Revisiting the relationship between unemployment rate and the size of the shadow economy for United States using Johansen approach for cointegration

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1 Revisiing he relaionship beween unemploymen rae and he size of he shadow economy for Unied Saes using Johansen approach for coinegraion ADRIANA ANAMARIA ALEXANDRU Naional Scienific Insiue for Labour and Social Proecion 6-8 Povernei Sree, Buchares, ROMANIA Saisics and Economerics Deparmen Academy of Economic Sudies Buchares 5-7, Calea Dorobanilor, Buchares, ROMANIA ION DOBRE Economic Cyberneics Deparmen Academy of Economic Sudies Buchares 5-7, Calea Dorobanilor, Buchares, ROMANIA CATALIN CORNELIU GHINARARU Naional Scienific Insiue for Labour and Social Proecion 6-8 Povernei Sree, Buchares, ROMANIA Absrac: The paper revisis and invesigaes he possible co-inegraion and direcion of causaliy beween unemploymen rae(ur) and he size of he shadow economy(se) in case of USA, by employing Johansen and Granger approaches, using quarerly daa covering he period The shadow economy is esimaed as percenage of official, using MIMIC model and heir dimension is decreasing over he las wo decades. The empirical resuls reveal he exisence of a long run relaionship beween he wo variables. Furhermore, he Granger causaliy ess idenify a unidirecional causaliy ha runs from unemploymen rae o he size of shadow economy. Keywords: shadow economy, unemploymen rae, MIMIC model, coinegraion, Johansen approach, VECM, Granger causaliy, USA.. Inroducion The relaionship beween he shadow economy 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. 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 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 0 Ialian regions beween ISSN: ISBN:

2 The paper examines he possible co-inegraion relaionship beween unemploymen rae and he size of he shadow economy and ess he direcion of causaliy beween hese variables.. Daa and Mehodology The sudy used quarerly daa covering he period The size of he U.S. shadow economy is esimaed as % of official using a paricular ype of srucural equaions models-mimic model. The unemploymen rae is expressed in %, aen from U.S. Bureau of Saisics, Labour Force Saisics from Curren Populaion Survey. 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 [4]. The possible causes of shadow economy considered in he model are: ax burden decomposed ino personal curren axes ( X ), axes on producion and impors( X ), axes on corporae income( X 3 ), conribuions for governmen social insurance( X 4 ) and governmen unemploymen insurance( X 5 ), unemploymen rae( X 6 ), self-employmen in civilian labour force ( X 7 ), governmen employmen in civilian labour force ( X 8 ) 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 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 8.8 pacage, we normalized he coefficien of he index of real ( λ = ) o sufficienly 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 8--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 [0]. Afer we esimae he size of he shadow economy, we invesigae he naure of he relaionship beween he wo variables. The Augmened Dicey-Fuller (ADF) and Phillips- Perron (PP) Uni Roo Tess are employed o es he inegraion level and he possible co-inegraion among he size of he shadow economy esimaed using MIMIC model and he unemploymen rae ([7], []). Afer he order of inegraion is deermined, coinegraion beween he series should be esed o idenify any long run relaionship. Johansen race es is used for he co-inegraion es in his sudy. Cheung and Lai [3] menion ha he race es is more robus han he maximum eigenvalue es for co inegraion. The Johansen race es aemps o deermine he number of co-inegraing vecors among variables. There should be a leas one co-inegraing vecor for possible co inegraion. This procedure [9] can be expressed in he following VAR model: = Π X Π K X K +µ e,.., T X + = () where X, X -,, X -K are vecors of curren and lagged values of P variables which are I() in he model; Π,.,Π K are marices of coefficiens wih (PXP) dimensions; µ is an inercep vecor i ; and e is a vecor of random errors. The number of lagged values, in pracice, is deermined in such a way ha error erms are no significanly auo-correlaed.. The ran of Π is he number of co inegraing relaionship(s) (i.e. r) which is deermined by esing wheher is Eigen values (λ i ) are saisically differen from zero. Johansen and Juselius [5] propose ha using he Eigen values of Π ordered from he larges o he smalles is for compuaion of race saisics. The race saisic (λ race ) is compued by he following formula 3 : This procedure is presened in deail in Kaircioglu S.T. Financial developmen, rade and growh riangle: he case of India, Inernaional Journal of Social Economics, Vol. 34 No. 9, 007, pp Asympoic criical values are obained from Oserwald-Lenum (99). 3 A he beginning of he procedure, we es he null hypohesis ha here are no co inegraing vecors. If i can be rejeced, he alernaive hypohesis (i.e. r,, r n) are o be esed sequenially. If r=0 canno be rejeced in he firs place, hen here is no co inegraing relaionship beween he variables, and he procedure sops ISSN: ISBN:

3 λ race = T ln( λi ) () i = r+,, n- and he hypoheses are : H 0 : r = 0 H : r H 0 : r H : r H 0 : r H : r 3 If he series are I() and coinegraed, hen Granger Causaliy ess should be run under VECM framewor([0], [9]): 0 + iy i + αi X i + piect Y = C β + u (3) X = C 0 + γ i X i + ζ iy i + ηiect + ε (4) Where Y, X are he variables, p i is he adjusmen coefficien while ECT expresses he error correcion erm. In eq.(3), X Granger causes Y if α, are significanly differen from zero. In eq.(4) i p i Y Granger causes X if ζ i, ηi are significanly differen from zero. F-es alone is no enough o have causaion; -raio of ECM erm should be also negaive and saisically significan ogeher wih F value of he model o have causaion in he models. 3. Empirical resuls 3.. Esimaing he size of he shadow economy In order o esimae he size of he shadow economy, we have idenified he bes model as MIMIC 4-- 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). Taing ino accoun he reference variable Re al ( Y, ) he shadow economy is scaled up Re al 990 o a value in 990, 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 990 is lined o he index of changes of real as follow: Measuremen Equaion: 990 ~ η ~ η = 990 Table : Esimaes of he size of U.S.A. shadow economy (990) Auhor Mehod Size of Shadow Economy Johnson e. Al(998) Currency Demand 3.9% Approach Laco(999) Physical Inpu(Elecriciy) 0.5% Schneider and Ense(000) Currency Demand 7.5%* Approach Mean % *means for The esimaes of he srucural model are used o obain an ordinal ime series index for laen variable (shadow economy): Srucural Equaion: η~ = 0.4 X X X6 +.0 X7 (6) 990 The index is scaled o ae up o a value of 0.6% in 990 and furher ransformed from changes respec o he in he 990 o he shadow economy as raio of curren : ~ * η η ˆ η ~ = (7) η (5) ~ η I. is he index of shadow economy calculaed 990 by eq.(6); * η990 II. = 0.6% is he exogenous esimae of 990 shadow economy; ~ η990 III. is he value of index esimaed by eq.(6); 990 IV. 990 is o conver he index of changes respec o base year in shadow economy respec o curren ; ηˆ V. is he esimaed shadow economy as a percenage of official. ISSN: ISBN:

