Midterm Exam 2 answers

Taskin
Bitkent University
Department of Economics
Econ 301
Econometrics
Mid Term Exam II
December 13,Z0l4
Name
Indicate the test statistic,
for
he null hyp"tü*§-,nd iis economic interpretation
each hypothesisto
all your computations, complete the calculations
In vour numerical calculations: show
»
y/
.<J /
ll
"9/
rtıV
receive full points.
t|eJ_ are asked,
please, answer individual sections of each que§tion in the order
sheet, 4 y] _ *, ,; u.ı'' _ :__. .rl
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please do notwrite on the margins, you may u§e the backof each
1.
VARIABLES
equation:
(24 points) SÇALING OF
Öorİid.. the following
Y=Fr+B.X,+U,
which is estimated to
,]
be:
,
i=+.+o+0.869x
se. (I.23) (0.117)
a)
If the values of the
- }" İ"
! ), =
j ii, = 2 ?,
dby 2r,r"h_a, X,*
are multiplie
'
=
'i,.
i nç." -,' u",t.{ ? - çi''}
^:;-'{:,^
," 27
:' ,}
= ı4 Qt)r
X, x2, find
the numerical
of the following regression using the
values of intercept and the slope coefficient
yorn steps)
coefficient estimates above (show all
Y, = 1, + )"rX
b)
X,
=0.756
R2
'y-
*'.-,.'
*
r,
*u|
How wil1 the residual, ü,,
step by step.
VEr(,\),
t_stat and x_' be affected by this scaling, Illustrate
c)IfthevaluesoftheX,andY,arebothmultipliedby2suchasX,*=Xix2,and
of
values of intercept and the slope coefficient
Y,* = Y, x2; whatwill be the numerical
your steps),
the following regression (show all
Y*,=ar+arX*r,*i'
Yf..Y'"L
.l
"l
A.
/t
_
.7-.r-, , -? ' ' ') '
"<!yr, i*,, -|,' ':,_ *o'.ı'.,".,-_
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i,=Ç-',=-r'=
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Name
(con't)
Question 1 answers
14
C)
ı(*i-ı} vi;\- io) _
üı=
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x
#i K'
-
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rz i*
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Name
'.
(30
eTnh:§)e
y th" foılo*ing equation
log(D
= Fr+
Frlog(L,)+ğ |og(K,)+ Bot+u,
the time
input; K, is the capital input; and / is
The estimated equation is:
trend that takes the values |r2 ,3, ...,32.
where
-
5
}Z,
is the output; Z, is the labor
Dependent Variable: LOG(Y)
Method: Least Squares
(',
-ç
Date 12l09l10 Time:
^'r'6
23:21
Sample: 1 32
lncluded observations: 32
y- .,,/
..llv
coefficient
Std. Error
t-statistic
c
-o.206271
0.090808
0.144506
-2.271503
1o.76710
0.056,165
-1.109171
o.2768
2.542197
0.0168
1.555910
-0.062296
o.o2o077
LoG(L)
LoG(K)
TlME
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
a)
Prob.
Variable
0.993578
0.992890
0.076893
0.165553
38.82121
0.945304
0-007897
schwarz criterion
F-statistic
Prob(F-statistic)
F, f ,
0-0000
1.969834
0.911935
-2,176325
-1.993108
1444.083
0.000000
Mean dependent var
S.D. dependent var
Akaike info criterion
signs of the
Before the estimatiorı, explain the expected
0.0310
and B o (which is )
=01og(Y)/0f).
ğ ı1
,V'\gd{
Jgj!
c)
significant. (your formal test should include
Test the hypothesis that prareindividually
conclusion and interpretation,)
null and the altemative hypothesis, test statistics,
,*il
t[§,t
J
*/, A, /1:l
(what is the graphical ^'
coefficient?
the
of
interpretation
/o
*r* İ rİ"lİ;".,c
hypothesis t , )
function in a y and L space?) Test the
interpretatio nof Bofor the production
interpretatio
What are the mathematical and economic
that Ho : §o
=
0;
against the alternativ e thü
iog(t/ K,)= A+ Br|og(L,l K,)+u"
(Yo, need to
the restrictio n o^ pr,0. *d 4 .
equation.)
v§^wrt
arıd prcoeffıcients,
H, : fo> 0, What
If you estimate
what are
ıof B,
is your conclusion?
do simplifications in the first
h" d
to be
above restricted equation (in e) is calculated
If the sum of squared residual of the
0.38783 1, formally test this restriction,
-*
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Question 2 answers (con't)
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Name
a) Which one is the base category and write the equation that represents this category?
b) Formulate and test the hypothesis that the autonomous consrrmption is the same inthe
first and the fourth quarter.
br-y**roJi--
C)
lMü9Lr -2-
\
Formulate and test the hypothesis that the autonomous consumption is the same in the
second and the third quarter.
d) Formulate and test the hypothesis that marginal propensity to consume in the first
quarter is greater than the fourth quarter.
