Pitfalls of testing non-nested hypotheses by the lagrange multiplier method

In applied research in econometrics a general model determined from the current knowledge of economic theory often establishes a ‘natural’ method of embedding a number of otherwise non-nested hypotheses. Under these circumstances, significant tests of various hypotheses can be carried out within the classical framework, and tests of non-nested or separate families of hypotheses do not require development of new statistical methods. The application of some suitable variant of likelihood ratio testing procedure will be quite appropriate.There are, however, many ocassions in applied econometrics where the hypotheses under consideration are intended to provide genuine rival explanations of the same given phenomenon and the state of economic theory is not such as to furnish us with a general model that contains both of the rival hypotheses in a ‘natural’ and theoretically consistent manner. A number of investigators have advocated that even when a ‘natural’ comprehensive model containing both of the hypotheses under consideration cannot be obtained from theoretical considerations, it is still appropriate to base significant tests of non-nested hypotheses upon a combined model ‘artificially’ constructed from the rival alternatives. Moreover, in a recent paper on the application of Lagrange Multiplier (LM) tests to model specification, T.S. Breusch and A.R. Pagan (1980) have claimed that Cox's test statistic is connected to an LM or ‘score’ statistic derived from the application of the LM method to an exponentially combined model earlier employed by A.C. Atkinson (1970).Although the use of ‘artificially’ constructed comprehensive models fortesting separate families of hypotheses is analytically tempting, nevertheless it is subject to two major difficulties. Firstly, in many cases of interest in econometrics, the structural parameters under the combined hypothesis are not identified. Secondly, the log likelihood function of the artificially constructed model has singularities under both the null and alternative hypotheses.The paper firstly examines the derivation of LM statistics in the case of non-nested hypotheses and shows that Atkinson's general test statistic, or Breusch and Pagan's result, can be regarded as an LM test if the parameters of the alternative hypothesis are known. The paper also shows that unless all the parameters of the combined models are identified, no meaningful test of the separate families of the hypotheses by the artificial embedding procedure is possible, and in the identified case an expression for the LM statistic which avoids the problem of the singularity of the information matrix under the null and the alternative hypotheses is obtained.The paper concludes that none of the artificially embedding procedures are satisfactory for testing non-nested models and should be abandoned. It, however, emphasizes that despite these difficulties associated with the use of artificial embedding procedures, Cox's original statistic (which is not derived as an LM statistic and does not depend on any arbitrary synthetic combination of hypotheses) can still be employed as a useful procedure for testing the rival hypotheses often encountered in applied econometrics.     

Pitfalls of testing non-nested hypotheses by the lagrange multiplier method

The paper considers the problem of testing non-nested hypotheses by the application of the Lagrange Multiplier (LM) method to an exponentially combined likelihood function. It shows that the general test statistic derived by Atkinson (1970) and later by Breusch and Pagan (1980) can be regarded as an LM statistic only if it can be assumed that the parameters of the alternative model are known. When none of the parameters are known, the paper shows that a straightforward application of the LM method to testing non-nested hypotheses breaks down and it discusses the reasons for this failure.     

A lagrange multiplier interpretation of disturbance estimators with an application to testing for nonlinearity

This paper describes a Lagrange multiplier interpretation of LUF disturbance estimators and an associated means of constructing residuals and procedures for testing for certain kinds of misspecification. Together with a recent technique for partially ordering multivariate data, the methods are used to devise an F test for nonlinearity in some or all of the explanatory variables in multiple regression. Unlike several alternatives, the proposed test does not require all misspecified variables to be positively correlated. Power computations, and comparisons with other procedures, yield encouraging results.     

A test for randomness in behaviour

In biological analysis of behaviour, transition matrices occur of which the diagonal entries are essentially zero. For such transition matrices, a model of randomness is constructed, with a test for the hypothesis that this model holds.     

The effects of multiplier shifts in a hierarchical city-size model

Hierarchical city-size models based upon the tenets of central place theory have recently become an important research topic in urban-regional economics. It is the aim of this paper to examine one such model in a comparative statics framework. Some general policy considerations follow the analysis.     

The power of the Durbin-Watson test for regressions without an intercept

In the linear regression model without an intercept, the limiting power of the Durbin–Watson test (as correlation among errors increases) is shown to take only one of two values. This is either one or zero, depending on the underlying regressor matrix. Some examples and a simple rule to decide from a given regressor matrix which of these cases applies are also given.     

轮对电机磨合试验台测试系统的研发

电机在装车前,需对其进行性能测试,检测其相关参数是否正常,如电压、电流、转速、温度等。传统的办法是给电机上电后,通过电压表和电流表观测其工作电压和电流,用手持式测速仪测试电机转速等,这种肉眼观察的测量方式存在准确性与实时同步性的误差,给测试书面分析报告带来巨大的困难。为解决上述问题,文章研制了一套轮对电机磨合试验台测试装置,该装置由触摸屏、单片机、传感器(电压传感器、电流传感器、光电编码器、温度传感器)、信号处理电路板等器件组成,测量精度高,实时同步性强,更能完成数据自动记录,自动打印数据报告。其各项性能指标都能达到设计目标,能满足现场实际要求。     

The discrepancy distribution of stationary multiplier rules for rounding probabilities

The problem of rounding finitely many (continuous) probabilities to (discrete) proportions N _i/n is considered, for some fixed rounding accuracy n. It is well known that the rounded proportions need not sum to unity, and instead may leave a nonzero discrepancy D=(∑N _i) −n. We determine the distribution of D, assuming that the rounding function used is stationary and that the original probabilities follow a uniform distribution. Received: April 1999     

Shortages in an ageing labour market: an analysis of employers' behaviour

Different policies are being promoted to increase the labour supply in ageing labour markets. This article presents the results of a large-scale survey carried out among Dutch employers into their management of the constraints presented by a tight labour market. Organizations take different measures in response to staff shortages, which can in fact be distinguished as four strategies. The first relates to the recruitment of new groups of workers: groups that traditionally were perhaps not a preferred choice. The principal measures in this strategy are the recruitment of women and ethnic workers, and to a lesser extent the elderly. The second strategy focused on increasing the labour supply of existing workers. Overtime, encouraging part-timers to work extra hours and a structural increase in the length of the working week were part of this strategy. The measures constituting the third strategy were of a different type. Generally, these measures were adopted in order to cope with temporary peaks. Work was outsourced, a recruitment agency used, and higher wages offered to try to fill a vacancy. The fourth strategy focused on substituting technology/capital for labour. Regression analyses is carried out to explain which strategies organizations use to deal with shortages.     

