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.     

On the flexible functional forms

This note proposes a general structure of the so-called flexible functional forms able to describe direct utility functions. It is obtained by solving the functional equation:

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.     

Empirical factor demands and flexible functional forms: a bayesian approach

In this paper we compare classical econometrics, calibration and Bayesian inference in the context of the empirical analysis of factor demands. Our application is based on a popular flexible functional form for the firm's cost function, namely Diewert's Generalized Leontief function, and uses the well-known Berndt and Wood 1947–1971 KLEM data on the US manufacturing sector. We illustrate how the Gibbs sampling methodology can be easily used to calibrate parameter values and elasticities on the basis of previous knowledge from alternative studies on the same data, but with different functional forms. We rely on a system of mixed non-informative diffuse priors for some key parameters and informative tight priors for others. Within the Gibbs sampler, we employ rejection sampling to incorporate parameter restrictions, which are suggested by economic theory but in general rejected by economic data. Our results show that values of those parameters that relate to non-informative priors are almost equal to the standard SUR estimates, whereas differences come out for those parameters to which we have assigned informative priors. Moreover, discrepancies can be appreciated in some crucial parameter estimates obtained with or without rejection sampling.     

On Bayesian analysis and computation for functions with monotonicity and curvature restrictions

Our goal is inference for shape-restricted functions. Our functional form consists of finite linear combinations of basis functions. Prior elicitation is difficult due to the irregular shape of the parameter space. We show how to elicit priors that are flexible, theoretically consistent, and proper. We demonstrate that uniform priors over coefficients imply priors over economically relevant quantities that are quite informative and give an example of a non-uniform prior that addresses this issue. We introduce simulation methods that meet challenges posed by the shape of the parameter space. We analyze data from a consumer demand experiment.     

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.     

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.     

Imposing regional monotonicity on translog stochastic production frontiers with a simple three-step procedure

We show that the monotonicity condition is conceptually important in Stochastic Frontier Analysis (SFA). Despite its importance, most empirical studies do not impose monotonicity—probably because existing approaches are rather complex and laborious. Therefore, we propose a three-step procedure that is much simpler than existing approaches. We demonstrate how monotonicity of a translog function can be imposed regionally at a connected set (region) of input quantities. Our method can be applied not only to impose monotonicity on translog production frontiers but also to impose other restrictions on cost, distance, or profit frontiers.     

Preference symmetries,partial differential equations,and functional forms for utility

A discrete symmetry of a preference relation is a mapping from the domain of choice to itself under which preference comparisons are invariant; a continuous symmetry is a one-parameter family of such transformations that includes the identity; and a symmetry field is a vector field whose trajectories generate a continuous symmetry. Any continuous symmetry of a preference relation implies that its representations satisfy a system of PDEs. Conversely the system implies the continuous symmetry if the latter is generated by a field. Moreover, solving the PDEs yields the functional form for utility equivalent to the symmetry. This framework is shown to encompass a variety of representation theorems related to univariate separability, multivariate separability, and homogeneity, including the cases of Cobb–Douglas and CES utility.     

A remark on boundary restrictions in the Global Newton method

This remark shows how Smale's method of computing fixed points can be extended to problems involving very general boundary behavior.     

Some notes on discount factor restrictions for dynamic optimization problems

We consider dynamic optimization problems on one-dimensional state spaces. Under standard smoothness and convexity assumptions, the optimal solutions are characterized by an optimal policy function h mapping the state space into itself. There exists an extensive literature on the relation between the size of the discount factor of the dynamic optimization problem on the one hand and the properties of the dynamical system x_t+1=h(x_t) on the other hand. The purpose of this paper is to survey some of the most important contributions of this literature and to modify or improve them in various directions. We deal in particular with the topological entropy of the dynamical system, with its Lyapunov exponents, and with its periodic orbits.     

What restrictions do Bayesian games impose on the value of information?

In a Bayesian game players play an unknown game. Before the game starts some players may receive a signal regarding the specific game actually played. Typically, information structures that determine different signals, induce different equilibrium payoffs. In two-person zero-sum games the equilibrium payoff measures the value of the particular information structure which induces it. We pose a question as to what restrictions Bayesian games impose on the value of information. We provide answers for two kinds of information structures: symmetric, where both players are equally informed, and one-sided, where only one player is informed.     

Economic assumptions and choice of functional forms: comparison of top down and bottom up approaches

Two alternative model building approaches are analyzed and compared. The general to specific modeling (top down approach) starts with a general model and subjects it to a sequence of restrictions to determine an acceptable specific model. This approach can start with a series expansion and the concavity or homotheticity conditions can be imposed to modify it into a cost or a production function. The simple to general modeling (bottom up approach) starts with a well known simple model and extends it until a complete system is formed. This approach can start with a Cobb-Douglas function (which satisfies the concavity and homogeneity conditions) and extends it to include the desired complexity. Relative advantages and disadvantages of the two approaches are discussed and tabulated. The electricity generation data is applied to compare the performance of these two approaches.

A note on multinomial maximum likelihood estimation under ordered restrictions and the EM algorithm

A frequently occurring problem is to find the maximum likelihood estimation (MLE) of p subject to p∈C (C⊂ P the probability vectors in R ^k ). The problem has been discussed by many authors and they mainly focused when p is restricted by linear constraints or log-linear constraints. In this paper, we construct the relationship between the the maximum likelihood estimation of p restricted by p∈C and EM algorithm and demonstrate that the maximum likelihood estimator can be computed through the EM algorithm (Dempster et al. in J R Stat Soc Ser B 39:1–38, 1997). Several examples are analyzed by the proposed method.     

基于组态王的柔性制造生产系统监控技术研究

文章以Me093399型机电一体化教学系统为研究对象,以组态王为上位机监控软件,进行了实时控制系统的开发,模拟了实际现场工况,操作简单,实用性强。文章还介绍了系统的构成和网络结构形式,对组态王监控系统的设计与开发过程进行了重点研究。     

一种基于PLC的柔性自动化生产线系统

在对柔性自动化理论研究的基础上,文章设计了一条柔性自动化生产线系统,并且利用PLC强大的数据处理和数值运算功能,实现了该系统的编辑和仿真。     

上海公交价格需求弹性估计

本文估计得到上海地面公交的价格需求弹性为-0.129,低于欧美城市公交的价格需求弹性。上海公交价格弹性低于西方城市的现象,可以由从中国城市较低的经济发达程度、收入水平和较少的可选择交通工具来解释。     

A functional perspective on financial networks

The financial sector is a critical component of any economic system, as it delivers key qualitative asset transformation services in terms of liquidity, maturity and volume. Although these functions could in principle be carried out separately by specialized actors, in the end it is their systemic co-evolution that determines how the aggregate economy performs and withstands disruptions. In this paper we argue that a functional perspective on financial intermediation can be usefully employed to investigate the functioning of financial networks. We do this in two steps. First, we use previously unreleased data to show that focusing on the economic functions performed over time by the different institutions exchanging funds in an interbank market can be informative, even if the underlying topological structure of their relations remains constant. Second, a set of alternative artificial histories are generated and stress-tested by using real data as a calibration base, with the aim of performing counterfactual welfare comparisons among different topological structures.