2.1. Labor and economic activity indicators of slack

A standard national accounts statistical procedure is to update the base year to estimate the Gross Domestic Product (GDP) series. This process includes an important effort by the Mexican National Institute of Statistics and Geography (Instituto Nacional de Estadística y Geografía, INEGI) to update the value of the different goods produced in the economy. The GDP series is thus more accurate and the historic GDP series changes, both in terms of level and growth rates. This change may affect the measurement of economic activity and, as a result, the estimation of economic activity slack in real-time.⁴ However, labor market slack is not subject to this problem, because the variables used to compute this indicator are generally based on the number of employed or unemployed workers and is not subject to periodic revisions. These considerations highlight the importance of taking labor market information into account to evaluate slack in the economy in real-time.

2.2. Informal labor definition and identification

According to international criteria proposed by the International Labour Organization (^{ILO, 2003}), informal workers include self-employed persons and wage earners not registered in social security. Some informal workers, particularly the unregistered self-employed, may earn relatively high incomes and may work voluntarily in the informal sector, that is, they remain informal even if they have an opportunity to enter the formal sector. In contrast, involuntary informal workers-those who would rather have formal employment but cannot obtain ittend to concentrate in the group of informal wage earners (see ^{Alcaraz et al., 2015}; and ^{Fajnzylber and Maloney, 2007}). The World Bank flagship report Informality Exit and Exclusion (^{Perry et al., 2007}) finds that informal wage workers are more disadvantaged than their informal self-employed counterparts in several Latin American countries. ^{Alcaraz et al. (2015)} use a model of self-selection with entry barriers into the formal sector to detect endogenously involuntary informal workers and find a higher proportion of involuntary informal workers among wage workers. Informal wage earners may thus best represent disadvantaged workers and, consequently, behave similarly to unemployed workers. We therefore combine informal wage earners and unemployed workers to construct our extended indicator of slack in the Mexican labor market, defined as the extended indicator of the level of unemployment consistent with an environment of stable inflation. We use this indicator to analyze the evolution of slack in the Mexican labor market from 2005 to 2016. To evaluate the advantages of using this variable as an alternative to traditional measures, we also estimate the NAIRU using only the unemployment rate (NAIRU-trad) and compare the slack estimated with both indicators (slack-inf and slack-trad). By comparing these indicators through different stages of the economic cycle, we can evaluate their ability to indicate inflationary pressures.

In order to assess the participation of our proposed new indicator of labor slack slack-inf within the Economically Active Population (EAP), we calculate the EAP composition from the National Survey of Occupation and Employment (Encuesta Nacional de Ocupación y Empleo, ENOE) data, using expansion factors to obtain population-representative data, as shown in figure 2.⁵ The data correspond to the survey of the fourth quarter of 2016. Among the population aged 15 years and older, just over 35 million are economically active, and of these, 4.1 percent were unemployed. There were just under 34 million who were employed, almost 13.7 million of them were informal. In turn, informal wage earners (informal employees) represented 14.8 percent of the EAP in the fourth quarter of 2016. Our alternative rate of unemployment, taking informal labor into account, was 26.6 percent (the traditional unemployment rate of 4.1 percent plus the informal wage earners’ rate of 22.5 percent). It is important to notice that non-remunerated workers (workers that receive no wage) represented 6.8 percent of the EAP. These workers earn some kind of non-monetary income but it is not observable. Furthermore, in general, these workers have a particular type of labor relationship associated with family activity. In line with other empirical labor market studies, we exclude these workers from our analysis.

Note: Survey weights were used to obtain the population-representative figures.

Source: Authors’ calculations with data from ENOE, INEGI.

Figure 2 Labor market composition, urban areas, ENOE (Q4-2016) Percentage of total economically active population (EAP), 15 years and older 

2.3. Exogenous policy changes that could trigger changes in incentives between formal and informal labor

One potential problem with our alternative measure of slack is the possibility of legal or administrative actions aimed at reducing informal employment in the economy. If these measures are successful, such a reduction could take place regardless of the economic cycle, resulting in an erroneous attribution of the decline to the slack in the economy. We argue that this problem is not severe enough to offset the usefulness of our alternative indicator. Unfortunately, we can only provide circumstantial evidence for some cases, but for the rest, we have administrative data that allows us to quantify the effect of these measures on the number of formal workers.

