Immigration supply shocks, fixed effects and model interpretation

I'm new to this and I've been racking my brains for a couple days trying to understand this model and how to run it in Stata. More than programming help, I think I just don't understand the model well enough, and I'm hoping someone here might be able to offer some advice.

I'm trying to replicate the basic empirical specification from the Borjas and Monras (2016) paper on the Labor Market Consequences of Refugee Supply Shock.

This paper uses one "simple" model to estimate the effects of refugee induced supply shocks on native worker's wages over several different historical events--the famous Mariel boatlift case in the 1980s, the wave of Algerians going to France in the 1960s, or the Balkan refugees moving to different countries in Europe throughout the 1990s. The paper uses public, easily accessible IPUMS data.

I'm trying to replicate some of the analysis on the Balkan refugee shock in Europe, where there is cross-sectional data that comes from census in 1990 and 2000.

The study uses the following model:

$$\Delta log \cdot w_{rs} = \theta_r + \theta_s - \eta\cdot log \frac{L_{rs1}}{L_{rs0}}-\eta\cdot m_{rs} + \varepsilon_{rs}$$

Trying to be brief, the idea is that any given location is comprised of a number of labor market "cells". Prior to the refugee supply shock ($$t = 0$$), there are $$L_{rs0}$$ workers in region $$r$$ of skill type $$s$$.

The labor markets in the receiving country are then “shocked” by the political upheaval abroad. This upheaval sends an influx of $$M_rs$$ new refugees into each region-skill cell.

Furthermore "the wage change observed in cell ($$r, s$$) as a result of the refugee supply is given by equation above, where $$θr = Δ log pr + Δ log Qr$$, and is captured by a region-specific fixed effect; $$θs = Δ log αs$$, and is captured by a skill-specific fixed effect; and $$m_{rs} = M_{rs}/L_{rs1}$$."

"Note that $$m_{rs}$$ gives the relative size of the supply shock: the percent increase in the number of workers due to the entry of refugees into cell ($$r, s$$). In addition to the fixed effects $$θ_r$$ and $$θ_s$$, equation (4) has two regressors. Not surprisingly, the wage change depends on the refugee supply shock."

So the data for used for this has observations on the local labor force taken from a census in 1990 and 2000 ($$t=1$$, and $$t=0$$, respectively). Where you can tally up which workers are natives, who are refugees, whether they were unemployed or not in either of the two years.

I’ve managed to calculate both regressors, the change in the supply of local labor ($$log \frac{L_{rs1}}{L_{rs0}}$$) and the relative size of the refugee supply shock ($$m_{rs}$$), but I’m a bit lost on what to do next.

Should I be using OLS for this? Is this a panel regression with two time periods? (so in Stata, xtreg, for example).

Even more, I don’t know what to do about the two “fixed effect” parameters $$\theta_r$$ and $$\theta_s$$. I’ve tried to include these in some kind of fixed effects model, but I keep getting an error in Stata saying I have “insufficient observations”, and even more, all of the example fixed effects models I’ve seen in the literature usually have a $$t$$ component on the dependent variable, as well as on some \alpha intercept.

When I try to do this with OLS, I get a constant term returned, which I don’t think I see in this model (above).

I’m sure I’ve left out some more detail that would make this clear, but this is already way, way too long a post. I doubt anyone will read or reply, but if you have any helpful comments, I would be truly grateful.

Thanks.

• If it helps, it looks like Prof. Borjas provides access to Stata .do files for this paper on his website: sites.hks.harvard.edu/fs/gborjas/#section3. – AlexK May 25 at 23:57
• Thanks @AlexK. I've looked at the files. With that in mind, I'm wondering if the answer to my question are the different Stata commands for fixed effects. Namely, if one is running the areg command, even though Stata reports the constant term, is it correct that this term is meaningless? I've come across this somewhere that the constant terms that come in the output in the areg and xtreg commands have a different or possibly meaningless interpretation, but again, I don't know if this is correct. – anguyen1210 May 26 at 6:39
• There is a lot of info on this online, e.g., stackoverflow.com/questions/14179197/… – AlexK May 26 at 7:09