Multipliers with log-data in first differences

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Posts: 3
Joined: Tue Jul 14, 2015 5:58 am

Multipliers with log-data in first differences

I estimated fiscal multipliers (via Blanchard and Perotti decomposition) in levels, which is suggested by mentioned authors even if series are I(1). And I mostly got estimates that are broadly in line with relevant literature.

However, for the sake of robustness check, I want to test how would my results change if I imply the same procedure, but instead of using log levels, I will use log of first differences. This is, in the end, how textbook on time series taught us so, compared to the empirical literature (Blanchard and Perotti (2002), Perotti (2004),. etc.) => if variables are non-stationary (for example, I(1)), we should make them stationary - by calculating first differences. Problem is also that even on the internet, I couldn't find any paper at all that deals with estimation of structural VAR with log-data in first differences, with a goal to calculate multipliers.

All in all, my question is: how can multipliers, calculated by structural VAR with log-data in differences, be interpreted? (For log-data in levels it is easy -> if you increase X by one unit, what is the change in Y). And also, is there any particular reason why I couldn't find any paper dealing with this issue?

dakila
Posts: 350
Joined: Tue Nov 24, 2015 4:57 pm

Re: Multipliers with log-data in first differences

Just accumulate the impulse response function.

Posts: 23
Joined: Sat Dec 05, 2009 5:56 pm

Re: Multipliers with log-data in first differences

Hi. I see the thread below. I am trying to compute the following for the SVAR and the VECM that I have estimated:

1. Multipliers
2. Elasticities, for instance the elasticity of real GDP to shocks to tax cuts or real government expenditures.

I thought multipliers are coefficients that enter the impulse response computation as the latter includes a shock (say one sd). However, dakila seems to suggest that we simply add up the impulse responses. Any comments?

As for elasticities, if the multiplier is Dy/DX (assume levels, can I interpret it this way here?) seems to me I should multiply this by y/x to get the elasticity?

If original endogenous variables are in LNs then the multiplier would be Dln(y)/Dln(x), thus an elasticity? Does that mean the impulse responses in LNs are elasticities?

Thank you for any help. Best, BA