COMMENTS ARE IN BOLD LETTERS

         ECONOMETRICS SOFTWARE LIBRARY (ESL) PROGRAM -- VERSION 4.35
           Copyright (C) by Ramu Ramanathan --- All rights reserved
   Dept. of Econ., UC San Diego, La Jolla, CA 92093-0508, PH. (619)534-6787
            FAX (619)534-7040, Email address: ramu@weber.ucsd.edu

Reading header file data7-4.hdr
List of variables
  0) const       1) WLFP        2) YF          3) YM          4) EDUC      
  5) UE          6) MR          7) DR          8) URB         9) WH        
 10) D90       

period: 1, maxobs: 100, obs range: full 1-100, current 1-100
Reading datafile data7-4 BY OBSERVATIONS

PART I

?genr D90YF = D90*YF                 (Generate new variables)
Generated var. no. 11 (D90YF)
?genr D90UE = D90*UE
Generated var. no. 12 (D90UE)
?genr D90MR = D90*MR
Generated var. no. 13 (D90MR)
?square YF EDUC UE MR DR URB WH D90YF D90UE D90MR  ;
Created sq_YF = YF squared  as var no. 14
Created sq_EDUC = EDUC squared  as var no. 15
Created sq_UE = UE squared  as var no. 16
Created sq_MR = MR squared  as var no. 17
Created sq_DR = DR squared  as var no. 18
Created sq_URB = URB squared  as var no. 19
Created sq_WH = WH squared  as var no. 20
Created sq_D90YF = D90YF squared  as var no. 21
Created sq_D90UE = D90UE squared  as var no. 22
Created sq_D90MR = D90MR squared  as var no. 23

List of variables
  0) const       1) WLFP        2) YF          3) YM          4) EDUC      
  5) UE          6) MR          7) DR          8) URB         9) WH        
 10) D90        11) D90YF      12) D90UE      13) D90MR      14) sq_YF     
 15) sq_EDUC    16) sq_UE      17) sq_MR      18) sq_DR      19) sq_URB    
 20) sq_WH      21) sq_D90YF   22) sq_D90UE   23) sq_D90MR  

(The following is the basic model)

?ols WLFP const YF EDUC UE MR DR URB WH D90YF D90UE D90MR  ;

        OLS ESTIMATES USING THE 100 OBSERVATIONS 1-100
                 Dependent variable  - WLFP

  VARIABLE           COEFFICIENT         STDERROR      T STAT   2Prob(t > |T|)

  0) constant            47.6366           6.5784     7.24136    < 0.0001 ***
  2) YF               0.00477939     7.339485e-04     6.51189    < 0.0001 ***
  4) EDUC                0.27507        0.0455059     6.04471    < 0.0001 ***
  5) UE                 -1.06141         0.245591    -4.32186    < 0.0001 ***
  6) MR                -0.207293         0.104894    -1.97622   0.0512267 *
  7) DR                 0.281618         0.133697     2.10638   0.0379862 **
  8) URB              -0.0784652        0.0206237    -3.80462  0.00026013 ***
  9) WH                -0.111495        0.0242421    -4.59924    < 0.0001 ***
 11) D90YF           -0.00405375     6.821243e-04    -5.94282    < 0.0001 ***
 12) D90UE             -0.569355         0.327225    -1.73995   0.0853242 *
 13) D90MR              0.126361        0.0509756     2.47884    0.015066 **

Mean of dep. var.           53.869     S.D. of dep. variable           5.51914
Error Sum of Sq (ESS)      427.576     Std Err of Resid. (sgmahat)     2.19185
Unadjusted R-squared         0.858     Adjusted R-squared                0.842
F-statistic (10, 89)       53.8705     pvalue = Prob(F > 53.871) is < 0.0001
Durbin-Watson Stat.        1.98322     First-order auto corr coeff       0.007

MODEL SELECTION STATISTICS

SGMASQ          4.80422     AIC             5.32792     FPE            5.33268
HQ              5.98311     SCHWARZ         7.09599     SHIBATA        5.21642
GCV               5.398     RICE            5.48174

?genr usq = uhat*uhat                (Generate uhat squared)
Generated var. no. 24 (usq)

(The following is the Breusch-Pagan auxiliary regression for the error
variance.  The null hypothesis for no HSK is that the coefficients for
the squared terms are all zero.  This gives 10 restrictions.)