Since our empirical strategy allows for changes in the NAIRU over time, we do not expect that gradual changes in the informality rate caused by these measures will bias our results. In order to assess the magnitude of this problem, we list in table 1 all the actions taken during the study period that encouraged worker registration, and we link them to the informality rate over time (see figure 1). Mexico’s primary social security institution, the Mexican Social Security Institute (Instituto Mexicano del Seguro Social, IMSS), regularly sponsors campaigns to encourage formalization of employment. However, none of these campaigns seem to have resulted in a significant decrease in informal employment. The government also promoted a series of ‘first job’ programs encouraging young workers to register in 2007 and 2010. According to administrative data, these programs registered 25,000 workers per year. If we consider that approximately 700,000 new workers register at IMSS every year, it is clear that these programs did not meaningfully increase formality during the time span of our analysis.

In 2012, the Mexican Congress approved a labor law reform, which may have encouraged the registration of wage earners (see ^{Banco de México, 2012}). However, according to the Banco de México, the increase in the number of formal workers due to this reform would be gradual, over a few years. Given that our methodology allows for changes over time in the NAIRU, we do not consider this reform as a serious source of bias in our analysis. In 2014, the government launched the program Crezcamos Juntos (‘Let’s Grow Together’) to encourage the registration of small firms. This program might have led to an increase in the number of registered workers and thus a reduction in informal employment, but the increase was negligible. Finally, in the same year, IMSS and the tax authorities agreed to share information about registered workers. It is advantageous for employers to register workers and wages with the tax authorities because they receive tax deductions, but there is also an incentive not to register workers with IMSS, as the employer pays part of the cost of social security. It was expected that as a result of the sharing agreement, employers with more workers registered with the tax authorities than with IMSS would increase IMSS registration, so the numbers would match. This measure could thus have induced the formalization of workers. However, the effect of this measure might be limited by the fact that employers may assume that both institutions shared information with no need of agreement, and as a consequence, they regularly matched the workers’ registration in both institutions independently of the celebration of any agreement.

Figure 1 shows an important variation of informality over time, but we observe no relationship with any of the policy measures explained in this section. Even though there have been some changes in regulations that could bias our results, we conclude that the magnitude of this problem is not significant enough to affect them.

3.1 Econometric methodology

There are different methodological approaches in the literature to estimate the NAIRU and thus to calculate the corresponding unemployment gap. In this paper, we focus on the estimation of the NAIRU from equations that model inflation dynamics based on the Phillips curve. The consensus in the literature is that the most suitable conceptual framework for studying the NAIRU is a reduced-form Phillips curve approach. We use this approach to compute the NAIRU as the unemployment rate consistent with stable inflation, subject to an expectations-augmented Phillips curve. This relationship broadly establishes a negative link between inflation and the unemployment gap the difference between the observed unemployment rate and the NAIRU in the short run, such as the following:

where:

πt is the annual inflation rate and πte is the expected inflation rate;

ut-u- is the unemployment gap, defined as the difference between the observed unemployment rate ut and the NAIRU u- ; and

Xt represents a vector of variables controlling for the presence of supply shocks (e.g.,fluctuations in the real exchange rate, telecommunication and commodity prices, and external sector variables).

In order to better approximate the dynamics of the inflationary process, we generalize this relationship and, following ^{Staiger et al. (1997a} and ^1997b), we use the following empirical model to estimate inflation dynamics:

where:

Δ=1-L and L is the lag operator;

βL,γL    and δL are lag polynomials; and εt is and

εt error term.

The literature on the estimation of the NAIRU includes different interpretations of these ways of modeling inflation. ^{Gordon (1997} deliberately omitted inflation expectations and estimated the NAIRU from what he calls the triangle model of inflation. According to this model, the inflation rate depends on three basic determinants: inertia, demand, and supply. ^{Staiger et al. (1997a)} develop another interpretation: the random-walk model for inflation expectations, i.e., πte=πt-1 and thus πt-πte=Δπt . Under this assumption, inflation expectations are equal to past inflation. ^{Laubach (2001)} also uses the first difference of inflation, but justifies its use because it is the stationary transformation of inflation according to his data.⁶Finally, as discussed in ^{Restrepo (2008}, when inflation is stable, this particular case is also consistent with a model of adaptive expectations. Here, following this literature, we use the specification in equation (1) in our estimates.⁷

