The Importance Of Common Cyclical Features in VAR Analysis: A Monte-Carlo Study.

Despite the commonly held belief that aggregate data display short-run comovement, there has been little discussion about the econometric consequences of this feature of the data. We use exhaustive Monte-Carlo simulations to investigate the importance of restrictions implied by common-cyclical features for estimates and forecasts based on vector autoregressive models.Reduced rank models; model selection criteria; forecasting; variance decomposition

The Missing Link: Using the NBER Recession Indicator to Construct Coincident and Leading Indices of Economic Activity.

We use the information content in the decisions of the NBER Business cycle Dating Committee to construct coincident and leading indices of economic activity for United States. Specifically, we use canonical correlation analysis to filter out the noisy information contained in the coincident series. Finally, to construct our preferred coincident index of the U.S. business cycle, we take account of measurement error in the commonly used coincident series by using instrumental-variable methods. The resulting index is a simple linear combination of four coincident series that encompassed currently popular coincident indices.Coincident and Leading Indicators; Business Cycle; Canonical Correlation; Instrumental Variable Probit; Encompassing

Estimating the Stochastic Discount Factor without a Utility Function

In this paper we take seriously the consequences of the Pricing Equation in constructing a novel consistent estimator of the stochastic discount factor (SDF) using panel data. Under general conditions it depends exclusively on appropriate averages of asset returns, and its computation is a direct exercise, as long as one has enough observations to fit our asymptotic results. We identify the logarithm of the SDF using the fact that it is the serial correlation "common feature" in every asset return of the economy. Our estimator does not depend on any parametric function representing preferences, or on consumption data. This property allows its use in testing different preference specifications commonly employed in finance and in macroeconomics, as well as investigating the existence of several puzzles involving intertemporal substitution, such as the equity-premium puzzle. It is also straightforward to construct an estimator of the risk-free rate based on our SDF estimator. When applied to quarterly data of U.S.$ real returns from 1972:1 through 2002:4, our estimator of the SDF is close to unity most of the time and yields an equivalent average annual real discount rate of 2.46%. When we examined the appropriateness of different functional forms to represent preferences, we concluded that standard preference representations used in the literature on intertemporal substitution cannot be rejected by the data. Moreover, estimates of the relative risk-aversion coefficient are close to what can be expected a priori -- between 1 and 2, statistically significant, and not different than unity in testing. A direct test of the equity-premium puzzle using our SDF estimator cannot reject the null that the discounted equity premium in the U.S. has mean zero. However, when consumption-based SDF estimates are employed in the same test, the null is rejected. Further empirical investigation shows that our SDF estimator has a large negative correlation with the equity premium, whereas that of consumption-based estimates are usually too small in absolute value, generating the equity-premium puzzlecommon features, stochastic discount factor

A Common-Feature Approach for Testing Present-Value Restrictions with Financial Data

It is well known that cointegration between the level of two variables (labeled Yt and yt inthis paper) is a necessary condition to assess the empirical validity of a present-value model(PV and PVM, respectively, hereafter) linking them. The work on cointegration has been soprevalent that it is often overlooked that another necessary condition for the PVM to hold isthat the forecast error entailed by the model is orthogonal to the past. The basis of this resultis the use of rational expectations in forecasting future values of variables in the PVM. If thiscondition fails, the present-value equation will not be valid, since it will contain an additionalterm capturing the (non-zero) conditional expected value of future error terms. Our article has a few novel contributions, but two stand out. First, in testing for PVMs,we advise to split the restrictions implied by PV relationships into orthogonality conditions(or reduced rank restrictions) before additional tests on the value of parameters. We showthat PV relationships entail a weak-form common feature relationship as in Hecq, Palm, andUrbain (2006) and in Athanasopoulos, Guillén, Issler and Vahid (2011) and also a polynomialserial-correlation common feature relationship as in Cubadda and Hecq (2001), which representrestrictions on dynamic models which allow several tests for the existence of PV relationships tobe used. Because these relationships occur mostly with nancial data, we propose tests based ongeneralized method of moment (GMM) estimates, where it is straightforward to propose robusttests in the presence of heteroskedasticity. We also propose a robust Wald test developed toinvestigate the presence of reduced rank models. Their performance is evaluated in a Monte-Carlo exercise. Second, in the context of asset pricing, we propose applying a permanent-transitory (PT)decomposition based on Beveridge and Nelson (1981), which focus on extracting the long-runcomponent of asset prices, a key concept in modern nancial theory as discussed in Alvarez andJermann (2005), Hansen and Scheinkman (2009), and Nieuwerburgh, Lustig, Verdelhan (2010).Here again we can exploit the results developed in the common cycle literature to easily extractpermament and transitory components under both long and also short-run restrictions.The techniques discussed herein are applied to long span annual data on long- and short-term interest rates and on price and dividend for the U.S. economy. In both applications we donot reject the existence of a common cyclical feature vector linking these two series. Extractingthe long-run component shows the usefulness of our approach and highlights the presence ofasset-pricing bubbles.