Download handout 5 05/04/2017 File - Faculty of Business and Economics

EASTERN MEDITERRANEAN UNIVERSITY
Faculty of Business and Economics
Department of Business administration
MGMT 434 Research Method in Business Studies
Practical Computing Classes
SPRING 2016-2017
Handout 5: Project
By
Stata SE 11.0-14.0
Coordinator
Instructor
Prof. Dr. Sami Fethi
Mr. Amin Sokhanvar
[email protected]
[email protected]
Project
STATA SE 11.0
Sami Fethi
PROJECT
You are expected to investigate the relationship between quantity demanded of
chicken meat and its determinants by employing the data set in Table 1.
As a chief analyst, you have been asked to prepare a report for your managing
director on the impact of the quantity demanded of chicken and its determinants.
This report needs to address the concerns all the following:
(a) Introduction
(b) Brief information on the empirical literature (i.e. demand theory).
(c) An explanation of the model and the methodology used.
(d) Construct a correlation matrix as well as descriptive statistics
among the variables for the equation.
(e) A discussion of the coefficients associated with the regression
equation.
(f) Comparison of the regressions using the estimated results (t-stat,
F-stat, ANOVA).
(g) Any other comments you feel relevant to the issues being
addressed.
(h) Conclusion and recommendations.
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Tips
Tips for Demand Estimation
1. Using the data in Data set 1; specify a linear functional form for the demand
for chicken.
2. Based on the variables in the demand equation, estimate both the descriptive
statistics and the correlation matrix.
3. Create the natural log of the existing variables (LY, LPC, and LPB…). Also
create a constant and time trend by giving c and t respectively.
4. Run a regression to estimate the demand for Chicken consumption by
conducting OLS.
5. Having run the regression in step 4, we need to check the output result. When
we look at the result, we realize that there exists serial correlation. Or we can
just drop the most insignificant variable from the model.
6. What happens if we estimate the equation without the price of substitute?
Check whether the estimated Durbin-Watson statistics significant or not?
7. Find the short-run demand effects of the equation.
Hint: DLY = a + b DLPC+ c DLYD4 +………….+ i, t
8. Evaluate the regression results by examining signs of parameters, p-values
(or t-ratios), F-ratio and the R2.
9. Using the estimated demand equation’s results, find out income elasticity,
own-price elasticity, and cross-price elasticity (i.e. pork and beef).
10. Comment on chicken product whether is luxury consumption or not?
11. Based on its own price elasticity coefficient, discuss whether price is elastic
or not?
12. Is the demand for chicken affected by the variation in the prices of pork and
beef?
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SOURCE: © Gary Koop(2000) ‘Analysis of economic data’, John Wiley and Sons, Ltd, England.
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DATA SET 1: Annual Data for the demand of Chicken meat
Year
Y
PC
PB
PR
YD
1960
20.22
11.1
23.25
12.2
20.4
1961
20.78
9.5
25.95
10.1
20.2
1962
21.71
9.1
25.94
10.2
21.3
1963
22.46
9
27.22
10
19.9
1964
24.1
8.9
27.82
9.2
18
1965
25.63
8.4
29.77
8.9
19.9
1966
27.34
9.2
32.08
9.7
22.2
1967
28.95
7.1
32.62
7.9
22.3
1968
31.14
7.8
32.88
8.2
23.4
1969
33.24
9.2
34.9
9.7
26.2
1970
35.87
8.7
36.88
9.1
27.1
1971
38.6
7.3
36.74
7.7
29
1972
41.4
8.7
38.49
9
33.5
1973
46.16
14.7
37.01
15.1
42.8
1974
50.1
9.5
36.93
9.7
35.6
1975
54.98
9.3
36.7
9.9
32.3
1976
59.72
12.5
39.84
12.9
33.7
1977
65.17
11.7
40.71
12
34.5
1978
72.24
12.1
43.1
12.4
48.5
1979
79.67
13.6
46.64
13.9
66.1
1980
88.22
10.7
46.91
11
62.4
1981
97.65
10.8
48.45
11.1
58.6
1982
104.26
10.1
49.52
10.3
56.7
1983
111.31
12.4
50.83
12.7
55.5
1984
123.19
15.7
52.83
15.9
57.3
1985
130.37
14.4
54.81
14.8
53.7
1986
136.49
12.3
56.47
12.5
52.6
1987
142.41
10.5
60.27
11
61.1
1988
152.97
8.6
62.28
9.2
66.6
1989
162.57
14.2
66.17
14.9
69.5
1990
171.31
8.9
69.08
9.3
74.6
1991
176.09
6.8
72.12
7.1
72.7
1992
184.94
8.4
75.38
8.6
71.3
1993
188.72
9.8
77.14
10
72.6
1994
195.55
7.2
78.61
7.4
66.7
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1995
202.87
6.3
78.23
6.5
61.8
1996
210.91
6.4
81.42
6.6
58.7
1997
219.4
7.3
83.67
7.7
63.1
1998
231.61
7.8
83.89
8.1
59.6
1999
239.68
6.9
88.87
7.1
63.4
Introduction
Economics begins and ends with the “Law” of supply and demand.