Our methodological strategy is first to estimate a version of equation (1) for each of our two measures of unemployment in Mexico, assuming the NAIRU is constant. From this estimation, we conduct a simple statistical test with the null hypothesis of constant parameters (Chow test) that suggests that the NAIRU in Mexico might have changed in recent years. From these first results, we estimate models that allow us to obtain a time-varying NAIRU. Specifically, we consider two reduced-form approaches widely used in the literature: i) a deterministic NAIRU, i.e., a recursive estimation from equation (1), and ii) state-space specifications, which provide further flexibility regarding the dynamic properties of the NAIRU. We explain these specifications in further detail below.

NAIRU recursive estimation

In the specification of equation (1), the unemployment gap could have a contemporaneous and a lagged impact on inflation. In order to simplify the NAIRU estimation, we assume that βL=β , i.e., that the relationship is contemporaneous. We will see below that this is the resulting specification in our empirical application. We infer the NAIRU as follows:

such that if α^ and β^ are the OLS estimators in (2), the NAIRU (i.e., the unemployment rate that accomplishes Δπt=Δπt-1=0 ) can be estimated through the following relationship:

However, in order to allow the relationship between unemployment and inflation to vary over time, we compute the path of the NAIRU through a recursive estimation of equation (2), leaving the starting point of the sample fixed as follows:

Through this estimation, it is possible to infer the evolution of the NAIRU over time, since the most recent information is incorporated into the model. An alternative strategy could be a rolling window estimation of the model, but the size of the sample and the drastic behavior of the unemployment rate in the international financial crisis make these estimates very volatile.⁸

We model the NAIRU as an unobserved stochastic process, where we assume that its determinants are unknown but persistent (i.e., they follow a random walk). Starting from the simplest case, components that further explain the dynamics of the unemployment rate, such as lags and the output gap, can be gradually added to the system of equations to introduce additional structure into the model. We describe below the three cases we explore.⁹

NAIRU random walk

As in ^{Gordon (1997}, the evolution of the NAIRU is obtained from the following system of equations:

where errors are assumed to be i.i.d. N 0,σε2 and uncorrelated.¹⁰

NAIRU random walk and AR(2) unemployment gap

In addition to assuming a random-walk NAIRU, this methodology models the dynamics of the unemployment gap ut-u-t following ^{Laubach (2001}. We model this gap as an autoregressive process, which prevents the unemployment rate from deviating permanently from the NAIRU. In other words, the unemployment gap is a meanreverting process. The system of equations to estimate the NAIRU is given by:

Where ρ1 and ρ2 are parameters to be estimated, and the errors are assumed N 0,σ12 and uncorrelated, with i = e, ∈ .

NAIRU random walk and unemployment gap (Okun’s Law)

We expand the previous system of equations with the inclusion of an equation relating the unemployment gap to the output gap (Okun’s Law). The system of equations we use to estimate the NAIRU is the following:

Where φt is the time-varying Okun coefficient, modeled as a random walk, and errors are assumed to be N 0,σi2 and uncorrelated, with i=e,ϵ,r ¹¹ In this specification, we consider the output gap as an exogenous variable within the model, and estimate it using the ^{Hodrick-Prescott (HP) filter (Hodrick and Prescott, 1997}) with a tail correction method (^{St-Amant and Van Norden, 1997}).¹²

3.2 Data

We use monthly, seasonally-adjusted data for unemployment and prices from January 2005 to December 2016, obtained from INEGI. In all estimations, inflation πt corresponds to monthly core inflation, calculated as the annual change in the seasonally-adjusted Consumer Price Index (CPI).¹³ We use INEGI’s monthly statistics on unemployed workers, which are based on the international definition.¹⁴

The data on informal wage earners comes from INEGI’s ENOE, a quarterly household survey with a rotating panel structure, from 2005 to 2016. Every quarter, INEGI replaces one-fifth of the sample: each household is thus followed for five consecutive quarters. The purpose of the survey is to collect data on the employment situation of Mexicans aged 15 and older in rural and urban areas. It is possible to identify informal wage earners in this survey, as defined by the ^{ILO (2003)}. We assume that workers are informal if they are wage earners without any of the following mandatory benefits: IMSS (social security), ISSSTE (social security for government employees), Afore (retirement benefits), INFONAVIT (home loan), or private health insurance. For comparability purposes, we convert the quarterly informal labor data to monthly data using linear interpolation¹⁵ because the rest of the variables considered are available as monthly data.¹⁶

