The recurrent new waves of outbreaks worldwide over 2021 confirm that the COVID-19 economic crisis will have short- and long-term effects and severe economic repercussions worldwide.

According to the International Monetary Fund (2020), the projections are unfavorable for the economy, with a fall of -3% in 2020, and if the pandemic ceases, a global economic recovery could be expected in the middle of the year 2021, with a growth projection of 5.8%.

In Latin America and the Caribbean, the pandemic hit precisely in a recession, resulting in a negative economic impact of between 3 and 4% (CEPAL, 2020). Given that Mexico is one of the leading economies in Latin America, its projections are within these same ranges. The country's growth projection for Mexico is between 1.4 and 3% in 2021 (IMF, 2020), and such projections depend on the political decisions taken in the country and the efficient control of the spread of the virus. From the above estimations and described potential scenarios, it can be inferred that that the Mexican economic effects might present more profound structural effects, and this depends on its ability to cope and assimilate the effects of COVID-19 on the economy; some of these effects might be classified as short-run effects and others structural.

For this research, the impact of COVID-19 on the Mexican economy might come from two types of sources: "exogenous shocks" and what we call "structural effects."

The exogenous shocks in our country were observed at the end of the first quarter of 2020 when countries began implementing isolation measures. Given that Mexico is predominantly a tourism-dependent country, these external measures reflected Mexico's first shock in productivity (Esquivel, 2020). In addition to the isolation decisions taken in other countries, Mexico was forced to make decisions regarding this, and it was then that the policy of social distancing was proposed. This policy not only represented a measure to contain the virus but was also considered as part of the exogenous shock. Once the exogenous shock impacts (COVID-19), there are implications in the economy that are usually "structural effects." Structural effects refer to the interrelationships of the different existing economic agents, which produce complex relationships, and these relationships bring with them different implications in the markets (Sampedro and Cortina, 1969). For Mexico, the structural effects derived from COVID-19 can be divided into three forms:

1. 1. Supply side - real effects: the isolation brought the country's companies and industries to a standstill, and their supply chains and input production led to a reduction in aggregate supply.
2. 2. Demand side - real effects: the social distancing and the contraction of the aggregate supply triggered an increase in unemployment in the country and decreased families' economic capacity, resulting in a reduction in the demand for goods and services in the economy.
3. 3. Financial risk - uncertainty effects: due to the increase in external economic uncertainty, the Mexican economy experienced increases in interest rates, risk premiums, and Mexican Peso (currency) depreciation (Banco de México, 2020).

Identifying the sources of the economic impact will help us understand the repercussions that this impact will have on the markets, specifically for this study, and on the Mexican labor market.

Employment in Mexico represents a significant issue in the country's economic structure, partly due to the "duality" faced by its labor market (Maloney 2004; Moreno 2007).

The term "dual market" refers to the existence of a market outside the formal labor market, what Hart (1970) called the "informal sector." This definition was generalized when the International Labor Organization (ILO), in 1972, analyzed economic activities in Kenya that were neither registered nor protected there.

Since then, labor informality is one of the most sensitive variables to measure, not only in Mexico but also in many other Latin American countries, since they face an informal sector of almost 60% (OECD, 2019), and the challenge of quantifying it lies not only in the estimates but also in achieving an unbiased definition of both the informal sector and informal employment. The following subsection details the definition used in this study.

Table 1
Mexican labor market segments, before and during COVID-19

Source: Own estimation with ENOE data (2019 and 2020). Notes: the values expressed in percentages. The data presented is for the third quarter of each year.

Table 1 presents data on the differentiated situation between employment structure and gender before and during the COVID-19 pandemic. In both genders, the economically active population (PEA) decreased by 3 to 4 percentage points (pp), with a more significant proportion for men. Concerning its structure, it can be observed that informal employment was more affected since there was a decrease of 0.53 pp for men and 4.44 pp for women, and these losses concern the PEA. According to Samaniego (2020), the phenomenon of contraction in informal employment had not occurred in previous crises since informality used to be an escape valve for the economy when formal employment was affected.

