- Email: [email protected]
The informal sector: baby or bath water? A comment
Carnegie-Rochester Conference Series on Public Policy 45 (1996) 163- 171 North-Holland
T h e i n f o r m a l sector: b a b y or b a t h water? A comment Patrick K. Asea* [,:niverstly of (Talifornza
1
Introduction
A comrnon observation in ninny devdoping cottl,~ries is thal the infornmt sector comprises a large part of economic actix ilv. llowever, there is considerable disagreement on the role of the informal s,.'ctor in the growth process. The queslion I,oayza addresses in this paper is the relalionship ',)e~ween the size of the informal sector and economi, gr,m, th. This question is part of a broader queslion that has puzzled economists and policymakers: Why do some poor nations become rich, whih' others remain poor? Several generations of economists have sought the answer to Ibis question, th,:e':.tv, our appetite for the answer I,as increased with the toni rast between the successful development of the East Asian nations over the pasl three decades and the disappoirfl ing stagnation in Africa and lnany parts of central and Latin America. As Nobel Laureate Robert I,ucas !1993~ puts it. "'The consequences for human welfare involved in queslions like th,'se arc simply staggering. Once one slarts to think about lhen~, it is hard l,~ think about anything else.'" l,oayza attempts to move us clo~;er to ~n answer t)y focusing on the role of the informal sector in the growth process. While I do not agree with his conclusions .....that the informal sector i:: "'bath wat(r'" to be l hrown out .... the author makes a valuable contrilmlioil by drawing allentiolJ to an irnportant • Prepared for the Carnegie--Rochester ('tmfi'r,,n,'e on Public Policy held in t)ittsburgh. November 10--11, 1995. ! am gratefid to Josh ('oval for cc,mments. Financial support front the UCLA Academic Senate Committee on Research is yralefully acknowledged. The usual disclaimer applies 0167-2231/96/$15.00/~ 1996 - Elsevier Science B.V. All rights reserved. PII 0167-2231 (96)00022-X
feature, of developing countries that had hitherto not. played much role in the modern debate on the sources of growth. In&'ed, this paper provides a welcCme respite from the somewhat st .nlc discussion of 3 and cr convergence that has dominated the literature on gro x~.th ' over the• past couple of years, My comments will generally follow the outline of the paper, tlaving alrc.ady commented on the importance of the issue under discussion I will next discuss the research stra,tegy and theoretical framework and then turn to the empirical analysis.: 1.1
Strategy and anatytic,zl framework
To comment on the strategy and theoretical framework, it is instructive to summarize the prevailing views on the informal sector. The traditional view--pervasive among "dirigiste" types ............is that the infimna! sector is a backward part of the e('o:ic~ay with transitory employment and meagor wages, According to t b_is view the informal sector is the consequence of market imperfections inherent to developing countries. Policy recommendations based on this view reject laissez-faire and range from prohibition of informal sector activities to a poverty-alleviatio:a orientati,m. The neoclassical view is that the informal sector represents the optimal tesponse to the prevailing economic environnlent (the demand for urban services and small-scale manufacturing). According to this view the informal sector is dynamic and absorbs e.mlepreneurml "" talent, which in turn enhances its capacity to provide competiti',;e earnings. In other words there is Vohmtary self-selection into the informal sector. An obvious implication of the neoclassical view is that there is little role for government in te;vention in the tladitional sense. Policies would be limited !:o ensuring adequate access to capital markets at competitive rates for the accumulation of physical and human capital and reform of legal and political institutions. Since tliere is no agreed-upon position on the relative merits of these two l(ws. one way to improve our understanding of the relationship between the size of the informal sector ant growth would be to proceed as follows. First., adopt, one view (say, se.lf--.s~1( ....... tlon, ' ~as a "null hypothesis." Second, develop a simple model that stresses the .... ~:1I'nypolihesls ' " and obtain empirically • "refutable predictions, Third, carry out empitlcal analysiswhich Can speak to a, causal relationship bet~ee:: the: variables under consideration, The "~mii 5ypott!esis" adopted by the ,::uthor is that the informal sector -arises fi'om :i~,Svernment-~il~duced distortion:s (excessive taxes), tte then proceeds to develop a theoretical model ConsisCent witti tha,t view, That is, .the author develops a 2;sector:endogenous growth model in which the informal sector is:assumed tO arise from a n, oppressive regulatory: system with high :(above optimal) tax:rates and an inefIicientsystem of enforcement-. The k e y :feature of the model:that :leads t o t h e emcrgenCe0f the informal sector i s ~"' "