?ols usq const sq_YF sq_EDUC sq_UE sq_MR sq_DR sq_URB sq_WH sq_D90YF 
 sq_D90UE sq_D90MR  ;

        OLS ESTIMATES USING THE 100 OBSERVATIONS 1-100
                 Dependent variable  - usq

  VARIABLE           COEFFICIENT         STDERROR      T STAT   2Prob(t > |T|)

  0) constant           -17.3438          10.3559    -1.67478   0.0974871 *
 14) sq_YF          4.907542e-07     3.381952e-07      1.4511    0.150268
 15) sq_EDUC         -0.00491893       0.00112534    -4.37105    < 0.0001 ***
 16) sq_UE              0.105935        0.0697069     1.51973    0.132124
 17) sq_MR            0.00379377       0.00275609     1.37651    0.172118
 18) sq_DR           -0.00374629        0.0217432   -0.172297    0.863595
 19) sq_URB         9.345139e-04     5.051586e-04     1.84994   0.0676404 *
 20) sq_WH            0.00225127     5.806277e-04      3.8773 0.000201832 ***
 21) sq_D90YF      -4.613104e-07     3.332777e-07    -1.38416     0.16977
 22) sq_D90UE         -0.0546619        0.0879087   -0.621803    0.535661
 23) sq_D90MR          0.0042284       0.00177189     2.38638   0.0191337 **

Mean of dep. var.          4.27576     S.D. of dep. variable           7.59649
Error Sum of Sq (ESS)      4315.86     Std Err of Resid. (sgmahat)     6.96367
Unadjusted R-squared         0.245     Adjusted R-squared                0.160
F-statistic (10, 89)       2.88104     pvalue = Prob(F > 2.881) is 0.00368316
Durbin-Watson Stat.        1.73806     First-order auto corr coeff       0.128

MODEL SELECTION STATISTICS

SGMASQ          48.4928     AIC             53.7789     FPE             53.827
HQ              60.3922     SCHWARZ         71.6254     SHIBATA        52.6534
GCV             54.4862     RICE            55.3315

Excluding the constant, p-value was highest for variable 18 (sq_DR)
?genr LMBP = $nrsq          (Computes n times rsquared and saves it as LMBP)
Generated var. no. 25 (LMBP)
?pvalue 3 10 LMBP                   (Computes the pvalue)
For Chi-square (10), area to the right of 24.4549 is 0.00648026

(Because the pvalue < 0.01, we reject the null hypothesis of no HSK and
conclude that there is significant HSK.)

PART II

(The following command generates predicted uhat squared as observed minus
the residual and saves it as usqhat)

?genr usqhat = usq-uhat
Generated var. no. 26 (usqhat)

(If you rerun the above and print usqhat, you will note that several values 
are negative.  These have to be identified and replaced with the original
uhat squared values.)

II.1

?genr d = (usqhat>0)             [d = 1 if usqhat(t) > 0, 0 otherwise]
Generated var. no. 27 (d)

(The following genr sets the positive usqhat values to sigmasq and replaces
negative ones with the original uhat squared values)

?genr sgmasq = (d*usqhat)+((1-d)*usq)
Generated var. no. 28 (sgmasq)
?print -o usq usqhat sgmasq  ;     (Verify that the values are all positive)


