1. Econometrics I Professor William Greene Stern School of Business
Department of Economics

2. Econometrics I
Part 16 – Panel Data

4. Panel Data Sets Longitudinal data Cross section time series
British household panel survey (BHPS)
Panel Study of Income Dynamics (PSID)
… many others
Cross section time series
Penn world tables
Financial data by firm, by year
rit – rft = i(rmt - rft) + εit, i = 1,…,many; t=1,…many
Exchange rate data, essentially infinite T, large N

5. Benefits of Panel Data
Time and individual variation in behavior unobservable in cross sections or aggregate time series
Observable and unobservable individual heterogeneity
Rich hierarchical structures
More complicated models
Features that cannot be modeled with only cross section or aggregate time series data alone
Dynamics in economic behavior

15. Cornwell and Rupert Data
Cornwell and Rupert Returns to Schooling Data, 595 Individuals, 7 Years (Extracted from NLSY.) 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 BLK = 1 if individual is black 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. 15

17. 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.
Is unbalancedness due to nonrandom attrition from an otherwise balanced panel? This would require special considerations.

18. Application: Health Care Usage
German Health Care Usage Data, 7,293 Individuals, Varying Numbers of Periods This is an unbalanced panel with 7,293 individuals.  There are altogether 27,326 observations.  The number of observations ranges from 1 to 7.   (Frequencies are: 1=1525, 2=2158, 3=825, 4=926, 5=1051, 6=1000, 7=987).  (Downloaded from the JAE Archive) Variables in the file are
DOCTOR = 1(Number of doctor visits > 0) HOSPITAL = 1(Number of hospital visits > 0)
HSAT =  health satisfaction, coded 0 (low) - 10 (high)  
DOCVIS =  number of doctor visits in last three months HOSPVIS =  number of hospital visits in last calendar year PUBLIC =  insured in public health insurance = 1; otherwise = ADDON =  insured by add-on insurance = 1; otherswise = 0
HHNINC =  household nominal monthly net income in German marks /
(4 observations with income=0 were dropped) HHKIDS = children under age 16 in the household = 1; otherwise = EDUC =  years of schooling
AGE = age in years
MARRIED = marital status 18

19. An Unbalanced Panel: RWM’s GSOEP Data on Health Care
N = 7,293 Households

20. A Basic Model for Panel Data
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 ] = 0. Cov[xit,ci] = 0

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

22. 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

23. Assumptions for Asymptotics
Convergence of moments involving cross section Xi.
N increasing, T or Ti assumed fixed.
“Fixed T asymptotics” (see text, p. 348)
Time series characteristics are not relevant (may be nonstationary – relevant in Penn World Tables)
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

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

25. OLS in the Presence of Individual Effects

26. Estimating the Sampling Variance of b
s2(X ́X)-1? Inappropriate because
Correlation across observations (certainly)
Heteroscedasticity (possibly)
A ‘robust’ covariance matrix
Robust estimation (in general)
The White estimator
A Robust estimator for OLS.

27. Cluster Estimator

28. Application: Cornwell and Rupert

29. 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.

31. Using First Differences
Eliminating the heterogeneity

32. 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. Use OLS in first differences and use Newey-West with one lag.

33. 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

34. 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

35. Regression-Treatment Effects Model

36. 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

37. First Differences Model

38. Dealing with Attrition
The attrition issue: Appearance for the second interview was low for people with initial low QOL (death or depression) or with initial high QOL (don’t need the treatment). Thus, missing data at exit were clearly related to values of the dependent variable.
Solutions to the attrition problem
Heckman selection model (used in the study)
Prob[Present at exit|covariates] = Φ(z’θ) (Probit model)
Additional variable added to difference model i = Φ(zi’θ)/Φ(zi’θ)
The FDA solution: fill with zeros. (!)

39. Difference in Differences
With two periods,
This is a linear regression model. If there are no regressors,

40. 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,

41. Difference in Differences

42. 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

43. Difference in Differences

44. 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|M,79] = β81 + γL
It is assumed that unemployment growth in the two cities would be the same if there were no immigration.