'
164
a production technology in which tax financ,'d public services are sub.iect 1o congestion, l-'urthcrnlore, lh(' iaformal sector do(.'s no( l>ay taxes b~l~ is sltb.,ect to i)('nalt i(:s whidt are not used to i!nan(:(' public services. The )ln,
nor the very high costs of formality are necessarily the most irnporl ant determinants of size and level of formality. The point is that while the ob.served distribution of firms is clearly affected to some degree by the cost of participation, for a range of firms size may be unrelated to issues of regulatory and tax avoidance. In this context, such firms pay no taxes as a passive by-product of their small size. Levenson and Maloney point out that these firms do not choose to be small in order to avoid paying taxes. Their limited investment needs make stable property rights unimportant and personal ties may be an adequate contracting technology so that the firm will not need to seek formality along these dimensions. By incorporating the costs and benefits of participation in civic institutions within a model of firm dynamics, Levenson and Maloney conclude that neither the high rates of turnover nor the small size of firms necessar;ly reflect anything pathological about the informal sector. Although market )mperfections may be important issues, their existence is not required. Firms escape enumeration precisely because it is not cost. effective for the government to monitor the smallest, youngest, and least productive firms. In this sense, the large informal sectors observed in many developing countries may bc optimal. The research strategy Loavza adopts leads to the unsurprising conclusion that the size of the informal sector is negatively related to the growth rate. This conclusion ignores the extent to which thc informal sector may contribute to the creation of markets, increase financial resources, enhance entreprcneurship, and transform the legal, social, and econom;," institutions necessary for accumulation.
1.2
Empiricalanalysis
To evaluate the empirical analysis I will start by discussing some crucial features of the empirical methodology. Loayza uses a Multiple Indicator Multiple Cause (henceforth MIMIC~ model to estimate the size of the informal sector. This class of model exploits the fact that the causes and indicators of a latent (unobserved) variable are kn,~wn. The MIMIC model is a powerful vehicle for eslimaling lhe size of the informal sector because it allows the researcher to make statements abo,~t the fa<'tor:, inflt:encing the size and growth of the informal sector. At the sanw time it i)rovi(h:s est;mates of the impact of the informal sector on certain "indicators." The specification of the MIMIC model is as follows. The MIMIC model consists of two sets of relationships. A latent or unobserved variable I is linearly determined by a set of observable exogenous variables (causes'~. XI,
. . • ;Xk, l
__
,t
t
where IE(X. ~) = O. At the same time the unobserved variable I ddermincs
166
a set. of m observable endogenous vari.~bles (indicators), z l , . . . , =,~, Z = ¢ I +/~
~ ~ A:(O, E),
(2~
E = diag (a~ . . . . cry). The unknown parameters to be estimated are O = 1:¢. ¢ , Z, ¢~) are k + 2m + 1 in number. In Loay/~t's i,aper I is an n x I vector representing values of the unobserved informal sector; .\" repr,~ents the n x 2 matrix of observations of exogenous causes i.e., the tax burden, governn,, :at restrictions on labor markets and the efficiency of enforcement; Z represent.,, the ~, " '2 mat rix of indicators i.e., the rate of VAT (value added tax) evasion and the percent of Ilw labor force not. contributing to social security. The reduced form in terms of the observables is given by Z = I I ' X -r z,.
(3)
II,(u,ut : ' ) _- fl = i ¢ , r r ~ + v .,,.
(.1)
where
[I =
,7@'
From (1) and (2) it is apparent thai lhe model determines @ up to a scalar, Spanos (198,1). 30 see this, observe thai when
~:=
I,
~l =
rn-~
(y2
=
1
Loayza uses the most common normalization o~ = : This normalizalion constrains tile relative x ariances of th-" cause and t tw indicator ,list urbances to be constant.
