Prices and Inflation

Prices and inflation are measured using the CPI of the 46 cities in the sample and its 283 categories of expenditure (subclass-product). The base period is the second half of December 2010, and the series are monthly from January of 1990 to April 2017. The data come from the web page of Mexico’s statistics agency, INEGI (www.inegi.org.mx). The price series are adjusted for seasonality using ARIMA X-12 under the additive option applied to the first difference of the logarithm of the price index. Then, the seasonally adjusted variable in levels is recovered as the sum of the seasonally adjusted log-difference plus the first observation of the non-seasonal adjusted index, that is: $p_t^{\text{sa}}=p_0^{\text{nsa}}+{\displaystyle {\sum }_{s=1}^t\Delta p_s^{\text{sa}}}$.

The inflation rate used for the estimations is the month-to-month percent change of the seasonally adjusted price index and non-seasonally adjusted.

To capture the cross-section dependence of inflation across cities, we use a proxy variable. This proxy variable is the cross-city average of the inflation rates weighted by the inverse of the distance between cities. Our objective is to capture the linkages between cities in a way that the cities that are nearer get more importance.

Let this proxy variable be defined as ${\pi }_{it}^{\text{CS}}={\omega }_i^{\text{'}}{\pi }_t$, where π_t is a 46 × 1 vector of inflation rates of the 46 cities in time t and ω_i is a normalized weight vector (46 × 1) using the inverse of the Euclidean (linear) distance from city i to the rest of the j cities.⁴ This variable is calculated for each of the 46 cities using the other 45 cities.

Household Expenditure Survey

For the estimation of the household’s welfare loss, we use the 2010 Household Expenditure Survey. This database is available at inegi’s website and documented in INEGI (2011). Using this database, we build a new database that gathers the households’ aggregate expenditure by each component of the CPI. ⁵⁶⁷

These calculations must be approached with some caution because it is well known that some expenses in the survey are understated (e.g., liquor, cigarettes, and beer); and for some goods, the expenses are reported as zero —although, we take this last issue into account with a censored regression model.

A. The Difference in Differences Estimation

Table 1 and Table 2 show the summary statistics of inflation in border and non-border cities for seasonally and non-seasonally adjusted data. The descriptive statistics of the two groups match relatively well. Moreover, Figure 2 and Figure 3 show that the distributions broadly overlap and move in sync except in April of 1995 and January of 2014 when the VAT changes differ. These shifts and patterns are evidence that the two regions can be used as a counterfactual —we test this claim more formally later.

One problem in applications of panel data is the correlation of unobserved shocks across groups. For instance, trade between cities, regional factors, and spillovers could induce cross-correlation from one city to the others and bias the estimations; to control for this type of dependency, we include the cross-section inflation rate as a control. This variable is a weighted average of the inflation rates of all the cities, and the weights are proportional to the distance between them.⁹ The general equation form is the following:

where π_it is the monthly inflation rate, DT_t is a dummy variable set to 𝟙 at time t when the VAT changed and zero otherwise; DC_i is a dummy variable set to 𝟙 on the city i where the VAT changed and zero elsewhere. As previously described, ${\pi }_{it}^{\text{CS}}$ is the cross-section inflation of cities near city i, and finally, ε_it, is the unobservable characteristics of the cities. To introduce anticipatory effects and second-round effects, we include m leads and q lags of the variable DT_t+j (j = —q,...,m), with six months of data before and after the actual date when the VAT set in. We use this sample to have more degrees of freedom and to be able to test for cross-sectional dependence.¹⁰

Our parameter of interest is φ which captures the net effect of the VAT change on inflation once the unconditional mean μ₀ the time effect φ_T, the group effect φ_C, and other controls are taken into account.

Table 3 shows the estimated effects of the two VAT reforms. The higher and most significant effect is precisely at the month when the VAT reforms are adopted. Only the 1995 reform has significant second-round effects. For this reform, the estimated effect is between 1.2 and 2.0 on April; that makes the elasticity of the VAT between 0.2 and 0.4 percentage points. Accumulating the significant months from April to June, the elasticity goes up to 0.6 percentage points. Meanwhile, for the 2014 reform, only January is significant, and the estimates give an elasticity between 0.14 and 0.19 percentage points.

The coefficients of the regressions that include the cross-section inflation are lower than the ones that do not. In comparison, all the non-seasonally adjusted regressions present high cross-sectional dependence, as it is shown by CD Test (Pesaran, 2004) and the cross-correlation of the residuals (Table 3). These results are evidence, on the one hand, that inflation shocks are transmitted through geographical proximity; and, on the other, that there are strong seasonal patterns common to the cities that the DID cannot remove completely.

We believe that the change of coefficients over time is related to the level and persistence of inflation. In 1995, when Mexico’s inflation was higher and more persistent than in 2014, the VAT’s impact is higher and more persistent as well. This finding is consistent with Chiquiar, Noriega, and Ramos-Francia (2010) who estimate a reduction in the persistence of inflation set in January of 2001. Similarly, Schmidt-Hebbel and Werner (2002) and Mariscal, Powell, and Tavella (2018) show that since the adoption of inflation targeting, the Central Bank of Mexico has improved its credibility and dilute the effect of inflation’s shocks on inflation’s expectations.

Having said that, not all the pass-through reduction comes from the price stabilization. We find that part of the reduction is because the cities near the border face higher competition —in particular, those at the northern board. To get a sense of how much of the effect comes from price stabilization and how much from the asymmetric response of the regions to the VAT rate, we estimate the DID regressions with a sample that excludes the center cites and balances the north with the southern cities, and a sample that excludes the northern region for VAT reform of 2014.

We find that the coefficients on the regressions that exclude the center cites are lower than the regressions that include all the cities available (Appendix Table 5 and Appendix Table 7). Conversely, the coefficients in the sample that excludes the northern cities are higher than the coefficients in the sample that includes all cities (Appendix Table 8). Therefore, we estimate that the net reduction of the pass-through from 1995 to 2014 is about one percentage point instead of 1.3 that the full sample brings. However, this method of analysis has limitations. One needs to note that in the second set that excludes the northern cities, there are only two border cities to compare with the rest. This downsize in the number of cities reduces the confidence level and increases the margin of error.

As a point of comparison, we show in Table 4 and Figure 4 the results of the simple DID regression without the cross-section inflation and the pre/post-effects as controls. These estimates get the simple VAT effect of one month at the time but disregard the monthly effect of the VAT combined. That is, the regressions catch the effects per month unconditionally, instead of the effect of the current month conditional on the last and the next months. Note that the magnitudes of the coefficients are not widely different from Table 3. However, one needs to keep in mind that the simple DID overestimate the effect on the switching date and underestimate the effects outside this date.

Finally, we turn to a placebo test to check the assumption that the border and non-border cities are good counterfactuals. The idea is to show that a simultaneous VAT change in both border and non-border cities would affect the outcome of both groups in the same way. If so, one could use either of the groups as counterfactuals. This test is done by estimating the DID regressions on the reforms of 2010 and 1991 when the VAT rate change for both groups. Ideally one should find the parameter of interest (φ) to be insignificant.

The VAT effects of the border and the non-border cities are statistically insignificant in general (Appendix Table 3 and Appendix Table 4). However, the VAT reform of 2010 has a significant effect in January. Even after we exclude the center cities from the sample and add the cross-section inflation, the January effect remains significant (Appendix Table 6). In the next section, we will explore the composition of the effects and offer some explanations for this and other results shown in this section.

