- Email: [email protected]
Empirical estimation of per capita brandy demand in Armenia
Accepted Manuscript Empirical estimation per capita brandy demand in Armenia S.A. Movsisyan PII:
S1512-1887(17)30023-4
DOI:
10.1016/j.aasci.2016.09.016
Reference:
AASCI 90
To appear in:
Annals of Agrarian Sciences
Received Date: 9 November 2016 Accepted Date: 27 December 2016
Please cite this article as: S.A. Movsisyan, Empirical estimation per capita brandy demand in Armenia, Annals of Agrarian Sciences (2017), doi: 10.1016/j.aasci.2016.09.016. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Annals of Agrarian Science vol. 15, no.1, 2017
Empirical estimation per capita brandy demand in Armenia S. A. Movsisyan National Agrarian University of Armenia
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74 Teryan Str., Yerevan, 009, Republic of Armenia
Received: 09 November 2016; Accepted: 27 December 2016 Corresponding Corresponding author: Suren Movsisyan
SC
[email protected]
ABSTRACT
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The empirical estimations were based on linear and double-log regression models, which identified the factors influencing the average per capita brandy demand in Armenia. The model was estimated using quarterly time-series data on per capita brandy consumption, disposable income, prices of various alcoholic beverages for 1997-2015 periods. This is quantitative study based on secondary annual, quarterly and monthly data, and 5% significance level. The average annual per capita brandy consumption data for 1997-2007 periods was obtained from WHO’s website, whereas the 2008-2015 data was extracted from the National
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Statistical Service of the Republic of Armenia. For annual, quarterly and monthly periods from 1997 through 2015, the price data related to various alcoholic beverages, consumer price index were
provided
in
NSS
statistical
publications
of
“Socio-Economic Situation of RA”, ”Consumer price indexes (prices) in the Republic of
EP
Armenia”, “Prices and tariffs in the Republic of Armenia”. For 1997-2015 periods, the average monthly per capita monetary income data was obtained from “Living Standards of Population
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and Social Sphere” section of statistical yearbooks. The latter substituted the average per capita monthly disposable income data, since these data were unavailable. Meantime, since the data included numerous years, therefore, the nominal price and income data were adjusted for inflation using consumer price index with 2005 as base year. In conclusion, the average real prices of wine and vodka were statistically significant determinants of the average per capita brandy demand in Armenia, and the demand for brandy was inelastic. Keywords:
Per
capita
brandy
demand,
double-log
regression
model,
seasonality,
cross price elasticity, income elasticity ----------------------------------------------------------------------------------------------------------------
ACCEPTED MANUSCRIPT Introduction he average per capita brandy production was characterised by an increasing trend over the observed period, while the average per capita brandy consumption increased until 2007 and drastically reduced during subsequent years. Over the period 2005-2015, the compound annual growth rates of the average per capita brandy consumption and production were -3% and 8%
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accordingly [Fig. 1].
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6.71 7.0 6.21 6.11 6.5 5.64 6.0 5.17 5.5 5.07 5.0 4.56 4.15 4.5 4.0 3.22 3.5 2.90 2.79 3.0 2.23 2.24 2.5 2.0 1.5 1.0 0.5 0.18 0.21 0.23 0.22 0.22 0.08 0.08 0.07 0.07 0.08 0.07 0.06 0.12 0.0 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Per capita brandy consumption
Per capita brandy production
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Fig. 1. The average per capita brandy production and consumption in Armenia during 2003-2015 [1-3]
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Objectives and methods
First time in the Republic of Armenia, this study identifies the factors influencing the average per capita brandy demand over the period 1997-2015.
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Experimental section
The analysis have been conducted through STATA 10 statistical programming software and the
dataset encompassed annual, quarterly and monthly time series data ranging from 1997 through 2015.
The estimated linear brandy demand equation was as follows: Pcbrandyqt= β0 - β1·rl_pbrandyt + β2·rl_pwinet + β3·rl_pchampagnet + β4·rl_pbeert +
β5·rl_pvodkat + β6·rl_pcdpit + β7·trendt + ut
(Model 1)
Meantime, the following double-log brandy demand equation was estimated: ln_pcbrandyqt= β0 - β1·lnrl_pbrandyt + β2·lnrl_pwinet + β3·lnrl_pchampagnet + β4·lnrl_pbeert + β5·lnrl_pvodkat + β6·lnrl_pcdpit + β7·trendt + ut,
(Model 2)
ACCEPTED MANUSCRIPT where ln_pcbrandyqt is the natural logarithm of the average per capita brandy consumption in time period t; [1-4] lnrl_pbrandyt is the natural logarithm of the average real price of brandy in time period t; lnrl_pwinet is the natural logarithm of the average real price of wine in time period t; lnrl_pchampagnet is the natural logarithm of the average real price of champagne in time period
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t;
lnrl_pbeert is the natural logarithm of the average real price of beer in time period t;
lnrl_pvodkat is the natural logarithm of the average real price of vodka in time period t; [5-7]
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lnrl_pcdpit is the natural logarithm of the average real per capita disposable income in time period t; [8]
trendt is an artificially created variable equalling 1 for the first observation, followed by ut is the random error term;
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chronological increase;
β1, 2, .., 7 are the parameters to be estimated.
Results and analysis
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The Model Specification Issue
The number of statistically significant variables (given 5% significance level) in
double-log
regression model exceeded the same indicator in linear regression model and the values of adjusted R2 in both models were almost equal. Meantime, the parameter estimate associated with
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real price of brandy (i.e. rl_pbrandy) has a positive sign in linear regression model, which contradicts the “Law of Demand”, thus, the preference should be given to double-log regression
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model.
