Why Quarterly GDP Growth Cannot Determine Monthly Growth
Summary
The document explains why a quarterly growth rate does not uniquely determine the growth rates in its three constituent months. Compounding means the monthly rates multiply to produce the quarterly rate, giving one constraint for three unknowns. Dividing the quarterly percentage by three is therefore an assumption, not a deduction from the data.
It illustrates two possible assumptions: equal monthly growth, or a linear change in growth from a known prior month. Each produces a different monthly path consistent with the same quarterly total. The examples show how added assumptions or observations can make an estimate possible, but the document does not assess which assumption fits real GDP data best. Its central limitation is that quarterly observations alone leave many possible monthly patterns; a more reliable estimate would need additional information or a justified modeling choice.
Key ideas
- A quarterly growth rate constrains the compounded product of three monthly rates.
- The quarterly observation alone cannot identify each month's growth rate.
- Dividing a quarterly percentage by three assumes a particular monthly pattern.
- Equal growth and linearly changing growth are examples of assumptions that yield different estimates.
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# Estimating monthly GDP growth based on quarterly data # 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? ## Answer by Attack68 (score 1, accepted) https://quant.stackexchange.com/a/46060 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.
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