2.8 (i) We follow the hint, noting that qy = cl? (the sample average of c1 yi is 61 times the
sample average of y,) and 02x = c2)? . When we regress clyl- on czxi (including an intercept) we
use equation (2.19) to obtain the slope:
~ 2(szi _sz)(c1)7i 01?)
an , order th'FerentTaI equation:
of interest the 2nd, order dTc. eq. 75 o (172+ b%"-+oxo (h)
homogehous. constant coeFcrent , automous, lTnear
Remember the homo. sol. the ISt-order dTQ eq 0t oohstorrt- weff.,auto, and
how form, has the torm e t" the
Continuous Dynamic System (Shone, Economic Dynamics, 2/e, 2003)
2.1 Some denitions
0 Adifferential equation is an equation relating
a the derivatives of an unknown function,
b the function itself,
N57 . .49. '
c the variables in terms of which the functio
2012.11.06 () Homework III
(i) prtystr A expend A ,
, A , B A
, B , A
A B , .
. gen expendAxB = expendA *
. reg voteA prtystrA expendA expendB expendAxB
Layout the multiple regression model in matrix form and discuss the meaning
of each of Gauss-Markov assumptions.
Proof that OLS estimator is not only
unbiased, but also BLUE. (15 pts)
Prove that the OLS is a consistent estimator and deri
Note: There are four questions in this test. Please answer all of the questions. The
exam time is three hours. Calculator is allowed. Good luck!
(25 pts) Consider the multiple regression model with three independent variables,
under the clas
DI XII t
~"Xr2 t \' T
~ "X,< t
~K-tl Y. -t Vi"
'if = ~o t ~'XI T ~J.X2 t ,\-t ~J<Xt<
= ( ~O
XI -t ~J-X2 -t
Ho~ SI: Z>2=-'"
Multilevel Logistic Regression
y = + x
Show that iJzsls = (XX)X'Y and explain why
Suppose the probability that a person is a smoker is given by the logit model,
Z'X. ( 15 pts)
exp(a + ,&)/[1 + exp(a + fix)] where x is a dummy variable taking the
value one for
2012.10.23 () Homework II
. gen a =
exper + tenure
1. You want to estimate a log wage equation using all variables (including a square
d ummy variable equal to one if the person belongs to a union and zero otherwise.
The variable YR85 is