{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Econometrics-I-2

# Econometrics-I-2 - Applied Econometrics William Greene...

This preview shows pages 1–14. Sign up to view the full content.

Applied Econometrics William Greene Department of Economics Stern School of Business

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

View Full Document
Applied Econometrics 2. Regression and Projection
Statistical Relationship Objective :  Characterize the stochastic  relationship between a variable and a set of  'related' variables  Context:   An inverse demand equation,  P =   α   +   β Q  +   γ Y, Y = income.  Q and P are two  obviously related random variables.  We are  interested in studying the relationship between P  and Q. By ‘relationship’ we mean (usually) covariation.   (Cause and effect is problematic.)

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

View Full Document
Bivariate Distribution - Model for a Relationship Between Two Variables We might posit a bivariate distribution for Q and P,  f(Q,P)  How does variation in P arise?  With variation in Q, and  Random variation in its distribution.  There exists a conditional distribution f(P|Q) and a  conditional mean function, E[P|Q].  Variation in  P  arises  because of  Variation in the mean,  Variation around the mean,  (possibly) variation in a covariate, Y.
Implications Regression  is the conditional mean There is always a conditional mean It may not equal the structure implied by a theory What is the implication for least squares estimation? LS always estimates regressions LS does not necessarily estimate structures Structures may not be estimable – they may not be  identified .

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

View Full Document
Conditional Moments The conditional mean function is the   regression function . P  =  E[P|Q]  +  (P - E[P|Q])  =   E [P|Q] +  ε E[ ε |Q] = 0 = E[ ε ].  Proof:  (The Law of iterated expectations) Variance of the conditional random variable = conditional variance,  or the   scedastic function . A “trivial relationship” may be written as P = h(Q) +  ε , where the  random variable  ε =P-h(Q) has zero mean by construction.  Looks  like a regression “model” of sorts.  An extension:  Can we carry  Y  as a parameter in the bivariate  distribution?  Examine  E [P|Q,Y]
Sample Data (Experiment)

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

View Full Document
50 Observations on P and Q Showing Variation of P Around E[P]
Variation Around E[P|Q] (Conditioning Reduces Variation)

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

View Full Document
Means of P for Given Group Means of Q
Another Conditioning Variable E[P|Q,Y=1] E[P|Q,Y=2]

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

View Full Document
Conditional Mean Functions No requirement that they be "linear" (we will  discuss what we mean bylinear) No restrictions on conditional variances
Projections and Regressions We explore the difference between the linear projection  and the conditional mean function y  =   α   +   β x  +   ε   where   ε    x,  E( ε |x)  =  0              Cov(x,y)  =  Cov(x, α )  +   β Cov(x,x)  +  Cov(x, ε )

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