1. Introduction¹

During the Covid-19 health crisis, labor poverty (population whose income from work is insufficient to meet their basic food needs, according to the National Council for the Evaluation of Social Development Policy (^{CONEVAL, 2023}) increased and stood at 46% in the third quarter of 2020 (2020q3). This was an all-time high, ending a 10-quarter continuous decline that reached a low of 36.6% in 2020q1. By 2020q4, it had returned to its downward trajectory but the factors affecting these changes are not clear.

This paper uses quarterly data to incorporate a proposed analysis of the effects of income, inflation and interest rates on labor poverty in Mexico between 2005 and 2022. Three scenarios linking these Variables were estimated: i) real per capita product, inflation, real interest rate and labor poverty, while the remaining two scenarios replace income and inflation with ii) labor income and inflation of the income poverty line, and iii) inflation of the extreme income poverty line.

An impulse-response function was proposed to analyze these concepts, resulting from estimating VAR models and studying the short—and long-term effects on labor poverty using ^{Engle and Granger's (1987)} cointegration. The results suggest that the interest rate impacts poverty in both the short and long term; therefore, an economy with controlled inflation and higher growth is indispensable to reducing labor poverty.

The paper consists of five sections. In addition to this introduction, the second section reviews the literature on macroeconomics and poverty. The third section presents the data's methodology and construction, and the fourth section estimates and analyzes the different scenarios. Conclusions are given at the end.

2. Literature review

In the macroeconomics of the new consensus, the representation of the economy is usually based on the inclusion of three equations (^{Setterfield, 2006}) that describe the economy's behavior, as well as the economic policy response to shocks that deviate the product from its long-term trajectory.

For example, ^{Carlin and Soskice (2015)} identify the economy as a model represented by the commodity market through the IS curve, the labor market through the Phillips curve and a monetary rule of the Central Bank on the interest rate. The way this model works indicates that, when faced with a shock in the economy, the Central Bank will decide, based on its preferences, whether to incur costs between deviating from its inflation target or equilibrium products. In this respect, using the monetary rule is the best response. Finally, this will adjust the interest rate and influence aggregate demand.

Meanwhile, the literature focuses on the relationship between macroeconomic stability and poverty since a well-functioning macroeconomy reduces poverty (^{Ames et al., 2001}), and economic growth is the main factor affecting poverty reduction. However, the higher the poverty level, the longer it takes for growth to reduce it (^{Cashin et al., 2001}).

^{Romer and Romer (1998)} find differences between short—and long-term effects. For example, in the short term, an expansionary cycle generated by monetary policy improves the welfare of the poor; however, in the long term, an economy with low and stable inflation is better for this population's welfare. Meanwhile, ^{Ekobena (2014)} establishes that a restrictive monetary policy reduces poverty in the United States. However, the interest rate does not affect poverty or income distribution in low-income countries.

At the same time, ^{Azis (2008)} analyzes the relationship between fiscal and monetary policy and poverty. The effects of policy and the response of the poverty rate depend on the elasticity of poverty lines in relation to the price level and the elasticity of personal income in relation to the product level. For example, in the event of a shock destabilizing aggregate supply and demand, a stabilizing policy is necessary to reduce poverty. However, this could raise or lower the price level above or below the poverty line so that the product may be larger or smaller than the increase in the income of the poor. This depends on whether the policy response is fiscal or monetary.

By following this proposal, ^{Shahrier and Lian (2018)} find that, in the case of Thailand, an expansionary fiscal policy delivers better results than an expansionary monetary one in the short term. This is because it has a faster impact on the income of the bottom 20% of the population and does not generate distortions in the credit market. However, in the long term, a monetary policy that controls inflation impacts poverty reduction.

Continuing with evidence from countries such as Pakistan, ^{Saeed (2020)} finds that an increase in the monetary supply results in difficulties in reducing poverty and high interest rates. For Nigeria, ^{Abdulrahman et al. (2023)} argue that by implementing a monetary policy that leads to low inflation, the Central Bank will not only boost employment, output and institutions but also improve the welfare of the poor.

