Statistics and Econometrics ID- 4119l 2011/12 Level Essay

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.....