R. Carter Hill

Recreation Demand Equations: Functional Form and Consumer Surplus

The subject of recreation demand has increasingly attracted the attention of economic research. The demand equations resulting from this research follow the Hotelling-Clawson model of recreation demand, in which occasions (or days) recreated is specified as a function of average cost and average distance traveled per occasion and various combinations of other explanatory variables. Linear, quadratic, and semilog functional forms have been used widely in empirical applications of this model. Linear specifications have been employed often for computational or analytical ease (Burt and Brewer; Brown, Singh, and Castle; Cicchetti, Fisher, and Smith; Clawson and Knetsch). Other functional forms have been chosen frequently on the basis of statistical significance and consistency of the coefficients with theoretical expectations. Examples of a semilog form are Batie, Jensen, and Hogue; and Sawyer and Shulstad. A quadratic expression was chosen by Gum and Martin. A fourth functional form, log-log, also has appeared (Kalter and Gosse; Smith; Wetzstein and Green), but will not be considered here for reasons to be developed later. As the results of this study will demonstrate, the choice of functional form can have a significant effect on consumer surplus values derived from recreation demand equations. This paper presents a set of decision criteria for the choice between three popular functional forms that have been employed previously in recreation demand equations. The choice between linear and quadratic forms can be made via conventional hypothesis-testing procedures. The Box and Cox transformation procedure often allows choice between linear, semilog, and other power transformations of the dependent variable. The consequences of the choice of a particular functional form on consumer surplus also are investigated. The plan of the paper is first, to specify an appropriate set of regressors; second, to choose an appropriate functional form; and, finally, to demonstrate the effect of functional form on consumer surplus estimates derived from regression cost coefficients of recreation demand equations. The Choice of Regressors

Estimating Capital Asset Price Indexes

This paper introduces an improved procedure for estimating capital asset price indexes. We jointly estimate conventional hedonic and repeat sales models via maximum-likelihood procedures, thereby taking advantage of the unique features of the individual models and using all the data that are available. Our model captures depreciation within the repeat sales model and accounts for serial correlation in hedonic data. The improvement in precision obtained by estimating the joint model is illustrated by smaller standard errors and narrower interval estimates for the resulting price indexes. We also carry out a simulation experiment that shows estimation errors significantly smaller using the joint estimation technique than either of the individual models or the GLS estimator of Case and Quigley (1991).

Small Sample Properties of Probit Model Estimators

Abstract When maximum likelihood estimates of the coefficients in a nonlinear model such as the probit model are obtained there are a number of asymptotically equivalent covariance matrix estimators that can be used. These covariance matrix estimators are typically associated with different computer algorithms. For example, with the Newton–Raphson algorithm the inverse of the negative of the Hessian matrix from the log-likelihood function is used; with the method of scoring the inverse of the information matrix is used; and with a procedure proposed by Berndt, Hall, Hall, and Hausman (1974), the inverse of the outer product of the first derivatives of the log-likelihood function is used. Although these three estimators are asymptotically equivalent, their performance can vary in finite samples. The main objective of this article is to use a Monte Carlo experiment to investigate the finite sample properties of the three covariance matrix estimators, in the context of maximum likelihood estimation of the pr...

A random walk down main street

Abstract In this paper we provide a statistical test for the presence of a random walk component in house prices. This assumption is widely made when estimating repeat sales price index models. The surprising aspect of the test is that it is based on repeat sales data in which each house is observed to sell only twice. We do not have a time series of data on each house, nor a panel, and thus conventional tests for unit roots do not apply. Despite the fact that we have only two time series observations per house we show that our test, which is easy to apply with available software, has desirable characteristics. When applied to the well known Case and Shiller (1989) [Case, Karl E. and Robert J. Shiller, 1989. The efficiency of the market for single family homes. American Economic Review, 79, 125–137.] data the test reveals no evidence of a random walk component in four large U.S. cities.