In Mexico, literature on the effects of macroeconomics has focused on the link between social spending and poverty (^{Torres and Rojas, 2015}), the estimation of poverty and income elasticity by state (^{Campos and Monroy, 2016}) or the regional effects on reductions in extreme and moderate poverty (^{Mendoza Cota and Torres Preciado, 2022}).

Recently, ^{Esquivel (2023)} conducted a stylized factual review of the current decline in labor poverty. He highlights the increase in the minimum wage as one of the main factors in this reduction, despite episodes of high inflation and the pandemic shock. This is followed by exploring some stylized facts and explaining the methodology of the VAR and cointegration models for the different scenarios presented.

3. Some stylized facts and econometric methodology

In the first scenario, real income, inflation and the interest rate are related to the labor poverty rate. This is because it represents a structural scenario where macroeconomic effects impact poverty.

For the second and third scenarios, real income is replaced by real labor income (deflated with the basic food basket) and the inflation rate by the inflation of the income poverty line (IPL) and extreme income poverty line (EIPL), respectively. This substitution connects, so to speak, the macroeconomic effects in a microeconomic scenario. It connects the impact of monetary policy on the family nucleus since these Variables are a construction of micro-survey information.²

The series is quarterly from 2005 to 2022. For the first scenario, we use GDP per capita from the national accounts, which is the result of dividing quarterly GDP (^{INEGI, 2023b}) by the total population recorded in the National Occupation and Employment Survey (Encuesta Nacional de Ocupación y Empleo, ENOE) (^{INEGI, 2023a}). It was decided to undertake this transformation to obtain figures comparable to labor poverty. We also used the quarterly average for inflation (^{INEGI, 2023b}) and the 90-day interest rate (^{Banxico, 2024}). To measure income in scenarios two and three, we used real labor income and to measure inflation, we used the growth rate of poverty and extreme poverty lines by average income and by area of residence (^{CONEVAL, 2023}).

Figure 1 reports the evolution of the labor poverty rate or labor poverty, which refers to the percentage of the population whose labor income is insufficient to purchase a basic food basket (^{CONEVAL, 2023}). The complete series presents at least four relevant changes: 1) a decreasing trend between 2005q1 and 2007q2; 2) an increasing trend between 2007q3 to 2014q2; 3) a decrease between 2014q3 and 2020q1; finally, 4) the pandemic shock in 2020q3 -the historical peak of labor poverty- and its subsequent decline towards the end of the sample.

Source: compiled by the authors with information from ^{CONEVAL (2023)}.

Figure 1 Evolution of the percentage of the population living in labor poverty, 2005q1-2022q4 

The labor poverty rate seems to respond mainly to the income component. ^{Esquivel (2023)} points out that the increase between 2006 and 2015 is due to a stagnation in the population's income. Meanwhile, the downward phase before the pandemic can be explained by the fact that labor poverty is almost non-existent in the formally employed population, a phenomenon of informality that reduces all labor poverty.

Figure 2 shows the income mentioned above. First, it highlights the fact that both labor income deflated by the National Consumer Price Index (NCPI) and labor income deflated by the value of the basic food basket (FB) report a different trajectory from GDP per capita until 2014q4 when all three incomes enter an upward phase. This is because labor income measures only a part of the GDP per capita, as seen from the income side. In this respect, it is worth noting that labor income increased slightly until shortly before the financial crisis and, after that, it entered a downward phase until 2014q4. Meanwhile, following that crisis, GDP per capita entered an upward phase until the Covid-19 crisis, the breaking point of the three series. Finally, in the last eight quarters available, the three series entered an upward phase.

Source: compiled by the authors with data from ^{INEGI (2023b)} and ^{CONEVAL (2023)}.

