Firms' Relative Sensitivity to Aggregate Shocks and the Dynamics of Gross Job Flows

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Firms’ Relative Sensitivity to Aggregate Shocks and the Dynamics of Gross Job Flows Eugenio P. Pinto 2009-02 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Firms(cid:146)Relative Sensitivity to Aggregate Shocks and the Dynamics of Gross Job Flows EugØnio Pinto (cid:3) November 2008 Abstract We propose a measure for the importance of aggregate shocks for (cid:135)uctuations in job (cid:135)ows at the (cid:133)rm level. Using data for the Portuguese economy, we (cid:133)nd that largeandold(cid:133)rmsexhibithigherrelativesensitivitytoaggregateshocksandhave adisproportionalin(cid:135)uenceoverthedynamicsofaggregatejobreallocation. Inthe overall economy, since large and old (cid:133)rms reallocate jobs less procyclically than small and young (cid:133)rms, job reallocation is less procyclical than if (cid:133)rm size and age classes were equally sensitive to aggregate shocks. A similar result applies in the manufacturingandthetransportationandpublicutilitiessectors. However,inthe services and retail trade sectors the reallocation patterns are more similar across (cid:133)rm size and age, likely re(cid:135)ecting the expansion of existing and the creation of new industries. We conclude that large and old (cid:133)rms seem relatively more important to assess the state of the business cycle. JEL Classi(cid:133)cation: E24, E32, J23 Keywords: Aggregate Shocks, Gross Job Flows, Firm Heterogeneity Board of Governors of the Federal Reserve System (e-mail: eugenio.p.pinto@frb.gov). The views (cid:3) expressed in this paper are those of the author and do not necessarily re(cid:135)ect the views of the Board of Governors of the Federal Reserve System or its sta⁄. I would like to thank valuable comments on an earlier version of this paper from Bruce Fallick, Andrew Figura, John Haltiwanger, David Lebow, Michael Pries, and John Shea. All remaining errors are my own. I would also like to thank the Direc(cid:231)ªo-Geral de Estudos, Estat(cid:237)stica e Planeamento - MinistØrio da Seguran(cid:231)a Social, da Fam(cid:237)lia e daCrian(cid:231)a,forkindlyenablingmetoaccesstheQuadrosdePessoaldatabase,theUniversityofMinho for their hospitality, and Joªo Cerejeira and Miguel Portela for their help in extracting results.

1 Introduction Job reallocation is a signi(cid:133)cant and cyclically sensitive activity. The literature has identi(cid:133)edsubstantialheterogeneitiesacross(cid:133)rmclassesandeconomicsectorsintermsof themagnitudeandthevolatilityofjobcreationandjobdestruction. Inthispaper, after con(cid:133)rming some of these heterogeneities, we analyze how the importance of aggregate shocks for (cid:135)uctuations in gross job (cid:135)ows di⁄ers across (cid:133)rm size and age and how these di⁄erences a⁄ect the dynamics of aggregate job (cid:135)ows. Using the Longitudinal Research Database (LRD) data for the U.S. manufacturing sector, Davis and Haltiwanger (1990, 1992) and Davis et al. (1996) (cid:133)nd that job reallocation is countercyclical mostly because of large and old plants, as job destruction for these plants is substantially more volatile than job creation.1 Burgess et. al. (2000) emphasize the (cid:133)rm(cid:146)s lifecycle and conclude that young and dying (cid:133)rms account for about a third of all job reallocation. The countercyclical nature of job reallocation is later questioned by Boeri (1996) as it seemed to be speci(cid:133)c to manufacturing and result from a selection bias against small and young (cid:133)rms in the LRD data. Foote (1998) con(cid:133)rms this with Michigan unemployment insurance data, where the higher volatility of job destruction with respect to the volatility of job creation in manufacturing does not hold in other sectors like services and retail trade. Foote then argues that the cyclical properties of input reallocation are a function of the sector(cid:146)s trend growth rate. In analyzing the importance of composition e⁄ects for some of these facts, Davis and Haltiwanger (1999) conclude that, among four-digit manufacturing sectors, the relative volatility of job destruction is positively a⁄ected by (cid:133)rm size and age after controlling for trend growth. This suggests that the higher relative volatility of job destruction in manufacturing partly results from the predominance of large and old (cid:133)rms in this sector, with the opposite occurring in services. In this paper, we provide further evidence on how di⁄erent (cid:133)rm size and age classes in(cid:135)uence the cyclical properties of aggregate job reallocation. We begin by presenting (cid:133)rm-level job (cid:135)ows statistics for the Portuguese economy and four economic sectors, and later tabulate job (cid:135)ows by (cid:133)rm size and age. Our (cid:133)ndings are consistent with those in other international studies. Previous studies for Portugal, such as Blanchard and Portugal (2001), only contained information for the overall economy and the manufacturing sector and did not include an analysis of heterogeneities by (cid:133)rm size and age. 1Because job creation is procyclical and job destruction is countercyclical, if job reallocation is countercyclical then job destruction has a higher cyclical variability than job creation. 1

Based on a simple model of job (cid:135)ows dynamics, with both aggregate and idiosyncratic shocks, we propose the coe¢ cient of variation of gross job (cid:135)ows as a proxy for the importance of aggregate shocks for (cid:135)uctuations in job (cid:135)ows at the (cid:133)rm level. Since the coe¢ cient of variation is a scale-independent index of volatility, we interpret this proxy as a measure of (cid:133)rms(cid:146)relative sensitivity to aggregate shocks. In our data, for both the overall economy and the four economic sectors, we (cid:133)nd that large and old (cid:133)rms are more relatively a⁄ected by aggregate shocks than small and young (cid:133)rms. Therefore, large and old (cid:133)rms in(cid:135)uence more the dynamics of aggregate job (cid:135)ows than the average size of these (cid:135)ows. Given the markedly heterogeneous job reallocation patterns across (cid:133)rm size and age classes, we then analyze how the higher relative sensitivity to aggregate shocks of large and old (cid:133)rms a⁄ects the dynamics of aggregate job reallocation. In the overall economy, the higher sensitivity of large and old (cid:133)rms makes aggregate job reallocation less procyclical than if (cid:133)rm size and age classes were equally sensitive to aggregate shocks, as these (cid:133)rms have lower net job creation rates and less procyclical, or even countercyclical, job reallocation. A similar result applies in the manufacturing and the transportation and public utilities sectors, for both large and old (cid:133)rms, and in the services sector, for old (cid:133)rms. For the other cases, the above result does not apply because of more similar reallocation activity across (cid:133)rm classes. In particular, large (cid:133)rms make aggregate job reallocation in retail trade and services slightly more procyclical than if size classes were equally sensitive to aggregate shocks, as large (cid:133)rms exhibit even more procyclical reallocation than small (cid:133)rms. We conclude that the dynamics of aggregate job reallocation depends disproportionately on the cyclical behavior of large and old (cid:133)rms. Therefore, a relatively higher emphasis should be given to large and old (cid:133)rms when characterizing the business cycle. The conclusions of the paper appear also important for the literature that analyzes di⁄erences in the response to aggregate shocks across (cid:133)rm size and age. Similarly to Li and Weinberg (2003) and Campbell and Fisher (2004), we use a framework where (cid:133)rms face idiosyncratic and aggregate shocks. However, instead of focusing on the absolute responseofadjustmentratestoaggregateshocks, whichtendstobehigherforsmalland young (cid:133)rms, we analyze the absolute response relative to the average adjustment rate, which also tends to be higher for these (cid:133)rms as they are more exposed to idiosyncratic shocks. That is, we emphasize coe¢ cients of variation instead of standard deviations. Sincesmallandyoung(cid:133)rmsarecharacterizedbyhigheraverageratesofadjustment, the absolute volatility of gross job (cid:135)ows should also be higher due to the scale dependence 2

