Binary choice models with discrete regressors: Identification and misspecification

This paper explores the inferential question in semiparametric binary response models when the continuous support condition is not satisfied and all regressors have discrete support. I focus mainly on the models under the conditional median restriction, as in Manski (1985). I find sharp bounds on the components of the parameter of interest and outline several applications. The formulas for bounds obtained using a recursive procedure help analyze cases where one regressor’s support becomes increasingly dense. Furthermore, I investigate asymptotic properties of estimators of the identification set. I describe a relation between the maximum score estimation and support vector machines and propose several approaches to address the problem of empty identification sets when the model is misspecified.     

Masking identification of discrete choice models under simulation methods

We present examples based on actual and synthetic datasets to illustrate how simulation methods can mask identification problems in the estimation of discrete choice models such as mixed logit. Simulation methods approximate an integral (without a closed form) by taking draws from the underlying distribution of the random variable of integration. Our examples reveal how a low number of draws can generate estimates that appear identified, but in fact, are either not theoretically identified by the model or not empirically identified by the data. For the particular case of maximum simulated likelihood estimation, we investigate the underlying source of the problem by focusing on the shape of the simulated log-likelihood function under different conditions.     

Heteroskedasticity and spatiotemporal dependence robust inference for linear panel models with fixed effects

This paper studies robust inference for linear panel models with fixed effects in the presence of heteroskedasticity and spatiotemporal dependence of unknown forms. We propose a bivariate kernel covariance estimator that nests existing estimators as special cases. Our estimator improves upon existing estimators in terms of robustness, efficiency, and adaptiveness. For distributional approximations, we considered two types of asymptotics: the increasing-smoothing asymptotics and the fixed-smoothing asymptotics. Under the former asymptotics, the Wald statistic based on our covariance estimator converges to a chi-square distribution. Under the latter asymptotics, the Wald statistic is asymptotically equivalent to a distribution that can be well approximated by an F distribution. Simulation results show that our proposed testing procedure works well in finite samples.     

Pseudo-likelihood estimation and bootstrap inference for structural discrete Markov decision models

This paper analyzes the higher-order properties of the estimators based on the nested pseudo-likelihood (NPL) algorithm and the practical implementation of such estimators for parametric discrete Markov decision models. We derive the rate at which the NPL algorithm converges to the MLE and provide a theoretical explanation for the simulation results in Aguirregabiria and Mira [Aguirregabiria, V., Mira, P., 2002. Swapping the nested fixed point algorithm: A class of estimators for discrete Markov decision models. Econometrica 70, 1519–1543], in which iterating the NPL algorithm improves the accuracy of the estimator. We then propose a new NPL algorithm that can achieve quadratic convergence without fully solving the fixed point problem in every iteration and apply our estimation procedure to a finite mixture model. We also develop one-step NPL bootstrap procedures for discrete Markov decision models. The Monte Carlo simulation evidence based on a machine replacement model of Rust [Rust, J., 1987. Optimal replacement of GMC bus engines: An empirical model of Harold Zurcher. Econometrica 55, 999–1033] shows that the proposed one-step bootstrap test statistics and confidence intervals improve upon the first order asymptotics even with a relatively small number of iterations.     

Instrumental quantile regression inference for structural and treatment effect models

We introduce a class of instrumental quantile regression methods for heterogeneous treatment effect models and simultaneous equations models with nonadditive errors and offer computable methods for estimation and inference. These methods can be used to evaluate the impact of endogenous variables or treatments on the entire distribution of outcomes. We describe an estimator of the instrumental variable quantile regression process and the set of inference procedures derived from it. We focus our discussion of inference on tests of distributional equality, constancy of effects, conditional dominance, and exogeneity. We apply the procedures to characterize the returns to schooling in the U.S.     

Identification of binary choice models with social interactions

This paper provides a set of results on the econometric identifiability of binary choice models with social interactions. Our analysis moves beyond parametric identification results that have been obtained in the literature to consider the identifiability of model parameters when the distribution of random payoff terms is unknown. Further, we consider how identification is affected by the presence of unobservable payoff terms of various types as well as identification in the presence of certain forms of endogenous group membership. Our results suggest that at least partial identification may be achieved under assumptions that in certain contexts may be plausible.     

