ANALYSIS REGRESSION OF ENOE DATA

INTRODUCTION

• In this model we are going to study some variables which could have an impact on someone’s monthly income based on the ENOE’s data (Encuesta Nacional de Ocupación y Empleo).
• So according to the OLS method, we took some steps to carry out our analysis. First and foremost, we declared our variables; some of them were created as “dummy variables” in order to show the impact of each one on monthly income. Then we constructed our econometric model, based on some assumptions. After this, we ran our regression interpreting the results at the same time.

We declared some libraries to make our estimations. Then we loaded our data base.

library(haven)
library(car)
library(stargazer)
library(lmtest)
SDEMT118 <- read_dta(file.choose())

We have eliminated some lines.

SDEMT118 <- SDEMT118[SDEMT118$eda > 18,] # solo mayores de edad
SDEMT118 <- SDEMT118[SDEMT118$ingocup > 0,] # solo ingresos mayores a cero
SDEMT118 <- SDEMT118[SDEMT118$anios_esc != 99,] # años de escolaridad distintos a 99 (informacion no disponible)

Encoding some variables to make our regression easier.

SDEMT118$mujer <- recode(SDEMT118$sex, "1=0; 2=1") # mujer=1; 0=hombre
table(SDEMT118$mujer)

SDEMT118$casado <- recode(SDEMT118$e_con, "5=1; 1=0; 2=0; 3=0; 4=0; 6=0; 9=0") # mujer=1; 0= hombre
table(SDEMT118$casado)

Running the regression focusing on important variables. Then we summarized with “stargazer” the regression in order to interpret the results more easily.

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=================================================
                         Dependent variable:     
                    -----------------------------
                            log(ingocup)         
-------------------------------------------------
mujer                         -0.283***          
                               (0.004)           
                                                 
eda                           0.040***           
                               (0.001)           
                                                 
I(eda2)                      -0.0004***          
                              (0.00001)          
                                                 
anios_esc                     0.075***           
                              (0.0005)           
                                                 
casado                        0.038***           
                               (0.004)           
                                                 
hrsocup                       0.011***           
                              (0.0001)           
                                                 
Constant                      6.540***           
                               (0.017)           
                                                 
-------------------------------------------------
Observations                   112,660           
R2                              0.301            
Adjusted R2                     0.301            
Residual Std. Error      0.641 (df = 112653)     
F Statistic         8,081.319*** (df = 6; 112653)
=================================================
Note:                 *p<0.1; **p<0.05; ***p<0.01
                    0.5 %        99.5 %
(Intercept)  6.4952109637  6.5851018097
mujer       -0.2938389997 -0.2728216185
eda          0.0378879514  0.0419496415
I(eda^2)    -0.0004406711 -0.0003949861
anios_esc    0.0733600709  0.0757822642
casado       0.0276027273  0.0487996649
hrsocup      0.0109560386  0.0115236530

• In the regression, the variable mujer shows us that a woman tends to earn 28.3% less than a man.
• The second variable (eda) tells us that if a person is older by one more year, that person tends to earn 4% more.
• the third variable I(eda2) means that at a certain age, like if for example the person is 61 he will earn -0.8% less than the person who is 60. (The age of 60 is taken as the turning point of the age variable)
• Then the next variable (anios_esc) shows that for one more year of schooling, the person will earn 7.5% more than before.
• The variable (casado) says that a person who is married tends to earn 3.8% more than a person who is not (single). The next variable (hrsocup) tells us that for one more hour worked per week, the person will earn 1.1 more in his monthly income.
  
• The R squared tells us that our model explains only 30.1% on the variation of the monthly income.

Making an Hipothesis with our model: T TEST

summary(reg)

Call:
lm(formula = log(ingocup) ~ mujer + eda + I(eda^2) + anios_esc + 
    casado + hrsocup, data = SDEMT118)

Residuals:
    Min      1Q  Median      3Q     Max 
-5.0028 -0.3203  0.0398  0.3784  3.8213 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  6.540e+00  1.745e-02 374.824   <2e-16 ***
mujer       -2.833e-01  4.080e-03 -69.449   <2e-16 ***
eda          3.992e-02  7.884e-04  50.632   <2e-16 ***
I(eda^2)    -4.178e-04  8.868e-06 -47.117   <2e-16 ***
anios_esc    7.457e-02  4.702e-04 158.605   <2e-16 ***
casado       3.820e-02  4.115e-03   9.284   <2e-16 ***
hrsocup      1.124e-02  1.102e-04 102.014   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.6415 on 112653 degrees of freedom
  (7182 observations deleted due to missingness)
Multiple R-squared:  0.3009,    Adjusted R-squared:  0.3009 
F-statistic:  8081 on 6 and 112653 DF,  p-value: < 2.2e-16

We can assume that each variable is very significant at the significance level of 5%.

Then we created a graph (histogram) of the “ingocup” variable.

Doing a Breusch-Pagan test and a White test and interpreting the result.