45. Implications for Differences
If neither city exposed to migration
E[Yi,0|M,81] - E[Yi,0|M,79] = β81 – β79 (Miami)
E[Yi,0|L,81] - E[Yi,0|L,79] = β81 – β79 (LA)
If both cities exposed to migration
E[Yi,1|M,81] - E[Yi,1|M,79] = β81 – β79 + δ (Miami)
E[Yi,1|L,81] - E[Yi,1|L,79] = β81 – β79 + δ (LA)
One city (Miami) exposed to migration: The difference in differences is.
{E[Yi,1|M,81] - E[Yi,1|M,79]} – {E[Yi,0|L,81] - E[Yi,0|L,79]} = δ (Miami)

46. The Fixed Effects Model
yi = Xi + diαi + εi, for each individual
E[ci | Xi ] = g(Xi); Effects are correlated with included variables.
Cov[xit,ci] ≠0

47. The Within Groups Transformation Removes the Effects

48. Useful Analysis of Variance Notation
Total variation = Within groups variation
+ Between groups variation

49. WHO Data

50. Baltagi and Griffin’s Gasoline Data
World Gasoline Demand Data, 18 OECD Countries, 19 years Variables in the file are
COUNTRY = name of country
YEAR = year, LGASPCAR = log of consumption per car LINCOMEP = log of per capita income LRPMG = log of real price of gasoline
LCARPCAP = log of per capita number of cars
See Baltagi (2001, p. 24) for analysis of these data. The article on which the analysis is based is Baltagi, B. and Griffin, J., "Gasolne Demand in the OECD: An Application of Pooling and Testing Procedures," European Economic Review, 22, 1983, pp  The data were downloaded from the website for Baltagi's text.

51. Analysis of Variance

52. Analysis of Variance
| Analysis of Variance for LGASPCAR |
| Stratification Variable _STRATUM |
| Observations weighted by ONE |
| Total Sample Size |
| Number of Groups |
| Number of groups with no data |
| Overall Sample Mean |
| Sample Standard Deviation |
| Total Sample Variance |
| |
| Source of Variation Variation Deg.Fr Mean Square |
| Between Groups |
| Within Groups |
| Total |
| Residual S.D |
| R-squared MSB/MSW |
| F ratio P value |

53. Estimating the Fixed Effects Model
The FEM is a plain vanilla regression model but with many independent variables
Least squares is unbiased, consistent, efficient, but inconvenient if N is large.

54. Fixed Effects Estimator (cont.)

55. Least Squares Dummy Variable Estimator
b is obtained by ‘within’ groups least squares (group mean deviations)
a is estimated using the normal equations:
D’Xb+D’Da=D’y a = (D’D)-1D’(y – Xb)

56. Inference About OLS
Assume strict exogeneity: Cov[εit,(xjs,cj)]=0. Every disturbance in every period for each person is uncorrelated with variables and effects for every person and across periods.
Now, it’s just least squares in a classical linear regression model.
Asy.Var[b] =

57. Application Cornwell and Rupert

58. LSDV Results
Note huge changes in the coefficients. SMSA and MS change signs. Significance changes completely!
Pooled OLS

59. The Effect of the Effects

60. The Within (LSDV) Estimator is an IV Estimator

61. LSDV – As Usual

62. 2SLS Using Z=MDX as Instruments

63. A Caution About Stata and R2
For the FE model above,
R2 =
R2 =
The coefficient estimates and standard errors are the same. The calculation of the R2 is different. In the areg procedure, you are estimating coefficients for each of your covariates plus each dummy variable for your groups. In the xtreg, fe procedure the R2 reported is obtained by only fitting a mean deviated model where the effects of the groups (all of the dummy variables) are assumed to be fixed quantities. So, all of the effects for the groups are simply subtracted out of the model and no attempt is made to quantify their overall effect on the fit of the model.
Since the SSE is the same, the R2=1−SSE/SST is very different. The difference is real in that we are making different assumptions with the two approaches. In the xtreg, fe approach, the effects of the groups are fixed and unestimated quantities are subtracted out of the model before the fit is performed. In the areg approach, the group effects are estimated and affect the total sum of squares of the model under consideration.

