1. Econometric Analysis of Panel Data
William Greene Department of Economics Stern School of Business

2. Short Term Agenda for Simple Effects Models
Models with individual effects
Interpretation of models
Computation (practice) and estimation (theory)
Extensions
Nonstandard panels: Rotating, Pseudo-, Nested
Generalizing the regression model
Alternative estimators
Methods
Least squares: OLS, GLS, FGLS
MLE and Maximum Simulated Likelihood

3. Fixed and Random Effects
Unobserved individual effects in regression: E[yit | xit, ci]
Notation:
Linear specification:
Fixed Effects: E[ci | Xi ] = g(Xi). Cov[xit,ci] ≠0
effects are correlated with included variables.
Random Effects: E[ci | Xi ] = μ; effects are uncorrelated with included variables. If Xi contains a constant term, μ=0 WLOG. Common: Cov[xit,ci] =0, but E[ci | Xi ] = μ is needed for the full model

4. Convenient Notation Fixed Effects – the ‘dummy variable model’
Random Effects – the ‘error components model’
Individual specific constant terms.
Compound (“composed”) disturbance

5. Balanced and Unbalanced Panels
Distinction: Balanced vs. Unbalanced Panels
A notation to help with mechanics
zi,t, i = 1,…,N; t = 1,…,Ti
The role of the assumption
Mathematical and notational convenience:
Balanced, n=NT
Unbalanced:
Is the fixed Ti assumption ever necessary? Almost never. (Baltagi chapter 9 is about algebra, not different models!)
Is unbalancedness due to nonrandom attrition from an otherwise balanced panel? This will require special considerations.

6. Unbalanced Panels and Attrition ‘Bias’
Test for ‘attrition bias.’ (Verbeek and Nijman, Testing for Selectivity Bias in Panel Data Models, International Economic Review, 1992, 33,
Variable addition test using covariates of presence in the panel
Nonconstructive – what to do next?
Do something about attrition bias. (Wooldridge, Inverse Probability Weighted M-Estimators for Sample Stratification and Attrition, Portuguese Economic Journal, 2002, 1: )
Stringent assumptions about the process
Model based on probability of being present in each wave of the panel

8. Inverse Probability Weighting

9. An Unbalanced Panel: RWM’s GSOEP Data on Health Care
N = 7,293 Households
Some households exited then returned

10. Unbalanced Panel Data – Not Attrition (First 10 households in healthcare data)

11. Exogeneity Contemporaneous exogeneity
E[εit|xit,ci]=0  Not sufficient for regression
Doesn’t imply how to estimate β
Strict exogeneity – the most common assumption
E[εit|xi1, xi2,…,xiT,ci]=0
Can use first difference or fixed effects
Cannot hold if xit contains lagged values of yit
Sequential exogeneity?
E[εit|xi1, xi2,…,xit,ci] = 0
These assumptions are not testable. They are part of the model.

12. Assumptions for Asymptotics
Convergence of moments involving cross section Xi.
N increasing, T or Ti assumed fixed.
“Fixed T asymptotics” (see text, p. 175)
Time series characteristics are not relevant (may be nonstationary)
If T is also growing, need to treat as multivariate time series.
Ranks of matrices. X must have full column rank. (Xi may not, if Ti < K.)
Strict exogeneity and dynamics. If xit contains yi,t-1 then xit cannot be strictly exogenous. Xit will be correlated with the unobservables in period t-1. (To be revisited later.)
Empirical characteristics of microeconomic data

13. Estimating β β is the partial effect of interest
Can it be estimated (consistently) in the presence of (unmeasured) ci?
Does pooled least squares “work?”
Strategies for “controlling for ci” using the sample data
Using a proxy variable.

14. The Pooled Regression Presence of omitted effects
Potential bias/inconsistency of OLS – depends on ‘fixed’ or ‘random’

15. A Popular Misconception
If only one variable in X is correlated with , the other coefficients are consistently estimated. False.
The problem is “smeared” over the other coefficients.