 Obs           usq       usqhat       sgmasq

   1    0.68748907      5.50669      5.50669
   2    0.14560512      3.99406      3.99406
   3       10.1571      1.76374      1.76374
   4   0.026216664      7.74488      7.74488
   5       2.80372      1.28804      1.28804
   6       1.89808     -1.42704      1.89808
   7       2.14174      5.21556      5.21556
   8        5.4398      4.76749      4.76749
   9       10.3112      7.90545      7.90545
  10       11.0883      6.19231      6.19231
  11       1.13099     -3.39061      1.13099
  12       3.92053      5.21131      5.21131
  13  0.0091406273      6.54263      6.54263
  14       2.52377      8.19425      8.19425
  15     0.9258649      2.14816      2.14816
  16        4.8309       2.6072       2.6072
  17       1.48051      12.6637      12.6637
  18    0.49113359      3.05867      3.05867
  19    0.23995693      6.52814      6.52814
  20       4.58317      2.78921      2.78921
  21       1.01473      5.78155      5.78155
  22      0.308379      6.25909      6.25909
  23       7.75874      2.57918      2.57918
  24   0.029112688  -0.57548919  0.029112688
  25     0.5236997       6.6152       6.6152
  26    0.22151662   0.21554509   0.21554509
  27    0.81842342   0.42666579   0.42666579
  28    0.37616617      3.42857      3.42857
  29   0.045828205      2.69299      2.69299
  30       1.27472      9.84329      9.84329
  31       2.83837      3.22747      3.22747
  32        18.155      8.81967      8.81967
  33       3.70409      4.76784      4.76784
  34    0.27626281      2.39342      2.39342
  35       2.25453      5.94886      5.94886
  36       4.16959      4.23364      4.23364
  37    0.56818513       3.5591       3.5591
  38       2.25212      9.39795      9.39795
  39       40.7305      15.6303      15.6303
  40       10.4287   0.65782259   0.65782259
  41   0.058160771   0.47657583   0.47657583
  42       3.71531      10.2481      10.2481
  43       3.44954      5.93171      5.93171
  44       1.62882     -1.39253      1.62882
  45       1.60126   0.86065841   0.86065841
  46  0.0034100926       2.2915       2.2915
  47   0.082130157      1.03173      1.03173
  48       47.6634       14.905       14.905
  49       4.91974       3.5899       3.5899
  50  0.0023447083   0.48664814   0.48664814
  51    0.56138312       4.4758       4.4758
  52        12.985      7.81461      7.81461
  53       1.45911      5.33545      5.33545
  54  0.0081247783      7.55657      7.55657
  55       5.22004      7.72436      7.72436
  56       3.29199       2.0967       2.0967
  57       1.47803      9.00949      9.00949
  58       2.12256      1.82558      1.82558
  59        10.079      6.75067      6.75067
  60       2.21385      2.04564      2.04564
  61        9.5421     -2.05829       9.5421
  62    0.71987133      4.12353      4.12353
  63    0.17713808      4.75311      4.75311
  64    0.30629431      4.24565      4.24565
  65       1.10163      1.74992      1.74992
  66       2.50049      2.22751      2.22751
  67  8.6297884e-05       11.199       11.199
  68    0.21190474      2.00158      2.00158
  69  3.8913144e-05      2.54641      2.54641
  70    0.34496047      1.73867      1.73867
  71       1.94148      6.46542      6.46542
  72   0.056508863      4.42375      4.42375
  73       3.79082      2.84755      2.84755
  74     0.4748752  -0.55018888    0.4748752
  75    0.73594444      5.46408      5.46408
  76  0.0031647407   0.33948004   0.33948004
  77  0.0052992329  -0.73721002 0.0052992329
  78       19.8232      5.72342      5.72342
  79       15.6631      4.59239      4.59239
  80    0.99705393      9.60371      9.60371
  81  0.0096706428      2.75655      2.75655
  82       6.42913      5.17884      5.17884
  83       2.32619      1.06063      1.06063
  84       1.72351      2.43491      2.43491
  85       2.15926      5.28749      5.28749
  86        1.7854      5.84064      5.84064
  87       5.73747      2.74726      2.74726
  88       11.8454      5.42623      5.42623
  89       18.3551      10.3259      10.3259
  90       3.32227   0.44883926   0.44883926
  91   0.020937808  -0.75769266  0.020937808
  92       3.62211      7.16032      7.16032
  93       2.19249      7.48285      7.48285
  94   0.023355599      1.74849      1.74849
  95    0.99368981      8.24675      8.24675
  96     0.1225549       -6.014    0.1225549
  97       11.7987      3.01011      3.01011
  98       26.8563      11.8378      11.8378
  99       3.88779      2.08058      2.08058
 100    0.84130239      2.30298      2.30298

?genr wt = 1/sqrt(sgmasq)            (Compute the weights)
Generated var. no. 29 (wt)

(Obtain Weighted Least Squares estimates of the basic model)

?wls wt WLFP const YF EDUC UE MR DR URB WH D90YF D90UE D90MR  ;

