Choice Of Functional Form Research Articles

Functional Form and the Statistical Properties of Welfare Measures

AbstractThis paper uses Monte Carlo analysis to compare the variance of consumer's surplus for several functional forms for demand. Although the semilog and linear forms fit the data well by statistical criteria, the coefficients of variation for consumer's surplus generated by these forms were substantially larger than for the double log and linear‐log forms. While this paper is framed in the travel cost approach to recreational demand, there are implications for the choice of functional form whenever the measure of interest is a nonlinear transformation of the estimated parameters.

Nonrobustness of Dynamic Dual Models of the U.S. Dairy Industry

The robustness of dynamic dual model results across functional forms is examined for the U.S. dairy industry. Modified generalized Leontief (GL) and normalized quadratic (NQ) functional forms are compared by examining their consistency with properties of the competitive firm, estimated rates of adjustment for cows and labor, tests of technological change, and elasticities. Homogeneity and symmetry are maintained in both models. Convexity is not rejected by the GL and is not seriously violated by the NQ. Absence of technological change is rejected by both models, but quality indexes on labor and cows fully embody technological change occurring within labor and cows in the NQ but not in the GL. Policy-relevant elasticities differ greatly between the functional forms. Dynamic dual models are found to be non-robust in important ways to choice of functional form.

The Reliability of Estimates of Environmental Benefits from Recreation Demand Models

AbstractRecreation demand models are commonly employed tools of economists interested in valuing improvements in environmental amenities. Despite their importance, little comparative work has been undertaken to examine the ability of the models to accurately estimate welfare changes. A simulation study designed to compare the reliability of estimated welfare measures (compensating variation and consumer surplus) from several commonly employed recreation demand models is presented. Results of the study indicate that choice of functional form and model specification are important determinants of the resulting estimates of benefits.

An Evaluation of Alternative Estimation Techniques and Functional Forms in Developing Statistical Appraisal Models

This paper examines the combined effects of multicollinearity, parameter stability, and alternative function forms in hedonic regression models. The results indicate that the significance and stability of the regression coefficients as well as prediction accuracy are sensitive to the choice of functional form and estimation technique. In certain respects nonlinear models proved to be more effective than linear models and ridge regression techniques were generally superior to OLS estimation. Since no single estimation technique or functional form was superior in all respects, the appraiser may have to choose between minimizing the average prediction error or maximizing prediction stability.

Farm price responsiveness and the choice of functional form: An application to rice cultivation in West Malaysia

The estimated responsiveness of farmers to changes in the prices of output or inputs is in general very sensitive to the econometric model used. Using cross-section survey data for farms in marginal rice-growing districts in West Malaysia price elasticities based on estimated input demand equations derived from a quadratic restricted profit function were found to be superior to those derived from translog or Cobb-Douglas production functions or from a translog restricted profit function. The Cobb-Douglas production function is restrictive and should be used sparingly. Restricted profit functions are only believable if the available price data are of high quality.

Log Transformation Bias in Estimating Travel Cost Models

With the general acceptance of the travel cost method for estimating the demand for and value of recreation sites, increasing attention is being directed to the improvement of empirical methods in order to reduce errors in travel cost model estimation. Research has focused particularly upon how the choice of functional form (Ziemer, et al. 1980; Strong 1983; Smith 1975; Vaughan, et al. 1982; Sutherland 1982) and estimation methods (Bowes and Loomis 1980) influence the results of travel cost studies.

The choice of functional forms for hedonic price equations: Comment

Rosen [13], Freeman [4], Halvorsen and Pollakowski [6], and others have stressed that economic theory does not suggest an appropriate functional form for hedonic price functions. 1 1 The only theoretical restriction on the hedonic price function is that its price elasticity must lie in between the price elasticities of supply and demand. Since both the supply and demand curves are not observable, even this mild restriction is not very helpful in choosing functional forms. It consequently is reasonable to try several functional forms and utilize the multiple regression equation with the best performance. In this spirit, Halvorsen and Pollakowski [6] recommend using the Box-Cox flexible functional form for hedonic analysis and measuring best performance with a goodness of fit test. The Box-Cox methodology has also been adapted in hedonic studies by Goodman [5], Linneman [10], Blomquist and Worley [1], and Eberts and Gronberg [3]. 2 2 The Box-Cox functional form has been used in several other urban contexts by Kau and Lee [8], Kau and Sirmans [9], Sirmans et al. [14], Sirmans and Redman [15], and McDonald [11]. Some of the problems, for example with prediction, raised in this paper on hedonics apply to these uses as well. The Box-Cox is particularly suited for testing functional forms because many familiar forms such as semilog, log linear, and translog are subsets of the flexible Box-Cox permitting nested hypothesis testing. In this note, we illustrate that the formal hypothesis testing advantage of the Box-Cox functional form is purchased at the expense of other important goals. The goal of most hedonic studies is to estimate the prices of the characteristics, to measure the response to changes in the prices, and/or to predict future expenditures. Using a best fit criterion to choose functional forms does not necessarily lead to more accurate estimates of characteristic prices. In fact, the large number of coefficients estimated with the Box-Cox functional form reduces the accuracy of any single coefficient which could lead to poorer estimates of specific prices. Second, because any negative number raised to a noninteger real power is imaginary, the traditional Box-Cox functional form is not suited to any data set containing negative numbers. Third, the Box-Cox functional form may be inappropriate for prediction. Since the mean predicted value of the untransformed dependent variable need not equal the mean of the sample upon which it is estimated, the predicted untransformed variable (housing value) will be biased. The predicted untransformed dependent variable may also be imaginary. Fourth, the nonlinear transformation results in complex estimates of slopes and elasticities which are often too cumbersome to use properly. We discuss each of these drawbacks and quantify them when possible in the remainder of this note.

