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Abstract

http://archive-ouverte.unige.ch/unige:25568


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"Econometric Modeling of Informal Employmentin Latin-American Countries"

Thèse présentée à la Faculté des Sciences Économiques et Sociales de

l’Université de Genève

par Jorge Elías Dávalos Chacón

pour l’obtention du grade deDocteur ès Sciences Économiques et Sociales

mention Économétrie

Membres du jury de thèse :

Prof. Jaya KRISHNAKUMAR, directrice de thèse, Université de GenèveProf. Marcelo OLARREAGA, président du jury, Université de Genève

Prof. Yves FLÜCKIGER, Université de GenèveProf. Rafael LALIVE, Université de Lausanne

Genève le 10 décembre de 2012Thèse No 794


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La Faculté des sciences économiques et sociales, sur préavis du jury, a au-torisé l’impression de la présente thèse, sans entendre, par là, n’émettreaucune opinion sur les propositions qui s’y trouvent énoncées et qui

n’engagent que la responsabilité de leur auteur.

Genève, le 10 décembre de 2012

Le doyenBernard MORARD


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Contents

Abstract v

Résumé vii

Acknowledgements ix

1 Chapter I

Labour Exclusion and Informality

47 Chapter II

ILO’s Informal Employment Indicator and Heterogeneity

97 Chapter III

Informal Employment and Trade Openness

Thesis Concluding Remarks 137

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Informal employment is a pervasive economic feature in Latin American countries; eventhough its presence may have positive implications often related to entrepreneurship,it’s fundamentally related to poor working conditions, tax evasion and labour marketsdisequilibrium. From a labour econometrics perspective, informality has become a chal-lenging subject as several statistical concerns underlie the available data. Thus, thisThesis presents three papers dealing with fundamental micro and macro-econometrictopics of the informal employment literature.

The first paper presents a micro-econometric model of the dual informal labour marketobserved in Latin American countries. Informality is observed under two regimes: Ex-clusion and non-exclusion (or “voluntary” and “non-voluntary” informality). Model’sspecification searches to encompass the empirical literature in Latin American countrieswith a unifying theoretical framework being able to model a dualistic labour market.Exclusion is then modeled following a latent class econometric specification where classindicators are suggested by the theoretical framework. The model is estimated usingBrazil 2004 household survey and is specified so it could be replicated with standardhousehold survey data. Final results provide evidence that almost two thirds of informal

workers in the sample are excluded and corroborate the existence of a dualistic labourmarket that goes beyond informality attaining other labour status as well. It also sug-gest that education oriented policies may consistently reduce the weight of excludedworkers within the informal sector.

The second paper contributes to empirical literature by correcting for measurementerrors implied by the aggregate informal employment indicator published by the ILO.This indicator plays a crucial role in labour policy making and its availability is mainlyconcentrated in African and Latin American countries. Where available, informalitystatistics are hardly comparable across and within countries due to heterogeneity is-sues in the underlying informality definitions and statistical sources. By estimatingthe informality indicator conditioned on a set of homogeneity conditions, this paperproposes a corrected informality indicator. The econometric specification is chosen bya cross-validation analysis. The implied sample selection bias arising from the missingdata patterns is also tested and treated. The significant influence of the heterogeneityconcerns is not only verified by the parameters of the econometric model but also by thediscrepancies between the statistical properties of the “raw” and “corrected” informalemployment indicators.

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The third paper faces the challenge of obtaining micro-founded macroeconometric es-timates of the Informality - Trade openness relationship. Micro founded economicliterature on this matter often brings evidence of a positive relationship at some spe-

cific countries, with no clear implications at a macro level. From a simple theoreticalmodel, it is shown that a positive or negative relationship depends on country’s pricecompetitiveness. As a consequence, an implicit threshold for the Real Exchange Ratecan be defined. The relationship and its RER threshold are estimated for a panel of LAC where trade openness is considered as a latent unobservable measured with errorthrough two available indicators. The inaccurate small sample inference implied by theGMM estimator (under overidentified moment conditions) is treated by standard andRobust Exponential Tilting estimators.

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L’emploi informel est une caractéristique omniprésente des marchés du travail Latino-Américains. Même si sa présence peut avoir des implications positives liées à l’entre-preneuriat, il est fondamentalement lié à de mauvaises conditions de travail, à l’évasionfiscale et au déséquilibre des marchés du travail. Du point de vue économétrique, l’infor-malité est devenue un sujet de recherche important car plusieurs problèmes statistiquescaractérisent les données disponibles. Ainsi, cette Thèse présente trois articles traitantde sujets micro et macro-économétriques fondamentaux présents dans la littérature de

l’emploi informel.

Le premier article présente un modèle micro-économétrique du marché du travail in-formel dual dans les pays d’Amérique Latine où l’informalité est observée sous deuxrégimes : l’exclusion et la non-exclusion (ou informalité “volontaire” et “non volontai-re”). La spécification du modèle cherche à établir un lien entre la littérature empiriqueayant constaté cette dualité et un cadre théorique capable de la modéliser. L’exclusion,en tant que variable qualitative non observée, est modélisée comme une variable latentediscrète (dichotomique) qui se manifeste par des indicateurs objectifs proposés par lecadre théorique. Le modèle économétrique est estimé à partir de l’enquête des condi-

tions de vie des ménages brésiliens en 2004 (PNAD 2004) et sa spécification permetde répliquer le modèle sur d’autres économies étant donné la disponibilité des variablesimpliquées dans l’analyse. Les résultats montrent que près des deux tiers des travailleursdu secteur informel dans l’échantillon seraient “exclus” et corroborent l’existence d’unmarché du travail dual qui va au-delà du secteur informel. Il suggère également que lespolitiques visant à augmenter les niveaux d’éducation des travailleurs permettent deréduire le taux des travailleurs exclus dans le secteur informel.

Le deuxième article contribue à la littérature empirique en proposant une méthodologiede correction des erreurs de mesure implicites dans l’indicateur macroéconomique del’emploi informel publié par l’Organisation International du Travail. La disponibilitéde cet indicateur se concentre dans les pays africains et latino-américains où il joueun rôle important dans la recherche académique et l’élaboration des politiques éco-nomiques. Lorsqu’elles sont disponibles, les statistiques d’informalité sont difficilementcomparables entre et au sein des pays en raison de problèmes d’hétérogénéité dans lesdéfinitions sous-jacentes et les sources statistiques. À partir d’un modèle économétriqueet d’un ensemble de conditions d’homogénéité, cet article propose un indicateur de l’em-ploi informel corrigé. La spécification économétrique est choisie par une procédure de

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validation croisée et le biais de sélection découlant du schéma de données manquantesest également traité. L’influence significative des sources de hétérogénéité est non seule-ment vérifiée par les paramètres du modèle économétrique, mais aussi par les différencesentre les propriétés statistiques des indicateurs “standard” et “corrigé”

Le troisième article relève le défi d’obtenir des estimations macroéconométriques micro-fondées de la relation entre l’emploi informel et la libéralisation commerciale. La lit-térature économique visant à explorer cette relation trouve souvent des indices d’unerelation positive pour certains pays, mais sans implications claires au niveau macro-économique. À partir d’un modèle théorique simple et sous certaines hypothèses, il estdémontré que la relation (positive ou négative) est déterminée par la compétitivité desprix d’une économie. En conséquence, un seuil implicite pour le taux de change réelpeut être défini. Le modèle économétrique définissant la relation et le seuil de taux dechange réel est estimé pour un panel de pays de l’Amérique Latine; la libéralisationcommerciale est considérée comme une variable latente qui se manifeste par deux indi-

cateurs. Le modèle empirique qui en resulte implique un échantillon de petit taille etun système de conditions d’orthogonalité sur-identifié, dont l’estimation par la méthodeGMM soufre des problèmes d’inférence importants. Ainsi, deux variantes de la méthode“Empirical Likelihood" ayant de bonnes propiétés dans les échantillons de taille moderéesont implémentées (Exponential Tilting et Robust Exponential Tilting).

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To acknowledge the positive contribution of so many people (and circumstances) to myresearch in so little space is simply beyond my capabilities so let me start by apologizingfor the ingratitude of these very few lines. I should start by mentioning the effort of Professors Hugo Loza and Fabrizio Carlevaro who conceived a very competitive quan-titative economics master program in Bolivia in collaboration with the EconometricsDepartment of the University of Geneva. Such collaboration allowed motivated Boli-vian students to benefit of the academic and teaching skills of Professors such as Emilio

Fontela, Harry de Haan, Jaya Krishnakumar and Marcelo Olarreaga among others.But the most important contribution of this experience relied on its deep scientific com-mitment which finally traced my path towards the former ’DEA en Économétrie’ anddoctoral studies at the University of Geneva.

