Metaanalysis of alcohol price and income elasticities – with corrections for publication bias
 Jon P Nelson^{1}Email author
DOI: 10.1186/21911991317
© Nelson; licensee Springer. 2013
Received: 2 May 2013
Accepted: 2 July 2013
Published: 24 July 2013
Abstract
Background
This paper contributes to the evidencebase on prices and alcohol use by presenting metaanalytic summaries of price and income elasticities for alcohol beverages. The analysis improves on previous metaanalyses by correcting for outliers and publication bias.
Methods
Adjusting for outliers is important to avoid assigning too much weight to studies with very small standard errors or large effect sizes. Trimmed samples are used for this purpose. Correcting for publication bias is important to avoid giving too much weight to studies that reflect selection by investigators or others involved with publication processes. Cumulative metaanalysis is proposed as a method to avoid or reduce publication bias, resulting in more robust estimates. The literature search obtained 182 primary studies for aggregate alcohol consumption, which exceeds the database used in previous reviews and metaanalyses.
Results
For individual beverages, corrected price elasticities are smaller (less elastic) by 2829 percent compared with consensus averages frequently used for alcohol beverages. The average price and income elasticities are: beer, 0.30 and 0.50; wine, 0.45 and 1.00; and spirits, 0.55 and 1.00. For total alcohol, the price elasticity is 0.50 and the income elasticity is 0.60.
Conclusions
These new results imply that attempts to reduce alcohol consumption through price or tax increases will be less effective or more costly than previously claimed.
Keywords
Alcohol demand Price elasticity Health production Publication bias MetaanalysisBackground
The objective of a metaanalytic review is quantitative synthesis of a body of literature. There are a number of obstacles that must be overcome for a synthesis to be successful. First, primary studies in economics usually employ a variety of data and statistical methods, which results in a dispersion of estimates due to methodological differences. For example, estimates from surveybased studies may be incompatible with traditional econometric studies using aggregate data. Second, factual heterogeneity may be present; it is not clear if sample estimates obtained with, say, older data sets are generated by the same population of consumers as more recent data series. Relatively simple metaanalytic methods are available for handling unobserved heterogeneity. Third, empirical estimates typically contain outliers that reflect sampling problems, estimation methods, or artifacts associated with data and methods. It is important to recognize that, in a metaanalysis, outliers can occur for both effectsizes (elasticity estimates) and standard errors of the estimates. Fourth, the sample of estimates may contain publication selection bias, reflecting choices about “acceptable” estimates made by primary researchers, journal referees, and editors.^{a} Selection often means that reported estimates are biased toward larger, but less precise, values. Publication bias represents a threat to internal and external validity of all literature reviews, both traditional narrative reviews and quantitative syntheses.
This paper presents metaanalytic summaries of price and income elasticities for alcohol beverages, which correct for outliers and publication bias. The analysis builds on several recent metaanalyses, but those studies failed to give sufficient attention to these problems; see Fogarty [1], Gallet [2], and Wagenaar et al. [3]. The methods employed here are relatively straightforward, but underutilized in the metaanalysis literature. First, for outliers, trimmed samples are employed, but trimming is along two dimensions: effectsizes and size of primary standard errors. Due to weighting methods used in metaanalysis, especially the fixedeffect model, it is important that weighting is subjected to a sensitivity analysis. This can be accomplished by trimming samples for standard error outliers and by comparing fixed and randomeffect estimates. A 10% trimmed sample is used for this purpose. Second, publication bias is addressed using cumulative metaanalysis. Borenstein [4] initially proposed using cumulative metaanalysis, with ordering by precision, as a method for reducing publication bias; see also [5, 6]. Briefly, primary data are ordered from high to low precision, and metaanalyses are run in a stepwise fashion using the first (most precise) estimate, then the first two estimates, and so on until the entire sample is fully analyzed. While other methods are available, advantages of this approach are that the analysis is transparent and focused on estimates with greater information value due to their greater precision. Less precise estimates are those that are more likely to be biased on selectivity grounds. This also is a form of sensitivity analysis since results from cumulative analyses can be compared to full sample estimates or summary estimates can be examined for shifts and drift as more studies are added to the analysis [4, 7].
Previous metaanalyses provide a variety of summary averages for alcohol price and income elasticities, but for the most part these studies ignore publication bias. Gallet [2] presents unweighted medians by beverage and unweighted metaregressions that focus on methodological dispersion. However, his metaregressions pool all estimates, so marginal effects for various covariates are uniform across beverages. Gallet includes individuallevel survey studies as well as aggregate studies in the analysis, but many survey studies report tax elasticities rather than price elasticities e.g., [8–10]. Price and tax elasticities are not comparable unless tax elasticities are transformed [[11], p. 72]. All tax elasticities are excluded here. Wagenaar et al. [3] report unweighted mean elasticities by beverage. Separate results are reported for aggregate and individuallevel studies, but their analysis uses standardized effect sizes that are not interpretable as elasticities. While they demonstrate that increased prices have a negative effect on alcohol consumption, this leaves uncertain the magnitude of effects. Wagenaar et al. adjust for outliers by excluding a few estimates, but they fail to address publication bias. Fogarty [1] is more complete in several respects. He reports unweighted means and medians by beverage and provides average demand elasticities by country. Weighted metaregressions are reported that focus on methodological differences among pooled primary estimates. However, prior to weighting, it is important to consider the influence of outliers. Fogarty [[1], p. 458] discusses publication bias, but concludes it is important for only beer price elasticities. Results reported below demonstrate a greater level of concern for this problem.
The present paper departs in several important ways compared to prior analyses of alcohol demand elasticities. First, the literature search uncovered a number of alcohol demand studies that were not included in prior analyses. Both published and unpublished studies are included. Inclusion/exclusion criteria for the search are designed to insure that primary studies are of comparable quality. Second, outliers are deleted using 10% trimmed samples, which is important if weighted means are to be used as summary statistics. Both fixed and randomeffect means are reported for full and trimmed samples. Third, publication bias is examined using funnel graphs and Egger’s intercept test, with standard errors corrected for clustering by country groups. Fourth, given the importance of publication bias in primary estimates, results from cumulative metaanalyses are used to correct summary statistics for this bias. Average price elasticities obtained in this paper are generally smaller (less elastic) compared to results in prior analyses and consensus averages. Several policy implications of this finding are discussed, including alcohol taxation and minimum pricing.
Methods
Database review
Summary of database review – 578 alcohol studies
Review step  Results of data extraction 