To estimate the parameters O of a MIMI(' model subp'ct to a normalization condition, one must solve the two sets of equations ]I = ,~O' and ~1 = 0 ¢ ' + E uniquely fi)r O. A necessary condition for i,tentification is I
m k + .Sm(m + t ) - 2m - k) > 0. 'l'l,c log likelihood function of a .MIMI(I "qodel take,, the form
7' [logld,.t log E = cons! - .~-
)+
.
where .'S' - (I/T)(Z- X I 1 y ( Z - XII) ~2 = ~ ¢ ' + 2. Maximum likelihood estimation of the MIMIC model is concept ually straightforward, J~reskog and Golberger (191'5) . The log-likelihood function is well-defined if nonqality 167
is assumed; therefore all that is required is joint maximization of the loglikelihood function with respect to the unknown parameters. In practice, however, these computations become prohibitive as the number of causes and indicators increases. An alternative approach is provided by the EM algorithm developed by Dempster, Laird, and Rubin (1977). The EM algorithm is relatively simple to implement, and yields estimates that converge to the maximum likelihood estimates that follow from using the procedure outlined by Jfreskog and Goldberger. The EM approach is attractive because it is equipped with tests of overidentifying restrict'ons vhose number is 1
+ 1) - 2 m .
The over identifying restrictions can be tested using a likelihood ratio statistic ]
LRS(d) = T [log(det(fi) + tr(Pt-'S,) - l o g ( d e t S l ) - m], which is chi-square distributed ;',,ith d degrees of freedom. Tile over-identific~.,,ion test is extremely important because it can be ,sed to assess the appropriateness of the indicators chosen. The main advantages of the EM approach lelative to alternative methods such as the method of scoring are that it is easy to implement, free of computational difficulties, and "rough" parameter estimates are obtained fairly rapidly. One drawback is that it. converges linearly to a maximum. This implies that while it is able to yield parameter estimates in the region of the final estimate rapidly, it takes a while for the procedure to converge. Having discussed the specification and estimation of a MIMIC model, we are now in position to evaluate the empirical results reported by Loayza. The empirical analysis proceeds in two steps. First, he estimates the size of the informal sector; second, he ihcludes the size of the, informal sector in a Barro-Galton type OLS (ordinary least squares) growth regression, Barro (1991). From the first step, the estimated signs on the causal variables have the expected signs. How much faith can we place in these estimates ? One of the most important problems facing users of MIMIC models is model selection. In particular the modeling of the time dimension of the observed data i~ crucial. If the researcher incorrectly specifies (1), by perhaps ignoring any dynamics then such misspecification will contaminate equation (2) with adverse effects on the parameter estimates. It is therefore imperative that the researcher test for dynamic misspecification using the Durbin-Watson statistic and a Lagrange Multiplier test for k'th order autocorrelation. Loayza overlooks this important step. However, he does report several other diagnostic statistics which indirectly suggest that the model ma ')e 168
well-specified. Loayza does not report tests of the over-identifying restrictions so we cannot evaluate the appropriateness of the choice of indicators. It is comforting that the relative size of the informal sector for the countries in his sample appear to be consistent with one's intuition. In the second step of the empirical analysis, Loayza demonstrates that the size of the informal sector has a significant negative impact on real per capita GDP. How much confidence can we have in these estimates ? Unfortunately not much. Several researchers have pointed out that the Barro~-Galton regression that Loayza uses is seriously flawed, Pesaran and Smith (1995). In Barro-Galton regressions the dependent variable is a dine average of growth rates, right-hand-side variables are a combination of time averages of flows and beginning period stocks (index of education attainment beginning of period per capita GDP). There is likely to be omitted variables bias due to incorrect treatment of indi~'idual country specific effects. OLS estimates in a cross-section are consistent as long as the individual effects are uncorrelated with other right hand side variables. This is likely to be violated in most interesting cases. Finally. the assumption that the errors are uncorrelated with the covariates is likely to be wrong due to the dynamic nature of regressions. The problems associated with Barro-Galton regressions can be resolved by using Generalized Method of Moments (GMM) estimates of a dynamic panel specification, Asea (1996). tteuristically, GMM estimation of dynamic panels rt~quires two simple steps. First, di~I,,rence the growth equation to eliminate the individual effect. Second, instrument the right-hand-side variables using lagged values. This step eliminates inconsistency that arises from the potential endogeneity of the policy variables. The advantages of the GMM procedure are that it accounts for individualspecific and timespecific effects. Perhaps more iq~p.~rtantly, the GMM procedure relaxes the assumption of strict exogeneity of explanatory variables. There are several drawbacks. First, because GMM is based on timedifferencing, it reduces the "signal" variance and increases the "noise" variance of the estimates. Second, the procedure eliminates all purely cross ~-, sectional information. 2
Conclusion
So what hlive we learned ? T|w author has provided theoretical arguments and empirical evidence that suggest that economies with larger informal sectors have lower growth rates. From a theoretical standpoin; the result appears rea sotiab!e and qui!e sensible notwithstanding mv caveats on the wisdom of the author's research strat¢~v. However, from an empirical standpoint, it is iniportant to bear in mind that the estimates reported here are correlations. Even if these correlations were robust---which is an open ques169
tion because ro attempt at. robustness or sensitivily analysis was carried out by the author - - I remain unconvinced. Alternative interpretation.~ of reverse causation and spurious correlation seem likely at every turn. Extreme caution should be exercised ill interpreting tile evidence; otherwise to our dismay we may end up throwing the "baby out with the bath water."
