
on Econometrics 
By:  Liang Jiang (Singapore Management University); Xiaobin Liu (School of Economics, Academy of Financial Research, and Institute for Fiscal BigData & Policy of Zhejiang University); Peter C.B. Phillips (Cowles Foundation, Yale University); Yichong Zhang (Singapore Management University) 
Abstract:  This paper examines regressionadjusted estimation and inference of unconditional quantile treatment eï¬€ects (QTEs) under covariateadaptive randomizations (CARs). Datasets from ï¬ eld experiments usually contain extra baseline covariates in addition to the strata indicators. We propose to incorporate these extra covariates via auxiliary regressions in the estimation and inference of unconditional QTEs. We establish the consistency, limit distribution, and validity of the multiplier bootstrap of the QTE estimator under CARs. The auxiliary regression may be estimated parametrically, nonparametrically, or via regularization when the data are highdimensional. Even when the auxiliary regression is misspeciï¬ ed, the proposed bootstrap inferential procedure still achieves the nominal rejection probability in the limit under the null. When the auxiliary regression is correctly speciï¬ ed, the regressionadjusted estimator achieves the minimum asymptotic variance. We also derive the optimal pseudo true values for the potentially misspeciï¬ ed parametric model that minimize the asymptotic variance of the corresponding QTE estimator. Our estimation and inferential methods can be implemented without tuning parameters and they allow for common choices of auxiliary regressions such as linear, probit and logit regressions despite the fact that these regressions may be misspeciï¬ ed. Finitesample performance of the new estimation and inferential methods is assessed in simulations and an empirical application studying the impact of child health and nutrition on educational outcomes is included. 
Keywords:  Covariateadaptive randomization, Highdimensional data, Regression adjustment, Quantile treatment effects 
JEL:  C14 C21 I21 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2288&r= 
By:  Matei Demetrescu (University of Kiel); Robinson KruseBecher (University of Hagen and CREATES) 
Abstract:  Testing distributional assumptions is an evergreen topic in statistics, econometrics and other quantitative disciplines. A key assumption for extant distributional tests is some form of stationarity. Yet, under timevarying mean or timevarying volatility, the observed marginal distribution belongs to a mixture family with components having the same baseline distribution but different location and scale parameters. Therefore, distribution tests consistently reject when stationarity assumptions are violated, even if the baseline distribution is correctly specified. At the same time, timevarying means or variances are common in economic data. We therefore propose distribution tests that are robustified to such timevariability of the data by means of a local standardization procedure. As a leading case in applied work, we demonstrate our approach in detail for the case of testing normality, while our main results are extended to general locationscale models without essential modifications. In addition to timevarying mean and volatility functions, the data generating process may exhibit features such as generic serial dependence. Specifically, we base our tests on raw moments of probability integral transformations of the series standardized using rolling windows of data, of suitably chosen width. The use of probability integral transforms is advantageous as they accommodate a wide range of distributions to be tested for and imply simple raw moment restrictions. Flexible nonparametric estimators of the mean and the variance functions are employed for the local standardization. Shortrun dynamics are taken into account using the (fixedb) Heteroskedasticity and Autocorrelation Robust [HAR] approach of Kiefer and Vogelsang (2005, Econometric Theory), which leads to robustness of the proposed test statistics to the estimation error induced by the local standardization. To ease implementation, we propose a simple rule for choosing the tuning parameters of the standardization procedure, as well as an effective finitesample adjustment. The provided Monte Carlo experiments show that the new tests perform well in terms of size and power and outperform alternative tests even under stationarity. Finally, we find in contrast to other studies no evidence against normality of the aggregate U.S. real output growth rates after accounting for timevariation in mean and variance. 
Keywords:  Distribution testing, Probability integral transformation, Local standardization, Nonparametric estimation, Heteroskedasticity and autocorrelation robust inference 
JEL:  C12 C14 C22 E01 E32 
Date:  2021–05–20 
URL:  http://d.repec.org/n?u=RePEc:aah:create:202107&r= 
By:  Yong Cai 
Abstract:  Clustered standard errors and approximated randomization tests are popular inference methods that allow for dependence within observations. However, they require researchers to know the cluster structure ex ante. We propose a procedure to help researchers discover clusters in panel data. Our method is based on thresholding an estimated longrun variancecovariance matrix and requires the panel to be large in the time dimension, but imposes no lower bound on the number of units. We show that our procedure recovers the true clusters with high probability with no assumptions on the cluster structure. The estimated clusters are independently of interest, but they can also be used in the approximate randomization tests or with conventional clusterrobust covariance estimators. The resulting procedures control size and have good power. 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2106.05503&r= 
By:  Yuanhua Feng (Paderborn University) 
Abstract:  We first propose to extend the SAS (sinharcsinh) normal distribution (Jones and Pewsey, 2009) by allowing the transformed normal random variable to be unstandardized. A LogSAS transformation for nonnegative random variables is then defined, which results in a novel LogSAS normal distributions. Properties of those distributions are investigated. The SAS transformation can also be applied e.g. to BoxCox transformed data. Maximum likelihood estimation of the proposed distributions are developed. A chain mixed multivariate extension of the SAS normal distribution and its application to distributional regression are also proposed. Those approaches can e.g. help us to discover possible spurious or hidden bimodal property of a multivariate distribution. The proposals are illustrated by different examples. 