1.  Total alcoholrelated studies retrieved in search: 578 studies 
a. Excluded individuallevel studies and alcoholharms studies: 223 studies  
2.  Demand studies examined for inclusion in metaanalysis: 355 studies 
a. Excluded studies in Fogarty [4] or Gallet [5] or Wagenaar et al. [6]: 58. Reasons: taxation study–12; older data (pre1950)–9; std. errors missing–8; prices missing /income only–9 firm/brand/varietal/survey data–10;duplicate study–3; and linear model or other reason–7.  
b. Excluded aggregate studies in Wagenaar et al. [6]: 14. Reasons: taxation study–5; no. std. errors or no elasticities–5; and duplicate, older data or other–4.  
c. Excluded individuallevel studies in Wagenaar et al. [6]: 33  
3.  Remaining studies examined: 297 studies 
a. Additional excluded studies: 115. Reasons: taxation study–5; std.errors missing–7; prices missing/income only–27; duplicate study–5; firm/brand/varietal/survey data–28; no elasticities reported–2; and linear model or poor data22.  
4.  Total studies containing aggregate elasticities: 182 (any alcohol beverage or total alcohol) 
a. Included studies not reported in Fogarty [4] or Gallet [5]: 64  
b. Included studies not reported in Wagenaar et al. [6]: 135  
c. Type of publication for 182 studies: articles–127; chapters & books–17; reports–4; dissertations–8; working papers and reports–26  
5.  Total primary studies analyzed by beverage 
a. Comparable studies for beer elasticities: 112 (93 published, 19 unpublished)  
b. Comparable studies for wine elasticities: 104 (89 published, 15 unpublished)  
c. Comparable studies for distilled spirits elasticities: 111 (97 published, 14 unpublished)  
d. Comparable studies for total alcohol elasticities: 66 (55 published, 11 unpublished) 
Extraction of estimates
The present analysis is based on estimates obtained from 112 primary studies for beer elasticities, 104 studies for wine, 111 studies for distilled spirits, and 66 studies for total alcohol demand. Among the 182 studies, there are 64 studies that were not included in Fogarty [1] or Gallet [2], and 58 studies included in their analyses that are excluded here (reasons are detailed in Table 1). Compared to Wagenaar et al. [3], there are 47 studies excluded (mostly individuallevel survey studies) and 135 studies that were not included in their analysis. Data used in the present analysis reflect the following inclusion/exclusion criteria:

Aggregate studies are included that provide price and income elasticities for aggregate quantity consumed, and a reported standard error (tstatistic, pvalue, confidence interval) for the elasticity or for price and income coefficients. Household survey studies are included if they provide populationlevel elasticities and standard errors.

Aggregate studies are excluded that use alcohol taxes as proxies for prices. Aggregate studies and household surveys are excluded if prices are not included. Studies are excluded if based predominantly on older data (pre1950). Duplicates are excluded.

Individuallevel survey studies are excluded because alcohol consumption is selfreported, prices are imputed or taxes are used as price proxies, and “elasticities” cover a wide range of drinking behaviors (participation, prevalence, frequency, binging, etc.). These elasticities are not comparable to aggregate quantity elasticities.

Studies are excluded that use firmlevel data, brand data, and narrowlydefined beverage categories, such as vodka and wine varietals.

About 18% of included studies were found in the grey literature (working papers, reports, dissertations) compared to, say, only 3% in Wagenaar et al. [3].
Data from each study were collected and recorded by the author, including page or table numbers for primary estimates. No elasticity values were estimated, which is a reason for excluding most linear model estimates. Empirical studies in economics frequently report multiple estimates based on the same data or major portions of the same data set. Using all estimates creates intrastudy dependence or correlation, which will bias summary statistics. More weight is assigned to primary studies with multiple estimates than to studies with one or two estimates. Equally important, using multiple estimates will bias standard errors of summary statistics, with understatement of errors being the generally expected outcome [[7], p. 226]. There are several possible solutions to dependence problems, including intrastudy averages, hierarchical/multilevel models, and cluster robust standard errors [12]. Interstudy dependence also occurs when primary investigators use the same data to estimate different models in separate publications or different investigators use the same data or very similar data. Following Fogarty [[1], p. 437], collection of effect sizes was restricted to one or two estimates per primary study or model. In general, the primary author’s preferred result was selected from each study and an important variation was used to capture different model specifications or estimation methods. While this restriction reduces intrastudy dependence, it does not address interstudy dependence. In particular, several authors have published multiple studies using similar data sets, such as countrylevel models using annual time series. These authors also tend to use different econometric methods in each study, resulting in different “treatment effects.” Metaregressions reported below include cluster robust standard errors for seven different country groupings, which address potential data dependencies at this aggregate level. The extracted data are in Additional file 2.
Results
Results for summary averages
Average price and income elasticities for alcohol beverages
Study/sample (no. obs. price, income)  Price elasticity (se)  Income elasticity (se) 

