Introduction

Mexico has undergone various structural changes that have transformed its economic activities and its commercial relationships, going from a closed economy to an open one. With the enforcement of the North American Free Trade Agreement (NAFTA), the Mexico-United States bilateral relationship has developed within a context of great dynamism in commercial terms.

Because of its geographic location and economic potential, the United States is Mexico’s main commercial partner at the global scale. Just in the period of 1995 to 2012, Mexican exports to this country increased in 341.52 % and the imports in 243.88 % (INEGI, Banco de Información Económica; SE. Subsecretaría de Comercio Exterior).

From January to September 2013, 78.24 % of the Mexican exports were destined to the United States and only 20 %, approximately, were destined to other countries, despite the number of trade agreements that Mexico has signed. The behavior of exports sent to the US ranges between 77 and 92% (INEGI, Banco de Información Económica; SE. Subsecretaria de Comercio Exterior) of participation in total exports; in their part, the behavior in value of exports grew at a mean annual rate of 7.6 % for the total and 6.8 % for those towards the United States.

Exports by manufacturers are the main product sent to the United States, followed by the oil, agriculture and livestock, and extractive activities. From the percentage reported in January to September, 2013, 64.59 % of the participation corresponds to manufacturers, 10.34 % to oil exports, and 2.32 % and 0.96 % to agricultural and extractive products, respectively.

One of the main issues in the academic and political scope of international trade has been promoting the exporting sector to drive a greater growth of developing economies. Various studies¹ have attempted to respond to this questioning, trying to explain this relation under different perspectives and the application of econometric techniques, among which the following stand out: crossed section studies, neoclassic production functions and simultaneous equations, as well as temporal series of causality and cointegration.

^{Donoso and Martín (2009}) perform a study that reflects the main empirical studies that contrast the hypothesis of exports as motor for growth in an economy, under two types of methodologies: crossed section studies and temporal series. The crossed section studies show evidence that the exports promote economic growth in the countries under study, and that it depends on the level of development or rent. Under this approach, there are studies by ^{Krueger (1980}), ^{Tyler (1981}) and ^{Feder (1982}), among others.

^{Chow (1987}), ^{Ramírez (2005}), ^{Balaguer and Cantavella-Jordá (2001} and ²⁰⁰⁴) use time series of causality, cointegration and error correction models, obtaining results that are far from being similar, even when they analyze the same countries and use similar samples.

Of the studies carried out for Mexico, the one by Thornton (1996) for the period of 1895-1992 stands out; he finds that exports have a relation of causality in the sense of Granger² towards the Mexican domestic product. ^{Cuadros (2000)} analyzes the impact of trade openness from 1983 to 1997, finding after the application of an autoregressive vector and Granger’s causality contrast the absence of causality between the different categories of the total exports, of manufacturers, and of exports that include those performed in the maquila sector and the growth of net exports product. This author concludes that there is not a causality relation between the growth rate of exports and the net product growth rate of exports and that, therefore, the positive impact of trade openness on economic growth does not seem to be related to the increase in exports.

^{Fujii, Candaudap and Gaona (2005}) evaluate the effects in terms of economic growth for the decade of the 1990s of the industrial export model based on shared national production. Through the elaboration of different determination models of the imports of intermediate goods associated to exports, they find that the exporting sector depends strongly on the exterior in terms of input supply, which indicates there is weakness in the backward links among exporting companies and the different productive branches of the national economy.

^{Rodríguez and Venegas (2011}) analyze the effects of exports on Mexico’s economic growth for 1929-2009, using Johansen’s cointegration test and Granger’s causality analysis. Through the estimation of an error correction model, the existence of a long-term stable relationship is found between the exports and the real gross domestic product of Mexico, where the causality direction goes from exports towards product growth.

