The estimation of a state space model by estimating functions with an application

Conventionally the parameters of a linear state space model are estimated by maximizing a Gaussian likelihood function, even when the input errors are not Gaussian. In this paper we propose estimation by estimating functions fulfilling Godambe's optimality criterion. We discuss the issue of an unknown starting state vector, and we also develop recursive relations for the third- and fourth-order moments of the state predictors required for the calculations. We conclude with a simulation study demonstrating the proposed procedure on the estimation of the stochastic volatility model. The results suggest that the new estimators outperform the Gaussian likelihood.     

Simulation estimation of two‐tiered dynamic panel Tobit models with an application to the labor supply of married women

In this paper a computationally practical simulation estimator is proposed for the two‐tiered dynamic panel Tobit model originally developed by Cragg ( 1971 ). The log‐likelihood function simulated through procedures based on a recursive algorithm formulated by the Geweke–Hajivassiliou–Keane simulator is maximized. The simulation estimators are then applied to study the labor supply of married women. The rich dynamic structure of the labor force participation decision as well as hours worked decisions that are conditional on the participation of married women are identified by using the proposed simulation estimators. The average partial effects of the participation and hours worked decisions for married women in response to fertility decisions and increases in the husband's income are also investigated. It is found that the hypothesis that the fertility decision is exogenous and the hypothesis that the husband's income is exogenous to married women's labor supply function are both rejected in the dynamic and static two‐tiered models. Moreover, children aged between 6 and 13 years old may have a negative impact on the hours worked decision for married women that is conditional on their participation. However, these children may provide some positive incentives for married women to participate in the labor force. Copyright © 2009 John Wiley & Sons, Ltd.     

Diagnostic analysis for a vector autoregressive model under Student′s t‐distributions

In this paper, we use the local influence method to study a vector autoregressive model under Student^′s t‐distributions. We present the maximum likelihood estimators and the information matrix. We establish the normal curvature diagnostics for the vector autoregressive model under three usual perturbation schemes for identifying possible influential observations. The effectiveness of the proposed diagnostics is examined by a simulation study, followed by our data analysis using the model to fit the weekly log returns of Chevron stock and the Standard & Poor's 500 Index as an application.     

On the estimation of simultaneous-equations error-components models with an application to a model of developing country foreign trade

An empirical balance of payments model involving the demand and supply of imports and exports for 31 developing countries is estimated utilizing panel data over 1964-1987. In order to compute error-components 3SLS estimates of this model, which requires different instruments for different equations, we propose a generalization of the Fuller-Battese transformation to obtain GMM estimates. Our empirical results suggest that very little of the short-run adjustment in external imbalances is likely to be achieved by exchange rate policies, and most of the burden must fall on aggregate demand management.     

A discrete‐choice model with social interactions: with an application to high school teen behavior

We develop an empirical discrete‐choice interaction model with a finite number of agents. We characterize its equilibrium properties—in particular the correspondence between interaction strength, number of agents, and the set of equilibria—and propose to estimate the model by means of simulation methods. In an empirical application, we analyze the individual behavior of high school teenagers in almost 500 school classes from 70 schools. In our baseline model endogenous social interaction effects are strong for behavior closely related to school (truancy), somewhat weaker for behavior partly related to school (smoking, cell phone ownership, and moped ownership) and absent for behavior far away from school (asking parents' permission for purchases). Intra‐gender interactions are generally much stronger than cross‐gender interactions. In a model with school‐specific fixed effects social interaction effects are insignificant, with the exception of intra‐gender interactions for truancy. Copyright © 2007 John Wiley & Sons, Ltd.     

On Markov error‐correction models,with an application to stock prices and dividends

This paper considers Markov error‐correction (MEC) models in which deviations from the long‐run equilibrium are characterized by different rates of adjustment. To motivate our analysis and illustrate the various issues involved, our discussion is structured around the analysis of the long‐run properties of US stock prices and dividends. It is shown that the MEC model is flexible enough to account for situations where deviations from the long‐run equilibrium are nonstationary in one of the states of nature and allows us to test for such a possibility. An empirical specification procedure to establish the existence of MEC adjustment in practice is also presented. This is based on a multi‐step test procedure that exploits the differences between the global and local characteristics of systems with MEC adjustment. Copyright © 2004 John Wiley & Sons, Ltd.     

