From 1972 to 1991 changes in safety regulations increased the cost of building new automobiles by $900. Over this same period emission control regulations increased the costs of new automobiles by $1400. This paper develops and estimates a model that tests whether consumers valued the effects safety regulations had on the safety of vehicles by comparing the effects of changes in safety regulations on used vehicle prices to the effects of changes in emission control regulations.
Changes in emission control regulations have only one immediate impact on the used vehicle market. As consumers attempt to substitute the now relatively less expensive used vehicles for the new vehicles, the prices of used vehicles are bid up. Safety regulations cause this same substitution effect, but, assuming they are effective, they also increase the relative value of owning new vehicles (due to the latter's increased safety). This second effect depresses the prices of used vehicles, so a change in the costs of new automobiles due to a change in safety regulations has a lesser impact on the prices of used vehicles than does a similar change in the costs of new automobiles due to a change in emission control regulations. If the second effect is stronger than the first, the prices of used vehicles will fall in response to the change in safety regulations. As shown in section II, this implies that the change in safety regulations increases social welfare.
The empirical model, discussed in section III, can differentiate between two possible valuations consumers may place on safety regulations. If the effect of changes in both emission control and safety regulations on the prices of used vehicles are identical, then consumers place no value on safety regulations. If increases in safety regulations decrease the prices of used vehicles, then consumers value the safety induced by these regulations more than their costs. The empirical results presented in section IV show that used vehicle prices fall in response to an increase in mandated safety, implying that consumers value the safety induced by safety regulations more than the additional cost imposed by these regulations. This has the surprising implication that the implementation of the safety regulations resulted in an overall Pareto improvement in social welfare.
The new and used car markets are assumed to be competitive with the cost of building a new car, MC, a constant given by the sum of a per-vehicle cost, V, the cost of emission controls, E, and the cost of safety, S. All automobiles with a given safety level, S, produce the same level of service regardless of age and are scrapped at an age of T with a scrap value of zero. Consumers are identical with income, I, discount rate, r, and own exactly one vehicle. They derive utility from automobile consumption and from a generic consumption good, g. Because clean air is assumed to be a public good, the utility derived from the automobile is dependent only on the vehicle's safety. This utility is given by d(S) with d[prime](S) [greater than] 0 and d[double prime](S) [less than] 0. The price of using a vehicle for one period is its rental value. In equilibrium, it is a function of the level of emission controls and safety built into new vehicles, [C.sup.n] and [S.sup.n], respectively, and the vehicle's own safety level, S, and is given by R([C.sup.n], [S.sup.n]; S).(1) The utility from the generic consumption good is given by f(g) with f[prime](g) [greater than] 0 and f[double prime](g) [less than] 0. The price of the generic consumption good is assumed to be one giving the following utility function for consumers, U = f[I - R([C.sup.n], [S.sup.n]; S)] + d(S), where total expenditure on the generic good is equal to I - R([C.sup.n], [S.sup.n]; S).
In a steady-state equilibrium, competition ensures that the expected present value of the rental values of the vehicle equals its marginal cost of production (as well as its price). Perfect competition also ensures that firms select the safety level that maximizes consumer (and social) welfare (and the lowest level of emission controls allowed). This safety level is denoted by [S.sup.*] and is found by differentiating the consumer's utility with respect to safety and setting the result equal to zero.
(1) [Delta]U / [Delta]S = -f[prime]([center dot])[[R.sub.S]([center dot])] + d[prime](S)
= -rf[prime]([center dot])/(1 - [e.sup.-rT]) + d[prime](S) = 0.
The assumptions made above ensure that [S.sup.*] is a unique maximum. The second-order condition implies that when S [less than] [S.sup.*] then [Delta]U / [Delta]S [greater than] 0 and when S [greater than] [S.sup.*] then [Delta]U / [Delta]S [less than] 0. This relationship is critical in using changes in used vehicle prices to determine whether changes in safety regulations increased social welfare.
