  We propose an improvement of the finite sample approximation of the central limit theorems (CLTs) that were recently derived for statistics involving production efficiency scores estimated via Data Envelopment Analysis (DEA) or Free Disposal Hull (FDH) approaches. The improvement is very easy to implement since it involves a simple correction of the variance estimator with an estimate of the bias of the already employed statistics without any additional computational burden and preserves the original asymptotic results such as consistency and asymptotic normality. The proposed approach persistently showed improvement in all the scenarios that we tried in various MonteCarlo experiments, especially for relatively small samples or relatively large dimensions (measured by total number of inputs and outputs) of the underlying production model. This approach therefore is expected to produce more accurate estimates of confidence intervals of aggregates of individual efficiency scores in empirical research using DEA or FDH approaches and so must be valuable for practitioners. We also illustrate this method using a popular real data set to confirm that the difference in the estimated confidence intervals can be substantial. A stepbystep implementation algorithm of the proposed approach is included in the Appendix. 
Keywords:  DEA; signconstrained convex nonparametric least squares (SCNLS); LASSO; elastic net; big data 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:qld:uqcepa:145&r=all 
By:  Shi, Chengchun; Song, Rui; Chen, Zhao; Li, Runze 
Abstract:  This paper is concerned with testing linear hypotheses in high dimensional generalized linear models. To deal with linear hypotheses, we first propose the constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with foldedconcave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are χ2 distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow noncentral χ2 distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to ∞ at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures. 
Keywords:  High dimensional testing; linear hypothesis; likelihood ratio statistics; score test; Wald test 
JEL:  C1 
Date:  2019–10 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:102108&r=all 
By:  Yoonseok Lee (Center for Policy Research, Maxwell School, Syracuse University, 426 Eggers Hall, Syracuse, NY 13244); Yulong Wang (Department of Economics and Center for Policy Research, 127 eggers Hall, Syracuse University, Syracuse, NY 132441020) 
Abstract:  This paper develops new statistical inference methods for the parameters in threshold regression models. In particular, we develop a test for homogeneity of the threshold parameter and a test for linear restrictions on the regression coefficients. The tests are built upon a transformed partialsum process after reordering the observations based on the rank of the threshold variable, which recasts the crosssectional threshold problem into the timeseries structural break analogue. The asymptotic distributions of the test statistics are derived using this novel approach, and the finite sample properties are studied in Monte Carlo simulations. We apply the new tests to the tipping point problem studied by Card, Mas, and Rothstein (2008), and statistically justify that the location of the tipping point varies across tracts. 
Keywords:  Threshold Regression, Test, Homogeneous Threshold, Linear Restriction, Tipping Point 
JEL:  C12 C24 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:max:cprwps:223&r=all 
By:  Léopold Simar (Institut de Statistique, Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, B1348 LouvainlaNeuve, Belgium); Valentin Zelenyuk (School of Economics and Centre for Efficiency and Productivity Analysis (CEPA) at The University of Queensland, Australia) 
Abstract:  We propose an improvement of the finite sample approximation of the central limit theorems (CLTs) that were recently derived for statistics involving production efficiency scores estimated via Data Envelopment Analysis (DEA) or Free Disposal Hull (FDH) approaches. The improvement is very easy to implement since it involves a simple correction of the variance estimator with an estimate of the bias of the already employed statistics without any additional computational burden and preserves the original asymptotic results such as consistency and asymptotic normality. The proposed approach persistently showed improvement in all the scenarios that we tried in various MonteCarlo experiments, especially for relatively small samples or relatively large dimensions (measured by total number of inputs and outputs) of the underlying production model. This approach therefore is expected to produce more accurate estimates of confidence intervals of aggregates of individual efficiency scores in empirical research using DEA or FDH approaches and so must be valuable for practitioners. We also illustrate this method using a popular real data set to confirm that the difference in the estimated confidence intervals can be substantial. A stepbystep implementation algorithm of the proposed approach is included in the Appendix. 
