Abstract
This paper implements the technique suggested by Den Haan (J Monet Econ 46:3–30, 2000) to investigate contemporaneous as well as lead and lag correlations among economic data for a range of forecast horizons. The lead/lag approach provides a richer picture of the economic dynamics generating the data and allows one to investigate which variables lead or lag others, and whether the lead or lag pattern is short term or long term in nature. This technique is applied to monthly sectoral level employment data for the USA and shows that among the ten industrial sectors followed by the US Bureau of Labor Statistics, six tend to lead the other four. These six have high correlations indicating that the structural shocks generating the data movements are mostly in common. Among the four lagging industries, some lag by longer intervals than others and some have low correlations with the leading industries. These low correlations may indicate that these industries are partially influenced by structural shocks beyond those generating the six leading industries, but they also may indicate that lagging sectors feature a different transmission mechanism of shocks.
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Notes
These modern macroeconomic models owe much of their existence to the seminal work on Real Business Cycles by Kydland and Prescott (1982). Such models typically require simplicity somewhere in their formulation in order to remain manageable in dynamic settings, and aggregation is the most popular approach to achieving manageability.
The idea of differences in sectoral behavior has been around since work by Pigou (1927).
The data used in this paper came from the US Bureau of Labor Statistics and were obtained from the FRED data base maintained by the St. Louis Federal Reserve Bank. The paper refers to the various sectors by using the names given by the Bureau of Labor Statistics to each sector with the exception of referring to Total Manufacturing as simply Manufacturing. We also use the ampersand, &, when it is part of the name given to a sector by the Bureau of Labor Statistics. In order to be clear when we are referring to a particular industrial sector, the paper uses a convention of capitalizing the name of the sector.
Our objective here is to provide new summary statistics useful for developing better sectorial models of the economy. Some work, such as Clark (1998), Christiano and Fitzgerald (1998), Hornstein (2000), DiCecio (2009), Yedid-Levi (2009) and Foerster et al. (2011), have built models that match the general level of comovement recognized by the Business Cycle Dating Committee of the National Bureau of Economic Research. Recently, Chang and Hwang (2011) have focused on the comovement analysis of phase shifts (i.e. turning points of alternative business cycle phases) in US manufacturing industries. But these models to not capture the results that we find that some service sectors tend to be laggards, and even among the leaders, some seem to have different transmission mechanisms from each other.
Stock and Watson (1999) also use this lead and lag analysis to assess numerous data series comovements over the business cycle using log differenced data. A related approach is used in Christiano and Fitzgerald (1998) who detrend using the band-pass filter described in Christiano and Fitzgerald (2003).
Another popular measure of economic performance is output, but unfortunately, there is no source that is useful for our purposes. Although aggregate GDP is computed at a quarterly frequency by the US Commerce Department, sectoral output is only computed at an annual frequency. Alternative series on industrial production are computed at a monthly frequency by the Federal Reserve Bank. Unfortunately, these data tend to emphasize Manufacturing, Business Equipment, Mining and Electric & Gas Utilities and leave out many other important service industries. This missing service sector component is particularly important in part, because the service sectors have grown to such a large percentage of GDP, but also because our results below show that some of these service sectors are part of the group of sectors which lag the rest of the economy. Given these constraints, we regard the employment data as more suitable.
This analysis was also carried out using the band-pass filter advocated by Christiano and Fitzgerald (2003) with largely the same results. These results can be obtained from the authors upon request. Another alternative used in Stock and Watson (1999) is to take logarithmic differences of the data to focus on the growth rates of unit root processes. As is well known (Canova 1998, pp. 489–490), first-difference detrending implies cycles of short length, which emphasize high-frequency data dynamics.
In most of our analysis, we consider the Manufacturing sector as a whole. However, at times we have split this sector in Durable and Non-Durable subsectors in order to highlight some important results. Table 1 shows this extra decomposition in the last two rows.
This unusual data point in August 1983 is likely a miscode, but it could be because of employment changes arising from the break up of AT&T. However, regardless of its origin, since this is the way the data are reported, we did not want to change it. In all of the results reported below, we used the data exactly as reported. As a check, we also ran the calculations using a value of 2213, which was the average of the series 1 month before and 1 month after that date, and found qualitatively the same results.
Stock and Watson (1999) also use this approach with disaggregated data. An alternative approach for lead and lag analysis is to use VAR methods as in Fuhrer and Moore (1995). In contrast to the VAR approach suggested in this paper, the VAR approach followed by Fuhrer and Moore (1995) requires that all variables included in the VAR to be covariance stationary. So detrending of non-stationary variables is required prior to computing their comovement under Fuhrer and Moore’s approach. Space considerations kept us from including that analysis here, but sample assessments using this approach can be obtained from the authors on request.
Prescott (1986) choose GDP as the base series.
Some of the highest correlations appear to be equal to others with the two decimal place accuracy given in the table, but are higher if additional decimal places are considered. The additional decimal places are not reported to keep the table’s width narrow enough to fit on a page.
