{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# ps6 - Problem Set 6 Introduction to Econometrics Fall 2006...

This preview shows pages 1–2. Sign up to view the full content.

Problem Set 6 Introduction to Econometrics - Fall 2006 Due Date: Tuesday, December 12th, BEFORE CLASS. Each student is responsible for handing one handwritten solution. If working in groups, indicate the members of the group (to facilitate grading). PLEASE SHOW YOUR WORK . 1. The supply of bikes is given by the following equation: ln ( Q ) = β 0 + β 1 ln ( P ) + u where u denotes factors other than price that determine supply. You know that E ( u ) = 0 and var ( u ) = σ 2 u , where 0 < σ 2 u < . The demand of bikes is given by: ln ( Q ) = γ 0 + v where E ( v ) = 0 , var ( v ) = σ 2 v , 0 < σ 2 v < and cov ( u, v ) = 0 . All the variables in the supply and in the demand have nonzero fi nite fourth moments. a. Solve the two simultaneous equations and get ln ( Q ) and ln ( P ) as functions of u and v . b. Derive E [ln ( P )] and E [ln ( Q )] . c. Using the expression for ln ( P ) obtained in a. , derive cov [ln ( P ) , u ] . Are ln ( P ) and u correlated? d. Using the expression for ln ( P ) and ln ( Q ) obtained in a., derive var [ln ( P )] and cov [ln ( Q ) , ln ( P )] . e. You collect a random sample of 10000 observations ( Q i , P i ) and compute (ln ( Q i ) , ln ( P i )) for each i = 1 , ..., 10000 . You want to estimate the supply of bikes: ln ( Q i ) = β 0 + β 1 ln ( P i ) + u i In particular, you are interested in the coef fi cient β 1 . Is the OLS coef fi cient b β 1 an unbiased estimator of β 1 in this application? Explain. f. Use the fact that: b β 1 = s ln( Q ) ln( P ) s 2 ln( P ) p −→ cov [ln( P ) , ln( Q )] var [ln( P )] and your results in d. to show that the OLS estimator is inconsistent in this application. 2. Consider the following regression model: Y i = β 0 + β 1 X i + u i where corr ( X i , u i ) 6 = 0 . You want to use the variables Z 1 i and Z 2 i as instruments for X i . You check for instrument exogeneity using the overidentifying restrictions test and the value of the heteroskedasticity-robust J -statistic you obtain is J = 15 . 7 . Assume that the fi rst three assumption for IV regression hold, that the instruments are not weak and that your sample is large.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern