Mexico’s economic infrastructure: international benchmark and its impact on growth

The following paragraphs describe three of Mexico’s economic infrastructure trends, in three periods—namely 1970, 1990 and 2010, by countries (Brazil, Chile, Argentina, Turkey and South Africa⁷) and regions (Latin America or LAC, and a selection of industrialized countries—interchangeably used with “IND”⁸). The telecommunications sector variable is the sum of fixed telephone and mobile lines for every 1000 workers.⁹ The source is the World Development Indicators (WDI) from the World Bank. Latest years were manually updated for representative countries by reaching out to governments. Figure 1 presents an overview for telecommunications, with a 20-year gap in between each set. Technology has aided accessibility and affordability, which in turn have contributed to an extraordinary growth in stocks. Mexico depicts only 56 lines for every thousand workers in 1970, and then the sector expands in 2010 to an average of 2.1 lines per person.

In spite of the stock’s improvement over time, in 2010 Mexico lags from all comparing countries and regions by presenting the lowest penetration of telecommunication services. LAC presents a median of 2.5 line mixture per worker, which is still 0.4 more than Mexico’s figure. On the high end of the spectrum are Argentina, Chile, Turkey, and South Africa who average around the industrialized counties’ mean with figures above 3.0 lines per worker. On the other hand, Brazil keeps a lower bound of stocks with 2.3 lines per worker.

For the energy sector, the most accessible way of calculating infrastructure stocks is by the nation’s electricity generating capacity, measured by thousand KW per thousand workers.¹⁰ The pooled data present an average of 1.36 and a lower standard deviation than the telecom sector’s average of 1.91. Obtained from the U.S. Energy Information Administration (EIA), the data indicate that most countries have shown a gradual increase in the stock over time, except for South Africa, whose electric generating capacity increased in 1990, but then decreased by 0.48. Nonetheless, it still performed an overall-period increase of 0.81 KW by 2010 (see Fig. 2). Chile makes an astounding effort in the last period by increasing its stock from 0.71 to 1.14 thousand KW per worker. That is almost as much as Mexico or Brazil generated in total for 2010, and 0.43 more than the LAC median.

Notwithstanding the gradual increase in electric generating capacity stock in Mexico, it lags from most comparator countries, except Brazil. Still, it displays a performance than LAC, but lacks a substantial amount of stock to resemble the industrialized countries’ level. Chile and Turkey increased their figures from 1970 to 2010 to over 1 KW per worker (in thousands). Mexico was unable to increase that amount.

Transport infrastructure stocks are measured by total road length in kilometers divided by the country’s area. The source is the International Road Federation (IRF) and includes “all roads in a given area,” like motorways, highways, main or national roads, secondary or regional roads, and other roads such as rural. Like the telecom sector, some information was missing and it was necessary to reach out to each country’s government. In 2010, Mexico surpassed peer comparator countries’ road network per area from the LAC region—Brazil, Chile and Argentina,—as the region itself. There was a constant increase for every following period in Mexico (see Fig. 3). However, compared to South Africa,¹¹ Turkey and IND, Mexico has a considerable gap to close, particularly, with the industrialized countries. Turkey has around 3 times more than Mexico’s stock in 2010, and South Africa displays more than double the quantity offered by Mexico in 1990. Moreover, Mexico lags a whopping 1.139 from the median of IND in the last observation. Even though Mexico surpasses the comparator countries in the LAC region, these do not lag much behind. It is a tight situation where some of them, Brazil for example, may level the Mexican 2010 figure quickly.

This section adjusts the variables by eliminating the geographic and demographic variances that affect each of the sectors and their correlation to GDP, as done by Canning (1998). Adjusting the variables makes it possible to observe the residual, which remains as simply the variance from the other elements that conform the variable. The partial regressions for each infrastructure stock variable are given by:where \(z_{1,2,3} = {\text{Each}}\;{\text{of}}\;{\text{the}}\;{\text{infrastructure}}\;{\text{sectors}}\;{\text{variables}}\)

In this way, they are conditioned to area and population. The component area corresponds to each country’s land in square kilometers, and population corresponds to the number of people living in every country for every year. GDP per capita is adjusted by following the same procedure. It corresponds to Penn World Tables version 8.2, expenditure side of gross domestic product at current PPP per capita. Both residuals are graphed in a scatter plot for 1970 and 2010 to observe the behavior over time.

