IIIIIII III III II IIIIIIIIIIIII w _ 31300099 5104 THESIS 11:2 ' * * This is to certify that the thesis entitled AUTOMOBILE SCRAPPAGE AS AN ECONOMICALLY MOTIVATED EVENT presented by EDWARD ANTON WEBER has been accepted towards fulfillment of the requirements for _Eh_._D_.__dcgree in Economic S mar/L: Major professor Date October 9, 1981 0-7 639 RETURNING MATERIALS: IV1£31_] PIace in book drop to LIBRARJES remove this checkout from —;— your record. ELISE will be charged if book is returned after the date stamped below. r 3..- “94¢th 993 EN AUTOMOBILE SCRAPPAGE AS AN ECONOMICALLY MOTIVATED EVENT By Edward Anton Weber A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Economics 1981 ABSTRACT AUTOMOBILE SCRAPPAGE AS AN ECONOMICALLY MOTIVATED EVENT By Edward Anton Weber The reasons cited for scrapping or selling an auto are many: "the auto wore out," "the car was in an accident," "the car worked poorly," etc., etc. These reasons can all be attributed to economic decision making. In each case the cost of repairing the car is judged to be greater than the value of its future services. The main problem addressed by this dissertation is to incorporate the economics of scrappage into the main body of economic theory regarding the markets for durable goods. In previous studies of durable goods scrappage is presumed to be determined by technical factors relating to the good itself. Herein we have allowed scrappage to fluctuate with movements in economic factors, and we show that scrappage is highly sensitive to movements in economic variables, even after the effects of changes in the age distribution of autos are taken into account. Questions of technical and structural changes are addressed in empirical tests. The conclusions show that allowing for these changes has important effects on the results. To further pursue the effects of changes in the industry the data are disaggregated into age and make- groups. The findings demonstrate that real interest rates, Edward Anton Weber prices of complementary goods, and consumers' expectations about the future health of the manufacturer are all important determinants of scrappage. Finally, a model of the linkage between the market for new cars and scrappage is built. This model, in conjunction with empirical results, allows the validity of major assertions of previous auto demand models to be considered. The findings suggest that revisions should be made to many of the commonly used empirical models of auto demand. © Copyright by Edward Anton Weber 1981 To my parents iii ACKNOWLEDGMENTS One cannot complete a program of graduate study without the assistance and encouragement of a great many people who deserve recognition for their efforts. The assistance of Daniel B. Suits, my dissertation committee chairman, was always generously given. Dr. Suits displayed a willingness to teach me the fundamentals of put- ting together a project, and he always had something instruc- tive to add. His skills and encouragement made my task much easier. The other members of my committee: Kenneth Boyer, Bruce Allen, and Charles Larrowe were also extremely help- ful in providing technical advise, editorial assistance, and moral support. A number of other faculty members also provided assis- tance. In particular, Richard Anderson was very helpful. Many of my fellow graduate students have also contri- buted to this effort through their advise and encouragement. My thanks go out to Marie Connolly, Steven Husted, Paul Koch and Renee Stahle; all of whom helped tremendously in the completion of this project. Finally, Sandy Bolton deserves recognition for the care- ful and expedient way in which this manuscript was typed. iv LIST OF TABLES . LIST OF FIGURES CHAPTER ONE: CHAPTER TWO: CHAPTER THREE: TABLE OF CONTENTS INTRODUCTION AND SUMMARY . AGGREGATE AUTOMOBILE SCRAPPING . The Stock Adjustment Model of New Car Demand . . . . Automobile Holding . . . The Supply of Junk Autos . Demand for Junk Autos The Scrapping Function . Results . . . Vintage Effect . Conclusions and Summary Footnotes APPENDIX 2.1: EFFECTS OF ECONOMIC VARIABLES ON CHOICE OF SCRAP DATE APPENDIX 2.2: EXTENSION OF PRICE SERIES . . . . . . . . . . . EFFECTS OF ECONOMIC VARIABLES ON AGE GROUPS OF AUTOS . . . . Introduction . . The Regression Equations . The Variables in Detail General Considerations Results . . Pooled Regression . . Results of Pooled Regression . Conclusions and Summary Footnotes Page vii . viii CHAPTER FOUR: CHAPTER FIVE: MAKE-SPECIFIC SCRAPPAGE Data Considerations The G.M. Makes Other Makes . . . . . . . . The "Orphan Car" Influence . Choice of Time Period Summary and Conclusions Footnotes IMPLICATIONS FOR AUTO DEMAND MODELS The Market For New Cars and Scrappage . . . . External Influence Summary and Conclusions Footnotes VARIABLES AND DATA SOURCES LIST OF REFERENCES vi 80 83 86 87 88 91 Table 2. 2. l 2 .4a .4b LIST OF TABLES Estimates of the Age- Scrapping Relationship; 1930-1977 and Three Sub- Periods A Test for Homogeneity of the Age- Scrapping Relationship . . . . . . Scrappage as a Function of Price, Income, Vintage and Age Estimated Coefficients for Vintage Dummy Variables . . . . . . . . . Estimated Coefficients for Vintage Dummy Variables . . . . . . . Gain in Explanatory Power From Addition of Price, Income and Vintage Variables Homogeneity of Scrapping Functions with Price, Vintage, and Income Variables Extension of Price Series Estimates of Age- Specific Scrapping Functions . Significance of Loss Due to Pooling Age Groups Coefficient Estimates of Make-Specific Scrap- ping Functions . Partial R2 for Make . Scrappage Functions for Studebaker, Hudson, Nash, Packard, and Desoto . vii Page 15 l7 19 20 21 22 22 37 44 47 64 68 73 LIST OF FIGURES Fitted Values From the Age- Scrapping Relationships Over 1930- 1977 and Three Sub- Periods . . . . . . . . Percent Differences From Mean Scrap Rate for Five Makes Percent Differences From Mean Scrap Rate -- G.M. Makes Percent Differences From Mean Scrap Rate (1950-1956) Shift of New Car Supply and Effects on Scrappage . . Effects on Scrappage of a Shift in New Car Demand . . . . . . . . . . . . . . External Influences on the New Car Market and Scrappage viii Page 16 59 61 66 82 82 85 CHAPTER ONE INTRODUCTION AND SUMMARY This dissertation consists of three empirical essays which are linked through the use of a common data set. These essays explore the nature and determinants of auto- mobile scrapping in the U.S. The work herein builds on the theory of machine life, on the specification of demand functions for durable goods, and on the relationship between automobile make and expected life-span. Chapter Two develops the theory of automobile scrap- page from the micro-economics of machine life. This theory is then tested with an analysis of aggregate scrappage data. Scrappage is shown to be mainly influenced by age of auto. Large variations in rates of scrappage are, however, associated with movements in new car price, per capita in- come, and technical change in the auto itself. Chapter Two also shows how many commonly used auto demand functions can be improved with the addition of scrapping information. For example, changes in the age distribution of autos are shown to have large effects on scrappage, and therefore, on replacement demand. Existing auto demand models can easily be reworked to include this information. 2 The second essay (Chapter Three) deals with the in- fluence of the real interest rate, repair price, price of gasoline and demographic change on individual age groups of automobiles. The results show that, while the real interest rate has a negative overall effect on scrappage, this interest rate has a positive effect on the scrappage of very old automobiles. Therefore, the effects of increased real interest rate are that the age distribution of automobiles will be compressed. Changes in the age structure of the population are shown to have very large effects on auto scrappage. This is to be expected in a market which is dominated by the replacement motive. When the pool of prospective owners is generally younger, and at a low point in the life cycle of income, automobiles have a longer expected life-span. Repair prices have increased markedly over the postwar period, and this has had a major influence on scrappage. Rising repair prices are shown to have shortened the expected life-span of automobiles. The price of gasoline has had a generally small and negative effect on scrappage. Until recently, increased gasoline prices generally caused a delay in the replacement of autos. This effect may change as more efficient autos are developed. Chapter Three also looks at the question of the aggre- gation, across different age groups, of automobile scrappage rates. The results show that, while the loss from pooling 3 scrap rates of autos 6-11 years of age is statistically significant, the pooling operation provides benefits in finding the direction and magnitude of the effects on scrappage of economic variables. Tests of the pooling hypothesis do show, however, that information about the scrappage of very old or fairly new cars adds little to our understanding of scrappage as an economic event. The effect of automobile make on scrappage is the topic of Chapter Four. We show that large differences in scrap rate are make-related. Furthermore, it is also shown that these make-related differences in scrappage are not only the result of durability differences, but are largely affected by demand factors in the used car market. These three essays provide us with a new way of look- ing at scrappage as an economically motivated event. The importance of demand elements is stressed, and it is shown throughout that demand factors play an important part in the determination of scrap rates. Chapter Five explores the relationship between new car demand and scrappage. We show that new car prices have been mainly influenced by demand shifts over the prewar period, and since 1960. During the late 1940's and 1950's, however, new car prices were primarily affected by shifts in new car supply. The implications of these findings are that many common specifications of auto demand are subject to simultaneous equations bias over the periods when demand shifts are prevalent. CHAPTER TWO AGGREGATE AUTOMOBILE SCRAPPING In this chapter we examine the influences of economic forces on aggregate automobile scrapping. We build a model of automobile holding which is used to develop hypotheses about the economic aspects of the decision to sell or trade a car. These hypotheses are then tested with an analysis of automobile registration data. It is important to develop a scrappage model because scrappage is closely related to durable goods demand. We are able to show that scrappage is an economic event largely influenced by price, income, technical change, and the age distribution of the stock of autos. We also show that the age-scrapping relationship has undergone large changes over the past 50 years. Much of this structural change can be attributed to the postwar distortion in automobile markets and to technical change in the auto itself. The Stock Adjustment Model of New Car Demand The stock of automobiles is completely determined by new car sales and by scrappage. In this paper we examine the linkage between new car sales and the scrappage of old cars. We are interested in examining some of the 5 6 commonplace perceptions of the way in which scrapping occurs. In the literature the most common approach to the determination of the stock of autos maintains that the stock of autos (At) changes by some percentage (a) of the difference between the desired stock (A?) and the stock in the previous period (At-l): At - At-l = a(A§ - At-l) (2.1) The quantity of new cars purchased is equal to the change in the stock of autos plus scrappage. In its sim- plest version the model asserts that scrappage is equal to a fixed percentage (6) of the stock during the previous period, and that the desired stock is a