Download - Two-Period Panel Data Analysis
Two-Period Panel Data Analysis
According to CANA, more people are choosing cremation because it is (1) affordable, (2) environmentally friendly, (3) easier given our βgeography and population mobility, β and (4) increasingly acceptable to religious groups.
http://www.kates-boylston.com/NewsPage.aspx?newsID=2122
Cremation rate (%)
Natives, born in state (%)Year dummy
The 35 states are: AL, AZ, AR, CO, CT, FL, GA, ID, IN, IA, KS, KY, ME, MD, MA, MI, MN, MO, MT, NE, NV, NJ, NM, NC, ND, OR, PA, SC, SD, TX, UT, VT, WA, WI, and WY
πΆπ ππ‘=π½0+πΏ0ππ 2000+π½1π ππ‘+πππ‘
A simple empirical specification that focuses on Boylstonβs third explanation for the increasing proportion of people choosing cremation is:
(1)
Pooled OLS
πΆπ ππ‘=64.4+9.34 βππ 2000β0.757 βπ ππ‘
0 10 20 30 40 50 60 70 80 90 100051015202530354045505560657075
Cremation
Rate (%)
Native (% born in state)
π ππππ=β0.757πΆπ
ππ‘=2000πΆπ
ππ‘=1990
9.34
0 10 20 30 40 50 60 70 80 90 100051015202530354045505560657075
Cremation
Rate (%)
Native (% born in state)
Colorado
Georgia
Fewer people living in Colorado were born there than in Georgia and a lot of the variation in Native used to estimate is coming from between states and some of the variation is coming from within states over time.
State fixed effect () captures (time-invariant and unobserved) prices, regulations, environmental attitudes, religious attitudes. If they are observable, you are better off putting them into the equation as explanatory variables.
πππ‘=ππ+π’ππ‘
Time varying error (idiosyncratic error) βunobserved factors that affect cremation rates and vary over time
πΆπ ππ‘=π½0+πΏ0ππ 2000+π½1π ππ‘+πππ‘
πΆπ ππ‘=π½0+πΏ0ππ 2000+π½1π ππ‘+ππ+π’ππ‘
Fixed Effects Model
(2)
(1)
Pooled OLS
Pooled OLS is not substantially different from single-time-period OLS. If you have an omitted variable problem due to stuff in the error term, pooling the data doesnβt eliminate it.
πΆπ ππ‘=π½0+πΏ0ππ 07+π½1 π ππ‘+πππ‘
For simplicity, suppose
πΆπ ππ‘=π½0+πΏ0ππ 07+π½1 π ππ‘+π½2 π 2πΈππ‘+π’ππ‘
EβοΏ½ β βοΏ½ β βοΏ½+
downward bias
πΆπ π2000=π½0+πΏ0+π½1 π π2000+ππ+π’π 2000
πΆπ π1990=π½0+π½1 π π1990+ππ+π’π1990
βπΆπ π=πΏ0+π½1βπ π+βπ’π
First-difference equation: eliminates
First Differences
(3)
Estimating Fixed Effects Models
πΆπ ππ‘=π½0+πΏ0ππ 2000+π½1π ππ‘+ππ+π’ππ‘(2)
Estimating First-Differencing Models
βπΆπ π=πΏ0+π½1βπ π+βπ’π(3)
Estimating First-Differencing Models βπΆπ π=πΏ0+π½1βπ π+βπ’π(3)
Estimating Fixed Effects Models
πΆπ ππ‘=π½0+πΏ0ππ 2000+π½1π ππ‘+ππ+π’ππ‘(2)
οΏ½ΜοΏ½0
οΏ½ΜοΏ½1
οΏ½ΜοΏ½0
οΏ½ΜοΏ½1
Demonstrates that models using fixed effects are using variation within states (or cities, counties, colleges, etc.) to estimate parameters
πΆπ ππ‘=π½0+πΏ0ππ 07+π½1 π ππ‘+πππ‘
πππ‘=ππ+π’ππ‘
βπΆπ π=πΏ0+π½1βπ π+βπ’π
Key Assumption is uncorrelated with
This assumption holds if the idiosyncratic error (u) at each time period is uncorrelated with the explanatory variable in both time periods.
Costs and Benefits of Fixed Effects Model
Benefitβcontrols for unobserved factors that vary across states, cities, collegesβ¦ Costs1. More expensive data collection2. Can reduce or eliminate variation in explanatory variables.