The Empirical Evidence of Mean Diversion in the U.S. Labor Market

Transcription

1 Inernaional Journal of Economics and Finance Vol. 3, No. 1; February 2011 The Empirical Evidence of Mean Diversion in he U.S. Labor Marke John Silvia, Chief Economis Wells Fargo Securiies, LLC One Wachovia Cener, 301 Souh College Sree, NC0602 Charloe, NC , USA Tel: Fax: Azhar Iqbal (Corresponding Auhor) Vice Presiden and Economerician Wells Fargo Securiies, LLC, One Wachovia Cener, 301 Souh College Sree, NC0602 Charloe, NC , USA Tel: Fax: Acknowledgemen: Iniial draf of his paper was presened a he 79 h Annual Meeings of he Souhern Economic Associaion, November 2009, San Anonia, TX, USA. We are graeful o he audience of he conference for heir useful commens. The views expressed in his sudy are hose of he auhors. Neiher Wells Fargo Corporaion nor is subsidiaries is responsible for he conens of his aricle. Absrac Policy makers love o speak abou resoring he economy and he associaed good obs as voers imagine hey were in he pas. Bu is such economic nosalgia reasonable in a dynamic global economy? Our work here suggess ha he labor marke has been consanly evolving since 1970 and ha here is no endency o reurn o normal if such a normal were o be defined as i was in he good old days. Since 1970 he mean and sandard deviaion of employmen growh had acually been decreasing for each decade up unil he For he mos recen ( ) period, he sandard deviaion shows an upick and a significan reducion in he mean. We find ha he rend coefficien is saisically significan and has a negaive sign. Tha implies he employmen growh rae has a decreasing paern over ime. Our resuls sugges, he level of he employmen growh raes is mean-divering and subec o a srucural break. Second, in he presence of he ARCH effec, OLS sandard errors can be misleading, wih a spurious regression possibiliy. Finally, he ARCH effec and uni roo problem have serious consequences for forecasing and he forecas band could be narrower han he acual. Keywords: Employmen, Srucural Change, ARCH, Mean Diversion JEL Classificaion: C10; J21; J30 Inroducion Policy makers love o speak abou resoring he economy and he associaed good obs as voers imagine hey were in he pas. Bu is such economic nosalgia reasonable in a dynamic global economy? Moreover, has i acually been rue ha he economy, and paricularly he labor marke, were ever as sable as we imagine? This paper seeks o characerize he behavior of he U.S. employmen growh rae over he economic cycle. We raise hree fundamenal quesions which are; firs, does he employmen growh over ime exhibi a mean-revering behavior? Tha is, does he growh in employmen exhibi a endency o reurn o some average value? Second, how volaile are employmen and does his volailiy obscure he message of employmen growh? Finally, do employmen growh raes vary beween decades/ sub-samples? In his paper we divide he U.S. employmen growh rae ino decades since We es if all he daa share he same saisical momens average and sandard deviaion. We also esimae an insabiliy raio, he sandard deviaion as a percen of mean, where he higher value of he insabiliy raio is an indicaion of higher volailiy. In addiion, we es wheher here is any change in he characer (linear vs. non-linear) of he rend in employmen growh over ime. The nex issue would be o es wheher employmen growh is mean-revering or no. We employ uni roo mehodology on he series and es wheher employmen growh conains a uni roo or no. If a series does no conain a uni roo we call i saionary and, oherwise, non-saionary. Moreover, a saionary series flucuaes around a consan long-run mean ha implies he series, employmen growh in his case, has a finie variance which does no depend on ime, hence mean reversion. On he oher hand, if a series is non-saionary (conains a uni roo) ha implies he series has no endency o reurn o he long run mean and he variance of he series is ime dependen. Therefore, he bes way o es wheher he employmen growh series is mean revering would be o es wheher employmen growh conains a uni roo (no mean reversion) or no (mean reversion). 44

2 Inernaional Journal of Economics and Finance Vol. 3, No. 1; February 2011 Dickey and Fuller (1979, 1981) inroduced he eminen and firs sandard process for uni roo esing and heir es is known as ADF (Augmened Dickey-Fuller) uni roo es. However, here are some ohers uni roo ess, oher han he ADF es, available in he lieraure. For insance, Phillips and Perron (1988) proposed an alernaive o he ADF es, called he PP es, and Kwiakowski, Phillips, Schmid, and Shin (1992) inroduced KPSS es. Due o he serious issues relaed wih he radiional uni roo ess, which are he ADF, PP, and KPSS, recen lieraure proposed o employ he mos efficien ess of uni roo developed by Ellio, Rohenberg, and Sock (1996) (hence afer ERS) as well as Ng and Perron (2001) (afer here NP). However, here is anoher poenial issue which is very imporan and ha is he presence of a srucural break in he ime series. Perron (1989) found ha he sandard ADF ess are biased owards he null hypohesis in he presence of a srucural break in he ime series. In oher words, he ADF ess failed o reec he null of a uni roo even hough he ime series is saionary and ha happened because of a srucural break in he ime series. Perron (1989) suggesed ha i is no necessary ha mos macroeconomic ime series are characerized by a uni roo process no mean reversion, bu raher ha persisence arises only from large and infrequen shocks and many macroeconomic ime series reurn o heir long run mean afer small and frequen shocks. Baneree e al. (1992), Chrisiano (1992) and Zivo and Andrews (1992) criicize Perron s idea of an exogenous srucural break and hey suggesed ha he srucural break would be endogenous. Zivo and Andrews (1992) suggesed a uni roo es wih endogenous break. The above menioned ess assumed ha here is a break-poin and deermined he break dae eiher exogenously or endogenously. Bu he imporan quesion is; if here is no break poin and we ener a break poin ino he regression hen wha happened o he uni roo ess resuls? Nunes e al. (1997) and Bai (1998) provided he answer