1. Consider the linear regression model y=x11+x22 + , where y, x and x2 are N...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
1. Consider the linear regression model y=x11+x22 + , where y, x and x2 are N x 1 column vectors, and e is an N x 1 vector of regression errors; B1 and B2 are scalar parameters. Assume that x1 is endogenous, while X2 is exogenous, i.e. E[xe] 0, while E[x2] = 0. (a) [25%] Show that the OLS estimator B2 of 32 cam be expressed as =2+ (x2(IN Px)x2)2 (IN - Px), - where I is the identity matrix of dimension N and the matrix Px =x1(xx)1. (b) [25%] Use the result in (a) to show that B2 is unbiased if the re- gressors X and x2 are orthogonal, irrespective of the endogeneity of X1. (c) [25%] Suppose an N x 1 vector z is available that is considered as an instrument for X. State the conditions that z needs to satisfy to be a valid instrument for X, and explain how it can be used to obtain an unbiased estimator for 3' = (B1, B2). (d) [25%] Show that the IV estimator for B2 is equivalent to the OLS estimator for B2 when X and x2 are orthogonal. 1. Consider the linear regression model y=x11+x22 + , where y, x and x2 are N x 1 column vectors, and e is an N x 1 vector of regression errors; B1 and B2 are scalar parameters. Assume that x1 is endogenous, while X2 is exogenous, i.e. E[xe] 0, while E[x2] = 0. (a) [25%] Show that the OLS estimator B2 of 32 cam be expressed as =2+ (x2(IN Px)x2)2 (IN - Px), - where I is the identity matrix of dimension N and the matrix Px =x1(xx)1. (b) [25%] Use the result in (a) to show that B2 is unbiased if the re- gressors X and x2 are orthogonal, irrespective of the endogeneity of X1. (c) [25%] Suppose an N x 1 vector z is available that is considered as an instrument for X. State the conditions that z needs to satisfy to be a valid instrument for X, and explain how it can be used to obtain an unbiased estimator for 3' = (B1, B2). (d) [25%] Show that the IV estimator for B2 is equivalent to the OLS estimator for B2 when X and x2 are orthogonal.
Expert Answer:
Related Book For
Statistics Principles And Methods
ISBN: 9780470904114
7th Edition
Authors: Richard A. Johnson, Gouri K. Bhattacharyya
Posted Date:
Students also viewed these economics questions
-
You are holding a team meeting to discuss the financial targets provided in the organisational and April bistro budgets. What information do you need to communicate to the team to ensure they...
-
"internet radios" for streaming audio, and personal video recorders and players. Describe design and evaluation processes that could be used by a start-up company to improve the usability of such...
-
There are three general methods of allocating overhead costs: plantwide rates, rates for each expense category, and departmental rates. Describe when each is the most useful.
-
Digital Controls, Inc. (DCI), manufactures two models of a radar gun used by police to monitor the speed of automobiles. Model A has an accuracy of plus or minus 1 mile per hour, whereas the smaller...
-
(a) Find the dot product. (b) Find the angle between v and w; (c) State whether the vectors are parallel, orthogonal, or neither. v = 2i + j, w = i - 2j
-
Lynn Goldsmith is a photographer known for her photographs of famous musicians. In 1981, Goldsmith had a photography session with the singer Prince. Three years later, Vanity Fair obtained a license...
-
Kelly Pitney began her consulting business, Kelly consulting P.C., on April 1, 2012. The accounting cycle for Kelly Consulting for April, including financial statements, was illustrated on pages...
-
Consider the Solow model we studied in class, with the production function given by: Y =AKN1. tttt In this question, we distinguish between the labor force (L) and the total population (Pop). The...
-
1. Bare cost and total cost (incl. O&P) of formwork for spread footings (20 pts, specify which lines (or index) in RSMeans data are used) 2. Bare cost and total cost of reinforcement for spread...
-
Discuss the presuppositions involved in a modern evaluation of indigenous traditions and practices. What aspects of indigenous traditions struck you? What seems on the basis of evidence a valid way...
-
About 8 0 2 . 3 8 0 2 . 3 Ethernet, hubs and switches ( ( i ) ) Early 1 0 1 0 Mbps 8 0 2 . 3 8 0 2 . 3 Ethernet is 1 1 - Persistant CSMA / / CD ( ( CSMA:Carrier Sense Multiple Access, CD: Collision...
-
How to communicate between a Labview application and a Python server?
-
In the context of marginal accounting, what does the term "marginal cost" refer to? A) The total cost incurred for producing a certain quantity of goods. B) The average cost per unit of production....
-
The Alcanza, Corp. adds the materials at the beginning of its production process and the conversion costs are added uniformly. At the beginning of June 20xx, the inventory in process was 25%...
-
Lecture 3 Handout 1 Acquisition Method for Consolidation in After negotiations with the owners of Smallport, BigNet agrees to pay for 100% of Small Port's voting stocks, and the four separate...
-
Mantz Engines, Inc., is a privately owned company that was founded seven years ago by Sydney and Claire Mantz. The company manufacturers farm engines used primarily in farm equipment. Mantz has...
-
Evenflow Power Co. is considering a new project that is a little riskier than the current operations of the company. Thus, management has decided to add an additional 1.5% to the company's overall...
-
A random sample of 130 business executives was classified according to age and the degree of risk aversion as measured by a psychological test. Do these data demonstrate an association between risk...
-
The weights (oz) of nineteen babies born in Madison Wisconsin are summarized in the computer output. (a) Locate a measure of variation and also calculate the sample variance. (b) Calculate the...
-
Suppose a fair die has its even-numbered faces painted red and the odd-numbered faces are white. Consider the experiment of rolling the die once and the events A = [2 or 3 shows up] B = [Red face...
-
Go to the PMI Web site and examine the link Membership. What do you discover when you begin navigating among the various chapters and cooperative organizations associated with the PMI? How does this...
-
Go to http://www.pmi.org/business-solutions/casestudies and examine some of the cases included on the Web page. What do they suggest about the challenges of managing projects successfully? The...
-
Using your favorite search engine (Google, Yahoo!, etc.), type in the keywords project and project management. Randomly select three of the links that come up on the screen. Summarize what you find.
Study smarter with the SolutionInn App