Estimation of errors-in-latent-variable models on business survey data

Abstract

To estimate a theoretical model on business survey data, which consist only of qualitative information, requires a specific econometric analysis. First, the statistical specification is obtained by means of an errors-in-variable linear model. Second, the variables entering the theoretical model are interpreted as latent variables which, in turn, reveal the categorical survey response when they cross certain thresholds. The estimation is performed in two steps. First, the correlation matrix of the latent variables is estimated using the theory of the polychoric correlation coefficient. Second, this correlation matrix is the input for a method of moments: The estimates of the model parameters are derived either by maximum likelihood or by weighted least squares when a correct asymptotic covariance of the correlation matrix may be obtained. An example using business surveys of French manufacturing industry is presented.