What are the Mincerian Determinants of Wages?
A Panel Data Approach
1 Preliminaries
The code for this document is largely based on the public materials of the econometric academy.
1.1 Watch and discuss
1.2 Clarify your workflow
1.3 Load packages
library(tidyverse) # Modern data science library
library(plm) # Panel data analysis library2 Data Import and Tidying
dataWage <- read_csv("https://github.com/ds777/sample-datasets/blob/master/dataWage.csv?raw=true")Declare the dataset as panel data
dataWage <- plm.data(dataWage, index=c("id","t"))use of 'plm.data' is discouraged, better use 'pdata.frame' instead2.1 View tabular data
dataWage3 Exploratory Data Analysis
summary(dataWage) id t exp wks occ
1 : 7 1:595 Min. : 1.00 Min. : 5.00 Min. :0.0000
2 : 7 2:595 1st Qu.:11.00 1st Qu.:46.00 1st Qu.:0.0000
3 : 7 3:595 Median :18.00 Median :48.00 Median :1.0000
4 : 7 4:595 Mean :19.85 Mean :46.81 Mean :0.5112
5 : 7 5:595 3rd Qu.:29.00 3rd Qu.:50.00 3rd Qu.:1.0000
6 : 7 6:595 Max. :51.00 Max. :52.00 Max. :1.0000
(Other):4123 7:595
ind south smsa ms
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:1.0000
Median :0.0000 Median :0.0000 Median :1.0000 Median :1.0000
Mean :0.3954 Mean :0.2903 Mean :0.6538 Mean :0.8144
3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
fem union ed blk
Min. :0.0000 Min. :0.000 Min. : 4.00 Min. :0.00000
1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:12.00 1st Qu.:0.00000
Median :0.0000 Median :0.000 Median :12.00 Median :0.00000
Mean :0.1126 Mean :0.364 Mean :12.85 Mean :0.07227
3rd Qu.:0.0000 3rd Qu.:1.000 3rd Qu.:16.00 3rd Qu.:0.00000
Max. :1.0000 Max. :1.000 Max. :17.00 Max. :1.00000
lwage tdum1 tdum2 tdum3
Min. :4.605 Min. :0.0000 Min. :0.0000 Min. :0.0000
1st Qu.:6.395 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
Median :6.685 Median :0.0000 Median :0.0000 Median :0.0000
Mean :6.676 Mean :0.1429 Mean :0.1429 Mean :0.1429
3rd Qu.:6.953 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
Max. :8.537 Max. :1.0000 Max. :1.0000 Max. :1.0000
tdum4 tdum5 tdum6 tdum7
Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
Mean :0.1429 Mean :0.1429 Mean :0.1429 Mean :0.1429
3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000
Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
exp2
Min. : 1.0
1st Qu.: 121.0
Median : 324.0
Mean : 514.4
3rd Qu.: 841.0
Max. :2601.0
4 Panel Data Regression Modeling
4.1 Variable Definitions
Y <- cbind(dataWage$lwage)
X <- cbind(dataWage$exp, dataWage$exp2, dataWage$wks, dataWage$ed)4.2 Pooled OLS estimator
pooling <- plm(Y ~ X, data=dataWage, model= "pooling")
summary(pooling)Pooling Model
Call:
plm(formula = Y ~ X, data = dataWage, model = "pooling")
Balanced Panel: n = 595, T = 7, N = 4165
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-2.16057670 -0.25034526 0.00027256 0.26792139 2.12969386
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) 4.9080e+00 6.7330e-02 72.8945 < 2.2e-16 ***
X1 4.4675e-02 2.3929e-03 18.6701 < 2.2e-16 ***
X2 -7.1563e-04 5.2794e-05 -13.5552 < 2.2e-16 ***
X3 5.8270e-03 1.1826e-03 4.9271 8.673e-07 ***
X4 7.6041e-02 2.2266e-03 34.1511 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 886.9
Residual Sum of Squares: 635.41
R-Squared: 0.28356
Adj. R-Squared: 0.28287
F-statistic: 411.624 on 4 and 4160 DF, p-value: < 2.22e-164.3 Between estimator
between <- plm(Y ~ X, data=dataWage, model= "between")
summary(between)Oneway (individual) effect Between Model
Call:
plm(formula = Y ~ X, data = dataWage, model = "between")
Balanced Panel: n = 595, T = 7, N = 4165
Observations used in estimation: 595
