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The estimation of economic depreciation for Canadian farm machinery Bell, Paul Kevin Thomas 1985

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THE ESTIMATION OF ECONOMIC DEPRECIATION FOR CANADIAN FARM MACHINERY by PAUL KEVIN THOMAS BELL A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES A g r i c u l t u r a l Economics We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 1985 © P a u l K e v i n Thomas B e l l , 1985 9 0 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of //^,CJ'TWKJ trca^^Uj The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 D E - 6 r v f m ABSTRACT THE ESTIMATION OF ECONOMIC DEPRECIATION FOR CANADIAN FARM MACHINERY by . . . Paul B e l l The objective of this thesis was to estimate the rate at which four types of farm machinery lose value in Canada. S p e c i f i c a l l y , ,Canadian data on used machinery prices was u t i l i z e d to produce estimates of economic depreciation for two-wheel-drive tractors, combines, square balers and large round balers. The data used in this thesis to make these estimates are special for two reasons. F i r s t of a l l , they represent the only extensive record of Canadian used farm equipment prices available. Most previous studies have based their estimates on American data, assuming that they apply equally well to the Canadian s i t u a t i o n . Secondly, these data record actual transactions in the used market and these transactions have been reported in an unaveraged format. This i s valuable because information on options, horsepower, condition, and, most importantly, hours of use was retained for each machine. The a v a i l a b i l i t y of thi s information permitted richer and more s p e c i f i c estimates of depreciation. In p a r t i c u l a r , the inclusion of hours of use in the models enabled a d i s t i n c t i o n to be made in this thesis between the component of depreciation which is d i r e c t l y attributable to age and that component which is d i r e c t l y a t t r i b u t a b l e to accumulated hours of use. It i s f e l t that t h i s d i s t i n c t i o n provides a beginning point for the study of depreciation due to simple "wear and tear", and that depreciation which i s due to obsolescence and technological change. As well, this thesis extensively reviewed the l i t e r a t u r e on depreciation in an e f f o r t to determine the best approach to follow. The method f i n a l l y adopted was the "remaining value approach"; however, the thesis went further than the t y p i c a l remaining value approach because an attempt was made to estimate the pattern as well as the rate of depreciation. This was done by i n i t i a l l y adopting a functional form which was f l e x i b l e enough to l e t the data "choose for themselves" between the commonly used depeciation rules of thumb (declining balance, s t r a i g h t - l i n e and one-hoss-shay patterns). This was possible by using the Box-Tidwell procedure. This Box-Tidwell procedure when applied to the extensive tractor data indicated that tractors in Canada follow a decl i n i n g balance (geometric) pattern of depreciation. This was taken as support for the adoption of semi-log models to estimate depreciation. i i i The main findings of t h i s thesis are, f i r s t , that depreciation rates vary among assets (from approximately 9% for tr a c t o r s to to nearly 16% for large round balers), and, secondly, that these rates are less than those allowed by the government for tax purposes. It was concluded that t h i s generosity on the part of the government would be acceptable i f i t applied equally to a l l depreciable assets, but the divergence in depreciation rates found in thi s thesis indicate that generous blanket depreciation charges give more advantage to some than to others. i v T a b l e of Co n t e n t s 1 . INTRODUCTION 1 1.1 Problem Statement 1 1.2 O b j e c t i v e 3 1.3 P l a n of the T h e s i s 4 2. HISTORICAL OVERVIEW 7 2.1 The Development of the T r a c t o r 8 2.2 Combine H a r v e s t e r s 13 2.3 B a l e r s 16 3. LITERATURE REVIEW 18 3.1 Economic V e r s u s P h y s i c a l D e p r e c i a t i o n 21 3.2 I n d i r e c t Measures of D e p r e c i a t i o n 25 3.3 R e n t a l Approach 29 3.4 Remaining V a l u e Approach 30 3.4.1 Hedonic P r i c e F u n c t i o n s and D e p r e c i a t i o n .36 3.4.2 Other Remaining V a l u e S t u d i e s 39 3.5 S p e c i f y i n g a Model 40 3.5.1 F u n c t i o n a l Form 46 4. SOME METHODOLOGICAL ISSUES 51 4.1 Lemons and Other Problems 51 4.2 Tax C r e d i t s and F i r s t Year D e p r e c i a t i o n 54 4.3 Censored Sample B i a s 55 5. DATA AND PRELIMINARY MODEL 61 6. TRACTORS 66 6.1 L i n e a r Model 66 6.2 S e m i - l o g F u n c t i o n a l Form 67 6.3 A n a l y z i n g the S t a b i l i t y of the E s t i m a t e s 70 v 6.4 Pooled Cross-section Time Series 72 6.5 Interpreting the Beta C o e f f i c i e n t s 78 6.6 Age Versus Use Depreciation 81 6.7 Results of Adding Interactive Terms to Model ..83 6.7.1 The Effect of Horsepower on Depreciation 84 6.7.2 Makes E f f e c t s and Depreciation 85 6.8 The Effect of Options on Depreciation 87 7. COMBINES AND BALERS 90 7.1 Combines 90 7.2 Balers 93 7.3 Square Balers 94 7.4 Round Balers 96 8. SUMMARY AND IMPLICATIONS FOR POLICY 98 8.1 Depreciation for Taxation 99 8.2 Suggestions for Further Research 105 REFERENCES 106 vi LIST OF TABLES TABLE PAGE 1 Summary of Resu l ts fo r Var ious Remaining Value Formulat ions 36 2 Age Versus Time Ma t r i x 41b v i i LIST OF FIGURES FIGURE PAGE 1 P o s s i b l e Forms fo r the Remaining Value P r o f i l e s 23 2 P o s s i b l e Forms fo r the E f f i c i e n c y P r o f i l e s 2h v i i i ACKNOWLEDGEMENTS I would l i k e to express my sincere gratitude to those who assisted and guided me during the writing of this thesis. In p a r t i c u l a r I would l i k e to thank Dr. C. Short, Dr. T. Hazledine and Dr. L. Staley. I would also l i k e to thank Gus Blackburn. It was he more than any other who helped me understand the complications that depreciation involves. i x 1. INTRODUCTION The depreciation of durable assets, such as machinery, i s a major cost in any business. Estimates, of depreciation are required for the valuation of assets in the construction of balance sheets. These in turn may r e f l e c t how the business i s seen by external creditors and those.with an equity position in the firm. Depreciation is also the major non-cash item used to estimate the p r o f i t a b l i t y of the firm. . Depreciation i s a concern of tax o f f i c i a l s because depreciation, in the form of c a p i t a l cost allowances, is tax deductible..The amount of this allowance should be in accord with actual depreciation, or as i s sometimes the case, be appropriately greater than actual depreciation in order to stimulate s p e c i f i c areas of investment. F i n a l l y , depreciation i s also a major issue in the management of durable assets themselves. Maintenance and repairs of assets, replacement decisions, and buy versus rent decisions a l l depend, in part, upon the depreciation of those assets. 1.1 PROBLEM STATEMENT Because depreciation cannot be d i r e c t l y observed while the asset is s t i l l in use, one of a number of rules of thumb i s generally adopted to estimate i t . These require that the form of depreciation follow one of the t r a d i t i o n a l patterns ( s t r a i g h t - l i n e , declining balance 1 2 etc.) as well as specifying the rate of depreciation for broad classes of assets. Thus, for tax purposes, farm tractors, combines and balers are each assumed to follow a s p e c i f i c rate and form of depreciation. Farm tractors, for example, are assumed to depreciate 30% of their remaining value per year throughout their l i f e (that i s , following a declining balance pattern of depreciation). Some empirical studies show, however, a pattern of high i n i t i a l depreciation followed by a constant declining balance pattern thereafter (e.g. American Society of A g r i c u l t u r a l Engineers (ASAE) 1979). The widely used ASAE estimate for die s e l t r a c t o r s , for example, i s 32% depreciation when new and 8% per year thereafter. Other studies, however, support the s t r a i g h t - l i n e depreciation assumption (e.g.Peacock and Brake 1970). There are a number of problems with a l l of these studies. None, for example, considers a complete l i s t of factors which influence remaining value. Some consider only the effect of age on remaining value. However, because in theory the price or the remaining value of a machine i s determined by the present value of the expected earnings of that machine, other factors besides age must be considered. For example, horsepower, make, special features, and hours of use w i l l a f f e c t the expected returns from the machine. While most of the studies l i s t e d below address some of these factors, none addresses a l l of them together, and no study is l a i d out in a manner which 3 f a c i l i t a t e s hypothesis t e s t i n g . The fact that no study considers the e f f e c t that cummulative hours use w i l l have on remaining value i s s i g n i f i c a n t . It i s important because hours of use, through i t s e f f e c t on repair and maintenance costs, should have a strong negative influence on expected returns and hence, remaining value. This has implications for d i f f e r e n t farm sizes which use machinery more or less i n t e n s i v e l y . For example, i f large farming operations use machinery more intensively than small operations, then t h e i r machinery may exhibit a more rapid rate of depreciation. Yet no study to date has considered cummulative hours use. Furthermore, few studies have considered the Canadian s i t u a t i o n . American estimates may not be v a l i d in Canada due to d i f f e r e n t climactic conditions, commodities or produced/* tax rules. However, much of the Canadian farm management l i t e r a t u r e s t i l l uses American, estimates of depreciation simply because comprehensive Canadian information has not been a v a i l a b l e . 