When the price of a commodity change it result in a change in consumer income is known as?

Am J Public Health. 2013 November; 103(11): 1954–1961.

Abstract

Pricing policies such as taxes and subsidies are important tools in preventing and controlling a range of threats to public health. This is particularly so in tobacco and alcohol control efforts and efforts to change dietary patterns and physical activity levels as a means of addressing increases in noncommunicable diseases.

To understand the potential impact of pricing policies, it is critical to understand the nature of price elasticities for consumer products. For example, price elasticities are key parameters in models of any food tax or subsidy that aims to quantify health impacts and cost-effectiveness.

We detail relevant terms and discuss key issues surrounding price elasticities to inform public health research and intervention studies.

PRICING POLICIES PLAY a critical role in preventing and controlling threats to public health. In particular, tobacco taxes are a key intervention in tobacco control,1,2 as are alcohol taxes in reducing alcohol-related harm.3 Specific taxes are being used to decrease soft drink consumption4 and to prevent obesity and chronic diseases.5 Countries such as Denmark, Finland, Norway, and Hungary apply taxes on various high-sugar and high-fat foods.6 Denmark introduced a specific saturated fat tax in 2011 (although it was subsequently discontinued) and France a sweetened drink tax in 2012.7 There is evidence that food pricing that increases the relative cost of unhealthy foods is a health-protecting intervention.5,8–10

In low-income countries food subsidies are often used on staple foods to enhance food security, whereas in some high-income countries certain basic foods are exempt from sales taxes. In certain countries, there are calls to eliminate value-added taxes on groups of “healthy foods.” A mix of taxes and subsidies may be most effective, with some models suggesting that “a targeted food tax combined with the appropriate subsidy on fruits and vegetables could reduce deaths from [cardiovascular disease] and cancer.”11(p1324)

Pricing policies are also relevant in infectious disease control (e.g., subsidies on bed nets to prevent malaria12) and health service delivery in terms of user fees.13 In all pricing and health relationships, there is a need for an understanding of the association between price and demand for the good or service in question. That is, how does consumer demand for a good change in response to an alteration in the price of that good or of other goods or services?

The conceptual basis of pricing policies is the notion that changing the price of a good (via taxes or subsidies) alters its consumption and has flow-on health effects (e.g., tobacco taxes result in less tobacco-related disease). Price elasticities (PEs) are the empirical foundation of any epidemiological or other type of modeling. Here we detail terms and consider key issues to equip epidemiologists and public health workers with a basic knowledge of PEs, their conceptual foundation, and (roughly) how they are estimated through econometric methodology (i.e., applying mathematic and statistical methods). We also highlight a number of issues of relevance to modeling that have not been well described in econometric derivations of PEs.

KEY ISSUES SURROUNDING PRICE ELASTICITIES

In the sections to follow, we describe key issues relating to PEs, particularly from a public health perspective.

Elasticities of Demand

Economic theory posits that consumers choose the best consumption bundle they can afford. Thus, for given preferences, consumption depends on commodity prices and consumer incomes. Elasticity of demand is a unit-free measure of how consumption varies with a ceteris paribus change in price (price elasticity of demand) or income (income elasticity of demand). Price elasticity of demand is most important to epidemiologists and public health workers seeking to understand the effects of taxes and subsidies.

There are 2 types of PEs: own-price elasticities (OPEs) measure how much the consumption of a particular good changes with a change in the price of the good itself, whereas cross-price elasticities (CPEs) measure how much consumption of a given good changes with a change in another good’s price, holding everything else constant. Addressing OPEs first, Figure A (available as a supplement to the online version of this article at http://www.ajph.org) shows a demand curve indicating how the quantity of a good purchased varies with the price of the good (holding all other prices and income constant); as price increases, quantity purchased decreases. The OPE at any point along the demand curve is calculated as the slope of the curve at that point multiplied by the ratio of price over quantity. Thus, OPEs are generally different at every point on the demand curve.

The magnitude of the slope and the ratio of price over quantity also depend on the shape of the demand curve, which is determined by consumers’ preferences. The exact positioning of the curve depends on the levels of fixed prices of other goods and income. Thus, OPE values are, in general, different for different commodities and consumers, as well as at different prices and incomes.

