Estimates of the demand for medical care under different functional forms

We estimate price and income elasticities from a linear, log-linear, and the almost ideal demand model (with and without an adjustment for selectivity bias) in an effort to show that special attention should be paid to the underlying assumptions of consumer behaviour when estimating a medical care demand model. The literature on medical care utilization is extended by incorporating two major components of spending as separate demands in a system of medical care spending. We find that estimates of elasticities vary depending on the functional form of the estimating equation, thus questioning the usefulness for policy purposes of single estimates of elasticities.     

Simultaneous equations models in applied search theory

This paper shows how standard simultaneous equations models arise in the analysis of survey data on wages and unemployment durations in the light of job search theory. Log-linear approximations to the key functional relations lead to ordinary log-linear simultaneous equations in which, moreover, specification error or heterogeneity terms are absorbed into the structural form error terms. Identifiability of structural parameters by exclusion restrictions can then be examined. An illustrative application of the method to data on elapsed durations and asking wages is given with results not inconsistent with search theory.     

Testing the Technology of Human Capital Production: A General-to-Restricted Framework

Studies of childhood development have suggested human capital is accumulated in complex and nonlinear ways. Nonetheless, empirical analyses of this process often impose a linear functional form. This paper investigates which technology assumptions matter in quantitative models of human capital production. I propose a general-to-restricted procedure to test the production technology, placing constraints on a modified McCarthy function, from which transcendental, constant elasticity of substitution, log-linear and linear models are obtained as special cases. Applying the procedure to data on child height from the Young Lives surveys, as well as cognitive skills, I find that the technology of human capital production is neither log-linear nor linear-in-parameters; rather, past and present inputs act as complements. I recommend that maintained hypotheses underlying functional form choices should be tested on a routine basis.     

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.     

A multiplicative model for efficiency analysis

This paper develops theory and algorithms for a “multiplicative” Data Envelopment Analysis (DEA) model employing virtual outputs and inputs as does the CCR ratio method for efficiency analysis. The frontier production function results here are of piecewise log-linear rather than piecewise linear form.     

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 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 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.     

Bayesian semiparametric multivariate GARCH modeling

This paper proposes a Bayesian nonparametric modeling approach for the return distribution in multivariate GARCH models. In contrast to the parametric literature the return distribution can display general forms of asymmetry and thick tails. An infinite mixture of multivariate normals is given a flexible Dirichlet process prior. The GARCH functional form enters into each of the components of this mixture. We discuss conjugate methods that allow for scale mixtures and nonconjugate methods which provide mixing over both the location and scale of the normal components. MCMC methods are introduced for posterior simulation and computation of the predictive density. Bayes factors and density forecasts with comparisons to GARCH models with Student-t$t$ innovations demonstrate the gains from our flexible modeling approach.     

Wealth concerns and equilibrium

Most properties of the classical general equilibrium model without externalities fail to extend to the wildest forms of consumption externalities. The recent interest for wealth concerns, a kind of externality associated with herding behavior and other-regarding preferences, motivates a study of the general equilibrium exchange model with those externalities. The diffeomorphism of the equilibrium manifold with a Euclidean space, the smoothness and properness of the natural projection and its non-zero degrees are shown to hold true for endowment spaces with variable total resources. Other properties of the classical exchange model without externalities are fragile in the sense that they do not resist the introduction of wealth concerns even in models where consumers preferences are represented by the simplest forms of utility functions like the log-linear (or Cobb–Douglas) functions. The most notable fragile properties are the uniqueness and regularity of equilibrium at equilibrium allocations and the stability of no-trade equilibria.     

Incorporating monotonicity and concavity conditions in flexible functional forms

Empirical economists using flexible functional forms often face the disturbing choice of drawing inferences from an approximation violating properties dictated by theory or imposing global restrictions that greatly restrict the flexibility of the functional form. Focusing on the cost function, this paper presents an alternative approach which imposes monotonicity and concavity properties only over the set of prices where inferences will be drawn. An application investigating elasticities for Berndt-Wood data set using the translog, generalized Leontief, and symmetric generalized McFadden flexible functional forms illustrates the technique. © 1996 John Wiley & Sons, Ltd.     

Estimating demand with distance functions: Parameterization in the primal and dual

Our purpose is to investigate the ability of different parametric forms to ‘correctly’ estimate consumer demands based on distance functions using Monte Carlo methods. Our approach combines economic theory, econometrics and quadratic approximation. We begin by deriving parameterizations for transformed quadratic functions which are linear in parameters and characterized by either homogeneity or which satisfy the translation property. Homogeneity is typical of Shephard distance functions and expenditure functions, whereas translation is characteristic of benefit/shortage or directional distance functions. The functional forms which satisfy these conditions and include both first- and second-order terms are the translog and quadratic forms, respectively. We then derive a primal characterization which is homogeneous and parameterized as translog and a dual model which satisfies the translation property and is specified as quadratic. We assess functional form performance by focusing on empirical violations of the regularity conditions. Our analysis corroborates results from earlier Monte Carlo studies on the production side suggesting that the quadratic form more closely approximates the ‘true’ technology or in our context consumer preferences than the translog.     

