Testing the specification of multivariate models in the presence of alternative hypotheses

In this paper we propose a non-nested hypothesis test for testing the specification of a multivariate econometric model in the presence of an alternative model which purports to explain the same phenomenon. We demonstrate that the new test statistic tends to minus the same random variable as the CPD test statistic introduced by Pesaran and Deaton (1978), provided that the truth is ‘close’ to the null hypothesis. Since the new test is simpler to compute than the multivariate CPD test, it would seem to be the procedure of choice.     

Error Correction Testing in Panels with Common Stochastic Trends

This paper develops panel data tests for the null hypothesis of no error correction in a model with common stochastic trends. The asymptotic distributions of the new test statistics are derived and simulation results are provided to suggest that they perform well in small samples. Copyright © 2015 John Wiley & Sons, Ltd.     

Bayesian routes and unit roots: De rebus prioribus semper est disputandum

This paper provides detailed responses to the following eight discussants of my paper ‘To criticize the critics: an objective Bayesian analysis of stochastic trends’: Gary Koop and Mark Steel; Edward Learner; In-Moo Kim and G. S. Maddala; Dale J. Poirier; Peter C. Schotman and Herman K. van Dijk; James H. Stock; David DeJong and Charles H. Whiteman; and Christopher Sims. This reply puts new emphasis on the call made in the earlier paper for objective Bayesian analysis in time-series; it underlines the need for a new approach, especially with regard to posterior odds testing; and it draws attention to a new methodology of Bayesian analysis developed in a recent paper by Phillips and Ploberger (1991a). Some new simulations that shed light on certain comments of the discussants are provided; new empirical evidence is reported with the extended Nelson-Plosser data supplied by Schotman and van Dijk; and the new Phillips-Ploberger posterior odds test is given a brief empirical illustration.     

Robust adaptive rate-optimal testing for the white noise hypothesis

A new test is proposed for the weak white noise null hypothesis. The test is based on a new automatic selection of the order for a Box–Pierce (1970) test statistic or the test statistic of Hong (1996). The heteroskedasticity and autocorrelation-consistent (HAC) critical values from Lee (2007) are used, allowing for estimation of the error term. The data-driven order selection is tailored to detect a new class of alternatives with autocorrelation coefficients which can be o(n^−1/2)$o\left(n^{-1/2}\right)$ provided there are sufficiently many of such coefficients. A simulation experiment illustrates the good statistical properties of the test both under the weak white noise null and the alternative.     

Agglomeration and Congestion in the Economics of Ideas and Technological Change

Urban economists have long recognized that space is economically important. Evidence of the importance of urban agglomeration and the offsetting effects of congestion are provided in a number of studies of productivity and wages. Little attention has been paid to this evidence in the economic growth literature. The new growth research focuses on technological change. We extend the production function for new ideas common to this research in a way that allows for congestion and agglomeration in innovation and test the hypothesis that these forces are important in explaining innovation. Strong evidence is found that agglomeration and congestion are important in explaining the vast differences in per capita patent rates across US states. This suggests an important new agenda in linking studies of urban economics with the rapidly advancing field of endogenous growth.     

Testing for a unit root in a random coefficient panel data model

This paper proposes new unit root tests in the context of a random autoregressive coefficient panel data model, in which the null of a unit root corresponds to the joint restriction that the autoregressive coefficient has unit mean and zero variance. The asymptotic distributions of the test statistics are derived and simulation results are provided to suggest that they perform very well in small samples.     

Testing parametric conditional distributions using the nonparametric smoothing method

This paper proposes a new goodness-of-fit test for parametric conditional probability distributions using the nonparametric smoothing methodology. An asymptotic normal distribution is established for the test statistic under the null hypothesis of correct specification of the parametric distribution. The test is shown to have power against local alternatives converging to the null at certain rates. The test can be applied to testing for possible misspecifications in a wide variety of parametric models. A bootstrap procedure is provided for obtaining more accurate critical values for the test. Monte Carlo simulations show that the test has good power against some common alternatives.     

Semiparametric tests of conditional moment restrictions under weak or partial identification

We propose two new semiparametric specification tests which test whether a vector of conditional moment conditions is satisfied for any vector of parameter values θ₀. Unlike most existing tests, our tests are asymptotically valid under weak and/or partial identification and can accommodate discontinuities in the conditional moment functions. Our tests are moreover consistent provided that identification is not too weak. We do not require the availability of a consistent first step estimator. Like Robinson [Robinson, Peter M., 1987. Asymptotically efficient estimation in the presence of heteroskedasticity of unknown form. Econometrica 55, 875–891] and many others in similar problems subsequently, we use k-nearest neighbor (knn) weights instead of kernel weights. The advantage of using knn weights is that local power is invariant to transformations of the instruments and that under strong point identification computation of the test statistic yields an efficient estimator of θ₀ as a byproduct.     

