The Incidence of Social Security Taxes in Economies with Partial. Compliance: Evidence from the SS Reform in Mexico

Transcription

1 The Incidence of Social Secuity Taxes in Economies ith Patial Compliance: Evidence fom the SS Refom in Mexico Gecia M. Maufo Abstact Looking at impovements in social secuity benefits in Mexico, this pape evaluates hat faction of the ne mandated benefits can be shifted to ages in economies hee thee is a lage pevalence of non-compliance ith the egulation. I depat fom pevious studies on the effects of labo egulations in economies hee thee is a lage faction of uncoveed okes that use Diffeences-in-Diffeences methods compaing coveed and uncoveed okes. These methods equie the composition of the contol goup to be constant hen egulation changes. Evidence fom Mexico challenges this assumption since labo eallocated toads the coveed secto afte social secuity benefits impoved. Instead of elying on the Diffeence-in-Diffeence estimato, I evaluate the egulation using a to-secto geneal equilibium model ith labo mobile beteen sectos. In this model, I explicitly deive the effects of labo eallocation on ages induced by changes in taxes and benefits. I extend Habege s to-secto model to account fo social secuity taxation and intoduce social secuity benefits into it. I also extend his model by explicitly modeling oke s selection into the coveed secto using

2 a Genealized Roy Model. The model shos the age diffeential beteen the coveed and the uncoveed sectos depends on changes in the composition of okes acoss sectos, but also on the equilibium effect caused by changes in elative supply. Unde this scenaio, incidence of the egulation cannot be calculated based solely on changes in the age diffeential, even afte contolling fo selection. JEL Classification: J38, H42, O54 Gecia M. Maufo The Cente fo Reseach on Economic Development and Policy Refom CREDPR Landau Economics Building 579 Sea Mall Stanfod, CA

3 Intoduction This pape makes to contibutions. Fist, it deives an analytical fameok fo undestanding the effects of social secuity taxation on ages and employment hen noncompliance is substantial. Second, it uses a 997 Social Secuity Refom in Mexico to compae estimates based on idely used Diffeences-in-Diffeences methods ith estimates deived fom an econometic geneal equilibium model. This pape shos that Diffeences-in-Diffeences methods geneate inaccuate estimates of the incidence of the egulation on ages. In Mexico, the substitution of the Pay-As-You-Go fo Individual Retiement Accounts inceased coveed okes benefits by 7 to 9 pecent of thei age. Incemental benefits measued by Diffeencesin-Diffeences ee only 2.4 pecent, hile estimates based on age esponses pedicted by the model implied incemental benefits of pecent. Many studies on the effects of labo egulations in economies hee thee is a lage faction of uncoveed okes use Diffeences-in-Diffeences methods; the common identifying assumption is that uncoveed okes ae an ideal contol goup 2. This identification stategy equies that the efom does not change the composition of the contol goup. Intuitively, this is a stong assumption since changes in egulations ill induce labo eallocation acoss sectos. Fist, gains fom efoms vay acoss demogaphic and skill goups. Second, social secuity taxes In Mexico 37% of pivate secto employees ok at a fim that does not comply ith the egulation. Non-compliance ith social secuity coveage is substantial in many Latin Ameican counties. 2 See Kugle 999, Mondino and Montoya 2. See Gube 997 and Kugle and Kugle 2, although they do not use uncoveed okes as a contol they ignoe composition and equilibium effects on ages paid by 3

4 distot labo costs in the coveed secto elative to the uncoveed secto. When a efom contaminates the contol goup, Diffeences-in-Diffeences fail to contol fo compositional bias and geneal equilibium effects. I find evidence fo Mexico that justifies these concens. To yeas afte the legislation the social secuity system as impoved in Mexico, labo eallocated toads the coveed secto. Coveage inceased among those demogaphic goups that benefited fom the ne etiement system. In fact, thee is no change in the shae of labo employed in the uncoveed secto among okes ho ill etie unde the old egime Figues and 2. The faction of okes employed by fo non-complying fims deceased fom 4.5 pecent just befoe the ne la as announced to 34.2 in the thid quate of 999 Figue 3. Futhe, eallocation effects ee stonge in sectos typically coveed by social secuity Figue 4. Instead of elying on the Diffeence-in-Diffeence estimato ith its eak empiical fomulation, I evaluate the egulation using a to-secto geneal equilibium ith labo mobile beteen sectos. In this model I explicitly deive the effects of labo eallocation on ages induced by changes in taxes and benefits. I extend Habege s to-secto model to account fo social secuity taxation and intoduce social secuity benefits into it. In the model, coveed employees eceive the benefits of the pogams financed ith this tax and theefoe, complying fims can pay loe ages in exchange fo social secuity benefits. I also extend his model by explicitly consideing ho okes select into the coveed secto. I deive labo supply unde to scenaios: a okes ae homogenous in tastes and skills and b okes ae heteogeneous in thei benefits fom coveage and poductivity diffeentials. When okes ae homogenous labo supply beteen the coveed and uncoveed secto is completely elastic and age diffeential beteen sectos equals diffeences in benefits. In this scenaio, the model esembles Habege s oiginal model. Hoeve, the homogeneity complying fims. 4