o he quesion and he answer is spurious break. More explicily, when he disurbances of a regression model follow an I(1) process, order of inegraion one, here is a endency o esimae a break poin in he middle of he sample, even hough a break poin does no acually exis. Therefore, uni roo ess are no reliable in hese cases; (1) when a break poin exiss and did no include in he es regression, (2) if a break poin does no exis and did include in he es regression, and (3) he use of incorrec break dae in he es regression. Recenly, Kim and Perron (2009) proposed a uni roo es wih srucural break ha address hese issues and provide a more efficien esing procedure. Kim-Perron (2009) uni roo es allows a break a unknown ime under boh he null and alernaive hypoheses. The es also ackles he issue of spurious break and proposed a pre-es for a break ha is valid wheher he noise componen is inegraed or saionary (see Kim-Perron, 2009 for more deail). We employ a comprehensive uni roo mehodology and use ADF, PP, KPSS, ERS, NP, Perron, Zivo-Andrews and Kim-Perron ess on he U.S. employmen growh rae series and es wheher he employmen series is mean revering. Once we deermine he economeric se-up for mean reversion hen we would explore he volailiy of he employmen growh. We address he volailiy issue in wo differen ways. Firs, we calculae he mean, sandard deviaion, and he insabiliy raio for each decade. This would provide a picure for each decade and, based on sandard deviaion and insabiliy raios, we can evaluae which decade has higher employmen volailiy, higher sandard deviaion and insabiliy raio. Second, we employ an Auoregressive Condiional Heeroscedasiciy (ARCH) approach on he employmen growh and he benefis of he ARCH are numerous. For insance, if we find he ARCH effec in a ime series ha indicaes he series has volailiy clusering he deviaion from he mean is no consan over ime and ha he deviaion is smaller for some periods han ohers, and vice versa. Recenly, Hamilon (2008) proposed he use of ARCH in macroeconomics and suggesed ha even if our primary ineres is in he esimaion of he condiional mean (mean reversion or no), correcly modeling he condiional variance (volailiy of he series) can sill be quie imporan for wo reasons. Firs, due o he correcion for ouliers and high-variance episodes esimaed parameers would be more accurae. Second, if we don make he correcion hen he resul would be a spurious regression (see Hamilon (2008) for more deail). Our effors sugges ha since 1970 he mean and sandard deviaion of employmen growh had acually been decreasing up unil he For he mos recen ( ) period, we see an upick in he sandard deviaion and a significan reducion in he mean. Moreover, when we evaluae he enire period as a whole, , we find ha he rend coefficien is saisically significan and has a negaive sign. Tha implies he employmen growh rae has a decreasing paern over ime. In addiion, he sandard deviaion (1.79%) is higher han he mean (1.73%); his is evidence of high volailiy in he employmens series. Indeed, he growh of employmen is volaile over ime. Summing up, our empirical analysis suggess ha he level of he employmen growh raes is mean-divering and subec o a srucural break. In addiion, he ARCH effec in he employmen growh series implies he employmen series has a volailiy cluser he deviaion from he mean is no consan over ime and ha he deviaion is smaller for some periods han ohers, and vice versa. Finally, he ARCH effec and uni roo problem have serious consequences for forecasing and he forecas band could be narrower han he acual. The res of he paper is organized as follows. In secion 2 we discuss heory and daa for he employmen growh. Secion 3 inroduces he economeric se-up of he sudy and secion 4 explains he resuls. The concluding remarks of he paper are discussing in secion 5. Published by Canadian Cener of Science and Educaion 45

3 Inernaional Journal of Economics and Finance Vol. 3, No. 1; February 2011 Dynamic Economy: Dynamic Labor Marke They re closing down he exile mill across he railroad rack Foreman says hese obs are going boys and hey ain coming back o your homeown. My Homeown, Bruce Springseen from Born in he U.S.A., 1984 The old obs are gone and are no coming back. Moreover, obs seldom say in he same place forever and are no likely o pay he same real wage and benefis over ime. These are he cold hard facs ha poliical rheoric consanly aemps o shield from he public. As economiss our ob is very differen oday han i was hiry years ago and cerainly is no in he same locaion many of us grew up. Moreover, he exile and shoe obs of New England are gone and so was he relaive sandard of living associaed wih hose obs. In addiion, many of he obacco, exile, furniure and apparel obs of he Souh are also gone. The hegemony of Deroi s auo indusry is gone. Ye in heir place are many healh, educaion, informaion echnology and business services obs ha did no exis a he end of World War II. Therefore, i seems ha here is no mean reversion in he obs daa and here is no going back o he old economy. Exhibi I provides dramaic visual evidence of he evoluion of he American labor marke since us Over ha period ob growh has been generally posiive wih he expeced declines in employmen during recessions. Wha is surprising o some exen is he decline in he pace of ob growh over ha same ime period. Job growh since 1970 has seadily declined in he U.S.A of Bruce Springseen. I is rue ha he share of obs going o manufacuring has declined while he share going ino services has risen since (Noe 1) Reail and wholesale service secor employmen has risen bu he larges percenage increase has been in governmen employmen which has quadrupled over ime. Some would describe his paern as he arrival of he pos-indusrial sae. In Exhibi II, he reurns o educaion for workers are readily apparen. Jus over he las six years we have winessed he income dispariy beween workers of differen educaion no only persis bu acually increase over his period. Wih shif, on a percenage basis, from consumer demand for goods o services and he applicaion of echnology in he producion of boh goods