64. Examining the Effects with a KDE
Mean = 4.819, Standard deviation =

65. Robust Covariance Matrix for LSDV Cluster Estimator for Within Estimator
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
|OCC | |
|SMSA | ** |
|MS | |
|EXP | *** |
| Covariance matrix for the model is adjusted for data clustering. |
| Sample of observations contained clusters defined by |
| observations (fixed number) in each cluster |
|DOCC | |
|DSMSA | |
|DMS | |
|DEXP | *** |

66. Time Invariant Regressors
Time invariant xit is defined as invariant for all i. E.g., sex dummy variable, FEM and ED (education in the Cornwell/Rupert data).
If xit,k is invariant for all t, then the group mean deviations are all 0.

67. FE With Time Invariant Variables
| There are 2 vars. with no within group variation. |
| FEM ED |
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
EXP |
WKS |
OCC |
SMSA |
FEM | (Fixed Parameter)
ED | (Fixed Parameter)
| Test Statistics for the Classical Model |
| Model Log-Likelihood Sum of Squares R-squared |
|(1) Constant term only |
|(2) Group effects only |
|(3) X - variables only |
|(4) X and group effects |

68. Drop The Time Invariant Variables Same Results
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
EXP |
WKS |
OCC |
SMSA |
| Test Statistics for the Classical Model |
| Model Log-Likelihood Sum of Squares R-squared |
|(1) Constant term only |
|(2) Group effects only |
|(3) X - variables only |
|(4) X and group effects |
No change in the sum of squared residuals

69. Fixed Effects Vector Decomposition Efficient Estimation of Time Invariant and Rarely Changing Variables in Finite Sample Panel Analyses with Unit Fixed Effects Thomas Plümper and Vera Troeger Political Analysis, 2007

70. Introduction
[T]he FE model … does not allow the estimation of time invariant variables. A second drawback of the FE model … results from its inefficiency in estimating the effect of variables that have very little within variance.
This article discusses a remedy to the related problems of estimating time invariant and rarely changing variables in FE models with unit effects

71. The Model

72. Fixed Effects Vector Decomposition
Step 1: Compute the fixed effects regression to get the “estimated unit effects.” “We run this FE model with the sole intention to obtain estimates of the unit effects, αi.”

73. Step 2
Regress ai on zi and compute residuals

74. Step 3
Regress yit on a constant, X, Z and h using ordinary least squares to estimate α, β, γ, δ.

75. Step 1 (Based on full sample)
These 2 variables have no within group variation.
FEM ED
F.E. estimates are based on a generalized inverse.
| Standard Prob Mean
LWAGE| Coefficient Error z z>|Z| of X
EXP| ***
WKS| *
OCC| *
IND|
SOUTH|
SMSA| **
UNION| **
FEM| (Fixed Parameter)
ED| (Fixed Parameter)

76. Step 2 (Based on 595 observations)
| Standard Prob Mean
UHI| Coefficient Error z z>|Z| of X
Constant| ***
FEM| **
ED| ***

77. Step 3!
| Standard Prob Mean
LWAGE| Coefficient Error z z>|Z| of X
Constant| ***
EXP| ***
WKS| ***
OCC| ***
IND| ***
SOUTH|
SMSA| ***
UNION| ***
FEM| ***
ED| ***
HI| *** D-13

79. What happened here?

80. The Random Effects Model
ci is uncorrelated with xit for all t;
E[ci |Xi] = 0
E[εit|Xi,ci]=0

81. Notation

82. Error Components Model
A Generalized Regression Model

83. Notation

84. Convergence of Moments

85. Random vs. Fixed Effects
Random Effects
Small number of parameters
Efficient estimation
Objectionable orthogonality assumption (ci  Xi)
Fixed Effects
Robust – generally consistent
Large number of parameters

86. Ordinary Least Squares
Standard results for OLS in a GR model
Consistent
Unbiased
Inefficient
True variance of the least squares estimator

87. Estimating the Variance for OLS

88. OLS Results for Cornwell and Rupert
| Residuals Sum of squares = |
| Standard error of e = |
| Fit R-squared = |
| Adjusted R-squared = |
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
Constant
EXP
EXPSQ D
OCC
SMSA MS
FEM
UNION ED