Figure 2 Evolution of real per capita output and real labor income, 2005q1-2022q4 

Figure 3 shows the evolution of general inflation and the growth rate of poverty lines, in other words, inflation of poverty and extreme income poverty. The most noteworthy fact is that poverty line inflation is more volatile than general inflation in most of the samples; however, from 2020 onwards, it seems to behave in the same way. Nevertheless, the poverty lines represent the basic needs and basic food needs that the population would need to access, which could, in turn, imply a greater relationship between these phenomena and labor poverty.

Source: compiled by the authors with data from ^{INEGI (2023b)} and ^{CONEVAL (2023)}

Figure 3 Inflation and growth rates of poverty and extreme income poverty lines, 2005q1-2022q4 

These facts reveal several relevant implications. First, labor income represents 60% of household income (^{INEGI, 2021}). Second, labor income is the reference for measuring labor poverty (^{CONEVAL, 2023}). Third, the monetary policy transmission channels of the Bank of Mexico (^{Banxico, n.d.}) indicate that the interest rate impacts future spending by discouraging investment and consumption, decreasing aggregate demand and, therefore, inflation. Finally, other prices impact the welfare of families, such as the value of basic food baskets.

In this respect, replacing GDP per capita with labor income and general inflation by the inflation of the two poverty lines would show that monetary policy not only has effects on aggregate variables but also has an impact on households and their members and therefore, on poverty, demonstrating the need to rethink not only the current transmission channels and the effects of each policy decision on the interest rate, but also to rethink the objectives of the banks.

Regarding the econometric methodology, a VAR model in differences³ is estimated for each scenario. The order of integration is analyzed using the Augmented Dickey-Fuller (ADF) test. Furthermore, to analyze whether there is a short and long-term macroeconomic relationship with poverty, a cointegration model with error correction is estimated, following the procedure of ^{Engle and Granger (1987)}.

In this respect, the VAR model can be described as follows:

where Y_t is the vector of the model's endogenous variables, Yt-1 is the vector of the k-period lagged Variables, A is the parameter matrix, and U_t is the vector of the error term.

To select the optimal number of lags in the VAR models, we followed the recommendations of ^{Catalán (n.d.)} and ^{Loría (2007)}, which used the information criteria and the final forecast error as decision criteria. Furthermore, based on ^{Lütkepohl (2005)}, the test of the stability assumption that takes into consideration the eigenvalues of the A matrix and the correct specification tests were used, especially the autocorrelation tests: if a VAR with ρ lags does not present autocorrelation, it should be chosen for the impulse response analysis. In this respect, the impulse response analysis is performed using the Cholesky breakdown.

Where Pob_t is labor poverty, X_t is the vector of explanatory variables of the scenarios (income, inflation and interest rate), γ is the estimator associated with the error correction model (ECM). In other words, the lagged error series of the long-term equation, and v_t is the error related to this specification.

The equilibrium relationship is tested by estimating the long-term relationship with the ADF test. Finally, its correct specification is checked using conventional tests.

4. Econometric estimates of the scenarios of interest

Next, we seek to test whether there is a mechanism that associates macroeconomic fundamentals with the poverty rate. In this respect, the scenarios contribute to a better understanding of shocks to the product, the effects on inflation, the monetary policy response of central banks and the change in labor poverty.

The series were transformed into natural logarithms. Table 1 shows the summary statistics and the z-statistic of the ADF unit root test for the seven variables in relation to level and first difference. The ADF test was performed without intercept or trend, with four lags. In addition, to confirm these results, the Z(t) statistic of the Phillips-Perron (PP) test, including trend and constant with the same lags, is reported. The series is order 1 stationary.

Scenario I. GDP per capita, inflation, interest rate and labor poverty

The first model corresponds to an estimation that links the main macroeconomic variables with labor poverty. Table 2 shows the information criteria associated with different specifications of the VAR model. It was decided to estimate specifications from 1 to 8 lags, or lagged effects from one quarter to two years. The Jarque-Bera normality and LM autocorrelation tests with 4 lags are also shown as criteria for choosing the best estimation.

