Specification and estimation

We utilized data on reported quantities () and expenditures () for cigarettes consumption as recorded in the household survey across three waves. These data reflect the assumption that households within a specific locality are subject to common market prices during each wave. However, because direct information on cigarette prices is unavailable in the dataset, the Deaton’s methodology exploits the commonality of prices within localities, which is implicitly reflected in the and unit values ().

In Deaton’s model, the primary identifying assumption is that inter-cluster price variation serves as an instrumental variable (IV) for demand. This assumption remains valid for our panel data context: while households within a cluster face a uniform price at any given time point, these prices may exhibit temporal variation across waves. Such variation requires careful adjustments in unit values and budget share regressions (Equation 1 and 2) but does not invalidate the underlying identification and estimation strategy discussed below. Based on these information sets and assumptions, we estimated unit values () and budget-share () regression using the following specifications:

(1)

(2)

In these specifications, denotes the logarithm of unit values derived in the preceding step and represents the budget share for cigarette consumption: . The variable denotes the logarithm of total household consumption, and represents a vector of household-specific socioeconomic characteristics—such as household size, age and gender composition, and the attributes of household head—which serve as covariates that shift both unit values and budget share. Furthermore, and represent cluster-specific and year specific fixed effects, respectively, and and denote idiosyncratic error terms in the respective equations. In line with Deaton’s original framework, these error terms are assumed to incorporate the measurement errors in both unit values and budget shares. Notably, Equation 1 excludes cluster fixed effects because, as Deaton [13] elaborates, conditional on cross-sectional (and temporal, which we add to accommodate panel set-up) variation in prices, unit values are preliminary driven by quality effects and measurement errors. The term represents unobserved prices, which are assumed to remain constant within clusters once year specific fixed effects are controlled for. We estimated these equations omitting and, later, recovered the associated coefficients using the analytical expressions proposed by Deaton [13]. The relationship between the two error terms, and , was used to correct the price elasticity of demand for cigarettes.

In the pooled OLS set-up of Equations 1 and 2, we account for potential biases that may arise from repeated measurements across the three waves. These biases originate from temporal trends in unit values and budget shares, temporal correlation in the error terms, or unobserved shifts in cigarette consumption patterns that might be correlated with the covariates. We address these issues as follows:

1. We incorporate year-specific fixed effects to ensure that inter-cluster variation in the unit value and budget share regressions is free from temporal trends. This step preserves the fundamental requirements for applying Deaton’s demand model.
2. In equation 1 and 2, within-cluster variation may be attributed to: (i) shifts in cigarette consumption preferences over the three-year period, (ii) temporal correlation in the error terms of Equations 1 and 2, and (iii) measurement error (correlation between the error terms of Equations 1 and 2). While (iii) is central to Deaton’s correction strategy for the measurement error, we minimize bias that may result from (i) and (ii) through the following adjustments:
   • We account for temporal correlation in and by allowing the errors to cluster over time during the estimation of the measurement error in the Equation 5.
   • We assume that policy-driven shifts in cigarette preferences were minimal during the survey period. The stable, marginal fluctuations in cigarette prices and taxes between 2016 and 2018 (Table 1) support this assumption.
   • Cigarette consumption typically exhibits a stable pattern over short intervals. A one-year gap between survey waves makes preference shifts unlikely; evidence from longitudinal studies suggest that transitions between smoking states are rare within such a timeframe [24].

By implementing these assumptions and adjustments, the coefficient estimates from the pooled OLS remain unbiased, and the measurement error corrections retain the structural properties of the original Deaton (1988) model.

Next, using Equations 1 and 2, we derived the demand for cigarettes () and their corresponding unit values () at the cluster level after removing the effects of total household consumption, socio-demographic variables, household head’s attributes, and year-specific fixed effects. These residual values were then aggregated and averaged to the cluster level. The primary objective was to estimate elasticity based on cluster-level unit values () and budget share (). These values capture the commonality of market price and cigarette purchasing patterns within each specific cluster. From equations (3) onwards, the analysis relies on cluster-level averages, having purged the influence of systematic household characteristics and temporal effects. At this stage, the estimation procedure becomes identical to Deaton’s standard cross-sectional approach.

(3)

(4)

Using the cluster-level values derived in the previous step, we estimated the regression coefficient of cluster-level demand () on cluster level unit values () following the expression in equation 5. We employed a standard errors-in-variables regression to correct for measurement errors by utilizing the covariance and variance of error terms. In this step, we account for correlation among households over time to address the autocorrelation in error terms () of Equation 1 and 2.

(5)

In the final step, we used a quality correction formula developed by Deaton [13] to derive the price elasticity of cigarette demand (). This step allowed us to isolate genuine price responses from variations in unit values that reflect differences in brand or product quality.

(6)

In equation 6, represents the sample mean of the share of total household consumption expenditure allocated to cigarettes. The estimated parameters and correspond to the coefficients on the unobserved cluster-level cigarette prices in Equations 1 and 2, respectively. We recovered these values using the following expressions proposed by Deaton (1988).

(7)

(8)

(9)

We also recovered the expenditure elasticity of demand using the following expression proposed by Deaton (1988),

(10)

We used R-programming for statistical computing for data management and analysis. Specifically, we employed the tidyverse package for data management, fixest for estimating fixed-effect regression models, and the survey package to generate survey-weighted estimates. Additionally, we used the boot package to calculate bootstrapped standard errors [25–28].

