Semiparametric efficient estimation of dynamic panel data models

This paper extends the semiparametric efficient treatment of panel data models pursued by Park and Simar [Park, B.U., Simar, L., 1994. Efficient semiparametric estimation in stochastic frontier models. Journal of the American Statistical Association 89, 929–936] and Park et al. [Park, B.U., Sickles, R.C., Simar, L., 1998. Stochastic frontiers: a semiparametric approach. Journal of Econometrics 84, 273–301; Park, B.U., Sickles, R.C., Simar, L., 2003. Semiparametric efficient estimation of AR(1) panel data models. Journal of Econometrics 117, 279–309] to a dynamic panel setting. We develop a semiparametric efficient estimator under minimal assumptions when the panel model contains a lagged dependent variable. We apply this new estimator to analyze the structure of demand between city pairs for selected U.S. airlines during the period 1979 I–1992 IV.     

Generalized reduced rank tests using the singular value decomposition

We propose a novel statistic to test the rank of a matrix. The rank statistic overcomes deficiencies of existing rank statistics, like: a Kronecker covariance matrix for the canonical correlation rank statistic of Anderson [Annals of Mathematical Statistics (1951), 22, 327–351] sensitivity to the ordering of the variables for the LDU rank statistic of Cragg and Donald [Journal of the American Statistical Association (1996), 91, 1301–1309] and Gill and Lewbel [Journal of the American Statistical Association (1992), 87, 766–776] a limiting distribution that is not a standard chi-squared distribution for the rank statistic of Robin and Smith [Econometric Theory (2000), 16, 151–175] usage of numerical optimization for the objective function statistic of Cragg and Donald [Journal of Econometrics (1997), 76, 223–250] and ignoring the non-negativity restriction on the singular values in Ratsimalahelo [2002, Rank test based on matrix perturbation theory. Unpublished working paper, U.F.R. Science Economique, University de Franche-Comté]. In the non-stationary cointegration case, the limiting distribution of the new rank statistic is identical to that of the Johansen trace statistic.     

Inverse probability weighted estimation for general missing data problems

I study inverse probability weighted M-estimation under a general missing data scheme. Examples include M-estimation with missing data due to a censored survival time, propensity score estimation of the average treatment effect in the linear exponential family, and variable probability sampling with observed retention frequencies. I extend an important result known to hold in special cases: estimating the selection probabilities is generally more efficient than if the known selection probabilities could be used in estimation. For the treatment effect case, the setup allows a general characterization of a “double robustness” result due to Scharfstein et al. [1999. Rejoinder. Journal of the American Statistical Association 94, 1135–1146].     

SCAD‐penalized quantile regression for high‐dimensional data analysis and variable selection

The present penalized quantile variable selection methods are only applicable to finite number of predictors or do not have oracle property associated with estimator. This technique is considered as an alternative to ordinary least squares regression in case of the outliers and the heavy‐tailed errors existing in linear models. The variable selection through quantile regression with diverging number of parameters is investigated in this paper. The convergence rate of estimator with smoothly clipped absolute deviation penalty function is also studied. Moreover, the oracle property with proper selection of tuning parameter for quantile regression under certain regularity conditions is also established. In addition, the rank correlation screening method is used to accommodate ultra‐high dimensional data settings. Monte Carlo simulations demonstrate finite performance of the proposed estimator. The results of real data reveal that this approach provides substantially more information as compared with ordinary least squares, conventional quantile regression, and quantile lasso.     

Testing for short- and long-run causality: A frequency-domain approach

The framework of Geweke (1982. Journal of the American Statistical Association 77, 304–324.) and Hosoya (1991. Probability Theory and Related Fields 88, 429–444.) is adopted to construct a simple test for causality in the frequency domain. This test can also be applied to cointegrated systems. To study the large sample properties of the test, we analyze the power against a sequence of local alternatives. The finite sample properties are investigated by means of Monte Carlo simulations. Our methodology is applied to investigate the predictive content of the yield spread for future output growth. Using quarterly US data we observe reasonable leading indicator properties at frequencies around one year and typical business cycle frequencies.     

Semiparametric efficient adaptive estimation of asymmetric GARCH models

In this paper we derive a semiparametric efficient adaptive estimator of an asymmetric GARCH model. Applying some general results from Drost et al. [1997. The Annals of Statistics 25, 786–818], we first estimate the unknown density function of the disturbances by kernel methods, then apply a one-step Newton–Raphson method to obtain a more efficient estimator than the quasi-maximum likelihood estimator. The proposed semiparametric estimator is adaptive for parameters appearing in the conditional standard deviation model with respect to the unknown distribution of the disturbances.     