Table 2 Information criteria and teste of correct specification on ρ order VARs: Scenario I 

ρ-lags	FFE	AIC	HQIC	SBIC	JB	LM
0	3.00E-09	-19.916	-19.916	-19.916	-	-
1	7.70E-10	-21.294	-21.066	-20.700	0.000	0.000
2	4.10E-10	-21.945	-21.4875*	-20.7553*	0.000	0.237
3	4.10E-10	-21.963	-21.277	-20.179	0.001	0.776
4	4.00E-10	-22.041	-21.126	-19.662	0.106	0.401
5	3.5e-10*	-22.274	-21.131	-19.300	0.801	0.413
6	4.50E-10	-22.203	-20.831	-18.634	0.387	0.284
7	6.60E-10	-22.045	-20.444	-17.881	0.000	0.167
8	5.40E-10	-22.598*	-20.768	-17.840	0.141	0.045

Notes. FFE: Final forecost error; AIC: Akaike criterion; HQIC: Honnon^uin criteria; SBIC: Bayesian criterion. For mote details on tftese criteria, see ^{Lütkepohl (2005)}. Resuhs witfi * indicate the best model according to the estimated criterion parameters. JB: Jaique Bera nonnality test. LM: Autocorrelation test on Lagrange multipters. The associated pvalues are reported. For the LM, the probabi1ty associated with the fourth Iag is reported. All specifications incorporate the following dummies: 2009ql, 2020q2 and 2020q3.

Source: own estimates.

The results in Table 2 are varied. However, using the correct specification tests, the model whose lags provide more information for understanding the phenomenon is the order 5 VAR. The analysis strategy is as follows: Figure 1 shows the impulse analysis of the macroeconomic variables—income, inflation and interest rate—in labor poverty, while Figure 2 reports the impulse and causality response of the three equations (^{Carlin and Soskice, 2015}).

The results in Figure 4 regarding the response of the labor poverty rate to a shock in the system variables show: a) a boost in income corresponds to a correction in long-term poverty by equilibrating it to four periods after a shock; b) the effect of inflation lingers on poverty by moving as a wave. In this respect, it diverts it from its equilibrium path; c) the effect of a boost in the interest rate increases poverty in the first period. However, the effect dissipates quickly over time and d) poverty per se does not seem to have inertial effects on itself.

Source: Own estimates.

Figure 4 Impulse-response on the poverty rate, scenario I 

The effects of Figure 5 indicate that a) an income shock diverts inflation from its equilibrium for several periods; b) the Central Bank raises the interest rate to control the shock with some lag periods before returning the economy to its equilibrium; c) this increase in the interest rate causes delays in the adjustment of inflation; finally, d) this increase diverts the product from its long-term trend, as it takes some periods to return to equilibrium.

Source: own estimates.

Figure 5 Macroeconomic Effects of Scenario I 

In turn, two more effects are added: the increase in poverty and its impact on interest (e) and income (f). An increase in poverty results in a reduction in the interest rate that lasts about five periods before it begins to return to its normal level while diverting income from its equilibrium for several periods.

The mechanism by which the effect in (e) occurs could be due to the causes that generated the increase in poverty. Since this population is mainly salaried (^{Department of Economic and Social Affairs, 2009}), this may be due to the rise in unemployment, which causes lower wages. In this respect, based on the analytical framework of ^{Carlin and Soskice (2015)}, there is less inflation than there should be, which could deviate it from its target. This would lead to an adjustment by lowering the interest rate, implying an increase in income, leading to a recovery in wages and, subsequently, inflation, returning the system to its long-term equilibrium.

Scenario III. Labor income, extreme income poverty line, interest rate and labor poverty

Unlike the previous scenario, scenario III substitutes inflation of the IPL for that of the extreme income poverty line. In this respect, given the information criteria and the specification tests, the lags that provide more information to the model are order 2. The results for this and the models up to 8 lags are reported in Table 4.