16. OLS with Individual Effects Bias turns on the group means

17. Mundlak’s Estimator
Mundlak, Y., “On the Pooling of Time Series and Cross Section Data, Econometrica, 46, 1978, pp

18. Chamberlain’s (1982) Approach
Use a linear projection, not necessarily the conditional mean.
This “regression” can be computed T times, using one year at a time.
How would we reconcile the multiple estimators of each parameter?.

19. Chamberlain’s (1982) Approach

20. Proxy Variables
Proxies for unobserved effects: e.g., Test score for unobserved ability
Interest is in δ(xit,ci)=E[yit|xit,ci]/xit
Since ci is unobserved, we seek APE = Ec[δ(xit,ci)]
Proxy has two characteristics
Ignorable in the model: E[yit|xit,zi,ci] = E[yit|xit,ci]
‘Explains’ ci in that E[ci|zi,xit] = E[ci|zi]. In the presence of zi, xit does not further ‘explain ci.’
Then, Ec[δ(xit,ci)] = Ez{E[yit|xit,zi]/xit}
Proof: See Wooldridge, pp
Loose ends:
Where do you get the proxy?
What is E[yit|xit,zi]? Use the linear projection and hope for the best.

21. Estimating the Sampling Variance of bOLS
s2(X ́X)-1?
Correlation across observations => No
Possible heteroscedasticity
Find a “robust” covariance matrix
Robust estimation (in general)
The White estimator
A Robust estimator for OLS.

22. A ‘Cluster’ Estimator

23. Cluster Estimator (cont.)

24. Cornwell and Rupert Data
Cornwell and Rupert Returns to Schooling Data, 595 Individuals, 7 Years Variables in the file are
EXP = work experience WKS = weeks worked OCC = occupation, 1 if blue collar, IND = 1 if manufacturing industry SOUTH = 1 if resides in south SMSA = 1 if resides in a city (SMSA) MS = 1 if married FEM = 1 if female UNION = 1 if wage set by union contract ED = years of education LWAGE = log of wage = dependent variable in regressions
These data were analyzed in Cornwell, C. and Rupert, P., "Efficient Estimation with Panel Data: An Empirical Comparison of Instrumental Variable Estimators," Journal of Applied Econometrics, 3, 1988, pp  See Baltagi, page 122 for further analysis.  The data were downloaded from the website for Baltagi's text.

25. Application: Cornell and Rupert

26. Bootstrapping
Some assumptions that underlie it - the sampling mechanism Method: 1. Estimate using full sample: --> b 2. Repeat R times: Draw n observations from the n, with replacement Estimate  with b(r). 3. Estimate variance with W = (1/R)r [b(r) - b][b(r) - b]’

27. Bootstrap Application
matr;bboot=init(7,21,0.)$ Store results here name;x=one,occ,…,exp$ Define X regr;lhs=lwage;rhs=x$ Compute b calc;i=0$ Counter Proc Define procedure regr;lhs=lwage;rhs=x;quietly$ … Regression matr;{i=i+1};bboot(*,i)=b$... Store b(r) Endproc Ends procedure exec;n=20;bootstrap=b$ 20 bootstrap reps matr;list;bboot' $ Display results

28. Results of Bootstrap Procedure

29. Bootstrap Replications
Full sample result
Bootstrapped sample results

30. Bootstrap variance for a panel data estimator
Panel Bootstrap = Block Bootstrap
Data set is N groups of size Ti
Bootstrap sample is N groups of size Ti drawn with replacement.