Finite sample multivariate structural change tests with application to energy demand models

This paper considers finite sample motivated structural change tests in the multivariate linear regression model with application to energy demand models, in which case commonly used structural change tests remain asymptotic. As in Dufour and Kiviet [1996. Exact tests for structural change in first-order dynamic models. Journal of Econometrics 70, 39–68], we account for intervening nuisance parameters through a two-stage maximized Monte Carlo test procedure. Our contributions can be classified into five categories: (i) we extend tests for which a finite-sample theory has been supplied for Gaussian distributions to the non-Gaussian context; (ii) we show that Bai et al. [1998. Testing and dating common breaks in multi-variate time series. The Review of Economic Studies 65 (3), 395–432] test severely over-rejects and propose exact variants of this test; (iii) we consider predictive break test approaches which generalize tests in Dufour [1980. Dummy variables and predictive tests for structural change. Economics Letters 6, 241–247] and Dufour and Kiviet [1996. Exact tests for structural change in first-order dynamic models. Journal of Econometrics 70, 39–68]; (iv) we propose exact (non-Bonferonni based) extensions of the multivariate outliers test from Wilks [1963. Multivariate statistical outliers. Sankhya Series A 25, 407–426] to models with covariates; (v) we apply these tests to the energy demand system analyzed by Arsenault et al. [1995. A total energy demand model of Québec: forecasting properties. Energy Economics 17 (2), 163–171]. For two out of the six industrial sectors analyzed over the 1962–2000 period, break and further goodness-of-fit and diagnostic tests allow to identify (and correct) specification problems arising from historical regulatory changes or (possibly random) industry-specific effects. The procedures we propose have potential useful applications in statistics, econometrics and finance (e.g. event studies).     

Identification and estimation of econometric models with group interactions,contextual factors and fixed effects

This paper considers identification and estimation of structural interaction effects in a social interaction model. The model allows unobservables in the group structure, which may be correlated with included regressors. We show that both the endogenous and exogenous interaction effects can be identified if there are sufficient variations in group sizes. We consider the estimation of the model by the conditional maximum likelihood and instrumental variables methods. For the case with large group sizes, the possible identification can be weak in the sense that the estimates converge in distribution at low rates.     

Inconsistency of the MLE and inference based on weighted LS for LARCH models

This paper considers a class of finite-order autoregressive linear ARCH models. The model captures the leverage effect, allows the volatility to be arbitrarily close to zero and to reach its minimum for non-zero innovations, and is appropriate for long memory modeling when infinite orders are allowed. However, the (quasi-)maximum likelihood estimator is, in general, inconsistent. A self-weighted least-squares estimator is proposed and is shown to be asymptotically normal. A score test for conditional homoscedasticity and diagnostic portmanteau tests are developed. Their performance is illustrated via simulation experiments. It is also investigated whether stock market returns exhibit some of the characteristic features of the linear ARCH model.     

Moving average stochastic volatility models with application to inflation forecast

We introduce a new class of models that has both stochastic volatility and moving average errors, where the conditional mean has a state space representation. Having a moving average component, however, means that the errors in the measurement equation are no longer serially independent, and estimation becomes more difficult. We develop a posterior simulator that builds upon recent advances in precision-based algorithms for estimating these new models. In an empirical application involving US inflation we find that these moving average stochastic volatility models provide better in-sample fitness and out-of-sample forecast performance than the standard variants with only stochastic volatility.     

Heteroskedasticity, autocorrelation, and spatial correlation robust inference in linear panel models with fixed-effects

This paper develops an asymptotic theory for test statistics in linear panel models that are robust to heteroskedasticity, autocorrelation and/or spatial correlation. Two classes of standard errors are analyzed. Both are based on nonparametric heteroskedasticity autocorrelation (HAC) covariance matrix estimators. The first class is based on averages of HAC estimators across individuals in the cross-section, i.e. “averages of HACs”. This class includes the well known cluster standard errors analyzed by Arellano (1987) as a special case. The second class is based on the HAC of cross-section averages and was proposed by Driscoll and Kraay (1998). The ”HAC of averages” standard errors are robust to heteroskedasticity, serial correlation and spatial correlation but weak dependence in the time dimension is required. The “averages of HACs” standard errors are robust to heteroskedasticity and serial correlation including the nonstationary case but they are not valid in the presence of spatial correlation. The main contribution of the paper is to develop a fixed-b asymptotic theory for statistics based on both classes of standard errors in models with individual and possibly time fixed-effects dummy variables. The asymptotics is carried out for large time sample sizes for both fixed and large cross-section sample sizes. Extensive simulations show that the fixed-b approximation is usually much better than the traditional normal or chi-square approximation especially for the Driscoll-Kraay standard errors. The use of fixed-b critical values will lead to more reliable inference in practice especially for tests of joint hypotheses.     

