Shift-share IV Flashcards
Write the equation for the shift-share instrument and explain the components in the setting of Chinese import exposure.
Z_i = \sum_{j=1}^Js_{ij}g_j
where $z_i$ is the change in predicted import exposure per worker, $g_j$ in Industry $j$’s growth in Chinese imports (among 8 non-U.S high-income countries) and $s_{ij}$ is the lagged share of manufactory industry $j$ in the total employment of location $i$.
Do we need exogeneity in both the shift or the shares?
For identification, we only need exogeneity in the shares or the shift. We should pick only one approach which should be based on an ex-ante assessment of whether shares or shocks are exogenous.
Describe identification from the share in SSIV
Here we assume that the shares are exogenous (randomly asigned) and the shock is “fixed”.
Using shares as identification, i.e., assuming shares are the exogenious source of variation, it takes a DiD-like approach. We need to assume parallel trends, i.e., the shares should evolve similarly in absense of the shock/shift?
Describe how we obtain \hat\beta when identifications comes from the shares in SSIV
In this setting, the $\hat \beta$ can be obtained by using an over-identified GMM procedure that uses $J$ share instruments $s_{ij}$ and a weight matrix based on the shocks $g_j$. That is, we use the shares as the instrument and the shocks as weights. We are thus pooling all the did-iv’s from each industry. If instead assuming exogenous shocks, we we only have one moment condition.
What is the assumption when using identification from shares in SSIV?
Share exogeneity
What do we need to show when doing SSIV with identification from the shares?
- Calculate Rotemberg weights and show that they are not negative. This since we are kind of doing a DiD we could potentially have a problem with heterogeneity.
- Calculate the F-statistic and show that no instrument (each share are a specific instrument) is weak
Describe Share exogeneity and how we can argue for this in a paper.
Shares $s_{ij}$ are exogenous for each $j$. This is similar to parallel trends for each industri. If instead assuming exogenous shocks, we only have one moment condition.
Arguing for share-exogeneity implies that we assume that all unobservables are uncorrelated with anything about the local share distribution. That is, the all places $i$should have evolved similarly if it was not for the shock. This we should argue with economic reasoning.
What can we do to strenghten the exogeneity argument?
- Balance checks/pre-trend tests
- $z_i$ do not predict past outcomes or predetermined characteristics of the location $i$.
- Overident-ification tests
E.g., we could show that the predicted exposure to Chinese imports is unrelated to previous employment growth in some location. That is, it would not make sense that exposure now would predict employment before the exposure, otherwise, it would not be exogenous. Then it would capture some location characteristics.
How do we get \beta\hat when we assume identification from the shocks/shift?
In this setting, the $\hat \beta$ can be obtained by using an over-identified GMM procedure where now the shares are weights to the shocks.
What are the identifying assumptions we need to consider when we are using identification from shocks in a shift share IV?
With identification from shocks, we need to identifying assumptions to hold:
- Shocks are exogenious conditioned on the shares
- There are many uncorrelated shocks
If Assumption 1 and 2 holds and the instrument is relevant, then $\hat \beta \to^{p} \beta$. That is, shock-level IV is consistent. This goes both if we choose to use the SSIV or the shock-level IV.
What is shock-level IV?
Aggregating on the on the shock level, weighting with the shares.
What can we do if we have problem with incompleate shares
Having incomplete shares (shares not summing to 1) is not a problem as long as we control for the number of shares in our regression. We thus as $S_j$ as a control in our regression.
Can we add controls in SSIV?
Adding controls in SSIV is no problem since SSIV is simply 2SLS. It is also possible to do so with shock level regression but then we first need to residualize the variables, then aggregate them using weights.
How can we test our assumptions when we have identification from shifts/shocks?
Assumption 1 (exogeneity) is untestable. But we could do:
- Balancing checks => shock have no effect on pre-determined covariates
- Adding controls => this should not change estimates
Assumption 2 (no correlation among shocks)
- Show that the herfindal index goes to zero as the number of locations goes to infinity. No industry should be super important.
- Show that the shocks are mutually uncorrelated. This is hard.
When should we go for identification by shares in SSIV?
When the shock cannot naturally be viewed as an instrument, because there are to few shocks or when the shocks are hard to verify exogenously. Then it is better to assume that the shares are exogenous. This is than the did-setting where we have a non-exogenous reform.
When should we go for identification by shift/shock in SSIV?
We would use this if our IV is based on a set of shocks which can be themselves thought of as an instrument (i.e. many shocks that are plausibly quasi-randomly assigned.
“If we have an exogenous shock that affects different local areas with different amount due to their exposure to the shock by some “initial share” thing. Like, there are already different shares of Italian students in different U.S states, then if there is an Italian policy which makes it easier to study abroad, this would be an exogenious should that affects different industries with different amount. ”
Tycker den här beskrivningen stämmer bättre med shares???.