Keywords:  Data Envelopment Analysis, DEA; Free Disposal Hull, FDH; Statistical Inference; Production Efficiency; Productivity. 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:qld:uqcepa:144&r=all 
By:  Takuya Ishihara 
Abstract:  In this study, we explore the identification and estimation of the quantile treatment effects (QTE) using panel data. We generalize the changeinchanges (CIC) model proposed by Athey and Imbens (2006) and propose a tractable estimator of the QTE. The CIC model allows for the estimation of the potential outcomes distribution and captures the heterogeneous effects of the treatment on the outcomes. However, the CIC model has the following two problems: (1) there lacks a tractable estimator in the presence of covariates and (2) the CIC estimator does not work when the treatment is continuous. Our model allows for the presence of covariates and continuous treatment. We propose a twostep estimation method based on a quantile regression and minimum distance method. We then show the consistency and asymptotic normality of our estimator. Monte Carlo studies indicate that our estimator performs well in finite samples. We use our method to estimate the impact of an insurance program on quantiles of household production. 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2001.04324&r=all 
By:  Shi, Chengchun; Lu, Wenbin; Song, Rui 
Abstract:  The divide and conquer method is a common strategy for handling massive data. In this article, we study the divide and conquer method for cubicrate estimators under the massive data framework. We develop a general theory for establishing the asymptotic distribution of the aggregated Mestimators using a weighted average with weights depending on the subgroup sample sizes. Under certain condition on the growing rate of the number of subgroups, the resulting aggregated estimators are shown to have faster convergence rate and asymptotic normal distribution, which are more tractable in both computation and inference than the original Mestimators based on pooled data. Our theory applies to a wide class of Mestimators with cube root convergence rate, including the location estimator, maximum score estimator, and value search estimator. Empirical performance via simulations and a real data application also validate our theoretical findings. Supplementary materials for this article are available online. 
Keywords:  cubic rate asymptotics; divide and conquer; Mestimators; massive data; P01 CA142538 
JEL:  C1 
Date:  2018–10–02 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:102111&r=all 
By:  Shi, Chengchun; Song, Rui; Lu, Wenbin 
Abstract:  Precision medicine is an emerging medical paradigm that focuses on finding the most effective treatment strategy tailored for individual patients. In the literature, most of the existing works focused on estimating the optimal treatment regime. However, there has been less attention devoted to hypothesis testing regarding the optimal treatment regime. In this paper, we first introduce the notion of conditional qualitative treatment effects (CQTE) of a set of variables given another set of variables and provide a class of equivalent representations for the null hypothesis of no CQTE. The proposed definition of CQTE does not assume any parametric form for the optimal treatment rule and plays an important role for assessing the incremental value of a set of new variables in optimal treatment decision making conditional on an existing set of prescriptive variables. We then propose novel testing procedures for no CQTE based on kernel estimation of the conditional contrast functions. We show that our test statistics have asymptotically correct size and nonnegligible power against some nonstandard local alternatives. The empirical performance of the proposed tests are evaluated by simulations and an application to an AIDS data set. 
Keywords:  conditional qualitative treatment effects; kernel estimation; nonstandard local alternatives; optimal treatment decision making 
JEL:  C1 
Date:  2019–08–01 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:102109&r=all 
By:  Chainarong Amornbunchornvej; Elena Zheleva; Tanya Y. BergerWolf 
Abstract:  Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of the effect time series is influenced by a combination of other time series with a fixed time delay. However, the assumption of the fixed time delay does not hold in many applications, such as collective behavior, financial markets, and many natural phenomena. To address this issue, we develop variablelag Granger causality, a generalization of Granger causality that relaxes the assumption of the fixed time delay and allows causes to influence effects with arbitrary time delays. In addition, we propose a method for inferring variablelag Granger causality relations. We demonstrate our approach on an application for studying coordinated collective behavior and show that it performs better than several existing methods in both simulated and realworld datasets. Our approach can be applied in any domain of time series analysis. 
