Joint coefficients

[Burak Turgut]

Dear Statalist users,
This is my first post here and sorry in advance if the post does not fully comply with the advices on posting.

I run the following regression:
ivreg2 lfood self_employed_1 self_employed_1#i.year log_income_diff age agesq lnhh housesq i.year (lperm = private_car sex)

I have the following regression output:

lfood	Coef.	Std. Err.	z	P>z	[95% Conf.	Interval]
lperm	.2890392	.0059375	48.68	0.000	.2774019	.3006766
self_employed_1	.03577	.0073481	4.87	0.000	.021368	.0501719
self_employed_1#rok
1 2005	.0082357	.010991	0.75	0.454	-.0133062	.0297776
1 2006	.0190306	.0107994	1.76	0.078	-.0021358	.040197
1 2007	.007384	.0106777	0.69	0.489	-.0135438	.0283119
1 2008	.0069638	.010619	0.66	0.512	-.013849	.0277767
1 2009	.0049704	.0105409	0.47	0.637	-.0156893	.0256301
1 2010	.0025309	.0101807	0.25	0.804	-.0174229	.0224848
1 2011	-.0074874	.0102216	-0.73	0.464	-.0275215	.0125466
1 2012	.0129113	.0102845	1.26	0.209	-.0072459	.0330685
1 2013	.0061358	.010411	0.59	0.556	-.0142694	.0265411
1 2014	.0287141	.0104055	2.76	0.006	.0083198	.0491084
1 2015	.0187668	.0104033	1.80	0.071	-.0016233	.039157
1 2016	-.0033278	.0102994	-0.32	0.747	-.0235142	.0168587
1 2017	0	(omitted)

The interaction coefficients for self_employed_1*i.year are not statistically significant 2005, 2007-2013, and 2016. So, effect of self_employed_1 on lfood is same in these yars and the base year (2017).
However, when I use lincom, the joint coefficients of these interaction terms with self_employed_1 is statistically significant at 1% level. For example for year 2005, I have:

(	1)	self_employed_1 + 1.self_employed_1#2005b.rok =	0
	lfood Coef. Std. Err. z P>z	[95% Conf.	Interval]
	(1) .0440057 .0082907 5.31 0.000	.0277561	.0602552

My question is the following:
How should I interpret these results? Should I interpret there is no change of under-reporting in year 2005 relative to the baseline year 2017 because the interaction coefficient is not significant and impact of self_employment_1 on lfood in year 2005 is .03577?
Or should I look at the results from lincom and say the impact of self_employment_1 on lfood in year 2005 is .0440057?

I am little confused and your help would be greatly appreciated.
Thank you.

[Phil Bromiley]

Welcome to Statalist. Please try to follow the FAQ on asking questions-provide Stata code in code delimiters readable Stata output, and sample data using dataex.

The interactions between year and self-employed appear to be statistically insignificant in most years. This means you cannot reject the hypothesis that there are the same, which is different than saying they're actually the same.

Suppose the parameters on the interactions were all zero. Then the main effect would be the effect for all the other years. That is why you get a significant coefficient when you add the main effect and the effect for 2005 – the main effect is significant and the effect for 2005 doesn't seem to make a difference.

Remember, the true parameter for every year is the main effect plus the parameter for that year's interaction. I would test the joint hypothesis that all of the interactions with the years equal zero. If you cannot reject this, then it gives you a justification for not including the year interactions. However, you may get a significant interaction because of 2014 and 2015. One of the problems with entering all these year dummies is that it becomes exceedingly hard to interpret. Is there something unusual about 2006, 14, and 15? Sometimes people include continuous interactions with year #c.year) Instead of including interactions with dummies for each year.