Essays on Nonlinear Dynamics and their Estimation

Abstract

Economic outcomes often depend not only on individual shocks or policies, but also on the state of the economy, the interaction between mechanisms, and the order in which events occur. This dissertation demonstrates the importance of such nonlinear dynamics and develops methods for estimating them using all available information. <br/>

The first chapter examines the interaction of trade and financial sanctions. Combining cross-country evidence with a nonlinear two-country macroeconomic model, it shows that the effects of sanctions depend on their sequencing: financial sanctions weaken the target country’s banking sector and thereby amplify subsequent trade sanctions, whereas the reverse sequence produces no comparable amplification. <br/>

The remaining chapters study nonlinear state-space models whose state variables are observed in some, but not all, periods. These occasional observations contain information that standard methods treating the states as fully latent leave unused. The dissertation derives a likelihood that incorporates this additional information and accommodates endogenous observation patterns. It then develops a recursive numerical method for computing the likelihood, allowing the parameters of nonlinear state-space models to be estimated more accurately. The dissertation establishes consistency and asymptotic normality for both the exact and numerically approximated maximum likelihood estimators. Finally, after estimating the model parameters, it develops methods for inferring the remaining missing observations while accounting for parameter uncertainty. Together, these contributions make nonlinear dynamic models more empirically operational.