and services here have been increased demands upon workers hemselves o acquire new skills and work in new obs ha were unknown before he 1970s. Jobs for less-skilled workers have declined while workers in informaion-processing, communicaions and managerial areas have increased. (Noe 2) Therefore, he employmen growh may be mean-divering and subec o a srucural change. I is worhwhile o menion ha we are no he firs who is going o apply uni roo ess on he employmen daa. Several researchers have had employed uni roo es on he employmen series and here is mixed evidence wheher employmen is mean-revering or no. Nelson and Plosser (1982) applied ADF es on he 14 U.S. macroeconomic series including employmen. They used annual daase for ime period and concluded ha employmen series is mean-divering. Since hen many researcher have used Nelson-Plosser daase and have differen conclusions for he employmen. For insance, Perron (1989) include a srucural break for he 1929 crash and concluded ha employmen is mean-revering and subec o a srucural break. Zivo and Andrews (1992) concluded ha employmen is mean-divering. Lee and Srazicich (2003) included wo breaks and based on he LM es concluded ha employmen is mean-divering. (Noe 3) Bu in his paper we are no going o use he Nelson-Plosser daase for he following reasons; Firs, many researchers in he pas, inroduced or modified uni roo es and compared heir es s performance wih he exising uni roo ess and Nelson-Plosser daase is good for comparison bu obecive of our sudy is no o inroduce a new uni roo es. In addiion, we are ineresed o analyze he behavior of he employmen growh and for ha purpose laes employmen daa is more appropriae. Second, we are examining he employmen behavior by decades since Third, we also concenrae on he volailiy of he employmen growh and apply ARCH approach. Finally, we apply a comprehensive uni roo mehodology on he employmen growh. We use he U.S. nonfarm payrolls, year-over-year percen change, and source of daa series is Bureau of Labor Saisics (BLS). Our employmen growh analysis begins wih 1970:Q1 (quarerly daa series). We do no exend back o he end of he World-War-II (WWII) because he U.S. economy could no funcion properly by mid or lae 1960s. For insance, he U.S. economy slipped five imes ino recession beween he end of he WWII and Therefore, he sar dae for our analysis is 1970:Q1. We divide he daa series ino four decades ( , , and :Q3); he fourh is no a complee decade. Oher possible choices could have been o divide he daa ino business cycles, from rough o peak, ec. Alhough, daa division according o he business cycle is a good choice, i does no fi ino our analysis. For insance, each business cycle does no equal in duraion and he duraion varies from 4 quarers o 30 quarers. Moreover, our analysis is based on regression analysis, i.e., esimaion of he rend as well as applicaion of he ARCH approach. For esimaion purposes, more observaions wih bigger ime span are always beer han he fewer observaions. Therefore, we divide he daa ino decades and each decade has a leas one recession and ha implies ha each decade conains business cycle properies, e.g., peak and rough. 46

4 Inernaional Journal of Economics and Finance Vol. 3, No. 1; February 2011 Economerics of Mean Reversion Uni Roo Tesing: Inroducion Dickey and Fuller (1979, 1981) inroduced he idea of a uni roo and proposed a sandard uni roo esing procedure which is known as ADF (Augmened Dickey-Fuller) es of uni roo. Bu uni roo esing became popular in economics, especially among macro-economiss, afer he publicaion of he seminal paper by Nelson and Plosser (1982). Nelson and Plosser employed uni roo mehodology on 14 U.S. macroeconomic ime series and hey could reec he null hypohesis of a uni roo for only one ime series, which was he unemploymen rae. In addiion, Nelson and Plosser concluded ha many macroeconomic series are non-saionary. Tha implies many macroeconomic series exhibi rending behavior or a non-saionary mean pu simply, no mean-revering. Therefore, uni roo ess can be used o characerize a ime series. There are many oher uni roo ess, oher han ADF es, available in he lieraure. For insance; Phillips-Perron (1988) (PP), and Kwiakowski-Phillips-Schmid-Shin (1992) (KPSS) ess of uni roo (also known as radiional uni roo ess); ess inroduced by Ellio-Rohenberg-Sock (1996) (ERS) and Ng-Perron (2001) (also known as efficien uni roo ess). We employ all hese ess on he U.S. employmen series and es wheher he employmen series is mean revering. (Noe 4) Uni roo Tess and Srucural Breaks Perron (1989) challenged Nelson-Plosser s conclusion, ha is, mos macroeconomic ime series conain a uni roo. Perron argued ha in he presence of a srucural break, he sandard ADF ess are biased owards he non-reecion of he null hypohesis. He concluded ha mos macroeconomic ime series are no characerized by a uni roo bu raher ha persisence arises only from large and infrequen shocks. In addiion, Perron used he Nelson-Plosser daase and incorporaed an exogenous srucural break for he 1929 Crash. He reversed he Nelson-Plosser s conclusion for 10 of he 13 macroeconomic ime series. However, Perron s assumpion of known break dae (also known as exogenous break) was criicized, mos noably by Chrisiano (1992) as daa mining. Chrisiano argued ha he daa based procedures are ypically used o deermine he mos likely locaion of he break and his approach invalidaes he disribuion heory underlying convenional esing. Since hen, here are wo maor views abou he break dae, which are (a) known or exogenous break dae and (b) unknown or endogenous break dae. Perron (1989) proposed an exogenous (known) srucural break uni roo es. Several oher sudies have developed using differen mehodologies for endogenously deermining he break dae, including Zivo and Andrews(1992), Baneree e al. (1992), Perron and Vogelsand (1992), Lumsdaine and Papell(1997) and many ohers(see Byrne and Perman, 2006 for survey). (Noe 5) The above menioned ess assumed ha here is a break-poin and deermined he break dae eiher exogenously or endogenously. Bu he imporan quesion is; if here is