Chaojun LI(李超君) 5101209122
Engel’s Law
To test the effectiveness of the Engel’s law in China, a survey is conducted to interview 5394 families in different areas in China.
Descriptive statistics
The average of food consumption per capita, total consumption per capita and total income per capita are separately1158.633, 2432.697,and 1675.590 from which we can see that food consumption accounts for a lot total consumption and there is not much left after consumption. What’s more, there is a great disparity in total income per capita, as well as in food consumption and consumption. The highest income is more than 1000 times as the lowest.
Food Consumption and Total Income
Using scatter plots, we can see people with the same income spend quite different amounts of money on food. There is a trend that with the more the total income, the larger the food consumption, though the trend is not that clear.
If we run the regression between log(food) and log(totcinc), we can get the equation that
Log(food)=0.238log(totcinc)+5.229759+ u, [j1]
which verifies that when there is an increase in total income, there is very likely an increase in food consumption.
The Proportion of Food in Consumption and Income
The scatter plots of log(totcinc) and food/totcincshow a blur trend that with the increase of total income, the proportion of food in total consumption will decrease. If we run the regression, we can get the equation that
food/totcper=-0.075737logtotcinc+1.091566+ u.
When income doubles, the proportion will decrease by 0.02[j2]. And this verifies the effectiveness of the Engel’ law in China.
- Differences between Regions
If we run the regression of the relevant data in different regions, we can get different equations.
- Food consumption and total income
Nationwide: Log(food)=0.238log(totcinc)+5.229759+ u
Coast: Log(food)=0.199595log(totcinc)+5.674036+ u
Middle: Log(food)=0.210753log(totcinc)+5.304185+ u
West: Log(food)=0.285119log(totcinc)+4.920871+ u
When getting more income, people in different regions will increase their food consumption. However, when seeing an increase in income, people in the west will increase their food consumption more.
- The proportion of food in consumption and total income
Nationwide: food/totcper=-0.075737logtotcinc+1.062599+ u
Coast: food/totcper=-0.073852logtotcinc+1.091566+ u
Middle: food/totcper=-0.048399logtotcinc+0.881135+ u
West: food/totcper=-0.083344logtotcinc+1.194551+ u
The Engel’s law holds for all regions in China. What’s more, when income increases, the proportion of food decreases the most.
Income Determination
This report is a further investigation into the relation of the income of average people with education and experience. With the basic sum of these data has already been given, this time regression will be mainly used.
- Income, Education and Experience
The regression model we use is that:
log(income) = β0 +β1edu +β2expr + u,
where β0 means the amount of money that a person with no education and no experience can earn, β1, Β2 separately will show by how much log(income) will change if he has one more year of education or one more year of working experience.
After running the regression, we get the equation:
log(income) = 7.307423+0.159746edu -0.002961expr+ u.
From the equation we can see that without any education or working experience, one may get a yearly income of 7.307423[j3]. From the signs of the estimates we can see the more educated you are, the more salary you will get. However, very surprisingly, the equation shows that with more working experience, the less income you will get.
Specifically, if a person has an education of 10 years and working experience with 5 years, then the log(income ) is most likely to be E(log(income│edu=10, expr=5))= 7.307423+0.159746*10-0.002961*5+0=8.890303. σ=1.130683.E(log(income))=exp(8.890303+1.1306832/2)=13760.01255.
- The Augment effect of Education
To examine whether with the increase of education, a person can be overeducated for money making, we use the model:
log(income) = β0 +β1edu +β2expr+ β3edu2+ u.
After we run the regression, we get the equation that
log(income) = 7.551570+0.071511edu-0.002986expr+0.005598edu2+ u
From the coefficient of edu2 we can see that there is a continuous augment effect of education. That is, the increase of increase in education will bring better income, one will not be overeducated.
[j1]It’d be better if you include in this estimated equation the standard errors of the estimates, R square, and sample size.
[j2]My calculation is 0.05, which is obtained by -0.075737 *log(2). Note that the logarithm here is the natural log.
[j3]This is not correct. Note that the explained variable is log(income), not income itself.