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Topics in Microeconometrics University of Queensland Brisbane, QLD July 7-9, 2010 PowerPoint PPT Presentation


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William Greene Department of Economics Stern School of Business. Topics in Microeconometrics University of Queensland Brisbane, QLD July 7-9, 2010. Lab 3-1 Panel Data in Nonlinear Models. Unbalanced Panel Data Set. Load healthcare.lpj Create group size variable

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Topics in Microeconometrics University of Queensland Brisbane, QLD July 7-9, 2010

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William greene department of economics stern school of business

William Greene

Department of Economics

Stern School of Business

Topics in MicroeconometricsUniversity of QueenslandBrisbane, QLDJuly 7-9, 2010


Lab 3 1 panel data in nonlinear models

Lab 3-1Panel Data in Nonlinear Models


Unbalanced panel data set

Unbalanced Panel Data Set

Load healthcare.lpj

Create group size variable

Examine Distribution of Group Sizes

Sample ; all$

Regress ; Lhs=one ; Rhs=one ; Panel ; Str=id$

Create ; _obs=Ndx(id,1)$ (Obs. Number in group)

Reject ;_obs < _groupti $ (Keep last obs. in group)

Histogram ; rhs=_obs$


Group sizes

Group Sizes


Cluster correction

Cluster Correction

PROBIT ; Lhs = doctor

; Rhs = one,age,female,educ,married,working

; Cluster = ID $

Normal exit: 4 iterations. Status=0. F= 17448.10

+---------------------------------------------------------------------+

| Covariance matrix for the model is adjusted for data clustering. |

| Sample of 27326 observations contained 7293 clusters defined by |

| variable ID which identifies by a value a cluster ID. |

+---------------------------------------------------------------------+

Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X

--------+-------------------------------------------------------------

|Index function for probability

Constant| -.17336** .08118 -2.135 .0327

AGE| .01393*** .00102 13.691 .0000 43.5257

FEMALE| .32097*** .02378 13.497 .0000 .47877

EDUC| -.01602*** .00492 -3.259 .0011 11.3206

MARRIED| -.00153 .02553 -.060 .9521 .75862

WORKING| -.09257*** .02423 -3.820 .0001 .67705

--------+-------------------------------------------------------------


Fixed effects models

Fixed Effects Models

? Fixed Effects Probit.

Sample ; All $

Namelist ; X = age,hhninc,educ,married $

Probit ; Lhs = doctor ; Rhs = X ; FEM ; Marginal ; Pds = _groupti$

Probit ; Lhs = doctor ; Rhs = X,one ; Marginal $


A fixed effects probit model

A Fixed Effects Probit Model

Probit ;lhs=doctor ; rhs=age,hhninc,educ,married

; fem ; pds=_groupti ; Parameters $

+---------------------------------------------+

| Probit Regression Start Values for DOCTOR |

| Maximum Likelihood Estimates |

| Dependent variable DOCTOR |

| Weighting variable None |

| Number of observations 27326 |

| Iterations completed 10 |

| Log likelihood function -17700.96 |

| Number of parameters 5 |

| Akaike IC=35411.927 Bayes IC=35453.005 |

| Finite sample corrected AIC =35411.929 |

+---------------------------------------------+

+---------+--------------+----------------+--------+---------+----------+

|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|

+---------+--------------+----------------+--------+---------+----------+

AGE .01538640 .00071823 21.423 .0000 43.5256898

HHNINC -.09775927 .04626475 -2.113 .0346 .35208362

EDUC -.02811308 .00350079 -8.031 .0000 11.3206310

MARRIED -.00930667 .01887548 -.493 .6220 .75861817

Constant .02642358 .05397131 .490 .6244

These are the pooled data estimates used to obtain starting values for the iterations to get the full fixed effects model.


Fixed effects model

Fixed Effects Model

Nonlinear Estimation of Model Parameters

Method=Newton; Maximum iterations=100

Convergence criteria: max|dB| .1000D-08, dF/F= .1000D-08, g<H>g= .1000D-08

Normal exit from iterations. Exit status=0.

