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Abstract

Estimating the magnitude of the shadow economy in the U.S. and various European countries has been a topic of some interest since the late 1970's. Several indicators (measurements) have been proposed and attempts have been made to link the magnitude of the shadow economy (as a percentage of GNP) to causal variables such as the tax rate on personal income, the extent of government regulation in the conduct of business, etc. These attempts, while provocative in their findings, do not recognize (with but one exception) the obvious latent structure involved in this estimation problem. No one has yet attempted to estimate a latent variable model for the shadow economy using time series data. In this paper we construct and estimate a dynamic latent variable model of the MIMIC form (multiple indicators, multiple causes, one latent variable) on annual U.S. data covering the period 1939-82. A number of different specifications are considered. The maximum likelihood estimation procedure is patterned after a method used by Engle and Watson. It involves a first-stage Kalman filter followed by an application of the EM algorithm. As to substantive results, we find that the autoregressive structure in the latent variable and serial correlation in the measurement equation errors are responsible for much of the "action". Among the causal factors considered, tax "burden" and "tax morality" are statistically significant with a positive influence on the magnitude of the shadow economy in many of the models we present. Some of the available indicators are clearly more important than others, as measured by the estimated coefficients that link them to the shadow economy. Finally, prediction of the size of the shadow economy from our models indicates a minimum in the mid-sixties, growing to upwards of 29% of official GNP by 1982.

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