This Thesis would not have been possible without the contribution of many people. Iwould like to start by thanking my supervisor Prof. Jaya Krishnakumar for her effec-tive supervision and trust. Very special thanks to Prof. Manfred Gilli for his supportand sense of humor, to Prof. Ronchetti for his availability and wise advices and toProf. Carlevaro for being the last of the Mohicans, this is, for having that philosophical(but sometimes stubborn) approach of Econometrics and for not being responsible of supervising my research with his sharp eye and "Ockham’s Razor". Big thanks to themembers of my jury, Professors Rafael Lalive, Yves Flückiger and Marcelo Olarreaga fortheir significant contribution to the final version of the Thesis. A special thanks shouldbe addressed to my mistakes, at least to those from which I’ve learned something.

Thanks to my colleagues: Juan Tellez, Cristian Ugarte, Carlos de Porres, David Zavaleta,Reto Schumacher, Ilir Roko, David Neto and many others for sharing their academicexperience. Thanks to Paola for her intellectual and moral support from the beginningto the end.

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CHAPTER I

Labour Exclusion and Informality in a LatinAmerican Country, a Latent Class ModelApproach

Jorge Davalos ∗

Department of Economics, University of Geneva

Switzerland

Abstract

This paper presents an econometric model of the dual informal labour market observed inLatin American countries. Informality is observed under two regimes: Exclusion and non-exclusion (or “voluntary” and “non-voluntary” informality). Model’s specification searches toencompass the empirical literature in Latin American countries with an unifying theoretical

framework being able to model a dualistic labour market. Exclusion is then modeled followinga latent class econometric specification where class indicators are suggested by the theoreticalframework. The model is estimated using Brazil 2004 household survey and is specified soit could be replicated with standard household survey data. Final results provide evidencethat almost two thirds of informal workers in the sample are excluded and corroborates theexistence of a dualistic labour market that goes beyond informality attaining other labourstatus as well. It also suggest that education oriented policies may consistently reduce theweight of excluded workers within the informal sector.

Keywords: Microeconometric, Labour Exclusion, Informal Labour, Latent class.

∗I would like to thank Professors Jaya Krishnakumar, Rafael Lalive, Yves Flückiger, Marcelo Olar-reaga and Tobias Müller for their valuable comments. Any errors or omissions are the author’s respon-sibility. ([email protected] )


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Chapter I List of Figures

Contents

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1 Dualistic labour market: empirical evidence . . . . . . . . . . . . . . . . 93 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.1 The econometric model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1.1 Latent regime specification (R) . . . . . . . . . . . . . . . . . . . 163.1.2 Indicators’ specification . . . . . . . . . . . . . . . . . . . . . . . . 173.1.3 Identification Analysis . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2 Estimation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2.1 Unconditional exclusion probabilities . . . . . . . . . . . . . . . . 243.2.2 Exclusion probabilities conditioned on labour status . . . . . . . . 283.2.3 Wage and labour status estimated equations . . . . . . . . . . . . 313.2.4 About the conditional correlation structure . . . . . . . . . . . . . 323.2.5 The job seeking indicator (J ) . . . . . . . . . . . . . . . . . . . . 333.2.6 Exclusion and labour status patterns . . . . . . . . . . . . . . . . 33

4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34A Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36A.1 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36A.2 Estimated equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

A.3 Burdett and Mortensen model . . . . . . . . . . . . . . . . . . . . . . . . 39

List of Figures

1 Model’s structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Distribution of labour productivities, supply and demand. . . . . . . . . . . . 173 Exclusion probability and potential experience (by ethnic groups ) . . . . . . 264 Exclusion probability and years of education . . . . . . . . . . . . . . . . . 275 Conditional Exclusion probability P [R = 1|S , x] . . . . . . . . . . . . . . . 296 Conditional Exclusion probability P [R = 1|S , x] . . . . . . . . . . . . . . . 30

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List of Tables

1 Preference for independent employment (% of workers) . . . . . . . . . . 102 Reported reasons to be informal self-employed in Brazil (% of workers) . 113 Endogenous variables densities and cdf’s . . . . . . . . . . . . . . . . . . 184 Unconditional exclusion probability (P [R = 1]), logit estimated parameters. . 255 Exclusion-Education slopes . . . . . . . . . . . . . . . . . . . . . . . . . . 286 Conditional correlations (between unobservables) . . . . . . . . . . . . . . . 327 Estimated labour status and exclusion regime distribution . . . . . . . . . . . 348 Education years by region, labour and job seeking status . . . . . . . . . . . 369 Main job income by region, labour and job seeking status . . . . . . . . . . . 3610 Wage equations estimated parameters. . . . . . . . . . . . . . . . . . . . . . 3711 Mixed multinonial logit estimated parameters(P [S|R, x]). . . . . . . . . . . . 38


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Introduction

1 Introduction

Informality can be best defined from Hussmanns (2004) legalistic concept where theinformal economy term is used as referring to “all economic activities by workers andeconomic units that are, in law or in practice, not covered or insufficiently covered byformal arrangements”. Informality was first considered a consequence of segmentation(Harris and Todaro, 1970). From this approach, informal workers are “excluded” froma primary labour market and are then constrained to lower quality (informal) jobs. Butmore recent empirical evidence based on job satisfaction surveys revealed that informal-ity was also an exit from poverty potentially leading to better living conditions (Perry,Maloney, Arias, Fajnzylber, Mason and Saavedra-Chanduvi, 2007). This new evidencewas theoretically supported by a competitive approach and has been verified empiri-cally by Magnac (1991) for the women labour market in Colombia and by Günther andLaunov (2012) for the urban labour market in the Ivory Coast among others. This du-ality has important implications in policy making as poverty and inequality may showheterogenous responses between these two regimes

Despite of the fact that this new evidence clearly show the existence of dualistic labourmarkets, there is no consensus about the theoretical approach that would better describethe exclusion-informality phenomena. Such a theoretical approach would be crucial todefine informality and exclusion under an integrated framework and would give newdirections for the statistical measurement of both concepts. Moreover, other than sub-

jective surveys, there is no theory based methodologies that would allow researchers toidentify workers that are “excluded” in Harris and Todaro’s sense, i.e. those who are

constrained to accept a given job.

This paper aims to bring to light that a theoretical unifying framework exists in the formof equilibrium job search models which succeeded to introduce information uncertaintyinto labour market models. From this approach, El Badaoui, Strobl and Walsh (2010)specify a theoretical model of informality based on Burdett and Mortensen (1998).This framework introduces imperfect information related to workers partial knowledgeof market’s job offers; Workers receive wage offers at a random frequency, where theexpected number of offers can be held constant or not across workers, a limiting casebeing this expectation tending to infinity (perfect information case) which yields per-fect competition equilibria. Under the original model (Burdett and Mortensen, 1998)

assumptions, this paper suggests that excluded workers, in Harris and Todaro’s sense,can be identified with those lacking of information and opportunities regarding the joboffers in the labour market. Therefore, exclusion can be modeled by means of differen-tiated average arrival rates, where excluded workers are identified as those having thelower arrival rates of job offers. From this paper approach, exclusion1 is an omnipresentcharacteristic, not only attaining informal workers but other labour status as well.

1Defined as the lack of information and opportunities regarding the job offers in the labour market

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Chapter I Literature review

To identify “non-excluded” informality, also known as “voluntary” informality, job

satisfaction (subjective) surveys have been implemented; unfortunately they are notwidely available in latin-american countries and are heterogenous and not comparableacross countries. To overcome the identification problem, this paper proposes a latentclass econometric model for classification. The resulting econometric model can beimplemented from standard survey data and is estimated using Brazil’s PNAD-survey(2004)which, with respect to other LAC, has the advantage to report the legal regis-tration status of workers’ jobs2. Final results verify some stylized facts such as theimportance of ethnic discrimination and working experience into exclusion and the co-existence of excluded and non-excluded workers within the informal sector.

Results confirm that the unemployed and informal labour forces are mainly constituted

by excluded workers. At an aggregate level and from model estimates, there would betwice as much excluded informal workers than non-excluded informals. Estimates alsosuggest that working at urban centers, lack of working experience and ethnic discrimi-nation are the main exclusion determinants. The observed increase in low skilled labourdemand since the early 90’s is also captured by the model as exclusion increases slightlywith the level of education.

