The causal relationship between unemployment rate and U.S. shadow economy. A Toda-Yamamoto approach

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1 Recen Researches in Applied Mahemaics, Simulaion and Modelling The causal relaionship beween unemploymen rae and U.S. shadow economy. A Toda-Yamamoo approach Adriana AnaMaria Alexandru, Ion Dobre and Caalin Corneliu Ghinararu Absrac The paper analyses he causal relaionship beween U.S. shadow economy (SE) and unemploymen rae (UR) using Toda-Yamamoo approach for quarerly daa covering he period 9-9. The size of he shadow economy as % of official is esimaed using a MIMIC model wih four causal variables(axes on corporae income, conribuions for governmen social insurance, unemploymen rae and self-employmen) and wo indicaors (index of real and civilian labour force paricipaion rae). Their dimension is decreasing over he las wo periods. The evidence generally suppors he exisence of a unidirecional causaliy ha runs from unemploymen rae o shadow economy for he case of Unied Saes. Keywords shadow economy, unemploymen rae, MIMIC model, Toda-Yamamoo approach, USA. I. INTRODUCTION The relaionship beween he shadow economy (SE) and he level of unemploymen is one of major ineres. People wor in he shadow economy because of he increased cos ha firms in he formal secor have o pay o hire a worer. The increased cos comes from he ax burden and governmen regulaions on economic aciviies. In discussing he growh of he shadow economy, he empirical evidence suggess wo imporan facors: (a) reducion in official woring hours, (b) he influence of he unemploymen rae (UR). Ense [] poins ou ha he reducion of he number of woring hours below worer's preferences raises he quaniy of hours wored in he shadow economy. Early reiremen also increases he quaniy of hours wored in he shadow economy. In Ialy, Berola and Garibaldi [] presen he case ha an increase in payroll axaion can have effec on he supply of labour and he size of he shadow economy. An increase in ax Manuscrip received May,. Adriana AnaMaria Alexandru, PhD suden and eaching assisan, Deparmen of Saisics and Economerics, Buchares Academy of Economic Sudies, Romania and scienific researcher, Romanian Scienific Research Insiue in he Field of Labour and Social Proecion(adrianaalexandru@yahoo.com). Ion Dobre, PhD, Deparmen of Economic Cyberneics, Buchares Academy of Economic Sudies, Romania (dobrerio@ase.ro). Caalin Corneliu Ghinararu, principal researcher, Romanian Scienific Research Insiue in he Field of Labour and Social Proecion(ghinararu@incsmps.ro ). and social securiy burdens no only reduces official employmen bu ends o increase he shadow labour force. This is because an increase in payroll ax can influence he decision o paricipae in official employmen. Also, Boeri and Garibaldi [] show a srong posiive correlaion beween average unemploymen rae and average shadow employmen across Ialian regions during he period Dell Anno and Solomon [] find a posiive relaionship beween unemploymen rae and shadow economy using a SVAR analysis, showing ha a posiive aggregae supply shoc will cause in increase in he shadow economy by abou % above he baseline. The paper analyzes he causal relaionship beween shadow economy and unemploymen rae using Toda-Yamamoo approach. II. DATA AND METHODOLOGY II..DATA ISSUES The daa series used in he sudy are quarerly, seasonally adjused covering he period 9:Q o 9:Q. The main source of daa is U.S. Bureau of Economic Analysis, U.S. Bureau of Labour Saisics Daa and Federal Reserve Ban. The series in levels or differences have been esed for uni roos using he Augmened-Dicey Fuller (ADF) es and PP ess. All he daa has been differeniaed for he achievemen of he saionariy. While all he variables have been idenified lie inegraed on firs order, he laen variable is esimaed in he same ransformaion of independen variables (firs difference). II.. METHODOLOGY The size of he U.S. shadow economy is esimaed as % of official using a paricular ype of srucural equaions models-mimic model. The MIMIC model- Muliple Indicaors and Muliple Causes model (MIMIC model), allows o consider he SE as a laen variable lined, on he one hand, o a number of observable indicaors (reflecing changes in he size of he SE) and on he oher, o a se of observed causal variables, which are regarded as some of he mos imporan deerminans of he unrepored economic aciviy []. ISBN:

2 Recen Researches in Applied Mahemaics, Simulaion and Modelling The model is composed by wo sors of equaions, he srucural one and he measuremen equaions sysem. The equaion ha capures he relaionships among he laen variable (η) and he causes ( q ) is named srucural model and he equaions ha lins indicaors (Y p ) wih he laen variable (non-observed economy) is called he measuremen model. A MIMIC model of he hidden economy is formulaed mahemaically as follows: Y λη + ε () η γ + ξ () η is he scalar laen variable(he size of shadow economy); is he vecor of indicaors of he laen Y ( Y,... Y p ) variable;,... ) is he vecor of causes of η ; ( q λ( p ) and γ ( q ) ε ( p ) and ξ( q ) vecors of parameers; vecors of scalar random errors; ε and ξ are assumed o be muually uncorrelaed. The ' s Subsiuing () ino (), he MIMIC model can be wrien as: Y Π + z (3) ' Π λγ, z λξ + ε. The esimaion of () and () requires a normalizaion of he parameers in (), and a convenien way o achieve his is o consrain one elemen of λ o some pre-assigned value ([]-[]). The possible causes of shadow economy considered in he model are: ax burden decomposed ino personal curren axes ( ), axes on producion and impors( ), axes on corporae income( 3 ), conribuions for governmen social insurance( ) and governmen unemploymen insurance( 5 ), unemploymen rae( ), self-employmen in civilian labour force ( 7 ), governmen employmen in civilian labour force ( ) called bureaucracy index. The indicaor variables incorporaed in he model are: real gross domesic produc index ( Y ), currency raio M M ( Y ) and civilian labour force paricipaion rae ( Y 3 ). The variables used ino he esimaion of he shadow economy are also quarerly and seasonally adjused covering he period 9-9. All he daa has been differeniaed for he achievemen of he saionariy. In order o esimae he MIMIC model, by Maximum Lielihood, using he LISREL. pacage, we normalized he coefficien of he index of real ( ) o sufficienly λ idenify he model. This indicaes an inverse relaionship beween he official and shadow economy. In order o idenify he bes model, we have sared wih MIMIC model --3 and we have removed he variables which have no srucural parameers saisically significan. A deailed descripion and implemenaion of he MIMIC model for he USA shadow economy is provided in [5]. Afer we esimae he size of he shadow economy, we invesigae he naure of he relaionship beween he wo variables using Toda-Yamamoo approach. Toda and Yamamoo [33] causaliy es is applied in level VARs irrespecive of wheher he variables are inegraed, coinegraed, or no. Toda and Yamamoo [33] argue ha F- saisic used o es for radiional Granger causaliy may no be valid as he es does no have a sandard disribuion when he ime series daa inegraed or coinegraed. The Toda-Yamamoo procedure basically involves esimaion of an augmened VAR ( +) model, where is he opimal lag lengh in he original VAR sysem and is maximal order of inegraion of he variables in he VAR sysem. The Toda-Yamamoo causaliy es applies a modified Wald (MWALD) es saisic o es zero resricions on he parameers of he original VAR () model. The es has an asympoic (chi-square) disribuion wih degrees of freedom. The es essenially involves wo sages. The firs sage deermines he opimal lag lengh () and he maximum order of inegraion (d) of he variables in he sysem. The lag lengh, is obained in he process of he VAR in levels among he variables in he sysem by using differen lag lengh crierion such as AIC or SBC. The uni roo esing procedure, such as Dicey-Fuller [] ADF and Phillips-Perron [9] ess may be used o idenify he order of inegraion, d. The second sage uses he modified Wald procedure o es he VAR () model for causaliy. The opimal lag lengh is equal o p [d(max)]. In he case of a bivariae (Y, ) relaionship, Toda and Yamamoo[33] causaliy es is represened as follows: Y a + b i Y + b i Y + c i + c i + e () d + e i + e i + f i Y + f i Y + e (5) Y SE, UR, e e, are he residuals of he models. The Wald ess were hen applied o he firs coefficiens marices using he sandard χ saisics (Duasa[7]). Le c vec( c, c,..., c ) be he vecor of he firs VAR coefficiens. The null hypohesis ha does no cause Y is consruced as follows: H c, i,...,. : i Similarly he second null hypohesis ha Y does no cause is formulaed as follows: H f, i,...,. The : i sysem given by equaions ()-(5) is esimaed using he ISBN:

3 Recen Researches in Applied Mahemaics, Simulaion and Modelling Seemingly Unrelaed Regression echnique (Rambaldi and Doran[3]). A Wald es is hen carried ou o es he hypohesis. The compued Wald-saisic has an asympoic chi-square disribuion wih degrees of freedom. III. EMPIRICAL RESULTS III.. ESTIMATING THE SIZE OF SHADOW ECONOMY In order o esimae he size of he shadow economy, we have idenified he bes model as MIMIC -- wih four causal variables (axes on corporae income, conribuions for governmen social insurance, unemploymen rae and selfemploymen) and wo indicaors (index of real and civilian labour force paricipaion rae). Taing ino accoun he reference variable ( Y, Re al Re al ) he shadow economy is scaled up o a value in, he base year, and we build an average of several esimaes from his year for he U.S.A. shadow economy (able ). The index of changes of he shadow economy ( η ) in Unied Saes measured as percenage of in he is lined o he index of changes of real as follow: Measuremen Equaion: ~ η ~ η I. Esimaes of he size of U.S.A. shadow economy () Auhor Mehod Size of Shadow Economy Johnson e. Al(99) Currency Demand 3.9% Approach Laco(999) Physical Inpu(Elecriciy).5% Schneider and Ense() Currency Demand 7.5%* Approach Mean.% *means for -993 The esimaes of he srucural model are used o obain an ordinal ime series index for laen variable (shadow economy): Srucural Equaion: η~ The index is scaled o ae up o a value of.% in and furher ransformed from changes respec o he in he o he shadow economy as raio of curren : ~ η η ~ η 7 () (7) * () ˆ η I. ~ η * η is he index of shadow economy calculaed by (7); II..% is he exogenous esimae of shadow economy; III. IV. ~ η is he value of index esimaed by (7); is o conver he index of changes respec o base year in shadow economy respec o curren ; V. ηˆ official. shadow economy % of off. is he esimaed shadow economy as a percenage of shadow economy as % of off Fig.. The size of he shadow economy in Unied Saes as % of official The shadow economy measured as percenage of official records he value of 3.% in he firs rimeser of 9 and follows an ascendan rend reaching he value of.77% in he las rimeser of 9. A he beginning of 93, he dimension of USA shadow economy begins o decrease in inensiy, recording he average value of % of a he end of 7. For he las wo year and 9, he size of he unrepored economy i increases slowly, achieving he value of 7.3% in he second quarer of 9. The resuls are no far from he las empirical sudies for USA ([], [3], [3]).Schneider esimaes in his las sudy, he size of USA shadow economy as % of, a he level of 7.9% in 5, respecively % in. III..THE RELATIONSHIP BETWEEN UNEMPLOYMENT RATE AND U.S. SHADOW ECONOMY In many empirical sudies, is has been found ha ax burden is he bigges causes of shadow economy. Also he size of shadow economy is influenced by he level of unemploymen. An increase in unemploymen raes reduces he proporion of worers employed in he formal secor his leads o higher labor paricipaion raes in he informal secor. ISBN:

4 Recen Researches in Applied Mahemaics, Simulaion and Modelling The graphical evoluion of he shadow economy versus unemploymen rae reveal he exisence of a srong posiive relaionship beween he wo variables, quanified by a value of abou. of correlaion coefficien. II. ADF and PP ess for Uni Roo analysis shadow economy % of off shadow economy as % of off. unemploymen rae Fig.. Shadow economy vs. Unemploymen rae in Unied Saes Giles ([], []) saes ha he effec of unemploymen on he shadow economy is ambiguous (i.e. boh posiive and negaive). An increase in he number of unemployed increases he number of people who wor in he blac economy because hey have more ime. On he oher hand, an increase in unemploymen implies a decrease in he shadow economy. This is because he unemploymen is negaively relaed o he growh of he official economy (Oun s law) and he shadow economy ends o rise wih he growh of he official economy. III... EVALUATING THE RELATIONSHIP BETWEEN SHADOW ECONOMY AND UNEMPLOYMENT RATE. A TODA-YAMAMOTO APPROACH The applicaion of he Toda-Yamamoo approach requires informaion abou he lag lengh () and he maximum order of inegraion ( ) of he variables. d max The order of inegraion of he variables is iniially deermined using he ADF and PP uni roo ess. The resuls are presened in able II. The size of he shadow economy seems o be saionary in ADF es a level, bu his is no jusified by PP es. Furher more, boh ess reveal ha he variables are nonsaionary a heir levels bu saionary a heir firs differences, being inegraed of order one, I(). Therefore, he maximum order of inegraion in he VAR sysem, d. max Given ha boh series were found o be inegraed of order one, we specify he bivariae VAR model by