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 ìbestî empirical model developed without common cycle restrictions need not nest the ìbestî 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.

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 in this 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 so prevalent that it is often overlooked that another necessary condition for the PVM to hold is that the forecast error entailed by the model is orthogonal to the past. The basis of this result is the use of rational expectations in forecasting future values of variables in the PVM. If this condition fails, the present-value equation will not be valid, since it will contain an additional term 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 show that PV relationships entail a weak-form common feature relationship as in Hecq, Palm, and Urbain (2006) and in Athanasopoulos, Guillén, Issler and Vahid (2011) and also a polynomial serial-correlation common feature relationship as in Cubadda and Hecq (2001), which represent restrictions on dynamic models which allow several tests for the existence of PV relationships to be used. Because these relationships occur mostly with nancial data, we propose tests based on generalized method of moment (GMM) estimates, where it is straightforward to propose robust tests in the presence of heteroskedasticity. We also propose a robust Wald test developed to investigate 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-run component of asset prices, a key concept in modern nancial theory as discussed in Alvarez and Jermann (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 extract permament 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 do not reject the existence of a common cyclical feature vector linking these two series. Extracting the long-run component shows the usefulness of our approach and highlights the presence of asset-pricing bubbles.

Using common features to understand the behavior of metal-commodity prices and forecast them at different horizons

The objective of this article is to study (understand and forecast) spot metal price levels and changes at monthly, quarterly, and annual frequencies. Data consists of metal-commodity prices at a monthly and quarterly frequencies from 1957 to 2012, extracted from the IFS, and annual data, provided from 1900-2010 by the U.S. Geological Survey (USGS). We also employ the (relatively large) list of co-variates used in Welch and Goyal (2008) and in Hong and Yogo (2009). We investigate short- and long-run comovement by applying the techniques and the tests proposed in the common-feature literature. One of the main contributions of this paper is to understand the short-run dynamics of metal prices. We show theoretically that there must be a positive correlation between metal-price variation and industrial-production variation if metal supply is held fixed in the short run when demand is optimally chosen taking into account optimal production for the industrial sector. This is simply a consequence of the derived-demand model for cost-minimizing firms. Our empirical evidence fully supports this theoretical result, with overwhelming evidence that cycles in metal prices are synchronized with those in industrial production. This evidence is stronger regarding the global economy but holds as well for the U.S. economy to a lesser degree. Regarding out-of-sample forecasts, our main contribution is to show the benefits of forecast-combination techniques, which outperform individual-model forecasts - including the random-walk model. We use a variety of models (linear and non-linear, single equation and multivariate) and a variety of co-variates and functional forms to forecast the returns and prices of metal commodities. Using a large number of models (N large) and a large number of time periods (T large), we apply the techniques put forth by the common-feature literature on forecast combinations. Empirically, we show that models incorporating (short-run) common-cycle restrictions perform better than unrestricted models, with an important role for industrial production as a predictor for metal-price variation.

The missing link: using the NBER recession indicator to construct coincident and leading indices 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 the United States. We identify the coincident index by assuming that the coincident variables have a common cycle with the unobserved state of the economy, and that the NBER business cycle dates signify the turning points in the unobserved state. This model allows us to estimate our coincident index as a linear combination of the coincident series. We establish that our index performs better than other currently popular coincident indices of economic activity.

The missing link: using the NBER recession indicator to construct coincident and leading indices 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 the United States. We identify the coincident index by assuming that the coincident variables have a common cycle with the unobserved state of the economy, and that the NBER business cycle dates signify the turning points in the unobserved state. This model allows us to estimate our coincident index as a linear combination of the coincident series. We establish that our index performs better than other currently popular coincident indices of economic activity.

The missing link: using the NBER recession indicator to construct coincident and leading indices 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 the United States. We identify the coincident index by assuming that the coincident variables have a common cycle with the unobserved state of the economy, and that the NBER business cycle dates signify the turning points in the unobserved state. This model allows us to estimate our coincident index as a linear combination of the coincident series. We compare the performance of our index with other currently popular coincident indices of economic activity.