Keywords:  Extended SAS distribution, LogSAS distribution, MLE, chain mixed multivariate distribution, distributional regression, spurious and hidden bimodality 
JEL:  C14 C51 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:pdn:ciepap:142&r= 
By:  Martin GarciaVazquez (University of Minnesota) 
Abstract:  This paper provides a novel constructive identification proof for nonstationary Hidden Markov models. The identification result establishes that only two periods of time are required if one wants to identify transition probabilities between those two periods. This is achieved by using three conditionally independent noisy measures of the hidden state. The paper also provides a novel estimator for nonstationary hidden Markov models based on the identification proof. Montecarlo experiments show that this estimator is faster to compute than maximum likelihood, and almost as precise for large enough samples. Moreover, I show how my identification proof and my estimator can be used in two different relevant applications: Identification and estimation of Conditional Choice Probabilities, initial conditions and laws of motion in dynamic discrete choice models when there is an unobservable state; and identification and estimation of the production function of cognitive skills in a child development context when skills and investment are unobserved. 
Keywords:  identification, Child Development, cognitive skills, investment in children 
JEL:  C10 J24 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:hka:wpaper:2021023&r= 
By:  Kohtaro Hitomi (Kyoto Institute of Technology); Keiji Nagai (Yokohama National University); Yoshihiko Nishiyama (Institute of Economic Research, Kyoto University); Junfan Tao (JSPS International Research Fellow (Kyoto University), Institute of Economic Research, Kyoto University) 
Abstract:  Currently, because online data is abundant and can be collected more easily , people often face the problem of making correct statistical decisions as soon as possible. If the online data is sequentially available, sequential analysis is appropriate for handling such a problem. We consider the joint asymptotic properties of stopping times and sequential estimators for stationary firstorder autoregressive (AR(1)) processes under independent and identically distributed errors with zero mean and finite variance. Using the stopping times introduced by Lai and Siegmund (1983) for AR(1), we investigate the joint asymptotic properties of the stopping times, the sequential least square estimator (LSE), and the estimator of U+03C3U+00b2. The functional central limit theorem for nonlinear ergodic stationary processes is crucial for obtaining our main results with respect to their asymptotic properties. We found that the sequential least square estimator and stopping times exhibit joint asymptotic normality. When U+03C3U+00b2 is estimated, the joint limiting distribution degenerates and the asymptotic variance of the stopping time is strictly smaller than that of the stopping time with a known U+03C3U+00b2. 
Keywords:  Observed Fisher information, joint asymptotic normality, functional central limit theorem in D[0,U+221E), Anscombebe's Theorem 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:kyo:wpaper:1060&r= 
By:  Griffin, Jim E.; Mitrodima, Gelly 
Abstract:  We consider jointly modeling a finite collection of quantiles over time. Formal Bayesian inference on quantiles is challenging since we need access to both the quantile function and the likelihood. We propose a flexible Bayesian timevarying transformation model, which allows the likelihood and the quantile function to be directly calculated. We derive conditions for stationarity, discuss suitable priors, and describe a Markov chain Monte Carlo algorithm for inference. We illustrate the usefulness of the model for estimation and forecasting on stock, index, and commodity returns. 
