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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.

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

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.

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 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

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.

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.

In this paper, we derive a new algebraic property of two scales estimation in high frequency data, under which the effect of sampling times is canceled to high order. This is a particular robustness property of the two scales construction. In general, irregular, asynchronous, or endogenous times can cause problems in estimators based on equidistant observation of (trade or quote) times. The new algebraic property can be combined with pre-averaging, giving rise to the smoothed two-scales realized volatility (S-TSRV). We derive a finite sample solution to controlling edge effects and for handling irregular and endogenous observation times and asynchronously observed multivariate data. In connection with this development, we use the algebraic approach to define a version of the S-TSRV which has particularly small edge effect in microstructure noise. The main result of the paper is a representation of the statistical error of the estimator in terms of simple components. As an application of this representation, the paper develops a central limit theory for multivariate volatility estimators. The approach can also handle leads and lags in the signal process.

Using the marked empirical processes, this paper develops a test of parametric specification in a nonlinear cointegrating regression model. Unlike the kernel-smoothed U -statistic considered in Gao et al. (2009) and Wang and Phillips (2012), our new test statistic avoids the use of bandwidth, which has some advantages for practitioners. Simulations and a real data example show that our new test has a good finite sample performance. Other contributions of this paper are to provide a rigorous proof on weak convergence for a class of martingales and construct a simulated estimator of the limiting null distribution, which are interesting in their own rights.

The paper introduces a robust testing procedure for network generated cross sectional dependence in the endogenous variables, exogenous variables and/or disturbances. Empirical researchers often face situations where they are unsure about how to model the proximity between cross sectional units in a network. The tests considered provide the empirical researcher an important degree of robustness in such situations. They generalize the Moran (1950) I test for dependence in spatial networks. The asymptotic properties of the tests are established under general conditions. The paper also discusses the use of the test statistics in situations where the network topology is endogenous.

Based on the Girsanov theorem, this paper obtains the exact distribution of the maximum likelihood estimator of structural break point in a continuous time model. The exact distribution is asymmetric and tri-modal, indicating that the estimator is biased. These two properties are also found in the finite sample distribution of the least squares (LS) estimator of structural break point in the discrete time model, suggesting the classical long-span asymptotic theory is inadequate. The paper then builds a continuous time approximation to the discrete time model and develops an in-fill asymptotic theory for the LS estimator. The in-fill asymptotic distribution is asymmetric and tri-modal and delivers good approximations to the finite sample distribution. To reduce the bias in the estimation of both the continuous time and the discrete time models, a simulation-based method based on the indirect estimation (IE) approach is proposed. Monte Carlo studies show that IE achieves substantial bias reductions.

Cross-sections of financial returns are characterized by common underlying factors and exhibit fat tails that may be captured by α -stable distributions. This paper focuses on estimating factor models with independent latent factors and idiosyncratic noises featuring a multivariate α -stable distribution constant over time (static factor models) or a time-varying conditional multivariate α -stable distribution (GARCH factor models). Although the simulation of such a distribution is straightforward, the estimation of its parameters encounters difficulties. These difficulties are overcome in this paper by implementing the indirect inference estimation method with the multivariate Student’s t as the auxiliary distribution.

Corresponding publicationsWorking Paper | Generating Univariate Fractional Integration within a Large VAR(1) 〈halshs-01944588〉; International audience; This paper shows that a large dimensional vector autoregressive model (VAR) of finite order can generate fractional integration in the marginalized univariate series. We derive high-level assumptions under which the final equation representation of a VAR(1) leads to univariate fractional white noises and verify the validity of these assumptions for two specific models.

This paper proposes a first-order zero-drift GARCH (ZD-GARCH(1, 1)) model to study conditional heteroscedasticity and heteroscedasticity together. Unlike the classical GARCH model, ZD-GARCH(1, 1) model is always non-stationary regardless of the sign of the Lyapunov exponent $\gamma_{0}$ , but interestingly when $\gamma_{0}$ = 0, it is stable with its sample path oscillating randomly between zero and infinity over time. Furthermore, this paper studies the generalized quasi-maximum likelihood estimator (GQMLE) of ZD-GARCH(1, 1) model, and establishes its strong consistency and asymptotic normality. Based on the GQMLE, an estimator for $\gamma_{0}$, a test for stability, and a portmanteau test for model checking are all constructed. Simulation studies are carried out to assess the finite sample performance of the proposed estimators and tests. Applications demonstrate that a stable ZD-GARCH(1, 1) model is more appropriate to capture heteroscedasticity than a non-stationary GARCH(1, 1) model, which suffers from an inconsistent QMLE of the drift term