of standard deviations. On the contrary, coe¢ cients of variation are scale independent and show that large and old (cid:133)rms are relatively more a⁄ected by aggregate shocks. The paper is organized as follows. In section 2, we present gross job (cid:135)ows statistics for the Portuguese economy and four one-digit sectors. In section 3, we propose a measure for (cid:133)rms(cid:146)relative sensitivity to aggregate shocks. In section 4, we analyze heterogeneities across (cid:133)rm size and age classes and how the higher sensitivity to aggregate shocks of large and old (cid:133)rms a⁄ects the dynamics of aggregate job reallocation. We conclude in section 5. Three appendices contain a description of the database and the methods we use to obtain gross job (cid:135)ows, an outline of the model simulations and proofs in section 3, and additional details on the decompositions in section 4. 2 Gross Job Flows in the Portuguese Economy Inthissection, wepresentevidenceonthedynamicsofgrossjob(cid:135)owsinthePortuguese economy. We use Quadros de Pessoal (QP), a longitudinal employer-employee matched database, with annual data covering the period 1985-2000.2 As background, we present a summary of some macroeconomic developments in the Portuguese economy during this period. From the mid-1980s to the late-1990s, Portugal went through a process of modernization in infrastructure and market regulations. After joining the European Union (EU) in 1986, Portugal bene(cid:133)ted from large amounts of European Structural Funds to promote investment in infrastructure. Until the mid-1990s, Portugal also adopted reformstoenhancecompetitionandliberalize(cid:133)nancialmarkets, akeystepinthecreation of an economic union in Europe. In addition, from the late-1980s to the early-1990s there was a wave of privatizations of public utilities. As a result of these structural reforms, and the increased liberalization of trade in the EU during this period, some traditional manufacturing sectors, such as textiles, su⁄ered hard, while new opportunities emerged, especially in the retail trade and services sectors. To summarize the business cycle in the period under analysis, (cid:133)gure 2 plots the annual real growth rate of GDP, the unemployment rate, and the net job creation rate among continuing (cid:133)rms.3 The late-1980s was a period of high growth with a declining unemployment rate. This expansion was followed by a downturn in economic activity 2In appendix A, we describe the QP database and the methods we use to obtain gross job (cid:135)ows by sector and by (cid:133)rm size and age. 3The sources are SourceOECD, for the (cid:133)rst two variables, and QP, for the net job creation rate. 3

that hit the bottom in 1993. The ensuing upturn was mild and net job creation reacted only slowly to the improving economy. It is apparent from(cid:133)gure 2 that net job creation has a high positive correlation with growth of real GDP, and that the unemployment rate is countercyclical. We present in table 1 the evolution of gross job (cid:135)ows for the overall economy during the period under analysis.4 The values for gross job (cid:135)ows are comparable to other international evidence, such as Davis et al. (1996) and Baldwin et al. (1998). Both the rates of job creation and job destruction and the contribution of births and deaths to gross (cid:135)ows are large. Most job reallocation consists of excess reallocation, with net job creation accounting for only a small fraction. Job creation and job destruction vary procyclically and countercyclically with the business cycle, respectively, and in a way consistent with (cid:133)gure 2. In table 2, we present some statistics of job (cid:135)ows for the overall economy and four one-digit sectors: manufacturing, services, retail trade, and transportation and public utilities.5 In general, there is considerable reallocation activity and signi(cid:133)cant crosssector di⁄erences in the magnitude and cyclical behavior of job (cid:135)ows. Consistent with Foote (1998), sectors with higher net job creation (services and retail trade) exhibit more procyclical reallocation. However, for the overall economy, the average net job growth rate is notably positive while reallocation is only marginally procyclical. As we show in section 4, this result can be partially explained by the behavior of large and old (cid:133)rms.6 Table 2 also reveals the structural changes that occurred in the Portuguese economyduringthisperiod. Inparticular,manufacturingandtransportationandpublic utilities industries su⁄ered large drops in employment share, whereas services and retail trade industries registered steep gains. This is then re(cid:135)ected in the much higher net job creation rates in the last two sectors. 4In this paper, we only present gross job (cid:135)ows at the (cid:133)rm level. Although job (cid:135)ows at the establishment level are a little larger than job (cid:135)ows at the (cid:133)rm level, essentially due to excess reallocation, the di⁄erences in terms of covariation properties are small. 5To obtain equivalent one-digit SIC87 sectors, we use the following correspondence in terms of CAERev1codes: manufacturing(3),services(6:3+8:3:2+8:3:3+9:2+9:3+9:4+9:5),retailtrade (6:2), and transportation and public utilities (7+4). The rates of gross job (cid:135)ows presented in tables 1 and 2, for the overall economy and the manufacturing sector, are close in magnitude to those in BlanchardandPortugal(2001). Ourvaluesareslightlysmallerbecausetheunitofanalysisisthe(cid:133)rm in our paper and the establishment in Blanchard and Portugal. 6The large negative correlation between reallocation and net job growth in the transportation and public utilities sector results from the dominance of large and old (cid:133)rms, most of them owned by the government, in the industries that comprise this sector. 4