Previsão de preços de ativos usando restrições do modelo de valor presente

Motivados pelo debate envolvendo modelos estruturais e na forma reduzida, propomos nesse artigo uma abordagem empírica com o objetivo de ver se a imposição de restrições estruturais melhoram o poder de previsibilade vis-a-vis modelos irrestritos ou parcialmente restritos. Para respondermos nossa pergunta, realizamos previsões utilizando dados agregados de preços e dividendos de ações dos EUA. Nesse intuito, exploramos as restrições de cointegração, de ciclo comum em sua forma fraca e sobre os parâmetros do VECM impostas pelo modelo de Valor Presente. Utilizamos o teste de igualdade condicional de habilidade de previsão de Giacomini e White (2006) para comparar as previsões feitas por esse modelo com outros menos restritos. No geral, encontramos que os modelos com restrições parciais apresentaram os melhores resultados, enquanto o modelo totalmente restrito de VP não obteve o mesmo sucesso.

Estimating sectoral cycles using cointegration and common features

This paper investigates the degree of short run and long run co-movement in U.S. sectoral output data by estimating sectoraI 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; 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. Indeed. sectors cyclical components appear as one. In a variance decomposition analysis, prominent sectors such as Manufacturing and Wholesale/Retail Trade exhibit relatively important transitory shocks.

Common cycles in macroeconomic aggregates

Reduced form estimation of multivariate data sets currently takes into account long-run co-movement restrictions by using Vector Error Correction Models (VECM' s). However, short-run co-movement restrictions are completely ignored. This paper proposes a way of taking into account short-and long-run co-movement restrictions in multivariate data sets, leading to efficient estimation of VECM' s. It enables a more precise trend-cycle decomposition of the data which imposes no untested restrictions to recover these two components. The proposed methodology is applied to a multivariate data set containing U.S. per-capita output, consumption and investment Based on the results of a post-sample forecasting comparison between restricted and unrestricted VECM' s, we show that a non-trivial loss of efficiency results whenever short-run co-movement restrictions are ignored. While permanent shocks to consumption still play a very important role in explaining consumption’s variation, it seems that the improved estimates of trends and cycles of output, consumption, and investment show evidence of a more important role for transitory shocks than previously suspected. Furthermore, contrary to previous evidence, it seems that permanent shocks to output play a much more important role in explaining unemployment fluctuations.

Common factors in Latin America's business cycles

This paper constructs new business cycle indices for Argentina, Brazil, Chile, and Mexico based on common dynamic factors extracted from a comprehensive set of sectoral output, external trade, fiscal and financial variables. The analysis spans the 135 years since the insertion of these economies into the global economy in the 1870s. The constructed indices are used to derive a business cyc1e chronology for these countries and characterize a set of new stylized facts. In particular, we show that ali four countries have historically displayed a striking combination of high business cyc1e volatility and persistence relative to advanced country benchmarks. Volatility changed considerably over time, however, being very high during early formative decades through the Great Depression, and again during the 1970s and ear1y 1980s, before declining sharply in three of the four countries. We also identify a sizeable common factor across the four economies which variance decompositions ascribe mostly to foreign interest rates and shocks to commodity terms of trade.

Life Cycle Models, Heterogeneity of Initial Assets,and Wealth Inequality

Life cycle general equilibrium models with heterogeneous agents have a very hard time reproducing the American wealth distribution. A common assumption made in this literature is that all young adults enter the economy with no initial assets. In this article, we relax this assumption – not supported by the data - and evaluate the ability of an otherwise standard life cycle model to account for the U.S. wealth inequality. The new feature of the model is that agents enter the economy with assets drawn from an initial distribution of assets, which is estimated using a non-parametric method applied to data from the Survey of Consumer Finances. We found that heterogeneity with respect to initial wealth is key for this class of models to replicate the data. According to our results, American inequality can be explained almost entirely by the fact that some individuals are lucky enough to be born into wealth, while others are born with few or no assets.