I have a question regarding the Bartik Instrument.

I understand that this instrument is a particularly important tool that is used in labor economics. From my understanding, this instrument attempts to isolate demand shocks from supply shocks.

Consider the following thought experiment:

Say that we have an equilibrium quantity determined both the labor demand and labor supply. Call it total labor employed in period t in region i. We can express it as:$$L_{it}=\sum_{j}L_{ijt}$$ where the RHS is the summation over all industries hiring labor in this region.

Now, the problem is as follows: the changes in total labor hired in each industry is a result of both supply and demand shocks. What the Bartik Instrument does is that it constructs local labor demand shocks in the following manner:$$\tilde{L_{it}}=\sum_{j}\omega_{jt}L_{ijt-1}$$ where the LHS is region $i's$ predicted employment. The summation is basically a weighted average using weights which corresponding to growth rates in national level employment in industry $j$ times the labor force employed in industry j by region $i$ at time $t$. In a sense, these are changes that are unrelated to local labor supply shocks. The Bartik instrument is then calculated as $\frac{\tilde{L_{it}}-L_{it-1}}{L_{it-1}}$

This is where I am lost. Once I construct this 'instrument', what would be my first stage? Do I need a first stage anymore? My intuition tells me yes. What I mean is that is this already the predicted value that we obtain after a first stage? Let me phrase my question in a more intuitive manner:$$L=f(L^{d},L^{s})$$

As a result,$$dL=f_{L^d}dL^{d}+f_{L^S}dL^{s}$$

Now, in a stochastic environment:$$dL=f_{L^D}dL^{d}+f_{L^S}dL^{s}+v =f_{L^D}dL^{d}+\epsilon$$ where I assume that $$cov(dL^{d},\epsilon)=0$$ or that demand shocks and supply shocks are unrelated. In the first stage then, is the RHS the constructed Bartik instrument? In that case, I would regress the total observed change in labor on the Bartik instrument and obtain $\hat{dL}$ . Or is it the case that the constructed Bartik instrument by itself serves as $\hat{dL}$ ?

Thanks a lot!


2 Answers 2


I think the "first stage" would be $L_{it}$ on $\tilde{L_{it}}$. In the Peri paper above, the Bartik instrument is actually just included directly as $\tilde{L_{it}}$ as a control variable because it is an exogenous regressor in that form. If you are running labor supply elasticity regressions (and thus want to see the effect of $L_{it}$ itself on labor supply), if you can argue that the Bartik instrument is in fact exogenous, you can use it as an instrument for $L_{it}$. But, putting it directly in, as you suggested, would amount to something very similar (i.e., the Reduced Form rather than the Structural Eq.).

  • $\begingroup$ Perfect. This is what I was looking for. $\endgroup$
    – ChinG
    Mar 7, 2016 at 14:48

The Bartik instrument (from Bartik, 1991), also known as the shift-share instrument, is used as a typical instrument using 2-stage least squares regression. Here is an interesting example, using an explicit Bartik instrument. Hope this helps.

Note that the required exogeneity condition of this instrument is not always satisfied.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.