A Different Approach to Deriving Price and Income Elasticities: Applications to Telecommunications and Gasoline & Motor Oil

Abstract

The primary purpose of this chapter is to demonstrate how a framework developed from data embodied in surveys of households’ consumer expenditures can be used to calculate complete arrays of own- and cross-price elasticities. The procedure is illustrated for simulated changes of ±10% in the price of telecommunications and for ±50% and −50%/+75% changes in the price of gasoline & motor oil. The engine for the analysis is a matrix of “intra-budget” coefficients that represent the direct relationships amongst the different categories of expenditure in households’ budgets. A strength of the framework is that price changes can be translated immediately into real-income effects, which in turn allows for straightforward separation of income and substitution effects.

Appendices

Appendices

Appendix 1

Definitions of Expenditures in BLS Survey of Consumer Expenditure: 14 Categories of Expenditure.

Food includes expenditures on food at home referring to expenses for grocery stores and food by the consumer on trips; food away from home accounting for all meals at fast food, take-out, delivery, concession stands, buffet and cafeteria, full-service restaurants, vending machines, and mobile vendors; and other miscellaneous venues.

Alcoholic beverages include beer and ale, wine, whiskey, gin, vodka, rum, and other alcoholic beverages.

Housing includes expenditures on owned dwellings like interest on mortgages, property taxes, and repairs and maintenance; rented dwellings like rent and maintenance, utilities like natural gas and electricity; fuels like fuel oil and coal; public services like water, garbage, and telephone; housekeeping supplies; household textiles; furniture; floor coverings; major and small appliance; and other miscellaneous equipment purchases.

Apparel includes expenditures on men’s and boy’s apparel; women’s and girl’s apparel; apparel for children under 2; footwear; and other apparel products and services.

Transportation includes expenditures for vehicle purchases; vehicle finance charges; gasoline and motor oil; maintenance and repairs; vehicle insurance; public transportation; and vehicle rental, leases, licenses, and other charges.

Health Care includes expenditures on health insurance; medical services like hospital services and physicians’ services; eye and dental care; lab tests and X-rays, convalescent and nursing home care; medical appliances and equipment; and both non-prescription and prescription drugs.

Entertainment includes expenditures on fees and admissions; television, radio, and sound equipment; pets, toys, hobbies, and playground equipment; and other miscellaneous entertainment equipment and services like bicycles, hunting and fishing equipment, boats, photographic equipment and supplies, fireworks, electronic video games, etc.

Personal care products and services includes products for the hair, oral hygiene products, shaving needs, cosmetics and bath products, electric personal care appliances, other personal care products, and personal care services for males and females.

Reading includes subscriptions for newspapers and magazines; books through book clubs; and the purchase of single-copy newspapers, magazines, newsletters, books, and encyclopedias and other reference books.

Education includes tuition; fees; and textbooks, supplies, and equipment for public and private nursery schools, elementary and high schools, colleges and universities, and other schools.

Tobacco products and smoking supplies includes cigarettes, cigars, snuff, loose smoking tobacco, chewing tobacco, and smoking accessories (such as cigarette or cigar holder pipis flint and pipe cleaner).

Miscellaneous includes safety deposit box rental, checking account fees and other bank service charges, credit card memberships, legal fees, accounting fees, funerals, cemetery lots, union dues, occupational expenses, expenses for other properties, and finance charges other than those for mortgages and vehicles.

Cash contributions includes cash contributed to persons or organizations outside the consumer unit, including alimony and child support payments; care of students away from home; and contributions to religious, educational, charitable, or political organizations.

Personal insurance includes expenditures on life insurance; endowments; mortgage insurance; and other premiums for personal liability, accident, and disability, and other non-health insurance other than for homes and vehicles. (Source: U.S. Bureau of Labor Statistics, available at http://www.bls.gov/cex/csxgloss.htm.)

Appendix 2

When the large discrepancy (in absolute value) in the change in expenditures for gasoline & motor oil for all households for the ±50% price changes was first encountered (−$329 vs. $194) in Table 2.7, my reaction was that a coding error almost certainly had to be involved. However, this was not the case, for the difference in fact arises from the manner in which the budget constraint is imposed, specifically, in simulations using Expression (2.3), whether the budget constraint is imposed as in Expression (2.18), or as in:

$$y^{k} = w^{k} z + Ay^{k - 1} ,$$

(2.19)

[where (as before) $w^{k} = \frac{{y^{0} }}{{y^{k - 1} }}$], or as in:

$$y* = w*\hat{y},$$

(2.20)

where

$$\hat{y} = \lim (z + Ay^{k - 1} ),k \to \infty$$

(2.21)

and where

$$w^{*} = \frac{{y^{0} }}{{\hat{y}}}.$$

(2.22)

In the event, it turns out that y^* in Expression (2.20) is equal to the solution vector y from Expression (2.5)—as in Table 2.7 for the ±50% price changes. That this is the case can be seen numerically in Tables 2.13A and 2.13B. The numbers appearing in columns 1 and 3 of this show changes in gasoline & motor oil expenditures from the first 10 iterations of Expression (2.18) for a 50% decrease in the gasoil price (column 1) and a 50% increase (column 3). Columns 2 and 4 show the same for simulations using

Table 2.13A Means of intra-budget expenditures regression coefficients: 18 categories of U.S. Consumption expenditure (2006 Q1–2012 Q4)

Table 2.13B Means of intra-budget expenditures regression coefficients: 18 categories of U.S. Consumption expenditure (2006 Q1–2012 Q4)

$$y^{k} = z + Ay^{k - 1} .$$

(2.23)

Convergence values (i.e., −$297.10, −$399.76, etc.) are shown as well.²² At the bottom of the table, it is seen that the total expenditure that is associated with values of −$399.76 and $399.76 corresponding to Expression (2.18)—in which the budget constraint of $12, 220 is not imposed—are $9062 and $15,378, respectively, yielding values for w* in Expression (2.22) of 1.3485 (12,220/9062) and 0.7846 (12,220/15,378). When these two factors are applied to the $\widehat{y}$s [from Expression (2.21)] in Expression (2.17) to take the budget constraint of $12,220 into account, the result is budget-constrained expenditures for gasoline & motor oil of $274.17 for the 50% price decrease and $786.88 for the 50% price increase.²³ Subtraction of base expenditures of $603.04 from these quantities then yields the −$328.90 and $193.81 of Expression (2.3) (Table 2.14).

Table 2.14 Changes in gasoline & motor oil expenditures from ±50% changes in gasoline & motor oil price: first 10 iterations of Expressions (2.15) and (2.18) (all households)

Amongst other things, what this exercise illustrates is that (as discussed in detail in Chapter 4 of Internal Structure) the way in which a budget constraint is imposed in this framework is a matter of choice. This is both a strength and a weakness, a weakness because different methods lead to different results, but a strength in that the method used can be tailored to the question at hand. The method to be used can turn on whether the question of interest involves dynamics or a steady state. Dynamics can then be identified with iterative solutions involving the structural form per Expression (2.3) and a steady state with reduced-form solutions per Expression (2.5). Dynamics, accordingly, can usefully be associated with the sequential effects on expenditures from a price change under the assumption that total expenditure is constant. This allows for the initial effect on the good whose price has changed to be isolated from the effects that arise through feedbacks from other goods. Goods that might appear to be Giffen in the long run can thus be seen to behave normally in the short run. The simulations exercises for both telecommunications and gasoline & motor oil, using Expression (2.18), represented in Table 2.12 and Fig. 2.1 provide illustration.