Assessing the Impact of the Real Exchange Rate on Okun’s Misery Index in Mexico

Abstract

The exchange rate is among the main variables determining foreign trade, as it affects the prices of both exports and imports. Meanwhile, Okun’s misery index (MI) attempts to synthesize the main issues affecting a society by combining two major macroeconomic variables—unemployment and inflation. This study examines how Mexico’s bilateral real exchange rate index with the United States influences Okun’s misery index from 2005Q1 to 2023Q3. A quantitative analysis considering both the long- and short-run relationship between Okun’s MI and the real exchange rate was performed. The results show a unidirectional relationship between the exchange rate and the misery index in the long term, as indicated by the Toda–Yamamoto test. An unrestricted vector autoregressive model was used for the short-run analysis and found that depreciation increases the MI. A variance decomposition analysis shows that the real exchange rate considerably explains variations in the MI, whereas a historical decomposition analysis suggests that this relationship primarily occurs during periods of crisis.

1. Introduction

Exchange rate is a key indicator of foreign trade, influencing the prices of both imports and exports. Depreciation tends to raise import prices and lower export prices (Bakhshi & Ebrahimi, 2016; Krugman et al., 2023). As noted by Bush and López Noria (2021, p. 704), “The exchange rate is the key financial variable that connects the domestic economy with the rest of the world”.

The misery index (MI), developed by Arthur Okun, combines two critical economic indicators—unemployment and inflation—into a single measure of societal well-being (Clemens et al., 2022; Riascos, 2009). Okun’s MI provides an alternative approach to evaluating economic challenges from a macroeconomic perspective (Grabia, 2012) and is increasingly recognized as a useful well-being indicator, especially in light of recent inflation and unemployment surges in industrialized countries (Clemens et al., 2022).

Inflation erodes purchasing power, while higher unemployment rates make finding a job more difficult. Therefore, a combination of high unemployment and inflation is detrimental to the well-being of the ordinary citizen (Grabia, 2012). Additionally, the MI has been shown to negatively affect various aspects of human development, such as health and education (Singh, 2024), and contributes to income inequality (Bayar & Aytemiz, 2019). Thus, a higher MI typically signals poorer economic performance (Büyüksarıkulak & Suluk, 2022).

This study aims to explore the relationship between Mexico’s bilateral real exchange rate index with the United States (U.S.) and the original MI in Mexico from 2005Q1 to 2023Q3. Notably, while Sánchez (2022) developed a model involving both a modified MI and the real multilateral exchange rate, their study focused on the effect of the compensated misery index (CMI) on outbound tourism. Topbie et al. (2024) examined the relationship between the MI and official exchange rate in Nigeria, and Gakuru and Yang (2024) suggested incorporating the exchange rate into the MI. This study, therefore, is one of the first to analyze the impact of exchange rates on the MI.

The long-run analysis is based on the Toda and Yamamoto (1995) test, as the series are $I\left(1\right)$ but not cointegrated. The short-run analysis was conducted using a bivariate, unrestricted vector autoregressive (VAR) model whose lag structure was determined by means of the traditional information criteria. The Toda–Yamamoto test results confirm that the real exchange rate influences the MI unidirectionally, a finding consistent with the short-run analysis.

We believe that this document will be of interest for researchers and policy makers, as it provides solid evidence on the positive effect that the bilateral real exchange rate exerts on the standard Okun’s MI, which provides empirical evidence in favor of Gakuru and Yang’s (2024) index. Additionally, as the quantitative analysis was carried out by means of a VAR model, we have elaborated on variance and historical decomposition analyses, which has permitted us not only to measure the impact of the real exchange rate on the MI but also to locate in time the periods in which both variables were most closely related.

The remainder of this paper is organized as follows: Section 2 provides the literature review. Section 3 introduces the variables used in this study and their sources, followed by a subsection detailing the econometric methods employed. Section 4 presents the econometric results. Finally, Section 5 discusses the conclusions and offers recommendations.

2. Literature Review

2.1. Okun’s Misery Index

Okun’s MI, as described by Dornbusch et al. (2002) and Sánchez (2020), is computed by adding the unemployment and inflation rates, as shown in Equation (1):

$$MI=U+\dot{p}$$

(1)

where $U$ and $\dot{p}$ denote unemployment and inflation rates, respectively.

Okun’s MI has been widely criticized for its oversimplification of the economic issues that affect society (Lovell & Tien, 2000; Riascos, 2009). The MI’s specification assumes that citizens have an equal aversion to inflation and unemployment, as its indifference curves have a marginal rate of substitution of $-1$ (Lovell & Tien, 2000).

Despite these criticisms, the MI has proven useful in several contexts. Dornbusch et al. (2002) mention that the MI is associated with the political–business cycle. Adrangi and Macri (2019) found that the MI influences the approval ratings of U.S. presidents. Wang et al. (2019) suggested that economic misery is a significant factor affecting GDP. Açcı and Çuhadar (2021) found that higher MI levels correlate with increased crime rates. Alam et al. (2016) observed that economic misery negatively impacts life expectancy, while Yang and Lester (1999) found that the MI is a good predictor of suicide rates. Using a modified MI, Sánchez (2022) showed that economic misery reduces outbound tourism.

