Non-nested Hypotheses Research Articles

Testing for short-run money neutrality in a small open economy: The case of Canada

This paper adopts an econometric methodology which is based on standard nested-hypotheses testing in order to test the policy ineffectiveness proposition in the context of the Canadian economy. It thus avoids some problems associated with the non-nested hypotheses framework used by Barro and numerous other writers.

On Point-Optimal Cox Tests

This paper is concerned with the general problem of testing one form of covariance structure against another in a normal linear regression. It is shown that all the point-optimal tests recently proposed by King and his associates can be interpreted as special cases of a Cox test for non-nested hypotheses. This provides a synthesis of a whole range of point-optimal tests as well as demonstrating that King and his associates have exposed a class of Cox tests which have an exact distribution.

Alternative non-nested specification tests of time-series investment models

This paper develops and compares non-nested hypothesis tests for linear regression models with first-order serially correlated errors. It extends the non-nested testing procedures of Pesaran, Fisher and McAleer, and Davidson and MacKinnon, and compares their performance on four conventional models of aggregate investment demand using quarterly U.S. investment data from 1951:I to 1983:IV. The data and the non-nested hypothesis tests initially indicate that none of the models are correctly specified. The tests are also intransitive in their assessments. Before rejecting these conventional models of investment demand, we investigate the small-sample properties of these different non-nested test procedures through a series of Monte Carlo studies. We find that these non-nested tests can have significant finite-sample size and power biases.

Monte Carlo Methodology and the Finite Sample Properties of Statistics for Testing Nested and Non-Nested Hypothesis

Using recently developed Monte Carlo methodology, this paper investigates the effect of dynamics and simultaneity on the finite sample properties of maximum likelihood and instrumental variables statistics for testing both nested and non-nested hypotheses. Numerical-analytical approximations (response surfaces) to the unknown finite sample size and power functions of those statistics are obtained for dynamic one-and two-equation models. The results illustrate the value of asymptotic theory in interpreting finite sample properties and certain limitations for doing so. Two practical finite sample results arise: the F form of the Wald statistic is strongly favored over its chi-squared form; and the effects of "large-sigma" and a small effective sample size are particularly pronounced for Sargan's (1958) instrumental variables statistic and Ericsson's (1983) Cox-type instrumental variables statistic. Re-examining Pesaran and Deaton's (1978) empirical example illustrates the additional information gained from the instrumental variables statistics.

Segmented labour markets and the estimation of wage functions

This paper uses a stratified random sample of private sector employees to estimate wage equations for both the male labour market as a whole and six ‘segments’ of the labour market, segement which are defined with respect to the industry and size characteristics of the employing establishmen. Highly conventional results are obtained when wage equations are estimated for the male labour market as a whole, or within two segements, comprising almost half the survey population. However, one can reject conclusively the hypothesis that the same estimating equation is appropriate for modelling wage determination in all segments and if a ‘human capital’ (HK) model is, within segements, tested against more appropriate alternative hypotheses for wage determination using the Davidson and Mackinnon (1981) methodology for the testing of non-nested hypotheses, the conclusion is that one should reject the HK specification and not reject the alternative. It is therefore argued that the disaggregation of labour market dat...

A note on specification of climate variables in models of population migration.

"In the literature on population migration, increasing attention has been devoted to quality-of-life factors. Measures of temperature (as proxies for climate) have frequently been employed in empirical work regarding the determinants of population migration decisions. A wide range of such specifications have been used, most of which imply restrictions on the preferences of migrants. In this paper, a variety of temperature variable specifications are analyzed and interpreted. Statistical tests for nested and nonnested hypotheses are used to compare and choose among the various specifications." The model is used to analyze interstate migration in the 48 contiguous states of the United States for the period 1975-1980.

Selecting the best linear regression model

In this paper, we apply the model selection approach based on Likelihood Ratio (LR) tests developed in Vuong (1985) to the problem of choosing between two normal linear regression models which are not nested in each other. First we compare our model selection procedure to other model selection criteria. Then we explicitly derive the procedure when the competing linear models are non-nested and neither one is correctly specified. Some simplifications are seen to arise when both models are contained in a larger correctly specified linear regression model, or when at least one competing linear model is correctly specified. A comparison of our model selection tests and previous non-nested hypothesis tests concludes the paper.

The Putty-Clay Perspective on the Capital-Energy Complementarity Debate

This paper argues that capital-energy complementarity is a short-run phenomenon reflecting the fixed ex post nature of factor employment in a putty-clay technology. When an empirical specification is employed that measures firms' ex ante choice of technique, capital and energy are found to be long-run substitutes. However, further analysis of the standard translog and putty-clay models with nonnested hypothesis tests reveals that neither specification is an adequate representation of technology. The results suggest that there is a dynamic adjustment process in the data that is not fully captured in either model. Copyright 1987 by MIT Press.