170
References
Asea, P.K., (1996). The Miracle of (:ulture or the Culture of Miracles, unpublished manuscript, UCI,A. Ba:ro, R. J., (1991). Economic Growth in a ('ross S('(tion of ('ountries. Qtu:rtt:rl!~ Journal of Economics. 108 (2): 107-1,t-t. l)cmpster, A.P., Laird. N.M.. and Rubin, I).B., (1977). Ma"!..mm l,il:clihood From Incomplete Data via the EM Algorithm. do,trnal of lbc Royal Statistical Society, Ser. B, 39: 1-38. JSreskog, K.C. and Goldberger, A.S., (1.q75). Estimation of a Mo,H wilh Multiple Indicator.,, and Multiple ('auscs of a Single Latent Variable. ,Io~r~;,~l of lb¢ American Statistical Association, 70:631 639. l,evcnson, A. R. and Maloney, W.I'., (i996). Modeling the Informal Sector: q'hcx~rv and F.mpirical Evidence from Mexico. u l, published manu.,:cripl. Lucas, R.E...Jr., (1!)93). Making a Mirad,.. lfconomttrica. 61(2): 251 72. Pesaran, M.It. and Smith. R.. (1995). Esl treating Long-Run Relalionships from Dynamic l lelerogeneous Panels. Journal cf Eco~omttrics, 68/1): 79113. Spanos. A.. (1!)8-1). Liquidity as a l,atcm Variable An Application of the MIMIC Model. O.rford Bullttm of lfconomir., and S'lati.,t~c.,. 46(2): 125-.13.
171
T h e i n f o r m a l sector: b a b y or b a t h water? A comment Patrick K. Asea* [,:niverstly of (Talifornza
1
Introduction
A comrnon observation in ninny devdoping cottl,~ries is thal the infornmt sector comprises a large part of economic actix ilv. llowever, there is considerable disagreement on the role of the informal s,.'ctor in the growth process. The queslion I,oayza addresses in this paper is the relalionship ',)e~ween the size of the informal sector and economi, gr,m, th. This question is part of a broader queslion that has puzzled economists and policymakers: Why do some poor nations become rich, whih' others remain poor? Several generations of economists have sought the answer to Ibis question, th,:e':.tv, our appetite for the answer I,as increased with the toni rast between the successful development of the East Asian nations over the pasl three decades and the disappoirfl ing stagnation in Africa and lnany parts of central and Latin America. As Nobel Laureate Robert I,ucas !1993~ puts it. "'The consequences for human welfare involved in queslions like th,'se arc simply staggering. Once one slarts to think about lhen~, it is hard l,~ think about anything else.'" l,oayza attempts to move us clo~;er to ~n answer t)y focusing on the role of the informal sector in the growth process. While I do not agree with his conclusions .....that the informal sector i:: "'bath wat(r'" to be l hrown out .... the author makes a valuable contrilmlioil by drawing allentiolJ to an irnportant • Prepared for the Carnegie--Rochester ('tmfi'r,,n,'e on Public Policy held in t)ittsburgh. November 10--11, 1995. ! am gratefid to Josh ('oval for cc,mments. Financial support front the UCLA Academic Senate Committee on Research is yralefully acknowledged. The usual disclaimer applies 0167-2231/96/$15.00/~ 1996 - Elsevier Science B.V. All rights reserved. PII 0167-2231 (96)00022-X
feature, of developing countries that had hitherto not. played much role in the modern debate on the sources of growth. In&'ed, this paper provides a welcCme respite from the somewhat st .nlc discussion of 3 and cr convergence that has dominated the literature on gro x~.th ' over the• past couple of years, My comments will generally follow the outline of the paper, tlaving alrc.ady commented on the importance of the issue under discussion I will next discuss the research stra,tegy and theoretical framework and then turn to the empirical analysis.: 1.1
Strategy and anatytic,zl framework
