Analysis of Job Transitions in Mexico with Markov Chains in Discrete Time

Abstract

In this paper, we suggest a holistic explanation for the role currently played by self-employment in less developed countries and, consequently, a reason for its persistence and growth in recent years. At the same time, we link this explanation with current discussions on the role of very small economic units and informality and their relation to unemployment rates. In general, countries where the combined share of self-employment and very small units is high exhibit lower unemployment rates than countries of similar levels of development, but where the small units’ share is less significant. Using a rich set of labor data for Mexico, we examined flows between seven different labor statuses. Equilibrium vectors estimated through Markov matrices show that flows are linked to the economic cycle and that there exists a gender difference in behavior in these flows. We found that a dichotomic explanation of self-employment persistence (entrepreneurial reservoir/survival strategy) is not supported by evidence. We also found that strong links exist between the size of the self-employed sector and unemployment rates. With the help of a set of surveys on very small economic units, we identified a three-tier structure for very small economic units in Mexico. Thus, self-employment and small-sized economic units are both a source of income and a source of cheap goods for lower-income sectors. They serve as a buffer against unemployment and help to provide subsistence conditions for the poorest segment of the population. Finally, we discuss some questions that were raised along the text that help to guide future research.

1. Introduction

In Latin America, the average share of self-employed workers who work independently, without paid help (save for unpaid family workers), is well above 25% of the total labor force, in sharp contrast with the European Union (below 15%) or the United States, whose rate is 9% [1]. Its relative size and persistence in less developed economies have remained a sort of puzzle for economists, who have struggled to explain its persistence comprehensively. In this paper, we hypothesize that, in less developed countries, self-employment and very small economic units (with less than five workers) play a double role in the economy. On the one hand, because of the complete lack (or minimal coverage) of unemployment insurance schemes, these sectors act as an income source for those who are unable to obtain a job. On the other, they provide low-cost services and products for the working people, allowing for their reproduction and helping to maintain low wages.

In the following sections, we present a theoretical discussion of self-employment activities. On this issue, we can find three different explanations: one that stresses the entrepreneurial component of self-employment and, thus, implies that its size and dynamics are derived from an individual (rational) choice in a situation where access to a waged job is restricted [2]; a second one that emphasizes the fact that these kinds of activities are, most of the time, a survival strategy of poor workers, and thus can be understood as the result of constrained choices [3]; and a third one that considers self-employment as an expression of a reserve army of labor [4]. There is also a variant of the third explanation that considers self-employed works as a marginal sector under capitalism [5].

We discuss the practical implications of the different explanations for the existence and persistence of self-employment.

Next, we examine the theoretical issues on the links between open unemployment and self-employment in the context of low median income levels: As a starting point, the insights discussed in the classic contribution contained in Gunnar Myrdal’s Asian Drama [6] are still relevant. In general, countries where the share of self-employment and very small units is high exhibit lower unemployment rates than countries of similar levels of development, but where the small units share is smaller. Thus, there is a strong connection between self-employment and unemployment in less developed countries. We link this explanation with current discussions on the role of very small economic units and informality.

To deliver an integrated analysis of how people earn their livelihoods in the modern world, any theoretical analysis must deal with the issues of people being in and out of work, moving through several different conditions of activity during different periods (short or long) of their life courses.

We find two parallel processes operating, which are a clear expression of the current polarization in the global economy: on the one hand, the insufficient creation of stable and well-paid jobs in medium and large units; and, on the other hand, the growing share of employment created by micro-units, where remuneration levels are notoriously low.

In many analyses, a simple model of flows between three occupational statutes, namely employed, unemployed, and out of the labor force, is used to gain a general understanding of the general dynamics of the labor force [7]. In this paper, we estimate flows to and from seven categories: self-employed workers, unpaid family workers, wage workers (in units with five or fewer workers, and those on larger units), employers, unemployed persons, and those who are out of the labor force.

The analysis of the transitions between those seven categories allowed us to support our assertions about the roles played by own-account workers We used labor data from Mexico to compute those flows, and we estimated equilibrium vectors for the Markov processes derived from transitions between these categories for several years, starting in 2006 and ending at the beginning of 2020. The years were chosen to reflect different points in the Mexican business cycle, including the 2008/2009 crisis.

We examine flows between different labor statuses at various moments of recent business cycles, and we look at differences by gender, using an ample source of labor data from Mexico, a country whose labor structure dynamics have been widely used to test mainstream theories of labor markets.

In the current phase of capitalist development, the social role of the state has been redefined and metamorphosed, focusing its action on creating global conditions for the best economic performance of markets while dismantling essential components of its social protection policies. In this scenario, the small units (including self-employed workers), acting as a mechanism for obtaining income for a significant number of people, have functioned as an “obstacle” to open unemployment at massive levels. Their presence is limited to sites where there is a potential market for the products or services they offer. Consequently, the growth of these activities is determined by the global income in the cities, so it is in the medium and large cities where the most significant proliferation of micro-businesses can be observed.

Today, small-scale activities represent a mechanism through which capitalism can reproduce itself, allowing the persistence of low wages while minimizing conflicts arising from a lower capacity to absorb the labor force. A fraction of the small units plays a role analogous to that traditionally played by the peasantry in countries such as many less developed economies as the Latin-American countries: they do not directly collaborate in the accumulation process, as their productivity levels are low. However, they take charge of the reproduction of important volumes of the labor force, but, at the same time, self-employment includes workers who strive to become employers. Thus, we posit a division of the self-employed into three types: survival, traditional, and transitional.

Some of our results confirm previous findings, while others cast doubt on the validity of former findings.

2. Review of the Relevant Literature

In many advanced economies, including the USA, Great Britain, and EU members, the notion of self-employment includes own-account workers and employers that are paid from their profits. Since this definition is not uniformly used throughout the world, care should be taken when comparing developed and less developed countries regarding the extent and nature of self-employment.

A vast share of the current literature on self-employment and entrepreneurship in the developing world can be summarized by considering four elements. The first element includes the problems involved in estimating the amount of self-employment using available data sources. The second one is the issue of voluntary versus constrained self-employment. The third is the extent to which self-employment in the developing world can be regarded as “true” entrepreneurship. The fourth element is the links between self-employment, productivity, and economic growth. A comprehensive survey paper [8] developed each element.

Regarding the first question, measures of the size of self-employment vary because of several factors. The first factor is the inclusion or exclusion of family farms and household enterprises, since they involve unpaid contributing family workers. Second, estimates have used individual-based data sources, firm-based information, and expert surveys, but the paper stresses the relevance of using individual-based data. Third, depending on the level of detail required, different individual-based data sets can be used, and so there is a warning against the use of imputed data and non-representative surveys Lastly, it is argued that there is a compelling need to use standard (and common) definitions when comparing self-employment rates across countries.

On the controversy between self-employment by choice or by constraints issue, the survey enlists a series of conditions that have an impact on the size of self-employment. To begin with, it considers the existence of Social Protection schemes that diminish the need for subsistence self-employment and argues that labor market rigidities are a source of higher self-employment rates. The business environment, including business registration and licensing processes, access to finance, widespread corruption, and the quality of judicial systems, were stressed as important determinants of the share of voluntary self-employment and the overall level of wage employment. The existence or not of labor market regulations and the payroll taxes/wage subsidies were also identified as factors that could influence the levels of wage employment and the share of subsistence self-employment in a country. Overall, these arguments are milder versions of explanations of the existence of an unregistered or underground economy [9].

Margolis’s discussion about the share of “real” entrepreneurship concludes that roughly one-third of self-employed people in the developing world are entrepreneurs in the traditional sense, meaning that they are people who have initiative and exhibit risk-taking and profit-seeking behavior. This result contrasts with the analyses performed for advanced economies, where the proportions are higher [10,11,12]. However, it should be noted that there exists a discussion of the definition of “entrepreneurship” [13] that periodically repeats itself in the literature, leading to the identification of self-employment with entrepreneurship [14].

Two important observations in Margolis’s paper must be made: The first is the need for governments in the developing world to confront the high level of self-employment, because, in these countries, it tends to be relatively unproductive, and higher productivity levels can induce faster growth and higher levels of income. The second is that, as countries develop and their institutions evolve, self-employment rates tend to fall, and wage employment becomes the primary source of jobs.

However, the above discussion of the magnitude and role of self-employment in less developed countries creates the need for a further analysis of the connection between open unemployment and the so-called “informality” in these countries. On the one hand, there is a recognition that self-employment might act as a buffer for unemployed workers or as a destination where workers arrive at late stages of their life course, after getting experience and training in the wage sector of the economy. The first assertion can be readily demonstrated, under certain conditions, using labor flows, as we demonstrate later in this paper. The second assertion has been proved wrong already in Reference [15] but keeps coming up in the literature.

Although the purpose of this paper is not a broad discussion about the notion of informality, we turn to briefly present some issues about informality. There are several good discussions of the origin and standard use of the notion of informal sector, including Reference [16] and Reference [17], to mention two relevant papers. Three elements have to be highlighted: The first one is that, in spite of an ILO official definition, the literature is filled with many different notions, including the identification of informality with underground (or shadow) economies, as in Reference [9], or in Reference [18] for the case of Mexico. In a series of papers [19,20], Thomas and Roubaud made definite critiques to the methods used to measure the size of shadow economies (or what they call “informal activities”). We must add that, in spite of these definitive criticism, those methods are still in use [21].

A second point is that, before ILO introduced the notion of informal employment [22], informality included most of the self-employed workers and very small economic units, since the notion was defined by using economic elements (in contrast with legalistic definitions, which stressed social protection). Thus, as Reference [16] comments, behind the original definition of informal sector lies the need to explain the low levels of unemployment in many less developed countries. This observation was performed by Myrdal in Reference [6] and was developed to become the “luxury unemployment hypothesis” [23], which briefly states the idea that, in less developed countries, unemployment is a luxury few can afford. Recent empirical support for that hypothesis can be found in Reference [24].

The third point is that the current ILO definition includes workers in very small economic units and unprotected workers in registered businesses, mixing two different economic logics. Unprotected workers exist in registered units as part of a cost-reducing strategy that has no counterpart in the very small-scale units; thus, there is no common economic element that links both group as the current definition is legal based [17].

Labor-Market Transitions in México

For the Mexican case, with diverse levels of depth and geographic or temporal coverage, the problem of transitions between employment and unemployment has been studied by various authors, starting with the work of R. Cruz [25], who uses information derived from the ENEU (National Survey of Urban Employment) to study the entrance and exit into economic activity in the case of women. An important result is that women who are married or have children are more likely to be in small-scale activities or to work part-time. None of these works makes the distinction between exits from employment due to open unemployment or transition to economic inactivity.

On the other hand, in Pacheco and Parker [26], there is a comparison of the bilateral transitions between employment and open unemployment in two moments of recent economic history, 1987 and 1995. Additionally, they make an analysis of some of the determinants of unemployment. It is worth noting the fact that the authors, in addition to considering the open unemployed according to the ILO’s meaning, add to the standard definition of open unemployment the people referred to as “discouraged unemployed”, that is, those who do not have a job but did not search for one because they “considered that they could not obtain it”. The result is to increase the unemployment figures and skew the duration results in unemployment. Another early contribution is Reference [27], which presents an analysis of transitions between what the author calls “position at work” and examines, using simple survival analysis, the determining factors of permanence in activities where the worker has access to medical services or, more generally, to social security. One feature of that text is that the author ignores the standard definitions of job position, and unemployment as workers who did not have a job at some point in the last twelve months prior to the ENEU interview, had already worked before, or were not working at the time of the interview are considered unemployed. Due to changes in the usual definitions, his results are incomparable with those of other authors, as he produces higher unemployment rates than the ones really observed in Mexico.

In the case of Maloney [28], the analysis assumed that the labor market incudes both wage workers and own-account workers and employers, thus extending the notion of market for labor. In fact, own-account workers and employers do not sell their labor force; what they sell is a product. Thus, there is no justification for using theories devised to explain the earnings of workers (for example, those based on the notion of Human Capital). In a series of papers [29,30], some authors have delved into the dynamics of unprotected labor in several Latin-American countries, including México. In Reference [31], continuous-time Markov chain analysis was used to compare Argentina, Brazil, and México.

A couple of their research results stand out: labor markets are not segmented by informal activities, and firms in the sector have a similar behavior to those of more advanced economies. Reference [2] argued that most, if not all, activities in the unprotected sector (informal sector) are voluntary.

