Chapter 73 Nonparametric identification

A variety of single equation and simultaneous equation models have been employed to test the hypothesis that interest group campaign contributions influence congressional voting. Although contributions exhibited the anticipated positive effect in all models, the simultaneous equations estimates generally indicated much lower significance levels for the contribution coefficients than did the single equation models. The lower significance levels are apparently attributable to a lack of precision of the simultaneous model estimates (indicated by large standard errors) as well as possible bias of the single equation models. It was also found that qualitative results from the more sophisticated simultaneous probit-Tobit models were quite similar to those obtained from 2SLS estimation of the linear probability model.

This paper provides empirical evidence in favor of the Schumpeterian hypothesis using single equation models. A simultaneous equation model is then developed which examines the interaction of R & D, growth and profitability.

We develop a bivariate probit selection model of consumer access and adoption that accounts for the cross equation correlations of the errors. The Survey of Consumers, collected by the University of Michigan, is the database used to estimate the model. We find a significant cross equation correlation between consumers’ perceived access and their use of computer banking. Based on our results, the bivariate selection model provides asymptotically more efficient estimates than does a single equation model because the bivariate selection model accounts for the sample selection bias associated with access. In addition, the bivariate selection model has a higher percentage of correctly predicted adopters than does the corresponding single equation (univariate) model.

The theory and practice of econometrics: George G. Judge, William E. Griffiths, Helmut Lutkepohl, and Tsoung-Chao Lee. 2nd ed. New York: John Wiley & Sons, Inc., 1985. 1019 pp. $46.95 ISBN 0-471-89530-X

Estimation of parametric multiple time series models has been a major topic in recent work in statistics and econometrics (e.g., Hannan [1970], Wilson [1973], Dhrymes and Erlat [1974], and Hatanaka [1976]). However, relatively little has been reported on their prediction property, particularly when the involves autocorrelated errors. For the with uncorrelated errors, Goldberger, Nagar and Odeh [1962] and Dhrymes [1973] have obtained the asymptotic distribution of the reduced form coefficient estimates derived from the structural form estimates. It obviously serves as the asymptotic distribution of the one period ahead prediction of the model. Schmidt [1974] recently derived the asymptotic distribution of multiperiod ahead predictions for such a model, i.e., simultaneous equation autoregressive (or alternatively called dynamic model in econometrics) with exogenous variables (ARX) (see also Brissimis and Gill [1978]). When the disturbances of the models are autocorrelated, it is known that the derivation of the simplified prediction scheme, not to mention its asymptotic distribution, becomes complicated even for the single equation model. Bloomfield [1972] and Yamamoto [1978] derived the asymptotic mean square error of one period and multiperiod predictions for the single equation autoregressive moving average (ARMA) models, respectively. In this paper, first we derive the optimal prediction scheme for multiperiod prediction of a simultaneous equation autoregressive with exogenous variables, whose disturbances obey either autoregressive or moveing average process. The complication due to the error autocorrelation is handled by the introduction of the backward representation of the model, and the optimal predictor is given by a relatively simple formula with matrix notations. Secondly, for the unknown parameter case, we derive the asymptotic distribution of the optimal prediction scheme with the consistent estimates of the parameters. Our results are quite general, and we show, with a few examples, that they are easily modified to various single and simultaneous equation models of simpler specifications. The scope of this paper is as follows. Section 2 presents two types of representation. The first is the state variable representation suggested by

Introduction The maximum likelihood framework set out in Part ONE is now applied to estimating and testing regression models. This chapter focusses on linear models, where the conditional mean of a dependent variable is specified to be a linear function of a set of exogenous variables. Extensions to this basic model are investigated in Chapter 6 (nonlinear regression), Chapter 7 (autocorrelation) and Chapter 8 (heteroskedasticity). Single equation models include the linear regression model and the constant mean model. For single equation regression models, the maximum likelihood estimator has an analytical solution that is equivalent to the ordinary least squares estimator. The class of multiple equation models includes simultaneous equation models with multiple dependent and exogenous variables, seemingly unrelated systems and recursive models. In this instance, the maximum likelihood estimator is known as the full information maximum likelihood (FIML) estimator because the entire system is used to estimate all of the model parameters jointly. The FIML estimator is related to the instrumental variable estimator commonly used to estimate simultaneous models and, in some cases, the two estimators are equivalent. Unlike linear single equation models, analytical solutions of the maximum likelihood estimator for systems of linear equations are only available in certain special cases. Many of the examples considered in Part ONE specify the distribution of the observable random variable, y t . Regression models, by contrast, specify the distribution of the unobservable disturbance, u t , which means that maximum likelihood estimation cannot be used directly because this method requires evaluating the log-likelihood function at the observed values of the data.