Identifying interdependent behaviour in an empirical model of labour supply

In this paper we test a particular form of interdependent behaviour, namely the hypothesis that individuals' choices of hours of work are influenced by the average hours of work in a social reference group. There are problems in empirically disentangling the effects of interdependent behaviour and preference variation across groups. We show that panel data or data from several points in time are needed. In the empirical analysis we combine cross-section data from 1973, 1980, and 1990. Our results support the hypothesis of interdependent behaviour. The implication is that conventional tax policy predictions, in which preference interdependencies are neglected, will tend to underestimate the effect of a tax reform on hours of work. Our point estimates suggest that conventional calculations would capture only about a third of the actual change in hours of work. Copyright © 1999 John Wiley & Sons, Ltd.     

Status inconsistency: an antecedent to bullying behaviour in groups

This paper draws on frameworks developed by the strategic international human resource management (HRM) literature to analyse human resource practices in foreign-invested enterprises in China and their affiliates. It argues that such strategies can be best understood in the context of global commodity chains. Drawing on data from a study of 27 China-based enterprises in two industries, garments and consumer electronics, it contests that strategy is a good determinant of HRM policies. Moreover, most of the enterprises are following cost reduction strategies but with certain quality levels, based on standardized mature products and production processes. Industry sector is also important, as is the institutional milieu of China.     

Armax model specification testing,with an application to unemployment in the Netherlands

In this paper we present a consistent standard normal model specification test for ARMAX models. The null hypothesis is that the ARMAX model represents the conditional expectation of the dependent variable relative to the entire past of the economic vector time series process under review. This null is tested against the general alternative hypothesis that the null is false. The test is applied to testing the rational expectations-natural rate (RE-NR) hypothesis for the Netherlands according to the approach of Sargent (1976). It appears that RE-NR hypothesis has to be rejected.     

Public service motivation and customer service behaviour: testing the mediating role of emotional labour and the moderating role of gender

ABSTRACT

Prior research indicates that public service motivation (PSM) provides a motivational base for effective emotion regulation. This study extends this body of research by investigating how service workers in different gender groups regulate their emotions during service transactions. Analysis of survey data from public service workers in Thailand showed that ‘deep acting’ is the primary emotional labour strategy-linking PSM and customer service behaviour (CSB), whereas ‘surface acting’ does not play a mediating role. The results further revealed that PSM has a stronger association with male workers’ CSB only via deep acting. Theoretical and practical contributions are discussed.     

Different orders of one-sided scale elasticities in multi-output production

In this paper we explore properties of different orders of one-sided scale elasticities in multi-input multi-output production using the theoretical framework developed by Hadjicostas and Soteriou (Eur J Oper Res 168:425–449, 2006), Krivonozhko et al. (J Oper Res Soc 55:1049–1058, 2004), and others. That framework includes as a special case the well-known operations research method of data envelopment analysis (DEA). A special case of the theory in this paper is the Banker-Morey (Oper Res 34:513–521, 1986a) DEA model for data that include both discretionary and non-discretionary inputs and outputs. Several inequalities among different orders of one-sided scale elasticities are presented. An example is used to illustrate many of the results and ideas of the paper. Finally, we show how the theory and results of this paper can be used to shed some light on implicit Hicks input technical change.     

The effect of unions on the innovative behaviour of firms in Canada

Survey data on a sample of Canadian establishments are used to examine the influence of unions on technological change. The analysis indicates that unionism is not a significant determinant of the rate of technological change. However, union presence does appear to affect the way in which innovation takes place.     

Type I error and test power of different tests for testing interaction effects in factorial experiments

A simulation study was conducted to investigate the effect of non normality and unequal variances on Type I error rates and test power of the classical factorial anova F‐test and different alternatives, namely rank transformation procedure (FR), winsorized mean (FW), modified mean (FM) and permutation test (FP) for testing interaction effects. Simulation results showed that as long as no significant deviation from normality and homogeneity of the variances exists, generally all of the tests displayed similar results. However, if there is significant deviation from the assumptions, the other tests are observed to be affected at considerably high levels except FR and FP tests. As a result, when the assumptions of factorial anova F‐test are not met or, in the case those assumptions are not tested whether met, it can be concluded that using FR and FP tests is more suitable than the classical factorial anova F‐test.     

Drug testing in the transportation industry: The maritime case

The maritime industry provides an interesting case study of the design and implementation of drug-testing programs in the transportation industry during the 1980s. It is clear that such programs were designed and implemented less because of empirical evidence of safety problems than for political reasons. The results in the maritime industry are indicative of a program that is expensive to operate, intrusive with regard to employee privacy, and which will have little or no impact on safety. Focusing such programs on the issue of impairment rather than on the issue of drug usage per se is likely to improve the outcome of the programs. Although, despite common belief, there is little evidence that drug usage or the “drug problem” in U.S. society as a whole had gotten worse in the preceding years (Schonsheck, 1989, 250–251).