Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter

Maravall and del Río (2001), analized the time aggregation properties of the Hodrick-Prescott (HP) filter, which decomposes a time series into trend and cycle, for the case of annual, quarterly, and monthly data, and showed that aggregation of the disaggregate component cannot be obtained as the exact result from direct application of an HP filter to the aggregate series. The present paper shows how, using several criteria, one can find HP decompositions for different levels of aggregation that provide similar results. We use as the main criterion for aggregation the preservation of the period associated with the frequency for which the filter gain is ½this criterion is intuitive and easy to apply. It is shown that the Ravn and Uhlig (2002) empirical rule turns out to be a first-order approximation to our criterion, and that alternative —more complex— criteria yield similar results. Moreover, the values of the parameter λ of the HP filter, that provide results that are approximately consistent under aggregation, are considerably robust with respect to the ARIMA model of the series. Aggregation is seen to work better for the case of temporal aggregation than for systematic sampling. Still a word of caution is made concerning the desirability of exact aggregation consistency. The paper concludes with a clarification having to do with the questionable spuriousness of the cycles obtained with HP filte

Time aggregation and the Hodrick-Prescott filter

En este trabajo se analizan las propiedades de agregacion del filtro Hodrick- Prescott (HP), utilizado en la descomposicion de series temporales en tendencia y ciclo, para observaciones anuales, trimestrales y mensuales. La agregacion de los componentes obtenidos con la serie desagregada no se pude interpretar (de forma exacta) como el resultado de aplicar directamente un filtro HP a la serie agregada (y viceversa). No obstante, utilizando varios criterios se encuentran descomposiciones del tipo HP que proporcionan resultados muy similares. Finalmente, el criterio propuesto para encontrar filtros HP 'casi equivalentes' para distintas frecuencias de observacion es de facil aplicacion, y no depende de la serie temporal objeto de analisis, ni del modelo de esta. (am) (ad

Ciclos Económicos e Inversión en Bolivia

Los ciclos económicos en Bolivia son estables en el largo plazo pero no en el corto plazo, aun así los ciclos límite muestran que existe equilibrio. Tanto el acelerador como el tiempo de fabricación de nuevos bienes de capital dependen de las percepciones de las políticas del gobierno, si estas políticas permiten que el tiempo de fabricación de nuevos bienes de capital se reduzca o el impacto del acelerador fuera mayor, mejoraría el impacto de la inversión sobre el producto, teniendo como resultado ciclos estables en el corto plazo y largo plazo.Ciclos Económicos; Inversión; Equilibrio; Estabilidad; Corto Plazo; Largo Plazo; Acelerador; Producto

Modelling Italian potential output and the output gap

The aim of the paper is to estimate a reliable quarterly time-series of potential output for the Italian economy, exploiting four alternative approaches: a Bayesian unobserved component method, a univariate time-varying autoregressive model, a production function approach and a structural VAR. Based on a wide range of evaluation criteria, all methods generate output gaps that accurately describe the Italian business cycle over the past three decades. All output gap measures are subject to non-negligible revisions when new data become available. Nonetheless they still prove to be informative about the current cyclical phase and, unlike the evidence reported in most of the literature, helpful at predicting inflation compared with simple benchmarks. We assess also the performance of output gap estimates obtained by combining the four original indicators, using either equal weights or Bayesian averaging, showing that the resulting measures (i) are less sensitive to revisions; (ii) are at least as good as the originals at tracking business cycle fluctuations; (iii) are more accurate as inflation predictors.potential output, business cycle, Phillips curve, output gap

MULTIVARIATE TREND–CYCLE EXTRACTION WITH THE HODRICK–PRESCOTT FILTER

The Hodrick–Prescott filter represents one of the most popular methods for trend–cycle extraction in macroeconomic time series. In this paper we provide a multivariate generalization of the Hodrick–Prescott filter, based on the seemingly unrelated time series approach. We first derive closed-form expressions linking the signal–noise matrix ratio to the parameters of the VARMA representation of the model. We then show that the parameters can be estimated using a recently introduced method, called “Moment Estimation Through Aggregation (META).” This method replaces traditional multivariate likelihood estimation with a procedure that requires estimating univariate processes only. This makes the estimation simpler, faster, and better behaved numerically. We prove that our estimation method is consistent and asymptotically normal distributed for the proposed framework. Finally, we present an empirical application focusing on the industrial production of several European countries

The effects of shocks in early life mortality on later life expectancy and mortality compression: A cohort analysis

I study how shocks in cohort-level early life conditions, as represented by deviations from trend in mortality before age 5, affect later mortality. I use data for six European countries and find that shocks that increase infant mortality decrease later life expectancy between ages 5-30. The effect is strong for England and Wales but small or insignificant for other countries. Shocks that increase mortality at ages 1-5 increase life expectancy between ages 5-30 and compress the mortality distribution. For both shocks the effects are weak at older ages. These results suggest that early life conditions have a transitory effect and potentially only little influence on old-age mortality.cohort effects, early life conditions, mortality

Countercyclical Labor Productivity: The Spanish Anomaly

The cyclical pattern of labor productivity has been a subject of discussion in the economic literature for long time with important theoretical implications. Many authors point out the role of labor market institutions as determinants of the cyclical pattern. For these authors, the loss of procyclicality experimented in the United States since the mid-1980s could be explained by decrease of rigidities in labor market. Following the literature, this paper explores the role of labor regulation by analyzing the case of Spain, which has gone in a few years from a strongly procyclical pattern to a counterciclycal one. Our results suggest that the high rigidity in wages and the great flexibility in labor, related to the temporary workers after the 1984 legislative reform, is the main cause of the countercyclical pattern of the Spanish labor productivity. Our findings are in line with previous papers highlighting the crucial influence of labor market institutions over the cyclical pattern