The paper’s structure is structured as follows. A second section, that follows thisintroduction, presents a literature review about informality and Burdett and Mortensenmodel, the latter being complemented in the Appendix. The third section developsthe latent class model for the exclusion regime. Finally the last section presents andcomments the model estimates and ends with concluding remarks.

2 Literature review

Informal Employment has been a major concern in developing countries since the 1970’s.Its undesired effects on public finance, respect of law and economic policy efficiency arewidely documented in the economic literature (Feige, 2005b; Feige, 2005a ; Albrecht,Navarro and Vroman, 2006). Even though several statistical definitions are avail-able, Informal Employment in Latin American countries is mainly characterized bythe avoidance of government regulation, a non-regular labour status and tax evasion(Loayza, 1997; De Soto, 1989).

Formal economic models tend to explain informality from two rather complementaryapproaches. The first one refers to labour market segmentation , whereas the secondrefers to informality as a “voluntary” labour status. The labour segmentation liter-ature has its roots in Harris and Todaro (1970), and identifies the informal sectorto a residual or disadvantaged sector that results from a labour market disequilib-

2The informal status membership obtained by this definition makes possible to differentiate informalworkers from formal independent ones

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Literature review

rium. This approach points to labour market segmentation as informality’s major

cause (Rauch, 1991; Feige, 1989). The alternative approach considers informality asa “voluntary” labour status i.e. that informality is the result of an utility maximizationprocedure Hirschman (1970). Recent empirical studies in Latin American countries,based on labour satisfaction surveys, show that the majority of informal self-employedworkers seem to voluntarily chose their current informal labour status (Mondino andMontoya, 2002; Maloney, 1999; Saavedra and Chong, 1999).

The first attempts to unify and test the competitive and segmented hypothesis wereproposed by Dickens and Lang (1985) and Magnac (1991). The latter proposed a singlemarket model that could either be segmented (unconstrained model) or competitive(constrained model) and without nonpecuniary earnings or compensating differentials

between sectors (formal-informal). The former proposed a dual market model (switch-ing regime model) that nested competitiveness and segmentation assuming the existenceof compensating differentials and other strong assumptions criticized by Heckman andHotz (1986)3. More recently, Günther and Launov (2012) tested for the existence of anunknown number of clusters within the informal labour market of the Ivory Coast; fromtheir econometric approach, they find statistical evidence of the existence of a dualisticinformal labour market.

Compensating wage differentials

Two main implications arise from the compensating differentials perspective. First, job

seekers consider job’s advantages and disadvantages i.e. nonpecuniary compensations,therefore formal-informal wage differentials will not be explained solely by workers pro-ductivity. Second, a priori compensating differentials do not establish which labourstatus (formal or informal) receives higher wages(Maloney, 1999; Magnac, 1991). Onthe one hand informal workers may receive higher earnings to compensate for the ab-sence of some social benefits; on the other hand, they may receive lower earnings tocompensate for the value of some facilities related to informality such as flexible work-ing environment, tax evasion, autonomous work, etc.

Equilibrium search models

Equilibrium search models provide a formal framework to model labour market equilib-riums under agents’ limited information assumptions. Burdett and Mortensen (1998)model4 assumes imperfect information and homogenous agents where firms have het-erogenous profit maximization strategies. Every firm strategy is characterized by a

3The main criticisms were related to (i) labour market, segmented or competitive, is rather multi-sectoral while the model assumed a single sector at both regimes (ii) agents are “utility” maximizersnevertheless “utility” is reduced to a monetary definition, the net present value of future wages (iii)mobility costs should not be neglected (iv) distributional assumptions were unrealistic.

4See the appendix A.3 for a review of the model.

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Chapter I Literature review

particular incentive to offer higher wages so as to achieve low quit rates, thus the equi-

librium wage across firms is not unique but stochastic i.e. characterized by a distributionfunction. The non-participation decision is explained by the lower expected earningsrelated to any job search effort when compared to the reservation wage. An extensionto the basic model assuming heterogenous agents was developed by the author and byBontemps, Robin and Van den Berg (1999)5, yielding well behaved theoretical wagedensities. This approach is not in contradiction with standard labour supply theorywhich is based on perfect information and the leisure and working hours trade-off. Itrather introduces more realistic assumptions like imperfect information that enables arealistic job search behavior.

El Badaoui et al. (2010) extends Burdett and Mortensen (1998) model to account for

informality. The model is characterized by firms who may decide to become informalby defaulting taxes. As in the original model, bigger firms pay higher wages, exceptnow, firms’ probability of being controlled depends positively on its size, thus biggerfirms not only pay higher wages but are less likely to default. At the steady state,defaulting firms (informals) are those whose size (in number of employees) lies belowan endogenous threshold.

El Badaoui’s model inherits the core characteristics of Burdett and Mortensen’s suchas the temporary nature of the lower paid jobs even under homogeneous job arrivalrates. Given that informal (formal) firms, offer lower (higher) wages, its labour forcewill be mainly concentrated on newer (senior) rather than senior (newer) workers. Froma worker’s perspective who faces formal and informal offers, the choice relies solely on

the offered wage, which by definition, is expected to be higher when coming from formalfirms. If by any chance a higher offer comes from the informal sector, it will be accepteduntil a higher one (expected from the formal sector) arrives. This causes informal jobsto be considered rather “temporary” when compared to formal ones.

The following section (3) presents an econometric specification of informality and labourexclusion inspired on Burdett and Mortensen’s approach; Exclusion, defined as the lackof information and opportunities in the labour market, is identified to lower job offersarrival rates.

Exclusion under the job search framework

To better understand how this framework may nest a two regime model (exclusion ornot) let us consider the model review in appendix A.3. The model is first presentedwith different arrival rates for employed (λ0) and unemployed (λ1) individuals, where

5The authors show that the theoretical wage distribution function can be estimated by non para-metric methods.

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Literature review

arrival rates model information availability concerning job offers6. Given that the wage

offer distribution H (w) is unique, it can be shown that the expected accepted wage ishigher for the category with the highest arrival rate other things been equal.

The following proposition thats allows labour exclusion to be interpreted based on Bur-dett and Mortensen’s framework is introduced :

Barriers to entry into the labour market constrain the set of available job offers, which in terms of Burdett and Mortensen model implies lower arrival rates .

Therefore, in its simplest specification, labour exclusion may be defined as the lack of information availability and opportunities, arising from barriers to entry and related

characteristics e.g. ethnic discrimination, oligopsony in urban or rural markets, etc. Interms of El Badaoui et al. (2010) and Burdett and Mortensen (1998) model, this wouldimply lower arrival rates for the excluded workers. The econometric specification of theexclusion dichotomy to be presented in the next section is inspired on this approach.

The “non-voluntary” informality term needs to be interpreted with care as theoreticalmodels under an utility maximization framework consider discrete choices and decisionsmaking processes under a set of constraints. Extremely constrained problems may leadto particular solutions where the available choice set (after controlling by problem’sconstraints) has few, a single or no choice alternatives; in that sense informality maybe referred in the literature as “non-voluntary”. As this paper adopts the theoreticalframework given by Burdett and Mortensen (1998) and El Badaoui et al. (2010), the

exclusion definition is preferred to the “non-voluntary” term.

2.1 Dualistic labour market: empirical evidence

Different informality indicators are available across Latin American countries, neverthe-less the most common informal job definition is given by the ILO . According to ILO’sdefinition, informal jobs comprise non-professional self employed, employers and em-ployees in small firms with cut points varying from 5 to 15 employees. Only Brazil hasa registration card system that allows a more precise identification of informal workers.Independent workers in LAC are closely related to informality due to the higher avoid-ance of certain labour regulations within this sector. Thus, the share of independent

workers is often considered as an informality indicator. Empirical evidence (see table 1)shows that the percentage of urban formal workers that would prefer an independent jobis far from being negligible. The shares of informal workers (salaried and independent)that prefer an independent job exhibits even higher proportions (from 40% in Colombiato 75% at the Dominican Republic).