Keywords:  Bayesian nonparametrics; Predictive density; Stationarity; Transformation models 
JEL:  C1 J1 
Date:  2020–06–10 
URL:  http://d.repec.org/n?u=RePEc:ehl:lserod:105610&r= 
By:  John List; Azeem Shaikh; Atom Vayalinkal 
Abstract:  List et al. (2019) provides a framework for testing multiple null hypotheses simultaneously using experimental data in which simple random sampling is used to assign treatment status to units. As in List et al. (2019), we rely on general results in Romano and Wolf (2010) to develop under weak assumptions a procedure that (i) asymptotically controls the familywise error rate  the probability of one or more false rejections  and (ii) is asymptotically balanced in that the marginal probability of rejecting any true null hypothesis is approximately equal in large samples. Our analysis departs from List et al. (2019) in that it further exploits observed, baseline covariates. The precise way in which these covariates are incorporated is based upon results in Lin (2013) in order to ensure that inferences are typically more powerful in large samples. 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:feb:natura:00732&r= 
By:  Blankmeyer, Eric 
Abstract:  . Ordinary least squares, twostage least squares and the NISE estimator are applied to three data sets involving equations from microeconomics and macroeconomics. The focus is on simultaneity bias in linear least squares and on the ability of the other estimators to mitigate the bias. 
Keywords:  simultaneity bias, instrumental variables, least squares regression 
JEL:  C3 
Date:  2021–04 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:108179&r= 
By:  Jonas E. Arias; Juan F. RubioRamirez; Minchul Shin 
Abstract:  We document five novel empirical findings on the wellknown potential ordering drawback associated with the timevarying parameter vector autoregression with stochastic volatility developed by Cogley and Sargent (2005) and Primiceri (2005), CSPSV. First, the ordering does not affect point prediction. Second, the standard deviation of the predictive densities implied by different orderings can differ substantially. Third, the average length of the prediction intervals is also sensitive to the ordering. Fourth, the best ordering for one variable in terms of logpredictive scores does not necessarily imply the best ordering for another variable under the same metric. Fifth, the best ordering for variable x in terms of logpredictive scores tends to put the variable x first while the worst ordering for variable x tends to put the variable x last. Then, we consider two alternative ordering invariant timevarying parameter VARSV models: the discounted Wishart SV model (DWSV) and the dynamic stochastic correlation SV model (DSCSV). The DWSV underperforms relative to each ordering of the CSPSV. The DSCSV has an outofsample forecasting performance comparable to the median outcomes across orderings of the CSPSV. 
Keywords:  Vector Autoregressions; TimeVarying Parameters; Stochastic Volatility; Variable Ordering; Cholesky Decomposition; Wishart Process; Dynamic Conditional Correlation; Outofsample Forecasting Evaluation 
JEL:  C8 C11 C32 C53 
Date:  2021–06–03 
URL:  http://d.repec.org/n?u=RePEc:fip:fedpwp:92355&r= 
By:  David M. Kaplan (Department of Economics, University of Missouri); Xin Liu (Department of Economics, University of Missouri) 
Abstract:  With standard instrumental variables regression, kclass estimators have the potential to reduce bias, which is larger with weak instruments. With instrumental variables quantile regression, weak instrumentrobust estimation is even more important because there is less guidance for assessing instrument strength. Motivated by this, we introduce an analogous kclass of estimators for instrumental variables quantile regression. We show the firstorder asymptotic distribution under strong instruments is equivalent for all conventional choices of k. We evaluate finitesample median bias in simulations. Computation is fast, and the "LIML" k reliably reduces median bias compared to the k=1 benchmark across a variety of datagenerating processes, especially with greater degrees of overidentification. We also revisit some empirical estimates of consumption Euler equations. All code is provided online. 
Keywords:  bias, weak instruments 
JEL:  C21 C26 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:umc:wpaper:2104&r= 
By:  Mateusz Buczyński (Interdisciplinary Doctoral School, University of Warsaw); Marcin Chlebus (Faculty of Economic Sciences, University of Warsaw) 
Abstract:  This study proposes a new GARCH specification, adapting a long shortterm memory (LSTM) neural network's architecture. Classical GARCH models have been proven to give substantially good results in the case of financial modeling, where high volatility can be observed. In particular, their high value is often praised in the case of ValueatRisk. However, the lack of nonlinear structure in most of the approaches entails that the conditional variance is not represented in the model well enough. On the contrary, recent rapid advancement of deep learning methods is said to be capable of describing any nonlinear relationships prominently. We suggest GARCHNet  a nonlinear approach to conditional variance that combines LSTM neural networks with maximum likelihood estimators of probability in GARCH. The distributions of the innovations considered in the paper are: normal, t and skewed t, however the approach does enable extensions to other distributions as well. To evaluate our model, we have executed an empirical study on the log returns of WIG 20 (Warsaw Stock Exchange Index) in four different time periods throughout 2005 and 2021 with varying levels of observed volatility. Our findings confirm the validity of the solution, however we present several directions to develop it further. 