A CPE is calculated in exactly the same way, except that the relationship the curve represents is that between consumption and the price of some other commodity. CPEs can be very important in instances in which there are close substitutes or complements. For example, price discounts on fresh fruits and vegetables may appear to almost certainly be health enhancing. However, this may not necessarily be the case, in that a change in the price of one commodity affects consumption of not only that commodity but also consumption of all of the other commodities that are substitutes or complements to it. For instance, salty foods may be complements to fruits and vegetables (and thus the CPE of salty foods with respect to a change in the price of fruits and vegetables is negative), meaning that salt intake increases when the only price change is a subsidy on fresh fruits and vegetables. Thus, the net health impact of any tax or subsidy on food is a delicate balance of OPEs and CPEs, the baseline distribution of foods consumed, assumptions about whether total expenditures on food remain fixed, and other factors.

Several elements influence PE magnitudes.14 First, if there is no close substitute for a good (e.g., there is no margarine available when the price of butter changes), the change in consumption with the change in price will be less pronounced (i.e., less “elastic”). Second, the nature of the good also influences its PE; for example, necessities have lower PEs than luxuries (Table 1).14 Third, the larger the budget share of a good in a consumer’s overall expenditures, the higher the PE, because consumers are more sensitive to the price of an expensive good than that of a cheaper one. Fourth, when consumers have more time to adjust to a change in price, PEs are normally larger. Consumers who purchase at high frequencies or volumes are more price sensitive than consumers who do so at low frequencies or volumes.19 Of importance to public health, if consumers are addicted to the good in question (e.g., as in the case of tobacco or other drugs), PEs tend to be less elastic or lower.

TABLE 1—

Key Terms Relating to Demand Elasticities

Term	Definitions and Comments (Partly Based on Previous Work15)
Elasticities of demand	A measure of how much demand for a quantity of a good changes in response to changes in prices or consumer incomes: specifically, the percentage change in demand for quantity with respect to a 1% change in a single price or income, holding all else the same. This tool is useful because it is a unit-free measurement and provides information on the nature of a good (necessity or luxury) and the relationship between different goods (substitutes or complements). Demand elasticities are also useful for policymakers because they may want to control the consumption of a particular good (e.g., tobacco), particularly in the case of households at certain income levels. Elasticities can also inform future tax revenues after increases in price (e.g., on tobacco or alcohol).
Own-price elasticity (OPE)	A quantitative measure of how demand for a quantity of a good responds to a change in the price of the good. OPEs are calculated by dividing the percentage change in demand for a quantity of a good by the percentage change in price: OPEs are normally negative (i.e., demand decreases as price increases), but in some cases they can be positive. OPEs for a “normal” good (one for which consumption increases when income increases) are always negative. OPEs for Veblen goods are positive; for example, the demand for luxury cars increases as their price increases. If the price elasticity (PE) is greater than 1 in absolute value (i.e., the percentage change in the demand for a quantity of a good is greater than the percentage change in its price), demand is said to be price elastic or relatively more responsive to price changes. For example, research has shown that when the price of whole milk increases by 1%, the quantity demand for whole milk decreases by 1.12% (i.e., a PE of −1.12).16 The higher the PE in absolute value, the more sensitive the quantity demand for price changes. If the PE is smaller than 1 in absolute value, demand is said to be price inelastic or relatively less responsive to price changes. This is the case for tobacco, alcohol, and most food products.
Cross-price elasticity (CPE)	A quantitative measure of how demand for a quantity of a good responds to a change in the price of another good. CPEs are calculated by dividing the percentage change in demand for a quantity of a good by the percentage change in price: CPEs can be positive or negative depending on the relationship between the goods in question (substitute, complement, or independent). If the CPE of demand is positive, good A and good B are substitutes or good B is consumed instead of good A (e.g., an estimate of the CPE for pork and poultry in European countries is 0.3, which means that if the price of poultry increases by 1%, the demand for pork increases by 0.3%17). If the CPE of demand is negative, good A and good B are complements or good B is consumed together with good A (e.g., research has shown that the CPE for milk and cereals is −0.17, meaning that if the price of milk increases by 1%, the demand for cereals decreases by 0.17%18).
Income elasticity of demand	A measure of how much demand for a quantity of a good changes in response to a change in consumer incomes. Income elasticity is calculated by dividing the percentage change in demand for a quantity of a good by the percentage change in income: If the income elasticity of demand is positive, the good is defined as a normal good; if the income elasticity of demand is greater than 1, the good is defined as a luxury good. If the income elasticity is positive but less than 1, the good is classified as a necessary good. If the income elasticity of demand is negative, the good is referred to as an inferior good.
Expenditure elasticity of demand	The term used when expenditure is employed as a proxy for income.

