Sectoral Dynamics and Business Cycles

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Sectoral Dynamics and Business Cycles Manjola Tase 2016-066 Please cite this paper as: Tase, Manjola (2016). “Sectoral Dynamics and Business Cycles,” Finance and Economics DiscussionSeries2016-066. Washington: BoardofGovernorsoftheFederalReserveSystem, http://dx.doi.org/10.17016/FEDS.2016.066. 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.

Sectoral Dynamics and Business Cycles Manjola Tase∗ July 20, 2016 Abstract I construct an index of sectoral dynamics to characterize changes in the sectoral composition of economic activity. There is evidence of asymmetry in different phases of business cycles with recessions being associated with larger changes in sectoral composition than expansions. I find that the correlation between dynamics in sectoral employment and aggregate output has weakened since the 1990s. Also, sectoral changes appear to be smaller and spread across more sectors, while their contribution to aggregate volatility has been increasing. I also perform a simulation exercise and replicate these documented facts. The results suggest that shifts in the sectoral composition of the economy likely contribute to the formation of business cycles. Also the duration of recessions implied by the impulse response functions from a VAR model of sectoral dynamics and aggregate output growth matches the duration of recessions observed in the data. Keywords: Structural changes, business cycles, labor share, employment JEL Classification: E32, E24 ∗BoardofGovernorsoftheFederalReserveSystem,DivisionofMonetaryAffairs. Email: manjola.tase@frb.gov. IwouldliketothankGeorgeHall,ZeynepSenyuz,DavidMillerandseminarparticipantsatBrandeisUniversityand the Board of Governors of the Federal Reserve System for helpful comments. The analysis and conclusions set forth are my own and do not necessarily reflect the views of the Board of Governors or the staff of the Federal Reserve System. 1

1 Introduction Isthestructureoftheeconomymoredynamicinrecessionsorexpansions? Whatisthecontribution of these sectoral dynamics to aggregate volatility? In answering these questions, I investigate changes in the allocation of economic activity across sectors over time and explore how these sectoral dynamics relate to business cycles and GDP growth volatility. I construct a simple index of sectoral dynanamics based on changes in sectoral shares of total output over time; I also construct a similar index using employment data. The larger the index, the more pronounced are the changes in the sectoral composition of the economy. The index is constructedfordifferentlevelsofsectoraldisaggregation, coverage, andtimefrequency. Idocument the following facts about sectoral dynamics, GDP growth, and volatility. First, recessions are associated with large changes in sectoral composition. For example, over the period 1948–2010, sectoral shifts were about 1.7 times larger in recessions than in expansions. Furthermore, the larger the changes in sectoral composition, the more severe the recessions were. Second, starting from the 1990s, there is a weakening of the correlation between the index of sectoral dynamics using employment data and output growth. This finding is consistent with the decline in the labor share of output both in aggregate and within industries as documented by Elsby et. al (2013) and Karabarbounis and Neiman (2013). As the labor share of output decreases, the contribution of labor dynamics to growth dynamics would be expected to decrease as well. Third, while until the 1990s, business cycles were characterized by large cyclical changes in the share of the Durables sector, afterwards the sectoral dynamics were smaller and spread across more sectors. Fourth, the contribution of sectoral dynamics to GDP growth volatility has been continuously increasing. While GDP growth volatility has declined since the 1990s, sectoral 2