Homicide and Deterrence: A Reexamination of the United States Time-Series Evidence

Since the publication of Isaac Ehrlich's controversial articles [6; 9] on murder and capital punishment, there has been extensive criticism of his findings. Using regression analysis with U.S. time-series data, Ehrlich found that increases in the relative frequency of arrest, the relative frequency of conviction given arrest and the relative frequency of execution given conviction, reduce the number of homicides per capita and that the magnitudes of these effects are consistent with sharp predictions-the elasticity conditionsderived from the hypothesis that potential murderers act as if they were maximizing expected utility.' Among the criticisms of Ehrlich's time-series work on homicide, the most important are: (1) The FBI data used by Ehrlich to measure homicides and the probabilities of punishment is highly suspect, especially during the 1930s [3]. (2) Ehrlich's results are sensitive to the inclusion of additional explanatory variables and the choice of functional form [3; 19; 26]. (3) Ehrlich's regressions are unstable over the 1960s [26]. (4) The negative correlations between the homicide rate and the probabilities of punishment found by Ehrlich may be explained by the effect of the homicide rate on the probabilities of punishment not vice versa [17]. Ehrlich has responded to these criticisms in some detail [7; 8; 9; 11]; perhaps his strongest rebuttal is his cross-sectional study of homicide [9] which replicated the deterrence findings reported in his 1975 time-series article. Recently, however, Ehrlich's crosssectional results have also come under fire. McManus [25] and Leamer [22; 23] have argued that Ehrlich's cross-sectional finding that capital punishment is a deterrent to homicide is sensitive to one's prior beliefs concerning the variables to be included in the homicide regression. The purpose of this paper is not to debate the merits of Ehrlich's research but to move the debate forward by presenting new updated time-series estimates of the U.S. homicide function. Within the context of the new estimates presented in this paper, the criticisms of

Partial vs. general equilibrium analysis and choice of functional form: Implications for policy modeling

In formulating empirically tractable, economywide models, researchers are often forced to employ “convenient” functional forms. These forms embody restrictive maintained hypotheses. Alternatively, flexible functional forms may be utilized in a partial equilibrium setting. Estimation and incorporation of flexible functions into computable general equilibrium models is considerably more demanding of research resources. Assuming that shortcuts will continue to be necessary for researchers attempting to respond to current policy problems, this paper compares these two alternatives. Specifically, a general equilibrium model for New York State is employed to evaluate the relative performances of flexible partial equilibrium models and their more restrictive, general equilibrium counterpart. In the particular application considered, the former approach is found to dominate the latter.

An Engel Curve Analysis of Household Expenditure in New Zealand*

In this paper we estimate systems of Engel curves for expenditure on eight commodity groups by New Zealand households. Six model specifications are considered, and the preferred results are based on the Almost Ideal Demand System. The estimated expenditure elasticities and marginal budget shares are quite insensitive, at the sample mean, to the choice of functional form. The results are compared with those from other Australasian, British and American studies.

