Essays in Honor of Cheng Hsiao: Volume 41

It is shown in the literature that the Arellano–Bond type generalized method of moments (GMM) of dynamic panel models is asymptotically biased (e.g., Hsiao & Zhang, 2015; Hsiao & Zhou, 2017). To correct the asymptotical bias of Arellano–Bond GMM, the authors suggest to use the jackknife instrumental variables estimation (JIVE) and also show that the JIVE of Arellano–Bond GMM is indeed asymptotically unbiased. Monte Carlo studies are conducted to compare the performance of the JIVE as well as Arellano–Bond GMM for linear dynamic panels. The authors demonstrate that the reliability of statistical inference depends critically on whether an estimator is asymptotically unbiased or not.

Measurement of diminishing or divergent cross section dispersion in a panel plays an important role in the assessment of convergence or divergence over time in key economic indicators. Econometric methods, known as weak σ-convergence tests, have recently been developed (Kong, Phillips, & Sul, 2019) to evaluate such trends in dispersion in panel data using simple linear trend regressions. To achieve generality in applications, these tests rely on heteroskedastic and autocorrelation consistent (HAC) variance estimates. The present chapter examines the behavior of these convergence tests when heteroskedastic and autocorrelation robust (HAR) variance estimates using fixed-b methods are employed instead of HAC estimates. Asymptotic theory for both HAC and HAR convergence tests is derived and numerical simulations are used to assess performance in null (no convergence) and alternative (convergence) cases. While the use of HAR statistics tends to reduce size distortion, as has been found in earlier analytic and numerical research, use of HAR estimates in nonparametric standardization leads to significant power differences asymptotically, which are reflected in finite sample performance in numerical exercises. The explanation is that weak σ-convergence tests rely on intentionally misspecified linear trend regression formulations of unknown trend decay functions that model convergence behavior rather than regressions with correctly specified trend decay functions. Some new results on the use of HAR inference with trending regressors are derived and an empirical application to assess diminishing variation in US State unemployment rates is included.

This chapter examines the limit properties of information criteria (such as AIC, BIC, and HQIC) for distinguishing between the unit-root (UR) model and the various kinds of explosive models. The explosive models include the local-to-unit-root model from the explosive side the mildly explosive (ME) model, and the regular explosive model. Initial conditions with different orders of magnitude are considered. Both the OLS estimator and the indirect inference estimator are studied. It is found that BIC and HQIC, but not AIC, consistently select the UR model when data come from the UR model. When data come from the local-to-unit-root model from the explosive side, both BIC and HQIC select the wrong model with probability approaching 1 while AIC has a positive probability of selecting the right model in the limit. When data come from the regular explosive model or from the ME model in the form of 1 + n^α/n with α ∈ (0, 1), all three information criteria consistently select the true model. Indirect inference estimation can increase or decrease the probability for information criteria to select the right model asymptotically relative to OLS, depending on the information criteria and the true model. Simulation results confirm our asymptotic results in finite sample.

This chapter extends the univariate forecasting method proposed by Wang, Luc, and Hsiao (2013) to forecast the multivariate long memory model subject to structural breaks. The approach does not need to estimate the parameters of this multivariate system nor need to detect the structural breaks. The only procedure is to employ a VAR(k) model to approximate the multivariate long memory model subject to structural breaks. Therefore, this approach reduces the computational burden substantially and also avoids estimation of the parameters of the multivariate long memory model, which can lead to poor forecasting performance. Moreover, when there are multiple breaks, when the breaks occur close to the end of the sample or when the breaks occur at different locations for the time series in the system, our VAR approximation approach solves the issue of spurious breaks in finite samples, even though the exact orders of the multivariate long memory process are unknown. Insights from our theoretical analysis are confirmed by a set of Monte Carlo experiments, through which we demonstrate that our approach provides a substantial improvement over existing multivariate prediction methods. Finally, an empirical application to the multivariate realized volatility illustrates the usefulness of our forecasting procedure.

This chapter contributes to the growing global VAR (GVAR) literature by showing how global and national shocks can be identified within a GVAR framework. The usefulness of the proposed approach is illustrated in an application to the analysis of the interactions between public debt and real output growth in a multicountry setting, and the results are compared to those obtained from standard single country VAR analysis. We find that on average (across countries) global shocks explain about one-third of the long-horizon forecast error variance of output growth, and about one-fifth of the long-run variance of the rate of change of debt-to-GDP. Evidence on the degree of cross-sectional dependence in these variables and their innovations are exploited to identify the global shocks, and priors are used to identify the national shocks within a Bayesian framework. It is found that posterior median debt elasticity with respect to output is much larger when the rise in output is due to a fiscal policy shock, as compared to when the rise in output is due to a positive technology shock. The cross-country average of the median debt elasticity is 1.45 when the rise in output is due to a fiscal expansion as compared to 0.76 when the rise in output follows from a favorable output shock.

