MPA Munich Personal epec Archive Wage, Produciviy and Unemploymen Microeconomics Theory and Macroeconomic Daa Weshah azzak 1 November 2014 Online a hps://mpra.ub.uni-muenchen.de/61105/ MPA Paper No. 61105, posed 5 January 2015 05:57 UTC
Wage, Produciviy and Unemploymen Microeconomics Theory and Macroeconomic Daa W A azzak 1 November 2014 Absrac We confron microeconomic heory wih macroeconomic daa. Unemploymen resuls from wo main micro-level decisions of workers and firms. Mos of he efficiency wage and bargaining heories predic ha over he business cycle, unemploymen falls below is naural rae when he worker s real wage exceeds he reservaion wage. However, hese heories have weak empirical suppor. Firm s decision predics ha when he worker s real wage exceeds he marginal produc of labor, unemploymen increases above is naural rae. Accouning for his microeconomic decision helps explain almos all he flucuaions of U.S. unemploymen. JEL Classificaion numbers: D21, E24 Keywords: Wage, produciviy and unemploymen 1 razzakw@gmail.com. I am hankful o Francisco Nadal De Simone and Imad Moosa for valuable commens. W. azzak, 2014
1 1. Inroducion The U.S. unemploymen rae increased beween December 2007 and June 2009 because of he Grea ecession, bu began o fall, slowly since he early 2010. I dropped from 9.8 percen in March 2010 o 6.7 percen in March 2014. This is sill higher han he average unemploymen rae of 5.8 percen over he period 1948-2014. Labor marke oucomes, especially he unemploymen rae, are criical o U.S. moneary policymakers. The modern heories of unemploymen include, for example, efficiency wage (e.g., Shapiro and Sigliz, 1984) and he dynamic search and maching (e.g., Morensen and Pissarides, 1994). The empirical suppor for efficiency wage and dynamic search and maching models is weak. Dynamic search and maching models of unemploymen predic ha he volailiy of he employmen vacancy raio and average labor produciviy are he same while he U.S. daa show ha he sandard deviaion of he unemploymen-vacancy raio is 20 imes larger han ha of average labor produciviy, Shimer (2005). Essenially, one canno analyze unemploymen dynamic wihou analyzing he relaionship beween wages, produciviy, and unemploymen. Efficiency wage and bargaining models have such relaionship, which is called he wage curve, e.g., Blanchflower and Oswald (1994). Blanchard and Kaz (1997) show ha models of unemploymen based on efficiency wages, maching or bargaining models, and compeiive wage deerminaion, all generae such a wage curve relaionship. In he wage curve, he dependen variable is he naural log of real wage. The independen variables are he naural log of he reservaion wage, he produciviy level, and he rae of unemploymen (could be a naural log-ransformed measure of unemploymen). Given he level of produciviy, he relaionship beween he log of real wages relaive o he reservaion wage, and he unemploymen rae, is negaive. These heories inerpre his correlaion ha when unemploymen is high, he real wage falls given produciviy. However, here is a microeconomic inerpreaion. A worker faced wih a decision o accep or rejec a job wih a paricular wage offer would ake he job if he real wage rae is greaer han his or her reservaion wage, given he level of produciviy. Hence, W. azzak, 2014
2 he unemploymen rae o fall. The worker rejecs he job offer if he real wage is less han his or her reservaion wage, hence, unemploymen increases. However, hese models do no accoun for anoher imporan decision, i.e., he firm s decision. In he Beveridge curve (BC) analysis of vacancy and unemploymen, for example, here is no represenaion of he firm s demand for labor, Daly e al. (2012). They suggesed adding a job creaion curve o he BC. The decision is ha firms coninue o hire workers over he business cycle as long as he real wage rae is less han he marginal produc of labor; sops hiring when he real wage is equal o he marginal produc of labor; and layoffs workers when he real wage is higher han he marginal produc of labor. The objecive of his paper is o examine he effecs of hese wo micro-level decisions on unemploymen. We explain unemploymen dynamics by empirically esing he conribuions of he wo imporan micro-level decisions. We will show ha he firs decision could explain up o 50 percen of he dynamics of unemploymen, and ha he weak empirical suppor of unemploymen heories is due o ignoring he firm s decision. The firm s decision and he