Random coefficient first-order autoregressive models

This paper discusses the random coefficient model applied to panel data in a time-series context. Some of the basic issues involved in pooling problems are studied. An analysis of a first-order autoregressive model, where the autoregressive coefficients across units are regarded as a random sample from a beta distribution, is presented and illustrated by an example using real data. Generalizations to higher-order models are discussed.     

A note on multi-step forecasting with functional coefficient autoregressive models

This paper presents and evaluates alternative methods for multi-step forecasting using univariate and multivariate functional coefficient autoregressive (FCAR) models. The methods include a simple “plug-in” approach, a bootstrap-based approach, and a multi-stage smoothing approach, where the functional coefficients are updated at each step to incorporate information from the time series captured in the previous predictions. The three methods are applied to a series of U.S. GNP and unemployment data to compare performance in practice. We find that the bootstrap-based approach out-performs the other two methods for nonlinear prediction, and that little forecast accuracy is sacrificed using any of the methods if the underlying process is actually linear.     

A note on autoregressive error components models

The purpose of this paper is to shed some light on the asymptotic behavior of a wide class of estimators for a dynamic error components model when only the number of individuals tends to infinity, the number of time periods being kept fixed. In particular, it is shown that this asymptotic behavior is highly dependent on the assumption about the initial observations and that it offers very good approximations to the small sample behavior of the various estimators under consideration.     

Bayesian analysis of random coefficient logit models using aggregate data

We present a Bayesian approach for analyzing aggregate level sales data in a market with differentiated products. We consider the aggregate share model proposed by Berry et al. [Berry, Steven, Levinsohn, James, Pakes, Ariel, 1995. Automobile prices in market equilibrium. Econometrica. 63 (4), 841–890], which introduces a common demand shock into an aggregated random coefficient logit model. A full likelihood approach is possible with a specification of the distribution of the common demand shock. We introduce a reparameterization of the covariance matrix to improve the performance of the random walk Metropolis for covariance parameters. We illustrate the usefulness of our approach with both actual and simulated data. Sampling experiments show that our approach performs well relative to the GMM estimator even in the presence of a mis-specified shock distribution. We view our approach as useful for those who are willing to trade off one additional distributional assumption for increased efficiency in estimation.     

Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances

This study develops a methodology of inference for a widely used Cliff–Ord type spatial model containing spatial lags in the dependent variable, exogenous variables, and the disturbance terms, while allowing for unknown heteroskedasticity in the innovations. We first generalize the GMM estimator suggested in  and  for the spatial autoregressive parameter in the disturbance process. We also define IV estimators for the regression parameters of the model and give results concerning the joint asymptotic distribution of those estimators and the GMM estimator. Much of the theory is kept general to cover a wide range of settings.     

Fixed effects instrumental variables estimation in correlated random coefficient panel data models

We provide a set of conditions sufficient for consistency of a general class of fixed effects instrumental variables (FE-IV) estimators in the context of a correlated random coefficient panel data model, where one ignores the presence of individual-specific slopes. We discuss cases where the assumptions are met and violated. Monte Carlo simulations verify that the FE-IV estimator of the population averaged effect performs notably better than other standard estimators, provided a full set of period dummies is included. We also propose a simple test of selection bias in unbalanced panels when we suspect the slopes may vary by individual.     

The association between two random elements: A complete characterization and odds ratio models

For random elements X and Y (e.g. vectors) a complete characterization of their association is given in terms of an odds ratio function. The main result establishes for any odds ratio function and any pre-specified marginals the unique existence of a corresponding joint distribution (the joint density is obtained as a limit of an iterative procedure of marginal fittings). Restricting only the odds ratio function but not the marginals leads to semi-parmetric association models for which statistical inference is available for samples drawn conditionally on either X or Y. Log-bilinear association models for random vectors X and Y are introduced which generalize standard (regression) models by removing restrictions on the marginals. In particular, the logistic regression model is recognized as a log-bilinear association model. And the joint distribution of X and Y is shown to be multivariate normal if and only if both marginals are normal and the association is log-bilinear.Acknowledgements The author thanks both referees for their helpful comments which improved the first draft of the paper.     

Certificate-of-need regulation and the diffusion of innovations: A random coefficient model

In this paper, we examine empirically the effect that certificate-of-need regulation by state health planning organizations has had on the speed of diffusion of a relatively new medical technology—haemodialysis. Specifically, we test the hypothesis that a requirement that investments be subject to certificate-of-need review has significantly slowed the rate of adoption of this particular treatment modality. In subjecting this hypothesis to empirical verification, we estimate a random coefficient model. This approach allows us to make more efficient use of the available data than the traditional two-stage approach to modelling diffusion processes wherein separate logistic functions are first estimated over the time series observations followed by hypothesis tests conducted over the cross-sectional observations. We find evidence that certificate-of-need regulation slows the spread of haemodialysis technology.     

