Multiple imputation techniques, multinomial logistic regression for a categorical variable. (StataCorp, 2013a) and predictive mean matching for a continues ...
Appendix Computing alcohol price, purchasing and consumption Questions about purchasing of alcohol were asked using detailed loops in the International Alcohol Control Survey: respondents were asked how often they consume and purchase alcohol from a range of types of on- and off-premise venues, what they usually purchase at each venue type, and how much they consume. So if a respondent stated that he or she went to a ‘liquor barn’ (a warehouse-style off-premise store) once a month; they were then asked what alcohol beverage types they would purchase on a usual visit and how much of each type they would purchase. Separately, the survey then asked how much this purchase cost, either per unit of choice or in total, while they were asked where they would usually consume each beverage type (e.g. at home, someone’s home or restaurant) and how much they consumed. Respondents could give their responses in the units of their choice – for example, they could refer to a six-pack of regular strength beers; the number of ASD equivalent to the response was calculated by researchers after the interview. Information on the amount and cost of alcohol purchased allowed calculation of a unit price per standard drink across different beverage and outlet types. Implausible prices per standard drink were investigated – in 0.8% of cases it was decided that the respondent meant to state that they were giving the price in total, rather than per unit, or vice-versa. For instance if a respondent stated that they bought 24 cans of beer and paid $50 per beer (a common price for 24 beers) it was assumed that this price was meant to be given for the total amount. A further 0.1% of price based responses were deemed implausible and recoded as missing. No dollar figures were amended as part of this cleaning process. The survey questionnaire, methodology and sample design are reported in detail in the Australian IAC technical report (Jiang et al., 2014).
Marginal effects In a Tobit analysis approach, there are three marginal effects on the latent dependent variable for a change in price (Cong, 2000), namely: 1) the marginal effect on the latent dependent variable is
𝜕𝐸[𝑄𝑖∗ ] 𝜕𝑃𝑘
= 𝛼𝑘 ;
2) the marginal effect on the unconditional dependent variable is
𝜕𝐸[𝑄𝑖 ] 𝜕𝑃𝑘
𝑃𝑖 𝛼 ); and 𝜎 𝜕𝐸[𝑄𝑖 |𝑄𝑖 >0] 𝑃𝛼 = 𝛼𝑘 {1 − λ(a) [ 𝜎𝑖 𝜕𝑃𝑘
= 𝛼𝑘 (Φ
3) the marginal effect on the uncensored conditional dependent variable is
+ λ(a)] 𝑃}.
For policy purposes we believe the unconditional elasticity is more relevant (Collis et al., 2010). The elasticities of unconditional model is given by 𝜀𝑄𝑖, 𝜕𝐸[𝑄𝑖 ] 𝑃𝑘 ( ) 𝜕𝑃𝑘 𝐸[𝑄𝑖 ]
and the analysis assesses the factors affecting the actual amount of alcohol consumed by all observed individuals.
1
𝑃𝑘
=
Variables in the estimation There are eleven Tobit regression models in the paper, based on different alcoholic beverages at on- and off-premises sectors. The list of variables in regression models are listed in Table A.1. A consumer’s gender, age, household income, education levels, marital status and number of people in their household over the legal drinking age may affect drinking preferences, quantity demand and affordability for alcohol products (Morrison et al., 2015; Treno et al., 2006). Impacts of regional variations were considered in models by including state and rurality variables. Furthermore, whether a respondent consumes a particular type of alcohol beverage was developed as instrumental/dummy variables in our models. The dummy variables for consumed or not on different types of alcohol allows us to capture respondents’ personal preferences and their drinking culture (Soursa, 2014). For