
on Econometrics 
By:  Alyssa Carlson (Department of Economics, University of Missouri); Riju Joshi (Department of Economics, Portland State University) 
Abstract:  In this paper, we propose a parametric estimation procedure for linear panel data models with sample selection and heterogeneous coefficients. We allow heterogeneous coefficients in both outcome model as well as in the selection model. Our twostep estimation procedure accounts for endogeneity from the selection process as well as endogeneity due to correlation between the individual unobserved heterogeneity and the observed covariates. Conditional linear projections are used to establish a tractable control function approach that builds upon the original Heckman correction to sample selection. We derive the consistency and âˆšnasymptotic normality of the proposed twostep procedure and provide an asymptotic variance formula that allows for arbitrary correlation over time. Monte Carlo simulations illustrate the finite sample properties of our estimator and demonstrate that our proposed estimator outperforms standard estimators that ignore the presence of parameter heterogeneity and heteroskedastic sample selection. We apply the proposed approach to estimate gender differences in highstakes time constrained decisions using Elo ratings data from the World Chess Federation. When addressing both sources of endogeneity, we find a much larger gender skill gap and substantial differences across the gender in strategically selecting into time constrained matches. 
Keywords:  panel data, sample selection, heterogeneous coefficients, control function, conditional linear projections 
JEL:  C23 C33 
Date:  2021 
URL:  http://d.repec.org/n?u=RePEc:umc:wpaper:2103&r= 
By:  Giuseppe Cavaliere (Department of Economics, Exeter Business School, Department of Economics, University of Bologna,); Indeewara Perera (Department of Economics, The University of Sheffield); Anders Rahbek (Department of Economics, University of Copenhagen) 
Abstract:  This paper develops tests for the correct specification of the conditional variance function in GARCH models when the true parameter may lie on the boundary of the parameter space. The test statistics considered are of KolmogorovSmirnov and Cramérvon Mises type, and are based on a certain empirical process marked by centered squared residuals. The limiting distributions of the test statistics are not free from (unknown) nuisance parameters, and hence critical values cannot be tabulated. A novel bootstrap procedure is proposed to implement the tests; it is shown to be asymptotically valid under general conditions, irrespective of the presence of nuisance parameters on the boundary. The proposed bootstrap approach is based on shrinking of the parameter estimates used to generate the bootstrap sample toward the boundary of the parameter space at a proper rate. It is simple to implement and fast in applications, as the associated test statistics have simple closed form expressions. A simulation study demonstrates that the new tests: (i) have excellent finite sample behaviour in terms of empirical rejection probabilities under the null as well as under the alternative; (ii) provide a useful complement to existing procedures based on LjungBox type approaches. Two data examples are considered to illustrate the tests. 
Keywords:  GARCH model, bootstrap, specification test, KolmogorovSmirnov test, Cramérvon Mises test, marked empirical process, nuisance parameters on the boundary, 
Date:  2021–05–25 
URL:  http://d.repec.org/n?u=RePEc:kud:kuiedp:2106&r= 
By:  Arulampalam, Wiji (University of Warwick); Corradi, Valentina (University of Surrey); Gutknecht, Daniel (Goethe University Frankfurt) 
Abstract:  We propose various semiparametric estimators for nonlinear selection models, where slope and intercept can be separately identifed. When the selection equation satisfies a monotonic index restriction, we suggest a local polynomial estimator, using only observations for which the marginal distribution of instrument index is close to one. Such an estimator achieves a univariate nonparametric rate, which can range from a cubic to an 'almost' parametric rate. We then consider the case in which either the monotonic index restriction does not hold and/ or the set of observations with propensity score close to one is thin so that convergence occurs at most at a cubic rate. We explore the finite sample behaviour in a Monte Carlo study, and illustrate the use of our estimator using a model for count data with multiplicative unobserved heterogeneity. 
Keywords:  irregular identification, selection bias, local polynomial, trimming, count data 
JEL:  C14 C21 C24 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:iza:izadps:dp14364&r= 
By:  Jinyong Hahn (UCLA); Zhipeng Liao (UCLA); Geert Ridder (USC); Ruoyao Shi (Department of Economics, University of California Riverside) 
Abstract:  This paper studies semiparametric twostep estimators with a control variable estimated in a firststep parametric or nonparametric model. We provide the explicit influence function of the twostep estimator under an index restriction which is imposed directly on the unknown control variable. The index restriction is weaker than the commonly used identification conditions in the literature, which are imposed on all exogenous variables. An extra term shows up in the influence function of the semiparametric twostep estimator under the weaker identification condition. We illustrate our influence function formula in a mean regression example, a quantile regression example, and a sample selection example where the control variable approach is applied for identification and consistent estimation of structural parameters. 