Several modifications have been proposed to improve Okun’s MI. For instance, Hortalà i Arau and Rey Miró (2011) and Gaddo (2011) suggested subtracting the real gross domestic product (GDP) growth rate from the MI. Ramoni-Perazzi and Orlandoni-Merli (2013) proposed incorporating informal sector employment. Lovell and Tien (2000) used a version of the MI that considers $\left|\dot{p}\right|$ instead of $\dot{p}$, acknowledging the negative effects of deflation on an economy. Dynamic specifications of the MI have also been introduced by Cohen et al. (2014) and Tule et al. (2017). Dynamic specifications of the MI, as defined by Cohen et al. (2014), consider the natural rate of unemployment and an output gap, which is computed as the difference between actual and potential output growth. Murphy (2016) further refined the MI by elaborating on state-level indices. More recently, Gakuru and Yang (2024) proposed a version of the MI that incorporates bank lending and exchange rates, while subtracting real GDP per capita. Wiseman (1992) outlined various modifications to the MI and presented their indifference maps.

This study adds to the existing literature by examining both the long- and short-term effects of the bilateral real exchange rate on the MI. In the long term, the Toda and Yamamoto (1995) test reveals that the real exchange rate Granger-causes the MI. In the short term, depreciation is shown to increase the MI.

2.2. Misery Index and Exchange Rate

As previously discussed, Gakuru and Yang (2024) incorporated the exchange rate into an MI, which can be expressed using the notation proposed by the authors as $(U+I+R+EX)-RGDP$, where $U$ represents the unemployment rate, $I$ is the inflation rate, $R$ is the bank lending rate, $EX$ is the exchange rate, and $RGDP$ is the real GDP per capita. This specification assumes that depreciation of the national currency exacerbates economic malaise.

According to Gakuru and Yang (2024, p. 16), this MI formulation “includes exchange rate to reflect the value of country’s currency relative to other currencies, affecting international trade and investment”. The exchange rate negatively impacts corporate investment as it is linked to company leverage, a relationship that tends to be more pronounced in emerging markets owing to lower financial development and higher dependency on foreign funding (Banerjee et al., 2022). Conversely, in Mexico, currency depreciation has been shown to positively affect foreign direct investment (FDI) (Vélez & Peña, 2024).

Different studies suggest a positive relationship between Okun’s MI and the exchange rate. Sánchez (2022) found, using an unrestricted VAR model, that the multilateral real exchange rate (MREX) has a positive but marginally significant effect on the CMI. MREX accounted for 7.026% of the variations in the CMI, with the effect appearing stronger during times of crisis. Similarly, Topbie et al. (2024) found that Nigeria’s official exchange rate increased the MI, using multivariate linear regression.

However, Gaite and Marturet (2022) noted that traditional views on national currency depreciation suggest that, in the presence of idle resources, depreciation can have expansionary effects on the economy. Depreciation raises the prices of imports, which encourages domestic consumers to favor national over foreign goods and services (Bakhshi & Ebrahimi, 2016; Krugman et al., 2023), thus boosting employment. Similarly, depreciation reduces the price of exports, enhancing competitiveness and, with stability in other sectors, can increase exports and employment (Bakhshi & Ebrahimi, 2016).

In contrast, the Latin American structuralist school introduced the contractionary devaluation theory in the 1960s, arguing that in semi-industrialized economies, devaluation leads to contractions in both economic activity and employment (Gaite & Marturet, 2022).

As noted by Gaite and Marturet (2022), the contractionary devaluation theory gained traction following the research of Krugman and Taylor (1978), which, besides being conducted in a developed country, sparked an academic debate. Krugman and Taylor’s (1978) model established that devaluation can lead to economic contraction under three conditions: a trade deficit, when “there are differences in consumption propensities from profits and wages”, and when the government can increase its revenue by way of devaluating. This last condition assumes that government’s saving propensity is equal to 1 in the short run.

If depreciation has contractionary effects on the economy, the positive impact of GDP on economic misery is diminished, leading to an increase in the MI. As Hortalà i Arau and Rey Miró (2011) pointed out, the negative sign attributed to GDP in modified misery indices suggests that economic contraction contributes to rising misery. Additionally, economic contraction often leads to higher unemployment (Okun, 1962), further increasing the MI. However, as Lizondo and Montiel (1989, p. 182) noted, “the direction of the impact effects of devaluation on real output is ambiguous on analytical grounds”.

The literature presents mixed findings on the relationship between exchange and unemployment rates. Ani et al. (2019) found that increases in the real exchange rate stimulate unemployment in Nigeria. Chang (2011) showed that exchange rate uncertainty is linked to higher unemployment in the short run in South Korea and Taiwan. Conversely, in Israel, Djivre and Ribon (2003) found that depreciation boosts economic activity, leading to a decrease in unemployment. In a study focused on industrial employment in Latin America, Galindo et al. (2007) found that depreciation can positively impact employment. However, the authors cautioned that higher levels of liability dollarization can reverse this positive effect, potentially leading to a negative overall impact in industries with high liability dollarization.

