Economics Job Market Rumors Topic: Interaction of fixed effects
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Economics Job Market Rumors Topic: Interaction of fixed effectsen-USMon, 06 Feb 2023 22:48:18 +0000http://bbpress.org/?v=1.0.2<![CDATA[Search]]>q
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Economist on "Interaction of fixed effects"
https://www.econjobrumors.com/topic/interaction-of-fixed-effects/page/2#post-4318672
Sat, 23 Jun 2018 22:47:48 +0000Economist4318672@https://www.econjobrumors.com/<p>Third year grad student here trying to understand two-way FE. </p>
<p>So suppose we have firm-state-year level data (denoted y_{fst}) and there are multiple firms within a state-year. Then including state-year FE (group(state year) or i.state#i.year in Stata) non-parametrically controls for state-year shocks. That is we control for state level heterogeneity that varies by year (separate intercept for (state1, year1) and (state1, year2)) and also allows year effects to vary by state (separate intercept for (state1, year1) and (state2, year1)). So the variation left over to identify the remaining regression parameters is from firms within state-year?</p>
<p>Someone clarify whether I am on the right track. Also given our data environment, would state-year FE be generally preferred over state, year FE entering separately?
</p>Economist on "Interaction of fixed effects"
https://www.econjobrumors.com/topic/interaction-of-fixed-effects/page/2#post-4101350
Thu, 08 Mar 2018 02:55:22 +0000Economist4101350@https://www.econjobrumors.com/<p>Please someone tell me the hyperbolic paraboloid guys are trolls.
</p>Economist on "Interaction of fixed effects"
https://www.econjobrumors.com/topic/interaction-of-fixed-effects/page/2#post-4101009
Wed, 07 Mar 2018 23:15:34 +0000Economist4101009@https://www.econjobrumors.com/<blockquote><p>Good point. I'm reading this as though they are indicator variables.<br />
But if it is a strict value interaction, then it makes no sense at all, because it will assign some value to the rank of states (which makes no sense). Using Stata's standard for indicator (i) vs. continuous (c) variables:<br />
i.state#i.year ––> state-specific annual effects, flexibly controls for common annual shocks at the state level<br />
i.state#c.year ––> state-specific trends, controls for common trends at the state level<br />
c.state#c.year ––> makes no friggin' sense, since it would assume that the state variable has some interpretable numeric value, and now we're in log(NAICS) territory </p>
<blockquote><blockquote>I feel like I'm taking crazy pills over here. Both of the following should yield the same results:<br />
y = x + i.state#i.year<br />
or<br />
egen thing = group(state year)<br />
y = x + i.thing
</p></blockquote>
<p>Look at the notation in the original post. \gamma_{s}*\lambda_{t} or alternatively \delta_{st} are parameters to be estimated. Not indicator variables. If they were the latter then they'd yield identical fixed effects estimates, so your statement i quoted above is correct of course.<br />
</blockquote></blockquote>
<p>Haha not quite that bad. The states wouldn't be ordered arbitrarily, they would be ranked by which has the highest vs lowest \gamma. Same with years -- you're interacting a fixed effect for each year, not the numeric value of the year. So you're fitting state*year onto the surface of a hyperbolic parabaloid y=\delta*\lambda. State identities and years would be arranged in unpredictable ways along the axes, since the axes are 'fixed effect' values associated with state and year. Whichn't make any sense to me still, but if i took some shrooms maybe i could come up with something.
</p>Economist on "Interaction of fixed effects"
https://www.econjobrumors.com/topic/interaction-of-fixed-effects/page/2#post-4100998
Wed, 07 Mar 2018 23:08:18 +0000Economist4100998@https://www.econjobrumors.com/<p>Good point. I'm reading this as though they are indicator variables.</p>
<p>But if it is a strict value interaction, then it makes no sense at all, because it will assign some value to the rank of states (which makes no sense). Using Stata's standard for indicator (i) vs. continuous (c) variables:</p>
<p>i.state#i.year ––> state-specific annual effects, flexibly controls for common annual shocks at the state level<br />
i.state#c.year ––> state-specific trends, controls for common trends at the state level<br />
c.state#c.year ––> makes no friggin' sense, since it would assume that the state variable has some interpretable numeric value, and now we're in log(NAICS) territory </p>
<blockquote><blockquote>I feel like I'm taking crazy pills over here. Both of the following should yield the same results:<br />
y = x + i.state#i.year<br />
or<br />
egen thing = group(state year)<br />
y = x + i.thing
</p></blockquote>
<p>Look at the notation in the original post. \gamma_{s}*\lambda_{t} or alternatively \delta_{st} are parameters to be estimated. Not indicator variables. If they were the latter then they'd yield identical fixed effects estimates, so your statement i quoted above is correct of course.