The Multicollinearity Issue In the regression of ln_pcbrandyq on lnrl_pbrandy, lnrl_pwine, lnrl_pbeer, lnrl_pvodka, lnrl_pchampaign, ln_rl_pcdpi, trend we find overall R2 = 0.5945 is comparatively high, but all partial
correlations
among
regressors,
i.e.
r21,2
=
-0.09,
r21,3
=
0.25,
r21,4 = 0.31, r21,5 = 0.25, r21,6 = -0.33, r21,7 = -0.26, r21,8 = 0.12, r21,9 = 0.04, r21,10 = 0.09, r21,11 = 0.17 are comparatively low, in absolute value, thus, we suspect that there is a multicollinearity issue in the data (Table 1) [9].
ACCEPTED MANUSCRIPT Table 1. Partial Correlation among regressors Correlation
Significance
Lnrl_pbrandy
-0.09
0.47
Lnrl_pwine
0.25
0.04
Lnrl_pvodka
0.31
Lnrl_pchampagne
0.25
Lnrl_pbeer
-0.33
Lnrl_pcdpi
-0.26
Trend
0.12
q4
0.04
0.01 0.04
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q3
0.04
0.01
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q2
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Variable
0.33
0.77
0.09
0.46
0.17
0.16
Since the Variance Inflation Factor (VIF) of all regressors, besides ln of the average real quarterly price of vodka and seasonal dummy variables (i.e. q2, q3, q4) exceeded 10 and
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Tolerance Level (TOL) of most of regressors is very close to 0, therefore, we conclude that there is a multicollinearity issue in the data (Kleinbaum, Lawrence, Kupper, Muller, 1988) [9]. Since the R2 values of 0.9938, 0.9918, 0.9683, 0.9494, 0.9431, 0.9431 obtained from auxiliary regressions are greater than the overall R2 of 0.5945, thus, according to Klien’s rule of thumb,
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we suspect that there is multicollinearity issue in the data (Table 2) [10]. Since the condition number of 731.1977 is between 100 and 1000, we conclude that there is moderate to strong multicollinearity. Meantime, the conditional index (CI) = √731.1977 = 27.04
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is between 10 and 30, therefore, we conclude that there is moderate to strong multicollinearity in the data (Table 2) [9].
As correlation coefficients between lnrl_pwine and lnrl_pbrandy of 0.94, lnrl_pwine and lnrl_pchampagne of 0.93, lnrl_pbrandy and lnrl_pvodka of 0.92, ln_rl_pwine and lnrl_pbeer of 0.91, lnrl_pwine and lnrl_pcdpi of 0.93, lnrl_pbeer and lnrl_pchampagne of 0.92, lnrl_pbeer and lnrl_pcdpi of 0.91, lnrl_pcdpi and trend of 0.99 are greater than 0.9, thus, we suspect that there is severe multicollinearity in the data (Table 3) [9]. The average real prices of beer and brandy have comparatively high correlation coefficient of 0.90. In addition, initial estimation results indicated that the parameter estimate associated with the independent variable of the average real price of beer was negative, indicating that beer and
ACCEPTED MANUSCRIPT brandy were complements. Nevertheless, in theory beer and brandy are substitutes. Therefore, in order to remedy the issues of multicollinearity and the wrong sign of the parameter estimate, the average real price of beer was dropped from the final estimation. Table 2. Multicollinearity diagnostics
1 2 3 4
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5 6 7
11
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10
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8 9
17.58 4.19 31.51 5.61 7.97 2.82 19.76 4.45 17.57 4.19 160.77 12.68 1.53 1.24 1.56 1.25 1.78 1.34 122.62 11.07 Eigenvalue 8.5724
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ln of the average real price of brandy ln of the average real price of wine ln of the average real price of vodka ln of the average real price of beer ln of the average real price of champagne ln of the average real per capita monetary income Seasonal dummy variable for 2-nd quarter Seasonal dummy variable for 3-rd quarter Seasonal dummy variable for 4-th quarter Trend
SQRT VIF
Condition number
Tolerance
R-squared
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VIF
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Position
0.0569 0.9431 0.0317 0.9683 0.1255 0.8745 0.0506 0.9494 0.0569 0.9431 0.0062 0.9938 0.6528 0.3472 0.6416 0.3584 0.5608 0.4392 0.0082 0.9918 Conditional Index 1.0000
1.0003
2.9274
1.0000
2.9279
0.2441
5.9264
0.1812
6.8790
0.0013
80.8526
0.0005
131.0056
0.0001
243.1614
0.0001
257.6150
0.0000
677.5232
0.0000
731.1977
731.1977
The Serial Autocorrelation Issue Observing “Residuals vs. Year” plot, we see that residuals are changing their signs from negative to positive, while tend to have the same sign from one period to the next (i.e. ut-1 is positive and ut tends to be positive; or ut-1 is negative and ut tends to be negative), thus, there is an evidence of positive serial autocorrelation among residuals (Fig. 2) [11].
1995
2000
2005 year
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-.4
-.2
Residuals 0 .2
.4
.6
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2010
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Fig. 2. Residuals vs. Year
2015
0.94
1.00
0.92
0.85
1.00
0.90
0.93
0.81
1.00
0.90
0.91
0.82
0.92
1.00
0.93
0.76
0.84
0.91
1.00
0.84
0.89
0.72
0.80
0.90
0.99
1.00
-0.01
0.01
0.00
0.03
0.01
-0.02
-0.01
1.00
0.00
0.01
0.00
0.01
0.01
0.01
0.01
-0.33
1.00
0.00
0.01
-0.01
-0.02
-0.01
0.07
0.04
-0.33
-0.33
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0.87
Trend
Seasonal dummy variable for 4-th quarter
Seasonal dummy variable for 3-rd quarter
ln of the average real price of champagne
Seasonal dummy variable for 2-nd quarter
ln of the average real per capita monetary income
ln of the average real price of beer
ln of the average real price of vodka
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1.00
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ln of the average real price of brandy ln of the average real price of wine ln of the average real price of vodka ln of the average real price of champagne ln of the average real price of beer ln of the average real per capita disposable income Trend Seasonal dummy variable for 2-nd quarter Seasonal dummy variable for 3-rd quarter Seasonal dummy variable for 4-th quarter
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Position
ln of the average real price of wine
ln of the average real price of brandy
Table 3. Pair-wise correlation coefficients of independent variables
1.00
ACCEPTED MANUSCRIPT From “Standardized Residuals vs. Year” plot we see that residuals are changing their signs from negative to positive, while tend to have the same sign from one period to the next, consequently
2000
2005 year
2010
2015
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1995
SC
-2
-1
Standardized residuals 0 1
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2
there is an evidence of positive serial autocorrelation among residuals [Fig. 3] [9].
