# New York University ECON-SHU ECON-SHU 360 Measurement Error In this problem, we’ll go through the basics of what happens with measurement error in a model. Suppose that one knows a model to…

New York University ECON-SHU ECON-SHU 360 Measurement Error In this problem, we’ll go through the basics of what happens with measurement error in a model. Suppose that one knows a model to…

# Measurement Error In this problem, we’ll go through the basics of

what happens with measurement error in a model. Suppose that one knows a model to be, Yi = β0 + β1Xi + Ui and that the OLS assumptions are satisfied. In fact, we will go further and assume that U and X are independent. Suppose that you only have a noisy measure of Xi : X∗ i = Xi + ei (1) Let ei be independent of Xi and ui . Also, denote variance by σ 2 for each random variable. 1 Measurement error is pervasive in the social sciences. For example, when asked to report their compensation, people will often round to a whole number, report last year’s income, or forget parts of their income (e.g., return on savings). Our question is what happens in the situation that you, an econometrician, run this model: Yi = β0 + β1X∗ i + Ui (2) a. Prove that, Cov(X∗ , Y ) = Cov(X, Y ) Hint: If e is independent of X and U it must be independent of Y . What’s this mean for the covariance? b. Now show, V ar(X∗ ) = σ 2 X + σ 2 e c. Conclude that for model (2): βˆOLS 1 = β1 × σ 2 X σ 2 X + σ 2 e Hint: Remember that the OLS estimator is the covariance of the independent and dependent variables, over the variance of the independent variable. You’ll use this fact twice.

Don't use plagiarized sources. Get Your Custom Essay on
New York University ECON-SHU ECON-SHU 360 Measurement Error In this problem, we’ll go through the basics of what happens with measurement error in a model. Suppose that one knows a model to…
Just from \$5/Page

## Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)

### Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

### Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

### Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

### Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.