Maximum likelihood estimation of search costs

In a recent paper Hong and Shum [2006. Using price distributions to estimate search costs. Rand Journal of Economics 37, 257-275] present a structural method to estimate search cost distributions. We extend their approach to the case of oligopoly and present a new maximum likelihood method to estimate search costs. We apply our method to a data set of online prices for different computer memory chips. The estimates suggest that the consumer population can be roughly split into two groups which either have quite high or quite low search costs. Search frictions confer a significant amount of market power to the firms: Despite more than 20 firms operating in each of the markets, we estimate price-cost margins to be around 25%. The paper also illustrates how the structural method can be employed to simulate the effects of the introduction of a sales tax.     

Maximum likelihood estimation for vector autoregressions with multivariate stochastic volatility

This paper analyzes the maximum likelihood estimation for vector autoregressions with stochastic volatility. The stochastic volatility is modeled following Uhlig (1997). The asymptotic distribution of the maximum likelihood estimate is discussed under mild regularity conditions. The maximum likelihood estimate can be obtained via an iterative method. In that case, the maximum likelihood estimate becomes the iteratively reweighted least squares estimate analyzed in Rubin (1983). The iteratively reweighted least squares estimate is computationally much simpler than the Bayesian method offered by Uhlig (1997).     

Maximum likelihood estimation of the Rotterdam model under two different conditions

This letter describes maximum likelihood (ML) procedures for the Rotterdam model (1) when the model is formulated in relative prices and (2) under the constraints of the theory of rational random behavior.     

Stochastic unit root processes: Maximum likelihood estimation,and new Lagrange multiplier and likelihood ratio tests

We show in this study that the maximum likelihood estimators of stochastic unit root (STUR) processes are consistent and asymptotically normally distributed. We also present two new tests for STUR. We first propose a Lagrange multiplier test and show that it has a standard χ² distribution asymptotically. We also propose a likelihood ratio test and show that it has an asymptotic distribution of 50–50 mixture of χ² and a point mass at 0. As an empirical example, we test the existence of STUR in the Canadian real exchange rate and explore the implication of STUR on the validity of purchasing power parity.     

Estimating the trans-log cost function with insufficient observations

If the production technology is non-homothetic, efficient estimation of the trans-log approximation requires joint estimation of the cost and share equations. In this note we adopt the method of extraneous estimation to obtain a method of efficient joint estimation when there are insufficient observations on the cost equation.     

Efficient estimation of partially linear varying coefficient models

In this paper, we consider the problem of estimating a semiparametric partially linear varying coefficient model. We derive the semiparametric efficiency bound for the asymptotic variance of the finite-dimensional parameter estimator. We also propose an efficient estimator for estimating the finite-dimensional parameter of the model. Simulation results show substantial efficiency gain of our proposed estimator over a conventional estimator as considered in Ahmad et al. (2005).     

Maximum likelihood estimation of time-varying parameters: an application to the Athens Stock Exchange index

The problem of maximum likelihood estimation of time-varying parameters is considered. A hierarchical approach is proposed that involves, first, the estimation of the model order and parameters when they are assumed time-invariant. Second, for each parameter, an autoregressive (AR) model, with constant coefficients, is developed. This allows the parameters to change over time. Finally, the estimates of the AR coefficients for each parameter are used as initial conditions to a time-varying model with AR coefficients, which are allowed to change over time subject to some regularity constraints. This approach is then applied to the Athens Stock Exchange index, where the dominant forces affecting this index are analysed.     

Maximum likelihood estimators of the dagum model parameters

This paper will show the sample size needed to provide good maximum likelihood estimators of the Dagum model parameters. The principal goal of this study is to verify the asymptotic properties of these estimators for finite sample sizes comparable to the ones employed in the real surveys (for example, the Labor Force Survey).     

On Lindley-like mean correction in the improved estimation of linear regression models

The risks of estimators incorporating the correction to the sample mean in the spirit of Stein and Lindley are approximated in the case of small disturbances.     

Closed-form likelihood function of Markov-switching models

For a class of Markov-switching models, the likelihood function and inferred state distributions for a given sample are shown to have closed-form representations under a set of sufficient conditions. Based on these results, it is demonstrated that the closed-form partial derivatives (when exist) of the likelihood function can be readily found. These results may be used to improve the efficiency of numerical optimization techniques used for estimating the Markov-switching models.     

On maximum likelihood estimation of functional form and heteroskedasticity

The maximum-likelihood procedure has been developed to estimate the Box-Cox functional form parameter and the degree of heteroskedasticity simultaneously. By using an illustrative example, it is shown the likelihood ratio tests conditional on homoskedastic prior can sometimes yield misleading results.     

A maximum likelihood approach to estimating dynamic models with unobserved independent variables

A maximum likelihood method to estimate the parameters of dynamic models containing unobserved independent variables is proposed. The approach is to maximize the likelihood of the residuals produced by the recursive Kalman filter equations applied to the model in state-space form. A simulation study is presented comparing the proposed method to the instrumental variable approach. An example using real data is given which estimates models of the Permanent-Income Hypothesis.     

Maximum-likelihood estimation of misspecified models

Misspecified models occur frequently in econometric practice. It is therefore important to study the sampling distribution of maximum-likelihood estimators of parameters of misspecified models. This note exhibits the asymptotic covariance matrix of the ML estimator of a misspecified model. It points out that the expression for this matrix given by White is incorrect except for the very special case, rarely occuring in econometrics, that each observation is independent and identically distributed. An illustration using the standard linear regression model is provided.     

FIML estimation of models with multiple regimes and covariance restrictions

This paper examines the FIML estimator for a system of simultaneous equations in which a structural change, at a known time, has taken place in one or two of the equations, while the rest are unaffected.     

Robust estimation of models of Engel curves

Both standard and robust methods are used here to estimate models of Engel curves for three household commodities, namely, food, transport, and tobacco and alcohol in Canada. The income elasticities of demand computed from the various methods differ significantly for the transport and tobacco-alcohol consumption where there are obvious outliers and zero expenditures problem. Robust estimators point to lower income elasticities and have better performance than the standard LS and Tobit estimator. These results are analyzed in the light of the information on finite-sample performance obtained in a previous Monte Carlo study. First version received: July 2000/Final version received: July 2001 RID="*" ID="*"  I wish to thank Victoria Zinde-Walsh, John Galbraith, Clint Coakley, two anonymous referees and an associate editor for helpful comments. I would also like to thank Anastassia Khouri for kindly providing the 1992 Family Expenditure Survey of Canada data.     

On uniqueness of the conditional maximum likelihood estimation for a binary panel model

This paper considers an estimation method for a binary panel model with incidental parameters as individual effects. The necessary condition for the conditional maximum likelihood approach proposed by Andersen (1970) is investigated and we show that unique sufficient statistics exist only for logit models in a two-wave panel.     

On linear models with rational expectations which admit a unique solution

Based on a generalization of Doob's theorem, the method used in this paper is applied to derive the unique reduced form a general linear model containing rational expectations of the current endogenous variables made in several previous periods. In this procedure there is no need for assumptions on the structure of the policy instruments.     

General instrumental variables estimation under stochastic linear restrictions

This letter extends the Theil-Goldberger ‘mixed’ regression estimator, for models subject to stochastic linear restrictions, to the case of stochastic regressors. A general instrumental variables ‘mixed’ estimator is discussed. The asymptotic distribution of the estimator is obtained, and an asymptotic test of the compatibility of the sample and prior information is presented.