The informal Labour Market in Mexico: A Job Search Model

by

Carlo Eduardo Alcaraz Pribaz

Banco de México, 2007

Abstract

We propose a simple on-the-job search model of informal labour that helps us to understand somestylized facts about informality in the Mexican labour market. In testing the implications of themodel, we found evidence of wage di¤erentials between the two types of labour. We also found theprobability of transit from informal to formal is three times higher than that of transiting in theopposite direction. Finally, we found evidence that changes in productivity alone cannot explainworkers�transition probabilities between the formal and informal sectors.

0.1 Introduction

Studies of informality can be divided into two main groups: dual labour market models, and

models that explain informality as a result of a maximization problem of economic agents.

The informal labour literature began with Hart (1973). In this paper, informality is linked

with underemployment, and with small or micro-businesses that are the result of individual

or family self-employment. In addition, the existence of the informal labour market (ILM)

is explained as a consequence of weaknesses in Developing Countries�(DCs) economies that

prevent the incorporation of the majority of the economically active population (EAP) in

the formal labour market. In DCs, a large proportion of workers and their families are too

poor to a¤ord even small periods of unemployment, and while searching for suitable work

many start working as informal workers, either as self-employed workers or as employees in

micro-business informal �rms. Informal employment becomes like a survival strategy. These

informal �rms are typically characterized by undercapitalization, low productivity and small

size enterprises, and workers remain in the ILM only until they �nd a job in the formal

market.

Since the end of the 1980s, some researchers have proposed an alternative explanation

for the existence of ILMs. De Soto (1989) and Tokman (1992) argue that informality exists

because some agents want to take advantage of the dynamic unregulated informal labour

market. A fundamental characteristic of this approach is that workers choose to be informal

as a result of a maximization process. In other words, rather than a survival strategy,

informal labour is seen as voluntary. Under this framework, some �rms choose to have

1

the best of both worlds: they can maintain a proportion of the labour force under formal

regulations, while the remainder consists of informal workers.

We think that informal labour in DCs is better explained by a combination of these

two theories. A job search model with an informal sector can shed light on the informality

problem. With a job search model we can link these two versions: we have formal workers,

informal workers queuing to get a formal job and the associated higher wages, and both

formal and informal workers are integrated in the same labour market, with no restrictions

on entry to the formal sector (i.e., a non-segmented labour market).

In this paper, we present a theoretical model to explain some stylized facts of a labour

market with informal labour. We develop a simple on-the-job-search model, in which workers

are allowed to search for a job while working. Burdett, Lagos and Wright (2003) extend an

equilibrium search model of crime, unemployment and inequality by incorporating on-the-

job search. Based on this model, by relating crime with informal labour, we study the

relationship between informal and formal labour.

Several interesting results emerge. Informal workers do not pay taxes but have a higher

likelihood of losing the job, and this acts as a "punishment device" for informal workers.

As workers� wages increase, the cost of losing the job also rises. There will be a wage

level (informal wage) above which workers are better o¤ if they pay taxes and become

formal. This theoretical framework links tax level and the probability of losing the job with

informality size. It predicts higher wage dispersion among informal workers, and higher

workers�probability of moving from informal to formal than moving in the opposite direction.

2

We test some of the theoretical predictions. We test wage di¤erentials with three alter-

native methods: counterfactual density functions, residual analysis and quantile regression.

We also �nd higher wage dispersion among informal workers, and that informal workers

are more likely to lose their job than formal workers.

Finally, we analyze the e¤ects of changes in workers�productivity on the implications of

the job search model.

This paper is organized as follows: In Section 2, we review the literature on job search

models. In Section 3, we present a job search model with informal labour. Section 4

puts forward di¤erent econometric speci�cations to test the empirical implications of the

theoretical model. Section 5 contains the concluding remarks.

0.2 Theoretical review, job search models

One of the main assumptions in classic economic theory is that all participants in any market

have perfect information. In the particular case of the labour market, perfect information

implies that each worker has information about all the job o¤ers available in the market,

and that employers know of all the people who are looking for a job. Without market

imperfections, the only decision that workers have to face is how many hours they will

work (zero is one alternative). In consequence, in this economy there is no involuntary

unemployment. The �rst economist to analyze imperfect information was Stigler (1961).

Job search models were introduced in 1970, when McCall published his in�uential paper on

the "Economics of information and job search." Another important paper published in the

3

same year was "Job search, the duration of the unemployment, and the Phillips Curve" by

Mortensen (1970).

The main assumption of job search models is that the job seeker does not know the wage

each �rm is paying. As a result, a worker needs to keep searching for a job until he or she �nds

one with an attractive enough wage. In the basic model, workers cannot search for jobs while

employed, and the cumulative wage distribution is exogenous. The standard procedure is to

�nd the workers�reservation wage: i.e., the wage at which workers are indi¤erent between

accepting the job and remaining unemployed. Once the reservation wage is obtained, it is

possible to conduct static comparative analysis, to examine how di¤erent variables (what

workers receive when unemployed, interest rate, probability of losing the job, arrival rate

of job o¤ers) a¤ect the reservation wage. The determination of reservation wages allows

us to predict how their change a¤ects the level and duration of unemployment and post-

unemployment wages.

Equilibrium search model and crime In the models we have discussed so far, workers

may �nd themselves in two possible states: employed or unemployed. One of the extensions

of the equilibrium search models (Burdet, Lagos and Wright, 2003) adds another possible

state for workers: being in jail.

In this paper, the authors propose to model workers�behavior, given that they have the

opportunity to commit a crime. Some workers will commit a crime if the opportunity arises.

When they commit a crime they receive an extra income, but if they are caught they

lose their job, and they will spend a period of time in prison. In this labour market there

4

are two relevant wages: the reservation wage and the crime wage.

The reservation wage is the same as in the previous models, while the crime wage de-

termines whether a worker is willing to commit a crime or not. For workers with wages

above the crime wage, it will not be worth risking committing a crime because the cost of

losing the job is too high. For those workers with wages below the crime wage, it is worth

taking their chances and committing a crime if they have the opportunity, since the cost of

losing the job is lower. An interesting aspect of this model is that it links crime with the

traditional parameters of equilibrium search models, such as job o¤er arrival rates and the

instantaneous gain of being unemployed.

Informality and job search models The "toreros" (bull�ghters) are at the bottom

rank among street traders, these workers use to carry small quantities of cheap products

in order to sale them on the street, as soon as an inspector is in sight the toreros hastily

pick their products and move to another location. If they are caught by the inspector all

their products are con�scated. On the other extreme of the street vendors, there are workers

that are registered in the council, pay monthly fees and have permit to work on the street.

