# Estimating monthly GDP growth based on quarterly data

Apologies for this newbie question. Given the following quarterly GDP growth:

Quarter      %
---------------
2017-01-01  3.9
2017-04-01  4.2
2017-07-01  4.8
2017-10-01  5.1
2018-01-01  4.3
2018-04-01  7.6
2018-07-01  4.9
2018-10-01  4.1


How can I estimate the monthly growth? just divide the percentage by three?

• These look to me like annualized figures. – Alex C Jun 12 at 4:23
• I took these figures from CCAR historic data – ps0604 Jun 12 at 12:30
• CCAR documentation says: "The three variables for each country or country block: the percent change (at an annual rate) in real GDP, the percent change (at an annual rate) in the CPI or local equivalent, and the level of the U.S.dollar exchange rate.". – Alex C Jun 12 at 13:37
• So how do I convert to monthly values? divide by 12? – ps0604 Jun 12 at 13:57

Suppose your (first) Quarter on Quarter growth rate was 3% and that spanned 3 months and you want to know how much each month grew. That is you want to know the growth rate for Jan, Feb and Mar, call them $$\alpha, \beta, \gamma$$.

The only information you have is that:

$$(1+\alpha)(1+\beta)(1+\gamma) = 1 + 3\%$$

This is one equation for 3 unknowns and therefore has 2 degrees of freedom. You have an unlimited number of potential solutions.

### One possible solution..

If you choose to make the assumption that the growth rate in each period is the same then then you have 1 equation for 1 unknown, and this implies that:

$$(1+\alpha)^3 = 1 + 3\% \qquad \implies \qquad \alpha = 0.99\%$$

### A second possible soultion..

If you knew that December's growth rate was, say, 0.4% and you assumed there was linear increase in growth across all 3 months this would form a different set of equations:

$$(1+\alpha)(1+\alpha+x)(1+\alpha+2x) = 1 + 3\%$$
$$\alpha-0.4\%=x$$ (this is the change from Dec to Jan)

This implies that: $$(1+0.4\%+x)(1+0.4\%+2x)(1+0.4\%+3x) = 1+3\%$$ and $$x = 0.295\%$$

so under this assumption the growth rates in Jan, Feb and Mar are 0.695%, 0.99% and 1.285%.

Basically you can't create information from nothin so you have to form your own assumptions.