This dissertation consists of three essays on testing for cross-sectional dependence and specification in large panel data models. The first two essays are based on the papers joint with Prof. Badi H. Baltagi and Prof. Chihwa Kao; the third essay is based on the working paper joint with Prof. Lee. The first essay considers testing for Sphericity with non-normality in a fixed effects panel data model. The second essay considers testing for cross-sectional dependence in heterogeneous large N and large T panel data models allowing error serial correlation. The third essay considers the tests of specification in large N and large T dynamic panel data models.
The first essay proposes a test for sphericity in a fixed
effects panel data regression model which is robust to non-normality of the
disturbances. It builds up on the work of Chen, Zhang and Zhong (2010) who
use $U$-statistics to test for sphericity of the variance-covariance matrix
in statistics. Since the errors are unobservable, the residuals from the
fixed effects regression are used. The limiting distribution of the proposed
test statistic is derived. Additionally, its finite sample properties are
examined using Monte Carlo simulations.
The second essay considers the problem of testing cross-sectional dependence in
large panel data models with serially correlated errors. It finds that
existing tests for cross-sectional independence encounter size distortions
with serial correlation in the errors. To control the size, it
proposes a modification of Pesaran's CD\\ test to account for serially
correlation of an unknown form in the error term. We derive the limiting
distribution of this test as $\\left( N,T\\right) \\rightarrow\\infty$. The test
is distribution free and allows for unknown forms of serial correlation in the
errors. Monte Carlo simulations show that the test has good size and power for
large panels when serial correlation in the errors are present.
The third essay considers the tests of specification,
including the tests for serial correlation and the tests of overidentifying
restrictions, for large dynamic panel data models.\\ The test statistics are
built upon the two-step GMM estimations using three different instrument
matrices: the block-diagonal matrix with a full set of all available
instruments, the block-diagonal matrix with a subset of all available
instruments and the collapsed matrix with a subset of all available
instruments. It shows that the conventional Sargan's test of overidentifying
restrictions (Arellano and Bond (1991)) does not approximate to the chi-square
distribution, when the number of instruments used, is relatively as large as
$N$; therefore it proposes corrected Sargan's tests with different instrument
matrices. The limiting distributions of all the tests of specification are
derived as $N$ and $T$ go to infinity simultaneously. Power properties are
discussed under varieties of alternatives, The results show that the tests for
serial correlation are powerful against different alternatives, and the power
of corrected Sargan's tests only increases as $N$ increases. Monte Carlo
simulations confirm our theoretical findings, especially showing that the
corrected Sargan's tests have the correct size. Besides, it suggests using the
collapsed instrument matrix for the practical testing purpose.
","abstract_html":"<p>This dissertation consists of three essays on testing for cross-sectional dependence and specification in large panel data models. The first two essays are based on the papers joint with Prof. Badi H. Baltagi and Prof. Chihwa Kao; the third essay is based on the working paper joint with Prof. Lee. The first essay considers testing for Sphericity with non-normality in a fixed effects panel data model. The second essay considers testing for cross-sectional dependence in heterogeneous large N and large T panel data models allowing error serial correlation. The third essay considers the tests of specification in large N and large T dynamic panel data models.</p> <p>The first essay proposes a test for sphericity in a fixed</p> <p>effects panel data regression model which is robust to non-normality of the</p> <p>disturbances. It builds up on the work of Chen, Zhang and Zhong (2010) who</p> <p>use $U$-statistics to test for sphericity of the variance-covariance matrix</p> <p>in statistics. Since the errors are unobservable, the residuals from the</p> <p>fixed effects regression are used. The limiting distribution of the proposed</p> <p>test statistic is derived. Additionally, its finite sample properties are</p> <p>examined using Monte Carlo simulations.