On the other hand, formal employment presents an increase in its proportion between 1 to 3 pp for both genders. This effect could be related to the third quarter of 2020 since some of the economic sectors were already operating, reflecting employment recoveries. This fact (adverse effect on employment) is presented in several studies that have focused on analyzing formal employment with social security data and report that the fall occurred from February to May 2020 (Esquivel, 2020; Samaniego, 2020; Ramirez, 2020), this inflection point has been cataloged as the most severe of the previous crises, surpassing by 5.7% the minimum point observed in the 2008-2009 crisis.

For the analysis, a homologation of two existing employment surveys carried out, the National Urban Employment Survey (ENEU) for the years 1987 to 2004 and the National Occupation and Employment Survey (ENOE) for the years 2005 to 2019. The bases were standardized to build aggregate data series from the micro-foundations of the labor market.

The INEGI publishes the ENEU and the ENOE to capture data on our country's employment and sociodemographic characteristics.

The surveys have the particularity of being a dynamic panel—that is, they follow an individual for five quarters and thus allow us to alternate each quarter to 20% of the sample. For the present research, we used the benefits of cross-sectional data to construct quarterly aggregate data (i.e., employment time series) because we are interested in obtaining the behavior in the aggregate of these series.

As a measure of production at the national level, we used the quarterly real gross domestic product (base 2013=1) from 1987 to 2019; this series is obtained directly from INEGI's statistical bank data. The GDP time series is used since we are interested in the demand for labor as a function of the aggregate production of this country.

Based on the above, and for this research, the construction of the time series is limited to the employment growth rates of individuals between the ages of 16 and 65 who are working and receiving a monetary payment greater than zero, thus excluding individuals who work without receiving any payment or remuneration.

The employment series was divided by gender and by structure³. The employment structure was divided according to the definition established in section 2.2.1.

For the analysis, six time series are constructed at the national level: male formal employment growth rate, female formal employment growth rate, male informal employment growth rate, female informal employment growth rate, GDP growth rate, and real hourly wage growth rate.

Finally, all rural areas are excluded from the country to homologate both databases since the ENEU only includes urban areas of Mexico.

The relationship between productivity and employment has been a relevant topic of study over the years. One of the most studied hypotheses is known as "Okun's Law," and this model measures the inverted relationship between unemployment and growth (Okun, 1962). Despite being a general reference framework, this model can identify structural changes in supply and demand; therefore, in this study, we refer to a neoclassical model proposed by Arrow et al. (1961), which studies the relationship between economic productivity and employment.

The model is based on the assumption of a perfectly competitive labor market where production is maximized by equating the technical marginal rate of substitution to real wages. On the other hand, the marginal product of labor can be derived from a CES-type production function and constant elasticity of substitution (Arrow et al., 1961; Akkemik, 2007). The CES production function is defined as follows:

Where 𝑄 is the production, 𝐾 is the capital factor, and 𝐿 is the labor factor. 𝛽 is a parameter that lies between zero and one, and it determines the distribution of income among the factors of production; 𝜃 measures technological progress, s measures the returns to scale, and 𝜌 is the parameter that measures the elasticity of substitution between the factors of production (𝜌>0). As mentioned above, optimality is reached when the marginal product of capital and labor equals their respective payments (the return to capital and the wage):

From equation (2) and taking (1) as a base, the following expression is obtained:

Once equation (3) is found, logarithms are taken and rewrite the equation used for estimations:

The terms ${\alpha }_0$, ${\alpha }_1$ and ${\alpha }_2$ represent the following:

It can be observed that the expected effect of an increase in production is positive on employment and vice versa. This theoretical model will estimate the causal impact of the economy on employment in the following section.

Given the nature of the theoretical model and the simultaneous interactions that productivity and employment variables represent, an unrestricted reduced-form vector autoregressive (VAR) econometric model is presented. If the VAR model is presented in the reduced form, the model equations' contemporaneous values are not represented as explanatory variables in the model. In addition, it should be noted that the lags of each variable in the east are the exogenous variables; on the other hand, the fact that the model is unrestricted means that each variable appears in each of the equations as explanatory variables.