In general, it can be observed that the results found by the studies mentioned before are far from coinciding and they corroborate that the relation between exports and economic growth of a country is more complex and unstable. In this sense, and taking NAFTA and Mexico’s trade policy as starting point, this study uses a methodology based on the decomposition of time series to determine: first, whether there is a positive and significant relation between exports and Mexico’s Gross Domestic Product; and, second, to verify whether the Mexican economy responds to positive or negative disturbances of the United States economy.

The hypothesis by which this study is guided is that the behavior of exports and economic growth in Mexico is correlated with the variations in the United States economy due to two factors. Firstly, because the signing of the North American Free Trade Agreement took place within the context of fostering economic growth through the exporting sector and, more specifically, as a result of the expansion effect that would be expected towards domestic productive activities. Secondly, due to the close commercial relation there is currently with the United States, since it is the main destination of Mexican exports.

Materials and Methods

As has been pointed out, the objective is to determine the possible relations between Mexico’s GDP, the United States GDP, and Exports sent to this country. The information used for the analysis period of 1995.I-2013.III is a database made up of these variables with three-month periodicity.

The series of the Mexican GDP was taken from the National Statistics and Geography Institute (Instituto Nacional de Estadística y Geografía, INEGI); the exports sent to the United States were obtained from the Ministry of Economy (Secretaría de Economía, SE); finally, the United States GDP comes from the Bureau of Economic Analysis. To convert the exports series and the US GDP into MX pesos, the exchange rate reported by Banco de México for the study period was used.

In the study of data ordered in time, a time series can be defined as a record of the characteristics of a variable at fixed intervals of time. The time series exhibit behaviors that are not directly observable and which, therefore, cannot be obtained through conventional econometric techniques and methods. To carry out inferences, many times it is useful to decompose a time series into its principal components: seasonality, trend, cycle and irregularity, which can be done with the Hodrick and Presscot filter, which if used appropriately is superior to alternative methods (^{Pedregal and Young, 2001}).

Seasonality (E _t ) exhibits a repetitive pattern of duration equal to one year. It is influenced by institutional, climate and technical factors that evolve gradually in the long term.

Trend (T _t ) represents the evolution or behavior of the series in the long term. It is usually associated to the determinants of economic growth (technology, physical capital, qualification of the workforce).

Cycle (C _t ) is oscillatory movements around the trend and their duration varies between two and eight years. Irregularity (I _t ) or sporadic movements do not follow a specific pattern.

Based on the components described before, ^{Meza (2012)} considers that some authors have suggested that the variable that will be predicted Y(t) can be the result of the application of the following relations:

Additive scheme: Y(t)=E(t)+T(t)+C(t)+I(t)

Multiplicative scheme: Y(t)=E(t) X T(t) X C(t) X I(t)

Mixed scheme: Y(t)=E(t) X T(t) X C(t)+I(t)

Starting from the unobservability of the components, it becomes necessary to specify each one in function of nature, periodicity of the data, and needs of the research. ^{Guerrero (2011)} mentions that a simple way of representing the behavior of a series is through the model of unobservable components, which, even when not observed separately are present in the study phenomenon. In this sense, an element which will always be present and which in fact justifies the statistical analysis is the random component, which has the volatility of the series, that is, the unpredictable portion.

In the econometric literature, there is a set of techniques for the decomposition of temporal series, among which there is the methodology of the Hodrick-Prescott Filter.

A filter is any procedure carried out on an original time series to obtain a new series, whose magnitude is free from a specific effect that will make the correct interpretation of their values difficult. The Hodrick-Prescott Filter does not require the construction of a statistical model; it is enough to suggest a relation in form of a model with the unobservable components.

According to this method, the series that have a periodicity of more than one year do not require deseasonalizing; therefore, the series to be used Ytt=1N will be considered as the sum of the two components: one of trend, T _t and one cyclic C _t :

Y _t =T _t +C _t for t=1, 2, 3,..., N

where Y _t : is the variable observed at time t; T _t : is the trend component; C _t : is the cyclic component.