</p> <p>The second essay considers the problem of testing cross-sectional dependence in</p> <p>large panel data models with serially correlated errors. It finds that</p> <p>existing tests for cross-sectional independence encounter size distortions</p> <p>with serial correlation in the errors. To control the size, it</p> <p>proposes a modification of Pesaran's CD\\ test to account for serially</p> <p>correlation of an unknown form in the error term. We derive the limiting</p> <p>distribution of this test as $\\left( N,T\\right) \\rightarrow\\infty$. The test</p> <p>is distribution free and allows for unknown forms of serial correlation in the</p> <p>errors. Monte Carlo simulations show that the test has good size and power for</p> <p>large panels when serial correlation in the errors are present.</p> <p>The third essay considers the tests of specification,</p> <p>including the tests for serial correlation and the tests of overidentifying</p> <p>restrictions, for large dynamic panel data models.\\ The test statistics are</p> <p>built upon the two-step GMM estimations using three different instrument</p> <p>matrices: the block-diagonal matrix with a full set of all available</p> <p>instruments, the block-diagonal matrix with a subset of all available</p> <p>instruments and the collapsed matrix with a subset of all available</p> <p>instruments. It shows that the conventional Sargan's test of overidentifying</p> <p>restrictions (Arellano and Bond (1991)) does not approximate to the chi-square</p> <p>distribution, when the number of instruments used, is relatively as large as</p> <p>$N$; therefore it proposes corrected Sargan's tests with different instrument</p> <p>matrices. The limiting distributions of all the tests of specification are</p> <p>derived as $N$ and $T$ go to infinity simultaneously. Power properties are</p> <p>discussed under varieties of alternatives, The results show that the tests for</p> <p>serial correlation are powerful against different alternatives, and the power</p> <p>of corrected Sargan's tests only increases as $N$ increases. Monte Carlo</p> <p>simulations confirm our theoretical findings, especially showing that the</p> <p>corrected Sargan's tests have the correct size. Besides, it suggests using the</p> <p>collapsed instrument matrix for the practical testing purpose.</p>","abstract_has_math":true,"creators":["Peng, Bin"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Economics","degree_department":null,"school":null,"contributors":["Chihwa Kao"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-07-01T07:00:00Z","date_published":"2016-07-01T07:00:00Z","updated_at":"2026-07-24T04:55:13Z","subjects":["Cross-sectional Dependence","Large N Large T","Panel Data Models","Serial Correlation","Sphericity","Tests of Specification","Social and Behavioral Sciences"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://surface.syr.edu/etd/524","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chihwa Kao"]},{"key":"dc:creator","label":"Author","values":["Peng, Bin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Economics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Cross-sectional Dependence","Large N Large T","Panel Data Models","Serial Correlation","Sphericity","Tests of Specification","Social and Behavioral Sciences"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://surface.syr.edu/etd/524"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This dissertation consists of three essays on testing for cross-sectional dependence and specification in large panel data models. The first two essays are based on the papers joint with Prof. Badi H. Baltagi and Prof. Chihwa Kao; the third essay is based on the working paper joint with Prof. Lee. The first essay considers testing for Sphericity with non-normality in a fixed effects panel data model. The second essay considers testing for cross-sectional dependence in heterogeneous large N and large T panel data models allowing error serial correlation. The third essay considers the tests of specification in large N and large T dynamic panel data models.
The first essay proposes a test for sphericity in a fixed
effects panel data regression model which is robust to non-normality of the
disturbances. It builds up on the work of Chen, Zhang and Zhong (2010) who
use $U$-statistics to test for sphericity of the variance-covariance matrix
in statistics. Since the errors are unobservable, the residuals from the
fixed effects regression are used. The limiting distribution of the proposed
test statistic is derived. Additionally, its finite sample properties are
examined using Monte Carlo simulations.
The second essay considers the problem of testing cross-sectional dependence in
large panel data models with serially correlated errors. It finds that
existing tests for cross-sectional independence encounter size distortions
with serial correlation in the errors. To control the size, it
proposes a modification of Pesaran's CD\\ test to account for serially
correlation of an unknown form in the error term. We derive the limiting
distribution of this test as $\\left( N,T\\right) \\rightarrow\\infty$. The test
is distribution free and allows for unknown forms of serial correlation in the
errors. Monte Carlo simulations show that the test has good size and power for
large panels when serial correlation in the errors are present.
