Dear All,

I am looking to the impact of Syrian mass migration on the firm-level performance measures.
I have city level immigration densities (immigrants/city population) and I match these densities with firm level Census data.

I run the two different specifications and I have conflicting results that I am not able to explain it.
First specification (model 1) is difference in difference model.

Model 1: lnlp=a1+a2 High_immigrant + a3dd+a4 gr_ylf
gen time=(year>2012) &!missing(year)
dd=High_immigrant*time
High immigrant is a dummy for cities which have average immigration density (immigrants/city population) >1.5.,
gr_ylf is the growth of the young labor force aged population in the city (age 15 to 25) which is exogenous to the immigrant labor supply. I include this to control city level effects.

Note that immigration starts at 2013. The city level immigration density is time-varying during 2013-2015. For example, according to my definition city a can be in the treatment region in year 2013 as the average is above 1.5%.
Immigration density for City a in 2013: 0.5.
Immigration density for City a in 2014: 2.
Immigration density for City a in 2015:5
average=2,5
Question 1: Is there any way to control this?

The second model is the following:
Model 2: lnlp=b1 +b2time+b3time_id +b4gr_ylf
gen time=(year>2012) &!missing(year)
time_id=immigration density*time where immigration density is 0 before 2013.
In the dd models, I am interested in the coefficient of dd (a3). In the second model I am interested in the coefficient of b3. Negative and significant coefficient of a3 will show that the productivity level is lower in the high immigrant regions during 2013-2015 relative to low immigrant regions. Positive b3 indicates as immigration level increase during immigration period we expect higher (lower) productivity during immigration period.


However, their signs are opposite.
Question 2: What might be the reason?
Thanks in advance for your time and support.
Nazlı


(1) (3)
VARIABLES Model 2 - Dose Response - Level Model 1 - DD - Level
time -0.0264***
(0.00503)
time_id 0.0221***
(0.00125)
im_den
dd -0.0601***
(0.00857)
HighImmigrant 0.110***
(0.00577)
gr_ylf 0.0421*** 0.0632***
(0.00597) (0.00586)
Constant 6.389*** 6.324***
(0.00281) (0.00465)
Observations 212,175 212,175
R-squared 0.003 0.003
Year FE NO NO
N 212175 212175