Yes, impulse response function and forecast error variance decomposition both can be used.

What is the level of your study? Macroeconomic or microeconomic?

in a specific case you might use some theory about this, but more in the field how smes and men’s behave in international supply chains. But more qualitative research

I think you can use the impulse response function for this purpose.

I do not understand, why autoregressivity should have an important role for explaining the effect of exchange rate movements on import prices. I think a simple DL (without AR) approach (which could be seen as a IRF approach) will be sufficient.

I think that in his answer Anton Rainer has his reasons and the results that will be obtained will be will be sufficient. Perhaps the purpose of the analysis will determine what is sufficient and whether it is necessary to examine the autoregressivity in explaining the effect of the exchange rate movements on import prices.

IRF can help but clarifying whether it is at the micro or macro level could help in giving precise suggestions.

Yes, IRF is a good tool to complement your studies on ARDL. It provides an understanding of how the the shocks to the exchange rate model will behave.

Thank you for the answers. My study is at macroeconomic level. Some of the literature that I have reviewed uses ARDL method.

I think that many econometricians use ARDL, although there is no reason to assume feed-backs, mainly because it looks more scientific than simple diagrammatic approaches, correlations and OLS, and to replace own thinking. Therefore, it is no surprise to find it often in the literature.

What is the meaning of "macroeconomic level" in this study. The main (only?) independent variable(s) is(are) exchange rates, which seem to be more micro than macro. They concern every exporting and importing firm and everyone who buys from or travels to other countries. On the import price side, the effects are likely to be different for the prices of different imported goods and services. This means one should choose a level between micro and macro (i.e. an overall import price indicator or deflator should not be taken as the only dependent variable).

This is an extension of Anton Rainer 's answer. Different markets will respond in different ways to exchange rate changes and you need to look at these rather than the macro position. even if you get good results from you proposed analysis it will be very difficult to interpret them.

If you consider imported goods prices and prices and exchange rates are measured correctly then the identity

import price = export price in foreign country X exchange rate

for every item traded

Regressions involving

log(import price) = b_1 + b_2 log(export price) +b_3 log ( exchange rate) + lags

will only reveal problems in the calculation of the price indices rather than the pass-through of the exchange rate or in the aggregation methods used.

Your exchange rate is likely to be trade-weighted by country of origin.

Your import price is probably weighted by the currency of the transaction. For example, oil is likely to be priced in US$ rather than country of origin. For that matter, oil is often bought forward at long intervals. In such a case the forward price of the oil is the export price.

Are the index formulae used in the calculation of the indices consistent (Laspeyres, Paasch, Fisher indices)? Are the trade indices unit value indices?

There are probably many other questions relevant to the Indian economy that may impinge on your analysis.

If you can manage to manipulate the exchange rate you may possibly cause some export prices to your country to change. Any apparent non-passthrough is in effect a change in the foreign export price. If you wish to study the effect on the foreign export price you will need to do a very disaggregated analysis. Perhaps looking at oil, some food, or other large markets. This will not be easy

IRF in itself shows how shocks to the system will behave both in the short run or the long run and how quickly the shocks can be absorbed by the system. Using the IRF to explain ARDL results at the macroeconomic level should be possible since ARDL is applicable to both nonstationary time series as well as for time series with mixed order of integration

Impulse Response Function (IRF) is based on VAR or VECM model. It is not a necessary step for ARDL method. Indeed, ARDL does not need to fulfill stationary criteria while VAR requires this precondition. However, you can generate/take IRF for ARDL from VAR or VECM but it will be incorrect when elaborate the results because the estimates will be different. Even if you try to restrict VECM according to ARDL restrictions, the results may not be the same. Please, take care for this. Good luck!

My previous comments related to the data and economics or the problem. I would like to add some comments relating to the econometrics.

I am a little confused about the meaning of an IRF in the context of an ARDL model, If all the variables are stationary the ARDL method estimates the short-run elasticities or marginal effects using OLS. If your model is

y(t) = b0 + b1 y(t-1) + b2 x(t) + b3 x(t-1) (1)

then the long-run marginal effects or elasticities are estimated from this equation by equating the lags of a variable to its current value to get

y = b0 + b1y + b2 x + b3 x

(You probably have more lags and more variables bet the principle is the same). This gives

y = b0/(1-b1) + (b2+b3)/(1-b1) x (2)

and (b2+b3)/(1-b1) is your long run marginal effect or total pass through.

The right-hand side variables must be exogenous for the estimation to be valid. This implies that an impulse is uncorrelated with the explanatory variables. The impulse can not change the explanatory variables.

In a VAR an impulse in one variable feeds into the values of all variables. (All current variables are endogenous). When you have identified your VAT using either structural restrictions or using orthogonalization you can then calculate your IRFs. Note that the IRF's depend on the order in which you present your variables. The orthogonalization is completed silently by your software but you are supposed to determine using economic theory which order is appropriate. If you don't understand try to calculate your IRFs using different orders of your variables in your VAR estimation and see the difference.

If your variables are endogenous the conditions required for the validity of an ARDL estimation are not satisfied.

More complicated variations of these comments also hold for when you have non-stationary variables.

Ambili, it seems that your aim is not to find out effects of exchange rate changes (which exchange rates? which currencies?) on import prices (which import prices? which goods and services?), but to get some exercise in applications of econometric methods. That is ok, but I think that exchange rate-import price-relations are not suitable for ARDL applications, because I assume that the effects of past import price changes on later import price changes are negligible. At least, I find no good economic arguments for such effects.

we should be careful when using non-parametric results either in interpretation or relate to parametric estimation like in this case to ARDL parameters

@Anton Rainer my dependent variable is Aggregate Indian imports in USD. Explanatory variables are.. Crude oil price, domestic cost, foreign cost, domestic demand, foreign demand and Rupee

Ambili, from your original question I concluded that you wanted to estimate import price equations, but, in fact, you try to estimate an import equation. I assume that you have time series for your dependent (imports including services?) and explaining variables. I think, Rupee is the exchange rate vis-a-vis the USD. I do not know what cost variables you use and if these data are reliable. I am surprised, that you do not use an import price (deflator?) apart from the oil price. If you wish to estimate only one equation (e.g. because it is only for exercising econometrics or it should be part of a highly aggregated model), you can, of course, try different methods, but one should start with the simplest ones (diagrams, correlations, OLS). One should split up domestic demand. Public expenditure, construction and private consumption will e.g. likely have lower import propensities than investment in machinery or exports.

If you really want to find a good explanation for Indian imports, it seems preferable to estimate several equations for important import positions. As you include oil price as an explaining variable, I think, that oil imports make a big amount and that you - correctly - assume, that these imports "behave" differently from other imports. This may also be true for other positions.

Whatever procedure you choose, you should first analyse the composition of Indian imports in more detail and try to find out special movements compared with movements of the explaining variables. This can help you to establish a theoretical model which you can test by econometrics.

For imports, too, I find no convincing argument, why imports should have a relevant influence on imports of later periods. Therefore, an application of ARDL does not seem feasible (see e.g. John C Frain's answers).

Thank you for your answer... I will definitely look into the Indian important composition...