Revealing the New Nexus in Urban Unemployment Dynamics: The Relationship between Institutional Variables and Long-Term Unemployment in Colombia

3.1 Specification and Estimation of Autoregressive Vector Models – VAR

For this type of analysis, the estimation of Autoregressive Vector models consistent with the original proposal of Sims (1986) is considered. A model is then specified where Y t = ( x 1 , x 2 , x 3 , . . . , x 4 ) is a vector of ( n x 1 ) series of variables, where Y t corresponds to the set of endogenous variables integrated I(0) and I(1) and seasonally adjusted in period (t). The model is suitable as it assumes that the endogenous variables within the system are influenced by the lagged values of all variables in the system. This approach helps us avoid issues of endogeneity since the VAR model treats the entire system as one of endogenous variables. This is particularly appropriate in contexts where there is no theoretical consensus that allows us to confidently infer exogeneity conditions or correct endogeneity problems. These models offer a more practical and consistent alternative to traditional multi-equational models. To begin with, let’s examine a version of a lower triangular reduce vector autoregressive form model in – Var (1):

where i is the number of lags, and ϵ t is a vector n x 1 of innovations or processes without serial autocorrelation, white noise and with zero expectation and matrix of variances σ ε i 2 and covariances σ ij constant over time. Thus, the residuals are distributed as white noise identically in time with zero mean and constant variance: ε t ∼ N ( 0 , σ 2 ) , cov ( ε ti , ε tj ) = 0 , ∀ t i ≠ t j . (see Section 4.2. Robustness tests) This model representation helps address bias issues in estimation and mitigates potential identification problems. It explains how the estimated shock in each endogenous variable is incorporated into the impulse response function, assuming that all variables in the system are endogenous (Beaton et al., 2009). Now, the immediate reactions and the subsequent effects following the shock in the endogenous variables can be examined through the impulse-response functions, typically represented as:

where r t , jt − i measures the response of the variation in the LAPU to each endogenous variable j of the system in the previous periods, that is, in its lags corresponding to the vector Y t = ( x 1 , x 2 , x 3 , … , x 4 ) , each of the variables is expressed as a function of the accumulated random disturbances. Hence, for every shock, there exist as many accumulated impulse-response functions as there are variables. In this study, we estimate the generalized impulse-response functions developed by Pesaran and Shin (1998), which generate impulse-response functions wherein the ordering of variables in the VAR does not affect the outcomes. Consequently, the identification issue in this study adheres to Sims’ (1986) perspective, wherein no arbitrary restrictions are imposed on the model. This approach considers that none of the variables in the system of equations within the estimated VAR model possess adequate theoretical or empirical support to be deemed exogenous.

The analysis of decomposition of variance will be carried out considering its usefulness to get the proportion of the movements in the explained variables due to their “own” shocks, compared to the shocks of other endogenous variables^[1].

A crash in the ith variable will directly affect that variable, by its auto-regressive component, but it will also be transmitted to all other variables of the system through the dynamic structure of VAR. Two models are estimated: VAR 1 and VAR 2. In the first model, the vector of endogenous variables of the system of equations is composed by: LAPU, the ratio – gap between people with written contracts and people with verbal contracts, non-labor income, unemployed people with subsidies and unemployed people, people with severance payments, and unionized employed people, and one control variable: Control economic monitor CEM – as follows for VAR_1:

An additional model (VAR 2) is estimated that will only include variables that capture cash transfers: unemployed people with subsidies and people who receive severance payments, to determine their impact on LAPU, and one control variable: Control economic monitor CEM- as follows:

The series that showed signs of seasonality were seasonally adjusted with the TRAMO-SEATS method^[2]. Dickey-Fuller and Phillips-Perron unit tests have been implemented at the level and in the first difference with tendency and intercept for effects of greater rigor in the results. See Appendix 1. Similarly, the order of lags for VAR 1, VAR 2 and 14 and 2, respectively, has been determined considering the lag inclusion test based on AKAIKE information criterion (Appendix 2). Appendix 3 presents the LM Test serial self-correlation test. None of the models have serial auto-correlation problems.

Hypothesis 1 for VAR Model 1. Shocks in the vector of endogenous variables Y t ( x 1 , x 2 , x 3 , … , x 6 ) corresponding to institutional variables impact the duration of unemployment in Colombia and the LAPU. In this hypothesis, it is anticipated that a positive shock in the number of unionized individuals, the gap ratio between individuals with written and verbal contracts, non-monetary income, and individuals receiving unemployment benefits will affect LAPU.