In the baseline estimation, unemployment ut corresponds to INEGI’s national unemployment rate, ut=100*UnemtEAPt where Unemt is the number of people without a job and actively searching for one, and EAPt is the economically active population¹⁷ (unemployed plus employed) within the total population aged 15 or older. In the estimation including informal employment (NAIRU-inf), we calculate an extended measure of unemployment u-extendedt ,which includes INEGI’s national series for both unemployment and informal wage earners, u-extendedt=100*Unemt+InftEAPt where Inft is the number of informal wage earners within the EAPt . Figure 3 shows both the traditional unemployment rate and the extended unemployment rate used in our estimation. These variables show a high level of correlation: 0.92. However, unlike the traditional unemployment rate, it seems that the extended unemployment indicator did not return to the levels observed prior to the 2009 crisis.

Source: INEGI and authors’ calculations with data from ENOE, INEGI

Figure 3 Traditional and extended unemployment rate % 

We estimate the output gap Ytgap using the HP filter with tailcorrection on INEGI’s economic activity index (IGAE). Some of the variables tested as alternatives to control for supply shocks in equation (1) include the monthly annual change in the following series: the Bank for International Settlements (BIS) real effective exchange rate index for Mexico, the Banco de México Mexican import price index, the West Texas Intermediate and Mexican mix oil prices in U.S. dollars per barrel, the U.S. CPI, and the telecommunications component of the Mexican CPI. These variables are not included in the estimation simultaneously, but are tested as alternatives to obtain a parsimonious and statistically valid model according to the diagnostic and specification tests described in section 4. Using the conventions of the NAIRU-related literature, we subtract the mean from Xt to induce a zero-mean sample, avoiding bias from the constant component. Thus, supply shocks are zero, on average, in the specification for inflation dynamics.

4.1 Results A first approach to the NAIRU

Figure 4 shows scatter plots of the change in annual inflation against the two measures of unemployment. First, it should be noted that there is indeed a negative relationship between the variables. The correlation between the changes in annual inflation and u-extendedt is-0.18, and with ut is -0.21, both statistically different from zero at the 5 percent level. Thus, lower levels of unemployment, in any of its measurements, are associated with higher inflation.

Source: Authors’ calculations with data from INEGI.

Figure 4 Relationship between the change in annual inflation and unemployment in Mexico, 2005:01-2016:12 

From the intersection of the line of best fit with the x-axis (i.e., when the change in inflation is zero), we can infer that the NAIRU-trad is 4.4 and the NAIRU-inf is 27.3.¹⁸ However, this analysis would omit the inertial effects of inflation and the possible effect of supply shocks. The results of the estimation of equation (1) for both measures of unemployment are shown below.¹⁹

NAIRU-inf:

NAIRU-trad:

Where πt is core annual inflation and Δπt its first difference, utifor i ϵinf,trad is the traditional (trad) or extended (inf) unemployment rate, and Δrect is the first difference of the annual change of the real exchange rate (increase means appreciation). The standard errors are shown in parentheses. The sum of the coefficients related to the lags of the control variables is statistically significant and shows the expected sign, and there are no substantial changes in its magnitude when different unemployment measures are used.²⁰ R-2 is the R-squared measure adjusted by the number of predictors, and σ^ε is the standard error of the model. We include two tests for heteroskedasticity: the autoregressive conditional heteroskedasticity test, F _ARCH(1) , and the White test, F _het . For serial correlation, we run a Lagrange multiplier test, F _ar(1) , and we use the Jarque-Bera test, JB, for normality. All tests indicate that the model presents no problems of ARCH errors, autocorrelation, heteroskedasticity, or non-normality.²¹ We report the p-values of these diagnostic tests. To arrive at these well-behaved equations of inflation dynamics, we test different numbers of lags for all supply-shock variables, unemployment, and inflation. We use this same specification of inflation dynamics for all methodologies (including the state-space models), so that in all cases the variables included and the structure of lags are the same.

