The exchange rate effect is mainly depdndent on the composition and the measurement (n LC, $ or in relation to GDP or population) of external debt. I think that real exchange rates are not important in this respect. For cross-sectional analyses one should be cautious to use the usual trade opness definition, because this variable depends strongly on the size of countries. Small countries' import and export are likely much higher.

I also do not understand, why inflations should have much influence on external debt (unless, may be, via the exchange rate.

One should also take into acount possible different determaants for public and private debt.

The macro estimate of external debt is directly computed from the national accounts (expenditure table) identity. Y = C + G + I + X - M

S = Y - C -G , => S = I + X - M or S - I = X - M where S - I is the internal gap and X - M is the external gap.

Y = GDP, C= Household Consumption, G = Gov't Expenditure, I = Private Investment, X = exports and M = imports

Hence some countries follow an export promotion policy where exports are greater than imports to offset government spending.

Other countries will follow an import substitution policy to develop domestic industry .

Fred's hint on the National Accounts identities is important, because it shows, that the difference between exports and imports will likely explain much more than the sum of the two variables (as % of GDP) conserning the development of external debt ED). This link is easy to test: dED= a*X-M +u, where a should be significantly near 1 and u near 0. Nevertheless, in practice, there may be much more influences., i.e value changes because of changing exchange rates, interest payments, repayments, direct investments, emigration or immigration of creditors etc. Before a more comprensive estimation, one should put enough effort in a good specification of the model. One has to pay attention to possible multicollinearities. Example: Exchange rates will likely affect X and M (supposedly in different directions), but they will also have a direct effect on ED by changing its "value".

Thanks for Anton Rainer and Fred Campano comments.

Actually, in my project, there is one variable. So the total independent is four variables. I used macro accounting estimates, precisely the three sectoral balances from Godley (and Wray).

the results were good. R2 square is more than 95% and passed all the classical tests from the panel data.

I doubted my result because I didn't use Log/LN for my ExchRate (LCU/$). My worries about the min-max were too high. (Min:1 Max:14000).

some friends advised me to use Log/LN, which will distort my last result.

actually my Dependent parameters in $ (real values), just like ExchRates. I didn't use any d.ED and d.ExchRates. I thought it was a data transformation.

If you are looking at several countries it is better to use a consistent conversion to dollars. The data set for this is the United Nations Statistical Office GDP by Expenditure in constant 2015 US dollars. It is available to 2021,but 2022 should be appearing soon. This data is comparable across countries. The IMF offers the same data as the UN with a slight modification on the trade of precious metals. Do the work in constant dollars and do not try to predict the exchange rate of each country. It is better to do scenarios about the future exchange rate in each country based upon what the countries' options may be.

Thank you so much, Sir.

Using LCU/$ (Local Currency Unit per Dollar) as the measure of exchange rates in your analysis is not inherently wrong. It is a commonly used measure in economic research and can provide valuable insights into the relationship between exchange rates and external debt.

However, there are a few considerations to keep in mind:

1. Scaling: When exchange rates vary widely across countries, it may be challenging to compare the magnitude of the effect of exchange rates on external debt directly. For example, a change of 1 LCU/$ may have a different economic impact in a country where the exchange rate is 1 LCU/$ compared to a country where the exchange rate is 10,000 LCU/$. In such cases, you might consider using a logarithmic transformation (such as Log or LN) of the exchange rate variable to normalize the data and facilitate meaningful comparisons.

2. Interpretation: The interpretation of the coefficients in your regression model will depend on the chosen unit of measurement for the exchange rate variable. Using LCU/$ as the unit will provide you with information on the change in external debt associated with a one-unit change in the exchange rate. On the other hand, if you use the logarithmic transformation, the coefficients can be interpreted as elasticities, representing the percentage change in external debt corresponding to a 1% change in the exchange rate.

Ultimately, the choice between using LCU/$ or a logarithmic transformation depends on the specific objectives of your analysis, the characteristics of your data, and the interpretability of the results.

Mohannad Alobid's recommendation is important for understanding the debt in term's of international concerns. I would add that further clarification of the debt from a domestic point of view is gained when the debt is expressed in Purchasing Power Parity (PPP). This helps adjust between the US$ version of the debt and the local buying power.

To use absolute values or its logs in a regression must not be made dependent on the dimension of the variables, but only on the functional relation between the explaining and the dependent variable. If you assume a linear relationship like Debt = a0 + a1*ER +...., it is not allowed to use ln(ER). For an exponential relation one should, of course, not use ER but ln(ER).

Nevertheless, I fear that your model is misspecified. It seems that you estimate a linear relation between extDebt (how measured?) ER, Inflation (%-change of CPI) and TradeOpenness. Apart from that the last two variables (I think) have only a minor (unclear) effect on extDebt, this approach can only deliver spurious results. I think you should put much more effort into a good specification of the model/equation you want to estimate. This could also help you to handle the different dimensions of ER between countries.

Interesting discussion from Mr. Alobid, Mr. Campano, and Mr. Rainer. ​

Using LCU from various countries will certainly provide different results in the meaning of PPP. Apart from that, using LN means we don't use original data, which has advantages and disadvantages. The first advantage is normality.

But, using real data allows us to predict the future with the data we have. Isn't it?

For example: we have the regression Y = a + b1X1 + b2X2 + e.

We can predict Y in the future with data X1 and X2.

For forecasts, it is not necessary to use real (obviously you mean original, i.e. non-transformed) data. If, for example, you have a function lnY=a+b1*X1+b2*lnY2 or Y=a+b1*lnX1+b2*X22 or any other similar function , you can, in principle, estimate a, b1 and b2 by OLS (with sufficient data), but for a forecast of Y you need forecasts of X1 and X2. To find an appropriate function and feasible data transformations is one main aim of the model specification.

By the way, I do not understand the advantage of (which?) normality when using logs.

What is your measure of external debt: million or billion US-$, EUR or Local currency, per capita, percent of GDP or....? Because the effect of ER-changes will be rather different dependent on how debt is measured.

Apart from that, I think that the trade balance (= exports-imports; see Fred's irst reply) and interest rates are much more important explaining variables than inflation and trade openness.

The normality I mean is one of Classical assumption.

I measure the external debt with Million of USD. Thanks for your advice about the variable.

I have never heard of normality as a classical assumption for log-transformations.

What concerns extDebt in million USD, I see no relation between the $-ER and this debt level. Why should e.g. France (EUR as LC) with an ER of 0.9 per US-$ have a higher or lower extDebt than Japan with about 145 Xen/$ or Hungary wth about 350 Forint/$?

Another example: Some years ago, Croatia changed from Kuna (about 7/$) to the EURO. Do you think that this change has changed its debt level?

every LC/$ increase the ED by millions of dollars. Note that all countries can form a linear regression.