dynamicsseemstohaveplayedamoreprominentrole.1 Upuntilthe1990s,theaveragecontribution of sectoral dynamics to growth volatility fluctuated between 25 and 45 percent, while during the Great Moderation, it increased continuously and accounted for 50 to 60 percent of the GDP growth volatility. I also perform a simple simulation exercise to replicate the stylized facts on the relationship between sectoral dynamics and business cycles. The simulated sectoral growth rates are drawn to match the joint distribution of the sectoral growth rate in the historical data, accounting for the comovement across sectors. I find that the simulated data replicate the negative correlation between sectoral dynamics and the GDP growth during recessions. Furthermore, the duration of recession in the impulse response functions from a VAR of sectoral dynamics and GDP growth rate matches the recession duration observed in the data. The results are consistent with Phelan and Trejos (2000), in that an one-time change in the sectoralcompositionoftheeconomycanleadtoanaggregatedownturn. Theindexpresentedinthis paperissimilartothatinLilien(1982). Lilien(1982)constructsameasureofstructuralshiftswithin the labor market and argues that sectoral shifts are represented by a positive correlation between the dispersion of the employment growth rate across sectors and the level of the unemployment rate.2 The advantage of constructing an index of sectoral dynamics based on output, as in this paper, is that it fully captures sectoral dynamics in the economy. A decrease in employment in a 1The decline in GDP growth volatility in the U.S since the mid–1980s, a period known as the Great Moderation, iswelldocumentedintheliterature(KimandNelson(1999),McConnellandPerez-Quiros(2000)andBlanchardand Simon (2001)). 2AbrahamandKatz(1986)showthatthemeasureproposedbyLiliendoesnotdistinguishbetweenapuresectoral shift and a pure aggregate demand explanation of the unemployment rate. They show that aggregate demand movements alone can produce a positive correlation between the dispersion of the employment growth rates across sectors and the unemployment rate. They isolate the structural component from the aggregate component by using the detrended series of the unemployment rate after accounting for the aggregate shock measured by unanticipated growth in the money supply. Rissman (1997) develops a measure that is similar to Lilien’s but which addresses the criticism of Abraham and Katz by applying a Kalman filter to a simple model of industry employment growth to construct a measure of dispersion that is free from cyclical effects. 3

given sector might be due to changes in labor intensity in that sector rather than representing a change in that sector’s share in total output. Furthermore, an implicit assumption in constructing the index using employment data is that there is no variation in the labor share over time. As shown in Table 2, there is a variation in the labor share across sectors. For example, over the period 1960–2005, the average labor share in sectoral value added varied from 0.25 for “Oil and gas extraction” to 0.87 for “Construction”. In addition, as shown in Figure 2, the average labor share across sectors has been declining, from an average of 0.67 in the 1960s and 1970s to about 0.56 in the later period. This paper is organized as follows: Section 2 presents the data. Section 3 presents various specifications of the index of sectoral dynamics and its relationship to aggregate growth. Section 4 shows the contribution of sectoral dynamics to growth volatility. Section 5 concludes. 2 Data and Stylized Facts Iuseindustry-leveldataonvalueadded,employmentandoutputfromdifferentsourcesasdescribed in this section with sectoral coverage, disaggregation, time frame and frequency varying across datasets. Bureau of Economic Analysis (BEA) Industry Accounts The data from BEA are available at an annual frequency for the period 1947–2010 for 22 broad sectors of the economy.3 The list of sectors is given in Table 1. These sectors correspond to the two-digit level of the 2002 North American Industry Classification System (NAICS), and they fully representtheeconomy. Moredisaggregateddataareavailableonlyfrom1987. Thesectoralshareis measured as the sector’s value added as a percentage of GDP. I also construct a less disaggregated 3See http://www.bea.gov/industry/gdpbyind data.htm. 4

data set (15 sectors) based on the sector-level classification from the Input-Output Table. Dale Jorgenson’s 35-Sectors KLEMS This database contains data on output and input usage for 35 sectors at an annual frequency for the period 1960–2005.4. I calculate the sector’s value added as the difference between the value ofoutputandthevalueofintermediateinputs. AsshowninTable 2, theKLEMSdatasetprovides more disaggregated data for manufacturing than the 22-sector BEA data. The advantage of these two data sets compared to Current Employment Statistics and the Federal Reserve Board’s Index of Industrial Production is that they contain information on the entire economy. Current Employment Statistics (CES) CESincludeemployment,hours,andearningsseries.5 Thedataareatamonthlyfrequency,and most employment series start from 1990. I use the seasonally adjusted employment series (number of workers) by major industry sector (generally two-digit NAICS) which is available from 1939 to 2013, and I compute the sector’s employment as a percentage of nonfarm employment. The list of sectors is shown in Table 3. The Federal Reserve Board’s Industrial Production (IP) This database provides a monthly index of IP, related capacity indexes, and capacity utilization rates for manufacturing, mining, and electric and gas utilities.6 The production index measures real output, and it is expressed as a percentage of real output in a base year, currently 2007. I use the seasonally adjusted quarterly series for the period 1972q1–2013q4, corresponding to the industry structure classification of IP as shown in Table 4. I measure sectoral dynamics as the average change in the sectoral shares of total output over 4See http://scholar.harvard.edu/jorgenson/data. 5See http://www.bls.gov/ces/. 6See http://www.federalreserve.gov/Releases/g17/download.htm. 5

