Econometrics Question 8. The objective of a recent study was to determine the ca

Question

Econometrics

Question 8. The objective of a recent study was to determine the casual effect of education on fertility in a developing country. The researchers proposed the following regression model: children-?0 + ?1 educ + ?2age + ?3age2 + u where children, the number children born to given mother is the dependent variable, which is explained by educ (years of education), age (age in years) and age2 A sample drawn from a survey of 890 women in Botswana, which records information on the number of children, years of education, age, and mother's date of birth, is used to estimate this model. (i) Explain why the estimation of model (8.1) by OLS is unlikely to provide an unbiased estimate of (ii) An alternative to OLS is the Instrumental Variable (IV) estimator. A potential instrumental variable for educ is frsthalf which is a dummy variable equal to 1 if the woman was born during the first six months of the year, and is 0 otherwise. There is evidence that women born in the second half of the year tend to receive less education due to a delayed start to schooling related to the harvest season. What conditions must frsthalf satisfy in order to be an instrumental variable for educ? Explain whether these conditions can be tested (ii) It would be useful to test whether educ is endogenous in model (8.1). Outline one test for the endogeneity of educ in model (8.1) (iv) Based on the sample of 890 observations, the following estimates were obtained: Table of Model Estimates children educ 0.1015-0.3591 (0.0137) (0.1004) 0.3560 0.3527 (0.0380 (0.0450) 0.0029 -0.0034 (0.0006) (0.0008) age age 4.507 (0.552) (1.354) constanit 2.640 IV 0.301 Estimato OLS 0.609 NOTE: standard errors reports in parentheses O Construct the 95% confidence interval for the IV estimate of ?| : is the OLS estimate within that interval ?

Explanation / Answer

i) Our error term u is likely to contains variable which is correlated to education. Thus, making OLS estimator biased due to endogeneity.

ii) Following two condition must be satisfied for an variableto be used as an IV:

a) It must be correlated with the endogenous variable(This can be tested by calculating the correlation)

b) It must not be correlated with the error term(This cannot be tested)

iii) We can use Hausmann's test for endogeneity.

iv) 95% conf interval for IV estimated of beta1 is

-0.3591 +/- (1.96)(0.1004) = (-0.3591-0.196, -0.3591+0.196) = (-0.5551, -0.1631).

The OLS estimate is outside this interval.

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