A Reduction in Labor Wedge when Efficiency Units are Used

Transcription

1 A Reducion in Labor Wedge when Efficiency Unis are Used Chung Gu Chee Deparmen of Economics, he Ohio Sae Universiy Absrac I invesigae composiion bias in measuring he labor wedge. The counercyclical discrepancy beween he Marginal Rae of Subsiuion and he Marginal Produc of Labor (MPL) is observed in he U.S. daa, and i is called he labor wedge. Wha I poin ou in his paper is how o correcly calculae MPL. The aggregae number of hours worked is radiionally used for he labor inpu in calculaing MPL. owever, he rue labor inpu is no aggregae hours worked bu aggregae efficiency unis. Moreover, using aggregae hours worked as he labor inpu resuls in composiion bias, in ha aggregae hours worked increase during expansions, even hough mos newly employed workers are low-skilled workers. This means ha aggregae efficiency unis do no increase as much as aggregae hours worked. During recessions, he opposie phenomenon akes place. In order o measure MPL and he labor wedge correcly, I exrac a ime series of aggregae efficiency unis from he Curren Populaion Survey (CPS) daa. Then, I find ha he sandard deviaion of aggregae efficiency unis is 12% less han ha of aggregae hours worked, and he sandard deviaion of he labor wedge decreases by 11% when aggregae efficiency unis are used as he labor inpu. 1

2 Ⅰ. Inroducion The neo-classical heory expecs he sysemaic movemen among consumpion, hours worked, and produciviy due o he imposed srong resricions on hem. In models on ha heory, he economy works more and consumes more in a period of high produciviy, so he correlaion beween simulaed hours and produciviy (or wage) is highly posiive. owever, as observed in Figure 1, hours worked is no highly correlaed wih labor produciviy (MPL) in daa. Even, he correlaion of hose wo variables from daa is very low (.2). Such a low correlaion is known o be one of he mos apparen shorcomings of he RBC models. This discrepancy resuled in he considerable amoun of wedge beween MRS and labor produciviy in he labor marke opimaliy condiion. Figure 2 shows he cyclical movemens of hours and wedge. According o Figure 2, i can be seen ha he wedge is very counercyclical. From his high counercyclicaliy, some economiss view such measured wedges as a fundamenal driving force behind business cycles (all (1997), Chari, Kehoe and McGraan (29)). Or some ohers view i as inefficiency due o he failure of labor marke clearing (Gali, Gerler and Lopez-Salido (27)). Wedge may be a possible driving-force of business cycle or jus a resul of marke fricion as hose previous papers insis. owever, we need o be careful o he aggregaion bias which was poined ou by several researchers such as Sockman (1983), Bils (1985) and Solen e al (1984). These sudies show low-wage workers 1 paricipae more in he labor marke during expansions and exi more during conracions, so a couner-cyclical composiion bias is creaed in labor inpu. This makes he measured hours more volaile han he hours in effecive unis as Cho (1988) 2, ansen (1993) and Kydland and Presco (1989) 3 have shown. owever, up o now he wedge has been measured based on he homogenous-agen model which reas all hours as idenical, while in fac low-skilled workers like he inexperienced young produce less in a given hour han someone who has been accumulaing human capial over many years. In ha he rue labor inpu is no he oal amoun of hours worked bu he oal amoun of efficiency inpu, we can conjecure ha he measured wedge is ained by he composiion bias, and is also oversaed and ha he size of wedge hrough business cycle may be reduced o some exend if we use he aggregae hours in effecive 1 We can inerpre low-wage as low-produciviy. 2 Theoreically he shows ex-pos heerogeneiy in skill level across individuals brings abou flucuaions in oal hours which are significanly larger han hose in efficiency unis. 3 Acually ansen (1993) and Kydland and Presco (1989) did he same work. Boh show he cyclical flucuaions displayed by he efficiency unis series are smaller on average han hose displayed by hours worked. The former used CPS daa (quarerly daa during 1955~1988) and he laer used PSID (annually daa during 1969~1982). Bu he volailiy (percenage sandard deviaion) is reduced by 5% in he former, bu decreased by 28% in he laer. 2