6The perfect competition equilibria is obtained under a perfect information assumption, whichimplies worker’s perfect knowledge about all available job offers in the market (λ →∞)

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Tab. 2: Reported reasons to be informal self-employed in Brazil (% of workers)Would you like to leave your current job for a job with a signed contract? (Informal self employed)

Male FemaleResponse All 15 - 18 19 - 24 25 - 54 55 - 70 All 15 -18 19 -24 25 - 54 55 - 70

years years years years years years years yearsNo 67.9 29.9 52.6 68.3 80.6 55.5 24.6 41.8 55.2 71.2

Motivations to prefer an unprotected job (Self-employed)Male Female

Reason All 15 - 18 19 - 24 25 - 54 55 - 70 All 15 -18 19 -24 25 - 54 55 - 70years years years years years years years years

Earn more in current job 18 13.4 17.6 21 9.6 10.6 5.1 13.3 12.1 3.9Needed to care for home 0.2 0 0 0.1 0.4 26.9 15.3 22.8 27.5 28.8Need time for other 2.9 7.5 3.2 2.5 3.2 6.7 6.8 7.9 6.6 6.8activitiesHappy in current job 64.9 69.5 68.3 64 67.6 44.1 59.3 47.7 44.8 39Did not want the 10.1 8 9.8 10 10.6 7.5 8.5 7.6 6.9 9.8commitmentNo answer 4 1.6 1.1 2.2 8.6 4.1 5.1 0.8 2.2 11.6Percent of sample 73.5 0.8 5 51.3 13.7 26.5 0.3 1.7 20 3.9Percent of gender 100 1.1 6.8 69.8 18.6 100 1 6.3 75.4 14.8

Source : Perry et al. (2007), based on “Pesquisa Nacional por Amostra de Domicilios 1990”.

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Chapter I The model

Labour exclusion - Brazil

This paper defines labour exclusion as the lack of information and opportunities regard-ing the job offers in the labour market; in that sense, labour market segmentation maybe considered as its main determinant. From this definition, exclusion is not boundedto informality but can attain other labour status as well. Moreover, the importance of information availability has been already considered to model informality in El Badaouiet al. (2010).

Labour supply pressures play an important role given its obvious implications on thescarcity of job offers. The Brazilian labour force rose at 2.6 % on average during the1992-2004, a high increase when compared with worldwide rates of about 1.5%. As inother LAC, much of this increase is caused by demographic factors (rising in fertility

rates and in women participation into the labour market).

From the labour demand side, an important change has been observed since the late1990’s. A structural shift of the production towards lower productivity but labour in-tensive sectors(Ernst, 2008). The sudden shift in the share of the demand of low skilledcaused an occupational mismatch that raised the unemployment pressures at some sec-tors. The new jobs generated by this shift were mostly concentrated in the formalsector, raising the exclusion concerns at self-employment and informality.

3 The model

Empirical evidence presented in the previous section shows that both, formal and in-formal workers, may be classified either as willing to keep or not their current labourstatus. At the same time it’s suggested that the equilibrium search approach is able tonest this duality. This can be done by assuming that workers with more informationand opportunities in the labour market (higher arrival rates of job offers) are morelikely to be matched with “better” jobs. Empirically, this implies that workers with lessinformation (lower arrival rates of job offers) are more likely to be observed at unem-ployment, lower quality (temporary, informal) or lower paid jobs. Thus, defining labourexclusion as the lack of information and opportunities in the labour market implies thatexclusion is not bounded to stay in the informal sector but that it can be related to

other status and observed characteristics as well.

This section presents a latent class model for the unobserved labour exclusion statewhich is specified by exploiting the relationships suggested by the empirical evidenceand economic theory. Exclusion (R) is modeled as an endogenous dichotomous statethat manifest through observed characteristics. Exclusion (R) itself is endogenous asit is conditioned on worker’s characteristics. Such specification may also be interpreted

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The model

as a MIMIC7 model with a discrete latent variable.

From the equilibrium search approach, the excluded labour may be assumed to havelower arrival rates, hence when controlling for workers characteristics, excluded oneswould be expected to stay longer in lower quality or underpaid jobs. Thus, the higherthe exclusion the lower the accepted wage or the job quality related to it others thingsbeen equal. As a consequence the following observable manifestations of exclusion areconsidered :

Observed wages (w) Excluded workers receive less job offers, thus their received wageis expected to be lower other things being equal.

Job seeking status (J ) Excluded workers will be prone to seek for a better paid ormore satisfactory job.

Labour status (S ). Excluded workers will tend to stay longer at lower quality jobs jobs until a better job offer arrives. Economic literature identifies informality per-seas the most widely used indicator of job quality (Pagés and Madrigal, 2008), thus alabour status indicator that considers formality, informality and unemployment couldbe considered as an indirect exclusion indicator. As, it will be discussed in the econo-metric section, this variable not only serves as an indicator but also corrects for sampleselection in the observed wages equation.

3.1 The econometric model

As shown in the previous paragraphs, the framework provided by Burdett and Morten-sen model gives helpful insights for the expected relationships between relevant vari-ables. Thus, the following econometric specification exploits such relationships in theform of a latent class model i.e. the econometric model does not pretend to fully testfor the empirical validity of the theoretical model. The latent class model presentedbelow distinguishes three kind of variables: First, the latent class which is unobserved,endogenous and qualitative (R) ; second, the observed endogenous indicators that couldbe continuous (w) or qualitative (S ,J ) which by definition are determined by the latentclass. Finally the exogenous variables (x) on which all others are conditioned.

7Multiple Indicators and Multiple Causes

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Chapter I The model

wage

X R labour status

job seek

Fig. 1: Model’s structure

The presence of unobserved skills (or unobserved heterogeneity) in the model can bedetected through the conditional correlations (dotted lines in figure ??) e.g. higher(unobserved) skills will increase to likelihood of receiving a higher wage and of beingin a better quality job, causing w and S unobservables to be correlated. Controllingfor unobserved skills has important econometric implications as it corrects for the po-tential correlation between the human capital regressors within wage equations and thecorresponding residual terms.

This model may also be written as a structural equation model (SEM) of interrelatedcontinuous endogenous variables and latent traits :

w = hw(x,R,S ) + uw

S ∗s = hS (x,R,S ) + us

J ∗ = hJ (x,R) + uJ

R∗ = hR(x) + uR

where h() is a linear function of its arguments while the random vector u has a fullcorrelation structure, u ∼ D(0, Σ). As it can be noticed, the SEM representation of theLC model is based on categorical variables’ underlying latent traits (S ∗,J ∗,R∗). Thus,

the mapping from the latent traits to the observed indicators is given by :

R =

1 Excluded if R∗ ≥ 00 Non-excluded otherwise

J =

1 Job-seeking if J ∗ ≥ 00 Not seeking for a job otherwise

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The model

S = Argmaxs S ∗s ; s = 1, 2, 3, 4.

where S ∗s denotes the labour status latent trait at a given status s.

The simplest LC model

For the sake simplicity, the following presents the formal definition of a Latent Class(LC) model when a single dichotomous indicator (J R) is available. Identification anal-ysis is omitted on purpose as it is explained and applied to the final econometric modelat the end of this section. Let’s consider the latent trait R∗ linearly determined by thecovariates and unobservables defined above:

R∗ = δ ′1x + uR and P [R = 1] = F uR(δ ′1x) (1)

where R∗ is a continuous random variable determined by individual observed characte-ristics (x) and unobservables are modeled by uR, a random variable with distributionfunction (F uR).

As R is not observed, the dichotomous exclusion indicator (J R) classifies individualswith error in two groups (R = {0, 1}) with probabilities :

J R = 1 (Excluded); P [J R = 1]= P[J R = 1 ∩R = 1] + P [J R = 1 ∩R = 0]0 (Non-excluded); P [J R = 0] = P [J R = 0 ∩R = 1] + P[J R = 0 ∩R = 0]

where probabilities of observing a correct(false) classification are indicated in bold (stan-dard) characters8. These probabilities may be represented by probit specifications (Φ)conditioned on individual characteristics (x):

P [J R = 1|R = 1] = Φ(δ ′2x) ; P [J R = 0|R = 0] = Φ(δ

′3x)

which yields the following probabilities of observing J R:

J R =

1 (Excluded); P [J R = 1] = Φ(δ

′2x)FuR(δ 1x) + Φ(−δ

′3x)F uR(−δ

′1x)

0 (Non-excluded); P [J R = 0] = Φ(−δ ′2x)F uR(δ

′1x) + Φ(δ

′3x)FuR(−δ

′1x)

This specification corresponds to a (unidentified) latent class model with a single indi-cator. It may also be described as a MIMIC model with a discrete latent variable. The

8Correct and false classification probabilities are written as :

P [J R ∩ R] = P [J R|R] P [R]

where P [J R|R] is interpreted as the probability of observing an exclusion indicator(J R) given anunderlying regime(R)

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The model

π

g(π)

I.

tR = 1 R = 0 π

g(π)

II.

t1 t2R = 1 R = 1R = 0

Fig. 2: Distribution of labour productivities, supply and demand.