Component selection norms for principal components regression

Multicollinearity or near exact linear dependence among the vectors of regressor variables in a multiple linear regression analysis can have important effects on the quality of least squares parameter estimates. One frequently suggested approach for these problems is principal components regression. This paper investigates alternative variable selection procedures and their implications for such an analysis.

Environmental Protection, Agency Motivations, and Rent Extraction: The Regulation of Water Pollution in Louisiana

Direct environmental regulation has been in place in the United States for more than twenty-five years. Yet there has been little study of what actually affects regulatory enforcement levels. This study examines enforcement issues by focusing on water quality enforcement by the Louisiana Department of Environmental Quality. The study finds that penalties are more likely to occur, and are likely to be higher, the more serious a firms violation of a regulation. Penalties are also more likely, and likely to be higher, if a firm has a previous record of environmental violations. In contrast to other studies, however, we do not find that enforcement varies across regional offices. In addition, we did not find any systematic effects of the Weingast and Moran (1983) theory of legislative dominance. We did, however, find evidence of rent extraction, along the lines of McChesney (1987; 1991).

TEST STATISTICS AND CRITICAL VALUES IN SELECTIVITY MODELS

The Heckman two-step estimator (Heckit) for the selectivity model is widely applied in Economics and other social sciences. In this model a non-zero outcome variable is observed only if a latent variable is positive. The asymptotic covariance matrix for a two-step estimation procedure must account for the estimation error introduced in the first stage. We examine the finite sample size of tests based on alternative covariance matrix estimators. We do so by using Monte Carlo experiments to evaluate bootstrap generated critical values and critical values based on asymptotic theory.

The economics of choice in the allocation of Federal grants: An empirical test

Concluding remarksIn this paper, we have provided strong evidence in favor of the Niskanen model of bureaucratic behavior and against the ‘public interest’ hypothesis by considering the selection process used by HUD in awarding Urban Development Action Grants. Specifically, we did not find that any distress measures specified in regulations dealing with the program were statistically significant in explaining the awarding of grants. The only consistently significant factors of those considered were the level of private commitment to the project and the ratio of private funds committed to total amount requested. We argue that use of these variables, especially the latter, as primary selection criteria by HUD bureaucrats reflects their desire to enhance their budgetary environment by making what the market perceives to be the best investments available to them, avoiding risk and spreading available UDAG funds as widely as possible.We conclude that HUD officials may attempt to limit the number of projects in severely distressed cities (despite contrary regulations) and to maximize the spread of available resources among funded projects.

An Optimal Property of Principal Components in the Context of Restricted Least Squares

Abstract A new optimal property for principal components regression is presented. In particular, it is shown that the trace of the covariance matrix for estimators obtained by deleting principal components associated with the smallest eigenvalues is at least as small as that for any other least-squares estimator with an equal or smaller number of linear restrictions. This property is useful in suggesting data transformations and determining the maximum variance reduction obtainable from the introduction of linear restrictions on the parameter space.

Political and economic influences on the bureaucratic allocation of federal funds: The case of Urban Development Action Grants

Abstract The distributive theory of politics predicts that federal budget allocations will be responsive to the committee position of congressmen and their majority/minority party status. But such political allocations are less likely where bureaucrats rather than legislators make the allocative decisions. In such cases we must take into account bureaucratic motivations as well. Niskanens bureaucratic budget maximization theory emphasizes such bureaucratic maximands and the efficient production of output or activity by the budget constrained bureau. In this paper the two theories are tested using data from the Urban Development Action Grant program, a capital subsidy program operated by the Department of Housing and Urban Development. A set of political and bureaucratic decision criteria is employed as independent variables in a series of logit and Tobit models in order to predict the likelihood of projects being funded and the amounts they will receive. The political criteria are not significant in any specifications, but the bureaucratic criteria suggest an investment-maximizing, risk-avoidance strategy on the part of HUD bureaucrats. Thus the results support the Niskanen theory, but do not support the distributive theory.