Table 1.

Summary Statistics: Monthly Inflation (NSA)

Sources: INEGI and authors’ calculations. Notes: Month-to-month percent change of the non-seasonally adjusted price index by city.

Table 1.

Summary Statistics: Monthly Inflation (NSA)

	Border Cities						Non-Border Cities
Dates	N	Mean	Std.Dev.	Median	Min	Max	N	Mean	Std.Dev.	Median	Min	Max
Nov-91	7	2.07	0.37	2.03	1.43	2.48	28	2.15	0.48	2.08	1.37	3.15
Dec-91	7	2.02	0.43	2.26	1.46	2.48	28	2.11	0.36	1.99	1.57	2.94
Jan-92	7	1.63	0.30	1.56	1.33	2.25	28	1.68	0.24	1.61	1.31	2.44
Mar-95	8	5.71	0.94	5.50	4.55	7.53	38	5.45	0.73	5.26	4.44	7.39
Apr-95	8	6.58	0.36	6.53	6.08	7.11	38	7.85	0.78	7.84	6.51	9.79
May-95	8	3.58	0.60	3.54	2.89	4.34	38	4.05	0.37	4.04	3.32	4.95
Dec-09	8	0.27	0.18	0.31	0.04	0.51	38	0.36	0.20	0.35	0.05	0.71
Jan-10	8	0.89	0.23	0.83	0.67	1.28	38	1.16	0.43	1.07	0.37	2.44
Feb-10	8	0.34	0.35	0.40	-0.44	0.65	38	0.53	0.28	0.51	-0.22	1.41
Dec-13	8	0.42	0.26	0.43	-0.06	0.86	38	0.47	0.31	0.44	-0.20	1.25
Jan-14	8	1.77	0.41	1.67	1.36	2.45	38	0.82	0.38	0.78	0.12	1.72
Feb-14	8	0.08	0.36	0.05	-0.51	0.64	38	0.22	0.25	0.19	-0.41	0.83

Sources: INEGI and authors’ calculations. Notes: Month-to-month percent change of the non-seasonally adjusted price index by city.

View Table

Table 1.

Summary Statistics: Monthly Inflation (NSA)

	Border Cities						Non-Border Cities
Dates	N	Mean	Std.Dev.	Median	Min	Max	N	Mean	Std.Dev.	Median	Min	Max
Nov-91	7	2.07	0.37	2.03	1.43	2.48	28	2.15	0.48	2.08	1.37	3.15
Dec-91	7	2.02	0.43	2.26	1.46	2.48	28	2.11	0.36	1.99	1.57	2.94
Jan-92	7	1.63	0.30	1.56	1.33	2.25	28	1.68	0.24	1.61	1.31	2.44
Mar-95	8	5.71	0.94	5.50	4.55	7.53	38	5.45	0.73	5.26	4.44	7.39
Apr-95	8	6.58	0.36	6.53	6.08	7.11	38	7.85	0.78	7.84	6.51	9.79
May-95	8	3.58	0.60	3.54	2.89	4.34	38	4.05	0.37	4.04	3.32	4.95
Dec-09	8	0.27	0.18	0.31	0.04	0.51	38	0.36	0.20	0.35	0.05	0.71
Jan-10	8	0.89	0.23	0.83	0.67	1.28	38	1.16	0.43	1.07	0.37	2.44
Feb-10	8	0.34	0.35	0.40	-0.44	0.65	38	0.53	0.28	0.51	-0.22	1.41
Dec-13	8	0.42	0.26	0.43	-0.06	0.86	38	0.47	0.31	0.44	-0.20	1.25
Jan-14	8	1.77	0.41	1.67	1.36	2.45	38	0.82	0.38	0.78	0.12	1.72
Feb-14	8	0.08	0.36	0.05	-0.51	0.64	38	0.22	0.25	0.19	-0.41	0.83

Sources: INEGI and authors’ calculations. Notes: Month-to-month percent change of the non-seasonally adjusted price index by city.

Table 2.

Summary Statistics: Monthly Inflation

Sources: INEGI and authors’ calculations. Notes: Month-to-month percent change of the seasonally adjusted price index by city.

Table 2.

Summary Statistics: Monthly Inflation

	Border Cities						Non-Border Cities
Dates	N	Mean	Std.Dev.	Median	Min	Max	N	Mean	Std.Dev.	Median	Min	Max
Nov-91	7	1.55	0.33	1.50	1.17	1.96	28	1.79	0.46	1.71	1.18	2.82
Dec-91	7	1.30	0.30	1.37	0.87	1.70	28	1.39	0.33	1.27	0.89	2.22
Jan-92	7	1.15	0.21	1.07	0.95	1.57	28	1.12	0.22	1.10	0.72	1.82
Mar-95	8	5.66	0.89	5.68	4.58	7.42	38	5.47	0.80	5.27	4.38	7.49
Apr-95	8	6.33	0.41	6.47	5.69	6.79	38	7.91	0.78	7.95	6.43	9.93
May-95	8	3.95	0.83	3.91	2.98	5.64	38	4.28	0.37	4.25	3.31	5.11
Dec-09	8	0.21	0.19	0.26	-0.03	0.44	38	0.18	0.18	0.21	-0.17	0.47
Jan-10	8	0.49	0.24	0.39	0.28	0.93	38	0.92	0.43	0.79	0.30	2.13
Feb-10	8	0.40	0.20	0.42	0.15	0.71	38	0.53	0.25	0.51	-0.11	1.20
Dec-13	8	0.33	0.25	0.32	-0.04	0.82	38	0.32	0.23	0.32	-0.14	0.93
Jan-14	8	1.27	0.78	1.02	0.59	2.77	38	0.56	0.31	0.49	-0.02	1.25
Feb-14	8	0.16	0.17	0.16	-0.05	0.45	38	0.18	0.21	0.20	-0.31	0.72

Sources: INEGI and authors’ calculations. Notes: Month-to-month percent change of the seasonally adjusted price index by city.

View Table

Table 2.

Summary Statistics: Monthly Inflation

	Border Cities						Non-Border Cities
Dates	N	Mean	Std.Dev.	Median	Min	Max	N	Mean	Std.Dev.	Median	Min	Max
Nov-91	7	1.55	0.33	1.50	1.17	1.96	28	1.79	0.46	1.71	1.18	2.82
Dec-91	7	1.30	0.30	1.37	0.87	1.70	28	1.39	0.33	1.27	0.89	2.22
Jan-92	7	1.15	0.21	1.07	0.95	1.57	28	1.12	0.22	1.10	0.72	1.82
Mar-95	8	5.66	0.89	5.68	4.58	7.42	38	5.47	0.80	5.27	4.38	7.49
Apr-95	8	6.33	0.41	6.47	5.69	6.79	38	7.91	0.78	7.95	6.43	9.93
May-95	8	3.95	0.83	3.91	2.98	5.64	38	4.28	0.37	4.25	3.31	5.11
Dec-09	8	0.21	0.19	0.26	-0.03	0.44	38	0.18	0.18	0.21	-0.17	0.47
Jan-10	8	0.49	0.24	0.39	0.28	0.93	38	0.92	0.43	0.79	0.30	2.13
Feb-10	8	0.40	0.20	0.42	0.15	0.71	38	0.53	0.25	0.51	-0.11	1.20
Dec-13	8	0.33	0.25	0.32	-0.04	0.82	38	0.32	0.23	0.32	-0.14	0.93
Jan-14	8	1.27	0.78	1.02	0.59	2.77	38	0.56	0.31	0.49	-0.02	1.25
Feb-14	8	0.16	0.17	0.16	-0.05	0.45	38	0.18	0.21	0.20	-0.31	0.72

Sources: INEGI and authors’ calculations. Notes: Month-to-month percent change of the seasonally adjusted price index by city.