These street vendors have big stands with important number of products. There also traders

with establishment that sell groceries to locally, these workers generally count with council

permit and pay a fee to the local government. In Mexican cities it is possible to spot "taxis

piratas" (pirate taxis) these taxis are not registered in the local council and do not pay any

tax, generally charge smaller fees than normal taxis and are in very bad condition, if a taxi

pirata is caught by the police their car is con�scated temporally and they have to pay a

5

�ne. Registered taxis on the other hand, their cars are in better condition, they do not risk

to be caught and stop working for a period of time but they have to pay a fee to the local

government. Manufacturing �rms can also hire informal workers do not pay tax but risk to

be caught by the Social Security inspectors and stop working for a period of time. it seems

that there is a threshold under which workers are beeter of being formal and pay taxes.to

avoid losing the job if the inspector or police arrives.

Job search models can shed some light on the dynamics and the causes of informal

labour. We consider that two important characteristics of informality, tax payment and

the probability of being caught by governmental inspectors, can be easily and naturally

incorporated into the process of �nding a job in a job search model.

We present a simple on-the-job-search model with exogenous wage distribution focused

on workers�behaviour1 . The higher likelihood of informal workers losing their job acts as a

"punishment device." As workers�wage increases, the cost of losing the job also rises. There

will be a wage level (informal wage) at which workers are better o¤ if they are formal.

0.3 On-job-search model with informal labour

In this section we describe and analyze workers�behaviour. First assume that there is a

continuous in�nite lived and risk neutral number of workers [0; 1], and there is a continuous

in�nite lived and risk neutral number of �rms N; N 2 [0; 1]. Therefore N is the �rm-worker

ratio. Firms and workers are ex ante identical. Each �rm pays w to its workers, and hires

1 Burdet, Lagos and Wright (2003) present an equilibrium search model in which the wage distributionis endogenous. The wage distribution is obtained by examining the equilibrium between workers and �rms.

6

any worker that it contacts and is willing to accept w. F (w) is the wage distribution of the

wage o¤ers.

There are two types of labour in the economy: formal and informal. Formal labour pays

a lump sum tax t per worker, while informal labour does not pays tax. At any given moment

in time, a worker can be formally employed, informally employed or unemployed. Let the

payo¤ in these states be de�ned by, VF (w), VI(w) and VU . If the worker is unemployed,

he or she receives an income �ow of b. We de�ne the reservation wage (R) such that

VF (R) = VU or VI(R) = VU2: At the reservation wage, workers are indi¤erent between

working and staying unemployed. Formal and informal workers obtain wage w: Employed

and unemployed workers receive job o¤ers at rate � from a random draw from F (w). The

exogenous job destruction rate is � and is the same for formal and informal labour. When a

worker �nds a job, he or she has the option of being informal and not paying tax, or being

formal and paying tax t. If the worker decides to be informal, he or she has the probability

�3 of being caught by tax inspectors and losing the job.

The discounted expected utility (Bellman equation) for unemployed workers is

VU =1

1 + rdt[bdt+ �dtEx fmax(VI(x); VF (x); Vu)g+ (1� �dt)Vu] : (1)

Where r is the exogenous interest rate, then 11+rdt

is the discount factor over a short

interval of time dt: The unemployed worker receives a job o¤er with probability �dt that he

2 As explained later, just one of these two cases can exist.

3 � can re�ect any factor that increase the probability of losing the job for informal workers. Streetinsecurity, governmental regulations, lack of access to �nancial market, etc.

7

will accept if the expected utility of working in the new job (formal or informal) is higher

than remaining unemployed (VI(x) > VU or VF (x) > VU). With probability (1 � �dt) the

worker does not receive any job o¤er and stays unemployed.

By multiplying both sides of (1) by 1+rdt and rewriting, we obtain the following equation:

rVU = b+ �Exmax(VI(x)� VU ; VF (x)� VU ; 0): (2)

This equation has a alternative interpretation than equation 1. It shows that, at any

moment, the discounted expected �ow of income of unemployment rVU is equal to b; to

which is added the average income �Exmax(VI(x) � VU ; VF (x) � VU ; 0) due to a possible

change in the unemployed status. This term is also known as the expected capital gain of a

job seeker status change.

The Bellman equation for an informal worker is

VI(w) =1

1 + rdt

26666664wdt+ (1� �dt)(1� �dt)(1� �dt)max(VI(w); VF (w); VU)

+(1� (1� �dt)(1� �dt)(1� �dt))VU+

(1� �dt)(1� �dt)�dtEx fmax(V I(x); V F (x); V F (w); V I(w); V U)g

37777775(3)

At a given wage, every worker has to make two decisions. The �rst is whether to work

or remain unemployed, and the second is whether he or she wants to be formal or informal.

The decision procedure is re�ected in the term max(VI(w); VF (w); VU) in the informal work-

ers�value function. Informal workers may lose their job for two reasons: job destruction

(�) or if they are caught by the tax inspector (�), in which case they get VU : The worker

8

may not lose the job and receive a job o¤er with probability (1 � �dt)(1 � �dt)�dt: In this

case, the worker faces another set of decisions (Ex fmax(VI(x); VF (x); VF (w); VI(w); VU)g)

he or she can keep his current wage and decide to be formal, informal or unemployed

(VF (w); VI(w); VU) or accept the job o¤er and decide whether to be formal or informal

at the new wage. (VI(x); VF (x)).

Multiplying both sides of equation 1 by 1 + rdt and rearranging we have

rVI(w) = w � (1� � � � � �)max(VI(x)� VU ; VF (x)� VU ; 0) + (4)

�Ex fmax(VI(x)� VI(w); VF (x)� VI(w); VF (w)� VI(w); VU � VI(w); 0)g

This equation shows that, at every moment, the discounted expected �ow of an informal

workers�income equals his or her wage, to which is added the average income that comes

from a possible change in the worker�s status (capital gain).

The expected value of being formal is:

rVF (w) = w � t+ (1� � � �)max(VI(x)� VU ; VF (x)� VU ; 0) + (5)

�Exmax f(VI(x)� VF (w); VF (x)� VF (w); VI(w)� VF (w); VU � VF (w); 0)g :

Formal workers have to pay tax t, but they have a lower likelihood of losing their job,

because they do not lose their job if there is a tax inspection.

The optimal search strategy As noted above, at a given wage workers face two decisions:

�rst they have to decide whether to accept the job or not, and second, whether to be formal

9

and pay tax, or not pay tax and risk being caught by the tax inspector and losing the job.

Deciding between accepting the job and remaining unemployed: To obtain

the reservation wage, we substitute equations 4 and 5 in 2 and we solve for w :

R = b (6)

Any unemployed worker that receives a job o¤er with wage below b will not accept the

job and will keep searching. If an unemployed worker receives a job o¤er above b he or she

will accept the job.

Deciding between being formal and informal Because VI(w) and VF (w)are in-

creasing in w; employed workers will accept any o¤er above the current wage. To analyze

informality decisions, we obtain the informal value function when workers prefer to be in-

formal.

