Essays in formulating and estimating DSGE models
From the seminal work of Kydland and Prescott (1982) a huge amount of ef- fort and work has been devoted in order to improve our understanding of how an economy works. After the breakthrough of general equilibrium analysis, macroeconomics rapidly became a mathematical science based on the paradigm that economies can be described as intertemporal equilibria. A Dynamic Stochastic General Equilibrium model (DSGE) describes the over time evolution of an economy as function of primitive objects, so called deep pa- rameters, which relate to preference, technology and endowments of economic agents, namely firms, households and government. It is a Stochastic model as the source of economic fluctuations is provided by random shocks. Those latter can be measured and named, but their ultimate explanation is left out of the model. It is Dynamic General Equilibrium since agents take optimal intertem- poral decisions (under the constraints they face) which are mutually consistent, without being necessarily optimal from a social welfare point of view. This thesis is an attempt to add one further page to the book of knowledge of DSGE models. In particular, in each chapter I treat a different issue concerning the link between exogenous shocks and macroeconomic variables. In the first chapter I answer the following: 'How does credit relate to the transmission mechanism of shocks into macroeconomic variables ?' We introduce liquidity frictions into a standard Real Business Cycle model. While stan- dard models assume that business projects can immediately find financing, in our set-up we introduce a lengthy search process for potential Entrepreneurs to match with loans from financial intermediaries. Every period spent on the search process entails a cost. When a match occurs the Entrepreneur can start a business and she is willing to give up part of her profit to the intermediary in exchange for not getting back into the search process. This is a kind of liquidity premium which is paid by active firms on top of the risk-free rate: when credit markets are tight, meaning that Entrepreneurs are abundant compared to avail- able loans, the premium is higher. We show that when labor markets are perfect, the effects of our liquidity premium on economic dynamics are small. Instead, when also labor markets are subject to frictions, i.e. workers and firms are in another search process to find one another, credit frictions can either accelerate or reduce the impact of the stochastic shocks hitting the economy, depending on the value of deep parameters. For realistic calibrations of the model, based one US data, an accelerating effect seems to be in place. The second chapter deals with the econometric estimation of DSGE mod- els. Earlier contributions used simple models as small laboratory experiments which could be calibrated in order to reproduce relevant features of an econ- omy. As the discipline evolved, models were taken to the data by the means of more formal econometric techniques. Our second question is as follows: 'Pro- vided the generating process of shocks is unknown to researchers what is the best way to bring a model to the data ?'. This work relaxes one of the com- mon assumption used in the literature, that is the statistical form of exogenous shocks is known to the researcher. We extend Kalman Filter Maximum Like- lihood methods to cope with the problem at hand. We report better estimates of the deep parameters of the economy (i.e. more in line with those obtained by using other sources of data) and a large and statistically significant improve- ment in out-of-sample forecast of macroeconomic variables. We also provide empirical reasons to believe that long memory can be a relevant issue concern- ing DSGE models, a feature much overlooked in the literature. The ingenuity of our method is that it is an effective way of filtering out from the data the amount of persistence which would be left unexplained by the model. In the last chapter I take a Bayesian point of view to estimating DSGE mod- els. A bayesian researcher uses not only the set of data at hand, but also his prior knowledge. The contribution of the chapter is twofold. On the one hand we investigate some earlier problematic results, namely those of Negro and Schorfheide (2008). A critical issue in their procedure is fully exposed and some ways to solve it are outlined. Then we propose a simple way of eliciting priors, which is to use information concerning so called impulse response functions. Impulse responses are the responses of macroeconomic variables, conditional on some exogenous shock occurring in the economy. Those are the most stud- ied object in modern macroeconomics and they constitute an ideal source of prior knowledge. Some implications of the use of impulse responses as prior knowledge are explored in this chapter. The technical evolution of the chapters (from calibration to Bayesian Esti- mation) reflects the evolution of the literature on DSGE models and also the learning process of the author himself. ; (ECON 3) -- UCL, 2010