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Distribution of Monthly Inflation (NSA) Rate

Citation: IMF Working Papers 2018, 240; 10.5089/9781484381632.001.A001

Sources: INEGI and authors’ calculations.Notes: Month-to-month percent change of the non-seasonally adjusted price index by city. Shapes display the Gaussian kernel density estimation.

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Distribution of Monthly Inflation Rate

Citation: IMF Working Papers 2018, 240; 10.5089/9781484381632.001.A001

Sources: INEGI and authors’ calculations.Notes: Month-to-month percent change of the seasonally adjusted price index by city. Shapes display the Gaussian kernel density estimation.

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Table 3.

Extended DID on Inflation and CD Test

Sources: INEGI and authors’ calculations. Notes: The full report of the difference in differences estimations is available in the Appendix A, Table 1 and Table 2. CS-lnflation: regression that includes weighted average cross-section inflation rate of the near cities defined in Section II. CD Test: Pesaran (2004) test for HO of cross-sectionally independent residuals. Avg. Rho CS: average correlation coefficient for cross-sectional dependence in panels. BGW Test: Breusch-Godfrey-Wooldridge test for serial correlation in panel models, the null is that there is no serial correlation. Block-bootstrap standard errors in parentheses (correct for serial correlation), * p < 0.10, ** p < 0.05, *** p < 0.01.

Table 3.

Extended DID on Inflation and CD Test

			Inflation (NSA)	Inflation (NSA) CS-lnflation	Inflation	Inflation CS-lnflation
VAT 1995 (Mar)			-0.097	-0.152	0.120	0.150
			(0.342)	(0.333)	(0.391)	(0.432)
VAT 1995 (Apr)			1.436***	1.218***	1.888***	1.987***
			(0.199)	(0.207)	(0.369)	(0.413)
VAT 1995 (May)			0.637***	0.537**	0.636***	0.688***
			(0.236)	(0.239)	(0.240)	(0.263)
VAT 1995 (Jun)			0.427**	0.376**	0.682**	0.734**
			(0.172)	(0.189)	(0.302)	(0.354)
		CD Test	72.27***	14.81***	64.15***	10.32***
Avg.Rho CSD			0.62	0.13	0.55	0.09
	BGW Test		340.59***	238.75***	327.67***	266.03***
VAT 2013 (Dec)			-0.053	0.022	0.026	0.027
			(0.125)	(0.144)	(0.112)	(0.121)
VAT 2014 (Jan)			0.952***	0.787***	0.722**	0.744**
			(0.154)	(0.171)	(0.281)	(0.318)
VAT 2014 (Feb)			-0.137	-0.146	-0.008	-0.014
			(0.147)	(0.141)	(0.062)	(0.063)
		CD Test	33.58***	3.04***	35.16***	-0.77
Avg.Rho CSD			0.29	0.03	0.27	0.01
	BGW Test		191.48***	178.11***	35.16***	13.69

Sources: INEGI and authors’ calculations. Notes: The full report of the difference in differences estimations is available in the Appendix A, Table 1 and Table 2. CS-lnflation: regression that includes weighted average cross-section inflation rate of the near cities defined in Section II. CD Test: Pesaran (2004) test for HO of cross-sectionally independent residuals. Avg. Rho CS: average correlation coefficient for cross-sectional dependence in panels. BGW Test: Breusch-Godfrey-Wooldridge test for serial correlation in panel models, the null is that there is no serial correlation. Block-bootstrap standard errors in parentheses (correct for serial correlation), * p < 0.10, ** p < 0.05, *** p < 0.01.

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Table 3.

Extended DID on Inflation and CD Test

			Inflation (NSA)	Inflation (NSA) CS-lnflation	Inflation	Inflation CS-lnflation
VAT 1995 (Mar)			-0.097	-0.152	0.120	0.150
			(0.342)	(0.333)	(0.391)	(0.432)
VAT 1995 (Apr)			1.436***	1.218***	1.888***	1.987***
			(0.199)	(0.207)	(0.369)	(0.413)
VAT 1995 (May)			0.637***	0.537**	0.636***	0.688***
			(0.236)	(0.239)	(0.240)	(0.263)
VAT 1995 (Jun)			0.427**	0.376**	0.682**	0.734**
			(0.172)	(0.189)	(0.302)	(0.354)
		CD Test	72.27***	14.81***	64.15***	10.32***
Avg.Rho CSD			0.62	0.13	0.55	0.09
	BGW Test		340.59***	238.75***	327.67***	266.03***
VAT 2013 (Dec)			-0.053	0.022	0.026	0.027
			(0.125)	(0.144)	(0.112)	(0.121)
VAT 2014 (Jan)			0.952***	0.787***	0.722**	0.744**
			(0.154)	(0.171)	(0.281)	(0.318)
VAT 2014 (Feb)			-0.137	-0.146	-0.008	-0.014
			(0.147)	(0.141)	(0.062)	(0.063)
		CD Test	33.58***	3.04***	35.16***	-0.77
Avg.Rho CSD			0.29	0.03	0.27	0.01
	BGW Test		191.48***	178.11***	35.16***	13.69

Sources: INEGI and authors’ calculations. Notes: The full report of the difference in differences estimations is available in the Appendix A, Table 1 and Table 2. CS-lnflation: regression that includes weighted average cross-section inflation rate of the near cities defined in Section II. CD Test: Pesaran (2004) test for HO of cross-sectionally independent residuals. Avg. Rho CS: average correlation coefficient for cross-sectional dependence in panels. BGW Test: Breusch-Godfrey-Wooldridge test for serial correlation in panel models, the null is that there is no serial correlation. Block-bootstrap standard errors in parentheses (correct for serial correlation), * p < 0.10, ** p < 0.05, *** p < 0.01.

Table 4.

Simple DID on Inflation

Sources: INEGI and authors’ calculations. Notes: The full report of the difference in differences estimations is available in the Appendix A, Table 1 and Table 2. Block-bootstrap standard errors in parentheses (correct for serial correlation), * p < 0.10, ** p < 0.05, *** p < 0.01.

Table 4.

Simple DID on Inflation

	Inflation (NSA)	Inflation
VAT 1995 (Mar)	0.519*	0.982***
	(0.323)	(0.207)
VAT 1995 (Apr)	1.534***	1.768***
	(0.409)	(0.382)
VAT 1995 (May)	0.734*	0.516
	(0.418)	(0.494)
VAT 1995 (Jun)	0.525	0.562
	(0.387)	(0.384)
VAT 2013 (Dec)	-1.348	0.096
	(1.12)	(0.138)
VAT 2014 (Jan)	1.005***	0.696**
	(0.238)	(0.315)
VAT 2014 (Feb)	-0.085	-0.035
	(0.164)	(0.119)

Sources: INEGI and authors’ calculations. Notes: The full report of the difference in differences estimations is available in the Appendix A, Table 1 and Table 2. Block-bootstrap standard errors in parentheses (correct for serial correlation), * p < 0.10, ** p < 0.05, *** p < 0.01.

View Table

Table 4.

