Labor Supply of Married Females
Dede Dolkar
October 10, 2016, Version 1.0
Rensselaer Polytechnic Institute
1.Setting
library(Ecdat)
project1 <- WorkinghoursSystem Under Test
Data were drawn from 1987 cross section of the Michigan Panel Study of Income Dynamics. selected married couples with nonnegative family total income, where wife was of working age (18-64) and not self-employed. The study consists of 3382 observations and 12 variables.
A dataframe containing:
- hours : wife working hours per year
- income: the other household income in thousands of dollars
- age: age of the wife
- education: education years of the wife
- child5 : number of children for ages 0 to 5
- child13 : number of children for ages 6 to 13
- child17 : number of children for ages 14 to 17
- nonwhite : 0= white, 1= other race
- owned: 1= owner, 0 = otherwise
- mortgage: 1 = home on mortgages, 0 = otherwise
- occupation: occupation of the husband
- unemp: local unemployment rate
head(project1)## hours income age education child5 child13 child17 nonwhite owned
## 1 2000 350 26 12 0 1 0 0 1
## 2 390 241 29 8 0 1 1 0 1
## 3 1900 160 33 10 0 2 0 0 1
## 4 0 80 20 9 2 0 0 0 1
## 5 3177 456 33 12 0 2 0 0 1
## 6 0 390 22 12 2 0 0 0 1
## mortgage occupation unemp
## 1 1 swcc 7
## 2 1 other 4
## 3 0 swcc 7
## 4 1 other 7
## 5 1 swcc 7
## 6 1 other 7Factors and Levels
Factors and Levels of each factor is listed below:
The 4 factors being studied include:
owned (convert from integer to factor)
project1$owned <-as.factor(project1$owned)
str(project1$owned)## Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 1 1 ...- 0 = Doesn’t own house
- 1 = Does own house
nonwhite (convert from integer to factor)
project1$nonwhite <-as.factor(project1$nonwhite)
str(project1$nonwhite)## Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...- 0 = white
- 1 = nonwhite
mortgage (convert from integer to factor)
project1$mortgage <-as.factor(project1$mortgage)
str(project1$mortgage)## Factor w/ 2 levels "0","1": 2 2 1 2 2 2 1 2 1 1 ...- 0 = non mortgage holder
- 1 = mortgage holder
occupation (factor w/ 4 levels)
levels(project1$occupation)## [1] "other" "mp" "swcc" "fr"- mp = manager professional
- swcc = sales worker
- fr = farm-related market
- other = other
Continuous Variables
- hours : wife working hours per year
- income: the other household income in thousands of dollars
- education: education years of the wife
Reponse Variables
The response variable is hours the labor supply of married females measured in hours per year
The Data: How is it organized and what does it look like?
The study consists of 3382 observations and 12 variables. A new dataset is created by subsetting the data using the 4 factors discussed above.
myvars <- c("hours", "owned", "nonwhite", "mortgage", "occupation")
newdata <- project1[myvars]
head(newdata)## hours owned nonwhite mortgage occupation
## 1 2000 1 0 1 swcc
## 2 390 1 0 1 other
## 3 1900 1 0 0 swcc
## 4 0 1 0 1 other
## 5 3177 1 0 1 swcc
## 6 0 1 0 1 otherstr(newdata)## 'data.frame': 3382 obs. of 5 variables:
## $ hours : int 2000 390 1900 0 3177 0 0 1040 2040 0 ...
## $ owned : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 1 1 ...
## $ nonwhite : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ mortgage : Factor w/ 2 levels "0","1": 2 2 1 2 2 2 1 2 1 1 ...