Fig. 3. Standardized Residuals vs. Year From “Residuals vs. Residuals lagged one year” plot we see that most of the residuals are bunched in the 2nd
(northeast)
and 4th
quarters suggesting a strong positive autocorrelation
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-.4
-.2
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Residuals 0 .2
.4
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.6
among residuals (Fig. 4) [9].
(southwest)
-.5
0 Lresid_m4
.5
Fig. 4. Residuals vs. Residuals lagged one year
H0: No positive autocorrelation
H1: No negative autocorrelation The calculated Durbin-Watson d-statistic for n=76 and k’=11 (number of explanatory variables) equals 0.4780797, while lower (dL) and upper (dU) critical d-statistics (approximated with the closest number of n=75 observations, k’=11 given in Durbin-Watson table) equal 1.308 and 1.970 respectively (12). Since the estimated d-statistic of 0.4780797 lies in between 0 and dL,
ACCEPTED MANUSCRIPT thus, we reject the null hypothesis and conclude that the error terms are positively autocorrelated, given 95% confidence level [9]. The Heteroscedasticity Issue There are 4 outliers present in relation to the observations in the sample, thus, we expect the
-4.5
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0
.1
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resid_sq .2
.3
.4
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error variance in double-log regression model to be heteroscedastic (Fig. 5) [9].
-4
-3.5 Linear prediction
-3
-2.5
Fig. 5. Squared Residuals vs Estimated LNPCBRANDYQ Glejser Test for Heteroscedasticity
Abs_resid^t = -0.0852298 - 0.0852298·ln_pcbrandyq^t (0.1995825) (0.0567069)
t=
(-0.33)
p=
(0.741)
R2 = 0.0296
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se =
(-1.50)
(0.137)
Adjusted R2= 0.0165
df = 76-2 = 74
F1, 74, 0.05 = 2.26
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H0: There is homoscedasticity in the data
H1: There is heteroscedasticity in the data
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Since the p-value associated with ln_pcbrandyq^t of 0.137 is greater than α=0.05 level of significance, therefore, we conclude that there is a statistically insignificant relationship between the resid_sq^t and ln_pcbrandyq^t variables at the 5% significance level. Thus, according to
Glejser test, if β2 is statistically insignificant, we fail to reject H0 (there is homoscedasticity in the data), and conclude that there is no heteroscedasticity in the error variance [9].
Newey-West Method to Remedy Heteroscedasticity and Autocorrelation Newey-West method overestimated the standard errors, thus, underestimated t-values in absolute value. Newey-West corrected ordinary least squares (OLS) standard errors in terms of
ACCEPTED MANUSCRIPT autocorrelation and heteroscedasticity, so we get heteroscedasticity and autocorrelation consistent (HAC) standard errors (Newey and West, 1987) (Table 4) [9].
Table 4. Estimation results
ln of the average real brandy price ln of the average real wine price ln of the average real vodka price ln of the average real champagne price ln of the average real per capita disposable income
-0.269
NeweyWest Std. Error 0.443
0.794
0.322
2.47
0.016
0.152
1.437
0.530
0.292
1.82
0.074
-0.052
1.112
0.030
0.625
0.05
0.962
-1.216
1.276
-0.436
0.624
-0.7
0.487
-1.682
0.809
Trend
-0.015
0.020
-0.73
0.467
-0.055
0.026
Constant
-4.876
6.139
-0.79
0.43
-17.124
7.372
R2 F-test Prob>F
0.5352 10.24 0.0000
P>|t|
95% Confidence Interval
-0.61
0.547
-1.153
0.616
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t
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Coefficient
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Position
The own-price elasticity (OPE) = -0.269, which means that for every 1% increase in the real price of brandy, the quarterly per capita consumption of brandy decreases by 0.269%, everything else held constant. The estimated own-price elasticity of less than 1 in absolute value indicates
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that brandy faced an inelastic demand.
The cross price elasticity of wine (CPEw) = 0.794, which means that for every 1% increase in the
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real price of wine, the quarterly per capita consumption of brandy increases by 0.794%, everything else held constant. Since the p-value associated with the parameter estimate of ln of average real price of wine equals 0.016 and is less than α=0.05 level of significance, thus, we
reject the null hypothesis (i.e. H0: β2=0) and conclude that the parameter estimate of lnrl_pwine is statistically significant, given 5% significance level. The cross price elasticity of vodka (CPEv) = 0.530, which means that for every 1% increase in the real price of vodka, the quarterly per capita consumption of brandy increases by 0.530%, everything else held constant.
