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The first two influential books on economic forecasting are by Henri Theil [1961, second edition 1965. Economic Forecasts and Policy. North-Holland, Amsterdam] and by George Box and Gwilym Jenkins [1970. Time Series Analysis, Forecasting and Control. Holden Day, San Francisco]. Theil introduced advanced mathematical statistical techniques and considered a variety of types of data. Box and Jenkins introduced ARIMA models and how they are used to forecast. With these foundations, the field of economic forecasting has considered a wide range of techniques and models, wider and deeper information sets, longer horizons, and deeper questions including how to better evaluate all forecasts and how to disentangle a forecast, a policy, and the outcomes. Originally, forecasts were just for means (or expectations) then moved to variances, and now consider predictive distributions. Eventually, multivariate distributions will have to be considered, but evaluation will be difficult.

This paper estimates a panel model with endogenously time-varying parameters for COVID-19 cases and deaths in U.S. states. The functional form for infections incorporates important features of epidemiological models but is flexibly parameterized to capture different trajectories of the pandemic. Daily deaths are modeled as a spike-and-slab regression on lagged cases. The paper's Bayesian estimation reveals that social distancing and testing have significant effects on the parameters. For example, a 10 percentage point increase in the positive test rate is associated with a 2 percentage point increase in the death rate among reported cases. The model forecasts perform well, even relative to models from epidemiology and statistics.

This paper reestablishes the main results in Bai (2003) and Bai and Ng (2006) for generalized factor models, with slightly stronger conditions on the relative magnitude of N (number of subjects) and T (number of time periods). Convergence rates of the estimated factor space and loading space and asymptotic normality of the estimated factors and loadings are established under mild conditions that allow for linear, Logit, Probit, Tobit, Poisson and some other single-index nonlinear models. The probability density/mass function is allowed to vary across subjects and time, thus mixed models are also allowed for. For factor-augmented regressions, this paper establishes the limit distributions of the parameter estimates, the conditional mean, and the forecast when factors estimated from nonlinear/mixed data are used as proxies for the true factors.

It is a common practice to conduct principal component analysis (PCA) using standardized data, which is equivalent to applying PCA to the correlation matrix rather than the covariance matrix. Yet little research has been done about such differences in the context of high frequency data. This paper bridges this gap. We derive the analytical forms of the asymptotic biases and variances for the estimators of the integrated eigenvalues and eigenvectors. Furthermore, we propose a novel jackknife-type estimator of the asymptotic variance of the integrated volatility functional estimator. This new variance estimator shows much better finite sample performances compared to other existing ones. This paper also proposes several statistical tests for some commonly tested hypotheses in the literature. Simulation results show that one will get misleading results if one uses the analytical results of the covariance case when applying PCA on the correlation matrix.

This paper introduces novel approaches to forecast pooling methods based on a nonparametric prior for a weight vector combining predictive densities. The first approach places a Dirichlet process prior on the weight vector and generalizes the static linear pool. The second approach uses a hierarchical Dirichlet process prior to allow the weight vector to follow an infinite hidden Markov chain. This generalizes dynamic prediction pools to the nonparametric setting. Efficient posterior simulation based on MCMC methods is also examined. Detailed applications to short-term interest rates, realized covariance matrices and asset pricing models demonstrate that the nonparametric pool forecasts well. The paper concludes with extensions and an application for calibrating and combining predictive densities.

This paper studies the efficient estimation of betas from high-frequency return data on a fixed time interval. Under an assumption of equal diffusive and jump betas, we derive the semiparametric efficiency bound for estimating the common beta and develop an adaptive estimator that attains the efficiency bound. We further propose a Hausman type test for deciding whether the common beta assumption is true from the high-frequency data. In our empirical analysis we provide examples of stocks and time periods for which a common market beta assumption appears true and ones for which this is not the case. We further quantify empirically the gains from the efficient common beta estimation developed in the paper.

The incidence of tax and other policy changes depends on their impact on equilibrium wages. In a standard model of labor supply, the impact of wage changes on a worker’s welfare equals current labor supply times the induced wage change. Worker heterogeneity implies that wage changes vary across workers. In this context, in order to identify welfare effects one needs to identify the causal effect of policy changes on wages conditional on baseline labor supply and wages. This paper characterizes identification of such outcome-conditioned causal effects for general vectors of endogenous outcomes. Even with exogenous policy variation, outcome-conditioned causal effects are only partially identified for outcome vectors of dimension larger than one. We provide assumptions restricting heterogeneity of effects just enough for point-identification and propose corresponding estimators. This paper then applies the proposed approach to analyze the distributional welfare impact (i) of the expansion of the Earned Income Tax Credit (EITC) in the 1990s, using variation in state supplements in order to identify causal effects, and (ii) of historical changes of the wage distribution in the US in the 1990s. For the EITC, we find negative welfare effects of depressed wages as a consequence of increased labor supply, in particular for individuals earning around $20,000 per year. Looking at historical changes, we find modest welfare gains rising linearly with earnings.

