two-period panel data analysis
DESCRIPTION
Two-Period Panel Data Analysis. Pooled OLS. According to CANA, more people are choosing cremation because it is (1) affordable, (2) environmentally friendly, (3) easier given our “geography and population mobility, ” and (4) increasingly acceptable to religious groups. . - PowerPoint PPT PresentationTRANSCRIPT
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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 “geography and population mobility, ” 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
𝐶𝑅𝑖𝑡=𝛽0+𝛿0𝑌𝑟 2000+𝛽1𝑁 𝑖𝑡+𝜀𝑖𝑡
A simple empirical specification that focuses on Boylston’s third explanation for the increasing proportion of people choosing cremation is:
(1)
Pooled OLS
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𝐶𝑅𝑖𝑡=64.4+9.34 ∙𝑌𝑟 2000−0.757 ∙𝑁 𝑖𝑡
0 10 20 30 40 50 60 70 80 90 100051015202530354045505560657075
Cremation
Rate (%)
Native (% born in state)
𝑠𝑙𝑜𝑝𝑒=−0.757𝐶𝑅
𝑖𝑡=2000𝐶𝑅
𝑖𝑡=1990
9.34
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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.
![Page 4: Two-Period Panel Data Analysis](https://reader035.vdocument.in/reader035/viewer/2022081502/56815f24550346895dcdf012/html5/thumbnails/4.jpg)
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.
𝜀𝑖𝑡=𝑎𝑖+𝑢𝑖𝑡
Time varying error (idiosyncratic error) —unobserved factors that affect cremation rates and vary over time
𝐶𝑅𝑖𝑡=𝛽0+𝛿0𝑌𝑟 2000+𝛽1𝑁 𝑖𝑡+𝜀𝑖𝑡
𝐶𝑅𝑖𝑡=𝛽0+𝛿0𝑌𝑟 2000+𝛽1𝑁 𝑖𝑡+𝑎𝑖+𝑢𝑖𝑡
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 doesn’t eliminate it.
![Page 5: Two-Period Panel Data Analysis](https://reader035.vdocument.in/reader035/viewer/2022081502/56815f24550346895dcdf012/html5/thumbnails/5.jpg)
𝐶𝑅𝑖𝑡=𝛽0+𝛿0𝑌𝑟 07+𝛽1 𝑁 𝑖𝑡+𝜀𝑖𝑡
For simplicity, suppose
𝐶𝑅𝑖𝑡=𝛽0+𝛿0𝑌𝑟 07+𝛽1 𝑁 𝑖𝑡+𝛽2 𝑅2𝐸𝑖𝑡+𝑢𝑖𝑡
E⃝� – ⃝� – ⃝�+
downward bias
![Page 6: Two-Period Panel Data Analysis](https://reader035.vdocument.in/reader035/viewer/2022081502/56815f24550346895dcdf012/html5/thumbnails/6.jpg)
𝐶𝑅𝑖2000=𝛽0+𝛿0+𝛽1 𝑁 𝑖2000+𝑎𝑖+𝑢𝑖 2000
𝐶𝑅𝑖1990=𝛽0+𝛽1 𝑁 𝑖1990+𝑎𝑖+𝑢𝑖1990
∆𝐶𝑅𝑖=𝛿0+𝛽1∆𝑁 𝑖+∆𝑢𝑖
First-difference equation: eliminates
First Differences
(3)
![Page 7: Two-Period Panel Data Analysis](https://reader035.vdocument.in/reader035/viewer/2022081502/56815f24550346895dcdf012/html5/thumbnails/7.jpg)
Estimating Fixed Effects Models
𝐶𝑅𝑖𝑡=𝛽0+𝛿0𝑌𝑟 2000+𝛽1𝑁 𝑖𝑡+𝑎𝑖+𝑢𝑖𝑡(2)
![Page 8: Two-Period Panel Data Analysis](https://reader035.vdocument.in/reader035/viewer/2022081502/56815f24550346895dcdf012/html5/thumbnails/8.jpg)
Estimating First-Differencing Models
∆𝐶𝑅𝑖=𝛿0+𝛽1∆𝑁 𝑖+∆𝑢𝑖(3)
![Page 9: Two-Period Panel Data Analysis](https://reader035.vdocument.in/reader035/viewer/2022081502/56815f24550346895dcdf012/html5/thumbnails/9.jpg)
Estimating First-Differencing Models ∆𝐶𝑅𝑖=𝛿0+𝛽1∆𝑁 𝑖+∆𝑢𝑖(3)
Estimating Fixed Effects Models
𝐶𝑅𝑖𝑡=𝛽0+𝛿0𝑌𝑟 2000+𝛽1𝑁 𝑖𝑡+𝑎𝑖+𝑢𝑖𝑡(2)
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Demonstrates that models using fixed effects are using variation within states (or cities, counties, colleges, etc.) to estimate parameters
![Page 10: Two-Period Panel Data Analysis](https://reader035.vdocument.in/reader035/viewer/2022081502/56815f24550346895dcdf012/html5/thumbnails/10.jpg)
𝐶𝑅𝑖𝑡=𝛽0+𝛿0𝑌𝑟 07+𝛽1 𝑁 𝑖𝑡+𝜀𝑖𝑡
𝜀𝑖𝑡=𝑎𝑖+𝑢𝑖𝑡
∆𝐶𝑅𝑖=𝛿0+𝛽1∆𝑁 𝑖+∆𝑢𝑖
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.
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Costs and Benefits of Fixed Effects Model
Benefit—controls for unobserved factors that vary across states, cities, colleges… Costs1. More expensive data collection2. Can reduce or eliminate variation in explanatory variables.