Nonparametric transformation to white noise

We consider a semiparametric distributed lag model in which the “news impact curve” m is nonparametric but the response is dynamic through some linear filters. A special case of this is a nonparametric regression with serially correlated errors. We propose an estimator of the news impact curve based on a dynamic transformation that produces white noise errors. This yields an estimating equation for m that is a type two linear integral equation. We investigate both the stationary case and the case where the error has a unit root. In the stationary case we establish the pointwise asymptotic normality. In the special case of a nonparametric regression subject to time series errors our estimator achieves efficiency improvements over the usual estimators, see Xiao et al. [2003. More efficient local polynomial estimation in nonparametric regression with autocorrelated errors. Journal of the American Statistical Association 98, 980–992]. In the unit root case our procedure is consistent and asymptotically normal unlike the standard regression smoother. We also present the distribution theory for the parameter estimates, which is nonstandard in the unit root case. We also investigate its finite sample performance through simulation experiments.     

Natural conjugate priors for the instrumental variables regression model applied to the Angrist–Krueger data

We propose a natural conjugate prior for the instrumental variables regression model. The prior is a natural conjugate one since the marginal prior and posterior of the structural parameter have the same functional expressions which directly reveal the update from prior to posterior. The Jeffreys prior results from a specific setting of the prior parameters and results in a marginal posterior of the structural parameter that has an identical functional form as the sampling density of the limited information maximum likelihood estimator. We construct informative priors for the Angrist–Krueger [1991. Does compulsory school attendance affect schooling and earnings? Quarterly Journal of Economics 106, 979–1014] data and show that the marginal posterior of the return on education in the US coincides with the marginal posterior from the Southern region when we use the Jeffreys prior. This result occurs since the instruments are the strongest in the Southern region and the posterior using the Jeffreys prior, identical to maximum likelihood, focusses on the strongest available instruments. We construct informative priors for the other regions that make their posteriors of the return on education similar to that of the US and the Southern region. These priors show the amount of prior information needed to obtain comparable results for all regions.     

Semiparametric time series regression modeling with a diverging number of parameters

Variable selection and error structure determination of a partially linear model with time series errors are important issues. In this paper, we investigate the regression coefficient and autoregressive order shrinkage and selection via the smoothly clipped absolute deviation penalty for a partially linear model with a divergent number of covariates and finite order autoregressive time series errors. Both consistency and asymptotic normality of the proposed penalized estimators are derived. The oracle property of the resultant estimators is proved. Simulation studies are carried out to assess the finite‐sample performance of the proposed procedure. A real data analysis is made to illustrate the usefulness of the proposed procedure as well.     

Short and long run causality measures: Theory and inference

The concept of causality introduced by Wiener [Wiener, N., 1956. The theory of prediction, In: E.F. Beckenback, ed., The Theory of Prediction, McGraw-Hill, New York (Chapter 8)] and Granger [Granger, C. W.J., 1969. Investigating causal relations by econometric models and cross-spectral methods, Econometrica 37, 424–459] is defined in terms of predictability one period ahead. This concept can be generalized by considering causality at any given horizon h$h$ as well as tests for the corresponding non-causality [Dufour, J.-M., Renault, E., 1998. Short-run and long-run causality in time series: Theory. Econometrica 66, 1099–1125; Dufour, J.-M., Pelletier, D., Renault, É., 2006. Short run and long run causality in time series: Inference, Journal of Econometrics 132 (2), 337–362]. Instead of tests for non-causality at a given horizon, we study the problem of measuring causality between two vector processes. Existing causality measures have been defined only for the horizon 1, and they fail to capture indirect causality. We propose generalizations to any horizon h$h$ of the measures introduced by Geweke [Geweke, J., 1982. Measurement of linear dependence and feedback between multiple time series. Journal of the American Statistical Association 77, 304–313]. Nonparametric and parametric measures of unidirectional causality and instantaneous effects are considered. On noting that the causality measures typically involve complex functions of model parameters in VAR and VARMA models, we propose a simple simulation-based method to evaluate these measures for any VARMA model. We also describe asymptotically valid nonparametric confidence intervals, based on a bootstrap technique. Finally, the proposed measures are applied to study causality relations at different horizons between macroeconomic, monetary and financial variables in the US.     