Simple DID on Inflation

	Inflation (NSA)	Inflation
VAT 1995 (Mar)	0.519*	0.982***
	(0.323)	(0.207)
VAT 1995 (Apr)	1.534***	1.768***
	(0.409)	(0.382)
VAT 1995 (May)	0.734*	0.516
	(0.418)	(0.494)
VAT 1995 (Jun)	0.525	0.562
	(0.387)	(0.384)
VAT 2013 (Dec)	-1.348	0.096
	(1.12)	(0.138)
VAT 2014 (Jan)	1.005***	0.696**
	(0.238)	(0.315)
VAT 2014 (Feb)	-0.085	-0.035
	(0.164)	(0.119)

Sources: INEGI and authors’ calculations. Notes: The full report of the difference in differences estimations is available in the Appendix A, Table 1 and Table 2. Block-bootstrap standard errors in parentheses (correct for serial correlation), * p < 0.10, ** p < 0.05, *** p < 0.01.

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DID Estimates of VAT Pass-through

Citation: IMF Working Papers 2018, 240; 10.5089/9781484381632.001.A001

Sources: INEGI and authors’ calculations.Notes: The estimates come from a simple difference in differences model. The full report of the difference in differences estimations is available in the Appendix A, Table 1 and Table 2.

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B. The Difference in Differences Estimation from a Bottom-Up Approach

This section will show the details of the VAT reforms by looking at the subclass components of the CPI. The approach is the same as the previous Section III. A but now running the difference in difference (DID) regression for each of the 283 CPI subclass components. We use a mean group estimation to summarize our findings and aggregate the 283 components into twelve categories of expenses, three categories of VAT regimes, and six categories of inflation components.

Overall the results are consistent with the previous section. The pass-through from changes in the VAT rate to inflation has decreased between 1995 and 2014. Nonetheless, the composition of such a decrease has been mixed within the subclasses.

The first aggregation presented in Table 5 shows the DID estimates aggregated by twelve categories of expenditure. One can see that the pass-through of tradable goods, which has been more exposed to foreign competition coming from trade, has decreased over time. We refer specifically to alcoholic beverages, tobacco, clothing, furniture, and transportation (e.g., tires, bicycles, cars, and motorcycles). However, for the non-tradable goods like communications, healthcare, and schooling, the pass-through has increased. Communications, for example, has the highest increase in the mobile phone plans, home phone plans, and long-distance calls. Meanwhile, in the healthcare business, the highest increases were in general healthcare facilities, laboratory studies, and diabetes medication. For the rest of goods and services, the effect has been insignificant or without a substantial change over time.

The next aggregation presented in Table 6 shows the bottom-up effect on inflation’s components. One can see that the primary driver of the overall effect is on core inflation. While the importance of core-merchandise has decreased over time, the core-services has increased and practically revert in magnitude. Again, this pattern suggests that merchandises have been more exposed to competition and the supply curve has become more elastic. Instead, core-services have kept its monopolistic power, but because the demand for these services has presumably increased, the effect of the VAT has increased as well.¹¹

Finally, on the aggregation by VAT regime, Table 7 shows the mean group estimations. The effect on the taxed goods is, as one would expect, the highest and most significant. A five-percentage-point increase in the VAT rate in 1995 increased the inflation rate of the VAT-taxed goods by more than two and a half percentage points giving a 50 percent pass-through; whereas, in 2014, the effect is closer to one percentage point or a 20 percent pass-through.

One can see that the effect on the zero-rate goods is not significant, but the prices of goods and services under the exempt regime do show a significant effect. This significance happens because businesses selling zero-rate goods can claim a rebate against the VAT paid on its inputs. However, businesses selling exempt goods cannot claim a credit against the VAT paid on its inputs —the VAT adds to their costs and is non-refundable. Therefore, businesses with exempt goods are more prone to pass on the VAT to its final price, and so the effect of the VAT turns to be significant.

At the end of the previous Section III. A we checked if the border and non-border cities were good as counterfactuals. While the VAT reform of 1991 passed our placebo test, we found evidence against the VAT Reform of 2010 —specifically in January when the legislation entered. Using the same framework as in the previous section, we turn now to the disaggregated components. We find that the failure of the placebo test in January of 2010 is more the result of the surge in the prices of fuels, transportation, and government tariffs that coincides with the VAT change.

Most of the effect in the inflation rate arises from the non-core components of the CPI and broadly affected all the VAT-regimes (Appendix Table 9 and Appendix Table 10). Meanwhile, with the other VAT reforms, the higher and most significant effects were concentrated on the core components of the CPI and the taxed goods. Moreover, when we clear the sample to exclude the center cities, we find transportation services, energy prices, and government tariffs to be still significant, but agricultural goods and overall inflation not to be significant anymore.

We have shown the outcome of the VAT on inflation and its composition, but now the question is how these changes have affected the households’ welfare. Before addressing the question, we need to define a measure of welfare and estimate a system of demand functions. Next section will take on these matters.

Table 5.

DID Bottom-Up Effect of VAT on Inflation by Type of Expense

Sources: INEGI and authors’ calculations. Notes: Inflation is seasonally adjusted. Mean group estimation of the DID VAT effect per category: $\widehat{\phi }=\frac{1}{N}{\Sigma }_i\widehat{{\phi }_i}$ equation (III.1). The full report of the DID per category is available at the online repository. CS-lnflation: regression that includes weighted average cross-section inflation rate of the near cities defined in Section II. The estimates exclude subway transportation, thus number of subclasses is 282. Standard errors in parentheses: $SE\left(\widehat{\phi }\right)=\sqrt{\frac{1}{N\left(N-1\right)}{\Sigma }_i{\left(\widehat{{\phi }_i}-\widehat{\phi }\right)}^2}$, and p-values come from a t-distribution: * p < 0.10, ** p < 0.05, *** p < 0.01.

Table 5.

DID Bottom-Up Effect of VAT on Inflation by Type of Expense

		VAT 1995 (Apr)		VAT 2014 (Jan)
	Count	Simple	CS-lnflation	Simple	CS-lnflation
1. Food and non-alcoholic beverages	96	0.18	-0.02	-0.14	-0.18
		(0.407)	(0.373)	(0.277)	(0.241)
2. Alcoholic beverages and tobacco	7	5.48***	5.18***	1.56**	1.57**
		(0.630)	(0.801)	(0.511)	(0.499)
3. Clothing and footwear	29	2.93***	3.03***	0.62***	0.61***
		(0.443)	(0.469)	(0.180)	(0.179)
4. Housing and utilities	7	0.59*	0.33*	2.04*	1.45
		(0.267)	(0.134)	(0.910)	(0.834)
5. Furniture and house supplies	38	2.13***	2.03***	1.09***	1.08***
		(0.384)	(0.410)	(0.351)	(0.350)
6. Health care	23	0.72*	0.73*	1.34***	1.35***
		(0.395)	(0.421)	(0.319)	(0.325)
7. Transportation	18	2.87***	2.20**	0.96	0.89*
		(0.883)	(0.884)	(0.561)	(0.511)
8. Communications	6	0.98	0.45	2.46**	2.29**
		(0.508)	(0.455)	(0.844)	(0.778)
9. Recreation and cultural activities	20	2.68***	2.61***	0.96**	0.96**
		(0.831)	(0.783)	(0.409)	(0.406)
10. Schooling	8	-0.04	0.03	0.20***	0.12**
		(0.166)	(0.182)	(0.044)	(0.036)
11. Restaurants and hotels	9	0.68	0.63	0.41	0.43
		(0.561)	(0.441)	(0.461)	(0.410)
12. Diverse goods and services	21	3.03***	2.99***	2.28***	2.25***
		(0.732)	(0.754)	(0.528)	(0.517)
Overall Inflation	282	1.50***	1.36***	0.73***	0.69***
		(0.202)	(0.197)	(0.137)	(0.126)

Sources: INEGI and authors’ calculations. Notes: Inflation is seasonally adjusted. Mean group estimation of the DID VAT effect per category: $\widehat{\phi }=\frac{1}{N}{\Sigma }_i\widehat{{\phi }_i}$ equation (III.1). The full report of the DID per category is available at the online repository. CS-lnflation: regression that includes weighted average cross-section inflation rate of the near cities defined in Section II. The estimates exclude subway transportation, thus number of subclasses is 282. Standard errors in parentheses: $SE\left(\widehat{\phi }\right)=\sqrt{\frac{1}{N\left(N-1\right)}{\Sigma }_i{\left(\widehat{{\phi }_i}-\widehat{\phi }\right)}^2}$, and p-values come from a t-distribution: * p < 0.10, ** p < 0.05, *** p < 0.01.

