Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis

This paper derives asymptotic power envelopes for tests of the unit root hypothesis in a zero‐mean AR(1) model. The power envelopes are derived using the limits of experiments approach and are semiparametric in the sense that the underlying error distribution is treated as an unknown infinite‐dimensional nuisance parameter. Adaptation is shown to be possible when the error distribution is known to be symmetric and to be impossible when the error distribution is unrestricted. In the latter case, two conceptually distinct approaches to nuisance parameter elimination are employed in the derivation of the semiparametric power bounds. One of these bounds, derived under an invariance restriction, is shown by example to be sharp, while the other, derived under a similarity restriction, is conjectured not to be globally attainable.     

Consistent Testing of Cointegrating Relationships

In this paper we investigate methods for testing the existence of a cointegration relationship among the components of a nonstationary fractionally integrated (NFI) vector time series. Our framework generalizes previous studies restricted to unit root integrated processes and permits simultaneous analysis of spurious and cointegrated NFI vectors. We propose a modified F‐statistic, based on a particular studentization, which converges weakly under both hypotheses, despite the fact that OLS estimates are only consistent under cointegration. This statistic leads to a Wald‐type test of cointegration when combined with a narrow band GLS‐type estimate. Our semiparametric methodology allows consistent testing of the spurious regression hypothesis against the alternative of fractional cointegration without prior knowledge on the memory of the original series, their short run properties, the cointegrating vector, or the degree of cointegration. This semiparametric aspect of the modelization does not lead to an asymptotic loss of power, permitting the Wald statistic to diverge faster under the alternative of cointegration than when testing for a hypothesized cointegration vector. In our simulations we show that the method has comparable power to customary procedures under the unit root cointegration setup, and maintains good properties in a general framework where other methods may fail. We illustrate our method testing the cointegration hypothesis of nominal GNP and simple‐sum (M1, M2, M3) monetary aggregates.     

Consistent Moment Selection Procedures for Generalized Method of Moments Estimation

This paper considers a generalized method of moments (GMM) estimation problem in which one has a vector of moment conditions, some of which are correct and some incorrect. The paper introduces several procedures for consistently selecting the correct moment conditions. The procedures also can consistently determine whether there is a sufficient number of correct moment conditions to identify the unknown parameters of interest. The paper specifies moment selection criteria that are GMM analogues of the widely used BIC and AIC model selection criteria. (The latter is not consistent.) The paper also considers downward and upward testing procedures. All of the moment selection procedures discussed in this paper are based on the minimized values of the GMM criterion function for different vectors of moment conditions. The procedures are applicable in time-series and cross-sectional contexts. Application of the results of the paper to instrumental variables estimation problems yields consistent procedures for selecting instrumental variables.     

THE ANALYSIS OF OUTLYING DATA POINTS USING ROBUST REGRESSION: A MULTIVARIATE PROBLEM-BANK IDENTIFICATION MODEL*

Because the eight largest bank failures in United States history have occurred since 1973 [24], the development of early-warning problem-bank identification models is an important undertaking. It has been shown previously [3] [5] that M-estimator robust regression provides such a model. The present paper develops a similar model for the multivariate case using both a robustified Mahalanobis distance analysis [21] and principal components analysis [10]. In addition to providing a successful presumptive problem-bank identification model, combining the use of the M-estimator robust regression procedure and the robust Mahalanobis distance procedure with principal components analysis is also demonstrated to be a general method of outlier detection. The results from using these procedures are compared to some previously suggested procedures, and general conclusions are drawn.     

Transition Modeling and Econometric Convergence Tests

A new panel data model is proposed to represent the behavior of economies in transition, allowing for a wide range of possible time paths and individual heterogeneity. The model has both common and individual specific components, and is formulated as a nonlinear time varying factor model. When applied to a micro panel, the decomposition provides flexibility in idiosyncratic behavior over time and across section, while retaining some commonality across the panel by means of an unknown common growth component. This commonality means that when the heterogeneous time varying idiosyncratic components converge over time to a constant, a form of panel convergence holds, analogous to the concept of conditional sigma convergence. The paper provides a framework of asymptotic representations for the factor components that enables the development of econometric procedures of estimation and testing. In particular, a simple regression based convergence test is developed, whose asymptotic properties are analyzed under both null and local alternatives, and a new method of clustering panels into club convergence groups is constructed. These econometric methods are applied to analyze convergence in cost of living indices among 19 U.S. metropolitan cities.     

Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection

The topic of this paper is inference in models in which parameters are defined by moment inequalities and/or equalities. The parameters may or may not be identified. This paper introduces a new class of confidence sets and tests based on generalized moment selection (GMS). GMS procedures are shown to have correct asymptotic size in a uniform sense and are shown not to be asymptotically conservative. The power of GMS tests is compared to that of subsampling, m out of n bootstrap, and “plug‐in asymptotic” (PA) tests. The latter three procedures are the only general procedures in the literature that have been shown to have correct asymptotic size (in a uniform sense) for the moment inequality/equality model. GMS tests are shown to have asymptotic power that dominates that of subsampling, m out of n bootstrap, and PA tests. Subsampling and m out of n bootstrap tests are shown to have asymptotic power that dominates that of PA tests.     

Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis

Seemingly absent from the arsenal of currently available “nearly efficient” testing procedures for the unit root hypothesis, that is, tests whose asymptotic local power functions are virtually indistinguishable from the Gaussian power envelope, is a test admitting a (quasi‐)likelihood ratio interpretation. We study the large sample properties of a quasi‐likelihood ratio unit root test based on a Gaussian likelihood and show that this test is nearly efficient.     

Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis

This paper considers nonstandard hypothesis testing problems that involve a nuisance parameter. We establish an upper bound on the weighted average power of all valid tests, and develop a numerical algorithm that determines a feasible test with power close to the bound. The approach is illustrated in six applications: inference about a linear regression coefficient when the sign of a control coefficient is known; small sample inference about the difference in means from two independent Gaussian samples from populations with potentially different variances; inference about the break date in structural break models with moderate break magnitude; predictability tests when the regressor is highly persistent; inference about an interval identified parameter; and inference about a linear regression coefficient when the necessity of a control is in doubt.     

A Decision Model for the Robot Selection Problem Using Robust Regression*

Industrial robots are increasingly used by many manufacturing firms. The number of robot manufacturers has also increased with many of these firms now offering a wide range of models. A potential user is thus faced with many options in both performance and cost. This paper proposes a decision model for the robot selection problem. The proposed model uses robust regression to identify, based on manufacturers' specifications, the robots that are the better performers for a given cost. Robust regression is used because it identifies and is resistant to the effects of outlying observations, key components in the proposed model. The robots selected by the model become candidates for testing to verify manufacturers' specifications. The model is tested on a real data set and an example is presented.     

THE USE OF MODERATED REGRESSION IN JOB REDESIGN DECISIONS*

This paper describes the use of moderated regression in job redesign decisions. The procedures outlined are intended to augment the job redesign strategy described by Hackman and his colleagues. Different regression models based on a theory of job design are shown to lead to different job redesign decisions. Comparisons are also made between the moderated regression procedures and the more commonly used subgroups analysis.     

Optimal Two‐Sided Invariant Similar Tests for Instrumental Variables Regression

This paper considers tests of the parameter on an endogenous variable in an instrumental variables regression model. The focus is on determining tests that have some optimal power properties. We start by considering a model with normally distributed errors and known error covariance matrix. We consider tests that are similar and satisfy a natural rotational invariance condition. We determine a two‐sided power envelope for invariant similar tests. This allows us to assess and compare the power properties of tests such as the conditional likelihood ratio (CLR), the Lagrange multiplier, and the Anderson–Rubin tests. We find that the CLR test is quite close to being uniformly most powerful invariant among a class of two‐sided tests. The finite‐sample results of the paper are extended to the case of unknown error covariance matrix and possibly nonnormal errors via weak instrument asymptotics. Strong instrument asymptotic results also are provided because we seek tests that perform well under both weak and strong instruments.     

多元长记忆SV模型及其在沪深股市的应用

对多元长记忆随机波动进行建模,并给出了相应的谱似然估计方法以及在多元随机波动模 型框架下分数维协整的检验步骤. 最后用上海和深圳的数据对所给的模型与方法进行了实证检验.     

Testing When a Parameter is on the Boundary of the Maintained Hypothesis

This paper considers testing problems where several of the standard regularity conditions fail to hold. We consider the case where (i) parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and (ii) there may be a nuisance parameter that appears under the alternative hypothesis, but not under the null. The paper establishes the asymptotic null and local alternative distributions of quasi‐likelihood ratio, rescaled quasi‐likelihood ratio, Wald, and score tests in this case. The results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models. Examples treated in the paper are: (i) tests of the null hypothesis of no conditional heteroskedasticity in a GARCH(1, 1) regression model and (ii) tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with (possibly) correlated random coefficients.     

Concepts,Theory, and Techniques ROBUST METHODS: AN ALTERNATIVE APPROACH FOR ANALYZING DATA SETS CONTAINING INFLUENTIAL DATA POINTS

Recent advances in statistical estimation theory have resulted in the development of new procedures, called robust methods, that can be used to estimate the coefficients of a regression model. Because such methods take into account the impact of discrepant data points during the initial estimation process, they offer a number of advantages over ordinary least squares and other analytical procedures (such as the analysis of outliers or regression diagnostics). This paper describes the robust method of analysis and illustrates its potential usefulness by applying the technique to two data sets. The first application uses artificial data; the second uses a data set analyzed previously by Tufte [15] and, more recently, by Chatterjee and Wiseman [6].     

