I. Introduction, 407. — II. The multiple-change approach, 409. — III. A general probabilistic framework, 412. — IV. The quasi-Paretian criterion, 418. — V. Concluding remarks, 423.

equation, yet estimates of the income elasticity of housing demand derived from micro data are systematically lower than estimates obtained from grouped (metropolitan-wide) data. The explanation proposed was based on the effects of common specification errors related to the housing price term. It was demonstrated theoretically that, given certain assumptions, the omission of the price term biases the ungrouped income elasticity estimate downward (whether stratified by metropolitan area or not) and the grouped estimate upward. It was also shown that the inclusion of a metropolitan-wide housing price index in the micro equation worsens the downward bias of the income elasticity estimate (and biases the corresponding price elasticity estimate toward zero). At the time the paper was written, the only empirical evidence directly relevant to this price misspecification hypothesis was contained in a study by Maisel, Burnham, and Austin [1]. It was shown that their income elasticity estimates were entirely consistent with the proposed explanation. Although their price elasticity results were not consistent, it was suggested that this could easily be attributed to sampling error. The purpose of this note is to discuss the relevance of some new empirical estimates of housing demand for the price misspecification hypothesis. These results are part of a broader study of housing demand undertaken by the author with D. T. Ellwood [3]. Since that study discusses the data and the specification of the equations in detail, the focus here is on those aspects of the data and results which are especially relevant to the price misspecification explanation.

The low estimates of the income elasticity of housing demand obtained when individual households are the unit of observation are theoretically reconciled with the high estimates obtained when metropolitan-wide averages are used. The omission of the housing price term biases the ungrouped (whether stratified by metropolitan areas or not) estimate(s) downward and the grouped estimate upward. The inclusion of a metropolitan-wide average housing price term worsens the downward bias of the unstratified ungrouped estimate. The corresponding price elasticity estimate is biased upward (toward zero). These results are interpreted in terms of the theory of residential location and used to explain the empirical evidence. For the evidence considered, the true income and price elasticities are approximately .75 and -.75, respectively.

A. Mitchell Polinsky, David T. Ellwood, An Empirical Reconciliation of Micro and Grouped Estimates of the Demand for Housing, The Review of Economics and Statistics, Vol. 61, No. 2 (May, 1979), pp. 199-205

This article surveys the theory of the public enforcement of law—the use of public agents (inspectors, tax auditors, police, prosecutors) to detect and to sanction violators of legal rules. We first present the basic elements of the theory, focusing on the probability of imposition of sanctions, the magnitude and form of sanctions, and the rule of liability. We then examine a variety of extensions of the central theory, concerning accidental harms, costs of imposing fines, errors, general enforcement, marginal deterrence, the principal-agent relationship, settlements, self-reporting, repeat offenders, imperfect knowledge about the probability and magnitude of fines, and incapacitation.