View Table

Table 5.

DID Bottom-Up Effect of VAT on Inflation by Type of Expense

		VAT 1995 (Apr)		VAT 2014 (Jan)
	Count	Simple	CS-lnflation	Simple	CS-lnflation
1. Food and non-alcoholic beverages	96	0.18	-0.02	-0.14	-0.18
		(0.407)	(0.373)	(0.277)	(0.241)
2. Alcoholic beverages and tobacco	7	5.48***	5.18***	1.56**	1.57**
		(0.630)	(0.801)	(0.511)	(0.499)
3. Clothing and footwear	29	2.93***	3.03***	0.62***	0.61***
		(0.443)	(0.469)	(0.180)	(0.179)
4. Housing and utilities	7	0.59*	0.33*	2.04*	1.45
		(0.267)	(0.134)	(0.910)	(0.834)
5. Furniture and house supplies	38	2.13***	2.03***	1.09***	1.08***
		(0.384)	(0.410)	(0.351)	(0.350)
6. Health care	23	0.72*	0.73*	1.34***	1.35***
		(0.395)	(0.421)	(0.319)	(0.325)
7. Transportation	18	2.87***	2.20**	0.96	0.89*
		(0.883)	(0.884)	(0.561)	(0.511)
8. Communications	6	0.98	0.45	2.46**	2.29**
		(0.508)	(0.455)	(0.844)	(0.778)
9. Recreation and cultural activities	20	2.68***	2.61***	0.96**	0.96**
		(0.831)	(0.783)	(0.409)	(0.406)
10. Schooling	8	-0.04	0.03	0.20***	0.12**
		(0.166)	(0.182)	(0.044)	(0.036)
11. Restaurants and hotels	9	0.68	0.63	0.41	0.43
		(0.561)	(0.441)	(0.461)	(0.410)
12. Diverse goods and services	21	3.03***	2.99***	2.28***	2.25***
		(0.732)	(0.754)	(0.528)	(0.517)
Overall Inflation	282	1.50***	1.36***	0.73***	0.69***
		(0.202)	(0.197)	(0.137)	(0.126)

Sources: INEGI and authors’ calculations. Notes: Inflation is seasonally adjusted. Mean group estimation of the DID VAT effect per category: $\widehat{\phi }=\frac{1}{N}{\Sigma }_i\widehat{{\phi }_i}$ equation (III.1). The full report of the DID per category is available at the online repository. CS-lnflation: regression that includes weighted average cross-section inflation rate of the near cities defined in Section II. The estimates exclude subway transportation, thus number of subclasses is 282. Standard errors in parentheses: $SE\left(\widehat{\phi }\right)=\sqrt{\frac{1}{N\left(N-1\right)}{\Sigma }_i{\left(\widehat{{\phi }_i}-\widehat{\phi }\right)}^2}$, and p-values come from a t-distribution: * p < 0.10, ** p < 0.05, *** p < 0.01.

Table 6.

DID Bottom-Up Effect of VAT on Inflation’s Components

Sources: INEGI and authors’ calculations. Notes: Inflation is seasonally adjusted. Mean group estimation of the DID VAT effect per category: $\widehat{\phi }=\frac{1}{N}{\Sigma }_i\widehat{{\phi }_i}$, as in equation (III.1). The full report of the DID per category is available at the online repository. CS-lnflation: regression that includes weighted average cross-section inflation rate of the near cities defined in Section II. The estimates exclude subway transportation, thus number of subclasses is 282. Standard errors in parentheses: $SE\left(\widehat{\phi }\right)=\sqrt{\frac{1}{N\left(N-1\right)}{\Sigma }_i{\left(\widehat{{\phi }_i}-\widehat{\phi }\right)}^2}$, and p-values come from a t-distribution: * p < 0.10, ** p < 0.05, *** p < 0.01.

Table 6.

DID Bottom-Up Effect of VAT on Inflation’s Components

			VAT 1995 (Apr)		VAT 2014 (Jan)
		Count	Simple	CS-lnflation	Simple	CS-lnflation
Core		229	1.85***	1.71***	0.87***	0.86***
			(0.182)	(0.188)	(0.124)	(0.119)
	Merchandise	183	2.07***	1.93***	0.68***	0.69***
			(0.210)	(0.217)	(0.131)	(0.129)
	Services	46	0.96***	0.87**	1.65***	1.57***
			(0.325)	(0.338)	(0.302)	(0.277)
Non-core		53	0.00	-0.22	0.13	-0.10
			(0.703)	(0.631)	(0.491)	(0.423)
	Agricultural	40	-0.47	-0.49	-0.16	-0.32
			(0.871)	(0.772)	(0.617)	(0.524)
	Energy and Govt. Tariffs	13	1.43	0.66	1.03	0.68
			(0.966)	(0.929)	(0.613)	(0.530)
Overall Inflation		282	1.50***	1.36***	0.73***	0.69***
			(0.202)	(0.197)	(0.137)	(0.126)

Sources: INEGI and authors’ calculations. Notes: Inflation is seasonally adjusted. Mean group estimation of the DID VAT effect per category: $\widehat{\phi }=\frac{1}{N}{\Sigma }_i\widehat{{\phi }_i}$, as in equation (III.1). The full report of the DID per category is available at the online repository. CS-lnflation: regression that includes weighted average cross-section inflation rate of the near cities defined in Section II. The estimates exclude subway transportation, thus number of subclasses is 282. Standard errors in parentheses: $SE\left(\widehat{\phi }\right)=\sqrt{\frac{1}{N\left(N-1\right)}{\Sigma }_i{\left(\widehat{{\phi }_i}-\widehat{\phi }\right)}^2}$, and p-values come from a t-distribution: * p < 0.10, ** p < 0.05, *** p < 0.01.

View Table

Table 6.