Another critical issue is the level of disaggregation of product groupings. For example, the OPE for the overall category of soft drinks (e.g., soda, fruit juice) has been estimated at −0.79.20 But when separate calculations are made for regular soft drinks and diet soft drinks, their estimated OPEs are −2.26 and −1.27, respectively.21 These higher OPEs are attributable to the presence of more immediate substitutes; consumers can swap from sugary to diet soft drinks if the price of (only) sugary drinks increases. This is obviously an important consideration for researchers seeking to model the impact of more specific subsidies and taxes, but it will also often signify a lack of quality estimates (or poor-quality estimates) of demand elasticities for more segmented groupings.

Demand behavior is determined by consumers’ preferences, so PEs also vary according to context. For example, a particular country or culture may have a strong preference for potato consumption, meaning that the demand for potatoes is likely to be relatively inelastic (i.e., close to zero). Models of the impact of price changes in a given country (and time) should ideally use PEs calculated for that country’s population. Because this is not always possible, care and sensitivity must be taken in applying PEs from one context to another.

Another relevant public health consideration is whether PEs vary according to social grouping. For example, it is now well accepted that younger and poorer smokers are more responsive to tobacco price increases22 (i.e., the PE varies by the person’s socioeconomic position). Empirically determining whether PEs vary by social groupings is challenging. However, it seems a reasonable starting position to assume that PEs will often be greater in poorer populations.

Data Used to Estimate Price Elasticities

Several different types of data are used in estimating PEs (Table A, available as a supplement to the online version of this article at http://www.ajph.org). Central to the quality of PE estimates are variations in price across units of observation. Ideally, prices and consumption data will be available at the individual product level.23 However, depending on the level of commodity aggregation, prices may be available as averages over multiple products. Thus, they may not accurately reflect the actual prices paid by households for a given food item, and as a result the estimated PEs might be incorrect.

Furthermore, the accuracy of consumer survey data is important. For example, PEs have been estimated to vary by 10% to 25% depending on the data collection method used.23 Time series data may produce substantial variations in relative prices and less pronounced variations in income levels, whereas cross-sectional data may produce limited variations in relative prices and substantial variations in incomes.24

Although micro-level data are becoming more available, they also present challenges. Household survey data, for example, are very rich in terms of household characteristics23 but include goods (e.g., flour, rice, and oil) for which no expenditures have been made during the recall period, which leads to complications in estimating econometric models.25 Such zero expenditures are typically addressed with a sample selection or 2-part hurdle model. The most common (and easy to implement) method is that suggested by Shonkwiler and Yen, a consistent 2-step estimation procedure that is a variant of the 2-part hurdle model.25 By contrast, scanner data (e.g., from supermarket purchases) are accurate with respect to the price and quantity of a good purchased, and they offer valuable information for public health researchers such as nutritional information; however, they typically do not reflect all household food expenditures.26,27 Although it seems almost inevitable that PE estimates will vary considerably depending on underlying data quality, this issue has not been given much prominence in the literature.

Short-Run vs Long-Run Price Elasticities

To appropriately determine the public health effects of taxes and subsidies, modelers must think in terms of medium- to long-run PEs. For example, governments are unlikely to change taxes repeatedly over a short duration; rather, they are likely to implement new taxes that will be in effect over a number of years. Thus, when PEs are employed as inputs in modeling, it is important to use estimates that approximate the long-term situation. There is no watertight set of recommendations here. Nevertheless, a panel study with repeated measures collected on people every 3 months (e.g., over a period of 4 years) in the context of rapidly increasing and decreasing market prices would result in very good estimates of short-run PEs if data were calculated only at each wave transition (i.e., changes in consumption and price over the 3-month lag) and relatively good long-run PEs if a well-constructed model was run with times series methods that could detect yearly consumption changes resulting from price changes.