worker s decision ogeher explain almos all he flucuaions of U.S. unemploymen. We use U.S. quarerly daa from 1999 o 2013. The daa and sources are in he ada appendix. There is one imporan poin ha he relaionships we are analyzing are hose ha occur over he business cycle. We show ha hese wo decisions can accoun for almos all he variaions of he U.S. unemploymen over he business cycle. The paper is organized as follows. Nex, we explain he worker s and he firm s decisions ha we call microeconomic level decisions, and how hey are relaed o unemploymen. In secion 3 we provide measuremens and ess. In secion 4 we discuss he relaionship wih he Phillips curve and he wage curve. Secion 5 concludes. 2. Microeconomic level decisions and measuremens 2.1 The worker s decision Consider he worker s decision o accep or rejec a wage offer, which is he mechanism underlying he wage curve. A worker who faces a decision o accep or rejec a wage offer compares he offered real wage o a reservaion wage, which is he W. azzak, 2014
3 wage equivalen of being unemployed. The reservaion wage is an unobservable variable. If he real wage rae is greaer han he reservaion wage, he worker acceps he offer, akes he job, and unemploymen falls. The opposie is rue. Thus, he covariance beween he wage gap, which is he real wage minus he reservaion wage, and he unemploymen rae, is negaive. How much of he variaion in unemploymen over he business cycle is accouned for by his mechanism? To answer his quesion we have o measure he real wage and he reservaion wage. The former is less complicaed han he laer, bu we do no have a unique way o measure hem because expeced inflaion or expeced price level are no direcly observable. The bes measure mus be robus o a variey of measures of expecaions. 2.1.1 Measuring he real wage e Le he real wage be w W / P, where W is he nominal wage rae, and P e is he expeced price level. We could also adjus he nominal wage o a measure of he expeced inflaion rae e. We can have a number of measures of e e P and depending on how many differen measures of expeced inflaion we have. We will use he CPI as a measure of he price level. Le he expeced price level be a 6-quarer moving average of he CPI. In addiion we consider four differen measures of expeced inflaion: (1) a 6-quarer moving average of he rae of change of he CPI; (2) he Philadelphia fed s survey measure of inflaion expecaions; and (3) he Michigan Universiy s survey measure of inflaion expecaions. Then we can adjus he average hourly wage rae o hese measures of expeced price level and expeced inflaion. We arrive a four differen measures of he real wage. Figure (1) plos he HP-filered measures. The real wage, w 1, is he associaed wih average inflaion measured as a 6-quarer moving average of CPI inflaion; w2 is associaed wih Philadelphia fed s survey measure of inflaion expecaions; w 3 is associaed wih he Michigan Universiy s survey measure of inflaion expecaions; and w4 is associaed wih he expeced price level. W. azzak, 2014
4 Clearly, hese measures are robus o various price and inflaion adjusmens. However, noe ha wha maers for us is he wage gap, he gap beween he real wage and he reservaion wage, which we will examine nex. 2.1.2 Measuring he reservaion wage The reservaion wage is he wage equivalen of being unemployed. Mos of he heoreical model of wage seing could be represened by he following wage equaion under simplifying assumpions abou he funcional form and indicaors of labor marke ighness: ln w ln w (1 ) ln y u, (1) Where w is he real wage, w is he reservaion wage, y is labor produciviy, where labor produciviy is GDP/working age populaion, and u is log ( U /1 U), where uppercase U is he unemploymen rae. i The parameer is [0, 1]. For example, in he efficiency wage model of Shapiro and Sigliz (1984) he shirking model produciviy does no influence wages direcly, hence 1. In he bargaining models, e.g., Morensen and Pissarides (1994), 0 1, since wages depend on he surplus from mach, hus on produciviy. Blanchard and Kaz (1999) argue ha he reservaion wage depends on he generosiy of benefis (unemploymen benefis and oher benefis), and oher income suppors he workers expec o have while hey are unemployed. The insiuional dependence of unemploymen benefis on pas wage level, may sugges ha he reservaion wage also depends on pas wages. The reservaion wage depends also, on wha he unemployed do wih heir ime he uiliy of leisure, which may include home producion and income ha could be earned in he informal secor. The reservaion wage may also depend on non-labor income. Under a Harrod-neural echnological progress, an increase in produciviy leads o an increases in boh labor and non-labor income. Thus, he reservaion wage may depend on boh pas wages and produciviy levels. They argue ha i is empirically reasonable o assume ha echnological progress does no lead o a persisen rend in unemploymen, which pus an addiional resricion ha is he reservaion wage is homogenous of degree one in he real wage W. azzak, 2014