The specification of this model is very useful when variables are simultaneously determined and helps us find persistence between variables in the long run (optimal specification of lags), and this is possible because no restrictions are imposed on the model, thus avoiding specification errors.

We start by defining our variables of interest represented in growth rates, with 𝑦_1𝑡 being the formal employment of men, 𝑦_2𝑡 the formal employment of women, 𝑦_3𝑡 men's informal employment, 𝑦_4𝑡 women's informal employment, 𝑦_5𝑡 real GDP, and, finally, 𝑦_6𝑡 the real hourly wage. Also, each vector has its respective autoregressive components and a vector of components associated with the white noise process, which is stationary and assumes a normal distribution. Another one of the characteristics associated with the specification of the empirical model is that all of its variables must comply with stationarity; these tests are detailed in the following section.

Thus, the reduced matrix version of the VAR can be represented in terms of its characteristic polynomials defined over the number of "L" lags, 𝑎(𝐿,𝜙) y 𝑏(𝐿,𝜙), as follows:

Given the time stability of the distribution of the series, it is possible to represent this process in terms of the Gaussian white noise process described in the following reduced form:

In this case, the new characteristic polynomial 𝑐(𝐿,𝜙,𝜃) is unique for each VAR process defined over the number of lags (L). We used the maximum likelihood method via the properties of the Gaussian process to recover the set of parameters associated with the original model, {𝜙,𝜃}. Finally, to know the optimal number of lags (L) in the estimation, we must perform a series of tests, which we present in the estimation and results section.

The variables used in the estimation are presented as growth rates, Augmented Dickey-Fuller (ADF), and Phillips-Perron unit root tests are performed to test their long-term stability.

Table 2 presents the stationarity tests for the growth rates of GDP, employment, and wages. It can be observed that, in both tests, all series are stationary, and, at the time, the variables are growth rates and were differenced once, so these series consist of order-one I(1) data.

Table 2
Z-statistics for hypothesis testing unit roots

p-value: 0.01***, 0.05**, 0.10*. Source: Own estimations with time series constructed and homologized of employment surveys (ENEU-ENOE). Seasonally adjusted series presented by growth rates.

The analysis uses an unrestricted VAR model, so one of the critical points to note is the order of the variables and the optimal number of lags for the model. Regarding the order of the variables in the VAR, there are several ordering techniques (variance decomposition and Cholesky factorization); in our study, we stuck to the theoretical model presented in section 3.2, which respects the following order of employment, GDP, and real wages.

Once the order was implemented, at least five selection criteria are used to estimate the model for the optimal choice of lags. Table 3 presents the statistics associated with the optimal selection.

As can be seen, in the study of the properties of the model, two groups of statisticians are proposing optimal lags: the first group (LL, LR, FPE, AIC) proposes that the number of lags should be 1, whereas the second group (HQIC, SBIC) proposes there should be 0 lags in the estimation.

In this research, we decided to integrate one lag in the estimation of the unrestricted VAR model, considering that four of the six tests show statistical consistency, and it is pointed out that the optimal number of lags is one.

Table 3
Selection criterion for optimal lags in VAR estimation

Source: Own estimations with time series constructed and homologized of employment surveys (ENEU-ENOE). Seasonally adjusted series presented by growth. Notes: Sample 127 observations. LL: log-likelihood, LR: likelihood ratio, FPE: final prediction error, AIC: Akaike's information criterion, HQIC: Hannan and Quinn information criterion, SBIC: Schwarz's Bayesian information criterion.

After selecting the specific criterion of the optimal lag selection in Table 4, the VAR model of interest on the impact on the different employment structures can be observed. Given the nature of the model and the high multicollinearity existing in it, it is not recommended to make individual inferences of the estimators. However, we can focus on the effects on the dependent variables of interest of each of the equations because it will support understanding the dynamics in employment when introducing the impact of COVID-19.

