Essay: Factors Affecting Marital Quality Of Women In Korea.

1. To begin with, understand the policy question.

a. What is the policy question of this analysis? What is the dependent variable and how is it measured? What is the key independent variable and how is it measured?

b. What is the population? What is the sample?

2.  Write a short paragraph which summarizes the distribution of the dependent variable and the distribution of the key independent variable using summary statistics. 

Summary Statistics

What factors influence the marital quality of women? The dependent variable is the marital quality and it is measured on a 7-point scale ranging from 1 to 7. The key independent variable is the husband’s income measured in 1,000 USD per month.

The population is all the Korean women aged between 20 and 64 while the sample is a survey of 2,682 women surveyed in the 2007 for the population.

Write a short paragraph which summarizes the distribution of the dependent variable and the distribution of the key independent variable using summary statistics.

The average marital quality of the sampled women was found to be 5.38 with the highest and the lowest marital quality recorded being 7 and 1 respectively. On the other hand, the average husband’s income per month was found to be 2,748.5 US dollars per month with the highest and lowest income recorded being 10,000 US dollars and 300 US dollars per month.

The above results shows that there is a weak positive non-linear relationship between husband’s income and the marital quality. The two variables are positively related as can be seen from the correlation test and the scatterplot.

Yes there is evidence of non-linear relationship. The non-linearity exhibited is the positive non-linearity between the two variables (husband’s income and marital quality).

The estimated regression equation is;

The estimated slope is 0.1403; this means that a unit increase in the husband’s income would result to an increase in the marital quality by 0.1403. Similarly, a unit decrease in the husband’s income would result to a decrease in the marital quality by 0.1403.

The hypothesis is;

Null Hypothesis (H₀): Slope is not significantly different from zero

Alternative Hypothesis (H_A):  Slope is significantly different from zero

From the results we reject the null hypothesis.

Justification using confidence interval;

The 95% confidence interval is between 0.1064 and 0.1742, this clearly shows that zero is not within the interval hence the rejection of the null hypothesis at 5% level of significance.

Justification using t statistics

The computed t-value is 8.12; this value is clearly greater than the critical t value from the tables (t = 1.96). This means that the null hypothesis is rejected at 5% level of significance.

Justification using p-value

The p-value is given as 0.000; this value is less than the α = 0.05; we therefore reject the null hypothesis at 5% level of significance.

The husband earned 2,500 USD per month.

Estimating the Relationship between Husband's Income and Marital Quality

The estimated marital quality is;

The actual marital quality in 2007 was 5.

Condition 1: The control variable (husband’s education in years) is intuitively thought to be correlated with the husband’s income. Husbands with higher education levels (more years of education) tend to have higher income levels.

Condition 2: The control variable (husband’s education in years) affects the marital quality. Higher education years might result to higher martial quality.

Based on the above, omitting the years of education might make the estimated effect of the husband’s income upward biased. This is based on the fact that years of education is positively related with the marital quality.

The estimated regression equation is;

Interpret the estimated slope coefficient of hinc.

The estimated slope is 0.0828; this means that a unit increase in the husband’s income would result to an increase in the marital quality by 0.0828. Similarly, a unit decrease in the husband’s income would result to a decrease in the marital quality by 0.0828.

Yes the two conditions are satisfied based on the empirical evidence. As can be seen form the above table, there is positive relationship between husband’s education in years and husband’s income (r = 0.4339). There is also positive relationship between marital quality and husband’s education in years ( r = 0.1856)

Since the bias is greater than zero we can conclude that omitting the years of education might make the estimated effect of the husband’s income upward biased.

I do prefer model in Q5.c. This is based on the fact that an increase in the value of adjusted R-Squared is observed. In model Q4.a, the value of adjusted R-Squared was 0.0248 while for the model in Q5.c the value is 0.0414. This shows that a slightly higher proportion of the variation in the dependent variable is explained in model Q5.c as compared to model in Q4.a.

The estimated regression equation is;

1. Interpret each and every slope coefficient of the work hours.

The estimated slope for is 0.0742; this means that a unit increase in the husband’s income would result to an increase in the marital quality by 0.0742. Similarly, a unit decrease in the husband’s income would result to a decrease in the marital quality by 0.0742.

The estimated slope for  is 0.0588; this means that a unit increase in the husband’s education in years would result to an increase in the marital quality by 0.0588. Similarly, a unit decrease in the husband’s education in years would result to a decrease in the marital quality by 0.0588.

Controlling for Husband's Education and Work Hours

The estimated slope for  is 0.2303; this means that husbands who work for between 40 to 50 hours per week have higher marital quality by approximately 0.2303 as compared to the husbands who work 60 hours or more per week.

The estimated slope for  is 0.1160; this means that husbands who work for between 50 to 60 hours per week have higher marital quality by approximately 0.1160 as compared to the husbands who work 60 hours or more per week.

Test a null hypothesis that the husband’s work hours do not matter to marital quality against its alternative hypothesis. Using “β”s related to the husband’s work hours, re-write the null hypothesis and write the alternative hypothesis. Can you reject the null hypothesis at 1% significance level? Provide your evidence.