Fogarty [1] – unwt. medians  
beer (154, 121)  −0.33  0.67 
wine (155, 123)  −0.55  1.00 
spirits (162, 123)  −0.76  1.24 
alcohol  na  na 
Gallet [2] – unwt. means  
beer (315, 278)  −0.36  0.39 
wine (300, 240)  −0.70  1.10 
spirits (294, 245)  −0.68  1.00 
alcohol (263, 250)  −0.50  0.50 
Wagenaar et al. [3] – unwt. means  
beer (105)  −0.46  na 
wine (93)  −0.69  na 
spirits (103)  −0.80  na 
alcohol (91)  −0.51  na 
Full samples – unwt. medians  
beer (191, 169)  −0.32  0.66 
wine (197, 172)  −0.57  1.06 
spirits (202, 179)  −0.67  1.24 
alcohol (117, 88)  −0.54  0.70 
Trimmed samples – FE means  
beer (172, 151)  −0.26 (.01)  0.49 (.01) 
wine (178, 155)  −0.34 (.01)  0.64 (.01) 
spirits (182, 160)  −0.49 (.01)  0.87 (.01) 
alcohol (105, 77)  −0.46 (.01)  0.48 (.01) 
Trimmed samples – RE means  
beer (172, 151)  −0.35 (.02)  0.58 (.03) 
wine (178, 155)  −0.58 (.03)  1.12 (.06) 
spirits (182, 160)  −0.64 (.03)  1.15 (.04) 
alcohol (105, 77)  −0.58 (.03)  0.66 (.04) 
Unweighted averages are similar for the several analyses, suggesting that prior analyses are not biased on sampling grounds. Average beer price elasticities range from 0.32 to 0.46, with the largest average reported in [3]; wine prices, 0.55 to 0.70, with the largest reported in [2]; spirits prices, 0.67 to 0.80, with the largest reported in [3]; and total alcohol prices, 0.50 to 0.54. For income, the ranges are beer, 0.39 to 0.67; wine, 1.00 to 1.10; spirits, 1.00 to 1.24; and total alcohol, 0.50 to 0.70. Combing results, “consensus” averages for price elasticities are approximately: beer price, 0.40; wine price, 0.65; spirits price, 0.75; and total alcohol price, 0.50. Unweighted averages for income elasticities are approximately: beer, 0.60; wine, 1.00; spirits, 1.20; and total alcohol, 0.60.
Results for weighted means indicate less elastic demands, especially FE means for prices. The FE and RE means for trimmedsamples are: beer price, 0.26 and 0.35; wine price, 0.34 and 0.58; spirits price, 0.49 and 0.64; and total alcohol price, 0.46 and 0.58. For income, FE and RE means are: beer, 0.49 and 0.58; wine, 0.64 and 1.12; spirits, 0.87 and 1.15; and total alcohol, 0.48 and 0.66. Hence, using the RE model increases price and income elasticities. The results illustrate the importance of different weighting schemes. Because randomeffects account for the secondlevel variance at study levels, it is the preferred approach when unobserved heterogeneity is known to be present. However, if publication bias is detected, the estimates need to be refined further. As pointed out by Borenstein et al. [[7], p. 378], “. . . if these studies are a biased sample of all possible studies, then the mean effect reported by a metaanalysis will reflect this bias”.
Results for publication bias
This section reports tests for publication bias using two techniques. First, funnel graphs are presented for price elasticities for beer, wine, and spirits. Graphs for total alcohol and income elasticities are omitted in the interest of space, but can be obtained by request. Second, results for Eggerintercept tests are reported using metaregressions. Funnel plots and metaregressions indicate moderate to severe publication bias for all samples and estimates, except for beer income elasticities.
where t _{ i } is the tstatistic for the ith observation, 1/Se _{ i } is its precision, and υ _{ i } is an error term corrected for heteroskedasticity. Estimating Equation (2) by OLS is equivalent to estimating Equation (1) by weighted leastsquares with inverse variance weights. In Equation (2), a test of H_{0}: β _{ 1 } = 0 is a test of absence of publication bias or the funnelasymmetry test (FAT). If FAT rejects symmetry, the estimate of β _{ 0 } is interpreted as the effect size corrected for bias, referred to as the precisioneffect test (PET); see [16].
Results for regression tests for publication bias
Alcohol beverage  Intercept (se)  Precision (se) 