The laws of supply and demand are an important beginning in the
attempt to answer vital questions about the working of a market
system.
Demand for a good or service is defined as quantities of a good or
service that people are ready (willing and able) to buy at various
prices within some given time period, other factors besides price held
constant.
Every market has a demand side and a supply side. The demand side
can be represented by a market demand curve which shows the
amount of commodity buyers would like to purchase at different
prices. Demand curves are drawn on the assumption that buyers’
tastes, income, the number of consumers in the market and the price
of related commodities are unchanged.
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Literature Review
Consumer demand theory postulates that the quantity demanded of a
commodity per time period increases with a reduction in its price, with an
increase in the consumer’s income, with an increase in the price of substitute
commodities and a reduction in the price of complementary commodities,
and with an increased taste for the commodity. On the other hand, the
quantity demanded of a commodity declines with the opposite changes.
The inverse relationship between the price of the commodity and the
quantity demanded per period is referred to as the law of demand. A
decrease in the price of a good, all other things held constant (ceteris
paribus), will cause an increase in the quantity demanded of the good. An
increase in the price of a good, all other things held constant, will cause a
decrease in the quantity demanded of the good.
Economic Theory
Background: The general demand function shows the relationship between
quantity demanded and the following six factors can be expressed in the next
equation:
Qd=f (P, I, PR, T, PE, N)
Qd is quantity demanded of the good and service, P is price of
the good and service, I is consumer’s income per capita, PR is
price of the related goods and services, T is taste patterns of
consumers, PE is expected price of the good in some future period
and N is number of consumers in the market.
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The Theory says:
Qd=f (P, I, PR, T, PE, N)
-, +/-, +/-,+, +, +
N/I, S/C
DATA AND MODEL
It is worth stressing that the data set used in this study was obtained from
http://salvatore.swlearning.com. The data, cover the period between 1960
and 1999, are annually time series.
Y= a PCb PBc PRd YDe - this is nonlinear form of the demand equation.
This can be transformed by taking natural logarithms into the following loglinear specification:
Ln Y = Ln a + b ln PC + c Ln PB + d Ln PR + e ln YD
Y is per capita chicken consumption in pounds, PC is the price of chicken in
cents per pound; PB is the price of beef in cents per pound, PR is the price of
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pork in cents per pound; YD is the US per capita disposal income in hundred
of dollars.
The Theory says:
Qd=f (PC, PB, PR, YD)
- ,+ ,+ ,+
MODEL ESTIMATION
First step: Correlation Matrix
corr ly- lyd
(obs=40)
|
ly
lpc
lpb
lpr
lyd
-------------+--------------------------------------------ly |
1.0000
lpc | -0.0806
1.0000
lpb |
0.9834 -0.2118
1.0000
lpr | -0.1430
0.9947 -0.2732
1.0000
lyd |
0.9492
0.0894
0.9109
0.0272
1.0000
or
pwcorr ly lpc lpb lpr lyd, obs sig
|
ly
lpc
lpb
lpr
lyd
-------------+--------------------------------------------ly |
1.0000
|
|
40
|
lpc | -0.0806
1.0000
|
0.6210
|
40
40
|
lpb |
0.9834 -0.2118
1.0000
|
0.0000
0.1895
|
40
40
40
|
lpr | -0.1430
0.9947 -0.2732
1.0000
|
0.3787
0.0000
0.0881
|
40
40
40
40
|
lyd |
0.9492
0.0894
0.9109
0.0272
1.0000
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|
|
0.0000
40
0.5832
40
0.0000
40
Sami Fethi
0.8678
40
40
NOT: It is expected to have low correlation between explanatory variables and high
correlation between the dependent variables. As can be seen from the table above, the
correlation coefficient between ly and lpc .is slightly low. The other coefficients seem
that they do not create any fragile results. In the table above, the top number is the
correlation coefficient itself, the number below is the two-tailed p-value for the
correlation, and bottom number is the sample size. This step also gives us further
evidence for regression analysis.
