A simple decomposition of the variance of output growth across countries. by Christopher Phillip Reicher

Transcription

1 A smple decomposton of the varance of output growth across countres by Chrstopher Phllp Recher No May 2011

2 Kel Insttute for the World Economy, Hndenburgufer 66, Kel, Germany Kel Workng Paper No May 2011 A smple decomposton of the varance of output growth across countres * Chrstopher Phllp Recher Abstract: Ths paper outlnes a smple regresson-based method to decompose the varance of an aggregate tme seres nto the varance of ts components, whch s then appled to measure the relatve contrbutons of productvty, hours per worker, and employment to cyclcal output growth across a panel of countres. Measured productvty contrbutes more to the cycle n Europe and Japan than n the Unted States. Employment contrbutes the largest proporton of the cycle n Europe and the Unted States (but not Japan), whch s nconsstent wth the dea that hgher levels of employment protecton n Europe dampen cyclcal employment fluctuatons. Keywords: decomposton. Intensve margn, eensve margn, productvty, busness cycles, varance JEL classfcaton: C32, E24, E32. Chrstopher Phllp Recher Kel Insttute for the World Economy Kel, Germany Telephone: +49 (0) E-mal: chrstopher.recher@fw-kel.de * The author wshes to thank Chrstan Merkl and Denns Wesselbaum. All errors are naturally hs own. The responsblty for the contents of the workng papers rests wth the author, not the Insttute. Snce workng papers are of a prelmnary nature, t may be useful to contact the author of a partcular workng paper about results or caveats before referrng to, or quotng, a paper. Any comments on workng papers should be sent drectly to the author. Coverphoto: un_com on photocase.com

3 A smple decomposton of the varance of output growth across countres Chrstopher Phllp Recher a Kel Insttute for the World Economy Ths verson: May 24, 2011 Abstract: Ths paper outlnes a smple regresson-based method to decompose the varance of an aggregate tme seres nto the varance of ts components, whch s then appled to measure the relatve contrbutons of productvty, hours per worker, and employment to cyclcal output growth across a panel of countres. Measured productvty contrbutes more to the cycle n Europe and Japan than n the Unted States. Employment contrbutes the largest proporton of the cycle n Europe and the Unted States (but not Japan), whch s nconsstent wth the dea that hgher levels of employment protecton n Europe dampen cyclcal employment fluctuatons. a Contact nformaton: Hndenburgufer 66, Kel, Germany. Emal: chrstopher.recher@fw-kel.de; Phone: +49 (0) JEL: C32, E24, E32. Keywords: Intensve margn, eensve margn, productvty, busness cycles, varance decomposton. The author wshes to thank Chrstan Merkl and Denns Wesselbaum. All errors are naturally hs own.

4 A smple decomposton of the varance of output growth across countres 1. Motvaton In 2008 and 2009, the global economy suffered from a severe recesson. Dfferent economes behaved qute dfferently. In the Unted States, GDP per workng-age person fell by 3.5% n log terms, and n western Germany GDP per workng-age person fell by 5.0%. 1 Employment per head fell by 4.5% n the Unted States and actually rose n western Germany by 0.1%. As one mght magne, hours per worker make up some of the dfference. Hours per worker fell by 1.6% n the Unted States and fell by 2.9% n western Germany. Nonetheless, a large dscrepancy remans. Measured output per hour grew at a 2.6% rate n the Unted States but shrank by 2.3% n western Germany. Nearly half of the fall n output n Germany came from a fall n measured productvty, not from a fall n measured labor nput. France and the UK show a smlar pattern to Germany, wth productvty absorbng much of the fall n output. Durng the most recent epsode, dfferent countres appear to have adjusted to the fall n output along dfferent margns. Ths paper dscusses the degree to whch these dfferences are systematc. As s well known, labor market nsttutons are very dfferent across Europe, Asa, and the Anglo-Saxon world, wth contnental European countres and Japan exhbtng a hgh degree of employment protecton. Nonetheless, lttle cross-sectonal work has been done on how ths translates nto macroeconomc outcomes. Ths paper follows up on the work of Merkl and Wesselbaum (forthcomng), who compare fluctuatons n labor nput between the Unted States and Germany usng a smple covarance decomposton developed by Fujta and Ramey (2009). Merkl and Wesselbaum fnd that fluctuatons n the ntensve margn of labor nput do not contrbute much to the cycle n ether country; most fluctuatons come on the eensve margn, and the eensve margn s as mportant n Germany as n the Unted States. Ths paper eends ther work n two ways by showng that the Fujta-Ramey decomposton can be calculated smply through a seres of regressons for any accountng dentty and by showng that measured productvty s an mportant cyclcal adjustment margn n Germany as t s n most of contnental Europe and Japan. Nonetheless, employment remans as mportant of an adjustment margn n Europe as n the Unted States; the dfference comes from a 1 The data are from the OECD and from German natonal sources; they are descrbed n Secton 3. 1