     WEIGHTED LEAST SQUARES ESTIMATES USING THE 100 OBSERVATIONS 1-100
     Dependent variable  - WLFP,   Variable used as weight - wt

  VARIABLE           COEFFICIENT         STDERROR      T STAT   2Prob(t > |T|)

  0) constant            45.4119          3.96181     11.4624    < 0.0001 ***
  2) YF               0.00493523     4.460831e-04     11.0635    < 0.0001 ***
  4) EDUC               0.230463        0.0342447     6.72988    < 0.0001 ***
  5) UE                 -1.05302         0.178193    -5.90946    < 0.0001 ***
  6) MR                -0.119943        0.0764895    -1.56809    0.120408
  7) DR                 0.206505         0.110025     1.87689   0.0638097 *
  8) URB              -0.0726509       0.00934068    -7.77791    < 0.0001 ***
  9) WH                -0.115439         0.017933    -6.43725    < 0.0001 ***
 11) D90YF           -0.00415985     4.012242e-04    -10.3679    < 0.0001 ***
 12) D90UE             -0.521182         0.169354    -3.07747  0.00277468 ***
 13) D90MR              0.134905        0.0250202     5.39183    < 0.0001 ***

STATISTICS BASED ON RESIDUALS FOR THE WEIGHTED MODEL

R-squared is suppressed because it is not meaningful.  F-statistic tests the
hypothesis that each coefficient (including the constant term) is zero.

Error Sum of Sq (ESS)      101.719     Std Err of Resid. (sgmahat)     1.06907
F-statistic (11, 89)         86513     pvalue = Prob(F > 86512.963) is < 0.0001
Durbin-Watson Stat.        1.90357     First-order auto corr coeff       0.046

STATISTICS BASED ON RESIDUALS FOR THE ORIGINAL MODEL

R-squared is computed as the square of the corr. between observed and
predicted dep. var.

Mean of dep. var.           53.869     S.D. of dep. variable           5.51914
Error Sum of Sq (ESS)      439.722     Std Err of Resid. (sgmahat)     2.22277
Unadjusted R-squared         0.855     Adjusted R-squared                0.839

MODEL SELECTION STATISTICS

SGMASQ           4.9407     AIC             5.47927     FPE            5.48417
HQ              6.15308     SCHWARZ         7.29757     SHIBATA        5.36461
GCV             5.55135     RICE            5.63746

Excluding the constant, p-value was highest for variable 6 (MR)
Residuals for the unweighted model are saved as uhat.  Type:
  genr newname = uhat    to use it in the future

(Because MR has the highest pvalue, which implies that its coefficient is
least significant, it is omitted next)

?omit MR  ;  

     WEIGHTED LEAST SQUARES ESTIMATES USING THE 100 OBSERVATIONS 1-100
     Dependent variable  - WLFP,   Variable used as weight - wt

  VARIABLE           COEFFICIENT         STDERROR      T STAT   2Prob(t > |T|)

  0) constant            39.7111          1.58716     25.0202    < 0.0001 ***
  2) YF               0.00513826     4.303251e-04     11.9404    < 0.0001 ***
  4) EDUC               0.200728        0.0287456      6.9829    < 0.0001 ***
  5) UE                -0.981892         0.173713    -5.65237    < 0.0001 ***
  7) DR                 0.135551           0.1011     1.34077     0.18337
  8) URB              -0.0704736       0.00931147    -7.56848    < 0.0001 ***
  9) WH                -0.115057        0.0180761    -6.36514    < 0.0001 ***
 11) D90YF           -0.00424018     4.011532e-04      -10.57    < 0.0001 ***
 12) D90UE             -0.554991         0.169332    -3.27753  0.00148892 ***
 13) D90MR              0.128176        0.0248485     5.15831    < 0.0001 ***

STATISTICS BASED ON RESIDUALS FOR THE WEIGHTED MODEL

R-squared is suppressed because it is not meaningful.  F-statistic tests the
hypothesis that each coefficient (including the constant term) is zero.

Error Sum of Sq (ESS)      104.529     Std Err of Resid. (sgmahat)      1.0777
F-statistic (10, 90)         93646     pvalue = Prob(F > 93645.992) is < 0.0001
Durbin-Watson Stat.        1.89077     First-order auto corr coeff       0.053

STATISTICS BASED ON RESIDUALS FOR THE ORIGINAL MODEL

R-squared is computed as the square of the corr. between observed and
predicted dep. var.

