The effect of international visitors on poverty alleviation in Mexico: an approach from the misery index

Figures & data

Table 1. Breakpoint unit root tests, 2000Q2 – 2020Q2

Series	Innovation Outlier				Additive Outlier
	A	B	C	D	A	B	C	D
$ln\mathit{V}$	−1.691	−1.688	−1.323	−1.738	−2.104	−2.259	−3.464	−3.387
$\mathit{CMI}$	−5.476***	−5.520***	−5.425**	−5.576***	−5.586***	−5.520***	−5.795***	−6.986***
$\dot{v}$	−10.02***	−10.31***	−10.24***	−9.740***	−9.743***	−9.862***	−10.51***	−11.94***

A, intercept only; B, trend and intercept (intercept); C, trend and intercept (trend and intercept); D, trend and intercept (trend); lag length: Schwarz criterion; Max. lags = 8; Breakpoint selection: Dickey–Fuller min-t; *** and ** denote rejection of the unit root hypothesis at the 1% and 5% significance levels, respectively; Symbolization: $\dot{v}=\mathrm{\Delta }ln\mathit{V}$; CMI = compensated misery index.

Table 2. VAR model

Variables	${\dot{v}}_{\mathit{t}}$	$\mathit{CM}$
${\dot{v}}_{\mathit{t}-1}$	−0.161627	−6.999327
	[−1.29509]	[−2.70742]
${\dot{v}}_{\mathit{t}-2}$	−0.159319	−1.920905
	[−1.29082]	[−0.75131]
$\mathit{CM}{I}_{\mathit{t}-1}$	−0.002209	0.352802
	[−0.59366]	[4.57718]
$\mathit{CM}{I}_{\mathit{t}-2}$	0.002827	0.160034
	[0.77079]	[2.10632]
$\mathit{Intercept}$	−0.005529	2.227147
	[−0.29822]	[5.79898]
${\delta }_t$	0.001601	2.151934
	[0.14988]	[9.72402]
$D_{2020\mathit{Q}2}$	−1.129461	17.74181
	[−28.5761]	[21.6693]
R-squared	0.927308	0.910846
Adj. R-squared	0.921164	0.903312
F-statistic	150.9528***	120.8956***

t-statistic in []; *** denotes rejection of the null hypothesis at the 1% significance level.

Table 3. Unrestricted VAR joint correct specification tests

Test	Statistic	Probability
Doornik-Hansen Normality Test:
Skewness	3.4340	0.1796
Kurtosis	1.6453	0.4392
Jarque-Bera	5.0794	0.2792
Serial Correlation LM test (12)	0.2638	0.9007
White heteroskedasticity test (no cross terms)	36.3301	0.3162
White heteroskedasticity test (cross terms)	60.7744	0.5561

A full test of serial correlation is presented in Table A1 in the appendix.

Figure 1. Unrestricted VAR simulation (Broyden’s algorithm).

Table 4. Structural factorization normality test

Skewness	Kurtosis	Jarque-Bera
2.6491	0.6724	3.3216
(0.2659)	(0.7145)	(0.5055)

Probabilities are in parentheses.

Figure 2. Response to structural VAR innovations ± 2 S. E.

Table 5. VAR Granger causality test

Null hypothesis	${\chi }^2$	df	Probability
$\dot{v}$ does not Granger-cause $\mathit{CMI}$	7.454425	2	0.0241**
$\mathit{CMI}$ does not Granger-cause $\dot{v}$	0.677691	2	0.7126

**denotes rejection of the null hypothesis at the 5% significance level.

Table 6. Variance decomposition using structural VAR factors

Period	Decomposition of ${\dot{v}}_{\mathit{t}}$		Decomposition of $\mathit{CM}{I}_t$
	${\dot{v}}_{\mathit{t}}$	$\mathit{CM}{I}_t$	${\dot{v}}_{\mathit{t}}$	$\mathit{CM}{I}_t$
1	100.00	0.000	3.983	96.016
5	99.575	0.424	18.131	81.868
10	99.574	0.425	18.210	81.789
15	99.574	0.425	18.210	81.789
20	99.574	0.425	18.210	81.789

Only the first three decimal positions are considered in the data.

Figure 3. Historical decomposition using structural VAR weights.

Table A1. VAR serial correlation LM test

	^aNo serial correlation at lag h				^aNo serial correlation at lags 1 to h
Lag	LRE statistic	Probability	Rao F-statistic	Probability	LRE statistic	Probability	Rao F-statistic	Probability
1	5.069847	0.2802	1.281781	0.2802	5.069847	0.2802	1.281781	0.2802
2	1.685449	0.7934	0.420870	0.7934	6.993308	0.5374	0.877264	0.5375
3	6.126506	0.1899	1.554956	0.1899	13.11442	0.3608	1.105386	0.3614
4	7.177717	0.1268	1.828821	0.1268	18.59938	0.2900	1.182291	0.2912
5	2.394468	0.6636	0.599471	0.6636	20.87507	0.4045	1.053908	0.4069
6	9.006782	0.0609	2.310373	0.0609	29.84301	0.1900	1.280296	0.1932
7	2.635040	0.6206	0.660281	0.6206	36.06673	0.1409	1.337878	0.1451
8	3.852030	0.4264	0.969545	0.4264	36.65898	0.2615	1.171855	0.2695
9	5.383119	0.2502	1.362550	0.2502	43.83184	0.1734	1.261154	0.1828
10	1.684846	0.7935	0.420719	0.7935	44.18341	0.2993	1.124005	0.3150
11	2.403458	0.6620	0.601742	0.6620	45.58226	0.4061	1.039371	0.4279
12	1.059130	0.9007	0.263868	0.9007	51.74342	0.3299	1.089093	0.3573

^aIndicates the null hypothesis.

Table A2. Variance inflation factors (VIF)

Variable	VIF
${\dot{v}}_{\mathit{t}-1}$	1.171234
${\dot{v}}_{\mathit{t}-2}$	1.057610
$\mathit{CM}{I}_{\mathit{t}-1}$	1.274311
$\mathit{CM}{I}_{\mathit{t}-2}$	1.250782
${\delta }_t$	1.012809
$D_{2020\mathit{Q}2}$	1.140469

$1<\mathit{VIF}<5$ indicates moderate correlation. The test does not apply for constants.

Data Availability Statement

The data that support the findings of this study are openly available at Mendeley Data at https://doi.org/10.17632/hzgysvg55k.1