PRACTITIONERS CORNER: Lag Order and Critical Values of a Modified Dickey-Fuller Test

ABSTRACTS This study examines some finite-sample properties of a new modified Dickey-Fuller test, called the DF-GLS test, which has been shown to be more powerful than standard unit-root tests. The study shows the lag order can significantly affect the critical values of the test. This points to the importance of correcting for the lag order effect in implementing the DF-GLS test. Approximate lag-adjusted finite-sample critical values for the DF-GLS test are provided, which can be straightforwardly computed from response surface equations.     

Generating the efficient frontier of a class of bicriteria generalized fractional programming

In this paper, a particular class of bicriteria maximization problems over a compact polyhedron is considered. The first component of the objective function is the ratio of powers of affine functions and the second one is linear. Several theoretical properties are provided, such as the pseudoconcavity of the first criterium of the objective function, the connectedness and compactness of both the efficient frontier and the set of efficient points. The obtained results allow us to propose a new simplex-like solution method for generating the whole efficient frontier; to better clarify the use of the suggested algorithm, several examples are described and the results of a computational test are presented.     

Fluctuation Tests for a Change in Persistence*

In this paper, we develop a set of new persistence change tests which are similar in spirit to those of Kim [Journal of Econometrics (2000) Vol. 95, pp. 97–116], Kim et al. [Journal of Econometrics (2002) Vol. 109, pp. 389–392] and Busetti and Taylor [Journal of Econometrics (2004) Vol. 123, pp. 33–66]. While the exisiting tests are based on ratios of sub‐sample Kwiatkowski et al. [Journal of Econometrics (1992) Vol. 54, pp. 158–179]‐type statistics, our proposed tests are based on the corresponding functions of sub‐sample implementations of the well‐known maximal recursive‐estimates and re‐scaled range fluctuation statistics. Our statistics are used to test the null hypothesis that a time series displays constant trend stationarity [I(0)] behaviour against the alternative of a change in persistence either from trend stationarity to difference stationarity [I(1)], or vice versa. Representations for the limiting null distributions of the new statistics are derived and both finite‐sample and asymptotic critical values are provided. The consistency of the tests against persistence change processes is also demonstrated. Numerical evidence suggests that our proposed tests provide a useful complement to the extant persistence change tests. An application of the tests to US inflation rate data is provided.     

储能电池与检测认证

储能电池是新能源产业链中的重要一环,市场前景良好。本文主要分析了储能电池产业的现状与未来发展趋势、国内外检测认证机构现状,汇总了相关的检测标准与规范,并针对相关关键检测项目,指出了检测试验室建设中需要注意的问题,为相关科技工作者提供参考。     

A non-parametric spatial independence test using symbolic entropy

In the present paper, we construct a new, simple, consistent and powerful test for spatial independence, called the SG test, by using the new concept of symbolic entropy as a measure of spatial dependence. The standard asymptotic distribution of the test is an affine transformation of the symbolic entropy under the null hypothesis. The test statistic, with the proposed symbolization procedure, and its standard limit distribution have appealing theoretical properties that guarantee the general applicability of the test. An important aspect is that the test does not require specification of the W matrix and is free of a priori assumptions. We include a Monte Carlo study of our test, in comparison with the well-known Moran's I, the SBDS (de Graaff et al., 2001) and τ test (Brett and Pinkse, 1997) that are two non-parametric tests, to better appreciate the properties and the behaviour of the new test. Apart from being competitive compared to other tests, results underline the outstanding power of the new test for non-linear dependent spatial processes.     

Testing rational expectations by the use of overidentifying restrictions

A simple econometric test for rational expectations in the case in which unobservable, rationally expected variables appear in a structural equation is presented. Using McCallum's instrumental variable estimator as a base, a test for rational expectations per se and a joint test of rational expectations and hypotheses about the structural equation are presented. The new test is shown to be a new interpretation of Basmann's test of overidentifying restrictions. As an illustration, the hypothesis that the forward exchange rate is the rationally expected future spot exchange rate is tested and rejected.     