two consecutive periods across all sectors, as shown in ( 1): 1 (cid:88) SecDynamics = |ω −ω |, (1) t i,t i,t−1 n i where ω denotes sector’s i(cid:48)s share of total output at time t. i,t Figure 1 plots the index for various levels of sectoral disaggregation using value added or employment data. Summary statistics for the index over stages of the business cycles and over time are shown in Table 5. Both Figure 1 and Table 5 show that recessions are associated with larger values of this index than expansions, suggesting that most of the reallocation of economic activity across sectors occurs during recessions. Furthermore, the larger the value of the index, the larger is the drop in GDP growth. Focusing on recession periods only, the negative correlation suggests that the larger the sectoral dynamics, the more pronounced the recessions are. These results are robust across a variety of levels of disaggregation (15, 22, and 35 sectors) as well as the basis for the construction of sectoral shares (value added or employment). Looking at the period after 1990, the correlation between the index of sectoral dynamics based on the labor data and GDP growth is significantly lower, suggesting a disentangling between the labor market and the aggregate economy. This pattern is consistent with the decline in the share of labor in output. Figure 2 plots the labor share of value added for the U.S. economy and the averagelaborshareacrosssectors. Bothseriesshowadeclineinthelaborshare, whichisevenmore pronouncedfortheaveragelaborshare,implyingashiftawayfromthelabor-intensivesectors. This observationisconsistentwithElsbyet.al(2013)whoarguethattheoffshoringofthelabor-intensive component of the U.S. supply chain is a leading potential explanation of the decline in the U.S. labor share. Karabarbounis and Neiman (2013) document that a global decline in the labor share is occurring within the large majority of countries and industries. They show that the decrease in 6

the relative price of investment goods, inducing firms to shift away from labor and toward capital, explains roughly half of the observed decline in the labor share. While recessions are associated with large sectoral shifts, the magnitude and distribution of these shifts have been changing over time. Figure 3 shows that the range of the change in the sectoral shares was wider before the mid–1980s. However, the standard deviation of the change in sectoral shares in largely unchanged. Intheperiodsbeforethemid–1980s,thelargestchangesinthesectoralshareswereconcentrated in the “Durables goods” sector, with the share of Durables shrinking in recessions and increasing in expansions. During the period 1948–1983, there were 16 recession years and 10 expansion years. Durables had the largest drop in sectoral share in 10 out of the 16 recession years and the largest increase in 10 out of the 10 expansion years. The period 1984–2010 shows a different picture. More sectorsexhibitedlargechangesinbothrecessionsandexpansions. Outofthe6recessionyearsinthe period 1984–2010, Durables had the largest drop in 3 years, followed by Construction and Mining. Duringtheexpansionsyears,FinanceandInsurance,ProfessionalServicesandTransportationwere thesectorswiththelargestincreases. Hence, eventhoughtherangeofchangesinthesectoralshare is narrower in the period after the mid–1980s, more sectors exhibit changes in their share of GDP. While before the mid–1980s the cycles were mostly mirroring the change in the manufacturing activity, in the later period, distinct sets of sectors drove recessions and expansions suggesting a larger role for structural changes. These structural shifts can provide an explanation for the stagnant employment during the recoveries since the 1990s, also known as jobless recoveries.7 The argument is that if a recession corresponded to the permanent shrinking of some industries and the expansion of other industries, 7Starting from the 1990s, the nature of the recoveries following the recessions has changed. Expansions after the recessionsof1990–91,2001,and2007–09(theGreatRecession)werelabeled“joblessrecoveries”. Unliketheprevious recoveries, they did not see an increase in employment, corresponding to the growth in output. 7

