Understanding and interpreting the large coefficients of control variables in my results table

[James Sonela]

Hi,

I am running a panel regression with a DiD setup and fixed-effects. I have obtained significant results for the years that I am interested in. However, there is one thing that worries me. Although my did estimators (interaction btw post & treated) have negative and significant coefficients (which proves my hypotheses), their impact might be dwarfed by the larger impact of the control variables (GDP Growth, INFLATION, UNEMPLOYMENT, RATES). For instance, the impact of rates are 17 (?) which seems very large compared to my did estimator. My dependent variable is loan growth.

I made sure that each of them scaled to the same style (i.e., loan growth = 0.02, gdp growth = 0.01 etc.)

Now, while I am writing this post, I realized what might be an issue. My dependent variable is loan growth which is calculated as annual % changes between years. But the control variable interest rates is not. They are the average duration of 10Y Government Bond yields in a given year (i.e, 2016 = 1%, 2017 = 2. this control variable is not calculated as % changes from year to year). On the other hand, the coefficient of GDP growth is rather small. Perhaps this is because it is calculated as the growth between the GDP between years. So it is consistent with the dependent variable.

I am confused about interpreting this result and would like to receive your valuable insights.

dependent variable: loan growth	(1)	(2)	(3)
VARIABLES	2019	2020	2021
did_estimator_2019	-0.0487***
	(0.0161)
post2019	0.0186*
	(0.0112)
GDP Growth	0.234***	0.230***	0.237***
	(0.0765)	(0.0763)	(0.0756)
UNEMPLOYMENT	2.644***	2.491***	3.071***
	(0.343)	(0.351)	(0.360)
INFLATION	2.148***	3.240***	1.828***
	(0.293)	(0.609)	(0.288)
INTEREST RATES	17.55***	16.18***	17.33***
	(1.024)	(0.751)	(0.696)
did_estimator_2020		-0.0353***
		(0.0119)
post2020		-0.0140
		(0.0111)
did_estimator_2021			-0.0224*
			(0.0121)
post2021			0.0416***
			(0.00482)
Constant	-0.418***	-0.389***	-0.434***
	(0.0213)	(0.0127)	(0.0129)
Observations	2,227	2,227	2,227
R-squared	0.535	0.535	0.543
Number of ID	373	373	373

[Emil Alnor]

James Sonela large coefficients are not a problem per se. As I don't know your data in detail or the theory you are using, I cannot provide you with very specific guidance on your guidance, however I think the following generic advice may be useful: as a beginners guide, interpreting coefficients in regression tables involves three things (assuming that data and design are dealt with): 1) direction (negative/positve), 2) significance level and importantly but often omitted 3) size of coefficient. It seems what worries you is, that the size of the coefficients of your variable of interest is small relative to that of the control variables. I would advice you to take some steps in order to assess the size of the coefficients of your variable of interest in itself. This could include:
1) what is the change of the expected value of the dependent variable, when the indepedent variable goes from observed min to observed max (or 25. percentile to 75. percentile). Use your substantive knowledge to assess whether this is substantial (e.g. what would this change mean in the real world).
2) how many standard deviations does the expected value of the dependent variable change, when the independent variable changes 1 standard deviation. Use your substantive knowledge to assess whether this is substantial.

As a side note, most philopsophy of science scholars would say that you cannot prove you hypotheses. You can find support for it.