Keywords:  control variable approach, generated regressors, influence function, semiparametric twostep estimation 
JEL:  C14 C31 C32 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:ucr:wpaper:202107&r= 
By:  Laura Liu; Alexandre Poirier; JiLiang Shiu 
Abstract:  Average partial effects (APEs) are generally not pointidentified in binary response panel models with unrestricted unobserved heterogeneity. We show their pointidentification under an index sufficiency assumption on the unobserved heterogeneity, even when the error distribution is unspecified. This assumption does not impose parametric restrictions on the unobserved heterogeneity. We then construct a threestep semiparametric estimator for the APE. In the first step, we estimate the common parameters using either conditional logit or smoothed maximum score. In the second step, we estimate the conditional expectation of the outcomes using local polynomial regression given generated regressors that depend on firststep estimates. In the third step, we average this conditional distribution over a subset of conditioning variables to obtain a partial mean which estimates the APE. We show that this proposed threestep APE estimator is consistent and asymptotically normal. We then evaluate its finitesample properties in Monte Carlo simulations, and illustrate our estimator in a study of determinants of married women's labor supply. 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2105.12891&r= 
By:  Jiang, Peiyun; Kurozumi, Eiji 
Abstract:  In this paper, we develop a new test to detect whether break points are common in heterogeneous panel data models where the time series dimension T could be large relative to crosssection dimension N. The error process is assumed to be crosssectionally independent. The test is based on the cumulative sum (CUSUM) of ordinary least squares (OLS) residuals. We derive the asymptotic distribution of the detecting statistic under the null hypothesis, while proving the consistency of the test under the alternative. Monte Carlo simulations and an empirical example show good performance of the test. 
Keywords:  CUSUM test, panel data, structural change, common breaks 
JEL:  C12 C23 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:hit:hiasdp:hiase107&r= 
By:  Canepa, Alessandra (University of Turin) 
Abstract:  Johansen (2000) Bartlett correction factor for the LR test of linear restrictions on cointegrated vectors is derived under the i.i.d. Gaussian assumption for the innovation terms. However, the distribution of most data relating to financial variables are fattailed and often skewed, there is therefore a need to examine small sample inference procedures that require weaker assumptions for the innovation term. This paper suggests that using a nonparametric bootstrap to approximate a Bartletttype correction provides a statistic that does not require specification of the innovation distribution and can be used by applied econometricians to perform a small sample inference procedure that is less computationally demanding than estimating the pvalue of the observed statistic. 
Date:  2021–03 
URL:  http://d.repec.org/n?u=RePEc:uto:dipeco:202108&r= 
By:  Martin Bruns (University of East Anglia); Helmut Lütkepohl (DIW Berlin and The Free University of Berlin) 
Abstract:  Different local projection (LP) estimators for structural impulse responses of proxy vector autoregressions are reviewed and compared algebraically and with respect to their small sample suitability for inference. Conditions for numerical equivalence and similarities of some estimators are provided. A new LP type estimator is also proposed which is very easy to compute. Two generalized least squares (GLS) projection estimators are found to be more accurate than the other LP estimators in small samples. In particular, a lagaugmented GLS estimator tends to be superior to its competitors and to perform as well as a standard VAR estimator for sufficiently large samples. 
