On univariate time series methods and simultaneous equation econometric models

Systematic testing of the implications of the structural assumptions for the properties of the final equations and transfer functions associated with a dynamic econometric model, as proposed by Zellner and Palm (1974–1975), proved to be useful in model building. This paper contains several remarks on the use of univariate time series methods to empirically check out the implications of a linear dynamic simultaneous equation model.     

Recursive estimation of simultaneous equation models

A recursive instrumental variable estimator is derived. For simultaneous equation estimation, the choice of the instruments is discussed. A computationally simple and asymptotically efficient recursive estimator is proposed in this context.     

A note on a heteroscedastic model

In this article the author considers a regression model where the variance of the error term is a linear combination of certain independent variables and compares four different estimators of the coefficients of this linear combination, They are (1) the estimator proposed by Goldfeld and Quant and called the Modified Glejser Method, (2) the estimator proposed by Hildreth and Houck, (3) the generalized least squares method, and (4) the maximum likelihood estimator. It is shown that the first two are asymptotically not fully efficient whereas the last two are.     

A note on least squares estimation and the blue in a generalized linear regression model

In a generalized linear regression model, least squares and Gauss-Markov estimators differ, in general, if the variance-covariance matrix of the disturbances is singular. In the present note it is shown that, nevertheless, the conventional least squares procedure leads to a Gauss-Markov estimator if it is applied to a modified model which results from adding dummy constraints to the original model. These constraints reflect the effects of the singularity of the variance- convariance matrix. As a consequence, a Gauss-Markov estimate may always be obtained by standard least squares minimization, which offers considerable computational advantages.     

Monotonicity preserving regression techniques for interest rate term structure estimation: A note

Alternative methodologies are compared for measuring the term structure of interest rates via monotone approximations to the discount function. Some empirical comparisons using coupon bond data show that a simple linear methodology based on rational tension spline parametrizations turns out to yield the most efficient compromise between the conflicting goals of goodness of fit and smoothuess of the interpolaut Work supported by M.U.R.S.T. funds.     

Semiparametric three‐step estimation methods for simultaneous equation systems

This paper proposes a new method for estimating a structural model of labour supply in which hours of work depend on (log) wages and the wage rate is considered endogenous. The main innovation with respect to other related estimation procedures is that a nonparametric additive structure in the hours of work equation is permitted. Though the focus of the paper is on this particular application, a three‐step methodology for estimating models in the presence of the above econometric problems is described. In the first step the reduced form parameters of the participation equation are estimated by a maximum likelihood procedure adapted for estimation of an additive nonparametric function. In the second step the structural parameters of the wage equation are estimated after obtaining the selection‐corrected conditional mean function. Finally, in the third step the structural parameters of the labour supply equation are estimated using local maximum likelihood estimation techniques. The paper concludes with an application to illustrate the feasibility, performance and possible gain of using this method. Copyright © 2005 John Wiley & Sons, Ltd.     

FIML estimation of the dynamic simultaneous equations model with ARMA disturbances

A method is presented for the estimation of the parameters in the dynamic simultaneous equations model with vector autoregressive moving average disturbances. The estimation procedure is derived from the full information maximum likelihood approach and is based on Newton-Raphson techniques applied to the likelihood equations. The resulting two-step Newton-Raphson procedure involves only generalized instrumental variables estimation in the second step. This procedure also serves as the basis for an iterative scheme to solve the normal equations and obtain the maximum likelihood estimates of the conditional likelihood function. A nine-equation variant of the quarterly forecasting model of the US economy developed by Fair is then used as a realistic example to illustrate the estimation procedure described in the paper.     

A note on estimation based on record data

In data-processing standpoint, an efficient algorithm for identifying the minimum value among a set of measurements are record statistics. From a sequence of n independent identically distributed continuous random variables only about log(n) records are expected, so we expect to have little data, hence any prior information is welcome (Houchens, Record value theory and inference, Ph.D. thesis, University of California, Riverside, 1984). In this paper, non-Bayesian and Bayesian estimates are derived for the two parameters of the Exponential distribution based on record statistics with respect to the squared error and Linear-Exponential loss functions and then compared with together. The admissibility of some estimators is discussed.     

A ridge-like method for simultaneous estimation of simultaneous equations

In the context of full information estimation in a linear simultaneous equations model, this paper considers a ridge-like modification of the 3SLS estimator. The proposed method is particularly desirable where the square matrix of the 3SLS normal equationsis singular (or near-singular) leading to non-existence (or poor performance) of the estimator. Furthermore, the type of solution suggested here does seem to result in the existence of the finite sample moments of the estimator even when the degrees of over identification are as low as zero (just identified models). This paper considers only a simple scalar form of the ‘ridge-matrix” with a relatively simple choice of the modifying scalar that preserves the asymptotic properties of the 3SLS estimator. A value of this scalar is derived which minimizes an appropriatequadratic risk criterion. The approximate quadratic risk function is based upon the asymptotic approximation of the relevant moments in the manner of Nagar (1959). A range of risk reducing values of the ‘ridge-scalar” is also given.     

A note on the Bayesian estimation of Solow's distributed lag model

This note develops the Bayesian estimation of the parameters of Solow's distributed lag model with implicit autocorrelation of disturbances in its autoregressive form. The estimation technique extends Chetty's method for independent disturbances. The results of some Monte Carlo experiments are given comparing point estimates from the posterior distributions with the maximum likelihood estimates. The characteristics of the Bayesian and maximum likelihood estimates are very similar.     

An econometric model of a retail firm

Existing models of retail resource allocation generally specify response functions in a somewhat ad hoc manner. These are not usually derived from an explicit model of consumer maximization, and they generally do not explicitly consider the supply side of the market. This paper shows how the model of Ehrlich and Fisher (1982) can be used to provide insights into the proper specification of these functions. We illustrate the application of this model on data from a retail chain; our application extends work in Ratchford and Stoops (1988) to the demand side of the market. Potential areas of application of the model are to understanding the demand for labor and advertising services by consumers, and to the measurement of retail productivity.     

An econometric procedure for estimation of a generalized systemic gravity model under incomplete information about the system

Gravity spatial interaction models have a long history and a wide scope of empirical applications, Alonso (1973) proposed a generalized model whose structure subsumes major versions of the gravity model in the literature as special cases. Little attention has been given to how the general model might be estimated, or if it is estimable at all. This paper develops an econometric procedure for situations where all places in a geographic system are not included in the observations. The general model and various constrained versions are empirically estimated on a sample of intermetropolitan migration data and compared.