A significant portion of the literature links exchange rate volatility to unemployment. Bush and López Noria (2021) argued that under a floating exchange rate regime, some volatility is expected and even necessary, as it helps correct macroeconomic imbalances. However, excessive volatility can have negative effects on investment, thereby hindering economic growth. Following Feldmann (2011), some scholars suggest that in the presence of strong trade unions, exchange rate volatility may lead to wage hikes, which can result in reduced employment. Feldmann’s (2011) findings indicate that exchange rate volatility is associated with higher unemployment in the subsequent year, although the effect is small. Similarly, in Türkiye, Akarsu (2020) found that exchange rate volatility increases unemployment.

Regarding inflation, Krugman et al. (2023) noted that depreciation raises import prices, impacting local consumers, as most consumption baskets contain imported goods. Depreciation can also create inflationary pressure in an economy at full employment (Gaite & Marturet, 2022).

Depreciation can have opposing effects on the MI. For example, it may improve exports and boost the demand for national goods and services, stimulating employment creation and thus reducing the MI. Conversely, as suggested by Krugman and Taylor (1978), depreciation can have contractionary effects, increasing economic misery. Furthermore, depreciation can exert inflationary pressure by raising the prices of imports, which increases the MI.

In this document, we have elaborated on an unrestricted VAR model relating Okun’s MI and the bilateral real exchange rate, finding that the exchange rate exerts a positive effect on economic misery. This effect, as mentioned by Sánchez (2022), is stronger during times of crisis.

3. Data and Model Design

3.1. Variables and Sources

For this study, the following series were retrieved from the National Institute of Statistics and Geography (INEGI, 2023): the unemployment rate and the national consumer price index (INPC). The bilateral real exchange rate index of Mexico with the U.S. $\left(\pi \right)$ was sourced from Banco de México (2023). The analysis used quarterly data from 2005Q1 to 2023Q3 $\left(N=75\right)$, with the series seasonally adjusted using the Census X12 filter. All models, tests, and figures were generated using EViews^® 12 University Version.

Okun’s MI was calculated by determining the inflation rate as the growth rate of the seasonally adjusted INPC, then adding it to the seasonally adjusted unemployment rate, as shown in Equation (1).

To test the integration order of the variables, unit root tests with Dickey–Fuller min-t (DF min-t) breakpoint selection were applied (

Table 1. Unit root tests, 2005Q1–2023Q3 (Breakpoint selection: DF min-t).

Series	Innovation Outlier				Additive Outlier
	I	II	III	IV	I	II	III	IV
$\pi$	−3.998	−3.330	−3.628	−2.825	−3.643	−3.397	−3.550	−2.952
$MI$	−3.281	−4.644 *	−4.622	−4.041	−3.759	−4.745 *	−4.758	−3.218
$\ln \pi$	−4.083	−3.644	−3.515	−2.781	−3.677	−3.411	−3.500	−2.917
$∆\pi$	−9.274 ***	−9.225 ***	−8.910 ***	−7.886 ***	−9.313 ***	−9.331 ***	−8.834 ***	−8.026 ***
$∆MI$	−12.85 ***	−13.01 ***	−13.02 ***	−13.03 ***	−14.37 ***	−14.40 ***	−13.82 ***	−4.931 ***
${\dot{\pi }}_t$	−8.618 ***	−8.569 ***	−8.350 ***	−7.759 ***	−8.693 ***	−8.708 ***	−8.392 ***	−7.901 ***

Notes: I, intercept only; II, trend and intercept (intercept); III, trend and intercept (trend and intercept); IV, trend and intercept (trend). * and *** signify $p<0.1$ and $p<0.01$, respectively. Notation: ${\dot{\pi }}_{\mathrm{t}}=∆\ln \pi$.

). The Schwarz information criterion (SIC) was used to determine the appropriate number of lags for the unit root tests.

The unit root test results confirm that both the bilateral real exchange rate and its natural logarithm are $I\left(1\right)$ series. Similarly, Okun’s MI is also an $I\left(1\right)$ series. However, specification II of both versions of this unit root test suggests that the MI is a stationary series at the 10% significance level.

3.2. Empirical Design

To analyze the relationship between the MI and $\pi$, the traditional VAR model approach was employed. Since both series used in this study were $I\left(1\right)$ (Table 1), a bivariate VAR model was calculated with the series in levels to test for the existence of an equilibrium relationship, as shown in Equation (2):

$$\begin{array}{c}M{I}_t={\alpha }_1+{\displaystyle \sum _{i=1}^k}{\beta }_{1,i}M{I}_{t-i}+{\displaystyle \sum _{i=1}^k}{\theta }_{1,i}{\pi }_{t-i}+{\epsilon }_{1,t}\\ {\pi }_t={\alpha }_2+{\displaystyle \sum _{i=1}^k}{\beta }_{2,i}M{I}_{t-i}+{\displaystyle \sum _{i=1}^k}{\theta }_{2,i}{\pi }_{t-i}+{\epsilon }_{2,t}\end{array}$$

(2)

To estimate the number of lags in Equation (2), five criteria were used, as suggested by Sánchez (2022, p. 6): “sequential modified LR test statistic (LR), final prediction error (FPE), Akaike (AIC), Schwarz (SIC), and Hannan–Quinn (HQ)”. The LR criterion recommended $k=4$ as the ideal number of lags, while the other criteria suggested $k=2$ as the best choice (

Table 2. Optimal number of lags.