no break poin and we ener a break poin ino he regression hen wha happened o he uni roo ess resuls? Nunes e al. (1997) and Bai (1998) provided he answer o he quesion and he answer is spurious break. More explicily, when he disurbances of a regression model follow an I(1) process, order of inegraion one, here is a endency o esimae a break poin in he middle of he sample, even hough a break poin does no acually exis. Therefore, uni roo ess resuls are no reliable in hese cases; (1) when a break poin exiss and did no include in he es regression, (2) if a break poin does no exis and did include in he es regression, and (3) he use of incorrec break dae in he es regression. The good hing of he Perron (1989) ype s ess is ha hey are invarian o he break parameers and hus heir performance does no depend on he magniude of he break. Recenly, Kim-Perron (2009) proposed a uni roo es wih srucural break ha address hese issues and provide a more efficien esing procedure. For insance, Perron (1989) es allows for a break under he null and alernaive hypoheses bu assume exogenous break and, on he oher hand, Zivo-Andrews (1992) es assume endogenous break bu did no allow break under he null hypohesis. In addiion, boh ess did no alk abou he spurious break. Kim-Perron (2009) uni roo es allows a break a unknown ime under boh he null and alernaive hypoheses. The es also ackles he issue of spurious break and proposed a pre-es for a break ha is valid wheher he noise componen is inegraed or saionary (see Kim-Perron; 2009). Uni Roo ess wih Exogenous Break: Perron ess Perron (1989) inroduced he firs sandard uni roo ess wih srucural break and all ohers ess are exension or modificaion of he Perron s es and hereby we sar wih he Perron es. Perron suggesed hree models. The models ake ino accoun he exisence of hree kinds of srucural breaks: a crash model (Model A), which allows for a break in he level (or inercep) of he series; a changing growh model (Model B), which permis for a break in he slope (or rae of growh); and lasly one ha includes boh effecs o occur simulaneously (Model C), i.e. one ime change in boh he level and he slope of he series. Model (A) y 1 DU d DTB) 1 p ( y ime y (1) 1 Published by Canadian Cener of Science and Educaion 47

5 Inernaional Journal of Economics and Finance Vol. 3, No. 1; February 2011 Model (B) Model (C) y y DT 1 * y 1 1 DU d DTB) ime p 1 y 1 p ( DT y ime y (3) 2 Where y is dependen variable and employmen growh in our case. Time is a ime variable or ime dummy. The inercep dummy DU represens a change in he level; 1 if TB DU (4) 0 oherwise * The slope dummy DT (also DT ) represens a change in he slope of he rend funcion; if TB D * T (5) 0 oherwise The crash dummy model; 1 if TB 1 DTB (6) 0 oherwise TB is he break dae. I is worh menioning ha each of he hree models has a uni roo wih a break under he null hypohesis, as he dummy variables are incorporaed in he regression under he null. The alernaive hypohesis is a broken rend saionary process. Uni Roo ess wih Endogenous Break: Zivo-Andrews Tess The endogenous srucural break es of Zivo and Andrews (1992) is a sequenial es which uilizes he full sample and uses a differen dummy variable for each possible break dae. The selecion crierion for he break dae is based on he -saisic from an ADF es and a minimum (i.e. mos negaive) value of -saisic will be he indicaion of he break dae. Consequenly, a break dae will be chosen where evidence is leas favorable for he uni roo null hypohesis. The Zivo-Andrews minimum -saisic es has is own asympoic heory and criical values. The laer are more negaive han hose provided by he Perron (1989) and may be sugges greaer difficuly in reecing he uni roo null hypohesis. Zivo-Andrews es evaluaes he oin null hypohesis of a uni roo wih no break in he series. As a consequence, acceping he null hypohesis in he conex of Zivo-Andrews es does no imply uni roo bu raher uni roo wihou a break. The criical values for Zivo-Andrews ess are derived under he assumpion of no srucural breaks under he null hypohesis. Efficien Uni Roo ess wih Break: Kim-Perron Tess Kim and Perron (2009) es allows break under boh he null and alernaive hypoheses and, when a break is presen, he limi disribuion of he es is he same as in he case of a known break dae, hereby allowing increased power while mainaining he correc size. If here is no break in he rend hen we can apply he sandard ADF or any uni roo es wih no break dummies. Hence, we need a pre-es o assess wheher a break is presen or no. Kim and Perron (2009) proposed he procedure ha has he correc size and powerful wheher he noise is saionary or inegraed. (Noe 6) The esing procedure is based on a quasi-gls approach using an auoregression of order one for he noise componen, which a runcaion o 1 when is in some neighborhood of 1, and a bias correc. For a given break dae, one consrucs he F-es for he null hypohesis of no srucural change in he deerminisic componens. Kim and Perron (2009) labeled he es as Exp-W FS. The es has he same asympoic size wheher he noise is saionary or inegraed (see Kim-Perron; 2009 for more deail). We apply Perron (1989), Zivo-Andrews (1992) and Kim-Perron (2009) ess on he employmen growh and es wheher he employmen series is mean-revering as well as subec o a srucural change. Macroeconomics and ARCH: Hamilon (2008) Once we seled he issue of he mean-reversion hen he naural quesion would be does employmen series has a volailiy cluser? Moreover, we would like o know he behavior of he variance of he employmen series. To answer all hese quesions we employ he Auoregressive Condiional Heeroscedasiciy (ARCH) approach on he employmen and he benefis of he ARCH are numerous. For insance, if we find he ARCH effec in a ime series, employmen growh in his case, hen ha indicaes he series has volailiy clusering, i.e., some periods are more volaile han ohers. In oher words, he deviaion from he mean is smaller for some periods han ohers, and vice versa. Recenly, Hamilon (2008) proposed use of he ARCH in macroeconomics and suggesed ha even if our primary obecive is he esimaion of he condiional mean (mean reversion or no) having a correc descripion of he condiional variance (volailiy of he series) can sill be quie imporan for wo reasons. Firs, OLS sandard errors can be misleading, wih a spurious regression possibiliy in which a rue null hypohesis is asympoically reeced 1 (2) 48

