Date of Award

July 2016

Degree Type


Degree Name

Doctor of Philosophy (PhD)




Chihwa Kao


Cross-sectional Dependence, Large N Large T, Panel Data Models, Serial Correlation, Sphericity, Tests of Specification

Subject Categories

Social and Behavioral Sciences


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.


Open Access