Lag	LR	FPE	AIC	SIC	HQ
0	NA	116.2548	10.43153	10.49735	10.45758
1	184.5155	7.331994	7.667882	7.865317	7.746007
2	16.11427	6.373693 *	7.527377 *	7.856436 *	7.657587 *
3	2.462904	6.899910	7.605732	8.066414	7.788025
4	10.55843 *	6.492230	7.543093	8.135398	7.777470
5	1.104440	7.192347	7.642774	8.366703	7.929234
6	2.288530	7.799099	7.719797	8.575349	8.058341
7	2.379900	8.441051	7.793432	8.780608	8.184060
8	7.849587	8.188671	7.755844	8.874643	8.198555

Note: * best number of lags according to the criterion. NA—Not applicable.

).

Based on the results in Table 2, Johansen’s cointegration test was conducted, first using two lags and then four lags, to assess an equilibrium relationship between the MI and the bilateral real exchange rate. However, for all five test types, the cointegration hypothesis was rejected based on both the trace and maximum eigenvalue specifications of the test (

Table 3. Summary of Johansen’s cointegration test.

Data Trend	None	None	Linear	Linear	Quadratic
Test Type	No Intercept No Trend	Intercept No Trend	Intercept No Trend	Intercept Trend	Intercept Trend
Two Lags
Trace	0	0	0	0	0
Max-Eig	0	0	0	0	0
Four Lags
Trace	0	0	0	0	0
Max-Eig	0	0	0	0	0

Note: Tests at the 5% significance level.

). As a result, the long-term analysis focused on applying the Toda–Yamamoto test to determine the direction of the relationship between the variables.

The Toda–Yamamoto procedure was deemed suitable because it “involves estimation of a vector autoregressive (VAR) model in levels, a method that minimizes the risks associated with incorrect identification of the order of integration of the respective time series and co-integration among the variables” (Amiri & Ventelou, 2012, p. 542). Additionally, as mentioned by Toda and Yamamoto (1995, p. 226), the usual Wald test utilized to perform the Granger causality test in VAR models with series in levels “[…] not only has a nonstandard asymptotic distribution but depends on nuisance parameters in general if the process is $I\left(1\right)$”.

Toda and Yamamoto’s (1995) approach to Granger causality involves estimating a $\mathrm{V}\mathrm{A}\mathrm{R}\left(k+d_{\mathrm{m}\mathrm{a}\mathrm{x}}\right)$, where $d_{\mathrm{m}\mathrm{a}\mathrm{x}}$ represents the maximum order of integration in the series. More precisely, “the Toda–Yamamoto long-run causality test artificially augments the correct order of the VAR, $k$, by the maximum order of integration, $d_{max}$, and ensures that the usual test statistics for Granger causality have the standard asymptotic distribution” (Amiri & Ventelou, 2012, p. 542).

According to Amiri and Ventelou (2012), a VAR model with these characteristics, adapted to the variables used in this study, can be written as shown in Equation (3):

$$\begin{array}{c}M{I}_t=c_1+{\displaystyle \sum _{i=1}^k}{\gamma }_{1,i}M{I}_{t-i}+{\displaystyle \sum _{j=k+1}^{d_{\mathrm{m}\mathrm{a}\mathrm{x}}}}{\gamma }_{2,j}{\mathrm{MI}}_{t-j}+{\displaystyle \sum _{i=i}^k}{\phi }_{1,i}{\pi }_{t-i}+{\displaystyle \sum _{j=k+1}^{d_{\mathrm{m}\mathrm{a}\mathrm{x}}}}{\phi }_{2,j}{\pi }_{t-j}+{ϵ}_{1,t}\\ {\pi }_t=c_2+{\displaystyle \sum _{i=1}^k}{\delta }_{1,i}M{I}_{t-i}+{\displaystyle \sum _{j=k+1}^{d_{\mathrm{m}\mathrm{a}\mathrm{x}}}}{\delta }_{2,j}{\mathrm{MI}}_{t-j}+{\displaystyle \sum _{i=i}^k}{\vartheta }_{1,i}{\pi }_{t-i}+{\displaystyle \sum _{j=k+1}^{d_{\mathrm{m}\mathrm{a}\mathrm{x}}}}{\vartheta }_{2,j}{\pi }_{t-j}+{ϵ}_{2,t}\end{array}$$

(3)

The model in Equation (3) was computed using $k=2$, as recommended by most of the criteria in Table 2, and considering that both series in the model were $I\left(1\right)$ (Table 1). After estimating the model in Equation (3), the Granger causality test was applied. However, as noted by Gujarati and Porter (2009), the Granger causality test requires the no-autocorrelation assumption to be satisfied. This was tested using a serial-correlation LM test. The stability condition was also verified.