Trivariate non‐Gaussian copulas to analyze the spatial behavior of rat sightings

The brown rat lives with man in a wide variety of environmental contexts and adversely affects public health by transmission of diseases, bites, and allergies. Understanding behavioral and spatial correlation aspects of pest species can contribute to their effective management and control. Rat sightings can be described by spatial coordinates in a particular region of interest defining a spatial point pattern. In this paper, we investigate the spatial structure of rat sightings in the Latina district of Madrid (Spain) and its relation to a number of distance‐based covariates that relate to the proliferation of rats. Given a number of locations, biologically considered as attractor points, the spatial dependence is modeled by distance‐based covariates and angular orientations through copula functions. We build a particular spatial trivariate distribution using univariate margins coming from the covariate information and provide predictive distributions for such distances and angular orientations.     

Bartlett correction in the stable second‐order autoregressive model with intercept and trend

This paper derives the Bartlett factors that can be used to obtain higher‐order improvements for testing hypotheses about the autoregressive (AR) parameters in the stable AR(2) model with possible intercept and linear trend. The factors are obtained for testing hypotheses about individual parameters (φ₁ and φ₂) as well as their sum. Moreover, the effect of deterministic terms on the correction factors is found explicitly. All corrections are non‐decreasing in the AR parameters. Furthermore, the Bartlett corrections for φ₁ and φ₂ tend to infinity as φ₂ approaches 1, whereas the correction for φ₁ + φ₂ tends to infinity as φ₁ + φ₂ is close to 1. The effectiveness of these Bartlett corrections in finite samples is evaluated by simulations.     

On the specification and estimation of macro rural-urban migration functions: with an application to Indian data

The authors suggest several extensions and modifications to the existing specifications of macro migration functions as suggested by Todar through a more careful investigation of the micro theory underlying migration decisions. They use a probabilistic migration model to examine internal migration in India and present evidence that migration tends first to rise and then to fall as rural income rises     

A method for estimating the timing interval in a linear econometric model, with an application to Taylor's model of staggered contracts

This paper describes and implements a procedure for estimating the timing interval in any linear econometric model. The procedure is applied to Taylor's model of staggered contracts using annual averaged price and output data. The fit of the version of Taylor's model with serially uncorrelated disturbances improves as the timing interval of the model is reduced.     

Application of one‐step method to parameter estimation in ODE models

In this paper, we study application of Le Cam's one‐step method to parameter estimation in ordinary differential equation models. This computationally simple technique can serve as an alternative to numerical evaluation of the popular non‐linear least squares estimator, which typically requires the use of a multistep iterative algorithm and repetitive numerical integration of the ordinary differential equation system. The one‐step method starts from a preliminary ‐consistent estimator of the parameter of interest and next turns it into an asymptotic (as the sample size n →∞ ) equivalent of the least squares estimator through a numerically straightforward procedure. We demonstrate performance of the one‐step estimator via extensive simulations and real data examples. The method enables the researcher to obtain both point and interval estimates. The preliminary ‐consistent estimator that we use depends on non‐parametric smoothing, and we provide a data‐driven methodology for choosing its tuning parameter and support it by theory. An easy implementation scheme of the one‐step method for practical use is pointed out.     

From a var model to a structural model,with an application to the wage–price spiral

In this paper a VAR model is considered as a general framework in which a structural model can be tested. We carefully describe the hypotheses defining a structural model; this leads us to discuss various notions such as: predeterminedness, non-causality, exogeneity, contemporaneous identification, overall identification, weak and strong structural forms. Then we propose a test procedure, based on the asymptotic least-squares method, which allows successive testing of each aspect of a structural model. This procedure is applied to the wage–price spiral.     

A class of flat prior distributions for the Poisson‐gamma hierarchical model

A wide class of prior distributions for the Poisson‐gamma hierarchical model is proposed. Prior distributions in this class carry vague information in the sense that their tails exhibit slow decay. Conditions for the propriety of the resulting posterior density are determined, as well as for the existence of posterior moments of the Poisson rate of either an observed or an unobserved unit.     

