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M.R. Jamilov, R.M. Jamilov: Factor-Augmented J-Curve

M.R. Jamilov, R.M. Jamilov: Factor-Augmented J-Curve

rotation convergence. The rotation matrix will report the important values of factor
loadings of each industry on each of the previously extracted factors. We will suppress
small factor score coefficients of below 0.1 in both the baseline and the rotated matrices.
This allows us to focus our vision on the bigger coefficients, which correspond to better
loadings on our extracted factors. Coefficient suppression is a rather common procedure
in factor analysis literature. Finally, we save the rotated score matrix as a group of 9
separated series (in our case, it is the “factorial trade balances”).
The second stage of our estimation strategy employs the Auto-Regressive
Distributed Lag model approach to cointegration, which is best described in Pesaran
et al. (2001). The ARDL methodology is beneficial on several levels and primarily
because it allows us to estimate both the short-run effects and the long-run
cointegrating equation estimates of a given model. In addition, this method solves
the problem of variable endogeneity and the inability to test hypotheses on the
estimated coefficient. Narayan (2005) claims that the performance of the ARDL-
based bounds testing approach in small samples is superior to that of multivariate
cointegration, a claim which is particularly useful for our case due to our small
sample sizes. Moreover, ARDL regressions do not require the variables in the model
to be non-stationary in level forms; ARDL works regardless of whether there exists
a unit root in the regressors or not. However, we will still perform and present
results from the Augmented Dickey-Fuller test (Dickey and Fuller, 1979; 1981). It is
important to ensure that variables are stationary at least in first differences, since I(2)
processes will not work with the ARDL framework.
We can now set up a very simple single-equation trade balance model in its
ARDL form:

Where , stand for the trade balance and the bilateral exchange rate

parameters, respectively. Trade balance is defined as the ratio of exports to imports;
the exchange rate is the ln-transformed USD/YUAN bilateral exchange rate. ,
are the constant and the elasticity estimates, respectively. is the stochastic
component. Small-cased , , refer to the factor, time, and lag-length indexes,

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