32. Bootstrapping Naïve bootstrap: Why is it naïve? Cases when it fails
Time series
“Clustered data”
Order statistics
Parameters on the edge of the parameter space
Alternatives
Block bootstrap
“Wild” bootstrap (injects extra randomness)

33. Using First Differences
Eliminating the heterogeneity

34. OLS with First Differences
With strict exogeneity of (Xi,ci), OLS regression of Δyit on Δxit is unbiased and consistent but inefficient.
GLS is unpleasantly complicated. In order to compute a first step estimator of σε2 we would use fixed effects. We should just stop there. Or, use OLS in first differences and use Newey-West with one lag.

35. Two Periods With two periods and strict exogeneity,
This is a classical regression model. If there are no regressors,

36. Difference-in-Differences Model
With two periods and strict exogeneity of D and T,
This is a linear regression model. If there are no regressors,

37. Difference in Differences

39. Outcome is the fees charged.
Activity is collusion on fees.

40. Treatment Schools: Treatment is an intervention by the Office of Fair Trading
Control Schools were not involved in the conspiracy
Treatment is not voluntary

43. Treatment (Intervention) Effect = δ

44. In order to test robustness two versions of the fixed effects model were run. The first is Ordinary Least Squares, and the second is heteroscedasticity and auto-correlation robust (HAC) standard errors in order to check for heteroscedasticity and autocorrelation.

48. Natural Experiment: Do Motorcycle Helmets Save Lives?
In the three years after Michigan repealed a mandatory motorcycle helmet law, deaths and head injuries among bikers rose sharply, according to a recent study.
Deaths at the scene of the crash more than quadrupled, while deaths in the hospital tripled for motorcyclists. Head injuries have increased overall, and more of them are severe, the researchers report in the American Journal of Surgery.

49. D-in-D Model: Natural Experiment
With two periods and strict exogeneity,
This is a classical regression model. If there are no regressors,

50. D-i-D – Natural Experiment
Card and Krueger: “Minimum Wages and Employment: A Case Study of the Fast Food Industry in New Jersey and Pennsylvania,” AER, 84(4), 1994,
Pennsylvania vs. New Jersey
1991, NJ raises minimum wage
Compare change in employment PA after the change to change in employment in NJ after the change.
Differences cancel out other things specific to the state that would explain change in employment.

51. A Tale of Two Cities
A sharp change in policy can constitute a natural experiment
The Mariel boatlift from Cuba to Miami (May-September, 1980) increased the Miami labor force by 7%. Did it reduce wages or employment of non-immigrants?
Compare Miami to Los Angeles, a comparable (assumed) city.
Card, David, “The Impact of the Mariel Boatlift on the Miami Labor Market,” Industrial and Labor Relations Review, 43, 1990, pp

52. Difference in Differences

53. Applying the Model c = M for Miami, L for Los Angeles
Immigration occurs in Miami, not Los Angeles
T = 1979, 1981 (pre- and post-)
Sample moment equations: E[Yi|c,t,T]
E[Yi|M,79] = β79 + γM
E[Yi|M,81] = β81 + γM + δ
E[Yi|L,79] = β79 + γL
E[Yi|L,79] = β81 + γL
It is assumed that unemployment growth in the two cities would be the same if there were no immigration.

54. Implications for Differences
Neither city exposed to migration
E[Yi,0|M,81] - E[Yi,0|M,79] = [β81 + γM ] – [β79 + γM] ( Miami)
E[Yi,0|L,81] - E[Yi,0|L,79] = [β81 + γL ] – [β79 + γL] (LA)
Both cities exposed to migration
E[Yi,1|M,81] - E[Yi,1|M,79] = [β81 + γM ] – [β79 + γM] + δ(Miami)
E[Yi,1|L,81] - E[Yi,1|L,79] = [β81 + γL ] – [β79 + γL] + δ(LA)
One city (Miami) exposed to migration: The difference in differences is.
Miami change - Los Angeles change
{E[Yi,1|M,81] - E[Yi,1|M,79]} – {E[Yi,0|L,81] - E[Yi,0|L,79]} = δ (Miami)