Keywords:  ValueatRisk, GARCH, neural networks, LSTM 
JEL:  G32 C52 C53 C58 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:war:wpaper:202108&r= 
By:  James Mitchell; Martin Weale 
Abstract:  This paper develops methods for the production and evaluation of censored density forecasts. Censored density forecasts quantify forecast risks in a middle region of the density covering a specified probability, and ignore the magnitude but not the frequency of outlying observations. We propose a new estimator that fits a potentially skewed and fattailed density to the inner observations, acknowledging that the outlying observations may be drawn from a different but unknown distribution. We also introduce a new test for calibration of censored density forecasts. An application using historical forecast errors from the Federal Reserve Board and the Monetary Policy Committee at the Bank of England illustrates the utility of censored density forecasts when quantifying forecast risks after shocks such as the global financial crisis and the COVID19 pandemic. 
Keywords:  Forecast uncertainty; Outliers; Fan charts; Skewed densities; Best critical region; Density forecasting; Censoring; Forecast evaluation 
JEL:  C24 C46 C53 E58 
Date:  2021–05–27 
URL:  http://d.repec.org/n?u=RePEc:fip:fedcwq:92109&r= 
By:  JIN SEO CHO (Yonsei Univ); MATTHEW GREENWOODNIMMO (University of Melbourne); YONGCHEOL SHIN (University of York) 
Abstract:  We review the literature on the Autoregressive Distributed Lag (ARDL) model, from its origins in the analysis of autocorrelated trend stationary processes to its subsequent applications in the analysis of cointegrated nonstationary time series. We then survey several recent extensions of the ARDL model, including asymmetric and nonlinear generalisations of the ARDL model, the quantile ARDL model, the pooled mean group dynamic panel data model and the spatiotemporal ARDL model. 
Keywords:  Autoregressive Distributed Lag (ARDL) Model; Asymmetry, Nonlinearity and Threshold Effects; Quantile Regression; Panel Data; Spatial Analysis 
JEL:  C22 
Date:  2021–04 
URL:  http://d.repec.org/n?u=RePEc:yon:wpaper:2021rwp186&r= 
By:  Johann Pfitzinger 
Abstract:  Adoption of deep neural networks in fields such as economics or finance has been constrained by the lack of interpretability of model outcomes. This paper proposes a generative neural network architecture  the parameter encoder neural network (PENN)  capable of estimating local posterior distributions for the parameters of a regression model. The parameters fully explain predictions in terms of the inputs and permit visualization, interpretation and inference in the presence of complex heterogeneous effects and feature dependencies. The use of Bayesian inference techniques offers an intuitive mechanism to regularize local parameter estimates towards a stable solution, and to reduce noisefitting in settings of limited data availability. The proposed neural network is particularly wellsuited to applications in economics and finance, where parameter inference plays an important role. An application to an asset pricing problem demonstrates how the PENN can be used to explore nonlinear risk dynamics in financial markets, and to compare empirical nonlinear effects to behavior posited by financial theory. 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2106.05536&r= 
By:  Minsu Chang (Georgetown University); Xiaohong Chen (Cowles Foundation, Yale University); Frank Schorfheide (University of Pennsylvania, CEPR, PIER, NBER) 
Abstract:  We develop a statespace model with a statetransition equation that takes the form of a functional vector autoregression and stacks macroeconomic aggregates and a crosssectional density. The measurement equation captures the error in estimating log densities from repeated crosssectional samples. The log densities and the transition kernels in the law of motion of the states are approximated by sieves, which leads to a nitedimensional representation in terms of macroeconomic aggregates and sieve coeï¬€icients. We use this model to study the joint dynamics of technology shocks, per capita GDP, employment rates, and the earnings distribution. We nd that the estimated spillovers between aggregate and distributional dynamics are generally small, a positive technology shock tends to decrease inequality, and a shock that raises the inequality of earnings leads to a small but not signiï¬ cant increase in GDP. 
Keywords:  Bayesian Model Selection, Econometric Model Evaluation, Earnings Distribution, Functional Vector Autoregressions, Heterogeneous Agent Models, Statespace Model, Technology Shocks 
JEL:  C11 C32 C52 E32 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:cwl:cwldpp:2289&r= 
By:  Laura Coroneo; Fabrizio Iacone 
Abstract:  We revisit the Diebold and Mariano (1995) test, investigating the consequences of having autocorrelation in the loss differential. This situation can arise not only when a forecast is suboptimal under MSE loss, but also when it is optimal under an alternative loss, or it is evaluated on a short sample, or when a forecast with weakly dependent forecast errors is compared to a naive benchmark. We show that the power of the Diebold and Mariano (1995) test decreases as the dependence increases, making it more difficult to obtain statistically significant evidence of superior predictive ability against less accurate benchmarks. Moreover, we find that after a certain threshold the test has no power and the correct null hypothesis is spuriously rejected. Taken together, these results caution to seriously consider the dependence properties of the selected forecast and of the loss differential before the application of the Diebold and Mariano (1995) test, especially when naive benchmarks are considered. 