ACCEPTED MANUSCRIPT The cross price elasticity of champagne (CPEc) = 0.030, which means that for every 1% increase in the real price of champagne, the quarterly per capita consumption of brandy increases by 0.030%, everything else held constant. The income elasticity (IE) = -0.436, which means that for every 1% increase in the quarterly real per capita disposable income, the quarterly per capita consumption of brandy decreases by
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0.436%, everything else held constant. According to theory, brandy is a normal good, but since income elasticity of -0.436 is less than 0, implies that brandy is an inferior good. Since the pvalue associated with the parameter estimate of ln of average real price of vodka equals 0.074 and is less than α=0.08 level of significance, thus, we reject the null hypothesis (i.e. H0: β3=0)
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and conclude that the parameter estimate of lnrl_pvodka is statistically significant, given 8% significance level.
The parameter estimate associated with Trend variable was -0.015, implying that for quarterly
quarter.
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periods from 1997 through 2015 the per capita brandy consumption rate decreased 1.5% per
The parameter estimates associated with the independent variables of lnrl_pwine, lnrl_pvodka, lnrl_pchampagne are greater than 0, consequently wine, vodka and champagne are substitute products for brandy, as hypothesized. H0: β1 = β2 = …= β6 = 0
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H1: at least one β ≠ 0
Since the p-value of estimated F6, 69, 0.05 = 0.0000 and is less than α=0.05 level of significance, thus, we reject the null hypothesis (i.e. H0: β1 = β2 = …= β6 = 0), and conclude that all independent variables are jointly statistically significant, given 5% significance level.
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R-squared = 0.5352, which means that 53.52% of the total variation in log of quarterly per capita consumption of brandy (i.e. ln_pcbrandyq) is explained by the total variation in log of quarterly real prices of brandy, wine, champagne, vodka, per capita disposable income and trend.
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According to Frisch-Waugh theorem, the inclusion of dummy variables in the regression model not only removes the seasonality in our dependent variable (i.e. per capita consumption of brandy), but also removes the seasonality, if any, in our quantitative independent variables, therefore, seasonality was tested using joint F-test of seasonal dummy variables and there was no evidence of statistically significant seasonality in the dataset [9].
Conclusion and recommendations This paper aims at identifying the average per capita brandy demand in Armenia. Therefore, the linear
and
double-log
regression
models
were
estimated
based
on
quarterly
ACCEPTED MANUSCRIPT time-series data. The estimation results revealed negative correlation between real price of brandy and average per capita consumption of brandy. Meantime, brandy faced an inelastic demand in the Republic of Armenia over the period 1997-2015. Consequently, in the short-run, the producers of Armenian brandy can increase the brandy price, trying to maximize their total revenue.
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The cross-price elasticities of brandy with respect to wine, vodka and champagne showed that these alcoholic beverages were substitutes for brandy. Most importantly, based on the absolute values of the parameter estimates associated with substitute alcoholic beverages, wine and vodka were relatively stronger competitors for brandy. Therefore, Armenian producers of brandy need
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comprehensive analysis of wine and vodka industries.
Negative income elasticity implied that brandy was an inferior good. The inclusion of artificially created trend variable into double-log regression model indicated that the per capita brandy in
the
Republic
of
Armenia
experienced
a
downward
trend.
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demand
The average real prices of wine and vodka were statistically significant determinants of the average per capita brandy demand.
The limitation of current study, was due to the fact that the differentiated data on consumption of domestically produced and imported brandy wasn’t available.
Future research shall concentrate on double log regression models for obtaining the system of
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equations for various types of alcoholic beverages, therefore revealing a more comprehensive overview of the brandy industry in Armenia.
References
pure
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[1] World Health Organization, Alcohol, recorded per capita (15+) consumption (in litres of alcohol),
from
2000
by
country,
multipurpose
table
in
Excel
format.
http://apps.who.int/gho/data/node.main.A1026?lang=en, 2016 (accessed 05.10.2016), (in
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English).
[2] National Statistical Service of the Republic of Armenia, Food consumed at home during 2008-2014, Excel tables. http://www.armstat.am/en/?nid=452,
2015
(accessed
01.10.2016),
(in
Armenian).
World Health Organization, Global alcohol report, Appendix I, Alcohol Consumption. http://www.who.int/substance_abuse/publications/global_alcohol_report/msb_gsr_2014_3.pd f, 2014 (accessed 06.10.2016), (in English).
[3] World Health Organization, Alcohol, recorded per capita (15+) consumption (in litres of pure alcohol), 1980-1999 by country, multipurpose table in Excel format.
ACCEPTED MANUSCRIPT http://apps.who.int/gho/data/node.main.A1024?lang=en, 2000 (accessed 05.10.2016), (in English). [4] Consumer price indexes (prices) in the Republic of Armenia, 2000-2015. National Statistical Service of the Republic of Armenia, Yerevan, 2001-2016 (in Armenian).
Republic of Armenia, Yerevan, 2011 (in Armenian).
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[5] Statistical Yearbook of Armenia - Prices and tariffs, National Statistical Service of the
[6] Socio-Economic Situation of RA, 1999-2015, National Statistical Service of the Republic of Armenia, Yerevan, 2000-2016 (in Armenian).
[7] Statistical Yearbook - Living Standards of Population and Social Sphere, 1997-2015,
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National Statistical Service of the Republic of Armenia, Yerevan, 2001 (in Armenian). [8] D.N. Gujarati, Basic Econometrics, fourth ed., Tata McGraw Hill, Berkshire, 2004,
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[9] C.F. Lee. Advances in Quantitative Analysis of Finance and Accounting, Volume 6, World Scientific Publishing Co. Ptc. Ltd., Singapore, 2008.
[10] Cengage Learning (EMEA) Ltd, Autocorrelation: A Problem with Time-Series Regressions.
http://www.cengage.com/resource_uploads/downloads/0030348064_54176.pdf,
2004
(accessed 02.10.2016), (in English).
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[11] Alma Mater Studiorum, Università di Bologna, Durbin-Watson Significance Tables. http://www.dm.unibo.it/~simoncin/Durbin_Watson_tables.pdf, 2016 (accessed 01.10.2016),
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(in English).
