Fixed effects using OLS vs linearmodels

[ethanmetzger]

Here I try to include state and year fixed effects using OLS:

df['year'] = df['year'].astype('category')
reg3 = smf.ols('fatalityrate ~ sb_useage + speed65 + speed70 + ba08 + drinkage21 + np.log(income) + age + state + year + EntityEffects + TimeEffects', df).fit()
reg3.summary()

Here I try to do the same thing but using the linearmodels method:

df2 = df.dropna().set_index(['state', 'year'])
md = linearmodels.RandomEffects.from_formula("fatalityrate ~ 1 + sb_useage + speed65 + speed70 + ba08 + drinkage21 + np.log(income)", data=df2)
mdf = md.fit() 
mdf

Why do I get different results? Why is one of them (the OLS way, I'm guessing) wrong? I'm especially confused because in R I got the same results whether I used OLS or plm.

[ethanmetzger]

I'm also getting slightly different results for these two regressions:

reg2 = smf.ols('fatalityrate ~ sb_useage + speed65 + speed70 + ba08 + drinkage21 + np.log(income) + age + state', df.dropna()).fit()
reg2.summary()

and...

md = smf.mixedlm("fatalityrate ~ sb_useage + speed65 + speed70 + ba08 + drinkage21 + np.log(income) + age", data=df.dropna(), groups=df["state"]) 
mdf = md.fit() 
mdf.summary()

[jmbejara]

I'm not sure why this works:

df['year'] = df['year'].astype('category')
reg3 = smf.ols('fatalityrate ~ sb_useage + speed65 + speed70 + ba08 + drinkage21 + np.log(income) + age + state + year + EntityEffects + TimeEffects', df).fit()
reg3.summary()

It seems like this would fail. The ols method doesn't know what to do with the EntityEffects and TimeEffects arguments in the formula. That seems confusing to me. To compute the fixed effects regression, you need to use the linearmodels.PanelOLS function. Also note that linearmodels.RandomEffects and linearmodels.PanelOLS are not the same thing. A fixed effects models is not the same thing as a random effects model (though they are closely related).

[jmbejara]

For your second question, including state in the OLS regression doesn't seem like should make sense. It's a categorical variable, right?

[ethanmetzger]

Re: "It seems like this would fail," I mistakenly included Entity and Time Effects in that line of code. I meant to write:

df['year'] = df['year'].astype('category')
reg3 = smf.ols('fatalityrate ~ sb_useage + speed65 + speed70 + ba08 + drinkage21 + np.log(income) + age + state + year', df).fit()
reg3.summary()

[ethanmetzger]

I've since tried:

df2 = df.set_index(['state', 'year'])
reg = linearmodels.PanelOLS.from_formula("fatalityrate ~ sb_useage + speed65 + speed70 + ba08 + drinkage21 + np.log(income) + EntityEffects + TimeEffects", data=df2)
reg.fit()

I am getting something closer to what I am getting through

df['year'] = df['year'].astype('category')
reg3 = smf.ols('fatalityrate ~ sb_useage + speed65 + speed70 + ba08 + drinkage21 + np.log(income) + age + state + year', df).fit()
reg3.summary()

but still slightly different (not sure if you're okay with discussing precise values on this forum).

Re: "For your second question, including state in the OLS regression doesn't seem like should make sense. It's a categorical variable, right?" I was under the impression that by making state and year categorical variables and running an OLS regression I'm essentially doing the same thing that I'd be doing if I were to use something like linear models.PanelOLS. Is this incorrect?

[jmbejara]

If you're turning year and state into individual dummy variables, then it's the same thing. It doesn't look like that's what you're doing. So, in that case, it would be different.