I'm confused about what the overall effect of my independent variable, voteshare, on my dependent variables, car1 car2 car3 and car4. Voteshare is related to year, so I ran an additional regression using an interaction between the two. Does the regression without the interaction tell me the direct effect, and the regression with the interaction tell me the indirect effect via the year interaction?
What do the coefficients of the year dummy tell me in both regressions? The interaction regression outputs two sets of coefficients for year.




sum

Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
name | 0
firmid | 304 48.01645 29.19554 1 98
date | 304 19441.88 1381.175 16915 21804
year | 304 2012.855 3.78447 2006 2019
industry | 304 34.95395 18.39782 1 76
-------------+---------------------------------------------------------
voteshare | 304 19.31845 14.06176 .53 91.6
eventday | 304 1 0 1 1
eventid | 304 152.5 87.90146 1 304
car1 | 304 -.0049372 .0422174 -.2426251 .1450617
car2 | 304 -.0059204 .0497666 -.315154 .2163311
-------------+---------------------------------------------------------
car3 | 304 -1.86e-06 .0801375 -.4143263 .3033057
car4 | 304 -.0025896 .0938644 -.4573294 .4463808
car5 | 304 .0043219 .3897267 -.9783255 1.144717
car6 | 304 .0089991 .4212142 -1.005563 1.264166

.
**Regressions without Interaction
. eststo: quietly regress car1 voteshare i.year, cluster(name)
(est1 stored)

. eststo: quietly regress car2 voteshare i.year, cluster(name)
(est2 stored)

. eststo: quietly regress car3 voteshare i.year, cluster(name)
(est3 stored)

. eststo: quietly regress car4 voteshare i.year, cluster(name)
(est4 stored)

.
. esttab

----------------------------------------------------------------------------
(1) (2) (3) (4)
car1 car2 car3 car4
----------------------------------------------------------------------------
voteshare -0.000295 -0.000247 -0.000342 -0.000282
(-1.37) (-1.02) (-1.14) (-0.83)

2006.year 0 0 0 0
(.) (.) (.) (.)

2007.year 0.00126 -0.00186 0.0125 0.0134
(0.10) (-0.13) (0.62) (0.51)

2008.year 0.0251 0.0254 0.0881** 0.116**
(1.86) (1.54) (2.72) (3.10)

2009.year 0.00638 0.0266 0.0917* 0.126**
(0.32) (0.95) (2.22) (2.70)

2010.year 0.0360* 0.0504** 0.149*** 0.162***
(2.44) (3.16) (7.68) (5.36)

2011.year 0.0178 0.0290* 0.0828*** 0.110***
(1.83) (2.28) (4.50) (5.53)

2012.year 0.0218* 0.0265** 0.0842*** 0.105***
(2.52) (2.68) (4.21) (5.02)

2013.year 0.0114 0.0145 0.0552** 0.0682**
(1.02) (1.20) (2.73) (3.13)

2014.year 0.0159 0.0163 0.0864*** 0.0988***
(1.85) (1.66) (4.48) (4.31)

2015.year 0.0107 0.0145 0.0496** 0.0646***
(1.22) (1.48) (3.14) (3.48)

2016.year 0.0257* 0.0322** 0.0944*** 0.112***
(2.29) (3.00) (5.18) (5.14)

2017.year 0.0110 0.0157 0.0432* 0.0443
(1.19) (1.51) (2.47) (1.97)

2018.year 0.00305 0.000419 0.0501* 0.0533**
(0.21) (0.03) (2.49) (2.67)

2019.year -0.00988 -0.00732 0.0261 0.0391
(-0.68) (-0.45) (1.27) (1.52)

_cons -0.0128 -0.0196* -0.0608*** -0.0787***
(-1.61) (-2.16) (-4.36) (-4.78)
----------------------------------------------------------------------------
N 304 304 304 304
----------------------------------------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001

. estimates clear

.
**Regressions with Interaction

. eststo: quietly regress car1 c.voteshare##i.year, cluster(name)
(est1 stored)

. eststo: quietly regress car2 c.voteshare##i.year, cluster(name)
(est2 stored)

. eststo: quietly regress car3 c.voteshare##i.year, cluster(name)
(est3 stored)

. eststo: quietly regress car4 c.voteshare##i.year, cluster(name)
(est4 stored)

. *eststo: quietly regress car5 c.voteshare##i.year, cluster(name)
. *eststo: quietly regress car6 c.voteshare##i.year, cluster(name)
.
. esttab

----------------------------------------------------------------------------
(1) (2) (3) (4)
car1 car2 car3 car4
----------------------------------------------------------------------------
voteshare -0.00136 -0.00175 -0.00156 -0.00479**
(-1.47) (-1.59) (-0.66) (-2.68)

2006.year 0 0 0 0
(.) (.) (.) (.)