DID Bottom-Up Effect of VAT on Inflation’s Components

			VAT 1995 (Apr)		VAT 2014 (Jan)
		Count	Simple	CS-lnflation	Simple	CS-lnflation
Core		229	1.85***	1.71***	0.87***	0.86***
			(0.182)	(0.188)	(0.124)	(0.119)
	Merchandise	183	2.07***	1.93***	0.68***	0.69***
			(0.210)	(0.217)	(0.131)	(0.129)
	Services	46	0.96***	0.87**	1.65***	1.57***
			(0.325)	(0.338)	(0.302)	(0.277)
Non-core		53	0.00	-0.22	0.13	-0.10
			(0.703)	(0.631)	(0.491)	(0.423)
	Agricultural	40	-0.47	-0.49	-0.16	-0.32
			(0.871)	(0.772)	(0.617)	(0.524)
	Energy and Govt. Tariffs	13	1.43	0.66	1.03	0.68
			(0.966)	(0.929)	(0.613)	(0.530)
Overall Inflation		282	1.50***	1.36***	0.73***	0.69***
			(0.202)	(0.197)	(0.137)	(0.126)

Sources: INEGI and authors’ calculations. Notes: Inflation is seasonally adjusted. Mean group estimation of the DID VAT effect per category: $\widehat{\phi }=\frac{1}{N}{\Sigma }_i\widehat{{\phi }_i}$, as in equation (III.1). The full report of the DID per category is available at the online repository. CS-lnflation: regression that includes weighted average cross-section inflation rate of the near cities defined in Section II. The estimates exclude subway transportation, thus number of subclasses is 282. Standard errors in parentheses: $SE\left(\widehat{\phi }\right)=\sqrt{\frac{1}{N\left(N-1\right)}{\Sigma }_i{\left(\widehat{{\phi }_i}-\widehat{\phi }\right)}^2}$, and p-values come from a t-distribution: * p < 0.10, ** p < 0.05, *** p < 0.01.

Table 7.

DID Bottom-Up Effect of VAT on Inflation by VAT-Regime

Sources: INEGI and authors’ calculations. Notes: Inflation is seasonally adjusted. Mean group estimation of the DID VAT effect per category: $\widehat{\phi }=\frac{1}{N}{\Sigma }_i\widehat{{\phi }_i}$, as in equation (III.1). The full report of the DID per category is available at the online repository. CS-lnflation: regression that includes weighted average cross-section inflation rate of the near cities defined in Section II. The estimates exclude subway transportation, thus number of subclasses is 282. In December of 1995 the Law changed medical and laboratory analysis from taxed to exempt; and in January of 2014 pet’s food from zero-rate to taxed. Standard errors in parentheses: $SE\left(\widehat{\phi }\right)=\sqrt{\frac{1}{N\left(N-1\right)}{\Sigma }_i{\left(\widehat{{\phi }_i}-\widehat{\phi }\right)}^2}$, and p-values come from a t-distribution: * p < 0.10, ** p < 0.05, *** p < 0.01.

Table 7.

DID Bottom-Up Effect of VAT on Inflation by VAT-Regime

	VAT 1995 (Apr)			VAT 2014 (Jan)
	Count	Simple	CS-lnflation	Count	Simple	CS-lnflation
Zero-Rate	110	0.15	-0.03	109	0.05	0.01
		(0.357)	(0.329)		(0.245)	(0.215)
Taxed	149	2.55***	2.47***	148	1.26***	1.21***
		(0.222)	(0.229)		(0.156)	(0.151)
Exempt	23	1.17**	0.84*	25	0.61*	0.59*
		(0.486)	(0.437)		(0.340)	(0.327)

Sources: INEGI and authors’ calculations. Notes: Inflation is seasonally adjusted. Mean group estimation of the DID VAT effect per category: $\widehat{\phi }=\frac{1}{N}{\Sigma }_i\widehat{{\phi }_i}$, as in equation (III.1). The full report of the DID per category is available at the online repository. CS-lnflation: regression that includes weighted average cross-section inflation rate of the near cities defined in Section II. The estimates exclude subway transportation, thus number of subclasses is 282. In December of 1995 the Law changed medical and laboratory analysis from taxed to exempt; and in January of 2014 pet’s food from zero-rate to taxed. Standard errors in parentheses: $SE\left(\widehat{\phi }\right)=\sqrt{\frac{1}{N\left(N-1\right)}{\Sigma }_i{\left(\widehat{{\phi }_i}-\widehat{\phi }\right)}^2}$, and p-values come from a t-distribution: * p < 0.10, ** p < 0.05, *** p < 0.01.

View Table

Table 7.

DID Bottom-Up Effect of VAT on Inflation by VAT-Regime

	VAT 1995 (Apr)			VAT 2014 (Jan)
	Count	Simple	CS-lnflation	Count	Simple	CS-lnflation
Zero-Rate	110	0.15	-0.03	109	0.05	0.01
		(0.357)	(0.329)		(0.245)	(0.215)
Taxed	149	2.55***	2.47***	148	1.26***	1.21***
		(0.222)	(0.229)		(0.156)	(0.151)
Exempt	23	1.17**	0.84*	25	0.61*	0.59*
		(0.486)	(0.437)		(0.340)	(0.327)

Sources: INEGI and authors’ calculations. Notes: Inflation is seasonally adjusted. Mean group estimation of the DID VAT effect per category: $\widehat{\phi }=\frac{1}{N}{\Sigma }_i\widehat{{\phi }_i}$, as in equation (III.1). The full report of the DID per category is available at the online repository. CS-lnflation: regression that includes weighted average cross-section inflation rate of the near cities defined in Section II. The estimates exclude subway transportation, thus number of subclasses is 282. In December of 1995 the Law changed medical and laboratory analysis from taxed to exempt; and in January of 2014 pet’s food from zero-rate to taxed. Standard errors in parentheses: $SE\left(\widehat{\phi }\right)=\sqrt{\frac{1}{N\left(N-1\right)}{\Sigma }_i{\left(\widehat{{\phi }_i}-\widehat{\phi }\right)}^2}$, and p-values come from a t-distribution: * p < 0.10, ** p < 0.05, *** p < 0.01.

A. Estimation of a Quadratic Almost Ideal Demand System

The Quadratic Almost Ideal Demand System (quaids) is a general model that captures the non-linear term in the Engel’s curves that the simple demand system of Deaton and Muellbauer (1980) does not. This non-linearity can be tested empirically and has valuable implication as Banks, Blundell, and Lewbel (1997) show.

On the other hand, household surveys usually have censoring problems reporting zero expenditure for some goods or services. A censor-correction aims to reduce the bias and inconsistency in the estimation. We extend the demand system and incorporate a bias-correcting term known as the inverse Mills ratio. We estimate the demand system using a two-step approach a la Heckman (1979) with independent probits and Non-linear Seemingly Unrelated Regressions (NLSUR).¹³ Tauchmann (2005) has proven how this approach is, in general, more efficient than most of the estimations available.

The system of demand equations is the following:

where w_ih is the share of expenditure good i in the household h, In p_j is the logarithm of the price index for good j, y_h is the total household expenditure, and ${\widehat{R}}_{ih}$ is the inverse Mills ratio estimated in the first stage with a probit model.¹⁴ The functions In a(p) and b(p) are, respectively, the price index and the Cobb-Douglas price aggregator:

Finally, the following restrictions must be imposed to assure the system of equations (IV. 1) represent demand functions consistent with the economic theory:

The parameters in (IV. 1) with restrictions (IV.2) are estimated by iterated feasible generalized nonlinear least-squares. One can exclude the n-th equation since it will be redundant given the restrictions stated in (IV.2).

Table 9 present the summary of the income and own-price estimated elasticities using the censored-augmented QUAIDS model.¹⁵ The numbers show that all the aggregates are normal goods as they have negative price elasticities. Food, beverages, tobacco, clothing, and footwear are necessary goods because the estimated income elasticity is less than one and the coefficient on the squared expenditure, λ_i, is negative —which gives concave-shaped Engel curves. Meanwhile, healthcare, transportation, and schooling have the highest price elasticities as these categories are likely to have close substitutes or a public-sector provider. Schooling, furniture, house supplies, recreation, and cultural activities, stand as a luxury with a large income elasticity and a steep convex Engel curve. The diverse goods’ price-elasticity may seem odd, but this category includes housekeeping products, personal care, funerals, government fees, and other diverse goods that makes the variance across goods large.