Since both $∆MI$ and $\dot{\pi }$ are stationary series (Table 1), the short-run analysis was conducted using a bivariate unrestricted VAR model, as shown in Equation (4):

$$\begin{array}{c}{∆MI}_t=a_1+{\displaystyle \sum _{i=1}^n}{\varphi }_{1,i}∆{MI}_{t-i}+{\displaystyle \sum _{i=1}^n}{\omega }_{1,i}{\dot{\pi }}_{t-i}+{\lambda }_1{D}_t+{\eta }_{1,t}\\ {\dot{\pi }}_t=a_2+{\displaystyle \sum _{i=1}^n}{{\varphi }_{2,i}∆MI}_{t-i}+{\displaystyle \sum _{i=1}^n}{\omega }_{2,i}{\dot{\pi }}_{t-i}+{\lambda }_2{D}_t+{\eta }_{2,t}\end{array}$$

(4)

In Equation (4), $D_t$ is a dummy variable included to help the model accurately account for atypical observations. It is introduced into the VAR model as an exogenous variable. Equation (5) illustrates the definition of the variable $D_t$.

$$D_t=\left\{\begin{array}{cc}1& if t=2008Q4; 2020Q2\\ 0& Otherwise\end{array}\right.$$

(5)

Equation (4) was approached by estimating a VAR$\left(2\right)$ model, as this specification satisfies all the statistical assumptions associated with these types of models. This specification was recommended by both the AIC and FPE criteria (

Table 4. Optimal number of lags (unrestricted VAR).

Lag	LR	FPE	AIC	SIC	HQ
0	NA	0.000497	−1.932124	−1.799417	−1.879685
1	22.23605 *	0.000392	−2.169558	−1.904145 *	−2.064680 *
2	8.495226	0.000384 *	−2.189932 *	−1.791813	−2.032617
3	6.810211	0.000386	−2.186138	−1.655312	−1.976383
4	1.634125	0.000424	−2.094106	−1.430575	−1.831914
5	1.092194	0.000471	−1.993120	−1.196882	−1.678489
6	1.004325	0.000524	−1.891222	−0.962278	−1.524152
7	5.577000	0.000533	−1.881550	−0.819899	−1.462041
8	8.029342	0.000513	−1.927616	−0.733259	−1.455668

Note. * Selected number of lags. The test is performed in the presence of variable $D_t$. NA—Not Applicable.

). Although most criteria suggested one lag as optimal, under such a specification, the model does not meet the assumption of homoskedasticity.

For the short-run analysis, no cointegration test is needed since the variables in Equation (4) are stationary, as shown in Table 1 (Charemza & Deadman, 1997; Enders, 2015).

The VAR method has been criticized for its lack of parsimony in representing a time-series vector, which can lead to estimation issues such as overfitting and multicollinearity (Jaramillo, 2009). Additionally, Guzmán and García (2008) argued that the number of coefficients in each VAR equation is proportional to the number of variables in the model, which may reduce forecasting accuracy.

To avoid over-parameterization, only two variables were included and, as noted earlier, the number of lags was determined by two information criteria (Table 4). According to Gujarati and Porter (2009), each equation in a VAR model can be treated as a linear regression. Using this approach, variance inflation factors (VIFs) were estimated to check for multicollinearity. Additionally, the so-called Quandt–Andrews unknown breakpoint test was performed to identify potential structural breaks.

However, as Guzmán and García (2008) pointed out, working with a low-dimensional VAR can lead to issues with omitted variables. Great care was taken to ensure that the model met the assumption of no serial correlation. Gujarati and Porter (2009) noted that autocorrelation may indicate the exclusion of relevant variables from the model. To address this, both the serial correlation LM test and residual portmanteau tests for autocorrelations were applied, confirming that the model met the no-autocorrelation requirement in both tests.

4. Econometric Results and Discussion

4.1. Long-Run Analysis

Based on Equation (3) and the results in Table 1 and Table 2, the augmented VAR model used to perform Toda and Yamamoto’s (1995) test was estimated, as shown in

Table 5. Augmented VAR model.

Variable	${\mathit{M}\mathit{I}}_{\mathit{t}}$	${\mathsf{\pi }}_{\mathit{t}}$
${MI}_{t-1}$	0.478737 [3.98217]	0.074604 [0.06398]
${MI}_{t-2}$	0.225245 [1.78380]	−0.573589 [−0.46833]
${\pi }_{t-1}$	0.038671 [3.00923]	1.065944 [8.55179]
${\pi }_{\mathrm{t}-2}$	−0.030162 [−1.55877]	−0.225278 [−1.20033]
$Intercept$	0.780846 [1.14093]	11.82874 [1.78191]
${MI}_{t-3}$	0.191187 [1.67823]	−0.306813 [−0.27767]
${\pi }_{t-3}$	−0.011081 [−0.80242]	0.083919 [0.62655]
$R^2$	0.677962	0.895723
Adjusted $R^2$	0.648235	0.886097

Note: t-statistics in [].

.

As previously mentioned, the model met the assumptions of no serial correlation (

Table A1. Augmented VAR serial correlation LM test.

	* No Serial Correlation at Lag h				* No Serial Correlation at Lags 1 to h
Lag	LRE Statistic	p-Value	Rao F-Statistic	p-Value	LRE Statistic	p-Value	Rao F-Statistic	p-Value
1	5.362173	0.2521	1.358754	0.2521	5.362173	0.2521	1.358754	0.2521
2	8.017090	0.0910	2.053383	0.0910	11.99129	0.1516	1.536009	0.1518
3	5.963363	0.2019	1.514759	0.2019	14.65726	0.2607	1.244841	0.2614
4	3.297755	0.5093	0.828727	0.5093	18.96221	0.2706	1.209208	0.2721
5	6.116185	0.1906	1.554535	0.1907	22.59555	0.3091	1.150382	0.3119
6	2.125974	0.7126	0.531751	0.7126	22.70972	0.5370	0.946069	0.5415
7	0.118539	0.9983	0.029412	0.9983	22.92288	0.7369	0.803206	0.7420
8	5.578133	0.2329	1.414708	0.2330	30.56466	0.5392	0.951003	0.5495
9	5.762430	0.2176	1.462535	0.2176	32.53910	0.6340	0.888995	0.6469
10	1.102395	0.8939	0.274603	0.8939	35.64930	0.6664	0.869849	0.6831
11	3.605337	0.4620	0.907143	0.4621	37.50537	0.7446	0.819598	0.7633
12	3.554283	0.4697	0.894114	0.4697	43.08476	0.6741	0.865624	0.7025

Note: * Null hypotheses.