3 Gross Flows and Sensitivity to Aggregate Shocks In this section, we propose a measure of (cid:133)rms(cid:146)relative sensitivity to aggregate shocks using a simple model of job (cid:135)ows dynamics. Although the model is mostly descriptive and not entirely built from microfoundations, it allows a clear motivation for the empirical analysis in section 4. Similarly to Bertola and Caballero (1990), in the study of durable goods consumption, and Foote (1998), in the analysis of the cyclical volatility of gross job (cid:135)ows, we use a simple model of (S;s) adjustment with aggregate shocks. In this model of employment adjustment, (cid:133)rms face proportional adjustment costs andaresubjecttobothidiosyncraticandaggregateshocks. Inparticular,intheabsence of adjustment costs, the (cid:133)rm(cid:146)s optimal employment is determined by, e = a +(cid:27) w , a = (cid:22)t+(cid:27) w , (1) (cid:3)t t i i;t t a a;t where e is the frictionless log-employment at time t, a and (cid:27) w are the aggregate (cid:3)t t i i;t andidiosyncraticcomponentsofemployment, (cid:22)isthetrendgrowthparameter, andw a;t and w are the aggregate and idiosyncratic shocks, which follow independent Wiener i;t processes. In summary, the log-growth rate of employment has mean (cid:22) and (cid:135)uctuates around this constant due to normally distributed aggregate and idiosyncratic shocks with mean 0 and variances (cid:27)2 and (cid:27)2, respectively. For example, optimal employment a i could be described as in (1) for a perfectly competitive (cid:133)rm facing a Cobb-Douglas production function and random-walk productivity shocks. The model assumes that (cid:133)rms choose employment in order to minimize the costs of deviating from frictionless employment, simply modelled as b (e e )2, net of propor- 2 t (cid:0) (cid:3)t tional adjustment costs, given by c (cid:1)e , with future net costs discounted at a rate (cid:26). t (cid:1) Although (cid:133)rms would continuously react to incoming shocks, if adjustment was costless, the non-di⁄erentiable adjustment costs imply that (cid:133)rms adjust employment only intermittently. The optimal employment policy is then characterized by two trigger points, l and u, de(cid:133)ned over the employment gap, e e . These trigger points de(cid:133)ne t (cid:0) (cid:3)t themaximumdeviationsallowedbeforeadjustmentoccurs. Withthetriggerpointsand the stochastic properties of the shocks it is possible to derive an ergodic distribution for each (cid:133)rm(cid:146)s employment gap. While this micro-level distribution is time-invariant, the cross-sectional distribution of (cid:133)rms over the employment gap varies over time. In fact, aggregate shocks cause all (cid:133)rms to move similarly in the gap space, resulting in a parallel shift of the cross-sectional distribution. 5

In appendix B, we show that, when the ergodic distribution is used as an approximation for the cross-sectional distribution, the coe¢ cients of variation of gross job creation (jc) and job destruction (jd) can be simply expressed as the ratio of the standard deviation of the aggregate shock, (cid:27) , over the standard deviation of employment a shocks, (cid:27), which is a composite of aggregate and idiosyncratic shocks, (cid:27) cv(jc) = cv(jd) = a , (cid:27)2 = (cid:27)2 +(cid:27)2. (2) (cid:27) a i Intuitively, the coe¢ cient of variation of gross job (cid:135)ows can be interpreted as a measure of the relative importance of aggregate shocks for (cid:135)uctuations in gross job (cid:135)ows at the (cid:133)rmlevel. Therefore,wecallthisratiothe(cid:133)rms(cid:146)relative sensitivitytoaggregateshocks. Since the time-series variation in gross job (cid:135)ows is due in part to changes in the cross-sectional distribution, the above result does not hold exactly when we use this time-varying distribution. However, we show by numerical simulation that the crosssectional distribution preserves the positive relation between the ratio (cid:27) =(cid:27) and the a coe¢ cients of variation of gross job (cid:135)ows.7 We calibrate the model to match the time-series means and standard deviations of job creation and destruction among continuing (cid:133)rms in the overall economy. The parameter values are the following: an annual discount rate of 2%, (cid:26) = 0:02; an annual trend growth rate of employment of 2:3%, (cid:22) = 0:023; an annual standard deviation of employment shocks of 21:4 percentage points, (cid:27) = 0:214; an annual standard deviation of aggregate employment shocks of 1:1 percentage points, (cid:27) = 0:011; an annual cost of a adjustment equal to 3:3 times the annual cost of deviating from optimal employment, foranadjustmentanddeviationequaltotheaveragejobcreationanddestructionrates, c=(b=2 m(jc+jd)=2) = 3:3.8 Theimpliedtriggerpointsarel = 0:152 andu = 0:169. (cid:2) (cid:0) Therefore, the(cid:133)rmonlydecidestohireafteremploymentfallsbelowitstargetby15:2% and only decides to (cid:133)re when employment rises above its target by 16:9%. Associated with this policy, the time-series average rates of job creation and destruction are 7:7% and 6:6%, respectively, the coe¢ cients of variation are 0:14, and the ratio of standard deviations is 0:86.9 7In appendix B, we provide an outline of how we simulate the model with a time-varying crosssectional distribution. 8To solve the indeterminacy, the value of c is normalized to 100. 9Althoughtheprecisevaluesofthesestatisticsdependonthedrawnsequenceofrandomaggregate shocks, we have not attempted to optimize this sequence. In fact, we use this model only to motivate the empirical analysis in section 4, and we are not concerned about estimating the parameters in the model. 6

With this calibration in hand, we vary (cid:27) around its reference value and analyze the relation between the coe¢ cients of variation of job creation and destruction and the ratio (cid:27) =(cid:27) (keeping (cid:27) (cid:133)xed). In (cid:133)gure 1, we can see that the coe¢ cients of variation a a obtained from the simulated ergodic distribution satisfy very closely the relationship presented in (2). We can also see that the dynamics of the cross-sectional distribution accounts for a sizable fraction of the cyclical variation of gross job (cid:135)ows. Notwithstanding this, the coe¢ cients of variation based on the cross-sectional distribution preserve the positive dependence on the ratio (cid:27) =(cid:27). Indeed, in the cross-sectional distribution a case, the relation appears to be linear, with the coe¢ cients of variation being proportional to the ratio (cid:27)=(cid:27) . Therefore, our interpretation for the coe¢ cients of variation a of gross job (cid:135)ows based on equation (2), as a measure of (cid:133)rms(cid:146)relative sensitivity to aggregate shocks, remains valid even if we account for the impact of aggregate shocks on the cross-sectional distribution. The sensitivity to aggregate shocks is particularly interesting for comparing di⁄erent classes of (cid:133)rms, as the literature has not directly analyzed potential heterogeneities in this dimension of gross job (cid:135)ows. In the next section, we analyze how heterogeneous are (cid:133)rm size and age classes along this dimension and the implications of these heterogeneities for the dynamics of aggregate job reallocation. 4 Sensitivity to Aggregate Shocks by Size and Age Inthissection, we(cid:133)rstdescribehowtheimportanceofaggregateshocksfor(cid:135)uctuations in gross job (cid:135)ows varies by (cid:133)rm size and age, and then we analyze the in(cid:135)uence of these (cid:133)rm heterogeneities on the dynamics of aggregate job reallocation. In order to adopt relative and sector-speci(cid:133)c de(cid:133)nitions of small versus large and young versus old (cid:133)rms, we partition the set of all (cid:133)rms in two classes, in such a way that each class contains approximately 50% of total employment.10 Due to the higher prevalence of entry and exit among small and young (cid:133)rms, we restrict our attention to job (cid:135)ows for continuing (cid:133)rms.11 Tables 3 and 4 contain statistics for size and age classes, respectively. From the size 10The transportation and public utilities sector is the only exception due to the high incidence of large and old (cid:133)rms. After using other alternative partitions, the conclusions of the paper seem robust to the adopted partition rule. 11Although job creation due to entry and job destruction due to exit are more concentrated among young and small (cid:133)rms, their impact on the cyclical properties of aggregate job reallocation is limited because these (cid:135)ows are less sensitive to aggregate conditions than (cid:135)ows for continuing (cid:133)rms. 7

