1. PANEL REGRESSION (T≥2) (plm package)
By Mike Jadoo

2. Purpose Bring about an awareness
Enable individuals to properly create analysis
Select the most appropriate model(s).

3. Special Thank you
MLK library Digital commons lab

4. Lecture Structure
Slides, code, datasets are in the groups Meetup files section

5. Lecture Structure Using R i386 3.2.3 or R studio
Can follow lecture and code or code after
There will be some web exercises

6. R i386 3.2.3 (32 bit)/ R-Studio Plm Lmtest XLCONNECT fBasics Tseries
PACKAGE
task
Plm
panel regression model
Lmtest
additional statistical tests
XLCONNECT
Read in excel files
fBasics
for the Jarque Bera Test
Tseries
ADF test
stargazer
for nice reports
PSYCH
Describe( ) descriptive statistics

7. Data series SNAP benefits data from USDA
Civilian population estimates from Census
Food store employment data from BEA

8. Orientation (TYPES OF DATA)
Cross-sectional datasets- observing many subjects at one point in time (i.e. OLS model)
Pooled Cross Sectional-multiple variables over two periods of time
Time series- one variable over multiple periods of time
Panel data- multiple variables over multiple periods of time
This is worth going over

9. Orientation (Terminology Clarification)
Longitudinal data
Pooled Cross sectional
Time series
Panel Data
Longitudinal data: Collection of samples observations about a particular individual(s), firms, or place over multiple periods of time.
Represents combination of regression (linear regression) and time series analysis where a subject (category) is observed over time but unlike time series data many subjects which are observed more than once.
Terminology clarification:
Be advised that Panel data model is often times called longitudinal data model (regression) as it is done so in biostatistics. **Be aware of this whenever researching/googleing the subject. **

10. History of Panel Data Regression
Sir George Biddell Airy's 1861 analysis of astronomical data
R. A. Fisher 1925 explained more fully the concepts and methods of both fixed-effects and random effects
First Paris Conference 1977 experts started to convene and share ideas
Sir George Airy
Sir George Biddell Airy's 1861 analysis of astronomical data was the first person to use this method- he used a random effects model.
R. A. Fisher was noted as explaining more fully the concepts and methods of both fixed-effects and random effects in 1925.
After many papers and attempts to modernize the model in 1977 the First Panel Data Conference was held called “first Paris Conference” and was established to bring together experts to share ideas and new discovers of panel data methodologies.
R.A. Fisher

11. Why use panel regression model?
Gives more observations to analyze
More complicated characteristics and behavioral hypothesis can be tested
Better analysis of the nature of unobserved errors and individual [idiosyncratic] errors
2. Observe same individual units over time so a more complicated dynamics and behavioral hypothesis can be tested rather than a linear regression model where it is one- dimensional data.
3. Provide a means for analyzing more fully the nature of unobserved errors (idosencatic errors) disturbance terms. Disturbance terms are supposed to measure the effects of all kinds of other external factors.

12. Statistical Modeling Find the data Check the data Estimate the model
Review topics theory or use past experience
Formulate a initial model
Find the data
Check the data
Estimate the model
Reformulate the model
Check the Parameter estimates
Interpret your results

13. Statistical modeling process review
Create the hypothesis
- What are you trying to analyze or predict
Go over the topics relative theory
-May involve extensive reading but it is the good first start!!

14. Finding the data sources
Government sources are the good first start!! Can’t find the data your looking for? Staff is there to help. There are more providers of data, some have a cost.
(Data source list presented)
longitudinal:

15. Panel data sets sources
Web exercise
Please see R – code text file for a list of resources

16. Methodology
Review the data series methodology (document that tells you how the data is made), is this acceptable?
Web exercise bls.gov/mfp

17. Data structure
An example

18. Data structure

19. Panel Regression Pooled (OLS) Fixed effects Random effects
First Differencing
R demonstration is per Ani Katchova lecture and Sayed Hossain.
Econometrics Academy Introduction, Ani Katchova:
Hossain Academy
Pooled: putting all observations together and running an ols regression. Taken out the cross section and time series feature of the data table.
Combing observations we den the heterogeneity or individual effects that may exist.
Assume all categories are the same.
Fixed effects: allows for heterogeneity or individuality among categories (individuals) with different intercept terms. Categories are not the same.
Random effects: all categories have common mean value, common intercept.
First-difference: used when time is not invariant (same values across time)