89. Alternative Variance Estimators
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] |
Constant
EXP
EXPSQ D
OCC
SMSA MS
FEM
UNION ED
Robust – Cluster___________________________________________
Constant
EXP
EXPSQ D
OCC
SMSA MS
FEM
UNION ED

90. Generalized Least Squares

91. Generalized Least Squares

92. Estimators for the Variances

93. Practical Problems with FGLS

94. Stata Variance Estimators

95. Other Variance Estimators
x´ does not contain a constant term in the preceding.

96. Fixed Effects Estimates
Least Squares with Group Dummy Variables
LHS=LWAGE Mean =
Residuals Sum of squares =
Standard error of e =
These 2 variables have no within group variation.
FEM ED
F.E. estimates are based on a generalized inverse.
Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X
EXP| ***
EXPSQ| *** D
OCC|
SMSA| **
MS|
FEM| (Fixed Parameter)
UNION| **
ED| (Fixed Parameter)

97. Computing Variance Estimators

98. Application
Random Effects Model: v(i,t) = e(i,t) + u(i)
Estimates: Var[e] =
Var[u] =
Corr[v(i,t),v(i,s)] =
Lagrange Multiplier Test vs. Model (3) =
( 1 degrees of freedom, prob. value = )
(High values of LM favor FEM/REM over CR model)
Fixed vs. Random Effects (Hausman) = (Cannot be computed)
( 8 degrees of freedom, prob. value = )
(High (low) values of H favor F.E.(R.E.) model)
Sum of Squares
R-squared
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
EXP
EXPSQ D
OCC
SMSA MS
FEM
UNION ED
Constant

99. Testing for Effects: An LM Test

100. Application: Cornwell-Rupert

101. Testing for Effects Regress; lhs=lwage;rhs=fixedx,varyingx;res=e$
Matrix ; tebar=7*gxbr(e,person)$
Calc ; list;lm=595*7/(2*(7-1))*
(tebar'tebar/sumsqdev - 1)^2$
LM =

102. A Hausman Test for FE vs. RE
Estimator
Random Effects
E[ci|Xi] = 0
Fixed Effects
E[ci|Xi] ≠ 0
FGLS
(Random Effects)
Consistent and Efficient
Inconsistent
LSDV
(Fixed Effects)
Consistent
Inefficient
Possibly Efficient

103. Computing the Hausman Statistic
β does not contain the constant term in the preceding.

104. Hausman Test +--------------------------------------------------+
| Random Effects Model: v(i,t) = e(i,t) + u(i) |
| Estimates: Var[e] = D-01 |
| Var[u] = D+00 |
| Corr[v(i,t),v(i,s)] = |
| Lagrange Multiplier Test vs. Model (3) = |
| ( 1 df, prob value = ) |
| (High values of LM favor FEM/REM over CR model.) |
| Fixed vs. Random Effects (Hausman) = |
| ( 4 df, prob value = ) |
| (High (low) values of H favor FEM (REM).) |

105. Fixed Effects +----------------------------------------------------+
| Panel:Groups Empty , Valid data |
| Smallest 7, Largest |
| Average group size |
| There are 2 vars. with no within group variation. |
| ED FEM |
| Look for huge standard errors and fixed parameters.|
| F.E. results are based on a generalized inverse. |
| They will be highly erratic. (Problematic model.) |
| Unable to compute std.errors for dummy var. coeffs.|
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
|WKS | |
|OCC | |
|IND | |
|SOUTH | |
|SMSA | ** |
|UNION | ** |
|EXP | *** |
|EXPSQ | *** D |
|ED | (Fixed Parameter) |
|FEM | (Fixed Parameter) |

106. Random Effects +--------------------------------------------------+
| Random Effects Model: v(i,t) = e(i,t) + u(i) |
| Estimates: Var[e] = D-01 |
| Var[u] = D+00 |
| Corr[v(i,t),v(i,s)] = |
| Lagrange Multiplier Test vs. Model (3) = |
| ( 1 df, prob value = ) |
| (High values of LM favor FEM/REM over CR model.) |
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
|WKS | |
|OCC | *** |
|IND | |
|SOUTH | |
|SMSA | * |
|UNION | *** |
|EXP | *** |
|EXPSQ | *** D |
|ED | *** |
|FEM | *** |
|Constant| *** |