π − t corresponds to the latent trait (R∗) in equation (1). From workers’ perspective,

P [π < t] is calculated over workers productivity distribution (blue) where the thresholdis implicitly defined by functions’ intersection.

In the second and most general scenario (II) the latent regime could be modeled asa trichotomy by assuming three productivity states, nevertheless this would increasethe complexity of the econometric estimation. Instead, a simpler specification may beadopted by defining the exclusion probability as a non linear function:

P [R = 1] = P [(π − t1)(π − t2) > 0] (2)

= P [α1π2 − α2π + α3 > 0] ; (α1, α2, α3) = (1, t1 + t2, t1 t2)

where P [R = 1] at the first scenario is a nested model if (α1, α2, α3) = (0, 1, t).

Worker’s latent productivity being unobservable, it may be explained by minceriancovariates (z ) and a random component which leads to the reduced form:

P [R = 1] = P [β̃ ′z̃ + θ̃ε < uR] (3)

where the z̃ vector contains the reduced form variables resulting from the quadraticequation (2) whereas θ̃ε is introduced to control for unobserved heterogeneity i.e. un-observed that determine productivity. This equation implies the inclusion of higher

order polynomials for π in order to model the underlying productivities scenario, thusfinal estimates presented in the next section show evidence in favor of scenario I (table4).

3.1.2 Indicators’ specification

The econometric model has a compact representation in the form of the i-th observationlikelihood function. Let’s first define the notation to be used for endogenous indicatorsdensity or probability functions :

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Chapter I The model

Tab. 3: Endogenous variables densities and cdf’s

Definition Specification

P [J |x,R] Probability of the dichotomous

job seeking indicator J . Logit∗

P [S|x,R]

Probability of observing theLabour status where S is qual-itative and nominal. The fourlabour status categories in S areformal, independent, informaland unemployed

Mixed multinomial logit∗

f u(w|x,R,S ) Observed wage density function ,where u stands for the residualterm.

Linear regression∗

P [R|x] Probability of the underlying di-

chotomous regime∗ Logit∗

∗ Linked to the other model equations through the mixing distribution ψ(ε)

Thus, for conditional independent J , S and w, the conditional mixture distributiong( . |x) is obtained as:

g(w,J ,S ,R|x) =r

f (w|x,R,S )P [J |x,R]P [S|x,R]P [R|x] (4)

=

r={0,1}

f (w,J ,S|x,R = r]P [R = r|x]

= g(w,J ,S ,R|x)

Nevertheless, the conditional independence assumption could be unrealistic in the pres-ence of unobserved heterogeneity like individual unobserved skills, leading to incon-sistency of the ML estimator. Thus, dependence between indicators and the latentregime is induced by means of mixing10 distribution function d ψ(ε). The new mixturedistribution h( . |x) for the i-th observation is:

10In the statistics literature, the weighted average of several functions es called a mixed functionand the density that provides de weights is the denoted as the mixing distribution

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The model

h(w,J ,S ,R, ε|x) = r

f (w|x,R,S , ε)P [J |R, ε , x]P [S|R, ε , x]P [R|ε, x] dψ(ε)

=

r={0,1}

f (w, J ,S|R = r, ε, x]P [R = r|ε, x] dψ(ε) (5)

Alternative interpretation Let’s consider the model without the job seeking indicator(J ) and the latent regime (R). The resulting model would consist of two endogenousvariables, the offered wage (w) and labour status (S ). Such a model corresponds to a

multinomial tobit specification where (w) is the censored variable observed at differentlabour status (S )11. Thus, the introduction of the latent regime (R) leads to a tworegimes multinomial tobit model. Under this interpretation the additional indicator(J ) enters the model only to contribute to the statistical identification of the latentregime.

Dependencies within S The assumption of multivariate normality for the latent traitthat determines S would lead to a computationally burdensome estimation proceduredue to the multidimensional integrals involved in the multivariate normal distributionfunction. An alternative approach consists to specify probabilities from a simpler mul-

tivariate distribution function (like a multivariate normal with non correlated randomvariables or a multinomial logit) and to introduce a common random regressor (ε) toinduce dependence between categories(McFadden and Train, 2000; Train, 2002). Thisis the role of ε, not only to avoid conditional independence within S but to createdependencies between the endogenous variables in the system. Let’s define us as therandom term that underlies the latent trait determining P [S = s|.],

us = θsε + us ; s = 1,...4 (6)

for simplicity a multinomial logit specification is assumed,

P [S = s|R, ε , x] = eα

′sx+θsε

1 +3

τ =1 eα′τ x+θτ ε

(7)

which implies that us follows a Type-I extreme value distribution (log-Weibull), where εand us are independent and V (us) = π

2/6, ε ∼ N (0, 1). Thus, the implicit conditionalcorrelation between labour status s and p is given by:

11This a multiple groups generalization of the Heckman’s sample selection model (Tobit II).

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Chapter I The model

θsθ p (θ2s + π

2/6)(θ2 p + π2/6)

The constraint V (ε) = 1, frees the correlation sign between status s and p by lettingthe θ parameter to take positive or negative values.

Other implied correlations The observed hourly wage at a given regime (R) is cen-sored and observed at status s = 1, 2, 3 (S = 4 corresponds to unemployment) :

ln w∗s = ln ws = a

′sx + λsε + ǫs if S = s

− otherwise(8)

where the as parameters represent the hourly wage returns on individuals’ characteris-tics (x). Both ε and ǫ are iid across workers and normally distributed . As mentionedearlier, unobserved heterogeneity is modeled by the random term ε which induces con-ditional correlations between and within indicators.

From a multinomial tobit perspective it could be interesting to define and test for theconditional correlation between S = s and ln ws, i.e. the correlation between us andthe wage equation residual (λsε + ǫs) :

θsλs

(θ2s

+ π2/6)(λ2s

+ σ2ǫ

)

while the correlation between the wage equation residuals s and p is given by :

λsλ p (λ2 p + σ

2ǫ )(λ

2s + σ

2ǫ )

The parameters (λ, θ,σ2ǫ ) related to the above correlation structure are identified fromsecond order moments, which makes numerical identification very difficult if two correla-tion structures at both regimes (R) are estimated, thus an unique correlation structurefor both regimes is assumed 12.

The job seeking dichotomous indicator (J ) has a logit specification P [J |ε,x,R,S ] and

is conditioned on the random component (ε). Again the conditional correlation betweenJ and ln ws and s may be easily written as:

λsδ (λ2s + σ

2ǫ )(δ

2 + π2/3), ;

θsδ (θ2s + π

2/6)(δ 2 + π2/3)

where δ is the parameter that multiplies ε within the logit covariates.

12The theoretical identification of the implied correlations has been established from rank and orderconditions as suggested in Walker, Ben-Akiva and Bolduc (2007)

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The model

3.1.3 Identification Analysis

Theoretical identification of latent class models with categorical indicators has beendiscussed in the literature by Goodman (1974) and Hagenaars and McCutcheon (2002)among others. The necessary and sufficient conditions for identification may be consid-ered as special cases of more general approaches like the one described in Skrondal andRabbe Hesketh (2004). In order to discuss the identification of this paper’s model asimpler version dealing with two categorical indicators (J ,S ) would be first considered,thus the complete model analysis will follow with the introduction of the wage indicator.

As J and S have 2 and 4 categories respectively it’s possible to generate a new categorialvariable (M ) to code their equivalent 8 possible combinations, for simplicity the IIA isassumed. Thus the joint probability from which the i-th observation likelihood function

may be written has the form :

P [J ,S ] =s

j

r

P [J = j |R = r]1[J = j]P [S = s|R = r]1[S =s] P [R = r]

As can be seen the probits (J ,R) and multinomial logit (S ) imply the estimation of nine vector parameters:

P [J = j |R = r]] Two vector parameters (one for every exclusion regime).P [S = s|R = r] Six (mlogit) parameters (three for every exclusion regime)

P [R = r] One vector parameter.

