Main Question: How are the coefficients of the second-order differenced explanatory variables to be interpreted? (See the attached screenshot of my result.)
- I examine the determinants for capital in- and outflows of country x for the period Q1.1990-Q4.2007.
- Quarterly data are seasonally-adjusted and outliers are corrected.
- The different scales of various macroeconomic variables are corrected using "scale" function in R. Specifically, the column means of variables are subtracted and the (centered) variables are divided by their standard deviations.
- To make my time-series data stationary the second-order differencing was necessary.
- The regression analysis was successful in the sense that the sign of the variables of interest was as expected and the statistical significance was also confirmed.
The attached screenshot is a result of my regression analysis. The dependent variable is capital export of country X. EX_GIIPS is exports of goods from country X to GIIPS countries. IM_GIIPS is imports of goods from GIIPS countries to country X.
Aside from other explanatory variables, how should the coefficients of these two variables be interpreted? I'm well aware of what the second-order differencing does: (𝑋𝑡−𝑋𝑡−1)−(𝑋𝑡−1−𝑋𝑡−2) as Ben formulated in the hyperlinked discussion above.
My current interpretation is very general: "A positive relationship between capital exports from country x and exports of goods from country x to GIIPS countries for the period Q1.1990-Q4.2007 can be confirmed at conventional significance levels."
Can this interpretation become more specific? What I imagine is like the clear-cut interpretation of log-first difference which approximately corresponds to the growth rate... This is the first time I needed the second-order differencing and fail to interpret the coefficients precisely...
Any idea is welcome! Thanks!