5 assumption equies that thee ae compaable jobs in each secto fo evey oke in the economy o else that complying and non-complying fims ae andomly allocated acoss sectos. Because the cost of avoiding egulatoy agencies vaies among economic sectos, in equilibium thee ae economic sectos that ae typically coveed by social secuity as ell as economic sectos ithout coveage 3. As a esult, a oke s poductivity in the coveed secto may not be equal to his poductivity in the uncoveed secto. When okes ae heteogeneous in skills they select into the coveed secto based on thei pefeences fo coveage, but also based on thei compaative advantage. The implications of the model ae to. Fist, if the complying and the non-complying sectos have diffeent technologies, then social secuity taxes distot the compaative advantage of okes acoss sectos. In this case, social secuity taxes foce okes to move fom the secto hee they ae moe poductive to a secto hee they ae less poductive. Second, the equilibium age diffeential beteen the coveed and the uncoveed sectos depends on the distibution of okes acoss sectos and theefoe, tax incidence cannot be calculated based solely on changes in the age diffeential, even afte contolling fo selection. An additional advantage of using the model to deive the effects of social secuity taxation on ages is that I can sepaate age effects of educing social secuity taxes fom the effects of tying okes benefits to thei contibutions. Pevious studies based on age diffeentials beteen the coveed and uncoveed secto 4 do not anse the key empiical question that the analysis of the incidence of social secuity taxation equies: What faction of the cost of social secuity can the fim shift to okes in fom of loe ages? Inability to anse this questions aises fom the fact that most social secuity efoms combine changes in benefits ith tax eductions, thus shifting both labo demand and supply. Besides the limitations of ignoing 3 Coveage in lage manufactuing fims is about 85% hile coveage in non-tadable sectos is about 28%. 4 Mondino and Montoya 2, Cox-Edads 2 5

6 equilibium effects of labo eallocation, Diffeences-in-Diffeences methods cannot isolate the effects that changes in benefits had on equilibium ages fom changes in the tax ate. The pape is oganized as follos. Section 2 descibes the main featues of the ne Social Secuity legislation implemented in July 997. Section 3 pesents the geneal equilibium model and deives deteminants of the shifting of taxes and benefits to ages. Section 4 pesents estimates on the valuation of ne benefits based on Diffeence-in-Diffeence estimatos methods. Section 5 descibes the empiical methods used to estimate the econometic geneal equilibium model and compae these esults ith diffeence-in-diffeence estimatos. Section 6 concludes the pape and suggests diections fo futue eseach. 2 Social Secuity Refom in Mexico The Refom in 997 substituted the Pay-As-You-Go etiement system fo a system based on Individual Retiement Accounts. Contibutions to the Individual Retiement Accounts inceased fom 2% to 3.5%. The efom has distinctive cohot effects, okes olde than 5 ae moe likely to etie unde the old egime ules and theefoe, have no diect benefits fom the pivatization of the etiement pension 5. Evidence fom the Social Secuity efom in Mexico challenges empiical methods that equie a constant contol goup, since labo eallocates acoss sectos depending on benefits. Fist, coveage inceased moe among those demogaphic goups that benefited the most fom the ne etiement system. In fact, thee is no change in the shae of labo employed in the noncomplying secto among okes ho ill etie unde the old egime. Second, the shae of labo 5 See Appendix A fo a detailed desciption of the elements of the efoms as ell as the compaison of benefits in the old egime and ne egime fo diffeent skills and demogaphic goups. 6

7 employed in the non-complying secto deceased acoss all economic sectos. Thid, eallocation effects ee stonge in secto typically coveed by social secuity. The efom clealy affects young and old okes diffeently. Olde okes, moe than 5, ae moe likely to etie unde the old egime ules and theefoe eceive no diect benefits fom the pivatization of the etiement pension. Hoeve, olde okes could claim Pay-As- You-Go benefits only if they ee egisteed befoe the ne legislation as implemented in July 997. Figue shos olde okes moved aay fom the uncoveed secto to the coveed secto to be entitled to Pay-As-You-Go benefits. In addition, eallocation toads the coveed secto did not incease futhe afte the la as implemented. The late is consistent ith the fact that old oke had no futhe gains fom sitching sectos afte July 997. Figue 2 shos young okes eallocated toads the coveed secto afte the ne la as implemented in July 997. Coveage inceased hen benefits impoved, figue 3 shos the faction of okes employed by fo non-complying fims deceased fom 4.5 pecent just befoe the ne la as announced to 34.2 in the thid quate of 999. Evidence fom the efom in Mexico shos that changes in the egulation do not affect all economic sectos equally. Intuitively, in economies ith lage pevalence of non-compliance, changes in the egulation ill be stonge to complying fims o fims that ae at the magin of compliance. Figue 4 shos eallocation effects ee stonge in economic sectos typically coveed by social secuity. Diffeences in eallocation in the manufactuing secto, a secto ith taditionally high compliance ates and in the sevice secto, a secto ith lo coveage, ae not small. The coveed secto is pimaily composed of lage fims hile the uncoveed secto is composed mainly of fims ith 6 o fee okes. In this sense, egulation inceases the elative cost of labo to lage fims. As the Social Secuity efom educes the elative cost of labo in the complying secto, e expect employment to move aay fom small fims toad lage fims. Figue 5 and Figue 6 sho that this is the case; afte 997, the distibution of 7

8 employment acoss fim sizes moved aay small fims toads lage fims afte being constant fom 993 to Model I extend Habege s to-secto geneal equilibium model to account fo social secuity taxation and intoduce social secuity benefits into it. In the model, coveed employees eceive benefits fom the pogams financed ith this tax and theefoe, complying fims can pay loe ages in exchange fo social secuity benefits. I also extend his model by explicitly consideing ho okes select into the coveed secto. I deive labo supply unde to scenaios: a okes ae homogenous in tastes and skills and b okes diffe in thei benefits fom coveage and poductivity in the to sectos. The analysis of the to-secto model shos that the Social Secuity tax is an implicit tax to fims that have highe cost of avoiding the egulation, and theefoe it is an implicit tax to goods poduced by economic sectos poviding social secuity. I find that even if ages adjust completely beteen the complying and the non-complying secto fo diffeences in benefits, social secuity taxes distot the compaative advantage beteen sectos hen the fims ith high cost of avoiding the egulation diffe in thei poduction technology to the est of the economy and benefits ae not equal to contibutions. Also, I find that educing social secuity taxes is not equivalent to tying benefits to contibutions. The model has the folloing empiical implication, idely used Diffeences-in- Diffeences methods fail to contol fo compositional bias and geneal equilibium effects. Fo example, an incease in benefits in the coveed secto eallocates labo supply fom the coveed secto to the uncoveed secto, inceasing the equilibium age in the uncoveed secto and deceasing ages in the coveed secto. 8