1.2 OBJECTIVE This study i s a response to the need for t h i s more complete information on the depreciation of farm machinery in Canada, and the need for the incorporation of more detailed data into the estimation of th i s depreciation. The purpose of thi s research is to estimate both the rate and the form of economic depreciation of farm 4 tractors, combines and, balers in Canada. The approach u t i l i z e s used market price data to estimate "age-price" p r o f i l e s ( i . e . remaining value p r o f i l e s ) from which i t i s possible.to infer.economic depreciation. This approach is based ,upon the. assumption that the value of a machine in equilibrium j s reflected by the machine's price in the market for used machines... -1.3 PLAN OF THE THESIS The following chapter .briefly outlines the history of the development of farm machinery. The key is^sue is the extent to which major innovations have caused instant obsolescence on older vintages. Waves of obsolescence disrupt the procedures used to estimate depreciation, a l l of which rely on the assumption that value declines smoothly over the l i f e of the machine. In chapter three, the theore t i c a l model and l i t e r a t u r e review, the l i t e r a t u r e on the remaining value and the hedonic approaches is taken up. As well, t h i s section includes a review of some of the indire c t approaches to the estimation of depreciation. These past attempts help to define the model to be used in the present research. The subject of the correct functional form i s also raised here. The model arrived at is semi-log and thi s form i s tested using the Box-Tidwell procedure. The results support the use of semi-log models for estimating depreciation and t h i s , in turn, implies that the 5 frequently made assumption of constant geometric depreciation i s j u s t i f i e d . Chapter four outlines some methodological problems involved with the used market approach to depreciation. Chapter five .describes the preliminary model and the steps involved in deriving the f i n a l cross-sectional model which forms the basis for a l l other investigations in this research. A description of the data i s also included in thi s chapter. The data are interes t i n g because they are Canadian and because they include information on a large number of s p e c i f i c transactions. These, 'individual transactions data', contain' information on hours use which i s not available from the average price data which i s t y p i c a l l y used in studies of depreciation. The representativeness of the nineteen eighty cross-section is also considered here by comparing i t with three other cross-sections and by placing i t in a larger pooled cross-section time series model. Chapter six extends the model to cover combines and balers, and in chapter seven some implications for the taxation of durable farm assets and their treatment in the tax schedules are drawn. F i n a l l y , in chapter eight, some conclusions are drawn. To summarize,the object of the research i s to u t i l i z e a market-price based approach to estimate the pattern and rate of depreciation for Canadian farm machinery. This research does not represent an attempt at innovative theory so much as an attempt to apply a established technique towards the resolution of some important questions in Canadian agriculture ,notably, the depreciation of farm assets. It is f e l t that these estimates are c r u c i a l information, relevant to a number research areas (investment studies based on the durable goods model, taxation, e t c . . . ) . The intention, however, simply to offer evidence which can be used by others to resolve those questions. 2 . HISTORICAL OVERVIEW As in a l l studies of depreciation based on used machinery prices, the question arises as to what proportion of the decline in value r e f l e c t s obsolescence (due to general technological improvement in the breed) and what proportion is-due to depreciation as defined in this paper. A technological breakthrough may depress the value of those machines already in use for a number of reasons, some of which are psychological (eg.the 'keeping up with the Jones effect') Unfortunately a l l these factors cannot be accurately quantified. Hal l [1968] has in fact shown mathematically the i m p o s s i b i l i t y of separating the e f f e c t of obsolescence from the e f f e c t s of either age or time, given only information on average p r i c e s . However, in spite of t h i s , i t i s s t i l l possible to roughly check the impacts of innovation by surveying the history of the machines in question. This should permit the i d e n t i f i c a t i o n of the major technological advances that may have affected machinery value, and so warn us i f the timing of these i s l i k e l y to e f f e c t the procedure for estimating depreciation. In t h i s chapter the f i r s t section i s devoted to t h i s question as i t relates to the history of the tractor s p e c i f i c a l l y . The second section b r i e f l y outlines the history of the combine harvester and the l a s t section deals with the baler. 7 8 2.1 THE DEVELOPMENT OF THE TRACTOR In his work on-tractor depreciationy G r i l i c h e s [1960] argued that most of the r e a l l y revolutionary changes in tractor design, had been made by the 1920.'s'. • There i s no denying that in the period.after the 1920's there has been a steady trend towards larger more sophisticated and refined machines. However, i t is also true that nothing as s i g n i f i c a n t as the one piece frame, the three point hitch or the internal combustion engine has been introduced in the period since then and this is e s p e c i a l l y so of the last twenty years - the period of concern in this study. The refinements that have been made in these last twenty years, such as better and more extensive use of hydraulics, and better operator comfort features (e.g. cabs and a i r - c o n d i t i o n i n g ) , are not the types of changes that render old machines obsolete. On the other hand, these refinements may have some effect on the prices of older machines that i s unrelated to the economics of operation . The h i s t o r i c a l evidence suggests, however, that these post-1930 changes occured in a smooth progressive fashion that did not d i s t o r t the values of used machines made in one year more than machines of any other year. The tractor developed from the need for a horseless plow. The very f i r s t applications of mechanization to farming were in the form of stationary engines to which large belts could be attached and numerous tasks 9 performed. Some of these stationary engines found their way to the edges of.fields,from which point plowing could be done using cables or.chains to.draw the plow across the f i e l d . Soon these stationary-engines were replaced by great mobile steam engines. These could do a l l the work of the stationary engine and could be moved to d i f f e r e n t areas as reguired. However, they were s t i l l very awkward beasts and were wasteful of land and labour. This i s because they required large areas at the end of f i e l d s to turn around and small armies of labour to fetch water and f u e l . In fact, because steering was s t i l l so primitive, some even required teams of horses to turn them. Such huge machines did not catch on readily with the owners of small farms. About the turn of the century the internal combustion engine began to be used to power tr a c t o r s . I n i t i a l l y these were almost as large and heavy as the steam engines which preceded them, but the trend towards smaller, l i g h t e r tractors was becoming evident. This trend was completed with the introduction of the Fordson in 1917. Previously i t had been believed that massive ladder-type frames were necessary for torsional r i g i d i t y (which had been more important for steam tractors) and to add weight for t r a c t i o n . However, the Fordson's unit-block frame and l i g h t weight disproved t h i s theory. 1 1The Wallis Cub of 1913 also had a frameless type of construction, but i t was of plate s t e e l not l i k e the single piece of cast iron that was the Fordson's frame. 10 "One l o o k a t . t h e Fordson r e v e a l s how e a s i l y heavy and c o s t l y impedimenta c o u l d be d i s p e n s e d w i t h , w i t h o u t i m p a i r i n g e f f i c i e n c y , the most noteworthy example be i n g the e n t i r e absence of the u s u a l frame w i t h i t s cross-members and b r a c k e t s . The machine i n r e a l i t y was a power u n i t and t r a n s m i s s i o n gear en.bloc mounted on p a i r s of wheels t o g e t h e r w i t h the s i m p l e s t s t e e r i n g arrangements." [Wright 1962 p. 31,] W i t h the i n t r o d u c t i o n of the of the F o r d s o n , the farm t r a c t o r l o o k e d remarkably modern. The f o l l o w i n g year (1 918) I n t e r n a t i o n a l H a r v e s t e r i n t r o d u c e d a p r a c t i c a l power t a k e - o f f t o r e p l a c e the cumbersome f l y w h e e l and b e l t arrangement and a l s o e l i m i n a t e the need f o r a u x i l a r y e n g i n e s ( i n most a p p l i c a t i o n s ) t o power machinery i f the t r a c t o r was b e i n g used t o p u l l them. T h i s i n n o v a t i o n was q u i c k l y adopted by the r e s t of the i n d u s t r y . N o t i c e t h a t a l l t h i s had been a c c o m p l i s h e d p r i o r t o the 1920's. The o n l y r e v o l u t i o n a r y change t o come about a f t e r t h i s decade was the pneumatic t i r e which was i n t r o d u c e d by F i r e s t o n e i n 1932. A l l i s - C h a l m e r s was the f i r s t m a n u f a c t u r e r t o o f f e r t h e s e t i r e s on t h e i r t r a c t o r s and they " i n a u g u r a t e d a t r e n d t h a t put the t r a c t o r i n d u s t r y on a i r " [Wright 1962 p . 2 6 ] . G r i l i c h e s summarizes h i s argument w i t h a comment from Gray and D i e f f e n b a c h [ 1 9 5 7 ] : "From the s t a n d p o i n t of development, 1920 t r a c t o r , t a k e n c o l l e c t i v e l y , embodied fundamental e n g i n e e r i n g and d e s i g n i n g found perhaps i n more r e f i n e d form, i n t r a c t o r s of the p r e s e n t day. The o n e - p i e c e c a s t - i r o n frame, r e p l a c e a b l e w e a r i n g p a r t s , f o r c e - f e e d and p r e s s u r e gun l u b r i c a t i o n , e n c l o s e d t r a n s m i s s i o n , c a r b u r e t o r m a n i f o l d i n g , a i r c l e a n e r , e l e c t r i c l i g h t i n g and s t a r t i n g , a n t i f r i c t i o n b e a r i n g s , a l l o y and h e a t t r e a t e d s t e e l s and power t a k e - o f f had a l l been i n t r o d u c e d . " [p.393] 11 Refinements of t h i s b a s i c form, however, were numerous i n the years f o l l o w i n g 1920. For example, the Irishman Harry Ferguson made extensive c o n t r i b u t i o n s t o t h i s refinement process i n c l u d i n g improved h i t c h e s (the three p o i n t h i t c h ) , and the use of h y d r a u l i c s to c o n t r o l implement depth [Royal Commission on Farm Machinery 1971]. Another refinement was the adoption of the d i e s e l engine for the t r a c t o r i n the.l950's as the p r i c e of d i e s e l f u e l became c o m p e t i t i v e . In the next decade turbochargers became more common, t r a n s m i s s i o n s improved with more gear r a t i o s , and the use of h y d r a u l i c s was extended to s t e e r i n g , brakes and t r a n s m i s s i o n s to make o p e r a t i o n e a s i e r . T h i s decade was a l s o marked by i n c r e a s e s in t r a c t o r horsepower. The decade of the 1970's might be c a l l e d the "ergonomic decade" as the concern f o r the o p e r a t o r ' s h e a l t h and s a f e t y was emphasized. Engines were b e t t e r m uffled to prevent h e a r i n g damage. The operator was b e t t e r i n s u l a t e d from v i b r a t i o n to reduce back and i n t e r n a l i n j u r i e s by the adoption of s u p e r i o r s e a t i n g . R o l l - o v e r p r o t e c t i o n was i n c o r p o r a t e d to reduce the number of f a t a l i t i e s from t r a c t o r s t i p p i n g over, and cabs and a i r - c o n d i t i o n i n g became more common to p r o t e c t the operator from e x c e s s i v e heat and dust. G e n e r a l l y , then, changes were made to make the t r a c t o r s a f e r and the operator more e f f i c i e n t . While a l l of these are s i g n i f i c a n t refinements to the b a s i c t r a c t o r 1 2 d e s i g n they a r e p r o b a b l y not the k i n d s of changes t h a t would i n s t a n t l y render a l l p r e v i o u s machines o b s o l e t e . These changes c o u l d not be r e p r e s e n t e d by a d i s c o n t i n u o u s r a t e of t e c h n i c a l change. That i s , t h e s e changes d i d not lower c o s t s of p r o d u c t i o n enough t o make p r o d u c e r s who d i d not adopt them u n c o m p e t i t i v e . In t h i s sense G r i l i c h e s 1 o b s e r v a t i o n i s b a s i c a l l y c o r r e c t . Most s i g n i f i c a n t i n n o v a t i o n i n t r a c t o r d e s i g n was complete by the decade of the t w e n t i e s and s i n c e then the t r a c t o r has undergone a " c o n t i n u i n g stream of s m a l l improvements " [ G r i l i c h e s 1960 p.190] Another i s s u e r e l a t e d t o o b s o l e s c e n c e i s the a v a i l a b i l i t y of p a r t s t o r e p a i r the o l d e r machines. Some have argued t h a t equipment m a n u f a c t u r e r s d e l i b e r a t e l y " f o s t e r o b s o l e s c e n c e by f r e q u e n t model changes," [ R o y a l Commission on Farm Mac h i n e r y 1971, p . 