# Converting Annual GDP Growth Rate into Monthly GDP Growth Rate

I am researching the effects of Euroarea fiscal stimulus on inflation expectations during the crisis. The data for fiscal stimulus is given as an annual percentage of GDP, e.g. 1.5% of Euro Area GDP in 2009.

Therefore, I am not sure if I could convert it to monthly data (by simply assuming 1.5% in every month for 2009) to show the effects of this stimulus on inflation expectations during this particular period.

P.S I need monthly data as my data for inflation expectations is monthly.

Can someone help with this please? Thanks.

• What is the 1.5%? Is it the amount of fiscal stimulus (injected at one point or during a period)? Or is it the estimated effect of fiscal stimulus on GDP? If it is the latter, then I would be careful about assuming that the effect of fiscal stimulus was distributed evenly over the months. It's unlikely that by pure chance this was indeed the case, unless you have some other information telling you that. Feb 24 '15 at 10:00
• Hi, thanks for your comment. The 1.5% is the total amount of stimulus injected in 2009 (during the 12 months) Feb 24 '15 at 10:51
• So you would like to assume that the stimulus was injected in even amounts over the 12 months? I think this is a strong assumption. You had better try locate some monthly (or even finer) data for the execution of the stimulus instead of making this strong assumption. Also, inflation expectations could be mostly affected by the announcement of stimulus. If the announcement is credible, why should anyone react to its implementation if it fits with what was announced? Feb 24 '15 at 12:59
• My idea was that if the stimulus for 2009 was 1.5% in 2009 in the Euroarea, I would find the month that it was announced (eg. June) and use this value of fiscal stimulus as a proxy. The problem lies in the fact that since I am analysing the Euroarea as a whole, and fiscal stimulus is implemented with differing amounts between each member state, I would need a total figure for the Euroarea (as my data for inflation expectations correspond to the Euroarea as a whole) Feb 24 '15 at 13:11
• I don't quite understand... If you have stimulus for Euro area as a whole and inflation expectation for Euro area as a whole, what is the problem? The two seem to match each other alright. Also, you could benefit from updated the original post with all the relevant details you revealed in the comments. Then it would be easier for others to follow and contribute. Feb 24 '15 at 13:32

I don't think you can do this. See the following counter example. Assume the GDP at the beginning of 2009 was $100$. If it grew 1.5% every month, it would have been equal to $100\cdot1.015^{12} = 119.56$ at the end of 2009. However, since it grew 1.5% over the whole year the actual value at the end of 2009 was $101.5$. In order to get the correct average monthly compounding growth rate, you need a different approach.
Let $r$ be the average monthly compounding growth rate, $GDP_B$ the GDP at the beginning of 2009 and $GDP_E$ the GDP at the end of 2009. Then, the following holds: $GDP_E = GDP_B \cdot (1+r)^{12}$. So you need to rearrange this in order to get the correct $r$:
$GDP_E = GDP_B \cdot (1+r)^{12} \\ GDP_E/GDP_B = (1+r)^{12} \\ r = (GDP_E/GDP_B)^{(1/12)} - 1$
This means you get $r = (101.5/100)^{(1/12)} - 1 = 0.00124148771$.