and age cuto⁄s between classes, we conclude that the size and age distributions are quite di⁄erent across the four sectors, likely re(cid:135)ecting technological and institutional factors. In particular, the transportation and public utilities and the manufacturing sectors tend to be more populated by large and old (cid:133)rms, whereas the retail trade and the services sectors exhibit a high concentration of small and young (cid:133)rms. We also observe considerable heterogeneities across size and age classes. Small and young (cid:133)rms have high gross job creation and job destruction rates, accounting for a greater share of job reallocation than suggested by their employment share. Moreover, small and young (cid:133)rms exhibit higher net job growth, and, in line with Foote (1998), reallocation tends to be more procyclical for these (cid:133)rms. More importantly, small and young (cid:133)rms have lower coe¢ cients of variation of gross job (cid:135)ows. This suggests that (cid:135)uctuations in job reallocation at the (cid:133)rm level are less determined by aggregate shocks in the case of small and young (cid:133)rms than in the case of large and old (cid:133)rms. As a result, we expect large and old (cid:133)rms to in(cid:135)uence proportionately more the cyclical variation of aggregate job (cid:135)ows than the average size of these (cid:135)ows. These inferences appear consistent with a theory of learning and growth, where (cid:133)rms go through an intensive learning process after entry and adjust according to performance, a process that makes idiosyncratic shocks more determinant foremploymentadjustmentsofsmallandyoung(cid:133)rms(LiandWeinberg2003,Campbell and Fisher 2004). We now analyze how the higher relative sensitivity to aggregate shocks of large and old (cid:133)rms a⁄ects aggregate job reallocation. The cyclical properties of job reallocation are usually summarized by the coe¢ cient of correlation between the rates of job reallocation and net job creation, cc(rea;net).12 The following expression for this coe¢ cient suggests that we can also use the ratio of variances as a proxy for the cyclical behavior of job reallocation,13 1 v(jd) cc(rea;net) = (cid:0) v(jc) , (3) 2 1+ v(jd) 4cc(jc;jd)2 v(jd) v(jc) (cid:0) v(jc) r (cid:16) (cid:17) where we consider the de(cid:133)nitions rea = jc+jd and net = jc jd. In addition, equation (cid:0) 12Inwhatfollows,m(x),v(x),andsd(x)standforthetime-seriesmean,variance,andstandarddeviationofx,respectively,andcov(x;y)andcc(x;y)standforthetime-seriescovarianceandcorrelation between x and y, respectively. 13Note that cc(rea;net) declines when v(jd)=v(jc) increases, if cc(jc;jd) is (cid:133)xed and less than 1. 8

(2) above suggests the use of coe¢ cients of variation to measure the relative sensitivity to aggregate shocks of (cid:133)rms in each class. Therefore, we decompose the variances and covariances of aggregate gross (cid:135)ows approximately as weighted sums of each class ratio of variances (a proxy for cyclical behavior), where the weights depend on the coe¢ cients of variation. In the empirical analysis below, we analyze how these weights would change if all classes had equal coe¢ cients of variation and the implications of these changes for cc(rea;net), which summarizes the cyclical behavior of aggregate job reallocation, and for cc(jc;jc ) and cc(jd;jd ), which re(cid:135)ect the importance of each i i class for the dynamics of aggregate gross (cid:135)ows. For the case of two (cid:133)rm classes, where p represents the employment share of class i i, we consider the following decomposition of the variance of job destruction v(jd ) v(jd ) sd(jd )sd(jd ) v(jd) = A2 w2 1 +w2 2 +2w w cc(jd ;jd ) 1 2 , (4) 1v(jc ) 2v(jc ) 1 2 1 2 sd(jc ) sd(jc ) (cid:18) 1 2 1 2 (cid:19) where A = (p sd(jc )+p sd(jc )) and the weights are de(cid:133)ned as 1 1 2 2 p sd(jc ) i i w = , i = 1;2. i p sd(jc )+p sd(jc ) 1 1 2 2 Thisdecompositionexpressesthevarianceofjobdestructionapproximatelyasaweighted sumof eachclass varianceor, alternatively, asaweightedsumof eachclassratioof variances, v(jd )=v(jc ). Now, since sd(jc ) = cv(jc )m(jc ), we adjust the weights by i i i i i assuming that both classes are equally sensitive to aggregate shocks, cv(jc ) = cv(jc ), 1 2 so that the adjusted weights are de(cid:133)ned as p m(jc ) i i w~ = , i = 1;2. i p m(jc )+p m(jc ) 1 1 2 2 In appendix C, we present similar decompositions for the variance of job creation and the covariance of job creation and job destruction, which, together with the decomposition (4) and expression (3), allow a comparison between the unadjusted and adjusted correlations between job reallocation and net job creation. In appendix C, we also presentadecompositionthatallowsacomparisonbetweentheunadjustedandadjusted correlations between each class and aggregate gross job (cid:135)ows.14 14In applying these decompositions, we assume that the employment share of each class is constant over time. Because this assumption does not hold in the data, we also derive the unadjusted variances and covariances using the decompositions above (with unadjusted weights). 9