Estimation of Economies of Scale in Banking Using a Generalized Functional Form

THIS PAPER ADDRESSES four issues that arise in the estimation of economies of scale in the commercial banking industry. First, a common assumption underlying many of the studies of economies of scale in banking is the assumption of a Cobb-Douglas production function with exogenous input prices. The use of a Cobb-Douglas production function facilitates the estimation of the output elasticity of cost. However, there does not appear to be any other reason, a priori, for such an assumption. This paper utilizes a Box-Cox (hereafter B-C) generalized functional form methodology to directly test the assumption of an underlying Cobb-Douglas production function. Second, if the assumption of a Cobb-Douglas production function is inappropriate as a description of the production process of the financial firm, estimates of the output elasticity may be biased. The sensitivity of the estimates of this elasticity to the choice of functional form can also be examined through the use of a generalized functional form methodology. Third, no general consensus has been reached regarding the appropriate definition of bank output. Thus, a diversity of measures of bank output have been employed in previous estimates of economies of scale in banking. The sensitivity of the estimated output elasticity of cost to the selection of several alternative measures of output is examined through the use of the generalized functional form methodology. Finally, the B-C estimates of the cost function for commercial banks can be used

Modelling Price Expectations in Intertemporal Consumer Demand Systems: Theory and Application

ONE of the most puzzling dichotomies in economics is that between the microeconomic theory of consumer demand and the consumption function of macroeconomics. Although there is now a highly developed literature on the specification and estimation of systems of consumer demand equations, this is basically a theory of allocation, i.e., given the level of consumption, how is it to be allocated among the various categories of consumer goods? This literature takes as given the allocation of current income between consumption and savings, and hence contributes very little to the specification of the consumption function. A notable exception to this dichotomy is the Extended Linear Expenditure System (ELES) proposed by Lluch (1973), an intertemporal model of consumer decision making which endogenizes not only the allocation of consumption across commodities, but also the consumption-saving decision, and hence generates a consumption function which is firmly based in microeconomic theory. However, ELES is based on the rather special Klein-Rubin instantaneous utility function, which will be shown below to have quite restrictive implications. In fact, when the problem is set up in terms of the indirect utility function, generalizations of the Klein-Rubin form are easily incorporated into the intertemporal optimization problem. A second generalization of ELES relates to price expectations. Most empirical applications of ELES, for example, Lluch, Powell and Williams (1977), Lluch and Williams (1975) and Powell (1973) have generally assumed static price expectations and have depended upon the continual replanning assumption to justify observed price movement through time. Where price expectations have been considered, it has usually been in an ad hoc manner. Additionally, these models have generally assumed constant (current) nominal interest rate expectations,'which would appear to be inconsistent with an assumption of stationary price expectations, since the current nominal rate of interest will include a premium for inflation. In a previous paper (Cooper and McLaren (1980a)), an initial attempt was made to integrate a model of the formation of price expectations into an intertemporal consumer decision making model at the optimization stage. Two weaknesses of this model were the restriction to the case of a Klein-Rubin utility function, and the inconsistency of the assumptions made about interest rate expectations with those on price expectations. In the following two sections we present a reasonably general model of intertemporal consumer decision making incorporating price and interest rate expectations which overcomes these two weaknesses. Section IV presents the estimating forms based on a particular choice of functional forms, and estimates using Australian data are presented in section V.

Household Demand for Money in an Underdeveloped Economy : A Case Study of India

The paper tries to overcome some of the empirical problems that are associated with the estimation of demand-for-money function in an underdeveloped economy. It deals explicitly with the choice of functional form and inclusion of interest rate as an explanatory variable to serve as opportunity cost of holding money in the money demand function using both narrow and broad definitions of money. The paper concludes that short- or long-period interest rates serve as an opportunity cost of holding money in India only when a narrow definition of money is used. Time deposits were found to be sensitive to the maturity structure of financial instruments. As regards the choice of functional form, the paper holds that it makes no difference whether the function is estimated by linear form or by log-linear form. The paper also confirms for India the results of Friedman's seminal study for the United States.

Corporate Financial Reporting: A Methodological Review of Empirical Research

* University of New South Wales; tStanford University. This paper benefited from comments of participants in workshops at Baruch College CUNY, Cornell University, Monash University, Stanford University, University of Chicago, University of New South Wales, University of Pennsylvania, University of Rochester, and Washington University. A special thanks is due to detailed criticisms from G. Biddle, S. Datar, L. DeAngelo, P. Dodd, N. Dopuch, J. Elliott, N. Gonedes, C. Horngren, M. Jensen, A. Kirby, R. Leftwich, J. Magliolo, R. Morris, C. Purvis, K. Schipper, D. Shores, R. Watts, G. Whittred, M. Wolfson, and J. Zimmerman. Foster's contribution was sponsored by the Stanford Program in Accounting, contributors to which are: Arthur Andersen & Co.; Arthur Young & Company; Coopers & Lybrand; Deloitte Haskins & Sells; Ernst & Whinney; Peat, Marwick, Mitchell & Co.; and Price Waterhouse & Co. 1 Buchler [1961, p. 125] distinguishes and methodology in these terms:... in the broadest sense 'methodological' questions are those dealing with as their subject matter, questions pertaining to the origin, scope, nature and relative value of methods. Webster's Third New International Dictionary defines method as procedure or process for attaining an object ... a particular approach to problems of truth or knowledge. Methodology is defined as body of methods, procedures, working concepts, rules and postulates employed by a science, art or discipline ... a science on the study of method. We take research methods to include the selection of dependent and independent variables, sample selection, choice of functional forms, experimental controls, statistical inference, etc.

