Universität zu Köln

Kutzker, Tim (2020). Specification Testing in Econometric Models. PhD thesis, Universität zu Köln.

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Abstract

The thesis consits of three independent articles. First, specification tests for the m-dimensional spatial autoregressive (SAR) panel model are provided. Therefore, we derive the limiting distribution of the specification test statistics and examine size and power properties in finite sample simulations. In the empirical application we analyze the Euro Stoxx 50 returns. Regarding this, a 3-dimensional SAR panel model incorporating global dependencies, dependencies inside industrial branches and local dependencies is assumed. The investigation shows the tests’ ability to detect inaccurate Value-at-Risk forecasts. Secondly, we propose a new non-parametric test for detecting relevant breaks in copula functions. We assume that the data is driven by two non-equal copulas C1 and C2. Under the null hypothesis, the copula difference within an appropriate norm is smaller than a certain positive adjustable threshold . Within the alternative hypothesis, the copula difference exceeds the fixed value. The test is based on a cumulative sum approach of the empirical copula with sequentially estimated marginals. We propose a bootstrap procedure to compute critical values. The Monte Carlo simulation study indicates that the test results in a reasonable sized and powered testing procedure. A real data application of the DAX30 up to cross sectional dimension N = 30 shows the test’s ability to detect relevant break points. Finally, we propose a novel consistent specification test for quantile regression models where we allow the covariate effects to be quantile dependent and nonlinear. To achieve this, we parameterize the conditional quantile functions by appropriate basis functions, rather than parametrically and hence allowing to test for functional forms beyond linearity while retaining the linear cases as special cases. Due to the dependence on the quantile itself covariate-quantile relations can differ for distinct quantiles. The induced class of conditional distribution functions can finally be tested with a Cramér-von Mises type test statistic. We derive the theoretical limit distribution and propose a practical bootstrap method. To increase the power of our test, we suggest a modified test statistic using quantile regression splines. A detailed Monte Carlo experiment shows that the test results in a reasonable sized testing procedure with large power. An application to conditional income disparities between East and West Germany over the period 2001 − 2010 indicates that there are still significant differences across the quantiles of the conditional income distributions, when conditioning on age.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Kutzker, Tim tim.kutzker@uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-123231
Date:	18 August 2020
Language:	English
Faculty:	Faculty of Management, Economy and Social Sciences
Divisions:	Faculty of Management, Economics and Social Sciences > Economics > Econometrics and Statistics > Professorship for Statistics and Econometrics
Subjects:	Economics Mathematics
Uncontrolled Keywords:	Keywords Language Specification Tests English
Date of oral exam:	18 August 2020
Referee:	Name Academic Title Wied, Dominik Prof. Dr. Breitung, Jörg Prof. Dr. Hess, Dieter Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/12323