Estimation and inference for spatial models with heterogeneous coefficients: An application to US house prices

This paper considers the estimation and inference of spatial panel data models with heterogeneous spatial lag coefficients, with and without weakly exogenous regressors, and subject to heteroskedastic errors. A quasi maximum likelihood (QML) estimation procedure is developed and the conditions for identification of the spatial coefficients are derived. The QML estimators of individual spatial coefficients, as well as their mean group estimators, are shown to be consistent and asymptotically normal. Small‐sample properties of the proposed estimators are investigated by Monte Carlo simulations and results are shown to be in line with the paper's key theoretical findings, even for panels with moderate time dimensions and irrespective of the number of cross‐section units. A detailed empirical application to US house price changes during the 1975–2014 period shows a significant degree of heterogeneity in spatiotemporal dynamics over the 338 Metropolitan Statistical Areas considered.     

Tailored randomized block MCMC methods with application to DSGE models

In this paper we develop new Markov chain Monte Carlo schemes for the estimation of Bayesian models. One key feature of our method, which we call the tailored randomized block Metropolis–Hastings (TaRB-MH) method, is the random clustering of the parameters at every iteration into an arbitrary number of blocks. Then each block is sequentially updated through an M–H step. Another feature is that the proposal density for each block is tailored to the location and curvature of the target density based on the output of simulated annealing, following  and  and Chib and Ergashev (in press). We also provide an extended version of our method for sampling multi-modal distributions in which at a pre-specified mode jumping iteration, a single-block proposal is generated from one of the modal regions using a mixture proposal density, and this proposal is then accepted according to an M–H probability of move. At the non-mode jumping iterations, the draws are obtained by applying the TaRB-MH algorithm. We also discuss how the approaches of Chib (1995) and Chib and Jeliazkov (2001) can be adapted to these sampling schemes for estimating the model marginal likelihood. The methods are illustrated in several problems. In the DSGE model of Smets and Wouters (2007), for example, which involves a 36-dimensional posterior distribution, we show that the autocorrelations of the sampled draws from the TaRB-MH algorithm decay to zero within 30–40 lags for most parameters. In contrast, the sampled draws from the random-walk M–H method, the algorithm that has been used to date in the context of DSGE models, exhibit significant autocorrelations even at lags 2500 and beyond. Additionally, the RW-MH does not explore the same high density regions of the posterior distribution as the TaRB-MH algorithm. Another example concerns the model of An and Schorfheide (2007) where the posterior distribution is multi-modal. While the RW-MH algorithm is unable to jump from the low modal region to the high modal region, and vice-versa, we show that the extended TaRB-MH method explores the posterior distribution globally in an efficient manner.     

Maximum likelihood estimation and Lagrange multiplier tests for panel seemingly unrelated regressions with spatial lag and spatial errors: An application to hedonic housing prices in Paris

This paper proposes maximum likelihood estimators for panel seemingly unrelated regressions with both spatial lag and spatial error components. We study the general case where spatial effects are incorporated via spatial errors terms and via a spatial lag dependent variable and where the heterogeneity in the panel is incorporated via an error component specification. We generalize the approach of Wang and Kockelman (2007) and propose joint and conditional Lagrange multiplier tests for spatial autocorrelation and random effects for this spatial SUR panel model. The small sample performance of the proposed estimators and tests are examined using Monte Carlo experiments. An empirical application to hedonic housing prices in Paris illustrate these methods. The proposed specification uses a system of three SUR equations corresponding to three types of flats within 80 districts of Paris over the period 1990-2003. We test for spatial effects and heterogeneity and find reasonable estimates of the shadow prices for housing characteristics.     