3 2 ] . Another c o m p l a i n t i s l a c k of p a r t s s t a n d a r d i z a t i o n . However, as p o i n t e d out by i n d u s t r y o f f i c i a l s t h e r e has been c o n s i d e r a b l e s t a n d a r d i z a t i o n i n a r e a s of power t a k e - o f f , V - b e l t s , and h y d r a u l i c and e l e c t r i c a l components. A l s o as of 1971 f o u r p r o v i n c e s - A l b e r t a , M a n i t o b a , P.E.I., and Saskatchewan have had Farm Mac h i n e r y A c t s which among i o t h e r t h i n g s r e q u i r e , " t h a t the company s e l l i n g the implement w a r r a n t t h a t a s u f f i c i e n t s u p p l y of r e p a i r p a r t s be made a v a i l a b l e f o r a p e r i o d of t e n y e a r s from the date of the machines purchase and t h a t they be a v a i l a b l e w i t h i n a r e a s o n a b l e t i m e . " [ R o y a l Commission, 1971, p.547]. 13 T h e o r e t i c a l l y , a machine of a p a r t i c u l a r v i n t a g e c o u l d be so r a d i c a l l y s u p e r i o r , i n the extreme c a s e , as t o render a l l p r e v i o u s machines w o r t h l e s s . F a i l u r e t o a l l o w f o r t h i s t y pe of o c c u r r e n c e would l e a d t o an o v e r e s t i m a t e of d e p r e c i a t i o n . The b r i e f r e v i e w of the h i s t o r y of the development of the t r a c t o r , however, p r o v i d e s no e v i d e n c e of such extremes i n the l a s t twenty y e a r s which i s the p e r i o d of c o n c e r n i n t h i s study ( t h e o l d e s t t r a c t o r s c o n s i d e r e d a r e from the m i d - s i x t i e s ) . What the h i s t o r i c a l e v i d e n c e does i n d i c a t e i s a smooth, g r a d u a l p r o c e s s of improvement i n t h a t p e r i o d which i s c o n s i s t e n t w i t h a c o n t i n u o u s a g e - p r i c e r e l a t i o n s h i p . T h e r e f o r e , t o the e x t e n t t h a t t h i s t r e n d of improvements i s s t e a d y and i n e x o r a b l e , the e s t i m a t e s are r e l i a b l e . 2.2 COMBINE HARVESTERS • The h i s t o r y of the development of the combine h a r v e s t e r , u n l i k e t r a c t o r s , c o u l d not be d e s c r i b e d as a p r o c e s s of c o n t i n u a l r e f i n e m e n t . W h i l e the i n c o r p o r a t i o n of b e t t e r h y d r a u l i c s , cabs and remote s e n s i n g m o n i t o r s i n t o the b a s i c d e s i g n c o u l d be c a l l e d r e f i n e m e n t s , r e c e n t developments i n r o t a r y g r a i n s e p a r a t i o n or " a x i a l f l o w " type combines c o n s t i t u t e a major i n n o v a t i o n which i s l i k e l y d e s t i n e d t o r e p l a c e the c o n v e n t i o n a l combine. A l t h o u g h work on the c o n v e n t i o n a l combine began much e a r l i e r (Massey. H a r r i s began development i n Canada i n 1906), the combine was not i n t r o d u c e d u n t i l t he 1930's and 1 4 d i d not become common u n t i l a f t e r the war. The combine was an attempt t o reduce l a b o u r r e q u i r e m e n t s and "combine" the o p e r a t i o n s of c u t t i n g , t h r e s h i n g and c l e a n i n g . Some of the v e r y e a r l i e s t u n i t s were p u l l e d by h o r s e s and the t u r n i n g of the wheels powered,the machinery. L a t e r t r a c t o r s were used t o tow, ' p u l l - t y p e ' combines whose mechanisms were powered by a u x i l a r y e n g i n e s b e f o r e the advent of l a r g e , h i g h horsepower t r a c t o r s w i t h power t a k e - o f f . A l l combines c o n s i d e r e d i n t h i s s t u d y , however, a r e of the s e l f - p r o p e l l e d v a r i e t y which was i n t r o d u c e d l a t e r . In the c o n v e n t i o n a l machine the g r a i n i s c u t and passed t o a c e n t r a l l y l o c a t e d e l e v a t o r by means of an auger. Next the g r a i n i s passed up the e l e v a t o r t o a t h r e s h i n g c y l i n d e r which i s o r i e n t e d w i t h i t s a x i s r u n n i n g a c r o s s the machine, 90 degrees t o the d i r e c t i o n of t r a v e l . T h r e s h i n g t a k e s p l a c e as the g r a i n p asses between t h i s (convex) c y l i n d e r and what i s known as the "concave". G r a i n , c h a f f and straw a r e then p a s s e d t o s h a k e r s w h i c h , by r e c i p r o c a t i n g a c t i o n , s e p a r a t e the straw from the g r a i n and c h a f f . The g r a i n . a n d c h a f f drop down th r o u g h t h e s e s h a k e r s and by a c o m b i n a t i o n of s i e v e and fan the c h a f f i s s e p a r a t e d . The s e p a r a t e d g r a i n i s s t o r e d i n t a n k s . A l l t h i s s h a k i n g and v i b r a t i o n i s r e s p o n s i b l e f o r the f a c t t h a t c o n v e n t i o n a l combines wear out v e r y q u i c k l y . The N a t i o n a l Farm and Power Equipment D e a l e r s A s s o c i a t i o n O f f i c i a l Guide i n f a c t a d v i s e s t h a t , r e l a t i v e t o o t h e r machines, combines may d e p r e c i a t e r a p i d l y , and o l d e r 1 5 machines a r e l i k e l y t o have o n l y "junk v a l u e " [ s p r i n g 1983 p . F - 2 ] . S i n c e most of the p r i c e s r e p o r t e d i n t h i s study a r e f o r the s e c o n v e n t i o n a l combines i t i s e x p e c t e d t h a t combines w i l l e x p e r i e n c e h i g h e r r a t e s of d e p r e c i a t i o n than t r a c t o r s , f o r example. However, t h e r e i s a r e l a t i v e l y new type of combine t e c h n o l o g y a v a i l a b l e - the r o t a r y s e p a r a t i o n type (or a x i a l f l o w ) - which s h o u l d e x p e r i e n c e much s l o w e r r a t e s of d e p r e c i a t i o n . In the r o t a r y s e p a r a t i o n type of combine, the t h r e s h i n g c y l i n d e r s , b e a t e r s and s h a k e r s (or straw w a l k e r s ) a r e r e p l a c e d by a l a r g e i n c l i n e d , t u r b i n e - l i k e r o t o r t h a t s p i n s w i t h i t s a x i s o r i e n t e d p a r a l l e l t o the d i r e c t i o n the combine i s t r a v e l l i n g . The g r a i n i s g r a d u a l l y t h r e s h e d by a r u b b i n g a c t i o n as i t s p i r a l s up t o the back of the r o t o r . The open-grate c o n s t r u c t i o n of the "concave" p e r m i t s the g r a i n t o drop out as soon as i t i s t h r e s h e d . T h i s i n n o v a t i o n r e p r e s e n t s a major change f o r a number of r e a s o n s . F i r s t , " m u l t i p l e r u b b i n g " t h r e s h i n g i s both g e n t l e r and more th o r o u g h , y i e l d i n g a b e t t e r q u a l i t y g r a i n . Second, the r o t a r y system i s not a f f e c t e d by h i l l s , so t h a t e x p e n s i v e a u t o m a t i c l e v e l l i n g systems a r e not needed. T h i r d l y , the u n i t can be made much more compact. L a s t l y , the r o t a r y system i n v o l v e s fewer r e c i p r o c a t i n g p a r t s , i m p l y i n g t h a t t h e r e i s l e s s v i b r a t i o n and wear. For t h e s e reasons r a t e of p h y s i c a l d e p r e c i a t i o n , and hence of economic d e p r e c i a t i o n , s h o u l d be much lower f o r a x i a l f l o w type combines. I t has a l r e a d y been noted t h a t 16 combines (of the c o n v e n t i o n a l t y p e ) s h o u l d show a more r a p i d r a t e of d e p r e c i a t i o n t h a n , say, t r a c t o r s . T h i s more r a p i d . r a t e of d e p r e c i a t i o n f o r c o n v e n t i o n a l combines c o u l d be f u r t h e r a c c e l e r a t e d by the i n t r o d u c t i o n of the r o t a r y s e p a r a t i o n combine s i n c e t h i s t y p e s h o u l d be a b l e t o produce a s u p e r i o r 'sample' of g r a i n f o r a lower c o s t ( r e p a i r c o s t s l o w e r , r e m a i n i n g v a l u e h i g h e r e t c . ). 2.3 BALERS Wh i l e i t has been argued above t h a t t r a c t o r s have e x h i b i t e d a n e a r l y l i n e a r p a t t e r n of development i n the l a s t twenty or t h i r t y y e a r s , and t h a t combines have d i s p l a y e d a more lumpy p r o g r e s s , w i t h new d e s i g n s r e p l a c i n g o l d , the h i s t o r y of the b a l e r i s more one i n which i n n o v a t i o n s have d e v e l o p e d s i m u l t a n e o u s l y and have c o - e x i s t e d w i t h o u t one type d i s p l a c i n g a l l o t h e r s . The one t r e n d t h a t i s e v i d e n t t h r o u g h o u t i s the attempt t o make b a l i n g a s i n g l e person o p e r a t i o n - a l t h o u g h the means of a t t a i n i n g t h i s end Vary g r e a t l y . The f i e l d p i c k - u p b a l e r i n t r o d u c e d i n 1932 i s a b l e t o e l i m i n a t e two h a n d l i n g s of the c r o p . By 1940 b a l e r s which c o u l d s e l f - t i e were a v a i l a b l e and 1958 saw the i n t r o d u c t i o n of s e l f - p r o p e l l e d b a l e r s . Most b a l e r s today are of a r e of the s m a l l r e c t a n g u l a r v a r i e t y , but f o r some a p p l i c a t i o n s the l a r g e round b a l e r s i n v o l v e l e s s l a b o u r . An added advantage of the l a r g e round b a l e s i s t h e i r a b i l i t y t o shed r a i n and thus r e t a i n more of t h e i r water 17 s o l u a b l e n u t r i e n t s . U n f o r t u n a t e l y , l a r g e round b a l e s a r e d i f f i c u l t t o t r a n s p o r t so t h a t i f the hay or st r a w i s t o be s o l d then r e c t a n g u l a r b a l e r s a r e s t i l l used. For the same reason w i r e i s o f t e n used i n p l a c e of t w i n e i n square b a l e r s . There are many o t h e r t y p e s of b a l i n g equipment. Some machines compress the c r o p i n t o s m a l l cubes t h a t can be han d l e d l i k e a f l u i d and t h e r e a r e a u t o m a t i c s t a c k makers. A l l t y p e s a re s u i t e d t o p a r t i c u l a r a p p l i c a t i o n s , and a l l e x i s t s i m u l t a n e o u s l y . No one type i s so s u p e r i o r as t o render a n o t h e r o b s o l e t e . In e f f e c t , they each s e r v e a d i f f e r e n t f u n c t i o n even though t h e y a r e a l l c a l l e d b a l e r s . Only the s m a l l r e c t a n g u l a r and l a r g e round t y p e of b a l e r s a r e c o n s i d e r e d i n t h i s s t u d y , but the two t y p e s a r e d i s t i n g u i s h e d from each o t h e r so t h a t t h e i r r e l a t i v e r a t e s of d e p r e c i a t i o n can be compared. W i t h i n the p e r i o d of study c o n t i n u o u s t e c h n i c a l change can be assumed f o r bo t h these t y p e s of b a l e r s . To summarize t h i s c h a p t e r , t h e g e n e r a l r e s u l t o b t a i n e d from a review of the h i s t o r y of farm machinery i s t h a t , w i t h the p o s s i b l e e x c e p t i o n of a x i a l - f l o w combines (and the impact of t h e s e s t i l l remains t o be d e m o n s t r a t e d ) , i n n o v a t i o n over the l a s t twenty y e a r s , a t l e a s t , has come t o the i n d u s t r y i n the form of a s t e a d y stream r a t h e r than r a d i c a l o b s o l e s c e n c e c r e a t i n g changes. •3. LITERATURE REVIEW In o r d e r t o come t o an u n d e r s t a n d i n g of the model adopted i n t h i s s tudy i t i s n e c e s s a r y t o u n d e r s t a n d the p a t h t h a t the l i t e r a t u r e on d e p r e c i a t i o n has t a k e n . At i t s v e r y s i m p l e s t l e v e l , d e p r e c i a t i o n has been approached u s i n g s i m p l e and u n t e s t e d r u l e s of thumb. These r u l e s of t h u m b , - s t i l l common f o r