From these results, we observe that both the traditional unemployment measure and the proposed indicator have statistically significant effects on inflation. We also obtain a first estimate of the NAIRU, where we assume it is constant over time. Under this assumption we obtain NAIRU-trad = 4.43 (0.27) and NAIRU-inf = 27.46 (0.48).²² We test the assumption of a constant NAIRU by applying a test of structural change, the classical Chow test of structural change with the null hypothesis of constant parameters,²³ which divides the sample in two and tests whether the coefficients related to the NAIRU estimation are equal in both subsamples. Figure 5 illustrates the results of this test for different periods. In most periods the null hypothesis of constant parameters is rejected at the conventional significance levels. We can thus conclude from the analysis that the NAIRU-trad and the NAIRU-inf show trajectories that vary over time.

Source: Authors’ calculations using data from INEGI.

Figure 5 Evidence of time-varying NAIRU for Mexico, 2005:01-2016:12 F-Statistic 

Time-varying NAIRU

We next present in graphical form the results of the methodologies for estimating a time-varying NAIRU for both measures of unemployment. Appendix B presents detailed results for each estimated model. In figure 6, we show the results of the NAIRU and labor market slack using both the traditional indicator of labor underutilization, unemployment (slack-trad), and the extended indicator (slack-inf), estimated with the four models described in the previous section. In general, our results show that the estimations of both NAIRU-trad and NAIRUinf increase slightly over time, and that slack-trad and slack-inf follow a similar trajectory.

Figure 6 Estimation of NAIRU and NAIRU-inf1/%, s.a. 

Now we compare the four estimations, highlighting their major differences. The recursive estimation seems to jump slightly in mid2009 and then start a slight upward trend through the end of the sample period. These jumps are not observed in any of the state-space models because those are estimated with double smoothing using the Kalman filter. However, we can see that all the specifications coincide in a final NAIRU that is greater than at the beginning of the period. If we focus on the three state-space models, which differ only in how we model non-observable variables, we can distinguish some of the modeling differences. For example, the results of the random-walk model show a NAIRU with a clear upward trend, which slows down in the final years of the sample. These results contrast with those of the model in which the unemployment gap follows a second-order autoregressive process (see equation 4). In this specification, the unemployment gap tends to revert to its zero mean, which makes the slope of the NAIRU flatter than that of the random-walk models.

Finally, in contrast to the other three models, when we include the relationship between the unemployment gap and the output gap, as described by equations 5 and 5.1, the NAIRU drops after 2011, particularly when the extended unemployment measure is used. Figure 7 shows the output gap and the unemployment gaps for both indicators of slack in this estimation, and the trajectory over time of Okun’s coefficient φT The results show that toward the end of the sample period, although the output gap suggests the existence of slack in the goods and services market, the gap in the labor market has been closed. This result can be explained, in part, by the fact that the statistical relationship established by Okun’s Law has changed over time and, in particular, has weakened in the final years of the estimation period. In fact, this relationship becomes positive although statistically significant only in the case of the model that uses the traditional unemployment rate. It is noteworthy that these estimates of the NAIRU modeling Okun’s Law have smaller confidence intervals than the rest of the estimates (see figure 6D). In this model, we are not estimating the output-gap endogenously, but with an HP filter with tail-correction, and the greater rigidity in the structure of this model could explain this result. As the results of ^{Laubach (2001} suggest, providing more structure to the model reduces the confidence intervals.

Note: 90% confidence interval. Seasonally adjusted data.

Source: Authors’ calculations with data from INEGI.

Figure 7 Output gap, unemployment gap and Okun’s Coefficient 

Despite these differences, all our measures of labor slack seem to be consistent with the economic cycle, i.e., a first period characterized by tightness in the labor market, a post-crisis period with important labor slack, and a reduction in this slack beginning in 2014. In addition, the indicators derived from both indicators of slack show a gradual decrease that becomes more pronounced in the final year, when the unemployment rate is below NAIRU, a difference that is statistically significant. Figure 8 shows the average of all estimations. For the sake of simplicity, in sections 4.3 and 5 we use these averages to analyze employment in the economic cycle with both indicators of labor slack, the traditional measure and the one including informal employment.

Note: The confidence interval corresponds to two average standard deviations among all estimations. Seasonally adjusted data.

Source: Banco de México

Figure 8 Average estimations of NAIRU-trad and NAIRU-inf %, s.a. 