Date:  2019–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1912.10829&r=all 
By:  Jinwoo Park 
Abstract:  The only input to attain the portfolio weights of global minimum variance portfolio (GMVP) is the covariance matrix of returns of assets being considered for investment. Since the population covariance matrix is not known, investors use historical data to estimate it. Even though sample covariance matrix is an unbiased estimator of the population covariance matrix, it includes a great amount of estimation error especially when the number of observed data is not much bigger than number of assets. As it is difficult to estimate the covariance matrix with high dimensionality all at once, clustering stocks is proposed to come up with covariance matrix in two steps: firstly, within a cluster and secondly, between clusters. It decreases the estimation error by reducing the number of features in the data matrix. The motivation of this dissertation is that the estimation error can still remain high even after clustering, if a large amount of stocks is clustered together in a single group. This research proposes to utilize a bounded clustering method in order to limit the maximum cluster size. The result of experiments shows that not only the gap between insample volatility and outofsample volatility decreases, but also the outofsample volatility gets reduced. It implies that we need a bounded clustering algorithm so that maximum clustering size can be precisely controlled to find the best portfolio performance. 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2001.02966&r=all 
By:  Adam Dearing; Jason R. Blevins 
Abstract:  We propose a new sequential Efficient PseudoLikelihood (EPL) estimator for structural economic models with an equality constraint, particularly dynamic discrete choice games of incomplete information. Each iteration in the EPL sequence is consistent and asymptotically efficient, and iterating to convergence improves finite sample performance. For dynamic singleagent models, we show that Aguirregabiria and Mira's (2002, 2007) Nested PseudoLikelihood (NPL) estimator arises as a special case of EPL. In dynamic games, EPL maintains its efficiency properties, although NPL does not. And a convenient change of variable in the equilibrium fixed point equation ensures EPL iterations have the same computational simplicity as NPL iterations. Furthermore, EPL iterations are stable and locally convergent to the finitesample maximum likelihood estimator at a nearlyquadratic rate for all regular Markov perfect equilibria, including unstable equilibria where NPL encounters convergence problems. Monte Carlo simulations confirm the theoretical results and demonstrate EPL's good performance in finite samples. 
Date:  2019–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1912.10488&r=all 
By:  Hossein Alidaee; Eric Auerbach; Michael P. Leung 
Abstract:  Social network data can be expensive to collect. Breza et al. (2017) propose aggregated relational data (ARD) as a lowcost substitute that can be used to recover the structure of a latent social network when it is generated by a specific parametric random effects model. Our main observation is that many economic network formation models produce networks that are effectively lowrank. As a consequence, network recovery from ARD is generally possible without parametric assumptions using a nuclearnorm penalized regression. We demonstrate how to implement this method and provide finitesample bounds on the mean squared error of the resulting estimator for the distribution of network links. Computation takes seconds for samples with hundreds of observations. Easytouse code in R and Python can be found at https://github.com/mpleung/ARD. 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2001.06052&r=all 
By:  Victor Chernozhukov; Denis Chetverikov; Kengo Kato; Yuta Koike 
Abstract:  This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its distribution plays a key role in many highdimensional econometric problems. Using a novel iterative randomized Lindeberg method, the paper derives new bounds for the distributional approximation errors. These new bounds substantially improve upon existing ones and simultaneously allow for a larger class of bootstrap methods. 
Date:  2019–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1912.10529&r=all 
By:  Joshua Angrist; Brigham Frandsen 
Abstract:  Machine learning (ML) is mostly a predictive enterprise, while the questions of interest to labor economists are mostly causal. In pursuit of causal effects, however, ML may be useful for automated selection of ordinary least squares (OLS) control variables. We illustrate the utility of ML for regressionbased causal inference by using lasso to select control variables for estimates of effects of college characteristics on wages. ML also seems relevant for an instrumental variables (IV) first stage, since the bias of twostage least squares can be said to be due to overfitting. Our investigation shows, however, that while MLbased instrument selection can improve on conventional 2SLS estimates, splitsample IV and LIML estimators do better. In some scenarios, the performance of MLaugmented IV estimators is degraded by pretest bias. In others, nonlinear ML for covariate control creates artificial exclusion restrictions that generate spurious findings. ML does better at choosing control variables for models identified by conditional independence assumptions than at choosing instrumental variables for models identified by exclusion restrictions. 