6 Inernaional Journal of Economics and Finance Vol. 3, No. 1; February 2011 wih probabiliy one. Second, he inference abou he condiional mean can be inappropriaely influenced by ouliers and high-variance episodes. Consequenly, if we incorporae he condiional variance direcly ino he esimaion of he mean hen he esimaes of he mean would be more efficien (see Hamilon (2008) for more deail). Therefore, we uilize he ARCH approach. Resuls Simple Saisics: The Mean, Sandard deviaion, Insabiliy Raio, and Trend We broke up he employmen growh daa since 1970 ino decades which roughly approximaes four disinc periods of economic performance and poliical policy orienaions. We esimae a mean, sandard deviaion and insabiliy raio for each decade. The insabiliy raio, sandard deviaion as percen of mean, represens he volailiy of he employmen series in each decade where he higher value of he insabiliy raio is an indicaion of higher volailiy. One vial benefi of he insabiliy raio is ha i idenifies he magniude of he volailiy of employmen growh by decade. Wihou an insabiliy raio, i is hard o specify employmen volailiy by decades for researchers. For insance, if we se he sandard deviaion as he volailiy crierion, hen he 1970s has highes sandard deviaion. If we sick wih his crierion, hen he 1970s is mos volaile. Bu he problem wih his crierion is ha he 1970s also has he highes mean. Therefore, sandard deviaion alone is no he bes measure of volailiy especially when we compare differen decades. Indeed, we need o consider boh mean and sandard deviaion o deermine volailiy in he employmen growh by decades. The insabiliy raio includes boh mean and sandard deviaion and gives us informaion abou which decade has a higher sandard deviaion relaive o he mean for employmen growh. Based on he insabiliy raio we conclude ha is mos volaile and 1990s is mos sable decade for employmen growh. For he 1970s period, see Table 1 for resuls, employmen growh conains a rend, in ha, he coefficiens of he ime variable (ime dummy) are saisically significan and ha he rend is linear and upward, since coefficien of he ime variable is posiive. In addiion, 1970s conain highes mean (2.49%) and sandard deviaion (2.15%) and we esimae an insabiliy raio (sandard deviaion is percen of he mean). There are several reasons behind he high sandard deviaion of he 1970s. For insance, oil prices quadrupled following he Arab Oil Embargo in lae 1973; here was a financial crisis/sock marke collapse and a subsanial slowdown in he global economy. These facors may accoun for he volailiy of he employmen growh during he 1970s. As we coninue esing over subsequen decades we find ha he resuls of he 1970s are no repeaed during he 1980s a decade of apparen prosperiy and sock marke gains relaive o he 1970s. During he 1980s, he sandard deviaion of employmen growh appears large relaive o is average value; sandard deviaion (1.91%) is higher han he mean (1.87%). We find a non-linear rend for he 1980s, a U-shaped rend. In addiion, he insabiliy raio (102.14) is higher han during 1970s. The 1980s also had an oil shock and global economic aciviy urned down. There was a financial crisis/sock marke crash and nonfarm employmen umbled 3.1 percen during he recession. The 1990s also follows a non-linear rend, U-shaped rend, and a decline in he mean (1.8%) as well as in sandard deviaion (1.26%). Bu he decline in he sandard deviaion is much more han he decline in he mean. Consequenly, he insabiliy raio (70) is smalles in he 1990s hereby his decade is mos sable for he employmen growh. The maor facors behind his insabiliy are ha he grea moderaion and he Informaion Technology (IT) boom. During he 1990s U.S. economy experienced a boos in he produciviy and ha is known as he grea moderaion and during ha period oupu per-worker increased. (Noe 7) The IT boom bring in many new obs, however, he ou-sourcing ob process also go more aenion. Overall, he 1990s is mos sable decade for he employmen growh. For he mos recen period ( ), employmen growh does no follow he decreasing paern of he las hree decades and ha is reducion in he mean and sandard deviaion. Insead, he curren period shows a significan decline in he mean and an upick in he sandard deviaion. The insabiliy raio (191.2) is highes in all decades and hereby mos volaile decade for employmen growh. In addiion, here is no evidence of a rend ha is he coefficien of he ime variable is saisically insignifican. There are some maor reasons for his high volailiy as well as he reducion in he mean, (1) bus of he IT bubble, (2) more ob ou-source during 1 s half of 2000s, (3) 2001 recession had a ob-less recovery and (4) recession has he highes ob loss since pos WW-II. (Noe 8) Our effors sugges ha since 1970 he mean and sandard deviaion of employmen growh had acually been decreasing up unil he mos recen ( ) period. The mos recen period shows a significan decline in he mean and an upick in he sandard deviaion. When we evaluae he enire period as a whole, , we find ha he rend coefficien is saisically significan and has a negaive sign. Tha implies he employmen growh rae has a decreasing paern over ime. In addiion, he sandard deviaion (1.79%) is higher han he mean (1.73%), his is evidence of high volailiy in he employmen series. Indeed, he growh of employmen is volaile over ime as picured by Exhibi I. Overall; his paern suggess ha he characer of employmen growh changes over ime due o changing underlying economic forces and/or policy changes. Uni Roo Tess wihou Srucural Break Table 2 shows resuls based on uni roo ess and hese ess do no consider a srucural break in he es regression as well as in he null and he alernaive hypoheses. We sar wih he ADF es s resuls. Firs case we consider Published by Canadian Cener of Science and Educaion 49