Local polynomial estimation of nonparametric simultaneous equations models

We define a new procedure for consistent estimation of nonparametric simultaneous equations models under the conditional mean independence restriction of Newey et al. [1999. Nonparametric estimation of triangular simultaneous equation models. Econometrica 67, 565–603]. It is based upon local polynomial regression and marginal integration techniques. We establish the asymptotic distribution of our estimator under weak data dependence conditions. Simulation evidence suggests that our estimator may significantly outperform the estimators of Pinkse [2000. Nonparametric two-step regression estimation when regressors and errors are dependent. Canadian Journal of Statistics 28, 289–300] and Newey and Powell [2003. Instrumental variable estimation of nonparametric models. Econometrica 71, 1565–1578].     

Optimal estimation under nonstandard conditions

We analyze optimality properties of maximum likelihood (ML) and other estimators when the problem does not necessarily fall within the locally asymptotically normal (LAN) class, therefore covering cases that are excluded from conventional LAN theory such as unit root nonstationary time series. The classical Hájek–Le Cam optimality theory is adapted to cover this situation. We show that the expectation of certain monotone “bowl-shaped” functions of the squared estimation error are minimized by the ML estimator in locally asymptotically quadratic situations, which often occur in nonstationary time series analysis when the LAN property fails. Moreover, we demonstrate a direct connection between the (Bayesian property of) asymptotic normality of the posterior and the classical optimality properties of ML estimators.     

The modified second-round estimator in the general qualitative response model

This paper suggests a modification of the method of scoring in the general multivariate qualitative response model to attain simpler computation when there are many observations per cell. The paper shows that the proposed estimator is asymptotically efficient even in the cases when the generalized Berkson's estimator (see Amemiya, Journal of the American Statistical Association, June 1976) is not.     

Exponentially tilted likelihood inference on growing dimensional unconditional moment models

Growing-dimensional data with likelihood function unavailable are often encountered in various fields. This paper presents a penalized exponentially tilted (PET) likelihood for variable selection and parameter estimation for growing dimensional unconditional moment models in the presence of correlation among variables and model misspecification. Under some regularity conditions, we investigate the consistent and oracle properties of the PET estimators of parameters, and show that the constrained PET likelihood ratio statistic for testing contrast hypothesis asymptotically follows the chi-squared distribution. Theoretical results reveal that the PET likelihood approach is robust to model misspecification. We study high-order asymptotic properties of the proposed PET estimators. Simulation studies are conducted to investigate the finite performance of the proposed methodologies. An example from the Boston Housing Study is illustrated.     

Gaussian semiparametric estimation of multivariate fractionally integrated processes

This paper analyzes the semiparametric estimation of multivariate long-range dependent processes. The class of spectral densities considered is motivated by and includes those of multivariate fractionally integrated processes. The paper establishes the consistency of the multivariate Gaussian semiparametric estimator (GSE), which has not been shown in other work, and the asymptotic normality of the GSE estimator. The proposed GSE estimator is shown to have a smaller limiting variance than the two-step GSE estimator studied by Lobato [1999. A semiparametric two-step estimator in a multivariate long memory model. Journal of Econometrics 90, 129–153]. Gaussianity is not assumed in the asymptotic theory. Some simulations confirm the relevance of the asymptotic results in samples of the size used in practical work.     

Global yield curve dynamics and interactions: A dynamic Nelson–Siegel approach

The popular Nelson–Siegel [Nelson, C.R., Siegel, A.F., 1987. Parsimonious modeling of yield curves. Journal of Business 60, 473–489] yield curve is routinely fit to cross sections of intra-country bond yields, and Diebold–Li [Diebold, F.X., Li, C., 2006. Forecasting the term structure of government bond yields. Journal of Econometrics 130, 337–364] have recently proposed a dynamized version. In this paper we extend Diebold–Li to a global context, modeling a potentially large set of country yield curves in a framework that allows for both global and country-specific factors. In an empirical analysis of term structures of government bond yields for the Germany, Japan, the UK and the US, we find that global yield factors do indeed exist and are economically important, generally explaining significant fractions of country yield curve dynamics, with interesting differences across countries.     