JEL:  C21 C26 C52 C55 J01 J08 
Date:  2019–12 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:26584&r=all 
By:  Chen, Yunxiao; Li, Xiaoou; Liu, Jingchen; Ying, Zhiliang 
Abstract:  Item response theory (IRT) plays an important role in psychological and educational measurement. Unlike the classical testing theory, IRT models aggregate the item level information, yielding more accurate measurements. Most IRT models assume local independence, an assumption not likely to be satisfied in practice, especially when the number of items is large. Results in the literature and simulation studies in this paper reveal that misspecifying the local independence assumption may result in inaccurate measurements and differential item functioning. To provide more robust measurements, we propose an integrated approach by adding a graphical component to a multidimensional IRT model that can offset the effect of unknown local dependence. The new model contains a confirmatory latent variable component, which measures the targeted latent traits, and a graphical component, which captures the local dependence. An efficient proximal algorithm is proposed for the parameter estimation and structure learning of the local dependence. This approach can substantially improve the measurement, given no prior information on the local dependence structure. The model can be applied to measure both a unidimensional latent trait and multidimensional latent traits. 
Keywords:  item response theory; local dependence; robust measurement; differential item functioning; graphical model; Ising model; pseudolikelihood; regularized estimator; Eysenck personality questionnairerevised; R01GM047845 
JEL:  C1 
Date:  2018–09–01 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:103181&r=all 
By:  Shi, Chengchun; Fan, Ailin; Song, Rui; Lu, Wenbin 
Abstract:  Precision medicine is a medical paradigm that focuses on finding the most effective treatment decision based on individual patient information. For many complex diseases, such as cancer, treatment decisions need to be tailored over time according to patients' responses to previous treatments. Such an adaptive strategy is referred as a dynamic treatment regime. A major challenge in deriving an optimal dynamic treatment regime arises when an extraordinary large number of prognostic factors, such as patient's genetic information, demographic characteristics, medical history and clinical measurements over time are available, but not all of them are necessary for making treatment decision. This makes variable selection an emerging need in precision medicine. In this paper, we propose a penalized multistage Alearning for deriving the optimal dynamic treatment regime when the number of covariates is of the nonpolynomial (NP) order of the sample size. To preserve the double robustness property of the Alearning method, we adopt the Dantzig selector, which directly penalizes the Aleaning estimating equations. Oracle inequalities of the proposed estimators for the parameters in the optimal dynamic treatment regime and error bounds on the difference between the value functions of the estimated optimal dynamic treatment regime and the true optimal dynamic treatment regime are established. Empirical performance of the proposed approach is evaluated by simulations and illustrated with an application to data from the STAR∗D study. 
Keywords:  Alearning; Dantzig selector; model misspecification; NPdimensionality; optimal dynamic treatment regime; oracle inequality 
JEL:  C1 
Date:  2018–06–01 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:102113&r=all 
By:  Budnik, Katarzyna; Rünstler, Gerhard 
Abstract:  We study the identification of policy shocks in Bayesian proxy VARs for the case that the instrument consists of sparse qualitative observations indicating the signs of certain shocks. We propose two identification schemes, i.e. linear discriminant analysis and a nonparametric sign concordance criterion. Monte Carlo simulations suggest that these provide more accurate confidence bounds than standard proxy VARs and are more efficient than local projections. Our application to U.S. macroprudential policies finds persistent effects of capital requirements and mortgage underwriting standards on credit volumes and house prices together with moderate effects on GDP and inflation. JEL Classification: C32, E44, G38 
Keywords:  Bayesian proxy VAR, capital requirements, discriminant analysis, mortgage underwriting standards, sign concordance 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:ecb:ecbwps:20202353&r=all 
By:  Yann Bramoullé (AixMarseille Univ, CNRS, EHESS, Ecole Centrale, AMSE, Marseille, France.); Habiba Djebbari (AixMarseille Univ, CNRS, EHESS, Ecole Centrale, AMSE, Marseille, France. and IZA); Bernard Fortin (Laval University (Economics Department), CRREP, CIRANO and IZA.) 