4.2 Inflation-predicting performance of each measure of the unemployment gap

In this section, we evaluate the forecasting accuracy of the eight unemployment gaps estimated in the previous subsection. We use the methodology developed by ^{Hansen et al. (2011} that allows us to obtain a subset of superior models for its predictive capacity. The methodology identifies the subset of the models we use that have the best inflation forecasting ability, using the confidence interval acquired through the estimation of a parameter to obtain the model confidence set (MCS) constructed from a predictive equivalence test and elimination rule. This procedure can be summarized as follows: (i) the set of models to be evaluated is chosen in terms of their predictive capacity; (ii) the null hypothesis is that all models have the same predictive ability, while the alternative is that at least one of the models is inferior; and (iii) if the null hypothesis is not rejected, we have a superior set of models. If the null hypothesis is rejected, then the inferior model is removed from the procedure and we return to the previous step. This procedure, unlike other predictive equivalence tests, does not require the choice of a reference model to implement the test.

Specifically, to test whether the models have equivalent predictive performance, ^{Hansen et al. (2011} propose the following test statistic:

where M is the full set of models considered in the predictive evaluation, d-ij=n-1∑t=1ndij,t=Li,t-Lj,t and Li,t is the loss function of model i in the period t, which in our case is a quadratic loss function. Thus, d-ij is the mean squared error (MSE) of model i relative to the MSE of model j. The var^d-ij statistics is calculated using bootstrap. TR,M compares pairs of models.

The exercises are carried out to evaluate the predictive capacity of the models with different measures of unemployment gaps. This is a pseudo-out-of-sample exercise for different forecast horizons, h = 1,2,...12 , and the average of these horizons. For this exercise, we use the subsample that covers from 2006:12 to 2016:12, with a rolling window of 60 observations.²⁴ The sample for the forecast evaluation considers approximately 35 percent of the full sample (2013:1-2016:12), which corresponds to 48 forecast periods.

Table 2 shows the results of this exercise. Practically all the models for all horizons show an equivalent predictive capacity. A possible exception is the Okun’s law model with the informality unemployment rate that is discarded in some horizons. Thus, the results do not indicate a clear difference in the ability of the unemployment gaps to predict the dynamics of inflation.

4.3 Measuring inflationary pressures in difficult times

As shown in the previous analysis, there is no clear statistical difference between the two measurements of labor slack in predicting inflation. However, from the policymaker’s point of view, there could be periods when it is especially important to have accurate indicators of inflationary pressures, such as when the unemployment gap is declining and approaching toward zero. Because this type of situation could trigger demand pressures, the policymaker needs the most accurate possible indicator of the unemployment gap. On the other hand, when unemployment is well above the natural unemployment rate, there is little uncertainty that there are no inflationary pressures coming from the labor market.

In this section, we evaluate which labor market slack indicator is more accurate in detecting inflationary pressures when the unemployment gap is close to zero. We use the threshold regression model of the inflation equation that we have used in the previous estimates. The threshold is endogenously estimated in the model. First, as baseline regression we estimate a basic model with no thresholds:

where Slackttrad and Slacktinf are the average gaps of the traditional and expanded unemployment rate (with informality), respectively.

In this subsection, we use the average of the four estimation models for each unemployment measurement. Table 3 shows the results. Column (1) exhibits the results of the traditional unemployment gap, column (2) of the extended unemployment gap, and column (3) shows the results with both unemployment measures in the same equation. When the coefficients of the gaps are estimated separately they are significant and their levels are not statistically different. However, when both measures are included in the inflation specification, their magnitude is reduced by almost half and their standard error more than doubled,²⁵ an obvious indication that the two measures of labor market slack are closely related.²⁶ Figure 9 illustrates the unemployment gaps from the average of the estimates, that is, the gaps calculated from the average estimates of NAIRU-trad and NAIRUinf reported in Figure 8. The gaps are standardized (divided by their standard deviation in the sample) so that their magnitudes can be directly compared. Throughout the sample period the gaps show similar trajectories, but there are some periods with more than subtle differences.

Source: Authors’ calculations with data from INEGI.

Figure 9 Average estimations of the unemployment gap (standardized values) 

We then estimate the threshold regression model. This model allows us to specify a regime change that occurs when a predetermined variable crosses an unknown threshold to be estimated. In particular, we focus on the simplest case of a single threshold (τ ), that is, a model with two regimes described below:

Where βtradj and βinfj are the coefficients related to the gaps in each regime j, for j=1,2. Note that between regimes only the coefficients related to the gaps change; those related to the control variables are not a function of the threshold.