The VAR equations are presented in the order presented above. From the approach of this model, it is possible to observe the importance of the division of employment by structure and gender because there are differentiated effects between formal and informal employment and differences between genders.

In Table 4, the second and fourth columns pertain to the estimated equation for the formal employment of men and women, and it is observed that both genders react to changes in the economy. However, particularly for women, employment is more dynamic and interdependent to the different employment structures. In addition, there is a certain complementarity with men's employment (formal and informal); this effect could be contrary to what is expected in specific gender employment literature (Humphries, 1988) in which female employment has a substitution effect on male employment. On the other hand, some literature on human capital has supported complementarity in employment, given that men and women build a structure in the household where both complement each other, which is why the expected effect is positive (Becker, 1986). Finally, there is a dynamic for women and persistent adjustment in their long-term equilibrium (i.e., the behavior of formal employment adjusts to the same dynamics). In contrast, men only show complementarity with informal employment.

As for informal employment, its behavior does not react to economic changes. Again, this is true for both genders. In other words, evidence on this segment of the market suggests it is relatively inelastic to economic changes.

Table 4
VAR model: structure and dynamic on the Mexican labor market

p-value: 0.01***, 0.05**, 0.10*. Source: Own estimations with time series constructed and homologized of employment surveys (ENEU-ENOE). Seasonally adjusted series presented by growth rates.

Once the dynamics and structure of employment have been analyzed, we can proceed to our sensitivity and impact analysis on the employment structure, emphasizing the "economic shock" of COVID-19 and the long-term trend.

In this section, we present the main contribution of this paper: to quantify and isolate the impact of COVID-19 and what we call the "structural effect" on employment in Mexico⁶. We rely on impulse response functions using productivity (GDP) as the impulse and response variables as the different employment structures by gender to estimate the impact. The observed change in Mexico's real GDP for the first quarter of 2020, which was -2.2 % (INEGI, 2020), is introduced as the initial shock of COVID-19. Figure 1 shows the impulse response functions differentiated by employment structure and gender. This figure shows the growth rate projections for the different employment segments once the I-shock COVID-19 was incorporated into the impulse response functions.

It can be observed that the shock in the short term (period t+1) is harmful to the formal employment of men and women in Mexico in both series, as estimated in several sources for IMSS-registered workers (Banxico, 2020). On the other hand, our estimate shows persistent employment loss throughout the five periods⁷ and a more profound loss for women than men.

As for informal employment, an independent dynamic is observed in both genders, as mentioned in the dynamics of the model (Table 4), where informal employment seems to have self-determined behavioral dynamics (i.e., it is inelastic to economic shocks and only shows a persistence to its own series). This fact coincides with the findings of Huesca and Camberos (2009), who analyzed the counterfactual dynamics between the formal and informal markets for the years 1992-2001 in Mexico. These authors find that the informal sector presents relatively greater inequality than the formal sector due to the heterogeneity and higher dispersion of remunerations in this market.

These impulse response functions allow us to model the I-shock observed in Mexico derived from COVID-19 in the first quarter of 2020. These functions are taken as results in order to differentiate the first shock of the pandemic, and with the support of the estimates of the trend and employment observed in the four quarters of 2020, we can differentiate between the employment losses derived from the exogenous shock and the losses derived from the structural effects triggered by the COVID-19 crisis. Of course, only considering the initial economic shock of the pandemic may represent a limitation to this analysis. However, it allows us to quantify the magnitude of the COVID-19 I-shock represented in employment for Mexico.

4.3.1 Formal employment by gender

Formal employment, as discussed above, tends to be elastic to changes in the economy, so when there was an impact (I shock COVID-19) on formal employment, both men and women reacted.