3 unis insead of oal hours worked of people. In his paper, I exrac wo series - average hours worked and average efficiency unis - from CPS daa (198~26). From his empirical work, I found ha he volailiy of aggregae efficiency inpu is less han he volailiy of aggregae hours by 12%. As well, he volailiy of aggregae wedge can be reduced by 11% when aggregae efficiency is used as an inpu of labor raher han aggregae hours. 4 In secion Ⅱ, I explain briefly how o measure labor wedge in aggregae level and deal wih he measuremen issue abou a rue aggregae labor inpu. In secion Ⅲ, I measure aggregae efficiency unis. And in secion Ⅳ, resuls on he size of labor wedge are described. And I conclude his paper in secion Ⅴ. Ⅱ. Measuring labor-marke wedge On he assumpion of a represenaive agen, opimal allocaion of consumpion and hours worked means he marginal rae of subsiuion (MRS) should be he same wih he marginal produc of labor (MPL). For illusraion, he sand-in household has he following uiliy and budge consrain: 11/ (1) U ( C, ) ln C B[ /(1 1/ )] s. ( 1 r ) A W C A 1 where he parameer represens he labor-supply 5. Wih he assumpion of Cobb-Douglas producion echnology, Y K 1, he opimaliy condiion in labor marke is: (2) Y B C 1/ 1 The LS is MPL and he RS is MRS. The labor-marke wedge is defined as he raio beween he MRS and labor produciviy: 1/ Y (3) lnwedge ln ln consan. 1 C Figure 1 shows movemens of MPL and MRS. The gap beween hose wo variables flucuaes and his generaes a counercyclical wedge shown in Figure 2. Bu in he same figure, we can find hours 4 If he size of he volailiy of efficiency inpu is similar o wha Kydland and Presco (1989) found, he size of he volailiy of wedge would be much smaller. 5 I use =1.5 as usual macroeconomic lieraure does. 3

4 and wedge have a very highly negaive correlaion each oher. From his observaion, we can guess ha if he sandard deviaion of becomes smaller, hen he volailiy of wedge can be reduced. In addiion, equaion 3 can be wrien as Y (1 (4) 1/ lnwedge ln ln ) consan C From Figure 3 we can noice ha boh of oupu-consumpion raio and hours co-move in general bu he sizes in movemens are differen. our is more volaile han oupu-consumpion raio. Tha is, hough posiive shocks make boh of hours and oupu-consumpion raio increase, much faser han 1 1 / is Y / C, which makes wedge counercyclical. This is he evidence ha if is less volaile, hen he volailiy will decrease. In addiion, usually aggregae hours ( hi, d ) is used as an aggregae labor inpu in producion echnology. Bu in ha case, he qualiy of hours is ignored. So aggregae efficiency unis ( L x h i i,, d ) is a correc measure of aggregae labor inpu raher han hours. So, if he volailiy of L is smaller han he volailiy of, we can ge less volaile wedge by replacing more volaile wih less volaile L. A his poin, we need o be careful a lile bi. In equaion 3, boh MPL and MRS include. If we replace boh wih L, i s a wrong specificaion. The reason is ha aggregae labor inpu is L for firms, so in MPL L should be used. Bu when an individual makes an employmen decision given wage rae per hour, she chooses her working hours and consumpion level. Tha is, in MRS should be used as a labor-supply. So revised wedge is as follows; 1/ Y (5) lnwedge ln ln consan 1 L C Now he nex ask is o ge aggregae efficiency unis and o check wheher i is less volaile han hours and how much. Ⅲ. Measuring Efficiency Unis In his secion, I measure he size of composiion bias and correc he amoun of rue labor inpu from acual daa. Using he correced labor inpu, I also remeasure wedge. There are wo previous sudies relaed o his work: Kydland and Presco (1989) use PSID o measure aggregae labor inpu. Because PSID is a se of panel daa, hey could derive he average produciviy of each 4