Much of the analysis of panel data has been based on an assumption of strict exogeneity. Distributions are specified for outcome variables conditional on a latent individual effect and conditional on observed predictor variables at all dates, with the future values of the predictor variables assumed to have no effect on the conditional distribution. The paper relaxes this assumption in order to allow for lagged dependent variables and, more generally, for feedback from lagged dependent variables to current values of the predictor variables. Such feedback would arise in an evaluation study if the treatment variable is randomly assigned only conditional on the individual effect and on previous outcomes. An information bound is derived for a semiparametric regression model with sequential moment restrictions, with the information set increasing over time. The bound is then applied to a model with a (scalar) multiplicative random effect. The mean of the random effect conditional on the predictor variables is not restricted, so that the random effect can control for various omitted variables. This conditional mean is the nonparametric component of the semiparametric regression model. There is a transformation that eliminates the random effect and leads to a set of sequential moment restrictions in which the moment function depends on only a finite-dimensional parameter. The information bound for this simpler problem coincides with that of the original problem. The form of the optimal instrumental variables is derived. The paper also considers the identification problems that arise when the random effect is a vector with two or more components.

This paper proposes an asymptotically valid permutation test for heterogeneous treatment effects in the presence of an estimated nuisance parameter. Not accounting for the estimation error of the nuisance parameter results in statistics that depend on the particulars of the data generating process, and the resulting permutation test fails to control the Type 1 error, even asymptotically. In this paper we consider a permutation test based on a martingale transformation of the empirical process to render an asymptotically pivotal statistic, effectively nullifying the effect associated with the estimation error on the limiting distribution of the statistic. Under weak conditions, we show that the permutation test based on the martingale-transformed statistic results in the asymptotic rejection probability of α in general while retaining the exact control of the test level when testing for the more restrictive sharp null. We also show how our martingale-based permutation test extends to testing whether there exists treatment effect heterogeneity within subgroups defined by observable covariates. Our approach comprises testing the joint null hypothesis that treatment effects are constant within mutually exclusive subgroups while allowing the treatment effects to vary across subgroups. Monte Carlo simulations show that the permutation test presented here performs well in finite samples, and is comparable to those existing in the literature. To gain further understanding of the test to practical problems, we investigate the gift exchange hypothesis in the context of two field experiments from Gneezy and List (2006). Lastly, we provide the companion RATest R package to facilitate and encourage the application of our test in empirical research.

In this paper we investigate to what extent the bootstrap can be applied to conditional mean models, such as regression or time series models, when the volatility of the innovations is random and possibly non-stationary. In fact, the volatility of many economic and financial time series displays persistent changes and possible non-stationarity. However, the theory of the bootstrap for such models has focused on deterministic changes of the unconditional variance and little is known about the performance and the validity of the bootstrap when the volatility is driven by a non-stationary stochastic process. This includes near-integrated exogenous volatility processes as well as near-integrated GARCH processes, where the conditional variance has a diffusion limit; a further important example is the case where volatility exhibits infrequent jumps. This paper fills this gap in the literature by developing conditions for bootstrap validity in time series and regression models with non-stationary, stochastic volatility. We show that in such cases the distribution of bootstrap statistics (conditional on the data) is random in the limit. Consequently, the conventional approaches to proofs of bootstrap consistency, based on the notion of weak convergence in probability of the bootstrap statistic, fail to deliver the required validity results. Instead, we use the concept of ‘weak convergence in distribution’ to develop and establish novel conditions for validity of the wild bootstrap, conditional on the volatility process. We apply our results to several testing problems in the presence of non-stationary stochastic volatility, including testing in a location model, testing for structural change using CUSUM-type functionals, and testing for a unit root in autoregressive models. Importantly, we work under sufficient conditions for bootstrap validity that include the absence of statistical leverage effects, i.e., correlation between the error process and its future conditional variance. The results of the paper are illustrated using Monte Carlo simulations, which indicate that a wild bootstrap approach leads to size control even in small samples., This research was supported by the Danish Council for Independent Research, Denmark (DSF Grant 015-00028B), by the University of Bologna, Italy (ALMA IDEA 2017 Grant), and by the Italian Ministry of University and Research, Italy (PRIN 2017 Grant 2017TA7TYC).

This paper develops estimators of the transition density, filters, and parameters of multivariate jump–diffusion models. The drift, volatility, jump intensity, and jump magnitude are allowed to be state-dependent and non-affine. It is not necessary to diagonalize the volatility matrix. Our density and filter estimators converge at the canonical rate typically associated with exact Monte Carlo estimation. Our parameter estimators have the same asymptotic distribution as maximum likelihood estimators, which are often intractable for the class of models we consider. The results of this paper enable the empirical analysis of previously intractable models of asset prices and economic time series.