) and stability (Figure A1). After confirming that the augmented VAR model satisfied these prerequisites, a Granger causality test was conducted, with the results presented in

Table 6. VAR Granger causality test (Toda–Yamamoto approach).

Null Hypotheses	${\mathit{\chi }}^{\mathbf{2}}$	d.f.	p-Value
${\pi }_t$ does not Granger cause ${MI}_t$	9.666012	2	0.0080 ***
${MI}_t$ does not Granger cause ${\pi }_t$	0.265825	2	0.8755

Note: d.f. is the degrees of freedom. *** $p<0.01$.

.

The results show that the MI is Granger-caused by $\dot{\pi }$ at the 1% significance level. However, the reverse effect is rejected at all traditional significance levels (Table 6).

4.2. Short-Run Analysis

Based on Equation (4), an unrestricted VAR model was used to analyze the relationship between the variables selected in this study, with the results presented in

Table 7. Unrestricted VAR model.

Variables	${\dot{\mathit{\pi }}}_{\mathit{t}}$	$∆{\mathit{M}\mathit{I}}_{\mathit{t}}$
${\dot{\pi }}_{t-1}$	0.128823 [1.31272]	3.819202 [3.02555]
${\dot{\pi }}_{t-2}$	−0.030660 [−0.28781]	1.670138 [1.21883]
$∆{MI}_{t-1}$	−0.003668 [−0.40536]	−0.530535 [−4.55862]
$∆{MI}_{t-2}$	−0.008184 [−0.96880]	−0.278505 [−2.56302]
$Constant$	−0.003381 [−0.75140]	−0.047239 [−0.81612]
$D_t$	0.169423 [6.16693]	0.723980 [2.04870]
$R^2$	0.382458	0.333405
Adjusted $R^2$	0.335675	0.282905

Note: t-statistics in [].

.

After estimating the unrestricted VAR model, the standard assumptions were verified by applying traditional joint correct specification tests, with the results shown in

Table 8. Correct specification tests.

Test		Value	p-Value
Doornik–Hansen normality test
	Skewness	0.865978	0.6486
	Kurtosis	0.228025	0.8922
	Jarque–Bera	1.094002	0.8952
White heteroskedasticity test (no cross-terms)		37.03463	0.0944
White heteroskedasticity test (cross-terms)		55.19198	0.2214

Note: The stability test and the full tests of autocorrelation are presented in Appendix A.

.

Table 8 demonstrates that the model met the assumptions of normality and homoskedasticity. As noted earlier, particular attention was given to the no-autocorrelation assumption. To assess this, the VAR residual portmanteau tests for autocorrelations (

Table A2. VAR residual portmanteau tests for autocorrelations.

Null Hypothesis: No Residual Autocorrelations Up to Lag h
Lags	Q-Statistic	p-Value *	Adj Q-Statistic	p-Value *	d.f.
1	0.392710	---	0.398241	---	---
2	1.400316	---	1.434635	---	---
3	4.833822	0.3048	5.017424	0.2855	4
4	8.001211	0.4334	8.371131	0.3981	8
5	12.48405	0.4076	13.18852	0.3555	12
6	13.76411	0.6163	14.58494	0.5552	16
7	13.99566	0.8307	14.84143	0.7854	20
8	17.76590	0.8142	19.08294	0.7476	24
9	24.21756	0.6700	26.45627	0.5480	28
10	25.02663	0.8049	27.39584	0.6989	32
11	27.25165	0.8528	30.02208	0.7479	36
12	28.40836	0.9148	31.41014	0.8323	40

Note: * In VAR$\left(k\right)$, this test is useful only for lags larger than $k$. d.f. is the degrees of freedom. This test was performed in the absence of the variable $D_t$, as the p-values are not accurate for models containing exogenous variables.

) and the VAR serial correlation LM test (

Table A3. VAR serial correlation LM test.