## $ occupation: Factor w/ 4 levels "other","mp","swcc",..: 3 1 3 1 3 1 3 2 4 1 ...summary(newdata)## hours owned nonwhite mortgage occupation
## Min. : 0 0:1079 0:2382 0:1597 other:1314
## 1st Qu.: 0 1:2303 1:1000 1:1785 mp : 962
## Median :1304 swcc :1021
## Mean :1135 fr : 85
## 3rd Qu.:1944
## Max. :58402. Experimental Design
How will the experiment be organized and conducted to test the hypothesis?
This experiment will use a multi-factor analysis of variance by subsetting the data as shown in the previous section. The analysis will use various attributes as factors such as owned, nonwhite, mortgage, occupation.
What is the rationale for this design?
The rationale for this type of design is to analyze the variation among and between the factors.
Randomize: What is the Randomization Scheme?
There was no randomization, because the dataset was a set of observation.
Replicate: Are there replicates and/or repeated measures?
The data was generated by selecting unique married couples. There is no mention of any repeated measures or replicates of this study.
Block: Did you use blocking in the design?
No blocking was used in this analysis, because subsetting of the data down to the four relevant factors already minimizes variace of error caused by nuisance factors.
3. (Statistical) Analysis
(Exploratory Data Analysis) Graphics and descriptive summary
Based on these boxplots, we can conclude that all of the four factors had some sort of effect on the labor supply of married females. “Mortgage Holder” factor seemed to show the greatest difference between levels.
Testing
In order to determine the statistical significance of the results of the factorial experiment, an ANOVA test will be conducted.
model1 <- aov(hours ~ owned*nonwhite*mortgage*occupation, data = newdata)
summary(model1)## Df Sum Sq Mean Sq F value Pr(>F)
## owned 1 1.850e+06 1849655 2.391 0.12213
## nonwhite 1 6.666e+05 666609 0.862 0.35332
## mortgage 1 5.089e+07 50889477 65.785 6.98e-16 ***
## occupation 3 1.751e+07 5835515 7.544 4.99e-05 ***
## owned:nonwhite 1 1.462e+06 1462354 1.890 0.16925
## nonwhite:mortgage 1 1.279e+06 1278941 1.653 0.19860
## owned:occupation 3 1.214e+07 4045207 5.229 0.00134 **
## nonwhite:occupation 3 5.758e+06 1919279 2.481 0.05923 .
## mortgage:occupation 3 3.260e+06 1086695 1.405 0.23943
## owned:nonwhite:occupation 3 9.422e+05 314061 0.406 0.74871
## nonwhite:mortgage:occupation 3 2.769e+05 92304 0.119 0.94878
## Residuals 3358 2.598e+09 773577
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The summary of the ANOVA gives the p-values for each factor as well as the p-value for the interactions between the factors. The null hypothesis states that the variation in the response variable, hours, cannot be explained by anythng other than randomization. This ANOVA summary supports the null hypothesis. There are no significant p-values for owned, nonwhite, mortgage, occupation and all interactions, except:
- owned: occupation
Because the p-values are greater than alpha of 0.05, they are not significant. This leads us to not reject the null hypothesis and conclude that the variation in hours is explained by randomization alone.
Diagnostics/Model Adequacy Checking
par(mfrow = c(1,1))
qqnorm(residuals(model1))
qqline(residuals(model1))
The Q-Q Normality Plot of the residuals shows that the points falls along a line in the middle of the graph, but curve off in the extremities. This usually means that the data has more extreme values that would be expected is they truly came from a Normal distribution.
plot(fitted(model1), residuals(model1))
Residual = Observed - Predicted
- Positive values on the y-axis (residual) means prediction was too low
- Negative valyes mean that prediction was too high.
- 0 means the guess was exactly correct
Therefore…
- The plot above shows that they’re pretty symmetrically distributed, tending to cluster towards the middle of the plot
- Overall there aren’t clear patterns
4. References to the literature
Montgomery, Douglas C. Design and analysis of experiments. John Wiley & Sons, 2008.
Journal of Applied Econometrics, Vol. 10, No. 2 (Apr. - Jun., 1995), pp. 187-200