LOCAL ASYMPTOTIC POWER OF THE IM-PESARAN-SHIN PANEL UNIT ROOT TEST AND THE IMPACT OF INITIAL OBSERVATIONS

In this note we derive the local asymptotic power function of the standardized averaged Dickey–Fuller panel unit root statistic of Im, Pesaran, and Shin (2003, Journal of Econometrics, 115, 53–74), allowing for heterogeneous deterministic intercept terms. We consider the situation where the deviation of the initial observation from the underlying intercept term in each individual time series may not be asymptotically negligible. We find that power decreases monotonically as the magnitude of the initial conditions increases, in direct contrast to what is usually observed in the univariate case. Finite-sample simulations confirm the relevance of this result for practical applications, demonstrating that the power of the test can be very low for values of T and N typically encountered in practice.

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ASYMPTOTICALLY UMP PANEL UNIT ROOT TESTS—THE EFFECT OF HETEROGENEITY IN THE ALTERNATIVES

Econometric Theory ◽

10.1017/s0266466614000656 ◽

2014 ◽

Vol 31 (3) ◽

pp. 539-559 ◽

Cited By ~ 5

Author(s):

I. Gaia Becheri ◽

Feike C. Drost ◽

Ramon van den Akker

Keyword(s):

Unit Root ◽

Generalized Least Squares ◽

Applied Economics ◽

Unit Root Tests ◽

Finite Sample ◽

Asymptotic Power ◽

Optimal Tests ◽

Independent Panel ◽

Local Asymptotic Power ◽

Uniformly Most Powerful

In a Gaussian, heterogeneous, cross-sectionally independent panel with incidental intercepts, Moon, Perron, and Phillips (2007, Journal of Econometrics 141, 416–459) present an asymptotic power envelope yielding an upper bound to the local asymptotic power of unit root tests. In case of homogeneous alternatives this envelope is known to be sharp, but this paper shows that it is not attainable for heterogeneous alternatives. Using limit experiment theory we derive a sharp power envelope. We also demonstrate that, among others, one of the likelihood ratio based tests in Moon et al. (2007, Journal of Econometrics 141, 416–459), a pooled generalized least squares (GLS) based test using the Breitung and Meyer (1994, Applied Economics 25, 353–361) device, and a new test based on the asymptotic structure of the model are all asymptotically UMP (Uniformly Most Powerful). Thus, perhaps somewhat surprisingly, pooled regression-based tests may yield optimal tests in case of heterogeneous alternatives. Although finite-sample powers are comparable, the new test is easy to implement and has superior size properties.

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THE IMPACT OF PERSISTENT CYCLES ON ZERO FREQUENCY UNIT ROOT TESTS

Econometric Theory ◽

10.1017/s0266466613000066 ◽

2013 ◽

Vol 29 (6) ◽

pp. 1289-1313 ◽

Cited By ~ 4

Author(s):

Tomás del Barrio Castro ◽

Paulo M.M. Rodrigues ◽

A.M. Robert Taylor

Keyword(s):

Unit Root ◽

Unit Root Test ◽

American Statistical Association ◽

Unit Root Tests ◽

Statistical Association ◽

Finite Sample ◽

Finite Sample Properties ◽

Augmented Dickey Fuller ◽

Frequency Unit ◽

The Impact

In this paper we investigate the impact of persistent (nonstationary or near nonstationary) cycles on the asymptotic and finite-sample properties of standard unit root tests. Results are presented for the augmented Dickey–Fuller (ADF) normalized bias and t-ratio-based tests (Dickey and Fuller, 1979, Journal of the American Statistical Association 745, 427–431; Said and Dickey, 1984; Biometrika 71, 599–607). the variance ratio unit root test of Breitung (2002, Journal of Econometrics 108, 343–363), and the M class of unit-root tests introduced by Stock (1999, in Engle and White (eds.), A Festschrift in Honour of Clive W.J. Granger) and Perron and Ng (1996, Review of Economic Studies 63, 435–463). We show that although the ADF statistics remain asymptotically pivotal (provided the test regression is properly augmented) in the presence of persistent cycles, this is not the case for the other statistics considered and show numerically that the size properties of the tests based on these statistics are too unreliable to be used in practice. We also show that the t-ratios associated with lags of the dependent variable of order greater than two in the ADF regression are asymptotically normally distributed. This is an important result as it implies that extant sequential methods (see Hall, 1994, Journal of Business & Economic Statistics 17, 461–470; Ng and Perron, 1995, Journal of the American Statistical Association 90, 268–281) used to determine the order of augmentation in the ADF regression remain valid in the presence of persistent cycles.