Hypothesis 2 for the VAR Model 2. Shocks in the vector of endogenous variables Y t = ( x 1 , x 2 … , x 4 ) corresponding to cash transfers of employment protection impact the LAPU. The hypothesis predicts that positive shocks in monetary transfers related to labor market regulations, such as severance payments and unemployment benefits, will affect LAPU.

3.2 Variables and Data

Machin and Manning (1999) identify two primary sources for unemployment duration data: labor force surveys and administrative records. They suggest that administrative measurements may be influenced by idiosyncratic factors, making population and labor force surveys more reliable. This study systematically organizes microdata from DANE’s Great Integrated Household Survey (GEIH) to analyze the Colombian labor market from 2010 to 2021. The research focuses on 24 main urban labor markets in Colombia, including major capital cities and metropolitan areas. The GEIH database has evolved methodologically over time to adhere to international standards set by the International Conference of Labor Statistics (ICLS) and the International Labor Organization (ILO). The dataset includes information on employment duration, collected consistently across various survey modules. The data are weighted to ensure the representativeness of the target population, accounting for dwelling density in surveyed segments at the time of data collection.

The current research takes the period January 2010 to October 2021 as a sample to perform the econometric analyses. It avoids potential biases due to the methodological changes reported by DANE. The variables that report the number of people are expressed in thousands. Table 2 lists the variables by category, source, and estimated model. In this same way, it is a synthesis of data treatment and calculation of variables.

The construction of the long-term unemployment variable is derived from question Q7320 of the unemployed people’s module of the Great Integrated Household Survey of DANE (GEIH)^[3]: “How long ago did you stop working?” In Colombia, people are considered to be long-term unemployed when they have been unemployed for more than 52 weeks. Therefore, a filter is applied to the monthly microdata provided by question Q7320 to identify all individuals with a total of 52 weeks or more of unemployment.

The LAPU variable is then measured as the total number of people who have been unemployed for 1 year or more over the total number of people unemployed a year ago. The indicator measures the percentage of people who were unemployed a year ago and are still unemployed 1 year later (Webster, 2005). The calculation of this indicator is as follows:

Table 3 provides a summary of the central tendency, dispersion, and range of values for each variable. Each variable has monthly observations for the analysis period. The average duration of long-term unemployment is approximately 120 weeks, with moderate variability indicated by a standard deviation of around 10.44 weeks. However, there is a considerable range between the minimum and maximum durations, spanning about 53 weeks, highlighting significant variation in long-term unemployment durations. Notably, the mean duration accounts for roughly 19.79% of total unemployed respondents who reported their last employment status, indicating a substantial proportion of long-term unemployed individuals among surveyed Colombian households.

Figure 1 shows an increase in the number of long-term unemployed and LAPU because of the recent pandemic crisis in contrast to a decrease in the average number of weeks in long-term unemployment. This decrease could be explained by the transition of the unemployed to inactivity resulting from the sharp contraction in economic activity that worsens the situation of the unemployed in Colombia.

Figure 1

Time series at the level. Source: The data used in this study was obtained from the Great Integrated Household Survey (GEIH) conducted by DANE. However, data for certain variables such as rental payments, unemployment benefits, written and verbal contracts, and unionized employees was not available for March, April, May, June, and July 2020 due to limitations in survey application caused by the COVID-19 pandemic. As a result, missing values were imputed using the Nearest Neighbor Imputation method.

Figure 1 reveals a significant increase in the gap between individuals with written contracts and those with verbal contracts since 2014. However, during the recent COVID-19 crisis, this gap notably reduced, suggesting an interesting procyclical behavior – greater formalization during periods of growth compared to periods of crisis.

From 2012 to 2014, the number of unionized workers grew steadily, thanks to an increase in collective bargaining agreements (Urrea-Giraldo et al., 2020). This growth coincided with the rise in the unionization rate that began with Juan Manuel Santos’s presidential term in 2010. However, a subsequent negative trend suggests a decline in unionization. This could possibly reflect corporate governance policies that oppose collective bargaining processes. Figure 1 also highlights a marked fluctuation and increase in the number of unemployed individuals receiving unemployment benefits from 2014 to 2021. In contrast, non-labor income showed a downward trend, with a brief recovery between 2018 and January 2020, followed by a contraction likely caused by COVID-19 containment measures.

