Advanced

Testing Homogeneity and Unit Root Restrictions in Panels

Blomquist, Johan LU (2012) In Lund Economic Studies
Abstract (Swedish)
Popular Abstract in Swedish

Denna avhandling består av sex kapitel. Det första kapitlet är en introduktion medan de resterande fem innehåller avhandlingens huvudsakliga bidrag. De tre första kapitlen är samförfattade med Joakim Westerlund.



Kapitel två har sin utgångspunkt i Westerlund (Empirical Economics 37:517-531, 2009) som visar på en svaghet i det populära LLC (Levin et al. Journal of Econometrics 98:1-24, 2002) testet för enhetsrötter. Westerlund (2009) visar att styrkan hos LLC testet kan vara mycket låg och starkt beroende av hur korrigeringen för autokorrelation sker. I kapitel två föreslås därför ett alternativt test. Genom att utföra stokastiska simuleringar undersöks egenskaperna hos de båda... (More)
Popular Abstract in Swedish

Denna avhandling består av sex kapitel. Det första kapitlet är en introduktion medan de resterande fem innehåller avhandlingens huvudsakliga bidrag. De tre första kapitlen är samförfattade med Joakim Westerlund.



Kapitel två har sin utgångspunkt i Westerlund (Empirical Economics 37:517-531, 2009) som visar på en svaghet i det populära LLC (Levin et al. Journal of Econometrics 98:1-24, 2002) testet för enhetsrötter. Westerlund (2009) visar att styrkan hos LLC testet kan vara mycket låg och starkt beroende av hur korrigeringen för autokorrelation sker. I kapitel två föreslås därför ett alternativt test. Genom att utföra stokastiska simuleringar undersöks egenskaperna hos de båda testen och resultaten visar att det nya testet har överlägset bättre styrka. Vi illustrerar nyttan med det nya testet genom att analysera köpkraftsparitetsteoremet för växelkurser.



I kapitel tre fortsätter vi analysen av paneldatatest för enhetsrötter. I detta kapitel analyserar vi PANIC (Bai and Ng Econometrica 72:1127-1177, 2004) som är ett av litteraturens mest generella och populära test. Ett problem med PANIC testet är att det förutsätter att forskaren vet om en deterministisk trend ska vara med i modellen eller inte, vilket i många fall är ett orealistiskt antagande. Målet med kapitel tre är att generalisera PANIC testet så att det kan implementeras utan förkunskap om en eventuell deterministisk trend.



I kapitel fyra analyserar vi svensk brottslighet med hjälp av data över antalet rapporerade brott i de svenska länen över tidsperioden 1975 till 2010. Vi fokuserar på utvecklingen över tiden och samvariationen mellan länen. Våra resultat indikerar att de tre brottstyperna i fokus (stöld, inbrottsstöld och stöld av fordon) är icke-stationära och kointegrerade mellan länen. Detta implicerar att traditionella paneldata metoder inte bör användas för att analysera orsakerna bakom brottsligheten. Vi avslutar kapitlet med att analysera sambandet mellan arbetslöshet och brottslighet med hjälp av nya estimeringsmetoder som kan hantera att variablerna är icke-stationära och kointegrerade. Resultaten indikerar att det inte finns något samband mellan arbetslöshet och de tre brottstyper som undersöks.



I kapitel fem föreslås en ny metod för att testa om lutningsparametrarna i en paneldatamodell är lika för alla enheter i panelen (homogenitetstest). Det nya testet är en generalisering av det test som föreslagits av Pesaran and Yamagata (Journal of Econometrics 142:50–93, 2008) och kan användas i paneler där residuerna är autokorrelerade och/eller heteroskedastiska. Testets asymptotiska fördelning härleds och simuleringsresultaten visar att det nya testet har goda egenskaper jämfört med andra test.



Kapitel sex fördjupar analysen i kapitel fem genom att föreslå ett homogenitetstest som kan användas då residuerna uppvisar både autokorrelation och tvärsnittsberoende. Kapitlet föreslår också ett nytt sekventiellt test som möjliggör en gruppering av enheter, där lutningsparametrarna är lika inom en grupp men skiljer sig mellan grupper. Testens asymptotiska fördelningar härleds och en bootstrap-algoritm för att ta fram kritiska värden presenteras. Simuleringsresultaten visar att de nya testen fungerar väl, även i små stickprov. (Less)
Abstract
This thesis is divided into two distinct parts. The first part contains three chapters, co-authored with Joakim Westerlund, that deal with the analysis of unit root testing, and the second part consists of two chapters on slope homogeneity testing.



Chapter 2 continues and extends the analysis in Westerlund (Empirical Economics 37:517–531, 2009), who demonstrates that the performance of the popular LLC (Levin et al., Journal of Econometrics 98:1–24, 2002) panel unit root test depends critically on the choice of lag truncation used when correcting for serial correlation, and that it is only when this parameter is set as a function of time that the power raises above size. The purpose Chapter 2 is to propose a modified test... (More)
This thesis is divided into two distinct parts. The first part contains three chapters, co-authored with Joakim Westerlund, that deal with the analysis of unit root testing, and the second part consists of two chapters on slope homogeneity testing.



Chapter 2 continues and extends the analysis in Westerlund (Empirical Economics 37:517–531, 2009), who demonstrates that the performance of the popular LLC (Levin et al., Journal of Econometrics 98:1–24, 2002) panel unit root test depends critically on the choice of lag truncation used when correcting for serial correlation, and that it is only when this parameter is set as a function of time that the power raises above size. The purpose Chapter 2 is to propose a modified test that does not suffer from this drawback. The new test is not only simpler to compute but also superior in terms of small-sample performance, which is illustrated using as an example purchasing power parity for less developed countries.



Chapter 3 considers panel unit root testing when there is uncertainty about the deterministic trend. In doing so, it takes PANIC (Bai and Ng, Econometrica 72:1127-1177, 2004), one of the most general and popular panel unit root tests, and demonstrates how it can be modified to determine the extent of both the deterministic trend and non-stationarity of the data.



Chapter 4 offers an in-depth analysis of the dynamic and cross-sectional properties of crime using data covering 21 Swedish counties from 1975 to 2010. The results suggest that the crimes considered are non-stationary, and that this cannot be attributed to county-specific disparities alone, but that there are also a small number of common stochastic trends to which groups of counties tend to revert. With this result in mind, we investigate the relationship between unemployment and crime using novel panel cointegration techniques. Overall, the results do not support cointegration, and suggest that previous findings of a significant relationship between unemployment and crime might be spurious.



Chapter 5 proposes a test of slope homogeneity for panel data models that is robust to unspecified error serial dependence and heteroscedasticity. The proposed test is an adjusted version of the dispersion-type test suggested by Pesaran and Yamagata (Journal of Econometrics 142, 50–93, 2008) and is shown to have a standard normal distribution, as N, T → ∞. Using Monte Carlo experiments, it is demonstrated that the proposed test performs well in small samples, even when the degree of serial dependence is large.



Chapter 6 considers the issue of slope homogeneity testing in panel data models with non-spherical errors. It proposes a bootstrap test of the slope homogeneity hypothesis that is robust to cross-sectional and serial dependence in the errors. The chapter also proposes a bootstrap sequential test that enables differentiation between units with a common slope coefficient vector and units for which the hypothesis of equal slope coefficients fails. Asymptotic properties of the bootstrap tests are derived by letting the time series dimension of the panel increase to infinity, and a small Monte Carlo study is conducted to investigate the small-sample properties. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Kongsted, Hans Christian, University of Copenhagen
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Non-stationary panels, Panel unit root tests, Cross-sectional dependence, Homogeneity testing
in
Lund Economic Studies
pages
178 pages
defense location
EC3:211, Holger Crafoords Ekonomicentrum, Tycho Brahes väg 1
defense date
2012-06-11 10:15
language
English
LU publication?
yes
id
a8e9fdd2-0d25-47d2-8f25-c1ebaa2ae89f (old id 2540994)
date added to LUP
2012-05-16 11:04:52
date last changed
2016-09-19 08:45:17
@misc{a8e9fdd2-0d25-47d2-8f25-c1ebaa2ae89f,
  abstract     = {This thesis is divided into two distinct parts. The first part contains three chapters, co-authored with Joakim Westerlund, that deal with the analysis of unit root testing, and the second part consists of two chapters on slope homogeneity testing.<br/><br>
<br/><br>
Chapter 2 continues and extends the analysis in Westerlund (Empirical Economics 37:517–531, 2009), who demonstrates that the performance of the popular LLC (Levin et al., Journal of Econometrics 98:1–24, 2002) panel unit root test depends critically on the choice of lag truncation used when correcting for serial correlation, and that it is only when this parameter is set as a function of time that the power raises above size. The purpose Chapter 2 is to propose a modified test that does not suffer from this drawback. The new test is not only simpler to compute but also superior in terms of small-sample performance, which is illustrated using as an example purchasing power parity for less developed countries.<br/><br>
<br/><br>
Chapter 3 considers panel unit root testing when there is uncertainty about the deterministic trend. In doing so, it takes PANIC (Bai and Ng, Econometrica 72:1127-1177, 2004), one of the most general and popular panel unit root tests, and demonstrates how it can be modified to determine the extent of both the deterministic trend and non-stationarity of the data.<br/><br>
<br/><br>
Chapter 4 offers an in-depth analysis of the dynamic and cross-sectional properties of crime using data covering 21 Swedish counties from 1975 to 2010. The results suggest that the crimes considered are non-stationary, and that this cannot be attributed to county-specific disparities alone, but that there are also a small number of common stochastic trends to which groups of counties tend to revert. With this result in mind, we investigate the relationship between unemployment and crime using novel panel cointegration techniques. Overall, the results do not support cointegration, and suggest that previous findings of a significant relationship between unemployment and crime might be spurious.<br/><br>
<br/><br>
Chapter 5 proposes a test of slope homogeneity for panel data models that is robust to unspecified error serial dependence and heteroscedasticity. The proposed test is an adjusted version of the dispersion-type test suggested by Pesaran and Yamagata (Journal of Econometrics 142, 50–93, 2008) and is shown to have a standard normal distribution, as N, T → ∞. Using Monte Carlo experiments, it is demonstrated that the proposed test performs well in small samples, even when the degree of serial dependence is large.<br/><br>
<br/><br>
Chapter 6 considers the issue of slope homogeneity testing in panel data models with non-spherical errors. It proposes a bootstrap test of the slope homogeneity hypothesis that is robust to cross-sectional and serial dependence in the errors. The chapter also proposes a bootstrap sequential test that enables differentiation between units with a common slope coefficient vector and units for which the hypothesis of equal slope coefficients fails. Asymptotic properties of the bootstrap tests are derived by letting the time series dimension of the panel increase to infinity, and a small Monte Carlo study is conducted to investigate the small-sample properties.},
  author       = {Blomquist, Johan},
  keyword      = {Non-stationary panels,Panel unit root tests,Cross-sectional dependence,Homogeneity testing},
  language     = {eng},
  pages        = {178},
  series       = {Lund Economic Studies},
  title        = {Testing Homogeneity and Unit Root Restrictions in Panels},
  year         = {2012},
}