Meta-analysis of e-cigarette price elasticity

Data

This meta-analysis was registered with the Center for Open Science’s OSF Registries on January 20, 2022 (https://doi.org/10.17605/OSF.IO/9HBWQ), following Cochrane guidelines for systematic reviews where applicable (https://training.cochrane.org/handbook). This pre-registration was based on updating the results of the previously published study²⁴ (research questions 1 and 2 above), and while conducting the present research a number of results on the cross-price elasticity of cigarettes with respect to ENDS price (question 3, the inverse of research question 2 above) were found. Thus, we extended the pre-registration following the same methods as pre-registered analyses for research question 3 above.

Studies on tobacco product elasticity were sourced from peer-reviewed publications and National Bureau of Economic Research (NBER) working papers in the PubMed and Google Scholar databases using the two separate search terms ‘e-cigarette’ + ‘own-price’, and ‘e-cigarette’ + ‘cross-price’. Pre-registration authors independently screened search results for eligibility in blinded and duplicate fashion. Conflicts were resolved through discussion. The inclusion criteria were primary sources of all study designs and groups of participants with relevant elasticity outcomes. No limits were applied to date of publication or language; regardless, all articles retained for review were in English.

Studies on elasticity examined how changes in price (or tax, which, due to a high pass-through fraction, is equivalent to a change in price^22,23), of a product impacted one of two measures of demand.

Data were extracted manually by reviewing the full text of each manuscript, including the geographic region, age group (adults/adolescents), ENDS product type (disposable; reusable/rechargeable; liquid/cartridges; or multiple), price elasticity type (own/cross), effect size (elasticity value), 95% confidence interval (CI), standard errors (SEs), and p-values. When multiple models were presented in a single study with a range of independent control variables, results were taken from the model with the most controls for the most realistic estimate (typically the ‘main result’).

Where effects were not reported in the original texts, estimates were derived from figures. Where only SEs were reported, Wald-type 95% CIs were estimated as $\mathrm{CI}=\text{effect size}\pm \left(1.95996\times \text{standard error}\right)$. Similarly, where only CIs were reported, SEs were estimated conservatively as $\text{standard error}=max\left(\frac{\mathrm{LCL}-\text{effect size}}{-1.95996},\frac{\mathrm{UCL}-\text{effect size}}{1.95996}\right)$. Because the underlying studies do not always report what kind of distribution their SEs are based on, we assume a normal distribution of SEs. Where only p-values were reported, SEs and CIs were conservatively estimated following the methodology of Altman and Bland.²⁶ Elasticities expressed on the scale $\alpha =e^{\text{elasticity}}$ were transformed by taking the natural logarithm ($\text{elasticity}=ln\alpha$).

Statistical analysis

Meta-analytic summary statistics were estimated via a method of moments random-effects model with the two-step DerSimonian and Laird estimator.²⁷ A random-effects model was selected because these studies are estimating effects that are related but not identical²⁸; studies use different designs, and examined different product types (as described above) across different years. The summary effect in the present study is therefore an estimate of the mean of the distribution of underlying effects.²⁹ The two-step DerSimonian and Laird estimator was selected over alternatives such as the original one-step DerSimonian and Laird estimator and the Paule-Mandel estimator because the latter have been shown to introduce bias.³⁰ As a sensitivity test, the one-step estimator were also implemented.

Three separate models were implemented with these methods. The first analyzed the own-price elasticity of ENDS; the second the cross-price elasticity of ENDS with respect to cigarette price; the third the cross-price elasticity of cigarettes with respect to ENDS price. Where studies presented different effect estimates for different product types (e.g. one for disposable ENDS and another for reusable ENDS), both were included as separate effects in the same model, as they originate from different data. Some studies also provided both own-price and cross-price effects; each was used in the corresponding models above.

Heterogeneity of effects was assessed with the Q statistic, tested for statistical significance as a chi-square score with degrees of freedom $\mathrm{df}=\text{number of studies}-1$ and $\text{alpha}=0.05$. The I² statistic and its CI was also calculated to reflect the overlap of individual studies’ CIs.³¹ Finally, the T² statistic was calculated to provide a sample estimate of the standard deviation of underlying effects$\mathrm{T}=\sqrt{{\mathrm{T}}^2}$ around the mean effect.

Analyses were conducted in Python version 3.7.6 with the packages Numpy version 1.18.1, Pandas version 1.0.1, Matplotlib version 3.1.3, Scipy version 1.4.1, and Zepid version 0.9.0.