These last estimations can provide some insight into the uniform rates discussion. For some studies, the VAT exemptions and zero-rates are a source of erosion. Dalsgaard (2000) and Huesca and Serrano (2005) estimate that the implicit subsidy of the zero-rate is between 1.6 to 1.8 of the GDP. Moreover, they argue that the zero-rate on food and other necessary goods is mostly capitalized by the top deciles as they get between 20 to 30 percent of the subsidy. According to these studies, the system would be more efficient under a uniform rate.

Our estimates show that the price-elasticities are relatively elastic and different from zero. This result is important for the goods that are exempt or under the zero-rate statute. Since the price-elasticity is not zero, if there were a positive VAT rate in these goods, the quantity exchanged in the market would go down, and the tax revenues would be lower than what the authors estimate. One could expect more efficiency from mixed VAT rates that are inversely proportional to the price elasticities of the goods (Diamond, 1975), while considering the complementarity of goods with leisure (Corlett and Hague, 1953). Not to mention that the VAT on food products could induce tax evasion with informal transactions; as Abramovsky, Attanasio, and Phillips (2015) show, approximately 47 percent of the expenditure on food, clothing, and footwear occur in informal establishments in Mexico.

Table 8.

Expenditure Shares by Deciles (Percentage points)

Sources: INEGI, 2010 Household Survey (ENIGH) and authors’ calculations. Notes: Expenditure in the mapping bundle of the 283 CPI goods and services for urban and rural households.

Table 8.

Expenditure Shares by Deciles (Percentage points)

	Deciles
Expenditure Category	1	2	3	4	5	6	7	8	9	10	Overall
1. Food and non-alcoholic beverages	36.61	37.05	35.86	33.41	31.05	29.72	26.78	23.98	20.12	14.43	29.30
2. Alcoholic beverages and tobacco	0.41	0.48	0.43	0.44	0.51	0.39	0.47	0.42	0.45	0.41	0.44
3. Clothing and footwear	3.84	4.35	4.83	5.24	5.37	5.57	5.81	6.00	6.38	6.33	5.32
4. Housing and utilities	34.18	28.47	26.12	25.90	25.54	25.68	25.81	25.63	26.24	26.29	27.11
5. Furniture and house supplies	2.23	1.99	2.10	2.12	2.26	2.23	2.37	2.50	2.94	3.44	2.40
6. Health care	1.92	1.81	1.68	1.65	1.69	1.67	1.74	1.99	2.23	2.44	1.88
7. Transportation	4.70	5.96	6.81	7.39	7.82	8.01	8.31	8.61	8.52	8.67	7.40
8. Communications	1.54	2.16	2.75	3.19	3.72	4.14	4.73	5.32	6.03	7.87	4.04
9. Recreation and cultural activities	1.78	2.40	2.73	3.30	3.56	4.09	4.53	5.36	5.89	7.01	3.97
10. Schooling	1.99	2.87	3.49	3.83	4.63	4.86	5.32	5.77	6.40	7.55	4.57
11. Restaurants and hotels	2.50	3.66	4.31	4.87	5.35	5.60	6.23	6.88	7.54	9.45	5.53
12. Diverse goods and services	8.29	8.80	8.89	8.66	8.51	8.04	7.89	7.56	7.26	6.10	8.04

Sources: INEGI, 2010 Household Survey (ENIGH) and authors’ calculations. Notes: Expenditure in the mapping bundle of the 283 CPI goods and services for urban and rural households.

View Table

Table 8.

Expenditure Shares by Deciles (Percentage points)

	Deciles
Expenditure Category	1	2	3	4	5	6	7	8	9	10	Overall
1. Food and non-alcoholic beverages	36.61	37.05	35.86	33.41	31.05	29.72	26.78	23.98	20.12	14.43	29.30
2. Alcoholic beverages and tobacco	0.41	0.48	0.43	0.44	0.51	0.39	0.47	0.42	0.45	0.41	0.44
3. Clothing and footwear	3.84	4.35	4.83	5.24	5.37	5.57	5.81	6.00	6.38	6.33	5.32
4. Housing and utilities	34.18	28.47	26.12	25.90	25.54	25.68	25.81	25.63	26.24	26.29	27.11
5. Furniture and house supplies	2.23	1.99	2.10	2.12	2.26	2.23	2.37	2.50	2.94	3.44	2.40
6. Health care	1.92	1.81	1.68	1.65	1.69	1.67	1.74	1.99	2.23	2.44	1.88
7. Transportation	4.70	5.96	6.81	7.39	7.82	8.01	8.31	8.61	8.52	8.67	7.40
8. Communications	1.54	2.16	2.75	3.19	3.72	4.14	4.73	5.32	6.03	7.87	4.04
9. Recreation and cultural activities	1.78	2.40	2.73	3.30	3.56	4.09	4.53	5.36	5.89	7.01	3.97
10. Schooling	1.99	2.87	3.49	3.83	4.63	4.86	5.32	5.77	6.40	7.55	4.57
11. Restaurants and hotels	2.50	3.66	4.31	4.87	5.35	5.60	6.23	6.88	7.54	9.45	5.53
12. Diverse goods and services	8.29	8.80	8.89	8.66	8.51	8.04	7.89	7.56	7.26	6.10	8.04

Sources: INEGI, 2010 Household Survey (ENIGH) and authors’ calculations. Notes: Expenditure in the mapping bundle of the 283 CPI goods and services for urban and rural households.

Table 9.

Estimated Income and Own-Price Elasticities

Sources: INEGI, 2010 Household Survey (ENIGH) and authors’ calculations. Notes: Estimates come from a Quadratic Almost Ideal Demand System (QUAIDS) using a Non-linear system of Seemingly Unrelated Regressions (NLSUR) with data from the household survey and the CPI aggregated at 12 categories of expenditure.

Table 9.

Estimated Income and Own-Price Elasticities

Expenditure Category	Percent of Expenditure	Income Elasticities	Own-Price Elasticities (Compensated)	Own-Price Elasticities (Uncompensated)
1. Food and non-alcoholic beverages	29.30	0.14	-0.86	-0.95
2. Alcoholic beverages and tobacco	0.44	0.73	-0.91	-0.94
3. Clothing and footwear	5.32	0.94	-0.93	-1.00
4. Housing and utilities	27.11	1.17	-0.84	-1.05
5. Furniture and house supplies	2.40	2.06	-1.00	-1.04
6. Health care	1.88	1.96	-74.77	-74.80
7. Transportation	7.40	1.31	-1.39	-1.48
8. Communications	4.04	1.31	-0.97	-1.03
9. Recreation and cultural activities	3.97	1.66	-0.43	-0.51
10. Schooling	4.57	2.24	-1.10	-1.23
11. Restaurants and hotels	5.53	1.32	-0.94	-1.04
12. Diverse goods and services	8.04	1.18	-159.37	-159.43

Sources: INEGI, 2010 Household Survey (ENIGH) and authors’ calculations. Notes: Estimates come from a Quadratic Almost Ideal Demand System (QUAIDS) using a Non-linear system of Seemingly Unrelated Regressions (NLSUR) with data from the household survey and the CPI aggregated at 12 categories of expenditure.