Analysis of Intertemporal Efficiency Trends Using Rank Statistics With an Application Evaluating the Macro Economic Performance of OECD Nations

This paper presents two applications of rank statistics to evaluate efficiency performance trends using productive efficiency measures derived through various Data Envelopment Analysis (DEA) models. The paper starts with a discussion of the difficulties in obtaining consistent ranks from DEA efficiency ratings. Next, a procedure is proposed to identify intertemporal performance trends using any one of several possible efficiency measures. Another procedure is then developed to test the stability over time of the rank positions of the analyzed units. For each statistical procedure, a small numerical example involving DEA efficiency measures is provided to illustrate the proposed technique. Finally, the new procedures are applied to data reflecting the macro-economic performance of 17 OECD nations in 1979–1988. The outcomes of the application are discussed and contrasted with previous research in this area.     

The Hausman test and weak instruments

We consider the following problem. There is a structural equation of interest that contains an explanatory variable that theory predicts is endogenous. There are one or more instrumental variables that credibly are exogenous with regard to this structural equation, but which have limited explanatory power for the endogenous variable. Further, there is one or more potentially ‘strong’ instruments, which has much more explanatory power but which may not be exogenous. Hausman (1978) provided a test for the exogeneity of the second instrument when none of the instruments are weak. Here, we focus on how the standard Hausman test does in the presence of weak instruments using the Staiger–Stock asymptotics. It is natural to conjecture that the standard version of the Hausman test would be invalid in the weak instrument case, which we confirm. However, we provide a version of the Hausman test that is valid even in the presence of weak IV and illustrate how to implement the test in the presence of heteroskedasticity. We show that the situation we analyze occurs in several important economic examples. Our Monte Carlo experiments show that our procedure works relatively well in finite samples. We should note that our test is not consistent, although we believe that it is impossible to construct a consistent test with weak instruments.     

Robust trend inference with series variance estimator and testing-optimal smoothing parameter

The paper develops a novel testing procedure for hypotheses on deterministic trends in a multivariate trend stationary model. The trends are estimated by the OLS estimator and the long run variance (LRV) matrix is estimated by a series type estimator with carefully selected basis functions. Regardless of whether the number of basis functions K is fixed or grows with the sample size, the Wald statistic converges to a standard distribution. It is shown that critical values from the fixed-K asymptotics are second-order correct under the large-K asymptotics. A new practical approach is proposed to select K that addresses the central concern of hypothesis testing: the selected smoothing parameter is testing-optimal in that it minimizes the type II error while controlling for the type I error. Simulations indicate that the new test is as accurate in size as the nonstandard test of Vogelsang and Franses (2005) and as powerful as the corresponding Wald test based on the large-K asymptotics. The new test therefore combines the advantages of the nonstandard test and the standard Wald test while avoiding their main disadvantages (power loss and size distortion, respectively).     

A point optimal test for autoregressive disturbances

This paper is concerned with testing for first-order autoregressive disturbances in the linear regression model and recommends an alternative test to the Durbin-Watson test. The new test is most powerful invariant in a given neighbourhood of the alternative hypothesis parameter space. An empirical power comparison indicates that the test is generally more powerful than the Durbin-Watson test. The comparison also suggests that for many economic applications, the difference in power will be small, although circumstances do exist in which the power advantage of the new test is very real. Selected bounds for the test's significance points are tabulated.     

A new test for fourth-order autoregressive disturbances

This paper proposes a new test for simple fourth-order autoregressive disturbances in the linear regression model. The test is shown to be most powerful invariant in a given neighourhood of the alternative hypothesis for all design matrices. An empirical power comparison suggests that the test is generally more powerful than the Wallis test, the difference in power probably being slight for most economic applications, although for certain design matrices, the power advantage of the new test is very real. Selected bounds for the test's significance points are tabulated.     

Autoverkopen en autopark in Nederland, 1950–1970

Summary  This is a study of the demand for the ownership of new or firsthand cars, i.e. the demand of 'first owners' who habitually buy new cars which are then traded in long before they are obsolescent. Upon combining the evidence of various surveys with time-series for 1950-64 it is found that this ownership has an income elasticity of 2 and a price elasticity of – 1.25 in respect of the constant-quality index of new car prices earlier provided. On the average new cars are traded in after three years so that roughly one third of the existing stock is replaced every year. These values together determine an equation for purchases of new cars which accurately predicts new registrations in 1965 and 1966. Projections for the years 1967-70 are provided.
In the model employed the total number of cars (including used cars) is determined by the active demand exerted by 'first owners' on one hand and by the hitherto fairly constant scrappage rates on the other. Projections of the overall ownership rate can therefore be derived from the forecasts of new registrations. The ownership rate will approach 80% around 1970, and it is likely that at that stage the current scrappage rates will cease to apply in view of the greater predilection for comparatively younger cars.