Breusch-Pegan test

bptest(reg)

    studentized Breusch-Pagan test

data:  reg
BP = 4151.9, df = 6, p-value < 2.2e-16

White test

bptest(reg, ~fitted(reg) + I(fitted(reg)^2))

    studentized Breusch-Pagan test

data:  reg
BP = 2774.6, df = 2, p-value < 2.2e-16

conclusion: There is heteroskedasticity given the fact that 2.2e-16 < 0.05 So we are going to adjust using-robust estandar errors.

reg3 <- coeftest(reg, hccm) 
reg3

t test of coefficients:

               Estimate  Std. Error  t value  Pr(>|t|)    
(Intercept)  6.5402e+00  1.9203e-02 340.5831 < 2.2e-16 ***
mujer       -2.8333e-01  4.1152e-03 -68.8489 < 2.2e-16 ***
eda          3.9919e-02  9.0704e-04  44.0102 < 2.2e-16 ***
I(eda^2)    -4.1783e-04  1.0794e-05 -38.7079 < 2.2e-16 ***
anios_esc    7.4571e-02  5.2625e-04 141.7019 < 2.2e-16 ***
casado       3.8201e-02  4.2141e-03   9.0651 < 2.2e-16 ***
hrsocup      1.1240e-02  1.3675e-04  82.1904 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

stargazer(reg, reg3, type = "text")

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=============================================================
                               Dependent variable:           
                    -----------------------------------------
                            log(ingocup)                     
                                 OLS              coefficient
                                                     test    
                                 (1)                  (2)    
-------------------------------------------------------------
mujer                         -0.283***            -0.283*** 
                               (0.004)              (0.004)  
                                                             
eda                           0.040***             0.040***  
                               (0.001)              (0.001)  
                                                             
I(eda2)                      -0.0004***           -0.0004*** 
                              (0.00001)            (0.00001) 
                                                             
anios_esc                     0.075***             0.075***  
                              (0.0005)              (0.001)  
                                                             
casado                        0.038***             0.038***  
                               (0.004)              (0.004)  
                                                             
hrsocup                       0.011***             0.011***  
                              (0.0001)             (0.0001)  
                                                             
Constant                      6.540***             6.540***  
                               (0.017)              (0.019)  
                                                             
-------------------------------------------------------------
Observations                   112,660                       
R2                              0.301                        
Adjusted R2                     0.301                        
Residual Std. Error      0.641 (df = 112653)                 
F Statistic         8,081.319*** (df = 6; 112653)            
=============================================================
Note:                             *p<0.1; **p<0.05; ***p<0.01

• In this case, there is no heteroskedasticity anymore, because we have made more robust our estimated errors so we can not reject the assuption of homoskedasticity.

Creating three dummy variables to run the new regression and see what is the effect of being single female/male, and married female/male.

stargazer(reg2, type = "text")

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=================================================
                         Dependent variable:     
                    -----------------------------
                            log(ingocup)         
-------------------------------------------------
marrfem                       -0.352***          
                               (0.006)           
                                                 
singmal                       -0.085***          
                               (0.005)           
                                                 
singfem                       -0.319***          
                               (0.005)           
                                                 
eda                           0.040***           
                               (0.001)           
                                                 
I(eda2)                      -0.0004***          
                              (0.00001)          
                                                 
anios_esc                     0.074***           
                              (0.0005)           
                                                 
hrsocup                       0.011***           
                              (0.0001)           
                                                 
Constant                      6.617***           
                               (0.019)           
                                                 
-------------------------------------------------
Observations                   112,660           
R2                              0.302            
Adjusted R2                     0.302            
Residual Std. Error      0.641 (df = 112652)     
F Statistic         6,971.641*** (df = 7; 112652)
=================================================
Note:                 *p<0.1; **p<0.05; ***p<0.01

• We can see in the first variable (marrfem) that a woman that is married tends to earn 35.2% less that a man who is married.
• In the second one (singmal) says that a man who is single tends to earn 8.5% than a man who is married.
• In the last one (singfem) we can see that a woman that is single tends to earn 31.9% less than a man that is married.

CONCLUSION

• Acording to the economic theory, there are no redundant variables because we have specified our variables correctly, and much less there is perfect collinearity with our independent variables.

• We wondered if it’s possible that some other variables exist which might have an influence on monthly income, so according to the ENOE data, we took into account the informal and formal job variable (job). We made the regression, and according to this, the variable shows that for the simple fact of having a formal job, someone could earn 40% more that someone who doesn’t. we use dummy varibles for this regression too.

SDEMT118$job <- recode(SDEMT118$emp_ppal, "1=0; 2=1") # empleo informal=1; 0=empleo formal
reg2 <- lm(log(ingocup) ~ job + mujer + eda + I(eda^2) + anios_esc + casado + hrsocup, data=SDEMT118)
stargazer(reg2, type = "text")

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=================================================
                         Dependent variable:     
                    -----------------------------
                            log(ingocup)         
-------------------------------------------------
job                           0.400***           
                               (0.004)           
                                                 
mujer                         -0.280***          
                               (0.004)           
                                                 
eda                           0.037***           
                               (0.001)           
                                                 
I(eda2)                      -0.0004***          
                              (0.00001)          
                                                 
anios_esc                     0.057***           
                              (0.0005)           
                                                 
casado                        0.019***           
                               (0.004)           
                                                 
hrsocup                       0.009***           
                              (0.0001)           
                                                 
Constant                      6.678***           
                               (0.017)           
                                                 
-------------------------------------------------
Observations                   112,660           
R2                              0.357            
Adjusted R2                     0.357            
Residual Std. Error      0.615 (df = 112652)     
F Statistic         8,939.598*** (df = 7; 112652)
=================================================
Note:                 *p<0.1; **p<0.05; ***p<0.01