SECOND STEP: Descriptive statistics
. summarize y-yd
summarize ly- lyd
Variable |
Obs
Mean
Std. Dev.
Min
Max
-------------+-------------------------------------------------------ly |
40
4.325927
.8271163
3.006672
5.479305
lpc |
40
2.255696
.2417019
1.84055
2.753661
lpb |
40
3.849958
.389262
3.146305
4.487175
lpr |
40
2.298974
.2355904
1.871802
2.766319
lyd |
40
3.735565
.4779164
2.890372
4.31214
This gives us a general idea about data in terms of mean, standard deviation etc…
THIRD STEP:
regress
ly lpc lpb lpr lyd
Source |
SS
df
MS
-------------+-----------------------------Model |
26.334994
4 6.58374851
Residual | .345739981
35 .009878285
-------------+-----------------------------Total |
26.680734
39 .684121385
Number of obs
F( 4,
35)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
40
666.49
0.0000
0.9870
0.9856
.09939
-----------------------------------------------------------------------------ly |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------lpc | -.0171159
.816133
-0.02
0.983
-1.673954
1.639722
lpb |
1.787105
.1442181
12.39
0.000
1.494327
2.079884
lpr |
.3047523
.8450215
0.36
0.721
-1.410733
2.020237
lyd |
.3135002
.1131904
2.77
0.009
.0837114
.543289
_cons | -4.387463
.4215806
-10.41
0.000
-5.243317
-3.531609
------------------------------------------------------------------------------
Diagnostic Tests Results
estat hettest
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Breusch-Pagan / Cook-Weisberg test for heteroskedasticity
Ho: Constant variance
Variables: fitted values of ly
chi2(1)
=
0.35
Prob > chi2 =
0.5522
Heteroskedasticity Another assumption of the OLS regression model is that residuals
are homoscedastic. If the residuals have a constant variance, they were said to be
homoscedastic, but if they are not constant, they are said to be heteroscedastic. The effect
of heteroscedastic are that even though the regression coefficients are still linear and
unbiased, they are no longer the best or minimum variance estimates, thus they are no
longer the most efficient coefficient. As a result, in the presence of heteroscedasticity, the
usual hypothesis testing routine is not reliable, raising the possibility of drawing
misleading conclusions. The model was tested whether error variance is constant or not.
The hypothesis is conducted as follows:
H0:
H1:
Б12 = Б22 (Homoscedasticity)
Б12  Б22 (Heteroscedasticity)
It seems that there is no heteroscedasticity problem in this case.
estat dwatson- Multicollonieary
Durbin-Watson d-statistic(
5,
40) =
1.163403
Multicollinearity is the existence of strong relation among some or all explanatory
variables of regression. Multicollinearity does not affect the best unbiased estimator of
OLS but since some coefficient have large standard errors; they tend to be insignificant,
thus making precise estimation to becoming difficult. For this pupose, you can use DW
statistics.
estat vif
Variable |
VIF
1/VIF
-------------+---------------------lpr |
156.47
0.006391
lpc |
153.63
0.006509
lpb |
12.44
0.080370
lyd |
11.55
0.086555
-------------+---------------------Mean VIF |
83.52
NOTE: When you check the estimated DW- statistic, the general rule of thumb tells us
the value should be around 2. A VIF of 1 means that there is no correlation among the
variables under inspection. The general rule of thumb is that VIFs exceeding 10 are signs
of serious multicollinearity requiring correction. As you can see, three of the variance
inflation factors such as, 11.55, 12.44 —are fairly large. The VIF for the predictor
Weight, for example, tells us that the variance of the estimated coefficient of Weight is
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inflated by a factor of 83.52 because Weight is highly correlated with at least one of the
other predictors in the model.