Assuming that both new and used vehicles must conform to the change in emission control and safety regulations, the steady-state effects of changes in emission control and safety regulations on the prices of used vehicles can be shown to be identical and increasing. Typically though, these regulations only affect new vehicles and leave standards for existing vehicles unchanged, allowing the immediate effects of changes in these regulations on used vehicle prices to differ.
Let [S.sup.u] be the level of safety built into existing vehicles and [S.sup.m] be a new mandated level of safety that exceeds the previous (possibly mandated) safety level. Equilibrium in the new and used automobile markets requires that the utility of consumers be the same regardless of the type of vehicle they own. This implies that
(2) f[I - [R.sup.m]([C.sup.n], [S.sup.m]; [S.sup.m])] + d([S.sup.m])
= f[I - [R.sup.u]([C.sup.n], [S.sup.m]; [S.sup.u])] + d([S.sup.u])
with the right-hand side of this equation giving the utility of the owners of new vehicles, the left-hand side giving the utility of the owners of used vehicles, and [R.sup.m]([center dot]) and [R.sup.u]([center dot]) representing the rental values of new and used vehicles, respectively. The impact of an increase in mandated safety on used vehicle rental values can be found by implicitly differentiating equation (2) with respect to [S.sup.m], the new safety standard, and solving for [Delta][R.sup.u]([center dot]) / [Delta][S.sup.m].
(3) [Delta][R.sup.u]([center dot]) / [Delta][S.sup.m] = f[prime][([center dot]).sup.(-1)][rf[prime]([center dot]) / (1 - [e.sup.-rT])]
+ (-1)f[prime][([center dot]).sup.(-1)]d[prime]([S.sup.m]).
As equation (3) shows, the impact of an increase in mandated safety has two effects on the rental values of vehicles built prior to the change in safety. These effects are illustrated in Figure 1 with the initial equilibrium rental value, [R.sup.a]([C.sup.n], [S.sup.u]; [S.sup.u]), given by the intersection of demand curve [D.sup.a] and the supply curve, S.(2) The first effect is given by f [prime][([center dot]).sup.(-1)][rf[prime]([center dot])]/(1-[e.sup.-rT]) in equation (3) and represents the increase in the rental values of used vehicles as consumers attempt to substitute used vehicles for the now relatively more expensive new vehicles. In Figure 1, this shifts the demand curve from [D.sup.a] to [D.sup.b]. The second effect, given by (-1)f[prime][([center dot]).sup.(-1)]d[prime]([S.sup.m]) in equation (3), is the decrease in the value of used vehicles as the relative (and absolute) safety of new vehicles increases. This effect is represented by a shift in the demand curve from [D.sup.b] to [D.sup.c], giving a new equilibrium rental value of [R.sup.c]([C.sup.n], [S.sup.m]; [S.sup.u]). The impact of a change in emission control regulations would be found in a similar manner except these regulations do not produce any direct benefits for the owner of the vehicle. This implies that only the first effect will be present(3) and the equilibrium rental value of used vehicles,[R.sup.b]([center dot]), would be found in Figure 1 as the intersection of demand curve [D.sup.b] and the supply curve. This shows that the change in emission control regulations has a greater impact on the rental values of used vehicles if consumers place some value on the safety induced by safety regulations (in other words when d[prime](S) is not zero implying that the second effect is present). This implies a test for the value consumers place on the safety induced by safety regulations. If the effect of a change in emission control regulations on the prices (which are equal to the present value of the vehicle's rental values) of used vehicles is equal to (or less than) the effect of a change in safety regulations, then consumers do not value the safety induced by safety regulations.