In order to find the number of identifiable vectors, the previous probability may berelated to an equivalent multinomial probability P [M ] (or reduced form model) thatdeals with eight observed categories :

P [M ] =m

P [M = m]1[M =m]

P [M ] ≡ P [J ,S ]

Therefore,

m

P [M = m]1[M =m] ≡s

j

r

P [J = j |R = r]1[J = j]P [S = s|R = r]1[S =s] P [R = r]

The left hand side is a multinomial probability with one reference category, where sevenidentifiable vector parameters exist. Given the equivalence between left and and righthand sides, for every m there is an equivalent (s, j) combination, thus the followingimplicit system of seven equations and nine unknown vectors is obtained :

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Chapter I The model

P [M = m] ≡r

P [J = j |R = r]1[J = j]P [S = s|R = r]1[S =s] P [R = r] , m = 1,...7

Having at least as many equations as unknowns is the necessary condition for identifi-cation, as a consequence the model is unidentified. If this condition would have beensatisfied, it follows that the Jacobian of the implicit system relating the reduced formparameters within (P [M ]) and the right hand side (structural) parameters must be fullrank in order to obtain local identification. Full rank of the Jacobian is then a sufficientcondition provided that there are as many equations as unknowns.

Let’s introduce wages at labour status s as an indicator, the overall probability becomes :

f (wm|M = m)P [M = m] ≡r

P [J = j |R = r]1[J = j][P [S = s|R = r]f (ws|R = r)]1[S =s] P [R = r]

The left hand side corresponds to a Multinomial Tobit 13 probability where seven vec-tor parameters14, composed by multinomial logit and wage equation parameters15, aretheoretically identified. Identification in mtobit models rely heavily on empirical ratherthan theoretical identification e.g. a bivariate normal tobit is theoretically identifiedbut is close to unidentified if f (wm|M = m) and P [M = m] are conditioned on the

same explanatory variables (Cameron and Pravin K., 2005). Regarding the right handside or Latent Class model, this suggests that even if necessary and sufficient conditionsfor theoretical identification are met, empirical identification could be a main concern.The count of unknown parameter vectors at the right hand side yields the same results,the only difference being in the definition of the mtobit probability :

P [S = s|R = r]f (ws|R = r)] Six (mtobit) parameters( three for every exclusion regime )

As can be noticed, adding wages as a continuous indicator does not change the numberof resulting equations, so the model stays unidentified; thus estimation can only beperformed over a constrained version of the model.

The econometric model presented in the next section tested for alternative constraintsets. Each constraint was evaluated by the economic coherence of its estimated pa-rameters and by its empirical identification (assessed by the condition number16). This

13Also known as switching regression model with endogenous switching14Multinomial logit and wage parameters can be represented as one mtobit parameter vector15The wage parameters for labour status other than unemployment16The ratio of the highest to the smallest eigenvalue of the log-likelihood Hessian matrix.

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The model

strategy pointed to a model where i) the job seek (J ) slope parameters were statisti-

cally close to zero without discarding ε17

and ii) the formal-excluded and formal-nonexcluded wage parameters exhibited similar slopes. Thus, to achieve theoretical identi-fication, the job seek logit parameters were fixed to the values suggested by the previousanalysis; zero for the slope parameters whereas its threshold is such that the likelihoodfunction is maximized. This reduces the number of structural vector parameters by twoand ensures that the order condition is met. A second constraint that enhances theempirical identification of the model implies the equality of the slope parameters at thewage equations across regimes in the formal sector. Model’s economic coherence needsto be addressed by several probability curves and estimated parameters. Moreover, asthis is a multivariate non linear model, the comparison (reporting) of alternative modelsbecomes cumbersome, thus this paper emphasizes on the explanation of the resulting

econometric identification and avoids reporting and comparison of alternative models.For a reference on analog latent regime models and implied constraints see Dickens andLang (1985) and Günther and Launov (2012).

3.2 Estimation results

The econometric model is estimated using Brazil’s household survey (PNAD-2004). Thesample consists of male individuals between 18 and 65 years old, not working or havinga single job only. A main concern with this criteria relies in the fact that workers havingmore than a single job may be related to informal activities which may be a source of a sample selection bias. Nevertheless, the share of workers in this situation is relativelysmall (about 2.5% of the male subsample). The female sample is not considered in

order to control for potential specification issues as parallel decision making processes(related to motherhood) may play an important role in the determination of the chosenlabour status and observed wages (see appendix A.1, for the descriptive statistics of model’s main variables).

The labour status (S ) has been generated from survey’s indicators and it distinguishesfour labour categories: formals, independents, informals and unemployed workers :

• Informality. Workers whose current job is not registered on their working card.Not registered jobs are not covered by the labour market regulation.

• Formality. Non independent workers whose current job is registered on theirworking card plus public sector workers and members of the national army.

• Independent. Workers classified as self-employed, domestic servants and familyor non remunerated workers with a registered job. In Brazil’s case independentworkers are not informals. Even though, being independent may also be consideredas an informal status in other LAC where the registration card system does notexist.

17Its parameter is identified from second order moments (the implied variance structure)

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Chapter I The model

• Unemployment. Economically active workers that do not belong to the previous

three categories.

The other endogenous variables (indicators) definitions are:

• Job seeking status(J ). Dummy variable equal to one if the worker was seekingfor a job during the last 30 days and zero otherwise. The average over the entiresample was about 5% and did not increase significantly when considering a longerhorizon (365 days).

• Logarithm of the hourly wage. Calculated from the declared working hoursper week and monetary wage received from the main labour activity.

The exogenous (x) variables definitions are:

• Years of education (Educ.years). Effective years of education (available inthe survey). This definition is more accurate that the nominal years of educationwhich tends to overestimate individual skills.

• Region (Urban). Dummy variable equal to one if workers’ region is urban andzero otherwise (available in the survey)

• Potential experience (Potl. Exp.). Quantitative variable calculated as thedifference between worker’s age and the estimated age of entry into the labour

market. The latter is calculated as the years of education plus the age of entry toelementary school.

• Ethnic group (White). Dummy variable equal to one if workers’ ethnic appar-tenance corresponds to ’white’ and zero otherwise.

• Postgraduate education (Educ.years(> 15)) Dummy variable equal to one if years of education is greater or equal than 15 and zero otherwise.

• Wage equations also include dummy variables to control for industry and occupa-tional wage differentials (see table 10).

3.2.1 Unconditional exclusion probabilitiesAccording to the Burdett and Mortensen (1998) framework presented in the previoussection, excluded workers receive less wage offers than their non excluded counterparts.Exclusion may also manifest in the way workers are distributed across the differentlabour status(S ) and in the job seeking (J ) decision(fig. 1), where the exclusion stateis a dichotomy modeled through equation (3) which depends on workers productiv-ity (π) and other characteristics. Table 4 presents the estimated parameters for thisrelationship.

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The model

Tab. 4: Unconditional exclusion probability(P [R = 1]), logit estimated param-eters.

Variable parameters

White(race) -1.3(0.15)

Years of education(Urban) -0.08(0.02)

Years of education 0.04a

(0.04)

Years of education(> 15) -0.84

(0.19)Urban 0.62

(0.19)

Potential Experience -0.53(0.06)

Sqrd. Potl. Exp. /100 0.73(0.08)

Educ.× Potl.Exper. /100 0.57(0.12)

anot significant at 5 % level.

b

not significant at 1 % level.Standard errors in parenthesis.

The retained specification is mainly explained by mincerian covariates and an ethnicdummy, where most of the higher order polynomials and crossed terms implied by sce-nario II were not significant or resulted in empirical non-identification of the overallmodel.

The next figure presents the exclusion probability curves with respect to potential expe-rience and ethnic groups based on table 4 estimates. Exclusion probability decreases asexperience increases until a certain experience level is achieved. Ethnic discriminationmay be verified for individuals not classified as ”white” by the survey as their exclusionprobabilities are statistically significant .

The non linear negative effect of experience into exclusion diminishes as experienceincreases, as shown by the positive ”Sqrd. Potential experience” coefficient. It also di-minishes with workers’ education as shown by the interaction coefficient.(Educ. × Potl.Exper.). The ethnicity dummy controls for a discrimination factor that may influencethe exclusion state and as can be seen in fig. 3, it plays a significant role.

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Chapter I The model

Fig. 3: Exclusion probability and potential experience (by ethnic groups )

Potential experience

E x c l u s i o n

P r o b a b i l i t y

0.2

0.4

0.6

0.8

10 20 30 40

factor(ethnic)

Other

White

Some counterintuitive results may be noticed, the first being the positive relationshipbetween the urban dummy and the exclusion probability. In Brazil, rural regions exhibitgreat heterogeneity as some of them may be populated by prosper rural societies (spe-cially in the southern country) while others may harbor important indigenous tribes.Thus, the urban dummy in the exclusion probability (4) only controls for some of thegeographic heterogeneity. Nevertheless, the higher exclusion probability at the urbanregion is in line with recent findings. Ernst (2008) shows that a systematic increase inurban unemployment since the early 90’s caused unemployment at urban regions to be10% against 1% in the rural one.