In tables 3 and 4, the adjusted correlations are signaled with [ ] in the last three (cid:1) columns. In the overall economy, the higher net job creation rates and lower sensitivity to aggregate shocks of small and young (cid:133)rms implies that, after adjustment, the correlation cc(rea ;net ) becomes higher and the correlations cc(jc ;jc ) and cc(jd ;jd ) c c c c;i c c;i become higher for small and young (cid:133)rms and lower for large and old (cid:133)rms. Therefore, the higher relative sensitivity of large and old (cid:133)rms makes aggregate job reallocation less procyclical than if size and age classes were equally sensitive to aggregate shocks and increases the importance of these (cid:133)rms for the dynamics of aggregate gross job (cid:135)ows. In comparison to the other sectors, manufacturing displays small di⁄erences in the sensitivity to aggregate shocks between the two (cid:133)rm size and age classes. However, reallocation patterns are strikingly opposite between the two classes: small and young (cid:133)rms exhibit positive net job creation and procyclical reallocation, while large and old (cid:133)rms exhibit negative growth and countercyclical reallocation. Thus, the adjusted correlations imply conclusions similar to the overall economy case: large and old (cid:133)rms in(cid:135)uence the dynamics of aggregate job (cid:135)ows more than proportionately to their in(cid:135)uence over the average size of these (cid:135)ows and lead job reallocation in manufacturing to be countercyclical. Theevidenceforthetransportationandpublicutilitiessectorisqualitativelysimilar to that for the manufacturing sector. However, the contrast between the two (cid:133)rm size and age classes is sharper than in manufacturing, as transportation and public utilities industries are mostly composed of large and old (cid:133)rms, with much higher sensitivities to aggregate shocks than small and young (cid:133)rms.15 Consequently, the di⁄erences between the adjusted and unadjusted correlations are even higher than in manufacturing, with largeandold(cid:133)rmsdeterminingthemarkedlycountercyclicalbehaviorofjobreallocation in the sector. Similarlytotheothersectors,largeandold(cid:133)rmsinservicesandretailtradearemore sensitive to aggregate shocks than small and young (cid:133)rms and have a disproportional in(cid:135)uence over the dynamics of gross job (cid:135)ows. However, contrary to the other sectors, the reallocation patterns in services and retail trade are, for the most part, quite similar between the two size and age classes. In particular, young and old (cid:133)rms in retail trade show nearly no di⁄erences in reallocation activity and the cyclical properties of aggregate reallocation would not change even if (cid:133)rms in these two classes were equally 15As above, this might re(cid:135)ect the fact that in transportation and public utilities industries we (cid:133)nd several large-scale government-owned (cid:133)rms that have remained in activity for a long time. 10

sensitive to aggregate shocks. Moreover, large (cid:133)rms in services and retail trade have higher net job creation rates and even more procyclical reallocation than small (cid:133)rms. Consequently, in these two particular cases, aggregate job reallocation would be a little lessprocyclicalifsmallandlarge(cid:133)rmswereequallysensitivetoaggregateshocks. There is one exception, though, to these similitudes: young (cid:133)rms in services have notoriously procyclical reallocation while old (cid:133)rms do not, and job reallocation in services is less procyclical than if young and old (cid:133)rms were equally sensitive to aggregate shocks. In table 2, the evolution of the sectoral employment shares between 1987 and 1999 seems helpful to understand some of the results identi(cid:133)ed above, with the manufacturing and the transportation and public utilities sectors registering large drops and the services and retail trade sectors showing steep gains. Manufacturing was subject to considerable structural changes mainly due to increased international competition, whichappearstohavehitharderlargeandold(cid:133)rms, particularlyduringtheearly-1990s downturn. In services, and especially in retail trade, the opposite occurred with the expansion of existing and the creation of new industries. The scale and the (cid:133)rst-mover advantages seem to have been important factors for success in sectors such as the bigretail segment and business and education services. This could then explain the highly procyclical reallocation activity among large (cid:133)rms in retail trade and services and old (cid:133)rms in retail trade. 5 Conclusion In this paper, we present job (cid:135)ows statistics for the Portuguese economy and four one-digit sectors, and analyze whether (cid:133)rm size and age classes di⁄er in the relative sensitivity to aggregate shocks. We (cid:133)nd that large and old (cid:133)rms are more sensitive to aggregate shocks than small and young (cid:133)rms, and conclude that large and old (cid:133)rms contribute proportionately more to the cyclical dynamics than to the average size of job (cid:135)ows. Because large and old (cid:133)rms tend to have lower net job creation rates and less procyclical (or even countercyclical) reallocation than small and young (cid:133)rms, then aggregate job reallocation is less procyclical, or more countercyclical, than if all (cid:133)rms were equally sensitive to aggregate shocks. This result applies in the overall economy and in the manufacturing and the transportation and public utilities sectors, for size and age classes, and in the services sector, for age classes. In the other cases, either young and old (cid:133)rms behave very similarly over the business cycle, as in retail trade, or 11

large (cid:133)rms exhibit even more procyclical reallocation than small (cid:133)rms, as in services and retail trade. The speci(cid:133)cities of the services and retail trade sectors, with respect to the overall economy, likely result from the structural changes that these sectors went through during the period under analysis. The paper shows that the higher relative sensitivity to aggregate shocks of large and old (cid:133)rms is important to understand the cyclical properties of aggregate job reallocation. The emphasis on a relative measure, as opposed to an absolute measure, of the sensitivity to aggregate shocks, appears also important for the literature that studies heterogeneities in the response to aggregate shocks across (cid:133)rm size and age. In particular, although small and young (cid:133)rms have higher absolute responses to aggregate shocks, we (cid:133)nd that relative to their average adjustment rates these responses are smaller than those of large and old (cid:133)rms. As some papers in this literature have emphasized, this might re(cid:135)ect the higher incidence of idiosyncratic shocks among small and young (cid:133)rms. In this sense, large and old (cid:133)rms appear relatively more useful to assess the state of the business cycle. Appendix A Gross Job Flows in Quadros de Pessoal QP is a Portuguese longitudinal database containing annual information on workers, establishments and (cid:133)rms. The database originates from a mandatory annual survey run by the Ministry of Employment,anditcoversalleconomicentities,excludingpublicadministration,withatleastoneworker. In this paper, we have access to data covering the period 1985-2000. The three linkable datasets contain anaverageof250,000(cid:133)rms,300,000establishments,and2,500,000workersperyear. Onlyabout5%of all establishments belong to multi-establishment (cid:133)rms, but these account for a more signi(cid:133)cant share of total employment since these (cid:133)rms are usually large. We de(cid:133)ne job creation (jc) and job destruction (jd), both for continuing and entering establishments/(cid:133)rmsasinDavisandHaltiwanger(1990). Weselectentering/exitingunitsattimetbyrequiring thatt/t 1wastheearliest/latestperiodtheiridshowedupinthedataset(withpositiveemployment). (cid:0) Because there is some incidence of temporary exits, especially among establishments, we recover all units with a temporary exit spanning only one year, and exclude all other units with temporary exits in years with missing values. For the recovered units, the missing value is taken to be the average of the two closest years. Information refers to March up to 1993, and to October since the reformulation of the survey in 1994. Inordertoadjustgrossjob(cid:135)owsproportionately,wecreateanewemploymentvariablereferring toMarch1994. Withprobability7=19thisnewvariableisrandomlyassignedthevalueinMarch1993, and with probability 12=19 it is randomly assigned the value in October 1994. The CAE industry classi(cid:133)cation system was revised in 1995. To enable the time-series analysis by economic sector, we adopt the following procedure. First, we reduce the amount of miscoding by converting all 6-digits CAE Rev 1 codes into 4-digits CAE Rev 1 codes. Second, we construct a correspondencetablebetween6-digitsCAERev2codesand4-digitsCAERev1codes. Third, weuse (cid:133)rms(cid:146)information in 1994 and 1995 to construct a probability transition matrix for this equivalence 12