Keywords:  Structural vector autoregression, local projection, impulse responses, instrumental variable 
JEL:  C32 
Date:  2021–05–28 
URL:  http://d.repec.org/n?u=RePEc:uea:ueaeco:202104&r= 
By:  Marina Dias; Demian Pouzo 
Abstract:  We propose a method for conducting asymptotically valid inference for treatment effects in a multivalued treatment framework where the number of units in the treatment arms can be small and do not grow with the sample size. We accomplish this by casting the model as a semi/nonparametric conditional quantile model and using known finite sample results about the law of the indicator function that defines the conditional quantile. Our framework allows for structural functions that are nonadditively separable, with flexible functional forms and heteroskedasticy in the residuals, and it also encompasses commonly used designs like difference in difference. We study the finite sample behavior of our test in a Monte Carlo study and we also apply our results to assessing the effect of weather events on GDP growth. 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2105.10965&r= 
By:  Karlsson, Sune (Örebro University School of Business); Mazur, Stepan (Örebro University School of Business); Nguyen, Hoang (Örebro University School of Business) 
Abstract:  With uncertain changes of the economic environment, macroeconomic downturns during recessions and crises can hardly be explained by a Gaussian structural shock. There is evidence that the distribution of macroeconomic variables is skewed and heavy tailed. In this paper, we contribute to the literature by extending a vector autore gression (VAR) model to account for a more realistic assumption of the multivariate distribution of the macroeconomic variables. We propose a general class of generalized hyperbolic skew Student's t distribution with stochastic volatility for the error term in the VAR model that allows us to take into account skewness and heavy tails. Tools for Bayesian inference and model selection using a Gibbs sampler are provided. In an empirical study, we present evidence of skewness and heavy tails for monthly macroe conomic variables. The analysis also gives a clear message that skewness should be taken into account for better predictions during recessions and crises. 
Keywords:  Vector autoregression; Skewness and heavy tails; Generalized hyper bolic skew Students t distribution; Stochastic volatility; Markov Chain Monte Carlo 
JEL:  C11 C15 C16 C32 C52 
Date:  2021–05–20 
URL:  http://d.repec.org/n?u=RePEc:hhs:oruesi:2021_008&r= 
By:  Gaillac, Christophe; Gautier, Eric 
Abstract:  This paper studies point identification of the distribution of the coefficients in some random coefficients models with exogenous regressors when their support is a proper subset, possibly discrete but countable. We exhibit tradeoffs between restrictions on the distribution of the random coefficients and the support of the regressors. We consider linear models including those with nonlinear transforms of a baseline regressor, with an infinite number of regressors and deconvolution, the binary choice model, and panel data models such as singleindex panel data models and an extension of the Kotlarski lemma. 
Keywords:  Identification; Random Coefficients; Quasianalyticity; Deconvolution 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:tse:wpaper:125629&r= 
By:  Eric Auerbach 
Abstract:  This paper provides additional results relevant to the setting, model, and estimators of Auerbach (2019a). Section 1 contains results about the large sample properties of the estimators from Section 2 of Auerbach (2019a). Section 2 considers some extensions to the model. Section 3 provides an application to estimating network peer effects. Section 4 shows the results from some simulations. 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2105.10002&r= 
By:  Stauskas, Ovidijus (Department of Economics, Lund University) 
Abstract:  A recent study proposed by Westerlund (CCE in Panels with General Unknown Factors, Econometrics Journal, 21, 264276, 2018) showed that a very popular Common Correlated Effects (CCE) estimator is significantly more applicable than it was thought before. Contrary to the usual stationarity assumption, common factors can in fact be much more general and not unit root only. This also helps to alleviate the uncertainty over deterministic model components since they can be treated as unknown, similarly to unobserved stochastic factors. While very promising, these theoretical results concern only the pooled (CCEP) version of the estimator for the homogeneous parameters, which does no take heterogeneous effects into account. Therefore, it is natural to generalize these findings to the case of unitspecific slopes. It is especially interesting, because many previous studies on heterogeneous slopes did not rigorously account for the usual situation when the factors are proxied by more explanatory variables than needed. As a result, the current setup introduces more uniformity to the CCE theory. We demonstrate that save for some regularity conditions, CCEP and the mean group (CCEMG) estimators are asymptotically normal and unbiased under heterogeneous slopes and general unknown factors. 
Keywords:  Panel data; CCE; NonStationarity; Factors; Heterogeneity 
JEL:  C12 C23 C33 
Date:  2021–05–18 
URL:  http://d.repec.org/n?u=RePEc:hhs:lunewp:2021_009&r= 
By:  Odendahl, Florens; Rossi, Barbara; Sekhposyan, Tatevik 
Abstract:  We propose a novel forecast comparison methodology to evaluate models' relative forecasting performance when the latter is a statedependent function of economic variables. In our benchÂ¬mark case, the relative forecasting performance, measured by the forecast loss differential, is modeled via a threshold model. Importantly, we allow the threshold that triggers the switch from one state to the next to be unknown, leading to a nonstandard test statistic due to the presence of a nuisance parameter. Existing tests either assume a constant outofsample forecast performance or use nonparametric techniques robust to timevariation; consequently, they may lack power against statedependent predictability. Importantly, our approach is applicable to point forecasts as well as predictive densities. Monte Carlo results suggest that our proposed test statistics perform well in ï¬ nite samples and have better power than existing tests in selecting the best forecasting model in the presence of state dependence. Our test statistics uncover "pockets of predictability" in U.S. equity premia forecasts; the pockets are a statedependent function of stock market volatility. Models using economic predictors perform signiï¬ cantly worse than a simple mean forecast in periods of high volatility, but, in periods of low volatility, the use of economic predictors may lead to small forecast improvements. 