function of price (P) and income (Y): scrappage = 6 A (2.2) t-l A? = f(P, Y) (2.3) The demand function for new cars is obtained by sub- stituting (2.3) into (2.1), and adding scrappage to both sides:1 At - At_1 + a At__1 = o:[f(P, Y) - At_1] + a At_1 (2.4) One theoretical problem with this model concerns the desired stock of automobiles. It is not clear hOW'We arrive at the desired stock. If stock demand is our primary motivation, then scrappage should be endogenous to the model so that we can adjust the stock by altering the rate of scrapping. Another theoretical deficiency is the assertion that scrappage will be equal to a fixed proportion of the pre- vious period's stock. This neglects both the impact of changes in the age distribution of autos on scrappage and the effects of economic variables on scrapping. Older cars are more likely to be scrapped than are late model cars; therefore when the stock is older we would expect scrappage to be greater. Scrappage is also an economic event in that changes in prices, incomes, etc., may all affect economic actors who collectively determine the stock of autos. Westin (1975) shows that a large portion of the pre- vious period's stock is irrelevant to new car demand in the context of infrequent replacement. Replacement demand, which dominates the automobile market, should be highly volatile because replacement can easily be delayed. The stock adjustment model, however, views replacement as a constant percentage of the stock during the previous period. To improve on this view of replacement demand we build a model of automobile holding. From this model hypotheses regarding the economic motivations to replace an automobile are developed. Automobile Holding An automobile is held as long as the present value of its expected future services is greater than the present 8 value of the expected cost of these services. The quasi- h rent of the ith consumer or firm from the jt automobile in time, t, (QRijt) is equal to the discounted difference between the value imputed to the services of the car (IV ) and the expected operating cost of the vehicle ijt (0C ). plus the discounted expected resale value of the ijt machine (VjT) at the time of resale (T). For the sake of convenience we net out intermediate trades so that T is the scrap date while VT is the scrap value of the car. T QRijt = [O (Ivijt - oc ) e'rt dt + v. e‘rT (2.5) ijt 3T We posit that the imputed value of the services of a specific auto to an individual (IV. ) will decline over ljt time as the auto ages. We also believe that (IV ) will ijt depend upon the price of substitute autos (Pi), income (Yit)’ and a portmanteau vector (Xit) to account for consumers' tastes. Operating costs are believed to increase with time as the vehicle ages, and to be a positive function of the prices of goods and services which are complementary to automobiles (Pg). Substituting these arguments into equation (2.5) yields: T _ S C -rt (2.6) -rT + VijT e By examining the effects of these arguments on the 9 quasi-rent of the individual we can determine the causes of variation in the scrap date. From the determination of scrap date a theory of the supply of junk autos can be obtained. The Supply of Junk Autos The supply schedule for scrap autos consists of the number of autos that owners or car dealers are willing to sell at any given price. The individual owner chooses the date of sale by attempting to maximize the quasi-rent ' available from a given auto with respect to this sale or trade date.2 .(PC, T)] e‘rT J -rT -rT _ d(QR)/dT = [IVij(PS, T, Y, X) - 0ci (2 7) ‘ rVijT Equation (2.7) states that the automobile should be replaced when the discounted net benefits are equal to the discounted costs of operation. The second order condition for this maximum.requires that: §__%§ < 0 d T We can see from equation (2.7) that increased operating cost, interest rate, or scrap value will cause the maximum to occur at an earlier date. Increased imputed value will move the maximum to a later date; prolonging the life of the car. Therefore: 10 dT03nd-aY—>O. dP A formal derivation of these effects is shown in Appendix 2.1. The marginal owners' quasi-rent is equal to the value of the car. An increase in operating cost, interest rate, or scrap value will cause the quasi-rent of the marginal owner to be less than the value of the car. Likewise, a decline in the price of substitute autos indicates a rela- tive abundance of substitutes, and the value imputed by the marginal owner to the services of his automobile will decline. Decreased quasi—rent of the marginal owner implies that quasi-rent will be less than the value of the car -- causing the marginal owner to either trade the car, or to personally scrap it. By aggregating across all car owners we can postulate a supply relation between the quantity of junk autos offered for sale and the scrap price. Arguments of the quasi-rent function, aside from scrap price, are shift variables for the supply of junk autos (QS). Increased 'price of substitute autos will shift the supply function to lower quantities: s ig_< O BPS 11 Increased interest rate (r), prices of complement goods (PC), or income (Y) will shift the supply function to higher quantities: S S S S 2.9_>029_>02Q_>029_>0. 8V ’ 3r ’ 3Pc ’ BY The supply function for junk autos is: Q8 = f(V. r. PS. Y. x. Pc) (2.8) Demand for Junk Autos Demand for junk autos by scrap dealers is closely related to automobile age. Late model cars have many valuable parts which can be resold. The parts in early models are generally not as valuable, and therefore the price of a junk car is largely determined by its age. In our model we segment junk autos by age. The price of junk autos of a given age, A, is a function of the quantity of junk autos in that age group (QA), and a vector of other variables that affect the demand for junk (2): vT = g(QA. 2) (2.9) The intersection of the supply and the demand for junk automobiles determines the quantity of vehicles to be scrapped. By substituting equation (2.9) into equation (2.8) we solve for the quantity of vehicles to be junked: 0A = h(2t, rt, Pi, Yt, it, P?) (2.10) 12 This reduced form can be used to test hypotheses regarding the behavior of scrappage with respect to economic events. The ScrappinggFunction The most important determinant of the probability that a car will be scrapped during a given year is its age. By simply considering scrappage as a function of automobile age we can improve on the stock adjustment mechanism. To investigate the age—scrappage function we estimated equa- tions in which scrap rate was regressed on automobile age. Auto registration data collected by the R. L. Polk Co. were used to obtain a working definition of scrapping. These data consist of the number of registered autos in each vintage cohort for each year of the sample. The number of vehicles scrapped during a year is mainly in- fluenced by the size of the stock of autos. To avoid this influence in our time series we calculated rates of scrapping (SV,t) by subtracting the quantity of vintage, V, autos in year t+1, (QV,t+l) from the stock of the same vintage autos in year t, (QV,t)' The difference was divided by QV,t to estimate the rate of scrapping.3 The great majority of vehicles which are de-registered are also scrapped. Some measurement error is created by export of used vehicles and temporary de-registrations, but among older autos measurement error is a small percentage of de-registrations. Scrappage data for relatively young 13 cars is of much lower quality; so we truncated these data to eliminate consideration of cars less than 5 years of age. Younger autos have low rates of scrapping; scrap rates are expected to increase with age until a maximum.is reached. Scrappage rates of still older vehicles (some are collector's items) tend to fall below the maximum. There- fore the functional form chosen must be at least flexible enough to capture this behavior. A good candidate for this job is the cubic spline function. We estimated cubic spline functions in two knots via O.L.S. (Suits, Mason, Chan, 1978): _ 2 3 3 SV,t — bO + blAv + b2Av + b3A.V + b4(Av - 7) D1 (2.11) 3 where: {0; A 3,7} {0; A < 10 D = D = — 1 l;A>7 2 l;A>lO} at is a random disturbance term. The knots were arbitrarily placed at ages 7 and 10. Because of the structural distortion in auto markets immediately after World War II, due to the absence of 1943- 1945 vintages, we fitted scrapping functions over four separate time periods: 1930-1942, 1947-1959, 1960-1977, 1930-1977. These three sub-periods were chosen because our data set includes cars up to 14 years of age, and therefore 14 the vintage dislocation of 1943-1945 leaves our data set in 1959 with the absence of 14 year old cars during that year. Coefficients of equations fitted to the three sub-periods are given in Table 2.1. The results indicate that from 40 to 90 percent of the variation in scrappage rates is associated with age of vehicle. The lowest R2 is found for the immediate post World War II period, when the absence of wartime production and postwar distortions resulted in particularly low scrappage rates for cars of any age. In addition, as shown in Figure 2.1 and as confirmed by analysis of covariance, calculated age-specific scrap rates vary significantly among the time periods. Figure 2.1 shows that the age-scrapping function has changed markedly over time. The lowest scrap rates are for the 1948-1959 subset of the data, while the highest levels of scrapping occurred during the prewar period. In Table 2.2 we test the significance of the difference between scrappage functions estimated over the three subsets. The calculated F-ratio is highly significant; showing that significant changes have occurred in the age-related scrap- page. Changes in rates of scrappage may be caused by changes in automobile prices, by technical change in the auto itself, by changes in the production and distribution technology of automobiles, by changed incomes of consumers, by demographic shifts, and by institutional factors such as 15 Table 2.1: Estimates of the age-scrapping relationship; 1930-1977 and three sub-periods.* Tbme Period 1930-1977 1930-1942 1948-1959 1969-1977 Isgggggiggt Coefficient Estimates Constant .299498 .938977 -1.29252 .633661 AGE .131829 0.483810 .637776 .262423 (.974) (1.854) (1.525) (.506) (A08)2 .019544 .083456 -.103741 .035027 (.150) (.285) (.235) (.078) (AGE)3 .000728 -.004372 .005672 .001296 (.008) (.014) (.012) (.004) (AGE - 7)3 01 .000131 .006386 -.009169 .000319 (.009) (.018) ( 014) (.005) (AGE - 10)3 02 .001912 -.00234 .008552 .001665 ( 005) (.009) (.007) (.002) SSE .67063 .986034 .312282 .143033 R2 .54 .65 .46 .90 # Observations 360 117 81 162 F (8's = 0) 82.0 41.0 13.0 283.9 * Standard errors are in parentheses. 16 Scrap Rate .5 ' .4 - . x .3 x O * * . x 1 .2 ' )1 * o x 7" . x * o o o o l * o i x o o * 0l___ ’3 ° 5 6 7 8 9 10 ll 12 13 Age Key: - = 1930-1942 0 = 1948-1959 * = 1960-1977 x = 1930-1977 Figure 2.1: Fittgd values from the age-scrapping relation- ships over 1930-1977 and three sub-periods. 17 Table 2.2: A test for homogeneity of the age-scrapping relationship. Mean QEMEzBeEie unrestricted 1.441349 342 .004214 sum of squares restricted-unrestricted sum of squares 1.229281 12 .1024401 24.3095 the absence of wartime production. To incorporate these explanations into our analysis of scrapping we add variables to the scrapping function. The income variable is NNP per capita over the age of sixteen; deflated by the CPI. We expect the income effect to become larger over time as auto markets are increasingly dominated by the replacement motive. As a price variable we used the new car component of the CPI deflated by the CPI for all items.