A structural analysis of the correlated random coefficient wage regression model

We estimate a dynamic programming model of schooling decisions in which the log wage regression function is set within a correlated random coefficient model. We show that estimates of the dynamic programming model can be used to obtain a number of treatment effects, including the local average treatment effect (LATE). However, unlike LATE parameters obtained in a standard IV framework, our LATE estimates are obtained without imposing separability between individual specific heterogeneity and schooling choices and are therefore not subject to a “monotonicity” restriction. We find that returns to schooling are characterized by a high degree of dispersion across individuals.     

A bayesian analysis of a random coefficient model in a simple keynesian system

The marginal propensity to consume in a simple Keynesian model is treated as a random coefficient. This gives rise to the problem of quotient of random variables, i.e., the Fieller-Creasy problem. The Bayesian and maximum likelihood estimators are compared in sampling experiments. The Bayesian estimators have smaller mean squared errors than the maximum likelihood estimators. Marginal posterior probability density functions for a given sample are also presented.     

Estimation and forecasting in vector autoregressive moving average models for rich datasets

We address the issue of modelling and forecasting macroeconomic variables using rich datasets by adopting the class of Vector Autoregressive Moving Average (VARMA) models. We overcome the estimation issue that arises with this class of models by implementing an iterative ordinary least squares (IOLS) estimator. We establish the consistency and asymptotic distribution of the estimator for weak and strong VARMA(p,q) models. Monte Carlo results show that IOLS is consistent and feasible for large systems, outperforming the MLE and other linear regression based efficient estimators under alternative scenarios. Our empirical application shows that VARMA models are feasible alternatives when forecasting with many predictors. We show that VARMA models outperform the AR(1), ARMA(1,1), Bayesian VAR, and factor models, considering different model dimensions.     

GMM and 2SLS estimation of mixed regressive,spatial autoregressive models

The GMM method and the classical 2SLS method are considered for the estimation of mixed regressive, spatial autoregressive models. These methods have computational advantage over the conventional maximum likelihood method. The proposed GMM estimators are shown to be consistent and asymptotically normal. Within certain classes of GMM estimators, best ones are derived. The proposed GMM estimators improve upon the 2SLS estimators and are applicable even if all regressors are irrelevant. A best GMM estimator may have the same limiting distribution as the ML estimator (with normal disturbances).     

A reconsideration of the link between vertical externality and managerial incentives

Previous research revealed that the strategic role of delegation contracts disappears if two quantity‐setting firms outsource input production to a monopolistic supplier. I show that this role is restored if the assumption of a downstream duopoly is relaxed. Thus, delegation contracts allow downstream profit‐maximizing owners to commit their firms to a behavior that differs from their preferences. This behavior varies nonmonotonically with the number of firms in the downstream market. Corresponding deviations from profit maximization are larger if the upstream monopolist makes a price precommitment. But little to no deviation occurs if the number of firms is large.     

Estimation in threshold autoregressive models with a stationary and a unit root regime

This paper treats estimation in a class of new nonlinear threshold autoregressive models with both a stationary and a unit root regime. Existing literature on nonstationary threshold models has basically focused on models where the nonstationarity can be removed by differencing and/or where the threshold variable is stationary. This is not the case for the process we consider, and nonstandard estimation problems are the result.     

Discriminating between autoregressive forms: A Monte Carlo comparison of Bayesian and ad hoc methods

The paper considers the problem of discriminating between the autoregressive forms of a Koyck distributed lag model and a regression model with autocorrelated distrubances. Several interpretations of an ad hoc rule-of-thumb suggested by Griliches are compared with Bayesian posterior odds analysis in a Monte Carlo experiment. The Bayesian analysis is generally superior to the rules-of-thumb, the latter exhibiting large probabilities of type I error, and low power. The rules-of-thumb excessively favour the distributed lag model, while the Bayesian method is free from such bias. All methods improve with increased sample size.     

A new measure of association between random variables

We propose a new measure of association between two continuous random variables X and Y based on the covariance between X and the log-odds rate associated to Y. The proposed index of correlation lies in the range [\(-1\), 1]. We show that the extremes of the range, i.e., \(-1\) and 1, are attainable by the Fr\(\acute{\mathrm{e}}\)chet bivariate minimal and maximal distributions, respectively. It is also shown that if X and Y have bivariate normal distribution, the resulting measure of correlation equals the Pearson correlation coefficient \(\rho \). Some interpretations and relationships to other variability measures are presented. Among others, it is shown that for non-negative random variables the proposed association measure can be represented in terms of the mean residual and mean inactivity functions. Some illustrative examples are also provided.