The predetermined variable which helps us to determine the threshold is the square of the traditional unemployment rate gap, Slackttrad2 which is illustrated in figure 10.²⁷ This is intuitively simple: Slackttrad2 represents how far the slack in the labor market is from zero. We analyze whether for periods in which Slackttrad2 is close to zero (values, regardless of the sign, of the traditional unemployment gap closer to zero) there is a statistically valid partition in which the information of each gap is exploited. A model with its corresponding threshold is estimated for each constraint, and we choose the best model according to the information criteria. Table 4 reports the main results; the full results and constraints can be found in Appendix C. In this methodology (^{Bai and Perron, 2003}), the threshold is determined endogenously using the information criteria from the global minimization procedure.

Source: Authors’ calculations with data from INEGI.

Figure 10 Variable of interest to determine the regimes: square of the traditional unemployment gap, τ= 0.52 

Column (1) of table 4 shows the result of the non-constrained classical threshold regression model, in which a regime change is permitted in the parameters βtradj and βinfjSlackttrad is only significant in regime 2 τ^≤Slackttrad2 ; whereas Slacktinf is marginal in regime 1 Slackttrad2<τ^ ; and not statistically significant in regime 2. Column (2) shows a restricted version of the model, in which we assume that βtrad1=0 and βinf2=0 In this case, Slacktinf has a significant impact on inflation when the variable Slackttrad2 is less than the estimated threshold, while Slackttrad is significant in regime 2 when τ^≤Slackttrad2 In fact, according to the information criteria (AIC, BIC, and HQ) and the R-2 , this is the best model among those considered. The estimated threshold value τ^=0.54 is shown in figure 10. Finally, columns (3) and (4) present other variants of the model in which just one of the gaps is a function of the threshold, while the coefficient of the other remains constant between regimes. Column (3) assumes that only Slacktinf depends on the regimes, while in column (4) Slackttrad remains constant between regimes. In none of these variants are the coefficients significant. Thus, according to our results, the best partitioned specification, the one in column (2), implies that Slackttrad is relatively better suited to explain inflation tan Slackttrad in periods where it is more difficult to know if there is slack or not.

These results might be explained by a period with a high rate of job creation where slack-trad reflects a tight labor market. However, if this period also showed a high rate of low-quality informal labor growth, slack-inf might show a different history, one with a higher level of slack, given that it accounts for this low-quality employment. In such a case, slack-inf could reflect inflationary pressures more accurately.²⁸ The specification of the inflation equation can be decomposed into terms for the determinants of slack, inertia, and supply shocks. In figure 11 we compare the contribution to inflation of the slack components of models (1) and (2) in table 3 with that of the preferred model resulting from threshold regression analysis in table 4. We see that around 2007 the Slackttrad measure does not indicate inflationary pressures, while the Slacktinf measure does. Towards the end of the sample period, beginning in 2016, we see the opposite: the Slackttrad measure shows inflationary pressures, while Slacktinf showsno upward pressures until the end of the year. In the following section we analyze these observations in more detail.

Source: Authors’ calculations with data from INEGI.

Figure 11 Comparison of the contribution to inflation of the unemployment gap measures 

Period I (2005Q1-2008Q4)

During this period, inflation began to pick up (figure 13). The Mexican economy showed some tightness: the GDP gap was positive and statistically significant (figure 12) and wages showed important gains (figure 14d). In addition, unit labor costs in both the manufacturing and service sectors were particularly high throughout this period (figure 14e and 14f).²⁹ However, increases in international food and energy prices also contributed to local inflation (^{Banco de México, 2008}). Slack-inf showed greater tightness than slack-trad, particularly in 2008 (figure 8), which is consistent with the inflationary pressures suggested by other sources of information in the economy. This may indicate that through this period, slack-inf was a better indicator of the Mexican labor market than slack-trad to detect inflationary pressures.