‘I The construc- tion of these variables is described in detail in the data appendix. Technical change in the automobile is very important in the explanation of the differences between prewar rates of scrapping and postwar scrappage. These technical changes are modeled by including dummy variables for the different vintages in the study. We expect that postwar vintage autos will be more durable than those built before the war; with the exception of cars built in the late thirties which survive the war. 18 The scrapping function resulting from the addition of price, income, and vintage effects has the form: _ 2 3 SV,t — a0 + a1 Av + a2 Av + a3 A.v 3 3 + as (AV - 10) D2 + 06 Pt + a7 Yt (2.12) + 1 "MS 1 mi Vi + €v,t where: _ ;At>7 ; otherwise - A > 10 ’ t D2 = { 1 0 l 0; otherwise 1; in vintage i 0 ; otherwise Results The addition of price, income, and vintage variables adds greatly to the explanatory power of the scrapping functions, as shown in Table 2.5. The largest gains in explanatory power are the 31 percent gain over the full data set and the 30 percent gain in the 1948-1959 subset. These gains in R2 are large but, as shown by analysis of covariance in Table 2.6, the addition of these variables does not homogenize the scrapping relationship. The F-ratio calculated in Table 2.6 is highly signi- ficant. This shows that the age-scrapping relationship has l9 Table 2.3: Scrappage as a function of price, income, vin- tage and age.* full Variable sample 1930-1942 1948-1959 1960-1977 Constant .561121 1.41209 -.236818 .077083 AGE .204589 -.602406 365641 .268998 (.560) (1.368) (1.080) (.323) (A08)2 .029672 .101221 -.061874 .036359 (.086) (.210) (.166) (.050) (AGE)3 .001233 -.005343 .003653 .001365 (.004) (.011) (.008) (.003) (AGE - 7)3 D1 .000503 .007938 -.006871 .000260 (.005) (.013) (.010) (.003) (AGE - 10)3 02 .001528 -.003546 .008235 .001660 (.003) (.006) (.005) (.002) Price .172414 -.253395 -.352950 .246827 .051028) (.169100) (.155259) .111979) Income .022689 .018358 -.021168 .065613 .013439) (.026147) (.054146) .008574) F-ratio for vintage** 9.536 3.561 1.755 5.816 R2 .87 .85 .80 .97 SS .739395 .420107 .114359 .047215 # Observations 360 117 81 162 * Standard errors are in parentheses. ** F-ratio for vintage tests the null hypothesis that Estimated vintage effects there are no vintage effects. are shown in Table 2.4. .mmwmucfl> amm3umn GOmHHmano mo mmmm Mom oumw ou 85m ou vmcwmuumcoo Goon o>m£ muaofiofimmmoo mwmuafi> « 20 asomuo. 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HN> H50000.: 00> 000000.: 00> 0000HN. 00> 0NNON0. 00> 000000.: 50> 00000H. 0H> 000000.: 50> 000050.: 00> 005HOH. 0H> 0NOHHO.: 00> H50000.: 00> 00000H. 50> ucmfluwmmmoo manmwnm> ucmwowmmmou manmwum> unmfiofimmmoo mHQMflHm> 550H:000H 06m 6068 Hash ¥.mmanmwum> 05550 mwmucfi> How mucmwowwmooo vmumawumm "500 0.0 maan 22 Table 2.5: Gain in explanatory power from addition of price, income and vintage variables. 1930- 1930- 1948- 1960- 1977 1942 1959 1977 R2(with Price Income 84 80 72 96 and Vintage) ' ° ° ° -2 . . R (Without Pr1ce Income and Vintage) .53 .63 .42 .90 A R2 .31 .17 .30 .06 Table 2.6: Homogeneity of scrapping functions with price, vintage, and income variables. Mean d: Square F-Ratio unrestricted sum of squares :581681 275 .002115 restricted-unrestricted sum of squares .157714 25 .006309 2.98277 23 changed over the past 50 years. ,As regards the differences between the 1930-1942 scrappage function and the 1948-1959 function, these findings confirm Walker's (1968) observa- tion of large differences in scrap rate between the prewar and postwar periods. Walker did not attempt to explain this, but it is fairly clear that the absence of wartime vintage auto caused individuals to preserve, in use, prewar vintages. To explore this further we can see from Table 2.4 that the coefficients estimated for vintage dummy variables are all negative for cars produced during the 1930's and early 1940's. This indicates that these automobile vintages had lower than average scrap rates. This could be explained by quality differences. It is highly likely that the quality of new cars improved greatly from 1917 to 1942, and it is also quite reasonable that cars produced immediately after the war were of generally poor quality. Materials shortages and the ease of selling new cars into a market characterized by excess demand probably had an adverse affect on quality. These two explanations: quality differences and the absence of wartime vintages, are sufficient for understand- ing the changes in the age-scrapping relationship between the 1930-1942 and 1948-1959 periods. This structural change has important effects on the market for new cars. Interesting findings regarding these effects are shown in the scrapping functions (Table 2.3) which include income and price variables. 24 The price coefficient is negative and highly signifi- cant over 1930-1942. The price coefficient estimated over the 1948-1959 period is also negative and very significant. Over the 1960-1977 period, however, this coefficient is positive and significant at the .05 level. The price coefficient estimated over the full sample is negative and highly significant. In Chapter Five we address the possible causes of this change in sign, and we find that this has major implications for the use of some common specifications of auto demand.6 The income coefficient estimated over the full sample (1930-1977) is significantly positive at the .05 level. The positive influence of income on scrap rate implies that the income elasticity of demand for used cars has generally been negative. Over the first sub-sample (1930-1942) the income coefficient is positive, but insignificant. This is evidence of a trend towards saturation in auto demand. The income coefficient estimated over 1948-1959 is negative and insignificant. This supports the view that the postwar automobile scarcity disrupted the scrapping relationship. The income elasticity of used car demand apparently became positive as a reaction to the shortage of automobiles. Since 1960, used cars have apparently returned to their status as inferior goods. The income coefficient estimated over 1960-1977 is positive and highly significant. In Park's (1977) study he was unable to find any 25 evidence of an income effect on scrapping. He used a series of scrap rates which includes the entire postwar period. Our results suggest that the income effect changed from negative to positive over 1948-1977. These income effects apparently offset one another when the entire series was used. Consideration of the postwar vintage dislocation has helped us isolate the income effect and to understand why it has changed. Vintage Effect The effect of vintage on aggregate scrapping is very strong. The addition of vintage dummy variables to the scrapping functions adds about ten percent each to the explanatory power of the 1930-1942 and to the 1948-1959 regressions. The increase in R2 due to the addition of vintage variables is only about .04 for the 1960-1977 equations, but R2 increases by .20 when vintage dummies are added to the equation estimated over the full sample. The F-ratio for vintage (Table 2.3) tests the signifi- cance of these increases in explanatory power. The contribution of vintage to explanatory power is significant at the .01 level for the full sample and for the equations estimated over the 1930-1942 and the 1960-1977 time periods. The contribution of vintage to the equation estimated over 1948-1959 is significant at the .05 level. The vintage effects (Table 2.4) estimated over the 26 period 1930-1942 are for automobiles built between 1917 and 1937. These coefficients generally become smaller from 1917 to 1937 indicating that scrappage was lower for later models. This is the result of the advancements in auto- mobile technology, and the wartime scarcity of autos. The vintages with the highest scrap rates are: those cars built in the early 1920's, cars built right after the war (1946-1953), and cars built during the late 1950's (1957- 1959). Cars built immediately after the war were probably of low quality due to the materials shortages, and the ease of selling cars into a market characterized by excess demand. The high rates of scrappage associated with autos assembled during the late 1950's may be related to style changes and to the high level of experimentation with mechanical components which took place during this era. For example, electronic accessories such as air condition- ing, power window lifts, and power seats came into much wider use during this period. Gadgets which were introduced during this period include the retractable steel top, swivel seats, the push-button transmission, and electronic eyes which adjusted the rear view mirror upon sensing over- taking headlights.7 During this period the industry was also involved in a horsepower race (Fisher et al., 1962) and cars became more powerful. It is quite possible that the physical durability of the automobile suffered from these changes. 27 On the demand side of the market obsolescence became an important factor. The styling changes of 1956-1961 were so frequent as to cause autos to look out of date shortly after their introduction. Tail fins, dual headlights, dual ratio antennae, and colored tires adorned the latest models. The effect of this obsolescence was to reduce the value imputed to the services of a used car; leading to more frequent trade-ins, and hence more scrapping. Autos built in the early and mid 1960's were more durable than average. During this period considerable consumer backlash to the styling excesses of the late fifties surfaced. Volkswagen started.making serious in- roads into the domestic market in 1957; by 1961 the domes- tic manufacturers had responded with compact automobiles. These cars were much simpler than the standard size autos. They did not feature yearly re-stylings, tremendous horse- power, or electrical wizardry. The simplicity of these autos, in conjunction with their large market share, probably enhanced the durability of autos built in the early and mid 1960's. On the demand side of the used car market the longer life-spans of 1961-1967 autos may be partly the result of abnormally high demand for used cars in the early 1970's. These demand conditions could be caused by the tremendous influx of young people into auto markets as a result of the baby boom of 20 years prior. The 1961-1967 vintage autos were 7 years old or older during 1968-1974. During this 28 time the children born from 1952 to 1957, peak years for the baby boom, were between 16 and 22 years of age. Given the low incomes associated with young persons, the demand for these older cars may have increased due to this demo- graphic change. Conclusions and Summary In this paper we have shown that automobile scrapping is highly influenced by age, new car price, income, and vintage. The results concerning the age-scrapping function show that, in the context of an annual model, we can improve on the commonly used stock adjustment mechanism. By simply specifying scrappage as a function of these variables we can eliminate one assumption (equation (2.2)) from this model. The results concerning the heterogeneity of the age scrapping function are interesting from a methodological point of view. Both Walker (1968) and Boulding (1955) commented on the effect of postwar vintage dislocation on scrappage. Walker found large differences between prewar and postwar auto scrapping. Boulding's paper looks at the effect of vintage dislocation on the new car market. White (1971) implicitly allows for the effects of vintage dis- location by only considering postwar vintages. Parks, in some more recent studies (1979, 1977), does not allow for any structural change in the scrapping func- tion. The importance of this is borne out in our result 29 regarding the income effect. By not considering the causes of structural change, important results can be overlooked. 30 Footnotes For examples of this type of auto demand model, see Analysis of the Wharton EFA Automobile Demand Model (1979), Hess (1977) or Faucett (1976). 2 By allowing operating costs and scrap value to be exogenously determined, we are implicitly limiting the choices of consumers to the choice of scrap date. For an analysis in which consumers simultaneously choose mainten- ance program and scrap date see Nafislund (1967). 