Beer prices  
(n = 172, R^{2} = 0.238)  −1.425 (.217)*  −0.172 (.045)* 
Beer income  
(n = 151, R^{2} = 0.272)  1.266 (1.20)  0.405 (.183)* 
Wine prices  
(n = 178, R^{2} = 0.230)  −2.057 (.509)*  −0.228 (.037)* 
Wine income  
(n = 155, R^{2} = 0.176)  3.113 (.852)*  0.388 (.183)* 
Spirits prices  
(n = 182, R^{2} = 0.353)  −1.530 (.450)*  −0.388 (.083)* 
Spirits income  
(n = 160, R^{2} = 0.459)  2.299 (.640)*  0.657 (.141)* 
Total alcohol prices  
(n = 105, R^{2} = 0.284)  −1.830 (.917)*  −0.316 (.135)* 
Total alcohol income  
(n = 77, R^{2} = 0.419)  2.113 (.327)*  0.322 (.068)* 
Results for cumulative metaanalyses
Once there is evidence of bias, there are several possible ways it might be dealt with as a statistical problem [18, 23]. Although bias is probably present in most literatures, its extent can be modest [22, 24]. Correcting for bias helps ensure that resulting summary statistics are robust. Borenstein [[4], p. 198] proposed cumulative metaanalysis as a correction method:
For this purpose the studies would be sorted in the sequence from largest to smallest (or of most precise to least precise), and a cumulative metaanalysis preformed with the addition of each study. If the point estimate has stabilized with the inclusion of the larger studies and does not shift with the addition of smaller studies, then there is no reason to assume that the inclusion of smaller [or less precise] studies has injected a bias (i.e., since it is the smaller studies in which study selection is likely to be greatest).
Borenstein’s proposal leaves uncertain the meaning of “stabilized” or magnitude of a “shift,” which might vary by analyst. A fixed or prior standard for cumulative averages makes for a transparent correction, although any method used should also allow for a sensitivity analysis. The analysis here uses the 50th percentile as a cutoff (median cumulative average). For a sensitivity analysis, results also are reported for 25th and 75th percentiles. Reflecting a concern with heterogeneity among estimates, summary averages use randomeffects models. Hence, the cumulative weighted averages reported here are corrected for outliers, dependence, heterogeneity, and publication bias.
Cumulative metaanalysis for alcohol price and income elasticities
Study/sample  Price elasticity (se)  Income elasticity (se) 

Cumulative analysis: 50th percentile (no. obs. for price, income)  
beer (86, 76)  −0.29 (.02)  0.51 (.05) 
wine (89, 78)  −0.46 (.04)  0.99 (.08) 
spirits (91, 80)  −0.54 (.04)  1.00 (.06) 
alcohol (52, 38)  −0.49 (.05)  0.59 (.05) 
Additional results: 25th percentile (no. obs. for price, income)  
beer (43, 38)  −0.26 (.03)  0.51 (.07) 
wine (44, 39)  −0.43 (.05)  0.83 (.11) 
spirits (46, 40)  −0.52 (.06)  0.83 (.07) 
alcohol (26, 19)  −0.46 (.08)  0.54 (.06) 
Additional results: 75th percentile (no. obs. for price, income)  
beer (129, 113)  −0.33 (.02)  0.55 (.04) 
wine (134, 116)  −0.52 (.03)  1.09 (.07) 
spirits (136, 120)  −0.61 (.03)  1.14 (.05) 
alcohol (79, 58)  −0.51 (.04)  0.63 (.04) 
In summary, the beer price elasticity is estimated to be 0.29 (95% confidence interval 0.25 to 0.33); wine price, 0.46 (0.38 to 0.54); spirits price, 0.54 (0.46 to 0.62); and alcohol price, 0.49 (0.39 to 0.59). The beer income elasticity is 0.51 (95% confidence interval 0.41 to 0.61); wine income, 0.99 (0.83 to 1.15); spirits income, 1.00 (0.88 to 1.12); and alcohol income, 0.59 (0.49 to 0.69).
Have price and income elasticities changed over time?
Price and income elasticities vary across studies for many possible systematic reasons, including primary study methodology, country of origin, publication date, sample time period, and so forth. Fogarty [1] and Gallet [2] report metaregression results for numerous potential moderators, especially methodological covariates. However, in both cases, the metaregressions combine elasticities across beverages, leaving results at the beverage level uncertain. As demonstrated above, there are noticeable differences across beverages for price and income elasticities, especially for beer. One interesting relationship explored by Fogarty [1] is the possibility of a time trend in elasticity estimates. Using average dates from primary study data, he projects that alcohol beverages are modestly more price elastic after 1953 and less income elastic after 1965. Although precise explanations for these results are not given, it is reasonable to expect that changes in consumer attitudes toward alcohol might play some role. In any event, additional tests of the magnitude of change are in order.
Cumulative metaanalysis by primary sample time period
Beverage (no. obs., price, income)  Price elasticity (se)  Income elasticity (se) 

