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I want to interpret the output of a fixed effects regression and need help with interpreting the country-fixed effects. The regression is the following:

pm.alldata <- pdata.frame(alldata , index = c("country", "year") )
a.fixedtwo <- plm(log(production) ~ log(temp) + log(rain) + drought + flood + storm + log(labour) + log(fertilizer) +log(capital) +log(area) , data = pm.alldata, model = "within", effect = "twoways")

enter image description here

The dependent variable is agricultural production. I want to look at how temperature and precipitation affect agricultural production (although this is rather irrelevant to the question I have). The country fixed effects refer to 28 countries. The county-fixed effects are as follows:enter image description here

As I understand it, we can say that country 5 (Ecuador) has an unobservable negative effect (-5,99469) on agricultural production. Am I right?

Now I come to my main question: I have divided these 28 countries into two subgroups (poor and rich countries). If I regress only the 14 poor countries, the coefficients of the country-fixed effects change to the following: enter image description here

Now the effect of country 5 (Ecuador) is suddenly positive (7.5768). This would mean that Ecuador has positive unobservable effects on agricultural production. Is it normal for the signs to change when this is subdivided into a subgroup?Which of the two values of Ecuador should I use for interpretation when comparing the value of Ecuador with the value of a rich country (e.g. Argentina)?

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  • $\begingroup$ Let $\alpha_i$ be $i$'s intercept. If FE of $i$, say $\mu_i$, is defined as $\alpha_i - \bar\alpha$, it is possible and natural that $\mu_i$ depends on $\bar\alpha$. To me, the sign change looks OK especially if the countries in the subgroup have small $\alpha_i$. Ecuador has positive unobserved effects in comparison to the countries in the subgroup. I know Stata defines FE that way, but I don't know how plm does it. $\endgroup$
    – chan1142
    Mar 15, 2021 at 2:57
  • $\begingroup$ What happened to the difference $\delta_{ij} := \alpha_i - \alpha_j$ in country fixed effects for a pair $(i,j)$ of countries? $\endgroup$
    – Jesper Hybel
    Mar 15, 2021 at 3:28

1 Answer 1

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Fixed effects model is estimated as:

$$ y_{i t} − \bar{y_i} = ( X_{i t} − \bar{X_i} ) \beta + ( \alpha_i − \bar{\alpha_i} ) + ( u_{it} − \bar{u_i} )$$

So the country fixed effect is always relative to the average fixed effect.

If a country has negative fixed effect that means it is less productive than average country in your sample. If you choose different sample results might change.

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  • $\begingroup$ Thank you @csilvia, now I think my interpretation about the estimates might be also wrong! Assume that the beta for temperature is -1.6.Does it then imply that if temperature increases by 1%, agricultural production will decrease by 1.6%? OR If temperature increases by 1%, does agricultural production decrease relative to average agricultural production? I'm actually a bit confused right now and I'm handing in my bachelor thesis soon. $\endgroup$
    – mag123
    Mar 15, 2021 at 9:37
  • $\begingroup$ Im confused by this- isnt your notation demeaning at the group level, and hence the fixed effect $\alpha_i$ is purged completely? and if estimated by dummy variables then should it give the mean of the within group residual for each group? $\endgroup$
    – Steve
    Mar 15, 2021 at 17:27
  • $\begingroup$ @mag123 yes fixed effects regression uses within estimator so you are not regressing $y$ on $x$ but $y-\bar{y}$ on $x-\bar{x}$ this is why if there is no change in $x$ or $y$ you get error. So beta is effect of $x$ when it changes from mean on change in $y$ from the mean. If you are doing thesis talk about this with your advisor he or she can also tell you how to interpret it taking in account relevant literature $\endgroup$
    – csilvia
    Mar 15, 2021 at 20:07

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