We modify equation 4 for w s.t. VI(w) > VF (w); VI(w) > VU and we obtain

rVI(w) = w � (� + � + �)(VI(x)� VU) + �Exmaxf(VI(x)� VI(w); VF (x)� VI(w)g (7)

The second term represents the average expected value of receiving a job o¤er under

which the worker prefers to be formal and job o¤ers under which the workers prefer to be

informal.

10

Conditions that determine workers to be formal

In this case, we modify equation 5 for w s.t. VI(w) < VF (w); VF (w) > VU

rVF (w) = w � t� (� + �)(VF (x)� VU) + �Exmaxf(VI(x)� VF (w); VF (x)� VF (w)g (8)

Rearranging equations 7 and 8 we obtain the relation between the value function of

informal and formal workers and wages:

VI(w) =w + (� + � + �)VU + �[�I ]

r + � + � + �(9)

VF (w) =w � t+ (� + �)VU + �[�F ]

r + � + �(10)

Where �I = Exmaxf(VI(x) � VF (w); VF (x) � VF (w)g and �F = Exmaxf(VI(x) �

VF (w); VF (x)�VF (w)g: From these equations we know that the pendent of the formal value

function is higher than that of the informal value function (@(VI(w)�VF (w))@w

< 0). This implies

that the worker will be less inclined to be informal as the wage increases. This situation

arises because, when a worker loses a high paid job, he or she will not be able to �nd a good

job for a period of time. He or she will remain unemployed until he or she receives a job

o¤er higher than his reservation wage. Therefore, the higher the wage, the higher the cost

of losing the job.

At this point, we can de�ne the informality wage I as VI(I) = VF (I) > VU ; from equating

equations 9 and 10 and solving for w we can obtain the informality wage:

11

I =t(r + � + �)

�+ t+ VUr � �[

Z 1

I

(VF (x)� VF (w))dF (x)] (11)

Notice that, at wage I; workers will not accept any job o¤er from the informal sector:

this is re�ected in the second term of the equation. If the workers�wage is below I; the

relevant value function is VI (workers prefer to be informal). As the wage increases, there

is informal wage (I);at which informal workers are better o¤ if they pay taxes and become

formals, and VF becomes the relevant value function.

To analyze the di¤erent cases in our labour market, we obtain an alternative way of

expressing Bellman equations for formal and informal workers:

rVI(w) = w�(�+�+�)(VI(x)�VU)+�Z I

R

[VI(x)� VI(w)] dF (x)+Z 1

I

[VF (x)� VI(w)] dF (x):

(12)

The expected capital gain of job seekers can be represented as an addition of integrals.

The �rst is integrated over the informal wage range, and includes the gain from �nding an

informal job (VI(x) � VU) times the probability of �nding an informal job (dF (x)): The

second is integrated over the formal wage range and includes the gain from �nding a formal

job (VF (x)� VU) times the probability of �nding a formal job (dF (x)):

rVF (w) = w � t� (� + �)(VF (x)� VU) + �Z 1

I

[VF (x)� VF (w)] dF (x) (13)

In this case, the expected value of receiving a job o¤er includes only formal sector o¤ers

(only those o¤ers are acceptable).

12

Let w and w be the upper and lower supports of F (w). We have three possible situations:8>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>:

1) if VF (w) > I then VF (w) > R for all w � R and there is no informality in the economy,

VF (I) = R.(case 1)

2) if VI(w) < I then VF (w) < I; for all w � R and all the economy is informal,

VI(I) = R: (case 2)

3) if VI(w) < I < VF (w) therefore exists I such that VI(w) > VF (w) if w < I

and VI(w) < VF (w) if w � I. There is formal and informal labour in the economy,

VI(I) = R: (case 3)

VI

VF

w

VI, VF

VI

VF

w

VI, VF

Case 1 Case 2

VI

VF

VF before tax

tax

w

VF, VI

I

VF(I)=VI(I)

Case 3

13

Notice the concave shape of the value functions, this re�ects the fact that at higher wages

it is harder to get a better job (see equations 12.and 13).

We can obtain the relation between tax (t) and the probability of being caught (�) with

informality wage, (I) obtaining the derivative of equation 11 with respect to t and �4 :

� @I@t> 0: If the cost of being formal increases (tax), the wage at which workers are

willing to be informal also increases. If tax rises workers with higher wages are willing

to take their chances of becoming informal and risk of being caught and lose the job.

� @I@�< 0: If the probability to be caught increases, the expected value of being informal

decreases. Therefore some informal workers will be willing to become formal if � grows.

Workers decide to be informal at lower wages because the expected value of what they

would obtain by avoiding the payment of taxes is higher than what they would lose if they

were caught and lost their the job. At lower wages losing the job is not so problematic for

two reasons: �rst, the di¤erence between what they receive when they work and what they

receive when unemployed is not very large. Second, if they lose the job it is relatively easy

to �nd a new job with a similar wage given the high turnover in the informal labour.

Concluding, from this model we obtain some interesting results:

1. In this model, although workers are homogeneous, we can generate two types of labour,

in which the wages of formal workers are higher than those of informal workers.

4 There is a direct relationship between informality wage and proportion of informal workers in theeconomy.

14

2. An increase in the probability of being caught or a decrease in tax, will increase the

proportion of formal workers in the economy.

3. We also found that informal labour is characterized by lower wages, higher turnover

and that informal workers receive a higher number of acceptable job o¤ers, and have

a higher probability of losing the job.

4. Workers can transit from informal jobs to formal jobs, but have no incentive to go

directly from formal to informal. However, workers may lose formal jobs, spend some

time unemployed and obtain an informal job with a lower wage.

0.4 Empirical analysis

Since neither income taxes (t) nor tax compliance enforcement (�) in Mexico have changed

signi�cantly in recent years, we cannot assess the e¤ect of changes in these variables on the

informality level in the economy. However, the theoretical model we presented earlier in this

paper has other empirically testable implications:

1. Formal workers�wages are higher than informal workers�wages.

2. The probability of losing the job is higher for informal workers than for formal workers.

3. The workers�probability of going from informal to formal is higher than their proba-

bility of going from formal to informal5 .

5 Under the on-the-job search model we present here, the only way to observe a worker�s transition fromformal to informal is if the worker loses the formal job and �nds a new informal job in the period betweentwo interviews.

15

We use the data from the Encuesta Nacional de Empleo Urbano (ENEU).

0.4.1 Wage di¤erentials

The job search model predicts that the wages of informal workers are lower than the wages

of formal workers. This result is achieved assuming that formal and informal workers are

homogeneous.

Alcaraz (2006) found that formal workers have a higher level of education than informal

workers. Likewise, formal workers have higher wages than informal workers. We also know

that, for both formal and informal workers, there is a positive relationship between wages

and education. Wage di¤erentials between formal and informal workers can be entirely

explained by di¤erentials in education level between formal and informal workers. If that

is the case, then, when we control for education level, wage di¤erentials should become

zero. Other observable characteristics like workers age or workers economic sector could also

explain wage di¤erentials between formal and informal workers. Therefore to control for

workers observable characteristics is like to homogenize workers. However we can still have

bias if unobserved workers characteristics a¤ects wages. This can happen, for instance, if

unobserved workers abilty a¤ects wages and formal workers have on average more ability

than informal ones. The reported wages in the ENEU questionary are after taxes and include

all monetary income, non monetary income (i.e. social security benne�ts are not included)

The period of analysis goes from 1995 to 2001.

We use three alternative methods to analyze wage di¤erentials between formal and in-

formal workers: a non parametric approach (counterfactual distribution functions), a semi

16

parametric approach (quantile regression), and a parametric approach (residual analysis).

Despite the evident di¤erences between these three ways to test wage di¤erentials the mod-

els have two important characteristics in common: we control for observable characteristics

(age, square of age, sex, schooling, marital status and economic activity), and we analyze

wage di¤erentials through all the wage ranges.

Counterfactual functions The technique for decomposing changes in the density of

equivalent income is based upon the conditional re-weighting procedure developed by Di-

nardo, Fortin, and Lemieux (1996)� hereafter called DFL. This technique has also been

used by many authors in the recent literature (e.g., Chiquiar and Hanson, 2002; Daly and

Valletta, 2004; Valletta, 1997). This procedure is able to estimate the entire conditional

distribution.

The antecedent of this technique is the Oaxaca-Blinder. This decomposition is focused on

the mean of a distribution. The main problem with this estimation is that it only estimates

the mean of the wage distribution, and it does not take into account changes in the rest of the

distribution function (tails, for example). If the distribution function changes characteristics

other than the means, this method cannot show the wage di¤erentials.

We now construct the counterfactual densities that use the entire density of wages. Using

the conditional probability rule, we can write the Cumulative Density Function (CDF) of

observed wages in informal labour as the conditional wage distribution multiplied by the

marginals

17

F i=informal(wji = informal) =ZX2x

F i=informal(wjx)dpr(xji = informal) (14)

Where x is a set of all workers observable characteristics, F i=informal is the conditional

cumulative wage distribution for informal workers and pr(xji = informal) is the probability

of the workers� observable characteristics conditional to the workers� type of labour (i).

Meanwhile, the wage CDF of informal workers is

F i=formal(wji = formal) =ZX2x

F i=formal(wjx)dpr(xji = formal) (15)

With equations 14 and 15, we can construct the counterfactual CDF function for informal

workers (density of informal workers�wages if they are paid according to the prices of skills

for formal workers):

Fii=informal(wji = formal) =ZX2x

F i=informal(wjx)dpr(xji = formal) (16)

The former equation is equivalent to equation 15, except that it is integrated over the skill

distribution of formal workers. The term pr(xji = formal) (probability of workers�observ-

able characteristics given workers�status) is unknown. Assuming that the structure of wages

of informal workers (F i=informal(wjx)) does not depend on the distribution of attributes of

formal workers(pr(xji = formal)) we can rewrite 16:

F i=informal(wji = formal) =ZX2x

F i=informal(wjx)dpr(xji = formal)pr(xji = informal)pr(xji = informal)

(17)

18

The former equation can be written as

F i=informal(wjxi=formal) =ZX2x

�F i=informal(wjx)pr(xji = informal) (18)

where

� =pr(xji = formal)pr(xji = informal) (19)

The former equation is known as counterfactual CDF. The terms pr(xji = formal) and

pr(xji = informal) cannot be estimated. Fortunately, we can modify � applying Bayes rule6

. Bayes rule reverses the conditional probability to be estimated: instead to estimate the

probability of x given i; we have to estimate the probability of being formal given x:

pr(xji = formal) = pr(i = formaljx)pr(x)pr(i = formal)

(20)

pr(xji = informal) = pr(i = informaljx)pr(x)pr(i = informal)

(21)

If we substitute equations 20 and 21 in 19, we obtain

� =pr(i = formaljx)pr(i = informaljx)

pr(i = informal)

pr(i = formal)(22)

The nominator and denominator of the �rst term of equation 22 can be estimated with

a probit model. For each worker, we can estimate the probability of being formal given the

6 Bayes Rule: Let A1; A2; :::; An be a partition of , each Aj having a positive probability then

P (Aj jB) = P (BjAj)P (Aj)Pn1 P (BjAj)P (Aj)

19

worker�s observable characteristics. The counterfactual CDF can be estimated through the

empirical distribution function estimation. This procedure approximates a CDF function

from a random sample w1;w2;:::; wn;with weights �1; �2; :::; �n,Pn

i=1 �i = 1

After computing these weights we estimate the counterfactual wage CDF non-parametrically.

We apply the empirical distribution function to the sample of workers�wage:

F i=informal(wjxi=formal) =1

n

nXi=1

�i�

�w � wih

�:

Where n is the number of observations, h is the bandwidth, and �(:) is the accumulative

distribution function.

Figure 1 is the kernel estimation of the actual densities for formal and informal workers

for the 4th quarter of 2001 from the ENEU survey. The probability density function (PDF)

of observed wages for formal workers is shifted to the right, compared to the density of

observed wages for informal workers. That is evidence that informal workers earn less than

formal workers throughout all the distribution function. This graph also shows that informal

workers present higher wage dispersion than formal workers.

Figure 2 shows the cumulative wage distribution for formal and informal workers, in order

to establish whether this di¤erence is due exclusively to di¤erences in workers�characteristics.

The �gure 2 a) shows the unmodi�ed wage CDF for formal and informal workers, and the

�gure 2 b) shows the actual formal workers�wage CDF and the counterfactual informal wage

CDF.

In the counterfactual �gure, although both functions are closer, the informal counterfac-

20

0.2

.4.6

.8A

ctua

l for

mal

 200

1 de

nsity

/Act

ual i

nfor

mal

 200

1 de

nsity

4 6 8 10 12lingmens

Actual formal 2001 density Actual informal 2001 density

Figure 1: Formal and Informal workers wage distribution function

tual density function is still to the right of the formal wages density function throughout the

entire wage range. The formal wage function stochastic dominates the informal counterfac-

tual density function. That means that, at any quartile, wages of formal workers are higher

than wages of informal workers, when we have controlled for observable characteristics.

Residual analysis Another test for stochastic dominance can be conducted by regressing

the log wages on observable characteristics and obtaining the residuals. We then split the

residuals (i.e. actual wage minus predicted wage) between formal and informal workers.

Figure 3 shows that the quantile of distribution of wages for formal workers always lies

above than those are informal. Again, after controlling for observable characteristics, the

result proves stochastic dominance of the formal wage distribution over the informal wage

distribution.

21

0.2

.4.6

.81

cum

for/

cum

inf

4 6 8 10 12 14temp

cumfor cuminf

a) Actual

0.2

.4.6

.81

cum

for/

cum

cont

inf

4 6 8 10 12 14temp

cumfor cumcontinf

b) Counterfactual

Figure 2: Cumulative Wage Distribution Functions, Formal and Informal workers

Quantile regression Quantile regression (QR) was developed by Koenker and Basset

(1978). It is an extension of the Least Absolute Deviations (LAD). LAD estimator was �rst

proposed by Boskovich in the 18th century, to estimate astronomical distances. QR has

been used in a wide range of �elds, including biology, sociology and medicine. In economics,

QR methods have been used to study the determinants of wages, and trends in income and

inequality, among others topics.

There are two main advantages of this method:

1. Traditional Ordinary Least Squares estimations (OLS) can be seriously a¤ected by out-

lying observations. Compared to QR, OLS assigns a larger weight to larger deviations

from the regression causes7 . Quantile regression (QR) reduces this problem.

7 OLS minimizes the square of the di¤erence between the predicted estimation value and the observedvalue. On the other hand, quantile regression minimizes the absolute value of the same di¤erence. Thereforequantile regression predictor have smaller deviations from the mean.

22

­1­.

50

.51

resi

nf/r

esfo

r

.2 .4 .6 .8 1resinfFN/resforFN

resinf resfor

Figure 3: Residual analyisis

2. OLS regression is based on the mean of the conditional distribution of the dependent

variables. However, it may happen that the relation between the dependent and inde-

pendent variables changes at di¤erent levels of the independent variable. With QR it

is possible to obtain di¤erent estimations of the coe¢ cients of the independent variable

throughout all the conditional distribution function of the dependent variable.

QR regression estimator solves the following optimization problem:

�� = arg�min

8<: Xi:lnwi�x0i��

� jlnwi � xi��j+X

i:lnwi<x0i��

(1� �) jlnwi � xi��j

9=;Where lnwi is the logarithm of worker i wage, xi is a matrix with workers observable

characteristics (independent variables), including a dummy variable that indicates worker

status (1 if formal, 0 if informal), and � 2 [0; 1] represents the section of the wage distribution

in which � is estimated. The former optimization problem is also written as

23

min�

X��(lnwi � xi��)

where ��(�) is the piecewise linear function (check function) de�ned as

��(�) =

�� if � � 0

1� � if � < 0

The LAD estimator of � is a particular case of the optimization problem described above.

This is obtained setting � = 0:5 (median regression). The LAD estimation minimizes the

symmetrically weighted sum of absolute errors. For example, we can divide the population

by wages into four parts with equal proportions of workers (quartiles). Thus the �rst quartile

is obtained by setting � = 0:25: If we solve the maximization problem for many values of

� 2 [0; 1] ; we can trace the entire distribution of wi; conditional to xi:

The problem can be solved by linear programming methods. The con�dence intervals

are obtained by sample bootstrapping, and therefore there is no need to assume a particular

distribution of the residuals.

In the matrix of independent variables (X) is included as a dummy variable for formal

workers. The coe¢ cient of this variable captures the wage di¤erentials between formal and

informal workers.

Figure 4 shows the coe¢ cient of the dummy variable Formal across the di¤erent quan-

tiles. The grey line shows the 99 percent con�dence interval. From this �gure two interesting

results arise:

24

0.20

0.40

0.60

0.80

1.00

form

al2

0 .2 .4 .6 .8 1Quantile

Figure 4: Quantile regression

The �rst is that in all wage quantiles the coe¢ cient of the dummy variable Formal is

positive and signi�cant, which means that there exists a positive relationship between wages

and formality. This is again a sign of stochastic dominance of formal wages over informal

wages.

The second is that this e¤ect is decreasing as wages increase. A higher variance in the

informal wage distribution can produce this e¤ect.

Evidence of Informality Wage In �gure 5 we divide workers into three education

groups8 . Although the patterns are similar to those in the �rst �gure, the results show that

the e¤ect of being formal on wages for highly educated workers is larger in all the quantiles.

It is well known that workers of di¤erent education groups have di¤erent wage distrib-

8 Schooling 1: Up to primary school; Schooling 2: Up to high school; Schooling 3: University.

25

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

Coef

Qua

ntile Escol 1

Escol 2Escol 3

Figure 5: Quantile regression by education group

ution functions. The wage distribution function of workers with schooling level 3 is shifted

to the right with respect to those with schooling level 1 and 2.

Considering that the majority of informal workers are in schooling level 1 and 2 and that

the majority of workers with schooling level 3 are formal (see table 1), then if we truncate

both distribution functions at a particular wage (i.e. informality wage I) the number of

workers with schooling level 3 to the left of I9 will be lower than the number of workers with

schooling level 1 and 2 to the left of I. This situation shifts the wage curve for workers with

schooling level 3 to the left with respect to workers with schooling level 1 and 2 and provides

evidence of the existence of a wage I (informality wage) that sets the limit between formal

and informal workers.

9 Workers with wage lower than I are informal workers according with the job search model.

26

Formal Freq % % Acum.Scho 1 14,836 24.18 24.18Scho 2 28,340 46.18 70.36Scho 3 18,192 29.64 100Total 61,368 100InformalScho 1 12,350 46.45 46.45Scho 2 11,434 43.01 89.46Scho 3 2,802 10.54 100Total 26,586 100

Table 1: Formal and informal workers by schooling level, fourth quarter 2001

0.4.2 Labour market �ows

In this section, we analyze the transition probabilities between the three labour market

groups: formal, informal and unemployed workers. The ENEU uses the system of rotative

sampling. Every quarter one �fth of the sample is discarded and replaced by a new �fth. This

means that it is possible to follow one �fth of the workers through �ve quarters. This allows

us to calculate the workers�transition probabilities between the three states. The workers�

transition probabilities help us to test two predictions of the on-the-job search model:

1. In the theoretical model presented in this paper, informal workers have a higher prob-

ability of losing their job. In this section, we obtain the di¤erentials in the probability

of losing the job between formal and informal workers.

2. That model also predicted a higher likelihood of going from informal to formal. In this

section, we estimate the workers�probability of transiting from formal to informal, and

from informal to formal.

27

The transitions �ows between formality and informality can be easily estimated from our

data as follows.

Probability of transition To calculate the workers�probability of a change in status, we

select workers that were introduced into the sample in the last quarter of 2000, and we follow

them through �ve quarters. We estimate the probability of a formal worker losing his job

(estimated probability of transiting from formal to unemployed, epfu), the probability of an

informal worker losing his job (epiu), the probability of an unemployed worker �nding a job

(epue), the probability of a formal worker changing to informal (ep�) and the probability of

an informal worker getting a formal job (epif). We control for observable characteristics and

time, by using a multinomial probit model. From these probabilities, we can also obtain the

probability of losing the job if the worker is caught by a tax inspector �10 . From the job

search model, we know that formal workers lose their job only due to job destruction (�) :

epfu = pr(efi ! uijXi) = � = a (23)

Where Xi are the workers observable characteristics, efi is formal workers�employment

status and ui is unemployed workers�employment status. Informal workers lose their jobs

for two reasons: job destruction (�) and if they are caught by the tax inspector (�):

epiu = pr(eii ! uijXi) = � + (1� �)� = b (24)

10 � can also include all risks of losing the job associated with the fact of being informal, e.g., lack ofsecurity in the street, crime, di¢ culties to access to the �nancial market, etc.

28

Where eii is informal workers�employment status. From 23 and 24 we solve for � :

� =b� a1� a

Table 2 shows the probabilities of state transitions for all workers. Informal workers are

much more likely to lose their jobs than formal ones. From these probabilities we obtain �.

Informal workers have a probability equal to 0.02 of losing the job due to the risks associated

to informality. Unfortunately, we cannot compare this �gure with another results since this

is the �rst time that � is estimated, however this �gure seems too low to explain the existence

of informal workers. There is one possible explanation to this. There is a three moths period

between surveys in the ENEU. When a informal worker lose his job, is very likely that he

will be able to get a new informal job in a short period of time (few days). If a informal

worker lose the job and gets a new informal job between surveys the questionnaire does not

capture this information and the worker would appear like if just changed job (not being

unemployed). Therefore it is very likely that the � is underestimated.

Another result worth highlighting is the important di¤erence between pbif and ep�. The

probability of going from informal to formal is almost three times higher than the probability

of going from formal to informal. Unlike the estimation of � the ENEU data is suitable to

estimate these probabilities more accurately.

epue epfu epiu � epif ep�0.4061 0.0499 0.0695 0.0208 0.2898 0.0909

Table 2: Workers probability transition

29

0.4.3 Evaluating the e¤ects of changes in workers productivity in the contextof a on-the-job search model.

An essential requirement in explaining formal and informal labour is wage dispersion. In

an economy with wage dispersion, higher wages imply a higher cost of losing the job and,

as a consequence, there will be a threshold that sets the limit between formal and informal

workers. We can also obtain wage dispersion with heterogeneous productivity, and the

empirical implications of the model will be similar. In this section we analyze if changes in

workers productivity can also explain the results obtained in the empirical section.

Workers with heterogeneous productivity As in the job search model, workers can

decide to be formal or informal. If they choose to be formal they pay tax, if they decide to

be informal they will not pay tax but they have a probability � of being caught and losing

their job: Productivity for each worker i follows a moving average process

pit = �pit�1 + "it (25)

Where "it s N(0; �). We assume workers�bargaining power wit = pit: Workers will be

willing to work if w � R (reservation wage). If informal workers that are caught cannot work

for a �xed period of time, as in the job search model, the cost of losing the job is increasing

in wage.

The "punishment device" (higher probability of losing the job) acts in the same way as

in the previous model. Workers with wage higher than I will be better o¤ if they are formal.

Thus, we have an informality wage I that sets a limit between formal and informal workers.

In this model, we also have unemployment: if a worker is a¤ected by a shock in productivity

30

that reduces his or her productivity below R; the worker will remain unemployed until his

productivity again reaches at least R:

Workers may change their wages for two reasons: due to a stochastic shock " or because

they increase (or decrease) their productivity while working, �:

We simulate the transition probability between formal and informal workers that would

exist in an economy in which the labour market is explained by heterogeneous productivity.

Using data of the ENEU, we simulate equation 25 to see whether the estimated transition

probabilities can be explained exclusively by changes in workers�productivity.

We control for the following factors:

Informality wage across workers

So far, we have assumed that the informality wage is the same across workers; however, it

may happen that workers have di¤erent thresholds. This situation can a¤ect the probability

of transition.

Reservation wage across workers

Changes in the reservation wage across workers may also bias the results. Unfortunately,

ENEU�s lack of information on this subject makes impossible to estimate the workers�reser-

vation wage. In the appendix we assess the impact of the absence of the reservation wage

on our estimations, and we show that its absence does not a¤ect the �nal conclusions.

We divide the estimation into two parts: �rst, we estimate the wage distribution function

and the informality wage. In the second part, using the parameters obtained, we obtain the

transition probability between formal and informal labour.

31

Estimation of the wage distribution and wage shocks In this section we follow the

workers for �ve quarters. Thus, we have �ve wage observations in time per worker. This

allows us to estimate the wage distribution and shocks in wages. Sample selection may

arise because there may be some person characteristics that a¤ect the probability of being

working. Therefore the group of people being at work may not be a random sample, this may

bias the results. We control for sample selection (Heckman, 1979) and workers observable

characteristics.

The �rst stage of this method is to estimate the probability of being at work with a

probit model:

It = + Xt�+ et

where I is a dummy variable, which assumes the value 0 if worker�s wage is missing and

value 1 otherwise. We can estimate this equation with LS consistently.

The second stage is to estimate the following equations with LS:

LogWt = c+ �LogWt�1 + �Xt�+ ot�f(i)F (i)

+ "t

where t = + Xt�, and F is the cumulative distribution of a standard normal random

variable, and f is the density function.

From this regression we obtain the predicted wage average, LogWt, the predicted

variance of LogWt, �w , the variance of "t : �" and the predicted e¤ect of wages in t� 1 on

wages in time t: �:

32

Estimation of the threshold (informality wage) The informality wage ( I) is not

observed. However, we can use the data available to �nd the ranges within which the

real informality wage may lie. With censored regression methodology we can get unbiased

estimators of I:

We have �ve observations of wage and worker status (formal, informal or unemployed).

For employed workers we have three options:

Always formal If a worker was formal throughout the �ve periods, we know that the

real I for this worker should be lower than the minimum of the �ve wage observations.

Therefore we keep the lowest observation as the upper limit for the real I for this worker.

This observation is left censored.

Always informal If the worker was informal throughout �ve periods, from the theo-

retical model we know that the I for this worker must be above the maximum of the �ve

observed wages. For this worker we have one observation and it is right censored.

The worker has been formal and informal during the �ve quarters The max-

imum of his wages when in an informal job is considered as the lower limit of I; while the

minimum of the wages when the worker was formal is considered as the upper limit of I:

This observation is interval censored.

Thus we have three possible observations for each worker: left censored, right censored

and interval censored.

We use a more general version (Stata manual) of the standard log-likelihood for the Tobit

33

censored regression model (Tobin, 1958), to account for interval, left and right censored data

and for missing observations. The original Tobit censored model was created to deal with

left censored and point data. The generalization allows us to obtain an unbiased estimation

of the informality wage. This model deals with the following observation rule:

y�i � ILj if worker i has been formal through all �ve quarters.

y�i � IRj if worker i has been informal through all �ve quarters.