Recent contributions (References [32,33]) examined the impact of the 2008 global downturn and the 2008/2009 crisis in Mexico and found a distinctive gender behavior. Aguilar et al. also conclude “that in Mexico exists a duality in terms of self-employment, which is composed of a few people who look for capital accumulation and many others who just use it as economic survival”. This hypothesis had already been advanced by Reference [34], and it was framed in a different form by Reference [35]. The authors of Reference [36] argued that the Mexican informal sector has a dual structure, an upper tier and lower tier, that behaves as Fields had argued before.

3. Materials and Methods

From our initial discussion of the role played by self-employment in less developed economies, we can argue that any in-depth analysis must include a dynamic view of its role, and of that of very small economic units with waged labor. In our research, we relied on two household surveys that were implemented by the Mexican National Statistical Institute (INEGI, by his Spanish language acronym): National Survey of Occupation and Employment (ENOE, by his Spanish language acronym), which is a complex survey that gathers data at the national level and reports quarter data for rural and urban areas. It has a rotating panel structure that changes 20% of the sample each quarter, meaning that we can follow individuals for five quarters, allowing us to examine labor flows at a very detailed level. The survey started in 2005 and has been applied continuously since that date. Currently, it includes around 132,000 households Although we estimated flow matrices for the whole five quarters and four years selected, we show only the flows from the first to the second quarter of each year. The complete set of matrices is available on demand by emailing the corresponding author [37].

Using the subsample of those individuals who continued to be included in the sample for five quarters, starting at the beginning of 2006, 2009, 2013, and 2029, we built matrixes for each quarter for the whole population and for men and women, showing the flows between the following seven categories: waged workers in firms with 6 or more employees, waged workers in firms with less than five employees, self-employed (own-account) workers, unemployed workers, inactive persons (people out of the labor force), employers, and unpaid workers. A natural attrition process affects the survey each quarter and might reach a 20% loss from the first to the fifth quarter examined. Here we use the sample of those who were kept in the sample for the whole five-quarter period to build transition matrices for the following periods, both for the total working-age population and for men and women separately:

• 1st quarter 2006–1st quarter 2007, a growth period;
• 1st quarter 2009–1st quarter 2010, a crisis period;
• 1st quarter 2013–1st quarter 2014, a growth period;
• 1st quarter 2019–1st quarter 2020, a stagnation period.

It is possible to interpret transition matrices as Markov matrices, because, in each quarter, the probabilities of transition from one state to another (changes in activity condition) do not depend on the previous history; that is, they do not depend (in a probabilistic sense) on the situation in the previous period. With this interpretation, the question arises about the behavior of the transitions in the long term, that is, about the stability of the changes between states, if the economic conditions that generate the specific values of the Markov matrix entries remain constant.

A couple of remarks on the use of discrete-time Markov processes for this analysis are due. The first is that the labor flows that were examined do not happen in an uninterrupted way, day and night and every day of the week. The second thing is that the surveys used are quarterly surveys, gathered daily until they cover the total sample size. Thus, there is no compelling reason for the use of continuous-time Markov processes. Moreover, as we shall see, when we analyze the transition matrixes and the resulting equilibrium vectors, there are substantial variations between the results depending on the point of the business cycle where Mexico was at the time of each survey. Therefore, a continuous time process would miss these differences.

We use the Markov Chain Fundamental Theorem to answer the equilibrium question posed before. Let P represent a transition matrix for given two quarters, and let v₀ represents an initial distribution vector of labor status of the population aged fifteen and over. The question arises of whether or not there exists an equilibrium vector in the system? In other words, do repeated transitions represented by the same matrix converge to a finite limit?

Formally, we have the following:

Let vi = P v_i−1, then, do iterations P² v₁, …P^k v_k−1, …, converge?

Because each row of the matrix P has positive elements that add to one, it is known [38] that $\hat{\mathrm{P}}=\underset{\mathrm{k}\to \infty }{{\mathrm{lím}\mathrm{P}}^{\mathrm{k}}}$ exists and that $\hat{\mathrm{P}}$ has all its rows equal, and that, if π is any row of $\hat{\mathrm{P}}$, then π is an eigenvector of the original system, associated with the eigenvalue 1 [38,39,40,41]. In other words, we have the following:

π = P π

(1)

Moreover, it is also true that, for every i, if π_i is the i-th component of π, then ${\mathsf{\pi }}_{\mathrm{i}}=\frac{1}{{\mathsf{\lambda }}_{\mathrm{ii}}}$, where λ_ii is mean recurrence time, that is, the average number of steps to return to the i’th state starting on the i-th state [38].

