Quarterly GDP disaggregation to monthly levels - Gravity model estimation

[Annamaria Mazzoni]

Dear Forum,

I am currently working on a gravity model to estimate the effects on trade of an exogenous shock. In my research, I need to perform my analysis on a monthly level of detail (the period is 2016-2018). I am using the usual gravity regressors (GDP, distance, etc.). The data on trade (import and export) are already provided at a monthly level, while the data on GDP is only at a quarterly level.

As a first test, I initially tried to transform the quarterly data to monthly through a "naive" equal distribution among the three months of each quarter (M = Q/3). I tried this by assuming that there is a small variation of GDP produced between different months. I then run a simple regression (xtreg) with FE, and I obtained as a result that the beta coefficient of the GDP is negative (e.g.: -0.155), which is obviously wrong.
I have thus realized that this error is driven by the simplistic data disaggregation that I am using. When I tried to run the same regression at a quarterly level I have obtained the expected result (coef. = ~1 for GDP).

I would be extremely grateful if you can suggest a different methodology to disaggregate the GDP data from quarterly to a monthly level that will produce a more reliable and correct result.

Thank you in advance for your help.

Best,

Annamaria Mazzoni

[Andrew Musau]

GDP is a very slow-moving variable. In many cases, we take 5-year averages or 10-year averages to identify its effects. Even if monthly GDP estimates were to be available, I doubt how useful they would be.

[Justin Niakamal]

This can be done using mipolate (SSC) as shown here.

clear

local v = "GDPC1" // Real GDP
!curl -L https://fred.stlouisfed.org/series/`v'/downloaddata/`v'.csv > "`v'.csv"
insheet using "`v'.csv", comma clear
erase "`v'.csv"

gen quarter = qofd(date(date, "YMD"))
gen mdate = mofd(dofq(quarter)) + 1

tsset mdate
format mdate %tm
tsfill
sort mdate
rename value GDP
gen logGDP = log(GDP)

mipolate logGDP mdate, gen(logGDP2) pchip
gen iGDP = exp(logGDP2)


twoway connected iGDP mdate if yofd(dofm(mdate)) >= 2013, ms(+)  || scatter GDP mdate if yofd(dofm(mdate)) >= 2013 , ///
legend(order(1 "guessed" 2 "known"))  xtitle("") yla(, ang(h)) ytitle(GDP, orient(horiz))