Cross-sectional data will capture short-run PEs only if price changes vary rapidly over time and between areas. But if, for example, variations in price between different US states have been constant in relative terms for a number of decades (e.g., dairy products are cheaper in the Northeast than in the South), cross-sectional data may provide a reasonably good indication of long-run PEs as long as confounding between states is taken into account (e.g., variations in taste and cultural norms that may affect consumption levels). Thus, whether estimated PEs are classified as short run or long run depends on price variations (over both time and place), time lags, study design, and whether confounding is taken into account.

Econometric Models, Methods, and Assumptions

PEs are obtained from estimated demand functions that summarize the relationship between quantity demanded by consumers (dependent variable) and commodity prices and consumer income–utility (the satisfaction a consumer derives from consuming a particular bundle of goods and services; independent variables). The Marshallian demand function expresses the demand for a quantity of a good as a function of prices and consumers’ total incomes. By contrast, the Hicksian demand function expresses the demand for a quantity of a good as a function of prices and consumer utility. The decision of whether to use compensated PEs (obtained from a Hicksian demand function) or uncompensated PEs (obtained from a Marshallian demand function; see the Appendix, available as a supplement to the online version of this article at http://www.ajph.org) depends on whether the goal is to understand the pure price substitution effect or to understand that effect in combination with income effects.28–31 Relative to compensated PEs, uncompensated PEs tend to be higher in magnitude,32–35 are used more often in commodity models,36,37 and are more suitable for public health pricing interventions because they capture the full impact of price changes.

Given that it is impossible to estimate the demand for all commodities, there are 2 common approaches that can be used in selecting the commodity prices to include in a demand specification. One approach is to consider a complete demand system for all commodities but to assume that consumers’ preferences for the group of goods in question are independent of their preferences for other goods. This results in conditional (on the total expenditure on the goods of interest) demand functions (see the Appendix) that include the prices of those goods only in addition to the budget allotment to them. The prices of other goods are relevant only insofar as they determine the budget allotment to the goods of interest.

The second approach is to use an incomplete demand system by specifying demand for the goods of interest only. An important distinction between the elasticities yielded by these 2 approaches is that the incomplete demand system provides direct unconditional elasticities (see the Appendix) because total income is used as a regressor. The complete demand system can provide unconditional elasticities indirectly by estimating a 2-stage model. The difference between conditional and unconditional elasticities can be substantial. According to Klonaris and Hallam,38 unconditional OPEs are generally lower in absolute value than conditional OPEs.

A number of mathematical forms can be obtained in each of these demand functions (see the Appendix). The almost ideal demand system model, which specifies the budget share of a commodity as a linear function of the log of real total income and the log of prices, is a commonly used modeling approach.39–41 Another model used by many empirical researchers is the double-log model; however, these models can lead to problems with the internal consistency of results if they are applied to complete demand systems.23 A translog model can provide good-quality estimations, but a large number of parameters must be estimated.42

Another model in use, the Rotterdam model, can be applied to only a small number of goods; indeed, this model is generally too restrictive in that all goods must be substitutes and no goods can be inferior.43 The linear expenditure system model is more likely than the Rotterdam model to produce low PE estimates for food, tobacco, and alcohol.42 Finally, other models have been designed to address the absence of consumption of certain goods (e.g., the sample selection model and the 2-part hurdle model).

Uncertainty

There are many sources of uncertainty in PE estimates, and they appear to be afforded insufficient attention with respect to their application to epidemiological models and public health policies. First, the nature and quality of the underlying data are likely to alter estimates. Second, the grouping of products needs to align with the intended epidemiological model or the proposed public health intervention. For example, the interest may be in the impact of a tax on sugary drinks, but PE estimates are available only for all soft drinks combined (a model incorporating PEs for all soft drinks that is applied to only sugary soft drinks would likely lead to underestimation of the OPE44 and does not address the source of the CPE between sugary and nonsugary soft drinks).