then job losses in the recession would mostly be permanent. The job postings from the expanding industries would be new hires rather than rehires. The resulting structural unemployment would be more persistent than the cyclical one, as the newly unemployed people would need to acquire new skills to be employed in another industry. Furthermore, a new vacancy would take longer to fill than a rehire opening. Motivated by the “jobless recoveries”, Groshen and Potter (2003) distinguish between the cyclical component and the structural component by looking at the correlation of job flows by industry in recession and recovery. The industries that exhibit a positive correlation (jobs losses during both recession and recovery or job gains during both recession and recovery) are identified as predominated by structural changes. They find that the recoveries following the recessions of 1990–91 and 2001 saw larger structural changes than those following previous recessions. Panovska (2016) also finds that the composition of the structural shocks during recessions and the periods immediately following recessions has changed; the recessions before 1984 were followed by recoveries driven by positive permanent shocks to output, whereas the post–1984 recessions were followed by weak recoveries in demand. 3 Sectoral Dynamics and Business Cycles In this section, I perform a simple simulation exercise to replicate the stylized facts on the relationshipbetweensectoraldynamics andbusinesscycles. Thesimulatedsectoralgrowthratesaredrawn to match the joint distribution of the sectoral growth rate in the historical data, accounting for the comovement across sectors. I then follow with a VAR analysis of sectoral dynamics and GDP growth and compare the response time in the impulse response functions with recession duration in the historical data. 8

3.1 Simulation Approach First, IpresentaruletodefinetherecessionperiodsinthesimulatedGDPgrowthseries. Iconsider three candidate measures as a recession indicator: (1) negative GDP growth rate, (2) negative cyclical component of the GDP growth rate, and (3) negative cyclical component of the GDP growth rate by at least half the standard deviation of the cyclical component.8 Table 6 shows how these three indicators perform in defining business cycles in the data. “Correctly defined” corresponds to the percentage of times in the period 1948–2010 when the indicator defined the year to be a recession year when the true state was recession, and when the indicator defined the year to be an expansion year when the true state was expansion. Among these indicators, the third one - negative cyclical component of the GDP growth rate by at least half the standard deviation of the cyclical component- produces cycles that are closest to the cycles defined by the NBER. In the simulation procedure, I will use this indicator to define a recession year in the simulated series of the GDP growth rate. The simulation procedure is as follows: 1. Settheinitialsectoralsharestotheirvaluesin1948. Historicaldataarebasedonthe22-sector classification from the BEA for the period 1947–2010 as it provides the most comprehensive coverage. 2. For each time t and sector i, generate sectoral shocks (cid:15) , where µ and σ match the i,t (cid:15)i (cid:15)i,(cid:15)j average growth rate of sector i and the covariance between sector i and j in the data for the period 1948–2010. The sectoral growth rate is defined as g = ∆log(vaqi ), where vaqi i,t i,t denotes the chain-type quantity index for value added in the BEA industry data. 8The cyclical component corresponds to the deviations from the trend of the HP-filtered GDP growth rate. In the case of the normal distribution, P(z < −0.5) = 0.31, which matches the proportion of recessions in the period 1948–2010. 9

3. Compute the sectoral shares as ω = ω ∗(1+g ). i,t i,t−1 i,t 4. Repeat steps (2) and (3) for each time t. I set the number of periods to 100. (cid:80) 5. Compute the GDP growth rate as g = ω ∗(1+g ). GDP,t i,t i,t 6. Compute the index of sectoral dynamics as SecDynamics = 1 (cid:80) |ω −ω |. t n i i,t i,t−1 7. Define the recession periods. 8. Compute the correlation between the GDP growth rate and sectoral dynamics during recessions. Table 7 shows simulation results and how they compare with the historical data. Figure 4 plots a histogram of the ratio of the index of sectoral dynamics in recessions to the index of sectoral dynamics in expansions, and Figure 5 plots the correlation between the index of sectoral dynamics and GDP growth in the simulation data. The simulation data replicate the negative correlation between sectoral dynamics and business cycles. 3.2 VAR Approach The variables in the VAR are based on the seasonally adjusted quarterly data for IP for the period 1972q1–2013q4. The index of sectoral dynamics is calculated as the average deviation (in absolute value) of the sectoral growth rate from the IP growth rate. Figure 6 plots the index of sectoral dynamics and IP growth. The standard lag-length selections criteria recommend a recursive VAR with three lags. The stability conditions are satisfied, and the errors are not correlated. The results for the Granger test are shown in Table 8 and they are significant for all of the specifications. TheimpulseresponsefunctionsareshowninFigure 7. Alsoplottedisthe95percentconfidence interval for each of the impulse responses. An increase in the index of sectoral dynamics by 1 10