Period II (2009Q1-2014Q2)

During Period II, Mexican economic activity decelerated significantly and went through an important recession as a consequence of the international financial crisis. Wages and labor costs plunged deeply (figures 14d, 14e, and 14f) and are still today far from their pre-crisis levels. Banco de México quickly loosened monetary conditions by decreasing the policy interest rate from 8.25 to 4.5 percent (figure 13). In this period, both measures of slack showed an important increase. However, unlike during Period I, slack-inf suggested a greater degree of slack than slack-trad. Again, it appears that slack-inf better reflected the reality of the Mexican labor market.

Source: Authors’ estimations with INEGI data: ENOE and Economic Information Bank.

Figure 14 The context of the Mexican labor market A) IGAE gap and the negative of the unemployment gap 1/ % 

1/ The IGAE gap is shown as a percentage of the potential output. The negative of the unemployment gap refers to the average estimation for the NAIRU less the observed rate of unemployment.

2/ We present the IGAE gap, measured as a percentage of potential output, by sector. Source: Banco de Mexico estimates with data from INEGI.

Figure 15 B) IGAE gap ^2/ %, s.a. 

Figure 16 C) Informality rate by sector ^3/ % 

3/ Quarterly series. The graph shows the informality rate for the employed population aged 15 or older in urban areas with a population greater than 15,000.

4/ Quarterly data with and without Hodrick-Prescott filter (smooth line, λ=200). Employed population aged 15 or older in urban areas with a population greater tan 15,000. We eliminate wages lower than the 1st and greater than the 99th percentile. When the interviewee did not answer the question about wages with an actual figure, but answered in terms of the minimum wage equivalent, we calculated the monthly wage equivalent.

Source: Authors’ estimations with data from ENOE, INEGI.

Figure 17 D) Average monthly wages of the urban employed population ^4/ Real, MXN December 2010 

Period III (2014Q3-2016Q4)

Five years after the beginning of the crisis, the slack in the labor market, as measured both by NAIRU-trad and by NAIRU-inf, started declining and continued with this trend until the end of the period (figure 8). At first glance, the latter would suggest the presence of demand-pull inflationary pressures. However, the fact that wages barely grew during this period (figure 14d) and the output gap was still negative suggest no inflationary pressures coming from aggregate demand (figure 14a).

In order to understand this conundrum, we analyze this part of the cycle by separating economic activity in the service and industrial sectors. The slack in the IGAE during Period III is fully accounted for by the negative output gap in the secondary sector (with and without mining) since the end of 2015. In contrast, the tertiary sector (services) output gap closed and crossed into positive territory toward the end of the period (figure 14b). The tertiary sector is also more labor intensive and has a higher level of informal employment than the secondary sector (figures 14c, 14g, and 14h). Finally, the informal sector has considerably lower wages than the formal sector (figure 14d). These three factors provide a plausible explanation of why labor market conditions during this period did not translate into demand-pull inflationary pressures: the service sector, with the highest degree of informal employment and significantly lower wages, was the only productive sector that tightened. Thus, the labor market in Mexico seems to have allowed an adjustment in which workers without formal employment could be absorbed by the service sector into lower-paying jobs, without implying significant inflationary pressures from aggregate demand. During this period, both measures of slack start to suggest tighter labor market conditions. However, once again, slack-inf shows a subtle difference from slack-trad. Figure 8 shows that slack-inf suggests less tightness in the labor market than slack-trad, which is consistent with an absence of wage pressures and lower labor costs, both in the service and industrial sectors.

Figure 18 E) Labor productivity and unit labor cost ^5/ Manufactures 2008=100, s.a. 

5/ Productivity based on hours worked. Seasonally adjusted series. Trends and seasonal adjustment estimated by Banco de México.

Source: Banco de México using SCNM, ENOE, and INEGI data.

Figure 19 F) Labor productivity and unit labor cost ^5/ Services 2008=100, s.a. 

Figure 20 G) Urban employment by sector ^6/ % of total employment 

6/ Quarterly data. Employed population aged 15 years and older in urban áreas with a population greater than 15,000. 7/ Using original quarterly series on GDP at 2008 market prices.

Source: Authors’ estimations with INEGI data: ENOE and Economic Information Bank.

Figure 21 H) GDP by Sector ^7/ % of total GDP 

Finally, it is important to note that Banco de México started tightening monetary policy conditions in December 2015 (figure 13). However, it was emphatic that such pre-emptive policy rate increases were driven by other exogenous shocks at the time (most importantly, exchange rate depreciation) and not by demand-pull inflationary pressures (see ^{Banco de México, 2016}).