table. Fourth, foreach5-digitsCAERev2codes, welistallpossible4-digitsCAERev1codes. Fifth, startingin1995andgoingiterativelyuntil2000,we(cid:133)rstselectthecorrectlyenteredCAERev2codes, and check if in the previous year the unit has one of the 4-digits CAE Rev 1 codes appearing in the transformed equivalence table. If that is the case, it becomes the (cid:133)rm(cid:146)s equivalent 4-digit CAE Rev 1 code for the current year. If that is not the case, namely for new births, then we use the equivalence table to randomly select the 4-digits CAE Rev 1 code from the set of possible codes associated with the current year 5-digits Rev 2 code. Finally, for those 5-digits Rev 2 codes that are miscoded, we (cid:133)rst convert them into 3-digits Rev 2 codes and then apply the same procedure as above, using the appropriate equivalence table. Concerning the age of each unit, since the (cid:133)rm(cid:146)s year-of-birth variable is only available starting in 1995, we proxy it using the year-of-hiring variable from the workers dataset. Initially we correct or omit this variable for erroneous entries, and proceed in two steps. First, for each (cid:133)rm we calculate the mode, across all years, for each worker with a valid id. Then we take the minimum across all workers to be the year of entry by the (cid:133)rm. For those (cid:133)rms that do not have any worker with a valid id, we select the minimum year of hiring across all workers in each year, and then obtain the mode of this minimum across all years. B Outline of Model Simulation and Proofs As shown in Dixit (1993), the value function of the (cid:133)rm is given by b 2(cid:22)2 (cid:27)2 2(cid:22)z z2 V (z) = + j (cid:0) + +Ae (cid:11)z+Be(cid:12)z (cid:0)2 ( (cid:26)3 (cid:26)2 (cid:26) ) (cid:0) (cid:22) (cid:22)2+2(cid:26)(cid:27)2 (cid:22)+ (cid:22)2+2(cid:26)(cid:27)2 (cid:11) = (cid:0) ; (cid:12) = (cid:0) (cid:27)2 (cid:27)2 p p where z = e e . The two unknown constants of V and the values of l and u are found numerically (cid:3) (cid:0) by solving the following system of nonlinear equations V (l) = c, V (u)= c, 0 0 (cid:0) V (l) = 0, V (u)=0. 00 00 As in Bertola and Caballero (1990), by solving a system of equations, we can (cid:133)nd the continuoustimeergodicdistributionforthelocationoftheagentinthezstatespace. When(cid:22)=0,thecontinuous- 6 time density is de(cid:133)ned as16 2 (cid:22) exp 2 (cid:22) z f (z)= (cid:27)2 (cid:0) (cid:27)2 , z (l;u). c exp 2 (cid:22) l exp 2 (cid:22) u 2 (cid:0) (cid:27)2 (cid:0)(cid:8) (cid:0)(cid:9) (cid:27)2 We can view the Brownian motion(cid:8)proces(cid:9)s associa(cid:8)ted with(cid:9)z as the limit of a random walk when t the time interval (cid:1)t and the step size (cid:1)z go to zero simultaneously according to (cid:1)z = p(cid:27)2(cid:1)t. Following Bertola and Caballero (1990), we approximate the continuous-time process with a discretetime, discrete state-space Markov chain. Namely, we discretize the z state space into m points with an implied step size that satis(cid:133)es (cid:1)z = (cid:27)2(cid:1)t+(cid:22)2((cid:1)t)2. Given the step size and time interval, the probability of z increasing by (cid:1)z is giveqn by p = 1 1 (cid:22)(cid:1)t unconditionally, by p = 1 1 (cid:1)a conditionally on a positive aggregate shock, a z nd b 2 y p (cid:0) = (cid:1)z 1 1+ (cid:1)a conditionall z y j b on 2 a ne (cid:0) ga (cid:1) ti z ve (cid:0) zr 2(cid:1) (cid:1)z (cid:0) (cid:1) aggregate shock. The probability of a positive aggregate j shock is given by p = 1 1+(cid:22)(cid:1)t , where (cid:0) (cid:1) a 2 (cid:1)a (cid:1)a= (cid:27)2(cid:1)t+(cid:22)2((cid:1)t)2. (cid:0) (cid:1) a q 16For (cid:22)=0, the density is just given by the density of an uniform distribution. 13

Similarly to the continuous-time case, for given values of l and u, we can (cid:133)nd the (cid:133)rm(cid:146)s discretetime ergodic distribution. When (cid:22)=0, the discrete-time density is de(cid:133)ned as17 6 (1 p =q )(p =q )z=(cid:1)z f (z)= (cid:0) z z z z , z l+(cid:1)z;l+2(cid:1)z;:::;u 2(cid:1)z;u (cid:1)z , d (p =q )l=(cid:1)z (p =q )u=(cid:1)z 2f (cid:0) (cid:0) g z z z z (cid:0) (cid:16) (cid:17) where q =1 p . We obtain thediscrete-timecross-sectionaldistribution byapplyingtothis ergodic z z (cid:0) distributionthetransitionmatrix,conditionalonthetheaggregateshock,associatedwiththerandom walk approximation to z . In the numerical simulation, we use a grid for z with 1000 points and draw t a random sample of 100000 aggregate shocks, removing the initial 1000 realizations. The job creation rate is de(cid:133)ned as18, 19 f (l+(cid:1)z)q (cid:1)z (cid:27)2 E(jc) = d z f (l) =E(jc) . d (cid:1)t ! c 2 c For the variance of job creation, we have Var(jc) = p [E(jc b) E(jc) ]2+q [E(jc r) E(jc) ]2 d a j d(cid:0) d a j d(cid:0) d 2 2 q q q p q q = [E(jc) d ]2 8 p a a z j b q (cid:0) z j r +q a a z j r q (cid:0) z j b 9 " (cid:0) z (cid:1)# " (cid:0) z (cid:1)# < = p q = [E(jc) ]2 a a q q 2 d : q z 2 z j b (cid:0) z j r ; (cid:27)2 (cid:0) (cid:1) [E(jc) ]2 a =Var(jc) . ! c (cid:27)2 c where the second line uses E(jc i) = fd(l+(cid:1)z)qzi(cid:1)z =E(jc) qzi, i=b;r, and q =p q +q q , and the fourth line uses q q j d (cid:27)a as (cid:1) (cid:1) t t j 0. We conclu d de qz j that z a z j b a z j r z j b (cid:0) z j r ! (cid:27) ! Var(jc) (cid:27) cv(jc) = c = a, c E(jc) (cid:27) p c a relation that holds approximately in discrete time. A similar result could be derived for the job destructionrate. Thestatisticsassociatedwiththecross-sectionaldistributionareobtainedbyreplacing the ergodic distribution with the simulated cross-sectional distribution in the expressions above. C Decompositions of Variances and Covariances For the decomposition in equation (4), we assume that the employment share of each class is constant over time, so that v(jd)=v(p jd +p jd )=p2v(jd )+p2v(jd )+2p p cov(jd ;jd ). 1 1 2 2 1 1 2 2 1 2 1 2 We then divide and multiply each component by the corresponding class v(jc ) and simplify to get i explicit weights. An equivalent decomposition for the variance of job creation can be easily obtained 17See footnote 16. 18Note that we obtain analytical expressions for the gross job (cid:135)ows statistics in continuous time. 19When there are both (cid:133)xed and proportional adjustment costs, as considered in Bertola and Caballero(1990)andFoote(1998),wecanprovethatE(jc) =(l L)f (L)(cid:27)2 ,whereLandlrepresent c (cid:0) c0 2 the lower trigger and target points, respectively. 14

