Darryl Holden

Unit Roots and Cointegration for the Economist

Previous papers by one of the authors, Perman (1989, 1991), have proved popular amongst applied economists seeking an introduction to the new econometrics of unit roots and cointegration. The aim of the present paper is, as before, to provide a comprehensive overview of the field in a manner which minimises the technical knowledge required of the reader and which offers intuitive explanations wherever possible. Other useful surveys, at a slightly higher technical level, include the special issues of the Oxford Bulletin of Economics and Statistics (March 1986, August 1992), Dolado et al. (1990) and Campbell and Perron (1991). In this introduction we motivate the study of unit roots and cointegration, and outline the contents of the rest of the chapter.

Testing the Normality Assumption in the Tobit Model

This paper examines a number of statistics that have been proposed to test the normality assumption in the tobit (censored regression) model. It argues that a number of commonly proposed statistics can be interpreted as different versions of the Lagrange multiplier, or score, test for a common null hypothesis. This observation is useful in examining the Monte Carlo results presented in the paper. The Monte Carlo results suggest that the computational convenience of a number of statistics is obtained at the cost of poor finite sample performance under the null hypothesis.

The repeated application of shift-share: a structural explanation of regional growth?

The views put forward by Fothergill and Gudgin that structural factors account for variation in the growth rates of UK regions, and that such structural factors are identified by the repeated application of shift-share are examined. First, the conditions under which the growth rate of a region can be said to be structurally determined are considered. These conditions are not only restrictive, but are also at odds with the expressed views of those who support such a theory. Second, it is shown that, even if the identified conditions hold, the repeated application of the shift-share technique will lead, in general, to an incorrect measure of the importance of these structural factors. An accurate simple procedure is given as an alternative to shift-share in these circumstances. Last, analysis of variance is considered and it is shown that the assumptions required for this technique to be appropriate are essentially the same as those required for the regional growth rate to be structurally determined. Although the use of analysis of variance is not advocated, it is suggested that it is incorrect for shift-share to be portrayed as a superior alternative.

Factor subsidies, employment generation, and cost per job: a partial equilibrium approach

Factor subsidies in a perfectly competitive setting are analysed. A very general model is used to derive expressions for the effect of a factor subsidy on the price and quantity of output and the two factor inputs. These expressions are differentiated to generate qualitative results for the impact of changes in the product-demand, production-function, and factor-supply parameters on the subsidy effects. A similar procedure is used to investigate the exchequer cost per job of general labour and capital subsidies in an industry with Cobb — Douglas technology. The analysis is relieved with illustrative simulations in which ‘representative’ parameter values are used.

A Note on the Average Density Function in Urban Analysis

It is argued that the density function, commonly used in the study of urban spatial structure, is more appropriately described as the ‘marginal density function’. From such a marginal density function, it is possible to derive two types of average density function, each being concerned with a particular aspect of the spatial structure of population. The first type is consistent with the standard approach to the ‘average’ in economic analysis, while the second more completely takes account of the urban context. The two types of average density function are examined for different underlying forms of the marginal density function. Of the two types, the second has a greater applicability than the first in the analysis of urban spatial structure.

Annual Consumption Functions: A Scottish-UK Comparison, 1971–1985

HOLDEN D. R. and McgREGOR P. G. (1990) Annual consumption functions: a Scottish-UK comparison, 1971–1985, Reg. Studies 24, 247–259. This paper investigates the performance of a number of recently proposed ‘consumption functions’ using annual Scottish and UK data for the period 1971 to 1985. Whilst the exercise is ‘atheoretical’ in the sense that no attempt is made to tie estimated models to specific theories, the influences considered do reflect an underlying conviction that a full understanding of consumption functions ultimately necessitates an integrated framework for modelling household behaviour. In this context a number of recent models may be treated as non-competing and separate investigation of non-durable and durable expenditures may be helpful in evaluating competing explanations of recent consumption behaviour. Data coherent models of non-durable expenditures are obtained, although such specifications proved elusive for durables. Overall, there was some supporting evidence for the intuitive sy...

Testing for heteroskedasticity in the tobit and probit models

Non-constant variance across observations (heteroskedasticity) results in the maximum likelihood estimators of tobit and probit model parameters being inconsistent. Some of the available tests for constant variance across observations (homoskedasticity) are discussed and examined in a small Monte Carlo experiment.

The R&D boundaries of the firm: a problem solving perspective

Abstract This paper considers, theoretically and empirically, how different organization modes are aligned to govern the efficient solving of technological problems. The data set is from the Chinese consumer electronics industry. Following the problem-solving perspective (PSP) within the knowledge-based view (KBV), we develop and test several PSP and KBV hypotheses, whilst controlling for some relevant transaction cost economics and other variables, in an examination of the determinants of the firms’ R&D organization choice. The results show that a firm’s existing knowledge base is the most important explanatory factor. Problem complexity and decomposability are also found to be important, but it is suggested, contrary to the view of PSP, that they are better treated as separate variables, and that equity-based alliances tend to be reserved for the most complex problems.

The Regional Density Function and the Definition of Regional Boundaries

The population density function is usually applied at the level of the urban or metropolitan area. In this chapter, however, it is examined at the scale of the region, namely, an economic region of a nodal (rather than homogeneous) type. The regional density function to be employed has an inverse power form. This is shown to differ significantly from the negative exponential structure typically associated with urban areas. The primary purpose of the investigation is to explore the possibility of using the density function as a means of determining the boundary between adjacent economic regions. Initially, the boundary is examined in terms of a point and then, more conventionally, as a line. After discussing several possible extensions, the results are compared with findings of other theoretical models concerned with the specification of boundaries, but based on wholly different approaches.

Determining the appropriate deflation of nominal magnitudes in the UK consumption function: a non-nested test approach

This paper is concerned with the deflator(s) used to obtain series measured in real terms in ‘the’ consumption function. Since the precise deflator(s) to be used in any particular specification is not uniquely determined by theoretical considerations alone we consider ways of approaching the issue empirically. The starting point is to rearrange any given specification of ‘the’ consumption function so that a nominal consumption variable is explained. This implies that different deflators for consumption, and other variables in the initial specification which are expressed in real terms, define non-nested models. We therefore examine the issue of the appropriate method of deflation used non-nested tests. We consider the Davidson, Hendry, Srba and Yeo specification of the quarterly UK non-durable consumption function and find that the preferred method of deflating consumption and income variables is to use the total (durable and non-durable) consumption deflator. We also examine the quarterly UK consumption ...