55. The Tale
1979
1980
1981
1982
1983
1984
1985
In 79, Miami unemployment is 2.0% lower
In 80, Miami unemployment is 7.1% lower
From 79 to 80, Miami gets % better
In 81, Miami unemployment is 3.0% lower
In 82, Miami unemployment is 3.3% higher
From 81 to 82, Miami gets % worse

56. Application of a Two Period Model
“Hemoglobin and Quality of Life in Cancer Patients with Anemia,”
Finkelstein (MIT), Berndt (MIT), Greene (NYU), Cremieux (Univ. of Quebec)
1998
With Ortho Biotech – seeking to change labeling of already approved drug ‘erythropoetin.’ r-HuEPO

58. QOL Study Quality of life study
i = 1,… clinically anemic cancer patients undergoing chemotherapy, treated with transfusions and/or r-HuEPO
t = 0 at baseline, 1 at exit. (interperiod survey by some patients was not used)
yit = self administered quality of life survey, scale = 0,…,100
xit = hemoglobin level, other covariates
Treatment effects model (hemoglobin level)
Background – r-HuEPO treatment to affect Hg level
Important statistical issues
Unobservable individual effects
The placebo effect
Attrition – sample selection
FDA mistrust of “community based” – not clinical trial based statistical evidence
Objective – when to administer treatment for maximum marginal benefit

59. Regression-Treatment Effects Model

60. Effects and Covariates
Individual effects that would impact a self reported QOL: Depression, comorbidity factors (smoking), recent financial setback, recent loss of spouse, etc.
Covariates
Change in tumor status
Measured progressivity of disease
Change in number of transfusions
Presence of pain and nausea
Change in number of chemotherapy cycles
Change in radiotherapy types
Elapsed days since chemotherapy treatment
Amount of time between baseline and exit

61. First Differences Model

62. Finding
Optimal treatment. Conventional wisdom and assumption of policy.
Study finding
Note the implication of the study for the location of the optimal point for the treatment. Largest marginal benefit moves from the left tail to the center.

64. Most Helpful Customer Reviews
31 of 39 people found the following review helpful Too theoretical and poorly written
By Doktor Faustus on May 7, 2013
Format: Hardcover Econometric Analysis" by William Greene is one of the more widely use graduate-level textbooks in econometrics. I used it in my first year PhD econometrics course. This is unfortunate for several reasons. The book states that its first objective is to introduce students to applied econometrics, especially the basic techniques of linear regression. When reading the book, however, what the reader notices first is that the applications are essentially just footnotes; the meat of each chapter is dense econometric theory. An applied textbook would focus on working with data, but Greene's book has exercises that focus on proving obscure statistical properties (i.e. prove that the asymptotic variance of various estimators goes to zero). Useful for theorists, but not for applied work, which is what the book advertises itself as. Another problem with the book is its impenetrable text. Reading this book is drudgery even when not trying to make sense of the absurdly huge matrix equations. Greene uses academic, elevated language that does not belong in a technical textbook. Where the student needs clear explanation, he instead reads sentences like the following found in a chapter introduction: "We first consider the consequences for the least squares estimator of the more general form of the regression model. This will include assessing the effect of ignoring the complication of the generalized model and of devising an appropriate estimation strategy, still based on least squares". After reading that second sentence several times I still don't understand what Greene is trying to convey. Finally the book is much too large and expensive for a class textbook. The book is 1200 pages long and includes numerous asides in every chapter. If the objective of the book is to teach econometrics to graduate students (as it says in the book), then it would be better off focusing on important topics and applications, not on topics that are never used by the vast majority of economists. I do not recommend this book for anyone; there are better econometrics textbooks available for undergraduates, graduate students, and professionals.

65. October 13, 2014 By Daniel Pulido
This review is from: Econometric Analysis (7th Edition) (Hardcover)
The delivery was fine. But the book itself is the worst Econometric Analysis book
I have ever come across. No examples. Only a continuous list of theorems.
I would not recommend anyone this book.