Identification and Estimation of Regression Models with Misclassification

This paper studies the problem of identification and estimation in nonparametric regression models with a misclassified binary regressor where the measurement error may be correlated with the regressors. We show that the regression function is nonparametrically identified in the presence of an additional random variable that is correlated with the unobserved true underlying variable but unrelated to the measurement error. Identification for semiparametric and parametric regression functions follows straightforwardly from the basic identification result. We propose a kernel estimator based on the identification strategy, derive its large sample properties, and discuss alternative estimation procedures. We also propose a test for misclassification in the model based on an exclusion restriction that is straightforward to implement.     

A novel approach to regression analysis for the classification of quality attributes in the Kano model: an empirical test in the food and beverage industry

Since its introduction in the 1980s, Kano's two-dimensional model has become one of the most popular models with which to evaluate quality, finding a place in a wide range of industries. For decades, various approaches to regression analysis have been applied to explore asymmetric and non-linear relationships in the Kano model. Although a number of authors have questioned the use of these regression methods, there has been a lack of validity testing to evaluate their convergence with the results of the Kano questionnaire in classifying quality attributes. This study proposes a novel approach to regression analysis for the classification of quality attributes, including must-be, one-dimensional, attractive, and indifferent categories, as well as mixed-class distribution. Using popular tools and techniques for the measurement of customer satisfaction, the proposed approach is capable of simplifying the process of collecting data making it far easier to implement than the list of functional and dysfunctional questions initiated by Kano. An empirical study of a food and beverage chain showed that the proposed approach is capable of returning acceptable classification results, compared to the Kano questionnaire. A validity test indicated that the proposed approach significantly outperformed dummy variable regression and the moderated regression. In conclusion, the proposed approach provides a more practical implementation, while maintaining classification power on par with the Kano questionnaire.     

Estimating and Testing Structural Changes in Multivariate Regressions

This paper considers issues related to estimation, inference, and computation with multiple structural changes that occur at unknown dates in a system of equations. Changes can occur in the regression coefficients and/or the covariance matrix of the errors. We also allow arbitrary restrictions on these parameters, which permits the analysis of partial structural change models, common breaks that occur in all equations, breaks that occur in a subset of equations, and so forth. The method of estimation is quasi‐maximum likelihood based on Normal errors. The limiting distributions are obtained under more general assumptions than previous studies. For testing, we propose likelihood ratio type statistics to test the null hypothesis of no structural change and to select the number of changes. Structural change tests with restrictions on the parameters can be constructed to achieve higher power when prior information is present. For computation, an algorithm for an efficient procedure is proposed to construct the estimates and test statistics. We also introduce a novel locally ordered breaks model, which allows the breaks in different equations to be related yet not occurring at the same dates.     

Democracy,Redistribution, and Political Participation: Evidence From Sweden 1919–1938

In this paper, we compare how two different types of political regimes—direct versus representative democracy—redistribute income toward the relatively poor segments of society after the introduction of universal and equal suffrage. Swedish local governments are used as a testing ground since this setting offers a number of attractive features for a credible impact evaluation. Most importantly, we exploit the existence of a population threshold, which partly determined a local government's choice of democracy to implement a regression‐discontinuity design. The results indicate that direct democracies spend 40–60 percent less on public welfare. Our interpretation is that direct democracy may be more prone to elite capture than representative democracy since the elite's potential to exercise de facto power is likely to be greater in direct democracy after democratization.     

Applications and Implementation A SIMULATION STUDY OF THE RELATIVE EFFECTIVENESS OF ALTERNATIVE ANALYTICAL REVIEW PROCEDURES*

This paper evaluates the effectiveness of various analytical review (AR) procedures in detecting material errors in account balances. The study tested nine nonstatistical AR procedures based on common heuristic and ratio analyses and four AR procedures based on regression analysis. Simulated account balances were seeded with various magnitudes of errors and each AR procedure was used to detect the errors. It was found that the regression approaches tended to have fewer Type I and Type II errors than other AR procedures.     

TOTAL SETUP LOT SIZING WITH QUANTITY DISCOUNTS*

Often, order quantity decisions are made by purchasers facing a price schedule of quantity discounts. Traditional solution procedures have consisted of the evaluation of total cost at numerous price-break points in search of the lowest total cost. This approach is tedious and not particularly informative, especially when one is faced with lengthy schedules. This paper presents a total setup lot-sizing model that reduces the computations required to find the least-total-cost quantity, given parameters from a supplier's price schedule. The parameters are first obtained by simple regression (graphical or computer) and in themselves can provide valuable insight for the purchaser's decision making. A total setup lot-sizing model is next developed to define a “critical interval” that contains the solution. The model and algorithm are tested under a variety of conditions. Their application offers the decision maker a convenient alternative to determine the best quantity to order from a tendered price schedule.