9 3. Homogeneous Agents The economy is divided in to sectos Secto is the taxed secto and Secto is the untaxed non-complying secto. X, and X o ae espectively the output poduced in the taxed secto and the untaxed sectos. Assuming constant etuns to scale, 3. and 3.2 epesent the cost functions in each secto: C,, X c, t X = 3. C = 3.2,, X c, X Competition foces pices equal to maginal cost p = c, 3.3 t p = c, 3.4 Demand fo goods poduced in each secto ae given by: X X p, p, t L L K = 3.5 X X p, p, t L L K = 3.6 The factos demands ae: L d = X 3.7 c2, t c2, L d = X 3.8 K d = X 3.9 c, t c, K d = X 3. 9

10 Whee: p j is the pice of the good poduced in secto j t is the tax paid by the fim is the ental pice of capital is the age ate L j is the labo employed in secto j K j is the capital employed in secto j j c i Coesponds to the deivative of the i agument of the unitay cost function in secto j. The total tax ate is divided in to pats, so that the tax paid by the fim is given by: t = t t 2 t is the potion of the payoll tax that is allocated to pogams hose benefits ae peceived as public. t 2 coesponds to the potion of the Social Secuity tax that goes into the individual etiement accounts. The patition is ielevant fo the fim, hoeve, only t 2 detemines the elative labo supply beteen the coveed and the uncoveed secto. Each agent supplies a single unit of labo to the secto that gives them the highest benefits. Wages adjust in each secto so that no one is bette off sitching sectos. Assuming that thee ae no sitching costs e have that: b t = 2 o

11 Whee b t epesents the monetay equivalent of the benefits eceived in the coveed 2 secto. b t is a function of the tax paid by the fim since the evenues ae used to finance 2 pogams favoing okes employed in the coveed secto. Let a be the atio of benefits to contibutions. Then, bt 2 = at 2,. The solution of the model gives the folloing elationship 6 : d λσ mθldt σ θlk θkl dt λσ mθl adt2 σ θlk θk l adt2 = 3. λσ θ θ σ θ k θ l σ θ k θ l m l l l k l k Whee θ ij is the facto i shae on secto j σ j is the elasticity of substitution beteen capital and labo in secto j. L K λ L K The elative pice of poduction factos paid by complying fims,, inceases ith the Social Secuity tax. As a esult, employment ill eallocate to the uncoveed secto. If a= and dt=dt 2, that is okes ho ae coveed value thei benefits at thei exact cost, then dt 2 =- dt 2. Wages paid by complying fims ill decease by the same popotion as the tax. In this case, complying and non-complying fims face equal labo costs. If a=, the elative pice of factos t does not depend on the tax levied, no does the elative pice of the goods poduced in each secto depend on the tax. Unde this model diveting taxes to Individual 6 Appendix B deives the solution of the model and compaes esults ith Hagebe s oiginal model.

12 Retiement Accounts should decease ages by the same amount and thee ill not be any eallocation of okes toads sectos,, employment shaes in the coveed and the uncoveed secto should emain constant. Equation 3. shos that it is possible that the elative pice of labo ise in esponse to a eduction in the tax ate, even if ages in the complying secto do not adjust to benefits i.e. a=. Note that hen a=, complying fims absob all the cost of the egulation. The pevious analysis shos that even if okes ae homogenous, the elationship d dt does not povide any evidence on hat faction of the cost is shifted to ages. In ode to estimate this faction e need to evaluate the esponse of the elative pice of labo to capital to a change in taxes. The homogeneity assumption implies that labo supply is completely elastic beteen sectos and theefoe, complying fims ae not able to shift pue taxes to ages. If okes ae homogenous then the age diffeential beteen the coveed and uncoveed secto does not depend on the tax levied to fims. The homogenous model implies that hen benefits impove, ages in the coveed secto to fall by the same popotion and employment shaes emain constant The homogeneity assumption equies that thee ae compaable jobs in each secto fo evey oke in the economy o else that complying and non-complying fims ae andomly allocated acoss sectos. Because the cost of avoiding egulatoy agencies vaies among economic sectos, in equilibium thee ae economic sectos that ae typically coveed by social secuity as ell as economic sectos ithout coveage 7. As a esult, a oke s poductivity in the coveed secto may not be equal to his poductivity in the uncoveed secto. In the next section I extend the pevious model to deive the implications hen the coveed and uncoveed 7 Coveage in lage manufactuing fims is about 85% hile coveage in non-tadable sectos is about 28%. 2

13 secto demand diffeent types of skills and okes select into the taxed secto based on pefeence fo coveage but also based on thei compaative advantage. 3.2 Heteogeneous Wokes Each agent is endoed ith a pai of secto specific efficiency units of labo q i qi and. That is, an agent i supplies q i efficiency units of labo if he oks in the compliance secto o q i efficiency units of labo if he oks in the non-compliance secto. It is assumed that the distibution of secto specific efficiency units is given. q i q i The agent ith endoment, selects into the secto that yields him the highe benefits, but he can only ok at one secto at a time. Benefits in secto include, in addition to q i q i eanings, benefits coveed by social secuity. An agent ith endoment, ill ok in the coveed secto if benefits in Secto ae highe than benefits in Secto. Let j be the pice of secto specific efficiency units in secto j, an agent ill supply labo in the coveed secto if: qi at2 qi Whee: Numbe of okes employed at each secto is given by: N N q at2 = Nf q, q = Nf q, q q at2 dq dq dq dq 3

14 f q, q is the joint density of secto specific skills and, N is numbe of agents in the economy. Labo supply measued in efficiency units in each secto is given by: q at2 L = Nq f q, q dqdq 3.2 L = Nq f q, q q at2 dq dq 3.3 Equation 3.4 and 3.5 epesent the diffeentials of the labo supply evaluated at t 2 =: dl dl = 2 adt2 N q f A, q dq 3.4 = adt2 N qq f A, q dq 3.5 Whee A = q at2 Note that f A, q N is the numbe of okes ith specific capital q that ae indiffeent beteen sectos because total benefits ae equal in both sectos. Labo supply is not completely elastic because okes that have a significant compaative advantage in one secto ill not 4

