Statistics and Econometrics

ID- 4119L

2011/12 LEVEL

STATISTICS AND ECONOMETRICS

Present your data in a table showing the names of the variables. Make sure the full definitions and sources of each variable are given.

Birth Rates: (thousands)

Quarter1 (Q1)

Quarter2 (Q2)

Quarter3 (Q3)

Quarter4 (Q4)

GDP per capita (GDP)

The GDP data used was from http://earthtrends.wri.org/text/economics-business/variable-638.html in the table Economics, Business, and the Environment — GDP: GDP per capita, current U.S. dollars

Current U.S.$ per person

GDP

The equation to be estimated is:

BRi = b0 + b1 GDPi+ ui (i)

(i) In terms of the literature on demand for children, what would you expect to find for the coefficient on b1 ?

is expected to have a negative value. There is an indirect negative relationship between the birth rate and GDP per capita of a country. Generally, as the GDP per capita increases, the birth rate decreases [James M. 2009].

Explain how you would modify the model, implied by this equation, if there is an ‘Engel curve’ relationship in the demand for children.

For an Engel curve the income becomes dependent variable and plotted in the Y-axis and the service or good demanded becomes the independent variable and plotted on the X-axis [http://en.wikipedia.org/wiki/Engel_curve]. The model would change as follows:

GDPi = b0 + b1 BRi+ ui (ii)

(iii) Why is there a constant term in the equation with no variable attached?

The constant term b0 with no variable attached to it, gives the baseline Birth Rate, that is the Birth Rate when GDP is zero and GDP has no effect on Birth Rate.

(iv) Why do these types of equations have a ‘u’ term?

The term ui called the error term, is used to cater for the variation in the actual model and the fitted model.

3. Estimate equation (i) by OLS and present the results in a suitable table

Estimation by OLS

Dependent variable: Birthrate

Coefficient

Std. Error

t-ratio p-value const

9.86976

0.343927

28.6973

<�.00001

GDP

-0.000783

0.00012227

-6.4042

0.00037

Mean dependent var

7.74444

S.D. dependent var

0.66353

Sum squared resid

0.51352

S.E. Of regression

0.27085

R-squared

0.85421

Adjusted R-squared

0.83338

F (1, 7)

41.0132

P-value (F)

0.00037

Log-likelihood

0.11619

Akaike criterion

3.76761

Schwarz criterion

4.16206

Hannan-Quinn

2.91639

(i) Comment on result for the coefficient on the GDP variable.

The coefficient for GDP is -0.0008 and is statistically significant. This means that for every one unit increase in GDP, the Birth rate reduces by 0.0008.

(ii) Comment on the R. squared statistic.

The R-Squared statistic is 0.854. This means that 85.4% variation in Birth Rate can well be explained by change in GDP.

(iv) Derive estimates of the income elasticity of demand for children from your results.

Since the gradient is negative, the income elasticity of demand for children is negative and therefore this means that children are inferior goods. That is, as the income increases, the demand for children reduces.

4. Carry out the following hypothesis tests:

(i) b0=0 against the two sided alternative at the 1% level t (7; 0:005) = 3:499

Variable

Coefficient

99% confidence interval const

9.86976

8.6662

11.0733

GDP

0.00078303

0.00121091

0.000355151

The hypothesis is rejected.

(ii) b1=0 against the two sided alternative at the 5% level t (7; 0:025) = 2:365

Variable

Coefficient

95% confidence interval const

9.86976

9.0565

10.683

GDP

0.00078303

0.00107215

0.00049391

The hypothesis is accepted.

(iii) b0<� against the two sided alternative at the 5% level

The hypothesis is rejected.

(iv) b1<� against the two sided alternative at the 5% level

The hypothesis is accepted, b1 is less than 0.Therefore, there is a significant negative relationship between Birth Rate and GDP.

5. Differences in the pattern of births, over the calendar year, may cause serious problems with the accuracy of your results for this model. Outline the simple ‘seasonal dummy’ method of dealing with this and apply it to your data to produce a new set of results.

Note: sd Birthrate is the seasonal dummy variable after applying seasonal dummy method.