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Comparative Study of the Impact of Oil Rent on Healthcare in Nigeria and Cameroon: A Three Stage Methodical Approach

International Journal of Science and Management Studies (IJSMS) ◽

10.51386/25815946/ijsms-v2i1p107 ◽

2019 ◽

pp. 58-63

Author(s):

EWUBARE, Dennis Brown ◽

OBAYORI, Elizabeth Lizzy

Keyword(s):

Rural Areas ◽

Unit Root ◽

Capital Expenditure ◽

Unit Root Test ◽

Panel Cointegration ◽

Cointegration Test ◽

Panel Unit Root ◽

Long Run ◽

Oil Rents ◽

The Impact

The study comparatively examined the impact of oil rent on healthcare in Nigeria and Cameroon from 1995 to 2015. The objectives of the study are to; study the trend of oil rents and healthcare in Nigeria and Cameroon; examine the relationship between oil rent and healthcare of Nigerians and Cameroonians and determine the impact of mineral rent on the healthcare of Nigeria and Cameroon. To achieve these objectives panel data were collected on health, oil rent and mineral rent and analyzed using the econometric techniques of panel unit root test and panel cointegration test as well as graphical method. The panel unit root and cointegration test showed that all the series are indeed stationary and have long run equilibrium relationship. Comparatively, the graph showed that the rents from oil in Nigeria are lower than that of Cameroon. Also, Cameroon performs better in rents from minerals than Nigeria. Thus, Cameroon capital expenditure on health has steadily increased since 1995 up to 2015 while Nigeria seems not to take healthcare expenditure serious hence the dismal performance in the infant mortality rates. Based on the findings, it is recommended that revenue from oil should be towards inclusive growth, thereby impacting significantly on the healthcare and welfare of the citizens. Thus, there should be investment in primary as well as maternal health in the rural areas for the disadvantaged in society.

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A FIXED-b PERSPECTIVE ON THE PHILLIPS–PERRON UNIT ROOT TESTS

Econometric Theory ◽

10.1017/s0266466612000485 ◽

2012 ◽

Vol 29 (3) ◽

pp. 609-628 ◽

Cited By ~ 9

Author(s):

Timothy J. Vogelsang ◽

Martin Wagner

Keyword(s):

Unit Root ◽

Theoretical Explanation ◽

Unit Root Tests ◽

Nuisance Parameters ◽

Finite Sample ◽

Asymptotic Power ◽

Long Run ◽

Local Asymptotic Power ◽

One Step ◽

The One

In this paper we extend fixed-b asymptotic theory to the nonparametric Phillips–Perron (PP) unit root tests. We show that the fixed-b limits depend on nuisance parameters in a complicated way. These nonpivotal limits provide an alternative theoretical explanation for the well-known finite-sample problems of the PP tests. We also show that the fixed-b limits depend on whether deterministic trends are removed using one-step or two-step detrending approaches. This is in contrast to the asymptotic equivalence of the one- and two-step approaches under a consistency approximation for the long-run variance estimator. Based on these results we introduce modified PP tests that allow for asymptotically pivotal fixed-b inference. The theoretical analysis is cast in the framework of near-integrated processes, which allows us to study the asymptotic behavior both under the unit root null hypothesis and for local alternatives. The performance of the original and modified PP tests is compared by means of local asymptotic power and a small finite-sample simulation study.

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