Global and Partial Non-Nested Hypotheses and Asymptotic Local Power

This paper addresses two related issues in the literature of non-nested hypotheses testing. Firstly, by means of a measure of “closeness” of probability density functions, it shows how any two hypotheses can be placed into the nested and the non-nested categories with the latter category being subdivided further into “globally” and “partially” non-nested hypotheses. Secondly, by emphasizing the distinction between a “local null” and a “local alternative,” the paper shows that only in the case of partially non-nested hypotheses is it possible to specify local alternatives. In this case the paper derives the asymptotic distribution of the Cox test statistic under local alternatives and shows that it is distributed as a normal variate with a mean which is directly related to the measure of “closeness” of the alternative to the null hypothesis.

Statistical inference in non-nested econometric models

The purpose of this paper is to discuss some procedures that are available for testing non-nested (or separate) hypotheses in the statistics and econometrics literature. Since many of these techniques may also be exploited in other disciplines, it is hoped that an elaboration of the principal theoretical findings may make them more readily accessible to researchers in other disciplines. Several simple examples are used to illustrate the concepts of nested and non-nested hypotheses and, within the latter category, “global” and “partial” non-nested hypotheses. Two alternative methods of testing non-nested hypotheses are discussed and contrasted: the first of these is Cox's modification of the likelihood-ratio statistic, and the second is Atkinson's comprehensive model approach. A major emphasis is placed on the role of the Cox principle of hypothesis testing, which enables a broad range of hypotheses to be tested within the same framework. The problem associated with the application of the comprehensive model approach to composite non-nested hypotheses is also highlighted; Roy's union-intersection principle is presented as a viable method of dealing with this problem. Simulation results concerning the finite-sample properties of various tests are discussed, together with an analysis of some attempts to correct the poor size of the Cox and related tests.

Aggregate output with variable rates of utilization of employed factors

Empirical evidence has long shown that output varies more in the short run than do all factor inputs, including employment and hours worked. In such a context, long-run equilibrium involves the choice of average factor proportions and rates of utilization of employed factors, also referred to as operating rates, that minimize total cost of producing the desired level of output. In response to unexpected or temporary changes in demand or costs conditions, optimal temporary equilibrium involves some changes in factor demands coupled with the joint use of pricing and production decisions to make best use of the buffering capacity provided by inventories and factor utilization rates. Applying this framework to aggregate annual data, this paper concentrates on the econometrics of the production or operating rate decision, since the operating rate is the key adjusting variable in the short run. The operating rate decision also reveals most clearly the important consequences of quasi-fixity, and shows how our model contrasts with more conventional treatments. Non-nested hypothesis tests are used to compare the preferred specification with several alternatives.

The Underlying Structure of Nonnested Hypothesis Tests

A comparison between fitted and observed log likelihoods is used to study likelihood ratio statistics for both nested and nonnested hypothesis tests. A study of the geometry involved in the nonnested case clarifies the relationship between Cox's likelihood ratio test and the complete parametric Wald encompassing test of Mizon and Richard. Further it is shown why the asymptotic distribution of these test statistics is sometimes degenerate. Also, a new test statistic is proposed which combines the Cox and Mizon-Richard tests.

The Akaike Likelihood Ratio Index

In 1983, Horowitz proposed the use of an adjusted likelihood ratio index to select between alternative models. We define an alternative index based on the Akaike Information Criterion. The two indices incorporate different degrees-of-freedom corrections to the same measure of goodness-of-fit. The Akaike index favors more parsimonious models. We argue that the Akaike measure is the appropriate criterion for model selection. We utilize Horowitz's results on non-nested hypothesis testing for the new index.

The Encompassing Principle and its Application to Testing Non-Nested Hypotheses

The encompassing principle is used to develop a testing framework which unifies the literature on non-nested testing, allowing analysis of the relationship between alternative tests and in particular enabling asymptotic and finite sample equivalences and identities to be established easily when they exist, as well as embracing nested hypothesis testing. The concept of the implicit null hypothesis of a test is introduced to show that the effective acceptance region for some tests extends beyond the acceptance region corresponding to the null of interest, and so such tests can be inconsistent against fixed alternatives closely related to the nominal null and alternative. The analysis is illustrated by an application to two non-nested linear regression models, and it is shown that the conventional F test, as well as all the one degree of freedom non-nested tests, has an encompassing interpretation, and that the F test is a complete parametric encompassing test.

Post-Stimulation Analysis of Monte Carlo Experiments: Interpreting Pesaran's (1974) Study of Non-Nested Hypothesis Test Statistics

"Monte Carlo experimentation in econometrics helps 'solve' deterministic problems by simulating stochastic analogues in which the analytical unknowns are reformulated as parameters to be estimated." (Hendry (1980) With that in mind, Monte Carlo studies may be divided operationally into three phases: design, simulation, and post-simulation analysis. This paper provides a guide to the last of those three, post-simulation analysis, given the design and simulation of a Monte Carlo study, and uses Pesaran's (1974) study of statistics for testing non-nested hypotheses to illustrate the techniques described. A statistic is derived for testing for significant deviations between the asymptotic and (observed) finite sample properties. Further, that statistic provides the basis for analyzing discrepancies between the finite sample and asymptotic properties using response surfaces. The results for Pesaran's study indicate the value of asymptotic theory in interpreting finite sample properties and certain limitations for doing so. Finally, a method is proposed for adjusting the finite sample sizes of different test statistics so that comparisons of their power may be made. Extensions to other finite sample properties are indicated.