Dependent variable: sd Birthrate

Coefficient

Std. Error

t-ratio p-value const

0.421088

0.689097

0.6111

0.5636

GDP

0.000230674

0.000237893

0.9697

0.3697

Mean dependent var

0.225

S.D. dependent var

0.494975

Sum squared resid

1.48266

S.E. Of regression

0.497102

R2

0.135475

Adjusted R2

-0.008612

F (1; 6)

0.94023

P-value (F)

0.369666

Log-likelihood

4.609093

Akaike criterion

13.21819

Schwarz criterion

13.37707

Hannan-Quinn

12.14658

6. Compare your new set of results (from Q.5) with your original results (from Q.3). You may consider the following to be relevant:

(i) whether the new model offers a significant improvement in goodness of fit.

Using R2, the model in Q3 offers the best goodness of fit since 85.4% of the variation in Birth Rate can be explained by GDP. However, for the model in Q5, only 13.5% of the variation in Birth Rate can be explained by GDP.

(ii)assessing whether there has been any major change in estimated income elasticity.

Since the gradient has changed to positive, the demand for children now becomes a normal good, as the income increases, the demand for children increases.

(iii)assessing which quarters of the year tend to have, ceteris paribus, a higher or lower birth rate than others.

From the graph below, quarters 2 and 4 have high birth rates while quarters 1 and 3 have low birth rates.

7. You should now write a short report of 450-600 words. This should briefly summarize your findings but most of your answer should consist of further exploration of your data

(such as collecting further explanatory variables and estimating new regressions) and suggestions for improvement of the model you have estimated.

From the model of GDP and Birth Rate, it was found that GDP had a significant negative relationship with the Birth Rate. For every unit increase in GDP, the birth rate reduced by 0.0008. The model showed some seasonality. There were some quarters in which the birth rate was high and some in which it was low. Specifically birth rates were high in second and fourth quarters and low in first and third quarters.

When the method of simple seasonal was applied to the model, it completely changed. GDP and the constant variable did not have significant influence on the birth rate.

GDP alone is not enough to explain variation in birth rate; other factors need to be considered. The following may be taken into consideration [ http://www.birthrate.net/2008/02/04/factors-affecting-birth-rate/]:

a) Governmental policies — that is, whether the government is pro-natalist or anti-natalist. Countries like Japan and Thailand have natalist governments giving their citizens special incentives for bearing more children. China’s one-child only policy is the perfect example of anti-natilism.

b) Social Beliefs – This is usually heavily intertwined with religious beliefs since the predominant religion in the region affects society. Birth statistics can become skewed where there is gender or sex preference. For example, in certain countries female children are deemed worthless so that killing female infants before their births are even declared is common enough to affect birth statistics.

c) Religious Beliefs – Countries wherein the predominant religious belief is against contraception can be expected to have higher birth rates.

d) Abortion Rates – Abortion rates are affected by the other factors that affect birth rate. If it is high, then the birth rate reduces and vice versa.

e) Poverty/Economic prosperity – The ironic thing with this factor is that even though those that are more prosperous can afford to have more children they are usually the ones that have less, while poor families often have more children.

f) Literacy, with special emphasis on female literacy. Women should be educated on information about birth and be able to make informed decision on the way to go about it and the number of children they can have.

g) Infancy mortality rate – Countries with higher infant mortality rates generally have higher birth rates since families make it a point to have more children since the children are more likely to die.

h) Conflict – Pertaining to war, security, and safety. Countries that experience wars most of the time have low birth rates.

i) Urbanization-it brings with it all the necessary information needed for a country’s economic growth and therefore reduces birth rate so as to ensure the available resources can be enough for the population.

Therefore a good model should incorporate the above nine variables and access its significance on birth rate.

REFERENCE LIST

Birth rates in the U.S., accessed 19 Apr 2012
Economics, Business, and the Environment — GDP: GDP per capita, current U.S. dollars, accessed 18 Apr 2012

< http://earthtrends.wri.org/text/economics-business/variable-638.html>

Engel’s law, accessed 19 Apr 2012

James M. March 8, 2009 Society – GDP vs. Birthrate of a Country, accessed 19 Apr 2012