The signs from the OLS estimation concur with what is expected from the infrastructure sectors (see Table 1). For area, the larger the country’s land is, the harder it will be to have higher infrastructure stocks. Hence, all the infrastructure stocks present negative coefficients for area (land), where only telecom and transport are significant. On the contrary, with population, the higher the numbers, the higher the infrastructure stock will be. For all the infrastructure sectors, this coefficient is positive and highly significant.¹² The residuals emit high correlations among themselves in a similar manner to the unadjusted variables (see Appendix 3).

For telecommunications, the conditional comparison maintains a positive relationship with GDP. However, this correlation has weakened over time, from 0.8 in 1970 to 0.5 in 2010 (see Fig. 4). Telephone and mobiles lines’ comparative advantage of accessibility has been declining. Connectivity, such as internet, has substituted the service. Different regions converge in similar areas. Mexico, clustered around the LAC countries, stays below the regression lines for both periods observed and inside the 90% confidence intervals. In 1970, even though Mexico was below the mean, it stood ahead other LAC countries. However, it has drifted slightly from the regression line and other LAC countries—namely Chile, Argentina Panama and Uruguay—have gained advantage. Compared to the industrial countries in the sample, Mexico has been underperforming in the telecom sector. On the other hand, compared to most Sub-Saharan Africa and South Asia, Mexico is better off.

The energy infrastructure stocks’ behavior is different from telecom’s when eliminating the effects caused by population and area of each country (see Fig. 5). The sector exposes a general positive relation and, in contrast, shows a gain in correlation with GDP over time, from 0.82 in 1970 to 0.88 in 2010. Time has exposed the countries to different sources of energy as well as different technologies, keeping electricity as a main source of energy worldwide. Countries’ energy stocks are scattered in 1970. In 2010, the countries that lag mostly belong to Sub-Saharan Africa.

Compared to LAC countries, Mexico has a below average electricity stock. A better performing country is Panama, despite having similar adjusted GDP per capita. On the contrary, a LAC country with a lower adjusted GDP per capita is Paraguay, but it has increased the most its electricity generating capacity during the period.¹³ Still, Mexico has gotten closer to the world mean over time. On another front, in 1970, Mexico seemed to be following behind the industrialized countries, but in 2010, that gap has widened and now it is nowhere near any of them.

The transport sector displays a different behavior from both the previous sectors. This variable is more heterogeneous among countries. First, considering the adjustments, it is Mexico’s most underachieved infrastructure sector (see Fig. 6). For 1970, Mexico positions itself outside the confidence intervals of the regression, but later, in 2010, it manages to reach within. The country developed and improved over time, but still lags from the world mean. Surprisingly, Mexico’s underperformance in 1970 is so low, that it lies outside the confidence lines like Sudan and Thailand. In 2010, better transport infrastructure-providing LAC countries include Colombia, Bolivia, Argentina, Costa Rica and Brazil, all of them with lower adjusted GDP per capita than Mexico.

The regions in 1970 do not display a clear pattern of behavior in the transport sector like the others. In 2010, the behavior is more segregated by type of region: The industrialized countries have higher adjusted infrastructure stocks and adjusted GDP, while the African countries¹⁴ have from a medium-to-low transport stock and adjusted GDP. The transport sector is the clearest example of how adjustments affect the behavior of the variables, which may be overseen in simple comparisons. When looking at the stock level, it seems that Mexico has been improving, compared to others in the region. However, at the conditioned variables, there are others which excel its development, and besides, Mexico does not even reach the world mean in any of the sectors or terms observed.