2007.year -0.01000 -0.0174 0.00341 -0.0312
(-0.52) (-0.85) (0.10) (-0.92)

2008.year 0.0148 -0.0129 0.0343 0.0137
(0.66) (-0.51) (0.62) (0.23)

2009.year 0.00118 0.0171 0.118 0.101
(0.04) (0.40) (1.76) (1.35)

2010.year 0.00655 0.0323 0.134*** 0.121*
(0.26) (1.38) (3.83) (2.37)

2011.year -0.00875 -0.0145 0.0542 0.0321
(-0.51) (-0.71) (1.74) (1.08)

2012.year 0.0206 0.0188 0.110** 0.0999**
(1.31) (1.05) (3.06) (2.79)

2013.year -0.00219 -0.00150 0.0543 0.0270
(-0.12) (-0.08) (1.51) (0.80)

2014.year 0.00700 -0.00530 0.0962* 0.0708
(0.45) (-0.33) (2.04) (1.43)

2015.year -0.00291 0.00609 0.0412 0.0227
(-0.19) (0.37) (1.39) (0.77)

2016.year 0.0237 0.0188 0.0739 0.0446
(1.01) (0.95) (1.89) (1.12)

2017.year -0.0122 -0.00849 0.000661 -0.0413
(-0.79) (-0.52) (0.02) (-1.26)

2018.year 0.00151 -0.00550 0.0334 -0.00584
(0.06) (-0.19) (0.92) (-0.20)

2019.year 0.00779 0.0197 0.0147 0.0178
(0.27) (0.62) (0.35) (0.37)

2006.year#~e 0 0 0 0
(.) (.) (.) (.)

2007.year#~e 0.00102 0.00142 0.000972 0.00415*
(1.04) (1.22) (0.39) (2.10)

2008.year#~e 0.000923 0.00311 0.00427 0.00839**
(0.68) (1.61) (1.19) (2.91)

2009.year#~e 0.000393 0.000769 -0.00262 0.00190
(0.14) (0.29) (-0.55) (0.46)

2010.year#~e 0.00226 0.00156 0.00133 0.00379
(1.88) (1.19) (0.53) (1.63)

2011.year#~e 0.00204* 0.00329* 0.00222 0.00626**
(2.10) (2.58) (0.89) (3.16)

2012.year#~e 0.000470 0.000989 -0.000897 0.00202
(0.46) (0.79) (-0.34) (0.92)

2013.year#~e 0.00115 0.00142 0.000381 0.00385
(0.91) (1.02) (0.13) (1.59)

2014.year#~e 0.000881 0.00175 -0.000120 0.00318
(0.87) (1.46) (-0.04) (1.21)

2015.year#~e 0.00114 0.00104 0.000931 0.00400*
(1.15) (0.89) (0.38) (2.05)

2016.year#~e 0.000662 0.00135 0.00148 0.00514*
(0.60) (1.14) (0.58) (2.42)

2017.year#~e 0.00143 0.00174 0.00219 0.00566**
(1.54) (1.57) (0.91) (3.19)

2018.year#~e 0.000698 0.00111 0.00131 0.00477*
(0.48) (0.67) (0.51) (2.45)

2019.year#~e -0.0000682 -0.000177 0.00112 0.00336
(-0.04) (-0.10) (0.41) (1.32)

_cons -0.000644 -0.00242 -0.0468 -0.0270
(-0.05) (-0.17) (-1.68) (-1.02)
----------------------------------------------------------------------------
N 304 304 304 304
----------------------------------------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001




*Margins

. margins year, dydx(voteshare)

Average marginal effects Number of obs = 304
Model VCE : Robust

Expression : Linear prediction, predict()
dy/dx w.r.t. : voteshare

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
voteshare |
year |
2006 | -.0047905 .0017904 -2.68 0.009 -.008344 -.0012371
2007 | -.0006408 .0006799 -0.94 0.348 -.0019902 .0007086
2008 | .0035978 .0015916 2.26 0.026 .000439 .0067566
2009 | -.0028856 .0034362 -0.84 0.403 -.0097056 .0039343
2010 | -.0010043 .001627 -0.62 0.539 -.0042334 .0022248
2011 | .0014744 .0009406 1.57 0.120 -.0003924 .0033412
2012 | -.0027749 .0012215 -2.27 0.025 -.0051993 -.0003506
2013 | -.0009427 .0015342 -0.61 0.540 -.0039877 .0021022
2014 | -.0016129 .0017988 -0.90 0.372 -.0051829 .0019572
2015 | -.0007885 .0007218 -1.09 0.277 -.002221 .0006441
2016 | .0003467 .0011467 0.30 0.763 -.0019293 .0026227
2017 | .0008661 .0005954 1.45 0.149 -.0003155 .0020478
2018 | -.000025 .001056 -0.02 0.981 -.0021209 .0020709
2019 | -.0014304 .0018101 -0.79 0.431 -.0050228 .0021621
------------------------------------------------------------------------------