percentage points leads to an immediate decline in IP growth by 0.5 percentage point which lasts for two quarters and then it fades away after the third quarter. As a reference, the mean and the standard deviation are 1.78 and 0.73 for the index of sectoral dynamics and 0.55 and 1.55 for IP growth, where the units are percent. This result is similar to the duration of recession in the data. During the period 1972q1–2013q4, the length of a recession varied from 1.5 quarters (the 1980 recession) to 4.5 quarters (the Great Recession), with an average of 3 quarters. Since World War II, the average recession duration has been 2.71 quarters. 4 Sectoral Dynamics and Growth Volatility I compute the contribution of the sectoral dynamics to aggregate volatility using an approach similar to that Long and Plosser (1987). They use a one-factor model to extract a common shock, and they regress the aggregate volatility on the first component to compute the contribution of the common shock to aggregate volatility. The R2 of this regression shows the contribution of the common factor to aggregate volatility. Using monthly data for the 13-sector decomposition of the index of IP for the period 1948–1981, they find that the common factor accounted for 47 percent of the aggregate variance. In the spirit of Long and Plosser (1987), the contribution of the sectoral shocks to aggregate volatility is given by the R2 of the following regression: σ = β +β SecDyn +u , (2) GDP,t 0 1 t t Following the literature on the Great Moderation, σ denotes the instantaneous GDP GDP,t growth volatility. The instantaneous volatility is defined as σ = (cid:112)π |(cid:15) |, where (cid:15) is the estimated t 2 t t error term from the following AR(1) model of real GDP growth rates: ∆y = α +β∆y +(cid:15) , t t−1 t 11

where y is the log of real GDP. t I use a rolling-window estimation of regression 2 to capture the time dynamics of the contribution of sectoral dynamics to GDP volatility. Figure 8 plots a time series of the R2 from regression 2. The contribution of structural changes to GDP growth volatility has been increasing in the past two decades, from an average of about 30 percent until the 1990s to about 60 percent in 2010. DuringtheGreatModeration, sectoraldynamicsaccounted, onaverage, forhalfoftheannualvariation in GDP growth. This finding is in line with Foerster et.al (2011) who use a multisector growth model to adjust for the effects of input-output linkages in the factor analysis of quarterly IP data. They find that the Great Moderation was characterized by a fall in the importance of aggregate shocks while the volatility of sectoral shocks was essentially unchanged, leading to a considerable increase in the role of the idiosyncratic shocks. Carvalho and Gabaix (2013) and Tase(2013) find that the Great Moderation was the outcome of changes in the sectoral composition.9 5 Concluding Remarks This paper presents an index of structural dynamics that captures changes in the sectoral compositionofeconomicactivity. Thesesectoralshiftsareassociatedwithanaggregatedownturnlikewhat we would observe in the case of an aggregate productivity shock. In this regard, the sectoral shifts story can be considered an additional mechanism that generates business cycles. Furthermore the contribution of these sectoral dynamics to the aggregate volatility has been increasing. 9 Other explanations of the Great Moderation include: better monetary policy (Clarida, Gali and Gertler 2000, Cecchetti, Flores-Lagues and Krause 2006), and better inventory management (Kahn, McConnell, and Perez-Quiros 2002, McCarthy and Zakrajˇsek 2007, Irvine and Schuh 2005). 12

References [1] Abraham, Katherine G. and Lawrence F. Katz. 1986. “Cyclical Unemployment: Sectoral Shifts or Aggregate Disturbances?”. Journal of Political Economy, 94(3): 507–522. [2] Blanchard,Olivier,andJohnSimon.2001.“TheLongandLargeDeclineinU.S.OutputVolatility.”Brookings Papers on Economic Activity, no.1: 135–64. [3] Carvalho, Vasco, andXavierGabaix.2013.“TheGreatDiversificationandItsUndoing.”American Economic Review, 103(5): 1697–727. [4] Cecchetti, Stephen G., Alfonso Flores-Lagunes, and Stefan Krause. 2006. Has Monetary Policy Become More Efficient? A Cross-Country analysis. The Economic Journal 116: 408–33. [5] Clarida,Richard,JordiGal´ı,andMarkGetler.2000.MonetaryPolicyRulesandMacroeconomic Stability: Evidence and Some Theory. Quarterly Journal of Economics 115(1), 147-180. [6] Elsby, Michael W., Bart Hobijn and Aysegul Sahin. 2013. “The Decline of the U.S. Labor Share”. Brookings Papers on Economic Activity, Fall: 1-52. [7] Foerster Andrew T. , Pierre-Daniel G. Sarte, and Mark W. Watson. 2011. “Sectoral versus Aggregate Shocks: A Structural Factor Analysis of Industrial Production”. Journal of Political Economy, 119(1),1-38. [8] Gal´ı, Jordi and Luca Gambetti. 2009. On the Sources of the Great Moderation. American Economic Journal: Macroeconomics 1(1), 26-57. [9] Groshen, Erica L. and Simon Potter. 2003. “Has Structural Change Contributed to a Jobless Recovery?”. Federal Reserve Bank of New York Current Issues in Economics and Finance 9(8). 13

