"Productivity, Model Uncertainty, Home Production, and the New Home Sales Price in the U.S."

This dissertation investigates the role of productivity, model uncertainty, and home production in macroeconomics and the housing market, focusing on the resource allocation among different production sectors and the new home sales price.

In the first chapter, I construct sector-specific total factor productivity shocks in a two-sector DSGE model and study to what extent that the TFP shock in housing sector accounts for the rise and fall during the most recent housing market crisis. I solve the model using the methodology proposed by \cite{Hansen_Sargent_1995}. The discounted Linear Exponential Quadratic Gaussian control method successfully avoids computational difficulties such as high-dimensional state space, explosive value function, etc., and facilitates the simulation of the worst-case model to implement the likelihood ratio tests. I calibrate the parameters in the benchmark model by the simulated method of moments. The benchmark model, with TFP shocks alone, does a decent job in fitting the first and second moments of real-world data; it accounts for 32 percent of the increase and 40 percent of the decrease in the new home sales price. The implied changes in the resource allocation between the two sectors are also in line with data. Then I introduce model uncertainty into the benchmark framework and dedicate to answer the question that whether the fear of model misspecification help account for the boom-bust in the new home sales price, and I examine the first and second moments of the worst-case distribution of the TFP shocks. I allow a one-time temporary change in the model uncertainty level during the time span with enhanced dispersions of professional forecasts. The model uncertainty parameter is calibrated by the detection error probability as in \cite{Hansen_Sargent_2007}. When households hold a concern for model misspecification, they are seeking robust decision rules which perform well over a set of alternative models that are statistically indistinguishable from the not-fully-trusted approximating model. When model uncertainty level rises, the worst-case model distorts the Gaussian mean of TFP shocks negatively in households' minds but keeps the variance-covariance matrix of the TFP shocks almost unchanged. Since the TFP shock in housing production is more volatile, it receives a larger negative mean-shift effect than the TFP shock in the consumption goods sector from the robust state transition law. As a result, the new home sales price is pushed up even further. Thus with the one-time change in model uncertainty, the model is capable of accounting for 40 percent of the surge in new home sales price. The inclusion of the fear for model misspecification improves model's fitting with data.

The second chapter studies the implications of introducing home production into an otherwise standard two-sector production economy from the theoretical perspective. While the benchmark model shows reasonable impulse responses of the key economic variables to different productivity shocks in the two market production sectors, the existence of home production highlights more interesting mechanisms due to the substitution incentive between market-produced and home-produced goods. When there is a positive productivity shock in the nonhousing goods production sector, households are inclined to substitute market consumption for home consumption as it is relatively more efficient to work in the market. As a result, resources flow to the two market sectors as if the relative productivity change in the nonhousing sector to the housing sector were amplified. In the case with a positive productivity shock in the housing sector, although it is more efficient to produce housing goods, the increment of housing stock requires more home hours to pair with it in home production. Thus the effects on resource allocations in the market sectors driven by this relative productivity change are tempered. This substitution mechanism can help improve the two-sector model's performance in fitting of the correlations between factor inputs that observed in the data.