Post-simulation Analysis of Monte Carlo Experiments: Interpreting Pesaran's (1974) Study of Non-nested Hypothesis Test Statistics

Carlo experimentation in econometrics helps 'solve' deterministic problems by simulating stochastic analogues in which the analytical unknowns are reformulated as parameters to be estimated. (Hendry (1980)) With that in mind, Monte Carlo studies may be divided operationally into three phases: design, simulation, and post-simulation analysis. This paper provides a guide to the last of those three, post-simulation analysis, given the design and simulation of a Monte Carlo study, and uses Pesaran's (1974) study of statistics for testing non-nested hypotheses to illustrate the techniques described. A statistic is derived for testing for significant deviations between the asymptotic and (observed) finite sample properties. Further, that statistic provides the basis for analysing discrepancies between the finite sample and asymptotic properties using response surfaces. The results for Pesaran's study indicate the value of asymptotic theory in interpreting finite sample properties and certain limitations for doing so. Finally, a method is proposed for adjusting the finite sample sizes of different test statistics so that comparisons of their power may be made. Extensions to other finite sample properties are indicated.

The underlying structure of nonnested hypothesis tests

A comparison between fitted and observed log likelihoods is used to study likelihood ratio statistics for both nested and nonnested hypothesis tests. A study of the geometry involved in the nonnested case clarifies the relationship between Cox's likelihood ratio test and the complete parametric Wald encompassing test of Mizon and Richard. Further it is shown why the asymptotic distribution of these test statistics is sometimes degenerate. Also, a new test statistic is proposed which combines the Cox and Mizon-Richard tests.

An Evaluation of Alternative Investment Hypotheses Using Non-Nested Tests

Investment is an important determinant of aggregate economic performance in most macroeconomic models. There are, however, quite different hypotheses about the determinants of aggregate investment behavior. Several studies have evaluated the performance of alternative investment models based upon explanatory power and/or predictive ability.' A survey of the results of these studies reveals that, depending on the time period used for the evaluation, and the type of investment spending, the preferred models vary between studies. Unlike previous studies, we evaluate alternative econometric investment models utilizing hypothesis tests based on a structural norm. Because of differences in the theoretical foundations for the investment hypotheses, empirical specifications used for evaluating these hypotheses with available data are non-nested; i.e., the alternative specifications cannot be viewed as special cases of one another. Strictly speaking, the criterion of explanatory power is not correct when non-nested alternatives are being considered and the questions focus on comparative structural specifications. The choice of the most appropriate structure of econometric investment equations is important for two reasons. First, if one is interested in forecasting investment spending, a properly specified model will perform better over time than an improperly specified one. Confidence in model specification reduces the probability that the results are a statistical artifact or a result of spurious time series regressions [6, 202-204]. Second, if one is interested in evaluating the effects of policy changes on investment spending, model specification is crucial.2 Alternative specifications of investment equations have quite different implications for policy changes. For example, a change in the investment tax credit would have no direct impact in an accelerator model. This paper reports results from applying non-nested hypothesis tests to the evaluation of alternative investment models. The issue is which model specification is most appro-

Specification Tests of the Money Demand Function in an Open Economy

This paper addresses empirically the issues of selecting the appropriate opportunity cost and scale variables of the money demand function in the presence of alternative nonnested hypotheses. As part of the process of model specification, the role of currency substitution in the demand for money function in an open economy is examined. The tests are carried out with quarterly data from the open economy of Greece over the floating exchange rate period 1975-82.

Income or Wealth in Money Demand: An Application of Non-Nested Hypothesis Tests

The purpose of this paper to apply the new econometric literature on non-nested hypothesis testing to the issue of whether income or the appropriate scale variable in money demand functions. This important for two reasons. First, as MacKinnon points out empirical work using non-nested hypotheses tests still all but non-existent [11, 106]. Hence this paper helps fill one significant void in the applied econometrics literature. Second, the issue is it income or it wealth an important one, (as explained below) but, unfortunately, an unsettled one. Early research by Chow [1], Laidler [7] and Meltzer [12] that utilized a variety of goodness-of-fit and t tests generally concluded that the appropriate variable. The results of more recent research utilizing the same methodology are mixed. For example, Goldfeld [6] and Lieberman [10] argue income the appropriate variable, while Friedman [3] argues it wealth. The view taken in this paper that even though the argument over the proper scale variable an old one, it remains an important one and deserves to be examined through the prism of new econometric methods. The issue of the relevant scale variable remains important because the money demand function plays a crucial role in both monetary and fiscal policy. On the monetary side, successful implementation of an interest rate approach to money stock control rests on the Federal Reserve's use of the correct money demand function. If the Fed employs a misspecified money demand function, it will not know the federal funds rate that consistent with its money targets and, as a result, will miss those targets. Similarly, money demand plays a crucial role in fiscal policy. If money demand does not depend on wealth, then the often cited portfolio crowding out effect that monetarists claim offsets bond-financed fiscal stimuli [4] non-existent. Hence, even bond financed government purchases are expansionary.