7 Inernaional Journal of Economics and Finance Vol. 3, No. 1; February 2011 wihin he ADF es is he zero-mean case (no inercep and rend in he es regression). (Noe 9) We reec he null hypohesis ha he employmen series has a uni roo (no mean-reversion) in favor of he alernaive hypohesis ha he employmen series is saionary (mean-reversion). In second case, we incorporaed a consan (also known as drif parameer) in he es regression bu resuls did no show any change and he employmen series is sill mean-revering (saionary). The hird case which includes a consan and a linear rend in he es regression and he resul is as reecion of he null hypohesis of a uni roo. Therefore, based on he ADF es resuls, he employmen growh series is mean revering. The nex uni roo es we applied on he employmen growh series is he PP es. The PP es has he null hypohesis of a uni roo and he alernaive is saionary (mean-reversion). We ran hree differen regression equaions which are (i) equaion wih no inercep and rend, (ii) regression equaion wih consan and (iii) es equaion wih a consan and a linear rend. The resuls based on he PP es indicae srong evidence of mean-reversion. In oher words, in all hree cases we reec he null hypohesis of a uni roo and conclude ha he employmens series is mean-revering. We also applied he KPSS es on he employmen growh series. The null hypohesis of he KPSS es is ha he underline series is saionary (in our case, he employmen series is saionary) and he alernaive hypohesis is non-saionary. The KPSS es only considers wo cases, which are (a) es regression wih a consan and (b) regression equaion wih a consan and a linear rend. We failed o reec he Ho: he employmens series is saionary in boh cases hereby he KPSS es resuls indicae ha he U.S. employmen growh series is mean-revering. Ineresing, all hree uni roo ess have he same conclusion, ha is, he level of he employmen growh series is mean-revering. However, as we menioned earlier, he ADF, PP and he KPSS ess have some limiaions and may lead o a misleading conclusion. Therefore, we employ more efficien and reliable uni roo ess which are ERS (DF-GLS and Poin-opimal) and Ng-Perron ess. The resuls based on ERS and Ng-Perron ess are also available in Table 2. The DF-GLS es has he null hypohesis of a uni roo and he alernaive is saionary. We failed o reec he null hypohesis of a uni roo in boh cases; (i) a consan in he es regression and (ii) a consan and a linear rend in he regression. Therefore, he DF-GLS es resuls conradic he ADF, PP and KPSS ess resuls. Moreover, he DF-GLS es indicaes ha he level of he employmen growh series is no mean-revering. However, he firs difference of he employmen growh series is saionary. (Noe 10) The nex uni roo es we applied on he employmen series is he ERS Poin-opimal uni roo es which has he null hypohesis of a uni roo and he alernaive hypohesis is saionary (mean-reversion). When we include a consan in he es regression hen we reec he null hypohesis ha he employmen series has a uni roo a 10% level of significance. Tha implies he employmen growh series is mean revering. However, when we include a consan and a linear rend in he es regression hen he resul reecs he idea of he mean-reversion, he level of he employmen series has a uni roo. Bu he firs difference of he employmen growh series is saionary. Alhough he ERS poin-opimal uni roo es has a confusing conclusion, if we se he level of significance as 5% hen we fail o reec he null hypohesis of a uni roo. Now we proceed o he mos efficien es of uni roo and ha is Ng-Perron ess. The resuls based on he Ng-Perron ess indicae ha he employmen growh series conains a uni roo. In oher words, he employmens series is no mean revering. In sum, based on he uni roo ess wihou srucural break, we conclude ha he level of he U.S. employmen growh raes is no mean-revering. Alhough, he ADF, PP, and he KPSS ess resuls are in favor of he mean-reversion, hese ess have lower power han he ERS and Ng-Perron ess. Therefore, we give more imporance o hose resuls which are based on he ERS and Ng-Perron ess. (Noe 11) Uni Roo Tess wih Srucural Break In his secion of he sudy we discuss he resuls based on he uni roo ess which incorporae a srucural break (see Table 3 for resuls). We uilized he Perron (1989) es and consider 1973:Q4 as a break dae. (Noe 12) We failed o reec he null hypohesis of a uni roo wih a srucural break. Tha implies, he employmens series is no only mean divering bu also has a srucural break and he break dae is 1973:Q4. The nex es we applied on he employmen growh series is he Zivo-Andrews es. We es differen opions for a break dae. For insance, 1973:Q4-1975:Q1 (ime duraion of he recession) and 1981:Q3-1982:Q4 (ime duraion of he recession). We ry one by one each quarer of he above menioned ime period. We end up 1975:Q1 as a break dae. The null hypohesis of he Zivo-Andrews es is a uni roo wih no srucural break. The resuls based on he Zivo-Andrews es fail o reec he null hypohesis and conclude ha he employmen growh series is mean divering. The Zivo-Andrews es s resuls are no in favor of a srucural break bu he Perron es suppors he idea of a srucural break in he employmen growh series. The Zivo-Andrews es does no assume a srucural break under he null hypohesis bu he Perron es allows for a break under he null and alernaive hypoheses. Nunes e al. (1997) suggesed ha here may be some size disorion for Zivo-Andrews es. The firs sep of he Kim-Perron procedure is a pre-es for he break dae. We apply he EXP-W FS es and found ha employmen growh series has a srucural break and ha is 1973:Q4. Nex sep would be o follow he Kim-Perron uni roo es and deermine wheher employmen growh conains a uni roo. Based on he Kim-Perron es resuls, we fail o reec he null hypohesis ha employmen growh conains a uni roo as well as subec o a 50

