GMM Estimator : An Application to Intraindustry Trade

This paper investigates the determinants of intraindustry trade IIT , horizontal IIT HIIT , and Vertical IIT VIIT in the automobile industry in Portugal. The trade in this sector between Portugal and the European Union EU-27 was examined, between 1995 and 2008, using a dynamic panel data. We apply the GMM system to solve the problems of serial correlation and the endogeneity of some explanatory variables. The findings are consistent with the literature. The difference between per capita incomes and factor endowments present a positive sign. These results are according to Heckscher-Ohlin predictions. The economic dimension has a positive impact on trade. A negative effect of the distance on bilateral trade was expected and the results confirm this, underlining the importance of neighbour partnerships for all trade.


Introduction
The intraindustry trade IIT or two-way trade is explained by product differentiation and the existence of products belonging to the same category.The big push in the literature emerged with the work of Grubel and Lloyd 1 .The pioneering models of IIT, especially the horizontal differentiation as in Krugman 2 , Lancaster 3 , and Helpman and Krugman 4 , explained this type of trade based on monopolistic competition and economies of scale.In fact, the models of horizontal intraindustry trade HIIT do not predict the advantages theory as explanatory factor.HIIT is explained by consumers with similar characteristics and similar types of income.
In this respect, the vertical intraindustry trade VIIT admits different types of quality, that is, different types of preferences.The consumers have different types of income per capita, which emphasize the theoretical models of Falvey and Kierzkowski 5 and Shaked and Sutton 6 .

Literature Review
In recent years, emerged in the literature an explanation of international trade based on the transaction of intermediate goods.Fragmentation also called outsourcing of production has received attention from many scholars especially starting in the 1990s.
In fact, the conceptual model of Jones and Kierzkowski 7 demonstrated that the location of multinational firms was associated with economies of scale and factor endowments.In other words, a multinational company may have several branches located in several regional blocks.As Faustino and Leitão 11 referred, the term fragmentation has taken various forms outsourcing by Feenstra and Hanson 12 and vertical specialization by Hummels and Skiba 13 .Globalisation promotes regional clusters in the international economics.As Eiteam et al. 14 demonstrated, we have some countries as India, Russia, and Mexico that developed highly efficiently.The sector of parts and components for vehicles, aircraft, and software are generally referenced in the literature.According to Kol and Rayment 15 the exchange of intermediate goods may take two forms: horizontal intraindustry trade and vertical intraindustry trade.In fact horizontal intraindustry trade in intermediate goods cannot be explained by different types of quality.However, vertical intraindustry trade helps to explain the various stages of international production, since there are economies abundant in capital K and other factors in labour L .Thus, it is understood that the vertical intraindustry trade is explained by different types of quality.The application of the index of Grubel and Lloyd 1 and the methodology of Abd-el-Rahman 16 and Greenaway et al. 17  The study of Faustino and Leitão 18 examined the determinants of VIIT in the automobile components between Portugal and European Union countries and BRIC Brazil, Russia, India, and China for the period 1995-2006.The authors applied a dynamic panel data GMM System .Faustino and Leitão 18 demonstrated that the differences in per capita and transaction costs are the main determinants of fragmentation.Leitão 19 examines the long-term effects of IIT and its components-horizontal and vertical IIT, applied to the study case of the United States.Using GMM system, the study shows a negative correlation between factor endowments, and IIT.The findings also illustrate that there is no positive correlation between HIIT and HO Heckscher-Ohlin model.

Grubel and Lloyd Indexes
Grubel and Lloyd 1 define IIT as the difference between the trade balance of industry i and the total trade of this same industry.In order to make comparisons easier between industries or countries, the index is presented as a ratio, where the denominator is total trade: where X i and M i are export and import to partner country i.
The index is equal to 1 if all trade is intraindustry.If IIT it is equal to 0, all trade is inter-industry trade.
Grubel and Lloyd 1, page 22 proposed an adjustment measure to the country IIT index IIT calculated for all individual industries , introducing the aggregate trade imbalance.Aquino 20, page 280 also considered that an adjustment measure is required, but to a more disaggregated level, but for this, the Grubel and Lloyd method is inadequate.Following Aquino, we require an appropriate imbalance effect.The imbalancing effect must be equiproportional in all industries.So, the Aquino at the 5-digit level estimates "what the values of exports and imports of each commodity would have been if total exports had been equal to total imports."

HIIT and VIIT Indexes
To determine the horizontal HIIT it and vertical intraindustry trade VIIT it , Grubel and Lloyd 1 indexes and the methodology of Abd-el-Rahaman 16 and Greenaway et al. 17 are used, that is, the relative unit values of exports UV X it , and imports UV m it .Where HIIT it : where α 0.15.When the relative unit values of exports and imports are less than 15%, the trade flows are horizontally differentiated HIIT .The HIIT and VIIT indexes are also calculated with disaggregation at 5-digit Portuguese Economic Activity Classification from INE-Trade Statistics.
In Figure 1, the intraindustry trade between Portugal and the European Union EU is over 50% for the period 1995-2008.For all of the period in analysis, the VIIT is much higher than the HIIT.These values are in accordance with the fragmentation theory.

Econometric Model
The dependent variable used is the IIT Grubel and Lloyd 1 index, HIIT and VIIT indexes at five-digit level of the Standard International Trade Classification SITC .The explanatory variables are country-specific characteristics.The data sources for the explanatory variables are the World Bank Development Indicators 2011 .The source used for the dependent variable was data from INE, the Portuguese National Institute of Statistics.
This study uses a dynamic panel data GMM system .In static panel data models, Pooled OLS, fixed effects FEs , and random effects REs estimators have some problems like serial correlation, heteroskedasticity, and endogeneity of some explanatory variables.
The estimator GMM system GMM-SYS permits the researchers to solve the problems of serial correlation, heteroskedasticity and endogeneity for some explanatory variables.These econometric problems were solved by Arellano and Bond 21 , Arellano and Bover 22 , and Blundell and Bond 23, 24 , who developed the first-differenced GMM GMM-DIF estimator and the GMM system GMM-SYS estimator.The GMM-SYS estimator is a system containing both first differenced and levels equations.The GMM-SYS estimator is an alternative to the standard first differenced GMM estimator.To estimate the dynamic model, we applied the methodology of Blundell and Bond 23, 24 and Windmeijer 25 to small sample correction to correct the standard errors of Blundell and Bond 23, 24 .The GMM system estimator is consistent if there is no second-order serial correlation in the residuals m2 statistics .The dynamic panel data model is valid if the estimator is consistent and the instruments are valid.

Hypotheses and Definition of Explanatory Variables
Hypothesis 1.There is a negative positive correlation between differences in per capita income and IIT and HIIT VIIT .
LogDGDP is the logarithm of absolute difference in per capita GDP PPP, in current international dollars between Portugal and the trading partner.Loertscher  LogEP is a proxy for differences in physical endowments.It is the logarithm of the absolute difference in electric power consumption Kwh per capita between Portugal and its partners.Considering Hypothesis 2, the models of Helpman and Krugman LogDIM is the logarithm of average GDP of the two trading partners.Usually the studies utilized this proxy to evaluate the potential economies of scales and the variety of differentiated product.A positive sign is expected for the coefficient of this variable see, e.g, Greenaway et al. 17 LogDIST is the logarithm of geographical distance between Portugal and the partner country.Following the most empirical studies, we use kilometres between the capital cities of the trading partners.According to the literature, we expect a negative sign Badinger and Breuss 32 , Blanes 33 , Cieślik 34 , and Faustino and Leitão 11 .

Model Specification
We consider that where IIT it stands for IIT, HIIT, or VIIT, meaning Total, Vertical, or Horizontal Portuguese IIT index, and X is a set of explanatory variables.All variables are in the logarithm form; η i is the unobserved time-invariant specific effects; δt captures a common deterministic trend; ε it is a random disturbance assumed to be normal, and identically distributed with E ε it 0; Var ε it σ 2 > 0. Following the empirical work of Hummels and Levinsohn 29 , we apply a logistic transformation to IIT, HIIT, and VIIT because these indexes vary between zero and one.LOGISTIC IIT Ln IIT/ 1 − IIT .The same transformation is made for HIIT and VIIT.
The model can be rewritten in the following dynamic representation:

Estimation Results
Table 1 presents summary statistics for each variable.LogDGDP, LogEP, LogDIM, and LogDIST appear to have only little differences.However, this is not the case for the indexes of LogIIT, LogHIIT and LogVIIT.Before estimating the panel regression model, we have conducted a test for unit root of the variable.Table 2 presents the results of panel unit root test ADF-Fischer Chi square .
The most important variables such as the intraindustry trade LogIIT , horizontal intraindustry trade LogHIIT , vertical intraindustry trade LogVIIT , electric power consumption LogEP , economic dimension LogDIM do not have unit roots, that is, are stationary with individual effects and individual specifications.
In Figure 2 we can observe the distribution of intraindustry trade.Table 3 reports the determinants of IIT using a GMM system estimator.All explanatory variables are significant at 1% level LogIIT t−1 , LogDGDP, LogEP, LogDIM, and LogDIST .Our model presents consistent estimates, with no serial correlation m2 statistics .The specification Sargan test shows that there are no problems with the validity of instruments used.As expected for the Lagged dependent variable LogIIT t−1 the result presents a positive sign, showing the changes in IIT have a significant impact on long-term effects.The difference between per capita incomes, in logs LogDGDP , presents a positive sign.We can infer that countries have dissimilar demand.Following Falvey and Kierzkowski 5 , we introduced one proxy for the difference in factor endowments electric power .The variable, electric power in logs LogEP presents a positive sign.As Portuguese IIT is mainly vertical intraindustry trade VIIT , this is consistent with the neo-Heckscher-Ohlin trade theory, that is, the differences in physical endowments promote the IIT.
The coefficient economic dimension LogDIM has a significant and a positive effect on IIT.This result confirms the importance of scale economy and product differentiation.We can conclude that economic dimension influences the volume of intraindustry trade.The geographical distance LogDIST has been used as a typical gravity model variable.A negative effect of the distance on bilateral IIT was expected and the results confirm this, underlining the importance of neighbour partnerships for all trade.
The Table 4 presents the results using the horizontal intraindustry trade equation.The model presents consistent estimates, with no serial correlation m2 statistics .The specification Sargan test shows that there are no problems with the validity of instruments used.As expected for the Lagged dependent variable LogHIIT t−1 the result presents a positive sign.So we can infer that the changes in horizontal intraindustry trade have a a significant impact on the long-term effects.The absolute difference in electric power consumption LogEP is statistically significant, with positive sign.We can conclude that countries have dissimilar factor endowment.As expected, the variable LogDIM average of per capita GDP between Portugal and the partner consider has a significant and positive effect on trade.Therefore, the intensity of HIIT is positively correlated with the similarity in per capita income between trading partners.The coefficient of LogDIST geographical distance is negative as expected.The studies of Balassa and Bauwens 35 , Badinger and Breuss, 32 , Blanes 33 , Cieślik 34 , H. Egger and P. Egger 36 also found a negative sign.
In Figure 3 we present the distribution of horizontal intraindustry trade.Vertical intraindustry trade estimates are report in Table 5.All explanatory variables are significant.The results are according to previous studies.The model present consistent estimates, with no serial correlation and Sargan test validates the instruments used.
The hypothesis for economic differences between countries DGDP in logs presents a positive sign and is significant at 1% level.Falvey and Kierzkowski 5 suggest a positive effect of income difference on VIIT model.Kimura et al. 9 found positive relationship between income difference and VIIT for parts and components trade.We can conclude that VIIT occurs more frequently among economies that are dissimilar, that is, differentiation by quality of products.
In Figure 4 we can observe the distribution of vertical intraindustry trade.The coefficients electric power consumption EP and the economic dimension DIM are consistent with the expected sign.The result confirms that VIIT can be explained by Heckscher-Ohlin theory.
The difference in electric power consumption per capita LEP reflects the difference in endowments between Portugal and its trade partners.Regarding the hypothesis for   The null hypothesis that each coefficient is equal to zero is tested using one-step robust standard error.t-statistics heteroskedasticity corrected are in round brackets.P values are in square brackets; * * * / * statistically significant at the 1 percent and 10 percent levels.Ar 2 is tests for second-order serial correlation in the first-differenced residuals, asymptotically distributed as N 0,1 under the null hypothesis of no serial correlation based on the efficient two-step GMM estimator .The Sargan test addresses the overidentifying restrictions, asymptotically distributed X 2 under the null of the instruments' validity with the two-step estimator .The null hypothesis that each coefficient is equal to zero is tested using one-step robust standard error.t-statistics heteroskedasticity corrected are in round brackets.P values are in square brackets; * * * / * statistically significant at the 1, and 10 percent levels.Ar 2 is tests for second-order serial correlation in the first-differenced residuals, asymptotically distributed as N 0,1 under the null hypothesis of no serial correlation based on the efficient two-step GMM estimator .The Sargan test addresses the overidentifying restrictions, asymptotically distributed X 2 under the null of the instruments' validity with the two-step estimator .The null hypothesis that each coefficient is equal to zero is tested using one-step robust standard error.t-statistics heteroskedasticity corrected are in round brackets.P values are in square brackets; * * * / * statistically significant at the 1 percent, 5 percent, and 10 percent levels.Ar 2 is tests for second-order serial correlation in the first-differenced residuals, asymptotically distributed as N 0,1 under the null hypothesis of no serial correlation based on the efficient two-step GMM estimator .The Sargan test addresses the overidentifying restrictions, asymptotically distributed X 2 under the null of the instruments' validity with the two-step estimator .the geographical distance on VIIT, the empirical result support the idea that the gravity model is important to explain vertical intraindustry trade between partners.

Conclusion
The objective of this paper was to analyze the main determinants of intraindustry trade in automobile sector.The IIT between Portugal and the European Union countries is over 50% for the period 1995-2008.For all of the period in analysis, the VIIT is much higher than the HIIT.These values are in accordance with the fragmentation theory.The Lagged dependent variables LogIIT t−1 , LogHIIT t−1 , and LogVIIT t−1 are positive and less than one.So we can infer that the changes in intraindustry trade, horizontal and vertical IIT have a significant impact on the long-term effects.
The Linder theory considers that a difference in per capita incomes explains intraindustry trade and their components HIIT and VIIT .The variable LogDGDP used to evaluate the relative factor endowments presents a positive impact on IIT, HIIT and VIIT.In fact the decision of multinational corporations is associated with different factors as in localization, skilled labour and economies of scales.
In relationship to the variable differences in physical capital endowments LogEP , our results validate the hypothesis: VIIT occurs more frequently among countries that are dissimilar in terms of factor endowments.Our research confirms that fragmentation of production in the automobile sector is explained by the Heckscher-Ohlin.The difference in factor endowment allows showing that fragmentation is associated with vertical differentiation of products.This reveals that the decision-making of multinational corporations are based in reducing production costs; showing the importance of globalization to explain the phenomenon of fragmentation or outsourcing.
For the variable size of the market average of GDP , the study suggests that Portugal has size to attract this type of industry.In fact, the Euro Zone countries considered in the econometric analysis show that the removal of tariff and nontariff barriers promoted the increase of intraindustry trade with special focus on the VIIT.In future studies it will be interesting to extend our sample.
According to the literature we expected a negative sign to geographical distance.Usually the literature attributes a negative sign to geographical distance, that is, trade increases if the partners are geographically close.The findings support this hypothesis, that is, the gravity model are important to explain the composition of trade IIT, HIIT and VIIT within partners.
have allowed validating the conceptual model of Jones and Kierzkowski 7 .Empirical studies 8-11 have focused primarily on vertical products differentiation vertical intraindustry trade .The research of Ando 8 and Kimura et al. 9 validated the fragmentation and vertical intraindustry trade VIIT in East Asian countries.Leitão et al. 10 used a static panel data OLS with time dummies and Tobit model to explain the phenomena of fragmentation.The article of Leitão et al. 10 concluded that vertical specialization is explained by dissimilarities of per capita GDP, factor endowments and geographical distance.The last few years in the literature is emerging new and important developments on the intraindustry trade IIT .The dynamic analysis GMM system for intraindustry trade was introduced by Faustino and Leitão 18 .This analysis was also used by Faustino and Leitão 18 and Leitão 19 .

Figure 1 :
Figure 1: Trade between Portugal and European Countries for the period 1995-2008.

Hypothesis 3 .
4 and Hummels and Levinsohn 29 suggest a negative effect of physical endowment on IIT.Zhan et al. 31 use the absolute difference in electric power consumption in examining IIT for China.Zhang et al. 31 found a negative sign to IIT.The findings of Leitão 19 show a positive sign to VIIT.The economic dimension influences the volume of trade positively.
and Wolter 26 suggested a negative sign for the IIT model.Hypothesis 1, was formulated based the Linder 27 theory.Linder 27 considers that countries with similar demands have similar products.So, the Linder hypothesis suggests a negative sign for the IIT model Helpman 28 ; and Hummels and Levinsohn 29 .Regarding Hypothesis 1, Loertscher and Wolter 26 and Balassa 30 estimated a negative coefficient.The recent study of Leitão 19 also found a negative sign.The model of Falvey and Kierzkowski 5 suggests a positive impact between income difference and VIIT.The empirical works of Loertscher and Wolter 26 and Greenaway et al. 17 provide empirical support for a negative relation between difference in per capita income and HIIT.Hypothesis 2. IIT and HIIT occurs more frequently among countries that are similar in terms of factor endowments.
a VIIT predominate among countries that are dissimilar in terms of factor endowments.

Table 2 :
Panel unit root test results.