Academic journal article Journal of Money, Credit & Banking

Complementarities and Comovements

Academic journal article Journal of Money, Credit & Banking

Complementarities and Comovements

Article excerpt

POSITIVE COMOVEMENT between different sectors of the economy is a salient feature of business cycles. Over the period 1959-1986, for instance, the average pairwise correlation of annual employment growth for the 126 three-digit U.S. manufacturing industries used in this paper is 0.341. (1) For gross output and value added, the corresponding figures over 1960-1986 are 0.284 and 0.228. Similar evidence is presented in Long and Plosser (1987), Murphy, Shleifer and Vishny (1989a), and Cooper and Haltiwanger (1990).

Interindustry comovement is essential to aggregate output and employment volatility. To see this, suppose we approximate the growth rate of some aggregate activity measure, denoted q, as a weighted average of disaggregated industry growth rates:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where N is the number of sectors and SHAR[E.sub.i] equals sector i's steady-state share of aggregate activity. Then the variance of q is approximately

(2) SHARE * [PSI] * SHARE',

where SHARE is a 1-by-N vector of industry shares and [PSI] is the N-by-N variance-covariance matrix of disaggregated industry activity.

From (2), one can decompose the approximate variance of q into a term due to the diagonal elements of [PSI], and a "comovement" term due to the off-diagonal elements of [PSI]. Table 1 presents this decomposition for manufacturing employment, gross output and value added growth. The matrix [PSI] and the vector SHARE are estimated using annual data for 126 three-digit manufacturing industries from 1959-86 for employment and from 1960-86 for output and value added; the data are described in the appendix.

The results suggest that most aggregate volatility can be attributed to interindustry comovement. For instance, the actual standard deviation of annual manufacturing employment growth over the sample period is 4.31 percent. The approximate standard deviation implied by (2) is 4.42 percent. The standard deviation implied by the diagonal elements of [PSI] is just 0.99 percent, while the standard deviation implied by the off-diagonal elements of [PSI] is 4.31 percent; comovement thus accounts for almost 95 percent of the variance of manufacturing employment. Qualitatively similar results hold for output and value added. Comovement remains important at higher levels of aggregation; for instance, when I aggregate to twenty two-digit industries, the fraction of manufacturing employment variance attributable to comovement is over 86 percent.

In principle, interindustry comovement could be due entirely to the direct effects of common shocks. For instance, monetary policy may directly affect the demand for all durable goods. However, comovement may also be caused by complementarities that propagate shocks across sectors. For instance, monetary policy may generate comovement between cars and steel not because money affects steel directly, but because money affects cars and because shocks to cars are transmitted to steel. Recent research has suggested several potential sources of interindustry complementarity, including input-output linkages (Long and Plosser 1983; Horvath 1998 and 2000), consumption complementarities (Verbrugge 1998), external economies of scale (Baxter and King 1991; Farmer and Guo 1994), trading externalities (Diamond 1982), and aggregate demand spillovers (Murphy, Shleifer, and Vishny 1989b). The common implication of such theories is that the interindustry pattern of comovement depends on the interindustry pattern of linkage. Complementarities do not merely imply that A should comove with B; they imply that the amount of comovement between A and B should depend on the degree of linkage between A and B.

This paper assesses the importance of complementarities for short-run comovement. Using postwar U.S. data for disaggregated industries, I examine the relationship between the observed pattern of comovement and observable measures of complementarity suggested by three simple models. …

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