To comment on the strategy and theoretical framework, it is instructive to summarize the prevailing views on the informal sector. The traditional view--pervasive among "dirigiste" types ............is that the infimna! sector is a backward part of the e('o:ic~ay with transitory employment and meagor wages, According to t b_is view the informal sector is the consequence of market imperfections inherent to developing countries. Policy recommendations based on this view reject laissez-faire and range from prohibition of informal sector activities to a poverty-alleviatio:a orientati,m. The neoclassical view is that the informal sector represents the optimal tesponse to the prevailing economic environnlent (the demand for urban services and small-scale manufacturing). According to this view the informal sector is dynamic and absorbs e.mlepreneurml "" talent, which in turn enhances its capacity to provide competiti',;e earnings. In other words there is Vohmtary self-selection into the informal sector. An obvious implication of the neoclassical view is that there is little role for government in te;vention in the tladitional sense. Policies would be limited !:o ensuring adequate access to capital markets at competitive rates for the accumulation of physical and human capital and reform of legal and political institutions. Since tliere is no agreed-upon position on the relative merits of these two l(ws. one way to improve our understanding of the relationship between the size of the informal sector ant growth would be to proceed as follows. First., adopt, one view (say, se.lf--.s~1( ....... tlon, ' ~as a "null hypothesis." Second, develop a simple model that stresses the .... ~:1I'nypolihesls ' " and obtain empirically • "refutable predictions, Third, carry out empitlcal analysiswhich Can speak to a, causal relationship bet~ee:: the: variables under consideration, The "~mii 5ypott!esis" adopted by the ,::uthor is that the informal sector -arises fi'om :i~,Svernment-~il~duced distortion:s (excessive taxes), tte then proceeds to develop a theoretical model ConsisCent witti tha,t view, That is, .the author develops a 2;sector:endogenous growth model in which the informal sector is:assumed tO arise from a n, oppressive regulatory: system with high :(above optimal) tax:rates and an inefIicientsystem of enforcement-. The k e y :feature of the model:that :leads t o t h e emcrgenCe0f the informal sector i s ~"' "
'
164
a production technology in which tax financ,'d public services are sub.iect 1o congestion, l-'urthcrnlore, lh(' iaformal sector do(.'s no( l>ay taxes b~l~ is sltb.,ect to i)('nalt i(:s whidt are not used to i!nan(:(' public services. The )ln,
nor the very high costs of formality are necessarily the most irnporl ant determinants of size and level of formality. The point is that while the ob.served distribution of firms is clearly affected to some degree by the cost of participation, for a range of firms size may be unrelated to issues of regulatory and tax avoidance. In this context, such firms pay no taxes as a passive by-product of their small size. Levenson and Maloney point out that these firms do not choose to be small in order to avoid paying taxes. Their limited investment needs make stable property rights unimportant and personal ties may be an adequate contracting technology so that the firm will not need to seek formality along these dimensions. By incorporating the costs and benefits of participation in civic institutions within a model of firm dynamics, Levenson and Maloney conclude that neither the high rates of turnover nor the small size of firms necessar;ly reflect anything pathological about the informal sector. Although market )mperfections may be important issues, their existence is not required. Firms escape enumeration precisely because it is not cost. effective for the government to monitor the smallest, youngest, and least productive firms. In this sense, the large informal sectors observed in many developing countries may bc optimal. The research strategy Loavza adopts leads to the unsurprising conclusion that the size of the informal sector is negatively related to the growth rate. This conclusion ignores the extent to which thc informal sector may contribute to the creation of markets, increase financial resources, enhance entreprcneurship, and transform the legal, social, and econom;," institutions necessary for accumulation.