3 Using vintage and time subscripts (V, t) is equiva- lent to specifying an age and a time (a, t). Our change to the vintage subscript is only done to illuminate cohort features of vintage groups. 4 Calculation of a price index for the prewar period is shown in Appendix 2.2. 5 We also tried a specification which used dummy variables to allow for different intercepts in 2 of the 3 time periods. This specification did not significantly reduce the sum of squares. For examples of these auto demand models, see Suits (1958), Chow (1957) and Nerlove (1957). 7 A wealth of information on automobile features during the late 1950's can be found in the "Chronology of Events" sections of various editions of Ward's Automotive Yearbook, or the chapter dealing with the 1950‘s in Automofiiles of America, Automobile Manufacturers Associa- tion (1970). APPENDIX 2.1 Effects of interest rate, income, scrap price, prices of substitutes and prices of complementary goods on the choice of scrap date by an individual. From equation (2.7), scrap date is chosen when quasi- rent has been maximized. Taking the total differential of (2.7) and dividing out e-rT leaves: 31V 31V BIV BIV 30C WdT+-a——-PSdPS+-é—-X dX+_§Y_dY'—3T_dT- 2 (A2.l) 80C c d V ——— dP - dT - V(T) dr + = 0 8P° raT d'r2 Solving (A2.l) for the effect of interest rate on scrap date yields: dT = a? 800 ch + V(T) _ gig dPS _ 912 dX _ _;y dY 3L dzv aPcdr BPS—d? aXd? BYT dr—Z 81V _ 80c _ r av (A2.2) 8T' 8T HT We hold consumer tastes constant with respect to interest rate, E? = 0. Postulating that interest rates have a 3 positive effect on price of substitute (new) autos, dP > 0, H? a positive effect on the prices of complementary goods, 31 32 c - ' %%7 > 0, and have a negative influence on income, §§'< 0, allows us to evaluate the numerator of (A2.2). This numerator will be positive if (A2.3) holds: p0 2 BOCd 31V dY ]. d V aIV dPS 8Pc F + V(T) 8)! a? ' a; dTZ > 5‘3— (A2.3) The denominator of (A2.2) is negative because %%¥is negative md 330C is clearly positive while r 5% is small relative to the other arguments. Therefore, (A2.2) is negative and interest rate negatively affects the optimal holding period of the individual. We find the effect of income on scrap date by solving (112.1) for g; : dT = HY §_I__dPS+§_I_VdX+3_Y_BIV__EflgdPC_ V(T)d dr+d2Vl 3P3 ay— ax a? 3P6 ‘dr d—Tz a? (112.4) 300+ r dV _ Ely "8T HT 8T To simplify the evaluation of (A2.3) we rule out any effect that an individual's income may have on the interest rate, 3% = 0, or the price of substitute autos, %E: = 0. Clearly, increased income, particularly wage income, in- creases the value imputed to the services of an auto, %%¥ > 0. Income also has an effect on prices of complements. One of these complements is the time spent while having the vehicle serviced or while being otherwise inconvenienced by the vehicle. If increased income increases the value of 33 c . one's time then %%r > 0. Consumers' tastes would probably be changed to favor newer cars in the event of increased 81V dX income. Therefore, 75? HY < 0. The denominator of (A2.3) is positive because %%§ is positive and %%¥ is negative and r g¥ is presumed to be small. The evaluation of (A2.3) is indeterminant because we do not know whether the effect of income on imputed value is greater or less than the influence of income on tastes or operating cost: C 9.1.! 31V dx soc dP (A2.5) a—adYaPch AV However, it does seem likely that the right hand side of (A2.5) is larger than the left. The effect of scrap price on scrap date is found by solving (A2.1) for the effect of scrap price on scrap date. d1= EIV' idPs+§_I_V_dX+§_I_VdY__a_§_dPC_Vdr+d2Vl BPS-JV— ?) 3V BY 3V ape—dY— 3V dTZEI'Y' 129+r3V_£Y_ (A2.6) 8 ET 8 Scrap price is presumed to have no effect on consumers' tastes, prices of substitute autos, income or interest rate; %§;.= 0, 3% = 0, 5% = 0, 3% = 0. With these restric- tions the numerator of equation (A2.4) is clearly negative because scrap price has a positive influence of prices of 34 . c complementary goods (used parts), IR? > 0, and scrap price for a given car declines over time at a decreasing rate, Q3; < O dT The denominator of (A2.4) is clearly positive as operating costs rise over time, %%g~> 0, imputed value to the car falls over time, %%¥ < O and r 3% is presumed to be small. (A2.4) is negative, and therefore scrap price is negatively related to scrap date. Effects of prices of complementary goods on scrap date are found by solving (A2.1) for £fl%. dP £21.: dPC 2 81 dPS 81v dx 81v dY 30c dr dV 1 4———._—— + .——— + ——— -—— - ——— - V(T) ——— + -—— BPS ch 32‘ch BY ch ape ch d—TZch(A2 7) 800 av BIVI ' yr'*'r HT "81’ Changes in the prices of complementary goods probably have no effect on consumer tastes, income or interest rates; £2L-= 0, £9; = 0, £3; = 0. Changed prices of complementary ch ch dPC goods can affect the price of substitute autos. For example, the recent increases in the price of gasoline have caused manufacturers to redesign their autos; thereby affecting the price of new cars. The direction of this s effect is not generally known, however, and £23 could take dP s on different signs for other complements. If we let $25 dP equal zero, then (A2.7) is clearly negative because 2 £99 > 0, and-é—g 1 < 0. 8P° dT dPC 35 We find the effects of prices of substitute autos on scrap date by solving (A2.1) for 328-: dP £31.: dPS 2 81v 81v dX 81v dY 800 ch dv dV 1 __+——— +—————-—-—-—-V(T) _+—z—— 81>S 3X dPS BY dPS 8PC dPS dPS dT dPS(A2 8) _8_0__c_ + r dV _ 81V 81‘ ET 81‘ The price of substitutes probably has no effect on the prices of complements, income or scrap price; £9; = 0, dP s ch dv . ——§-= , ——5 = 0. If the prices of subst1tute autos have ‘1? ‘1? 8 IV dx any effect on consumers' tastes,then Tfi?'_—§ is probably dP negative. This is the case of conspicuous consumption. If we do not allow for this, then (A2.8) is clearly positive 2 as 31%.) 0 and 2_¥._l§ is presumed to be small. Therefore, 8P dT dP unless conspicuous consumption exerts a major influence on tastes, then the price of substitute autos will have a positive effect on the holding period. APPENDIX 2.2 EXTENSION OF PRICE SERIES The new car CPI was extended backward by adjusting Suits' (1957) series. Column (3) = the ratio of col. (1) to col. (2) % by 100. The ratio of col. (3) to col. (4) was computed for each available year, the mean value of this ratio (2.334) = col. (3) % col. (5). By looking at col. (5) 1949-1956 and comparing with col. (4), an idea of measurement error can be gotten. 36 37 00.00 0.00 00.000 0.000 0.000 0000 00.00 0.00 00.000 0.000 0.000 0000 00.00 0.00 00.000 0.000 0.000 0000 50.00 0.00 00.000 0.000 5.000 0000 00.00 0.50 50.000 0.000 0.000 0000 00.00 0.00 00.000 0.000 0.000 0000 00.00 0.00 00.000 0.000 0.000 0000 0.00 00.00 0.00 0.000 0000 0.00 00.00 0.00 0.000 0000 0.00 00.55 0.00 0.000 0000 0.00 00.00 0.00 0.000 0000 0.00 00.05 0.00 0.000 5000 5.00 00.00 0.00 0.500 0000 0.00 05.05 5.00 0.000 0000 0.00 00.05 0.50 0.000 0000 0.00 00.05 0.00 0.000 0000 0.00 00.05 0.00 0.000 0000 0.00 00.05 00 0.000 0000 0.00 00.00 0.05 0.000 0000 0.50 00.00 0.05 000 0000 moHHmm oo0um unocomaoo 000 magma 0mcwaoz :0 000 mo0umm mo0um oun< wouma 00mm Hmo 302 mmwnmm .muwam 00mqu 0000 .mu050 000 A00 000 000 000 .m00H00 mowum mo cowmamuxm "5.0 000mH CHAPTER THREE EFFECTS OF ECONOMIC VARIABLES ON AGE GROUPS OF AUTOS Introduction In this chapter, a system of regression equations is fitted to explore the influence on age-specific scrappage rates of real interest rates, gasoline prices, the prices of repair services, and the age structure of the population of potential automobile owners. The results show that, in general, these factors exert significant influences on scrapping. Age-specific scrappage rates tend to rise with increases in prices of repair services, and tend to decline with increases in real interest rates, increased gasoline prices and as the number of people under 35 grows in proportion to the total population over 16. The correlation of these variables with scrappage rates shows marked variation with the age of the automobile. Total R2 s of the regression equations are highest for vehicles aged 8 years and older. Contrary to expectations, however, estimated coefficients show little systematic trend over age classes. Indeed, age-to-age variation in coefficients is so erratic that pooling all age groups together into a single large regression provides a more accurate assessment of the direction of the impacts of 38 39 individual variables on age-specific scrappage rates that can be obtained from regressions fitted to individual age groups. The Regression Equations Age-specific scrappage rates are explored in terms of a series of regression equations in the form SR = O'a,0 + O‘a,l Pt + O'a,2 Yt + O'a,3 Rt + 0'a,4 Xt (3.1) + aa,5 PGt + aa,6 PRt + ua,t where 3 represents age of the automobile in years, and t t is the scrappage rate during year t of automobile a years old. As in earlier the year of observations. Thus SRa equations, P is the real price of new automobiles and Y is per capita income. The new variables under consideration are R, the real rate of interest, PG, real price of gaso- line, and PR, the real price of repair services. X represents the age structure of the population of potential automobile owners, expressed as the percentage of total population over 16 that falls in the 16 to 35 age bracket. The final term, u, is the residual, embodying all other factors that affect the scrappage rate of vehicles aged 3 during year t. 40 The Variables in Detail 1. Interest Rate Increased interest rate increases the cost to the buyer of a new car. This effect causes some people to delay replacement of their vehicle thereby reducing scrap rates. On the other hand, increased real interest rate reduces the present value of the stream of quasi-rents available from automobile ownership -- this effect causes rates of scrappage to rise as the total quasi-rent of the marginal buyer falls below price of the auto. The marginal buyer is probably looking at an older car while the person delaying replacement is likely to own a middle-aged car. The net effect of a higher real interest rate will be to compress the age distribution of cars as more older cars are scrapped and middle-aged cars are held longer. In keeping with the real values employed for monetary variables, real interest rates are used in the equations. For this purpose, the proxy for the real interest rate is defined as the difference between the 3-5 year treasury bond composite yield and the rate of inflation as measured by the annual rate of increase in the implicit price deflator of the GNP. 2. Gasoline Prices An increase in the price of gasoline should diminish the demand for new cars because gasoline and new cars are 41 complements. Since we are dealing with a market dominated by replacement purchases we expect this diminution of auto demand to imply delayed replacement, and therefore a higher gasoline price is expected to negatively affect scrappage. To whatever extent older vehicles get poorer gasoline mile- age than newer cars, a given increase in gasoline price will exert a greater effect on scrappage of older as com- pared to younger cars, but the differences should not be great and may easily be swamped by other factors. Price of gasoline is measured by the gasoline-price component of the CPI and is converted to real terms by division by the over-all CPI index. 3. Price of Repair Services The most frequent occasion for scrapping a vehicle arises when needed repairs cost more than the present value of the services available over the remaining life of the repaired vehicle. It follows that increasing repair costs raises scrappage rates of cars of any given age. In addition, of course, ordinary repairs are a normal part of operating cost, particularly of older cars, so an increase in repair prices reduces the value of services available over the remaining life of cars of any age which, in turn, contributes to higher scrappage rates. The price of repair services is measured by the corre- sponding component of the CPI and converted to real terms by division by the over-all CPI index. 