The third essay considers the tests of specification,
including the tests for serial correlation and the tests of overidentifying
restrictions, for large dynamic panel data models.\\ The test statistics are
built upon the two-step GMM estimations using three different instrument
matrices: the block-diagonal matrix with a full set of all available
instruments, the block-diagonal matrix with a subset of all available
instruments and the collapsed matrix with a subset of all available
instruments. It shows that the conventional Sargan's test of overidentifying
restrictions (Arellano and Bond (1991)) does not approximate to the chi-square
distribution, when the number of instruments used, is relatively as large as
$N$; therefore it proposes corrected Sargan's tests with different instrument
matrices. The limiting distributions of all the tests of specification are
derived as $N$ and $T$ go to infinity simultaneously. Power properties are
discussed under varieties of alternatives, The results show that the tests for
serial correlation are powerful against different alternatives, and the power
of corrected Sargan's tests only increases as $N$ increases. Monte Carlo
simulations confirm our theoretical findings, especially showing that the
corrected Sargan's tests have the correct size. Besides, it suggests using the
collapsed instrument matrix for the practical testing purpose.
"]},{"key":"dc:title","label":"Title","values":["Three Essays on Testing for Cross-Sectional Dependence and Specification in Large Panel Data Models"]}]}],"canonical_facts":{"dc:contributor":["Chihwa Kao"],"dc:creator":["Peng, Bin"],"dc:description.abstract":["This dissertation consists of three essays on testing for cross-sectional dependence and specification in large panel data models. The first two essays are based on the papers joint with Prof. Badi H. Baltagi and Prof. Chihwa Kao; the third essay is based on the working paper joint with Prof. Lee. The first essay considers testing for Sphericity with non-normality in a fixed effects panel data model. The second essay considers testing for cross-sectional dependence in heterogeneous large N and large T panel data models allowing error serial correlation. The third essay considers the tests of specification in large N and large T dynamic panel data models.
The first essay proposes a test for sphericity in a fixed
effects panel data regression model which is robust to non-normality of the
disturbances. It builds up on the work of Chen, Zhang and Zhong (2010) who
use $U$-statistics to test for sphericity of the variance-covariance matrix
in statistics. Since the errors are unobservable, the residuals from the
fixed effects regression are used. The limiting distribution of the proposed
test statistic is derived. Additionally, its finite sample properties are
examined using Monte Carlo simulations.
The second essay considers the problem of testing cross-sectional dependence in
large panel data models with serially correlated errors. It finds that
existing tests for cross-sectional independence encounter size distortions
with serial correlation in the errors. To control the size, it
proposes a modification of Pesaran's CD\\ test to account for serially
correlation of an unknown form in the error term. We derive the limiting
distribution of this test as $\\left( N,T\\right) \\rightarrow\\infty$. The test
is distribution free and allows for unknown forms of serial correlation in the
errors. Monte Carlo simulations show that the test has good size and power for
large panels when serial correlation in the errors are present.
The third essay considers the tests of specification,
including the tests for serial correlation and the tests of overidentifying
restrictions, for large dynamic panel data models.\\ The test statistics are
built upon the two-step GMM estimations using three different instrument
matrices: the block-diagonal matrix with a full set of all available
instruments, the block-diagonal matrix with a subset of all available
instruments and the collapsed matrix with a subset of all available
instruments. It shows that the conventional Sargan's test of overidentifying
restrictions (Arellano and Bond (1991)) does not approximate to the chi-square
distribution, when the number of instruments used, is relatively as large as
$N$; therefore it proposes corrected Sargan's tests with different instrument
matrices. The limiting distributions of all the tests of specification are
derived as $N$ and $T$ go to infinity simultaneously. Power properties are
discussed under varieties of alternatives, The results show that the tests for
serial correlation are powerful against different alternatives, and the power
of corrected Sargan's tests only increases as $N$ increases. Monte Carlo
simulations confirm our theoretical findings, especially showing that the
corrected Sargan's tests have the correct size. Besides, it suggests using the
collapsed instrument matrix for the practical testing purpose.
"],"dc:identifier":["https://surface.syr.edu/etd/524"],"dc:subject":["Cross-sectional Dependence","Large N Large T","Panel Data Models","Serial Correlation","Sphericity","Tests of Specification","Social and Behavioral Sciences"],"dc:title":["Three Essays on Testing for Cross-Sectional Dependence and Specification in Large Panel Data Models"],"thesis:degree_discipline":["Economics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T04:55:13Z"}