High frequency financial data has become an essential component of the digital economy, yielding an increasing number of estimators. However, it is hard to reliably assess the uncertainty of such estimators. The Observed Asymptotic Variance (observed AVAR) is a non-parametric estimator for (squared) standard error in high frequency data. The device is related to observed information in likelihood theory, but in this case it is non-parametric and uses the high-frequency data structure. An earlier paper has developed the estimator in the case where edge effects are small to moderate. In practical data, it is often more realistic to assume that edge effects can be large, and this is the problem that we tackle in the current paper. We here find a regression approach to observed AVAR which is highly robust to large edges. This approach covers most high frequency estimators.

This paper studies large sample properties of a Bayesian approach to inference about slope parameters $\gamma$ in linear regression models with a structural break. In contrast to the conventional approach to inference about $\gamma$ that does not take into account the uncertainty of the unknown break location $\tau$, the Bayesian approach that we consider incorporates such uncertainty. Our main theoretical contribution is a Bernstein-von Mises type theorem (Bayesian asymptotic normality) for $\gamma$ under a wide class of priors, which essentially indicates an asymptotic equivalence between the conventional frequentist and Bayesian inference. Consequently, a frequentist researcher could look at credible intervals of $\gamma$ to check robustness with respect to the uncertainty of $\tau$. Simulation studies show that the conventional confidence intervals of $\gamma$ tend to undercover in finite samples whereas the credible intervals offer more reasonable coverages in general. As the sample size increases, the two methods coincide, as predicted from our theoretical conclusion. Using data from Paye and Timmermann (2006) on stock return prediction, we illustrate that the traditional confidence intervals on $\gamma$ might underrepresent the true sampling uncertainty.

This paper computes semiparametric efficiency bounds for finite-dimensional parameters in discrete choice models with nonparametric regressors in the form of conditional expectations. These can include expectations about exogenous events as well as expectations about the choices of other agents. Thus, the models studied here include incomplete-information games, social-interactions models as well as single-agent discrete choice models with uncertainty as special cases. Our bounds rely on the assumption of rational expectations and on regularity conditions of equilibrium beliefs. The paper focuses on binary-choice models but the derivation of the bounds illustrates how our approach can be extended to multinomial choice cases. Explicit efficiency bound expressions for the models examined here had not been derived before. Furthermore, since we also characterize the efficient influence functions, our results can also potentially be used to construct semiparametrically efficient estimators for these models.

The present special issue features a collection of papers presented at the 2017 International Panel Data Conference, hosted by the University of Macedonia in Thessaloniki, Greece. The conference marked the 40th anniversary of the inaugural International Panel Data Conference, which was held in 1977 at INSEE in Paris, under the auspices of the French National Centre for Scientific Research. As a collection, the papers appearing in this special issue of the Journal of Econometrics continue to advance the analysis of panel data, and paint a state-of-the-art picture of the field. (c) 2020 Elsevier B.V. All rights reserved.

Numerous empirical studies employ regression discontinuity designs with multiple cutoffs and heterogeneous treatments. A common practice is to normalize all the cutoffs to zero and estimate one effect. This procedure identifies the average treatment effect (ATE) on the observed distribution of individuals local to existing cutoffs. However, researchers often want to make inferences on more meaningful ATEs, computed over general counterfactual distributions of individuals, rather than simply the observed distribution of individuals local to existing cutoffs. This paper proposes a consistent and asymptotically normal estimator for such ATEs when heterogeneity follows a non-parametric function of cutoff characteristics in the sharp case. The proposed estimator converges at the minimax optimal rate of root- n for a specific choice of tuning parameters. Identification in the fuzzy case, with multiple cutoffs, is impossible unless heterogeneity follows a finite-dimensional function of cutoff characteristics. Under parametric heterogeneity, this paper proposes an ATE estimator for the fuzzy case that optimally combines observations to maximize its precision.

Deviance information criterion (DIC) has been widely used for Bayesian model comparison, especially after Markov chain Monte Carlo (MCMC) is used to estimate candidate models. This paper first studies the problem of using DIC to compare latent variable models when DIC is calculated from the conditional likelihood. In particular, it is shown that the conditional likelihood approach undermines theoretical underpinnings of DIC. A new version of DIC, namely DIC L , is proposed to compare latent variable models. The large sample properties of DIC L are studied. A frequentist justification of DIC L is provided. Like AIC, DIC L provides an asymptotically unbiased estimator to the expected Kullback–Leibler (KL) divergence between the DGP and a predictive distribution. Some popular algorithms, such as the EM, Kalman and particle filtering algorithms, are introduced to compute DIC L for latent variable models. Moreover, this paper studies the problem of using DIC to compare misspecified models. A new version of DIC, namely DIC M , is proposed and it can be regarded as a Bayesian version of TIC. A frequentist justification of DIC M is provided under misspecification. DIC L and DIC M are illustrated using asset pricing models and stochastic volatility models.