S1512-1887(17)30023-4
DOI:
10.1016/j.aasci.2016.09.016
Reference:
AASCI 90
To appear in:
Annals of Agrarian Sciences
Received Date: 9 November 2016 Accepted Date: 27 December 2016
Please cite this article as: S.A. Movsisyan, Empirical estimation per capita brandy demand in Armenia, Annals of Agrarian Sciences (2017), doi: 10.1016/j.aasci.2016.09.016. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Annals of Agrarian Science vol. 15, no.1, 2017
Empirical estimation per capita brandy demand in Armenia S. A. Movsisyan National Agrarian University of Armenia
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74 Teryan Str., Yerevan, 009, Republic of Armenia
Received: 09 November 2016; Accepted: 27 December 2016 Corresponding Corresponding author: Suren Movsisyan
SC
[email protected]
ABSTRACT
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The empirical estimations were based on linear and double-log regression models, which identified the factors influencing the average per capita brandy demand in Armenia. The model was estimated using quarterly time-series data on per capita brandy consumption, disposable income, prices of various alcoholic beverages for 1997-2015 periods. This is quantitative study based on secondary annual, quarterly and monthly data, and 5% significance level. The average annual per capita brandy consumption data for 1997-2007 periods was obtained from WHO’s website, whereas the 2008-2015 data was extracted from the National
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Statistical Service of the Republic of Armenia. For annual, quarterly and monthly periods from 1997 through 2015, the price data related to various alcoholic beverages, consumer price index were
provided
in
NSS
statistical
publications
of
“Socio-Economic Situation of RA”, ”Consumer price indexes (prices) in the Republic of
EP
Armenia”, “Prices and tariffs in the Republic of Armenia”. For 1997-2015 periods, the average monthly per capita monetary income data was obtained from “Living Standards of Population
AC C
and Social Sphere” section of statistical yearbooks. The latter substituted the average per capita monthly disposable income data, since these data were unavailable. Meantime, since the data included numerous years, therefore, the nominal price and income data were adjusted for inflation using consumer price index with 2005 as base year. In conclusion, the average real prices of wine and vodka were statistically significant determinants of the average per capita brandy demand in Armenia, and the demand for brandy was inelastic. Keywords:
Per
capita
brandy
demand,
double-log
regression
model,
seasonality,
cross price elasticity, income elasticity ----------------------------------------------------------------------------------------------------------------
ACCEPTED MANUSCRIPT Introduction he average per capita brandy production was characterised by an increasing trend over the observed period, while the average per capita brandy consumption increased until 2007 and drastically reduced during subsequent years. Over the period 2005-2015, the compound annual growth rates of the average per capita brandy consumption and production were -3% and 8%
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accordingly [Fig. 1].
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SC
6.71 7.0 6.21 6.11 6.5 5.64 6.0 5.17 5.5 5.07 5.0 4.56 4.15 4.5 4.0 3.22 3.5 2.90 2.79 3.0 2.23 2.24 2.5 2.0 1.5 1.0 0.5 0.18 0.21 0.23 0.22 0.22 0.08 0.08 0.07 0.07 0.08 0.07 0.06 0.12 0.0 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Per capita brandy consumption
Per capita brandy production
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Fig. 1. The average per capita brandy production and consumption in Armenia during 2003-2015 [1-3]
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Objectives and methods
First time in the Republic of Armenia, this study identifies the factors influencing the average per capita brandy demand over the period 1997-2015.
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Experimental section
The analysis have been conducted through STATA 10 statistical programming software and the
dataset encompassed annual, quarterly and monthly time series data ranging from 1997 through 2015.
The estimated linear brandy demand equation was as follows: Pcbrandyqt= β0 - β1·rl_pbrandyt + β2·rl_pwinet + β3·rl_pchampagnet + β4·rl_pbeert +
β5·rl_pvodkat + β6·rl_pcdpit + β7·trendt + ut
(Model 1)
Meantime, the following double-log brandy demand equation was estimated: ln_pcbrandyqt= β0 - β1·lnrl_pbrandyt + β2·lnrl_pwinet + β3·lnrl_pchampagnet + β4·lnrl_pbeert + β5·lnrl_pvodkat + β6·lnrl_pcdpit + β7·trendt + ut,
(Model 2)
ACCEPTED MANUSCRIPT where ln_pcbrandyqt is the natural logarithm of the average per capita brandy consumption in time period t; [1-4] lnrl_pbrandyt is the natural logarithm of the average real price of brandy in time period t; lnrl_pwinet is the natural logarithm of the average real price of wine in time period t; lnrl_pchampagnet is the natural logarithm of the average real price of champagne in time period
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t;
lnrl_pbeert is the natural logarithm of the average real price of beer in time period t;
lnrl_pvodkat is the natural logarithm of the average real price of vodka in time period t; [5-7]
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lnrl_pcdpit is the natural logarithm of the average real per capita disposable income in time period t; [8]
trendt is an artificially created variable equalling 1 for the first observation, followed by ut is the random error term;
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chronological increase;
β1, 2, .., 7 are the parameters to be estimated.
Results and analysis
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The Model Specification Issue
The number of statistically significant variables (given 5% significance level) in
double-log
regression model exceeded the same indicator in linear regression model and the values of adjusted R2 in both models were almost equal. Meantime, the parameter estimate associated with
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real price of brandy (i.e. rl_pbrandy) has a positive sign in linear regression model, which contradicts the “Law of Demand”, thus, the preference should be given to double-log regression
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model.