107. The Hausman Test, by Hand
--> matrix; br=b(1:8) ; vr=varb(1:8,1:8)$
--> matrix ; db = bf - br ; dv = vf - vr $
--> matrix ; list ; h =db'<dv>db$
Matrix H has 1 rows and 1 columns. 1 1|
--> calc;list;ctb(.95,8)$
| Listed Calculator Results |
Result =

108. Hello, professor greene. 
I’ve taken the liberty of attaching some LIMDEP output in order to ask your view on whether my Hausman test stat is “large,” requiring the FEM, or not, allowing me to use the (much better for my research) REM.
Specifically, my test statistic, corrected for heteroscedasticity, is about 34 and significant with 6 df. 
I considered this a large value until I found your “assignment 2” on the internet which shows a value of 2554 with 4 df.  Now, I’d like to assert that 34/6 is a small value.

109. Variable Addition

110. A Variable Addition Test
Asymptotic equivalent to Hausman
Also equivalent to Mundlak formulation
In the random effects model, using FGLS
Only applies to time varying variables
Add expanded group means to the regression (i.e., observation i,t gets same group means for all t.
Use Wald test to test for coefficients on means equal to 0. Large chi-squared weighs against random effects specification.

111. Means Added to REM - Mundlak
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
|WKS | |
|OCC | |
|IND | |
|SOUTH | |
|SMSA | ** |
|UNION | ** |
|EXP | *** |
|EXPSQ | *** D |
|ED | *** |
|FEM | *** |
|WKSB | ** |
|OCCB | *** |
|INDB | |
|SOUTHB | |
|SMSAB | *** |
|UNIONB | ** |
|EXPB | *** |
|EXPSQB | |
|Constant| *** |

112. Wu (Variable Addition) Test
--> matrix ; bm=b(12:19);vm=varb(12:19,12:19)$
--> matrix ; list ; wu = bm'<vm>bm $
Matrix WU has 1 rows and 1 columns. 1 1|

113. A Hierarchical Linear Model Interpretation of the FE Model

114. Hierarchical Linear Model as REM
| Random Effects Model: v(i,t) = e(i,t) + u(i) |
| Estimates: Var[e] = D-01 |
| Var[u] = D+00 |
| Corr[v(i,t),v(i,s)] = |
| Sigma(u) = |
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
OCC |
SMSA |
MS |
EXP |
FEM |
ED |
Constant|

115. Evolution: Correlated Random Effects

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

117. Correlated Random Effects

118. Mundlak’s Approach for an FE Model with Time Invariant Variables

119. Mundlak Form of FE Model
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
x(i,t)=================================================================
OCC |
SMSA |
MS |
EXP |
z(i)===================================================================
FEM |
ED |
Means of x(i,t) and constant===========================================
Constant|
OCCB |
SMSAB |
MSB |
EXPB |
Variance Estimates=====================================================
Var[e]|
Var[u]|

120. Panel Data Extensions
Dynamic models: lagged effects of the dependent variable
Endogenous RHS variables
Cross country comparisons– large T
More general parameter heterogeneity – not only the constant term
Nonlinear models such as binary choice

121. The Hausman and Taylor Model

122. H&T’s 4 Step FGLS Estimator

123. H&T’s 4 STEP IV Estimator

125. Arellano/Bond/Bover’s Formulation Builds on Hausman and Taylor

126. Arellano/Bond/Bover’s Formulation Adds a Lagged DV to H&T
This formulation is the same as H&T with yi,t-1 contained in x2it .

127. Dynamic (Linear) Panel Data (DPD) Models
Application
Bias in Conventional Estimation
Development of Consistent Estimators
Efficient GMM Estimators

128. Dynamic Linear Model

129. A General DPD model

130. Arellano and Bond Estimator

131. Arellano and Bond Estimator

132. Arellano and Bond Estimator

133. Application: Maquiladora

134. Maquiladora

135. Estimates