Statistica Neerlandica

Kmenta, J.

doi: 10.1111/j.1467-9574.1991.tb01295.xpmid: N/A

Unobservable variables in econometrics are represented in one of three ways: by variables contaminated by measurement errors, by proxy variables, or by various manifest indicators and/or causes. This paper contains a discussion of models involving each of these representations, and highlights certain interesting implications that have been insufficiently emphasized or completely unrecognized in the literature.

Wansbeek, T.J.; Koning, R.H.

doi: 10.1111/j.1467-9574.1991.tb01296.xpmid: N/A

The underidentification of linear models with measurement error does not necessarily extend to panel data models, as has been shown by GAiliches and Hausman (1986). We discuss and extend some of their results for a simple case and address particular issues concerning identification and asymptotic variances.

Friedmann, R.; Mittag, H. J.; Brandtstater, A.

doi: 10.1111/j.1467-9574.1991.tb01297.xpmid: N/A

In the simple errors‐in‐variables model the least squares estimator of the slope coefficient is known to be biased towards zero for finite sample size as well as asymptotically. In this paper we suggest a new corrected least squares estimator, where the bias correction is based on approximating the finite sample bias by a lower bound. This estimator is computationally very simple. It is compared with previously proposed corrected least squares estimators, where the correction aims at removing the asymptotic bias or the exact finite sample bias. For each type of corrected least squares estimators we consider the theoretical form, which depends on an unknown parameter, as well as various feasible forms. An analytical comparison of the theoretical estimators is complemented by a Monte Carlo study evaluating the performance of the feasible estimators. The new estimator proposed in this paper proves to be superior with respect to the mean squared error.

Bekker, P.A.; Montfort, K.; Mooijaart, A.

doi: 10.1111/j.1467-9574.1991.tb01298.xpmid: N/A

We discuss a regression model in which the regressors are dummy variables. The basic idea is that the observation units can be assigned to some well‐defined combination of treatments, corresponding to the dummy variables. This assignment can not be done without some error, i.e. misclassification can play a role. This situation is analogous to regression with errors in variables. It is well‐known that in these situations identification of the parameters is a prominent problem. We will first show that, in our case, the parameters are not identified by the first two moments but can be identified by the likelihood. Then we analyze two estimators. The first is a moment estimator involving moments up to the third order, and the second is a maximum likelihood estimator calculated with the help of the EM algorithm. Both estimators are evaluated on the basis of a small Monte Carlo experiment.

Wegge, L.L.

doi: 10.1111/j.1467-9574.1991.tb01299.xpmid: N/A

This is an essay on a unified approach to the identifiability problem in static models with and without hidden endogenous variables. As is well known, when some of these variables are unobserved, the prior information requirements for models when all endogenous variables are observed, are still there. In addition, extra prior information that takes the place of the means and covariances of the missing variables will have to be supplied directly or indirectly by the statistical researcher. In the paper we characterize the quality and quantity of the required information for the general linear static model and apply it when the model is i) an econometric demand and supply model with missing observations on the quantity transacted, ii) a factor analysis model with observed characteristics of the test takers and iii) a LISREL Model without fixed exogenous variables. With unknown true parameters, the exact rank conditions are seldom verifiable but we do recommend an implementable check‐list that is adequate for almost all parameters.

Schneeweiss, H.

doi: 10.1111/j.1467-9574.1991.tb01300.xpmid: N/A

Summary: LISREL and PLS are two different ways of modelling latent variables and their relations to each other within a set of manifest variables. These two models are contrasted with each other. In the special case of two groups of manifest variables the relations that exist between corresponding parameters and latent variables of both types of models are revealed.

Mooijaart, A.; Bentler, P.M.

doi: 10.1111/j.1467-9574.1991.tb01301.xpmid: N/A

A condition is given by which optimal normal theory methods, such as the maximum likelihood methods, are robust against violation of the normality assumption in a general linear structural equation model. Specifically, the estimators and the goodness of fit test are robust. The estimator is efficient within some defined class, and its standard errors can be obtained by a correction formula applied to the inverse of the information matrix. Some special models, like the factor analysis model and path models, are discussed in more detail. A method for evaluating the robustness condition is given.

Satorra, A.; Saris, W.E.; Pijper, W.M.

doi: 10.1111/j.1467-9574.1991.tb01302.xpmid: N/A

In this paper we compare alternative asymptotic approximations to the power of the likelihood ratio test used in covariance structure analysis for testing the fit of a model. Alternative expressions for the noncentrality parameter (ncp) lead to different approximations to the power function. It appears that for alternative covariance matrices close to the null hypothesis, the alternative ncp's lead to similar values, while for alternative covariance matrices far from Ho the different expressions for the ncp can conflict substantively. Monte Carlo evidence shows that the ncp proposed in Satorra and Saris (1985) gives the most accurate power approximations.

Hsiao, C.; Taylor, G.

doi: 10.1111/j.1467-9574.1991.tb01303.xpmid: N/A

We demonstrate that despite the common worry about the possible correlations between the unobserved individual effects and the explanatory variables in panel data models the likelihood approach can provide a unified framework towards the study of the identification of a panel data model subject to measurement errors. In fact, it can also serve as a basis for deriving efficient estimation methods.

Faber, J.

doi: 10.1111/j.1467-9574.1991.tb01304.xpmid: N/A

The measurement of cooperation and conflict among nations differs greatly among several empirical studies of international relations. In the multidimensional approach to the measurement of both concepts, cooperation and conflict are considered to be unmeasured traits of various indicators in different areas of interest. Insight into the validity of the measurement theory can be gained from the fit of the estimated measurement model and from the estimates of the unknown parameters. These estimates are obtained through confirmatory factor analysis of data on observable policy Indicators of both concepts (see e.g., Jöreskog, 1969). The reliability of the estimated model can be investigated by means of multi‐sample confirmatory factor analysis, which allows one to fit a specified model to several data sets simultaneously. Maximum likelihood estimates of the unknown parameters of one‐sample and multi‐sample confirmatory factor analysis models, based on data available in COPDAB, can be obtained by using the LISREL‐VI program (see Jöreskog and Sörbom (1986). The results indicate that cooperation and conflict in foreign policies of nations have de‐escalating effects upon each other.