# Energy Consumption and Financial Development in NAFTA Countries, 1971-2015
## 3 Econometric Models  
Following the empirical literature, this article considers energy consumption (\(EC\)) as dependent on financial development (\(FD\)), Gross Domestic Product (\(GDP\)), the consumer price index (\(CPI\)), urbanization (URB), and trade openness (\(TO\)), and it can be expressed as follows:  
\[EC_{it}=\beta_{0 it}+\beta_{1i}FD_{it}+\beta_{2i}GDP_{it}+\beta_{3i}CPI_{it}\quad +\beta_{4i}URB_{it}+\beta_{5i}TO_{it}+e_{it}, \tag{1}\]where \(i\) indicates the cross section (the three countries), \(t\) is the time period of the data, and \(e_{it}\) represents the error term. The parameters \(\beta_{1}\), \(\beta_{2}\), \(\beta_{3}\), \(\beta_{4}\), and \(\beta_{5}\) represent the long-term elasticity of financial development, \(GDP\), prices, urbanization, and trade openness with respect to energy consumption, respectively. It is expected that \(\beta_{1}<0\) because incremental change in financial development can generate a decrease in energy consumption. When the coefficient \(\beta_{2}>0\) is positive, an increase in the level of economic activity generates an increase in energy consumption; when \(\beta_{3}<0\), a negative relationship between the price level and energy consumption is expected. \(\beta_{4}>0\) (or \(\beta_{4}<0\)) can be positive or negative, and it is difficult to determine the sign. On the other hand, \(\beta_{5}<0\), can be negative if the trade of more efficient goods and services helps to reduce energy consumption. One of the important problems in the time series are spurious regressions, so it is essential to verify the order of integration and prove the existence of long-term cointegration relationships between the study variables. However, the econometric literature suggests that unit root tests in panel data have greater power than unit time series root tests. That is, when combining cross-sectional data and time series, there are some advantages, such as the following: a greater number of observations, more degrees of freedom, more variability, less collinearity, and greater efficiency [24]. The most commonly used unit root tests with panel data include the tests of [PERSON], [PERSON], and [PERSON] (LLC) [25], [PERSON], [PERSON], and [PERSON] (IPS) [26], Fisher-type tests using ADF (Fisher-ADF) and PP (PP-Fisher) [27; 28]. The traditional tests mentioned above would not be adequate in the case of cross-section dependence. It is very important to apply unit root tests that generate consistent results in the absence of independence and heterogeneity in all countries of the panel [29], for which we also apply the two tests suggested by [PERSON] [30]. If the variables are cointegrated, the most common Ordinary Least Squares (OLS) technique to estimate the coefficients of panel data models turns out to be biased and produces inconsistent estimates. New methods for estimating cointegration relationships using panel data, such as the Fully Modified OLS (FMOLS) and Dynamic OLS (DOLS) estimators [31; 32; 33]. These approximations produce estimators of coefficients that are asymptotically unbiased and normally distributed [32; 33]. [PERSON] [32] argues that the FMOLS estimator behaves relatively well and even in small samples, it generates consistent estimates and allows controlling the endogeneity of its regressors and the serial correlation. Due to the above, this research will use both FMOLS and DOLS estimators for cointegrated heterogeneous panels. [PERSON] [34] points out that if the variables are cointegrated, there must be a causal relationship in at least one direction, so it is necessary to apply the causality test to determine the direction of causality between the variables. The heterogeneity of cross-sectional units is one of the important topics in the panel data econometrics, and this article considers a new proposal that has a standardized panel statistic with good properties in small samples.