example, drinking regular beer in the off-premises is likely to be strongly linked with drinking regular beer in the on-premises venues; drinking off-spirits might be associated with drinking off-Ready to Drinks as well. Table A.1 List of variables in Tobit regression models Dependent variables Quantity demand for on-regular beer Quantity demand for on-low- and midstrength beer Quantity demand for on-bottle wine Quantity demand for on-spirits Quantity demand for on-Ready to Drinks (RTDs) Quantity demand for off-regular beer Quantity demand for off-low- and midstrength beer Quantity demand for off-bottle wine Quantity demand for off-cask wine Quantity demand for off-spirits Quantity demand for off-Ready to Drinks (RTDs)
Explanatory variables Control variables Price for on-regular beer Age Price for on-low- and mid-strength beer Gender Price for on-bottle wine Price for on-spirits Price for on-Ready to Drinks (RTDs)
Household income Education level States variations
Price for off-regular beer Remoteness Price for off-low- and mid-strength beer Number of household aged 18 and over Price for off-bottle wine Marital status Price for off-cask wine Price for off-spirits Price for off-Ready to Drinks (RTDs)
Instruments/dummy variables Drink on-regular beer or not Drink on-low- and mid-strength beer or not Drink on-bottle wine or not Drink on-spirits or not Drink on-RTDs or not Drink off-regular beer or not Drink off-low- and mid-strength beer or not Drink off-bottle wine or not Drink off-cask wine or not Drink off-spirits or not Drink off-RTDs or not
It is worth noting that an enhanced household income variable was used in the estimation instead of the raw household income variable, due to a large number of respondents not reporting their household income in the survey (raw household income n=1366, missing = 654). To solve this problem, we selected the closest equivalent personal income of those who did not report a household income but also lived alone in their house (n=356) and recoded it as their household income. The new household income (n=1722) variable is a more appropriate measure of income than personal income to use in the price elasticity analysis, as
2
some people have personal incomes significantly lower than their household income. Furthermore, we assumed that the total annual amount of alcohol purchased by the participants may not only be consumed by themselves, but also by their partner or other household members. Multiple imputation for missing data Missing data were found in two control variables (respondents who reported “refused/ can’t say” in the survey questionnaire were coded as missing), namely household income and number of household aged 18 and over. Multiple imputation techniques, multinomial logistic regression for a categorical variable (StataCorp, 2013a) and predictive mean matching for a continues variable (StataCorp, 2013b), were applied to impute the missing data based on non-missing variables, such as age, gender, education level and state. The imputed variables were then inserted in Tobit regression models for price elasticity estimation to provide unbiased estimates. The missing data and imputed data information are summarized in the following table. Table A.2 Multiple Imputation for missing data in the control variables Variables
Data type
Household income Number of households over 17yrs
Categorical Continues
Missing data Missing N Observed N 298 1,722 248 1,772
Min 1 1
Max 3 21
Imputed data Complete Imputed 1722 298 1772 248
Total 2020 2020
Tobit models regression outputs Table A.3 Regression outputs of unconditional Tobit regression model N=2020 P(on-regbeer) P(on-midbeer) P(on-botwine) P(on-spirits) P(on-RTDs) P(off-regbeer) P(off-midbeer) P(off-botwine) P(off-caskwine) P(off-spirits) P(off-RTDs)