[10] Irvine, Owen and Scott Schuh. 2005. “The Roles of Comovement and Iinventory Investment in the Reduction of Output Volatility.” Federal Reserve Bank of Boston, Working Paper 05(9). [11] Kahn, James, Margaret M. McConnell, and Gabriel Perez-Quiros. 2002. On the Causes of the Increased Stability of the U.S. Economy. Federal Reserve Bank of New York Economic Policy Review 8(1), 183 - 202. [12] Karabarbounis, Loukas and Brent Neiman. 2013. “The Global Decline of the Labor Share”. National Bureau of Economic Research Working Paper19136. [13] Kim, Chang-Jin, and Charles R. Nelson. 1999. “Has the U.S. Economy Become More Stable? A Bayesian Approach Based on a Markov-Switching Model of the Business Cycle.” The Review of Economics and Statistics, 81: 608–16. [14] Lilien, David M. 1982. “Sectoral Shifts and Cyclical Unemployment”. The Journal of Political Economy, 90(4), 777–93. [15] Long, John B. and Charles I. Plosser. 1987. “Sectoral vs. Aggregate Shocks In The Business Cycle”. American Economic Review, Papers and Proceedings, 77(2): 333-36. [16] McCarthy, Jonathan and Egon Zakrajˇsek. 2007. “Inventory Dynamics and Business Cycles: What Has Changed?” Journal of Money, Credit, and Banking, 39(2-3), 591–13. [17] McConnell, Margaret and Gabriel Perez-Quiros. 2000. “Output Fluctuations in the United States: What Has Changed since the Early 1980s?”. American Economic Review, 90(5): 1464- 76. [18] Panovska, Irina. 2016. “What Explains the Recent Jobless Recoveries?” Macroeconomic Dynamics, http://dx.doi.org/10.1017/S1365100515000656. 14

[19] Phelan, Christopher and Alberto Trejos. 2000. “The Aggregate Effects of Sectoral Reallocations”. Journal of Monetary Economics, 45, 249-26., [20] Rissman, Ellen R. 1997. “Measuring Labor Market Turbulence?”. Federal Reserve Bank of Chicago Economic Perspectives 21(3), 2-14. [21] Stock, James and Mark Watson. 2003. “Has the Business Cycle Changed? Evidence and Explanations”. Federal Reserve of Kansas City, Economic Policy Symposium Proceedings, Jackson Hole, Wyoming, August 28-30. [22] Tase,Manjola.2013.“SectoralAllocation,RiskEfficiencyandtheGreatModeration”.Finance and Economics Discussion Series 2013-73. Board of Governors of the Federal Reserve System. 15

Sector 2002 NAICS Code Agriculture, Forestry, Fishing and Hunting 11 Mining 21 Utilities 22 Construction 23 Durable goods 33, 321, 327 Nondurable goods 31, 32 (except 321 & 327) Wholesale trade 42 Retail trade 44, 45 Transportation and Warehousing 48, 49 (except 491) Information 51 Finance and Insurance 52 Real estate, Rental, Leasing 53 Professional, Scientific and Technical Services 54 Management of Companies and Enterprises 55 Administrative and Waste Management Services 56 Education services 61 Health care and Social assistance 62 Arts, Entertainment and Recreation 71 Accomodation and Food services 72 Other Services, except Government 81 Federal Government na State and Local Government na Table 1: List of Sectors - Bureau of Economic Analysis. Value added, 22 sectors. 16