Productivity trends in U.S. manufacturing: Evidence from the NQ and AIM cost functions

In this paper, we take the econometric approach to productivity measurement in United States manufacturing, using KLEM data over the period from 1953 to 2001. We are also interested in technical change bias, price elasticities, and elasticities of substitution in the U.S. manufacturing industry. We present an empirical comparison and evaluation of the effectiveness of four well-known flexible cost functions—the locally flexible generalized Leontief (see Diewert [1971. An application of the Shephard duality theorem: a generalized Leontief production function. Journal of Political Economy 79, 481–507]), translog (see Christensen et al. [1975. Transendendal logarithmic utility functions. American Economic Review 65, 367–364]), and normalized quadratic (see Diewert and Wales [1987. Flexible functional forms and global curvature conditions. Econometrica 55, 43–68])—and the globally flexible asymptotically ideal model (see Barnett et al. [1991. Semi-nonparametric Bayesian estimation of the asymptotically ideal production model. Journal of Econometrics 49, 5–50]), the latter modified to introduce technical change by means of Thomsen's [2000. Short cuts to dynamic factor demand modelling. Journal of Econometrics 97, 1–23] factor-augmenting efficiency index approach.     

The size distribution of innovations revisited: An application of extreme value statistics to citation and value measures of patent significance

This paper focuses on the analysis of size distributions of innovations, which are known to be highly skewed. We use patent citations as one indicator of innovation significance, constructing two large datasets from the European and US Patent Offices at a high level of aggregation, and the Trajtenberg [1990, A penny for your quotes: patent citations and the value of innovations. Rand Journal of Economics 21(1), 172–187] dataset on CT scanners at a very low one. We also study self-assessed reports of patented innovation values using two very recent patent valuation datasets from the Netherlands and the UK, as well as a small dataset of patent licence revenues of Harvard University. Statistical methods are applied to analyse the properties of the empirical size distributions, where we put special emphasis on testing for the existence of ‘heavy tails’, i.e., whether or not the probability of very large innovations declines more slowly than exponentially. While overall the distributions appear to resemble a lognormal, we argue that the tails are indeed fat. We invoke some recent results from extreme value statistics and apply the Hill [1975. A simple general approach to inference about the tails of a distribution. The Annals of Statistics 3, 1163–1174] estimator with data-driven cut-offs to determine the tail index for the right tails of all datasets except the NL and UK patent valuations. On these latter datasets we use a maximum likelihood estimator for grouped data to estimate the tail index for varying definitions of the right tail. We find significantly and consistently lower tail estimates for the returns data than the citation data (around 0.6–1 vs. 3–5). The EPO and US patent citation tail indices are roughly constant over time, but the latter estimates are significantly lower than the former. The heaviness of the tails, particularly as measured by value indicators, we argue, has significant implications for technology policy and growth theory, since the second and possibly even the first moments of these distributions may not exist.     

Model averaging by jackknife criterion in models with dependent data

The past decade witnessed a literature on model averaging by frequentist methods. For the most part, the asymptotic optimality of various existing frequentist model averaging estimators has been established under i.i.d. errors. Recently, Hansen and Racine [Hansen, B.E., Racine, J., 2012. Jackknife model averaging. Journal of Econometrics 167, 38–46] developed a jackknife model averaging (JMA) estimator, which has an important advantage over its competitors in that it achieves the lowest possible asymptotic squared error under heteroscedastic errors. In this paper, we broaden Hansen and Racine’s scope of analysis to encompass models with (i) a non-diagonal error covariance structure, and (ii) lagged dependent variables, thus allowing for dependent data. We show that under these set-ups, the JMA estimator is asymptotically optimal by a criterion equivalent to that used by Hansen and Racine. A Monte Carlo study demonstrates the finite sample performance of the JMA estimator in a variety of model settings.     

Estimation of Markov regime-switching regression models with endogenous switching

Following Hamilton [1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57, 357–384], estimation of Markov regime-switching regressions typically relies on the assumption that the latent state variable controlling regime change is exogenous. We relax this assumption and develop a parsimonious model of endogenous Markov regime-switching. Inference via maximum likelihood estimation is possible with relatively minor modifications to existing recursive filters. The model nests the exogenous switching model, yielding straightforward tests for endogeneity. In Monte Carlo experiments, maximum likelihood estimates of the endogenous switching model parameters were quite accurate, even in the presence of certain model misspecifications. As an application, we extend the volatility feedback model of equity returns given in Turner et al. [1989. A Markov model of heteroskedasticity, risk, and learning in the stock market. Journal of Financial Economics 25, 3–22] to allow for endogenous switching.