	* No Serial Correlation at Lag h				* No Serial Correlation at Lags 1 to h
Lag	LRE Statistic	p-Value	Rao F-Statistic	p-Value	LRE Statistic	p-Value	Rao F-Statistic	p-Value
1	4.703049	0.3191	1.188372	0.3192	4.703049	0.3191	1.188372	0.3192
2	8.283749	0.0817	2.123120	0.0817	10.79898	0.2134	1.376061	0.2136
3	3.307509	0.5077	0.831142	0.5078	14.37428	0.2774	1.219006	0.2781
4	2.899300	0.5748	0.727389	0.5748	19.10525	0.2632	1.218680	0.2647
5	4.038284	0.4008	1.017716	0.4009	23.16568	0.2807	1.182002	0.2834
6	0.811291	0.9369	0.201870	0.9369	23.32726	0.5006	0.974510	0.5051
7	2.691945	0.6106	0.674814	0.6106	25.56886	0.5967	0.907047	0.6031
8	7.014688	0.1351	1.788810	0.1351	34.43723	0.3519	1.091143	0.3622
9	9.182917	0.0567	2.362018	0.0567	41.82470	0.2326	1.194874	0.2454
10	0.905700	0.9237	0.225445	0.9237	43.54280	0.3231	1.104845	0.3423
11	4.360221	0.3594	1.100251	0.3595	48.28636	0.3038	1.114701	0.3288
12	1.232252	0.8728	0.307125	0.8728	49.33318	0.4197	1.024552	0.4536

Note: * Null hypotheses.

) were conducted, confirming that the model satisfied the no-autocorrelation assumption. Additionally, the VAR model met the stability assumption, as shown in Figure A2. The Quandt–Andrews unknown breakpoint test (

Table A4. Quandt–Andrews unknown breakpoint test.

Statistic	$\mathbf{∆}\mathit{M}\mathit{I}$ Equation		$\dot{\mathit{\pi }}$ Equation
	Value	p-Value	Value	p-Value
Maximum LR F-statistic	1.722261	0.6065	2.314556	0.2738
Maximum Wald F-statistic	10.33356	0.6065	13.88734	0.2738
Exponential LR F-statistic	0.635868	0.4158	0.713582	0.3154
Exponential Wald F-statistic	4.115641	0.3489	4.983755	0.2003
Average LR F-statistic	1.249985	0.2285	1.380411	0.1579
Average Wald F-statistic	7.499911	0.2285	8.282463	0.1579

Note: 20% of trimmed data.

) and the VIFs (

Table A5. Variance inflation factors (VIFs).

Variable	VIFs
${\dot{\pi }}_{t-1}$	1.013801
${\dot{\pi }}_{t-2}$	1.174215
${∆MI}_{t-1}$	1.379386
${∆MI}_{t-2}$	1.232990
$D_t$	1.050168
$Constant$	NA

Note: NA = not applicable.

) further verified that the model met the assumptions of no structural breaks and no multicollinearity, respectively.

After confirming that the model met the statistical assumptions, impulse response analysis was conducted using the generalized response (Figure 1).

The impulse response analysis revealed that the bilateral real exchange rate positively affects Okun’s MI, though this effect remains statistically significant only during the second period (Figure 1a). Figure 1b shows that Okun’s MI has no significant impact on $\dot{\pi }$.

Since both series used in the unrestricted VAR model were stationary, a standard Granger causality test was conducted (

Table 9. VAR Granger causality test.

Null Hypotheses	${\mathit{\chi }}^{\mathbf{2}}$		p-Value
$\dot{\pi }$ does not Granger cause $∆MI$	11.65146	2	0.0030 ***
$∆MI$ does not Granger cause $\dot{\pi }$	0.938579	2	0.6254

Note: *** $p<0.01$.

) to provide additional statistical evidence supporting the results observed in Figure 1.

As shown in Table 9, Okun’s MI is Granger-caused by the real exchange rate, but not the other way around. These results align with those obtained using the Toda–Yamamoto approach (Table 6). To further complement this analysis, a variance decomposition analysis was conducted using Cholesky ordering (

Table 10. Variance decomposition Cholesky one S.D. (d.f. adjusted).

Period	$\mathbf{Decomposition}\mathbf{of}{\dot{\mathit{\pi }}}_{\mathit{t}}$		$\mathbf{Decomposition}\mathbf{of}{∆\mathit{M}\mathit{I}}_{\mathit{t}}$
	${\dot{\mathit{\pi }}}_{\mathit{t}}$	${∆\mathit{M}\mathit{I}}_{\mathit{t}}$	${\dot{\mathit{\pi }}}_{\mathit{t}}$	${∆\mathit{M}\mathit{I}}_{\mathit{t}}$
1	100.000	0.000	5.383	94.616
5	98.912	1.087	16.528	83.471
10	98.900	1.099	16.532	83.467
15	98.900	1.099	16.532	83.467
20	98.900	1.099	16.532	83.467

Note: Cholesky ordering: ${\dot{\pi }}_t$, $∆{MI}_t$.

).

The results in Table 10 align with those in Figure 1 and Table 9, showing that Okun’s MI explains only 1.09% of the changes in the bilateral real exchange rate by the end of the study period and 0% during the first period. In contrast, variations in the bilateral real exchange rate account for 5.38% of the changes in Okun’s MI during the first period and 16.53% during the last period. The model stabilized after the fifth period and was fully stable by the tenth period. Both Okun’s MI and the bilateral real exchange rate are highly autoregressive. These findings are consistent with the results in Table 9 and Figure 1.

The final step of the analysis involved a historical decomposition. This method “assigns responsibility for fluctuations in any one of the VAR’s variables, beyond a specified point in the available time series, among all the variables included in the system of equations comprising the VAR” (Burbidge & Harrison, 1985, p. 45). The relevance of each variable in the historical decomposition can be interpreted as follows: “The importance of the variable in each period is measured by the extent to which the baseline without the structural error of interest […] closes the gap between the actual value of the endogenous variable (vertical bars) and the baseline forecast […]” (Ouliaris & Rochon, 2018, pp. 13–14).

