This paper sets out a general criterion for the identifiability of a statistical system, based on Kullback's integral. It is shown that the general identification problem is equivalent to a maximisation problem, or where parameter restrictions are present, a problem in nonlinear programming. The relationship of this criterion to that based on the of the underlying distribution is also exhibited. THE COLLECTION OF results on the identification problem in econometrics is by now assuming the proportions of an imposing edifice. It is, however, a little surprising to note that this structure has been growing upwards and, more recently, outwards, without a corresponding strengthening in the foundations. It is true that in the case of work on linear simultaneous equation systems (and this, with the work of Koopmans and Reiersol [3] and Chapters 1-4 of Fisher [1] in particular, has almost assumed the status of a classical line of development), these results are founded on a pretty secure rock; to wit, the identifiability of the reduced form in the absence of any singularities in the data matrices. Nevertheless, with the development of other wings on our edifice, it seems desirable to look to more basic things. The recent paper by Thomas Rothenberg [5] provided a welcome attack on this subject. The identifiability of a parametric system is approached via the nonsingularity of R. A. Fisher's information matrix evaluated at the true value of the parameter. The present note generalizes this approach by providing a simple criterion for identifiability, which not only affords an approach to global identification, but also makes no assumptions about the regularity of the underlying distribution. Rothenberg's basic theorem emerges as a simple corollary to this result. The approach has a natural relationship with estimation theory and also provides a straightforward method for delineating the subspace of observationally equivalent parameters in the case of underidentification.

If prices have an allocational role, then in addition to their economic signalling, they may act as a statistical signal for the existence of selection bias in cross-sectional studies with some form of price (wages, rental, yield etc.) as dependent variable. Elements of competitive selection appear in the pricing theory of real or financial assets and in the determination of wage rates, where prices correlate the characteristics of the asset or job with those of the individuals, under the equilibrium allocation. If prices achieve such an allocation, then regressions with price as dependent variable are prima facie "mixed-index" in character, with adverse bias or consistency properties, no matter that the right-hand regressors are apparently exogenous. We set up a paradigm for competitive selection and use the concepts so generated to codify the conditions under which mixed index bias will occur. The problem may be regarded as one of selection bias, but does not necessarily derive from classical simultaneity, and is a problem of data-generation structures rather than sample selection.

Journal Article Non-linearity and Non-stationarity in Dynamic Econometric Models Get access Roger J. Bowden Roger J. Bowden University of Auckland Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 41, Issue 2, April 1974, Pages 173–179, https://doi.org/10.2307/2296711 Published: 01 April 1974

Journal Article Some Implications of the Permanent-Income Hypothesis Get access Roger J. Bowden Roger J. Bowden University of Auckland Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 40, Issue 1, January 1973, Pages 33–37, https://doi.org/10.2307/2296737 Published: 01 January 1973

abstract: the conventional approach to the design of stochastic systems operates, either directly or indirectly, by minimising the variance of the model. this procedure can be regarded as a natural extension of the stability analysis of a deterministic system, according to which the degree of stability is inversely related to the absolute value of its largest characteristic root. very often, however, the policymaker is not indifferent to the frequency composition of economic fluctuations. he may, for example, have a marked dislike for short-term fluctuations. we formalize this notion by setting up a spectral utility function as a criterion for steady-state optimisation, and show that the results from such an optimisation may conflict with those yielded by the conventional approach. large characteristic roots may not necessarily be bad! the scheme of the paper is as follows. because the ideas involved may be unfamiliar we shall spend some time on a rather intuitive motivation for what follows. this is done in section i. in section ii the notion of a spectral utility function is introduced and its evaluation discussed. we then return to the example of section i to give it a more precise treatment. section iii contains extensions, principally to the multivariate case.;

How does the consumer react to uncertainty in his future inconme receipts from human and nonhuman wealth? In answering this question, it is helpful to replace his stochastic life cycle problem with a certaintyequivalent problem in which expectations of future income receipts are adjusted by the subtraction of risk premiums, as a manifestation of risk aversion on the part of the individual. A recent paper by Keizo Nagatani utilizes this idea. B1v supposing the consumer to maximize a lifetime utility function subject to an intertemporal budget constraint in which incomes are replaced by their certaintv equivalents, he shows that with the unfolding of his y-ears, the individual's planned consumption at anv' future date will shift up or down. Thus suppose the consumer is now aged v years and is planning consumption for age t>v. Then Cv(t) will in general differ from Ct(t). However, the risk premiums on uncertain future inconme (from hunman wealth) that Nagatani uses are arbitrarily imposed, or exogenotus to the maximizing problem. This seems wrong. Such premiiiums should reflect not onl the variability of future incomes, but also the individual's reaction to such variability; or in other words, the nature of his intertemporal utility function. Further, there is a prior question of uniqueness; are the risk premliums in each period uniquely defined? To see that this might prove potentially troublesome, imagine a decision problem:

Recently developed methods in the analysis and measurement of latent factor models for time series are utilised to study international business cycles and their relationship to international stockmarket price behaviour. An advantage of these methods is that the duality properties between time domain and frequency domain approaches for investigating the properties of time series can be exploited to identify and model business cycles. The empirical results show that the six countries studied, which include the United States, Australia, Canada, United Kingdom, Germany and Japan, exhibit coherent national business cycles, although these cycles are not all alike. It is also found that international coherence in economic activity has increased in the flexible exchange rate period, although it is not as strong as it is for the national business cycles. The coherence between stockmarket prices and business cycles is not strong, both nationally and internationally, but international stockmarkets appear to show greater mutual coherence than do the corresponding economies.