When to use time dummies in multiple regression

Question

When is it appropriate to use time dummies in multiple regression analysis? I am using pooled ols, random effects model, and fixed effects model. I have a period of 3 years. I don´t know whether it is corrected but I think that time dummies should be included when the period under investigation is large, at least larger than 3 years. Then by using time dummies you can correct for time trends that are not observed by the model? Am I right or? And is it always included in fixed effects model?

Answer 1

Including dummies for each year allows your model to attribute some of the variation in your data to unobserved events that took place during each year, or otherwise characteristic features of that year besides specific events. Including dummies is not always done for the simple reason that they may not be necessary - meaning they might not improve your model. Reasons for this can be that other variables you already have explain the variation well, or that there is baseline difference in behavior across the years. Nevertheless, you may want to include dummies. Should you?

One way to think about this problem is to ask if including the dummies improves your model. Intuitively, if they do, you are explaining the structure of your data better. Based on the information you have provided, I am not sure if you should include dummies or not, but to check this for a basic fixed effects model you can perform a likelihood ratio (LR) test or use another model selection criterion, like the AIC. Here is how you can perform LR test in R for a basic, fixed effects model (here it is a logit, but this is not necessary):

mydata <- read.csv("http://www.ats.ucla.edu/stat/data/binary.csv")
mydata$rank <- factor(mydata$rank)
mylogit <- glm(admit ~ gre + gpa + rank, data = mydata, family = "binomial")
mylogit2 <- glm(admit ~ rank, data = mydata, family = "binomial")
test <- anova(mylogit, mylogit2, test = "LRT")

I dropped the GRE and GPA variables and tested if the model fit changed, but you could do this for dummies and no dummies in your case.

For mixed effects models, things are more complex. This post offers some pointers to approaches for using model selection, like the AIC, when you are working with these types of models.

If the data you are talking about is longitudinal, meaning you follow the same subjects over a period of time, I highly recommend this book. Even if your data is not longitudinal, it still has a lot of useful advice regarding the construction of mixed effects models.