UC Irvine

This dissertation comprises three chapters. Chapter 1 is based on my unpublished second-year paper "Estimation Methods of Adaptive Learning" In this chapter, I investigate the differences inherent in estimating New Keynesian models via the linearity assumptions of the Kalman filter and the more plausible Particle filter. As the computational abilities of econometricians continue to expand, the use of Nonlinear state space methods becomes a more viable methodology to capture realities and understand macroeconomic policy events. However, research on the empirical differences of new Keynesian models equipped with adaptive learning is limited. To fill this gap, I use U.S. macroeconomic data to estimate both a Kalman filter that incorporates a new Keynesian model via expectations formed via recursive least squares and compare this with a particle filter estimation procedure. I pay particular attention to the constant gain learning parameter along with the empirical likelihood, in order to understand which model is more realistic & why. My findings show that in the absence of a particle filter, overall SSE is 45\% greater, and a correspondingly higher likelihood. Additionally, I find the constant gain learning parameter in the standard 3 equation new-Keynesian model to be 16% higher under Particle filter estimation as opposed to the less plausible Kalman filter estimation. Chapter 2 is motivated by the recent monetary policy actions prompted by the federal reserve in response to Covid-19, In this chapter, I introduce a structural new Keynesian model with household wealth-in-utility and capital adjustment costs in the production process of intermediary firms. Using these features in the economic process, I additionally incorporate households and investors to form expectations about the future state of the economy via adaptive learning. To address the increasingly prevalent zero lower-bound central bankers face when making interest and balance sheet decisions, I enable households and firms to update their beliefs about the economy via Recursive least squares, while also allowing them to simultaneously learn the alternate equilibrium in which the federal funds rate reaches the floor of 0\% with an updated counting rule. Equipped with the following model of the economic process, I utilize U.S. financial

amp; macroeconomic data to estimate the model parameters of the model along with the counterfactual effects of alternative monetary policies. Due to the non-linear nature of the model, I utilize the particle filter in my resulting analysis. I find that I find more aggressive long-term asset purchases during the Great Recession and Dot-com Recession led to over \%1 higher output growth each quarter, with a close to a 0% net change in Inflation. I find that investment and demand shocks make up over a 20% contribution in explaining U.S. GDP growth, while expectations of future wealth amplify the effects of the business cycle. Chapter 3 extends the exercises conducted in Chapter 2 by incorporating financial frictions from collateral constraints placed on the intermediary firm along with a financial intermediary that receives deposits from households. Furthermore, Chapter 3 incorporates the novel feature of "anticipated utility" in which households, when forming consumption decisions, form expectations of their future infinite horizon of discounted wealth. Taking the following features into account, the chapter applies this model to Japanese macroeconomic amp; financial data and estimates model parameters to obtain key results. The paper finds BOJ asset purchases lead to output and inflation of approximately 0.80% and .35%. Particle Filter analysis suggests coordinating simultaneous interest rate cuts and LSAPs during the Global Financial Crisis and initiating equity LSAPs during the Dot-Com bubble would have resulted in increased output growth and inflation.