5 individual using wage daa hrough he sample periods. So he weighed sum 6 of hours of individuals is aggregae efficiency unis. Though hey find ha he sandard deviaion of labor inpu is much less han ha of oal hours by 28%, PSID is annual survey, so heir mehod canno be used o calculae quarerly wedge. ansen (1993) uses CPS daa o measure quarerly aggregae efficiency unis. Because CPS is no panel daa, each individual s produciviy canno be obained. So he uses group daa. e divides individuals ino several groups by sex and age and views one group as one individual 7. Then he could derive he average produciviy of each group, and using i as he weigh, he calculaed aggregae efficiency unis. owever, because his mehod ignores he composiion bias in each group, he series of aggregae efficiency unis are quie similar o he series of oal hours and he difference of volailiies of wo series is very small (5%). Thus o measure he aggregae efficiency uni and wedge I can use neiher of hese wo previous sudies mehods. The way o exrac efficiency unis in his paper is as followed: W i denoes hourly wage of individual i in period. One s hourly wage can be decomposed ino w and x i. ( W i = w * x i, w is he wage rae per effecive uni of labor a ime and x is efficiency unis (or produciviy) which individual i posses in period ). If h i, and L denoes hours worked of individual i in period, oal hours worked in period, and oal efficiency unis in period each, hen and h i, L x i i L are as follows: ere a problem occurs. From CPS, daa of each individual, i h i W i = x i canno be obained direcly hough we have hourly wage w * x i. I s because we don know w. So I use a subgroup which consiss of employed men of aged from 35 o 44 who graduaed high school. People in his group can be viewed having high and sable produciviy wih respec o employmen because enry and exi usually occur in low-produciviy groups hrough business cycles. Then we can conjecure ha an average efficiency uni ( x 3544 ) of his group is very sable. ere I assume x 3544 is consan hrough all sample period. 8 If W 3544 denoes average hourly wage of ha group, hen W 3544 (= w * x 3544 ) can be calculaed from CPS daa. If we divide ge each individual produciviy divided by a consan: W / W 3544 = i x / x i And using individual hours daa, h i, we can ge labor inpu as follows: i W i by W 3544, hen we can 6 Produciviy of each individual is one s weigh. 7 This mehod is used frequenly in CPS. 8 This assumpion is used by ansen (1993) o calculae weigh (produciviy) of each group. 5

6 L x3544 Because / = and i x / i h i x 3544 = i / insead of L. Le s denoe hiwi W3544 L x3544 / as L'. L' are he resuls in he CPS sample, I divide hem by he number of workers in E ) which is released he sample and muliply hem by he oal number of employmen (denoed by by BLS (Bureau of Labor Saisic) in order o obain oal hours and labor inpu in his economy. In his paper he sample period is from 198 o 26. Ⅳ. Resuls : Aggregae Efficiency Unis and Labor Wedge The resuls from CPS are summarized in Table 1. We can noice ha he volailiy of labor inpu is smaller han ha of oal hours by 12% and he volailiy of wedge calculaed using labor inpu is also smaller han ha using oal hours by 11%. Figure 4 gives he comparison of volailiies of oal hours and labor inpu. In Figure 5, we can see ha he labor produciviy using labor inpu is closer o MRS han labor produciviy using oal hours is close o MRS, which means opimaliy condiion is more saisfied when using rue labor inpu han using oal hours. This implies ha oal hours are ained from composiion bias. The source of composiion bias can be seen in Figure 7. In a recession he average produciviy per worker is relaively high and i is relaively low in a boom, which means ha in a recession low-produciviy workers exi more, so average produciviy is high and in a boom low-produciviy worker ener more, so average produciviy is low. This can also be checked from he correlaion beween he employmen level and average produciviy per worker in Table 2. I is -.47 which is highly negaive. This makes oal hours more volaile han rue labor inpu. Thus, from Figure 6 we can see ha he wedge measured using labor inpu is less ha he wedge measured using oal hours. One possible problem from his exercise is ha x 3544 may also suffer from he composiion bias hough ha group is relaive sable and highly produciviy. In order o exrac labor inpu I use x 3544, assuming x 3544 is consan in his paper. owever, if x 3544 is also ained by ha bias, hen i flucuaes couner-cyclically, which means he measured labor inpu is sill oversaed because L' L / x3544. So he volailiy of rue labor inpu should be less han.94 in he able. This makes sense in ha Kydland and Presco (1989) show he raio of volailiy in labor inpu and oal hours is 71% (=1.2/1.42) bu i is 89%(=1.2/1.35) in his paper. Therefore, if we correc he composiion bias more precisely, hen we can ge a beer labor inpu series which is much less volaile han wha his paper finds. Then he size of wedge would be measured much smaller. 6