4.1 Impulse-response Functions and Variance Decomposition

Considering the hypotheses formulated in the methodology section, the impulse-response functions that measure the reaction of each variable to a shock in each of the endogenous variables are presented below (refer to Figure 2). In this system of interrelationships, the number of impulse-response functions equals the number of endogenous variables. These functions depend on the elapsed time, and the size of the shock is conventionally one standard deviation.

Figure 2

Generalized impulse-response functions accumulated to a standard deviation. Source: Authors’ own elaboration based on VAR 1 estimation. Note: The time horizon for analysis in the impulse response function is 12 periods.

Therefore, in the case of a one standard deviation shock, the size of the effect on the system of endogenous variables is given in the unit of measurement of the considered variable. Specifically, in terms of the LAPU on the ordinate axis, a significant and positive response (0.02 LTUR measurement unit) is evident to a one standard deviation shock in itself between periods 1 and 5 after the shock. The blue line represents the response, while the red line represents the 95% confidence interval^[4].

It’s important to note that our interest lies in showing the direction of the effect. Given that in this type of VAR model, the logarithmic differentiation of the variables complicates the interpretation of the magnitude of the effect in terms of a unit of measurement. Therefore, the analysis ultimately focuses on the direction of the effect and its statistical significance.

The results reveal that the LAPU exhibits relatively inertial behavior, responding positively and significantly to shocks to itself approximately between periods 1 and 6; this is not surprising given that it is a measure of persistence in unemployment duration, in which the variability of the long-term unemployment ratio to total unemployment is very limited and low (Webster, 2005). Secondly, the LTUR responds negatively and significantly to a positive shock in the growth of the gap between the number of employed individuals with written contracts versus verbal contracts between periods 4 and 7 after the shock.

This finding allows inferring that explicit contracting mechanisms, such as written contracts, prevail as effective means to reduce the persistence of unemployment duration in Colombia. In conclusion, this study underscores the importance of labor formalization through written contracts as a means to reduce unemployment persistence in Colombia. This is consistent with Clark et al. (2009), who point out that labor market failures often stem from the security conditions of the labor market. The evidence indicates that addressing information asymmetries through transparent contracts can significantly enhance labor market efficiency by encouraging unemployed individuals to seek formal employment opportunities.

Third, LAPU responds positively and significantly to a shock in non-labor income growth between periods 7 and 10 after the shock. These findings reveal that the LAPU in Colombia responds positively and significantly to growth in non-labor income. This result is consistent with previous research such as that of Cardona-Arenas and Sierra-Suarez (2023) and Webster (2005), the latter of which suggests that income from activities other than primary employment may contribute to prolonging the duration of unemployment (e.g., remittances, rents, and transfers). This finding underscores the importance of considering not only variables directly related to the labor market, but also other socioeconomic aspects that may influence the dynamics of long-term unemployment, such as the effect that non-labor income has on reservation wages.

On the other hand, the VAR estimation results indicate that LAPU responds positively to shocks from unionized personnel in periods 1 and 3. Similarly, unionized personnel respond positively to LAPU in periods 2 and 11, demonstrating a co-movement. This is consistent with Hirsch’s (2008) assertion that if high union labor compensation does not lead to higher productivity or product prices, union profits can act as a “tax” on company profits, thereby limiting market competitiveness.

This dynamic impacts labor demand, as companies can only thrive with higher union costs if they can pass these cost increases onto consumers – a strategy that is often impractical. This situation can hinder companies with collective union bargaining. As a result, collective bargaining processes may introduce rigidity in Colombia, affecting the persistence of unemployment duration.

Contrary to expectations, the estimation shows that LAPU does not significantly respond to growth shocks among those receiving unemployment benefits. This suggests that it is not a determinant of unemployment duration persistence – at least at the time of the estimations. Figure 2 presents the generalized impulse response functions of the VAR_1 model.