1.2
Empiricalanalysis
To evaluate the empirical analysis I will start by discussing some crucial features of the empirical methodology. Loayza uses a Multiple Indicator Multiple Cause (henceforth MIMIC~ model to estimate the size of the informal sector. This class of model exploits the fact that the causes and indicators of a latent (unobserved) variable are kn,~wn. The MIMIC model is a powerful vehicle for eslimaling lhe size of the informal sector because it allows the researcher to make statements abo,~t the fa<'tor:, inflt:encing the size and growth of the informal sector. At the sanw time it i)rovi(h:s est;mates of the impact of the informal sector on certain "indicators." The specification of the MIMIC model is as follows. The MIMIC model consists of two sets of relationships. A latent or unobserved variable I is linearly determined by a set of observable exogenous variables (causes'~. XI,
. . • ;Xk, l
__
,t
t
where IE(X. ~) = O. At the same time the unobserved variable I ddermincs
166
a set. of m observable endogenous vari.~bles (indicators), z l , . . . , =,~, Z = ¢ I +/~
~ ~ A:(O, E),
(2~
E = diag (a~ . . . . cry). The unknown parameters to be estimated are O = 1:¢. ¢ , Z, ¢~) are k + 2m + 1 in number. In Loay/~t's i,aper I is an n x I vector representing values of the unobserved informal sector; .\" repr,~ents the n x 2 matrix of observations of exogenous causes i.e., the tax burden, governn,, :at restrictions on labor markets and the efficiency of enforcement; Z represent.,, the ~, " '2 mat rix of indicators i.e., the rate of VAT (value added tax) evasion and the percent of Ilw labor force not. contributing to social security. The reduced form in terms of the observables is given by Z = I I ' X -r z,.
(3)
II,(u,ut : ' ) _- fl = i ¢ , r r ~ + v .,,.
(.1)
where
[I =
,7@'
From (1) and (2) it is apparent thai lhe model determines @ up to a scalar, Spanos (198,1). 30 see this, observe thai when
~:=
I,
~l =
rn-~
(y2
=
1
Loayza uses the most common normalization o~ = : This normalizalion constrains tile relative x ariances of th-" cause and t tw indicator ,list urbances to be constant.
To estimate the parameters O of a MIMI(' model subp'ct to a normalization condition, one must solve the two sets of equations ]I = ,~O' and ~1 = 0 ¢ ' + E uniquely fi)r O. A necessary condition for i,tentification is I
m k + .Sm(m + t ) - 2m - k) > 0. 'l'l,c log likelihood function of a .MIMI(I "qodel take,, the form
7' [logld,.t log E = cons! - .~-
)+
.
where .'S' - (I/T)(Z- X I 1 y ( Z - XII) ~2 = ~ ¢ ' + 2. Maximum likelihood estimation of the MIMIC model is concept ually straightforward, J~reskog and Golberger (191'5) . The log-likelihood function is well-defined if nonqality 167
is assumed; therefore all that is required is joint maximization of the loglikelihood function with respect to the unknown parameters. In practice, however, these computations become prohibitive as the number of causes and indicators increases. An alternative approach is provided by the EM algorithm developed by Dempster, Laird, and Rubin (1977). The EM algorithm is relatively simple to implement, and yields estimates that converge to the maximum likelihood estimates that follow from using the procedure outlined by Jfreskog and Goldberger. The EM approach is attractive because it is equipped with tests of overidentifying restrict'ons vhose number is 1
+ 1) - 2 m .
The over identifying restrictions can be tested using a likelihood ratio statistic ]
LRS(d) = T [log(det(fi) + tr(Pt-'S,) - l o g ( d e t S l ) - m], which is chi-square distributed ;',,ith d degrees of freedom. Tile over-identific~.,,ion test is extremely important because it can be ,sed to assess the appropriateness of the indicators chosen. The main advantages of the EM approach lelative to alternative methods such as the method of scoring are that it is easy to implement, free of computational difficulties, and "rough" parameter estimates are obtained fairly rapidly. One drawback is that it. converges linearly to a maximum. This implies that while it is able to yield parameter estimates in the region of the final estimate rapidly, it takes a while for the procedure to converge. Having discussed the specification and estimation of a MIMIC model, we are now in position to evaluate the empirical results reported by Loayza. The empirical analysis proceeds in two steps. First, he estimates the size of the informal sector; second, he ihcludes the size of the, informal sector in a Barro-Galton type OLS (ordinary least squares) growth regression, Barro (1991). From the first step, the estimated signs on the causal variables have the expected signs. How much faith can we place in these estimates ? One of the most important problems facing users of MIMIC models is model selection. In particular the modeling of the time dimension of the observed data i~ crucial. If the researcher incorrectly specifies (1), by perhaps ignoring any dynamics then such misspecification will contaminate equation (2) with adverse effects on the parameter estimates. It is therefore imperative that the researcher test for dynamic misspecification using the Durbin-Watson statistic and a Lagrange Multiplier test for k'th order autocorrelation. Loayza overlooks this important step. However, he does report several other diagnostic statistics which indirectly suggest that the model ma ')e 168
