Interpretation of coefficients when dependent variable is in % of GDP

[Anne Tholen]

Hello everyone,

I have a question that is more statistical than specific to Stata, but I hope it will still be accepted here, since this community has proven to be extremely helpful to me before.

I am conducting various fixed effects regressions, where the dependent variables are all in terms of percentage of GDP (General government expenditure on different socio-economic functions). My explanatory variable of interest is a dummy variable, taking the value of one in years when a legislative election takes place.

Now to take one of my regressions as an example, I find a coefficient of 0.029 on the election dummy variable. The p-value is 0.014, making the coefficient significant at the 10% level. The descriptive statistics of my dependent variable are the following: mean=1.782, standard deviation=0.472.

Is the following interpretation correct?: In an election year, government expenditure increases by 0.029 percentage points when compared to non-election years. This implies that in election years, one can observe an 1.627 percent increase in expenditure on this socio-economic function (calculated as 1.782+0.029/1.782).

I am wondering whether this interpretation is statistically correct and economically reasonable here.

Best regards,
Anne

[Mads Moring]

Hi Anne Tholen

Would you kindly attach a regression output? From where I'm standing it sounds about right, although remember it's an average - and Ceteris paribus.

[Anne Tholen]

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
	GF01	GF02	GF03	GF04	GF05	GF06	GF07	GF08	GF09	GF10
Elections	0.160	-0.006	0.029*	0.022	0.010	0.026*	-0.002	0.015	0.046*	0.026
	(0.124)	(0.014)	(0.014)	(0.120)	(0.013)	(0.011)	(0.036)	(0.011)	(0.018)	(0.039)
COFOG(-1)1	0.478**	0.679***	0.733***	0.194***	0.673***	0.368	0.751***	0.727***	0.657***	0.791***
	(0.164)	(0.052)	(0.034)	(0.048)	(0.066)	(0.201)	(0.061)	(0.043)	(0.050)	(0.026)
Ln Real GDP pc	-0.955	-0.065	-0.126	-0.548	0.006	0.338	0.206	0.183	-0.086	-1.072*
	(1.060)	(0.168)	(0.122)	(1.200)	(0.123)	(0.342)	(0.283)	(0.114)	(0.178)	(0.450)
Real GDP growth	-0.032	-0.000	-0.003	-0.077	-0.004	-0.003	-0.023	-0.005	-0.027**	-0.155***
	(0.025)	(0.005)	(0.005)	(0.039)	(0.005)	(0.007)	(0.015)	(0.003)	(0.009)	(0.014)
Population 15-64	2.156	-0.078	-2.072	-16.502	0.551	-3.049	-5.027	-1.153	1.414	-3.600
	(8.104)	(1.124)	(1.332)	(18.805)	(1.307)	(3.555)	(3.151)	(1.273)	(1.657)	(3.842)
Population 65+	8.268	0.788	-1.549	-18.543	1.621	-4.166	-7.051	-0.478	-1.501	-4.971
	(10.608)	(1.393)	(1.263)	(13.322)	(1.759)	(4.073)	(3.448)	(1.656)	(2.814)	(7.778)
Eurozone	0.022	0.034	-0.028	-0.213	-0.002	0.092	0.012	0.015	-0.050	-0.150
	(0.117)	(0.032)	(0.042)	(0.233)	(0.019)	(0.059)	(0.042)	(0.033)	(0.046)	(0.100)
Output gap	-2.085	0.728*	0.784	6.389	1.314	0.169	-0.150	0.464	1.548	7.841*
	(2.738)	(0.339)	(0.842)	(9.229)	(0.966)	(1.003)	(1.320)	(0.475)	(1.098)	(2.869)
Constant	11.019	1.076	3.297***	23.268	-0.426	0.017	3.892	-0.573	1.905	17.050***
	(8.054)	(1.328)	(0.780)	(12.921)	(1.107)	(1.708)	(2.684)	(0.724)	(1.565)	(4.273)
N	520	520	520	520	520	520	520	520	520	520
R2	0.597	0.880	0.897	0.205	0.814	0.133	0.917	0.710	0.916	0.932
Note. Cluster robust standard errors in parentheses. p-value of tests * p < 0.05, ** p < 0.01, *** p < 0.001 1. COFOG(-1) shows the estimate of the lagged dependent variable in each column respectively.

[Jeff Wooldridge]

Anne: It appears that your dependent variable is a percent rather than a proportion (people mix these up all the time). Therefore, your interpretation is correct.


Do you really mean your p-value is .014? If so, you are rejecting at much smaller than the 10% level. t looks like the standard error is .014 in column (3), which means the coefficient is significant at the 5% level.

[Anne Tholen]

First of all sorry, for the late reply. I actually had solved the issue by looking at your textbook Mr. Wooldridge, so it is almost bizzare to me to have you answer here :D
Secondly, you're right about the significance level. From other publications I had in mind that one * always represents the 10% level. Looking at the Note under the table, however, revealed to me that Stata used the 5% level as default for one * here.

Again, thank you very much for your feedback!