Using the R package markovchain, written by Reference [42], we estimated equilibrium vectors for all the periods and for both sexes, so the interpretation of results was facilitated. The condition used to find equilibrium solutions for the transition matrixes was that the component sum of the final row was equal to one (up to four decimal places).

Additionally, we used data from the National Survey of Very Small (micro) Economic Units (ENAMIN for its Spanish language acronym [43]), a Survey that was conducted every two years, beginning in 1992, until it was phased out in 2012. This includes detailed data on self-employed individuals and very small economic units (less than 6 workers for units in the service or commerce sectors and less than 11 workers in the case of manufacturing units). This survey is representative for the whole country (to the best of our knowledge, there are few similar surveys; a recent example is Reference [44]). The richness of the information gathered makes it a relevant source of information on some qualitative characteristics of micro-units and their owners, whose general trends were relatively constant during the period when the survey was conducted every other year. Thus, it is a reasonable assumption, as we are only interested in the general structure and not the numbers themselves. In this text, we use a set of questions on the reasons to start a small-scale activity, as well as some others on the unit’s age.

4. Results

The following three tables show several interesting processes whose intensities vary with the cycle. They were chosen to illustrate differences in behavior throughout cycles.

Table 1. Total activity flows of first quarter of 2006 (stability).

1st to 2nd	Non-Micro-Wage Earner	Micro-Wage Earner	Own Account	Unemployed	Inactive	Employer	Unpaid Worker
Non-micro-wage earner	53.6	16.3	10.0	2.0	13.4	1.8	2.9
Micro-wage earner	8.3	80.1	2.8	1.7	5.9	0.8	0.4
Own account	9.4	4.5	62.1	1.0	15.7	4.9	2.4
Unemployed	14.8	29.5	9.0	18.7	23.7	1.7	2.6
Inactive	3.1	2.6	4.3	1.0	85.7	0.2	3.2
Employer	7.8	8.1	26.8	0.4	5.1	49.8	2.1
Unpaid worker	6.8	3.7	9.1	0.4	36.2	1.4	42.3

shows flows during a period of stability,

Table 2. Total activity flows for first quarter of 2009 (crisis).

1st to 2nd	Non-Micro-Wage Earner	Micro-Wage Earner	Own Account	Unemployed	Inactive	Employer	Unpaid Worker
Non-micro-wage earner	53.9	14.5	10.1	3.4	14.5	1.4	2.1
Micro-wage earner	9.2	78.5	2.7	2.9	5.6	0.6	0.4
Own account	8.8	3.8	60.9	1.7	15.1	6.4	3.3
Unemployed	17.3	20.6	9.3	23.3	26.7	1.0	1.8
Inactive	3.5	2.3	4.4	1.8	84.9	0.4	2.8
Employer	7.0	8.9	31.1	1.4	4.8	45.0	1.8
Unpaid worker	9.8	2.7	8.9	2.0	32.2	1.2	43.2

during a crisis, and

Table 3. Total activity flows for first quarter of 2019 (stagnation).

1st to 2nd	Non-Micro-Wage Earner	Micro-Wage Earner	Own Account	Unemployed	Inactive	Employer	Unpaid Worker
Non-micro-wage earner	54.6	13.7	10.4	2.1	15.0	1.6	2.6
Micro-wage earner	9.3	77.6	3.0	2.0	6.8	0.7	0.6
Own account	9.2	4.6	59.7	1.1	16.6	6.6	2.2
Unemployed	11.0	26.6	10.7	17.3	31.4	1.0	2.0
Inactive	3.9	2.7	5.5	1.3	83.8	0.5	2.4
Employer	9.9	6.6	32.9	1.3	9.4	38.1	1.8
Unpaid worker	10.5	2.2	12.6	0.4	37.0	1.6	35.6

during a stagnation period. Although we estimated flow matrices for the whole five quarters and four years selected, we show only the flows from the first to the second quarter of each year. The complete set of matrices is available upon request by emailing the corresponding author. In all of them, we can see that movements out of unemployment end up in very small-scale activities (self-employment and very small units with waged labor), while movements out of inactivity end up in the same sector as the former unemployed workers: that is, in very small-scale activities. At the same time, staying as an own-account worker has an estimated tenure time smaller than working in a very small unit, and this relationship holds for all of the periods analyzed. The movements described show the relevance of examining very small-scale activities, as discussed previously.

