using an econometric model and the gap between the black market rate and official rates and inflation as explanatory variable (gap is > 60%).
In my experience, you will need to adjust the model for the country (or countries) you are studying. That happens because black market is highly influenced by conjunctural factors, and patterns tends to be self-correlated (the gap may also be influenced by the black market structure, if it is getting stronger or not, and so on).
What I would do is the following:
(1) plot both official and black market exchange on a X-Y dispersion graph;
(2) Verify if they seems to have the same progression (if they are both linear or exponential, for example);
(3) assuming they do have similar progression pattern, with different wave patterns, I would build a linear model, using the variables you pointed out. So, it would be: Ebm = A + B (Eof) + C (Inf); where Ebm is black market exchange rate, Eof is official Exchange rate, and Inf is inflation. If both R² and DW are solid, and the others statistics tests show good results, I would keep the model. But I am betting that you will probably find a low DW. In that case I would follow some additional steps:
(4) I would take the residuals from the last model, and divide them by the observed black market exchange rate. Then I would plot the graph. This graph is called: Oscillatory Profile. This kind of graph allows you to manually identify conjunctural variations, where negative values (or positives) tends to follow one another. I would mark what were the years (or months, or days, whatever you are using) where the same conjuncture appears;
(5) Then I would build a model using a dummy to lessen the effect of conjunctural variations. If needed, I would use more then one dummy, although I would avoid that if possible. The model would be: Ebm = A + B (Eof) + C (Inf) + D (Dummy1).
(6) If, on this new regression I have solid statistical tests, I would proceed to forecast, using a multiple scenarios method.
Bare in mind, proper forecasting outcomes for unstable variables a very hard, and tend to give more a general tendency than a solid result. For a better result, you will have to put lot of effort on it. And use it wisely, avoiding to claim you found a definitive prediction or anything like that.
Dear Mohamed,
Steve Hanke has circulated a recent letter on his research on Venezuela's currency. He found that "changes in the black-market exchange rate can be reliably transformed into accurate measurements of countrywide inflation rates." I attach his file.
BLACK MARKET is part if the informal sector. There is no such a thing as data integrity of the black market. Whatever data it is, it is an estimate at best. Unless all black market participants volunteer their data, then a model may be used. The proposed data for black market is not supportable, the basic characteristic of data integrity: current, complete, accurate and relevant...may not be there. A model based on data lacking integrity is far from being or may be "optimal." It might not be such a thing as optimal model even in a nonblack market. In case of black market or under ground, it most likely is non-existent.