4 Table. ADF and PP Tess for Uni Roo Shadow Economy(SE) Unemploymen rae(ur) T&C C None T&C C None Level ADF *** lag (3) (3) (6) () () () PP lag (6) (6) (6) (6) (6) (7) Firs diff. ADF -3.43* -3.39** -3.33* -4.40* -4.7* -4.7* lag () () () (0) (0) (0) PP -6.99* -6.97* -6.73* -4.69* -4.5* -4.53* lag (5) (5) (6) (3) (3) (3) The shadow economy measured as percenage of official records he value of 3.4% in he firs rimeser of 980 and follows an ascendan rend reaching he value of 6.77% in he las rimeser of 98. A he beginning of 983, he dimension of USA shadow economy begins o decrease in inensiy, recording he average value of 6% of a he end of 007. For he las wo year 008 and 009, he size of he unrepored economy i increases slowly, achieving he value of 7.3% in he second quarer of 009. The resuls are no far from he las empirical sudies for USA ([], [4], [5]).Schneider esimaes in his las sudy, he size of USA shadow economy as average 004/05, a he level of 7.9 percenage of official. 3.. Evaluaion of he relaionship beween he shadow economy and he unemploymen rae under Johansen approach The main goal of he sudy is o invesigae he naure of he relaionship beween he wo variables and o idenify any possible direcion of causaliy beween hem. In order o idenify he level of inegraion of he wo series, ADF and PP uni roo ess were applied; he resuls are presened in able. 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 non-saionary a heir levels bu saionary a heir firs differences, being inegraed of order one, I(). 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: 54-55). *, ** and *** denoe rejecion of he null hypohesis a he %, 5% and 0% levels respecively. Tess for uni roos have been carried ou in E-VIEWS 6.0. Because he boh series are inegraed of he same order, I() we will apply Johansen and Juselius[5] coinegraion approach in order o invesigae if here is a long run relaionship beween he wo variables. Alhough he opimal number of lags is wo, esablished by SIC and HQ crierions, Pindyc and Rubinfeld [5] poined ou ha i would be bes o run he es for a few differen lag srucures and mae sure ha he resuls were no sensiive o he choice of lag lengh. In able are presened he resuls of co-inegraion ess using Johansen and Juselius approach(990) and confirms ha here is a unique co-inegraion vecor(a long run relaionship) beween he wo variables. According o he normalized parameer esimaes, we can conclude ha unemploymen rae has a posiive and elasic effec on he size of he shadow economy. When unemploymen rae grows by % he U.S. shadow economy will rise wih abou.34%. Because a long run equilibrium relaionship is found beween unemploymen rae and he size of he shadow economy, a VECM model is consruced o deermine he direcion of causaliy. Table 4 repors he F-saisics and -saisics for error correcion erm defined for he null hypohesis of no-causaliy. ISSN: ISBN:

5 Table 3.Conegraion ess using he Johansen (988) and Johansen and Juselius 990) approach Variables Trace saisic 5% Criical Value 4 % Criical Value Lag H 0 : r = 0 5.4** H : r Lag H o : r = 0.00** : r H Lag 3 H o : r = 0 3.3* H : r Lag 4 H o : r = H : r Noe: Trace es indicaes co inegraing equaion(s) a boh 5% and % levels for lag and, and coinegraing equaion a 5% level. *(**) denoes rejecion of he hypohesis a he 5% (%) level. Because he -raio of ECT is posiive and no saisically significan, we can conclude ha we don have any granger causaliy from SE o UR, bu we can say ha we have a unidirecional causaliy from UR o SE (-raio of ECT and F-raio are saisically significan a % and 5% levels, bu he ECT is no negaive). Table 4.Granger Causaliy Tess Null hypohesis UR does no Granger cause SE SE does no Granger cause UR F-sa.4* 39.37* Lag.63**.47 Lag Lag 3 ECT F-sa.94* 5.96*.40**.06 ECT F-sa.4* 9.99*.50**.78 ECT *and ** denoe significance for % and 5% levels. Table 5.Esimaion of he Granger Causaliy Tess wihin Bloc Exogeneiy Wald Tess Dependen variable:se χ Exclude Lag Lag Lag 3 Lag 4 Lag 5 UR 5.43* 4.30*.5**.50** 8.* Dependen variable: UR χ Exclude Lag Lag Lag 3 Lag 4 Lag 5 SE * and ** denoe significance for % and 5% levels. 4. Conclusions The paper has invesigaed he exisence of a long run relaionship and direcion of any causaliy beween unemploymen rae and he size of he U.S.A. shadow economy measured as % of official for he period The size of he shadow economy esimaed using he MIMIC model is decreasing over he las wo decades, from hireen o seveneen percen beween 980 and 983 up o 7 percen of official in 009. The empirical resuls poin ou he exisence of a unique co-inegraion relaionship beween he variables. Thus, here is a unidirecional causaion ha runs from unemploymen rae o shadow economy. Acnowledgemen The auhor Alexandru Adriana would lie o han Professor Salih Turan Kaircioglu (Deparmen of Baning and Finance, Easern Medierranean Universiy, Norh Cyprus) for valuable nowledge impared during The Fourh Inernaional Training Worshop on Economeric Modeling and Daa Analysis. References [] Berola, G., Garibaldi, P., The Srucure and Hisory of Ialian Unemploymen, CESifo Woring Papers, n.907, We have used he criical values of Oserwald-Lenum. ISSN: ISBN:

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