If the second effect from the increase in safety regulations overwhelms the first effect there will be a drop in the rental values and prices of used vehicles. This implies that the change in safety regulations improved social welfare because automobile manufacturers were initially building vehicles with less than the socially optimal safety level. This is shown by factoring (-1)f[prime][([center dot]).sup.(-1)] out of the right-hand side of equation (3):
(4) [Delta][R.sup.u]([center dot]) / [Delta][S.sup.m]
= (-1)f[prime][([center dot]).sup.(-1)][-rf[prime]([center dot]) / (1 - [e.sup.-rT])
The term in brackets is the first-order condition from equation (1) and is multiplied by (-1)f[prime][([center dot]).sup.(-1)], which is negative. If the initial safety level, [S.sup.c], and the mandated safety level, [S.sup.m], are less than the socially optimal safety level [S.sup.*], the change in safety regulations improves social welfare. The term in brackets will be positive by the second-order condition, making the entire expression negative and implying that the rental values and prices of used vehicles fall when the social-welfare improving regulations are implemented. If [S.sup.c] is greater than [S.sup.*], the change in safety regulations decreases social welfare and the term in brackets is negative making the entire expression positive, implying that the rental values and prices of vehicles increase.(4) This implies a simple test for the social welfare effects of safety regulations. If used vehicle prices increase in response to changes in mandated safety levels, then those changes decreased social welfare; if prices decrease then social welfare increased.
III. EMPIRICAL MODEL AND DATA
The price change of a used vehicle from one year to the next is equal to that vehicle's depreciation plus any changes in its value due to changes in emission control and safety regulations affecting new cars plus changes in any other factors that affect the value of a vehicle.(5) Preliminary estimates were made using the vehicle's price change as the dependent variable. The error term in these estimates was heteroskedastic with its variance proportional to the square of the price of the vehicle. To eliminate the heteroskedasticity, the entire equation was divided by the vehicle's price, [P.sub.y](a). This made the dependent variable in the estimated model, shown in equation (5) below, the vehicle's realized depreciation rate or ([P.sub.y+1] - [P.sub.y])/[P.sub.y]. Because of this correction, the emission control, safety, and fuel cost variables are expressed as a percentage of the price of the vehicle at the beginning of the period.
(5) [[P.sub.y+1](a + 1) - [P.sub.y](a)] /[P.sub.y] (a)
= [Alpha] + [[Beta].sub.1][DG.sub.1] + [[Beta].sub.2]DA1 + [summation over] [[Gamma].sub.a] DCa where a = 1 to 6
+ [summation over] [[Theta].sub.a] DSa where a = 1 to 6 + j + a + [Epsilon].
As discussed above, the dependent variable is the vehicle's realized depreciation rate as a percentage of its price at the beginning of the period. The intercept term, [Alpha], and a series of age and manufacturer dummies, a and j, capture the vehicle's expected depreciation.(6) The age dummies, denoted by A2 through A6, capture how the depreciation rate of a two-through six-year-old vehicle differs from a one-year-old vehicle. The five manufacturer dummies represent how the depreciation rate of vehicles of a specific make differ from other vehicles. There is one dummy for each domestic manufacturer active during the sample period (AMC, Chry, Ford, and GM) and one, Japan, for all Japanese manufacturers together. There are six emission control variables, given by DC1 through DC6, where DCa is equal to that year's change in the cost of new vehicles (as a percentage of the price of the vehicle) due to changes in emission control regulations if the vehicle is a years old and zero otherwise. This allows the effects of changes in emission control regulations on used vehicle prices to differ by vehicle age. For analogous reasons, there are six similarly defined safety variables, given by DS1 through DS6. The coefficients on the emission control and safety variables are given by [[Gamma].sub.a] and [[Theta].sub.a], respectively, for an a-year-old vehicle. There are also two terms denoted by DG1 and DA1, with coefficients [[Beta].sub.1] and [[Beta].sub.2] respectively, that are equal to the changes in the vehicle's and its substitute's expected fuel costs (as a percentage of the price of the vehicle) due to changes in expected fuel prices. Finally, the error term, [Epsilon], captures the effects of all other factors that affect a used vehicle's depreciation rate.