This paper provides a rigorous treatment on design-based estimating equation inference using complex survey data in the presence of nuisance functionals. The proposed design-based framework covers parameters from inequality measures and measures on performance evaluation in economic, business and financial studies but the scope of the paper is more broad. Unlike nuisance parameters in other settings where profile analysis is commonly used, the nuisance functionals are typically handled by using a “plug-in” estimator. We establish root- n consistency and asymptotic normality for parameters defined through survey weighted smooth or non-differentiable estimating functions even if the “plug-in” estimator for the nuisance functional has a convergence rate slower than root- n . A multiplier bootstrap procedure is proposed for three types of commonly used survey designs to tackle the challenge task of variance estimation. Results from a simulation study and an application to a real survey data set demonstrate the effectiveness of the proposed design-based inference on the Lorenz curve.

We propose a simple and fast approach to identify and estimate the unknown group structure in panel models by adapting the M-estimation method. We consider both linear and nonlinear panel models where the regression coefficients are heterogeneous across groups but homogeneous within a group and the group membership is unknown to researchers. The main result of the paper is that under certain assumptions, our approach is able to provide uniformly consistent estimation as long as the number of groups used in estimation is not smaller than the true number of groups. We also show that, asymptotically, our method may partition some true groups into further subgroups, but cannot mix units from different groups. When the true number of groups is used in estimation, all units can be categorized correctly with probability approaching one, and we establish the limiting distribution for the estimators of the group parameters. In addition, we provide an information criterion to select the number of groups, and establish the consistency of the selection criterion under some mild conditions. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed method. The findings in the simulation confirm our theoretical results in the paper. Applications to two real datasets also highlight the necessity to consider both individual heterogeneity and group heterogeneity in the model.

In this paper, we study the linear transformation model in the most general setup. This model includes many important and popular models in statistics and econometrics as special cases. Although it has been studied for many years, the methods in the literature are based on kernel-smoothing techniques or make use of only the ranks of the responses in the estimation of the parametric components. The former approach needs a tuning parameter, which is not easily optimally specified in practice; and the latter is computationally expensive and may not make full use of the information in the data. In this paper, we propose two methods: a pairwise rank likelihood method and a score-function-based method based on this pairwise rank likelihood. We also explore the theoretical properties of the proposed estimators. Via extensive numerical studies, we demonstrate that our methods are appealing in that the estimators are not only robust to the distribution of the random errors but also lead to mean square errors that are in many cases comparable to or smaller than those of existing methods., Comment: 6 tables and 2 figures

The policy relevant treatment effect (PRTE) measures the average effect of switching from a status-quo policy to a counterfactual policy under consideration. Estimation of the PRTE involves estimation of multiple preliminary parameters, including propensity scores, conditional expectation functions of the outcome and covariates given the propensity score, and marginal treatment effects. These preliminary estimators can affect the asymptotic distribution of the PRTE estimator in complicated and intractable manners. In this light, we propose an orthogonal score for double debiased estimation of the PRTE, whereby the asymptotic distribution of the PRTE estimator is obtained without any influence of preliminary parameter estimators as far as they satisfy mild requirements of convergence rates. To our knowledge, this paper is the first to develop limit distribution theories for inference about the PRTE.

This paper considers a treatment effect model in which individual treatment effect may be heterogeneous, even among observationally identical individuals. Specifically, by extending the classical instrumental-variables (IV) model with an endogenous binary treatment, the heteroskedasticity of the error disturbance is allowed to vary with the treatment variable so that the treatment generates both mean and variance effect on the outcome. In this endogenous heteroskedasticity IV (EHIV) model, the standard IV estimator can be inconsistent for the average treatment effect (ATE) and lead to incorrect inference. After nonparametric identification is established, closed-form estimators are provided under the linear EHIV specification for the mean and variance treatment effect, as well as the average treatment effect on the treated (ATT). Asymptotic properties of the estimators are derived. We use Monte Carlo experiments to investigate the performance of the proposed approach and then consider an empirical application regarding the effect of fertility on female labor supply. Our findings demonstrate the importance of accounting for endogenous heteroskedasticity.

Change point detection in time series has attracted substantial interest, but most of the existing results have been focused on detecting change points in the time domain. This paper considers the situation where nonlinear time series have potential change points in the state domain. We apply a density-weighted anti-symmetric kernel function to the state domain and therefore propose a nonparametric procedure to test the existence of change points. When the existence of change points is affirmative, we further introduce an algorithm to estimate the number of change points together with their locations. Theoretical results of the proposed detection and estimation procedures are given and a real dataset is used to illustrate our methods., to appear in Journal of Econometrics

For predictive quantile regressions with highly persistent regressors, a conventional test statistic suffers from a serious size distortion and its limiting distribution relies on the unknown persistence degree of predictors. This paper proposes a double-weighted approach to offer a robust inferential theory across all types of persistent regressors. We first estimate a quantile regression with an auxiliary regressor, which is generated as a weighted combination of an exogenous random walk process and a bounded transformation of the original regressor. With a similar spirit of rotation in factor analysis, one can then construct a weighted estimator using the estimated coefficients of the original predictor and the auxiliary regressor. Under some mild conditions, it shows that the self-normalized test statistic based on the weighted estimator converges to a standard normal distribution. Our new approach enjoys a nice property that it can reach the local power under the optimal rate T with nonstationary predictor and squared root of T for stationary predictor, respectively. More importantly, our approach can be easily used to characterize mixed persistence degrees in multiple regressions. Simulations and empirical studies are provided to demonstrate the effectiveness of the newly proposed approach. The heterogenous predictability of US stock returns at different quantile levels is reexamined.