Search results

PubMed searches for the two search term combinations ‘e-cigarette’ + ‘own-price’ and ‘e-cigarette’ + ‘cross-price’ returned five and seven results respectively. Google Scholar searches for the same combinations returned 102 results and 252 results respectively. After reviewing these results for eligibility, 23 studies that assessed relevant elasticities were retained. All excluded articles did not assess relevant elasticities.

Of the 23 studies retained, 10 did not use sales/purchases outcomes (e.g., they instead used prevalence/frequency or other outcomes). These 10 studies are summarized narratively because sales/purchases and prevalence/frequency/other outcomes are not appropriate for direct comparison, even in a random-effects model, and because each combination of outcome (current use, daily use) and population (adults, adolescents) had too few results for separate model-based meta-analyses.

Of the remaining 13 studies considered appropriate for inclusion, nine reported both own-price and cross-price elasticities, two reported only own-price elasticities, and two reported only cross-price elasticities. Reporting of different elasticities for different product types from these studies provided 14 separate own-price elasticities and 15 separate cross-price elasticities for modelling.

Of the 13 included studies, the majority were US-based, with the only exceptions being Stoklosa et al.³² which studied the EU, and Grace et al.³³ which studied New Zealand. Of the 14 own-price estimates, three examined disposable ENDS, three examined reusable or rechargeable ENDS, one examined e-liquid, and the remaining studies examined multiple product types. Of the 15 cross-price estimates, three estimates examined disposable ENDS, three examined reusable or rechargeable ENDS, two examined e-liquid, and the remaining studies examined multiple product types.

ENDS own-price elasticity

All studies estimated a negative own-price elasticity, and none of the CIs crossed zero. The random-effects model summary effect for ENDS own-price elasticity was -1.10 (95% CI: -1.39 – -0.80). As a sensitivity test, the one-step DerSimonian and Laird estimator provides a summary effect of -1.12 (-1.46 – -0.78) which is not meaningfully different from the two-step result. The Q statistic for the own-price two-step model was 310.2 with 13 degrees of freedom, providing a p-value <0.001, which indicates statistically significant heterogeneity. The I² statistic was 95.8% (94.3%–96.9%), which is high³¹ and is evidence that the underlying effects vary. Finally, the square root of the T² statistic provided a sample estimate of the standard deviation of underlying effects of 0.47 around the mean effect -1.10.

To explore the heterogeneity of these studies, subgroup analyses were undertaken. A subgroup analysis of those studies which analyzed multiple product types and which used commercial retail/market-level models (n=6 studies) yielded a Q statistic of 4.2 with five degrees of freedom, providing a p-value of 0.52. This indicates homogeneity across these studies. For this subgroup, the summary effect was -1.15 (-1.34 – -0.97), which is statistically consistent with the whole-group analysis, and implies that a 10% increase in ENDS price is associated with an 11.5% (9.7%–13.4%) decrease in ENDS demand. This subgroup represents the largest subgroup with a non-significant Q-statistic, and consists of a sufficient number of studies for meta-analysis.³⁴ Figure 1 shows the forest plot for ENDS own-price elasticities from this homogeneous group of studies.

Figure 1. Forest plot of own-price elasticity of ENDS.

CI: confidence interval.

Table 1 summarizes studies on ENDS own-elasticity which were excluded from the meta-analysis model because they used different outcome measures (e.g., prevalence) or non-comparable populations (e.g., adolescents or adult subpopulations). These studies all report negative own-elasticity of ENDS across product types and study models, consistent in direction and magnitude to the meta-analyzed studies in Figure 1. Increased ENDS price is associated with decreased ENDS purchase, ENDS use prevalence, and ENDS use frequency among adults and adolescents in these studies.

Cross-price elasticity of ENDS with respect to cigarette price

All studies examined adults and estimated a positive cross-price elasticity, with the CIs of eight of the 14 estimates crossing zero. The random-effects model summary effect for ENDS cross-price elasticity with respect to cigarette price was 1.75 (0.92–2.58), with the CI not crossing zero. As a sensitivity test, the one-step DerSimonian and Laird estimator provides a summary effect of 1.80 (0.84–2.76) which is not meaningfully different from the two-step result. The Q statistic for the cross-price two-step model was approximately 130.7 with 13 degrees of freedom, providing a p-value <0.001, which indicates statistically significant heterogeneity. The I² statistic was 90.0% (85.1%–93.4%), which is high³¹ and is evidence that the underlying effects vary. Finally, the square root of the T² statistic provided a sample estimate of the standard deviation of underlying effects of 1.18 around the mean effect 1.75.