+---------------------------------------------+

| FIXED EFFECTS Probit Model |

| Maximum Likelihood Estimates |

| Dependent variable DOCTOR |

| Number of observations 27326 |

| Iterations completed 11 |

| Log likelihood function -9454.061 |

| Number of parameters 4928 |

| Akaike IC=28764.123 Bayes IC=69250.570 |

| Finite sample corrected AIC =30933.173 |

| Unbalanced panel has 7293 individuals. |

| Bypassed 2369 groups with inestimable a(i). |

| PROBIT (normal) probability model |

+---------------------------------------------+

+---------+--------------+----------------+--------+---------+----------+

|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|

+---------+--------------+----------------+--------+---------+----------+

Index function for probability

AGE .06334017 .00425865 14.873 .0000 42.8271810

HHNINC -.02495794 .10712886 -.233 .8158 .35402169

EDUC -.07547019 .04062770 -1.858 .0632 11.3602526

MARRIED -.04864731 .06193652 -.785 .4322 .76348771


Computed fixed effects parameters

Computed Fixed Effects Parameters


Logit fixed effects models conditional and unconditional fe

Logit Fixed Effects Models Conditional and Unconditional FE

? Logit, conditional vs. unconditional

Logit ; Lhs = doctor

; Rhs = X ; Pds = _groupti $ (Conditional)

Logit ; Lhs = doctor

; Rhs = X ; Pds = _groupti ; Fixed $


With t 5 ip seems tolerable

With T ≈ 5, IP Seems Tolerable


Hausman test for fixed effects

Hausman Test for Fixed Effects

? Logit: Hausman test for fixed effects

?

Logit ; Lhs = doctor ; Rhs = X ; Pds = _groupti $

Matrix ; Bf = B ; Vf = Varb $

Logit ; Lhs = doctor ; Rhs = X,One $

Calc ; K = Col(X) $

Matrix ; Bp = b(1:K) ; Vp = Varb(1:K,1:K) $

Matrix ; Db = Bf - Bp ; DV = Vf - Vp

; List ; Hausman = Db'<DV>Db $

Calc ; List ; Ctb(.95,k) $


Random effects vs random constant

Random Effects vs Random Constant

? Random effects

? Quadrature Based (Butler and Moffitt) Estimator

Probit ; Lhs = doctor

; Rhs = X,One ; Random ; Pds = _groupti $

Calc ; List ; RhoQ = rho $

? Simulation Based Estimator

Probit ; Lhs = doctor ; Rhs = X,one

; RPM ; Pds = _groupti

; Fcn = One(N) ; Halton ; Pts = 25 $

Calc ; ks = col(x)+2 $

Calc ; List ; RhoRP = b(ks)^2/(1+b(ks)^2) ; RhoQ $


Using matrix algebra

Using Matrix Algebra

Namelists with the current sample serve 2 major functions:

(1) Define lists of variables for model estimation

(2) Define the columns of matrices built from the data.

NAMELIST ; X = a list ; Z = a list … $

Set the sample any way you like. Observations are now the rows of all matrices. When the sample changes, the matrices change.

Lists may be anything, may contain ONE, may overlap (some or all variables) and may contain the same variable(s) more than once


Matrix functions

Matrix Functions

Matrix Product: MATRIX ; XZ = X’Z $

Moments and Inverse MATRIX ; XPX = X’X ; InvXPX = <X’X> $

Moments with individual specific weights in variable w.

Σiwi xixi’ = X’[w]X.

[Σiwi xixi’ ]-1 = <X’[w]X>

Unweighted Sum of Rows in a Matrix

Σi xi = 1’X

Column of Sample Means

(1/n) Σi xi = 1/n * X’1 or MEAN(X)

(Matrix function. There are over 100 others.)

Weighted Sum of rows in matrix

Σiwi xi = 1’[w]X


Normality test for probit

Normality Test for Probit

Thanks to Joachim Wilde, Univ. Halle, Germany for suggesting this.