42 4. Age Distribution of the Population of Potential Car Owners Any demographic shift that alters the demand for automobiles of a given age will be reflected in correspond- ing shifts in relative values and hence in altered age- specific scrappage rates. Analysis of a cross-section of households by Kreinin (1959) showed that the proportion of used car buyers was higher among young married couples with children than in any other demographic group. Johnson (1978) showed that purchase of older cars tends to rise with family size, but to decline with age of family head. Both results suggest that demand for older cars would rise with an increase in the proportion of potential car owners who are in the younger age brackets. In an attempt to capture this effect, X is defined as the percentage of population over 16 years of age that is under age 35. A rise in this percentage should raise the relative values of used cars and reduce scrappage rates. General Considerations In general, it can be expected that the variables listed will exert relatively little influence on scrappage rates of cars at very young or very old ages. Scrappage of relatively new cars is the consequence of severe accidental damage, the occurrence of which is almost totally indepen- dent of economic factors. Older cars, on the other hand, are either so subject to the weaknesses of old age or are 43 so coveted as curiosities that the alteration of a few economic variables has little effect on the likelihood that they will be scrapped. It is in the middle of the age range that the effects of economic factors should be best evidenced. This implies that the total correlation of scrappage rates with economic variables should be lowest for the newest and oldest cars, and highest for ages in the middle. Results The series of fitted regression equations is presented in Table 3.1. As expected, total correlation is lowest for youngest ages. Indeed, the low R2 associated with the scrappage rates of 5 year old cars is not even statistically significant. Correlation rises in the middle range and is highest for 11, 12 and 13 year old cars. The sample does not contain cars old enough, however, to observe falling correlation for older ages. As in the previous chapter, prices of new cars are, in general, negatively correlated with scrap rates when the model is estimated over the full (1949-1979) time period. Coefficients of the price term, however, vary erratically from age to age and are subject to large standard errors. The partial correlation of income with scrappage is positive for ages greater than 5; in keeping with the character of used cars as inferior goods. The effect of income on scrap rates is highest for 10 year old cars and 44 .muouuo wumvfimum mum mommnucmumm G0 mumnabz % ANNH.V Ammo.o Aa~4.o Aowm.v Isms.v Amol.o 00.0 000000. 00. 000000.: 000000.: 55000.0: 000000. 050000.: 005000.: 00000.0 50 00 08mN.V Am00.0 Awam.v Aowm.0 0m0~.v 0500.0 00.0 000000. 05. 055000.: 000000.: 00000.0: 000005. 000000. 000000.: 00000.0 00 00 0500.0 0000.0 5005.0 5000.0 0000.0 0000.0 00.0 000500. 05. 000000.: 550000.: 00000.0: 000000. 000000. 000000.: 00050.0 00 00 0500.0 0000.0 0000.0 0000.0 Aq5~.0 0mm~.0 00. 000000. 05. 000050.: 505000. 50000.0: 005000. 000500. 000000.: 00555.0 00 00 0000.0 0000.0 0005.0 0000.0 5500.0 0000.0 50.0 000000. 05. 000000.: 000000. 00005.0: 000000. 000000. 000000.: 00000.0 00 0 0000.0 0000.0 5000.0 0000.0 0050.0 5000.0 00.0 050500. 05. 000000.: 500000. 00000.0: 000500. 000000. 000000.: 000000. 00 0 AwHH.V Ahqo.0 Anm~.0. Aom~.v Ammo.v Aouo.v 00.0 000000. 00. 000000. 505000. 500005.: 000050. 500000. 000000.: 000000. 50 5 Am5o.0 0000.0 0000.0 0000.0 0000.0 Aomo.0 00.0 050000. 00. 000500. 000000.: 000050.: 000000.: 000000. 000000. 000000.: 00 0 5000.0 0500.0 5050.0 0000.0 0500.0 0000.0 00.0 050000. 00. 000500. 005000.: 000500.: 000050. 000500.: 000000. 000000.: 00 0 3:0 000 M mufimamm ma00omm0 00:0mu00800 mumm 080050 mUHHm unmanaoo mGO0um> 000 0 umououQH :ummno a.” m. u a + new 08 + m. m. m. m. u a n uwm 05 + u0 05 + um 05 + u> 05 + um m 0d + m 08 u u m00 "coquUHMwoomm «.mcowuoaSM mawmmmuom owmwooam:mwm mo wmumaaumm "0.0 00008 45 is highly significant for 10 and 11 year age groups. The magnitude of the income coefficient is such that a 100 dollar increase in real per capita income would lead to a 3.5 percent increase in the scrappage of 10 year old cars (172,000 cars in 1979). The decline in the income effect for 12 and 13 year old cars presumably reflects the declining influence of income as automobiles become in- creasingly vulnerable to scrappage from unspecified causes as they get older. Real interest rates do not show any strong influences on cars less than 12 years of age. For 12 and 13 year age groups the effect of real interest rates is positive and very significant. This indicates that, for these older cars, the effect of interest rates is primarily on the present value of the future services of the car. Coefficient estimates for gasoline price are positive for 7 year to 10 year age groups, but are negative for 11, 12, and 13 year age groups. For the younger cars the positive sign may indicate a substitution effect whereby new cars getting better mileage are substituted for older less efficient models. The negative coefficient estimate for the 11 year to 13 year age groups probably indicates the presence of an income effect which causes replacement to be delayed. The negative coefficient may also indicate that higher gasoline price provides an incentive to drive less; thereby increasing vehicle life-span. For cars less than 7 years of age the price of repair 46 services shows the expected positive correlation with rates of scrappage. For cars in the 8 year to 13 year age groups the repair price coefficient is negative, but not very significant. This probably indicates that the major com- ponent of repair services (labor cost) is avoided by many owners of old cars. Much of the maintenance on old cars is probably performed by the owner, and when a serious mal- function occurs the car is scrapped. The demographic factor, reflecting age distribution of the population of potential car owners, shows the expected uniform negative influence on scrappage. In terms of partial correlations, this is the strongest single influence shown by any variable included in the system of equations. The Durbin-Watson statistics of the age specific regressions decline with age to a minimum at age 10, indicating the possibility of positive autocorrelation among the residuals of these equations. This autocorrelation probably indicates the presence of some vintage effect; which results from a trend in the durability of auto- mobiles.1 Pooled Regression Since Table 3.1 gives only weak evidence of systematic variation of coefficients by age class, another regression is fitted employing pooled data. The 5, 12 and 13 year age groups were dropped from the sample because these age groups do not respond to economic variables to the same 47 extent as do middle-aged autos. The pooled regression takes the form: SRa,t = b0 + bl Pt + b2 Yt + b3 Rt + b4 Xt PGt + b6 PRt + Q Ca Da + u (3.2) + b 5 a,t The D3 are dummy variables defined to have value 1 when the observation involves automobiles aged a and otherwise 0. All other variables have meanings as defined above. SRa t = .708718 - .076220 Pt + .333902 Yt ' (. 064) (.083) - .026141 Rt - 1. 64571 xt - .001147 PGt (.177) (. 242) (.043) + .027977 PRt - .135304 D6 - .111233 D7 (.089) - .072029 D8 - .025037 99 - .017997 D10 + .050197 011 + ua,t R2 = .88 observations = 167 SSE = .114237 Table 3.2: Significance of loss due to pooling age groups. SSE df F-Ratio Pooled Sample .114237 155 6-11 year age groups .078663 125 1.884304 48 Results of Pooled Regression The pooled regression shows that the major influence on scrappage, aside from age of auto, comes from demographic change in the population of potential owners. This is to be expected in a market which is dominated by the timing of the replacement decision. The coefficient on X is negative, ! large in absolute value, and highly significant. This 1 shows that the presence of younger drivers increases the demand for older autos; probably because of their low position in the life-cycle of income. b" Automobile age is shown, as before, to have a positive effect on scrappage. The coefficients on automobile age dummies are observed to grow with age. The net effects of income and repair prices on scrap- page are, as expected, positive and highly significant. The price of gasoline is shown to have an insignifi- cant negative overall effect on scrappage. The gasoline price effect is also very small in absolute value. This effect is caused by the complementary relationship between auto demand and gasoline. Increases in the price of gasoline apparently cause some individuals to delay the replacement of their autos for a short period of time. For example, if the rate of scrappage is constant over the course of a year, our model predicts that a 30 percent increase in the price of gasoline will lead to a one day delay in the replacement cycle of the stock of cars aged 6 through 11. This result will probably be altered as autos 49 are redesigned to use less gasoline. When the replacement of a car can significantly decrease gasoline consumption, then gasoline price may positively affect scrappage. The F-ratio, calculated in Table 3.2, shows that the loss in explanatory power which results from pooling is significant at the .01 level. Clearly, this loss would grow if the number of age groups pooled were to increase. This finding is interesting in that other authors, Walker (1968) and Parks (1977), pooled all available age groups. The causes of differences between the results of pooled vs. unpooled regressions are that some variables affect vehicles of different age groups differently. This is evident in our estimates of the coefficient on interest rate. For cars less than 12 years of age interest rate does not exhibit any clear sign, as in the pooled regres- sion. In the age-specific regressions, however, this coefficient is positive and highly significant for 12 and 13 year age groups. This anomaly is resolved by realizing that, while interest rate plays an important part in determining the present value of the future services of an automobile, interest rate is also a major determinant of the cost of a .substitute (new) car. Therefore, in the presence of high interest rate the owner of a middle—aged car may delay replacing it. At the same time this high interest rate may cause the owner of a 12 or 13 year old car to dispose of it in an attempt to improve his liquidity. The end result is 50 that a high real interest rate will cause the age distribu- tion of autos to be compressed, and a low real rate will cause the age distribution of autos to be more dispersed. Conclusions and Summary We have shown that a significant amount of information about scrapping is obscurred by the pooling of age—specific scrap rates. This explains why other researchers (Boulding, 1955; Walker, 1968; Parks, 1977) were unable to find the effects of interest rates, demographic variables, and the prices of complementary goods on automotive scrappage. Our methodology may be generalized and used to investi- gate movements in other types of durable goods, particularly investment goods. The model we have developed can go a long way towards helping us understand why the age distribution of durable goods changes. This understanding is basic to the development of a vintage-specific model of the capital stock. For example, we find a large positive effect of real interest rate on the scrap rates for 12 year and 13 year age groups. This shows