8 Inernaional Journal of Economics and Finance Vol. 3, No. 1; February 2011 srucural break for all hree models. The Kim-Perron uni roo es is he mos efficien es and hereby, based on he Kim-Peron es, we conclude ha employmen growh series conains a uni roo and subec o a srucural break in our sample period. ARCH Resuls We have found ha he level of he employmen growh series is non-saionary, mean-divering, ha implies ha he mean and/or variance of he employmens series are no consan over ime and may be ime dependen. Bu i is sill imporan o analyze he behavior of he employmens series variance and es wheher he variance is volaile over ime; i is also known as he ARCH effec. The ARCH effec has very serious consequences for modeling and forecasing. For insance, in he presence of he ARCH effec OLS sandard errors can be misleading, wih a spurious regression possibiliy (see Hamilon (2008) for more deail). Anoher issue could be ha he forecas band could be narrower han he acual. Therefore, we employ he ARCH approach which overcomes he consan variance problem. We divided he sample period ino decades and applied an ARCH Approach on each decade s daa as well as he complee sample ha is 1970:Q1-2009:Q3, see Table 1 for resuls. We found an ARCH effec for each decade as well as for he complee sample period. (Noe 13) The implicaion of he ARCH effecs is ha he employmen growh series has a volailiy cluser some periods are more volaile han ohers. In oher words, he variance of he employmen growh is no consan over ime and has episodes of high variance for some periods han ohers. Tha also implies, he forecas band, upper and lower band of he forecas, will no be consan and may be smaller for some ime period han ohers, and vice versa. If we sum-up our empirical analysis, hen he level of he employmen series is mean divering and subec o a srucural break. The ARCH effec ells us he employmen growh series has a volailiy cluser some periods are more volaile han ohers. Conclusion: Key findings of he Sudy Policy makers love o speak abou resoring he economy and he associaed good obs as voers imagine hey were in he pas. Bu is such economic nosalgia reasonable in a dynamic global economy? Moreover, has i acually been rue ha he economy, and paricularly he labor marke, were ever as sable as we imagine? Our work here suggess ha he labor marke has been consanly evolving since 1970 and ha here is no endency o reurn o normal if such a normal were o be defined as i was in he good old days. Moreover, labor marke policies buil on such nosalgia in an aemp o reurn o he pas are misplaced a bes and likely o hur workers more by providing false hopes and also lead o a misallocaion of economic resources han if forward looking policies were adoped o adap workers for he fuure of he labor marke. Our effors sugges ha since 1970 he mean and sandard deviaion of employmen growh had acually been decreasing up unil he mos recen ( ) period. The mos recen period ( ) shows a significan decline in he mean and an upick in he sandard deviaion. When we evaluae he enire period as a whole, , we find ha he rend coefficien is saisically significan and has a negaive sign. Tha implies he employmen growh rae has a decreasing paern over ime. In addiion, he sandard deviaion (1.79%) is higher han he mean (1.73%); his is evidence of high volailiy in he employmens series. Summing-up, our empirical analysis suggess ha he level of he employmen growh raes is mean-divering and subec o a srucural break. Therefore, he level of he employmen series is no appropriae for he modeling and forecasing purpose because of a uni roo problem. Second, due o he presence of a srucural break in he employmen series i would be beer o employ only hose echniques which are assuming a srucural break in he daa e.g., coinegraion ess wih a srucural break. Third, in he presence of he ARCH effec, OLS sandard errors can be misleading, wih a spurious regression possibiliy. Finally, he ARCH effec and uni roo problem have serious consequences for forecasing and he forecas band could be narrower han he acual. References Bai, J. (1998). A Noe on Spurious Break. Economeric Theory, vol. 14(05), pp Baneree, A., Lumsdaine, R. and Sock, J. (1992). Recursive and sequenial ess of uni-roo and he rend break hypoheses: heory and inernaional evidence. Journal of Business Economics and Saisics, 10, Bhargava, Alok. (1986). On he Theory of Tesing for Uni Roos in Observed Time Series. Review of Economic Sudies, vol. 53(3), pp Byrne J. and Perman, R. (2006). Uni Roos and Srucural Breaks: A Survey of he Lieraure. Working paper # 2006_10. Deparmen of Economics, Universiy of Glasgow, UK. Caner, M. and Kilian, L. (2001). Size disorions of ess of he null hypohesis of saionariy: evidence and implicaions for he PPP debae. Journal of Inernaional Money and Finance, vol. 20(5), pp Chrisiano, L. (1992). Searching for a break in GNP. Journal of Business Economics and Saisics, 10, Clemene, J., Monanes, A., and Reyes, M. (1998). Tesing for a uni roo in variables wih a double change in he mean. Economics Leers, 59(2), pages Published by Canadian Cener of Science and Educaion 51

9 Inernaional Journal of Economics and Finance Vol. 3, No. 1; February 2011 Dickey, D. and Fuller, W. (1979). Disribuion of he esimaors for auoregressive ime series wih a uni roo. Journal of he American Saisical Associaion, 74, pp Dickey, D. and Fuller, W. (1981). Likelihood Raio Saisics for Auoregressive Time Series wih a Uni Roo, Economerica, 49, Diebold, F. X. (2007). Elemens of Forecasing. 4 h ed., Thomson Souh-Wesern. Ellio, G., Rohenberg, T. & Sock, J (1996). Efficien Tess for an Auoregressive Uni Roo. Economerica 64, Fuller, W. A. (1976). Inroducion o Saisical Time Series. New York: John Wiley. Gordon, R. (2005). Wha caused he decline in US Business cycle volailiy? NBER working paper Hamilon J. (2008). Macroeconomics and ARCH, Forhcoming in Fesschrif in Honor of Rober F. Engle. Kim, D. & Perron, P. (2009). Uni roo ess allowing for a break in he rend funcion a an unknown ime under boh he null and alernaive hypoheses. Journal of Economerics,148, pp1 13. Kwiakowski, D., Phillips, P., Schmid, P. & Shin, Y. (1992). Tesing he null hypohesis of saionariy agains he alernaive of a uni roo: How sure are we ha economic ime series have a uni roo? Journal of Economerics 54(1-3): Lee, J. and Srazicich, M. (2003). Minimum Lagrange Muliplier Uni Roo Tes wih Two Srucural Breaks. The Review of Economics