Three researchers are estimating the relationship between expenditure on cinema tickets (Ci)and total monthly expenditure (Yi)using a cross-sectional survey of 1500 households in England during May 2014. All three have also been asked to look at the effect of children on cinema attendance and they have been given data on the number of children Ki in each household from which a dummy variable Di has been constructed taking the value 1 if Ki>0 and 0 otherwise. The variable Ei is the years of education of the head of household, and residuals for each of the three researchers' models are denoted varepsilon1,i ,varepsilon2,i , varepsilon3,i respectively, i is the household identifier.

Researcher 1 estimates the following relationship:

(1) Ci= 5.48 + 2.48 Yi - 0.25 Yi2- 1.328 Di + varepsilon1,i

(1.24) (2.41) (2.16)(4.21)

Number of observations = 1500

Researcher 2 estimates:

(2) ln Ci = 1.22 + 0.72 Yi- 0.38 Yi*Di - 0.42 Di + varepsilon2,i

(0.26) (5.13) (3.28)(2.72)

Number of observations = 1320

Researcher 3 estimates:

(3) ln Ci = 1.32 + 1.38 ln Yi - 0.11 Ki + 0.28 Ei + varepsilon3,i

(0.54) (6.56)(1.09) (1.10)

Number of observations = 1280

In all the above regressions, the numbers in brackets are absolute values of t-ratios.

Questions:

a)For each regression, discuss the effect of total monthly expenditure on cinema tickets expenditure.

b)Researcher 3 claims to be able to reject the hypothesis that the income elasticity of spending on cinema tickets is equal to 1. Do you agree? Explain your reasoning.

c)Which one of these three specifications provides evidence that the income elasticity depends on children? Find the income elasticity for those with and without children in this specification and in each case state whether cinema tickets are a necessity or a luxury.

d) Why do the three researchers' specifications have different numbers of observations? Does this worry you or suggest that any of the specifications are better than any of the others? Explain your reasoning.