The effect of education on exclusion probability (Figure 4 and Table 5), constitutesthe second counterintuitive result. Table 5 shows the exclusion-education slopes atseveral experience levels calculated from the exclusion logit parameters (equation 1).This relationship is determined by education interaction with experience and tends tobe positive at lower experience levels. Nevertheless, the impact of postgraduate studiesunambiguously diminishes the exclusion probability. This behavior points to a potentialexcess of labour supply of middle educated workers as highly educated workers are less

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The model

excluded. This phenomena is discussed in Ernst (2008) where the author suggests that

the structural change in Brazil’s labour market since the early 90’s, caused a systematicdecrease in the share of the highly skilled labour demand; this was also related to adecrease in labour conditions (increase in unemployment rates) of better educated andurban region workers. At the rural area, the education parameter is positive but nonsignificant, as a consequence, rural and urban probability curves share similar shapes.

Fig. 4: Exclusion probability and years of education

Years of education

E x c l u s i o n P r o b a b i l i t y

0.2

0.4

0.6

0.8

2 4 6 8 10 12 14

factor(POEXP)

6

10

15

35

The random component parameter(θ̃) introduced to control for unobserved heterogene-ity (skills) is not reported but its t-ratio is −9.58 and the implied conditional correlationwith formal workers wage residuals is a singnificant −60%. This is a sound result giventhat if wage equation unobservables and workers productivity are driven by unobservedskills, then an increase of the unobserved skills would imply a negative conditional cor-relation between the exclusion probability and wage equations.

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Chapter I The model

Tab. 5: Exclusion-Education slopes

Potential Experience level 0 6 10 15 35

Urban 0.43 0.47 0.49 0.52 0.63(0.16) (0.36) (0.45) (0.55) (1.3)

Rural 0.52 0.55 0.58 0.60 0.72(0.17) (0.35) (0.47) (0.57) (1.4)

Standard errors in parenthesis

3.2.2 Exclusion probabilities conditioned on labour status

The main drawback with probabilities calculated from 4 rely in the fact that they arenot labour status specific. The following figures show sample exclusion probabilitiesconditional on the labour status and other worker characteristics. These probabilitiesare calculated from the empirical sample and are not conditioned on wages, thus therelationships are represented as clouds of points relating exclusion probabilities to theexogenous characteristics.

For formal workers , potential experience and exclusion probabilities exhibit a clearnegative relationship, while for independent and informal workers exclusion is a nonlinear function of potential experience. To better understand these effects, let’s considerthe exclusion probability conditioned on the labour status and other regressors alsoknown as posterior probability :

P [R|S , x] = P [S|R, x] P [R|x]

P [S|x] (9)

As can be seen in figure 5, the resulting probability shapes with respect to potentialexperience do not correspond exactly to the quadratic one defined for P [R = 1|x] intable (4). The new shapes are modified by the composition effect of potential experience(x) on the labour status at both regimes. The composition effect may be defined as thechange in the composition of excluded/non excluded proportions within a given labourstatus (S ) i.e. the change in:

P [S |R = r, x]P [S|x]

, r = 0, 1

which once multiplied by P [R] yields the posterior probability.

The composition effect may be obtained from Table 11 estimates; e.g. consider informalworkers and a change in the years of education education, it can be seen that educationincreases (0.92) the informal probability given non exclusion while it decreases theinformal probability given exclusion (-1.4). The final effect over the posterior probability

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The model

results from the composition effect and the pure exclusion effect, the first and second

terms in the expression below :d P [R|S , x]

dx = P [R|x]

d (P [S|R, x]/P [S|x])

dx +

P [S|R, x]

P [S|x]

d P [R|x]

dx (10)

At the formal status, the conditional exclusion probability is always decreasing andseems to fit the quadratic shape of the unconditional exclusion probability discussedearlier. It does not shows the the upward sloping probability segment of the uncon-ditional probability (fig. 3) as potential experience beyond 40 years are less frequentin the sample. From the composition effect, potential experience effect on conditionalexclusion stays ambiguous18, therefore, the conditional exclusion probability for formalworkers is dominated by the exclusion effect.

Fig. 5: Conditional Exclusion probability P [R = 1|S , x]

Potential experience

C o n d i t i o n a l E x c l u s i o n P r o b a b i l i t y

0.0

0.2

0.4

0.6

0.8

0.0

0.2

0.4

0.6

0.8

Formal

Informal

10 20 30 40

Independent

Unemployed

10 20 30 40

In the case of independent workers , the conditional probability shape suggests that thefirst experience years will diminish exclusion, nevertheless staying longer would revert

18From table 11 coefficients, experience increases more the formal probability given exclusion thanthe formal probability under non exclusion. This slight difference in experience coefficients (0.25-0.19)is compensated by the experience squared (-1.13,-0.2) so the final effect stays ambiguous.

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Chapter I The model

this situation as additional years of experience will increase it. The complexity of the

shape is due to the quadratic (experience) terms within the labour status probabilities(P [S |R = 1, x], table 11). Informal workers exhibit a similar probability curve with aless dominant quadratic shape, it also presents higher exclusion probabilities at everypotential experience level when compared with independent workers.

For unemployed workers , exclusion probabilities remain constant and around 95% atalmost every potential experience level. The remaining 5% (non excluded) can beidentified to the non participation decision i.e. the economically active individualswithout a job and not seeking for one. Given that wages are unobserved for unemployedworkers its exclusion probability curve does not show the dispersion of the others.

Fig. 6: Conditional Exclusion probability P [R = 1|S , x]

Years of education

C o n d i t i o n a l E x c l u s i o n P r o b

a b i l i t y

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

Formal

0 2 4 6 8 10 12 14

Independent

0 2 4 6 8 10 12 14

Informal

0 2 4 6 8 10 12 14

Unemployed

0 2 4 6 8 10 12 14

P o.E x p.1 0 y r s

P o.E x p.2 0 y r s

P o.E x p.4 0 y r s

The formal workers probability shape (fig. 4) is similar to the unconditional one19

(fig. 6) and education still has and slight effect on exclusion as experience stays at

19These curves are not conditioned on the log of wages

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Chapter I The model

workers while for informal ones these differentials are positive for ’managers’ only.

Labour status (S ) m-logit estimates (Table 11) suggest that education increases theshare of non excluded within a given status. Under exclusion, the effect of working atan urban region leads workers to unemployment or formality while under non exclusionit leads workers to unemployment or self-employment. This seemingly counterintuitiveresult can also be explained by Ernst (2008) as the unemployment rates raised system-atically in the urban region since the early 90’s achieving a 10% against 1% in the ruralarea.

3.2.4 About the conditional correlation structure

The conditional correlation structure across endogenous variables (S , w, J , R) was

introduced in order to control for the unobserved heterogeneity which is believed to bemainly driven by workers unobserved skills. The same covariance structure is specifiedat both regimes by introducing one common factor (ε) so the estimation procedure couldstill be feasible23. This common factor has unit variance and shares the same loadingsor associated parameters across regimes. Correlations in the table below (table 6) takeas a reference category the unemployment status, as in the econometric model. Thesignificant correlation (66%) between the independent-informal status supports the factthe independent and informal workers not only share observed but also unobservedcharacteristics. As a consequence, the IIA assumption does not holds and corroboratesthe strong relationship between self-employment and informality in LAC.

Tab. 6: Conditional correlations (between unobservables)

Within labour status

S ♭

formal-independent

0.07(0.05)

formal-informal

0.09(0.06)

independent-informal

0.66(0.05)

Between wages and labour status a ♭

(ws;S = s)

formal0.05

(0.03)

independent0.54

(0.04)

informal0.40

(0.02)

Standard errors in parenthesis♭ Estimated from the implied mixed multinomial tobit model.a Correlation between the unobservables of labour status s and the corresponding wage equation

(log ws)residual

The second part of the table presents conditional correlations between the labour statusand wage equations. The significant correlations represent how the same unobservablesdetermine the received wage at a given status and the fact of being at the status itself;They also confirm that wage equations should be estimated following a Mixed Tobit

23Increasing the number of common factors also increases the dimension of the integral involved inlikelihood (eq. 5) calculation.

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The model

approach.