The econometric growth model to assess the impact of infrastructure on growth has a neoclassical approach, similar to Calderón and Servén (2004) and Loayza and Odawara (2010): where \(y\) is the log of output per capita, subscript i stands for country, t for period, the dependent variable \(\Delta y_{it}\) stands for the growth rate (Eq. 5), \(\mu_{t}\) and \(\eta_{i}\) are the unobserved time-specific and country-specific effects, respectively, and \(\varepsilon\) is the error term. The control variables are the infrastructure synthetic index (\(I_{i,t} )\), specified later, and (‘X) are a standard set of growth control variables suggested by Barro (1991) and Loayza et al. (2005). They are divided into four main groups: (1) capital, (2) structural policies and institutions, (3) stabilization policies and (4) external conditions.

Before further detailing the variables, it is important to mention that they are constructed under several-year averages for the empirical estimation. The first reason is that the variable of interest—infrastructure stocks—does not change much on a yearly basis. By averaging the stocks, the variance is observed better. The second is due to business cycles, because they directly affect infrastructure. When business cycles contract, the first thing to experience building constraints is infrastructure (Grebler and Burns 1982; Wheaton 2015). To eliminate the undesirable effects, 5-year averages are used observe the short-run relationship and 10-year averages for the long run (Calderón and Servén 2008; Loayza and Soto 2002). However, Male (2011) calculates that the business cycle for Mexico is 5.37 years. Since the business cycle falls short from being in the 5-year average, the regression is estimated with 6-year averages.¹⁵

Besides infrastructure, or physical capital, the estimation includes seven growth determinants from the standard set of variables widely used in growth literature: human capital, financial debt, trade openness, government burden, governance, inflation and terms of trade shocks.¹⁶ The focus of this investigation is on physical infrastructure, or as specified in the regression: \(I_{i,t}\). Infrastructure is a multi-dimensional concept that should be treated as an integral variable. With three economic infrastructure sectors included (telecommunications, energy and transport), principal component analysis (PCA) helps construct a synthetic index that considers the minimum dimensionality of the variables and, in some cases, the error variance as well. It keeps as much variance possible and transforms the information into new variables, called principal components, which are no longer correlated between them (Pradhan et al. 2014; Torres et al. 2015). The new components are ranked in such a way that the first few retain most of the variation present in the original values and the differences in measures from the infrastructure stocks are eliminated,¹⁷ e.g., kilometers and kilowatts (Alesina and Perotti 1996; Sánchez-Robles 1998; Jolliffe 2002; Calderón and Servén 2008). It estimates the aggregate effect to give a better approach, instead of modeling each of the sectors separately. The form used to calculate the index is:

In this equation, \({\text{Sd}}\) is the standard deviation, \(X_{ij}\) is the ith sector variable in the jth year and \(a_{ij}\) is a component load or weight derived by PCA. The synthetic infrastructure index used in this investigation corresponds to the first principal component constructed by the eigenvectors of the infrastructure sectors in logs.¹⁸ It captures 75% of the total variation and has a strong correlation with the original variables. The energy sector holds the highest correlation of 0.92, followed closely by the telecom sector with 0.91, and last is the transport sector with a correlation of 0.76. Based on the high correlations, it is safe to say the first principal component is a strong measure for infrastructure. The calculated weights are 0.60 for telecom, 0.61 for energy and 0.50 for transport.¹⁹ These were normalized to equal 1. The corresponding weights are expressed by:

Figure 7 displays how the index has evolved in all regions on 1970, 1990 and 2010.²⁰ Due to standardization, means will be 0. All the regions have improved their index score over time. As expected, the industrialized countries maintain the highest score in every period. Sub-Saharan Africa, on the other hand, lags from the rest of regions in all periods.

Human capital also has a direct role as a factor of production, and jointly with physical capital, serves as a complement to other factors by contributing to technology and efficiency, thus to growth. It is measured as the ratio of population attending secondary school, regardless of their age (Mankiw et al. 1992; Barro and Lee 2001; Loayza and Soto 2002; Lee and Lee 2016).