a c c o u n t i n g and t a x a t i o n p u r p o s e s , i n c l u d e ' s t r a i g h t - l i n e ' , ' d e c l i n i n g b a l a n c e ' and 'one-hoss-shay' p a t t e r n s of d e p r e c i a t i o n . A s t r a i g h t - l i n e p a t t e r n i m p l i e s t h a t the a s s e t i n q u e s t i o n l o s e s a c o n s t a n t p e r c e n t a g e of i t s o r i g i n a l v a l u e each y e a r . The i m p o r t a n t phrase here i s ' o r i g i n a l v a l u e ' . C o n s i d e r the f o l l o w i n g example. C o n s i d e r a $10,000 a s s e t which d e p r e c i a t e s a c c o r d i n g t o a s t r a i g h t - l i n e p a t t e r n of d e p r e c i a t i o n , a t a r a t e of 10% per y e a r . I t would l o s e $1000 of v a l u e i n the f i r s t y e a r , $1000 i n the second, $1000 i n the t h i r d , f o u r t h and f i f t h e t c . I t would be " v a l u e l e s s " by the e l e v e n t h y e a r . As the name s u g g e s t s , t h e r e f o r e , s t r a i g h t - l i n e d e p r e c i a t i o n i m p l i e s a l i n e a r a g e - p r i c e p r o f i l e , but the r a t e , i n terms of a p e r c e n t a g e of c u r r e n t v a l u e , i s a c t u a l l y i n c r e a s i n g each y e a r . In c o n t r a s t t o t h i s , d e c l i n i n g b a l a n c e d e p r e c i a t i o n s u g g e s t s t h a t an a s s e t l o s e s a c o n s t a n t p e r c e n t a g e of i t s c u r r e n t v a l u e each y e a r . Because t h i s o f t e n causes c o n f u s i o n , a nother example i s g i v e n . C o n s i d e r the same $10,000 a s s e t s t i l l d e p r e c i a t i n g a t a r a t e of 10% per y e a r . T h i s time assume i t f o l l o w s a d e c l i n i n g b a l a n c e 18 1 9 p a t t e r n of d e p r e c i a t i o n . Now the a s s e t l o s e s $1000 i n the f i r s t year ( 10% of 10,000), but o n l y $900 i n the second (10% of $9000). In the t h i r d year i t l o s e s $810 (10% of $8,1.00), and c o n t i n u e s t o l o s e t h i s c o n s t a n t p e r c e n t a g e each y e a r . T h e r e f o r e , an age p r o f i l e c o r r e s p o n d i n g t o t h i s p a t t e r n of d e p r e c i a t i o n i s not l i n e a r , but i s a convex g e o m e t r i c c u r v e . E s t i m a t i n g a g e o m e t r i c a g e - p r i c e p r o f i l e , such as t h i s , would r e q u i r e a s e m i - l o g model. The t h i r d commonly used r u l e of thumb i s the one-hoss-shay p a t t e r n of d e p r e c i a t i o n . In t h i s case the a s s e t l o s e s v a l u e s l o w l y a t f i r s t , but t h i s r a t e i n c r e a s e s s h a r p l y w i t h age. Here the r a t e i n c r e a s e s both as a p e r c e n t a g e of c u r r e n t v a l u e , and of o r i g i n a l v a l u e , so i t i s d i s t i n c t from t h e o t h e r two r u l e s of thumb mentioned. A l s o the form of t h e a g e - p r i c e p r o f i l e c o r r e s p o n d i n g t o t h i s p a t t e r n i s n e i t h e r l i n e a r nor convex, but r a t h e r concave t o the o r i g i n . E a r l y on H o t e l l i n g e x p r e s s e d d i s s a t i s f a c t i o n w i t h the r u l e s of thumb approa c h e s i n h i s a r t i c l e , "A G e n e r a l M a t h e m a t i c a l Theory of D e p r e c i a t i o n " [ 1 9 2 5 ] , He proposed a "fundamental f o r m u l a " t h a t gave t h e v a l u e of a machine as a f u n c t i o n of t i m e , v a l u e of o u t p u t , o p e r a t i n g c o s t , s c r a p v a l u e , u s e f u l l i f e and the r a t e of i n t e r e s t . H o t e l l i n g ' s a r t i c l e a l s o c o n t a i n e d the i d e a t h a t " . . . t h e v a l u e of a machine i s the sum of the a n t i c i p a t e d r e n t a l s w hich i t y i e l d s , each m u l t i p l i e d by a d i s c o u n t f a c t o r t o a l l o w f o r i n t e r e s t , p l u s the s c r a p or s a l v a g e , 20 a l s o d i s c o u n t e d , " [ 1 9 2 5 ] . T h i s n o t i o n i s an i m p o r t a n t one f o r i n the p r e s e n t s t u d y the assumption i s b e i n g made t h a t the sum of the a n t i c i p a t e d r e n t a l s which a machine i s ex p e c t e d t o y i e l d i s . r e f l e c t e d by the p r i c e of t h a t machine on the used market. Hence/ i n m o d e l l i n g d e p r e c i a t i o n , r e m a i n i n g v a l u e ( g i v e n by the p r i c e of the used machine) becomes the dependent v a r i a b l e . Another i m p o r t a n t n o t i o n was H o t e l l i n g ' s d e m o n s t r a t i o n t h a t s t r a i g h t - l i n e and geometric methods of d e p r e c i a t i o n a r e e x t r e m e l y s p e c i a l c a s e s of the more g e n e r a l t h e o r y of d e p r e c i a t i o n . Thus, the f u n c t i o n a l form must be chosen w i t h c a r e s i n c e t h e s e r u l e s of thumb are s p e c i a l c a s e s t h a t impose s p e c i a l r e s t r i c t i o n s on the form of t he a g e - p r i c e p r o f i l e , as shown above. Some attempt must be made t o ensure t h a t the chosen form i s r e a s o n a b l e g i v e n the d a t a . S i n c e H o t e l l i n g t h e l i t e r a t u r e on d e p r e c i a t i o n has, s p l i t i n t o t h r e e s t r e a m s . These streams c o u l d be c a l l e d the " i n d i r e c t " a p proach, the " r e n t a l " approach and the " r e m a i n i n g v a l u e " or "used market" approach. The l a s t stream has i t s e l f d i v i d e d i n t o t h r e e branches: a farm management and a nonfarm management r e m a i n i n g v a l u e b r a n c h , and a Hedonic b r a n c h . B e f o r e p r o c e e d i n g t o examine t h e s e , however, the d i s t i n c t i o n between economic and p h y s i c a l d e p r e c i a t i o n must be made c l e a r . 21 3.1 ECONOMIC VERSUS PHYSICAL DEPRECIATION Economic d e p r e c i a t i o n may be d e f i n e d as the d e c r e a s e i n the v a l u e of an a s s e t [ H o t e l l i n g 1925]. More s p e c i f i c a l l y , the r a t e of d e p r e c i a t i o n i s the r a t e of d e c l i n e i n an a s s e t ' s p r i c e w i t h age at a s i n g l e p o i n t i n time [ H u l t e n and Wykoff 1981]. Assuming t h a t used market p r i c e s do r e f l e c t the v a l u e of an a s s e t , i t s h o u l d be p o s s i b l e t o e s t i m a t e d e p r e c i a t i o n from used p r i c e s and i n f o r m a t i o n on age. However, i t must be s t r e s s e d t h a t economic and not p h y s i c a l d e p r e c i a t i o n i s e s t i m a t e d i n t h i s manner. Only economic d e p r e c i a t i o n can be e s t i m a t e d from a g e - p r i c e p r o f i l e s . E s t i m a t i n g p h y s i c a l d e p r e c i a t i o n would r e q u i r e a n a l y s i n g e f f i c i e n c y p r o f i l e s . The r e l a t i o n s h i p between th e s e two p r o f i l e s can be seen i n f i g u r e s 1 and 2. PRICE K \ \ STRAIGHT- \ \ .L INE \ \ \ \ \ \ \ . \ v ONE-HOSS-SHAY \ \ \ \ \ GEOMETRIC . \ v \ \ \ Figure 1. P o s s i b l e Forms fo r the Remaining Value P r o f i l e s Corresponding to D i f f e ren t Pa t te rns of Economic Dep rec i a t i on . EFFICIENCY INDEX FIGURE 2. P o s s i b l e Forms for the E f f i c i e n c y P r o f i l e s Corresponding to D i f f e ren t Pat terns of Phys ica l Dep rec ia t i on . ho iii 24 As.shown the a g e - p r i c e p r o f i l e s w i l l t a k e on d i f f e r e n t forms such as convex, l i n e a r , or concave which c o r r e s p o n d t o the t h r e e forms economic d e p r e c i a t i o n i s thought t o take:, g e o m e t r i c , s t r a i g h t - l i n e and one-hoss-shay. S i m i l a r l y , t he e f f i c i e n c y p r o f i l e s c o r r e s p o n d i n g t o p h y s i c a l d e p r e c i a t i o n can t a k e v a r i o u s forms: g e o m e t r i c convex, convex (but l e s s convex than g e o m e t r i c ) and "box shaped".(see f i g u r e 2 ) . These forms c o r r e s p o n d t o the t h r e e forms t h a t p h y s i c a l d e p r e c i a t i o n i s t y p i c a l l y thought t o f o l l o w . U n f o r t u n a t e l y , these a r e a l s o c a l l e d d e c l i n i n g b a l a n c e , s t r a i g h t - l i n e and one-hoss-shay ( h e n c e f o r t h OHS). As these f i g u r e s d e monstrate, however, i t i s o n l y i n the case of the geom e t r i c form a re the shapes of the two p r o f i l e s a r e e x a c t l y e q u i v a l e n t . The d i f f e r e n c e between the two p r o f i l e s i s seen by c o n s i d e r i n g the OHS p a t t e r n . A l i g h t b u l b , f o r example, f o l l o w s an OHS p a t t e r n of p h y s i c a l d e p r e c i a t i o n i n t h a t i t performs a t peak e f f i c i e n c y up u n t i l the moment i t burns o u t . Thus, the p h y s i c a l d e p r e c i a t i o n p a t t e r n f o r OHS i s box-shaped as shown. On the o t h e r hand, the economic d e p r e c i a t i o n p a t t e r n ( i . e . t he shape of the a g e - p r i c e p r o f i l e ) f o r a l i g h t b u l b would not be box-shaped, but concave as drawn. T h i s i s because even though the l i g h t b u l b i s o p e r a t i n g a t 100% of i t s maximum e f f i c i e n c y , i t i s n e a r i n g the end of i t s l i f e s p a n and i s c o n s e q u e n t l y worth l e s s . In o t h e r words, the a n t i c i p a t e d r e n t a l s , or the 25 e x p e c t e d r e t u r n s , from the o l d e r b u l b . a r e l e s s so t h a t the c o r r e s p o n d i n g a g e - p r i c e , p r o f i l e i s downward s l o p i n g t h r o u g h o u t . I t i s concave,, s i n c e the remaining, v a l u e of the b u l b drops p r e c i p i t o u s l y as the maximum age approaches. The e f f i c i e n c y , and the a g e - p r i c e p r o f i l e s , t h e r e f o r e , , a re v e r y d i f f e r e n t a n i m a l s and w i l l o n l y be the same i n the case of the ge o m e t r i c form as .is shown i n f i g u r e s 1 and 2 . 3.2 INDIRECT MEASURES OF DEPRECIATION , Gi v e n t h a t i s economic and not p h y s i c a l d e p r e c i a t i o n t h a t i s b e i n g e s t i m a t e d , t h e r e a r e s t i l l a number of ways t o approach t h i s e s t i m a t i o n . For example, t h e r e a r e a number of n o n - p r i c e or i n d i r e c t approaches t o measuring d e p r e c i a t i o n . There i s the inve s t m e n t approach [Coen 1975,80], the p o l y n o m i a l benchmark approach and the Bureau of Economic A n a l y s i s (BEA) approach. The BEA approach i s a c o m p l i c a t e d example of an i n d i r e c t approach [see H u l t e n and Wykoff 1981] which i s e x t r e m e l y a r b i t r a r y . A l t h o u g h i t i s d i r e c t e d towards an e s t i m a t i o n of p h y s i c a l d e p r e c i a t i o n , i t a c h i e v e s t h i s v i a some u n t e s t e d assumptions about economic d e p r e c i a t i o n . I t i s brought i n t o the d i s c u s s i o n f i r s t because i t h i g h l i g h t s how a r b i t r a r y the c h o i c e of economic d e p r e c i a t i o n p a t t e r n s o f t e n i s , and s e c o n d l y because i t a n t i c i p a t e s t h e importance of r e t i r e m e n t d i s t r i b u t i o n s t o the e s t i m a t i o n of economic d e p r e c i a t i o n . 