Figures 2 and 3 show the cumulative loss of employment compared with its trend as an impact of the COVID-19 crisis for men and women, respectively. Three series can be distinguished from the graph. The first one, the black one, represents observed employment obtained from the ENOE for our sample. Only the second quarter of 2020 is calculated from the Telephone Occupation and Employment Survey. This study was an extension of the ENOE because the second quarter of the employment survey took place in seclusion. The red dotted line estimates the long-term growth trend and has been forecasted from our VAR model. Finally, the gray line is the estimate of the COVID-19 negative I-shock on employment, and this projection is calculated from the impulse response function (adding the negative GDP shock), and the long-run employment growth is added (Pre-COVID trend).

The loss in employment was deeper for women than men. In percentage terms, the minimum point of the drop in employment for men was in the third quarter of 2020, representing -8.35%, while it was -9.6% for women in the same period. This result coincides with the scenarios presented by the BID (2020); in particular, it is close to their projections of loss of formal employment in the medium-term scenario, in which they project a 7.7% drop in employment derived from a recession presented for more than three quarters, which is what is observed in this country.

In terms of the number of jobs lost at the inflection point, both genders accumulated a loss of around 1 million jobs. However, men accumulated losses of 597,814 formal jobs, whereas women accumulated losses of 475,289 formal jobs.

Figure 1
Impulse response function to negative shock in PIB related to COVID-19
Time set: quarters after initial COVID-19 production shockSource: Own estimations with time series constructed and homologized of employment surveys (ENEU-ENOE). Seasonally adjusted series presented by growth rates. Notes: confidence intervals 95%

Regarding the drop in employment, for men, only 1.21% represents the effect of the first COVID-19 shock, whereas 7.14% is the equivalent of the structural effect. Thus, in terms of employment, the first COVID-19 shock was equivalent to losses of 86,629, whereas the structural effect was the critical determinant of the losses, amounting to 511,185. On the other hand, of the 9.6% drop in women's employment, the first shock of COVID-19 was 0.7%, and 8.9% was the structural effect. Thus, the first shock is equivalent to 34,656 formal jobs in terms of jobs lost, and the structural effect is equivalent to losses of 440,633.

Figure 2
COVID-19 shock and structural effect on men's formal labor market
Source: Own estimations with time series constructed and homologized of employment surveys (ENEU-ENOE).Notes: trend estimation using the VAR model. The data of employment observed of second 2020 quarterly was calculated of ETOE.

From the above analysis, we conclude that the I-shock of COVID-19 was more significant for men relative to women. In contrast, the effect of the structural economy has a more significant impact on women's formal employment; this means that women's employment reacts more strongly to structural effects (92%, versus 86% for men), whereas men's employment reacts more strongly to exogenous shocks (14%, versus 7% for women).

For this reason, women's formal employment recovers faster than men's. As a result, the model forecasts that women will reach pre-COVID-19 employment levels one quarter earlier than men. Moreover, in the case of women, this recovery will begin to be observed in the first quarter of 2021, whereas that of men will be observed in the middle of the year (2021:Q2).

Figure 3
COVID-19 shock and structural effect on women's formal labor market
Source: Own estimations with time series constructed and homologized of employment surveys (ENEU-ENOE).Notes: trend estimation by VAR model. The data of employment observed of second 2020 quarterly was calculated of ETOE.

4.3.2 Informal employment by gender

Informal employment represents one of the most severe problems in our country; trying to quantify it gives us an approximation of the size of the problem. Estimates show that informal employment in both genders is inelastic to changes in productivity.

In Figure 4, particularly for men, the first quarter seemed to be an escape valve for job losses in the economy since the formal employment losses derived from the COVID-19 I-shock were around 163,700 jobs. In contrast, in the same period (2020:Q1), informal employment captured 115,074 jobs, almost equivalent to the losses. However, this increase was unsustainable because, by the second quarter of 2020, there was already a 43% drop in informal employment for men, as expressed by Samaniego (2020), who explained this is the most relevant decrease in informal employment of all time. In this sense, it is considered that this drop is entirely the result of the supply effect derived from the confinement because this phenomenon was observed in April, May, and June, and, as a consequence, many companies or businesses had to close and dismiss personnel; in particular, the tertiary or service sector was the most affected (Esquivel, 2020). This effect coincides with that reported by Altamirano et al. (2020), who reported that the tertiary sector has a higher proportion of informal employment in Latin America, such as social or communal services, commerce, restaurants, and hotels, so it can be concluded that, due to the effects of the confinement and closures, employment was affected for the first time in Mexico to this extent.

