With ARDL cointegration (the bounds tests approach), why is the dependent variable stated in first differences in software such as Eviews? Please explain as simply as possible - my algebra is terrible.
The ARDL bounds test is based on the error-correction representation the involves combinations of differenced and levels (not differenced) variables. In this representation the levels (not differenced) variables only appear on the right-hand side of the model and therefore the dependent variable (on the left-hand side of the equation) is differenced. All differenced variables should be I(0) given the model assumes a maximum order of integration of each variable as 1. The (F) bounds test seeks to determine whether or not the combined levels (not differenced) variables on the right-hand side of the model are (jointly) I(0).
That is depend on behaviour of data for long term and its stationary test not on the software system
Dear Lars,
ARDL bond test is based on the analysis of combination of variable at different levels. It's a major combination of I(0)and I(1) variables.
Majorly, the differences variable I(1) appears on the left and represented as the dependent variable while the variable at levels I(0) appears on the right side and represented as the independent variable.
Regards
Conventionally, in the ARDL model, the variables are expressed in lags not first difference. But, their expression at level or first-difference depends on underlying theory, which essentially guides the intuition of the researcher. Generally, there are three variants of ARDL:
The first is the standard variant where all the variables are expressed in level form with no clear distinction between the short-run (SR) and the long-run (LR). This assumes that the relationships only exist in the LR, but you can still reparametrize to separate the SR from the LR model.
In the second variant, the variables are expressed in both level (LR) and first-difference (SR) forms, implying that the underlying theory supports the existence of both the short and long-run.
In the third variant, all the variables, with the exception of the error correction term (ECM), are expressed in first-difference; implying that the researcher is only interested in the SR as may be suggested by the underlying theory, but he or she can still differentiate between the SR and the LR if necessary (a classical case of the Augmented short-run model).
The ARDL Bounds Testing Approach is all encompassing regardless of which variable is I(0) or I(1). It is, therefore, not compulsory that your dependent variable must be expressed in first-difference. If E-views does not support a chosen variant of ARDL, you can easily move to other packages like STATA or to an integrated econometric and statistical software (OxMetrics) depending on the intuition of the researcher and in line with the theory underpinning the research.