</p></blockquote>Economist on "Interaction of fixed effects"
https://www.econjobrumors.com/topic/interaction-of-fixed-effects/page/2#post-4100991
Wed, 07 Mar 2018 23:02:19 +0000Economist4100991@https://www.econjobrumors.com/<p>And yes, it will control for state-specific year shocks. That's because the interaction of state and year allows for a different, flexible time effect, which varies by state, in each year. Take a single example of that combination, say Nevada in 1990. That interaction will take a value of 1 only when both state = Nevada and year = 1990 are true. Just like a state-by-year FE generated using the group command will take a value of 1 only for observations that correspond to Nevada in 1990.
</p>Economist on "Interaction of fixed effects"
https://www.econjobrumors.com/topic/interaction-of-fixed-effects/page/2#post-4100987
Wed, 07 Mar 2018 23:00:35 +0000Economist4100987@https://www.econjobrumors.com/<blockquote><p>I feel like I'm taking crazy pills over here. Both of the following should yield the same results:<br />
y = x + i.state#i.year<br />
or<br />
egen thing = group(state year)<br />
y = x + i.thing
</p></blockquote>
<p>Look at the notation in the original post. \gamma_{s}*\lambda_{t} or alternatively \delta_{st} are parameters to be estimated. Not indicator variables. If they were the latter then they'd yield identical fixed effects estimates, so your statement i quoted above is correct of course.
</p>Economist on "Interaction of fixed effects"
https://www.econjobrumors.com/topic/interaction-of-fixed-effects/page/2#post-4100962
Wed, 07 Mar 2018 22:45:21 +0000Economist4100962@https://www.econjobrumors.com/<p>I feel like I'm taking crazy pills over here. Both of the following should yield the same results:</p>
<p>y = x + i.state#i.year</p>
<p>or</p>
<p>egen thing = group(state year)<br />
y = x + i.thing
</p>Economist on "Interaction of fixed effects"
https://www.econjobrumors.com/topic/interaction-of-fixed-effects/page/2#post-4100943
Wed, 07 Mar 2018 22:39:08 +0000Economist4100943@https://www.econjobrumors.com/<blockquote><p>This is the worst thread in ejmmr history. State-yet fe is the same as interacted state and year for if and only if you have a valid instrument for the endogeneity.<br />
Go read some wooldridge or you all will fail the market horribly.
</p></blockquote>
<p>My mistake. I think Hawaii became a state because of good surfing, maybe you can use waves as an instrument?
</p>Economist on "Interaction of fixed effects"
https://www.econjobrumors.com/topic/interaction-of-fixed-effects/page/2#post-4100926
Wed, 07 Mar 2018 22:27:59 +0000Economist4100926@https://www.econjobrumors.com/<p>This is the worst thread in ejmmr history. State-yet fe is the same as interacted state and year for if and only if you have a valid instrument for the endogeneity. </p>
<p>Go read some wooldridge or you all will fail the market horribly.
</p>Economist on "Interaction of fixed effects"
https://www.econjobrumors.com/topic/interaction-of-fixed-effects/page/2#post-4100890
Wed, 07 Mar 2018 22:06:51 +0000Economist4100890@https://www.econjobrumors.com/<blockquote><p>Regression donkey here, refereeing paper and wanting to make sure of the interpretation of the interaction of two fixed effects. With panel data (say households i in state s at time t), the interaction of the state and time fixed effects \gamma_{s}*\lambda_{t} (is NOT the same as a state-time fixed effect \delta_{st} , right? The authors claim that the interaction term allows state-year specific shocks, and that seems wrong to me. Am I right? Thanks!</p></blockquote>
<p>Fine for op to ask this cause sometimes you get thrown off but there is way too much confusion in this thread.</p>
<p>Not the same. \delta_{st} allows state-year specific shocks. It's nonparametric in the state-year space. Their specification forces the state-year surface into a hyperbolic parabaloid. </p>
<p>It's likely they messed up notation -- they really want to interact the indicator variables for state, time to create the state-time indicator. Then you get \delta_{st} estimates as fixed effects. Estimating the parameters of a hyperbolic paraboloid is harder so I'm sure if they did this it would be obvious from the rest of the paper.
</p>