I have addressed this issue in my earlier comments. What do you mean by "good" May there is no long-term causality given your data. There is always some chance that it is not evident in your aggregated data.

There is no econometric method which can help to find out causalities without theory. In your equation, you mix-up two different concepts, demand and supply-side economics. From a Keynesian viewpoint, exports increase directly GDP of the same period, as does any internal demand. As, in general, also imported inputs are used for the production of exported goods, the GDP-eefect is accordingly lower. If the export "shock" is unforeseen and/or only short-run, it will not induce additional investment. If the increased export demamd is expected to exceed production capacity for a longer term, then it will lead to increased investment in following periods, thereby increasing GDP of these periods. In any case, additional income is created, and there will be a multiplier effect (dependent on how this income is distributed). As consumption and investment may react with lags to income, one will likely come to an equation like

dY = a*dX+b*dX(-1)+c*dX(-2)+.......(d is the first absolute difference)

But one could also estimate a small model with 3 endogenous variables (dC, dI, dY), where the last dY=dX is definitional. The advantage of a more detailed model is, that it can give more information on the magnitude of the coefficients and therefore make interpretation more easy.

In a New Classical model, production (=GDP) is determined by the supply of labor (dependent on the utility maximum (U=U(C,L) and the capital stock, according to a production function. Assuming a Cobb-Douglas production function, the regression equation is simply dlnY=a*dlnL+b*dlnK+c.

Respected Arize

Good means to obtain the required results through that method. Sir I have your paper and I have read that paper but you have derived the causality in multivariate framework. However, it short run, from individual from variables we able to obtain causality. but in long-run, the t-statistics value of ect show the causality from all variables including in the model. In addition, i want the long-term causality from exports only how i obtain it. this is my question either the strong causality as see in your paper as well as in many other paper is the long-term causality or it is something else. please comments on this point also. I am thankful

Regards

Irshad

@Respected Sayed, I was about to go to bed when I saw your question. Turning to your question:

You cannot obtain that because cointegration deals with a linear combination. Nevertheless, you can indirectly infer if you can have a ECT(-1) that is statistically significant based on WALD test  and also ECt(-1)  is Yt-1) X(-1)  and X(-1) is significant. To be clear, you can approach it from Hendry type modelling by entering  ECt not as a single variable.

thanks alot for valuable suggestions

Sorry for disturbance. One more question: what you mean by linear combination. Can the theory not support the linear combination between exports and gdp. Here i am modify my question link i want the long-term causality between exports and Real GDP please tell how i derive it please comments in detail

A Theory could support linear combination between real exports and real GDP, and you could try testing for that. But, you open your work to criticisms of omitted variable misspecification. That is, the results you found are because you have omitted some variables. That is, why I suggested that you show your multivariate results using ECT (-1) and indirectly confirm that exports Granger cause GDP by applying Hendry's approach. Maybe I will have an assistant send you more stuff on this. Today is a busy day and am not well at all. 

Sir thanks for kindness. Your answer is very valuable and raised very good points. Sir how i applied the hendry's approach i applied please send me the stuff and provide me the detail procedure. i am using Eview software. Sir i am stuck in my dissertation Please guide me in detail I am very thankful to you. Please sir comments on hendery's approach how it is applied and how it is derived in eview

Please refer the attached files where Hendry's approach is illustrated and this full document can be found in the paper "Exchange Rates, Policy Convergence, and the European Monetary System, by Ronald MacDonald and Mark P. Taylor. The Review of Economics and Statistics.

Chuck is, of course, right, if he points to the problem of omitted variables. Changes of GDP can have innumerable causes. Nevertheless, it is important to have a model before applying an econometric method. The direct effect of X on GDP is clear: As X is a compnent of GDP, an increase of X of one unit brings a one unit increase of GDP. But, in general, inputs are needed to produce dX, a part of which is imported. This dM may be very different for different exported goods. By the way, I do not take into account here that stocks may play a role (on both sides). The next question is the effect on income (in sum and distribution). If the price of exports is low and that of imported inputs is high, the effect on total income could be minor.  With distribution the model would become to complicated to be econometrically tractable. To hold it simple, I would propose a simple model:

Y=C+I+G+X-M

C=c0+c1*Y+c2*Y(-1), one could also take Y-tax instead of Y

M=m1*C+m2*I+m3*G+m4*X

(proposal: all varaibles in first differences)

It is no problem to solve this model and to calculate dY for dY holding I and G constant (i.e. dI=dG=0). As a next step one can simulate a certain effect on I of future periods, which is more a philosophical than an econometric question.

Respected Rainer

thanks for your kind corporation. Really appreciated your response and i will work on this type model in next time to see the export and growth nexus.

Regards

Irshad