A discrete‐choice model for large heterogeneous panels with interactive fixed effects with an application to the determinants of corporate bond issuance

What is the effect of funding costs on the conditional probability of issuing a corporate bond? We study this question in a novel dataset covering 5610 issuances by US firms over the period from 1990 to 2014. Identification of this effect is complicated because of unobserved, common shocks such as the global financial crisis. To account for these shocks, we extend the common correlated effects estimator to settings where outcomes are discrete. Both the asymptotic properties and the small‐sample behavior of this estimator are documented. We find that for non‐financial firms yields are negatively related to bond issuance but that the effect is larger in the pre‐crisis period.     

The performance of heteroskedasticity and autocorrelation robust tests: a Monte Carlo study with an application to the three‐factor Fama–French asset‐pricing model

This paper illustrates the pitfalls of the conventional heteroskedasticity and autocorrelation robust (HAR) Wald test and the advantages of new HAR tests developed by Kiefer and Vogelsang in 2005 and by Phillips, Sun and Jin in 2003 and 2006. The illustrations use the 1993 Fama–French three‐factor model. The null that the intercepts are zero is tested for 5‐year, 10‐year and longer sub‐periods. The conventional HAR test with asymptotic P‐values rejects the null for most 5‐year and 10‐year sub‐periods. By contrast, the null is not rejected by the new HAR tests. This conflict is explained by showing that inferences based on the conventional HAR test are misleading for the sample sizes used in this application. Copyright © 2007 John Wiley & Sons, Ltd.     

GMM estimators with improved finite sample properties using principal components of the weighting matrix,with an application to the dynamic panel data model

GMM estimators have poor finite sample properties in highly overidentified models. With many moment conditions the optimal weighting matrix is poorly estimated. We suggest using principal components of the weighting matrix. This effectively drops some of the moment conditions. Our simulations, done in the context of the dynamic panel data model, show that the resulting GMM estimator has better finite sample properties than the usual two-step GMM estimator, in the sense of smaller bias and more reliable standard errors.     

Tricks with the BoD model and an application to the e-Government Development Index

In this paper we examine the implications of the ideal and the anti-ideal decision-making units on the Benefit-of-the-Doubt (BoD) model. In particular, we verify that, in the presence of an ideal (anti-ideal) decision-making unit, the efficiency scores of the BoD (inverted BoD) model can be obtained without solving the relevant linear programming problems. In this case, it suffices to choose the largest (smallest) of the element-wise divided component indicators of the evaluated decision-making unit by those of the ideal (anti-ideal) decision-making unit. We then illustrate one practical use of this simple enumeration algorithm by providing empirical results for a BoD-based e-Government Development Index within a traffic-light reporting system.     

Investigating the impact of excess zeros on hurdle‐generalized Poisson regression model with right censored count data

Typically, a Poisson model is assumed for count data. In many cases, there are many zeros in the dependent variable, thus the mean is not equal to the variance value of the dependent variable. Therefore, Poisson model is not suitable anymore for this kind of data because of too many zeros. Thus, we suggest using a hurdle‐generalized Poisson regression model. Furthermore, the response variable in such cases is censored for some values because of some big values. A censored hurdle‐generalized Poisson regression model is introduced on count data with many zeros in this paper. The estimation of regression parameters using the maximum likelihood method is discussed and the goodness‐of‐fit for the regression model is examined. An example and a simulation will be used to illustrate the effects of right censoring on the parameter estimation and their standard errors.     

Macro‐integration with inequality constraints: an application to the integration of transport and trade statistics

Macro‐integration is the process of combining data from several sources at an aggregate level. We review a Bayesian approach to macro‐integration with special emphasis on the inclusion of inequality constraints. In particular, an approximate method of dealing with inequality constraints within the linear macro‐integration framework is proposed. This method is based on a normal approximation to the truncated multivariate normal distribution. The framework is then applied to the integration of international trade statistics and transport statistics. By combining these data sources, transit flows can be derived as differences between specific transport and trade flows. Two methods of imposing the inequality restrictions that transit flows must be non‐negative are compared. Moreover, the figures are improved by imposing the equality constraints that aggregates of incoming and outgoing transit flows must be equal.