15 espond to small changes in the elative pice of secto specific skills. Labo supply elasticity is highe the lage is the coelation beteen secto specific skills. To undestand the diection of the compositional bias note that labo maket equilibium is achieved hen no one is bette off sitching sectos. Equilibium is eached hen the ate at hich efficiency units in Secto ae conveted to efficiency units in Secto equals the elative pice. Identity holds fo maginal okes. Benefits fom sitching to Individual Retiement Accounts ae popotional to q, the ne etiement system ill attact okes employed in the uncoveed secto that have the highest atios of q i qi among uncoveed okes, but loe atio of qi qi among coveed okes. Theefoe, the diffeence in aveage efficiency units is educed. Note that it is not longe tue that dl = dl as it is the case hen okes ae homogenous in skills. Equation 3.8 shos that the ate at ith labo in Secto tansfoms into labo in Secto is equal to the convesion ate fo individuals ho ae at the magin. qq f A, q dq dl P q A 3.6 = β, dl 2 P q A q f A, q dq It ill be useful to define the labo supply elasticity beteen the coveed and the uncoveed secto: ln L = γ ln L 3.7 Accoding to Equations 3.6 and 3.8, the labo supply elasticity is given by: 5

16 2, q qq γ = f A, q Eq Eq Let j be the pice fo secto specific skill in secto j and be the use cost of capital. in each secto: Assuming constant etuns to scale in L j and K j, 3.2 and 3.3 epesent the cost functions = 3.8 C,, X c, t X, X = c, 3.9 C, X The solution of the model gives the folloing elationships 8 : d ln = [ η k g η η ] dt [ λγ η η γ ] adt D Whee η σ θ ε ε θ j = is the labo elasticity in secto j j lj jj D = η k g λγ η η γ kk lj Efficiency losses aise hen taxes distots the effective compaative advantage beteen sectos, focing okes to move fom the secto hee they ae moe poductive to a secto 8 Appendix B deives the solution of the model and compaes esults ith Hagebe s oiginal model. 6

17 hee they ae less poductive. If thee ae not changes in t o taxes used to finance public goods, e can decompose the Equation 3.2 in to tems: d ln η k g η η = a dt η k g λγ η η γ 2 adt The second tem in equation 3.2 coesponds to pass tough of benefits on ages. If thee ee no equilibium effects, then ages in the coveed secto ill decease by the same popotion to ne benefits. The fist tem coesponds to the incidence of the faction of the tax that is not elated to benefits. In othe ods, it coesponds to the incidence of pue taxes. The degee of shifting inceases ith demand elasticity in the coveed secto and deceases ith demand elasticity in the uncoveed secto and supply elasticity. 4 Evidence fom Diffeences-in-Diffeences Methods Gube 994 uses the Diffeences-in-Diffeences-in-Diffeences DDD estimato to detemine the faction of the cost of benefits that it shifted to ages. He compaes age diffeentials beteen contol and teatment goups beteen expeimental states hee the povision as mandated and states hee it as not. To follo Gube s 994 appoach, I ould have to compae the age diffeential beteen the coveed and uncoveed sectos fo young okes to the age diffeential fo old okes. Diffeences in taxes ill affect the age diffeential beteen the coveed and uncoveed okes, but ne benefits ill affect only the age diffeential among young okes. To calculate the faction of benefits that is shifted to 7

18 ages, I compae the DDD estimato ith fim s mandated contibutions to the Individual Retiement Accounts. The DDD equies seveal conditions to identify the effect of impoved benefits on ages. Fist, aggegate shocks have common effects on both sectos. Second, e ae able to contol fo changes in the composition of okes acoss sectos by conditioning eanings to vaiables e obseve. Thid, labo supply to the coveed secto has no positive slope, so changes in elative pices measue exactly the shift of the due to change in benefits. In othe ods, labo supply beteen sectos is completely elastic. 4. Data The empiical evidence is based on data fom the ENEU Encuesta Nacional de Empleo Ubano. The ENEU is a quately household suvey that coves the lagest uban aeas in Mexico. This suvey coves appoximately 6 pecent of uban population and 92 pecent of the cities ith populations geate than,. The sample includes non-agicultual pivate secto employees fom 6 to 65 yeas old, ho oked moe than 3 hous duing the eek pevious to the intevie. The sample size is appoximately 6, individuals fo each quate fom 994 to Compaison Goups 4.2. Coveed and Uncoveed Sectos The most extensive definition of the non-complying o uncoveed secto includes all employees that have a job ithout labo potection and the self-employed. Appoximately 5 pecent of the Mexican labo foce falls into to this categoy. The incidence of non-compliance is still high 9 The suvey stats in 987, but I esticted the sample to the yeas since the question about contactual fom is added until the fouth quate of 999. In addition, occupations and economic sectos ae coded diffeently 8

19 even if the self-employed ae excluded fom the sample. About 37 pecent of full time pivate secto okes belong to this moe nao definition of the non-complying secto. I estict the sample to pivate secto employees, and then I divide the sample accoding to the degee of potection eceived fom the fims they ok. The highest fom of compliance constitutes jobs that povide both social secuity and seveance payment coveage SSSP. This goup includes okes coveed by social secuity that eithe have a pemanent contact o do not have a itten contact. The second goup constitutes employees ho have social secuity coveage but ae hied unde a tempoay contact so that the seveance payment egulation does not apply to them SS. The last goup, hich I define as the ''uncoveed secto is compised of employees ho do have neithe social secuity no seveance payment potection. Table shos the sample aveages accoding to the goup they belong. Wokes in the coveed and uncoveed secto ae compaable in sex, age and expeience, but okes in the coveed secto have on aveage moe yeas of schooling. The most significant diffeence beteen okes in the complying and non-complying secto is the distibution of okes acoss fim sizes. About 83% of okes in the uncoveed secto ok in a fim that has fee than 6 employees, compaed to only 22% of the okes in I excluded self-employed fom the sample fo seveal easons. Fist, individuals become self employed to avoid othe egulations as ell. Maloney 998 shos that mico-entepises avoid fedeal and state teasuy egulation in addition to labo egulation. Second, eanings can only be computed ith lage measuement eo. The suvey epots the total income, hich includes in addition to eanings, the etun fo capital investment and may include eanings of the unpaid labo of elatives. Individuals ithout a itten contact ae included in this goup because the Conciliation Boad assumes the existence of a pemanent contact heneve thee is no itten contact, as long as the employee can pove that an employment elationship exists. Once a fim egistes a oke in the social secuity administation, it gives the employee the necessay documents to demand all benefits of a pemanent contact at the Conciliation Boad. Theefoe, an effective ay to avoid seveance egulations is to offe a tempoay contact athe than not offeing a itten contact. 9

