Malawi Household Survey

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The range of the dependent variable “mthpay” in this model is (75, 900000). Some observations with considerably high wages are outliers and they could mislead the interpretation of this model. To find those outliers, a scatter plot of EL and wage is created in Figure 3. As shown, the observations of wage higher than around 400,000 are considered as abnormal ones and should be removed from the sample data. Therefore, a new subset “wagenew” is created in R and set “mthpay” at the range from (75 to 400,000).

>summary(mod2)

Call:

lm(formula = mthpay ~ EL + EL2 + EL3 + F + G + U + PC + Age +

Age2)

Residuals:

Min 1Q Median 3Q Max

-153624 -9902 -2039 4794 274021

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 1736.770 7486.397 0.232 0.8166

EL 1757.618 1041.017 1.688 0.0916 .

EL2 -1130.811 156.340 -7.233 7.88e-13 ***

EL3 82.474 6.222 13.255

F 1139.858 1630.220 0.699 0.4845

G 1798.111 1881.441 0.956 0.3394

U 7299.578 1488.776 4.903 1.06e-06 ***

PC 2750.705 1638.741 1.679 0.0935 .

Age 448.769 377.699 1.188 0.2350

Age2 -2.167 4.637 -0.467 0.6403

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 25100 on 1352 degrees of freedom

Multiple R-squared: 0.5079, Adjusted R-squared: 0.5046

F-statistic: 155 on 9 and 1352 DF, p-value:

The new summary of model is listed above, as we can see, t-statistic of EL decreases more than twice from 4.345 to 1.688 and t-statistics of EL2, EL3, Age, Age2 and PC have decreased as well. Overall, the positive change in t-statistics of these 9 predictors and the increase in multiple R-squared, and the decline in standard errors could all infer that estimated sample value of parameters is now closer to their population means.

Task2

The internal rate of return, which is often used to measure the profitability of investment, refers to the rate of return that makes all the cash flows of a particular investment zero The present value refers to the current value of the sum of money or cash flow stream in the future given a particular rate of return in an investment.

Task3

summary(mod3)

Call:

lm(formula = mthpay ~ EL + EL2 + EL3 + F + F * PC + G + U + PC +

Age + Age2)

Residuals:

Min 1Q Median 3Q Max

-153625 -9910 -2017 4789 274022

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 1734.475 7489.551 0.232 0.8169

EL 1757.840 1041.428 1.688 0.0917 .

EL2 -1130.815 156.398 -7.230 8.04e-13 ***

EL3 82.472 6.225 13.249

F 1110.531 1898.468 0.585 0.5587

PC 2727.256 1814.216 1.503 0.1330

G 1800.099 1883.290 0.956 0.3393

U 7300.974 1490.045 4.900 1.08e-06 ***

Age 449.242 378.163 1.188 0.2351

Age2 -2.173 4.642 -0.468 0.6398

FPRC 108.074 3581.668 0.030 0.9759

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 25110 on 1351 degrees of freedom

Multiple R-squared: 0.5079, Adjusted R-squared: 0.5042

F-statistic: 139.4 on 10 and 1351 DF, p-value:

Adding the interaction of variables F:G changes the interpretation of F. In model 3, the coefficient of F is 1110.531, which means that the wage or monthly pay difference between male and female who are not employed by private companies in this sample are 1110.531. FPRC then refers to this differential on the condition of being employed by private companies, which is 108.074. Both coefficients are positive, meaning that wages of female are higher than male’s.

In model 3, the coefficient of 7300.974, estimates the urban and rural pay gap on the conditional mean monthly pay, the dependent variable while holding constant of any other variables. Therefore, this result implies only the estimated mean wage difference between urban and rural people but not between male and female, or any other conditions.

This new regression model can be written as: E(W)=a+β1EL+β2EL2+β3EL3+β4F+β5G+β6U+β7PC+β8Age+β9Age2+β10F*PC

The function of estimates dependent variable W is:

=a+b1EL+b2EL2+b3EL3+b4F+b5G+b6U+b7PC+b8Age+b9Age2+b10F*PC[pic 6]

Hypotheses Test 1

Test the hypothesis that the wage gap between men and women working in private companies is zero.

H0: β10=0

=b10- β010/SE(b10) =0.030[pic 7]

The t-statistic on the wage difference between men and women working in private companies is 0.030 which does not exceed the critical value of 1.646 for a test at the 5% significance