As part of the endogenous growth, or the decisions taken by the public sector, private sector and the whole economy, the second category—structural policies and institutions—includes four variables: financial depth, trade openness, government burden and governance. Financial depth consists of the financial resources provided to the private sector by domestic money banks as a share of GDP. Domestic money banks comprise commercial banks and other financial institutions that accept transferrable deposits, such as demand deposits. Trade openness results from the regression of the log of the ratio of exports and imports (2005 US$) on the log of area, population and dummies created for oil-exporting and landlocked countries. All variables were gathered from the WDI. Government burden describes the ratio of government consumption to GDP in 2005 US$ in logs. Finally, for this category, after the work by Mauro (1995), government behavior and society’s reaction to it has received much attention. By these means, a governance index is added. It is built in a similar manner to the synthetic infrastructure index, by using principal components, and introducing four variables—namely prevalence of law and order, quality of bureaucracy, absence of corruption and accountability of public officials. The information for governance variables is reported by the risk governance framework.

For the stabilization policies’ variables, the lack of price stability is represented by inflation, or the average annual percent changes in consumer prices. Finally, external conditions accounts for terms of trade shocks measured as the national account export price index divided by the imports price index, with 2005 equaling 100 (Easterly et al. 1993; Fischer 1993; Easterly et al. 1997).²¹

The absence of high correlations discards multicollinearity (see Appendix 5). The highest is held by the infrastructure index with GDP (0.78) and human capital (0.79). The infrastructure index maintains a positive correlation with almost all the variables except inflation and terms of trade; however, these are relatively small. In fact, these variables have negative correlations with almost all the variables. Inflation has a positive relationship with trade openness, government burden and inflation, but very close to zero. Terms of trade is correlated positively, but also very close to zero with government burden.

The empirical strategy is based on panel data relating economic growth to the reviewed set of controls, including the infrastructure index. The methodology assumes the process is dynamic and includes level of output per capita at the start of the corresponding period in the set of independent variables. Arellano and Bond (1991) evolved the first dynamic model developed by Holtz-Eakin et al. (1988) and named it generalized method of moments (GMM) difference. Later, Arellano and Bover (1995) and Blundel and Bond (1998) developed GMM system. The method is consistent and asymptotically efficient in the presence of heteroscedasticity.

The first estimator developed by Arellano–Bond allows the researcher to use lags of the dependent or independent variables as needed, if both (the lag and un-lagged observation) are available in the data. By using lagged observations, (1) endogeneity (or causality) is eliminated, and (2) the country time-invariant characteristics are removed from the explanatory variables that may be correlated. By using GMM you also (3) eliminate autocorrelation that arises because of the independent term: \(y_{i,t - 1}\) (from Eq. 4). Finally, (4) it also solves the problem of data scarcity, and the equations need models that allow a short time dimension and a larger country dimension to produce robust results.

The way the GMM methodology and its lags solve these problems is by (1) including endogenous regressors as instrumental variables eliminate endogeneity. It uses (2) first differences to transform the regressors and remove the fixed country effects. In this analysis, common factors are dealt with the inclusion of period-specific dummies and unobserved country effects are handled by differencing. To deal with (3) autocorrelation, the first differenced dependent variable is also instrumented by past observations. Finally, the (4) short panel data problem is corrected because this method can only use around t = 10. Larger T panels diminish the error term that includes the shocks of fixed effects with time; in the same manner, this effect occurs to the lagged variables in a model estimated with GMM.

Arellano and Bover (1995) suggested an extra set of moment conditions. So, Blundell and Bond (1998) evolved the first estimator by Arellano–Bond where, instead of just taking the lagged variable as an instrument, it subtracts the average of all future observations, allowing a minimal loss of data. This evolved model by Blundell and Bond (1998) is called system GMM. It is computable for all the observations, except for the last one. When the conditions are satisfied, the resulting estimator has better finite sample properties. The expanded estimator has a cost of involving a set of additional restrictions on the initial conditions of the process in generating the dependent variable, which in turn leads to system GMM creating a higher number of instruments, which are internal to the regression. These are based on lagged versions of the level variable (Arellano and Bond 1991; Roodman 2006), which may be endogenous or not strictly exogenous. The procedure uses a moment condition that is based on the level equations, together with the usual Arellano and Bond estimator-type orthogonality conditions (Table 2).

