# IRF interpretation

Hi,

My impulse response shows that 1$increase in government investment (shock at time 0) increases output by 0,4$ at time 0
0,7$after 1 year 1,03$ after 2 years
1,3$after 3 years 1,5$ after 4 years.

My question is what is the total increase in output in 4 years as a result of 1$increase in government consumption at time 0? Here is my calculation: 0,4+0,7+1,03+1,3+1,5 = 4,93$. Is this correct?

Best, J

Alternatively, we could say that:

1 p.p. increase in G_0/Y_0 at time 0 increases output by
0,4% at time 0
0,7% after 1 year
1,03% after 2 years
1,3% after 3 years
1,5% after 4 years.

My question is: which output is increased at time t=1?

At time=0 output Y_0 increases by 0,004Y_0. So we have Y_0_new=1,004Y_0.

But what happens at time t=1? Which of the following two cases is correct?

Case 1:
Y_1 = 1,007*Y_0

or

Case 2:

Y_1 = 1,007*Y_0_new.

Best, J.

Unless your Y is in growth rates, the deviations are from Y_0 and do not cumulate, i.e case 1 is correct.

Here are the results I want to interpret:

See p. 10 Figure 1.1

The methodology is explained on p. 8.

That is from a local projection. The specification suggests that still case 1 is correct.

Thank you very much for the answer.

Now, suppose that country’s G/Y ratio is 0.25, where G=9.000.000.000 EUR and Y=36.000.000.000 EUR. 1 p.p. increase in G/Y, i.e. delta G =360.000.000 EUR would generate (according to the estimated multipliers presented above) total increase in GDP amounting to 1.863.000.000 EUR in 4 years. In my opinion, this is very high. What do you think?

People usually calculate cumulative multiplier which takes into account the persistence of the shock. Am I right?

To calculate the cumulative multiplier, we would need the impulse responses for Y as well as the impulse responses for G. Am I right?

Then the cumulative fiscal multiplier would be calculated as:

sum of the impulse responses for Y/sum of the impulse responses for G. Am I right?

Yes, people more often consider the cumulative multiplier
\frac{\sum_{t=0}^h\Delta Y_{t,0}}{\sum_{t=0}^h\Delta G_{t,0}}

1.) If I understand correctly, in the paper the authors report the following multipliers:

delta Y_{t0+n}/ delta FI_{t0},

i.e. the multiplier in a future period n is the ratio of change in output in time t0+n to
an exogenous change in the fiscal policy instrument (FI) at time of impact t0.

According to the estimates, 1$increase in government investment (shock at time 0) increases output by 0,4$ at time 0
0,7$after 1 year 1,03$ after 2 years
1,3$after 3 years 1,5$ after 4 years.

Am I right?

2.) Further, the authors state that:
Four years after an unanticipated shock to government investment spending of 1 percentage point of GDP, the level of real output is 1.5 percent higher, which corresponds to a medium-term fiscal multiplier of about 1.4.

How do the authors calculate the value of 1.4? Does this value correspond to the cumulative multiplier calculated as:

sum delta Y_{t0+i}/sum delta FI_{t0+i}, where i=1,2,…n?

Thank you very much!

Sorry, but only the authors of the original paper can answer that question as there seem to be not details in their paper.