20 the coveed secto ok in a fim of ith fee than 6 employees. One explanation is that fims deciding not to comply must estict thei size in ode to avoid detection by the egulatoy agencies. The evidence suggests that fims that comply ae not andomly distibuted acoss sectos aising the possibility of poductivity diffeential in both sectos. Most of okes employed in the coveed secto have seveance payment benefits in addition to Social Secuity benefits. Wokes ith Social Secuity benefits but ithout seveance payment benefits constitute an ideal contol goup to analyze the effect of the efom. Hoeve, Social Secuity and seveance payment benefits ae bundled 2, and theefoe only a small faction of okes in the coveed secto have a tempoay labo contact. In addition, it is difficult to distinguish hethe a oke ith a tempoay contact is on a tial peiod o if he ageed not to have seveance payment coveage 3. Resticting the contol goup to tempoay okes ill implicitly estict the contol goup to okes ith lo tenue. I included all okes employed in the coveed secto in the contol goup to avoid compaison among goups of okes ith systematic diffeences in tenue levels. Table shos okes in the coveed secto ith seveance payment and okes ithout seveance payment coveage have simila skill and demogaphic chaacteistics. Futhemoe, they have simila occupational stuctue and skill distibution. Wokes employed in the coveed ae not less likely to have outside coveage than okes employed in the uncoveed secto. The vaiable outside coveage is a dummy equal to one if the individual lives in a household hee thee is somebody else that is coveed by a health plan and he is eligible to eceive medical teatment fom this plan 4. 2 Once a fim egistes a oke in the Social Secuity Administation, it is difficult not to comply ith the seveance payment egulation as ell. 3 Tial peiod contacts ae pohibited but extensively used by complying fims. 4 The citeia fo coveage ithin the household include public secto okes. Public secto okes eceive simila medical benefits than Social Secuity and ae also extended to the immediate family of the oke. 2

21 Diffeences in education ae moe evident hen e compae the distibution of yeas of schooling. The faction of okes in the uncoveed secto ith 6 o fee yeas of education is almost tice the faction than in the SSSP secto. Only 8 pecent of the uncoveed secto okes have moe than 2 yeas of education compaed to 2 pecent of SSSP okes. The fact that the complying secto is moe skill intensive does not peclude us to compae ages unless okes sot accoding to skill. Table 2 shos the distibution accoding to skill and age goups. Wokes ith highe schooling attainment ae moe likely to ok in the coveed secto. Hoeve, schooling does not detemine hich secto a oke is going to be employed. Moe than one thid of okes ith fee than 6 yeas of schooling ae employed in the coveed secto. At the same time, moe than one thid of okes ith college education ae employed in the uncoveed secto. The evidence shos that Social Secuity egulation does not impact all economic sectos equally, but thee is an impotant vaiation on the non-compliance incidence acoss economic sectos. Table 3 shos coveage by economic secto. The sample includes only male okes ith 7 to 9 yeas of education in ode to contol fo diffeences in the composition of okes acoss economic sectos. The incidence of non-compliance is tice as high in the sevice secto than in the manufactuing secto, this is elated to the fact that the scope of economies of scale is highe manufactuing secto. The incidence of non-compliance is paticulaly high in sectos ith seasonal demand fluctuations such as hotels, estauants and constuction. Supisingly, the shae of tempoay okes in the secto composed of hotels and estauants is loe than the aveage. A possible explanation could be that the to diffeent foms of non-compliance, Social Secuity and SP, complement each othe. Fo example, it is easie to avoid the SP egulation if okes ae not 2

22 egisteed in the Social Secuity, and at the same time is easie to avoid the Social Secuity tax if the employees ae eplaced constantly. To conclude, okes in the coveed secto ae compaable to okes in the uncoveed secto but fims ae not. Fims in the coveed secto ae skill intensive, ae lage and ae moe likely to be poducing goods in the manufactuing secto than in the sevice secto. The decision to choose a job ith benefits is linked to the decision on hich economic secto to be employed Teatment Goup and Contol Goups The 997 Social Secuity efom inceased the contibutions to the individual etiement accounts and educed the tax ate used to finance public pogams. The effect of this tax efom on ages is ambiguous. On one hand, a loe Social Secuity tax ill incease ages if labo supply is not pefectly elastic. But on the othe hand, a Social Secuity job becomes moe attactive and thus the labo supply in the coveed secto should incease and dive ages paid by complying fims don. Hoeve e can sepaate these effects by compaing age esponses of demogaphic goups ho ee affected diffeently by the efom. The efom has distinctive cohot effects. Wokes olde than 5 ae moe likely to etie unde the old egime ules and theefoe, have no diect benefits fom the pivatization of the etiement pension. Fo this goup of okes, the Refom in 997 implied a eduction in the Social Secuity tax ith no change in the benefits. 4.3 Diffeences-in-Diffeences Estimato I divided the sample beteen old and young okes to evaluate the impact of the change of the egulation on each demogaphic goup. I test fo stuctual change in the age diffeential beteen the taxed and the untaxed sectos tend. 22