In GMM system, the main conditions favor a panel analysis due to the consideration that fixed effects might be distributed arbitrarily and the time variation can be used to calculate the parameters. The estimators handle the invariance of fixed effects and endogeneity of regressors, while avoiding panel dynamic bias. Besides the idiosyncratic disturbances found in the fixed effects, heteroscedasticity and serial correlation may be present in patterns, which would remain uncorrelated across individuals.

Table 3 reports the results from the growth regression for 6-year averages, or t = 9 from the complete sample of 96 countries from 1960 to 2014, by using different two-step system GMM²² estimations. The difference from each estimation lays on the instruments, which were carefully selected to identify the best model. When using GMM, the ideal is to have a small t, or less than 10–12 periods per individual. The 6-year periods fit this description accordingly. Column 1 uses endogenous instruments, which means that since it is a two-step estimation, it uses its own differenced and lagged variables. These instruments include GDP per capita, infrastructure, financial depth, government burden, governance and human capital, and the respective periods. Column 2 follows the same procedure, but uses population as an exogenous instrument for infrastructure, Column 3 uses labor as an exogenous instrument for infrastructure, and Column 4 uses urban population for the same purpose as Columns 2 and 3.

The three exogenous variables—population, labor and urban population—all have in common that they are demographic variables. The main reason to use these as exogenous instruments for infrastructure is twofold: (1) Infrastructure may not be completely exogenous—future projects may be affected by stocks today and (2) there may be a measurement error in the data, as explained as one of the caveats for physical infrastructure in Introduction. In addition, because it is people who place demand for infrastructure, there is no reason to believe that these demographic variables have a systematic relation with the measurement error in infrastructure, including the rest of the standard set of growth variables.²³

The validity of the instruments may be checked through two channels: First, the number of instruments is validated²⁴ through the Hansen test.²⁵ Specifically, it addresses the instruments’ validity by analyzing the sample analog of the moments conditions used in the estimation process. The second validation is aqcuired by the first-order and second-order correlation. It verifies the correlation of the errors. The first-order serial correlation of the differenced error term is expected even if the original error term is uncorrelated, unless the latter follows a random walk. Second-order serial correlation of the differenced residual indicates that the original error term is serial correlated and follows a moving average process of at least order one. Failure to reject the null hypothesis gives support to the model. In the estimated models from Table 3, the Hansen test and second-order correlation confirm little evidence against the validity of the moment conditions chosen for all the model specifications, but the results from Column 4 are the preferred estimators due to the extra confidence that the external instrument delivers and the validity of the test results.

In all the models, regardless of the technique used, the variable of interest, infrastructure, is statistically significant and positive, ranging from 0.10 to 0.12. Also, initial GDP has a significant negative coefficient as evidence of “conditional convergence” (Barro and Sala-i-Martin 1992). As the tests conclude that Column 4 gives the best fit, infrastructure stocks and economic growth are positively associated with a coefficient of 0.117. Human capital (0.018), financial depth (0.091), inflation (0.0003), terms of trade shocks (0.161) and the governance index (0.009) foster growth, while government burden (− 0.062) and trade openness (− 0.064) affect it adversely. When using GMM, it is expected that trade openness displays a negative coefficient due to short-term adjustments and a probable nonlinear relationship (Gries and Redlin 2012; Huchet-Bourdon et al. 2011).

As a robustness check, by following previous literature estimations (Calderón and Servén 2008; Loayza and Odawara 2010), Table 4 reports different year averages (5, 6 and 10 years for each method, respectively) for system GMM with endogenous instruments (Columns 1–3) and urban population as an exogenous instrument (Columns 4–6). It is interesting to observe the evolution of the coefficients for different year averages, but for both methodologies, the specification tests select the 6-year average, specifically Column 5 (the same as Colum 4 in Table 3), as the preferred estimator.²⁶ The infrastructure index coefficient approximately doubles for the 10-year average, compared to the 6-year average and slightly improves from the 5-year average coefficients. Even though these are positive and highly significant in all models, the specification does not confirm, in either of them, any evidence in favor of the validity of the moment conditions chosen.