PPMLHDFE Interpretation of constant

[Noemi Seng]

Dear Community,

I'm doing a ppmlhdfe regression on bilateral FDI data on a destination country-origin country-sector-year level. My regression command looks like this:

local gravity_sectorlevel lngdp_o lngdp_d lndistw lnsumgdp
ppmlhdfe TotalassetsthUSD `gravity_sectorlevel', absorb(year destination_country_sector origin_country_sector) cluster(country_pair_encode)

My question is: How can I interpret the constant (of approx. -50) in my regression results? I have read that with ppmlhdfe, the constant is always the base category of the dummies, however, I have not included dummies in my regression except for the fixed effects, which are absorbed, though. Would you simply ignore the constant, then? What, if I did include a dummy as a regressor, e.g. member of EU. Would I then have to combine its coefficient somehow with the constant coefficient to interpret it correctly?

Thank you very much in advance!

These are my regression results:

HDFE PPML regression No. of obs = 260,825
Absorbing 3 HDFE groups Residual df = 3,901
Statistics robust to heteroskedasticity Wald chi2(4) = 142.91
Deviance = 7.87706e+11 Prob > chi2 = 0.0000
Log pseudolikelihood = -3.93854e+11 Pseudo R2 = 0.8285

Number of clusters (country_pair_encode)= 3,902
(Std. err. adjusted for 3,902 clusters in country_pair_encode)
------------------------------------------------------------------------------
| Robust
Totalasset~D | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
lngdp_o | 1.231354 .4589419 2.68 0.007 .3318448 2.130864
lngdp_d | 2.041791 .2959249 6.90 0.000 1.461789 2.621793
lndistw | -.475572 .0712738 -6.67 0.000 -.6152662 -.3358779
lnsumgdp | -.5925919 .1389968 -4.26 0.000 -.8650206 -.3201632
_cons | -52.90519 17.3977 -3.04 0.002 -87.00405 -18.80633
------------------------------------------------------------------------------

Absorbed degrees of freedom:
----------------------------------------------------------------------+
Absorbed FE | Categories - Redundant = Num. Coefs |
------------------------------+---------------------------------------|
year | 11 0 11 |
country_dest_sector_encode | 1766 1 1765 |
country_origin_sector_encode | 2043 34 2009 ?|
----------------------------------------------------------------------+
? = number of redundant parameters may be higher

[Joao Santos Silva]

Just ignore the constant; it is basically meaningless.

[Noemi Seng]

Dear Joao Santos Silva

many thanks for your response. What if I include dummies in my regression (e.g. now I have included dummies for secondary and tertiary sector). I would like to interpret the coefficients of those dummies and say sth like "In the secondary sector - compared to the primary sector - the FDI stock is by x larger". To determine this "x", I need to consider the constant, but I'm not quite sure how to calculate the difference in the outcome variable by dummy category. Could you help me with this maybe?

Best wishes
Noemi

[Joao Santos Silva]

Dear Noemi Seng,

I do not think you need the constant; from the coefficient of the dummy you can get the percent difference, just use the usual formula 100*[exp(b)-1]%.

Best wishes,

Joao

[Noemi Seng]

Dear Joao Santos Silva


thank you very much. And - just to make sure that I understand it correctly - when I have an interaction term between e.g. the secondary sector dummy and GDP as well as between the tertiary sector and GDP, the main effect for GDP (without interaction) would be the effect of GDP in the primary sector (as the base category)? And the coefficients on the interactions represent the differential effect in the secondary (tertiary) sector? If such a coefficient on the interaction term was, let's say, 0.8, how to interpret this number when I want to interpret it as the difference to the base category? In the secondary sector, the effect of GDP on the FDI stock is by (exp(0.8)-1)*100=122.55 % larger than in the primary sector?

Best
Noemi

[Joao Santos Silva]

Dear Noemi Seng,

The case of interactions with GDP is different. Presumably GDP is in logs, so the coefficient on GPD is the elasticity for the primary sector, and the sum of that with the coefficient on the interaction between GDP and the secondary sector dummy is the elasticity for the secondary sector. Does this make sense?

Best wishes,

Joao

[Noemi Seng]

Dear Joao Santos Silva

this makes sense. Strictly speaking, I have included GDP in levels as I estimate with PPML, but we interpret it as if I had included it in logs, correctly? However, can I now only interpret the coefficient on GDP (elasticity for primary sector) and the sum of this coefficient with the coefficient of the interaction term (elasticity of secondary sector)? Is there no way I could interpret the coefficient on the interaction term on its own, hence the difference between the elasticities of primary and secondary sector?

Best
Noemi

[Joao Santos Silva]

Dear Noemi Seng,

Please note that regressors such as GDP should be logged; what we do not log is the dependent variable. Yes, the coefficient in the interaction is the difference in elasticities.

Best wishes,

Joao

[Noemi Seng]

Dear Joao Santos Silva

oh of course, thanks for the hint; I got mixed up there. GDP is logged. OKay, so if the coefficient on the interaction is let's say 0.8, I would say the elasticitiy of GDP is by 0.8 larger in the secondary sector than in the primary sector. I do not use percentage neither do I have to transform the coefficient on the interaction in some way?

Thank you
Noemi

[Joao Santos Silva]

If it is an elasticity, you do not need to transform :-)