Li, Jinke
(2012)
Essays in business cycles: housing market, adaptive learning, and credit market imperfections.
PhD thesis, University of Nottingham.
Abstract
In this thesis, we focus on the housing sector, which is important to the economy but is under-researched in business cycles analysis. We discuss several housing sector related issues in dynamics stochastic general equilibrium (DSGE) models.
To begin with, we conduct a sensitivity analysis using a simple DSGE model with the feature of sticky prices and a fixed housing supply, which is similar with the basic model in Iacoviello (2005) but with representative agents. Then we introduce credit market imperfections in two different ways. The first case is referred to as 'borrowing to invest', in which entrepreneurs take loans and accumulate production housing, which is a factor of production. We observe the financial accelerator (or decelerator) effect since their borrowing is related to output directly. The second case is referred to as 'borrowing to live', in which impatient households take loans to buy housing and gain utility from it. In contrast with the first case, we do not find the financial accelerator (or decelerator) effect, since the borrowing is not directly related to output anymore.
First, we add a variable housing supply, thus we can discuss the supply side effect in the housing market, including both the direct effect and the feedback effect. The direct effect is the impact of a housing technology shock, and the feedback effect is the impact of a change in new housing production, which is caused by other shocks. We find, however, that the magnitudes of these two effects are negligible under the standard setting of the housing market that is commonly used in the literature of DSGE model with housing, such as Davis and Heathcote (2005), Iacoviello and Neri (2010). The key assumption in the standard setting is that every household trades housing in a given period. An empirical examination of the U.S. housing sector suggests us to (i) re-construct the housing market and (ii) introduce the feature of time to build to new housing production. After constructing the new setting for the housing market by introducing the probability of trading housing, we find that (i) the steady state ratios from the model are consistent with their empirical targets and (ii) the magnitudes of both the direct effect and the feedback effect are 60 times larger. Furthermore, the feature of time to build, together with the new setting of the housing market, allows us to observe overshooting behaviour on the real house price.
Second, we discuss the impact of the assumption of adaptive learning, as we are convinced that the house price bubble is partially contributed by this alternative way of forming expectations. After writing the Nottingham Learning Toolbox1, we find that, given the AR(l) learning model, in which variable is forecasted using its own lagged terms, the adaptive learning mechanism largely amplifies and propagates the effects of a goods sector technology shocks to the economy, and also, enlarges the impact of the time to build feature on the real house price. Furthermore, our sensitivity analysis shows that the values of initial beliefs are important to the mechanism but forecasting errors are not if the constant gain coefficient is small.
Then we consider the assumption of heterogeneous expectations. From the impulse response analysis, we find that (i) the adaptive learning mechanism also has amplification and propagation effects to the economy when only a fraction of the population are learning agents; (ii) when two types of agents have equal weights, the impulse responses from heterogeneous expectations are much closer to those from rational expectations than those from adaptive learning; (iii) when rational agents are fully rational, the adaptive learning mechanism has larger amplification and propagation effects on the economy than when rational agents are partially rational. From the sensitivity analysis, We find that fully rational agents always have larger impacts on model variables than partially rational agents.
Finally, we introduce credit market imperfections to the housing market, thus the mortgage market subjects to a costly verification problem. Our empirical analysis suggests that, while the default rate is countercyclical, the loan to value ratio is procyclical. Our impulse response analysis shows that, given a positive goods sector technology shock, the default rate is counter cyclical, but the loan to value ratio is also countercyclical. The reason we suppose is that, in our model, credit constrained households have less housing in an economic upturn, thus the volume of loans they receive also decreases, leading to a fall in the loan to value ratio. Moreover, we illustrate that, when the mean of the idiosyncratic shock is time-invariant, we always have a positive relation between the default rate and the loan to value ratio. In order to overcome this co-movement, we show that a time-varying mean is necessary.
1 The Nottingham Learning Toolbox is a series of Matlab files that can solve a general form of DSGE models under adaptive learning and heterogeneous expectations. The toolbox solves the model using the Klein's QZ decomposition method, and facilitates the impulse response analysis. The Cambridge Learning Toolbox provides helpful reference for this toolbox at the initial stage.
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