from the structure of equation (4). Similarly, the decomposition for the covariance between job creation and job destruction, which we use to adjust cc(jc;jd) in expression (2), is given by 2 2 sd(jc )sd(jd ) cov(jc;jd)=A w cc(jc ;jd ) i j , ij i j 0 sd(jd )sd(jc )1 i j i=1j=1 XX @ A were A= p p sd(jd )sd(jc ), and the unadjusted weights are de(cid:133)ned as i j i j i j P P p p sd(jd )sd(jc ) w = i j i j , i;j =1;2. ij p p sd(jd )sd(jc ) i j i j i j The decomposition of the coe¢PciePnt of correlation between aggregate gross job follows and each class gross job (cid:135)ows, for the case of job creation and class 1, is given by sd(jc ) sd(jc ) cc(jc;jc )=A w 1 +w cc(jc ;jc ) 2 =sd(jc), 1 1sd(jd ) 2 1 2 sd(jd ) (cid:18) 1 2 (cid:19) where A=p sd(jd )+p sd(jd ), sd(jc) is decomposed analogously to equation (4), and the weights 1 1 2 2 are de(cid:133)ned as p sd(jd ) w = i i , i=1;2. i p sd(jd )+p sd(jd ) 1 1 2 2 Similar expressions can be derived for the case of class 2 and/or job destruction. References Baldwin, J., Dunne, T. and Roberts, M. (1998), (cid:147)A Comparison of Job Creation and Job Destruction in Canada and the United States,(cid:148)Review of Economics and Statistics, 80 (3), 347-56. Bertola, G. and Caballero, R. (1990), (cid:147)Kinked Adjustment Costs and Aggregate Dynamics,(cid:148)in O. Blanchard and S. Fischer (eds.), NBER Macroeconomics Annual, MIT Press, Cambridge, MA, 237-88. Blanchard, O. and Portugal, P. (2001), (cid:147)What Hides Behind an Unemployment Rate: Comparing Portuguese and U.S. Labor Markets,(cid:148)American Economic Review, 91 (1), 187-207. Boeri, T. (1996), (cid:147)Is Job Turnover Countercyclical?,(cid:148)Journal of Labor Economics, 14 (4), 603-25. Burgess, S., Lane, J. and Stevens, D. (2000), (cid:147)The Reallocation of Labour and the Lifecycle of Firms,(cid:148)Oxford Bulletin of Economics and Statistics, 62 (Special Issue), 885-907. Campbell, J. and Fisher, J. (2004), (cid:147)Idiosyncratic Risk and Aggregate Employment Dynamics,(cid:148)Review of Economic Dynamics, 7 (2), 331-53. Davis, S. and Haltiwanger, J. (1990), (cid:147)Gross Job Creation and Destruction: Microeconomic Evidence and Macroeconomic Implications,(cid:148)in O. Blanchard and S. 15

Fischer (eds.), NBER Macroeconomics Annual, MIT Press, Cambridge, MA, 123- 68. Davis, S. and Haltiwanger, J. (1992), (cid:147)Gross Job Creation, Gross Job Destruction, and Employment Reallocation,(cid:148)Quarterly Journal of Economics, 107 (3), 819-63. Davis, S. andHaltiwanger, J. (1999), (cid:147)GrossJobFlows,(cid:148)inO.AshenfelterandD.Card (eds.), Handbook of Labor Economics, Vol. IIIB, Elsevier, Amsterdam, 2711-805. Davis, S., Haltiwanger, J. and Schuh, S. (1996), Job Creation and Destruction, MIT Press, Cambridge, MA. Dixit, A. (1993), The Art of Smooth Pasting, Harwood Academic Publishers, Chur, Switzerland. Foote, C. (1998), (cid:147)Trend Employment Growth and the Bunching of Job Creation and Destruction,(cid:148)Quarterly Journal of Economics, 113 (3), 809-34. Li, W. and Weinberg, J. (2003), (cid:147)Firm-Speci(cid:133)c Learning and the Investment Behavior of Large and Small Firms,(cid:148)International Economic Review, 44 (2), 599-625. 16

CCCoooeeeffffffiiiccciiieeennnttt ooofff VVVaaarrriiiaaatttiiiooonnn ooofff GGGrrrooossssss JJJooobbb FFFlllooowwwsss 000...222333 jjjccc jjjddd 000...111999 CCCrorroossssss S SSeeeccctittoiioonnnaaallljjjccc aaannndddjjddjd 000...111555 000...111111 EEErgrrggooodddiciiccjjjccc aaannndddjjddjd 000...000888 000...000444 000...000333777 000...000444777 000...000555666 000...000666666 000...000777666 000...000888666 RRReeefffeeerrreeennnccceee PPPaaarrraaammmeeettteeerrr VVVaaallluuueeesss Figure 1: Sensitivity to Aggregate Shocks

Portuguese Economy: 1987 1999 7.5 6.0 4.5 3.0 1.5 0.0 1.5 GDP real growth Unemployment rate 2.9 Net job creation (continuing) 1987 1990 1993 1996 1999 year Figure 2: Macroeconomic Performance

Table 1: Firm Job Flows in Portugal: 1987-1999 Year jc jc jd jd net rea c c 1987 6.9 12.3 5.1 8.9 3.4 21.2 1988 8.0 14.3 5.3 9.0 5.3 23.2 1989 8.4 15.2 5.6 8.7 6.5 23.9 1990 7.6 13.1 6.4 10.1 2.9 23.2 1991 7.5 13.7 7.5 11.1 2.5 24.8 1992 6.9 12.1 7.3 10.8 1.3 22.9 1993 5.9 11.2 8.9 13.1 1:9 24.4 (cid:0) 1994 5.2 11.3 6.8 11.1 0.2 22.4 1995 7.2 11.9 6.9 10.8 1.1 22.7 1996 7.8 12.3 6.9 10.6 1.6 22.9 1997 9.1 13.9 6.4 9.9 4.1 23.8 1998 9.1 14.4 6.5 10.6 3.8 25.0 1999 9.0 13.9 6.7 11.0 2.9 25.0 Notes: jcandjdaretheratesofjobcreationandjobdestruction amongallunits; jc andjd aretheratesofjobcreationandjob c c destruction among continuing units; net(= jc jd) is the net (cid:0) job creation rate; rea(=jc+jd) is the job reallocation rate. All rates are in %.

