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

On the Nature of Income Inequality Across Nations

In this paper, we investigate the nature of income inequality across nations by first estimating, testing, and distinguishing between two types of aggregate production functions: the extended neoclassical model and a mincerian formulation of schooling-returns to skills. Next, given our panel-data estimates, we proceed in decomposing the variance of the (log) level of output per-worker in 1985 into that of three distinct factors: productivity, human capital, and the dynamic incentives to accumulate capital. Finally, we classify a group of 95 countries according to their relative position (above or below average) for each of these factors. The picture that emerges from these last two exercises is one where countries grew in the past for different reasons, which should be considered for policy design. Although there is not a single-factor explanation for the difference in output per-worker across nations, it seems that productivity differences can explain a considerable portion of income inequality, followed second by dynamic inefficiencies and third by human capital accumulation.

Mixed causal–noncausal autoregressions with exogenous regressors

Mixed causal–noncausal autoregressive (MAR) models have been proposed to model time series exhibiting nonlinear dynamics. Possible exogenous regressors are typically substituted into the error term to maintain the MAR structure of the dependent variable. We introduce a representation including these covariates called MARX to study their direct impact. The asymptotic distribution of the MARX parameters is derived for a class of non-Gaussian densities. For a Student (Formula presented.) likelihood, closed-form standard errors are provided. By simulations, we evaluate the MARX model selection procedure using information criteria. We examine the influence of the exchange rate and industrial production index on commodity prices

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. First, we show that the "best" empirical model developed without common cycle restrictions need not nest the "best" model developed with those restrictions. This is due to possible differences in the lag-lengths chosen by model selection criteria for the two alternative models. Second, we show that the costs of ignoring common cyclical features in vector autoregressive modelling can be high, both in terms of forecast accuracy and efficient estimation of variance decomposition coefficients. Third, we find that the Hannan-Quinn criterion performs best among model selection criteria in simultaneously selecting the lag-length and rank of vector autoregressions

Estimating Sectoral Cycles Using Cointegration and Common Features

This paper investigates the degree of short run and long run comovement in U.S. sectoral output data by estimating sectoral trends and cycles. A theoretical model based on Long and Plosser (1983) is used to derive a reduced form for sectoral output from first principles. Cointegration and common features (cycles) tests are performed and sectoral output data seem to share a relatively high number of common trends and a relatively low number of common cycles. A special trend-cycle decomposition of the data set is performed and the results indicate a very similar cyclical behavior across sectors and a very different behavior for trends. In a variance decomposition exercise, for prominent sectors such as Manufacturing and Wholesale/Retail Trade, the cyclical innovation is more important than the trend innovation.

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. First, we show that the "best" empirical model developed without common cycle restrictions need not nest the "best" model developed with those restrictions. This is due to possible differences in the lag-lengths chosen by model selection criteria for the two alternative models. Second, we show that the costs of ignoring common cyclical features in vector autoregressive modelling can be high, both in terms of forecast accuracy and efficient estimation of variance decomposition coefficients. Third, we find that the Hannan-Quinn criterion performs best among model selection criteria in simultaneously selecting the lag-length and rank of vector autoregressions