The price data used to calculate the realized depreciation rates was collected from the July issues of the N.A.D.A. Official Used Car Price Guide (Eastern edition). The sample included 490 automobiles manufactured from 1970 to 1989. A vehicle was included if Consumer Reports had done a road test of that model. Approximately 20 to 30 models are road tested each year with at least three models of every vehicle class from sub-compacts to luxury vehicles being tested. Because Consumer Reports tends to do road tests of more popular vehicles, the earlier part of the sample is biased towards larger vehicles while the latter part of the sample is biased towards mid-sized and smaller vehicles. Price observations were collected for the years 1972 through 1991 on the sample vehicles when they were from one to seven years old.(7) All prices and costs (including regulatory and fuel) were deflated to $1990 using the (urban) consumer price index. First-differencing the prices of the vehicles (to calculate the depreciation rate) implies that the dependent variable can only be calculated for one- to six-year-old vehicles. This leaves 2477 observations of the dependent variable.
The yearly changes in the cost of new vehicles due to changes in emission control and safety regulations, measured in $1990, are summarized in Figure 2.(8) From 1972 through 1991, these regulations increased the cost of building new automobiles by $2300. Of those $2300, $900 was due to changes in safety regulations and $1400 was due to changes in emission control regulations. As shown in Figure 2, these costs do not increase at a stable rate. Episodes associated with changes in the regulations affecting occupant restraints occurring in 1973-1974 and 1989-1990 account for more than half of the increased costs due to safety regulations. The 1973-1974 cost increase was mainly due to the introduction of devices such as interlocking seatbelts and buzzers that warn a driver that a seatbelt is unbuckled. The 1989-1990 cost increase was due to the introduction of passive restraints such as automatically locking seatbelts.(9)
Episodes in 1974-1975 and 1980-1982 account for almost half of the increase in the cost of emission control regulations. The first is associated with the introduction of the emission standards for hydrocarbons, carbon monoxide, and nitrogen oxides. The second occurred as allowable emissions for these pollutants were cut by approximately 75% and as particulate emission standards were introduced. These changes resulted in the introduction of the catalytic converter.
Because fuel prices were so volatile in this time period, two variables are introduced in the latter four models to account for the effect of changes in expected fuel costs on used vehicle prices. DG1 equals the present value of the change in the vehicle's expected fuel costs due to changes in expected fuel prices. Its coefficient is expected to be negative, indicating that a vehicle's price is decreasing in its expected fuel costs. DA1 equals the present value of the change in the expected fuel costs of the vehicle's substitutes due to a change in expected prices. Its coefficient is expected to be positive indicating that a vehicle's price is increasing in its substitute's fuel costs. Fuel price expectations were separately estimated assuming current prices hold indefinitely into the future (static expectations) and using an ARMA process. The latter uses a secondary regression and required a correction in the estimated standard errors produced by the statistical package.(10)
The dependent variable, depreciation, is expressed as a negative. Therefore a negative coefficient on an independent variable implies that an increase in that variable simultaneously increases the vehicle's depreciation rate and decreases its price. The empirical model tests both hypotheses discussed in section II. If the coefficients on the safety regulatory variables are greater than or not significantly different from the coefficients on the analogous (in terms of age) emission control variables, then consumers place no value on the safety induced by these regulations. If the coefficients on the safety variables are negative and significantly different from zero, then used vehicle prices decrease in response to mandated increases in vehicle safety and these increases improve social welfare.
IV. EMPIRICAL RESULTS
The coefficient estimates for six different models are presented in Tables I and II. The second, fourth, and sixth models include year dummies (the coefficients on the year dummies are not reported) while the other three models exclude the year dummies. The first two models also exclude the fuel cost variables. The last four models include the fuel cost variables. Static expectations for fuel prices are assumed in the third and fourth models while an ARMA model is used to generate fuel price expectations in the fifth and sixth models. The coefficients on the intercept, age dummies, and manufacturer dummies are reported in Table I. These dummies indicate a depreciation rate of 17% to 25% depending on the age and manufacturer of the vehicle. This is consistent with previous estimates of automobile depreciation rates.(11)
The estimated coefficients on the emission control and safety variables are presented in Table II. The coefficients on the emission control variables are all positive, significantly different from zero, and tend to be smaller for older vehicles implying that an increase in the price of new vehicles due to changes in emission control regulations tends to have a greater impact on the prices of newer used vehicles than on older used vehicles. This is consistent with these regulations acting like a tax on new vehicles. The restriction that the coefficients on these variables are less than or equal to the coefficient on the analogous (in terms of age) safety variable could be rejected both as a group restriction and as a separate restriction at each age. This implies that an increase in the cost of new cars due to a change in emission control regulations has a greater impact on the price of used cars than an identical increase in the cost of new vehicles due to a change in safety regulations and that consumers value the safety induced by safety regulations.