To explore the heterogeneity of these studies, subgroup analyses were undertaken. A subgroup analysis of those studies which used commercial retail/market-level models (n=11 studies) yielded a Q statistic of 8.0 with 10 degrees of freedom, providing a p-value of 0.63. This indicates homogeneity across these studies. For this subgroup, the summary effect was 0.98 (0.57 – 1.38), which is directionally and statistically consistent with, but half the magnitude of, the whole-group analysis result, and implies that a 10% increase in cigarette price is associated with a 9.8% (5.7%–13.8%) increase in ENDS demand. This subgroup represents the largest subgroup with non-significant Q-statistic. Figure 2 shows the forest plot for cross elasticity of ENDS with respect to cigarette price from this homogeneous group of studies.

Figure 2. Forest plot of cross elasticity of ENDS with respect to cigarette price.

CI: confidence interval.

Table 1 summarizes studies which examined the cross-price elasticity of ENDS with respect to cigarette price. These were excluded from the meta-analysis model because they used different outcome measures (e.g., prevalence), non-comparable populations (e.g., adolescents or adult subpopulations), or because exact elasticities were not reported. Consistent with the meta-analysis in Figure 2, Snider et al.,³⁷ Pesko et al.,³⁸ Pesko and Warman,¹⁹ and Friedman and Pesko³⁹ suggest that higher cigarette price is associated with significantly increased number of ENDS purchased and increased ENDS use prevalence. Cotti et al.⁴³ and Pesko et al.⁴¹ find negative cross-price elasticity of ENDS with respect to cigarettes, however these results did not reach statistical significance. Most recently, Chan et al.,⁴⁴ analyzing data from 47 countries participating in the World Health Organization’s Global Youth Tobacco Survey, found significant associations between higher cigarette taxes and higher prevalence of adolescent ENDS use.

Cross-price elasticity of cigarettes with respect to ENDS price

All studies examined adults. The random-effects model summary effect for cigarette cross-price elasticity with respect to ENDS price was 0.002 (-0.009–0.014), with the CI including zero. As a sensitivity test, the one-step DerSimonian and Laird estimator provides a summary effect of 0.002 (-0.003–0.007) which is practically identical to the two-step result. The Q statistic for the cross-price two-step model was approximately 15.1 with seven degrees of freedom, providing a p-value of 0.035, which indicates statistically significant heterogeneity. The I² statistic was 53.7% (0.0%–79.1%), which is moderate³¹ and suggests approximately half of the observed variance represents real differences in effect size. Finally, the square root of the T² statistic provided a sample estimate of the standard deviation of underlying effects of 0.009 around the mean effect 0.002.

To explore the heterogeneity of these studies, subgroup analyses were undertaken. Subgroup analyses by specific product types and study types did not resolve the heterogeneity. However, a subgroup analysis of those studies published after 2017 (i.e., the most recent studies most relevant to the current cigarette and ENDS markets; n=6 studies) yielded a Q statistic of 11.1 with five degrees of freedom, providing a p-value of 0.50. This indicates homogeneity across these studies. For this subgroup, the summary effect was 0.114 (-0.054 – 0.282), which is non-significant and positive. This subgroup represents the largest subgroup with non-significant Q-statistic. This implies that a 10% increase in ENDS price is non-significantly associated with a 1.1% (-0.5%–2.8%) increase in cigarette demand. Figure 3 shows the forest plot for cross elasticity of cigarettes with respect to ENDS price from this homogeneous group of studies.

Figure 3. Forest plot of cross elasticity of cigarettes with respect to ENDS price.

Effects based on commercial retail/market-level models are shown as circles. Effects based on hypothetical purchasing experiments are shown as squares. The summary effect is shown as a diamond. CI: confidence interval.

Table 1 summarizes studies which examined the cross-price elasticity of cigarettes with respect to ENDS price. These were excluded from the meta-analysis model because they used different outcome measures (e.g., prevalence), non-comparable populations (e.g., adolescents or adult subpopulations), or because they contain unpublished findings. Pesko et al.,³⁸ Saffer et al.,⁴⁵ Abouk et al.,⁴⁶ and Friedman and Pesko³⁹ all find statistically significant positive cross-price elasticity, indicating that increased ENDS price is associated with increased cigarette smoking prevalence and propensity among adults. In as-yet unpublished work, Mathios reports that in hypothetical purchasing experiments, when faced with increased ENDS price, users immediately choose cigarettes rather than quitting ENDS (https://youtu.be/6K6dUA8KjOI). Among adolescents, Pesko and Warman¹⁹ report a significant positive association between ENDS cartridge price and number of cigarettes smoked, while other outcomes in this study and in Cantrell et al.⁴² did not reach statistical significance. Findings in this narrative summary are directionally consistent the meta-analysis in Figure 3.