The Multicollinearity Issue In the regression of ln_pcbrandyq on lnrl_pbrandy, lnrl_pwine, lnrl_pbeer, lnrl_pvodka, lnrl_pchampaign, ln_rl_pcdpi, trend we find overall R2 = 0.5945 is comparatively high, but all partial
correlations
among
regressors,
i.e.
r21,2
=
-0.09,
r21,3
=
0.25,
r21,4 = 0.31, r21,5 = 0.25, r21,6 = -0.33, r21,7 = -0.26, r21,8 = 0.12, r21,9 = 0.04, r21,10 = 0.09, r21,11 = 0.17 are comparatively low, in absolute value, thus, we suspect that there is a multicollinearity issue in the data (Table 1) [9].
ACCEPTED MANUSCRIPT Table 1. Partial Correlation among regressors Correlation
Significance
Lnrl_pbrandy
-0.09
0.47
Lnrl_pwine
0.25
0.04
Lnrl_pvodka
0.31
Lnrl_pchampagne
0.25
Lnrl_pbeer
-0.33
Lnrl_pcdpi
-0.26
Trend
0.12
q4
0.04
0.01 0.04
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q3
0.04
0.01
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q2
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Variable
0.33
0.77
0.09
0.46
0.17
0.16
Since the Variance Inflation Factor (VIF) of all regressors, besides ln of the average real quarterly price of vodka and seasonal dummy variables (i.e. q2, q3, q4) exceeded 10 and
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Tolerance Level (TOL) of most of regressors is very close to 0, therefore, we conclude that there is a multicollinearity issue in the data (Kleinbaum, Lawrence, Kupper, Muller, 1988) [9]. Since the R2 values of 0.9938, 0.9918, 0.9683, 0.9494, 0.9431, 0.9431 obtained from auxiliary regressions are greater than the overall R2 of 0.5945, thus, according to Klien’s rule of thumb,
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we suspect that there is multicollinearity issue in the data (Table 2) [10]. Since the condition number of 731.1977 is between 100 and 1000, we conclude that there is moderate to strong multicollinearity. Meantime, the conditional index (CI) = √731.1977 = 27.04
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is between 10 and 30, therefore, we conclude that there is moderate to strong multicollinearity in the data (Table 2) [9].
As correlation coefficients between lnrl_pwine and lnrl_pbrandy of 0.94, lnrl_pwine and lnrl_pchampagne of 0.93, lnrl_pbrandy and lnrl_pvodka of 0.92, ln_rl_pwine and lnrl_pbeer of 0.91, lnrl_pwine and lnrl_pcdpi of 0.93, lnrl_pbeer and lnrl_pchampagne of 0.92, lnrl_pbeer and lnrl_pcdpi of 0.91, lnrl_pcdpi and trend of 0.99 are greater than 0.9, thus, we suspect that there is severe multicollinearity in the data (Table 3) [9]. The average real prices of beer and brandy have comparatively high correlation coefficient of 0.90. In addition, initial estimation results indicated that the parameter estimate associated with the independent variable of the average real price of beer was negative, indicating that beer and
ACCEPTED MANUSCRIPT brandy were complements. Nevertheless, in theory beer and brandy are substitutes. Therefore, in order to remedy the issues of multicollinearity and the wrong sign of the parameter estimate, the average real price of beer was dropped from the final estimation. Table 2. Multicollinearity diagnostics
1 2 3 4
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5 6 7
11
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10
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8 9
17.58 4.19 31.51 5.61 7.97 2.82 19.76 4.45 17.57 4.19 160.77 12.68 1.53 1.24 1.56 1.25 1.78 1.34 122.62 11.07 Eigenvalue 8.5724
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ln of the average real price of brandy ln of the average real price of wine ln of the average real price of vodka ln of the average real price of beer ln of the average real price of champagne ln of the average real per capita monetary income Seasonal dummy variable for 2-nd quarter Seasonal dummy variable for 3-rd quarter Seasonal dummy variable for 4-th quarter Trend
SQRT VIF
Condition number
Tolerance
R-squared
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VIF
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Position
0.0569 0.9431 0.0317 0.9683 0.1255 0.8745 0.0506 0.9494 0.0569 0.9431 0.0062 0.9938 0.6528 0.3472 0.6416 0.3584 0.5608 0.4392 0.0082 0.9918 Conditional Index 1.0000
1.0003
2.9274
1.0000
2.9279
0.2441
5.9264
0.1812
6.8790
0.0013
80.8526
0.0005
131.0056
0.0001
243.1614
0.0001
257.6150
0.0000
677.5232
0.0000
731.1977
731.1977
The Serial Autocorrelation Issue Observing “Residuals vs. Year” plot, we see that residuals are changing their signs from negative to positive, while tend to have the same sign from one period to the next (i.e. ut-1 is positive and ut tends to be positive; or ut-1 is negative and ut tends to be negative), thus, there is an evidence of positive serial autocorrelation among residuals (Fig. 2) [11].
1995
2000
2005 year
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-.4
-.2
Residuals 0 .2
.4
.6
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2010
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Fig. 2. Residuals vs. Year
2015
0.94
1.00
0.92
0.85
1.00
0.90
0.93
0.81
1.00
0.90
0.91
0.82
0.92
1.00
0.93
0.76
0.84
0.91
1.00
0.84
0.89
0.72
0.80
0.90
0.99
1.00
-0.01
0.01
0.00
0.03
0.01
-0.02
-0.01
1.00
0.00
0.01
0.00
0.01
0.01
0.01
0.01
-0.33
1.00
0.00
0.01
-0.01
-0.02
-0.01
0.07
0.04
-0.33
-0.33
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0.87
Trend
Seasonal dummy variable for 4-th quarter
Seasonal dummy variable for 3-rd quarter
ln of the average real price of champagne
Seasonal dummy variable for 2-nd quarter
ln of the average real per capita monetary income
ln of the average real price of beer
ln of the average real price of vodka
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1.00
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ln of the average real price of brandy ln of the average real price of wine ln of the average real price of vodka ln of the average real price of champagne ln of the average real price of beer ln of the average real per capita disposable income Trend Seasonal dummy variable for 2-nd quarter Seasonal dummy variable for 3-rd quarter Seasonal dummy variable for 4-th quarter
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Position
ln of the average real price of wine
ln of the average real price of brandy
Table 3. Pair-wise correlation coefficients of independent variables
1.00
ACCEPTED MANUSCRIPT From “Standardized Residuals vs. Year” plot we see that residuals are changing their signs from negative to positive, while tend to have the same sign from one period to the next, consequently
2000
2005 year
2010
2015
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1995
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-2
-1
Standardized residuals 0 1
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2
there is an evidence of positive serial autocorrelation among residuals [Fig. 3] [9].