The differing impacts that changes in emission control and safety regulations have on the prices of the existing stock of used vehicles are illustrated in Figure 3. Based on the coefficient estimates from the first model and in the absence of any regulatory changes, the age-price profile of a vehicle that cost $8000 new is given by the solid black line with circles representing the vehicle's predicted price at each age. A change in emission control regulations that increased the prices of new automobiles by $500 would shift the age-price profile out to the mixed dashed line in Figure 3 (with squares representing the price of the vehicle at each age). On the other hand, a change in safety regulations that increased the prices of new vehicles by $500 would depress the prices of most used vehicles, shifting the age-price profile downward to the simple dashed line (with triangles to indicate the vehicle's price at each age).(12)
Three of the six coefficients on the safety variables (for age one, four, and five) are negative and significantly different from zero. Two of the other three are typically negative but not significantly different from zero while the last is positive and not significantly different from zero. Both the restriction that all safety coefficients were equal and the restriction that all safety coefficients were identically equal to zero could be rejected implying that the prices of used vehicles fell when new safety regulations were mandated. This implies that the mandated increases in automobile safety increased overall social welfare and that automobile companies were providing less than the socially optimal safety level.(13)
This implication, to say the least, is surprising because it is inconsistent with the automobile firms maximizing profits as given in equation (2). It may have at least two possible causes. Consumers could have lacked information on the optimal level of safety and changes in regulations caused them to update their priors, increasing the value they placed on safety. The irony of this is that if regulators overvalue safety,(14) then the decrease in vehicle prices in response to the change in regulations [TABULAR DATA FOR TABLE I OMITTED] [TABULAR DATA FOR TABLE II OMITTED] may not imply an increase in social welfare. Alternatively, the demand for safety may have been increasing throughout this period and automobile firms would have increased vehicle safety regardless of any changes in regulations. The regulations could have resulted in lower used vehicle prices and still decreased social welfare if they increased the cost of obtaining a given level of safety. Since safety regulations mandate specific design features and equipment rather than levels of safety or safety expenditures, this possibility is likely. This makes the empirical results indicating an increase in social welfare that much more surprising.
This paper examined the impact of changes in emission control and safety regulations on the prices of used automobiles as a method of evaluating whether consumers valued the additional safety induced by safety regulations. The empirical results rejected the hypothesis that consumers place no value on the safety induced by safety regulations. They also indicated that prices of used vehicles decreased in response to changes in safety regulations, implying that these regulations may have improved social welfare and that automobile firms may have been building vehicles with less than the socially optimal level of safety.
The analysis and conclusions presented here are those of the author and do not purport to represent the views of the Department of Justice. I would like to thank mark Bils, Greg Werden, the participants of the applied workshop at the University of Rochester, the editor of this journal, and three anonymous referees for helpful comments on previous drafts of this paper. Any remaining errors are my responsibility.
1. R([C.sup.n], [S.sup.n]; S) is the rental value of a vehicle with safety level S, when new vehicles have safety level [S.sup.n] and emission control level [C.sup.n]. Since new vehicles are the marginal source of vehicles, it is the safety and emission controls levels of new vehicles (and the safety level of the vehicle in question) that is relevant for determining the equilibrium rental value of a vehicle.