Since Manufacturing, Construction, Leisure & Hospitality Services and Professional & Business Services are highly contemporaneously correlated, we concluded that they lead the other sectors. As a robustness check of this conclusion, it is possible to recompute the table with either of these sectors as the benchmark sector. Such a computation yields results that are analogous to the ones presented here for Manufacturing and in the interest of space are not presented. However, in the analysis which uses our approach, we do describe the results for alternative benchmark industries.
In addition to Den Haan (2000), other applications of this approach include Den Haan and Sumner (2004), María-Dolores and Vázquez (2008) and Den Haan and Sterk (2011). Cassou and Vázquez (2010) show how to use Den Haan’s approach to investigate the lead–lag comovement between output and inflation in the context of a New Keynesian model.
Avoiding detrending of the data is useful because Den Haan (2000, p. 5) argues that the negative correlation between output and prices often found in the data could be an artifact of common detrending procedures used to make the data stationary.
Indeed, an important difference between the approach here and the one in Clark (1998) is that Clark uses methods to identify the sectoral and regional structural shocks.
One limitation of this approach is that it does not provide standard impulse response functions which show the responses of each endogenous variable to alternative structural shocks. However, Den Haan (2000) views this as a positive feature as he notes that such standard impulse response analysis requires an identification structure which is often the subject of some dispute.
As a robustness check, we also investigated a fairly large number of alternative forecasting equation specifications. Among them were a 2-variable VAR with 12 lags, a 10-variable VAR with 24 lags and a few 10-variable Bayesian VAR specifications (with Minnesota priors) with different number lags. We found the results to be qualitatively similar to the ones obtained from the 12-lag unrestricted VAR used here. A robustness analysis across a fairly large number of dimensions is contained in an appendix available upon request from the authors.
A complete set of diagrams can be obtained from the authors upon request.
The length of forecast error series used to compute the lead–lag correlations in this, and the remaining figures of the paper is 318. It is possible to use standard bootstrapping methods to find confidence bands around the correlation plots. Such confidence bands were generated using programs from Den Haan’s Web site and showed sufficiently wide bands that the individual correlation plots were not significantly different from each other. However, as in Prescott (1986) and Stock and Watson (1999), we still interpret maximal correlations that are different from the contemporaneous correlation as indicating a lead or lag. Because the bands did not indicated significance, they are not provided here, but sample plots can be obtained from the authors upon request.
This contemporaneous correlation plot is the one used by Den Haan (2000) for his analysis.
At this point, it is also possible to illustrate one of the methodological differences between this paper and the important work by Long and Plosser (1987). They also looked at forecast errors. However, they only looked at one step ahead forecast errors and did not look at lead and lag correlations. Their comovement statistic is roughly equivalent to the first correlation displayed on the left edge of the contemporaneous correlation line in our diagram.
Blankenau and Cassou (2009) document that Information Services as well as Education & Health Services, discussed below, have a higher-skilled labor percentage than Manufacturing, where skilled labor is defined as workers with college degrees.
Table 3 above suggested the Non-Durable subsector is leading total Manufacturing. This result would imply that the Non-Durable subsector should show a larger lead over Information Services than the one exhibited by Manufacturing. We have confirmed this intuition by estimating an 11-variable VAR(4) where Durable and Non-Durable subsectors are included in the original 10-variable VAR instead of total Manufacturing.
It may be useful to note that because of the symmetry with regard to the leads and lags, Figs 2, 3, 4, 5 and 6 also show how the plots would look when other industries are the reference. So for example, Fig. 2 shows how the plots would look when Information Services is the reference industry and correlations with Manufacturing are plotted. The only difference is that the line representing the lead (lag) correlation in Fig. 2 would now represent the lag (lead) correlation when Information Services is the reference industry.
Other less consequential differences are that the analysis here uses a multivariate approach based on forecast errors, while theirs uses a univariate band-pass filter. Moreover, our analysis uses employment data, while theirs uses hours worked. One may use the band-pass filter to obtain similar information as our approach based on VAR forecast errors. For instance, one may use the band-pass filter to isolate selected short-, medium- and long-term cyclical components of the data and then analyze whether the comovement properties of pairs of variables change with the definition of the cyclical component.
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Acknowledgments
We would like to thank Ramón María-Dolores and seminar participants at Kansas State University, Durham University, England, Heriot Watt University, Universidad del País Vasco, 16th Computing in Economics and Finance Conference and the 10th Annual Missouri Economics Conference for helpful comments on earlier drafts of this paper. We would also like to thank two anonymous referees and the editor of this journal for helpful comments on an earlier draft of the paper. Some of this research was supported by the Spanish Ministry of Education and Science, Grant Numbers SEJ2006-12793/ECON, SEJ2007-66592-C03-01-02/ECON and ECO2010-16970. 2006–2009, Basque Government grants IT-214-07 and GME0702. Cassou would also like to thank Ikerbasque for financial support.
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Cassou, S.P., Vázquez, J. Employment comovements at the sectoral level over the business cycle. Empir Econ 46, 1301–1323 (2014). https://doi.org/10.1007/s00181-013-0720-7
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DOI: https://doi.org/10.1007/s00181-013-0720-7