2 6 The method t a k e s a r e t i r e m e n t d i s t r i b u t i o n and a p p l i e s i t t o a p a r t i c u l a r y e a r ' s investment i n o r d e r t o s e p a r a t e a y e a r l y i nvestment f l o w i n t o s u b c a t e g o r i e s ("subcohorts") which a r e i d e n t i f i e d by a p a r t i c u l a r r e t i r e m e n t d a t e . Next, each subcohort i s d e p r e c i a t e d a c c o r d i n g t o some a r b i t r a r i l y chosen s c h e d u l e . For example, s t r a i g h t - l i n e economic d e p r e c i a t i o n might be a p p l i e d t o the f i r s t s u b cohort f o r the number of y e a r s d i c t a t e d by the r e t i r e m e n t d i s t r i b u t i o n . The p r o c e d u r e i s r e p e a t e d f o r a l l s u b c o h o r t s and t h e i r sum g i v e s t o t a l d e p r e c i a t i o n f o r the c o h o r t ( i . e . f o r the e n t i r e v i n t a g e ) . P h y s i c a l d e p r e c i a t i o n i s g l e a n e d from net c a p i t a l s t o c k w h i c h i s c a l c u l a t e d by a d d i n g the o r i g i n a l y e a r l y f l o w t o a p e r p e t u a l i n v e n t o r y of c u m u l a t i v e g r o s s i n v e s t m e n t , and a d d i n g d e p r e c i a t i o n d e d u c t i o n s t o the i n v e n t o r y of accumulated d e p r e c i a t i o n . Another i n d i r e c t approach (one which i s d i r e c t e d a t economic d e p r e c i a t i o n ) i s the investment approach d e v e l o p e d by Coen [1975, 1980], I t t r i e s t o i n f e r p a t t e r n s of economic d e p r e c i a t i o n from net c a p i t a l e x p e n d i t u r e s i n v a r i o u s m a n u f a c t u r i n g i n d u s t r i e s . Coen used t h i s i n d i r e c t a p proach, as opposed t o a d i r e c t a p p r o x i m a t i o n t e c h n i q u e , because he f e l t t h a t the absence of markets f o r many c a p i t a l goods l i m i t e d the v a l u e of a d i r e c t p r i c e - o r i e n t e d a p proach. ( N o t i c e , however, t h a t the w e l l d e v e l o p e d used markets f o r farm machinery do a l l o w f o r a more d i r e c t approach t o be taken here.) He assumed t h a t replacement 27 investment r e f l e c t s economic d e p r e c i a t i o n . Coen then r e l a t e d net investment ( i . e . net of r e p l a c e m e n t ) t o p a s t changes i n t h e d e s i r e d c a p i t a l s t o c k and shows t h a t t h i s net i n v e s t m e n t , and t h e . i m p l i c i t r e n t a l p r i c e of c a p i t a l depend b o t h on l e n g t h of s e r v i c e l i v e s and on the r a t e of p h y s i c a l d e p r e c i a t i o n . Because d a t a on t h i s p h y s i c a l r a t e of d e p r e c i a t i o n are s c a r c e , Coen made v a r i o u s assumptions about the r a t e of p h y s i c a l d e p r e c i a t i o n i n coming up w i t h h i s e s t i m a t i o n of economic d e p r e c i a t i o n . In f a c t Coen f i t t e d f i v e d i f f e r e n t c o m b i n a t i o n s of p h y s i c a l d e p r e c i a t i o n and s e r v i c e l i v e s t o time s e r i e s d a t a on e x p e n d i t u r e s f o r equipment and b u i l d i n g s i n h i s m a n u f a c t u r i n g i n d u s t r i e s . . Coen c o n c l u d e d t h a t the form of the p h y s i c a l d e p r e c i a t i o n f u n c t i o n i s not g e o m e t r i c as i s commonly assumed (which would i m p l y t h a t the form of economic d e p r e c i a t i o n a l s o i s not g e o m e t r i c ) , but more of a one-hoss-shay p a t t e r n . W h i l e Coen's approach i s an i n d i r e c t method of e s t i m a t i n g economic d e p r e c i a t i o n i t does l e n d i t s e l f more t o r e s e a r c h d i r e c t e d a t p h y s i c a l d e p r e c i a t i o n . In f a c t Penson, et al [1981] e x t e n d Coen's approach t o d e v e l o p an e s t i m a t e of c a p a c i t y , or p h y s i c a l d e p r e c i a t i o n f o r farm t r a c t o r s . In comparing t h i s t o e n g i n e e r i n g d a t a on p h y s i c a l d e p r e c i a t i o n they a l s o found the g e o m e t r i c p a t t e r n t o be a poor assumption f o r t r a c t o r s . N ote, however, t h a t t h e i r i n t e n t i o n was t o e s t i m a t e p h y s i c a l d e p r e c i a t i o n and n o t , as Coen had i n 28 mind, t o e s t i m a t e economic d e p r e c i a t i o n i n d i r e c t l y u s i n g p h y s i c a l d e p r e c i a t i o n . F i n a l l y , t h e r e i s the p o l y n o m i a l benchmark approach t o i n d i r e c t l y measuring d e p r e c i a t i o n . B r i e f l y t h i s c o n s i s t s of assuming t h a t , t h e c a p i t a l s t o c k i n any year ( t ) i s the r e a l g r o s s investment f o r t h a t year p l u s what i s l e f t from the p r e v i o u s year - t h a t i s , the p r e c e d i n g y e a r ' s u n d e p r e c i a t e d c a p i t a l s t o c k . T h i s same assumption i s made f o r the p r e c e d i n g year ( t - 1 ) . By assuming t h a t the d e p r e c i a t i o n i s bo t h g e o m e t r i c ( i e . a c o n s t a n t p r o p o r t i o n of r e m a i n i n g v a l u e i n any y e a r ) and g e o m e t r i c i n a l l y e a r s (the types of i n v e s t m e n t made i n 1970, 7 1 , . . . e t c . a l l d e p r e c i a t e g e o m e t r i c a l l y ) i t i s p o s s i b l e t o r e p e a t e d l y s u b s t i t u t e f o r the p r e c e d i n g y e a r ' s c a p i t a l s t o c k and o b t a i n an e x p r e s s i o n which d e f i n e s a p o l y n o m i a l . I f e s t i m a t e s of benchmark inv e s t m e n t a r e a v a i l a b l e [say K ( t ) and K ( t - 1 ) ] as w e l l as data on t h e inve s t m e n t s e r i e s , i t i s p o s s i b l e t o s o l v e f o r a unique v a l u e of d e p r e c i a t i o n , [see N i s h i m i z i 1974] T h i s i s an example of a t e c h n i q u e f o r the study of d e p r e c i a t i o n which r e q u i r e s the a s s s u m p t i o n of g e o m e t r i c ( d e c l i n i n g b a l a n c e ) d e p r e c i a t i o n f o r the proced u r e t o be t r a c t a b l e . U n f o r t u n a t e l y , an a t t e m p t t o check the soundness of t h i s a s s u m p t i o n , g i v e n the d a t a , i s r a r e l y made. » 29 3.3 RENTAL APPROACH An a l t e r n a t i v e approach t o the e s t i m a t i o n of economic d e p r e c i a t i o n i s to l o o k a t the change i n r e n t a l p r i c e s w i t h age. T h i s approach was adopted by Taubman and Rasche [1969] and i s the m o s t - d i r e c t approach of any mentioned so f a r . I t i s b a s i c a l l y an attempt t o e s t i m a t e a g e - r e n t p r o f i l e s i n s t e a d of a g e - p r i c e p r o f i l e s . T h i s i s p o t e n t i a l l y i n t e r e s t i n g because r e n t s can be r e l a t e d d i r e c t l y t o e f f i c i e n c y i n d e x e s . I t s second advantage i s t h a t . i t can s i d e s t e p the "lemons i s s u e " . The "lemons i s s u e " , which w i l l be taken up i n g r e a t e r d e t a i l below, d e a l s w i t h asymmetry of i n f o r m a t i o n i n the market f o r used a s s e t s . I t s u g g e s t s t h a t owners w i l l o n l y s e l l poor q u a l i t y machines and w i l l r e t a i n the good ones, so t h a t a f t e r a p e r i o d of t i m e , p r i c e s i n the second-hand market w i l l become d e p r e s s e d and be u n r e p r e s e n t a t i v e of the v a l u e of the whole c o h o r t . I f t h i s i s t r u e then d e p r e c i a t i o n e s t i m a t e s d e r i v e d s o l e l y from used market p r i c e s would tend t o o v e r e s t i m a t e a c t u a l d e p r e c i a t i o n . T h i s , however, i s not a problem i n the r e n t a l approach because l e a s i n g companies would not f i n d i t i n t h e i r i n t e r e s t t o l e a s e "lemons" t o t h e i r c l i e n t s . W h i l e these advantages e x i s t t h e r e i s another problem - the problem of l o n g - t e r m l e a s e s . Long-term l e a s e s a r e o f f e r e d t o reduce the occurence of i d l e (nonrented) machinery. However, t h e s e s p e c i a l d e a l s , a t a c o n s t a n t r e n t , t e n d t o d e s t r o y the c o n n e c t i o n between d e c l i n i n g 30 e f f i c i e n c y and the r e n t a l p r i c e . That i s , t h e r e may be no d e c l i n e i n r e n t a l p r i c e s w i t h age. However, i f the t h e o r e t i c a l c o n n e c t i o n between r e n t a l p r i c e and age was m a i n t a i n e d i n such a c a s e , the r e s u l t s would t e n d t o ( m i s l e a d i n g l y ) i n d i c a t e a one-hoss-shay p a t t e r n of e f f i c i e n c y d e c l i n e . Because of t h i s , i t has been suggested ( H u l t e n and Wykoff [1981]) t h a t a p r o p e r l y c o n d u c t e d used market study i s s u p e r i o r . 3.4 REMAINING VALUE APPROACH The r e m a i n i n g v a l u e approach t a k e s d a t a on the ages and p r i c e s of used a s s e t s and a t t e m p t s t o f i t an a g e - p r i c e p r o f i l e t o t h e s e d a t a . Peacock and Brake [1970] used t h i s approach t o show t h a t the s t a n d a r d r u l e s of thumb used i n a c c o u n t i n g f a i l t o c a p t u r e a c t u a l economic d e p r e c i a t i o n . They f i t t e d a model f o r t r a c t o r s i n the U n i t e d S t a t e s which gave r e m a i n i n g v a l u e as a l i n e a r f u n c t i o n of age: (1) RV(A) = 65.6 - 4.1(A) where 'A' r e p r e s e n t s age. In o t h e r words t h i s model i m p l i e s t h a t a machine l o s e s 34.6 % of i t s v a l u e i m m e d i a t e l y a f t e r p u r c h a s e 2 and 4.1 % of i t s o r i g i n a l v a l u e e v e r y y e a r t h e r e a f t e r . N o t i c e t h a t t h i s l i n e a r form i m p l i e s a s t r a i g h t - l i n e p a t t e r n of d e p r e c i a t i o n . 2 t h i s phenomenon has been c a l l e d "as soon as you d r i v e i t o f f the l o t " d e p r e c i a t i o n . 31 Another example of the r e m a i n i n g v a l u e approach a p p l i e d t o t r a c t o r s i s p r o v i d e d by the American S o c i e t y of A g r i c u l t u r a l E n g i n e e r s (ASAE). T h e i r f o r m u l a f o r r e m a i n i n g v a l u e i s as f o l l o w s . A (2) R v ( A ) = S v , ( S v 2 ) where RV(A) i s the r e m a i n i n g v a l u e of a t r a c t o r of age A, Sv, i s s a l v a g e v a l u e f a c t o r one and S v 2 i s s a l v a g e v a l u e f a c t o r two. For d i e s e l t r a c t o r s the ASAE has e s t i m a t e d Sv, = .68 and S v 2 = .92. Here the term Sv, i s i n c l u d e d t o account f o r the extreme i n i t i a l l o s s i n v a l u e and the term S v 2 i s i n c l u d e d t o account f o r the b a s i c a l l y c o n s t a n t (or g e o m e t r i c ) r a t e of y e a r l y l o s s i n v a l u e t h e r e a f t e r . T h i s form, t h e r e f o r e , i m p l i e s a c o n s t a n t or g e o m e t r i c p a t t e r n of d e p r e c i a t i o n a f t e r the f i r s t y e a r . T h i s ASAE f o r m u l a i s w i d e l y used t o approach d e p r e c i a t i o n and has a l s o been used as the b a s i s f o r Canadian s t u d i e s . For example, Andruchow and S h o r t r e e d [1976] used the ASAE f o r m u l a t o produce r e m a i n i n g v a l u e t a b l e s f o r farm machinery i n western Canada. M c N e i l l [1979] d e v e l o p e d a d i s t i n c t r e m a i n i n g v a l u e f o r m u l a f o r t r a c t o r d e p r e c i a t i o n u s i n g Canadian d a t a . He e s t i m a t e d the r e m a i n i n g v a l u e f u n c t i o n f o r farm t r a c t o r s i n t he s o u t h e r n i n t e r i o r of B.C. based on a sample of 32 used t r a c t o r s . The t r a c t o r s i n h i s sample were r a t e d f o r c o n d i t i o n on a s c a l e of one t o f o u r . T h i s i n n o v a t i o n was 32 p o s s i b l e s i n c e the compactness of the sample p e r m i t t e d f a m i l i a r i t y w i t h each c a s e . M c N e i l l ' s r i c h e r model was e x p o n e n t i a l i n form, i m p l y i n g g e o m e t r i c d e p r e c i a t i o n . -.4299 -.0436A + .0691C (3) RV(A) = I00e where A e q u a l s age, and C r e p r e s e n t s c o n d i t i o n . A s i m i l a r p a t t e r n was a l s o adopted i n the p r e s e n t s t u d y . Moving f u r t h e r i n t h i s d i r e c t i o n R e i d and B r a d f o r d [1983] have a l s o i n c l u d e d net farm income i n t h e i r model as w e l l as makes of machine and horsepower (measured a t the power t a k e - o f f ) . -.273 .242 -.305 -.121 -.263 (4) RV(A) = 368.7(A) HP NF MX MY .