that a high real interest rate causes the use of these older autos to become uneconomic. If we are able to apply our model to investment goods we can then try to answer questions relating, for example, to the effects of interest rates or other policy variables on the age distribution of the investment goods stock. The finding of a large interest rate effect on scrap- ping is particularly interesting in light of Parks' (1978, 51 p. 213) comment to the effect that higher interest rates will increase the probability that a given auto will be repaired rather than scrapped. Our work suggests that what Parks has actually looked at is the change in relative prices of new versus used autos caused by a change in the new car finance rate which was used in his work. We contend that Hess' (1977, p. 699) observation that, I ”The real rate of interest affects the demand for autos in several offsetting ways resulting in a small negative effect," is more correct. Our scrappage model can also be used in the analysis of policy. For example, suppose that an excise tax on gaso- line were under consideration, and that this tax would increase the real price of gasoline by 10 percent. The model can estimate the number of cars in each vintage group that will be scrapped or saved as a result of the tax. In the example given, the imposition of this tax would cause the scrap rate for 12 year old cars to decline by 2.38 percent (68,142 1967 automobiles in 1979). The calculation of the number of scrapped cars of each vintage is important because automobile regulation has occurred on a vintage by vintage basis. Use of our model can help in the quantification of the benefits flowing from auto regulation. In our example, the excise tax on gasoline would have delayed the scrappage of some 1967 automobiles; these older cars emit more pollutants and are less safe than the newer cars which would have replaced them” With 52 an estimate of the per car change in pollution and the per car change in fatalities, which would have occurred if these cars were not replaced, the costs of this tax in terms of increased pollution and increased mortality could be easily calculated. 53 Footnotes 1 We also tried a specification which included the scrap rate of age A-l cars in year t-l as an independent variable. The Durbin-Watson statistics were much larger with this specification, but a high degree of multi- collinearity between the independent variables became evident. CHAPTER FOUR MAKE-SPECIFIC SCRAPPAGE In this chapter we explore variations in automobile scrap rates by make of car. Scrap rates are shown to vary widely by make of car even after the influences of price, income, demographic change, and repair price are taken into account. The causes of these make-specific variations are considered, and in an effort to hold both the manufacturer and the basic design constant, we analyze the scrap rates for the General Motors makes. Differences in scrap rates among these makes are large and significant. They are also unrelated to the price of the car when new. This evidence shows that scrap rate variations are not simply the result of quality differences among cars. To further investigate this topic we expanded the group of automobile makes used in this study to include makes which are no longer produced. These makes are shown to have had higher rates of scrapping than did the makes which survived. Furthermore, these scrap rates generally increased after production of these makes had ceased. This finding suggests that consumers' expectations regarding the future of the manufacturer have a large effect on the scrap rate of a make-group. 54 55 Make-specific scrap rate differences are caused by differences in the durability of the car, or by differences in the success of the make in the used car market. Our findings show that holding the design and construction of the car relatively constant, as with the G.M. makes and as with those makes no longer produced, does not eliminate make-specific variations in scrap rate. The implication is F that the expected life-span of an automobile is not solely determined by technical considerations. 3 To investigate make-specific variations in scrap rates E we disaggregated the data into make-groups. Age-specific scrap rates are analyzed to find the extent of make- specific differences in scrappage. The extent of these scrap rate variations is found by fitting a regression which includes dummy variables (Dm) for automobile makes to a series of age and make-specific scrap rates. The other variables in the scrapping function are all defined as in Chapter Two. The equation has the form: SRa,m,t = a0 + 011 Pt + a2 Yt + 013 PRt + 014 Xt 11 (4.1) + Z a D + Z a D + e a=6 a a. n1 H) In a,m,t where Ea m t is a random disturbance term. Data Considerations The influence of the absence of war-time model years is avoided by estimating the equation over the 1960-1979 56 period. The makes included are: 'all of the General Motors makes (which are pooled into one scrap rate), Ford, Plymouth, Chrysler, and Dodge. Estimation was performed under the constraint that the make-specific dummies and the age dummies sum to zero. Results of the estimation of equation (4.1) are: SR = .998438 - .419080 Pt + .003353 Y am”: (.060) (.007) t - .082815 PRt - 1.17920 Xt - 1.03728 D6 (.102) (.331) - .061474 D7 - .009951 D8 + .032528 D9 (4.2) + .062683 D10 + .079943 Dll - .011327 DGM + .010308 DF0 + .007111 DPL - .008231 DCHR + .002139 DDO where R2 = .78, and numbers in parentheses are standard errors. The coefficient estimate for the demographic variable has the expected negative sign and is highly significant. Coefficient estimates for income and repair price are not significantly different from zero. The estimated coeffi- cients for age dummies increase with age as expected. The price coefficient is also negative and highly significant, but this was unexpected. In Chapter One we find that new car price has a positive effect on aggregate scrap rate over this period. Apparently, the disaggrega- tion of the scrap rate data into make-groups implies a 57 different price effect. It is likely that the demand schedules for a make in the used and new car markets move together. Therefore, an outward shift of a new car make- specific demand schedule tends to occur at the same time as an outward shift of the used car make-specific demand schedule, thereby reducing scrappage as new car price rises. Nevertheless, in the aggregate an outward shift of the new car demand schedule may occur as the aggregate used car demand schedule shifts towards lower prices and quan- tities; indicating that new car price may positively affect aggregate scrappage while make-specific scrap rates are negatively affected. Partial R2 for the make variables is .01, with F(4,556) = 6.614; significant at the .01 level. This shows that the amount of make-specific variation in scrap rates is small, but very significant. The estimates of make coefficients indicate that scrap rates for the G.M. cars are about 1.1 percentage points below average scrap rate, and that scrap rates for Ford automobiles tend to be about one percentage point greater than average scrap rate. This translates into a life expectancy of 6.32 years for G.M. cars at the end of their fifth year. Ford automobiles can be expected to survive 5.57 years from the end of their fifth year. These percentage point differences yield a difference in life expectancy of nearly a year between these tw0‘makes. To better interpret scrap rate differences we show 58 percentage differences from mean scrap rate for the five makes in Figure 4.1. Scrap rates for the G.M. cars are about 6 percent lower than mean scrap rate, while the Ford scrap rates are about 6 percent larger than mean scrap rate. The scrap rates for the Chrysler Corporation cars are highest for the lowest priced cars (Plymouth) and decline for the higher priced automobiles. The G.M. Makes This is not so for the G.M. makes. These makes use similar body shell, chassis, and drive train. By consider- ing scrap rate variations for these makes we are, in effect, holding the basic design and method of construction constant across several makes. We had expected that the higher quality, higher priced, makes would have lower rates of scrappage than the less expensive makes. This also provided us with a fairly rigorous test of the influences of design and construction methods on rates of scrappage. The specification and sample period are the same as in equation (4.2), except that the G.M. makes are dissaggre- gated into Cadillac (CA), Chevrolet (CH), Buick (BU), Pontiac (PO), and Oldsmobile (0L) automobiles. Results of this estimation are: 59 Percent Difference From Mean* .08 Ford .06 .067 .04 Plymouth .042 .03 .02 .01 Dodge .012 Chrysler -.04 -.049 -.O6 G.M. -.O67 *Actual mean scrap rate = 1.693. Figure 4.1: Percent difference from mean scrap rate for five makes. 60 SR = 1.072213 - .193845 F .+ .025293 Y aim't (.041) t (.004) t - .450026 PRt - 1.12250 xt - .112647 D6 (.074) (.255) - .073046 07 - .020809 08 + .030550 09 (4.3) + .074736 010 + .101215 011 - .021303 DCH + .004174 DBU + .026436 DPO + .024638 D0L - .033947 DCA where R2 = .88. Coefficient estimates for price, income, repair price, and demographic variable show the same signs as in equation (4.1), but these estimates have much smaller standard errors, probably because of the elimination of extraneous make-related sources of scrap rate variation from the data. The increase in R2 also shows that some disturbance has been eliminated from the model. Partial R2 for make is .08, with F(4,586) = 95.37. Clearly, there are large significant variations in these scrap rates which are associated with automobile make. In keeping with the results for Chrysler, the lowest scrap rates are for Cadillac automobiles, but these are followed in ascending order by scrap rates for Chevrolet. The find- ing of low scrap rates for Chevrolet cars indicates that price when new is not as much of a determinant of automobile life-span as is popularly supposed. Percentage differences from.mean scrap rate are shown in Figure 4.2. These differences are larger among the G.M. Percent Difference From Mean* Figure 4.2: .20 .18 .16 .14 .12 .10 .08 .06 .04 .02 .02 .04 .06 .08 .10 .12 .14 .16 .18 .20 61 Pontiac Olds- .154 mobile .144 Buick .02 Chevrolet -.125 Cadillac -.l98 * Actual mean scrap rate = .1716. Percent difference from mean scrap rate -- G.M. makes. 62 makes than among the makes included in Figure 4.1. A possible cause of this is competition among manufacturers. Ford, Chrysler, and G.M. generally compete in each market segment, and this may have the effect of standardizing durability in each segment. By looking at the five G.M. makes we may be looking at individual segments of the market. The variation among scrap rates for G.M. makes indicates that there is far more at work here than differ- ences in the design, quality, or construction of the auto- mobile itself. Other Makes To expand this study so as to encompass more automobile makes we included scrap rates for some makes which are no longer manufactured. The specification is the same as that for equation (4.1) except that the pool of makes has been expanded to include Packard, Hudson, Nash, Studebaker, and Desoto automobiles. The criteria for the selection of these makes are that the car was produced before World War II, and that the make attained large volume at some time.1 The model was estimated over three different time periods in order to look at scrap rates for these makes before manufacturing had ceased. The 1950-1956 period was chosen to consider the scrap rates for Hudson, Nash, and Packard before production of Hudson and Nash was discon- tinued in 1957, and before the Packard automobile was radically altered by Studebaker-Packard Corporation. 