Sector Description Labor Share 1 Agriculture 0.50 2 Metal mining 0.51 3 Coal mining 0.59 4 Oil and gas extraction 0.25 5 Non-metallic mining 0.51 6 Construction 0.87 7 Food and kindred products 0.63 8 Tobacco 0.39 9 Textile mill products 0.75 10 Apparel 0.82 11 Lumber and wood 0.70 12 Furniture and fixtures 0.79 13 Paper and allied 0.66 14 Printing, publishing and allied 0.74 15 Chemicals 0.51 16 Petroleum and coal products 0.41 17 Rubber and misc plastics 0.76 18 Leather 0.74 19 Stone, clay, glass 0.73 20 Primary metal 0.67 21 Fabricated metal 0.74 22 Machinery, non-electical 0.74 23 Electrical machinery 0.68 24 Motor vehicles 0.63 25 Transportation equipment and ordnance 0.87 26 Instruments 0.83 27 Misc. manufacturing 0.70 28 Transportation 0.67 29 Communications 0.44 30 Electric utilities 0.32 31 Gas utilities 0.34 32 Trade 0.77 33 Finance Insurance and Real Estate 0.34 34 Services 0.81 35 Government enterprises 0.59 Table 2: List of Sectors - Dale Jorgenson’s KLEMS. Value added, 35 sectors. 17

Industry Title CES Industry Code Mining and logging 10-000000 Construction 20-000000 Durable goods 31-000000 Nondurable goods 32-000000 Wholesale trade 41-420000 Retail trade 42-000000 Transportation and warehousing 43-000000 Utilities 44-220000 Information 50-000000 Financial activities 55-000000 Professional and business services 60-000000 Education and health services 65-000000 Leisure and hospitality 70-000000 Other services 80-000000 Table 3: List of Sectors - Current Employment Statistics (CES). Employment, 14 sectors. 18

Industry Title NAICS Industry Code Mining 21 Electric power generation, transmission, and distribution 2211 Electric and gas utilities 2211,2 Natural gas distribution 2212 Food, beverage, and tobacco 311,2 Textiles and products 313,4 Apparel and leather goods 315,6 Wood product 321 Paper 322 Printing and related support activities 323 Petroleum and coal products 324 Chemical 325 Plastics and rubber products 326 Nonmetallic mineral product 327 Primary metal 331 Fabricated metal product 332 Machinery 333 Computer and electronic product 334 Electrical equipment, appliance, and component 335 Motor vehicles and parts 3361-3 Aerospace and miscellaneous transportation 3364-9 Furniture and related product 337 Miscellaneous 339 Table 4: List of Sectors - Industrial Production. Output, 23 sectors. 19

SecDyn(35) SecDyn(22) SecDyn(15) SecDyn(CES, 16) mean(Index | recession) 0.134 0.158 0.225 0.199 mean(Index | expansion) 0.079 0.099 0.129 0.109 mean(Index|recession) 1.7 1.6 1.7 1.8 mean(Index|expansion) corr(Index, growth) -0.508 -0.600 -0.684 -0.681 corr(Index, growth)|recession -0.345 -0.588 -0.615 -0.661 corr(Index, growth)|before 1990 -0.567 -0.640 -0.719 -0.770 corr(Index, growth)|after 1990 -0.663 -0.508 -0.544 -0.177 mean(Index pre 90s) 0.099 0.116 0.153 0.137 mean(Index post 90s) 0.072 0.106 0.144 0.113 Table 5: Summary Statistics. SecDyn(35), SecDyn(22), and SecDyn(15) correspond to the index of sectoral dynamics where the sectoral share is given by the sector’s share of value added in total output. In SecDyn(CES, 16), the sectoral share is given by the sector’s employment as a share of total employment. The numbers in parentheses correspond to the number of sectors. The time coverage for SecDyn(35) is 1960–2005; for SecDyn(22) and SecDyn(15) 1947–2010; and, for SecDyn(CES, 16) 1939–2013. 20

GDPgrowth ≤ 0 CyclicalGDP ≤ 0 CyclicalGDP ≤ −sd/2 correctly defined 81% 79% 87% define recession | recession 45% 82% 73% define expansion | expansion 100% 78% 95% Table 6: Defining Phases in Business Cycles. The columns represent three alternative measures used in defining phases in business cycles. The figures correspond to the percent correctly defined. The (correctly defined) is given as a percentage of the total number of periods, 63 years (1948–2010). The (define recession | recession)andthe(define expansion | expansion)aregivenasapercentageofthenumberofrecessionyears (22) and expansion years (41), respectively. 21