This paper documents the extent to which wage persistence can be explained by permanent worker, employer, and match heterogeneity. Standard methods used to perform such decompositions for industry or racial wage gaps are inappropriate for decomposing wage persistence in dynamic panel data models because of the incidental parameter problem. When we apply these methods without bias correction, we find that the majority, 59.3 percent, of wage persistence is explained by worker heterogeneity, with employer and match heterogeneity explaining 29.7 and 11.0 percent, respectively. We evaluate three methods for addressing incidental parameter bias using a Monte Carlo study. An empirical application to Portuguese linked employer–employee data shows that the uncorrected estimates tend to understate wage persistence by around 24 to 42 percent, depending on the choice of the bias correction estimator used, and overstate the extent to which wage persistence arises from permanent unobserved heterogeneity. Furthermore, results indicate that the uncorrected estimates overstate the role of permanent worker heterogeneity, and understate the role of firm heterogeneity.

This paper estimates the break point for large-dimensional factor models with a single structural break in factor loadings at a common unknown date. First, we propose a quasi-maximum likelihood (QML) estimator of the change point based on the second moments of factors, which are estimated by principal component analysis. We show that the QML estimator performs consistently when the covariance matrix of the pre- or post-break factor loading, or both, is singular. When the loading matrix undergoes a rotational type of change while the number of factors remains constant over time, the QML estimator incurs a stochastically bounded estimation error. In this case, we establish an asymptotic distribution of the QML estimator. The simulation results validate the feasibility of this estimator when used in finite samples. In addition, we demonstrate empirical applications of the proposed method by applying it to estimate the break points in a U.S. macroeconomic dataset and a stock return dataset.

This paper considers linear panel data models with a grouped pattern of heterogeneity when the latent group membership structure and/or the values of slope coefficients change at a break point. We propose a least squares approach to jointly estimate the break point, group membership structure, and coefficients. The proposed estimators are consistent, and the asymptotic distribution of the coefficient estimators is identical to that under known break point and group structure even when the cross-sectional sample size is much larger than the length of time series. Monte Carlo simulations and an empirical example illustrate the use of the approach and associated inference.

This paper proposes to model and forecast realized volatility (RV) using the fractional Ornstein–Uhlenbeck (fO–U) process with a general Hurst parameter, H . A two-stage method is introduced for estimating parameters in the fO–U process based on discrete-sampled observations. In the first stage, H is estimated based on the ratio of two second-order differences of observations from different frequencies. In the second stage, with the estimated H , the other parameters of the model are estimated by the method of moments. All estimators have closed-form expressions and are easy to implement. A large sample theory of the proposed estimators is derived. Extensive simulations show that the proposed estimators and the large-sample theory perform well in finite samples. We apply the model and the method to the logarithmic daily RV series of various financial assets. Our empirical findings suggest that H is much smaller than 1 / 2 , indicating that the RV series have rough sample paths, and that the mean reversion parameter takes a small positive number, indicating that the RV series are stationary but have slow mean reversion. The proposed model is compared with many alternative models, including the fractional Brownian motion, ARFIMA, and HAR, in forecasting RV and logarithmic RV.

Methods for cluster-robust inference are routinely used in economics and many other disciplines. However, it is only recently that theoretical foundations for the use of these methods in many empirically relevant situations have been developed. In this paper, we use these theoretical results to provide a guide to empirical practice. We do not attempt to present a comprehensive survey of the (very large) literature. Instead, we bridge theory and practice by providing a thorough guide on what to do and why, based on recently available econometric theory and simulation evidence. To practice what we preach, we include an empirical analysis of the effects of the minimum wage on labor supply of teenagers using individual data., Accepted at Journal of Econometrics

This paper considers bootstrap inference in model averaging for predictive regressions. We first show that the standard pairwise bootstrap is not valid in the context of model averaging. This common bootstrap approach induces a bias-related term in the bootstrap variance of averaging estimators. We then propose and justify a fixed-design residual-based bootstrap resampling approach for model averaging. In a local asymptotic framework, we show the validity of the bootstrap in estimating the variance of a combined forecast and the asymptotic covariance matrix of a combined parameter vector with fixed weights. Our proposed method preserves non-parametrically the cross-sectional dependence between different models and the time series dependence in the errors simultaneously. The finite sample performance of these methods is assessed via Monte Carlo simulations. We illustrate our approach using an empirical study of the Taylor rule equation with 24 alternative specifications.