Normality test for probit1

Normality Test for Probit

NAMELIST ; XI = One,... $

CREATE ; yi = the dependent variable $

PROBIT ; Lhs = yi ; Rhs = Xi ; Prob = Pfi $

CREATE ; bxi = b'Xi ; fi = N01(bxi) $

CREATE ; zi3 = -1/2*(bxi^2 - 1) ; zi4 = 1/4*(bxi*(bxi^2+3)) $

NAMELIST ; Zi = Xi,zi3,zi4 $

CREATE ; di = fi/sqr(pfi*(1-pfi)) ; ei = yi - pfi

; eidi = ei*di ; di2 = di*di $

MATRIX ; List ; LM = 1'[eidi]Zi * <ZI'[di2]Zi> * Zi'[eidi]1 $


Endogenous variable in probit model

Endogenous Variable in Probit Model

PROBIT ; Lhs = y1, y2

; Rh1 = rhs for the probit model,y2

; Rh2 = exogenous variables for y2 $

SAMPLE ; All $

CREATE ; GoodHlth = Hsat > 5 $

PROBIT ; Lhs = GoodHlth,Hhninc

; Rh1 = One,Female,Hhninc

; Rh2 = One,Age,Educ $


Random parameters model

Random Parameters Model

? Random parameters specification

?

Logit ; Lhs = doctor

; Rhs = One,age,educ,hhninc,married

; Pds = _groupti ; RPM ; Halton ; Pts = 25 ; Cor

; Fcn = One(n),hhninc(n),educ(n) ; Marginal ; Parameters ; maxit=20 $

Sample ; 1 - 7293 $

Create ; binc = 0 $

Matrix ; bi = beta_i(1:7293,2:2) $

Create ; binc= bi $

Kernel ; Rhs = binc $


Random parameters with heterogeneity

Random Parameters with Heterogeneity

? Random parameters with heterogeneity

? Examine effect of heterogeneity.

Sample ; All $

Logit ; Lhs = doctor

; Rhs = One,educ,hhninc,married

; Pds = _groupti

; RPM = female,age

; Halton ; Pts = 15 ; Cor

; Fcn = One(n),educ(n),hhninc(n)

; Marginal

; Parameters $

Create; Bimum = beta_i(firm,2) $

Regress ; Lhs = Bimum ; Rhs = one,InvGood,RawMtl $


Latent class models

Latent Class Models

? Latent class models

Namelist ; X = one,educ,hhninc

Sample ; All $

Logit ; Lhs = doctor

; Rhs = X ; LCM

; Pds=_groupti ; Pts = 3 $

Logit ; Lhs = doctor

; Rhs = X ; LCM = female,age

; Pds=_groupti ; Pts = 3 $

Logit ; Lhs = doctor ; Rhs = X ; LCM ; Pds=_groupti ; Pts = 4 $

Logit ; Lhs = doctor ; Rhs = X ; LCM ; Pds=_groupti ; Pts = 5 $


Fixed and random effects

Fixed and Random Effects

Poisson or NegBin

;PDS=setting

Fixed Effects

  • Default is a conditional esitmator

  • ;FEM uses the unconditional estimator

  • The two are algebraically identical but use different algorithms

    Random Effects

  • Use ; RANDOM

  • Can be fit as a random parameters model with just a random constant


Random parameters

Random Parameters

Poisson

  • ; LHS = dependent variable

  • ; RHS = independent variable(s)

  • ; PDS = setting (may be ;PDS=1)

  • ; RPM ; PTS = number of Points

  • ; Halton (for smarter integration method)

  • ; Correlated if desired to fit correlated

    parameters model

  • ; FCN = variable(n) , variable(n), …

    to indicate which parameters are random


Latent class

Latent Class

Poisson (or NEGBIN)

  • ; LHS = dependent variable

  • ; RHS = independent variable(s)

  • ; LCM for a latent class model

    ; LCM = variables if probabilities are heterogeneous

  • ; PDS = setting (may be ;PDS=1)

  • ; PTS = number of latent classes


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