Choice of functional form for hedonic price equations

The appropriate functional form for a hedonic price equation cannot in general be specified on theoretical grounds. In this paper, a statistical procedure for the choice of functional form is proposed. A highly general functional form is specified that yields all other functional forms of interest as special cases. Likelihood ratio tests are used to test the appropriateness of alternative forms. The procedure is illustrated using cross section microdata for housing. For the case considered, the functional forms most commonly used in previous studies are strongly rejected.

Testing Linear and Log-Linear Regressions for Functional Form

It is often a problem to know what functional form to choose when specifying an econometric model since economic theory does not usually provide a very precise guide. The choice of functional form may, however, have important implications for subsequent statistical tests, for forecasts and for policy analysis, e.g. see Hall (1978)and Mizon (1977). Due to their simplicity, the specifications most commonly used are the linear and log-linear models. Sometimes the estimates of these two variants are compared with a view to choosing one of them as the correct representation. Although this comparison may be of interest in certain cases, in others it may be more appropriate to test linearity or log-linearity against a more general functional form rather than against each other. In this paper, we discuss two approaches to testing the adequacy of the linear and log-linear specifications against the more general alternative of the extended Box-Cox (1964) regression model considered by Savin and White (1978). The first of these procedures is based on the Lagrange multiplier approach discussed by Breusch and Pagan (1980) and by Godfrey and Wickens (1980), while the second is derived from work by Andrews (1971) on the selection of data transformations.1 Both approaches lead to tests which are easy to compute and which can reject both models as well as being capable of selecting one form rather than the other. The paper is set out as follows. In Section 2 we compare some existing procedures for testing the functional form of linear and log-linear models. In Section 3 we derive new large sample tests which are based on the Lagrange multiplier approach. The possibility of using small sample tests is discussed in Section 4 and a numerical example to illustrate the use of our new tests is given in Section 5.

Choice of Functional Form and the Demand for Air Quality

The quadratic Box-Cox approach is examined to determine its usefulness in demand research. In the absence of information about hedonic price and household demand structures, the flexible form is invaluable in both stages of the Rosen demand estimation procedure. The quadratic Box-Cox form permits a statistical investigation of a wide variety of specific hypotheses concerning specifications. Commonly-used functional forms in both the hedonic and demand stages are shown in the samples to be founded upon unacceptably restrictive hypotheses. The impact of changes in functional form upon demand-elasticity estimates and benefit estimates justify concern over the functional form-selection process. 8 references, 4 tables.

Disaggregate and aggregate car ownership forecasting in Great Britain

The first part of this paper argues that the variable ‘cars per household’, as well as the proportion of households owning more than a given number of cars, should be modelled by sigmoid functions with finite saturation levels. Next, a summary and critique of the work of the Regional Highway Traffic Model, group is presented. Problems relating to choice of functional form, interaction of effects, and the usefulness of the explanatory variable ‘Car Purchasing Income’ are discussed. This leads to an analysis of the concept of a saturation level, with a caution against using external data to determine it when the true functional form of the car ownership growth path is unknown. Following this, Transport and Road Research Laboratory work is discussed and its limitations highlighted. Data for the period 1953–1974 is reworked yielding the conclusion that there is no evidence that growth in this period has been non-logistic. This implies that previous overpredictions by TRRL were due to incorrect parameter estimates, rather than the choice of the wrong model form.

Estimating U.S. Demand for Meat With A Flexible Functional Form

One of the fundamental problems in applied econometric work is the choice of functional form. Economic theory is insufficient in suggesting the functional forms appropriate to the specification of economic relationships. Conventionally, the functional form of the regression equation is assumed a priori and parameter estimates are obtained according to certain desirable criteria, such as least squares. A wide variety of functional forms have been investigated empirically with respect to the demand function for food, yet no single functional form has been generally accepted among economists [2, 6, 7].

THE DEMAND FOR MEAT — AN EXAMPLE OF AN INCOMPLETE COMMODITY DEMAND SYSTEM*

Equations describing the demand for beef and veal, mutton, lamb, pork and chicken are estimated using the full information maximum likelihood estimator. Elasticity estimates are presented and the double logarithmic model is compared with a demand system which is derived from the indirect translog utility function. Estimates of the direct price and income elasticities are not particularly sensitive to model specification but the estimated cross‐price elasticities are sensitive to the choice of functional form. The results indicate that the double logarithmic specification may be less satisfactory than the alternative presented in cases where restrictions on the parameters are imposed during estimation.