2. The assumptions of this model imply that the supply of used vehicles in each period is fixed.
3. This simply means that d(S) and d[prime](S) are zero, making the second term in equation (3) also zero.
4. There is a third case in which the initial safety level is less than the socially optimal safety level and the mandated safety level exceeds the socially optimal level. To show the effect of the change in safety regulations on used vehicle prices and on social welfare requires integrating the change in rental value and utility, respectively, over the change in the safety level. Doing this shows that welfare-increasing changes in safety regulations will, as above, decrease used vehicle prices and welfare-decreasing changes will increase them.
5. Hall  shows that the intertemporal price change of a durable asset such as an automobile consists of three parts: deterioration, revaluation of the asset from changes in such factors as fuel costs and new vehicles prices (which may be due to changes in safety and emission control regulations), and obsolescence due to technical improvements in the quality of new vehicles. The regressions presented below specifically account for the first two factors but not the third one, which is assumed to be orthogonal to the included variables; and therefore its omission does not bias the coefficient estimates. The possibility that the omission of the obsolescence effect biases the coefficient estimates was tested by including a variable which explicitly accounted for the obsolescence effect. This variable represented the average change in the prices of new vehicles due to changes in their quality. The inclusion of this variable had no systematic impact on any of the coefficient estimates, indicating that the omission of obsolescence effects did not bias the coefficient estimates. These results are available on request.
6. Year dummies were excluded because their purpose is to capture year-specific changes affecting the depreciation rate. Because the regulatory cost changes are year specific, it is uncertain what the coefficients on the regulatory cost variables are measuring when the year dummies are included. Because of this, the models which exclude the year dummies variables will give more reliable estimates of the impact of changes in regulatory costs on the prices of used automobiles. The results of the models including the year dummies are presented; however, only the results from the models that exclude the year dummies will be discussed.
7. James Kahn provided me with 754 price observations on 156 models built from 1970-1976 used in Kahn . Some data were unavailable including the 1971 prices of 1970 model year vehicles and the prices of some six- and seven-year-old vehicles. No prices were collected after 1991, implying that prices for 1989 vehicles were only collected when they were one and two years old.
8. This figure is based on Bureau of Labor Statistics estimates found in the Motor Vehicles Manufacturers Association Motor Vehicle Facts and Figures, 1992, p. 87.
9. The possibility of adjusting the safety variable for those used vehicles that already conformed to the new safety standard was considered. However this produced unsatisfactory results. Because the Bureau of Labor Statistics data do not allocate how much of the change in vehicle costs is associated with each different safety regulatory change in a given year, it is impossible to separate the cost of each of the different safety regulatory changes in a given year. This made it difficult to allocate costs if the used vehicle in question conformed to only a subset of the changed standards. It also proved impossible to get information for all vehicles or even a large subset of them on which standards implemented after a vehicle was built that it conformed to.
10. See Murphy and Topel  for the details of this correction and Dunham  for more details on the fuel cost variables.
11. See Tables 6.6 and 6.7 in Wykoff for a summary of estimates from previous studies.
12. Figure 3 illustrates the effect of regulatory changes on the existing stock of vehicles. As noted in section II, the long-run effects (with the long-run being the time necessary for the vehicles affected by the change in regulations to completely replace the stock of vehicles existing at the time the regulations were implemented) of both types of regulatory changes are identical.
13. It may be argued that this does not account for the effect discussed in Peltzman  where making a vehicle safer for its driver makes the driver more reckless and a danger to other drivers and pedestrians. However, drivers should internalize this cost if it is reflected in the insurance rates of the vehicle.
14. See the Wall Street Journal, "Insurance-Claims Data Don't Show Advantages of Some Auto Safety Devices," 17 March 1994, Sec. A, p. 1, 7 for a discussion of several mandated safety features that have no impact on insurance claims and were possibly overvalued by regulators.
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Wayne R. Dunham: Economist, Antitrust Division of the Department of Justice, Washington, D.C., Phone 1-202-307-3704 Fax 1-202-307-3372 E-mail firstname.lastname@example.org…