Beer  
19752004 (98, 84)  −0.38 (.03)  0.63 (.05) 
19492004 (172, 151 )  −0.35 (.02)  0.58 (.03) 
Wine  
19752004 (108, 89)  −0.57 (.04)  1.10 (.07) 
19542004 (178, 155)  −0.58 (.03)  1.12 (.06) 
Spirits  
19752004 (100, 86)  −0.66 (.04)  1.09 (.06) 
19542004 (182, 160)  −0.64 (.03)  1.15 (.04) 
Alcohol  
19752005 (76, 60)  −0.60 (.04)  0.61 (.04) 
19602005 (105, 77)  −0.58 (.03)  0.66 (.04) 
Discussion
Results in this paper for price elasticities have important implications for alcohol policy debates. Interest in price elasticities by policymakers has heightened in recent years as attention has focused on reducing average populationlevel consumption as part of a policy for addressing problem drinking and abusive alcohol consumption [11, 27, 28]. In part, this concern is motivated by a lognormal singlepeaked (unimodal) distribution model or Ledermann hypothesis for alcohol consumption. This hypothesis holds that a society’s alcohol problems are directlyrelated to average levels of consumption, even if only a small percentage of the population is categorized as “problem drinkers” [29]. The relationship has been interpreted to indicate that average consumption causally determines heavy drinking prevalence, possibly through a contagious social environment or “drinking culture.” This view is expressed in the continuing interest in alcohol taxes [11], recent interest in minimum pricing of alcohol [30, 31], and concern with the increased “affordability” of alcohol beverages over time or across countries [32, 33]. However, as explained by Duffy [34], heavy drinkers account for a large proportion of total alcohol consumption, so a statistical relationship between average consumption in a country and the percentage of heavy drinkers should be expected, and does not necessarily imply a causal relationship.
Conclusions
The average price elasticities reported here imply that reducing alcohol consumption through price or tax increases will be less effective or more costly than previously suggested or claimed [35–38]. Cumulative average price elasticities are 2829% smaller than “consensus” estimates, with a price inelastic demand for all three beverages (0.30 to 0.55) and total alcohol (0.50). On the other hand, income elasticities are more substantial for all beverages. Affordability of alcohol is therefore likely to be significantly influenced by rising real incomes. Further, recent policy proposals, such as minimum pricing, fail to account for differences in elasticities according to drinking levels or patterns. Even if the distribution of consumption is lognormal, it does not follow that responses to prices are uniform across subpopulations of drinkers. Available evidence from survey studies indicates that demands by heavy drinkers are less responsive to price compared to the general population [39, 40]. While many moderate drinkers probably respond to changes in prices of most alcohol beverages, it does not follow that an acrosstheboard price or taxation policy will directly reduce heavy drinking. In sum, demand heterogeneity exists for alcohol beverages and alcohol consumers.
Endnotes
^{a}Card and Kruger [17] attribute publication bias to three sources: (1) reviewers and journal editors may be predisposed to accept papers that support conventional views such as large negative price elasticities; (2) reviewers and journals tend to favor papers with statistically significant results; and (3) primary researchers use tstatistics of two or more for the main covariates as a guide for model specification and selection. See also [41, 42].
^{b}The grey literature search was aided by files maintained by the author since 1990. A summary is: unpublished working papers and dissertations/reports with dates prior to year 2000 (11 items); and unpublished working papers and dissertations/reports with dates from 20002012 (22 items). All unpublished materials are listed in the Additional file 1.
^{c}Consider three price elasticity estimates and their standard errors: 0.10 (.01); 0.50 (.20); and 1.20 (.60). The median is 0.50 and the unweighted mean is 0.90. The FE mean uses inverse variances for weights, so the first estimate receives a weight proportional to 1/(.01)^{2} = 10,000, while the weights for the other two estimates are proportional to 25 and 2.8. The FE mean for this sample is 0.10 (.01) and the randomeffects mean is 0.37 (.22). The example illustrates the importance of outliers for standard errors in metaanalysis, especially FE models.
Abbreviations
 FE:

Fixedeffect
 RE:

Randomeffects
 FAT:

Funnelasymmetry test
 PET:

Precisioneffect test.
Declarations
Authors’ Affiliations
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