23 Since benefits fom the substitution of the Pay-As-You-Go to the Individual Retiement Accounts inceases ith schooling, I evaluate the impact of the efom at thee diffeent skill levels: okes ith less than 9 yeas of schooling, 2 okes that have beteen 9 and 2 yeas of schooling, and 3 okes that have moe than 2 yeas of schooling. The egession includes skill specific explanatoy vaiables, egional and industy dummies to isolate changes in the diffeential poduced by changes in the composition of okes and fims acoss sectos, t. The egession also includes skill-time inteaction vaiables to isolate changes in the diffeential poduced by vaiations in the skill pemium. The diffeential could be diven by the fact that ages old and young okes have a distinctive esponse to local demand shocks. To contol fo deviations in the young-old diffeential caused by shot-tem fluctuations in the labo maket I included employment goth ates by egion. Equation 4.3 shos the egession equation. I estimate the folloing egession fo young and old okes sepaately. To contol fo countefactual tends in the age diffeential, e identify the impact of the age diffeential by changes in the tend of the elative age that at the time of the efom. Wij = λ' X i n β s n n in β s β s n4 in n in d i β exp s i n5 in β s exp 2 i d * time β i ns2 in i β s s n6 in s3 in * time d * afte i i i m * time γ i i i i m T n α z i in 4.3 Whee: Wij is the log houly age of individual i in secto j. s in n=,2,3 is a dummy vaiable equal to if individual i belongs to skill level n. d i = is the individual oks at the taxed secto. exp i is potential labo maket expeience age-schooling yeas-6. 23

24 i im m =... is a dummy vaiable equal to if individual i oks in industy m z ip p =...5 is a dummy vaiable equal to if individual i lives in egion p. afte i is a dummy equal to one if the age is obseved afte June 997. X i is a set of vaiables that contol fo egional-time demand shocks. T is equal to the numbe of quately obsevations befoe the ne legislation as implemented in July 997. The effect of the efom on the age diffeential is given by the coefficients β 6, β 26 and β 36. These coefficients measue time tend change on the age diffeential fo peiods afte the efom. Table 4 shos the OLS estimates of β s6 to test if the tend of the taxed-untaxed secto diffeential changed upon the efom. Estimates ae shon fo diffeent demogaphic and skill goups. The sample is divided beteen young okes, those ho ill etie unde the ne egime, and old okes, those ho ill etie unde the old egimen. The t statistics ae consistent ith a change in the tend of the taxed-untaxed age diffeential in the sample of young okes in all specifications, hile it is consistent ith no change in the old okes taxed-untaxed secto age diffeential. The estimates on the fist column coespond to the specification that includes a single time tend fo all skill goups. A diffeent time tend fo each skill is specified in the second column. The thid column includes employment goth in the egion to contol fo distinctive cohot esponse to local demand shocks. I constucted the DDD estimato by subtacting s 6 young s 6 old β β. Table 5 compaes the DDD estimato ith incemental benefits fom substituting Pay-As-You-Go fo Individual 24

25 Retiement Accounts. The DDD estimato shos ages fo those ho benefited fom the efom fell by only 2.4 pecent, hich coesponds to 29 pecent of incemental benefits. 5 Econometic Geneal Equilibium Model 5. Pices of secto specific skills The amount of efficiency units of individual i in secto j is detemined by obseved individual chaacteistics Xi and a secto specific andom component Uij. Assuming that the function that maps skills into secto specific efficiency units is log linea in X i and U ij, Equation 6. epesents okes i potential supply of efficiency units to secto j. ln q i j = β j X i U ij 5. Equation 6.2 epesents eanings in secto j at time t. W ij t = ijt jt q ij ln W = ln ln q jt ij 5.2 Whee jt is the equilibium pice of efficiency units of labo in secto j The log age of individual i on secto j at time t is given by: ln W ijt = ln jt β j X i uij

26 In addition to eanings, okes employed in coveed secto eceive mandated social secuity benefits. Valuation of benefits vaies acoss individuals accoding to function a Zi. Whee: Z i =[R,X] is a vecto of obseved andom vaiables R is a vecto of obseved andom vaiables that detemines paticipation in the Social Secuity secto, but does not detemine eanings. R includes compliance ate in the city hee individuals lives, family size and yeas upon etiement. q An agent ith endoment i q i, ill ok in the coveed secto if: Define q i a z t2 q Di * = ln qi ln qi lnt ln a z t2 ln t 5.4 Whee: U d is a andom component on the pefeence fo coveage. Note that D* can be decomposed into to components: D i* = G Zi Uid 5.5 Whee: U id = U U i i D i if D * > = i

27 Assume that: i U,U ae unobseved andom vaiables ith mean zeo. ii U,U ae independent of R, X iii G Z is a non-degeneate andom vaiable conditional on X A useful tansfomation poposed by Heckman and Vytlacil 999 is to assume that U d ~Unif[,], thee is no loss of geneality if F Ud is stictly monotonic. In this case Gz=P[D= Z=z], since P[D= Z=z]=F Ud GZ. Given this tansfomation, Equation 6.7 epesents the conditional expectations of U and U 5 : E[ U E[ U E[ U E[ U P Z, X, D = ] = E[ U P Z, X, D = ] = E[ U P Z, X, D = ] = E[ U P Z, X, D = ] = E[ U U d U U d d U < P Z] < P Z] d P Z] P Z] 5.7 Eanings in Secto j ae composed by the sum of to functions: a knon linea function of individual chaacteistics X i, and by an unknon function of PZ i. E W E W t t X, P Z, D = = X X, P Z, D = = X it ' β K it t ' β K P Z t P Z 5.8 Whee: K ijt is the conditional expectation of Ui given that a oke belongs to secto j. K E U Z, D = j K P Z ijt i = ijt 5 See Heckman and Robb 986 fo deivation of this epesentation, also Heckman, Ichimua and Todd

