Advanced Econometrics — DU B.A. (Hons.) Economics Previous Year Question Papers

3 . The question paper iconsists of six questions. 7. Statistical tables are attached for your reference Q-1 Consider the multiple regression model: Yi --Po.+ P|X|i + P2X2i+ P3X3i + ui where. the CLRM assumptions MLR.1 through MLR.4 hold (1inearity, random sampling, no perfect collinearity, and zero conditional mean). Suppose the data are given as: a) Write the regression model in matrix notation, clearly defining all matrices. b) Using matrix algebra, calculate the OLS estimator A = rx'XJ-'.X'y. c) Suppose we are interested in the linear combination C) = 4j + ¢2 : (i) Show that ©= ¢/ +42 is an unbiased estimator of ©. e) Find the coefficient of determination R2 and interpret it. a) Suppose a linear probability model (LPM) yields a predicted value of Y that is equal to -0.4. Explain why this is problematic. b) Why are the coefficients of probit and logit models estimated using the method of maximum likelihood (MLE), rather than using the instrumental variables (IV) method? c) Your friend is analyzing survey data on individuals' exercise habits to study what predicts regular physical activity in your city. She asks if she should use a logit, probit, or linear probability model. What are the advantages and disadvantages of each model in this context? Which would you recommend, and why? d) Now suppose the dependent variable Yi represents the number of hours per week an individual exercises, but many individuals report zero hours. Explain why a Tobit model may be more appropriate in this case. Discuss how the Tobit model differs from the logit and probit models in both puxpose and interpretation. e) You are analyzing household spending on luxury goods, where some households report zero expenditure because they choose not to buy such goods. Describe how you could use a two-part model that combines a logit/probit model with an OLS or Tobit model to analyze this data. What does each stage of the model capture? 5*4 =20 Q-3 Suppose the market for milk can be described by the following system: Qs = ai + Pip + yizs + ui where gs and gd are quantity supplied and demanded, P is price, and Zs and Zd are exogenous supply and demand shifters re`spectively. In equilibrium, Qs = Qd = Q. a) Define what is meant by a structural equation and a reduced form equation in this context.. b) Explain why OLS estimation of the supply curve generally produces biased estimates of P I. c) Under what condition is the demand equation identified? What role does the variable Z's play in this identification? ` d) Describe how the two-stage least squares (2SLS) method would be used to estiinate the demand equation in this system. Q-4 Consider a school-level analysis examining the impact of health insurance coverage on healthcare utilization among high school students, modelled ,as follows: Hs= Po + Pilc + P2 Fp + P3Av + P,turban + ui where: fJs= percentage of students who visited a hospital in the past year, Jc= percentage of students with health insurance coverage,