The null hypothesis that the husband’s work hours do not matter to marital quality against its alternative hypothesis is rejected at 1% level of significance.

Using “β”s related to the husband’s work hours

Where  refers to the beta related to husbands work hours of between 40 to 50 hours per week. The p-value related with the beta is 0.000 (a value less than 1% level of significance), we thus reject the null hypothesis for this beta. And conclude that the beta () related to husbands work hours of between 40 to 50 hours per week is significantly different from zero at 1% level of significance.

Where  refers to the beta related to husbands work hours of between 50 to 60 hours per week. The p-value related with the beta is 0.125 (a value greater than 1% level of significance), we thus fail to reject the null hypothesis for this beta. And conclude that the beta () related to husbands work hours of between 50 to 60 hours per week is not significantly different from zero at 1% level of significance.

The adjusted R squared of the regression in Q6.a is 0.0472; this implies that only 4.72% of the variation in the dependent variable (marital quality) is explained by the three independent variables in the model.

we found some evidence of non-linearity between hinc and maritalq. To relieve the concern about wrong functional forms, let’s examine the possibility of the non-linear relationship for the regression in Q6.a.

To do so, create logged income of the husband by taking log of hinc. Then regress maritalq on the logged hinc and the control variables included in Q6.a. Interpret the estimated slope coefficient for the husband’s income. (*This question is related to our learning in Week 11. For preview, you can create logged variable1, named as logvariable1 (or use whatever name you like), as below:

Examining Non-Linear Relationship

gen logvariable1 = ln(variable1)

ln denotes natural log.

“l” in ln is the lower case of “L” (NOT number one).

The estimated slope for is 0.2486; since the coefficient is 0.2486, marital quality will change by 0.002486 units when the husband’s income changes by 1%. 

I do prefer model in Q7.a. This is based on the fact that an increase in the value of adjusted R-Squared is observed. In model Q6.a, the value of adjusted R-Squared was 0.0487 while for the model in Q7.a the value is 0.0495. This shows that a slightly higher proportion of the variation in the dependent variable is explained in model Q7.a as compared to model in Q6.a. Implying that model in Q7.a is better than model in Q6.a.

Create a table which reports results from four regression models from Q4.a, Q5.c, Q6.a, and Q7.a. To create the table, make it sure to read the attached “Guidelines for Presenting Statistical Information” and refer to example regression tables in the textbook (You do not have to report SER as the textbook tables do). Note this question is about visual presentation of your statistical work. Pay your attention to DETAILS. In addition, the table should look good when it gets printed. Hence, I suggest you edit the final version of your table using MS Word (rather than other programs such as Excel) and you check whether the table looks good when printed.

The following is the table that represents the results obtained in the above sections.

Table 1: Summary of Regression Analysis for Predicting Wives’ Marital Quality (N = 2682)

	Model 1	Model 2	Model 3	Model 4
	β	β	β	β
Husband's income	0.1403*	0.0828*	0.0742*
Husband's education (in years)		0.0624*	0.0588*	0.0539*
Number of working hours
Between 40 and 50			0.2303*	0.2118*
Between 50 and 60			0.116	0.1033
Log of husband's income				0.2486*
Constant	5.0074*	4.2966*	4.2092*	4.2710*
Adjusted R-Squared	0.0244	0.0421	0.0472	0.0495

* Significant at 1% level of significance 

This study sought to investigate the factors that affect the marital quality married women aged between 20 and 64 years old. Results showed that the key factor that influences the marital quality of women is their husband’s monthly income. Results showed that a 1% change in the husband’s income would result to a 0.002486 units change in the marital quality. Other factors that were found to influence the marital quality were the husband’s education in years as well as the husband’s working hours per week. In overall, even though the factors significantly influenced the marital quality of women, the factors were found to have very little effect since only 4.95% of the variation in the marital quality was explained by the factors. 

Based on the findings, the following policy recommendations would be ideal to contain the situation.

• There is serious need to have work life balance for the men. Results showed that women whose husband’s worked for longer hours a week tended to have low marital quality as compared those women whose husband’s worked for shorter hours a week. As such, there if therefore need to help come up with a work life balance that would enable men spent better time with their wives.
• Need to encourage learning by the men. Results showed that women whose husbands had higher number of education years had had better marital quality as compared to those whose husband’s had lower education levels (in years). This implies literacy levels tend to help improve marital quality. 

The internal validity of the analysis is threatened by the following;

Omitted variable bias; as could be seen from the initial model, the analysis suffers from omitted variable bias. This is true from even when checking the value of adjusted R-Squared we found that only a very small proportion of the variation is explained by the variables in the model. This clearly shows that other variables outside the model that would have greatly influenced the dependent variable have been omitted from the model.

Missing data could also introduce some bias in the results. It found that most data were missing for the variable husband’s income. So it could be that there was deliberate decision not to give information on income by the participants. This could possibly result to bias as a result of missing data. 

The study does not mention on the sampling procedure that was used. It is therefore very difficult to conclude that the results are generalizable hence external validity of the results is threatened.