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Panel data based on various longitudinal surveys have become ubiquitous in economics in recent years. Estimation using the analysis of covariance approach allows for control of various "individual effects" by estimation of the relevant relationships from the "within" dimension of the data. Quite often, however, the "within" results are unsatisfactory, "too low" and insignificant. Errors of measurement in the independent variables whose relative importance gets magnified in the within dimension are often blamed for this outcome. However, the standard errors-in-variables model has not been applied widely, partly because in the usual micro data context it requires extraneous information to identify the parameters of interest. In the panel data context a variety of errors-in-variables models may be identifiable and estimable without the use of external instruments. We develop this idea and illustrate its application in a relatively simple but not uninteresting case: the estimation of "labor demand" relationships, also known as the "short run increasing returns to scale" puzzle.