Third, as described earlier (and in the Appendix), the econometric model and demand functions matter. Fourth, although the confidence intervals (CIs) for elasticity estimates may be very wide, especially in the case of CPEs, many published estimations do not include a standard error (or even a P value) for each individual estimate. Finally, as noted, there are issues surrounding contexts and preferences.

These aspects of uncertainty may become more complex in epidemiological modeling of hypothesized taxes and subsidies. Typically, either uncertainty analyses are not explicitly included in models or these analyses are simplistic. At the least, simple sensitivity analyses focused on OPEs and influential CPEs should be included in future models.

PRICE ELASTICITIES RELEVANT TO PUBLIC HEALTH

Table 2 presents examples of OPEs for goods that are relevant to epidemiology and public health. However, the OPEs reported need to be viewed with caution because they were drawn from different studies and thus might differ with respect to model assumptions, types of data, time periods, regression techniques, and so on.

TABLE 2—

Selected Examples of Own-Price Elasticities (OPEs) of Relevance to Epidemiology and Public Health

The demand for most goods is price inelastic, with bed nets being the most inelastic goods (−0.12) and spirits being the least inelastic (−0.8). In the case of gasoline, the short-run PE is low relative to the long-run PE, presumably because people need time to adapt to changes in gasoline prices and find alternative transport modes.

In Figures 1 and ​2, we present data on food OPEs derived from a large multicountry study.52 It is apparent that the specific grouping with the lowest median OPE was cereals in Organisation for Economic Co-operation and Development (OECD) countries (−0.042) and that the grouping with the highest median was dairy products in other countries (−0.543). The pattern in all of the product groups was that higher income OECD countries had lower OPEs than non-OECD countries. This is in line with a key factor affecting PE magnitudes: if the budget share of a given food is low, demand for that food tends to be inelastic.

Own-price elasticities for food: 32 Organisation for Economic Co-operation and Development countries, 2005.

Note. F&V = fruits and vegetables; O&F = oils and fats. The bars represent range (maximum to minimum). The box (from top to bottom) shows ranges: percentile 75, percentile 50 (median), and percentile 25.

Source. Calculated from data in Seale et al.52

Own-price elasticities for food: 144 countries, 2005.

Note. F&V = fruits and vegetables; O&F = oils and fats. The bars represent range (maximum to minimum). The box (from top to bottom) shows ranges: percentile 75, percentile 50 (median), and percentile 25.

Source. Calculated from data in Seale et al.52

Examples of CPEs for various food groups are shown in Table B (available as a supplement to the online version of this article at http://www.ajph.org).17,34,39,52,53 The highest CPE (0.274) corresponds with a rise in the demand for fruit after an increase in the price of meat.34 That is (according to this UK study at least), fruit and meat are substitutes, in that as the price of meat rises, consumption shifts to fruit. In other studies, however, the reported CPE for meat (relative to fruit) was essentially zero (0.009; 95% CI = −0.053, 0.061) or even negative (−0.10).

Indeed, the general finding from Table B is that there is no pattern: for the first 8 CPEs shown (elicited from 2 UK studies and 1 US study), the correlations were negative or null or were modest at best. Thus, one can conclude only that there is much variation across contexts (including time) or that CPEs are unstable and measured with such imprecision as to be of limited utility in modeling. A final point is one that is particularly relevant for public health research: CPEs are critical to the impact of highly targeted fiscal policies such as subsidizing low-fat milk, in that we implicitly assume people will respond to relatively lower prices by shifting consumption from unhealthy to healthy complements (i.e., from high-fat to low-fat milk).

RECOMMENDATIONS FOR FUTURE ESTIMATION

Whereas the quality of current PE estimates for some types of goods (e.g., foods) is poor, estimates are relatively reliable for other goods (e.g., tobacco). The level of uncertainty (often not stated) in currently published estimates does not allow robust determinations of how population-wide diets and subsequent disease and health impacts will be affected by taxes and subsidies on foods. Some of this uncertainty is unfortunately unavoidable. For example, as a result of factors such as cultural changes and marketing programs, past PE estimates will not necessarily be correct in the future (or in a different context).