During the crisis period, unemployment rates rose, and more than a quarter of the unemployed workers who could not get a job quit job searching and became inactive. During the stagnation period, that share went up sharply, and very small economic units absorbed a greater proportion of the formerly unemployed. Table 1, Table 2 and Table 3 also show that the average time in unemployment moves anti-cyclically: it increases in periods of crisis and is lower in growth periods than in stagnation periods.

Summing up these initial results, we see that the data show strong evidence for considering very small economic activities as having an important role in absorbing former unemployed workers and maintaining an important proportion of the labor force, a fact that is reflected by the sum of the micro-wage share and self-employed share in absorbing unemployed workers, and in the constancy of the share of own-account and micro-wage work.

Nevertheless, analyzing the whole set of transition matrices is a tedious task, and many conclusions can be reached by examining only the equilibrium vectors.

The equilibrium vectors obtained through Markov’s transition matrices are shown in

Table 4. Employment-transition steady states in Mexico.

	Micro-Wage Earner	Non-Micro-Wage Earner	Own Account	Unemployed	Inactive	Employer	Unpaid Worker
2006-I- > 2006-II	0.110	0.217	0.127	0.015	0.467	0.023	0.041
2006-II- > 2006-III	0.118	0.223	0.135	0.022	0.429	0.028	0.045
2006-III- > 2006-IV	0.121	0.228	0.131	0.017	0.434	0.023	0.045
2006-IV- > 2007-I	0.118	0.212	0.120	0.022	0.467	0.025	0.035
2009-I- > 2009-II	0.121	0.195	0.132	0.028	0.461	0.025	0.038
2009-II- > 2009-III	0.115	0.217	0.148	0.035	0.420	0.024	0.041
2009-III- > 2009-IV	0.121	0.230	0.131	0.028	0.427	0.022	0.041
2009-IV- > 2010-I	0.111	0.188	0.125	0.026	0.497	0.023	0.031
2013-I- > 2013-II	0.124	0.210	0.140	0.026	0.437	0.025	0.037
2013-II- > 2013-III	0.111	0.223	0.130	0.027	0.447	0.022	0.040
2013-III- > 2013-IV	0.120	0.233	0.121	0.022	0.439	0.024	0.041
2013-IV- > 2014-I	0.113	0.214	0.118	0.026	0.475	0.019	0.035
2019-I- > 2019-II	0.126	0.193	0.145	0.018	0.463	0.025	0.030
2019-II- > 2019-III	0.132	0.208	0.138	0.018	0.449	0.027	0.028
2019-III- > 2019-IV	0.117	0.212	0.135	0.015	0.463	0.027	0.029
2019-IV- > 2020-I	0.123	0.205	0.129	0.015	0.478	0.025	0.025

. The first relevant aspect to highlight is that the persistence of the labor force in a specific type of occupation is associated with the economic cycle.

Prior to the crisis period of 2009, inactive workers tended to decrease; between the first quarter of 2006 and the third quarter of 2009, their weight in the economy had decreased from 46.7% to 42%. At the same time, self-employment became more important, which also grew in that period by more than four percentage points; however, the weight of unpaid workers and micro-wage earners increased to a lesser extent.

With the 2009 crisis, the growth of inactivity rebounded again; its weight increased by about seven percentage points from the second quarter of 2009 to the transition to the first quarter of 2010. This increase in inactivity is also reflected in the reduction in the weight of all other forms of employment, highlighting the decrease in non-micro-wage earners (−2.9%) and self-employment (−2.3%).

It is very clear from the data that, in periods of crisis or stagnation of unemployed, the labor force tends to transition to inactivity and not necessarily to other forms of precarious employment, which are also negatively affected in periods of crisis.

The situation for men and women in the labor market shows differences that can be seen with the data in

Table 5. Employment-transition steady states of men in Mexico.