63 Consideration of the 1950-1960 time period allows us to look at make-specific variations in scrap rate for Desoto. The 1950-1967 period is used to include Studebaker auto— mobiles. The model was estimated with two different data sets over the 1950-1960 period. One data set includes scrap rates for Packard, Nash and Hudson automobiles while the other does not. This was done to look at effects on Packard scrap rates of the Studebaker-Packard merger, and to look at the effects of the cessation of Hudson and Nash production on their scrap rates. Coefficient estimates of this specification are shown in Table 4.1. R2 is large for all of these equations, and the price, income, repair price, and demographic variables are shown to significantly influence scrap rate in each case. The coefficient estimates for the equation estimated over 1950-1956 are very different from those of the follow- ing three equations. This is undoubtedly caused by the postwar confusion in automobile markets. Scrap rates over the 1950-1956 period are generally very low because of the postwar scarcity of automobiles. The average scrap rate for cars aged 6 to 11 is about 9.6 percent. This implies a 10.37 year life expectancy for a 5 year old car. The equation estimated over 1950 to 1956 shows Hudson with the highest scrap rate followed by Nash, Packard, and Studebaker. The lowest scrap rate is found for Plymouth Table 4.1: Coefficient estimates of make-specific scrapping functions. Sample 1950-1956 1950-1960 1950-1960 1950-1967 Constant -5.832919 .663842 .242899 1.845044 Price 1.38720 .810383 .760802 -.7l4937 (.318) (.082) (.087) (.100) Income 1.28153 .36163 .26543 -.392832 (.379) (.124) (.131) (.107) Repair Price 2.17599 .626776 .548592 .471660 (.372) (.171) (.181) (.191) Demographic 4.97633 .70206 .23763 -3.26529 (2.161) (.663) (.700) (.630) Age 6 -.091868 .108495 .099299 -.097752 7 -.058718 .069213 .069512 -.059950 8 .004508 .012783 .017151 -.012981 9 .028349 .029955 .027074 .027587 10 .044713 .070429 .069706 .061947 11 .073016 .090107 .089182 .081148 Make G.M. -.028301 .028464 .002679 -.014732 Ford -.016320 .013398 .012040 .010054 Plymouth -.034217 .044673 .019235 -.009355 Chrysler -.024863 .032878 .002083 -.Oll970 Dodge -.034122 .037701 .012094 -.007506 Studebaker .014660 .010368 .035628 .033455 Desoto -.025124 .031659 .006221 Nash .039900 .057022 Hudson .075267 .084296 Packard .033119 .037087 R2 .87 .89 .89 .83 SSE .137127 .448309 .242492 .536402 65 automobiles, and this is followed by Dodge. The difference in scrap rates over this period are extremely large. The high scrap rate of Hudson automobiles translates into an average life expectancy, at 5 years of age, which is 4.5 years less than average. The scrap rates of Packard cars translates into a life expectancy at age 5 that is 2 years and 8 months less than average. The low scrap rates for Plymouth autos indicate a life expectancy at age 5 that is 5.25 years greater than average. Thus far we have established that scrap rates varied widely by make of car over this period, and that differences in scrap rates indicated large differences in life expectancy for different makes. Figure 4.3 shows percent differences from mean scrap rate for the 10 makes. All of the makes which have greater than average scrap rate have been discontinued. Moreover, the makes which were discontinued in 1957 (Hudson and Nash) had the highest rate of scrappage. The Packard automobile, which was not discontinued until 1959, but was radically altered in 1957 when Packard became a nameplate on Studebaker bodies, has the next highest scrap rate. Studebaker, which ceased production in 1967, has the third highest scrap rate. Desoto is the only make which even- tually ceased manufacturing that has a scrap rate which is lower than average. It is also clear that high priced cars did not have lower scrap rates than low priced autos. In fact, the 66 mam.) nusossam .Aommauommav mum» amuom some Scum moamHmMMfiw unmoumm «mm.l swoon pmmno mNommo. soakmo. kflmwso. mackao. mamama. mmm mm. «m. as. mm. mm. mm Ammo.v AMHNO.V ANHo.V Am~.HV Amoo.v chauuuommscma semoao. kmnamo. sommwo.- momoqm. somasmo. “mono sasso mmoowo. ohnsko. «amuse. namNAO. Hammmo. Han «mango. Nasaoo. mommmo. omaooo. ammooo. can maswmh. wflsmso. eqoqmo. qm~k~0.- mammmo. an Hoesoo. mammoo. osamoo. oasmoo.- aqmaoo.- ma mmuaoo.- ommsmo. soasmo.- Hossmo.- a-kmo.- an mnmmma.- mmomma. N8N~OH.- ommmmo.- soawoa.- on Aaoq.v Aaus.v Amm~.v Ama8.v Amam.v semmsm.- ooomom. omoma.a Hmoamq. «sqmmm. moaum Homamm Awas.v Am~3.V Anom.v Aoa.Hv Aeom.v on~c~.H- a~mo~.a- mqmso.m- maammm.- Nmmmm.a- canamuwoamo Amm~.v Aaok.v A8n3.v AmH8.V Ammn.v wNHNo.H mamqq.a mqomos.- ammnon. mmoams. maouaH Aoea.v Amafl.v Aaoa.v AaoH.v A¢~H.V mmoomm. ummoam. nsmama. smmsmo. mmoauo.- moaum mmmmNH.- mnomNH. Hmeoam. mmeosm.- amqmam. 88808800 £mNZ Gomfifim Uhmxuwm OUOme HMMMQmUDum u a 80 + sac + Han Has + can + OHs + mo ms + me Na + an on + on ms + see 88 + ux ms + u» as + um H8 + as u u.s.m "cowumowmaomam «.ouomon was .vuwxomm .Smmz .aowpsm .memnmpnum How mcowuocnm mwmmamuom "m.¢ magma 74 The results for Packard probably indicate that these old Packards were held as collector's items. The insignificant results for Desoto indicate that the public did not view Desoto as an orphan car probably because the manufacturer (Chrysler) did not leave the industry. We have shown that scrap rates for the cars which became orphans were generally higher than those for the surviving makes. The finding of higher scrap rates for the soon-to-be orphans may indicate some durability problem with these makes. The fact that scrap rates for some of these makes rose significantly after they became orphan cars shows that the orphan car influence did occur for some makes. The presence of an orphan car influence in the used car market probably indicates that this influence also has effects on the market for new cars. Summary and Conclusions Several writers have commented on make-specific scrap rate differentials, or differences in expected life-span among makes. The first observation of make—related differences in automobile life-span was that of Griffin (1926, p. 10) who observed that Ford cars had a longer expected life-span than did other makes. He attributed this longevity to the lack of obsolescence in style among Ford cars (the bulk of these Fords were Model T's), and to the simplicity of the internal mechanisms. Differences in the quality of construction of various 75 makes have been commented on by White (1971) and by Parks (1977). In White's study survival rates for Chevrolet, Ford, and Plymouth automobiles are calculated. He finds that, between 1953 and 1967, Chevrolet cars had survival rates that were generally larger than those for Plymouth and Ford automobiles. These differences are attributed to a variety of causes: Durability strategies of manufac- turers, different qualities of construction, and resale values. In Parks' (1977) study make-specific scrap rate differences were mainly attributed to the profit maximizing decisions of manufacturers. These other writers have all focused on the construc- tion car itself, or on pricing decisions of the firm as the causes of make-related differences in scrapping. We have shown that demand differences among makes are a very important cause of scrapping differences. It has been demonstrated that not only do scrap rates vary by make, but that these variations persist even in the absence of differences in manufacturer or in basic design. It has also been shown that the expectations of the consumer regarding the future of the manufacturer are important to the determination of scrap rates. These findings, and the correlation of explicit demand factors with make-specific scrap rate, all point to a theory of scrappage that has its basis in consumer demand. Automobile make has been shown to exhibit a declining influence on the determination of make-specific rates of 76 scrappage. This is probably the net result of the reduc- tion in the number of manufacturers, and of the model proliferation of the remaining automakers. The competition among the big three in each price and size category probably minimizes the make-specific variations. The end result of this process is that make-specific scrap rate differences are internalized, and become model-specific differences. These model-specific differences are probably respon- sible for the variations in scrap rates among the G.M. makes. While the body shell, chassis, and drive train for these makes are standardized, the model mixes of these makes are different. For example, Chevrolet may sell more compact sized automobiles than Oldsmobile, and if these compacts are more highly prized by used car buyers than are other sized autos, then they will have lower scrap rates. We have found that the orphan car influence has been an important element in the used car market on several occasions. It is probable that this orphan car influence carries over into the market for new cars as well. There- fore we have shown that expectations about the future of the manufacturer are important to the demand for used cars, and probably for new cars. This is one of the factors that separates the demand for durable goods from the demand for other goods, and it may be important to include these expectations about the future health of the manufacturer into a model of automobile, or other durable goods, demand. 77 Future work on this topic should address the role of consumers' expectations in the determination of automobile life-span, and model-specific causes of variation in scrappage. It is hoped that with a consideration of model- specific data that some of the questions raised herein can be answered . 78 Footnotes 1 Lincoln was dropped from the sample because we estimated a number of negative scrap rates for Lincoln. Willys was dropped because of their merger history, and because the majority of Willys automotive products are utility vehicles. CHAPTER FIVE. IMPLICATIONS FOR AUTO DEMAND MODELS The previous three chapters show that automobile age, prices of substitutes and complements, income, make of auto, interest rate, and demographic change are major determinants of automobile scrap rates. These variables, with the exception of age, are all components of automobile demand.‘ In this chapter we show the relationship between scrappage and the demand for new cars. The results of our work on automobile scrappage have serious implications for many commonly used models of automobile demand. The most common automobile demand specifications (e.g. see Introduction to Chapter One) are estimated as single equations. This specification yields correct estimates of the demand equation parameters only if the demand function is traced out by shifts in the supply schedule. We will show that this condition existed during the postwar period when automobile markets were disrupted by the absence of wartime production. Nevertheless, we will also show that during the early thirties, and since 1960, prices of new cars have been mainly affected by shifts of the new car demand function. Relative new car prices were shown to be positively 79 80 associated with aggregate automobile scrapping over the 1960-1977 period in Chapter One. Over the 1930-1942 period real new car prices were shown to be negatively associated with aggregate scrappage rates. We develop a model which shows that over both of these periods the major determinant of real new car price was shifts in the demand schedule for new cars. In general, we show that the positive relationship between new car price and scrappage indicates that new car price is mainly determined by shifts in the new car demand function. There are, however, exceptions to this framework which will be dealt with after the basic model is developed. The Market For New Cars and Scrappage The relationship between new cars and junk autos is one of substitution. The purchase of a new car adds one more auto to the stock. If the stock of autos were in static equilibrium, then one old auto would be scrapped for each new auto that is added. The same principle generally applies to a stock of autos which is in dynamic