That said, improvements are possible in estimations of PEs. First, both CPEs and OPEs should be reported with confidence intervals. Covariance or correlation matrices are also needed to inform the best possible epidemiological modeling. Second, it is a sine qua non of observational research that there need to be sufficient variations in the exposure in question (e.g., food prices) to reliably estimate changes in outcomes (purchasing and, hence, PEs). Researchers need to find, or generate themselves, high-quality data sets with sufficient variations in price. Third, the PEs of interest to public health workers may not be the same as those routinely used in other disciplines. In particular, public health research needs CPEs in addition to OPEs, particularly those for healthy or unhealthy substitutes (e.g., low-fat vs high-fat milk) and those underlying the apparent unintended consequences of certain price changes (e.g., possible trade-offs of foods high in saturated fat for less salty foods).

Finally, there is a dearth of experimental studies in the domain of PEs related to food; indeed, we know of none. We suggest the possibility of an experimental design with, for example, a virtual supermarket wherein participants are randomly allocated to varying prices as they “virtually” shop.54,55 Thus, price variations can be randomly manipulated to maximize the precision and accuracy of the PEs that are most important in subsequent epidemiological modeling. This seems to be a fertile area for research, one that combines randomized trials and econometric and biostatistical approaches.

RECOMMENDATIONS FOR PUBLIC HEALTH RESEARCHERS

In the meantime, policymakers need the best evidence on PEs that researchers can provide. Ideally, researchers would use estimates that are accurate and statistically precise for their own population, but this may rarely be achieved. Therefore, they should strive to provide a clear description of the limitations associated with PE input parameters.

Also, in PE sensitivity or uncertainty analyses, there are issues surrounding the internal consistency of the resulting PEs (i.e., the tabulated PE matrix comprising OPE results down the diagonal and CPE results on the off-diagonal) and meaningful consideration of disease modeling outcomes. This is because there are theoretical restrictions in the matrix, and a change in one PE value will ultimately lead to a change in other PEs to satisfy these restrictions.19 A PE matrix that does not address these restrictions could produce unrealistic changes in consumption levels and, hence, unrealistic changes in model disease outcomes. In addition, clear descriptions of data types, data sources, time periods, demand models, and types of PEs are necessary.

Finally, uncertainty in PEs should be explicitly modeled. This should ideally be done probabilistically, and specific distributions of uncertainty regarding each PE should be described. Usually, these distributions are fitted on the basis of random errors (i.e., confidence intervals); however, systematic errors (e.g., errors resulting from the use of PEs from other countries) may also need to be included, essentially widening the uncertainty distribution. In addition, correlations should be allowed for; if a high value is selected for the CPE of low-fat milk with high-fat milk in a Monte Carlo simulation, in all likelihood a high value would also be expected for the CPE of high-fat milk with low-fat milk. Without allowing for these (unfortunately many) correlations, uncertainty in final model outputs will most likely be overestimated.

An alternative to such probabilistic uncertainty analyses is a deterministic approach in which specific values are used (e.g., rerunning the model for only the 90th percentile values of the key PEs). This may be adequate, and even preferable, when the level of uncertainty about PEs is so large that scenario analyses (as opposed to probabilistic analyses) seem to be a more transparent and scientifically honest option.

SUMMARY

PEs are key parameters of economic and disease models used to assess the impact of price interventions designed to protect public health. Such interventions include tobacco taxes, alcohol taxes, and healthy food subsidies. An understanding of PEs is of growing importance for epidemiologists and public health workers as governments increasingly consider new types of taxes and subsidies. In particular, future estimations of PEs for use in public health research need to carefully consider the quality of consumption data and categorizations of food groupings of relevance to health. There is also a need to assess the internal consistency of the PE matrix and uncertainty around PE estimates.

Acknowledgments

This work was supported by the Health Research Council of New Zealand as part of the Burden of Disease Epidemiology, Equity and Cost-Effectiveness Program (grant 10/248).

Human Participant Protection

No protocol approval was needed because no person-specific data were used.

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