Spurious Rejections Research Articles

Semi-endogenous Versus Schumpeterian Growth Models: A Critical Review of the Literature and New Evidence

Abstract Several studies have tested semi-endogenous versus Schumpeterian growth models using different methodological approaches. This paper critically reviews these studies including their approaches and provides new evidence on this issue, by analyzing both time-series data from the United States and panel data from 19 OECD countries over the period 1980–2014. The review finds much support for Schumpeterian growth theory, but shows that all studies reviewed have several limitations. These limitations include conceptual problems associated with the use of the number/stock of patents as a measure of the flow/stock of knowledge, the possibility of spurious regressions due to non-stationary data, potential mismeasurement of R&D inputs due to possible interpolation and deflation errors, misspecification problems that can arise in difference models when variables are cointegrated, and potential spurious rejections of the unit root hypothesis for R&D intensity when the lag length in unit root tests is too small. The present study avoids these limitations and finds strong evidence in favor of semi-endogenous growth.

Accounting for multiple testing in the analysis of spatio-temporal environmental data

The statistical analysis of environmental data from remote sensing and Earth system simulations often entails the analysis of gridded spatio-temporal data, with a hypothesis test being performed for each grid cell. When the whole image or a set of grid cells are analyzed for a global effect, the problem of multiple testing arises. When no global effect is present, we expect alpha % of all grid cells to be false positives, and spatially autocorrelated data can give rise to clustered spurious rejections that can be misleading in an analysis of spatial patterns. In this work, we review standard solutions for the multiple testing problem and apply them to spatio-temporal environmental data. These solutions are independent of the test statistic, and any test statistic can be used (e.g., tests for trends or change points in time series). Additionally, we introduce permutation methods and show that they have more statistical power. Real-world data are used to provide examples of the analysis, and the performance of each method is assessed in a simulation study. Unlike other simulation studies, our study compares the statistical power of the presented methods in a comprehensive simulation study. In conclusion, we present several statistically rigorous methods for analyzing spatio-temporal environmental data and controlling the false positives. These methods allow the use of any test statistic in a wide range of applications in environmental sciences and remote sensing.

UNIT ROOT TESTS IN THE PRESENCE OF MULTIPLE BREAKS IN VARIANCE

Spurious rejections of the standard Dickey–Fuller (DF) test caused by a single variance break have been reported and some solutions to correct the problem have been proposed in the literature. Kim et al. (2002) put forward a correctly-sized unit root test robust to a single variance break, called the KLN test. However, there can be more than one break in variance in time series data as documented in Zhou and Perron (2008), so allowing only one break can be too restrictive. In this paper, we show that multiple breaks in variance can generate spurious rejections not only by the standard DF test but also by the KLN test. We then propose a bootstrap-based unit root test that is correctly-sized in the presence of multiple breaks in variance. Simulation experiments demonstrate that the proposed test performs well regardless of the number of breaks and the location of the breaks in innovation variance.

Fixed and Recursive Right-Tailed Dickey–Fuller Tests in the Presence of a Break under the Null

AbstractRight-tailed Dickey–Fuller-type unit root tests against the explosive alternative have become popular in economics and finance for detecting asset price bubbles. This paper studies the size properties of fixed sample and recursive right-tailed Dickey–Fuller tests if the relevant series contains a unit root, but a structural break in the drift parameter occurs. It is shown that positive size distortion and therefore spurious rejections of the unit root null hypothesis in favour of the explosive alternative can be a problem for both types of test. Some possible solutions to this problem are briefly discussed.

New empirical evidence on income convergence

This paper aims at providing further evidence on stochastic income convergence for a group of 30 countries over a century long period, from 1900 to 2008, utilizing novel econometric methods for determining structural breaks and unit roots. Recent studies have noted the problem of low power and size distortions in unit root tests, and spurious rejections that plague unit root tests which treat structural breaks asymmetrically. The proposed methodology used in this paper enables robust detection and estimation of breaks, and reliable inference regarding the presence of unit roots conditional on the presence or absence of breaks. We find that the periods of War, the Great Depression and oil price shocks to be possible reasons for the occurrence of breaks. The unit root test results indicate limited evidence of stochastic income convergence. We find none of the current upper-middle-income and lower-middle-income countries to show convergence, while high-income countries such as Australia, Canada, the Netherlands, Norway, Portugal and USA show signs of convergence toward the world average.

Time-series tests of income convergence with two structural breaks: evidence from 29 countries

This article uses data on real per capita incomes from 1900 to 2001 to test for stochastic convergence in a diverse group of 29 countries. We utilize LM unit root tests to endogenously determine the number and location of structural breaks for each country. These tests avoid spurious rejections that can occur in Dickey–Fuller-type endogenous break tests used in many previous studies. We find significant evidence that incomes are stochastically converging in 23 of the countries, with World War II most often identified as the time period of structural breaks.

