7. Data Analysis Results
7.1 Regression Results
Regression results of the full unrestricted model can be found below in Table 6.
Table 6 Unrestricted regression results
Variable
Coefficient (Std. Error)
t
(p-values)
Post*Morocco 1.830
(0.115)
15.79 (0.000)
Post 0.065
(0.048)
1.35 (0.176)
Morocco -1.631
(0.053)
-30.50 (0.000)
Urban 0.432
(0.050)
8.58 (0.000)
Wealth Index 0.629
(0.017)
35.59 (0.000) Post*Morocco*Female -0.229
(0.144)
-1.40 (0.163)
Post*Female 0.342
(0.069)
4.97 (0.000)
Morocco*Female -0.188
(0.075)
-2.49 (0.013)
Urban*Female 0.211
(0.071)
2.96 (0.003) Wealth Index*Female 0.484
(0.025)
19.31 (0.000)
Female -2.384
(0.078)
-30.39 (0.000)
Constant 5.533
(0.055)
100.46 (0.000)
-- -- --
R-Squared 0.1023
Observations 141, 402
Breusch-Pagan (p-value)
2543.36 (0.000)
I conducted a Breusch-Pagan/ Cook-Weisberg test for heteroskedasticity for this regression. Heteroskedasticity violates the fifth fundamental assumption of multiple linear regression, the homoscedasticity assumption, which is that variance is constant or, more precisely, ββ¦the error u [π in this model] has the same variance given any value of the explanatory variablesβ (Wooldridge 2013, p. 62). If this assumption is violated and there is heteroskedasticity present in the model, the estimated standard deviations and t-statistics are likely to be biased. However, even in the presence of heteroskedasticity, the estimated coefficients remain unbiased. For this test, the null hypothesis is that there is no
heteroskedasticity, or more specifically, that variance is constant. I found a π! value of 2453.36 with a 0.000 significance level, which means that null hypothesis is rejected and suggests that this data does suffer from heteroskedasticity.
I have corrected for this by using robust standard errors and t-statistics. This estimated model can be found below in Table 7.
Table 7 Unrestricted regression results with robust standard errors and t statistics
Variable
Coefficient
(Robust Std. Error)
t
(p-values)
Post*Morocco 1.830
(0.100)
18.36 (0.000)
Post 0.065
(0.051)
1.28 (0.202)
Morocco -1.631
(0.052)
-31.32 (0.000)
Urban 0.432
(0.051)
8.43 (0.000)
Wealth Index 0.629
(0.018)
34.28 (0.000) Post*Morocco*Female -0.229
(0.144)
-1.59 (0.111)
Post*Female 0.342
(0.073)
4.70 (0.000)
Morocco*Female -0.188
(0.073)
-2.58 (0.010)
Urban*Female 0.211
(0.073)
2.90 (0.004) Wealth Index*Female 0.484
(0.026)
18.72 (0.000)
Female -2.384
(0.080)
-29.97 (0.000)
Constant 5.533
(0.056)
98.02 (0.000)
-- -- --
R-Squared 0.1023
Observations 141, 402
Additionally, in order to identify the sources of heteroskedasticity in the model, I
estimated the model using the squared residuals as the dependent variable. The results of this are found below in Table 8.
Table 8 Regression on squared residuals
Variable
Coefficient (Std. Error)
t
(p-values)
Post*Morocco -3.592
(0.522)
-6.88 (0.000)
Post -0.184
(0.217)
-0.85 (0.397)
Morocco -9.203
(0.241)
--38.21 (0.000)
Urban -1.489
(0.227)
-6.56 (0.000)
Wealth Index 2.293
(0.080)
28.78 (0.000) Post*Morocco*Female 2.800
(0.741)
3.77 (0.000)
Post*Female 1.094
(0.310)
3.53 (0.000)
Morocco*Female -1.257
(0.340)
-3.70 (0.000)
Urban*Female 2.461
(0.322)
7.65 (0.000) Wealth Index*Female 0.454
(0.113)
4.02 (0.000)
Female -2.858
(0.353)
-8.09 (0.000)
Constant 24.040
(0.248)
96.89 (0.000)
-- -- --
R-Squared 0.0636
Observations 141, 402
These results indicate that there are many sources of heteroskedasticity in this model. The only independent variable above that is not significant in this regression is the Post variable, which differentiates between time periods. Again, I have attempted to correct for the
heteroskedasticity found in the model by using robust standard errors, the results of which are found above in Table 7.
As discussed, the most important coefficients are the treatment coefficients. For males, this is represented as π·π, and for females, this is equal to π·π+ π·π. The estimated value of the treatment effect is positive for both genders. For males, this value is 1.830, meaning that for males the treatment is associated with an increase of 1.830 years of education on average. For females, the value for this coefficient is 1.601, meaning that for females the treatment is
associated with an increase of 1.601 years of education on average. I tested the hypothesis that there is a significant treatment effect; specifically, the null hypothesis is that π½! =π½! = 0. This test has a result of f=286.50, with a p-value of 0.000. Thus, we can reject the null hypothesis that there is no treatment effect at the 99% significant level. Additionally, I used an F-test to test whether or not the treatment effect depends on gender. Specifically, the null hypothesis is that π½!
is equal to zero. This test has a result with a result of F=2.54 with a p-value of 0.111. Thus, we fail to reject the hypothesis that the treatment effect depends on gender. Thus, we can conclude that the treatment coefficients for males and females are not statistically significantly different.
These estimated values and statistical tests are consistent with the hypothesis that the Moudawana reform is associated with an increase in educational attainment.
Because this study period occurs over a relatively short period of time directly following the reform, one potential explanation for why the treatment effect doesnβt depend on gender is that the increased relative return on investment of girlsβ education as an incentive to increased educational attainment is not present. That is, an increase in women empowerment would in the long turn encourage families to send their daughters to school longer, as they will be able to make their own choices about employment or graduate school in the future and thus be better
able to reap the benefits of schooling. However, it seems unlikely that families would realize this so soon after the reform. Thus, the effect being roughly the same for males and females is
consistent with the short-term hypothesis that increasing women empowerment increases educational attainment for children.
Aside from this main conclusion, there are other interesting results of this study. The estimated wealth index coefficient, represented by π·π for males, is 0.629; for females,
represented by π·π+ π·ππ, the estimated value is 1.113. So, the estimated value for females is roughly twice that for males. This suggests that female education may be consumed as a luxury good, as it is positively correlated with a rise in income, whereas male education is seen as more of a necessity.
Both male and female education is significantly and positively correlated with urbanity.
This is expected, as education and attendance are typically better in cities. Additionally, as I will discuss later, there is evidence that there is a lack of knowledge about and enforcement of the Moudawana in rural areas, so this positive coefficient supports the hypothesis that the
Moudawana is correlated with this increase in educational attainment. The constant for males is 6.397, while the constant for females is 4.436, suggesting that average female educational attainment is still far behind average male educational attainment.
The small, positive values for the Post coefficient, representing change over time are expected and in accordance with a general increase in education over time. The negative values for π·π, the Morocco coefficient, are negative, which is unsurprising given that the educational system in Egypt is on the whole marginally more developed than in Morocco.