20. Models Assumptions Fixed Effects
1. The model has parameter estimates and unobserved effect ai.
2. Data comes from cross sectional random sample
3. X variables changes over time, no prefect linear relationships exists among X’s
4. For each period, the expected value of the idiosyncratic errors given all X’s and the ai is 0
5. Variance for the idiosyncratic error terms and the ai is constant
6. The idiosyncratic errors are uncorrelated
7. The idiosyncratic errors are independent and normally distributed
Wooldridge. Intro to econometrics

21. Models Assumptions Random Effects
1. The model has parameter estimates and there is an ai.
2. Data comes from cross sectional random sample
3. No prefect linear relationships exists among X’s
4. For each period, the expected value of the idiosyncratic errors given all X’s and the ai is 0. Also, the expected value of ai for each parameter equals the constant term
5. Variance for the idiosyncratic error terms given all X’s and the ai is constant. Also, the variance of ai is constant given all X’s
6. The idiosyncratic errors are uncorrelated

22. Fixed vs Random Effects
Fixed effects: assuming that the individual effects are correlated with the other X’s; study the causes of changes within a person [or entity]
Random effects: assuming that the individual effects are uncorrelated with the other X’s

23. Demonstration Hypothesis Data
“Does food stamp benefits effect grocery store employment? if so, by how much?”
Data
FOODEMPLY: Food store employment: BEA
SNAPP: average annual participation in SNAP
SNAPB: SNAP benefits distributed in thousands of dollars
CIVPOP: estimated civilian population
STATE: state identifier for all 50 states,
YRS: time variable years from 2008 to 2012
You can hack with your own data set.

24. Creating the Model
Create scatter plot, histogram
R-excerise

25. Creating the Model Examine the data Create the summary statistics
These statistical measures and illustrations should be included in your report.

26. Test the series for normality
JB Test

27. Checking for Prefect Collinearity
Correlation box of all variables
x <- newdata[3:6]
y <- newdata[3:6]
cor(x, y)
LSNAPP LSNAPB LFoodEmply LCivPop
LSNAPP
LSNAPB
LFoodEmply
LCivPop
Correlation box of just explanatory variables
newdata$LFoodEmply <-NULL
x <- newdata[3:5]
y <- newdata[3:5]
LSNAPP LSNAPB LCivPop
LSNAPP
LSNAPB
LCivPop

28. Panel Regression
Set the panel regression

29. Panel Regression
Create and save the results for the different types of panel models, use the LM test to find best one.
#Pooled OLS estimator:
ols<-plm(LFoodEmply~LSNAPP+LSNAPB+LCivPop,data=newdata, index=c("id","t"),model='pooling')
#first difference;
firstdiff<-plm(LFoodEmply~LSNAPP+LSNAPB+LCivPop,data=newdata, index=c("id","t"),model='fd')
#fixed effects(within):
fixed<-plm(LFoodEmply~LSNAPP+LSNAPB+LCivPop,data=newdata, index=c("id","t"),model='within')
# Random effects:
random<-plm(LFoodEmply~LSNAPP+LSNAPB+LCivPop,data=newdata, index=c("id","t"),model='random‘)
R-excerise

30. Panel Regression
To determine Fixed vs Random effects use the Hausman Test
# Hausman test for fixed versus random effects model
phtest(random, fixed)
Ho: random effect model is appropriate
Ha: fixed effect model is appropriate
Hausman Test
data: LFoodEmply ~ LSNAPP + LSNAPB + LCivPop
chisq = , df = 3, p-value = 3.803e-05
alternative hypothesis: one model is inconsistent

31. Test your model If your panel data has a long time period then:
Check for serial correlation
pbgtest(fixed)
Check for cross-sectional dependence (Baltagi) pcdtest()

32. Statistics of Fit R2 and Adjusted R2 (some say R2 doesn’t matter)
Residual Sum of Squares or Mean Squared Errors
F-statistics: p< 0.05
Parameter estimates R2
Residual Sum of Squares or MSE

33. Statistics of Fit

34. Statistics of Fit

35. Statistics of Fit

36. Interpretation of model
How you say it counts!!
Logs
Levels
Levels to log dependant variable
Random effects: when the average effect of X changes across time and between states by one unit, this causes _______ change in Y.
Fixed effects: Y changes _____ much overtime, on average per state, when X increases by one unit

37. Report findings
Stargazer: collects the essential parameter estimates in a nice format

38. Summary Orientation History Statistical model process Data sources
Data Structure of panel data model
Panel data model in R
Interpretation of models parameter estimates
Reporting

39. MORE TO EXPLORE!!!

40. Announcements

41. Special Thanks
Ani Katchova- Econometric Academy Sayed Hossain: Hossain Academy