-621 .205 T1 T2 T h i s i s a s i m p l i f i e d v e r s i o n of t h e i r f o r m u l a , where A r e p r e s e n t s age, HP i s horsepower, NF i s net farm income, and MX and MY are dummy v a r i a b l e s t o account f o r d i f f e r e n t makes. T1 and T2 a r e " t e c h n o l o g i c a l change time index dummy v a r i a b l e s " . N o t i c e t h a t t h i s model must be e s t i m a t e d i n l o g - l i n e a r form. In a n o t h e r s t u d y , Letham and Baker have argued t h a t f a c t o r s such as horsepower, i n f l a t i o n , the p r i c e of new machines and the make of the t r a c t o r a l l a f f e c t the r e m a i n i n g v a l u e of the second-hand machine. Letham and Baker [ 1 9 8 1 ] , t h e r e f o r e , d i s t i n g u i s h e d between d i e s e l and 33 g a s o l i n e t r a c t o r s and a l l o w e d f o r d i f f e r e n c e s i n horsepower as w e l l as i n f l a t i o n . T h i s model i s as f o l l o w s : „ A B2 e, (g)RV = B0B, I , C 0e Where C 0 r e p r e s e n t s new l i s t p r i c e , A r e p r e s e n t s age and I e q u a l s a machine p r i c e i n d e x . Elements of Letham and Baker's model were i n c l u d e d i n t h i s s tudy such as dummy v a r i a b l e s f o r d i f f e r e n t makes and horsepower ( i n t h e i r case drawbar horsepower not power t a k e - o f f or.PTO hor s e p o w e r ) . Dummies were not i n c l u d e d f o r f u e l t y p e and 4-wheel d r i v e i n t h i s s tudy because a l l t r a c t o r s i n the sample were d i e s e l and because 4-wheel d r i v e t r a c t o r s were not sampled. The source of Letham and Baker's d a t a was the O f f i c i a l Guide , an American p u b l i c a t i o n w hich l i s t s average p r i c e d a t a . T h i s c o n t r a s t s w i t h the Canadian d a t a source used here which quotes a c t u a l p r i c e s from i n d i v i d u a l t r a n s a c t i o n s . The use of average p r i c e d a t a , by Letham and Baker, does not p e r m i t them t o i n c l u d e v a r i a b l e s f o r c o n d i t i o n , as M c N e i l l [1979] has done, o p t i o n s on each machine, or i n c l u d e hours of use. A l l of t h e s e , however, a r e i n c l u d e d i n the p r e s e n t s t u d y . An i n t e r e s t i n g a s p e c t of t h e i r model, which was adopted h e r e , was the use of terms which i n t e r a c t w i t h age. These terms a l l o w the v a r i o u s independent v a r i a b l e s 34 such as d i e s e l or horsepower t o change the r a t e of d e p r e c i a t i o n . W i t h o u t t h e s e , the r a t e of d e p r e c i a t i o n would be f o r c e d t o be c o n s t a n t ( r e g a r d l e s s of whether the machine was gas or d i e s e l powered e t c ) . U n f o r t u n a t e l y , because of the way they s e t up t h e i r model, i t i s d i f f i c u l t t o t e s t any hypotheses on these terms. T h i s f u n c t i o n a l form must be e s t i m a t e d i n a l o g - l o g form. T h i s imposes an i n t e r e s t i n g s t r u c t u r e on the p a t t e r n of d e p r e c i a t i o n , r e q u i r i n g the r a t e t o d e c r e a s e each y e a r . T h i s p a t t e r n i s d i f f e r e n t from both the s t r a i g h t - l i n e ( l i n e a r form) and d e c l i n i n g b a l a n c e ( s e m i - l o g f o r m ) . Table 1 o u t l i n e s the r e s u l t s of the v a r i o u s r e m a i n i n g v a l u e f o r m u l a s a l t h o u g h t h e s e have been s i m p l i f i e d somewhat from t h e i r o r i g i n a l f o r m u l a t i o n . TABLE 1. Summary of Results f o r Various Remaining Value Formulations. AGE AUTHOR 0 1 y. 4 5 REMAINING VALUE: % o f o r i g i n a l P e a c o c k / B r a k e 65. 60 61. 50 57. 40 53. 30 49. 20 45. 10 ASAE jf 68. 00 62. 56 57.56 52.95 43. 71 44. 32 M c N e i l l 85. 77 79. 87 74. 33 69.27 64. 50 60. 07 R a i d / B r a d f o r d * 70. 00 70. 00 57.93 42.92 29. 40 13. 94 Hulten/Wyko-ff * 100. 00 89. 30 79.74 71.21 63. 59 56. 79 L s a t h a m / B a k e r * 62. 38 cc 94 50. 16 44.98 40. OO 36. 16 DEPRECIAT ION RATE : • 9 P e a c o c k / B r a k e 34. 40 6. 25 6. 67 7. 14 7. 69 8. o o ASAE "TO 00 a . 00 3. 00 S. 00 3. 00 a . 00., M c N e i l l * 14. •-JT 33 is. 33 6.33 6. S3 6. 38 Rei d/Brad-ford MA 30. 00 17. 24 25. 91 31. 51 O -J - 56 Hu11 en/Wyk a11 * 0. 00 10. 70 10. 70 10.70 10. 70 10. 70 Leatham/Baker * 37. 62 10. 33 10. 33 10.33 10. 33 10. 33 Indicates simplified results 3 6 3.4.1 HEDONIC PRICE FUNCTIONS AND DEPRECIATION The approach used i n the .'hedonic p r i c e ' l i t e r a t u r e i s v e r y s i m i l a r t o the approach used here t o e s t i m a t e d e p r e c i a t i o n . The "Hedonic H y p o t h e s i s " assumes t h a t any good can be viewed as a bundle of c h a r a c t e r i s t i c s or a t t r i b u t e s , each of which has i t s own i m p l i c i t p r i c e . The f i n a l p r o d u c t p r i c e i s , t h u s , a f u n c t i o n of the ' i m p l i c i t ' p r i c e s of the i n d i v i d u a l c h a r a c t e r i s t i c s . F u r t h e r m o r e , i t i s p o s s i b l e t o determine t h e s e i n d i v i d u a l i m p l i c i t p r i c e s by examining the p r i c e s of s l i g h t l y d i f f e r e n t v e r s i o n s of the same f i n a l good c o n t a i n i n g v a r i o u s l e v e l s of each c h a r a c t e r i s t i c . T h i s approach i m p l i e s the need f o r d a t a which a re s p e c i f i c enough t o g i v e the l e v e l s of the im p o r t a n t u n d e r l y i n g c h a r a c t e r i s t i c s . Important examples of t h i s approach a r e G r i l i c h e s [1961 ], Ohta and G r i l i c h e s [1974] and T r i p l e t t [ 1 9 7 4 ] . In the many Hedonic s t u d i e s the a u t h o r s were l o o k i n g a t a u t o m o b i l e s , but the approach used here f o r the study of farm machinery i s s i m i l a r . In the case of a u t o m o b i l e s many d i f f e r e n t examples of the same model can be examined, each h a v i n g d i f f e r e n t amounts of horsepower, numbers of c y l i n d e r s and o p t i o n s ( h a r d t o p s , power brakes e t c . ) From t h i s type of a n a l y s i s i t i s p o s s i b l e t o a s s i g n a v a l u e t o a u n i t of a p a r t i c u l a r c h a r a c t e r i s t i c ( s a y , the v a l u e of one horsepower or the v a l u e of a r a d i o ) . W h i l e not b i l l e d as such, the s t u d i e s done by R e i d and B r a d f o r d , and by Letham and Baker go some d i s t a n c e 37 down a H e d o n i c - l i k e p a t h . In t h e i r models, they assumed t h a t the r e m a i n i n g v a l u e of a machine can be r e p r e s e n t e d by, or broken down i n t o , v a r i o u s " e f f e c t s " . These e f f e c t s on the r e m a i n i n g v a l u e (or p r i c e ) a r e a l s o due t o d i f f e r e n t l e v e l s of v a r i o u s c h a r a c t e r i s t i c s such as horsepower, o p t i o n s and make. These s t u d i e s mark a t r e n d i n the r e m a i n i n g v a l u e l i t e r a t u r e towards the i n c o r p o r a t i o n of a very H e d o n i c - l i k e ( i . e . i m p l i c i t p r i c e ) approach. By e x t e n d i n g t h i s a n a l y s i s a c r o s s d i f f e r e n t makes i t i s then p o s s i b l e t o f i n d a more e x a c t i m p l i c i t v a l u e of a p a r t i c u l a r c h a r a c t e r i s t i c . The e x p e c t a t i o n i n the Hedonic l i t e r a t u r e i s t h a t the i m p l i c i t p r i c e of any c h a r a c t e r i s t i c s h o u l d be c o n s t a n t a c r o s s a l l makes and models, g i v e n t h a t the d e f i n i t i o n and break-down o f t h e c h a r a c t e r i s t i c s i s s u b t l e enough. The Hedonic approach and i t s v a l i d i t y i n a p r o d u c t i o n s e t t i n g , however, i s not the s u b j e c t of t h i s r e s e a r c h . I t i s mentioned because, i f the a n a l y s i s i s extended t o the second-hand market, and i f the age of a p r o d u c t o r i t s newness i s a d m i t t e d as a c h a r a c t e r i s t i c t o which an i m p l i c i t p r i c e i s a t t a c h e d , then i t i s p o s s i b l e t o examine d e p r e c i a t i o n v i a the hedonic a p p r o a c h . Ohta and G r i l i c h e s [1974] have done t h i s f o r a u t o m o b i l e s , and the r e s e a r c h b e i n g done here on farm machinery i s s i m i l a r . Because the d a t a used h e r e i n c o n t a i n i n f o r m a t i o n on make, horsepower, v a r i o u s o p t i o n s , hours used, c o n d i t i o n , and age, i t i s 38 p o s s i b l e t o s e p a r a t e the e f f e c t s each have on the r e m a i n i n g v a l u e of a machine. Other s t u d i e s h a v i n g o n l y d a t a on age and t o t a l p r i c e (or r e m a i n i n g v a l u e ) a r e lumping t o g e t h e r a m y r i a d of d i f f e r e n t i m p l i c i t p r i c e s and c a l l i n g t h i s the i m p l i c i t ( n e g a t i v e ) p r i c e of age or d e p r e c i a t i o n . - F o r some purposes t h i s i s a c c e p t a b l e s i n c e o n l y a net f i n a l f i g u r e i s r e q u i r e d . There a r e , however, c i r c u m s t a n c e s when knowing the pure age e f f e c t would be b e t t e r . F or example, knowing the pure i m p l i c i t p r i c e of age and t h e i m p l i c i t p r i c e of the o t h e r c h a r a c t e r i s t i c s i t i s p o s s i b l e t o combine them i n a p a i r w i s e f a s h i o n t o see i f c e r t a i n c h a r a c t e r i s t i c s d e p r e c i a t e a t a s l o w e r or more r a p i d r a t e There i s a l s o some b e n e f i t t o be g a i n e d from s e p a r a t i n g the n e g a t i v e i m p l i c i t p r i c e of age from the n e g a t i v e i m p l i c i t p r i c e of h o u r s , e s p e c i a l l y i n f o r m u l a s i n which b o t h appear. A n o t h e r b e n e f i t of a d e t a i l e d d a t a s o u r c e i s the a b i l i t y t o compare the pure age e f f e c t ( i e . t h e i m p l i c i t n e g a t i v e p r i c e of age) f o r d i f f e r e n t makes. Ohta and G r i l i c h e s [1974] would e x p l a i n such d i f f e r e n t i a l d e p r e c i a t i o n a c r o s s makes as the i n a b i l i t y of " m a k e - e f f e c t s " t o p e r s i s t i n the second-hand market. Here m a k e - e f f e c t s a r e d e f i n e d as l e f t - o u t v a r i a b l e s which t e n d t o o v e r r i d e measurable p h y s i c a l or q u a l i t a t i v e d i f f e r e n c e s (Ohta and G r i l i c h e s [ 1 9 7 4 ] ) . The i m p l i c i t p r i c e of age ( i . e . d e p r e c i a t i o n ) s h o u l d be c o n s t a n t a c r o s s a l l makes and t h i s h y p o t h e s i s can be t e s t e d i n t h i s s t u d y . Thus, a 39 g r e a t d e a l of r i c h n e s s of economic a n a l y s i s i s a f f o r d e d by the h i g h l y d e t a i l e d ( d i s a g g r e g a t e d ) d a t a s e t such as the one p r o v i d e d by the e a r l i e r i s s u e s of the M a r s h a l l ' s  Canadian Farm Equipment Guide 3 3.4.2 OTHER REMAINING VALUE STUDIES Another b r a n c h of the r e m a i n i n g v a l u e l i t e r a t u r e d e v e l o p e d o u t s i d e the farm management stream. A v e r y e a r l y attempt t o use market p r i c e s t o e s t i m a t e a c t u a l d e p r e c i a t i o n was Terborgh [ 1 9 5 4 ] . S e c o n d l y , G r i l i c h e s conducted a s t u d y of d e p r e c i a t i o n of farm t r a c t o r s from market d a t a i n [ 1 9 6 0 ] , He e x p r e s s e d d i s s a t i s f a c t i o n w i t h USDA c h o i c e s of the r a t e and form of d e p r e c i a t i o n and n o t e d : "Nowhere does the USDA e x p l i c i t l y d efend i t s c h o i c e of the d e p r e c i a t i o n r a t e . " [ p.197] He a l s o p r o v i d e d one of the f i r s t p i e c e s of r e a l e v i d e n c e , based on market d a t a , s u p p o r t i n g a p a r t i c u l a r d e p r e c i a t i o n form: "From an e x a m i n a t i o n of p r i c e s of used farm t r a c t o r s , ages one t o t h i r t e e n f o r ten d i f f e r e n t p o i n t s of time d u r i n g the y e a r s 1937-58, G r i l i c h e s c o n c l u d e s : ' t h e data p o i n t t o a d e c l i n i n g b a l a n c e d e p r e c i a t i o n model, w i t h a r a t e somewhat h i g h e r i n the 1930*s than i n the 1950's. 1" (Jorgenson p.214) B a s i c a l l y , G r i l i c h e s approach was t o p l o t a g e / p r i c e p r o f i l e s . He a l s o a d j u s t e d t r a c t o r p r i c e s f o r c r o p p r i c e s t o get some n o t i o n of " r e a l p r i c e s " . There have been numerous o t h e r " p r i c e - o r i e n t e d " s t u d i e s as l i s t e d by H u l t e n and W y k o f f [ l 9 8 l ] and 3 l a t e r i s s u e s went t o a more common average p r i c e format i n which most of t h i s d e t a i l was s a c r i f i c e d . 