Melbourne: Population density; distance; the relationship

The analysis of two earlier writers is replicated using a data base pertaining to Melbourne, Australia, for the period 1901 to 1976. Several alternative functional forms of the population density functions are tested to determine comparative goodness of fit to the data. Population estimates are obtained and contrasted to actual population figures, and finally density functions incorporating time as an argument are estimated.     

On information-improvement and its generalization

TheTheil's information-improvement and its generalized form are consequences of different forms of the branching property that these measures are required to satisfy. We consider a seemingly more generalized form of the branching property and show that it does not lead to new measures. We also form a functional equation in three variables through this generalized branching property and show that this lead to the same result.The work is supported by a Post Doctoral Fellowship awarded to the author by Council of Scientific and Industrial Research, India.     

MODELS FOR RESPONSE DATA SHOWING EXTRA-POISSON VARIATION

When count data show extra-Poisson variation, standard log-linear techniques to analyse the data may fail. In ihis paper a generalization of the log-linear modelling technique is proposed for the negative binomial model, as an extension of the Poisson model. An illustration is given by the analysis of a twoway classification of soldering failure data; extensions to more general classifications are possible.     

A log-linear approach to disaggregated micro-level population forecasts

"This paper proposes the use of a log-linear model to obtain long-range micro-level population projections from the aggregative projections. The proposed model is tested using U.S. data. The total population of households is decomposed into 120 subgroups on the basis of the household's region of location, age, size and the female's employment status. The estimated number of households from the log-linear technique is compared against the random-walk and time-trend methods. A comparison of the size of the observed and estimated subgroups for the years 1960 and 1980 suggests that the log-linear technique is superior to the other two methods. Five different measures of errors are used to evaluate the projections."     

The Effect of Technological Change and Technical Inefficiencies on the Performance of Functional Forms

Technological change is one of the most important determinants of the technological structure of the firm. Unfortunately, this crucial factor is often unobserved and must therefore be approximated. It is also well recognized that firms are not necessarily located on their efficient production frontier, a phenomenon known as technical inefficiency. This paper compares the performance of three flexible functional forms (the Translog, Symmetric McFadden and Symmetric Generalized Barnett) to properly infer theoretical properties and technology measurements when: (i) unobserved technological change is approximated by a time trend in the variable-cost-function specification and, (ii) firms may be technically inefficient. Our results indicate that no functional form dominates and that measuring the shifts of the production (cost) function has a clear and negative effect on the performance of the functional forms. Furthermore, we find that technical inefficiencies have a significant and negative effect on the measurement of, notably, returns to scale and the implicit rental price of capital. However, all forms over-reject theoretical properties and provide adequate technology measurements only on a sample-average basis. In addition, the performance of the functional forms is closely related to the true underlying rate of technological change.     

Planning pre-school services: A socio-demographic analysis

Data were collected from mothers with a child under 5 living in 3 small areas of Inner London. Information was provided by them about various aspects of pre-school provision and these were related to a number of socio-demographic factors. The concepts of demand, need, desire and take-up were discussed in the context of preschool services and it was shown by using log-linear models that desire for pre-school provision could be efficiently predicted by a combination of these socio-demographic variables. Some emphasis was placed on the use of log-linear models with sparse data and the models were replicated on fresh data.     

Intrametropolitan location of employment

Differences among employment density functions for members of different income and sex groups in Toronto in 1971 indicate that jobs held by females were more centralized than jobs held by males, jobs held by lower-middle income females were more centralized than jobs held by other females, and jobs held by high-income males were more centralized than jobs held by other males. It is also concluded that use of the negative exponential functional form involves a misspecification of the employment density function.     

On the flexibility of flexible functional forms: An empirical approach

This paper analyzes empirically the ability of the Translog and Generalized Leontief functional forms to approximate Constant Elasticity of Substitution utility functions. Although these flexible forms provide a good local approximation they do not always provide a good approximation over a range of observations. Hence the finding in practice of observations for which the regularity conditions required by economic theory are not satisfied need not imply the absence of an underlying utility-maximizing process, but may simply reflect the inability of the flexible form to approximate the true utility function over the range of the data.     

On testing separability restrictions with flexible functional forms

In this paper, we examine the implications of imposing separability on the translog and three other flexible forms. Our results imply that the Berndt-Christensen ‘nonlinear’ test for weak separability tests not only for weak separability, but also imposes a restrictive structure on the macro and micro functions for all currently known ‘flexible’ functional forms. For example, testing for weak separability using the translog as an exact form is in fact equivalent to testing for a hybrid of strong (additive) separability and homothetic weak separability with Cobb-Douglas aggregator functions. Our results show that these ‘flexible’ functional forms are ‘separability-inflexible’. That is, they are not capable of providing a second-order approximation to an arbitrary weakly separable function in any neighbourhood of a given point.     

Energy consumption and economic growth

The present paper discusses methods originally proposed by Adams and Miovic in 1968 (then refined and used later by many other authors) for calculating the output elasticity of useful energy consumption (?). We first show that this methodological approach is quite dubious. Better alternative methods of estimation are then proposed. We also stress that, since the marginal rate of interfuel substitution depends on the GDP functional form, the simulataneous use of several functional forms of GDP in energy studies leads obviously to misleading interpretations. Using thermal efficiency coefficients and OECD countries figures for the 1959–73 period, we finally found that ? did steadily fall from high values to values which are still higher than one.