Survey data, cluster definitions, and measurement

We utilized data from the Nepal Household Risk and Vulnerability Survey, a three-year (2016–2018) household panel. The survey was conducted based on the protocol approved by Central Bureau of Statistics (CBS) as per the Statistical Act (1958) [29]. Verbal consent was obtained from each respondent after a thorough introduction of the survey. All respondents were briefed about the voluntary nature of participation. Participants were assured that the information they share during the interview will be kept confidential and anonymous. These data were accessed in July 2022 from The World Bank data repository. Detailed survey methodology is provided by Walker et al. (2019) [30]. The survey instrument, which is based on World Bank’s Living Standards Measurement Survey, collected information on socio-demographics, consumption expenditure, income, and labor supply. The sampling frame included all households in rural municipalities, municipalities and sub-metropolitan areas of Nepal, stratified across 11 regions. In the first sampling stage, 400 wards were randomly selected, with the number per region proportional to its population share. In the second stage, 15 households were randomly selected per ward, resulting in a total of 6,000 households interviewed in 2016. Attrition remained low: 5,835 households (97.3%) were reinterviewed in 2017, and 5,696 (94.9%) in 2018. A total of 5,654 households (94.2%) completed all three waves. After excluding one household due to missing food expenditure data in 2017, we utilized a balanced, complete-cases sample of 5,653 households, yielding 16,959 observations for analysis.

In this analysis, we utilized clusters defined by the survey design, resulting in a total of 400 clusters. On average, each cluster contains 42.4 observations across the three waves stemming from the follow-up of each household between 2016 and 2018. This approach contrasts significantly with that of Vladisavljevic, Zubović, Đukić and Jovanović in Serbia [31] where clusters were defined as interaction of . Similarly, Chelwa and van Walbeek [32] conducted separate analyses for each survey wave in Uganda. In contrast, we utilized repeated observations within the clusters for three primary reasons: 1) to increase the cluster sizes, thereby enhancing the robustness of the estimates; 2) to improve the reliability of unit value computations, as each household reports consumption at three distinct time points; and 3) to increase the estimation efficiency by reducing error variance.

The survey questionnaire is utilized to collect data on primary variables used in this analysis. We utilized weekly household expenditure on cigarettes, the quantity of cigarettes purchased, and total annual household expenditure. To ensure a uniform recall period, annual expenditure was converted into weekly equivalents. All monetary values were adjusted to 2017 prices by using the Consumer Price Index provided by Nepal Rastra Bank [33].

As specified in the Equation 1 and 2, we incorporated several household-level socio-demographic variables, including household size, age and gender composition, number of male members, education level and gender of household head. We also accounted for maximum education level within the household, consumption quintiles, and place of residence. These variables were extracted from Sections 1 and 2 of the survey questionnaires, with the exception of consumption quintiles which were calculated based on total annual per capita consumption expenditure. Because the place of residence of the household was not explicitly categorized in the initial questionnaire, we defined rural households as those located in rural municipalities and urban households as those in municipalities and sub-metropolitan cities.

Policy relevance

The price and expenditure elasticity estimates are relevant to the policy makers as they provide idea about the impact of tax on cigarette demand and tax revenues in short and long run, respectively. First, the estimated elasticity, along with its lower and upper bounds, fall within the range of −1–0, indicating that cigarette consumption in Nepal is relatively inelastic. This pattern is consistent with evidence from other countries in the South Asian region. Specifically, a one percent increase in cigarette prices is associated with an approximate 0.6 percent reduction in cigarette demand. Consequently, a tax-increase that raises cigarette prices is likely to reduce cigarette demand only modestly. However, a positive and unitary elastic expenditure elasticity suggests that rising incomes or increases in household expenditure can partially offset the price-induced reduction in cigarette demand, thereby moderating the overall decline in cigarette consumption and reinforcing the persistence of cigarette demand. This suggests that cigarette taxation should be complemented by additional tobacco control measures—such as restrictions on smoking in public places, support for nicotine replacement therapies etc.—to effectively curb cigarette demand. Similar policy implications apply in other settings with inelastic cigarette demand, including India and Bangladesh.

Second, policymakers are also concerned with the revenue implications of cigarette taxation, as government revenue is directly influenced by consumers’ responsiveness to price changes and changes in purchasing power. Given the relatively inelastic demand for cigarettes, increases in excise tax are likely to generate higher tax revenues. When demand is inelastic, consumers are less responsive to price increases, allowing tax revenue to rise despite higher cigarette prices. Here, the positive and unitary expenditure elasticity plays a complementary role by indicating how consumption responds to rising incomes. A positive expenditure elasticity suggests that economic growth or increases in household expenditure may offset some of the consumption-reducing effects of higher prices, thereby sustaining or even expanding the tax base. In Nepal, a recent policy discussion paper on excise taxation in the 2024/25 budget examined the revenue effects of higher cigarette taxes [21]. The paper highlights that experience over the past three years demonstrates that increasing tobacco taxes has been an effective means of raising government revenues.

Limitations

Our approach to estimating the price elasticity of demand for cigarettes is not without limitations. First, due to the low frequency of reported cigarette consumption, we rely on repeated observations pooled from three-year panel surveys to estimate price elasticity. To address potential autocorrelation, we made adjustments as discussed in methodology section, which helps mitigate the possible bias. Second, unlike many other studies, we were unable to report disaggregated estimates of the price elasticity by policy-relevant variables because of the relatively low incidence of cigarette consumption within each cluster. Despite these limitations, our analysis provides a robust price elasticity estimate that is consistent with the existing literature in the South Asian context and relevant to current policy discussions in Nepal.