This paper studies the rationalization and identification of binary games where players have correlated private types. Allowing for correlation is crucial in global games and in models with social interactions as it represents correlated information and homophily, respectively. Our approach is fully nonparametric in the joint distribution of types and the strategic effects in the payoffs. First, under monotone pure Bayesian Nash Equilibrium strategy, we characterize all the restrictions if any on the distribution of players' choices imposed by the game-theoretic model as well as restrictions associated with two assumptions frequently made in the empirical analysis of discrete games. Namely, we consider exogeneity of payoff shifters relative to private information, and mutual independence of private information given payoff shifters. Second, we study the nonparametric identification of the payoff functions and types distribution. We show that the model with exogenous payoff shifters is fully identified up to a single location--scale normalization under some exclusion restrictions and rank conditions. Third, we discuss partial identification under weaker conditions and multiple equilibria. Lastly, we briefly point out the implications of our results for model testing and estimation., This paper was presented at Texas Metrics Camp 2013, the 2013 North American Summer Meeting of the Econometric Society at University of Southern California, and the 2013 Asian Meeting of the Econometric Society at National University of Singapore

This paper reviews the recent developments in nonparametric identification of measurement error models and their applications in applied microeconomics, in particular, in empirical industrial organization and labor economics. Measurement error models describe mappings from a latent distribution to an observed distribution. The identification and estimation of measurement error models focus on how to obtain the latent distribution and the measurement error distribution from the observed distribution. Such a framework is suitable for many microeconomic models with latent variables, such as models with unobserved heterogeneity or unobserved state variables and panel data models with fixed effects. Recent developments in measurement error models allow very flexible specification of the latent distribution and the measurement error distribution. These developments greatly broaden economic applications of measurement error models. This paper provides an accessible introduction of these technical results to empirical researchers so as to expand applications of measurement error models.

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 proposes new specification tests for conditional models with discrete responses, which are key to apply efficient maximum likelihood methods, to obtain consistent estimates of partial effects and to get appropriate predictions of the probability of future events. In particular, we test the static and dynamic ordered choice model specifications and can cover infinite support distributions for e.g. count data. The traditional approach for specification testing of discrete response models is based on probability integral transforms of a jittered discrete data which leads to continuous uniform i.i.d. series under the true conditional distribution. Then, standard specification testing techniques for continuous variables could be applied to the transformed series, but the extra randomness from jitters affects the power properties of these methods. We investigate in this paper an alternative transformation based only on original discrete data that avoids any randomization. We analyze the asymptotic properties of goodness-of-fit tests based on this new transformation and explore the properties in finite samples of a bootstrap algorithm to approximate the critical values of test statistics which are model and parameter dependent. We show analytically and in simulations that our approach dominates the methods based on randomization in terms of power. We apply the new tests to models of the monetary policy conducted by the Federal Reserve. (C) 2017 Elsevier B.V. All rights reserved. Support from the Ministerio Economia y Competitividad (Spain), grants ECO2012-31748, ECO2014-57007p, MDM 2014-0431, Comunidad de Madrid, grant S2015/HUM-3444, and Fundación Ramón Areces is gratefully acknowledged.

This paper introduces a representation theorem for a mixed VAR(p) process by distinguishing its causal and noncausal components. That representation is used to discuss the advantages and limitations of second-order identification in a mixed VAR. We show that it is possible to find the numbers of causal or noncausal components of the process from its multivariate autocovariance function, while nonlinear autocovariances are needed to distinguish between them. The paper introduces also a consistent semi-parametric estimator for mixed causal/noncausal multivariate non-Gaussian processes, called the Generalized Covariance (GCov) estimator, which relies on combined standard and nonlinear autocovariances of the process. The GCov does not require any distributional assumptions on the errors. The approach is illustrated by a simulation study and applied to commodity prices.

The paper develops a novel realized stochastic volatility model of asset returns and realized volatility that incorporates general asymmetry and long memory (hereafter the RSV-GALM model). The contribution of the paper ties in with Robert Basmann’s seminal work in terms of the estimation of highly non-linear model specifications (Basmann, 1988), especially for specifying causal effects from returns to future volatility. This paper discusses asymptotic results of a Whittle likelihood estimator for the RSV-GALM model and a test for general asymmetry, and analyzes the finite sample properties. The paper also develops an approach to obtain volatility estimates and out-of-sample forecasts. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The paper compares the forecasting performance of the new model with a realized conditional volatility model.

This paper considers a stochastic frontier model that contains environmental variables that affect the level of inefficiency but not the frontier. The model contains statistical noise, potentially endogenous regressors, and technical inefficiency that follows the scaling property, in the sense that it is the product of a basic (half-normal) inefficiency term and a parametric function of the environmental variables. The environmental variables may be endogenous because they are correlated with the statistical noise or with the basic inefficiency term. Several previous papers have considered the case of inputs that are endogenous because they are correlated with statistical noise, and if they contain environmental variables these are exogenous. One recent paper allows the environmental variables to be correlated with statistical noise. Our paper is the first to allow both the inputs and the environmental variables to be endogenous in the sense that they are correlated either with statistical noise or with the basic inefficiency term. Correlation of inputs or environmental variables with the basic inefficiency term raises non-trivial conceptual issues about the meaning of exogeneity, and technical issues of estimation of the model.

This paper studies the determinants of firm-level revenues, as a measure of the performance of firms in China’s domestic and export markets. The analysis of the determinants of the aforementioned outcomes calls for a mixed linear–nonlinear econometric approach. The paper proposes specifying a system of equations which is inspired by Basmann’s work and recent theoretical work in international economics and conducts comparative static analyses regarding the role of exogenous shocks to the system to flesh out the relative importance of transmissions across outcomes.