The cyclic C _t represents the deviations from the trend T _t ; that is:

C _t =Y _t -T _t

So the irregular I _t is no more than:

I _t =Y _t -T _t -C _t

To determine the trend component T _t , ^{Hodrick and Prescott (1997}) suggested the following minimization problem:

Which is equivalent to:

The first term of the equation corresponds to the sum of squares of the deviations (Y _t -T _t ). The second is a multiple λ of the sum of squares of the second difference of the trend component (T _t ).

The constant λ is the parameter of punishment or softness with which the acceleration of the trend component is controlled; that is, the variations in its growth rate, and it is chosen according to the periodicity of the data. The lambda parameter (λ) must be positive for the existence of a minimum to be guaranteed when obtaining the second derivate.

It represents the importance attributed to the degree of adjustment in relation to the degree of softness. If λ tends to 0, the trend is softer. If λ =0, the trend component (T _t ) is equal to the original series of time. Instead, if λ tends to the infinite the softness is maximized, so that the values of the trend follow the behavior dictated by the equation:

T _t -2T _t-1 +T _t-2 =0

which corresponds to a straight line.

Hodrick and Prescott chose the value of λ , with the assumption that the cyclic component (Y _t -T _t ) and the second difference of the trend (T _t -2T _t-1 -T _t-2 ) were independent variables, distributed, normal and with zero mean and variances σI2 and σT2 , respectively, then:

For series with trimester data, they obtained a value of λ=1600, for time series with monthly data suggesting the use of a value of λ=14400, and for time series with annual data which suggest a value of λ=100.

Therefore, the trend component according to ^{Almendra-Arao and González Estrada (2006)} can be estimated by solving the following minimization problem:

s.a: Y _t =T _t +I _t

Using L ^m T _t =T _t-m , m∈Z, then:

(1-L)² T _t =(1-2L+L ²)T _t =T _t -2T _t-1 +T _t-2 = (T _t -T _t-1 )-(T _t-1 -T _t-2 )

The problem is transformed into:

If it is defined as ∇=1L:

It implies that: ∇2Tt=1-L2Tt

Therefore, the minimization problem becomes:

Obtaining the conditions of first order:

Which is equivalent to:

Therefore:

The Hodrick-Prescott Filter to obtain the secular or trend component is:

Following the methodology proposed by ^{Hodrick-Prescott (1997}) and ^{Almendra-Arao and González Estrada (2006)}, the procedure to obtain the possible relations between the Mexican GDP, exports sent to the United States, and the United States GDP is the following:

The value of λ chosen for a trimester series is 1600. The software with which the data were analyzed was the statistical SAS package. Figures 1 and 2 show the behavior of the exports in relation to Mexico’s GDP and the United States GDP.

The pattern of behavior of the exports does not follow the Mexican GDP, since in growth periods of the exports, the Mexican GDP decreases. This is evidenced better since 2000, when the peaks of the series of exports differ compared to what Mexico’s GDP presents (Figure 1).

The contrary case is shown in Figure 2, where the Mexican exports sent to the United States follow a similar behavior to the United States GDP, which evidences the close relationship between the two study variables.

Conclusions

The results obtained allow the following conclusions:

The first is about the relationship there is between Mexico’s GDP and the exports sent to the United States, which implies that any disturbance that happens in the exporting sector will have an influence on the Mexican GDP. The magnitude will depend, among other things, on the participation that they have in generating the GDP, as well as the composition and dragging effect towards the other productive sectors. In this case, the average participation for the study period of exports in the Mexican GDP is 5.36 %; and, second:

Given the trade relation between exports and the United States economy shown at the beginning of the study, anyone would think that the ups and downs in that country would be reflected automatically in the behavior of exports. However, the coefficient of correlation found indicates that this sector is scarcely vulnerable to any shock in that economy, which leads us to conclude that for this period the demand in the United States for Mexican exports is scarcely variable in time, and, therefore, Mexico’s economic growth through exports is not influenced by the United States economy.