# Bins and Year Fixed Effects

I am trying to understand the difference between two regression models. Before more complex models are run (ie. quantile) I split an key independent variable into bins to see if the relationship is non-linear. I do this in two ways.

Model (1): The independent variable x is grouped into 10 bins based on the decile. A regression is then run with y regressed on the 10 bins and year-fixed effects.

Model (2): The independent variable x is grouped into 10 bins based on the decile within each year. A regression is then run with y regressed on the 10 bins and year-fixed effects.

If Model (1) is run without year fixed effects, then it would seem that the 10 bins can be picking up some sort of time trend. Therefore, the method of calculating bins in Model (2) seems better. My question is if including year fixed effects in Model (1) removes the correlation between the bin variables and the time trend?

In my basic undergrad textbook (Introductory Econometrics: A Modern Approach) it states that "to reflect the fact that the population may have different distribution in different time periods, we allow the intercept to differ across periods, usually years." Then it talks about how year dummies accomplish this. So, it would seem that the time trend is controlled for. However, the distribution for bins in each year would differ between Model (1) and Model (2). For example, in Model (2) there would be an equal number of observations in each bin. This will not be true for Model (1).

Any advice? I get two very different results when I run these two models and am not sure which one is correct or how to interpret the differences.

Thank you!

• I may be reading this wrong, but you say x is the dependent variable, but then say that y is regressed on the 10 bins of x, making it sound like y is the dependent variable. Can you clarify? I'm also curious to know why you think you need to transform a continuous variable onto an ordinal scale. Is it non-normal? Commented Jan 5, 2015 at 4:30
• Yes sorry, x is the independent variable. It is non-normal! Commented Jan 5, 2015 at 14:53
• You should not bin it, better to try a spline Commented Apr 5 at 14:06