Bridging cyclical DSGE models and the raw data

I propose a method to estimate cyclical DSGE models using the raw data. The approach links the observables to the model counterparts via a ‡exible speci…cation which does not require that the cyclical component is solely located at business cycle frequencies and allows the noncyclical component to take various time series patterns. Applying standard data transformation induces distortions in structural estimates and policy conclusions and explain the reasons for their emergence. The proposed approach recovers the features of the cyclical component in selected experimental designs. JEL classi…cation: E32, C32. Keywords: DSGE models, Filters, Structural estimation, Business cycles. 1 INTRODUCTION 1 1 Introduction There have been considerable developments in the speci…cation of DSGE models over the last 10 years. The original structure, featuring a single technological disturbance, has been enriched with shocks and frictions and our understanding of the propagation mechanism of important shocks enhanced. Steps forward have also been made in the estimation of these models. While a few years ago it was standard to informally calibrate their structural parameters, now researchers routinely use limited and full information estimation procedures and, perhaps more importantly, this trend is common in academic and policy circles (see, e.g., [28], [11], [30],[22], [27] among many others). Despite recent e¤orts, structural estimation of DSGE models is conceptually and practically di¢ cult. For example, classical estimation is asymptotically justi…ed only when the model is the generating process (DGP) of the actual data, up to a set of serially uncorrelated measurement errors, and standard validation exercises are meaningless without such an assumption. Identi…cation problems (see [8]) and numerical di¢ culties are widespread. Finally, the majority of the models investigators use is intended to explain only the cyclical portion of observable ‡uctuations but macroeconomic data contains many types of ‡uctuations, some of which is hardly cyclical. There are two reasons for why researchers prefer to work with ”cyclical”models. Jointly accounting for all types of ‡uctuations is still an ambitious task since there are very few known theoretical mechanisms able to propagate temporary disturbances for a su¢ ciently long time (we need e.g. R&D as in [13] or a Schumpeterian creative destruction) and it is empirically di¢ cult to measure non-cyclical ‡uctuations because samples are short and structural breaks likely to exist. In addition, it is convenient from the computation and the interpretation point of views, to assume that the mechanisms driving cyclical and non-cyclical ‡uctuations are distinct. The mismatch between what models are designed to explain and what the data contains creates headaches for applied investigators. In the literature a number of approaches have been used, all of which are far from ideal: Ignore the existence of non-cyclical movements and …t the cyclical model to demeaned data (see [15]). Such an approach is likely to arti…cially increase the persistence of estimated shocks and, potentially, distort important economic mechanisms present in the model. Fit the cyclical model to data …ltered with an arbitrary statistical device. Such an approach is popular, but problematic for at least three reasons. First, the cyclical component extracted by the majority of the statistical …lters can be represented as a symmetric, two-sided moving average of the raw data. Thus, as suggested long ago in [21], the timing of the information is altered by …ltering, and dynamic analyses become di¢ cult to interpret. Second, while it is typical to …lter each series separately and to remove non-cyclical ‡uctuations from real but not from nominal variables, there are consistency conditions that must hold a resource constraint need not be satis…ed if each variable is separately …ltered and many situations when not all the ‡uctuations in nominal