3.2.5 The job seeking indicator (J )

According to this indicator 5% of the sample declares to seek for a new job. Severalspecifications (explanatory variables) where considered for its logistic regression, nev-ertheless, none yielded reliable or significant results due to identification issues (seesection 3.1.3). Hence, the final specification fixes the logit threshold and includes arandom term (ε) which may be interpreted as modeling the job seeking indicator asfunction of unobservable skills. As the more skilled workers are less likely to be seekingfor a new job, other things been equal, the conditional correlations between J andwage equations are expected to be negative. This is verified by the estimated condi-

tional correlations between J (formal, independent and informal) wage equations whichare all about −20%24. Finally, the conditional correlation between J and R is +0.21%meaning that unobservables leading to exclusion also lead to job search.

3.2.6 Exclusion and labour status patterns

From model estimates, conditional exclusion probabilities may be calculated in orderto classify observations into their most likely labour status and regime. The followingtable shows this distribution for the estimated sample25 and brings into light a mainstylized fact : the incidence of exclusion on informality and unemployment; as can beseen, the ratios of excluded to non-excluded are 2.4 and 5 respectively whereas formal

(0.9) and independent (0.53) status are much less affected.

According to this paper informality definition, independent workers are considered as“formal” independent as their jobs are registered in their registration cards while otherinformality definitions (ILO) tend to aggregate both, independent and non registered

jobs. Nevertheless, as can be seen in the table below, such aggregation relates twohighly heterogenous groups when it comes to labour exclusion.

24Standard errors between 0.02 and 0.04. Similar results are also obtained from labour statuscorrelations.

25The sample includes the male population between 18 and 65 years old.

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Chapter I Concluding remarks

Tab. 7: Estimated labour status and exclusion regime distribution

formal independent informal unemployed

Non-excluded 0.25 0.15 0.05 0.02 0.47

Excluded 0.23 0.08 0.12 0.10 0.53

0.48 0.23 0.17 0.12

Based on estimated posterior probabilities

The degree to which the model estimates distinguishes between the latent regimes maybe evaluated by the following entropy measure (Ramaswamy, Desarbo, Reibstein and

Robinson, 1993) :

E = 1 −

i

k−πik log πikN log2

; i = 1, ..., N , k = 1, 2

where πik is the (i-th observation) estimated posterior probability of being at the latentclass indexed by k . A worker is classified as excluded if he(she) is more likely to be ex-cluded (πiR > 0.5), thus clearer classifications imply probabilities that are closer to zeroor one and different from 0.5. This entropy measure increases with clear classificationsand is bounded between 0 and 1 (it tends to 0 as πik’s are concentrated around 0.5 andto 1 if they are closer to 0 and 1). The entropy measure for the exclusion regime (R)is 0.42 which indicates a “fair” classification. The same measure can be calculated to

evaluate the overall model performance when dealing with labour status and exclusionclassification at the same time, that is, evaluating the classification underlying table 7posterior probabilities; thus the entropy measure increases to 0.8.

4 Concluding remarks

The exclusion classification based on Burdett and Mortensen framework under the la-tent class modeling approach verifies many stylized facts, as ethnic discrimination andlack of working experience have a significant effect on (unconditional) exclusion proba-bilities. Having lower levels of education or postgraduate degres will also reduce workers(unconditional) exclusion whereas middle education will increase it pointing out a po-

tential excess of labour supply of middle educated workers that enter the job market.This phenomena has been identified in the literature (Ernst, 2008) in the form of apositive relationship between unemployment rates and education levels due to the in-crease of low skilled labour demand since the early 1990’s. Another stylized fact is theincidence of exclusion on informality and unemployment (table 7) as their excluded tonon-excluded worker ratios are about 2.4 and 5 respectively26.

26Non-excluded unemployed may be interpreted as non participants.

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Concluding remarks

Model estimates show that the lack of experience is the main determinant of (uncondi-

tional) exclusion and that education by itself will not suffice to reduce it. The influenceof experience and education on exclusion constitutes a main finding as it points out theimportance of school to job transition policies that facilitate the access to the labourmarket in order to gain working experience.

Informality is estimated to be mainly constituted by excluded workers (70%), suggest-ing the importance of labour market policies aiming to specifically reduce excluded-informality. From the composition effect, it can be concluded that education is a keyfactor as it’s capable of increasing non-excluded informality while decreasing the ex-cluded one. On the contrary, the pure exclusion effect will tend to increase exclusionas mentioned in the first paragraph. At the end, the overall effect (see eq.10) will still

be dominated by the composition effect as shown in figure 6. Such a result implies thatreducing the excluded-informality without discouraging the non excluded one can beachieved by standard policy measures aiming to increase workers level of education.

The random component (ε) introduced to control for unobserved heterogeneity mayalso be interpreted as an unobserved skills latent factor. From its estimated factorparameters (loadings) the model verifies the negative relationship between unobservedskills and exclusion. It also verifies the positive relationship between observed wagesand unobserved skills, where unobserved skills have a greater influence on independentand informal wages determination.

The presented methodology tries to encompass the empirical findings in the informality-

exclusion literature presented in (Perry et al., 2007) with a theoretical framework(El Badaoui et al., 2010; Burdett and Mortensen, 1998) so that it could be easily imple-mented with standard household survey data. The main feature of this approach is theassumption of endogenous arrival rates determined by workers productivity level. Eventhough, the endogeneity assumption implied by the econometric model yields coherentempirical results, it differs from Burdett and Mortensen approach where this rate is as-sumed to be exogenous. Thus, the empirical results suggest that allowing arrival ratesto be endogenous is a natural extension to the theoretical framework.

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Chapter I Appendix

A Appendix

A.1 Descriptive Statistics

Tab. 8: Education years by region, labour and job seeking statusYears of Education

Average Median Std. Dev. Share

Formal 8.4 9 4.1 42.2%Independent 5.6 5 4.2 22.6%

Informal 5.8 5 4.2 22.3%Unemployed 6.7 7 4.5 12.9%

100%

Job seekers (yes) 7.4 8 4.4 5%(no) 6.9 7 4.1 95%

Urban 7.6 8 4.2 83%Rural 3.9 4 3.5 17%

Adult male population (


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Appendix

A.2 Estimated equations

Tab. 10: Wage equations estimated parameters.

formal independent informal

Non NonVariable excluded Excluded excluded Excluded

Years of education 0.11 0.14 0.02a 0.17 0.02(0.001) (0.004) (0.008) (0.006) (0.004)

Urban 0.08 -0.1a -0.05a 0.06a 0.00(0.014) (0.052) (0.04) (0.064) (0.016)

Potential Experience 0.05 -0.04 0.02 0.02 0.02(0.001) (0.006) (0.006) (0.006) (0.002)

Sqrd. Potl. Exp. ×100 -0.05 0.06 -0.04 -0.01a -0.03

(0.002) (0.01) (0.009) (0.01) (0.004)Agriculture 0.07 -0.51 -0.21 -0.37 -0.18

(0.002) (0.045) (0.053) (0.061) (0.019)Industry 0.27 -0.24a 0.02a 0.26a 0.04a

(0.025) (0.2) (0.14) (0.19) (0.086)Transp. and Comm. 0.12 -0.19 0.16b 0.06a 0.09

(0.008) (0.05) (0.063) (0.05) (0.021)Construction 0.14 -0.1 0.24 0.17 0.06

(0.01) (0.029) (0.034) (0.046) (0.018)Manager 0.55 0.86 -0.43a - 0.55

(0.014) (0.19) (0.27) - (0.014)Technician(middle) 0.24 0.17 0.8 0.35 0.3

(0.014) (0.17) (0.16) (0.056) (0.036)

constant -0.51 1.12 -0.24b

-0.62 -0.33(0.026) (0.11) (0.103) (0.105) (0.04)variance (Resid.) 0.32 0.6 0.09 0.67 0.1

anot significant at 5 % level.

b not significant at 1 % level.Standard errors in parenthesis.

Educational and regional wage differentials between both regimes seem to be coherent asnon excluded workers earn higher wages. Occupational and sectoral differentials seem alsocoherent for independent workers while they are ambiguous for informal ones. Nevertheless,wage differentials across exclusion regimes need to be interpreted with care as characteristicsdetermining exclusion also determine received wages. To be able to calculate wage differentialsfrom the slope parameters, both populations (excluded and non-excluded) need to overlap interms of the characteristics included in the wage equation. As exclusion is mainly driven

by the same determinants (education, experience, etc.) this condition is not met. A validcomparison would be available through matching and propensity score estimators.

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Chapter I Appendix

Tab. 11: Mixed multinonial logit estimated parameters(P [S|R, x]).

f

informal employment model

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