Wives' financial independence gained from their pension may increase the risk of marital dissolution, especially when wives are approaching retirement age (the older wives' independence hypothesis). Applying single and simultaneous equations probit models to data from the Panel Study of Income Dynamics, we investigate the effect of wives' pension holding in 1984 on the risk of subsequent marital dissolution. Results from the single equation model appear to support the older wives' independence hypothesis. However, results from the simultaneous equations model suggest that interpreting the single equation results as a sign of older wives' economic independence may be misleading. JEL classification: C33; D31; J12; J32

VII - A prolegomenon to econometric model building

Weak identification in discrete choice models

Empirical studies utilizing time-series of cross-section data are constantly appearing in virtually every field of economics. This has been made easier by the increasing availability of panel data, and the increasing capability of computers in handling large data sets. Some of the earlier studies include Mundlak [1961, 1963] and Hoch [1962] in the production function literature, Kuh [1959] in the investment function literature, and Balestra and Nerlove [1966] in the energy literature. More recent studies include Chamberlin and Griliches [1975], Hausman and Wise [1979], Lillard and Weiss [1979] in the labor literature, and Griffin [1979] and Pindyck [1980] in the energy literature, to mention only a few. Efforts to develop the econometric theory for pooling time-series of cross-section data have concentrated largely on the single equation error components model.2 More recently, Avery [1977] and Baltagi [1981b] extended this error components literature to the seemingly unrelated regressions and the simultaneous equations model, respectively. Asymptotic as well as small sample properties of various pooling estimators received adequate investigation in the single equation model.3 However, the same cannot be said about pooling estimators in the simultaneous equations case. This paper is an attempt to remedy this situation. The small sample performance of various pooling estimators in a two-equation simultaneous model are studied by means of Monte Carlo experiments. The main purpose is to provide the applied researcher with some guidelines on how to pool time-series of crosssection data in the simultaneous model. Monte Carlo studies for the classical simultaneous model are plentiful,4 as are

The study describes a number of short-term expost forecasts of econometric models and univariate model of autoregressive-integrated-moving average (ARIMA) model of Natural Rubber (NR) prices SMR20 (Standard Malaysia Rubber Grade 20) in the Malaysia market. The econometric models include single equation model using Vector Error Correction Method (VECM) and multivariate autoregressive-moving average (MARMA) model. The models were developed to determine the inter-relationships between NR production, consumption and prices, to forecast the price of NR (SMR20) and to determine which model is more efficient in their price forecasting accuracy. The models based on data from period January 1990-December 2008. Comparative forecasting models accuracy between single equation model, MARMA model and univariate model of ARIMA, were made in terms of their estimation accuracy based on RMSE, MAE, RMPE and (U-Theil) criteria. The results revealed that the values of the RMSE, MAE, RMPE and U of MARMA model were comparatively smaller than the values generated by single equation model and ARIMA model. These statistics suggested that MARMA model is more accurate and efficient measured in terms of its statistical criteria than single equation model and ARIMA model in forecasting the NR price of SMR20 in the next 6 months or so.

Generalized indirect inference for discrete choice models

In this chapter the identification problem in the most meaningful single-equation linear stationary models with rational expectation (RE) discussed in the previous pages is considered. As pointed out in Pesaran (1989, p. 119) “identification is fundamental to the empirical analysis of structural models. Unless a model is identified it will not be possible to give a meaningful interpretation to its parameter estimates.”1 In all the single equation models “the substitution of unobserved expectational variables by functions of observables poses the problem of whether the unknown parameters can be identified from the knowledge of the observables” (Pesaran, 1989, p. 119). In those containing future expectations, like the Cagan and Taylor type models, “the new problem which emerges ... is the multiplicity of solutions ... (which depends) ... on the arbitrary choice of martingale differences. The number of arbitrary processes depends on the structure of the model (the horizon of the expectations and the size of the model) and on the values of the structural matrices. ... Consequently in the case of linear stationary models identification concerns both kinds of parameters: the structural ones and the additional, or auxiliary, ones” (Broze and Szafarz, 1991, pp. 184–185).KeywordsIdentification ProblemType ModelExogenous VariableConsistent EstimateRational ExpectationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The supply of and demand for residential mortgages has been the subject of much discussion in the literature. Many of these studies have used single equation, partial adjustment models with the price specified as the contract rate. In this study, two of the assumptions that underlie these previous studies are tested empirically. First, the proper specification of the price of mortgage funds is tested by using both the contract rate alone and all of the terms of the mortgage as the price. Second, the speed of adjustment in the mortgage market is examined by estimating the model in both the instantaneous adjustment and partial adjustment forms. Both of these tests are carried out using a simultaneous equation rather than a single equation model. The empirical results indicate that the contract rate along with the loan initiation fees, the loan‐to‐value ratio and the maturity is the better specification of price and that the partial adjustment model performs better than the instantaneous model in the mortgage market.

To present and compare socioeconomic status (SES) rankings of households using consumption and an asset-based index as two alternative measures of SES; and to compare and evaluate the performance of these two measures in multivariate analyses of the socioeconomic gradient in malaria prevalence. Data for the study come from a survey of 557 households in 25 study villages in Tanzania in 2004. Household SES was determined using consumption and an asset-based index calculated using Principal Components Analysis on a set of household variables. In multivariate analyses of malaria prevalence, we also used two other measures of disease prevalence: parasitaemia and self-report of malaria or fever in the 2 weeks before interview. Household rankings based on the two measures of SES differ substantially. In multivariate analyses, there was a statistically significant negative association between both measures of SES and parasitaemia but not between either measure of SES and self-reported malaria. Age of individual, use of a mosquito net, and wall construction were negatively and significantly associated with parasitaemia, whilst roof construction was positively associated with parasitaemia. Only age remained significant when malaria self-report was used as the measure of disease prevalence. An asset index is an effective alternative to consumption in measuring the socioeconomic gradient in malaria parasitaemia, but self-report may be an unreliable measure of malaria prevalence for this purpose.