5 and produciviy in he long run. This is a esable hypohesis, which we will examine laer. Blanchard and Kaz (1999) assume he following simple illusraive equaion for he reservaion wage: ln w a ln w 1 (1 ) ln y, (2) where 0 1. Thus, we have a leas wo opions o measure he reservaion wage. Firs, we can esimae he Sae-Space Kalman filer sysem of equaion (1). We experimened wih wo differen specificaions, e.g., in levels, log levels, wih unemploymen, and wih cyclical unemploymen. We esimae he variances as addiional parameers. The log version fis very well. The signal equaion is: ln w ln w ln y u~ 1 ; (3) he sae equaion; ln w ln w ; and (4) 1 he variance of he shock 2 2, which is esimaed joinly. We esimae he sysem above using a Maximum Likelihood mehod. The unemploymen variable u ~ is he HP-filered log unemploymen as defined earlier, where he symbol denoes he cyclical componen. The oher measure of he reservaion wage is o calibrae equaion (2) using a number of values for. ii Table (1) repors he correlaion coefficiens beween some esimaes of he, HPfilered, log reservaion wage using boh of he mehods explained above, along wih log real wage. We use a sensiiviy analysis. The reservaion wage daa are denoed w w10 in addiion o he Kalman filer esimae. The firs six esimaes 1 w 1 w are 6 from calibraing equaion (2), where we impose he homogeneiy resricion on equaion (2). The values for are given below. W. azzak, 2014
6 Parameer values used o calibrae Homogeneiy resricion imposed w 1 [ a 2.65, 0.50] w 2 [ a 2.65, 0.75] w 3 [ a 2.65, 0.85] w 4 [ a 2.65, 0.90] w 5 [ a 2.65, 0.95] w 6 [ a 2.65, 0.99] ln w a ln w 1 (1 ) ln y - Parameer values used o calibrae ln w a 1 ln w 1 2 ln y - Homogeneiy resricion no imposed so he weighs on lagged wages and produciviy do no sum up o one w 7 a 2.65, 0.90, 0.15] [ 1 2 w 8 [ a 2.65, 1 0.95, 2 0.10] w 9 [ a 2.65, 1 0.95, 2 0.25] w 10 [ a 2.65, 1 0.99, 2 0.10] Finally, we have he reservaion wage esimaed using he Kalman filer and he real wage. Table (1) shows ha hese measures are highly correlaed over he business cycle regardless of wheher he homogeneiy resricion is imposed, or no. However, a small value of, e.g., 0.50, which means a larger weigh on produciviy, produces a reservaion wage esimae ha is less correlaed wih he oher esimaes. Essenially, he reservaion wage is dependen more on lagged wages han on produciviy. I suggess ha he value of is no necessarily equal o one as in Shapiro and Sigliz (1984) and o Blanchard and Kaz (1999). Figure (2) plos all he esimaes along wih he real wage (HP-filered). Given our esimaes of he real wage and he reservaion wage, we calculae he wage gap (he log real wage log reservaion wage), bu we drop he exreme esimaes, which correspond o he reservaion wages wih low value of, i.e., 0. 50 and 0. 75. We have wage gaps corresponding o he esimaed reservaion wages, W. azzak, 2014
7 and he Kalman filer. We plo he daa in figure (3). The esimaes are highly correlaed. The heory predics ha he covariance beween he wage gap and unemploymen is negaive because when he real wage is greaer han he reservaion wage he worker akes he job, hence unemploymen falls. We es he covariance for each esimae of he wage gap and he unemploymen rae. We es he correlaions using a confidence ellipse, which is disribued 2 1,0. 95. Figure (4) plo he confidence ellipses. Some correlaions are posiive, which are inconsisen wih he heory. These are found in plos 1, 2, 3, which correspond o wage gaps, where he reservaion wage are calibraed using equaion (2), and he weigh, is eiher low (0.50, 0.75 and 0.85) or he homogeneiy resricion is no imposed and he weigh on produciviy is > 0.10. There are wo cases, where he correlaion is posiive; hese are plos 7 and 9, which correspond o w 7 and w 9, where 90 1 0. and 2 0. 15 and 1 0. 95 and 2 0.25 for w 7 and w 9 respecively. Generally, he es suggess ha for he predicion of he heory o hold (i.e. he gap beween he real wage and he reservaion wage and unemploymen are negaively correlaed), he homogeneiy resricion need no be imposed, bu he weigh on produciviy in equaion (2) should sill be smaller han he weigh on lagged waged. In oher words, produciviy affecs he reservaion wage and he real wage, bu he effec is smaller han he effec of lagged wages. Table (2) repors a number of regressions using he wage gaps ha are, saisically significanly, negaively correlaed wih unemploymen in figure (4). The wage gap, depending on measuremen, can explain up o 50 percen of unemploymen s flucuaions over he business cycle. 3. The firm s decision The firm s decision o hire workers has no been empirically esed in macroeconomic models of unemploymen. Over he business cycle, he firm hires workers as long as he marginal produc of labor exceeds he real wage; i sops hiring addiional workers when he marginal produc of labor is equal o he real wage; and i lays-off workers when he marginal produc is lower han he real wage. The marginal produc of labor can deviae from he real wage over he business cycle, and for a number of reasons. W. azzak, 2014
8 Thurow (1968) provides some insigh. The wedge exiss because: (1) Taxes can creae a wedge if he incidence of he indirec axes is on labor. (2) Monopoly power can explain differences beween he marginal produc of facor inpus and heir prices. (3) Consan subsiuion beween facor inpus along growh pah could creae a wedge beween he real wage and he marginal produc of labor. As he sock of capial rises, labor is displaced. Given oupu, less labor inpu causes is marginal produciviy o be higher han is rae of reurn, i.e. real wages. This wedge can persis if he ransiion cos along he growh pah is high. (4) Firms se he wage rae by he marginal produc of he marginal worker raher han he marginal produc of he average worker, due o heerogeneiy. Maré and Hyslop, (2006, 2008) provide evidence ha less skilled labor is hired a he up-urn of he New Zealand business cycle. If his were he case, hen wages will have o be lower han he marginal produc of he average worker. (5) isk premiums creae a wedge beween he marginal produc of labor and he real wage. (6) When social reurns are no equal o privae reurns, acual reurns mus be correced for axes when possible. (7) Endogenous growh models assume an increasing reurn o scale raher (i.e., less han doubling facor inpus is needed o double oupu), which means ha capial and labor will more han exhaus oal oupu. The covariance beween he wedge (real wages minus he marginal produc of labor) and he unemploymen rae over he business cycle is posiive. Unemploymen increases when he wedge is > 0 because he firm lays-off workers. Compuing he wedge requires an esimae of he marginal produc of labor. We assume a simple represenaive agen, where producion is given by he Cobb Douglas producion funcion. The firs-order condiion would equaion he marginal produc of labor o he real wage. Le he producion funcion be a consan reurn o scale Cobb Douglas: Y AK 1 L, (5) Where Y is real GDP, K is he sock of capial and L is labor, which is measured eiher in hours-worked or working age populaion. The parameer is he share of labor. The marginal produc of labor is: W. azzak, 2014
9 Y h mpl AK 1 L 1 Y / h, (6) which we can calibrae given K, L, and. The sock of capial is measured using daa on fixed capial formaion, and an assumed value of he iniial sock of capial and he depreciaion rae. We assume ha he sock of capial in he U.S. is approximaely hree imes as big as GDP (e.g., Obsfeld and ogoff, 1996) and he depreciaion rae is somewhere beween 5 and 8 percen annually. For labor, we use he working age populaion (15-64). There are issues abou measuring he share of labor, Krueger (1999). Karabarbunis (2014) provides four measures, and repors he correlaion coefficiens. Firs is BEA unadjused, which is oal compensaion o employee / naional income. iii Second is BEA adjused, where he reas compensaions o employee as unambiguous labor income, proprieor s income and ne axes on producion and impors as ambiguous income, and all oher caegories such as renal income, corporae profis, and business ransfers as unambiguous capial income. Third is BLS corporae, which does no require impuaions of he labor earnings of sole proprieors, he uses labor share for he corporae secor. I is he raio of corporae compensaions o employee / gross value added of he corporae secor. iv Fourh is BEA corporae, which is he share in he non-financial secor. These measures are highly, saisically significanly, correlaed. Table (3) repors he correlaion marix. Figure (5) plos our esimaes of he share of labor as in BEA above, which urns ou o be sufficien for our purpose. I has been declining over ime. To calibrae he marginal produc of labor we use our esimaes of he sock of capial, working age populaion and he share of labor. Gali (2005) argued ha he ime series properies of hours worked and employmen or working age populaion can give rise o differences in measuremens. To check he robusness of our esimae we calibrae he marginal produc of labor using hours worked and working age populaion separaely. Figure (6) plos boh esimaes. We repor he correlaions beween various measures of he wedge in able (4). They differ in he way he real wage is compued. Figure (7) plos he four measures. Figure W. azzak, 2014
10 (8) plo he differen measures of he wedge wih unemploymen. The correlaion is significan and posiive as prediced by he heory. We summarize he effecs of he wage gap and he wedge on unemploymen using an unresriced VA. X c 1X 1 2X 2 p X p, (7) where, X is an ( n 1) vecor conaining hree variables, which are he HP-filered measures of he wage gap, he wedge and unemploymen. The wage gap is our measure of he difference he real wage and he reservaion wage. The real wage e is w W / P. We use he Kalman filer s measure of he reservaion wage (see figure 4). The wedge is he real wage minus he marginal produc of labor, which we presened earlier. The error erm is also a vecor, which is disribued i.i.d. N ( 0, ) Figure (9) plos he VA s generalized impulse response funcions of unemploymen o he innovaions of he wage gap and o he wedge. Ordering of he variables in he VA is no longer a problem since he generalized impulse response funcion since Pesaran and Shin (1998) describe he impulse response funcion, where hey consruc an orhogonal se of innovaions ha does no depend on he VA ordering. We use a Mone-Carlo wih 10000 ieraions o esimae he sandard errors. The wage gap shock decreases unemploymen and he wedge shock increases unemploymen over he business cycle. Variance decomposiion shows he growing imporance of he wage gap and he wedge beween he real wage and he marginal produc of labor on unemploymen. From period 6 o 12, hey explain more han 50 percen of he variance of unemploymen. Earlier we showed ha he wage gap explains abou 30 50 percen of he flucuaions in unemploymen over he business cycle. Table (5) repors some regression resuls o show ha he wedge and he change in he wedge can explain an addiional 40 percen of he flucuaions in unemploymen. The wo variables, he wage gap and he wedge, explain nearly 80 percen of unemploymen. Mos of he remaining unexplained variaion is he dynamic, which is aribued o smoohing he daa by he HP filer (azzak, 1997) W. azzak, 2014
11 4. Conclusion The empirical record of modern unemploymen heories and models such as he efficiency wage heory, e.g., Shapiro and Sigliz (1984) Shirking model and he dynamic search and maching of Morensen and Pissarides (1994) is weak. Dynamic search and maching models of unemploymen predic ha he volailiy of he employmen vacancy raio and average labor produciviy are he same while he U.S. daa show ha he sandard deviaion of he unemploymen-vacancy raio is 20 imes larger han ha of average labor produciviy, Shimer (2005). Unemploymen heories and models accoun for he wage gap, which is he difference beween he real wage and he reservaion wage only. In his seup, he increase in unemploymen reduces real wages given reservaion wages and produciviy. The wage gap beween he real wage and he reservaion wage is bes inerpreed as he decision he worker s make when faced wih a wage offer. The worker acceps he job offer wih a cerain real wage when he real wage exceeds his or her reservaion wage, given produciviy. There is, however, anoher microeconomic-level decision no accouned for by mos models of unemploymen. I is he firm s decision o hire labor. Over he business cycle, firms hire workers as long as he real wage is lower han he marginal produciviy of labor; hey sop hiring workers when he real wage is equal o he marginal produciviy of labor; and hey lay off workers when he real wage exceeds he marginal produciviy of labor. By modeling boh microeconomic decisions, he macroeconomic daa are consisen wih he micro decisions above. We use quarerly daa from 1999 o 2013 for he U.S. o measure he real wage, he reservaion wage, and he wedge beween real wage and he marginal produc of labor and show ha hese shocks have impulse response funcions as prediced by he microeconomic heory and heir variances explain more han 50 percen of he variaion of unemploymen. We also show ha while he wage gap explains up o 50 percen of he unemploymen dynamic, he wedge beween he real wage and he marginal produc of labor can explain an addiional 30 percen of W. azzak, 2014