	Micro-Wage Earner	Non-Micro-Wage Earner	Own Account	Unemployed	Inactive	Employer	Unpaid Worker
2006-I- > 2006-II	0.161	0.303	0.175	0.021	0.265	0.040	0.037
2006-II- > 2006-III	0.118	0.223	0.135	0.022	0.429	0.028	0.045
2006-III- > 2006-IV	0.160	0.287	0.174	0.021	0.274	0.041	0.043
2006-IV- > 2007-I	0.168	0.290	0.171	0.027	0.266	0.045	0.034
2009-I- > 2009-II	0.165	0.255	0.172	0.042	0.282	0.044	0.038
2009-II- > 2009-III	0.147	0.262	0.199	0.043	0.269	0.040	0.041
2009-III- > 2009-IV	0.154	0.293	0.165	0.038	0.269	0.037	0.044
2009-IV- > 2010-I	0.151	0.267	0.175	0.036	0.301	0.041	0.029
2013-I- > 2013-II	0.161	0.262	0.178	0.034	0.281	0.043	0.041
2013-II- > 2013-III	0.148	0.301	0.181	0.033	0.258	0.039	0.040
2013-III- > 2013-IV	0.158	0.307	0.153	0.032	0.268	0.039	0.043
2013-IV- > 2014-I	0.148	0.284	0.163	0.035	0.300	0.034	0.036
2019-I- > 2019-II	0.158	0.254	0.178	0.022	0.320	0.042	0.026
2019-II- > 2019-III	0.167	0.282	0.181	0.023	0.273	0.048	0.027
2019-III- > 2019-IV	0.141	0.270	0.157	0.020	0.340	0.044	0.028
2019-IV- > 2020-I	0.151	0.273	0.186	0.021	0.299	0.047	0.022

and

Table 6. Employment-transition steady states of women in Mexico.

	Micro-Wage Earner	Non-Micro-Wage Earner	Own Account	Unemployed	Inactive	Employer	Unpaid Worker
2006-I- > 2006-II	0.070	0.143	0.088	0.010	0.636	0.009	0.043
2006-II- > 2006-III	0.156	0.303	0.190	0.028	0.228	0.052	0.043
2006-III- > 2006-IV	0.086	0.182	0.092	0.013	0.572	0.008	0.047
2006-IV- > 2007-I	0.077	0.147	0.080	0.017	0.634	0.009	0.036
2009-I- > 2009-II	0.083	0.145	0.095	0.016	0.616	0.008	0.037
2009-II- > 2009-III	0.085	0.182	0.100	0.026	0.557	0.009	0.041
2009-III- > 2009-IV	0.091	0.175	0.099	0.019	0.568	0.009	0.039
2009-IV- > 2010-I	0.077	0.121	0.084	0.018	0.659	0.008	0.033
2013-I- > 2013-II	0.091	0.167	0.106	0.020	0.573	0.009	0.035
2013-II- > 2013-III	0.081	0.157	0.089	0.021	0.606	0.008	0.038
2013-III- > 2013-IV	0.086	0.169	0.093	0.014	0.589	0.010	0.039
2013-IV- > 2014-I	0.085	0.155	0.081	0.019	0.620	0.006	0.033
2019-I- > 2019-II	0.096	0.140	0.115	0.014	0.589	0.010	0.035
2019-II- > 2019-III	0.101	0.143	0.103	0.015	0.602	0.009	0.028
2019-III- > 2019-IV	0.097	0.164	0.114	0.011	0.573	0.011	0.031
2019-IV- > 2020-I	0.100	0.149	0.085	0.010	0.620	0.009	0.027

. The main characteristic is that, for both groups, cycles of crisis or stagnation result in a greater transition toward work inactivity. However, this effect is much stronger in the case of women: for example, during the 2009 crisis, the weight of inactivity increased by 3.2% for men and by 10.2% for women when comparing the second quarter of 2009 with the transition to the first semester of 2010.

In the stagnation period of 2019, the transitions followed by the different work status for men and women show opposite behaviors; inactivity increases for women and decreases for men. For women, there is a greater increase in the work status of non-micro-wage earners and self-employment, whose participations increase by 1.9% and 0.8%, respectively. Meanwhile, for men, the increase in inactivity is associated with a reduction in self-employment (−1.5%).

In general, the results show that, during periods of crisis or stagnation, inactivity increases, so people move from the various forms of work to a situation in which they no longer seek employment. Under these conditions, unemployment is reduced, because workers stop looking for work, and other forms of work do not allow these workers to be absorbed. This situation shows that, for economies such as Mexico’s, the unemployment rate is not a good indicator of what is happening in the labor market.

Up to this point, we have shown the relevance of self-employment and very small economic units for the absorption of flows from unemployment and inactivity. Now we turn to examine some of the inner structure of micro economic units by means of a very rich survey, ENAMIN (National Survey of Micro Economic Units [43]).

