PANEL REGRESSION
(plm package)
By Mike Jadoo
Purpose
• Bring about an awareness
• Enable individuals to properly create analysis
• Select the most appropriate model(s).
Special Thank you
Lecture Structure
• Slides, code, datasets are in the groups
Meetup files section
Lecture Structure
• Can follow lecture and code or code after
• You can use your own data sets
• There will be some web exercises
R-Studio
PACKAGE
task
Plm
Lmtest
XLCONNECT
fBasics
Tseries
stargazer
PSYCH
panel regression model
additional statistical tests
Read in excel files
for the Jarque Bera Test
ADF test
for nice reports
Describe( ) descriptive statistics
Data series
• SNAP benefits data from USDA
• Civilian population estimates from Census
• Food store employment data from BEA
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
Orientation
(Terminology Clarification)
Longitudinal data
• Pooled Cross sectional
• Time series
• Panel Data
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 shared ideas
Sir George Airy
R.A. Fisher
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
Statistical Modeling
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
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!!
Finding the data sources
Government sources
Can’t find the data your looking for?
Staff is there to help.
There are more providers of data, some have a
cost.
Panel data sets sources
Methodology
• Review the data series methodology
(document that tells you how the data is
made), is this acceptable?
Reproducibility-(the NSF study)
• The inability to reproduce scientific work has
lead to the distrust in scientific findings among
the public and experts.
• Efforts have been made across all scientific
backgrounds (including economics) to bring
awareness to this issue and improve
reproducibility of scientific work.
Reproducibility-(the NSF study)
Why is this important:
Improve scientific discovery
Enhancing and Clarifying Protocols
Increasing Sharing of Research Material
Enhancing Education and Training
Reproducibility-(the NSF study)
What can we do?
-Make your code available and easy to
read
-Document each step when creating your
model carefully and clearly
Data structure
Data structure
Panel Regression
• Pooled (OLS)
• Fixed effects
• Random effects
• First Differencing
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
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
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
Demonstration
• Hypothesis
“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
Creating the Model
• Create scatter plot, histogram
Creating the Model
• Examine the data
– Create the summary statistics
Test the series for normality
JB Test
Checking for Prefect Collinearity
Correlation box of all variables
x <- newdata[3:6]
y <- newdata[3:6]
cor(x, y)
LSNAPP
LSNAPP
1.0000000
LSNAPB
0.9924108
LFoodEmply 0.9028983
LCivPop
0.9497298
LSNAPB LFoodEmply LCivPop
0.9924108 0.9028983 0.9497298
1.0000000 0.8857668 0.9315922
0.8857668 1.0000000 0.9756423
0.9315922 0.9756423 1.0000000
• Correlation box of just explanatory variables
newdata$LFoodEmply <-NULL
x <- newdata[3:5]
y <- newdata[3:5]
cor(x, y)
LSNAPP
LSNAPB
LSNAPP
LSNAPB
LCivPop
1.0000000 0.9924108 0.9497298
0.9924108 1.0000000 0.9315922
LCivPop
0.9497298
0.9315922
1.0000000
Panel Regression
• Set the panel regression
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‘)
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 = 23.125, df = 3, p-value = 3.803e-05
alternative hypothesis: one model is inconsistent
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()
Statistics of Fit
• R2 and Adjusted R2
(some say R2 doesn’t matter)
• Residual Sum of Squares or Mean Squared
Errors
• T-statistics and p< 0.05
• Parameter estimates
Statistics of Fit
Statistics of Fit
Statistics of Fit
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
Report findings
Stargazer: collects the essential parameter estimates in a nice format
Summary
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Orientation
History
Statistical model process
Data sources
Data Structure of panel data model
Panel data model in R
Interpretation of models parameter estimates
Reporting
MORE TO EXPLORE!!!
• R for Data Science, Grolemund and Wickham:
http://r4ds.had.co.nz/
• Practical Regression and Anova using R, Faraway:
http://cran.mtu.edu/doc/contrib/Faraway-PRA.pdf
• Web Companion – Applied Regression:
http://socserv.socsci.mcmaster.ca/jfox/Books/Companion/app
endix.html
• Data cleaning in R:
http://cran.mtu.edu/doc/contrib/de_Jonge+van_der_LooIntroduction_to_data_cleaning_with_R.pdf
• Online:
– http://www.statmethods.net/index.html
– Coursera: https://www.coursera.org/
Training options in the DMV
• Montgomery college
http://cms.montgomerycollege.edu/iti/careers/bigdata.html
Announcements
• October 5th Data Viz
Special Thanks
Ani Katchova- Econometric Academy
Sayed Hossain: Hossain Academy