"
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'rtor,r,o.o')
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a"ozğ
*.o Pc;
a)
c **
k s Pı + FıYg +ıı[
b) Lonçtıo"yhö'*'"l
- .- *,
_
[HıNr: INTERCEPT sHows AUTONOMOUS CONSUMPTION AND sLoPE sHows MARGINAL
CONSUMPTIONI
[IIrNr: YOUR FORMAL TESTS SHOULD INCLUDE HYPOTHESIS, TEST STATISTICS,
CRITICAL STATICS AND INTERPRETATION]
Dç *}ıJt", Bo*."ç.-i*1-,ö, 4t
P(_ü,*ı_*,
tt^^r-ç.
Formulate the hypothesis and describe (but DO NOT TEST) how you will test that
quarters do not affect consumption behaviour.
r
uıv,:.rtlc-lı"+J
+-ö
Formulate the hypothesis and describe (but DO NOT TEST) how you will test that
marginal propensity to consume is tlıe same in all quarters.
'
"4 ğ""
1l.,",( {,d* *1,
Name
3.
(30 points)
DUMMY VARIABLES
The following is the statistical model used to estimate the consumption expenditure function
with quarterly data, for the period |974 Ql to 1984 Q4, in United Kingdom (ie. n:44)
C,
where
=
+ ü,|D|ı + a
F,
rDr, + ü3D3ı + §rY, + 01(D |,*Y,) + 02(D 2,*I ) + 9r(D r,*Y,) + u,
C, ls tne real total consumption expenditures for the quarter,
{
ls tne real personal disposable income for the quarter,
Q,ls
Drris
a dummy variable that takes the value of 1 for the first quarter and 0 otherwİse.
^
dummy variable that takes the value of 1 for the second quarter and 0 otherwise.
Qrls , dummy variable that
takes the value of 1 for the third quarter and 0 otheı"wise.
The results of the estimation is:
LS
//
Dependent Variable is
CONSUMPTION
Sample: 1974:1|984:4
Included obşervations: 44
Variable
C
D1
D2
D3
INCoME
R-squared
Adjusted R-squared
-0.630725
0.202615
0.5322
0.22ll92
l|.4264|
0.8262
0.|22342
-0.079313
-0.582536
-0.|69759
0.13ı093
o-941246
Mean dependent
0.120583
var
var
Akaike info criter
Schwarz criterion
F-statistic
Prob(F-statistic)
S.D. dependent
_371.5093
L.267609
Coefficient Covariance Matrix: Diagonal elements are VAR(
Bl
p1
o1
ğ2
cı3
p2
0l
02
03
22961355
-22967355
-22967355
-22967355
-432.7877
432.7877
432.7877
432.7817
cıl
-22967355
i39736049
a2
o3
-22967355
22967355
-22967355
22967355
22967355
22967355 ı aZallSOl*
22967355 : 22967355
432.7877
432.7877
-432.7877
-903.9751
-432.7877
432.7871
432.7877
-768.1134
]?:927?299
432.7877
-432.7871
-432.7877
-752.7958
0.8406
0.6289
0.4874l3
-0.076366
-0.020470
1242.388
55567012
Log likelihood
Durbin-Watson stat
4792.427
6303.654
6916.018
6266.817
0.090584
-3022.704
12,17.2l8
3370.955
1386.167
1.035047
0.929822
S.E. of regression
Sum squared resid
Prob.
Std.
_0.009703
D1,,INCOME
D2*INCOME
D3*INCOME
Error
t-statistic
coefficien
f)
0.9372
0.5638
0.8661
50234.07
4689.827
|4.4|255
14.73695
82.38969
0.000000
r"a off-diagonal
F2
,
0.0000
-432.78
432.7877
432;7877
432.7877
0.008205
-0.008205
-0.008205
-0.008205
e1
one§
are Cov( B,,
B)
02
03
432;l877
-432.7817
432.78,17
-432.7877
-0.008205
-903.9751
432.7877
432.7877
-432.7877
-432.7877
-752;7958
0.0ı4968
0.008205
0.017185
0.008205
-0.008205
0.008205
0.008205
0.014540
432.7877
-768.L|34
0.008205
0.008205
_0.008205
Name
4. (16 noints) TRLIE FALSE ON MULTICOLLINEARITY
Indicate and explain whether the following statements are True or False? Your explanations
should involve a clear explanation and/or formal proof of your statement. The completeness of
your answer will determine the points you will receive.
1) In a regression
and
X,
model Y = fr+ FrXr,+ §rXr,* U,;
increases, the
Var(Br1
and
as the correlation
Var(Pr) declines,
coefficient between
because more the variation
in
l
X1
can be
explained by the explanatory variables,
2) You will not obtain a high Rİ value in a multiple regression if all the partial slope coeffıcients
are individually statistically inşignificant on the basis of t-tests.
3) Even with perfect multicollinearitv the
6ü
\ı
,
V"f(F}=
"""d
{t *^
eE Çun
t P$&, *Çi,
LiLo*** V,i e'"*\
P,+PeXa,
ç,rrcrl*s'*i*
-
OLS estimates are B.L.U,E.
i,\ r*o
**s
Xı,
1^.n"ı-rı,-,
İl
.^r.-*"e
[oi,*i, C,l"$**lf
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