Three Essays in Financial Econometrics

Understanding how cross-sectional units interact with each other in a panel setting is an important question, given we are living in a more and more interconnected world. The effort to provide a solution to this question involves proposing statistical models that capture such features and obtain network datasets that characterize interdependency among entities. With a hope to contribute to this discipline, this thesis looks into the cross-sectional dependence in panel both theoretically and empirically. The first chapter develops a multi-country contagion model where the individual-specific Markov chains are interdependent. The second chapter studies a spatial factor model, which accommodates two distinct types of cross-sectional dependence in a panel. The chapter also utilizes a novel network dataset and empirically shows local interactions play a vital role in explaining comovement in equity returns. Chapter 3 studies peer groups of arbitrage characteristics. The details of the three chapters are summarized below: Sovereign Risk Contagion in Eurozone with Mutual Exciting Regime-Switching Model This paper proposes a new mutual exciting regime-switching model where crises can spread contagiously across countries. Each country has its own hidden stochastic process that determines whether the country is in a normal or crisis regime. Contagion is defined as a rise in the transition probability to the crisis regime when other countries are in crisis in the past state. Using this new approach, I revisit the sovereign risk contagion in the euro area. I find that there are striking shifts in market pricing functions for the sovereign bond spreads. Multi-country contagion plays a dominant role in driving such shifts, while common risk factors and country-specific fundamentals are much less important. News-Implied Linkages and Local Dependency in the Equity Market This paper studies a heterogeneous coefficient spatial factor model that separately addresses both common factor risks (strong cross-sectional dependence) and local dependency (weak cross-sectional dependence) in the equity returns. For a high-dimensional panel of equity returns, it is challenging to measure firm-to-firm connectivity. We use extensive business news to construct firms’ links via which local shocks transmit, and we use those news-implied linkages as a proxy for the connectivity among firms. We document a considerable degree of local dependency among S&P 500 stocks. From the asset pricing perspective, we derive the theoretical implications of no asymptotic arbitrage for the heterogeneous spatial factor model. Empirically, we show that adding spatial interactions to factor models significantly reduces mispricing and estimation errors. We also show that our news-implied linkages provide a comprehensive and integrated proxy for firm-to-firm connectivity, and it out-performs other existing networks in the literature. Dynamic Peer Groups of Arbitrage Characteristics This chapter proposes an asset pricing factor model constructed with semi-parametric characteristics-based mispricing and factor loading functions. We approximate the unknown functions by B-splines sieve where the number of B-splines coefficients is diverging. We estimate this model and test the existence of the mispricing function by a power enhanced hypothesis test. The enhanced test solves the low power problem caused by diverging B-splines coefficients, with the strengthened power approaches to one asymptotically. We also investigate the structure of mispricing components through Hierarchical K-means Clusterings. We apply our methodology to CRSP (Center for Research in Security Prices) and Compustat data for the US stock market with one-year rolling windows during 1967-2017. This empirical study shows the presence of mispricing functions in certain time blocks. We also find that distinct clusters of the same characteristics lead to similar arbitrage returns, forming a “peer group” of arbitrage characteristics