This paper studies finite sample minimax optimal randomization schemes and estimation schemes in estimating parameters including the average treatment effect, when treatment effects are heterogeneous. A randomization scheme is a distribution over a group of permutations of a given treatment assignment vector. An estimation scheme is a joint distribution over assignment vectors, linear estimators, and permutations of assignment vectors. The key element in the minimax problem is that the worst case is over a class of distributions of the data which is invariant to a group of permutations. First, I show that given any assignment vector and any estimator, the uniform distribution over the same group of permutations, namely the complete randomization scheme, is minimax optimal. Second, under further assumptions on the class of distributions and the objective function, I show the minimax optimal estimation scheme involves completely randomizing an assignment vector, while the optimal estimator is the difference-in-means under complete invariance and a weighted average of within-block differences under a block structure, and the number of treated units is determined by the Neyman allocation.

This paper studies second-order properties of the many instruments robust t -ratios based on the limited information maximum likelihood and Fuller estimators for instrumental variable regression models with homoskedastic errors under the many instruments asymptotics, where the number of instruments may increase proportionally with the sample size n , and proposes second-order refinements to the t -ratios to improve the size and power properties. Based on asymptotic expansions of the null and non-null distributions of the t -ratios derived under the many instruments asymptotics, we show that the second-order terms of those expansions may have non-trivial impacts on the size as well as the power properties. Furthermore, we propose adjusted t -ratios whose approximation errors for the null rejection probabilities are of order O ( n − 1 ) in contrast to the ones for the unadjusted t -ratios of order O ( n − 1 / 2 ) , and show that these adjustments induce some desirable power properties in terms of the local maximinity. Although these results are derived under homoskedastic errors, we also establish a stochastic expansion for a heteroskedasticity robust t -ratio, and propose an analogous adjustment under slight deviations from homoskedasticity.

Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. In this paper, we consider statistical inference for quantile regression with large-scale data in the "increasing dimension" regime. We provide a comprehensive and in-depth analysis of a convolution-type smoothing approach that achieves adequate approximation to computation and inference for quantile regression. This method, which we refer to as {\it{conquer}}, turns the non-differentiable quantile loss function into a twice-differentiable, convex and locally strongly convex surrogate, which admits a fast and scalable Barzilai-Borwein gradient-based algorithm to perform optimization, and multiplier bootstrap for statistical inference. Theoretically, we establish explicit non-asymptotic bounds on both estimation and Bahadur-Kiefer linearization errors, from which we show that the asymptotic normality of the conquer estimator holds under a weaker requirement on the number of the regressors than needed for conventional quantile regression. Moreover, we prove the validity of multiplier bootstrap confidence constructions. Our numerical studies confirm the conquer estimator as a practical and reliable approach to large-scale inference for quantile regression. Software implementing the methodology is available in the \texttt{R} package \texttt{conquer}., An R package conquer for fitting smoothed quantile regression is available in CRAN, https://cran.r-project.org/web/packages/conquer/index.html

The COVID-19 pandemic is one of the most pressing issues at present. A question which is particularly important for governments and policy makers is the following: Does the virus spread in the same way in different countries? Or are there significant differences in the development of the epidemic? In this paper, we devise new inference methods that allow to detect differences in the development of the COVID-19 epidemic across countries in a statistically rigorous way. In our empirical study, we use the methods to compare the outbreak patterns of the epidemic in a number of European countries.

In this paper, we model the trajectory of the cumulative confirmed cases and deaths of COVID-19 (in log scale) via a piecewise linear trend model. The model naturally captures the phase transitions of the epidemic growth rate via change-points and further enjoys great interpretability due to its semiparametric nature. On the methodological front, we advance the nascent self-normalization (SN) technique (Shao, 2010) to testing and estimation of a single change-point in the linear trend of a nonstationary time series. We further combine the SN-based change-point test with the NOT algorithm (Baranowski et al., 2019) to achieve multiple change-point estimation. Using the proposed method, we analyze the trajectory of the cumulative COVID-19 cases and deaths for 30 major countries and discover interesting patterns with potentially relevant implications for effectiveness of the pandemic responses by different countries. Furthermore, based on the change-point detection algorithm and a flexible extrapolation function, we design a simple two-stage forecasting scheme for COVID-19 and demonstrate its promising performance in predicting cumulative deaths in the U.S.

This paper introduces a spatial panel quantile model with unobserved heterogeneity. The proposed model is capable of capturing high-dimensional cross-sectional dependence and allows heterogeneous regression coefficients. For estimating model parameters, a new estimation procedure is proposed. When both the time and cross-sectional dimensions of the panel go to infinity, the uniform consistency and the asymptotic normality of the estimated parameters are established. In order to determine the dimension of the interactive fixed effects, we propose a new information criterion. It is shown that the criterion asymptotically selects the true dimension. Monte Carlo simulations document the satisfactory performance of the proposed method. Finally, the method is applied to study the quantile co-movement structure of the U.S. stock market by taking into account the input–output linkages as firms are connected through the input–output production network.