well-specified. Loayza does not report tests of the over-identifying restrictions so we cannot evaluate the appropriateness of the choice of indicators. It is comforting that the relative size of the informal sector for the countries in his sample appear to be consistent with one's intuition. In the second step of the empirical analysis, Loayza demonstrates that the size of the informal sector has a significant negative impact on real per capita GDP. How much confidence can we have in these estimates ? Unfortunately not much. Several researchers have pointed out that the Barro~-Galton regression that Loayza uses is seriously flawed, Pesaran and Smith (1995). In Barro-Galton regressions the dependent variable is a dine average of growth rates, right-hand-side variables are a combination of time averages of flows and beginning period stocks (index of education attainment beginning of period per capita GDP). There is likely to be omitted variables bias due to incorrect treatment of indi~'idual country specific effects. OLS estimates in a cross-section are consistent as long as the individual effects are uncorrelated with other right hand side variables. This is likely to be violated in most interesting cases. Finally. the assumption that the errors are uncorrelated with the covariates is likely to be wrong due to the dynamic nature of regressions. The problems associated with Barro-Galton regressions can be resolved by using Generalized Method of Moments (GMM) estimates of a dynamic panel specification, Asea (1996). tteuristically, GMM estimation of dynamic panels rt~quires two simple steps. First, di~I,,rence the growth equation to eliminate the individual effect. Second, instrument the right-hand-side variables using lagged values. This step eliminates inconsistency that arises from the potential endogeneity of the policy variables. The advantages of the GMM procedure are that it accounts for individualspecific and timespecific effects. Perhaps more iq~p.~rtantly, the GMM procedure relaxes the assumption of strict exogeneity of explanatory variables. There are several drawbacks. First, because GMM is based on timedifferencing, it reduces the "signal" variance and increases the "noise" variance of the estimates. Second, the procedure eliminates all purely cross ~-, sectional information. 2
Conclusion
So what hlive we learned ? T|w author has provided theoretical arguments and empirical evidence that suggest that economies with larger informal sectors have lower growth rates. From a theoretical standpoin; the result appears rea sotiab!e and qui!e sensible notwithstanding mv caveats on the wisdom of the author's research strat¢~v. However, from an empirical standpoint, it is iniportant to bear in mind that the estimates reported here are correlations. Even if these correlations were robust---which is an open ques169
tion because ro attempt at. robustness or sensitivily analysis was carried out by the author - - I remain unconvinced. Alternative interpretation.~ of reverse causation and spurious correlation seem likely at every turn. Extreme caution should be exercised ill interpreting tile evidence; otherwise to our dismay we may end up throwing the "baby out with the bath water."
170
References
Asea, P.K., (1996). The Miracle of (:ulture or the Culture of Miracles, unpublished manuscript, UCI,A. Ba:ro, R. J., (1991). Economic Growth in a ('ross S('(tion of ('ountries. Qtu:rtt:rl!~ Journal of Economics. 108 (2): 107-1,t-t. l)cmpster, A.P., Laird. N.M.. and Rubin, I).B., (1977). Ma"!..mm l,il:clihood From Incomplete Data via the EM Algorithm. do,trnal of lbc Royal Statistical Society, Ser. B, 39: 1-38. JSreskog, K.C. and Goldberger, A.S., (1.q75). Estimation of a Mo,H wilh Multiple Indicator.,, and Multiple ('auscs of a Single Latent Variable. ,Io~r~;,~l of lb¢ American Statistical Association, 70:631 639. l,evcnson, A. R. and Maloney, W.I'., (i996). Modeling the Informal Sector: q'hcx~rv and F.mpirical Evidence from Mexico. u l, published manu.,:cripl. Lucas, R.E...Jr., (1!)93). Making a Mirad,.. lfconomttrica. 61(2): 251 72. Pesaran, M.It. and Smith. R.. (1995). Esl treating Long-Run Relalionships from Dynamic l lelerogeneous Panels. Journal cf Eco~omttrics, 68/1): 79113. Spanos. A.. (1!)8-1). Liquidity as a l,atcm Variable An Application of the MIMIC Model. O.rford Bullttm of lfconomir., and S'lati.,t~c.,. 46(2): 125-.13.
171