and Saisics, vol 85(4), pp Lumsdaine, R.L. and Papell, D.H. (1997). Muliple rend breaks and he uni roo hypohesis. Review of Economics and Saisics, 79, Maddala, G. and Kim, I (2003). Uni Roo, Coinegraion, and Srucural Changes. Cambridge Universiy Press. Nelson, C. R. and Plosser, C. I. (1982). Trends and random walks in macroeconomics ime series: some evidence and implicaions. Journal of Moneary Economics 10, Ng, S. and Perron, P. (2001). Lag lengh selecion and he consrucion of uni roo ess wih good size and power. Economerica 69, Nunes, L.C., C-M. Kuan and P. Newbold (1997). Spurious regression. Economeric Theory, 11, pp Papell, D. H. and Prodan, R. (2003). Resriced Srucural Change and he Uni Roo Hypohesis. Working paper, Universiy of Houson Perron P. (1988). Trends and Random Walks in Macroeconomic Time Series: Furher Evidence from a New Approach. Journal of Economic Dynamics and Conrol, 12, Perron, P. (1989). The grea crash, he oil price shock and he uni roo hypohesis. Economerica, 57, pp Perron, P. (1997). Furher evidence on breaking rend funcions in macroeconomic variables. Journal of Economerics, 80, Perron, P. (2005). Dealing wih Srucural Breaks. Mimeo forhcoming in he Handbook of Economerics. Perron, P & Vogelsang, T.(1992). Tesing for uni roo in a ime series wih a changing mean: correcion and exension. Journal of Business and Economic Saisics, 10, Perron, P & Yabu, T. (2009). Tesing for shifs in he rend wih an inegraed or saionary noise componen. Journal of Business and Economic Saisics (in press). Phillips, P. & Perron, P. (1988). Tesing for a uni roo in ime series. Biomerika, 75, pp Schwer, W. (1989). Tes for Uni Roos: A Mone Carlo Invesigaion. Journal of Business and economic Saisics, 7, pp Silvia, John (2006).Domesic Implicaions of a Global Labor Marke. Business Economics, July Silvia, John. & Iqbal, Azhar. (2009). Mean Diversion: When Geing Back o he Old Economy Isn Possible. Souhern Economic Associaion, 79 h Annual Meeings, November 2009, TX, USA. Zivo, E. and Andrews, D.W.K. (1992). Furher evidence on he grea crash, he oil price shock and he uni roo hypohesis. Journal of Business and Economic Saisics, 10, Noes Noe 1. For some microeconomic fundamenals behind hese paerns please see Silvia (2006). Noe 2. U.S. Bureau of he Census, Saisical Absrac of he Unied Saes (Washingon, D.C., U.S. Governmen Prining Office, various issues. Noe 3. See Byrne and Perman (2006) for a survey Noe 4. Here we are no explaining hese ess in deail because of space limi. See Silvia and Iqbal (2009) for more deail. 52

10 Inernaional Journal of Economics and Finance Vol. 3, No. 1; February 2011 Noe 5. I is worh menioning ha many researchers are considering muliple srucural breaks. The argumen for incorporaing more han one break is ha only considering one break is insufficien and leads o a loss of informaion when acually more han one break exis. Lumsdaine and Papell (1997), Clemene e al. (1998), and Pappel and Prodan (2003) considered muliple breaks. Bu we are no using muliple breaks es in his sudy because our analysis sars, sample sar dae, from 1970 and i is relaively a shor hisory. Therefore, we only employ single break ess, boh exogenous and endogenous breaks es. Noe 6. I is worhwhile o menion ha his procedure originally inroduced by Perron and Yabu (2009). Noe 7. During he grea moderaion U.S. produciviy increased and he volailiy associaed wih he produciviy reduced. However, he causes and he consequences of he grea moderaion are debaable, see Gordon (2005) for more deail. Noe 8. The recession is no officially ended a he iming of his wriing. Noe 9. Ng and Perron (2001) suggesed ha he Modified Akaike Informaion Crierion (MAIC) is a beer choice for he lag order selecion hereby we selec lag lengh based on MAIC, see Ng and Perron (2001) for more deail. Noe 10. We only repor he resuls for he level of he employmen growh series because we are ineresed in he mean revering properies of he employmen growh series. However, we also esimae he resuls for he firs difference. All resuls and daa are available upon reques from auhors. Noe 11. Alhough, ERS poin-opimal es is reecing Ho: he employmen series has a uni roo, a 10% level of significance bu he sandard level of significance is 5% and a 5% ERS failed o reec he null hypohesis of a uni roo. Noe 12. We are considering 1973:Q4 as break dae because his dae is he beginning of he recession. This recession is famous for he iniial Pos World-War-II oil shock and, due o he oil shock, energy inpu prices rose sharply, producion echnologies were rendered obsolee and hence he employmen growh raes become volaile. Noe 13. I is worh menioning ha we used he level and 1s difference of he employmen growh series and found ARCH effec in boh cases. Table 1. Employmen Growh, Nonfarm Payrolls, Year-o-Year percen Change Period Mean S.D* Insabiliy Raio** Skewness Kurosis Trend ARCH Linear(posiive) ARCH effec Non-linear(U-shape) ARCH effec Non-linear(U-shape) ARCH effec No Trend ARCH effec Linear(negaive sign) ARCH effec *S.D. = Sandard Deviaion ** Insabiliy Raio = (S.D./Mean)*100 Table 2. Uni Roo Tess; Wihou Srucural Break Tes Opion Tes Name Consan Consan & Trend None ADF No No No PP No No No KPSS No No N/A DF-GLS Yes Yes N/A ERS No Yes N/A Ng-Perron Yes Yes N/A Published by Canadian Cener of Science and Educaion 53

11 Inernaional Journal of Economics and Finance Vol. 3, No. 1; February 2011 Table 3. Uni Roo Tess; Wih Srucural Break Tes Opion Tes Name Model A Model B Model C Perron* Yes Yes Yes Zivo-Andrews** Yes Yes Yes Kim-Perron*** Yes Yes Yes No = No uni roo --- Mean-reversion; Yes = Uni roo ---- No Mean-reversion; * Break Dae= 1973:4Q; ** Break Dae= 1975:Q1 *** Break Dae= 1973:Q4 Exhibi I 6% Nonfarm Employmen Growh Year-over-Year Percen Change 6% 5% 4% 3% 2% 1% 0% -1% -2% -3% -4% Year/Year Change: -4.2% -5% % 4% 3% 2% 1% 0% -1% -2% -3% -4% -5% Exhibi II $160 $140 $120 $100 $80 $60 $40 $20 Mean Family Income by Educaion of Head Thousands of 2007 Dollars $160 $140 $120 $100 $80 $60 $40 $20 $0 No High School Diploma High School Diploma Some College College Degree $0 54