Time Dummies for Testing for Structural Change
Data 7-19
Determinants of Cigarette Demand in Turkey and Effect of Public
Campaigns against Smoking
Ln q= log of Cigarette Consumption per adult per year=Dependent Variable
Quantitative Variables
Ln y= log of per capita real GDP in 1968 prices (in TL)
Ln p= log of real price of cigarettes in TL per kg
Ln ed1= log of ratio of enrollments in middle/high school to the population
Ln ed2= log of ratio of enrollments in universities to the population
Qualitative Variables (Dummy Variables)
D82=1 for 1982 onward, 0 otherwise (Starting date for the First public campaign)
D86= 1 for 1986 onward, 0 otherwise (Starting date for the Second public campaign)
MODEL A (with only quantitative variables)
Dependent Variable: LNQ
Method: Least Squares
Date: 11/08/05 Time: 15:00
Sample: 1960 1988
Included observations: 29
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
LNY
LNP
LNED1
LNED2
-5.117077
0.746634
-0.479355
-0.044643
0.006777
4.222757
0.453106
0.112883
0.256141
0.098863
-1.211786
1.647814
-4.246482
-0.174292
0.068547
0.2374
0.1124
0.0003
0.8631
0.9459
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.700545
0.650636
0.064131
0.098706
41.25296
1.021825
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
0.784827
0.108499
-2.500204
-2.264464
14.03639
0.000005
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MODEL B (with quantitative and intercept time dummies)
Dependent Variable: LNQ
Method: Least Squares
Date: 11/08/05 Time: 15:09
Sample: 1960 1988
Included observations: 29
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
LNY
LNP
LNED1
LNED2
D82
D86
-9.509262
1.171375
-0.140956
-0.226339
-0.141883
-0.126167
-0.105592
2.652959
0.282972
0.089356
0.164159
0.068069
0.028011
0.036964
-3.584398
4.139551
-1.577466
-1.378774
-2.084413
-4.504173
-2.856628
0.0017
0.0004
0.1290
0.1818
0.0489
0.0002
0.0092
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.898862
0.871278
0.038927
0.033337
56.99234
1.692424
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
0.784827
0.108499
-3.447748
-3.117711
32.58727
0.000000
We see here positive income elasticity, negative price elasticity and relative unpopularity of
cigarettes among the educated people. Moreover, intercept dummies D82 and D86 have
negative coefficients implying that these public campaigns indeed significantly reduced
cigarette consumption in Turkey after 1982 and then further after 1986.
LM Test
Step 1: Regress lnq on the above variables as well as some additional interactive
dummies and interactive terms and save the residuals (uhat). Then regress the uhat on all
the original variables (Model A) and intercept and interactive dummies/terms. This is
called the auxiliary regression.
New Variables created using the “generate” command in Stata:
D82lny, D86lnp, D82lned2, Lnylnp, Lnylned1, Lnylned2, Lnplned1,
Lnplned2, Lned1lned2 and other possibilities
2
Auxiliary Regression for LM test
Dependent Variable: uhat
Method: Least Squares
Date: 11/08/05 Time: 15:25
Sample: 1960 1988
Included observations: 29
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
LNY
LNP
LNED1
LNED2
D82
D86
D82LNED2
D86LNP
LNYLNP
LNYLNED1
LNYLNED2
LNPLNED1
LNPLNED2
LNED1LNED2
78.88732
-8.444417
-62.42377
10.15174
12.18011
-0.933135
-0.112997
-0.297774
0.030253
6.712299
-0.553646
-1.207149
-3.250171
-0.930393
1.212970
128.8360
14.00025
64.16996
15.70892
29.16306
0.444921
0.244640
0.163616
0.248495
6.917964
1.173282
3.143089
3.593546
1.165807
2.121436
0.612308
-0.603162
-0.972788
0.646240
0.417656
-2.097302
-0.461890
-1.819956
0.121745
0.970271
-0.471878
-0.384065
-0.904447
-0.798068
0.571768
0.5502
0.5560
0.3472
0.5286
0.6825
0.0546
0.6513
0.0902
0.9048
0.3484
0.6443
0.7067
0.3811
0.4382
0.5765
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.834180
0.668359
0.034192
0.016367
67.30729
2.265701
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
-2.86E-16
0.059373
-3.607399
-2.900177
5.030622
0.002326
Test statistic=29*0.834180=24.186 exceeds the critical value of the chi-square, so some of the
new variables added are significant and based on the p-value test, these are d82, d82lned2
lnylnp lnplned1 lnplned2 (Also keep the original lnp, lny, lned1, lned2)
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FINAL MODEL (after eliminating insignificant ones)
Dependent Variable: LNQ
Method: Least Squares
Date: 11/08/05 Time: 15:32
Sample: 1960 1988
Included observations: 29
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
LNY
LNP
D82
D82LNED2
LNYLNP
-2.504783
0.416469
-3.653049
-1.413943
-0.475105
0.416570
0.643911
0.079784
1.185994
0.213406
0.078118
0.141064
-3.889955
5.219984
-3.080159
-6.625593
-6.081882
2.953058
0.0007
0.0000
0.0053
0.0000
0.0000
0.0071
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.935344
0.921288
0.030440
0.021312
63.47975
2.471386
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
0.784827
0.108499
-3.964121
-3.681232
66.54564
0.000000
Note that Adj Rsq is the highest among all other tries and all variables are significant!
Moreover, d82lned2 has a negative and signicant coefficient which means that not only
1982 campaign was successful in reducing cigarette consumption (sign of D82 is
negative) but also it was even more effective among the university students! (sign of
D82lned2 is negative and significant) In other words, university education began to have
a negative influence on cigarette consumption especially after the year 1982.
Another point is worth pursuing: the interactive term lnylnp is significant and positive.
This means that both the income elasticity of demand (coefficient of lny) and the price
elasticity of demand (coefficient of lnp) depend on the level of price and level of income
respectively. Differentiating lnq with respect to lnp, we get –3.65+0.4165lny. This means
that price elasticity is smaller (less negative, more inelastic) as per capita income grows.
In addition, differentiating lnq with respect to lny, we get +0.416+0.4165lnp. This means
that higher the price, greater is the income elasticity of demand (more sensitive to income
demand gets at higher prices)
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