The effect of a variance shift on the Breusch–Godfrey's LM test

In this article, we study the impact of an abrupt change in variance on the Breusch–Godfrey's LM test for autocorrelation. It is demonstrated by Monte Carlo simulations that a break in variance can generate spurious rejections of the null hypothesis of no serial correlation. Hence, a researcher might conclude that the error terms are serially correlated when in fact the contrary is true. It has been found that the likelihood of making this mistake depends on three factors: (i) break size, (ii) break location and (iii) the number of lagged terms included in the LM test.

Spurious Rejections with Endogenous Break Unit Root Tests in the Presence of Outliers and Breaks

Unit root tests with structural break developed by Zivot and Andrews (1992) and Perron and Rodriguez (2003) in the presence of additive outliers and breaks are studied by simulation experiments. The results show that the Zivot–Andrews test appears to have size distortions due to the additive outliers whereas the Perron–Rodriguez test exhibits good properties of size and power. However, the two tests are biased when a second break is present but not taken into account. Furthermore, these endogenous break unit root tests tend to determine the break point incorrectly at one period behind the true break point, leading to spurious rejections of the unit root null hypothesis.

New innovational outlier unit root test with a break at an unknown time

The Perron test which is based on a Dickey–Fuller test regression is a commonly employed approach to test for a unit root in the presence of a structural break of unknown timing. In the case of an innovational outlier (IO), the Perron test tends to exhibit spurious rejections in finite samples when the break occurs under the null hypothesis. In the present paper, a new Perron-type IO unit root test is developed. It is shown in Monte Carlo experiments that the new test does not over-reject the null hypothesis. Even for the case of a level and slope break for trending data, the empirical size is near its nominal level. The test distribution equals the case of a known break date. Furthermore, the test is able to identify the true break date very accurately even for small breaks. As an application serves the Nelson–Plosser data set.

For which countries did PPP hold? A multiple testing approach

We employ a multiple testing technique to identify the countries for which purchasing power parity (PPP) held over the last century. The approach controls the multiplicity problem inherent in simultaneously testing for PPP on several time series, thereby avoiding spurious rejections. It has higher power than traditional multiple testing techniques by exploiting the dependence structure between the countries with a bootstrap approach. Our results show that, plausibly, thus controlling for multiplicity leads to a number of rejections of the null that is intermediate between that of traditional multiple testing techniques and that which results if one tests the null on each single time series at some level α.

Co-integration testing using local-to-unity detrending: the impact of structural change under the null

In recent research, Perron and Rodriguez [Perron, P. and Rodriguez, G., 2006, Residual based tests for cointegration with GLS detrended data. Econometric Theory, in press.] have shown the use of local-to-unity detrending via generalised least squares to increase the power of the Engle–Granger [Engle, R. and Granger, C., 1987, Cointegration and error correction: representation, estimation and testing. Econometrica, 55, 251–276.] test for co-integration. In this paper, the properties of the resulting test are examined in the presence of structural change under the null hypothesis. The results of Monte Carlo experimentation show the test to possess very different properties to those noted in the literature previously by Leybourne and Newbold [Leybourne, S. and Newbold, P., 2003, Spurious rejections by co-integration tests induced by structural breaks. Applied Economics, 35, 1117–1121.] for the Engle–Granger and Johansen tests. The findings obtained show the extent of oversizing exhibited by the presence of level breaks to be substantially smaller than that of alternative co-integration tests. Furthermore, the results obtained for trend breaks are in stark contrast to those for alternative tests, with the oversizing noted for the Engle–Granger and Johansen tests replaced by undersizing for the test. In summary, the present analysis shows the test to be far less prone to the problem of spurious co-integration than previously examined tests.

Multiple Comparison Procedures, Trimmed Means And Transformed Statistics

Multiple Comparison Procedures, Trimmed Means And Transformed Statistics

Testing the Null of Co‐integration in the Presence of Variance Breaks

Abstract. We show that changes in the innovation covariance matrix of a vector of series can generate spurious rejections of the null hypothesis of co‐integration when applying standard residual‐based co‐integration tests. A bootstrap solution to the inference problem is suggested which is shown to perform well in practice, redressing the size problems associated with the standard test but not losing power relative to the standard test under the alternative.

Taxation with Representation: Intergovernmental Grants in a Plebiscite Democracy

Economic theory predicts that unconditional intergovernmental grant income and private income are perfectly fungible. Despite this prediction, the literature on fiscal federalism documents that grant and private income are empirically non-equivalent. A large scale school finance reform in New Hampshire -- the typical school district experienced a 200 percent increase in grant income -- provides an unusually compelling test of the equivalence prediction. Most theoretical explanations for non-equivalence focus on mechanisms which produce public good provision levels which differ from the decisive voter's preferences. New Hampshire determines local public goods provision via a form of direct democracy -- a setting which rules out these explanations. In contrast to the general support in the literature for non-equivalence, the empirical estimates in this paper suggest that approximately 92 cents per grant dollar are spent on tax reduction. These results not only document that equivalence holds in a setting with a strong presumption that public good provision decisions reflect the preferences of voters, but also directly confirm the prediction of the seminal work of Bradford and Oates (1971) that lump-sum grant income is equivalent to a tax reduction. In addition, the paper presents theoretical arguments that grant income capitalization and heterogeneity in the marginal propensity to spend on public goods may generate spurious rejections of the equivalence prediction. The heterogeneity argument is confirmed empirically. Specifically, the results indicate that lower income communities spend more of the grant income on education than wealthier communities, a finding interpreted as revealing that the Engel curve for education is concave.

Revisiting the Martingale Hypothesis for Exchange Rates

Many structural models have attempted to explain the behaviour of exchange rates under the floating rate regime. Meese and Rogoff (1983) found that a random walk model performs at least as well as various structural and time series models for exchange rates in terms of out-of-sample forecast. But, the random walk model is often rejected when the variance-ratio test is employed. In this paper, we attempt to resolve these apparently contradictory empirical findings. Our view is that (i) when a model successfully passes a battery of independent out-of-sample tests, it is likely to describe the true process, and (ii) apart from the fact that the variance-ratio test is inherently an in-sample test, it might be possible that researchers fail to take into account all the relevant characteristics of the process when conducting the variance-ratio test. One characteristic we will focus on in this paper is possible structural breaks in the exchange rate process. We consider a simple random walk process, a special case of the Martingale model, which exhibits a deterministic break in its drift term, for instance, from positive to negative. This particular example can be a plausible model for a time series on exchange rates which displays a persistent currency appreciation period followed by a long depreciation era. We demonstrate both theoretically and by simulation that when the standard variance-ratio test is applied to this process, the phenomenon of spurious rejections of the Martingale hypothesis can occur. We discuss some implication of this finding on the previously uncovered empirical evidence against the Martingale hypothesis for exchange rates. We propose a modification of the variance-ratio test taking into account structural breaks in the process. We have found that the standard tests strongly reject the Martingale hypothesis while our tests do not. Our empirical findings strongly indicate that rejecting the Martingale hypothesis by the standard variance-ratio tests might have been induced by failing to incorporate structural breaks into the testing procedure.

Testing for ARCH in the Presence of Nonlinearity of Unknown Form in the Conditional Mean

Tests of ARCH are a routine diagnostic in empirical econometric and financial analysis. However, it is well known that misspecification of the conditional mean may lead to spurious rejections of the null hypothesis of no ARCH. Nonlinearity is a prime example of this phenomenon. There is little work on the extent of the effect of neglected nonlinearity on the properties of ARCH tests. This paper provides some such evidence and also new ARCH testing procedures that are robust to the presence of neglected nonlinearity. Monte Carlo evidence shows that the problem is serious and that the new methods alleviate this problem to a very large extent.

Spurious rejections by cointegration tests induced by structural breaks

The effects on three cointegration tests are examined when the series analysed are independent integrated processes, each with a structural break. Although there are differences in detail among the tests, the results indicate in all cases that, when structural breaks are neglected in the analysis, spurious rejections, indicating the presence of cointegration, can occur.

Unit root tests with a break in innovation variance

Abstract It is shown that an abrupt change in the innovation variance of an integrated process can generate spurious rejections of the unit root null hypothesis in routine applications of Dickey–Fuller tests. We develop and investigate modified test statistics, based on unit root tests of Perron for a time series with a changing level, or changing intercept and slope, which are applicable when there is a change in innovation variance of an unknown magnitude at an unknown location.

Seasonal unit root tests with seasonal mean shifts

This paper analyses additive outlier and innovational outlier tests for seasonal unit roots when seasonal mean shifts occur under the null hypothesis. When the magnitude of the breaks is large, simulation evidence reveals that, for three of the four testing procedures considered, the endogenously determined break point can be incorrectly estimated, resulting in spurious rejections of the null. A simple modification to one of the testing approaches is proposed which achieves a substantial improvement in test size.

Break Point Estimation and Spurious Rejections With Endogenous Unit Root Tests

This paper examines the accuracy of break point estimation using the endogenous break unit root tests of Zivot and Andrews (1992) and Perron (1997). We find that these tests tend to identify the break point incorrectly at one‐period behind (TB‐1) the true break point (TB), where bias in estimating the persistence parameter and spurious rejections are the greatest. In addition, this outcome occurs under the null and alternative hypotheses, and more so as the magnitude of the break increases. Consequences of utilizing these endogenous break tests are similar to (incorrectly) omitting the break term Bt in Perron's (1989) exogenous test.