Although we used data from the 2012 edition of the survey (the last one carried out), these results were similar for all the time periods when the survey was conducted, from 1992 to 2012. By means of these data, we show that there are segments of this group of units that include entrepreneurial activities, survival strategies, and family income supplementation processes (

Table 7. Reason to start a micro-unit in Mexico.

	Own-Account Worker	Employer (Hires Wage Workers)
By family tradition or inherited it	0.057	0.106
To supplement family income	0.284	0.110
To improve income	0.208	0.277
Had money and found a good opportunity	0.040	0.072
To exercise his/her trade, career, or profession	0.096	0.166
It was the only way to get income	0.125	0.076
Did not have experience required for a job	0.003	0.002
Did not have schooling or training required for a job	0.004	0.002
Was over trained	0.000	0.002
The jobs found were poorly paid	0.011	0.010
Required a flexible schedule	0.018	0.013
There were no other job opportunities	0.052	0.036
Another reason	0.102	0.129

Source: own calculation, ENAMIN [43].

).

If we now consider the age distribution of self-employed units and very small units with wage work, the large share of units that have been active for more than five years (

Table 8. Starting unit age for self-employed and employer led units.

Unit Age	Less than a Year	1 to 2 Years	3 to 5 Years	6 to 10 Years	11 to 15 Years	16 to 20 Years
Employer	7.0%	10.9%	14.1%	18.9%	14.1%	12.6%
Self-employed	11.8%	15.8%	18.3%	18.8%	11.0%	8.6%

) stands out; this is a fact that explains why workers in self-employment tend to stay in that condition, as shown by the transition matrices and the estimated equilibrium vectors. In fact, the table shows that the median age for self-employed and employer-led units lies in the 6-to-10-year interval.

5. Conclusions

The evidence presented in Section 4 shows that self-employment and very small economic units play a significant role in the creation of job opportunities at every point of the business cycle, and that they act as a buffer to absorb unemployed workers. While examining the absorption role of small-scale activities on the reduction of unemployment levels, we have also shown that those levels depend on at least two factors, the business cycle and the size of the sector of very small economic activities. However, unemployment itself, as an expression of a lack of jobs, depends on the possibility of surviving for a period without income. In absence (or decline) of social support systems, such as unemployment insurance or some sort of family income, self-employment and very small economic units represent an income-earning possibility. Thus, comparisons between countries that have differences in the relative importance of very small-scale activities and or in the institutional arrangements to support unemployed persons should be performed with greater care and detail. In other words, the world of labor is not flat, nor are regions flat from the point of view of jobs and jobs flows. Our results support a vision of small-scale activities as a disadvantaged segment, because flows from larger firms to small-scale activities increases in recessions, but, at the same time, we found evidence that small-scale activities are segmented in a non-rigid way. Further work should be performed to prove these assertions for a larger number of countries in Latin America.

In contrast with previous works such as Reference [2], our results support a vision of some small-scale activities as a disadvantaged segment, because flows from larger firms to small-scale activities increase in recessions, but, at the same time, we found evidences that small-scale activities are segmented in a non-rigid way that includes entrepreneurial activities, survival strategies, and family-income-complementation processes. This division complements the two-tier proposal of Reference [45] and contradicts the generalized assumption that self-employment is always a (rational) choice of entrepreneurial agents [46].

We put forward an explanation of the persistence of self-employment in less developed economies and its current surge in advanced economies: today, self-employment and very small economic activities represent a mechanism through which capitalism can reproduce itself, while minimizing the conflicts arising from a lower capacity to absorb the labor force. A fraction of the small units plays a role analogous to that traditionally played by the peasantry in countries such as many Latin-American countries: they do not directly collaborate in the accumulation process, as their productivity levels are low. However, they take charge of the reproduction of important volumes of the labor force. Further work should be performed to prove these assertions for a larger number of countries in Latin America.

Finally, a methodological note. The use of a discrete Markov chain process to model labor flows allowed us to reach relevant economic results, thus showing, in practice, that mathematical techniques, other than econometrics, can support economic analyses grounded in an empirical analysis that lead to new economic hypotheses and results. This movement, from an empirical question to a theoretical answer, and then back to empirics, can also be found in Reference [47].