# How to interpret fixed effects?

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")


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:

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:

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)?

• 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. Commented Mar 15, 2021 at 2:57
• What happened to the difference $\delta_{ij} := \alpha_i - \alpha_j$ in country fixed effects for a pair $(i,j)$ of countries? Commented Mar 15, 2021 at 3:28

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.

• 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. Commented Mar 15, 2021 at 9:37
• 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? Commented Mar 15, 2021 at 17:27
• @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 Commented Mar 15, 2021 at 20:07