Three essays on time-varying parameters and time series networks

This thesis is composed of three essays on time-varying parameters and time series networks where each essay deals with specific aspects thereof. The thesis starts with proposing a 2SLS based test for a threshold in models with endogenous regressors in Chapter 2. Many economic models are formulated in this way, for example output growth or unemployment rates in different states of the economy. Therefore, it is necessary to have tools available which are capable of indicating whether such effects exist in the data or not. Chapter 3 proposes, to my best knowledge, the first estimator for the inverse of the long-run covariance matrix of a linear, potentially heteroskedastic stochastic process under unknown sparsity constraints. That is, the econometrician does not know which entries of the inverse are equal to zero and which not. Such situations naturally arise, for example, when modelling partial correlation networks based on time series data. Finally, in Chapter 4 this thesis empirically investigates how robust two commonly applied network measures, the From- and the To-degree, are to the exclusion of central nodes in financial volatility networks. This question is motivated by the current empirical literature which excludes certain nodes such as Lehman Brothers from their analysis

Testing for a Threshold in Models with Endogenous Regressors

We show by simulation that the test for an unknown threshold in models with endogenous regressors - proposed in Caner and Hansen (2004) - can exhibit severe size distortions both in small and in moderately large samples, pertinent to empirical applications. We propose three new tests that rectify these size distortions. The first test is based on GMM estimators. The other two are based on unconventional 2SLS estimators, that use additional information about the linearity (or lack of linearity) of the first stage. Just like the test in Caner and Hansen (2004), our tests are non-pivotal, and we prove their bootstrap validity. The empirical application revisits the question in Ramey and Zubairy (2018) whether government spending multipliers are larger in recessions, but using tests for an unknown threshold. Consistent with Ramey and Zubairy (2018), we do not find strong evidence that these multipliers are larger in recessions

Testing for a Threshold in Models with Endogenous Regressors

We show by simulation that the test for an unknown threshold in models with endogenous regressors - proposed in Caner and Hansen (2004) - can exhibit severe size distortions both in small and in moderately large samples, pertinent to empirical applications. We propose three new tests that rectify these size distortions. The first test is based on GMM estimators. The other two are based on unconventional 2SLS estimators, that use additional information about the linearity (or lack of linearity) of the first stage. Just like the test in Caner and Hansen (2004), our tests are non-pivotal, and we prove their bootstrap validity. The empirical application revisits the question in Ramey and Zubairy (2018) whether government spending multipliers are larger in recessions, but using tests for an unknown threshold. Consistent with Ramey and Zubairy (2018), we do not find strong evidence that these multipliers are larger in recessions

Testing for a Threshold in Models with Endogenous Regressors

We propose two new parametric tests for an unknown threshold in models with endogenous regressors. They are both based on unconventional 2SLS estimators that use additional information about the linearity of the first stage. This information leads to more accurate residuals and therefore tests with better size properties than the Wald GMM test in Caner and Hansen (2004), which we show exhibits severe size distortions in small samples pertinent to empirical applications. We prove the bootstrap validity of our tests and evaluate their empirical relevance by revisiting the question whether government spending multipliers are larger in recessions. As Ramey and Zubairy (2018), we cannot rule out that they are the same in recessions or expansions

Testing for a Threshold in Models with Endogenous Regressors

Using 2SLS estimation, we propose two tests for a threshold in models with endogenous regressors: a sup LR test and a sup Wald test. Here, the 2SLS estimation is not conventional because it uses additional information about the first-stage being linear or not. Because of this additional information, our tests can be more accurate than the threshold test in Caner and Hansen (2004) which is based on conventional GMM estimation. We derive the asymptotic distributions of the two tests for a linear and for a threshold reduced form. In both cases, the distributions are non-pivotal, and we propose obtaining critical values via a fixed regressor wild bootstrap. Our simulations show that in small samples, the GMM test of Caner and Hansen (2004) can be severely oversized under heteroskedasticity, while the 2SLS tests we propose are much closer to their nominal size. We use our tests to investigate the common claim that the government spending multiplier is larger close to the zero lower bound, and therefore that the governments should have spent more in the recent crisis. We find no empirical support for this claim