Q(onregbeer) -239.55*** -19.82* -2.49 -7.19 -8.20 150.50*** -51.52 1.14 -49.33 -1.13 -12.48
Q(onmidbeer) -13.95 -134.20*** -3.37 3.53 -2.88 0.23 115.13*** -11.14 108.12 10.37 9.16
Q(onbotwine) 6.83 8.90 -49.09*** 2.89 19.48* 5.78 -26.24 14.42 69.02 -17.20 -6.31
Q(onspirits) -0.35 -13.08 -1.84 -54.50*** -2.59 23.95 -27.18 -0.55 -179.06 59.59*** 33.08*
Q(onRTDs) -2.33 0.38 -1.55 -13.77 -107.44*** 4.37 -86.51 -28.04 -193.67 2.93 35.87*
Q(offregbeer) 240.74*** 33.62 -27.24 -12.14 -74.7 -1972.19*** 929.39*** -48.43 180.27 81.30 62.47
Q(offmidbeer) 2.15 61.66*** 1.39 -24.26 -25.75 -462.45*** -891.23*** -41.30 111.74 54.54 25.45
Q(offbotwine) 49.57 8.62 120.39*** -2.52 17.50 -22.69 -7.21 -121.30*** -92.36 12.65 -116.82*
Q(offcaskwine) 5.70 -177.79 15.83 -20.78 -339.30 170.19 -591.59 -255.86 -2644.22*** 338.18 292.41
Q(offspirits) -3.30 -11.89 -33.00* 50.27*** 0.80 71.12 -129.53 11.63 208.95* -848.04*** 42.28
Q(offRTDs) -29.17 -149.73** -11.04 -7.54 52.02** -69.22 22.43 -27.58 -233.26 40.64 -491.49***
Income Age
-1.04 -0.37
2.30 6.10***
10.76** 2.84***
52.78* -7.88 ***
37.85 -5.58**
138.67* -14.28*
74.88 9.34**
148.36*** 17.61***
-858.64* 34.99
-111.07 -11.57
55.80 -5.88
3
Male (vs female) Education State
381.89*** -12.35
238.89** -20.39
-128.57*** 29.67*
-28.01 -1.18
8.30 -20.40
904.01*** -225.43**
244.99* -198.88***
-361.29*** 158.03***
-53.37 -165.58
-55.89 -89.93**
-80.59 -51.87
-147.35* -366.82*** -220.82 -270.22** -323.40 -372.18 -323.67
-44.77 -58.02 -117.44 -281.69** -297.90 614.35*** -627.34**
-21.13 -49.27 -4.26 -5.96 -65.93 142.31 -60.32
-51.10 35.99 -19.22 -108.32 -142.54 -101.72 70.45
-18.49 -27.10 -127.80 -61.74 -12.37 -1489.31 -29.28
84.46 -478.84 222.95 -60.67 335.73 -214.76 -773.76
-115.34 -86.33 -397.52** -139.58 -161.58 263.87 -393.24
-45.43 209.65 203.23 39.81 -461.02 506.61 265.47
1051.72 1195.71 1783.28 574.79 1225.33 -1627.08 2628.87
77.82 189.54 -163.85 15.39 38.53 -413.01 76.37
90.21 63.84 53.93 -65.84 -178.99 -268.11 412.50
174.47**
70.97
-57.39*
31.89
66.93
547.94**
208.17**
-228.50*
559.67
36.63
213.39*
7.29
-3.83
-9.47
5.12
8.95
88.35
22.44
-61.09
-298.67
-31.40
1.72
175.35**
74.09
-5.28
102.99*
80.15
-610.12**
-316.92*
-283.64**
881.14
35.16
-67.81
-101.83 113.66 43.08 -65.63
33.02 -17.55 22.83 299.74
4.33 -72.05 -64.95 -60.92
60.99 -86.42 -1.30 144.53
110.66 97.21 33.69 164.06 -
1979.46*** 350.79 466.54 -416.37 -1012.60
-240.11 723.67*** -25.10 -332.94 69.66
-51.38 -16.44 1642.57** 369.23 -188.00
721.04 -3142.60 519.23 -764.19 -2443.67
-108.28 -1.04 488.24 964.25*** 278.51
-9.80 -241.61 -16.13 251.02 1426.34**
Drink off-regbeer
515.4***
124.06
-8.56
64.23
-151.28*
-
681.21**
79.24
-386.96
116.41
20.11
Drink off-midbeer Drink off-botwine Drink off-caskwine Drink off-spirits Drink off-RTDs Constant Sigma Log-likelihood
-90.89 -81.36 202.12 85.96 -24.05 1362.2*** 716.12 1083.91
312.05*** -90.22 -213.02 -11.22 -220.74 1357.59*** 441.10 714.25
-9.47 289.02*** 86.37 26.40 -13.51 445.43*** 341.30 648.79
-182.33 23.62 -112.64 194.06*** 145.02 524.36** 410.04 845.13
-7.42 -7.62 -210.23 115.21 70.33 603.66*** 305.25 661.01
156.94 -379.22 304.53 -396.31 250.18 2632.52*** 2849.70 906.50
-126.15 -20.73 11.55 -193.76 1590.25** 950.23 839.92
-43.91 -598.35 240.11 -370.74 1545.67*** 1465.85 503.73
2621.40 233.69 4521.90* -765.69 9482.33** 3797.43 305.08
29.20 130.26 892.15 82.61 1155.13*** 1483.56 748.48
171.28 -144.36 301.42 68.59 976.09*** 763.39 551.67
New South Wales (ref) Victoria Queensland South Australia Western Australia Tasmania Northern Territory Australian Capital Territory Remote (vs Capital cities) Number of households aged 18 and over Married or de facto relationship (vs single, Divorced and widowed) Drink particular types of beverages Drink on-regbeer Drink on-midbeer Drink on-botwine Drink on-spirits Drink on-RTDs
Note: * p