28 I follo Heckman,. Ichimua and Todd 998 to estimate the patial linea egession model in Equation The estimation has to stages. In the fist stage lnw iit and each element of X it ae egessed against the estimated pobability P. P Z is estimated by logit egession. The vaiables used in the logit egession ae skill and skill specific time tends, expeience and its squae, city and industy dummies. It also includes yeas upon etiement, a dummy fo maied, the ate of egional employment goth and the city compliance ate 7. I estimate by local linea egession E W P Z, D = and E X P Z, D = using the sample of okes employed in the coveed secto 8. In the same ay, I estimate E W P Z, D = and E X P Z, D = using the sample of okes employed in the uncoveed secto. X On the second stage, I use the esiduals lnw E[lnW P Z, D j] and Z i i ijt ij it = E[ X P Z, D j] to constuct the OLS model epesented in Equation 6.9 to obtain it it it = unbiased estimates of β j. W ijt E W P, D = [ X E[ X P, D ]' β υ 5.9 tjt i i ti it it it j it Whee: E υ P, D = i t it ti 6 See Robinson 988 fo a detailed desciption of the patially linea model as ell as the asymptotic popeties of the estimatos. 7 See Appendix C fo details on the estimation of PZ. 8 See Heckman, Ichimua and Todd 998 fo details and Fan993 fo the distibution theoy of the local linea egession estimato. 28

29 Residuals fom the second stage fom a function of the constant tem and the conditional expectation of the eo tem U j. The late is a function of PZ. W X β = ln β K P Z 5. ijt it j jt oj jj it To identify ln β fom K P Z, e need to evaluate the function jt j jjt it β K P Z at values of PZ it hee K P Z =. Note that: j jj it jjt it E d U X, P Z =, D = = E U U < = E U = Altenatively, E d U X, P Z =, D = = E U U > = E U = The estimates of βoj ln jt coespond to the value of E[lnWijt X it β j P Z, D = ]. To identify o t β ln, I evaluated the estimated function K P at PZ it =.5. Ideally, I ould like to evaluate the conditional expectation oo Z it at PZ it =, but thee ae fe obsevations of okes in the non-complying secto hee PZ< To identify β o ln t, I evaluated the estimated function K P Z at t it PZ it =.975. Table 6 eplicates the calculations shon in Table 5 using pices of specific labo units instead of obseved ages. I compaed changes in the tend of the age diffeential beteen the coveed and uncoveed sectos fo young okes ith changes in the tend in the age 9 Although thee is enough obsevations in the cells ee PZ appoaches to one, thee is fe obsevations in the intevals hee PZ appoaches to zeo even fo the sample that includes only okes at the non-complying secto. 29

30 diffeential fo old okes. The estimates of the shifting ae highe once e contol fo changes in the composition of okes ithin each secto. The Diffeences-in-Diffeences estimato is: t ot E Ut dit = E Ut dit = The change in the age diffeential afte the efom is d t d t = [ E U d = E U d = E U d = E U d = ] t it t ot t t it ot t it t it 6.6 The fist to components of equation 6.6 coespond to the change in the equilibium age diffeential. The tems inside the backets is the change in the obseved age diffeential caused by a change in the composition of okes acoss sectos. Table 6 confims the pedicted diection of the bias, the Diffeence-in-Diffeence coected fo selection implies that ages fo young okes deceased by 6 pecent, an estimate that is close to the eduction of the net tax ated poduced by the substitution to Individual Retiement Accounts. Hoeve, the estimates not povide definite estimates of the shifting of taxes and benefits on ages. Estimates shon in Table 6 do not take into account the geneal equilibium effects on the elative pices of labo hen the ate at hich labo supply shifts fom one secto to anothe is not equal to minus one. 5.2 Labo Supply Elasticity Because egulation is not neutal acoss economic sectos, employment oppotunities in the uncoveed secto vay accoding okes skills. The individual selection model shos that an incease in the elative age in the coveed secto ill attact fist okes that ae indiffeent 3

31 beteen sectos at the pevious equilibium pices. A featue of selection models is that labo shifting beteen sectos depends on the esponse of maginal okes to changes in skill pices. Theefoe, labo supply elasticity fom Secto to Secto is detemined by the distibution paametes coesponding to maginal okes Accoding to the individual selection model, the labo supply elasticity is given by: 2, q qq γ = f A, q Eq Eq To estimate γ e only need to ecove the joint distibution of q i and q i at the points hee q = q at2, o q = q at2. Folloing Heckman and Honoe 99 identification theoem hen panel data on aggegate eanings is available and the distibution of skills does not change ith time 2, I estimated the joint distibution of q i and q i at this point. Note that if at2 q i qi ' at2 q i then: F q, q = P qi < q, qi2 < q2 = P qi F q close to '. ' at < q, q < q, at < q < q, qi io 2 q i 2 = P max q q q,max q, q, i, i i ' at i 2 at2 The density q,q q q f can be appoximated by F ' q, q F q, q hen is 2 Heckman and Honoe 99 Theoem 3

32 Using estimates of ln jt, I computed ln q i by subtacting ln t to Wi t ln to okes employed in the coveed secto. I estimated ln q i by subtacting employed in the coveed secto. t ln to ln Wi t to okes The efeence peiod used is 997: and 997:2 to obtain the elasticity coesponding to the date at hich the efom took place. In the efeence peiod d =.4 and t 2 is equal to zeo. The distibution of = max{ q i q } and Z = max{ q i, q '} Z, i ' i 2 is estimated using the Epanechnikov kenel. The bandidth as chosen folloing Silveman 986 optimal bandidth ule 22. Estimates of the functions γ using q,q f ae. When the equilibium pice atio is geate than, highe benefits in the coveed secto incease the faction of okes at the magin, and theefoe, supply is moe elastic. 5.3 Labo Demand Elasticities Assuming labo demand fo secto specific efficiency units is log linea in eal pices, Equation 6. epesents the demand of secto specific efficiency units in Secto j: j j jt j Pkt ln L jt = η ηll ln η k ln 5. Pjt k Pjt 2 Whee Z=q if the individual selects into the coveed secto and Z = q if the individual oks in the uncoveed secto. 22. h=akn -/6. Whee AK=2.4 fo a multivaiate Epanechnikov kenel of dimension 2. 32