It seems that there is a multicollinearity problem in this case.
estat durbinalt
Durbin's alternative test for autocorrelation
--------------------------------------------------------------------------lags(p) |
chi2
df
Prob > chi2
-------------+------------------------------------------------------------1
|
9.290
1
0.0023
--------------------------------------------------------------------------H0: no serial correlation
Autocorrelation (Serial Correlation)
Autocorrelation occurs when the results are not independent of each other. The OLS
regression model is a minimum variance, unbiased estimator only when the residuals are
independent of each other. If the autocorrelation exists in the residuals, the regression
coefficients are unbiased but the standard errors will be underestimated and the test of
regression coefficients will be unreliable. The most commonly used test for detecting
autocorrelation is the one that is developed by Durbin and Watson, known as DurbinWatson (DW) statistics. However, in order to test for autocorrelation, you can use chisquare statistics with the tabular values by testing the following null hypothesis:
H0:  = 0 (no autocorrelation)
H1:   0 (existence of autocorrelation)
Since calculated values are smaller than tabular values, estimate regression does not have
first order serial correlation. However, our case is other way around (9.29-estimated>3.84
critical value).
It seems that there is a Serial Correlation problem in this case.
Normality:
sktest resid
Skewness/Kurtosis tests for Normality
------- joint -----Variable |
Obs
Pr(Skewness)
Pr(Kurtosis) adj chi2(2)
Prob>chi2
-------------+--------------------------------------------------------------resid |
40
0.6128
0.0003
10.96
0.0042
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Normality shows us whether the residuals are normally distributed or not, as normal
distribution is one of the assumptions of the OLS. To check this assumption, you can use
the chi-square statistics employing the following hypothesis:
H0: ut = 0 (residuals are normally distributed)
H1: ut  0 (residuals are not normally distributed)
Since the equation indicates its calculated value of normality is bigger (10.96-chi-sq(2))
than the tabular value (5.99-chi-sq(2)), there is a problem in terms of normality. However
some other statistical programs indicate this problem other way around (i.e. the calculated
value is 1.048).
Functional Form:
estat ovtest
Ramsey RESET test using powers of the fitted values of ly
Ho: model has no omitted variables
F(3, 32) =
9.65
Prob > F =
0.0001
Functional form is a problem whether there is the presence of misspecification within
the estimation equation. Following hypothesis are tested for the presence of
misspecification:
H0:  = 0 (no misspecification)
H1:   0 (existence of misspecification)
Since the calculated figures are smaller than tabular ones, there is no variable omitted. In
other words, the empirical equation is consistent with the relevant theory.
In this case, there is a functional form problem although the other programs do not
confirm this result obtained from Stata.
FOURTH STEP
: Drop the most insignificant variable ( i.e., LPC) from the model
regress
ly
lpb lpr lyd
Source |
SS
df
MS
-------------+-----------------------------Model | 26.3349897
3 8.77832989
Residual | .345744326
36 .009604009
-------------+-----------------------------Total |
26.680734
39 .684121385
Number of obs
F( 3,
36)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
40
914.03
0.0000
0.9870
0.9860
.098
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-----------------------------------------------------------------------------ly |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------lpb |
1.786771
.1413271
12.64
0.000
1.500146
2.073395
lpr |
.2871495
.0963688
2.98
0.005
.0917046
.4825944
lyd |
.3132104
.1107734
2.83
0.008
.0885516
.5378692
_cons | -4.383231
.3649689
-12.01
0.000
-5.123422
-3.64304
Drop the most insignificant variable (i.e., LPR) from the model
regress
ly lpc lpb
lyd
Source |
SS
df
MS
-------------+-----------------------------Model | 26.3337092
3 8.77790307
Residual | .347024795
36 .009639578
-------------+-----------------------------Total |
26.680734
39 .684121385
Number of obs
F( 3,
36)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
40
910.61
0.0000
0.9870
0.9859
.09818
-----------------------------------------------------------------------------ly |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------lpc |
.2752426
.0932464
2.95
0.006
.0861301
.4643551
lpb |
1.777065
.1397851
12.71
0.000
1.493567
2.060562
lyd |
.3118099
.1117186
2.79
0.008
.0852342
.5383857
_cons | -4.301347
.3432137
-12.53
0.000
-4.997417
-3.605277
------------------------------------------------------------------------------
Drop the price of substitute variables from the model
regress
ly lpc lyd
Source |
SS
df
MS
-------------+-----------------------------Model | 24.7757981
2 12.3878991
Residual | 1.90493588
37 .051484754
-------------+-----------------------------Total |
26.680734
39 .684121385
Number of obs
F( 2,
37)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
40
240.61
0.0000
0.9286
0.9247
.2269
-----------------------------------------------------------------------------ly |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------lpc | -.5708903
.1509282
-3.78
0.001
-.8766998
-.2650808
lyd |
1.668583
.0763305
21.86
0.000
1.513923
1.823243
_cons | -.6194177
.4255991
-1.46
0.154
-1.481763
.242928
------------------------------------------------------------------------------
estat vif
Variable |
VIF
1/VIF
-------------+---------------------lpc |
1.01
0.992004
lyd |
1.01
0.992004
-------------+---------------------Mean VIF |
1.01
. estat dwatson
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Durbin-Watson d-statistic(
3,
Sami Fethi
40) =
.6139399
*When you check the outputs, you will realize that the output results are getting
better in terms of t-values.