12 unemploymen dynamics. The remaining unexplained dynamic of unemploymen is a saisical arifac relaed o he use of smoohing. W. azzak, 2014
13 eferences Barro,. J. Unanicipaed Money Growh and Unemploymen in he Unied Saes, American Economic eview, 67, 1977, 101-15. Baxer, M. and. King. Measuring Business Cycles Approximae Band-Pass Filers For Economic Time Series. eview of Economics and Saisics 81(4), 1999, 575-593. Blanchard, O. and L. Kaz. Wage Dynamics: econciling Theory and Evidence. American Economic eview 89 (3), 1999, 69-74. Chrisaino, L. J. and Fizgerald. The Band Pass Filer, Inernaional Economic eview, Vol.44, Issue 2, 435-465. Daly, C. B. Hobijn, A. Sahin and. Vallea. A Search and Maching Approach o Labor Markes: Did he Naural ae of Unemploymen ise? Journal of Economic Perspecives, 26(3), Summer 2012, 3-26. Gali, J. Trends in Hours, Balanced Growh and he ole of Technology in he Business Cycle. NBE, WP No. 11130, 2005. Karabarbounis, L. The Labor Wedge: MS vs. MPN. eview of Economic Dynamic, 17, 2014, 206-223. Karabarbounis, L. and B. Neiman. The Global Decline of he Labor Share. NBE WP No. 19136, 2013. Maré, D. C., and D.. Hyslop. Cyclical Earnings Variaion and he Composiion of Employmen. Saisics New Zealand, 2008. Maré, D. C., and D.. Hyslop. Worker-Firm Heerogeneiy and Maching: An analysis using worker and firm fixed effecs esimaed from LEED. Saisics New Zealand, LEED research repor, 2006. Morensen, D. and C. Pissarides. Job Creaion and Job Desrucion in he Theory of Unemploymen. The eview of Economic Sudies, Vol. 61, No. 3. July 1994, 397-415 Obsfeld, M. and K. ogoff. Foundaion of Inernaional Macroeconomics. MIT Press, 1996. Pesaran, M. Hashem and Yongcheol Shin. Impulse esponse Analysis in Linear Mulivariae Models. Economics Leers, 58, 1998, 17-29. azzak, W. A. The Hodrick-Presco Technique: A Smooher versus a Filer: An Applicaion o New Zealand GDP. Economics Leers 57, issue 2, 1997, 163-168. W. azzak, 2014
14 Shapiro, M. and J. Sigliz. Equilibrium Unemploymen as a Discipline Device. American Economic eview 74, June 1984, 433-444. Shimer,. The Cyclical Behaviour of Equilibrium Unemploymen and Vacancies, American Economic eview, 2005, 25-49. Thurow, L. C. Disequilibrium and Marginal Produciviy of Capial and Labor. eview of Economics and Saisics Vol. 50, No.1, 1968, 23-31. W. azzak, 2014
15 w 1 w 1 1.000000 w 2 w 3 w 4 w 2 0.650233 1.000000 w 3 0.460663 0.973860 1.000000 w 4 0.382314 0.950613 0.996266 1.000000 w 5 w 6 w 7 w 8 w 9 w 10 Table 1: eservaion Wage Correlaions (HP-filered) w 5 0.315967 0.926062 0.987421 0.997245 1.000000 w 6 0.269057 0.906512 0.978607 0.992632 0.998792 1.000000 0.450089 0.970710 0.999482 0.996755 0.989409 0.981082 1.000000 0.376595 0.948400 0.995391 0.999645 0.997904 0.993519 0.996729 1.000000 0.566496 0.994425 0.992383 0.978042 0.960621 0.945926 0.990434 0.976435 1.000000 w 7 w 8 w 9 w 10 Kalman reservaion wage 0.371603 0.946690 0.994886 0.999605 0.998238 0.994117 0.996278 0.999985 0.975274 1.000000 Kalman 0.232124 0.862254 0.937944 0.953891 0.962094 0.964621 0.941003 0.955216 0.903047 0.955942 1.000000 eservaion Wage 0.456463 0.955083 0.979319 0.975144 0.966935 0.957911 0.979904 0.975256 0.972599 0.974719 0.959104 1.000000 w1 w6 are calibraed reservaion wages using equaion (2) imposing he homogeneiy resricion, where a is 2.65, he mean of log real wages as defined log ( / e W P ), e W is he average hourly wage, and P is 6-quarer moving average of CPI; and is 0.50, 0.75, 0.85, 0.90, 0.95 and 0.99 for W1 o W6. For W7-W10 are calibraed reservaion wages using equaion (2) wihou imposing he homogeneiy resricions. w 7 1 0. 90 and 2 0. 15 ; w 8 1 0. 95 and 2 0. 10 ; w 9 1 0. 95 and 2 0.25 and w 10 1 0. 99 and 2 0. 10 W. azzak, 2014
16 Table 2 Dependen variable u ~ ln( U /1 ) (i) (1999Q2 2013Q3) Coefficien Esimaes (P values) wage gap5(ii) -0.36 - - - (0.0000) wage gap 6 (ii) - -0.41 - - (0.0000) wage gap8 (iii) - - -0.26 - (0.0001) wage gap (Kalman) (iv) - - - -0.16 (0.0001) 2 0.34 0.53 0.15 0.25 0.0012 0.0010 0.0014 0.0013 (i) u ~ is he HP filered series of ln( U /1 U), whereu is he unemploymen rae. (ii) Wage gaps are HP filered lnw lnw, where w is real wages and w is he reservaion wage. The real wage is average hourly wage deflaed by a 6-quarer moving average CPI. In wage gaps 5 and 6, w is calibraed using lnw a lnw 1 (1 )ln y, where a is he mean log real wage equal o 2.65, y is produciviy measured as GDP/working age populaion raio, and is 0.95 and 0.99 respecively. (iii) In wage gap 8, w is calibraed using lnw a 1 lnw 1 2 ln y, where 1 0. 95 and 2 0. 10 so ha he homogeneiy resricion is no imposed. (iv) The wage gap based on he Kalman filer s esimaes of he reservaion wage. (v) P values are in parenheses. (vi) Sandard errors and covariance marix are esimaed by he Newey-Wes mehod wih Barle Kernel bandwidh = 4). W. azzak, 2014
17 Table 3 The Correlaion Marix of Measures of he Labor Shares (HP filered) BEA unadjus BEA adjusedbls corporae BEA corporae BEA unadjused 1.00 BEA adjused 0.96 1.00 BLS corporae 0.85 0.86 1.00 BEA corporae 0.86 0.87 0.95 1.00 Source (Karabarbunis, 2014) Table 4 The Correlaion Marix of Measures of he Wedge (HP filered) Wedge 1 Wedge 2 Wedge 3 Wedge 4 Wedge 1 1.00 Wedge 2 0.98 1.00 Wedge 3 0.97 0.98 1.00 Wedge 4 0.98 0.97 0.96 1.00 Wedge is he real wage minus he marginal produc of labor. 0.4 0.60 1 The marginal produc of labor is 0.6K L, where L is working age populaion. Wedge1, 2, 3, and 4 differ in how he real wage is measured only. Wedge 1:real wage is he nominal wage adjused for expeced inflaion measure as a 6-quarer moving average of annual CPI inflaion. Wedge 2: real wage is he nominal wage adjused for expeced inflaion measured by he Philadelphia fed survey measure. Wedge3: real wage is he nominal wage adjused for expeced inflaion measured by he Universiy of Michigan survey measure. Wedge4: real wage is he nominal wage deflaed by a 6-quarer moving average of he CPI level. W. azzak, 2014
18 Table 5 egressions: Dependen variable u ~ ln( U /1 U )(i) Coefficiens Wage gap 5 (ii) -02.0 -- -- -- (0.0007) Wage gap 6 (ii) -- -0.24 -- -- (0.0000) Wage gap 8 (iii) -- -- -0.15 -- (0.0118) Wage gap (Kalman) (iv) -- -- -- -0.18 (0.0043) Wedge (v) 0.20 (0.0005) 0.17 (0.0009) 0.23 (0.0001) 0.23 (0.0001) Wedge 0.51 (0.0000) 0.43 (0.0000) 0.55 (0.0000) 0.53 (0.0000) 2 0.73 0.78 0.69 0.70 0.0008 0.0007 0.0008 0.0008 (i) u ~ is he HP filered series of ln( U /1 U), whereu is he unemploymen rae. (ii) Wage gaps are HP filered lnw lnw, where w is real wages and w is he reservaion wage. The real wage is average hourly wage deflaed by a 6-quarer moving average CPI. In wage gaps 5 and 6, w is calibraed using lnw a lnw 1 (1 )ln y, where a is he mean log real wage equal o 2.65, y is he naural log of produciviy measured as GDP/working age populaion raio, and is 0.95 and 0.99 respecively. (iii) In wage gap 8, w is calibraed using lnw a 1 lnw 1 2 ln y, where 1 0. 95 and 2 0.10 so ha he homogeneiy resricion is no imposed. (iv) The wage gap based on he Kalman filer s esimae of he reservaion wage. (v) Wedge: real wage is he nominal wage deflaed by a 6-quarer moving average of he CPI level. (vi) Boh, he dependen variable and he independen variable in he equaion above are deviaions from he HP filer. (vii) P values are in parenheses. (viii) Sandard errors and covariance marix are esimaed by he Newey-Wes mehod wih Barle Kernel bandwidh = 4). W. azzak, 2014
1999Q1 1999Q3 2000Q1 2000Q3 2001Q1 2001Q3 2002Q1 2002Q3 2003Q1 2003Q3 2004Q1 2004Q3 2005Q1 2005Q3 2006Q1 2006Q3 2007Q1 2007Q3 2008Q1 2008Q3 2009Q1 2009Q3 2010Q1 2010Q3 2011Q1 2011Q3 2012Q1 2012Q3 2013Q1 2013Q3 19 0.04 Figure 1 eal Wages (HP filer) 0.03 0.02 0.01 0-0.01 w1 w2 w3 w4-0.02-0.03 w 1 w 3 are average hourly wage adjused for expeced inflaion measures as 6-quarer moving average of CPI inflaion, he Philadelphia fed s survey of inflaion expecaions e and he Michigan Universiy s survey of inflaion expecaions respecively. w4 is log ( W / P ), e W is he average hourly wage, and P is 6-quarer moving average of CPI. W. azzak, 2014
