The case that you propose is really special and, despite my extensive experience in the field of index number, not ever anything like it: you're sure you have not made miscalculations?

Assuming that your index is measuring flexibility properly than the interpretation is the same as the coefficient on any other explanatory variable. It is the partial derivative of the dependent variable wrt the index number with a few caveats. 1. Your number seemes to be discreet (more like a Likert scale than an index number) this may or. may not be an issue of importance to you and may need to be delt wit in hour estimation (OLS assumes continuous variables).  2. An index number is unique only up to a scaling, so the magnitude of the coefficient on an index number is arbitrary. 3. Also, have a think about any omitted variables. 

Your question "which is better" would be very difficult to answer given provided information. You don't even provide the dependent variable. 

Suppose the index number ranges from 1-15, where the 1= pure fixed exchange rate system and 15= pure floating exchange rate system. If we move from 1 to 15, then the index shows that we are moving from fixed to flexible exchange rate system. For instance, the flexibility of 2 is smaller than the flexibility of 3 and so on. Now if we want to regress the growth rate on this index number with other regressors and the coefficient of this index number becomes negative, then can we say that flexible exchange rate is better, or, fixed exchange rate is better for growth?

Gioacchino de Candia

Logan James Kelly

Monir Ahmed

So your problem is not related to statistics and even the regressors/index numbers report.

It is to decide whether, for the economic growth of your country, is better a flexible or fixed exchange system.

In a country like Bangladesh it could be preferable to a fixed system, as long as the Central Bank adopts a stable economic and financial policy and the medium to long term.

However, the speech is very complex and leads to many facets to be exhausted in this place.

Some regressions require commenting of coefficient signs only and not magnitudes. It now depends on the appropriateness of the model used. Also important to note, is your variable magnitude in relation to other variables used, otherwise data transformation may be required. It is still not clear enough to give conclusion, but keep checking on regression principles if they are not violated.

It basically depends upon the nature of relation between the variables under study. 

Dear Mohir,

Your interpretation of the sign is alright, ceteris paribus. A serious issue is whether the index numbers are actually continuous because that interpretation assumes so.

One more question you need to answer, these are indices of what? You seem to worry about the negative sign as though you expected a positive one! If that is the case, you need to consider causes of endogeneity. It is possible that the effect of the index is drifted by simultaneity in the model. Consider all the possible interrelationships among your variables and control for them. 

See how it behaves. But if you said fully what you are doing, I think experts here would be of better help.

Regards,

MS

Given that the higher value indicates greater flexibility and the lower value indicates greater rigidity.

Now, If the coefficient is negative then the interpretation will ab as follows:

"" Negative coefficient with higher absolute value indicates greater flexibility in opposite direction and negative coefficient with lower absolute vale indicates greater rigidity in op posit direction."

A Negative coefficient shows a very high rate of flexibility while a lower value indicates a very high rate of rigidity

Index number is a measure of average (overall) change in a group of related variables.

It is to be defined clearly what is coefficient of index.

A positive coefficient indicates that as the value of the independent variable increases, the mean of the dependent variable also tends to increase. A negative coefficient suggests that as the independent variable increases, the dependent variable tends to decrease.