Interpretation when dependent and independent variables are percentages

[Jelle Arie]

Dear all,

I have a problem with the interpretation of my dependent variables. My dependent variable is GDP growth and my variable of interest is the change in human capital (HC). I regressed the following:

VARIABLES	GDP	GDP	GDP	GDP
m2	-1.112***	-0.612	0.0418	0.391
	(0.351)	(0.432)	(0.419)	(0.345)
conv2		1.263**	1.238**	1.263**
		(0.562)	(0.556)	(0.573)
c11			-1.971***	-1.198***
			(0.234)	(0.223)
HCchange				-70.29**
				(27.97)
xconst				0.0597***
				(0.0198)
RNNAchange				74.24***
				(4.804)
Constant	3.163***	2.648***	2.627***	0.521
	(0.305)	(0.434)	(0.429)	(0.487)
Observations	1,528	1,491	1,491	1,349
Number of country1	37	36	36	33

I would say that a 1% change in HC leads to a 70% decrease in GDP growth. However, my teacher stated that when HC doubles, GDP decreases with 70%.

GDP is GDP growth per capita (annual %) and the variable HC is the % change per year. Does someone know the correct interpretation?

Thank you in advance for your comments!

Kind regards,

Jelle

[FernandoRios]

Hi Jelle,
Before giving any advice on the interpretation, i would ask if you can provide a simple summary statistics of your data (for the sample you are using. That would help to understand the units of measures of the data.
Fernando

[Jelle Arie]

Hi Fernando,

Thank you for your reply. I don't know if it's feasible, but below you find a summary. I hope it's sufficient.

I calculated the change over the years of the variable HC1. HC1 is a human capital index. So I wonder how I can interpret 'HCchange'.

Kind regards,

Jelle

> -
Variable n Mean S.D. Min .25 Mdn .75 Ma
> x
------------------------------------------------------------------------------
> -
GDP 1203 2.74 3.47 -14.56 1.13 2.67 4.53 23.9
> 4
m2 1624 0.51 0.50 0.00 0.00 1.00 1.00 1.0
> 0
conv2 1624 0.13 0.33 0.00 0.00 0.00 0.00 1.0
> 0
c10 1624 0.15 0.36 0.00 0.00 0.00 0.00 1.0
> 0
HC1 1384 2.79 0.48 1.30 2.50 2.83 3.13 3.7
> 9
HCchange 1355 0.01 0.00 -0.00 0.01 0.01 0.01 0.0
> 4
xconst 1316 5.35 9.42 -88.00 7.00 7.00 7.00 7.0
> 0
RNNAchange 1356 0.03 0.02 -0.02 0.02 0.03 0.05 0
> .14
------------------------------------------------------------------------------
> -

[FernandoRios]

Hi Jalle,
First, i would suggest next time using "code wrappers" next time when posting things like Stata output, so its easier to read.
Second. avg GDP is 2.75 and average HC change is 0.01. The standard interpretation would be, if HC changes in 1 unit. (from 0.01 to 1.01) , GDP would decline in 70%.
However, it is more reasonable to say, if HC changes from 0.01 to 0.02, GDP would decline in 0.7%. This is more reasonable for what you want to explain.
It happens to be, in this case, that the average change is equal to doubling HCchange.
Third. It isnt clear how exactly hcchange is measured. So you will have to take that into consideration to make a better interpretation of the results.
In addition, seems really counter-intuitive that improvements in human capital reduces GDP, but considering you might be using panel data, and with only 30 obs, something else may be explaining those results.
Best
Fernando

[Marcos Almeida]

Unfortunately, we didn’t see what was typed. I assume it was regress. However, if the DV is a proportion, we should consider a glm model under a binomial family and a log link. There are several threads on this topic whose reading may be helpful.

[Jelle Arie]

Hi Fernando,

Thank you for your quick reply! I get it now, thank you

It is indeed strange that human capital causes GDP growth to reduce but it could be due to the limited observations.

If I am allowed to ask you an antoher question, m2, conv2, and c10 are dummy variables where m2 represents membership of the EU. Could you then say for m2 (I know the coefficient is not significant): membership causes GDP growth to increase by 39.1%?

Or is it even better to say that GDP growth will increase by 76.67%? (0.51+0.391/0.51)

Kind regards,

Jelle

[FernandoRios]

So, if m2 is a dummy, as setting aside its not significant, i would say, EU members have in average a GDP growth that is 0.391percentage points higher. Remember that your GDP is measure in percentage points.
SO, say, if GDPGrowth for non EU countries is 2 (percent peryear) , for EU countries your model predicts it would be 2.391%..
I would also be hesitate to say, EU membership causes GDP growth to increase, since causal relationships are much harder to obtain.
HTH
Fernando

[Jelle Arie]

You're amazing Fernando. Thank you!