Answer Happy

Q2 [30 MARKS). A researcher is interested in the demand for holiday travel and has estimated the following models for annual expenditure on holiday travel using data from a cross-sectional study of spending patterns in a representative sample of the UK households in 2015. InEXP_T;=antajlnP_T;+ azInP_Others; + a3lnY; + 04 Age: + as Adultsi + a6Children; + εi w_T; =Bo+B1InP_T;+ B2InP_Others; + B31nY; + B4Age; + B5Adults;+ B6Children; + ui (1) (2) where EXP_T; is the expenditure on holiday travel of household i; w_T; is the budget share for holiday travel of household i; P_T; is the price of holiday travel household i pays; P_Others; is the price of other goods household i pays; Y; is total income of household i; Age is the age of head of household i; Adults; is the number of adults in household i; Children; is the number of children in household i; & and ui are error terms. In indicates the natural logarithm. i is the household identifier. The researcher gets the following estimates: (1) InEXP T Coefficient Standard error InP T InP_Others In Y Age Adults Children R2 N -0.424 0.236 1.236 -0.271 -0.925 -0.312 0.128 1328 0.205 0.417 0.537 0.112 0.210 0.041 (2) w T Coefficient Standard error -0.285 0.195 0.021 0.006 0.445 0.221 -0.262 0.108 -0.285 0.195 -0.021 0.006 0.245 1300

(a) In regression (1), can we say if the demand for holiday travel is price elastic or price inelastic? How would you suggest adapting the specification to allow the income elasticity to depend on the number of adults? Would you consider such a modification to be advisable? Show the derivations in detail and explain the intuition. (b) It has been suggested that spending on 'adult goods' is a good indicator of household living standard, i.e. households spending the same amount on such goods are to be regarded as equally well off. Assume this is the case, and that holiday travel is an example of an adult good. (i) In model (1), if the number of children were to increase by one, by how much would the logarithm of total income need to increase to preserve the household's living standard? (ii) Discuss any problems that you think arise with using comparisons of spending on adult goods such as holiday travel to measure welfare differences across households with and without children. (c) In regression (2), test the hypothesis that In Y has no effect on the budget share for holiday travel at the 5% level of significance. Is this the same as saying the income elasticity is zero? Justify your answer. Why do regressions (1) and (2) have different numbers of observations? Which regression specification do you prefer? Explain why.