Historical Data Simulation Data mean(Index) | recession 0.158 0.144 mean(Index) | expansion 0.099 0.125 mean(Index|recession) 1.6 1.2 mean(Index|expansion corr(Index, growth) -0.600 -0.122 corr(Index, growth)|recession -0.588 -0.543 Table 7: Comparing Simulation Results with Data. Historical data are from the BEA’s Industry Accounts and are 22 sectors, value added, and the period 1947–2010. Simulation data are drawn to match the joint distribution of sectoral growth rates in the historical data. 22

Dependent Variable in Regression Regressor Prob >chi2 Sectoral dynamics IP growth 0.000 IP growth Sectoral dynamics 0.000 Table8: GrangerCausalityTest. Theentriesshowthep-valuesforF-teststhatlagsofthevariableinthe column Regressor do not enter the reduced-form equation for the variable in the column labeled Dependent Variable. The results were computed from a recursive VAR with 3 lags and over the 1972q1–2013q4 sample period. 23

.5 .4 .3 .2 .1 0 stniop egatnecrep 1950 1960 1970 1980 1990 2000 2010 Sectoral Dynamics(value added, 15) Sectoral Dynamics(value added, 22) Sectoral Dynamics(value added, 35) Sectoral Dynamics(employment, 14) Figure 1: Index of Sectoral Dynamics. The numbers in parentheses correspond to the number of sectors. 24

75 70 65 60 55 tnecrep 1960 1970 1980 1990 2000 Labor share of Value Added Recession Labor share of Value Added (sector average) Figure 2: Labor Share. 25

2 1.5 1 0.5 0 −0.5 −1 −1.5 −2 1940 1950 1960 1970 1980 1990 2000 2010 2020 stniop egatnecrep Recessions Recessions Min(Change in Sectoral Shares) Max(Change in Sectoral Shares) Sd(Change in Sectoral Shares) Figure 3: Range and Standard Deviation of the Change in Sectoral Share of GDP. BEA’s Industry Accounts, 22-sector disaggregation. 26

3000 2500 2000 1500 1000 500 0 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 )snoitalumis 000,01(tnuoc Mean(Index|recession)/Mean(Index|expansion) Figure 4: Simulation Results. Distribution of Mean(Index|recession)/Mean(Index|expansion) in the simulated data. 27

all periods 3000 2500 2000 1500 1000 500 0 −1 −0.5 0 0.5 )snoitalumis 000,01(tnuoc recession periods 3000 2500 2000 1500 1000 500 0 −1 −0.5 0 0.5 Corr(SecDyn, GDP growth) )snoitalumis 000,01(tnuoc Corr(SecDyn, GDP growth) Figure 5: Simulation Results. Distribution of the correlation between sectoral dynamics and growth volatility in the simulated data. 28

6 4 2 0 −2 −4 −6 −8 tnecrep 1972q2 1976q2 1980q2 1984q2 1988q2 1992q2 1996q2 2000q2 2004q2 2008q2 2012q2 Sectoral Dynamics Industrial Production Growth Recession Figure 6: Sectoral Dynamics (Industrial Production). 29

1 .5 0 −.5 )%( IRF: SecDyn −> IPgrowth 1 .5 0 −.5 0 5 10 lag )%( IRF: SecDyn −> SecDyn 0 5 10 lag 1 .5 0 −.5 )%( IRF: IPgrowth −> SecDyn 1 .5 0 −.5 0 5 10 lag )%( IRF: IPgrowth −> IPgrowth 0 5 10 lag Figure 7: Impulse Responses. The results were computed from a recursive VAR with 3 lags and over the 1972q1–2013q4 sample period. 30

70 60 50 40 30 20 10 1975 1980 1985 1990 1995 2000 2005 2010 tnecrep Figure 8: Contribution of Sectoral Changes to GDP Growth Volatility. This figure plots the R2 from the regression sigma =β +β1SecDyn +u , where sigma denotes the instantaneous GDP GDP,t 0 t t GDP,t growth volatility. 31