Mean of dep. var.           53.869     S.D. of dep. variable           5.51914
Error Sum of Sq (ESS)      465.809     Std Err of Resid. (sgmahat)     2.27501
Unadjusted R-squared         0.848     Adjusted R-squared                0.833

MODEL SELECTION STATISTICS

SGMASQ          5.17565     AIC              5.6894     FPE            5.69322
HQ              6.32203     SCHWARZ         7.38257     SHIBATA         5.5897
GCV             5.75073     RICE            5.82261

Excluding the constant, p-value was highest for variable 7 (DR)
Model selection statistics have decreased (i.e. improved) for 0 criteria

Residuals for the unweighted model are saved as uhat.  Type:
  genr newname = uhat    to use it in the future

II.2
(Note that all the model selection statistics have worsened.  This means
that the previous model is better.  Also note that the pvalue for DR is
now 0.183, whereas in the previous model it was 0.06 and significant at the
10% level.  This suggests strong multicollinearity problems.  In the first
model, the only coefficient not significant at 10% is MR, but pvalue is
only slightly above 0.10.  To avoid possible omitted variable bias and to
keep DR which is significant, we choose the first model as the best overall
because it has the lower model selection statistics and all coefficients
are highly significant except for MR.  If you choose to omit MR anyway, 
you will find that 7 out of 8 selection criteria improve but are still 
below those for the first model.  Therefore the first model is still the 
best and has two more variables.

II.3
To obtain the relationship for 1980, we first set D90 = 0 in the first
model.  This gives (I am using only three decimals)

WLFP hat = 45.4119 + 0.0049 YF + 0.2304 EDUC - 1.0530 UE - 0.1199 MR 
  
                   + 0.2065 DR - 0.0727 URB - 0.1154 WH
           
For 1990, set D90 = 1.  This gives D90YF = YF and similarly for UE and MR. 

WLFP hat = 45.4119 + 0.0049 YF + 0.2304 EDUC - 1.0530 UE - 0.1199 MR 

                   + 0.2065 DR - 0.0727 URB - 0.1154 WH
  
                   - 0.0042 YF - 0.5212 UE + 0.1349 MR

We should combine the coefficents for YF as 0.0049 - 0.0042 = 0.0007 and 
similarly for UE and MR.  The final expression is 

WLFP hat = 45.4119 + 0.0007 YF + 0.2304 EDUC - 1.5742 UE + 0.0150 MR 

                  + 0.2065 DR - 0.0727 URB - 0.1154 WH


The model explains 83.9 percent of the variation in WLFP. 

YF:  As female income rises, you would expect more women to enter the labor
force, that is, a positive coefficient.  For both 1980 and 1990, the
coefficients are positive with the 1990 value slighty lower.  This means
that fewer women responded positively to YF in 1990 than in 1980.

EDUC:  More education means more labor force participation.  The signs are
positive as expected and there is no significant difference between 1980
and 1990.

UE:  A higher unemployment rate might scare more women into not looking for
jobs.  This would lower WLFP, that is, a negative sign.  Both periods have 
negative signs but the coefficient is numerically larger in 1990.  This 
means a greater degree of "discouraged work effect" in 1990.

MR:  The coefficient for marriage rate in 1980 was -0.1199, but in 1990 it
was 0.015.  If the marriage rate increases, one might expect fewer women
to work or look for a job, but that is not the case in 1990.  The coefficient
is positive.  A possible reason might be that nowadays it needs both
husband and wife working to be able to afford a housing.  That might
make more married women join the labor force.

DR:  We would expect a positive effect for divorce because divorced women
are likely to enter the labor force to augment their income.  The observed
sign is positive, but no difference existed between 1980 and 1990.

URB:  If rural women help out in the farm, they are already in the labor 
force.  Hence a higher URB (i.e. lower farm population) might mean a lower 
WLFP.  The expected sign is negative and this checks out and there is no
significant difference between the two Censuses.

WH:  This effect could go either way (see discussion on Page 193).  The 
coefficient is negative, meaning that the more white females in a State,
the less the women's labor force participation.  There is no difference
in this between 1980 and 1990.