Fig. 3. Standardized Residuals vs. Year From “Residuals vs. Residuals lagged one year” plot we see that most of the residuals are bunched in the 2nd
(northeast)
and 4th
quarters suggesting a strong positive autocorrelation
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-.4
-.2
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Residuals 0 .2
.4
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.6
among residuals (Fig. 4) [9].
(southwest)
-.5
0 Lresid_m4
.5
Fig. 4. Residuals vs. Residuals lagged one year
H0: No positive autocorrelation
H1: No negative autocorrelation The calculated Durbin-Watson d-statistic for n=76 and k’=11 (number of explanatory variables) equals 0.4780797, while lower (dL) and upper (dU) critical d-statistics (approximated with the closest number of n=75 observations, k’=11 given in Durbin-Watson table) equal 1.308 and 1.970 respectively (12). Since the estimated d-statistic of 0.4780797 lies in between 0 and dL,
ACCEPTED MANUSCRIPT thus, we reject the null hypothesis and conclude that the error terms are positively autocorrelated, given 95% confidence level [9]. The Heteroscedasticity Issue There are 4 outliers present in relation to the observations in the sample, thus, we expect the
-4.5
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0
.1
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resid_sq .2
.3
.4
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error variance in double-log regression model to be heteroscedastic (Fig. 5) [9].
-4
-3.5 Linear prediction
-3
-2.5
Fig. 5. Squared Residuals vs Estimated LNPCBRANDYQ Glejser Test for Heteroscedasticity
Abs_resid^t = -0.0852298 - 0.0852298·ln_pcbrandyq^t (0.1995825) (0.0567069)
t=
(-0.33)
p=
(0.741)
R2 = 0.0296
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se =
(-1.50)
(0.137)
Adjusted R2= 0.0165
df = 76-2 = 74
F1, 74, 0.05 = 2.26
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H0: There is homoscedasticity in the data
H1: There is heteroscedasticity in the data
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Since the p-value associated with ln_pcbrandyq^t of 0.137 is greater than α=0.05 level of significance, therefore, we conclude that there is a statistically insignificant relationship between the resid_sq^t and ln_pcbrandyq^t variables at the 5% significance level. Thus, according to
Glejser test, if β2 is statistically insignificant, we fail to reject H0 (there is homoscedasticity in the data), and conclude that there is no heteroscedasticity in the error variance [9].
Newey-West Method to Remedy Heteroscedasticity and Autocorrelation Newey-West method overestimated the standard errors, thus, underestimated t-values in absolute value. Newey-West corrected ordinary least squares (OLS) standard errors in terms of
ACCEPTED MANUSCRIPT autocorrelation and heteroscedasticity, so we get heteroscedasticity and autocorrelation consistent (HAC) standard errors (Newey and West, 1987) (Table 4) [9].
Table 4. Estimation results
ln of the average real brandy price ln of the average real wine price ln of the average real vodka price ln of the average real champagne price ln of the average real per capita disposable income
-0.269
NeweyWest Std. Error 0.443
0.794
0.322
2.47
0.016
0.152
1.437
0.530
0.292
1.82
0.074
-0.052
1.112
0.030
0.625
0.05
0.962
-1.216
1.276
-0.436
0.624
-0.7
0.487
-1.682
0.809
Trend
-0.015
0.020
-0.73
0.467
-0.055
0.026
Constant
-4.876
6.139
-0.79
0.43
-17.124
7.372
R2 F-test Prob>F
0.5352 10.24 0.0000
P>|t|
95% Confidence Interval
-0.61
0.547
-1.153
0.616
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t
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Coefficient
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Position
The own-price elasticity (OPE) = -0.269, which means that for every 1% increase in the real price of brandy, the quarterly per capita consumption of brandy decreases by 0.269%, everything else held constant. The estimated own-price elasticity of less than 1 in absolute value indicates
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that brandy faced an inelastic demand.
The cross price elasticity of wine (CPEw) = 0.794, which means that for every 1% increase in the
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real price of wine, the quarterly per capita consumption of brandy increases by 0.794%, everything else held constant. Since the p-value associated with the parameter estimate of ln of average real price of wine equals 0.016 and is less than α=0.05 level of significance, thus, we
reject the null hypothesis (i.e. H0: β2=0) and conclude that the parameter estimate of lnrl_pwine is statistically significant, given 5% significance level. The cross price elasticity of vodka (CPEv) = 0.530, which means that for every 1% increase in the real price of vodka, the quarterly per capita consumption of brandy increases by 0.530%, everything else held constant.
ACCEPTED MANUSCRIPT The cross price elasticity of champagne (CPEc) = 0.030, which means that for every 1% increase in the real price of champagne, the quarterly per capita consumption of brandy increases by 0.030%, everything else held constant. The income elasticity (IE) = -0.436, which means that for every 1% increase in the quarterly real per capita disposable income, the quarterly per capita consumption of brandy decreases by
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0.436%, everything else held constant. According to theory, brandy is a normal good, but since income elasticity of -0.436 is less than 0, implies that brandy is an inferior good. Since the pvalue associated with the parameter estimate of ln of average real price of vodka equals 0.074 and is less than α=0.08 level of significance, thus, we reject the null hypothesis (i.e. H0: β3=0)
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and conclude that the parameter estimate of lnrl_pvodka is statistically significant, given 8% significance level.