20 Figure 2 w1 w6 are calibraed reservaion wages using equaion (2) imposing he homogeneiy resricion, where a is 2.65, he mean of log real wages as defined log ( W / P ), W is he average e hourly wage, and P is 6-quarer moving average of CPI; and is 0.50, 0.75, 0.85, 0.90, 0.95 and 0.99 for r w 1 w6 respecively. w7 w10are calibraed reservaion wages using equaion (2) wihou imposing he homogeneiy resricions. w 7 1 0. 90 and 2 0. 15 ; w 8 1 0. 95 and 2 0.10 ; w 9 1 0. 95 and 2 0. 25 ; and w 10 1 0. 99 and 2 0. 10 e W. azzak, 2014
21 Figure 3 W. azzak, 2014
U U U U U U U U U U U 22 Figure 4 The 2 0. 95es of he correlaion beween he wage gap and unemploymen (HP filered) (1) Lambda=0.50 (2) Lambda=0.75 (3) Lambda=0.85 (4) Lambda=0.90.6.6.6.6.4.4.4.4.2.2.2.2.0.0.0.0 -.2 -.2 -.2 -.2 -.4 -.4 -.4 -.4 -.6 -.03 -.02 -.01.00.01.02.03 -.6 -.012 -.008 -.004.000.004.008.012 -.6 -.008 -.004.000.004.008.012 -.6 -.008 -.004.000.004.008.012 WAGEGAP WAGEGAP WAGEGAP WAGEGAP (5) Lambda=0.95 (6) Lambda=0.99 (7) Lambda 1=0.90; Lambda 2=0.15 (8) Lambda 1=0.95; Lambda 2=0.10.6.6.6.6.4.4.4.4.2.2.2.2.0.0.0.0 -.2 -.2 -.2 -.2 -.4 -.4 -.4 -.4 -.6 -.008 -.004.000.004.008.012 -.6 -.008 -.004.000.004.008.012 -.6 -.008 -.004.000.004.008 -.6 -.008 -.004.000.004.008 WAGEGAP WAGEGAP WAGEGAP WAGEGAP (9) Lambda 1= 0.95; Lambda 2=0.25 (10) Lambda 1= 0.99; Lambda 2=0.10 Kalman Filer.6.6.6.4.4.4.2.2.2.0.0.0 -.2 -.2 -.2 -.4 -.4 -.4 -.6 -.008 -.004.000.004.008 -.6 -.008 -.004.000.004.008 -.6 -.015 -.010 -.005.000.005.010.015 WAGEGAP WAGEGAP WAGEGAP The wage gap is he HP-filered w w, where w is log real wages and w is he log reservaion wage. The real wage is average hourly wage deflaed by a 6-quarer moving average CPI. The reservaion wage is esimaed eiher by calibraing he log equaion lnw a lnw 1 (1 )ln y, where y is log produciviy, which is real GDP o working age populaion raio (plos 1-6); or by calibraing lnw a 1 lnw 1 2 ln y, where he homogeneiy resricion is no imposed (plos 7-10); or by esimaing lnw lnw (1 )ln y u ~ using he Kalman filer and Maximum Likelihood mehod. And, u ~ is he HP-filered ln( U /1 U), whereu is he unemploymen rae. W. azzak, 2014
23 Figure 5 The Share of Labor W. azzak, 2014
24 Figure 6 Marginal Produc of Labor W. azzak, 2014
25 Figure 7 Measures of he Wedge Figure 8 Measures of he Wedge and Unemploymen W. azzak, 2014
26.12 Figure 9 esponse o Generalized One S.D. Innovaions ± 2 S.E. esponse of unemploymen o he wage gap esponse of unemploymen o he real wage-mpl wedge.12.08.08.04.04.00.00 -.04 -.04 -.08 1 2 3 4 5 6 -.08 1 2 3 4 5 6 Variance Decomposiion Period S.E. Wedge Wage Gap Unemploymen 1 0.038496 26.63352 3.068642 70.29784 2 0.062935 28.48215 7.212507 64.30534 3 0.081093 28.60753 12.32417 59.06830 4 0.094627 27.40724 17.97096 54.62180 5 0.104680 25.40900 23.69166 50.89935 6 0.112047 23.18024 29.05839 47.76137 7 0.117355 21.23961 33.67698 45.08341 8 0.121166 19.99733 37.20395 42.79872 9 0.124018 19.70109 39.39692 40.90199 10 0.126402 20.38655 40.18942 39.42404 11 0.128717 21.85973 39.75057 38.38969 12 0.131227 23.74622 38.47569 37.77809 W. azzak, 2014
27 Daa Appendix Variable U Y P W e L Fixed capial formaion WAP Descripion and sources Seasonally adjused civilian unemploymen rae. Source: US Deparmen of Labor. Seasonally adjused real chain GDP. Source: Deparmen of Commerce, Bureau of Economic Analysis. Seasonally adjused CPI for all urban consumers, all iems. Source: U.S. Deparmen of Labor Saisics. Seasonally adjused average hourly earnings of producion and nonsupervisory Employees: Toal Privae. Source: U.S. Deparmen of Labor: Bureau of Labor Saisics. (1) Federal eserve Bank of Philadelphia Survey of inflaion expecaions. (2) The Universiy of Michigan Survey of inflaion expecaions. Seasonally adjused Working Age Populaion: Aged 15-64: All Persons for he Unied Saes. Source: OECD; and, average weekly hours. I is he employmen rae*oal annual hours worked / 52. Source: OECD. Gross Domesic Produc by Expendiure in Consan Prices: Gross Fixed Capial Formaion for he Unied Saes. Source: OECD. Seasonally adjused working age populaion: Aged 15-64: All Persons for he Unied Saes. Source: OECD i I does no really maer wheher we measured he unemploymen in log form or no. I is jus more convenien for inerpreing he coefficiens. In a log form we can inerpre regression coefficiens as elasiciy. For example, see Barro (1977). ii The HP filer, he Band Pass filer (Baxer-King, 1997) or he Chrisiano-Fizgerald (2005) produce similar cyclical resuls, albei he BP filer produces smooher cycles han he HP filer. iii The daa are line 1 and 2 of NIPA, able 1.12. iv The daa are in line 4 of NIPA, Table 1.14. W. azzak, 2014