Keywords:  Forecast evaluation; Pockets of Predictability; State Dependence 
JEL:  C52 C53 G17 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:15217&r= 
By:  Borusyak, Kirill; Hull, Peter; Jaravel, Xavier 
Abstract:  Many studies use shiftshare (or "Bartik") instruments, which average a set of shocks with exposure share weights. We provide a new econometric framework for shiftshare instrumental variable (SSIV) regressions in which identification follows from the quasirandom assignment of shocks, while exposure shares are allowed to be endogenous. The framework is motivated by an equivalence result: the orthogonality between a shiftshare instrument and an unobserved residual can be represented as the orthogonality between the underlying shocks and a shocklevel unobservable. SSIV regression coefficients can similarly be obtained from an equivalent shocklevel regression, motivating shocklevel conditions for their consistency. We discuss and illustrate several practical insights of this framework in the setting of Autor, Dorn, and Hanson (2013), estimating the effect of Chinese import competition on manufacturing employment across U.S. commuting zones. 
JEL:  C18 C21 C26 F16 J21 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:15212&r= 
By:  Dante Amengual (CEMFI, Spain); Gabriele Fiorentini (Università di Firenze, Italy; Rimini Centre for Economic Analysis); Enrique Sentana (CEMFI, Spain) 
Abstract:  We show that the information matrix test for a multivariate normal random vector coincides with the sum of the two moment tests that look at the means of all the different third and fourthorder multivariate Hermite polynomials, respectively. We also explain how to simulate its exact, parameterfree, finite sample distribution to any desired degree of accuracy for any dimension of the random vector and sample size. Specifically, we exploit the numerical invariance of the test statistic to affine transformations of the observed variables to simulate draws extremely quickly. 
Keywords:  Exact test, Hessian matrix, Multivariate normality, Outer product of the score 
JEL:  C30 C46 C52 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:rim:rimwps:2112&r= 
By:  Yong Shi; Wei Dai; Wen Long; Bo Li 
Abstract:  The Gaussian Process with a deep kernel is an extension of the classic GP regression model and this extended model usually constructs a new kernel function by deploying deep learning techniques like long shortterm memory networks. A Gaussian Process with the kernel learned by LSTM, abbreviated as GPLSTM, has the advantage of capturing the complex dependency of financial sequential data, while retaining the ability of probabilistic inference. However, the deep kernel Gaussian Process has not been applied to forecast the conditional returns and volatility in financial market to the best of our knowledge. In this paper, grid search algorithm, used for performing hyperparameter optimization, is integrated with GPLSTM to predict both the conditional mean and volatility of stock returns, which are then combined together to calculate the conditional Sharpe Ratio for constructing a longshort portfolio. The experiments are performed on a dataset covering all constituents of Shenzhen Stock Exchange Component Index. Based on empirical results, we find that the GPLSTM model can provide more accurate forecasts in stock returns and volatility, which are jointly evaluated by the performance of constructed portfolios. Further subperiod analysis of the experiment results indicates that the superiority of GPLSTM model over the benchmark models stems from better performance in highly volatile periods. 
Date:  2021–05 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:2105.12293&r= 
By:  Stefan Leknes; Sturla A. Løkken (Statistics Norway) 
Abstract:  Reliable local demographic schedules are in high demand, but small area problems pose a challenge to estimation. The literature has directed little attention to the opportunities created by increased availability of highquality geocoded data. We propose the use of empirical Bayes methods based on a model with three hierarchical geographic levels to predict small area fertility schedules. The proposed model has a flexible specification with respect to age, which allows for detailed age heterogeneity in local fertility patterns. The model limits sampling variability in small areas, captures regional variations effectively, is robust to certain types of model misspecification, and outperforms alternative models in terms of prediction accuracy. The beneficial properties of the model are demonstrated through simulations and estimations on fullcount Norwegian population data. 
