<p>The Bartik instrument  (from <a href="https://ideas.repec.org/b/upj/ubooks/wbsle.html" rel="nofollow">Bartik, 1991</a>), also known as the shift-share instrument, is used as a typical instrument using 2-stage least squares regression. <a href="http://ftp.iza.org/dp9436.pdf" rel="nofollow">Here</a> is an interesting example, using an explicit Bartik instrument. Hope this helps.</p>

<p>Note that the required exogeneity condition of this instrument is not always satisfied.</p>

CC BY-SA 3.0
2015-11-25T03:46:19.243Z
2015-11-25T03:46:19.243Z
emeryville
<p>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.). </p>

CC BY-SA 3.0
2016-03-07T14:48:53.323Z
Perfect. This is what I was looking for.
ChinG
CC BY-SA 3.0
2016-03-05T22:57:50.413Z
2016-03-07T10:42:16.553Z
2016-03-07T10:42:16.553Z
Peter
<p>I have a question regarding the Bartik Instrument.</p>

<p>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.</p>

<p>Consider the following thought experiment:</p>

<p>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. </p>

<p>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 $\frac{\tilde{L_{it}}-L_{it-1}}{L_{it-1}}$</p>

<p>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:$$L=f(L^{d},L^{s})$$</p>

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

<p>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 $\hat{dL}$
 ?</p>

<p>Thanks a lot! </p>

<econometrics><labor-economics>
Bartik Instrument Intuition
ChinG
# Bartik Instrument Intuition

(Asked by: username_0 on 2015-11-18)

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!

**Tags:** econometrics, labor-economics

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## 2 answers

### Answer by username_2 on 2016-03-05. Score: 3 | Accepted answer

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.).

> **Comments:**
> **username_0**: Perfect. This is what I was looking for.  

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### Answer by username_1 on 2015-11-25. Score: 1

The Bartik instrument (from [Bartik, 1991](https://ideas.repec.org/b/upj/ubooks/wbsle.html)), also known as the shift-share instrument, is used as a typical instrument using 2-stage least squares regression. [Here](http://ftp.iza.org/dp9436.pdf) 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.


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