The parameter estimate associated with Trend variable was -0.015, implying that for quarterly
quarter.
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periods from 1997 through 2015 the per capita brandy consumption rate decreased 1.5% per
The parameter estimates associated with the independent variables of lnrl_pwine, lnrl_pvodka, lnrl_pchampagne are greater than 0, consequently wine, vodka and champagne are substitute products for brandy, as hypothesized. H0: β1 = β2 = …= β6 = 0
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H1: at least one β ≠ 0
Since the p-value of estimated F6, 69, 0.05 = 0.0000 and is less than α=0.05 level of significance, thus, we reject the null hypothesis (i.e. H0: β1 = β2 = …= β6 = 0), and conclude that all independent variables are jointly statistically significant, given 5% significance level.
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R-squared = 0.5352, which means that 53.52% of the total variation in log of quarterly per capita consumption of brandy (i.e. ln_pcbrandyq) is explained by the total variation in log of quarterly real prices of brandy, wine, champagne, vodka, per capita disposable income and trend.
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According to Frisch-Waugh theorem, the inclusion of dummy variables in the regression model not only removes the seasonality in our dependent variable (i.e. per capita consumption of brandy), but also removes the seasonality, if any, in our quantitative independent variables, therefore, seasonality was tested using joint F-test of seasonal dummy variables and there was no evidence of statistically significant seasonality in the dataset [9].
Conclusion and recommendations This paper aims at identifying the average per capita brandy demand in Armenia. Therefore, the linear
and
double-log
regression
models
were
estimated
based
on
quarterly
ACCEPTED MANUSCRIPT time-series data. The estimation results revealed negative correlation between real price of brandy and average per capita consumption of brandy. Meantime, brandy faced an inelastic demand in the Republic of Armenia over the period 1997-2015. Consequently, in the short-run, the producers of Armenian brandy can increase the brandy price, trying to maximize their total revenue.
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The cross-price elasticities of brandy with respect to wine, vodka and champagne showed that these alcoholic beverages were substitutes for brandy. Most importantly, based on the absolute values of the parameter estimates associated with substitute alcoholic beverages, wine and vodka were relatively stronger competitors for brandy. Therefore, Armenian producers of brandy need
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comprehensive analysis of wine and vodka industries.
Negative income elasticity implied that brandy was an inferior good. The inclusion of artificially created trend variable into double-log regression model indicated that the per capita brandy in
the
Republic
of
Armenia
experienced
a
downward
trend.
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demand
The average real prices of wine and vodka were statistically significant determinants of the average per capita brandy demand.
The limitation of current study, was due to the fact that the differentiated data on consumption of domestically produced and imported brandy wasn’t available.
Future research shall concentrate on double log regression models for obtaining the system of
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equations for various types of alcoholic beverages, therefore revealing a more comprehensive overview of the brandy industry in Armenia.
References
pure
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[1] World Health Organization, Alcohol, recorded per capita (15+) consumption (in litres of alcohol),
from
2000
by
country,
multipurpose
table
in
Excel
format.
http://apps.who.int/gho/data/node.main.A1026?lang=en, 2016 (accessed 05.10.2016), (in
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English).
[2] National Statistical Service of the Republic of Armenia, Food consumed at home during 2008-2014, Excel tables. http://www.armstat.am/en/?nid=452,
2015
(accessed
01.10.2016),
(in
Armenian).
World Health Organization, Global alcohol report, Appendix I, Alcohol Consumption. http://www.who.int/substance_abuse/publications/global_alcohol_report/msb_gsr_2014_3.pd f, 2014 (accessed 06.10.2016), (in English).
[3] World Health Organization, Alcohol, recorded per capita (15+) consumption (in litres of pure alcohol), 1980-1999 by country, multipurpose table in Excel format.
ACCEPTED MANUSCRIPT http://apps.who.int/gho/data/node.main.A1024?lang=en, 2000 (accessed 05.10.2016), (in English). [4] Consumer price indexes (prices) in the Republic of Armenia, 2000-2015. National Statistical Service of the Republic of Armenia, Yerevan, 2001-2016 (in Armenian).
Republic of Armenia, Yerevan, 2011 (in Armenian).
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[5] Statistical Yearbook of Armenia - Prices and tariffs, National Statistical Service of the
[6] Socio-Economic Situation of RA, 1999-2015, National Statistical Service of the Republic of Armenia, Yerevan, 2000-2016 (in Armenian).
[7] Statistical Yearbook - Living Standards of Population and Social Sphere, 1997-2015,
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National Statistical Service of the Republic of Armenia, Yerevan, 2001 (in Armenian). [8] D.N. Gujarati, Basic Econometrics, fourth ed., Tata McGraw Hill, Berkshire, 2004,
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[9] C.F. Lee. Advances in Quantitative Analysis of Finance and Accounting, Volume 6, World Scientific Publishing Co. Ptc. Ltd., Singapore, 2008.
[10] Cengage Learning (EMEA) Ltd, Autocorrelation: A Problem with Time-Series Regressions.
http://www.cengage.com/resource_uploads/downloads/0030348064_54176.pdf,
2004
(accessed 02.10.2016), (in English).
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[11] Alma Mater Studiorum, Università di Bologna, Durbin-Watson Significance Tables. http://www.dm.unibo.it/~simoncin/Durbin_Watson_tables.pdf, 2016 (accessed 01.10.2016),
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(in English).