Temple University

Economics 615

Demand for Bread and Meat: Answer Key

1.a.

QB =

1.95423 +

.029601 Y + e

 

(.842)

2.321

(.00852)

3.47

1.b.

QB =

.4011 +

.0245 Y +

.4129 S -

.355 PB

+.57 PM + e

 

(1.03)

.39

(.00789)

3.10

(.112)

3.69

(.062)

5.73

(.161)

3.54

2.

tobs = 1.954/.842 = 2.32

P(-2.32 < t < 2.32) @ .974 Therefore reject the null.

 

3. i.





The observed F is above the critical value for any reasonable significance level, so reject the null.

3.ii.


tobs = .57/.161 = 3.53


Reject Ho at the 1% level of test.

4.

i.



ii.



iii.




iv.




5. For the meat equation when the observations with Qm=0 are omitted

QM =

7.512 +

.0389 Y -

.356 S +

.146 PB -

1.179 PM +

e

 

(.95)

7.91

(.008)

4.86

(.121)

2.94

(.061)

2.39

(.149)

7.91

 

When all the observations are used

QM = 7.815 + .0411 Y - .4367 S + .1625 PB - 1.2293 PM + e
(1.045)
7.47		 (.008)
5.13		 (.114)
-3.83		 (.063)
2.56		 (.163)
-7.54

a.

Delete Obs for which Qm=0 All Observations

At the 2.5% level reject Ho

b.

Exclude obs for which Qm = 0 All observations


Define

.1625+.0411(4.7719)=.3586

tobs = 6.306

Reject the null.

 .06352+(4.7719)2(.008)2+2(4.7719)(-.0002416)

          =.003184

tobs = 6.355

6. Your answers to the meat part of this question will depend on how you dealt with the zeros in QM. The choices are to delete those observations; inadvisable since you lose valuable information. When QM = 0, let ln(QM) = 0; inadvisable since you are saying that these households are equivalent to those that consumed QM = 1. When QM = 0, reset it to QM = (some small number); inadvisable since this will tilt the regression line unduly. Add 1 to every observation on QM; best idea yet, although households with low QM experience a bigger % shift than those with high QM. You should read the text or lecture notes to decide how best to deal with missing data.
Results when observations corresponding to Qm = 0 are deleted from both the Bread and Meat samples:

LnQB =

-.5633

(.465)

+.719 lnY

(.162)

+.33 ln S

(.132)

-1.196 ln PB

(.172)

+.066 ln PM

(.16)

+ e

LnQM =

-1.833

(1.54)

+1.514 lnY

(.54)

+.899 ln S

(..44)

+.642 ln PB

(.57)

-2.282 ln PM

(.54)

+ e
Use all data for bread and add 1 to Qm.

LnQB =

-.6433

(.4207)

+.7057 lnY

(.1319)

+.37 ln S

(.1075)

-1.1428 ln PB

(.1555)

+.6303 ln PM

(.1555)

+ e

LnQM =

-.8025

+1.213 lnY

-.847 ln S

+.5087 ln PB

-1.782 ln PM

+ e

a.


All observations Delete obs for which Qm = 0


tobs = .07581/.09958 = .76126
Do not reject the null.

 tobs = .761

b.



1.213-.8471-1 = -.6341

tobs = -1.041
Do not reject the null.

 tobs = -2.33