Indirect inference requires simulating realisations of endogenous variables from the model under study. When the endogenous variables are discontinuous functions of the model parameters, the resulting indirect inference criterion function is discontinuous and does not permit the use of derivative-based optimisation routines. Using a change of variables technique, we propose a novel simulation algorithm that alleviates the discontinuities inherent in such indirect inference criterion functions, and permits the application of derivative-based optimisation routines to estimate the unknown model parameters. Unlike competing approaches, this approach does not rely on kernel smoothing or bandwidth parameters. Several Monte Carlo examples that have featured in the literature on indirect inference with discontinuous outcomes illustrate the approach, and demonstrate the superior performance of this approach over existing alternatives., Comment: This paper is a revision of arXiv:1708.02365 and supersedes the earlier arXiv paper "Derivative-Based Optimization with a Non-Smooth Simulated Criterion"

The paper shows how to combine (historical) statistical data and (current) market prices to form conservative trading strategies for options. This gives rise to a “worst case” state price distribution, which provides sharp price bounds for all convex European options. The paper provides for existence and computational algorithms under conditions which can be understood as “no arbitrage”. The worst case distribution converges to a regular state price distribution if the number of traded options increases to span the space of possible option payouts.

The paper establishes a quasi-Bayesian local likelihood (QBLL) estimation methodology for a multivariate model with time varying parameters. The asymptotic validity of the resulting quasi-posterior distributions of the drifting parameters is proven in general and, in the special case of a Gaussian VAR model, a closed form time varying Normal-Wishart expression for the quasi-posterior distribution of the parameters is provided. In addition, this paper develops several Gibbs algorithms, which can sample from a VAR model with a mixture of time varying and time invariant parameters. The proposed estimators differ from existing state space approaches to VAR models in that they estimate parameter time variation nonparametrically, without imposing parametric stochastic processes on the parameters. The QBLL estimators are robust to misspecification of the state equation and exhibit good finite sample performance, even when compared to correctly specified parametric state space models, as illustrated by a Monte Carlo exercise. In addition, we demonstrate that the QBLL approach provides a remedy to the ‘curse of dimensionality’ by accommodating large dimensional VAR systems and delivers improvements in the out-of-sample forecasts of key macroeconomic variables. Finally, the paper makes an empirical contribution to the literature on changing inflation dynamics in the U.S., presenting evidence of a fall in inflation persistence and volatility during the Great Moderation period. Postprint Other

This paper develops the methodology and asymptotic theory for the estimation of longrun variance of continuous time process. We analyze the asymptotic bias and variance of the longrun variance estimator in continuous time, and provide the optimal bandwidth balancing them off and minimizing the asymptotic mean squared error. In the paper, we present not only how to consistently estimate the longrun variance of continuous time process, but also how to choose bandwidth optimally with data dependent procedures, using discrete samples. Our framework is also useful to analyze the high frequency behaviors of usual longrun variance estimators for discrete time series. In particular, we show that they all diverge to infinity as the sampling frequency increases. The relevance and usefulness of our continuous time framework and asymptotic theory are demonstrated by illustration and simulation.

This paper develops parameter instability and structural change tests within predictive regressions for economic systems governed by persistent vector autoregressive dynamics. Specifically, in a setting where all – or a subset – of the variables may be fractionally integrated and the predictive relation may feature cointegration, we provide sup-Wald break tests that are constructed using the Local speCtruM (LCM) approach. The new tests cover both parameter variation and multiple structural changes with unknown break dates, and the number of breaks being known or unknown. We establish asymptotic limit theory for the tests, showing that it coincides with standard testing procedures. As a consequence, existing critical values for tied-down Bessel processes may be applied, without modification. We implement the new structural change tests to explore the stability of the fractionally cointegrating relation between implied- and realized volatility (IV and RV). Moreover, we assess the relative efficiency of IV forecasts against a challenging time-series benchmark constructed from high-frequency data. Unlike existing studies, we find evidence that the IV–RV cointegrating relation is unstable, and that carefully constructed time-series forecasts are more efficient than IV in capturing low-frequency movements in RV.

Monitoring economic conditions in real time, or nowcasting, and Big Data analytics share some challenges, sometimes called the three “Vs”. Indeed, nowcasting is characterized by the use of a large number of time series (Volume), the complexity of the data covering various sectors of the economy, with different frequencies and precision and asynchronous release dates (Variety), and the need to incorporate new information continuously and in a timely manner (Velocity). In this paper, we explore three alternative routes to nowcasting with Bayesian Vector Autoregressive (BVAR) models and find that they can effectively handle the three Vs by producing, in real time, accurate probabilistic predictions of US economic activity and a meaningful narrative by means of scenario analysis.

Structural VAR models are routinely estimated by Bayesian methods. Several recent studies have voiced concerns about the common use of posterior median (or mean) response functions in applied VAR analysis. In this paper, we show that these response functions can be misleading because in empirically relevant settings there need not exist a posterior draw for the impulse response function that matches the posterior median or mean response function, even as the number of posterior draws approaches infinity. As a result, the use of these summary statistics may distort the shape of the impulse response function which is of foremost interest in applied work. The same concern applies to error bands based on the upper and lower quantiles of the marginal posterior distributions of the impulse responses. In addition, these error bands fail to capture the full uncertainty about the estimates of the structural impulse responses. In response to these concerns, we propose new estimators of impulse response functions under quadratic loss, under absolute loss and under Dirac delta loss that are consistent with Bayesian statistical decision theory, that are optimal in the relevant sense, that respect the dynamics of the impulse response functions and that are easy to implement. We also propose joint credible sets for these estimators derived under the same loss function. Our analysis covers a much wider range of structural VAR models than previous proposals in the literature including models that combine short-run and long-run exclusion restrictions and models that combine zero restrictions, sign restrictions and narrative restrictions.

This paper proposes a generalization of the class of realized semivariance and semicovariance measures introduced by Barndorff-Nielsen et al. (2010) and Bollerslev et al. (2020a) to allow for a finer decomposition of realized (co)variances. The new “realized partial (co)variances” allow for multiple thresholds with various locations, rather than the single fixed threshold of zero used in semi (co)variances. We adopt methods from machine learning to choose the thresholds to maximize the out-of-sample forecast performance of time series models based on realized partial (co)variances. We find that in low dimensional settings it is hard, but not impossible, to improve upon the simple fixed threshold of zero. In large dimensions, however, the zero threshold embedded in realized semi covariances emerges as a robust choice.

This paper estimates a discrete choice model of time allocation decisions made by university students. We consider investments in academic and non-academic activities, such as job placements or volunteering. Identification is achieved using data collected through a recent survey of UK university students on subjective expectations about the returns to these activities, and the enjoyment students derive from them. Unobserved heterogeneity in the choice set is addressed using a sufficient set logit method. The analysis reveals significant ethnic differences in the level of investments, expected academic and labour market returns, and enjoyment of academic and non-academic activities. Simulations suggest that existing constraints play an important role in explaining ethnic gaps in investments.

This paper investigates how migration and location choice decisions depend on a large set of location characteristics, with particular focus on measuring the importance and nature of non-monetary costs of moving. We employ a stated-preference approach to elicit respondents’ choice probabilities for a set of hypothetical choice scenarios, using two waves from the NY Fed’s Survey of Consumer Expectations. Our stated probabilistic choice approach allows us to recover the distribution of individual-level preferences for location and mobility attributes without concerns about omitted variables and selection biases that hamper analyses based on observed mobility choices alone. We estimate substantial heterogeneity in the willingness-to-pay (WTP) for location characteristics and in moving costs, both across and within demographic groups. We find moving costs to be strongly associated with attachment to the current neighborhood and dwelling and to social networks. Our results indicate evidence of sorting into current locations based on preferences for location attributes as well as a strong negative association between respondents’ non-monetary moving costs and their moving expectations and actual mobility decisions.

This paper considers estimation and inference about tail features when the observations beyond some threshold are censored. We first show that ignoring such tail censoring could lead to substantial bias and size distortion, even if the censored probability is tiny. Second, we propose a new maximum likelihood estimator (MLE) based on the Pareto tail approximation and derive its asymptotic properties. Third, we provide a small sample modification to the MLE by resorting to Extreme Value theory. The MLE with this modification delivers excellent small sample performance, as shown by Monte Carlo simulations. We illustrate its empirical relevance by estimating (i) the tail index and the extreme quantiles of the US individual earnings with the Current Population Survey dataset and (ii) the tail index of the distribution of macroeconomic disasters and the coefficient of risk aversion using the dataset collected by Barro and Urs{\'u}a (2008). Our new empirical findings are substantially different from the existing literature.

This paper develops generalized method of moments (GMM) estimation and inference procedures for quantile regression models. We propose a GMM estimator for simultaneous estimation across multiple quantiles. This estimator allows us to model quantile regression coefficients using flexible parametric restrictions across quantiles. The restrictions and simultaneous estimation lead to efficiency gains compared to standard methods. We establish the asymptotic properties of the GMM estimators when the number of quantiles used is fixed and when it diverges to infinity jointly with the sample size. As an alternative to GMM, we also propose a minimum distance estimator over a given subset of quantiles. Moreover, we provide specification tests for the imposed restrictions. The estimators and tests we propose are simple to implement in practice. Monte Carlo simulations provide numerical evidence of the finite sample properties of the methods. Finally, we apply the proposed methods to estimate the effects of smoking on birthweight of live infants at the extreme bottom of the conditional distribution.