# How to calculate Debt to GDP ratio quarterly?

I know the formula Debt to GDP ratio = Debt : GDP I have debt quarterly data and GDP (yearly and quarterly). The one that make me confuse is, when i use Debt Q1 2014, for example it wont match with GDP (since GDP is only for 3 months January-March). What type or Which GDP date should i use as denominator, GDP Q4 2013, or GDP Q4 2014?

• What do you mean by saying “it want match GDP (since GDP is only for 3 months January-March)? January-March is literary the first quarter (Q1) April-June is the second quarter (Q2) July-September is the third quarter (Q3) and finally October-December is the fourth quarter (Q4). So you just use the same quarter of debt and GDP.
– 1muflon1
Sep 12 '20 at 12:51
• One is a stock variable, the other is a flow. Any comparison method is somewhat arbitrary. Sep 12 '20 at 12:53
• Let's say GDP of country A is 1000 and debt of country A in 2018 is 200, so debt/gdp of country A on 2018 is 0.2. What i want to count is debt/gdp per 30 march 2019, i have gdp (for 1st quarter) and i have debt until 30 march. So how should i calculate debt/gdp ratio for 1st quarter? @1muflon. (Note: i also have GDP for full year 2019). Sep 13 '20 at 18:52

Debt is a stock variable, measured in dollars. (I will use “dollars” for the local currency for simplicity.)

GDP is a flow, with units of dollars per accounting period.

These two concepts are different, and so any ratio is a convention, without any “correct” answer.

Let’s assume that we want to follow the usual convention, and divide the stock of debt by the GDP generated during time it takes for the Earth to go around the sun. There are a number of standard ways of doing this.

• Take the debt level at the end of the year, divide by the total of GDP for the same year (sum of four quarters). This gives us an annual series.
• For any quarter, take the debt at the end of the quarter, and divide by the rolling 4-quarter sum of GDP.
• For any quarter, take the debt at the end of the quarter, and divide by the annualized quarterly GDP.

One could imagine even more alternatives, such as comparing the average level of debt in the year to annual GDP.

You just choose one, and explain your choice.

• +1. The second bullet is the sensible approach for quarterly updates, at least in normal times. At the end of each year it gives the same as the first, and is sensible for annual figures. But in 2020 the ratio will be distorted by the short-term effects of lockdown on top of the long term effects of extra borrowing and a recession; using the third bullet would only make this distortion worse Sep 14 '20 at 12:37