View Table

Table 9.

Estimated Income and Own-Price Elasticities

Expenditure Category	Percent of Expenditure	Income Elasticities	Own-Price Elasticities (Compensated)	Own-Price Elasticities (Uncompensated)
1. Food and non-alcoholic beverages	29.30	0.14	-0.86	-0.95
2. Alcoholic beverages and tobacco	0.44	0.73	-0.91	-0.94
3. Clothing and footwear	5.32	0.94	-0.93	-1.00
4. Housing and utilities	27.11	1.17	-0.84	-1.05
5. Furniture and house supplies	2.40	2.06	-1.00	-1.04
6. Health care	1.88	1.96	-74.77	-74.80
7. Transportation	7.40	1.31	-1.39	-1.48
8. Communications	4.04	1.31	-0.97	-1.03
9. Recreation and cultural activities	3.97	1.66	-0.43	-0.51
10. Schooling	4.57	2.24	-1.10	-1.23
11. Restaurants and hotels	5.53	1.32	-0.94	-1.04
12. Diverse goods and services	8.04	1.18	-159.37	-159.43

Sources: INEGI, 2010 Household Survey (ENIGH) and authors’ calculations. Notes: Estimates come from a Quadratic Almost Ideal Demand System (QUAIDS) using a Non-linear system of Seemingly Unrelated Regressions (NLSUR) with data from the household survey and the CPI aggregated at 12 categories of expenditure.

B. The Measurement of Welfare Loss

To analyze the welfare loss we introduce a measure of equivalent variation. We define the equivalent expenditure as the amount of money that allows a household to get the same utility level as before the VAT reforms.¹⁶ Given the change in prices, the equivalent expenditure is the amount of money that allows the household to reach a level of expenditure as good as the one they had before the reforms. The higher the equivalent expenditure is to the original expenditure, the higher is the welfare loss.

Formally, we define the household’s h change in welfare as follows:

Where e(⋅) is the expenditure function and V(⋅) is the value function.¹⁷ p is the vector of actual prices and $\tilde{p}$ is the imputed price vector from the VAT reforms using our estimates on Section III. ¹⁸ Finally, y_h, is the original expenditure and ${\tilde{y}}_h$, is the equivalent expenditure, which after some algebra one can show it to be:

Overall, we estimate that the average household lost 1.4 percent of its monthly expenditure from the 1995 reform and 0.7 from 2014. That makes a 0.27 and 0.15 percent loss of monthly expenditure for a one percent increase in the VAT rate respectively. The welfare loss from the 1995 VAT reform is higher than the 2014 reform because, as we discussed in the previous section, inflation was a higher and more persistent process, so shocks used to have a larger impact and a longer life in 1995 than in 2014.

We find that the welfare loss is progressive in absolute and relative terms. Table 10 shows the overall welfare loss and the breakdown by decile of monetary income. Normalizing the figures to a one percent increase in the VAT rate, the households in the 10th decile loss on average 0.28 percent of its total expenditure in 1995 and 0.16 percent in 2014. Meanwhile, the households in the lowest decile loss 0.26 and 0.13 percent (Figure 5).

Two reasons explain most of the progressive effect of the VAT on the households. First, the VAT is not uniform for all goods: low-income households tend to spend a higher share of their incomes in untaxed goods, like food and non-alcoholic beverages (Table 8). Second, the tax incidence on prices is quite heterogeneous as we showed earlier on Section III. The most affected prices from the reforms were communications, healthcare, and schooling, which are more intensively consumed by the high-income households. Therefore, high-income households will be relatively more taxed than the low-income households. These expenditure patterns are also consistent with the income-elasticities of the demand system previously estimated (Table 9).

We also identify a source of regressivity in the diverse goods and services. This regressivity happens because most of its components are taxed with the VAT, and the low-income households spend an important share on them (Table 8). These types of goods include housekeeping products, personal care, funerals, and government fees.

Table 10.

Distribution of Welfare Loss by Deciles

Sources: INEGI, 2010 Household Survey (ENIGH) and authors’ calculations. Notes: Estimates come from a Quadratic Almost Ideal Demand System (QUAIDS) using a Non-linear system of Seemingly Unrelated Regressions (NLSUR) with data from the household survey and the CPI aggregated at 12 categories of expenditure. The welfare loss is the compensating variation, calculated with equation (IV.3). The household deciles are calculated using the monetary income in the Survey (ENIGH).

Table 10.

Distribution of Welfare Loss by Deciles

	Monthly average per household (MX$ 2010)			Percent of original expenditure
	Original	Welfare Loss	Welfare Loss	Welfare Loss	Welfare Loss
Decile	Expenditure	VAT 1995	VAT 2014	VAT 1995	VAT 2014
1	3,071.1	-39.21	-19.49	-1.28	-0.63
2	3,966.4	-51.17	-25.87	-1.29	-0.65
3	4,587.0	-59.22	-29.92	-1.29	-0.65
4	5,454.9	-71.20	-36.65	-1.31	-0.67
5	6,365.5	-83.73	-43.66	-1.32	-0.69
6	7,246.0	-95.69	-50.21	-1.32	-0.69
7	8,531.9	-113.33	-60.04	-1.33	-0.70
8	10,284.3	-137.54	-73.67	-1.34	-0.72
9	13,522.8	-184.03	-101.51	-1.36	-0.75
10	24,323.2	-340.01	-196.04	-1.40	-0.81
Overall	8,733.1	-117.48	-63.69	-1.35	-0.73

Sources: INEGI, 2010 Household Survey (ENIGH) and authors’ calculations. Notes: Estimates come from a Quadratic Almost Ideal Demand System (QUAIDS) using a Non-linear system of Seemingly Unrelated Regressions (NLSUR) with data from the household survey and the CPI aggregated at 12 categories of expenditure. The welfare loss is the compensating variation, calculated with equation (IV.3). The household deciles are calculated using the monetary income in the Survey (ENIGH).

View Table

Table 10.

Distribution of Welfare Loss by Deciles

	Monthly average per household (MX$ 2010)			Percent of original expenditure
	Original	Welfare Loss	Welfare Loss	Welfare Loss	Welfare Loss
Decile	Expenditure	VAT 1995	VAT 2014	VAT 1995	VAT 2014
1	3,071.1	-39.21	-19.49	-1.28	-0.63
2	3,966.4	-51.17	-25.87	-1.29	-0.65
3	4,587.0	-59.22	-29.92	-1.29	-0.65
4	5,454.9	-71.20	-36.65	-1.31	-0.67
5	6,365.5	-83.73	-43.66	-1.32	-0.69
6	7,246.0	-95.69	-50.21	-1.32	-0.69
7	8,531.9	-113.33	-60.04	-1.33	-0.70
8	10,284.3	-137.54	-73.67	-1.34	-0.72
9	13,522.8	-184.03	-101.51	-1.36	-0.75
10	24,323.2	-340.01	-196.04	-1.40	-0.81
Overall	8,733.1	-117.48	-63.69	-1.35	-0.73

Sources: INEGI, 2010 Household Survey (ENIGH) and authors’ calculations. Notes: Estimates come from a Quadratic Almost Ideal Demand System (QUAIDS) using a Non-linear system of Seemingly Unrelated Regressions (NLSUR) with data from the household survey and the CPI aggregated at 12 categories of expenditure. The welfare loss is the compensating variation, calculated with equation (IV.3). The household deciles are calculated using the monetary income in the Survey (ENIGH).