Interpreting Figure 2a, as indicated by Ouliaris and Rochon (2018), the historical decomposition highlights two specific periods where the real exchange rate played a significant role in explaining variations in Okun’s MI: the international financial crisis and the COVID-19 outbreak. A similar pattern is observed in Figure 2b.

5. Conclusions and Recommendations

This study examined the relationship between Mexico’s bilateral real exchange rate index and Okun’s MI. The results indicate a unidirectional relationship between the exchange rate and the MI in the long run. A similar relationship was observed in the short run, with the impulse response analysis revealing that depreciation increases Okun’s MI. These findings are further supported by Granger causality and variance decomposition analyses. However, Figure 2 shows that this relationship is more pronounced during periods of crisis.

The positive impact of the exchange rate on Okun’s MI found in this study aligns with prior research by Sánchez (2022) in Mexico and Topbie et al. (2024) in Nigeria. Additionally, the results support the positive sign introduced by Gakuru and Yang (2024) when incorporating the exchange rate into their MI. However, these studies were conducted in developing countries where, as noted in the literature review, depreciation can lead to increased unemployment through economic contraction, thereby amplifying Okun’s MI. Moreover, as discussed earlier, in developing nations depreciation has a stronger negative effect on corporate investment owing to lower levels of financial development. Nevertheless, depreciation can also encourage foreign investment, as noted in the Mexican context. Future research should compare these results with evidence from developed nations.

As mentioned earlier, a prerequisite for depreciation to cause economic contraction is the presence of a trade deficit balance. According to Secretaría de Economía (2023), Mexico currently has 14 free trade agreements with more than 50 countries. Given this network of commercial agreements, Mexico should focus on increasing exports and attracting more FDI to reduce the risk of significant economic contractions due to depreciation, which could exacerbate the economic misery reflected in Okun’s MI. To achieve this, establishing clear protections for FDI in Mexico’s territories is crucial.

Additionally, as mentioned by Johnson (1987, p. 18), “Exchange rate policy influences the level of imports. It does so by affecting both the demand for imports and the foreign exchange available to finance imports”. Generally, a depreciation is a policy designed to alleviate current account deficits. A depreciation usually impacts on consumption habits, as citizens tend to substitute imported goods with national goods due to price increases. This effect will be stronger to the extent that domestic goods are similar to imported ones. Effectively, according to Johnson (1987, p. 19), “The impact of the relative price changes is greatly affected by the structure and the significance of consumption imports and the associated price elasticities of demand”.

Mexico is considered a high-risk country owing to cartel activity, which results in high levels of violence. It is important to note that “Countries classified as High Risk experience ongoing conflict, criminal activity or civil unrest. These countries have weak institutions and are incapable of effectively managing crises” (Faintuch & Chafetz, 2024). Additionally, Chafetz (2024) used a travel advisory map to show that only the Mexican states of Campeche and Yucatán are considered safe enough for normal travel, while border states should be avoided for nonessential travel.

Recently, President Donald Trump stated that the tariffs potentially imposed on Mexican and Canadian goods entering the U.S. were a response to the massive trafficking of fentanyl, emphasizing that this policy was unrelated to the U.S.–Mexico–Canada Agreement (Redacción AN/MDS, 2025). When these tariffs were confirmed by Karoline Leavitt, the current White House press secretary, the value of the U.S. dollar surged in Mexico, causing the Mexican peso to depreciate by 1.40% (Ayala, 2025). However, a last-minute agreement resulted in a one-month tariff truce, with Mexico committing to send 10,000 soldiers to the Mexican border with the U.S. (Camhaji, 2025). This led to a temporary appreciation of the Mexican peso, although potential volatility remains owing to U.S. trade policies (Expansión, 2025). Estimates suggest that the exchange rate could exceed 24 pesos per U.S. dollar if the U.S. imposes a 25% tax on Mexican goods entering the U.S., though depending on trade relations, the peso could stabilize at 23 units per dollar by year-end (Melgoza, 2025).

Imposing consumption taxes affects consumers by restricting their options and by preventing them from achieving their desired consumption level. This effect is amplified by a depreciation, as “Currency depreciation, by raising domestic prices, causes the real value of financial assets and of disposable income to fall” (Johnson, 1987, p. 20).

This situation underscores the critical need to restore peace within the country for sustained trade development. As Muhammad et al. (2013) noted, importers may turn to other countries with more stable and secure conditions, a decision that could become permanent. This dynamic, as seen in Mexico’s experience, can significantly affect the exchange rate market, contributing to a rise in the MI.

The importance of shaping economic and social policies to reduce the MI lies in its impact on key areas like education, health, and income—factors essential to human development (Singh, 2024). For Mexico, one of the first steps toward reducing economic misery is rebuilding trust with its primary trading partner by restoring peace.

Limitations

While this study offers valuable insights into the MI and the exchange rate through a bivariate unrestricted VAR model that meets the assumptions of this approach, several variables were omitted in the pursuit of a more parsimonious model. Future research should examine how other variables, especially those related to Mexico’s main trade partners, influence Okun’s MI.