5 slghtly less procyclcal hours margn n Europe. At a macroeconomc level, European employment s generally not rgd, though Japanese employment s. 2. A generalzaton of the Fujta-Ramey decomposton The data resde n a mean-zero k by T matrx of tme seres y t wth a covarance matrx Σ wth an accountng dentty lnkng t to an aggregate x t. The goal s to attrbute movements n the aggregate to movements n the orgnal seres. Let b equal a 1 by k matrx whch lnks the columns of y to the scalar aggregate x. Then one could wrte: x t = by t. (1) For each, regressng y on x and then multplyng by b gves the coeffcent: c 1 T T = ' yt ' b, (2) t= 1 t= 1 whch converges n probablty to: p 1 ( E( x t x t ' )) ( E( x t y t ' ) b c ). (3) Wrtng (3) as a functon of varances gves the lmt of c as a functon of the covarance matrx: c p 1 ( bσb ) ( bσ b ) '. (4) The rght hand sde s seres s contrbuton to the overall varance of the aggregate seres (that s, the varance of the aggregate seres condtonal on seres ), whle the left hand sde s the overall varance of the aggregate seres. Furthermore, the c coeffcents all sum up to one. It s n ths sense that the elements of c could be thought of as an accountng-based varance decomposton. 2

6 Ths decomposton s numercally dentcal to the one used by Fujta and Ramey (2009) when b s a vector of all ones. In that case the measured varance contrbuton c s gven as a functon of sample covarances, whch s obvous from the regresson formula: 1 T T c = ' yt ' b = cov( b yt, ) / var( ) = cov( y t= 1 t= 1 t, x ) / var( x ). (5) t t It s possble to vary b over tme, whch would be useful f one wshed (for nstance) to decompose fluctuatons n a chan-weghted ndex of GDP. It s also possble to add other terms to the rght hand sde of the regresson to decompose fluctuatons n an aggregate condtonal on some other state varable. 3. Decomposng the busness cycle across countres The analyss uses data from the OECD s Natonal Accounts and Annual Labor Force Statstcs databases from 1970 through 2007, the latter date chosen n order to avod the most recent crss. The data cover 24 major economes after omttng transton economes and those whose data begn after Data for western Germany are constructed by the author to be as comparable as possble across tme; data on output and employment come from the state-level economc accounts. Data on hours per worker come from the OECD, and unemployment data come from the natonal accounts, wth adjustments made usng the labor force mcrocensus. The analyss uses annual data because country-level quarterly data are only sporadcally avalable and are prone to transtory blps and dscontnutes. The data are detrended n log levels usng an HP flter wth a smoothng parameter of 100. The object of nterest s growth n output per person aged Output per person equals output per hour tmes hours per worker tmes the employment rate (on a labor force bass) tmes the labor force partcpaton rate. In logarthms, ths gves an accountng dentty n the form of (1), whch also holds n frst dfferences: Δ log( Y / N ) = Δ log( Y / H ) + Δ log( H / E) + Δ log( E / LF) + Δ log( LF / N ). (6) Table 1 shows the results of regressng the components on the rght hand sde of (6) on aggregate per capta output growth. It s nstructve to splt the table nto the Anglo-Saxon 3