FIFTH STEP SHORT-RUN
regress dly dlpc dlpb dlpr
dlyd
Source |
SS
df
MS
-------------+-----------------------------Model | .005183328
4 .001295832
Residual |
.01717825
34 .000505243
-------------+-----------------------------Total | .022361578
38 .000588463
Number of obs
F( 4,
34)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
39
2.56
0.0558
0.2318
0.1414
.02248
-----------------------------------------------------------------------------dly |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlpc |
.1588333
.1585995
1.00
0.324
-.1634795
.4811462
dlpb | -.2925925
.1339937
-2.18
0.036
-.5649005
-.0202845
dlpr | -.1466017
.1644654
-0.89
0.379
-.4808357
.1876322
dlyd |
.0868503
.0397139
2.19
0.036
.0061419
.1675587
_cons |
.0708367
.0056002
12.65
0.000
.0594557
.0822176
------------------------------------------------------------------------------
Drop the most insignificant variable (i.e., LPR) from the model
regress dly dlpc dlpb
dlyd
Source |
SS
df
MS
-------------+-----------------------------Model | .004781881
3
.00159396
Residual | .017579698
35 .000502277
-------------+-----------------------------Total | .022361578
38 .000588463
Number of obs
F( 3,
35)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
39
3.17
0.0361
0.2138
0.1465
.02241
-----------------------------------------------------------------------------dly |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------dlpc |
.0183891
.0180954
1.02
0.316
-.0183466
.0551248
dlpb | -.2605479
.1287019
-2.02
0.051
-.5218266
.0007308
dlyd |
.0767796
.0379611
2.02
0.051
-.0002856
.1538448
_cons |
.0703506
.0055572
12.66
0.000
.0590689
.0816323
-----------------------------------------------------------------------------
EMPIRICAL RESULTS
In the long run: Having estimated the log linear demand function, all slope coefficients
are partial elesticities of per capita consumption chickens (Y) with respect to the
appropriate the real disposable income per capita (its elasticity is about 0.32 percent), the
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retail price of chicken per pound (its own price elasticity is about -0.02 percent), the retail
price of pork per pound (its cross price elasticity is about 0.32 percent), and the retail
price of beef per pound(its cross price elasticity is about 1.32 percent). Individually,
income and cross-price elesticities of demand are statistically significant. The demand for
chicken with respect to its own price is price inelastic because absolute term of elasticity
coefficient is less than 1.The two cross-price elasticities are positive and suggesting that
the other two meats are competing with chicken however, the beef is only statistically
significant. Thus it seems that the demand for chicken is only affected by the variation in
the price of beef.
CONCLUSION
In this study, a demand model was investigated to find the relationship between quantity
demanded for consumption of chicken and its determinants in the case of US economy
for the period of 1960-1999. In order to see the impact of per capita consumption of
chicken on income, own price and cross price elesticities.
The empirical findings show that the demand for chicken is only affected by the variation
in the price of beef. It also indicates that the demand for chicken with respect to its own
price is price inelastic.
0
1
2
3
4
NOTE: Graphical presentation can be thought to add to the text.
mean of ly
mean of lpb
mean of lyd
mean of lpc
mean of lpr
17
Project
STATA SE 11.0
Y
PB
YD
Sami Fethi
PR
PC
18