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Likelihood-Based Panel Unit Root Tests for Factor Models
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics. (Time Series Econometrics)
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The thesis consists of four papers that address likelihood-based unit root tests for panel data with cross-sectional dependence arising from common factors.

In the first three papers, we derive Lagrange multiplier (LM)-type tests for common and idiosyncratic unit roots in the exact factor models based on the likelihood function of the differenced data. Also derived are the asymptotic distributions of these test statistics. The finite sample properties of these tests are compared by simulation with other commonly used unit root tests. The results show that our LM-type tests have better size and local power properties.

In the fourth paper, we estimate the spaces spanned by the common factors and the spaces spanned by the idiosyncratic components of the static factor model by using the quasi-maximum likelihood (ML) method and compare it with the widely used method of principal components (PC). Next, by simulation, we compare the size and power properties of established tests for idiosyncratic unit roots, using both the ML and PC methods. Simulation results show that the idiosyncratic unit root tests based on the likelihood-based residuals generally have better size and higher size-adjusted power, especially when the cross-sectional dimension is small and the time series dimension is large.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2014. , 35 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences, ISSN 1652-9030 ; 103
Keyword [en]
Panel unit root, Exact factor model, Dynamic factor model, Maximum likelihood, Principal components, Lagrange multiplier
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-233094ISBN: 978-91-554-9049-2 (print)OAI: oai:DiVA.org:uu-233094DiVA: diva2:750646
Public defence
2014-11-14, Hörsal 2, Ekonomikum, Kyrkogårdsgatan 10, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2014-10-24 Created: 2014-09-29 Last updated: 2015-01-23
List of papers
1. An LM-type Test for Idiosyncratic Unit Roots in the Exact Factor Model with Nonstationary Common Shocks
Open this publication in new window or tab >>An LM-type Test for Idiosyncratic Unit Roots in the Exact Factor Model with Nonstationary Common Shocks
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We consider an exact factor model with integrated factors and propose an LM-type test for unit roots in the idiosyncratic component. We show that, for a fixed number of panel individuals (N) and when the number of time points (T) tends to infinity, the limiting distribution of the LM-type statistic is a weighted sum of independent chi-square-one variables, and when T tends to infinity followed by N tending to infinity, the limiting distribution is standard normal. The test is derived under assumptions that are restrictive just enough to be able to rely on explicit maximum likelihood estimators, and should contribute to the challenging task of deriving likelihood or quasi-likelihood based unit root tests in dynamic factor models.

Keyword
Panel unit root, Dynamic factors, Maximum likelihood, Lagrange multiplier
National Category
Social Sciences
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-207291 (URN)
Projects
Solving Macroeconomic Problems Using Non-Stationary Panel Data
Available from: 2013-09-11 Created: 2013-09-11 Last updated: 2015-01-23
2. LM-type Tests For Idiosyncratic and Common Unit Roots in the Exact Factor Model with AR(1) Dynamics
Open this publication in new window or tab >>LM-type Tests For Idiosyncratic and Common Unit Roots in the Exact Factor Model with AR(1) Dynamics
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Recent developments within the panel unit-root literature have illustrated how the exact factor model serves as a parsimonious framework and allows for consistent maximum likelihood inference even when it is misspecified contra the more general approximate factor model. In this paper we consider an exact factor model with AR(1) dynamics and propose LM-type tests for idiosyncratic and common unit roots. We derive the asymptotic distributions and carry out simulations to investigate size and power of the tests in finite samples, as well as compare the performance with some existing tests.

Keyword
Panel unit root, Dynamic factors, Maximum likelihood, Lagrange multiplier
National Category
Social Sciences
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-207294 (URN)
Projects
Solving Macroeconomic Problems Using Non-Stationary Panel Data
Available from: 2013-09-11 Created: 2013-09-11 Last updated: 2016-03-30
3. A Lagrange multiplier-type test for idiosyncratic unit roots in the exact factor model
Open this publication in new window or tab >>A Lagrange multiplier-type test for idiosyncratic unit roots in the exact factor model
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper an exact factor model is considered and a Lagrange multiplier-type test for a homogenous unit root in the idiosyncratic component is derived. It is shown that the asymptotic distribution is independent of the distribution of the common factors, and that the factors are allowed to be integrated, cointegrated, or stationary. In a simulation study, size and power is compared with some popular second generation panel unit root tests. The simulations suggest that the statistic is well-behaved in terms of size and that it is powerful and robust in comparison with existing tests.

Keyword
Panel unit root, Dynamic factors, Maximum likelihood, Lagrange multiplier
National Category
Other Social Sciences not elsewhere specified
Identifiers
urn:nbn:se:uu:diva-233093 (URN)
Available from: 2014-09-29 Created: 2014-09-29 Last updated: 2016-02-22
4. Comparing idiosyncratic unit root tests based on the residuals estimated from ML and PC methods in a static factor model
Open this publication in new window or tab >>Comparing idiosyncratic unit root tests based on the residuals estimated from ML and PC methods in a static factor model
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics Other Social Sciences not elsewhere specified
Identifiers
urn:nbn:se:uu:diva-233090 (URN)
Note

For static factor models or dynamic factor models with static representations, the idiosyncratic components can be estimated either from the method of principal components (PC) or from the method of (quasi) maximum likelihood (ML). In this paper, we compare the size and power properties of some commonly used unit root tests under the two sets of residuals. We also compare the estimation efficiency of the common factors, factor loadings and the idiosyncratic components across the two methods when the factor model is either stationary or non-stationary. The simulation results show that when the number of cross-section individuals (N) is small and the number of the observations (T) is large, the ML method is superior to the PC method. When $N$ and $T$ are both large, the difference between the methods is negligible.

Available from: 2014-09-29 Created: 2014-09-29 Last updated: 2015-01-23

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