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

On the upper side, this study can open up a new stream of literature in this field,
with a methodological framework to be followed and expanded upon in future
studies. The remaining of this paper is structured as follows: Section 2 lays out the
empirical strategy and describes the dataset. Section 3 reports the estimation results.
Finally, Section 4 concludes.
1. Methodology and Data
Our empirical strategy consists of two fundamental components. First, we employ
the rather conventional existing techniques of exploratory factor analysis [There are many
good references on the general mechanics of factor analysis. Consult, for example, Vincent (1971) and Jae-
on and Mueller (1978) for an excellent treatment of the subject. Hamilton (2006) is recommended for
practical implementations on STATA]. Consider a generic function , where
are unobserved random variables and is a set of observable random variables with

means . Applying the generic formula to our study, the dependent variable becomes
the bilateral exchange rate, – the industry-specific trade balance volumes, and – the

unobserved common factors. The relationship between and is indirect, with the
factor matrix being the intermediary step. Our dimension reduction technique (factor
analysis) will reduce the matrix to , thus bridging the association gap.

Further, suppose that for some unknown parameters and the unobserved
variables , with and , and for every , we impose:

Where are the error terms with zero mean, , and finite but
heteroskedastic variance. The variance of is set at and is defined as:

Where is a diagonal matrix with all entries outside the main diagonal
THE JOURNAL OF ECONOMIC SCIENCES: THEORY AND PRACTICE, V.72, # 2, 2015, pp. 4-22
equal to zero. For simplicity, we can rewrite (1) in the following manner:

Where capital is the matrix of the of the unobserved coefficients .

Now, we assume that we have observations so that the dimensions of the matrix
components can be represented as , , and . Matrix is static across all
cases, while columns and are observation-specific. We impose three binding

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