For women (Figure 5), the drop was almost the same magnitude as for men (-42.9%), which had an unexpected impact on this sector. Despite the substantial employment losses in both groups, it can be observed that employment began to recover for both groups from 2020:Q3 onwards.

Figure 4
COVID-19 shock and structural effect on men's informal labor market
Source: Own estimations with time series constructed and homologized of employment surveys (ENEU-ENOE).Notes: trend estimation by VAR model. The data of employment observed of second 2020 quarterly was calculated of ETOE.

Concluding this section, to estimate a scenario of recovery in informal employment, another technique had to be considered because the model predicts with very little strength the fall in informal employment due to inelasticity in the face of economic changes. As an exercise, we apply the growth rates estimated with the impulse response functions plus the sum of the long-term trend and apply this growth rate to the last observation of observed employment (2020:Q4). For the male group, informal employment hypothetically began to recover by the beginning of 2022 (pre-COVID-19 employment level). On the other hand, by this same point (2022:Q1), women are expected to reach a level of employment approximate to the one observed at the end of 2018:Q4 (i.e., around 5 million jobs).

Figure 5
COVID-19 shock and structural effect on women's informal labor market
Source: Own estimations with time series constructed and homologized of employment surveys (ENEU-ENOE).Notes: trend estimation by VAR model. The data of employment observed of second 2020 quarterly was calculated of ETOE.

Finally, we performed a projection exercise on the recovery period of the formal labor market by focusing on the gap in permanent job losses as estimated by our model, using the latest available point data (2020:Q4) instead of the projections according to the COVID-19 initial shock.

Figure 6 shows an analysis of the formal labor market for men. The first point shows the pre-COVID-19 employment level, which was 7,159,142 in the fourth quarter of 2019. According to the projections of our VAR model, this employment level will recover in the middle of this year (7,217,580). Despite this recovery, there has been a gap in the permanent employment loss because, in that same period (2021:Q2), the pre-COVID-19 growth trend indicated there would be a level of 7,397,595 employed in our country. The difference between the pre-COVID-19 trends and the level of employment in 2021:Q2 is -2.5%. On the other hand, a growth trend at a constant rate (3.8%) was projected based on the last observation of current employment, which leads to the same conclusion as the VAR model. Therefore, the pre-COVID-19 employment level recovery is observed from 2021:Q2 if this growth rate prevails, but the gap of permanent employment loss would be less than 1%.

Figure 6
Men's formal employment recovery period: pre-COVID employment level vs. pre-COVID trend
Source: Own estimations with time series constructed and homologized of employment surveys (ENEU-ENOE).Notes: trend estimation by VAR model. The level of actual employment at the second 2020 quarterly was calculated with ETOE. The constant employment rate for 2020q4 was 3.8%.

Figure 7
Women's formal employment recovery period: pre-COVID employment level vs. pre-COVID trend
Source: Own estimations with time series constructed and homologized of employment surveys (ENEU-ENOE).Notes: trend estimation by VAR model. The level of actual employment at the second 2020 quarterly was calculated with ETOE. The constant employment rate for 2020q4 was 8.5%.

On the other hand, the analysis of the female labor market (Figure 7) shows a different picture. The pre-COVID-19 employment level was 4,936,569 for 2019:Q4, so the econometric model projects a faster recovery than that of men since the employment recovery should be observed by the end of the first quarter of 2021. If the level of employment projected by the VAR model (4,992,563) has been reached, there would be a permanent employment loss of around -2.2%. However, if the constant growth trend rate (8.5%) is applied from the last observation of current employment, the gap of permanent employment losses would be reversed, and there would be an increase in women's formal employment of 3%.

*Corresponding author: jorge.morenotr@uanl.edu.mx