This chapter re-examines the determinants of health care expenditure (HCE), using a panel of 32 Organization for Economic Cooperation and Development (OECD) countries from 1990 to 2012. In particular, a panel semiparametric technique (i.e., a partially linear model) is employed, with cross-sectional dependence allowed. Beside the study of coefficients, this chapter investigates the trending functions of HCE. After the common and individual trends of HCE are estimated via semiparametric methods, the authors calibrate them with polynomial specifications, leading to out-of-sample forecasting. The validities of the calibration are tested as well. Contrary to those studies that do not take into account time series properties, our finding suggests that medical care is not a luxury commodity. Other determinants, such as public financing, and the supply of doctors, are all positively related to HCE. Moreover, the calibrated trending models perform well in out-of-sample forecasting.

This chapter proposes semiparametric estimation of the relationship between growth rate of GDP per capita, growth rates of physical and human capital, labor as well as other covariates and common trends for a panel of 23 OECD countries observed over the period 1971–2015. The observed differentiated behaviors by country reveal strong heterogeneity. This is the motivation behind using a mixed fixed- and random coefficients model to estimate this relationship. In particular, this chapter uses a semiparametric specification with random intercepts and slopes coefficients. Motivated by Lee and Wand (2016), the authors estimate a mean field variational Bayes semiparametric model with random coefficients for this panel of countries. Results reveal nonparametric specifications for the common trends. The use of this flexible methodology may enrich the empirical growth literature underlining a large diversity of responses across variables and countries.

Importance sampling is a popular Monte Carlo method used in a variety of areas in econometrics. When the variance of the importance sampling estimator is infinite, the central limit theorem does not apply and estimates tend to be erratic even when the simulation size is large. The authors consider asymptotic trimming in such a setting. Specifically, the authors propose a bias-corrected tail-trimmed estimator such that it is consistent and has finite variance. The authors show that the proposed estimator is asymptotically normal, and has good finite-sample properties in a Monte Carlo study.

This chapter develops a structural framework for the analysis of scoring procurement auctions where bidder’s quality and bid are taken into account. With exogenous quality, the authors characterize the optimal mechanism whether the buyer is private or public and show that the optimal scoring rule need not be linear in the bid. The model primitives include the buyer benefit function, the bidders’ cost inefficiencies distribution and cost function, and potentially the cost of public funds. We show that the model primitives are nonparametrically identified under mild functional assumptions from the buyer’s choice, firms’ bids and qualities. The authors then develop a multistep kernel-based procedure to estimate the model primitives and provide their convergence rates. Our identification and estimation results are general as they apply to other scoring rules including quasi-linear ones.

The authors propose an Markov Chain Monte Carlo (MCMC) method for estimating a class of linear sum assignment problems (LSAP; the discrete case of the optimal transport problems). Prominent examples include multi-item auctions and mergers in industrial organizations. This contribution is to decompose the joint likelihood of the allocation and prices by exploiting the primal and dual linear programming formulation of the underlying LSAP. Our decomposition, coupled with the data augmentation technique, leads to an MCMC sampler without a repeated model-solving phase.

The authors consider how the mode of data collection (Internet vs. paper) alters individuals’ responses to different types of survey questions, including subjective, recall, and factual questions. The authors isolate the measurement effect of the mode from the sample selection effect by exploiting predata in a convenience consumer panel. The authors propose using panelists’ reward point balance as exclusion restriction to correct for differing response probabilities by mode, because the reward point balance depends on the timing of the survey invitations and is a source of random variation in response incentive. The authors evaluate average and quantile measurement effects in a mixed-mode Web/paper survey and find statistically significant evidence of mode effects in subjective and recall questions.

Peers and friends are among the most influential social forces affecting adolescent behavior. In this chapter, the authors investigate peer effects on post high school career decisions and on school choice. The authors define peers as students who are in the same classes and social clubs and measure peer effects as spatial dependence among them. Utilizing recent developments in spatial econometrics, the authors formalize a spatial multinomial choice model in which individuals are spatially dependent in their preferences. The authors estimate the model via pseudo maximum likelihood using data from the Texas Higher Education Opportunity Project. The authors do find that individuals are positively correlated in their career and college preferences and examine how such dependencies impact decisions directly and indirectly as peer effects are allowed to reverberate through the social network in which students reside.

Portfolios of mortgage loans played an important role in the Great Recession and continue to compose a material part of bank assets. This chapter investigates how cross-sectional dependence in the underlying properties flows through to the loan returns, and thus, the risk of the portfolio. At one extreme, a portfolio of foreclosed mortgage loans becomes a portfolio of real estate whose returns exhibit substantial cross-sectional and spatial dependence. Near the other extreme, almost all loans perform and yield constant returns, which do not correlate with other performing loan returns. This suggests that loan performance effectively censors the random returns of the underlying properties. Following the statistical properties of the correlations among censored variables, the authors build off this foundation and show how the loan return correlations will rise as economic conditions deteriorate and the defaulting loans reveal the underlying housing correlations. In this chapter, the authors (1) adapt tools from spatial statistics to document substantial cross-sectional dependence across house price returns and examine the spatial structure of this dependence, (2) investigate the nonlinear nature of correlations among loan returns as a function of the default rate and the underlying house price correlations, and (3) conduct a simulation exercise using parameters from the empirical data to show the implications for holding a portfolio of mortgages.