Keywords:  strong autocorrelation, Forecast evaluation, Diebold and Mariano Test, Long Run Variance Estimation. 
JEL:  C12 C32 C53 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:yor:yorken:21/03&r= 
By:  Aguirregabiria, Victor 
Abstract:  Firms make decisions under uncertainty and differ in their ability to collect and process information. As a result, in changing environments, firms have heterogeneous beliefs on the behavior of other firms. This heterogeneity in beliefs can have important implications on market outcomes, efficiency, and welfare. This paper studies the identification of firms' beliefs using their observed actions  a revealed preference and beliefs approach. I consider a general structural model of market competition where firms have incomplete information and their beliefs and profits are nonparametric functions of decisions and state variables. Beliefs may be out of equilibrium. The framework applies both to continuous and discrete choice games and includes as particular cases models of competition in prices or quantities, auction models, entry games, and dynamic investment games. I focus on identification results that exploit a natural exclusion restriction in models of competition: an observable variable that affects a firm's cost (or revenue) but does not have a direct effect on other firms' profits. I present identification results under three scenarios  common in empirical IO  on the data available to the researcher. 
Keywords:  identification; Nonequilibrium beliefs; Revealed beliefs approach; Structural models of competition 
JEL:  C57 D81 D83 D84 L13 
Date:  2020–06 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:14975&r= 
By:  Paul Glasserman; Mike Li 
Abstract:  We study the behavior of linear discriminant functions for binary classification in the infiniteimbalance limit, where the sample size of one class grows without bound while the sample size of the other remains fixed. The coefficients of the classifier minimize an expected loss specified through a weight function. We show that for a broad class of weight functions, the intercept diverges but the rest of the coefficient vector has a finite limit under infinite imbalance, extending prior work on logistic regression. The limit depends on the left tail of the weight function, for which we distinguish three cases: bounded, asymptotically polynomial, and asymptotically exponential. The limiting coefficient vectors reflect robustness or conservatism properties in the sense that they optimize against certain worstcase alternatives. In the bounded and polynomial cases, the limit is equivalent to an implicit choice of upsampling distribution for the minority class. We apply these ideas in a credit risk setting, with particular emphasis on performance in the highsensitivity and highspecificity regions. 
Date:  2021–06 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2106.05797&r= 
By:  Bobeica, Elena; Hartwig, Benny 
Abstract:  We document the impact of COVID19 on frequently employed time series models, with a focus on euro area inflation. We show that for both single equation models (Phillips curves) and Vector Autoregressions (VARs) estimated parameters change notably with the pandemic. In a VAR, allowing the errors to have a distribution with fatter tails than the Gaussian one equips the model to better deal with the COVID19 shock. A standard Gaussian VAR can still be used for producing conditional forecasts when relevant offmodel information is used. We illustrate this by conditioning on official projections for a set of variables, but also by tilting to expectations from the Survey of Professional Forecasters. For Phillips curves, averaging across many conditional forecasts in a thick modelling framework offers some hedge against parameter instability. JEL Classification: C53, E31, E37 
Keywords:  COVID19, forecasting, inflation, student's t errors, tilting, VAR 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:ecb:ecbwps:20212558&r= 
By:  Michel Lubrano (https://www.amseaixmarseille.fr/en); Zhou Xun (School of Economics and Management, Nanjing University of Finance and Economics, China) 
Abstract:  This survey paper reviews the recent Bayesian literature on poverty measurement. After introducing Bayesian statistics, we show how Bayesian model criticism could help to revise the international poverty line. Using mixtures of lognormals to model income, we derive the posterior distribution for the FGT, Watts and Sen poverty indices, then for TIP curves (with an illustration on child poverty in Germany) and finally for Growth Incidence Curves. The relation of restricted stochastic dominance with TIP and GIC dominance is detailed with an example on UK data. Using panel data, we show how to decompose poverty into total, chronic and transient poverty, comparing child and adult poverty in East Germany when redistribution is introduced. When a panel is not available, a Gibbs sampler is used to build a pseudo panel. We illustrate poverty dynamics by examining the consequences of the Wall on poverty entry and poverty persistence in occupied West Bank. 
Keywords:  Bayesian inference, mixture model, poverty indices, stochastic dominance, poverty dynamics 
JEL:  C11 C46 I32 I38 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:aim:wpaimx:2133&r= 