Table 4 Information criteria and tests of correct specification on the VARs of order ρ: Scenario Ill 

ρ-lags	FPE	AIC	HQIC	SBIC	JB	LM
0	2.30E-13	-17.730	-17.568	-17.318	-	-
1	7.90E-14	-18.825	-18.4481*	-17.8646*	0.000	0.095
2	6.6e-14*	-19.020	-18.428	-17.511	0.051	0.095
3	7.10E-14	-18.963	-18.155	-16.905	0.036	0.082
4	8.30E-14	-18.853	-17.829	-16.246	0.004	0.018
5	1.1E-13	-18.601	-17.362	-15.445	0.060	0.038
6	1.00E-13	-18.784	-17.329	-15.079	0.040	0.075
7	1.10E-13	-18.840	-17.170	-14.586	0.001	0.005
8	9.50E-14	-19.2293*	-17.343	-14.426	0.000	0.094

Notes: FPt Final forecast error; AlC: Akaike criterion; HQIC: HonnandJuin criterio; SBIC: Bayesian criterion. For more details on these criteria, see Ludcepohl (2005). Results with * indicate the bestmodel according to the estimated criterion porameters. JB: Jarque Bera normality test. LM: Autocorrekrtion test on Lagronge multipliers. The associated puolues are reported. For the LAE, the probability associated with the fourth Iag is reported. All specifications incorporate the following dummies: 2020q2,2020q3 and 2020q4.

Source: own estimates.

The results in Figure 7 indicate that a) income quickly balances poverty after a shock; b) inflation of the basic food basket first decreases and then increases the poverty rate. However, the adjustment takes place relatively quickly; c) the interest rate, like income, quickly adjusts income, bringing poverty toward its equilibrium value, while d) poverty does not generate inertia on its own.

Source: own estimates.

Figure 6 Impulse response on the poverty rate, scenario II 

Source: own estimates.

Figure 7 Impulse-response on the poverty rate, scenario III 

The effect in b) could be counterintuitive because an increase in the value of the basic food basket would have to increase poverty, at least in the early periods after the shock. However, with unequal income distribution, an increase in the poverty line does not necessarily translate into an increase in poverty (^{Shahrier and Lian, 2018}). An increase in the inflation of the basic food basket, by reducing purchasing power, incentivizes employment as work is less costly due to inflation, increasing income and, therefore, reducing poverty (^{Department of Economic and Social Affairs, 2009}). One of our objectives is to study the links between the short- and long-term discussed below.

5. Conclusions

The main result suggests that a monetary policy that promotes low inflation will reduce the labor poverty rate in Mexico. In this respect, the reaches of monetary policy are broader than acknowledged in the literature and inside central banks.

Throughout the analyzed period, the Mexican economy was characterized by cyclical behavior in most economic variables reviewed in this research. However, to contextualize the econometric results obtained, we should not lose sight of the two significant contractions in the GDP in 2009 and 2020 and inflationary episodes throughout the years considered.

Additionally, in the last five years (2018-2023), the Mexican economy reported an increase in minimum wages, a factor not recorded in several previous decades. After a five-year period of minimum wage increases well above inflation, although such a trend should continue in the short term, a suitable correction to the interest rate is also required in the context of a marked downward trend in the inflation rate and the monetary value of the basic food basket, in both cases, falling by 2025.

The results presented here assume that labor poverty is a given. In this respect, we need a better understanding of the main factors determining whether a person is subject to labor poverty. A better understanding of such factors will allow us to obtain more robust conclusions about the relationship between poverty and macroeconomics, economic policy, social policy, fiscal policy, etc. However, that is beyond the scope of this research.

Finally, the relationship between macroeconomics and poverty should be explored in greater detail from a theoretical and empirical perspective. The results presented here are hoped to stimulate discussion about the need to promote policies that correct and reduce poverty for the benefit of society as a whole.