7 Table 1 Volailiies of aggregae variables from CPS Variable Value Y 1.13 ( / Y ) 1.7 (.95) ( / ).94 (.83) L L Wedge( ) ( Wedge( ) Y / Y ) 1.35 (1.2) / Y ) Wedge(L) ( Wedge(L ) 1.2 (1.6) Corr(E, Average Eff per worker) -.47 Noes : All variables are logged and derended by he -P filer. The volailiy of oupu is measured by is sandard deviaion. ere I use 2. Ⅴ. Conclusion The cyclical behavior of aggregae consumpion, hours worked, and produciviy is hard o reconcile wih he equilibrium oucome of he represenaive agen wih sandard preferences. This phenomenon creaes he considerable amoun of wedge. And because he wedge is highly counercyclical o business cycle, some economiss inerpre such measured wedge as a fundamenal driving force behind business cycles or some ohers view i as inefficiency due o he failure of labor marke clear - like wage rigidiy. The purpose of his paper is no o deny such views, bu o emphasize aking i ino accoun he composiion bias which makes such wedge measured larger han rue size of wedge. By a simple empirical work using CPS daa, aggregae efficiency unis which is less volaile han aggregae hours by 12% can be derived. And when using his aggregae variable as a labor inpu, hen he sandard deviaion of wedge is measured less by 11%. I find he same daa series which also consisen wih wha are found in he modeled economy. As I noed in he previous secion, he procedure exracing he labor inpu series is no perfecly free from he composiion bias, so he size of volailiy of labor inpu from CPS is no reduced by much compared o he resul in Kydland and Presco (1989) paper or he resul from he model-simulaed daa. This is a furher research opic which should be done. 7

8 Ⅵ. References Cho, Jang-Ok, (1995), Ex pos heerogeneiy and he business cycle, Journal of Economic Dynamics and Conrol, 19, Kydland, Finn E., and Edward C. Presco (1989), Cyclical movemens of he labor inpu and is real wage, Federal Reserve Bank of Minneapolis Working paper No. 413 ansen, G.ary D., (1993), The Cyclical and Secular Behaviour of he Labor Inpu: Comparing Efficiency unis and hours Worked, Journal of Applied Economerics, 8, 71-8 Bil, Mark, (1985), Real Wages over he Business Cycle: Evidence from Panel Daa, Journal of Poliical Economy, 93, Chang, Yongsung, and Sun-Bin Kim, (26), From Individual o Aggregae labor Supply: A Quaniaive Analysis Based on a eerogeneous Agen Macroeconomy, Inernaional Economic Review, 47, 1-27 Chang, Yongsung, and Sun-Bin Kim, (27), eerogeneiy and Aggregaion: Implicaions for labor-marke Flucuaions, American Economic Review, 97,

9 Ⅶ. Appendix ln MPL ln MRS Figure 1. Deviaion of MPL and MRS from log rends, measured as an P filer wih parameer 1,6 (Daa) ln ln Wedge Figure 2. Deviaion of he labor wedge and hours worked from log rends, measured as an P filer wih parameer 1,6 (Daa). Wedge is counercyclical 9

10 ln ( 1+1/gamma) ln Wedge ln Y/C Figure 3. Deviaion of he labor wedge, 1 1 /, and C Y / from log rends, measured as an P filer wih parameer 1,6 (Daa). Counercyclical wedge is generaed because 1 1 / is more volaile han Y / C.3.2 ln ln L` Figure 4. Toal hours and Labor inpu from CPS. L is less volaile han 1

11 ln MRS ln Y/ ln Y/L` Figure 5. MRS and wo labor produciviies from CPS.4.3 ln Wedge from ln Wedge from L` Figure 6. Two differen wedges from CPS 11

12 ln E ln average efficiency unis Figure 7. Cyclicaliy of Employmen and average efficiency unis per workers 12