IILj � y�i � IIRj if worker i has been formal and informal thorough the �ve quarters.

where y�i is a latent variable that represents the unobserved informality wage for indi-

vidual i: ILj is the minimum of informal worker i wage (left censored data). IRj is the

maximum of formal worker i wage (right censored data) and IILj; IIRj is interval censored

data. Therefore, we can formalize the censored regression model as follows:

y�i = Xi� + ei; i = 1; 2; :::; N

y�i � ILj if worker i has been formal through all �ve quarters.

y�i � IRj if worker i has been informal through all �ve quarters.

IIRj � y�i � IILj if worker i has been formal and informal thorough the �ve quarters.

Where et is i.i.d. N(0; �2) and Xi is a matrix with workers observable characteristics.

This model describes three probabilities. The �rst is the probability of y�i � ILj given Xi :

34

pr fy�i � ILjg = pr fet � ILj �Xi�g = pr�et�� ILj �Xi�

�

�= �

�ILj �Xi�

�

�(26)

The second is the probability of y�i � ILj given Xi :

pr fy�i � IRjg = pr f�et � �(IRj �Xi�)g = pr��et�� �IRj �Xi�

�

�= 1��

�IRj �Xi�

�

�(27)

Finally, this model describes the probability of IIRj � y�i � IILj given Xi :

pr fIIRj � y�i � IILjg = pr fIIRj �Xi� � et � IILj �Xi�g

= pr

�IIRj �Xi�

�� et�� IILj �Xi�

�

�= �

�IILj �Xt�

�

�� �

�IIRj �Xt�

�

�(28)

Therefore, the log-likelihood function of the model can be written as:

L =Xj2L

log pr fy�i � ILjg+Xj2R

log pr fy�i � IRjg+Xj2Ilog pr fIIRj �Xt� � et � IILj �Xt�g

(29)

where L are left censored observations, R are right censored observations and I are

interval censored observations. By substituting 26, 27, 26 in 29 we obtain:

35

L =Xj2L

log

��

�ILj �Xi�

�

��+Xj2R

log

�1� �

�IRj �Xi�

�

��+Xj2Ilog

��

�IILj �Xi�

�

�� �

�IIRj �Xt�

�

��

The parameters can be estimated by a censored regression, using the maximum likeli-

hood method. If the model is properly speci�ed, the maximum likelihood method produces

consistent and e¢ cient estimators for � and �: From this estimation, we obtain the average

predicted value for I : I and the estimated variance of I: �I .

Simulation Using the regression estimators obtained above, we simulate a heterogeneous

productivity model. We generate wages for two periods and the informality wage I. We

repeat the operation 100 times. From the data obtained in the simulation, we obtain workers�

probabilities of change in status in the heterogeneous productivity model, in order to compare

them with the observed probabilities.

Simulation of wage shocks We obtain one observation from a random draw from a

normal distribution function that has the variance estimated above (�")

ei s N(0; �"); i 2 [1 100]

Simulation of wages We obtain the simulated workers� wage in period 1 from a

random draw from a normal distribution with median LogWtand variance �w :

36

W1;i s N( LogWt; �w )

In the second period we obtain one observation of wage from the wage of period one

times �; which is added to the wage shock e :

W2;i = �W1;i + ei

Informality wage I We obtain the simulated informality wage Is from random draws

of a normal distribution function with the median and variance of I obtained in the previous

section.

Is;i s N( I ; �I )

Transition probabilities In order to obtain the worker status in each period we com-

pare W1;i and W2;i with Is;i for each observation i:

First period

If W1;i < Is;i =)Worker is informal

If Is;i < W1;i =)Worker is formal

Second period

If W2;i < Is;i =)Worker is informal

37

If Is;i < W2;i =)Worker is formal

By comparing worker status in period one and period two, we can calculate the workers�

probability of change in status. The results are shown in table 3. spif is the simulated

probability of changing from informal to formal, and sp� is the simulated probability of

changing from formal to informal.

spif spfi epif epfi0.0761 .0626 0.2898 0.0909

Table 3: Workers probability transition, simulation of the heterogeneous productivity model

Now we can compare the estimated and the simulated probability of changing type of

labour. The results show that, as in the empirical section (epif; epfi), the probability of

changing from informal to formal (spif) is larger than changing from informal to formal

(spfi).

The coe¢ cient � (0.64)11 obtained in the estimation of the equation 25, pushes wages

upwards, making the probability of changing from formal to informal lower than the proba-

bility of changing from informal to formal. However, the di¤erence with the empirical results

is much smaller. The empirical results show that epif is three times larger than ep�, whereas

spif is less than 20 percent higher than sp�.

Productivity plays an important role in the dynamic of informal and formal labour.

However, it cannot explain all the transition probability betwen informal and formal em-

ployment. There is also a substantial proportion of workers that increase their wages (and

11 That means that workers increase their wages when employed.

38

go from informality to formality). This can be explained by a job search process in a labour

market with imperfect information.

0.4.4 Conclusions

Our job search model shows that it is possible to explain the existence of informal labour with

search frictions. From this model we obtained three interesting results: although workers in

this economy are homogeneous, the wages of formal workers are higher than those of informal

workers. Second, informal workers have a higher risk of losing their job because of the risk

associated with being informal. Third, we found that workers present higher probability of

going from informal to formal than transiting in the opposite direction. Finally we found

that an increase in the probability of being caught, or a decrease in tax, will increase the

proportion of formal workers in the economy.

In the empirical section, we then tested some of the theoretical predictions of our on-the-

job search model. Given that taxes and law enforcement did not signi�cantly change in the

period of study (between 1995 and 2001), we were able to test the �rst three implications of

the theoretical model. We estimated wage di¤erentials and dispersion as well as the proba-

bility of transition between formal and informal employment. We found that formal workers�

wage is higher than informal workers�wage, using three di¤erent methods: counterfactual

functions, residual analysis and quantile regression. Second, we found that there is higher

wage dispersion among informal workers than among formal workers. The third interesting

result was that informal workers have a higher probability of losing their job. From this

result, we obtained the di¤erential between formal and informal labour in the probability

39

of losing their job associated to the risk of being informal (�). Finally, we found evidence

that changes in productivity alone cannot explain workers transition probabilities between

the formal and informal sectors.

As explained before, unobserved workers�ability can also explain part of wage di¤erentials

between formal and informal labour. Alcaraz and Chiquiar (2006) using the same survey

followed workers that transit between formal and informal labour from the forth quarter

of 2000 to the forth quarter of 2001 they found that workers that transit from formal to

informal experiment a decrement of their wages of 13%. Because they used the wage of

the same person in formal and in informal employment they also controlled for unobserved

worker characteristics like ability.

A segmented labour market12 can also explain wage di¤erentials between identical formal

and informal workers. However, labour market segmentation cannot explain the higher

probability of going from informal to formal than transiting in the opposite direction, when

the economy is contracting.13

The most important implication of these results is that we can observe many of the

implications of a segmented labour market, without restrictions on entry to formal labour.14

12 For example, institutional reasons (minimum wage, strong unions, labour law) may restrict entry toformal labour. Because of these restrictions, two people with identical productivity may have di¤erent wagesif they are in di¤erent sectors.