40 J o r genson[1973] i n t h e i r s u r v e y s . For example, under the hea d i n g of " a u t o m o b i l e s " t h e s e i n c l u d e : Akerman[1973], Cagan[1971], Chow[l957 and.60], Ohta and G r i l i c h e s t 1 9 7 6 ] , Ramm[l970] and Wykof f [ 1 970]. As. w e l l p i c k - u p t r u c k s have been s t u d i e d by H a l l [1971]-, machine t o o l s by Biedleman [1976] s h i p s by .Lee [19.78] r e s i d e n t i a l h o u s i n g by C h i n l o y [ 1 9 7 7 ] and by M a l p e z z i , Ozanne and Thi b o d e a u [ 1 9 8 0 ] . 3.5 SPECIFYING A MODEL In the p r e v i o u s c h a p t e r s the a r b i t r a r y n a t u r e of n o n p r i c e approaches t o the e s t i m a t i o n of d e p r e c i a t i o n was d i s c u s s e d . There was a l s o a d i s c u s s i o n of the problems i n v o l v e d w i t h the r e n t a l approach t o the e s t i m a t i o n of d e p r e c i a t i o n , namely, the tendency f o r l o n g - t e r m l e a s e s t o i n d i c a t e a one-hoss-shay p a t t e r n of d e p r e c i a t i o n even when one does not e x i s t . F i n a l l y , i t was noted t h a t some a u t h e r s who used n o n p r i c e approaches d i d so s i m p l y because t h e r e was i n s u f f i c i e n t p r i c e i n f o r m a t i o n f o r the a s s e t s t h e y were s t u d y i n g . Because ample p r i c e i n f o r m a t i o n on farm a s s e t s i s a v a i l a b l e , and f o r the o t h e r reasons mentioned, a d i r e c t p r i c e , or r e m a i n i n g v a l u e approach i s t o be used h e r e . T h i s c h a p t e r d e s c r i b e s the b a s i c model. U s i n g e a r l i e r r e m a i n i n g v a l u e s t u d i e s as a base, the c h o i c e of t h e o r e t i c a l model i s much s i m p l e r . At the v e r y s i m p l e s t l e v e l , the f o l l o w i n g b a s i c model i s proposed i n a l l r e m a i n i n g v a l u e s t u d i e s . L e t t i n g the market 41 t r a n s a c t i o n p r i c e (P) be a f u n c t i o n of age (A) one can assume the f o l l o w i n g r e l a t i o n s h i p . (6) P = B0 + 3,A +n However, as o t h e r s t u d i e s have shown, P can a l s o be a f f e c t e d by o t h e r v a r i a b l e s such as i n f l a t i o n . T h i s e f f e c t i s independent of age so a pure time v a r i a b l e such as y e a r ( t ) c o u l d be i n c l u d e d : (7) P = B0 + B,s + B2t + n T h i s r e p r e s e n t a t i o n s e p a r a t e s the "pure age" e f f e c t s and "pure t i m e " e f f e c t s from one a n o t h e r t o f a c i l i t a t e a n a l y s i s . The pure time e f f e c t can be thought of as i n f l a t i o n and the pure age e f f e c t s as a c t u a l d e p r e c i a t i o n - t h a t e f f e c t which i s of most i n t e r e s t . In t h i s case the b e t a c o e f f i c i e n t on age (/3, ) can be i n t e r p r e t e d as a measure of pure economic d e p r e c i a t i o n . The c o e f f i c i e n t on time ( t ) , on the o t h e r hand, s h o u l d be i n t e r p r e t e d as the pure i n f l a t i o n or " c a p i t a l g a i n s " e f f e c t . In t h a t case the v a l u e s can be a r r a n g e d i n a m a t r i x as i n i n T a b l e A . Table 2. Example of Age vs. Time Matrix Separating the Pure Age Depreciation from the E f f e c t of I n f l a t i o n TIKE 1 f ! a : u I <: i i i i t i ( 1 , 1970) ( 1 , 1971) ( 1 , 1972) ( 1 , 1973) •! ( 2 , 1970) ( 2, 1971) ( 2, 1972) ( 2, 1973) ( 3 , 1970) ( 3 , 1 9 7 D ( 3 , 1972) . . . 1970) ( 5 , 1970) The rows of t h i s m a t r i x r e p r e s e n t the i n f l a t i o n e f f e c t s , t h a t i s , the change i n p r i c e over t i m e , h o l d i n g age c o n s t a n t . The columns r e p r e s e n t the pure age e f f e c t or the change i n the p r i c e of an a s s e t , w i t h age, h o l d i n g time c o n s t a n t . The columns, a c c o r d i n g t o the d e f i n i t i o n above f o r d e p r e c i a t i o n , c a p t u r e a c t u a l d e p r e c i a t i o n ( i . e . the r a t e of d e c l i n e . o f an a s s e t ' s p r i c e w i t h age a t a s i n g l e p o i n t i n time) assuming t h a t d i s c r e t e changes, ( g i v e n enough o b s e r v a t i o n s ) w i l l a p p r o x i m ate c o n t i n o u s changes. T h i s i s one method f o r d e a l i n g w i t h i n f l a t i o n ' s e f f e c t s on the r e m a i n i n g v a l u e s c h e d u l e . N o t i c e t h a t by drawing t h i s d i s t i n c t i o n i n t h i s way i t i s p o s s i b l e t o net out i n f l a t i o n ' s e f f e c t s c o m p l e t e l y by d o i n g a c r o s s - s e c t i o n a l a n a l y s i s f o r a s i n g l e y e a r . T h i s i m p l i e s h o l d i n g the time or i n f l a t i o n e f f e c t c o n s t a n t at a v a l u e of one so t h a t i t e n t e r s the i n t e r c e p t term r a t h e r than a s l o p e term. I f a number of c r o s s s e c t i o n s were done then i n f l a t i o n would e n t e r i n t o t h i s p a r t i c u l a r a n a l y s i s as a c u r v e s h i f t e r r a t h e r than a s l o p e term. The t r e n d i n the r e m a i n i n g v a l u e l i t e r a t u r e has been t o attempt t o d i s t i n g u i s h as many s e p a r a t e e f f e c t s on d e p r e c i a t i o n as p o s s i b l e . By d o i n g so i t i s p o s s i b l e to q u a n t i f y and g r e a t l y c l a r i f y the n a t u r e of t r u e d e p r e c i a t i o n . T h i s has 43 meant v a r i o u s a u t h o r s have added more v a r i a b l e s t o i n c l u d e the e f f e c t s t h a t horsepower, o p t i o n s and make have on r e m a i n i n g v a l u e . That i s , they not o n l y attempt t o s e p a r a t e the pure age e f f e c t from the pure time e f f e c t , but a l s o t o d i s t i n g u i s h t h e s e o t h e r e f f e c t s . Thus, "pure o p t i o n s " , "pure makes" and o t h e r e f f e c t s have been d i s e n t a n g l e d . An assumption of t h i s a pproach i s t h a t age (or newness), and o t h e r c h a r a c t e r i s t i c s of a good a r e s e p a r a b l e from the o t h e r e f f e c t s * To c a p t u r e these e f f e c t s an a d d i t i v e model was used. I t i s s i m i l a r t o H u l t e n and Wykoff's [ 1981 ] model except t h a t i t i n c l u d e s more independent v a r i a b l e s . That i s , t h i s model adds v a r i a b l e s t o c a p t u r e c o n d i t i o n , hours use, horsepower, o p t i o n s and make, because i t i s f e l t t h a t f a i l u r e t o do so would l e a d t o a measure of d e p r e c i a t i o n which i s confounded w i t h the e f f e c t s of t h e s e o t h e r c h a r a c t e r i s t i c s . Such e s t i m a t e s , t h e n , would not be s t r i c t l y comparable w i t h any o t h e r because the amount of each c h a r a c t e r i s t i c p r e s e n t i n each machine, and the c o n t r i b u t i o n i t makes t o the f i n a l p r i c e , would not be known. "At l e a s t t h i s h y p o t h e s i s i s m a i n t a i n e d a t the o u t s e t even though t h i s i s s t r i c t l y not t r u e i n the case of hours and c o n d i t i o n . A g a i n t h i s i s r e m i n i s c e n t of the Hedonic approach i n w h i c h every c h a r a c t e r i s t i c i s a s s o c i a t e d w i t h an i m p l i c i t p r i c e . ( see Ohta and G r i l i c h e S [ 1 9 7 4 ] i n p a r t i c u l a r ) . The p r e s e n t s t u d y , however, goes f u r t h e r i n the d i r e c t i o n of s e p a r a t i n g the v a r i o u s i n f l u e n c e s on p r i c e than any of the Hedonic s t u d i e s , because i t i n c l u d e s a term f o r c u m u l a t i v e hours of use. In t h e o r y , the number of hours a machine has been used s h o u l d a f f e c t the r e m a i n i n g v a l u e , s i n c e f o r a g i v e n age, a h i g h e r number of hours i m p l i e s g r e a t e r r e p a i r c o s t s . For the same reason a v a r i a b l e f o r c o n d i t i o n s h o u l d be i n c l u d e d as M c N e i l l has done. A priori , i t i s e x p e c t e d t h a t the s i g n s on th e s e v a r i a b l e s w i l l be p o s i t i v e , e x cept f o r hours and c o n d i t i o n , which s h o u l d e x e r t a n e g a t i v e i n f l u e n c e on the p r i c e . Thus, i t was b e l i e v e d t h a t the r e m a i n i n g v a l u e ( g i v e n by p r i c e ) s h o u l d be m o d e l l e d as some f u n c t i o n of age, hours of use, horsepower, c o n d i t i o n , o p t i o n a l equipment and make ( f o r a complete d e f i n i t i o n of the v a r i a b l e s see page 65) (8) P r i c e = f(AGE, CAB, DUALS, AIR, 3-PH, P-ST, FEL, HOURS, PTO-HP, HICOND, MAKE) Here AGE r e p r e s e n t s the age of the t r a c t o r i n y e a r s and GAB i s a dummy v a r i a b l e t o i n d i c a t e whether or not the t r a c t o r i s equipped w i t h an e n c l o s e d cab. L i k e w i s e , DUALS, AIR, 3-PH and P-ST are dummy v a r i a b l e s f o r d u a l r e a r wheels, a i r c o n d i t i o n i n g , t h r e e - p o i n t - h i t c h and power s h i f t t r a n s m i s s i o n . HOURS g i v e s the number of hours the t r a c t o r has been used, PTO-HP i n d i c a t e s the horsepower of the machine measured a t the p o w e r - t a k e - o f f , HICOND i s a dummy i n d i c a t i n g whether the machine was of e x c e p t i o n a l l y h i g h c o n d i t i o n and MAKE i s a dummy v a r i a b l e i n d i c a t i n g the make of the t r a c t o r . The r a t e of d e p r e c i a t i o n i n a l i n e a r model can be found by comparing the p r i c e s of machines of d i f f e r e n t ages. In a s e m i - l o g model the r a t e of d e p r e c i a t i o n i s taken d i r e c t l y from the c o e f f i c i e n t on age. A l s o i n t e r a c t i v e terms would be needed i f the v a r i o u s c h a r a c t e r i s t i c s a r e t o a f f e c t the r a t e of d e p r e c i a t i o n . However, a t t h i s p o i n t , the n u l l h y p o t h e s i s was t h a t the r a t e of d e p r e c i a t i o n would be c o n s t a n t r e g a r d l e s s of i t s make or o p t i o n s , so i n t e r a c t i v e terms were not i n c l u d e d i n i t i a l l y . I n o r d e r t o approach d e p r e c i a t i o n from t h i s p o i n t of view i t i s n e c e s s a r y t o have e x c e p t i o n a l l y d e t a i l e d i n f o r m a t i o n on a l a r g e sample of t r a n s a c t i o n s i n the second-hand market. Data on average p r i c e s would not be s u f f i c i e n t f o r they would mask the s p e c i f i c 46 c h a r a c t e r i s t i c s of the i n d i v i d u a l machine which p e r m i t the d e t e r m i n a t i o n of i m p l i c i t p r i c e s . F o r t u n a t e l y , M a r s h a l l ' s Canadian Farm Equipment Guide, p r o v i d e s data which l i s t a c t u a l t r a n s a c t i o n s and g i v e the p r i c e and the s p e c i f i c c h a r a c t e r i s t i c s of the machine which d e t e r m i n e t h a t p r i c e . These type o f . d a t a were used t o c r e a t e c r o s s - s e c t i o n s f o r 1980 f o r t r a c t o r s , combines, square b a l e r s and round b a l e r s . 