The results of the variance decomposition of LAPU (see Figure 3 below) reveal that non-labor income explains 28.49% of the variance, while the number of unionized individuals explains 7.45%, and the contract ratio gap explains approximately 17.91%. These findings provide evidence of the significant effect of institutional variables in the labor market on the persistence of unemployment duration in emerging countries like Colombia. According to the established variable system, approximately 53.85% of the LAPU variance is explained by this set of institutional variables. Finally, the ISE, a variable included as a control capturing the effect of the economic cycle, explains 10.49% of the variability of LAPU.

Figure 3

Variance Decomposition of LAPU at T = 20. Source: Authors’ own elaboration based on VAR1 estimation. T = 20 period in which the variance stabilizes. Cholesky’s order of the system: DLOG (CEM), DLOG (Non-labor income), DLOG (unionized), DLOG (Contract ratio – gap), DLOG (Unemployment benefits), LAPU. Note: The time horizon for variance decomposition analysis is 20 periods.

The results of the monetary transfer model are presented below (refer to Figure 4). These findings suggest that unemployment subsidies and severance payments do not influence the persistence of unemployment duration in Colombia. It’s important to note that the null effect of unemployment benefits on LAPU could be attributed to the low coverage of this unemployment protection benefit among the total number of unemployed individuals.

Figure 4

Generalized impulse-response functions accumulated to a standard deviation. Source: Authors’ own elaboration based on the VAR 2 estimation. Note: The time horizon for analysis in the impulse response function VAR 2 is 10 periods.

In this study, we calculated the average percentage of unemployed individuals who have received unemployment benefits, compared to the total number of unemployed individuals reported by the GEIH. The mean is 0.04%, the maximum value is 1%, and the minimum value is 0.002%. This calculation is based on a total of 142 observations in the time series. Given that these results are not significant, the variance decomposition analysis of the monetary transfer model is not carried out.

Taking into account the results of the VAR 2 model, the variance decomposition process agrees robustly with the results of the impulse response functions, since the variables that correspond to monetary transfers such as severance payments and unemployment benefits do not show significant effects on the LAPU; it is correct to indicate that the percentage of the variance of the LAPU that is explained by the growth in people receiving unemployment benefits and growth of people receiving severance payments is very low, that is, 4.63 and 2.29%, respectively; however, the growth of the ISE in this case explains about 21.09%, showing that cyclical economic activity has a greater impact on the LAPU than the variables corresponding to monetary transfers.

4.2 Robustness Checks

In the context of vector model estimation, the behavior of residuals is of utmost relevance as they depict the differences between observed and predicted values of the studied phenomenon. In our case, these residuals provide important information about the goodness of fit of the model and allow us to discard potential specification issues. In the case of VAR estimation in this study, we can infer from Figure 5 that the residuals exhibit a random behavior without discernible patterns, which is ideal as it implies the absence of serial autocorrelation, as further evidenced in Appendix 4 with the Breusch-Godfrey LM Test for the serial autocorrelation of VAR residuals. In conclusion, we can confidently affirm, based on our estimation, that there is no systematic relationship between residuals across different time periods. Additionally, as observed in Figure 3, residuals should exhibit a mean close to zero and a relatively constant variance over time. From the foregoing, the validity and reliability of the VAR model results can be assured.

Figure 5

VAR residuals. Source: Authors own elaboration based on VAR estimations.

Even when a VAR model is correctly specified, the issue of omitted additional lags may arise. However, this can be addressed by ensuring the normality of the disturbances. At a 99% confidence level and a 0.01 significance level, the null hypothesis that “The residuals are normally distributed” is accepted, as shown in Appendix 5. Additionally, the residual plot indicates a random walk process without discernible patterns. In empirical VAR model estimations, one should not assume transitive causal effects without a sufficient theoretical basis. Therefore, Granger causality tests (Granger, 1969) are useful for confirming or refuting unidirectional causality. The causality test results indicate no unidirectional causality, consistent with the model specification and the impulse-response function findings, affirming the endogeneity of these variables (Appendix 4).

We also included the historical variance decomposition of the variable of interest, “LAPU.” In the Figure 6, the historical decomposition shows the accumulated contribution of the jth shock to the variable of interest in the VAR over time. This analysis allows us to infer how changes in the variable of interest are explained by shocks in the system’s endogenous variables. In this case, based on the red line (baseline + variable behavior), we observe that non-labor income, unionization, and the contracts ratio closely and accurately explain the historical behavior of the LAPU variable.

Figure 6

Historical decomposition. Source: Authors own elaboration based on VAR estimations.