33 Whee: P kt is the pice fo intemediate input k. Includes index pice fo enegy, intemediate inputs in the secto, use cost of capital. To estimate Equation 5. I follo Heckman and Sedlacek 985. They estimate demand functions fo unmeasued tasks that ae secto specific using sectoal age bills in the manufactuing and sevices sectos. They obseve that total ages paid in each Secto j ae equal L jt times lnπ jt.. Substituting total aged paid in equation 6. gives: ln ln ln P η 5.2 j j j j j kt Wages Paid in Secto j = o β oj ηll ηll η k ln Pjt k ln Pjt Table 7 shos the estimates of demand elasticities. Wage bills and pices ae not aggegated in coveed and uncoveed sectos, instead these vaiables ae aggegated by industies. I selected industies that ae epesentative of the coveed and uncoveed sectos espectively to estimate. Fo example, data fo the coveed secto comes fom the Encuesta Industial Mensual. The Encuesta Industial Mensual is a fim based suvey that coves the lagest fims in the manufactuing secto, hee compliance is the highest. Data on ages paid in the uncoveed secto comes fom INEGI calculations based on the Encuesta Comecial Mensual. The Encuesta Comecial Mensual is an establishment-based suvey that coves small etailes and estauants. These industies have high non-compliance incidence. Pices of othe factos include: enegy pice index, investment index, intemediate good pice index and the net ate of etun of commecial bonds at 28 days Data on pices and inteest ates comes fom Cuadenos de Infomacion Economica, Banco de Mexico, vaious issues. 33

34 5.4 What Faction of the Tax is Shifted to Wages? The degee of shifting depend on the folloing paametes: the elative demand elasticities beteen coveed and uncoveed secto, as ell the joint distibution of. q i and q i coesponding to maginal okes, the coelation of benefits to taxes. Equation 3.2 sepaates the effect the egulation efom into to components: changes in the cost of poviding Social Secuity and changes in the benefits eceived by okes employed in the coveed secto. The fist tem is the shifting of the cost of poviding Social Secuity dt on ages.. The second tem detemines ho this diffeential is affected by changes in benefits. Table 8 shos the estimates of Equation 3.2 substituting the estimates peviously defined fo the hole sample and fo males beteen 2 and 4 yeas old. The estimates sho that inceasing the tax to finance Social Secuity pogams ile leaving benefits unchanged ill educe ages in the coveed secto by 43% of the tax incease. If the tax is not changed but benefits ae tied to contibutions at a one to one elationship, ages paid in the coveed secto ill decease by 57% of the value of benefits. Full shifting of the cost cannot be achieved unless labo supply is inelastic. The highe the elasticity of supply into the coveed secto the loe is the shifting of the tax in fom of loe ages. On the contay, highe elasticity of supply esults in lage shifting of benefits to ages. The model as specified to evaluate the effect of diveting pat of the tax to Individual Retiement Accounts. I defined benefits to be popotional to q to esemble deposits on the Individual Retiement Accounts. An incease in the faction of the age that fims deposit into the Individual Retiement Accounts ill attact okes employed in the coveed secto ith highe q q o atios. This ill ceate an excess of supply in Secto elative to Secto, diving the age diffeential don. 34

35 Table 6 compaes Diffeences-in-Diffeences estimatos ith estimates pesented in Table 7. Diffeences-in-Diffeences estimatos bias donad the value of shifting. Based on the estimates obtained in the Diffeences-in-Diffeences estimato and the assumptions that suppot these methods, homogenous okes, benefits can only be tansfeed to ages in 29 pecent. The Diffeences-in-Diffeences estimato is consistent only if okes ae homogenous in skills and tastes and theefoe labo supply is completely elastic. In this case, accoding to the homogenous agents model thee must be full shifting of benefits to ages but no shifting of pue labo taxes. The diffeence beteen pedicted and obseved shifting is diven by diffeences in benefits of Investment Retiement Accounts compaed to Pay-As-You-Go benefits. Diffeences-in-Diffeences estimatos povide an inaccuate measue of the incidence of the egulation on ages. To illustate this point, I computed the incemental benefits fom sitching fom Pay-As-You-Go to Individual Retiement Accounts fo the aveage oke and compaed this figue ith the estimates implied by Diffeences-in-Diffeences and the estimates based on the paametes pedicted by the model. While sitching fom Pay-As-You-Go to Individual Retiement Accounts implies a eduction in the aveage net tax ate of 7 to 9 pp, Diffeences-in-Diffeences estimates imply a eduction of only 2.4 pp hile the model implies a eduction of pp See Table 9. 6 Conclusions To contibutions ae pesented in this pape. Fist, it deives the fameok fo undestanding Social Secuity taxation hen thee is a secto that does not comply ith the egulation and okes self-select into the coveed secto. Second, it uses evidence on a Social Secuity efom in Mexico to compae Diffeences-in-Diffeences methods ith estimates fom the econometic geneal equilibium model. 35

36 Thee ae to impotant lessons deived fom the analysis. Fist, Social Secuity egulation distots the optimal allocation of labo and capital beteen poduction sectos. Second, evidence fom the Social Secuity efom in Mexico aises seious concens in Diffeences-in-Diffeences methods. Diffeences-in-Diffeences methods equie that the efom does not change the composition of the contol goup. Intuitively, this is a stong assumption since changes in egulations ill induce labo eallocation acoss sectos. Fist, gains fom efoms vay acoss demogaphic and skill goups. Second, social secuity taxes distot labo costs in the coveed secto elative to the uncoveed secto. When a efom contaminates the contol goup, Diffeences-in-Diffeences fail to contol fo compositional bias and geneal equilibium effects. A geneal equilibium analysis is equied to identify the effect of any labo egulation hen thee is a secto that does not comply because egulation is not neutal acoss economic sectos and because the composition of the teatment goup depends on ho benefits ae specified.. The model shos that efficiency losses aise because factos ae misallocated beteen sectos. In the case of labo, thee is a misallocation hen egulation affects the effective compaative advantage among sectos. In ode to educe this distotion is it equied that benefits in the coveed sectos to be popotional to eanings potentials. The analysis pesented in this pape assumes a given distibution of fims acoss sectos, futue ok ill benefit fom explicitly deiving fims decisions to comply. Findings pesented in this pape ill hold if the ne composition of fims acoss sectos did not sitch okes compaative advantage beteen coveed and uncoveed sectos. 36