7 economes, contnental European economes, and other economes, though dscusson wll concentrate on the bg fve economes of France, Germany, Japan, the Unted Kngdom, and the Unted States. The Anglo-Saxon economes wth the excepton of Australa and Ireland have much less procyclcal productvty than the European and Japanese economes. In the Unted States, productvty only contrbutes about 27% of the cycle and labor nput fourffths. Meanwhle, n France and Germany, productvty contrbutes 43% and 38% of the cycle, respectvely. Japan s more European than Europe n ths regard; productvty contrbutes 59% of the cycle there, whle Korea looks more lke the Unted States. In the Unted States, hours per worker contrbute 20% of the cycle and employment fluctuatons contrbute 52% of the cycle; the majorty of those are drven by fluctuatons n the employment rate and not by labor force partcpaton. In the Unted Kngdom, hours per worker are much more mportant. The UK looks lke an outler n ths regard; n most other countres, hours per worker do not contrbute much to the cycle. Even n Japan, hours contrbute only 19%. In most countres, the measured ntensve margn of labor adjustment s not partcularly mportant, and n fact, n France and Germany, t s less mportant than n the Unted States. The employment adjustment margn s the most mportant n the Unted States as n most countres; there, most employment adjustment happens n the employment rate wth an addtonal small contrbuton comng from procyclcal labor force partcpaton. Fluctuatons n the employment rate are about as mportant n the UK and contnental Europe, wth labor force partcpaton provdng more of a margn of adjustment n France and Germany. Some countres, lke Japan, see lttle fluctuaton n employment rates at all. Labor force adjustment n Europe s generally more procyclcal than n the Unted States, whch s nterestng but dffcult to nterpret. Nonetheless, comparng the bg fve countres shows that the eensve margn of employment adjustment s roughly equal n mportance n all countres except Japan. Employment comprses 48% of the cycle n the Unted Kngdom, 51% n the Unted States, 45% n France, and 51% n Germany. Only n Japan s the eensve margn relatvely unmportant, at 22% of the cycle. There are some countres where the estmates seem a lttle bt suspect, namely Span and Turkey. In Span, total labor nput accounts for more than the entre cycle, and measured productvty s n fact countercyclcal. In Turkey the estmates are even stranger; all forms of 4

8 labor nput are actually countercyclcal. Estmates from these countres should not be taken too lterally. 4. Concluson Ths paper has shown how the Fujta-Ramey decomposton can be calculated as a seres of lnear regressons, applyng t to a cross-country panel n order to determne the form that cyclcal fluctuatons take n dfferent countres. In much of Europe and Japan, productvty s more procyclcal than n the Unted States, whle employment s as procyclcal n Europe and much less procyclcal n Japan. Such behavor s nconsstent wth the dea that labor market rgdtes substantally dampen employment fluctuatons n European economes, though the Japanese labor market does appear to be very rgd at a macroeconomc level. 5

9 References Fujta, Shgeru, and Garey Ramey, The Cyclcalty of Separaton and Job Fndng Rates. Internatonal Economc Revew 50(2), pages Merkl, Chrstan, and Denns Wesselbaum, forthcomng. Eensve vs. Intensve Margn n Germany and the Unted States: Any Dfferences? Appled Economcs Letters. 6

10 Table 1: Contrbuton of dfferent components of cyclcal output growth, 24 countres Anglo-Saxon Economes Country Begn End Y/H H/E E/LF LF/N SD(Y/N) Australa Canada Ireland New Zealand Unted Kngdom Unted States Contnental European Economes Country Begn End Y/H H/E E/LF LF/N SD(Y/N) Austra Belgum Denmark Fnland France Germany (West) Greece Iceland Italy Netherlands Norway Portugal Span Sweden Swtzerland Other Economes Country Begn End Y/H H/E E/LF LF/N SD(Y/N) Japan Korea (South) Turkey Ths table contans the results of regressng each component of cyclcal growth n output per person aged on aggregate cyclcal growth. All varables are logged, HP-detrended wth a smoothng parameter of 100, and then taken n frst dfferences. 7