# Difference in differences with multiple time periods

I am assessing the economic impact of High-Speed Rail (HSR) between two cities using Difference-in-Differences. To do so I have a set of treated and control regions (indexed by i). I am assuming that treatment starts at the year t=2007, and I have data from 2000 all the way to the year 2016. My query is as follows:

I am running a panel data regression using package 'plm' in R to quantify treatment effect through difference-in-differences. I have created year dummies for all my years (2000-2016), and my treatment starts at year 2007, yet when I run the regression it does not use year 2015 and 2016, hence regresses t-2 instead of t-1.

I am regressing the equation

$$Y_{it}=\beta_{0} + \beta_1 \cdot Group + \delta \cdot DID + \beta_2 \cdot \text{year_dummies} + \beta_3 \cdot X$$

Year dummies are: y2000, y2001, y2002, y2003, y2004,..., y2016. Group is a dummy with 1 for treated and 0 for control regions and Treat is a dummy with 1 for post-treatment(2007-2016) and 0 for pre-treatment (2000-2006)). However, when I run pooled OLS, fixed effects or first differences regressions, the model only regresses up to y2014, omitted the last two year dummies.

I would really appreciate if you could help me out to resolve the matter!

• Obviously, your design matrix has col-linearity. The first column (for intercept) = Y2000+...,+Y2016. I think there is another collinearity. I have no data, so I cannot check it. But first one is true. If you can give the definitions of Group, DID and X, maybe I can give you the answer. – user158565 May 31 '17 at 1:23
• Thanks for your comment. Could you please further explain the fact that the design matrix has colinearity? In terms of my regression equation: Yit, the dependent variable corresponds to GVA. Year dummies are: y2000, y2001, y2002, y2003, y2004,..., y2016. The DID term is an interaction between treated group and post-treatment time, DID=Group*Treat_time. X represents a set of explanatory variables such as ln(population), ln(employment), ln(average salary), etc. – user163339 May 31 '17 at 1:30
• Group is a dummy: maybe 0 for control, 1 for treated. What is treat_time? – user158565 May 31 '17 at 1:40
• Group is a dummy, 0 for control, 1 for treated. treat_time is a dummy, 1 for post-treatment (2007-2016) and 0 for pre-treatment (2000-2006) – user163339 May 31 '17 at 1:42
• Yit is regressed with ln, as: ln(Yit) which corresponds to GVA for each region at each year. – user163339 May 31 '17 at 1:42