13 Alcaraz Chiquiar (2006) found the same patterns in the transition probability between formal andinformal labour during the period 2001-2002, when the formal sector was contracting.

14 Restrictions to entry to the formal sector have been decreasing in Mexico in recent years. The realminimum wage has been decreasing steadily, and nowadays it is widely accepted that the minimum wage isnot binding the labour market equilibrium. Additionally, the number of unionized workers as a proportion

40

It is important to underline some strengths and limitations of this analysis.

An important part of the modern literature on the informal labour market claims that

there is no evidence of wage di¤erentials between formal and informal workers in DCs (Mal-

oney, 1998, 1999, 2004; Tokman, 1992; among others). These studies emphasize that workers

may choose jobs in the informal rather than the formal sector, as the result of a decision

that takes advantage of the unregulated nature of the informal sector. Our framework is

a decision model, in which workers have the same productivity, and the choice between

being formal and informal is not conditioned by barriers to the entry in the formal sector.

However, after controlling for workers�observable characteristics, we found evidence of wage

di¤erentials between formal and informal workers.

Two factors can explain these di¤erences.

First, the papers described above consider all self-employed workers as informal workers.

Alcaraz (2006) shows that this is not entirely accurate: many self-employed workers are

registered with local and federal governments, pay taxes and comply with governmental

regulations. It is not unrealistic to consider that registered self-employed workers have

substantially di¤erent characteristics from those that are not registered, and that these

di¤erences are directly related with the problem of informality that we all want to describe.

Second, Maloney (2004) divides informal workers into three groups: informal salaried,

formal salaried, and commission workers. Although this division of informality has some

problems, as explained above, it allowed Maloney to present a more detailed vision of the

of the formal labour market has been decreasing. During this time the informal sector has maintained asteady proportion of informal labour.

41

nature of informality. He found that informal salaried workers are indeed disadvantaged

workers: they are younger, have very low wages, have lower education and little experience.

This speci�c group of workers would then be waiting for better opportunities, in order to

migrate to better jobs, rather than being in the informal sector by their own choice.

Given that we did not split informal workers into smaller groups, we cannot conclude

that all informal workers have lower wages in the informal sector.

Fields (1980, 1990, and 2004) and Gong and van Soest (2002), among others, found that

the majority of informal workers have lower income, and that these workers would prefer to

have formal jobs. However, they acknowledge that there also exists a proportion of informal

workers that are in the informal sector because they prefer to be there, because of the higher

wages that they receive there. However, if there is a group of workers that are better o¤ in

the informal sector, this group does not have a su¢ ciently strong e¤ect on informal wages

to reverse the wage di¤erentials we found between formal and informal workers.

Therefore, it is highly likely that our on-the-job-search model does not explain the be-

haviour of all informal workers. There are two options to follow in this line of research. First,

like Maloney and others, we can split informal workers into other categories, such as, for

example, employees, self-employed and commission workers, and perform an analysis of wage

di¤erentials and transitions probability, in order to identify if there is a particular group of

informal workers that has di¤erent characteristics from those we found in this paper. An-

other option would be to select, and analyze the characteristics of, workers that transit from

formal to informal, and to identify the workers that improve their condition (i.e., increment

42

their wages).

43

References

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0.5 Appendix

In order to estimate the reservation wage, we need an upper limit and/or a lower limit for

the reservation wage of each worker (see the estimation of the informality wage). From the

data available in the ENEU, we can obtain the upper limit for the reservation wage15 . Some

labour surveys ask unemployed workers what is their non-labour income, or what is the

minimum wage they are ready to accept if they receive a job o¤er. These data would allow

us to estimate the lower limit for the reservation wage. Sadly, the ENEU does not provide

this information, therefore it is not possible to estimate the reservation wage.16

There are two relevant questions to answer. The �rst is whether the absence of the

reservation wage in the simulation biases the results. The second is, if the bias exists, what

sign does it have? To answer these questions, we compare two cases, one with only informality

wage (Case 1, the case we simulated) and the other with reservation and informality wage

(Case 2).

We assume the same wage distribution function and same informality wage (I) in both

cases (see �gure 6): in Case 2, there exists a reservation wage that divides workers between

unemployed and employed.

Case 1 We have the following transition possibilities (see �gure 6)

Simulation with informality wage:

15 The minimum of the wage observations for each worker.

16 Kiefer and Neumann (1979) proposed a Tobit model, to estimate the reservation wage. In order toidentify the model they needed a variable that a¤ects the reservation wage but not the searching cost: thevariables they used were tenure on the previous jobs and wage at previous jobs. These variables are notavailable in ENEU.

46

Wages

Frequency

Wages

I yR xz

yx

1

2

Figure 6: Wage density �nctions: case 1 and case 2

a) Informal to formal (x to y)

b) Formal to informal (y to x)

Case 2: Simulation with reservation and informality wage:

a) Informal to formal (x to y)

b) Formal to informal (y to x)

c) Informal to unemployment (x to z)

d) Unemployed to informal (z to x)

e) Unemployed to formal (z to y)

f) Formal to unemployed (y to z)

47

To answer the �rst question, we analyze how transition probabilities c), d), e) and f)

would make transition probabilities a) and b) in Case 2 di¤erent from transition probabilities

a) and b) in Case 1.

The existence of c) does not a¤ect the probabilities a) and b) because it is equivalent to

going from informal to informal (with a lower wage) in Case 1.

d) does not a¤ect the probabilities a) and b) because is equivalent to going from informal

to informal (with a higher wage) in Case 1.

e) and f) can a¤ect the results by altering the probabilities of a) and b) between Case 1

and Case 2.

e) if a worker goes from z to y in the Case 2 (unemployed to formal), the same wage

change implies going from informal to formal. Therefore, taking into account this e¤ect,

Case 1 overestimates the probability of going from informal to formal.

f) if a worker goes from y to z in Case 2 he or she will be considered as going from formal

to unemployed. In case 1, however, he or she would be considered as going from formal to

informal in Case 1. Therefore, this transition leads Case 1 to overestimate the probability

of going from formal to informal.

e) and f) have e¤ects of opposite sign over a) and b). The question to answer here is

which of these e¤ects is stronger. When we estimated wage dynamics to do the simulations

we found that wage increases through the �ve quarters (� =0.63). This can also be explained

with the heterogeneous productivity model if workers increase their productivity as they gain

more experience. This term makes the e¤ect e) bigger than f).

48

Because e¤ect e) is more important than e¤ect f), the absence of reservation wage will

slightly17 overestimate the probability of going from informal to formal. This implies that

the direction of the bias has opposite direction to what we want to prove. Therefore, the

results of this exercise will be reinforced by this small bias.

17 As seen in �gure 6 in order to observe this transition workers need a large increment in wages in justone period.

49