In a seminal paper, Basmann (1985) introduced a serial correlation structure based on an intertemporal adjustment mechanism. Basmann’s 1985 paper of course was built on his previous pioneering work on estimation and identifiability in structural equations leading to 2SLS (Basmann, 1957, 1960). In this paper, we follow a similar path. We derive a non-standard unit root serial correlation formulation for intertemporal adjustments in the labor force participation rate. This leads to a tractable three-error component model, which in contrast to other models embeds heterogeneity into the error structure. Unlike in the typical i.i.d. three-error component two-tier stochastic frontier model, our equation’s error components are independent but not identically distributed. This leads to a complex nonlinear likelihood function requiring identification through a two-step estimation procedure, which we estimate using Current Population Survey (CPS) data. By transforming the basic equation linking labor force participation to the working age population, this paper devises a new method which can be used to identify labor market joiners and leavers. The method’s advantage is its parsimonious data requirements, especially alleviating the need for survey based longitudinal data.

This paper provides identification results for a class of models specified by a triangular system of two equations with binary endogenous variables. The joint distribution of the latent error terms is specified through a parametric copula structure that satisfies a particular dependence ordering, while the marginal distributions are allowed to be arbitrary but known. This class of models is broad and includes bivariate probit models as a special case. The paper demonstrates that having an exclusion restriction is necessary and sufficient for global identification in a model without common exogenous covariates, where the excluded variable is allowed to be binary. Having an exclusion restriction is sufficient in models with common exogenous covariates that are present in both equations. The paper then extends the identification analyses to a model where the marginal distributions of the error terms are unknown.

In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by subsampling; an approach that computes rescaled copies of the original statistic based on local stretches of high-frequency data, and then it studies the sampling variation of these. We show that our estimator is consistent both in frictionless markets and models with additive microstructure noise. We derive a rate of convergence for it and are also able to determine an optimal rate for its tuning parameters (e.g., the number of subsamples). Subsampling does not require an extra set of estimators to do inference, which renders it trivial to implement. As a variance–covariance matrix estimator, it has the attractive feature that it is positive semi-definite by construction. Moreover, the subsampler is to some extent automatic, as it does not exploit explicit knowledge about the structure of the asymptotic covariance. It therefore tends to adapt to the problem at hand and be robust against misspecification of the noise process. As such, this paper facilitates assessment of the sampling errors inherent in high-frequency estimation of volatility. We highlight the finite sample properties of the subsampler in a Monte Carlo study, while some initial empirical work demonstrates its use to draw feasible inference about volatility in financial markets.

This paper reviews the first forty years of the Journal of Econometrics. The focus of the paper is on collaboration patterns and the internationalization of research in econometrics. We report the most prolific authors, institutions and countries and we find that the share of collaborative articles has increased over time and that most contributions come from affiliations that are based in the USA (but decreasingly so). We also apply social network analysis and discover the most central authors, institutions and countries in the Journal of Econometrics. Moreover, we find that the coauthorship network has been increasingly integrated, exhibiting small-world properties.

Statistical applications of classical parametric max-stable processes are still sparse mostly due to lack of (1) efficiency of statistical estimation of many parameters in the processes, (2) flexibility of concurrently modeling asymptotic independence and asymptotic dependence among variables, and (3) capability of fitting real data directly. This paper studies a more flexible model, i.e. a class of copula structured M4 (multivariate maxima and moving maxima) processes, and hence CSM4 for short. CSM4 processes are constructed by incorporating sparse random coefficients and structured extreme value copulas in asymptotically (in)dependent M4 (AIM4) processes. It is shown that the new model overcomes all of the aforementioned three constraints. The paper illustrates new features and advantages of the CSM4 model using simulated examples and real data of intra-daily maxima of high-frequency financial time series. The paper also studies probabilistic properties of the proposed model, and its statistical inference.

Pre-averaging is a popular strategy for mitigating microstructure in high frequency financial data. As the term suggests, transaction or quote data are averaged over short time periods ranging from 30 s to five min, and the resulting averages approximate the efficient price process much better than the raw data. Apart from reducing the size of the microstructure, the methodology also helps synchronise data from different securities. The procedure is robust to short term dependence in the noise. Since averages can be subject to outliers, and since they can pulverise jumps, we have developed a broader theory which also applies to cases where M-estimation is used to pin down the efficient price in local neighbourhoods. M-estimation serves the same function as averaging, but we shall see that it is safer. Good choices of M-estimating function greatly enhance the identification of jumps. The methodology applies off-the-shelf to any high frequency econometric problem. In this paper, we develop a general theory for pre-averaging and M-estimation based inference. We show that, up to a contiguity adjustment, the estimated process behaves as if one sampled from a semimartingale (with unchanged volatility) plus an independent error. Estimating the efficient price is a form of pre-processing of the data, and hence the methods in this paper also serve the purpose of data cleaning.

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.