Keywords:  small area estimation; hierarchical linear models; empirical Bayes method; shrinkage; agespecific fertility 
JEL:  J13 R58 C13 C18 
Date:  2021–04 
URL:  http://d.repec.org/n?u=RePEc:ssb:dispap:953&r= 
By:  Thomas von Brasch; Arvid Raknerud (Statistics Norway) 
Abstract:  In a seminal paper, Feenstra (1994) developed an instrumental variable estimator which is becoming increasingly popular for estimating demand elasticities. Soderbery (2015) extended this estimator and created a routine which was shown to be more robust to data outliers when the number of time periods is small or moderate. In this paper, we extend the Feenstra/Soderbery (F/S) estimator along two important dimensions to obtain a more efficient estimator: we handle the cases where there are no simultaneity problems, i.e. when supply is either elastic or inelastic, and we generalize the current practice of choosing a particular reference variety by creating a pooled estimator across all possible reference varieties. Using a Monte Carlo study, we show that our proposed estimator reduces the RMSE compared to the F/S estimator by between 60 and 90 percent across the whole parameter space. 
Keywords:  Demand elasticity; Panel data; Twostage estimator 
JEL:  C13 C33 C36 
Date:  2021–04 
URL:  http://d.repec.org/n?u=RePEc:ssb:dispap:951&r= 
By:  Chemla, Gilles; Hennessy, Christopher 
Abstract:  Causal evidence from random assignment has been labeled "the most credible." We argue it is generally incomplete in finance/economics, omitting central parts of the true empirical causal chain. Random assignment, in eliminating selfselection, simultaneously precludes signaling via treatment choice. However, outside experiments, agents enjoy discretion to signal, thereby causing changes in beliefs and outcomes. Therefore, if the goal is informing discretionary decisions, rather than predicting outcomes after forced/mistaken actions, randomization is problematic. As shown, signaling can amplify, attenuate, or reverse signs of causal effects. Thus, traditional methods of empirical finance, e.g. event studies, are often more credible/useful. 
Keywords:  Causal effect; CEO; Corporate Finance; Government Policy; household finance; investment; random assignment; selection; signal 
JEL:  D82 E6 G14 G18 G28 G3 J24 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:15175&r= 
By:  Valencia Caicedo, Felipe 
Abstract:  This chapter surveys the usage of Instrumental Variables (IVs) and Regression Discontinuity Designs (RDDs) in economic history. I document the positive trends of economic history articles employing these methods using three different samples: top 20 journals in economics, top 5 journals in economic history and top five general interest journals in economics from 20002020. I detail two broad phases: seminal articles published from 2001 to 2011, and a second wave of studies refining these techniques appearing from 2012 to today (2020). I discuss some methodological refinements that have appeared recently in the econometrics fieldin the IV and RDD fronts. I then present a practical guide on regression diagnostics, acknowledging that there are other useful sources of identification available to tackle potential endogeneity issues. 
Keywords:  econometrics; economic history; instrumental variables; Regression Discontinuity Designs; survey 
JEL:  A33 C1 C26 C36 N01 
Date:  2020–08 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:15208&r= 
By:  Andrea Carriero; Todd E. Clark; Massimiliano Marcellino; Elmar Mertens 
Abstract:  Interest rate data are an important element of macroeconomic forecasting. Projections of future interest rates are not only an important product themselves, but also typically matter for forecasting other macroeconomic and financial variables. A popular class of forecasting models is linear vector autoregressions (VARs) that include shorter and longerterm interest rates. However, in a number of economies, at least shorterterm interest rates have now been stuck for years at or near their effective lower bound (ELB), with longerterm rates drifting toward the constraint as well. In such an environment, linear forecasting models that ignore the ELB constraint on nominal interest rates appear inept. To handle the ELB on interest rates, we model observed rates as censored observations of a latent shadowrate process in an otherwise standard VAR setup. The shadow rates are assumed to be equal to observed rates when above the ELB. Point and density forecasts for interest rates (short term and long term) constructed from a shadowrate VAR for the US since 2009 are superior to predictions from a standard VAR that ignores the ELB. For other indicators of financial conditions and measures of economic activity and inflation, the accuracy of forecasts from our shadowrate specification is on par with a standard VAR that ignores the ELB. 
Keywords:  Macroeconomic forecasting; effective lower bound; term structure; censored observations 
JEL:  C34 C53 E17 E37 E43 E47 
Date:  2021–03–29 
URL:  http://d.repec.org/n?u=RePEc:fip:fedcwq:91780&r= 