Indirect estimation of large conditionally heteroskedastic factor models,with an application to the Dow 30 stocks

We derive indirect estimators of conditionally heteroskedastic factor models in which the volatilities of common and idiosyncratic factors depend on their past unobserved values by calibrating the score of a Kalman-filter approximation with inequality constraints on the auxiliary model parameters. We also propose alternative indirect estimators for large-scale models, and explain how to apply our procedures to many other dynamic latent variable models. We analyse the small sample behaviour of our indirect estimators and several likelihood-based procedures through an extensive Monte Carlo experiment with empirically realistic designs. Finally, we apply our procedures to weekly returns on the Dow 30 stocks.     

No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects,jumps and i.i.d. noise: Theory and testable distributional implications

We develop a sequential procedure to test the adequacy of jump-diffusion models for return distributions. We rely on intraday data and nonparametric volatility measures, along with a new jump detection technique and appropriate conditional moment tests, for assessing the import of jumps and leverage effects. A novel robust-to-jumps approach is utilized to alleviate microstructure frictions for realized volatility estimation. Size and power of the procedure are explored through Monte Carlo methods. Our empirical findings support the jump-diffusive representation for S&P500 futures returns but reveal it is critical to account for leverage effects and jumps to maintain the underlying semi-martingale assumption.     

On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks

Likelihoods and posteriors of instrumental variable (IV) regression models with strong endogeneity and/or weak instruments may exhibit rather non-elliptical contours in the parameter space. This may seriously affect inference based on Bayesian credible sets. When approximating posterior probabilities and marginal densities using Monte Carlo integration methods like importance sampling or Markov chain Monte Carlo procedures the speed of the algorithm and the quality of the results greatly depend on the choice of the importance or candidate density. Such a density has to be ‘close’ to the target density in order to yield accurate results with numerically efficient sampling. For this purpose we introduce neural networks which seem to be natural importance or candidate densities, as they have a universal approximation property and are easy to sample from. A key step in the proposed class of methods is the construction of a neural network that approximates the target density. The methods are tested on a set of illustrative IV regression models. The results indicate the possible usefulness of the neural network approach.     

A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation

This paper presents a Bayesian approach to bandwidth selection for multivariate kernel regression. A Monte Carlo study shows that under the average squared error criterion, the Bayesian bandwidth selector is comparable to the cross-validation method and clearly outperforms the bootstrapping and rule-of-thumb bandwidth selectors. The Bayesian bandwidth selector is applied to a multivariate kernel regression model that is often used to estimate the state-price density of Arrow–Debreu securities with the S&P 500 index options data and the DAX index options data. The proposed Bayesian bandwidth selector represents a data-driven solution to the problem of choosing bandwidths for the multivariate kernel regression involved in the nonparametric estimation of the state-price density pioneered by Aït-Sahalia and Lo [Aït-Sahalia, Y., Lo, A.W., 1998. Nonparametric estimation of state-price densities implicit in financial asset prices. The Journal of Finance, 53, 499, 547.]     

A semiparametric panel model for unbalanced data with application to climate change in the United Kingdom

This paper is concerned with developing a semiparametric panel model to explain the trend in UK temperatures and other weather outcomes over the last century. We work with the monthly averaged maximum and minimum temperatures observed at the twenty six Meteorological Office stations. The data is an unbalanced panel. We allow the trend to evolve in a nonparametric way so that we obtain a fuller picture of the evolution of common temperature in the medium timescale. Profile likelihood estimators (PLE) are proposed and their statistical properties are studied. The proposed PLE has improved asymptotic property comparing the sequential two-step estimators. Finally, forecasting based on the proposed model is studied.     

Inference on an extended Roy model,with an application to schooling decisions in France

This paper considers the identification and estimation of an extension of Roy’s model (1951) of sectoral choice, which includes a non-pecuniary component in the selection equation and allows for uncertainty on potential earnings. We focus on the identification of the non-pecuniary component, which is key to disentangling the relative importance of monetary incentives versus preferences in the context of sorting across sectors. By making the most of the structure of the selection equation, we show that this component is point identified from the knowledge of the covariate effects on earnings, as soon as one covariate is continuous. Notably, and in contrast to most results on the identification of Roy models, this implies that identification can be achieved without any exclusion restriction nor large support condition on the covariates. As a by-product, bounds are obtained on the distribution of the ex ante   monetary returns. We propose a three-stage semiparametric estimation procedure for this model, which yields root-n$n$ consistent and asymptotically normal estimators. Finally, we apply our results to the educational context, by providing new evidence from French data that non-pecuniary factors are a key determinant of higher education attendance decisions.