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-0.978153 -0.220264 0.036574 0.250118 0.985629
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) 4.68303917 0.21009890 22.2897 < 2.2e-16 ***
X1 0.03815295 0.00569666 6.6974 4.953e-11 ***
X2 -0.00063127 0.00012568 -5.0228 6.757e-07 ***
X3 0.01309028 0.00406592 3.2195 0.001355 **
X4 0.07378378 0.00489848 15.0626 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 92.322
Residual Sum of Squares: 62.187
R-Squared: 0.32641
Adj. R-Squared: 0.32185
F-statistic: 71.4768 on 4 and 590 DF, p-value: < 2.22e-164.4 First differences estimator
firstdiff <- plm(Y ~ X, data=dataWage, model= "fd")
summary(firstdiff)Oneway (individual) effect First-Difference Model
Call:
plm(formula = Y ~ X, data = dataWage, model = "fd")
Balanced Panel: n = 595, T = 7, N = 4165
Observations used in estimation: 3570
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-2.0217 -0.0486 0.0157 0.0271 0.0873 2.4263
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
X2 1.7323e-03 7.0214e-05 24.6712 <2e-16 ***
X3 8.1012e-05 5.9103e-04 0.1371 0.891
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 118.06
Residual Sum of Squares: 128.92
R-Squared: 0.0040562
Adj. R-Squared: 0.003777
F-statistic: -300.514 on 1 and 3568 DF, p-value: 14.5 Fixed effects or within estimator
fixed <- plm(Y ~ X, data=dataWage, model= "within")
summary(fixed)Oneway (individual) effect Within Model
Call:
plm(formula = Y ~ X, data = dataWage, model = "within")
Balanced Panel: n = 595, T = 7, N = 4165
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-1.8120879 -0.0511128 0.0037112 0.0614250 1.9434065
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
X1 1.1379e-01 2.4689e-03 46.0888 < 2.2e-16 ***
X2 -4.2437e-04 5.4632e-05 -7.7678 1.036e-14 ***
X3 8.3588e-04 5.9967e-04 1.3939 0.1634
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 240.65
Residual Sum of Squares: 82.632
R-Squared: 0.65663
Adj. R-Squared: 0.59916
F-statistic: 2273.74 on 3 and 3567 DF, p-value: < 2.22e-164.6 Random effects estimator
random <- plm(Y ~ X, data=dataWage, model= "random")
summary(random)Oneway (individual) effect Random Effect Model
(Swamy-Arora's transformation)
Call:
plm(formula = Y ~ X, data = dataWage, model = "random")
Balanced Panel: n = 595, T = 7, N = 4165
Effects:
var std.dev share
idiosyncratic 0.02317 0.15220 0.185
individual 0.10209 0.31952 0.815
theta: 0.8228
Residuals:
Min. 1st Qu. Median 3rd Qu. Max.
-2.0439676 -0.1057048 0.0070992 0.1147499 2.0875839
Coefficients:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) 3.8294e+00 9.3634e-02 40.8974 <2e-16 ***
X1 8.8861e-02 2.8178e-03 31.5360 <2e-16 ***
X2 -7.7257e-04 6.2262e-05 -12.4083 <2e-16 ***
X3 9.6577e-04 7.4329e-04 1.2993 0.1939
X4 1.1171e-01 6.0572e-03 18.4426 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Total Sum of Squares: 260.94
Residual Sum of Squares: 151.35
R-Squared: 0.42
Adj. R-Squared: 0.41945
F-statistic: 753.113 on 4 and 4160 DF, p-value: < 2.22e-164.7 Tests for choosing between models
4.7.1 LM test for random effects versus OLS
plmtest(pooling)
Lagrange Multiplier Test - (Honda) for balanced panels
data: Y ~ X
normal = 72.056, p-value < 2.2e-16
alternative hypothesis: significant effects4.7.2 LM test for fixed effects versus OLS
pFtest(fixed, pooling)
F test for individual effects
data: Y ~ X
F = 40.239, df1 = 593, df2 = 3567, p-value < 2.2e-16
alternative hypothesis: significant effects4.7.3 Hausman test for fixed versus random effects model
phtest(random, fixed)
Hausman Test
data: Y ~ X
chisq = 6191.4, df = 3, p-value < 2.2e-16
alternative hypothesis: one model is 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