equilibrium; except that the supply and demand for used cars may fluctuate. Whether or not the purchase of a new auto leads to the scrappage of an old one depends on movements in the supply and demand for used cars. If the quantity of used cars supplied to the market increases as a result of an outward shift of new car 81 demand, then the price of used cars must decline and this leads to increased scrappage. If the quantity of used cars supplied does not increase with an outward shift of new car demand, then the stock is growing and there is no effect on scrappage. This framework of substitution can be used to develop hypotheses about the sources of price movements in new car markets. In Figure 5.1 we show a leftward shift from S1n to S2n in the new car supply function which results in a higher new car price. The price increase causes some persons who would be marginal new car buyers to substitute used autos for new cars. The substitution of used autos for new cars is indicated as a leftward shift in the supply of junk autos from Slj to SZj' This process causes the increase in new car price to be capitalized into the value of existing used cars. The leftward shift in the new car supply curve, in conjunction with the leftward shift in the supply schedule of junk cars, indicates that higher new car prices are associated with decreased scrappage (from Qlj to sz). Therefore, if we find that scrappage is negatively influenced by new car prices then the new car supply func- tion has generally traced out the new car demand function. This finding would indicate that the parameters of the demand function can be estimated without a large amount of simultaneous equations bias. In Figure 5.2 we show a change in tastes from used to P new cars Figure 5.1: P new cars Figure 5.2: 82 Zn In new cars 21 11 junk autos age A Shift of new car supply and effects on scrap- page. In new cars junk autos age A Effects on scrappage of a shift in new car demand. 83 new cars. The new car demand function shifts to the right (from D1n to D2n) and the price and quantity of new cars increases. There is net substitution of new cars for used cars and therefore the supply schedule for junk autos shifts to the right for all age groups (from S1j to SZj)° The increased price of new cars is associated with higher levels of scrapping. If we find that scrappage is positively influenced by new car prices, then shifts in new car demand schedule have been the prevalent reason for changes in new car prices. This finding would indicate that the estimation of a single equation demand model would not estimate the demand function. Instead of the demand function some reduced form combination of supply and demand forces would be estimated, and the coefficient estimates may be subject to a large amount of simultaneity bias. External Influences The foregoing theory is generally correct providing that l) shifts in the new car demand function are associated with a shift in the opposite direction of the supply schedule for junk autos, and that 2) shifts in the new car supply function are associated with a shift in the same direction of the supply schedule for junk autos. This framework could be disrupted by major changes in the demand for all automobiles. This type of major change in auto demand occurred dur- ing the early 30's. From 1930 to 1933 scrappage was at 84 very high levels, while at the same time new car demand was extremely depressed.1 This resulted in a decline of about 3 million units in the stock of registered autos in the U.S. The causes of this are related to the sharp decline in income over this period which probably caused many individuals to delay maintenance on their autos until these autos simply fell apart. In Figure 5.3 we consider the case of a falling stock of autos due to a decline in the demand for new cars and an increase in the supply of junk vehicles. The demand for new autos shifts from D1n to D2n’ At the same time the supply of junk cars increases from S1j to SZj' Increased scrappage in this model is associated with lower prices and the demand function for new autos is less stable than the supply function. The price coefficient estimated over 1930-1942 in Table 2.3 of Chapter Two is negative and highly signifi- cant. This indicates that movements in new car prices in the early 30's were mainly influenced by shifts in the demand function for new autos. In 1941 and 1942 new car prices were probably in- fluenced by the supply constraints of the early war effort as production was cut off in 1942. The negative price coefficient estimated over 1930-1942 is consistent with supply determined prices in 1941 and 1942, and with demand determination of prices during the early 30's. From 1934 to 1939 auto markets were more stable than at the ends of 85 P new VT cars 8 n D2n D1n new junk cars autos age A Figure 5.3: External influences on the new car market and scrappage. our sample sub-period. Therefore, it is not surprising that the sign of the price coefficient is dominated by occurrences in the early 1930's and early 1940's. From 1948 to 1959 the supply constraint of the absence of wartime vintages dominated the used car market. The negative price coefficient estimated over this period indicates that new car prices were mainly influenced by shifts in the supply schedule. Some of the most influential automobile demand models were developed during the late 1950's. In general, these ‘models are single equation demand models.2 This type of model is fully identified if a shifting supply function traces out the demand curve. The finding of a shifting supply schedule during the 1948-1959 period generally 86 supports the use of these models over that time period. The price coefficient estimated over the 1960-1977 sample is significantly positive at the .05 level. The inference which can be drawn from this is that new car prices, since 1960, have been influenced mainly by shifts in the new car demand schedule. This has important impli- cations for the continued use of single equation demand models. These single equation demand models estimate a locus of equilibrium points; which may be adequate for forecasting purposes. Nevertheless, these single equation models cannot correctly estimate demand elasticities if the demand curve shifts. Summary and Conclusions We have found that scrappage of automobiles is influenced by many elements of auto demand: price, income, interest rate, demographic change, repair prices and auto- mobile make choice of the used car buyer. We have developed a model of substitution between new and used cars, and used this model to look at shifts in the supply and demand functions for new cars and for junk autos. Our findings indicate that the specifications of many empirical auto demand models do not account for shifts in the new car demand function; which have occurred on a regular basis. This results in a simultaneity bias in the estimation of demand function parameters. 87 Footnotes 1 It has been suggested that this increase in scrappage is a data problem caused by widespread evasion of licensing regulations. Consideration of a separate data set shows that the percentage of cars traded in which were junked nearly doubled from 1928 to 1930 (National Automobile Chamber of Commerce, 1931, p. 65; Automobile Manufacturers' Association, 1935, p. 62). 2 For example, see: Chow (1957), Suits (1958), or Nerlove (1957). VARIABLES AND DATA SOURCES Income: The income variable used was Net National Product per capita over the age of sixteen. NNP is taken from Table B-l7 of The Economic Report of the President (1979). The population data used in my calculation of this variable are taken from, "Annual Estimates of the Popula- tion by Age, 1900-1970," Series A32-37 of Historical Statistics of the United States, Colonial Times to 1970 which is published by the Department of Commerce, Bureau of the Census. These data were updated to 1979 with Series No. 3, column heading, 16 years and older, of various editions of Statistical Abstracts of the United States, also published by the U.S. Department of Commerce, Bureau of the Census. Percent of Population over 16 years old that is less than 35 years old: This series is also calculated from data appearing in "Annual Estimates of the Population by Age, 1900-1970," series A32 and A33 of Historical Statistics of the United States, Colonial Times to 1970, published by the Department of Commerce, Bureau of the Census. These data were updated as were the per capita Income data. Automobile Price, Price of Gasoline, Auto Repair Price: These three price variables are relative prices and 88 89 were constructed by dividing the Consumers Price Index (CPI) for new autos, price of gasoline and the auto repair index respectively by the CPI for all items. The CPI for new autos, price of gasoline, auto repairs and all items is taken from table 128 respective row headings "automobiles new, gasoline, regular and premium," "auto repairs and maintenance," and "all items" of the Handbook of Labor Statistics, published by the U.S. Department of Labor, Bureau of Labor Statistics. These series were updated to 1977 with annual data which appears in table 23 next to the same row headings in August issues of the Monthly Labor Review, also published by the U.S. Department of Labor, Bureau of Labor Statistics for subsequent years. Rates of Scrappage (SR ): These were calculated a,m,t as: SR = Sa,m,t - Sa+1,1n,t+l a,m,t a,m,t where S = stock of make, m, age, a, autos in time, t. a,m,t Data for the calculation of scrapping rates comes from tables titled: "Passenger Cars in Operation by Year, Model and Makes,‘ or "U.S. Passenger Car and Truck Registrations by Year, Models, and Makes," in yearly editions of Wards' Automotive Yearbook, 1949-1977, published by the R. L. Polk Company of Detroit, Michigan, and used with their permission. Real Interest Rate Proxy: This was formed by sub- tracting the percentage change in the Implicit Price 9O Deflator from the Composite 3-5 Year Government Bond Rate. This bond rate was obtained from series 12.7 (p. 693), column heading "3-5 year issues" of Banking and Monetary Statistics 1941-1970, published by the Board of Governors of the Federal Reserve System, Washington D.C. 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By The University of Michigan Highway Safety Research Institute, a report to the Motor Vehézle Manufacturers' Association, September 1978, p. . Johnson, Terry R. "A Cross Section Analysis of the Demand for New and Used Automobiles in the United States." Economic Inquiry, 16 (October 1978), pp. 531-48. Kreinin, Mordechai. "Analysis of Used Car Purchases." Review of Economics and Statistics, 41 (November 1959), pp. 419-25. Langsworth, Richard M. The Last Onslaught on Detroit. Princeton, N.J.: Princeton Publishing Inc., 1975. Langsworth, Richard M. Studebaker: The Postwar Years. Osceola, Wis.: MotofboEks International,il979. Naaslund, Bertil. "Simultaneous Determination of Optimal Repair and Service Life." Swedish Economic Journal, 1 (1967), p. 63. National Automobile Chamber of Commerce. Facts and Figures of the Automobile Industry. Detroit: iNationaI'Auto- mobile Chamber of Commerce, 1931, p. 65. Nerlove, Marc. "A Note on Long Run Automobile Demand." 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Analysis of the Wharton EFA Automobile Demand Model. UMI Research Press,*l979, p._l3. Walker, Franklin. "Determinants of Auto Scrappage." The Review of Economics and Statistics, 50 (November 1968), pp. 503-506. Ward's Automotive Yearbook 1977, 39. Detroit: Wards Communications Inc., 1977, p. 153. Westin, Richard B. "Empirical Implications of Infrequent Purchase Behavior in a Stock Adjustment Model." American Economic Review, 65 (June 1975), p. 384. White, Lawrence J. The Automobile Industry Since 1945. Boston: Harvard University Press, 1971} Wykoff, Frank C. "Capital Depreciation in the Postwar Period: Automobiles." Review of Economics and Statistics, 52 (May 1970, pp. 168-172.