deermining he opimal lag lengh of level variables in he model. The opimum lag lengh () chosen by AIC, SC, FPE, HQ, LR is found o be. The diagnosic ess implemened (Breush-Godfrey Serial Correlaion LM and Whie ess) indicae ha he VAR model have no problem of serial correlaion and heeroscedasiciy. unemploymen rae(%) Noe: T&C represens he mos general model wih a drif and rend; C is he model wih a drif and wihou rend; None is he mos resriced model wihou a drif and rend. Numbers in braces are lag lenghs used in ADF es (as deermined by SCH se o maximum ) o remove serial correlaion in he residuals. When using PP es, numbers in braces represen Newey-Wes Bandwih (as deermined by Barle-Kernel). Boh in ADF and PP ess, uni roo ess were performed from he mos general o he leas specific model by eliminaing rend and inercep across he models (See Enders, 995: 5-55). *, ** and *** denoe rejecion of he null hypohesis a he %, 5% and % levels respecively. Tess for uni roos have been carried ou in E-VIEWS.. Since d max, we mus esimae a VAR (3) for he relaionship beween unemploymen rae and shadow economy: x A + A x + A x + A3 x 3 + A3 x 3 + e (9) SE a + a UR a a () () () (3) a SE + a () (3) a UR a e E ( e ) and ( e e e ' ) Σ (3) a SE + e 3 (3) a UR 3 e... () E. The Toda-Yamamoo es involves he addiion of one exra lag of each of he variables o each equaion and he use of he Wald es is o see if he coefficiens of he lagged oher variables (excluding he addiional one) are joinly zero in he equaion (Duasa [7]). To es ha UR does no Granger cause SE, we esimae he VAR (3) model and es ha UR, UR does no appear in SE equaion. Thus he null hypohesis is () () ( i) H : a where a are he coefficiens of a UR, i, i in he firs equaion of he sysem. The exisence of causaliy from unemploymen rae o shadow economy can be esablished hrough rejecing he above null hypohesis which requires finding he significance of he MWald saisic for he group of he lagged independen variables idenified above. ISBN:

5 Recen Researches in Applied Mahemaics, Simulaion and Modelling III. The resuls of he Toda-Yamamoo causaliy es Null hypohesis p MWald saisics H : UR does no Granger cause SE H : SE does no Granger cause UR p-values 3..* Decision Rejec H Do no rejec *, ** indicaes rejecion of he null a he % level, respecively 5% level According o he Toda-Yamamoo causaliy es resuls shown in Table III, here is srong evidence of causaliy running from unemploymen rae o shadow economy a he % level of significance. The resuls do no reveal causaliy from shadow economy o unemploymen rae. Therefore, we can conclude ha here is a uni-direcional direcion of causaliy ha runs from unemploymen rae o shadow economy for he case of Unied Saes. IV. CONCLUSIONS The paper has invesigaed he naure of he relaionship beween unemploymen rae and he size of he U.S.A. shadow economy measured as % of official for he period 9-9, using Toda-Yamamoo approach. The size of he shadow economy esimaed using he MIMIC model is decreasing over he las wo periods, achieving he value of abou 7.3% of official a he middle of 9. The empirical resuls poin ou ha here is srong evidence of uni-direcional causaliy running from unemploymen rae o shadow economy a he % level of significance. REFERENCES [] A, Alexandru, I., Dobre, C., Ghinararu, Revisiing he relaionship beween Unemploymen rae and he size of he shadow economy for Unied Saes using Johansen Approach for Coinegraion, Proceedings of he h WSEAS Inernaional Conference on Mahemaics and Compuers in Business and Economics, Iasi, Romania, june 3-5,, pg.99-, ISBN [] A., Alexandru, I., Dobre, C., Ghinararu, The relaionship beween unemploymen rae and he size of he shadow economy. The case of Unied Saes, Wseas Transacions on Business and Economics, issue, vol.7, pg , ocober, ISSN: [3]Alexandru A., Dobre, I., Ghinararu, C. 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6 Recen Researches in Applied Mahemaics, Simulaion and Modelling Applied Saisics No., 99, The Deparmen of Economerics, Universiy of New England. [3] F., Schneider, D.H., Ense Shadow economies: size, causes and consequences, Journal of Economic Lieraure 3,, pp [3] F., Schneider Shadow Economies and Corrupion all over he world: New esimaes for 5 Counries, Economics, 9, pp. -7. [33] H.Y.Toda, T. Yamamoo. Saisical inference in vecor auoregressions wih possibly inegraed processes. Journal of Economerics, Vol. /995, pp *** U.S. Economic Accouns *** U.S. Deparmen of Labour Saisics *** Eviews. sofware *** Lisrel. pacage ISBN: