Causal Modeling of the Effect of Foreign Direct Investment, Industry Growth and Energy Use to Carbon Dioxide Emissions

Application of path analysis for causal modeling has been widely used in many areas of studies, such as in social science, education, biology, medical, sociology, and economics. In this study, path analysis is applied to test a relationship model among variables: Foreign direct investment (FDI), industry growth (IND), energy use (ENR), and carbon dioxide (CO2) emissions. Aims of this study are to know whether there exist direct effect of FDI to IND, direct effect of FDI and IND to ENR, and direct effect of IND and ENR to CO2 emissions. Results of analysis show that there is a direct effect of FDI to IND where the effect is determined as 0.3597; parameter estimate is significant and meaningfulness. There is direct effect of FDI and IND to ENR. Effect of FDI to ENR is identified as 0.2736; parameter estimate is not significant, but the value is still meaningfulness. Direct effect of IND to ENR is −0.4975; parameter estimate is very significant. There is a direct effect of IND and ENR to CO2 emissions. Effect of IND to CO2 emissions is 0.0557; parameter estimate is not significant, but the value is still meaningfulness. Direct effect of ENR to CO2 emissions is 0.9597 where parameter estimate is very significant and meaningfulness.


INTRODUCTION
Causal modeling or path analysis was introduced by Wright (1921;1934) as a method to analyze direct and indirect effects of variables (Pedhazur, 1997). It is noted that path analysis is not a method to find the causes, but a method that can be used for testing causal model which have been formulated by a researcher. Therefore, path analysis is a useful method in testing theory rather than in generating model. It is a method of analysis to test a proposed model formulated by researcher. A system of relationships in the path diagram can be established among all the variables under investigation based on the hypotheses or by empirical grounds (Gilmour, 1978). Path analysis is an extension and application of traditional regression analysis, and data is used in standardize form, which requires additional assumptions but in turn provides additional information about the model under consideration. One of these assumptions is that the variables are linearly related in a causal fashion (Wonnacott and Wonnacott, 1990;Gilmour, 1978). In exchange for the assumption of linear, additive, and asymmetric relationships between variables, correlation between any two variables in the system can be decomposed into direct and indirect effects (Pedhazur, 1997;Loether and McTavish, 1980). It is expressed in terms of the links between them which leads through other intervening variables as well as the direct link between them (Gilmour, 1978). There are some approaches to estimate the parameters in path analysis, some use correlation approach (Pedhazur, 1997) and some use standardized multiple regression equation (Loether and McTavish, 1980;Wonnacott and Wonnacott, 1990). Aims of the application of path analysis is to compare a model of direct and indirect effects that are assumed to This Journal is licensed under a Creative Commons Attribution 4.0 International License be in between variables under study (Loether and McTavish, 1980). Path analysis model are generally illustrated by means of one headed-arrow connection among some variables included in the model (Pedhazur, 1997).
Application of path analysis has been used in many areas of studies, for example in social research path analysis is applied to data collected in social survey on community response to traffic noise in Tokyo (Osada et al., 1997), in transportation research (Gilmour, 1978), in business and marketing (Bagozzi, 1980). Causal models in the study of human biology and genetic can be found in some research conducted by Fields et al. (1996), Vogler (1985 and Phillips et al. (1987). The model can be found in the field of education conducted by Sewell et al. (1970) where the research aimed in explaining occupational attainment of Wisconsin high school students. In the field of sociology research, the model also can be found in some study conducted by Duncan (1966).
One of the advantages of path analysis or causal modeling is the ability to explain direct effect and indirect effect between variables. Path diagram are useful enough as a simple descriptive tool to describe direct and indirect effects of variables in the model. The coefficient p in the path analysis model is meant to quantify the causal impact on one variable to the other variable as connected by an arrow (Russo, 2009). In path analysis model, is was assumed that all variables used in regression model are in standard form, that is with mean zero and variance one. Therefore, the interpretation of the path coefficients is in standard deviation unit (Loehlin, 2004;Pedhazur, 1997;Wright, 1960); given a numerical value of path coefficient p, say the equation is y = px + u, claims that a unit standard deviation increase in x would in p unit standard deviation increase of y (Engelhardt and Kohler, 2009). Carbon dioxide (CO 2 ) emissions increased over past few decades (Goodall, 2007). The problem of massive emissions of CO 2 emissions from the energy used, especially fossil fuels, and their impact has become major scientific and political issues (Safaai et al., 2011). The study of CO 2 emissions has been conducted by many scientists all over the world and has become the concerns of many countries. Knapp and Mookerjee (1996) explored the nature of the relationship between global population growth and CO 2 emissions by using Granger causality. The study about the relationship between energy used and CO 2 emissions also have been conducted by many researchers (Lee and Ryu, 1991;Ruth, 1995;Kandpal, 1998, 1999;Noorman and Kamminga, 1998;Sun et al., 2010).

STATISTICAL MODELS AND METHOD OF ANALYSIS
Causal model of FDI, IND, ENR, and CO 2 emissions is formulated as follows: Based on Figure 1, structural model according to Wonnacott and Wonnacott (1981) can be written as follows: Model 1: IND = p 21 FDI + p 1 u 1 (1) Model 2: ENR = p 31 FDI + p 32 IND + p 2 u 2 (2) Model 3: CO 2 = p 42 IND + p 43 ENR + p 3 u 3 (3) Where, u 1 , u 2 , and u 3 are error terms. Based on the models (1), (2), and (3), there are three null hypotheses which will be tested, namely: (1) There is no direct effect of FDI to IND; (2) There are no direct effects of FDI and IND to ENR; and (3) There are no direct effects of IND and ENR to CO 2 emissions. The error terms can be calculated as follows: Furthermore, besides direct and indirect effects, a total effect from one variable to the other variables will also be calculated. Path analysis suggest that the total effect of one variable, say Z 1 , on another variable, say Z 0 , is defined as the change occurring in Z 0 when Z 1 change one unit of standard deviation, this concept is applied for all the changes in the intervening variables between Z 1 and Z 0 . Therefore, total effect is the sum of all paths following the arrows from Z 1 to Z 0 (Russo, 2009).

Decomposition of Correlations
Advantages of path analysis is considered as a method for decomposing correlation among variables, thereby enhancing the interpretation of correlation. One of the interesting applications of path analysis is the analysis of correlation in its components. Within a given causal model, it is possible to determine the part of a correlation between two variables because of the direct effects and the part which is due to indirect effect (Pedhazur, 1997 To find composition of correlation r 13 and r 23 , from model (2), both sides of model (2) (6) Second, both sides of model (2) is multiplied by IND and then expected values are taken such that, So that, r 23 = p 31 .r 12 + p 32 = p 31 .p 21 + p 32 r 23 = p 31 .p 21 + p 32 (7) To find composition of correlation r 24 and r 34 , from model (3), both sides of model (3)

RESULTS AND DISCUSSION
Data that used in this study are FDI (World Bank, 2019a), industry (Including infrastructure) annual % growth (IND) (World Bank, 2019b), energy used (kg of oil equivalent percapita) (ENR) (World Bank, 2019c), CO 2 emissions (metric tons per capita) (World Bank, 2019d). First step before data analysis, data are transformed into standardized form within mean zero and variance one.
From analysis of data for model (1), results are presented in Table 1.
From Table 1, to test null hypothesis whether there is no direct effect of FDI to IND, the F-test = 6.24 with P = 0.0165, therefore the null hypothesis is rejected, there is a direct effect of FDI to IND. R-squares = 0.1294, this means that 12.94% of the variation of IND can be explained by the model. From Table 2, the estimated parameter in model (1) is p 21 = 0.3597.
To test partial parameter of model (1) (to test Ho: p 21 = 0), it is calculated that t = 2.50 with P = 0.0165 and the null hypothesis is rejected. The value of p 12 = 0.3597 >0.05 which according to Land (1969) and Heisse (1969) and Pedhazur (1997) is meaningfulness. Figure 2 indicates positive trend which is in line with the value of estimated parameter, p 21 = 0.3597. Graph shows that if FDI increases, IND also increases. Therefore, according to Land (1969) and Pedhazur (1997), FDI has direct effect to IND. If FDI increases one standard deviation, IND will increase 0.3597 standard deviation. The error is identified as, p 1 = − = 1 0 1294 0 9331 . . .   From analysis of data for model (2), results are presented in Table 3.
From  Land (1969), Heisse (1969) and Pedhazur (1997), is still meaningfulness, therefore it is not needed to be deleted from the model. To test Ho: p 32 = 0, calculation presented that t = −3.38 with P = 0.0016 and the null hypothesis is rejected. Therefore, there are direct effects of FDI and IND to ENR. Analysis of data for model (3) are presented in Table 5.
Testing of null hypothesis whether there are no direct effect of IND and ENR to CO 2 emissions, Table 5 presents result as F-test = 152.54 with P ≤ 0.0001, therefore null hypothesis is rejected, so there are direct effects of IND and ENR to CO 2 . R-squares = 0.8815, which means 88.15% of the variation of CO 2 emissions can be explained by the model. From Table 6, the estimated parameters in model (3) are p 42 = 0.0557 and p 43 = −0.9597. To conduct partial test of the parameters in model (3), to test Ho: p 42 = 0, it is determined as t = 0.95 and P = 0.3347, so the null hypothesis is not rejected. But the value of p 42 = 0.0557 >0.05 which, according to Land (1969), Heisse (1969) and Pedhazur (1997), is still meaningfulness, therefore it is not needed to be deleted from the model. To test Ho: p 43 = 0, it is determined that t = 16.377 with P = 0.0001 and the null hypothesis is rejected. Therefore, there are direct effects of IND and ENR to CO 2 emissions.
According to Figure 5, contour fit plot of model (3)

Direct, Indirect, and Total Effects and Decomposition of Correlation
Correlation between variables and estimation of causal model are given below:    From the analysis, it is found that the estimated model (1) is Where unexplained variation is p 1 1 0 1294 0 9331 = − = .
Direct effect of FDI to IND is p 21 = 0.3597, this means that for everyone if standard deviation increases in FDI, IND will increase by 0.3597 standard deviation.
Equation (11) shows that there are direct effects of FDI and IND to ENR, the effect of FDI (p 31 = 0.2736) is positive and based on the "meaningfulness" criteria of Land (1969) and Heisse (1969), p 31 >0.05. Effect of IND (p 32 = −0.4975) is negative, very significance, and meaningfulness. From the path diagram ( Figure 6), the effect of FDI to ENR can be decomposed into direct and indirect effects as follows: Direct effect p 31 = 0.2736 Indirect effect p 21 .p 32 = (0.3597) (−0.4975) = −0.1789 Total effect p 31 + p 21 .p 32 = 0.0947 While the effect of IND to ENR has only direct effect as p 32 = −0.4975. The direct effect is negative.
Correlation between IND and ENR, r 23 = p 31 .p 21 + p 32 , can be explained as shown in Table 9.
Correlation between ENR and CO 2 (r 34 = p 42 .p 31 .p 21 + p 42 .p 32 + p 43 ) can be explained by Table 11. and −0.4975 respectively. FDI also has indirect effect to ENR, where the indirect effect is −0.1789. IND and ENR have direct effect to CO 2 where the direct effect of IND to CO 2 and ENR to CO 2 are 0.0557 and 0.9597 respectively. IND also has indirect effect to CO 2 emissions, where the indirect effect is −0.4775. Path analysis also has been used to explain correlation between variables by decomposition of correlation into direct and indirect components, where this study explains decomposition of correlation between FDI and IND,between FDI and ENR,between IND and ENR,between IND and CO 2 , and between ENR and CO 2 emissions.