ECONOMETRIC TECHNIQUES USING STATA 11
ECONOMETRICTECHNIQUES USING STATA
Thename of the class
Thename of the school
Thecity and state where it is located
Make a bar graph that shows average nett financial assets and average income for respondents of different family size, where you divide the respondents into the following five family-size groups: 1, 2, 3, 4, and 5 or more family members.
Make a bar graph that shows average nett financial assets and average income for respondents of different age groups, where you divide the respondents into three age groups of roughly equal size.
Describe and comment on the figures displayed in a) and b).
Thefirst figure shows that there may be some linear relationship in theaverage nett financial assets with the family dummies that may benegative. Income cases had a clear cut of high average mean whencompared to nettfa where the highest had an average of about 30 and aminimum of at least 10 and above. The average of income from thefamily size has a minimum of 30 and a maximum of 45.
Thesecond figure suggests that there may be a positive linearrelationship between income and the family dummies.
d) Estimate the following model
nettfa= ß0 + ß1Fsizedummies + u
nettacan be used to set prediction of the family size dummies in that anysingle change of unit in neffta leads to a negative change in familysize dummies 1 3 and 4 by 1.2 and a positive effect on family sizedummy 2 by 1 if all other factors are kept constant.
Wherethe term Fsizedummies represent family-size dummies that correspondto the family-size groups that you used in the figure in a).Interpret the estimated coefficients, and comment on the results ofthis regression compared to the figure in a). Report the regressionresult in a table where you also report the results from any furtherregressions that you do in Question 1.
Age 1.02477** -1.817775 -1.3565589**
(0.06177) (0.50403) (0.5132965)
Age2 0.03291 0.0274162**
Inc 0.96111** -0.2055086 -0.1650598**
Inc2 0.0101732 0.0099466**
Cons 22.539**-60.67212**21.3243951 17.3412293
adj. R2 0.0005370.16620.1957 0.1976
Standard errors in parentheses
* p < 0.10, ** p < 0.05
Interpretationof the estimated coefficients
Anincrease in family size from one group to the next reduces the nettfinancial assets by approximately 1.224 units, and if the familythere is no any unit change in family size then net financial assetsbecome 22.539 .The family size dummies had great significant inexplaining the nettfa in that all of their probabilities are lessthan the set p-value 0.05.The variability in the models is onlyaccounted by 16.6% as revealed by the adjusted R squared.
Withrespect to the figure in (a), it’s clear that average nettfinancial assets are reducing from the family dummy of 2 as weprogress to the family dummy of 5 and above.
Now forget about the family-size dummies and consider only the variables (age) and annual family income (inc). Based on your economic intuition, discuss whether you would prefer a model that captures only a linear effect of both age and income on wealth, or whether you prefer a model that captures a possible u-shaped (or inverted u-shaped) relationship between income and wealth and between age and wealth, respectively. Estimate both models and comment on the results. Find the turning points for age and income from the relevant model. The turning point for age is the value of age where the sign, in terms of the effect on wealth, changes. Explain briefly how you find these turning points.
Economictheory has wealth increasing as age increases, but age has adiminishing effect on wealth, therefore using the model were age iscaptured as a u-shaped (or inverted u-shaped) is better than usingthe linear model.
Themodel estimates are captured in the table above.
Getthe first partial derivative of the wealth equation with respect toboth age and income and equate it to zero then solve.
Add the family size dummies that you used in question 1 d) to your preferred model in e), and test the null hypothesis that the family dummies should not be included in the model. Based on the estimated coefficients on the dummies for family size provide some arguments for a reasonable way of reducing the number of dummies for family size report the results of this regression and compare them to your previous regression with more dummies for family size.
Themodel estimates are on the table in column (4)
Ho:family dummies have no effect
H1:family dummies have an effect
At0.05 level of significance F ~ F (1, 8681) = 3.84
SinceF=21.651 is greater than F (1, 8681) we reject Ho and conclude thatFamily dummies are statistically significant
Test the null hypothesis of homoscedasticity in each of your reported regressions, and consider whether this should have implications for the way you report your regression results.
Forthe model labeled (1)
Breusch-Pagan/ Cook-Weisberg test for Heteroskedasticity
Variables:fitted values of model1
Sincethe homoscedasciticity test the equality of sample variance settingthe null hypothesis that there is no any change of variance and thenull that there is no assumption of the equality in variance we failto reject the null hypothesis that the variances of the samples areequal in that the p-value 0.4969 which is less than the set p-value0.05 level of significance. We fail to reject Ho and conclude thatthe first model satisfies the assumption of homoscedasticity.
Forthe model labeled (2)
P-value<2.2e-16, Therefore model 2 has heteroscedasticity.
Forthe model labeled (3)
P-value<2.2e-16, reject Ho and conclude that there is evidence ofheteroscedasticity.
Forthe model labeled (4)
P-value<2.2e-16, reject Ho and conclude that there is evidence ofheteroscedasticity.
Ingeneral conclusion, the parametric test of homoscedasticity was fullysatisfied in the model parameters that the test of equality invariance relevant.
Discuss briefly what signs of the slope coefficients you would expect. Estimate the model and see whether your intuition is correct or not. Test the null hypothesis that age has no effect on the supply of labour.
hours= ß0 + ß 1educ + ß 2age + ß 3age2 + ß 4kidslt6 + ß 5kidsge6 + ß6nwifeinc + u
Theeffect of years of schooling on a number of hours worked per yearshould be positive since with more education comes more jobopportunities therefore ß1 should be positive. This clearindication shows that there is a positive relationship in Joopportunities and the number of schooling years.
Onewould also expect that increase with age directly increases hoursworked, but with a diminishing rate, thus ß 2revealing a negativeassociation positive while ß 3 depicting a negative association.
Havingmore kids irrespective of their age should reduce the number of hoursworked per year, therefore ß 5 and ß 6 should be negative.
hours= -307.009 + 56.220educ + 60.389age – 0.934age2 – 479.181kidslt6
-94.675kidsge6 – 10.889nwifeinc + u
Fromthe above-estimated model, the above intuition is valid.
H0:ß 2 =0 (no effect)
H1:ß 2 ≠0 (there is an effect)
t-statisticreported from strata is, t-value = 1.395
p-valueto this statistic is, p-value = 0.163531
Atthe level of significance of 0.05, we fail to reject the nullHypothesis that there is no any change in coefficients since thep-value, 0.163531 is greater than 0.05, and conclude that 0.05 levelof significance age has no any significant effect on effect on thesupply of labour.
There are a lot of observations where hours = 0. Estimate the model above for the subsample that is working. Compare the two sets of results. Discuss whether the explanatory variables have the same effect on the decision of whether or not to work (the extensive margin), and the decision of how many hours one wants to work given that one already has decided to work (the intensive margin).
hours= 930.6261 -16.1306educ + 50.3688age – 0.6795 age2 – 322.4621 kidslt6
-121.5067 kidsge6 – 4.7921nwifeinc + u
Fromthis new model, the parameter of education has a negative signimplying that for those working more and better education reduceshours of labour. It can be further elaborated that higher level ofeducation has a positive contribution to hours of working.
Ageas one of the factors that used in setting the prediction of working hours there is positive association and negative association for ageand age2 respectively as the previous model, but here an increase inage by one year increases hours of labour by 50.37 other than 60.39in the previous model. Hence given that one already works there isapproximately 10hrs decrease of hours of labour with respect toincrease in age by 1 year.
Thediminishing property of age on the hours of labour remains in thesecond model, but given that one already works then hours of labourreduces slower by approximately 0.25hours
Forkids of less than 6years of age the new model suggests that one morekid in this category reduces hours of labour by 322.46hours, this issmaller than that of the first model by approximately 156.721, hencegiven that a woman already works one more kid of less than 6years ofage reduces hours of labour at a slower rate.
Giventhat one already works an increase in nonwage income by a single unitreduces hours of labour slower, in the new model this reduction isapproximately 4.79hours other than the previous model that reduceshours of labour by 10.889hours.
Typically, we think that supply is likely to depend on the selling price of the supplied product. Discuss what effects this could have for your estimates in question (b).
Levelof education and the price of labour are related, so with price asalso another variable that is highly related to education level andalso affecting hours of labour, the coefficient estimate of educationshould increase to a higher value than -16.1306.
Allthe other variables including age, number of kids and the nonwageincome are also related to the price of wage labour, but since agehas an increasing effect on price of labour the coefficient estimateof age should increase.
Sincenonwage income is also related to the price of labour, we shouldexpect the coefficient of nwifeinc to increase.
Now include wage (in levels) in the model above and discuss the results.
hours= 852.3201 – 5.9093 educ + 51.8622age -0.6939age2 -321.3768 kidslt6
-123.8319kidsge6 – 4.4766nwifeinc -21.6696 wage+u
Thecoefficient of educ, age, kidslt6 and nwifeinc increases is a resultof their decreasing relationship of wage as a variable but the extentof the increase completely depends on the level of this correlationbetween these independent variables.
Discuss whether it is reasonable to believe that wage is an exogenous variable in the labour supply model.
Theproduction of labour does not affect wages. Therefore, the wholemodel has no effect on wages, but wages may affect the model.Therefore, wages is an exogenous variable.
Instead of using hours in levels, we log transform hours and reestimate the model with log hours as the dependent variable (including the wage variable in levels as an explanatory variable). Test and discuss whether you prefer the model with hours in levels or hours log-transformed.
Ho:Bi=0 (i=1, 2, 3, 4, 5, 6, 7)
Calculatingthe F statistic and the P-value for the whole data set gives
Hoursin levels: F-statistic: 4.988 on 7 and 420 DF, p-value: 1.926e-05
Hourslog-transformed: F-statistic: 7.917 on 7 and 420 DF, p-value:4.95e-09
Fromthis it would be clear that the model with the highest F-value and,therefore, the one with hours log-transformed should be the bestmodel, moreover comparing coefficient of determination R2 of the twomodels, the model with hours log-transformed has its independentvariables explaining more of the dependent variable that were verysignificant at 0.05.