Abstract:  We survey the recent, fastgrowing literature on peer effects in networks. An important recurring theme is that the causal identification of peer effects depends on the structure of the network itself. In the absence of correlated effects, the reflection problem is generally solved by network interactions even in nonlinear, heterogeneous models. By contrast, microfoundations are generally not identified. We discuss and assess the various approaches developed by economists to account for correlated effects and network endogeneity in particular. We classify these approaches in four broad categories: random peers, random shocks, structural endogeneity and panel data. We review an emerging literature relaxing the assumption that the network is perfectly known. Throughout, we provide a critical reading of the existing literature and identify important gaps and directions for future research. 
Keywords:  social networks, peer effects, identification, causal effects, randomization, measurement errors 
JEL:  C31 C21 C90 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:aim:wpaimx:1936&r=all 
By:  Stefan T\"ubbicke 
Abstract:  This paper introduces entropy balancing for continuous treatments (EBCT) by extending the original entropy balancing methodology of Hainm\"uller (2012). In order to estimate balancing weights, the proposed approach solves a globally convex constrained optimization problem. EBCT weights reliably eradicate Pearson correlations between covariates and the continuous treatment variable. This is the case even when other methods based on the generalized propensity score tend to yield insufficient balance due to strong selection into different treatment intensities. Moreover, the optimization procedure is more successful in avoiding extreme weights attached to a single unit. Extensive MonteCarlo simulations show that treatment effect estimates using EBCT display similar or lower bias and uniformly lower root mean squared error. These properties make EBCT an attractive method for the evaluation of continuous treatments. 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2001.06281&r=all 
By:  Florian Gunsilius 
Abstract:  This article extends the method of synthetic controls to probability measures. The distribution of the synthetic control group is obtained as the optimally weighted barycenter in Wasserstein space of the distributions of the control groups which minimizes the distance to the distribution of the treatment group. It can be applied to settings with disaggregated or aggregated (functional) data. The method produces a generically unique counterfactual distribution when the data are continuously distributed. An efficient practical implementation along with novel inference results and a minimum wage empirical illustration are provided. 
Date:  2020–01 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2001.06118&r=all 
By:  Bryan S. Graham 
Abstract:  Many economic activities are embedded in networks: sets of agents and the (often) rivalrous relationships connecting them to one another. Input sourcing by firms, interbank lending, scientific research, and job search are four examples, among many, of networked economic activities. Motivated by the premise that networks' structures are consequential, this chapter describes econometric methods for analyzing them. I emphasize (i) dyadic regression analysis incorporating unobserved agentspecific heterogeneity and supporting causal inference, (ii) techniques for estimating, and conducting inference on, summary network parameters (e.g., the degree distribution or transitivity index); and (iii) empirical models of strategic network formation admitting interdependencies in preferences. Current research challenges and open questions are also discussed. 
JEL:  C1 C23 C25 C31 D85 
Date:  2019–12 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:26577&r=all 
By:  Ulrich K. Müller; James H. Stock; Mark W. Watson 
Abstract:  We develop a Bayesian latent factor model of the joint evolution of GDP per capita for 113 countries over the 118 years from 1900 to 2017. We find considerable heterogeneity in rates of convergence, including rates for some countries that are so slow that they might not converge (or diverge) in centurylong samples, and evidence of “convergence clubs” of countries. The joint Bayesian structure allows us to compute a joint predictive distribution for the output paths of these countries over the next 100 years. This predictive distribution can be used for simulations requiring projections into the deep future, such as estimating the costs of climate change. The model’s pooling of information across countries results in tighter prediction intervals than are achieved using univariate information sets. Still, even using more than a century of data on many countries, the 100year growth paths exhibit very wide uncertainty. 
JEL:  C32 C55 O47 
Date:  2019–12 
URL:  http://d.repec.org/n?u=RePEc:nbr:nberwo:26593&r=all 