Table 2: Firm Job Flows in Portugal: 1987-1999 Sector esh esh m(jc) m(jd) m(net) m(rea) cc(rea;net) cc (net) 87 99 se All 13.0 10.4 2.6 23.5 0.09 Manu 45.7 34.1 10.2 9.9 0.2 20.1 0.03 0.93 Serv 14.2 23.2 17.2 10.8 6.4 28.0 0.56 0.78 Reta 8.1 11.4 16.6 11.1 5.6 27.7 0.54 0.65 Tran 9.0 6.6 7.5 7.3 0.2 14.8 0:55 0.81 (cid:0) Notes: esh andesh aretheemploymentsharesin1987and1999; m(x)isthemean 87 99 of x; cc(x;y) is the correlation between x and y; cc (x) is the correlation between se sectoral x and aggregate x; for other de(cid:133)nitions see table 1.

Table 3: Sensitivity to Aggregate Shocks: Size Classes Size esh m(jc ) m(jd ) cv(jc ) cv(jd ) cc(rea ;net ) cc (jc ) cc (jd ) c c c c c c cl c cl c Overall Economy 1 49 47:6 9:2 7:1 0:14 0:10 0:58 0:82 [0:94] 0:81 [0:87] (cid:0) 50 52:4 6:3 6:1 0:22 0:22 0:06 0:89 [0:75] 0:96 [0:93] (cid:0)(cid:1) 1 100:0 7:6 6:6 0:15 0:15 0:24 [ 0:45] (cid:0)(cid:1) Manufacturing 1 99 51:3 7:9 6:2 0:19 0:14 0:67 0:95 [0:98] 0:89 [0:88] (cid:0) 100 48:7 4:6 6:3 0:17 0:26 0:75 0:80 [0:72] 0:97 [0:97] (cid:0)(cid:1) (cid:0) 1 100:0 6:2 6:2 0:15 0:19 0:11 [ 0:17] (cid:0)(cid:1) (cid:0) Services 1 24 51:0 9:0 7:1 0:10 0:08 0:40 0:74 [0:89] 0:75 [0:88] (cid:0) 25 49:0 10:3 5:9 0:25 0:25 0:55 0:97 [0:87] 0:96 [0:87] (cid:0)(cid:1) 1 100:0 9:6 6:5 0:17 0:14 0:51 [ 0:44] (cid:0)(cid:1) Retail Trade 1 9 51:0 7:9 6:5 0:10 0:08 0:37 0:54 [0:72] 0:21 [0:62] (cid:0) 10 49:0 10:6 5:8 0:18 0:15 0:70 0:94 [0:84] 0:81 [0:46] (cid:0)(cid:1) 1 100:0 9:2 6:2 0:12 0:07 0:83 [ 0:78] (cid:0)(cid:1) Transportation and Public Utilities 1 999 38:7 8:4 5:9 0:20 0:28 0:05 0:84 [0:96] 0:67 [0:91] (cid:0) 1000 61:3 1:3 5:4 0:18 0:87 0:80 0:93 [0:79] 0:99 [0:84] (cid:0)(cid:1) (cid:0) 1 100:0 4:1 5:5 0:44 0:60 0:67 [ 0:01] (cid:0)(cid:1) (cid:0) Notes: cv(x) is the coe¢ cient of variation of x; cc (x) = cc(x ;x) is the correlation between cl i each class x and aggregate x; for other de(cid:133)nitions see tables 1 and 2. The numbers in [] are i (cid:1) obtained by using the adjusted weights, w~ . i

Table 4: Sensitivity to Aggregate Shocks: Age Classes Age esh m(jc ) m(jd ) cv(jc ) cv(jd ) cc(rea ;net ) cc (jc ) cc (jd ) c c c c c c cl c cl c Overall Economy 1 24 48:7 10:4 7:0 0:14 0:10 0:63 0:94 [0:98] 0:85 [0:89] (cid:0) 25 51:3 5:2 6:6 0:20 0:21 0:31 0:90 [0:83] 0:97 [0:95] (cid:0)(cid:1) (cid:0) 1 100:0 7:7 6:7 0:15 0:15 0:18 [ 0:47] (cid:0)(cid:1) Manufacturing 1 27 48:9 8:8 5:7 0:19 0:15 0:65 0:95 [0:97] 0:93 [0:93] (cid:0) 28 51:1 3:9 7:0 0:19 0:22 0:70 0:76 [0:70] 0:98 [0:98] (cid:0)(cid:1) (cid:0) 1 100:0 6:3 6:3 0:16 0:19 0:16 [ 0:07] (cid:0)(cid:1) (cid:0) Services 1 19 51:5 11:4 7:3 0:16 0:09 0:77 0:94 [0:98] 0:72 [0:75] (cid:0) 20 48:5 8:0 8:1 0:19 0:24 0:07 0:90 [0:81] 0:94 [0:92] (cid:0)(cid:1) 1 100:0 9:8 6:7 0:16 0:14 0:50 [ 0:68] (cid:0)(cid:1) Retail Trade 1 17 50:4 10:1 6:4 0:12 0:09 0:63 0:65 [0:73] 0:50 [0:75] (cid:0) 18 49:6 8:7 6:2 0:21 0:13 0:69 0:85 [0:78] 0:73 [0:46] (cid:0)(cid:1) 1 100:0 9:4 6:3 0:12 0:07 0:84 [ 0:83] (cid:0)(cid:1) Transportation and Public Utilities 1 34 21:5 11:9 6:3 0:18 0:20 0:59 0:86 [0:96] 0:56 [0:68] (cid:0) 35 78:5 1:9 5:5 0:63 0:76 0:85 0:97 [0:87] 1:00 [0:98] (cid:0)(cid:1) (cid:0) 1 100:0 4:1 5:6 0:44 0:62 0:75 [ 0:03] (cid:0)(cid:1) (cid:0) (cid:0) Notes: See table 3.