3.5.1 FUNCTIONAL FORM R e g a r d l e s s of the v a r i a b l e s used, an a p p r o p r i a t e f u n c t i o n a l form must a l s o be chosen. The c h o i c e of f u n c t i o n a l form i s a c r u c i a l a s p e c t of model s p e c i f i c a t i o n s i n c e any s i m p l e model r e s t r i c t s the form of the d e p r e c i a t i o n i n some manner. As was i n d i c a t e d above, many of the r e m a i n i n g v a l u e approaches r e s t r i c t e d the form t o be g e o m e t r i c , w h i l e o t h e r s r e s t r i c t e d the form t o be s t r a i g h t - l i n e and o t h e r s s t i l l had a form which does not c o r r e s p o n d t o any of the a c c o u n t i n g r u l e s of thumb. H u l t e n and Wykoff [1981] ( h e n c e f o r t h H-W) suggest u s i n g a Box-Cox power t r a n s f o r m a t i o n t o s i m u l t a n e o u s l y e s t i m a t e the form and the r a t e of d e p r e c i a t i o n as a way of s o l v i n g t h i s problem. In t h i s i n s t a n c e the s i m p l e model i s a l t e r e d by the a d d i t i o n of an e x t r a parameter t o each r e g r e s s o r : (8) P* = B0+B,k* +B2t* +M where, 47 X, P* =(P -1)/X ,, A* =(A - 1)/X 2 , X 3 t * =(t - 1)/X 3 , Now the B0 and B, parameters d e t e r m i n e the i n t e r c e p t and s l o p e as u s u a l , but the lambda parameters determine the f u n c t i o n a l form w i t h i n the Box-Cox f a m i l y . These lambda parameters can be e s t i m a t e d u s i n g maximum l i k e l i h o o d methods ( f o l l o w i n g H-W ). The t r a d i t i o n a l Box-Cox method o n l y t r a n s f o r m s the dependent v a r i a b l e , however, an extended v e r s i o n t r a n s f o r m s a l l the v a r i a b l e s . E s s e n t i a l l y , the proce d u r e i s t o s e a r c h over a s e r i e s of lambdas and f i n d t he maximum l i k e l i h o o d e s t i m a t e of the s e t of lambda. I t can be shown t h a t as lambda tends towards z e r o the v a r i a b l e i t i s t r a n s f o r m i n g approaches i t s l o g (see Kmenta [ 1 9 7 1 ] ) . Thus, i n the t r a d i t i o n a l Box-Cox t r a n s f o r m a t i o n , an e s t i m a t e d lambda of a p p r o x i m a t e l y z e r o i n d i c a t e s a s e m i - l o g f u n c t i o n a l form. A v a l u e of one would i n d i c a t e a l i n e a r form. I f the extended model i s chosen both the dependent and independent v a r i a b l e s a r e t r a n s f o r m e d a d d i n g more f l e x i b i l i t y . U n f o r t u n a t e l y a l l v a r i a b l e s must be t r a n s f o r m e d by t h e same lambda r e g a r d l e s s of whether they a r e dependent or ind e p e n d e n t . To a c h i e v e complete f l e x i b i l i t y a B o x - T i d w e l l t r a n s f o r m a t i o n (Box-Cox f o r the dependent v a r i a b l e and T i d w e l l f o r the independent v a r i a b l e s ) was used. T h i s g i v e s the d a t a the chance t o "choose f o r i t s e l f " the 48 f u n c t i o n a l form from any of t h e " n e s t e d " c l a s s i c a l forms ( l i n e a r , s e m i - l o g , l o g - l o g , i n v e r s e or l o g - i n v e r s e ) . S i n c e d e p r e c i a t i o n i s u s u a l l y t h o u g h t t o f o l l o w one of t h e s e forms, t h i s t r a n s f o r m a t i o n i s v e r y u s e f u l . N o t i c e t h a t i f the f a m i l y of lambda pa r a m e t e r s t u r n e d out t o be X =(1,1,1) then the model would be the s i m p l e l i n e a r one above. I f , on the o t h e r . h a n d , X=(0,1,1) t h e n , the model has s e m i - l o g form and c o r r e s p o n d s t o the g e o m e t r i c p a t t e r n of d e p r e c i a t i o n . F i n a l l y , X=(1,3,1) c o r r e s p o n d s t o a OHS p a t t e r n . The s e t of lambdas w h i c h b e s t f i t the d a t a can be found by s e a r c h i n g i t e r a t i v e l y t o maximize the l o g of l i k e l i h o o d f u n c t i o n . In t h i s way an e s t i m a t e of the form of d e p r e c i a t i o n can be d e r i v e d from the d a t a r a t h e r than imposing the form a priori . T h e o r e t i c a l l y the m a x i m u m - l i k e l i h o o d e s t i m a t e s of t h i s parameter a r e e s s e n t i a l l y showing the p o p u l a t i o n t h a t the sample i s most l i k e l y t o have come from (Kmenta [ 1 9 7 1 ] ) . I t i s as though the d a t a were b e i n g asked t o dete r m i n e the f u n c t i o n a l form f o r t h e m s e l v e s . U n f o r t u n a t e l y , i n p r a c t i c e , t h i s i s o n l y p a r t i a l l y t r u e . The f u l l B o x - T i d w e l l o p t i o n r e q u i r e s numerous i t e r a t i o n s b e f o r e c o n v e r g i n g on the maximum of the l i k e l i h o o d f u n c t i o n . I f more than one or two independent v a r i a b l e s a re used i t tends t o "blow-up" and no s o l u t i o n i s g i v e n . T h e r e f o r e , f o r the purposes of v e r i f y i n g the f u n c t i o n a l form o n l y a s e v e r e l y t r u n c a t e d model c o u l d be used: (Sb) P = f (AGE, PTO-HP) 49 T h i s i s tantamount t o r e s t r i c t i n g the c o e f f i c i e n t s on a l l o t h e r v a r i a b l e s t o be. z e r o (Ho:/33 = /3a = ...=/3= 0 ) , which i s e x p e c t e d b e f o r e hand t o be f a l s e . Thus, i n s p i t e of the e f f o r t t o impose no r e s t r i c t i o n s and l e t the "data d e c i d e " the f u n c t i o n a l form, i t i s n e c e s s a r y t o impose some r e s t r i c t i o n s . However, AGE i s an u m b r e l l a f o r hours and c o n d i t i o n . Thus, even w i t h o n l y t h e s e two v a r i a b l e s the f u n c t i o n a l form s h o u l d become e v i d e n t . The e s t i m a t e s of the c o e f f i c i e n t s however, w i l l not r e l a t e t o the f u l l model. The Box-Cox ( o r , more a c c u r a t e l y , the B o x - T i d w e l l ) p r o c e d u r e was used o n l y t o v e r i f y t h a t the assumed f u n c t i o n a l form was r e a s o n a b l e g i v e n type of d a t a which were used. The l i k e l i h o o d r a t i o t e s t was used t o see i f t h e r e a c t u a l l y i s a s i g n i f i c a n t d i f f e r e n c e between the e s t i m a t e d f u n c t i o n a l form and any o t h e r of the c l a s s i c a l f u n c t i ' o n a l forms i n the more g e n e r a l Box-Cox f a m i l y . The t e s t i n v o l v e s comparing the r a t i o of r e s t r i c t e d and u n r e s t r i c t e d f u n c t i o n a l forms ( t h e i n v e r s e of the l i k e l i h o o d r a t i o t e s t ) t o a c r i t i c a l v a l u e of the C h i - s q u a r e d i s t r i b u t i o n . As i t t u r n s o u t , two t i m e s t h i s r a t i o i s C h i - s q u a r e d i s t r i b u t e d w i t h degrees of freedom g i v e n by the number of r e s t r i c t i o n s p l a c e d on the u n r e s t r i c t e d model ( T h e i l [ 1 9 7 1 ] ) . Or, as Zarembka [1974] p u t s i t , the l i k e l i h o o d r a t i o i s a p p r o x i m a t e l y 1/2 C h i - s q u a r e d i s t r i b u t e d w i t h one degree of freedom. The r a t i o t e s t i n l o g form then i s t h e maximum of the l o g of l i k e l i h o o d f u n c t i o n r e s t r i c t e d minus the l o g of the l i k e l i h o o d f u n c t i o n of the u n r e s t r i c t e d form. To a n t i c i p a t e the r e s u l t s g i v e n below, t h i s t e s t showed t h a t t r a c t o r s f o l l o w e d a g e o m e t r i c p a t t e r n of d e p r e c i a t i o n . T h i s s u p p o r t s the use of the d e c l i n i n g b a l a n c e r u l e of thumb. 4. SOME METHODOLOGICAL ISSUES T h i s c h a p t e r i s devoted t o a d i s c u s s i o n of t h r e e problems which a re o f t e n c i t e d as reasons why the used market p r i c e s approach t o the e s t i m a t i o n of d e p r e c i a t i o n s h o u l d not be used. The f i r s t i s s u e c o n c e r n s the "lemons" problem and the second i s the e f f e c t t a x i n c e n t i v e programs have on c r e a t i n g a wedge between new p r i c e and the p r i c e of one y e a r - o l d machines. T h i r d i s the problem r a i s e d by c e n s o r e d sample b i a s . 4.1 LEMONS AND OTHER PROBLEMS The "lemons problem" r e f e r s t o asymmetry of i n f o r m a t i o n between buyers and s e l l e r s i n the used a s s e t market. The argument s t a t e s t h a t s e l l e r s of used equipment w i l l o n l y r e l e a s e the po o r e r q u a l i t y i tems which they know to be "lemons", onto the market and w i l l r e t a i n the b e t t e r machines ("creampuffs") f o r t h e m s e l v e s . A f t e r a p e r i o d of such b e h a v i o r buyers w i l l a d j u s t t h e i r o f f e r s downward i n l i n e w i t h the r e a s o n a b l e e x p e c t a t i o n of poor q u a l i t y . Thus, i n response t o t h i s p e r c e p t i o n t h a t poor machines are more h e a v i l y r e p r e s e n t e d i n the used market, the p r i c e s of the machines w i l l be l o w e r . T h e r e f o r e , a sample based e x c l u s i v e l y on second-hand p r i c e s w i l l be a b i a s e d e s t i m a t e of the v a l u e of the whole c o h o r t . I t w i l l not i n c l u d e the h i g h e r v a l u e d machines not o f f e r e d f o r r e s a l e r e s u l t i n g i n a downward b i a s i n v a l u e e s t i m a t e d or an o v e r e s t i m a t e of d e p r e c i a t i o n . T h i s would, t h e r e f o r e , 51 5 2 reduce the v a l i d i t y of the used market approach f o r d e t e r m i n i n g d e p r e c i a t i o n . The importance of the problem, however, depends on whether or not d e f e c t i v e , p o o r l y assembled machinery ( l e m o n s ) , r e p r e s e n t a s i g n i f i c a n t p o r t i o n of any c o h o r t of new machinery.. I f the number of "lemons" to come o f f a modern assembly l i n e i s s m a l l (two or t h r e e p e r c e n t ) then the importance of t h i s type, of b i a s may be so s m a l l as to not be w o r t h w o r r y i n g about. In o t h e r words i f most machines a r e " c r e a m p u f f s " , then s e l l e r s , even w i t h s u p e r i o r i n f o r m a t i o n , c o u l d not r e l e a s e "lemons" o n l y t o the market f o r r e s a l e . In the case of farm machinery t h i s q u a l i f i c a t i o n i s r e l e v a n t because farm machinery i s produced on assembly l i n e s where the p e r c e n t a g e of t r u e lemons may be v e r y s m a l l . S e c o n d l y , even i f "lemons" were t o c o n s t i t u t e a s i g n i f i c a n t p e r c e n t a g e of the p o p u l a t i o n of new machines i t would s t i l l remain t o be shown t h a t buyers of used machines cannot t e l l a good machine from a bad one. The "lemons q u e s t i o n " h i n g e s on the c l a i m t h a t b u y e r s , unable t o d i s t i n g u i s h a good a s s e t from a poor one, but h a v i n g been " s t u n g " once, assume a l l second-hand machines t o be " l e m o n s " j u s t t o be on the s a f e s i d e . Buyers of a u t o m o b i l e s may behave t h i s way, but farm equipment p u r c h a s e r s can be c o n s i d e r e d e x p e r t s s i n c e t h e i r o c c u p a t i o n i n c l u d e s the r e p a i r and maintenance of s i m i l a r machines. I f t h e y do know a g r e a t d e a l about machinery, then i t f o l l o w s t h a t 53 they would o f f e r , f o r a machine, what i t i s worth and not s y s t e m a t i c a l l y u n d e r v a l u e t h e i r o f f e r s as a s t r a t e g y f o r d e a l i n g , w i t h unknown q u a l i t y . One way t o e m p i r i c a l l y t e s t f o r the e x i s t e n c e of the problem would be t o compare the maintenance r e c o r d s of machines when new t o t h o s e . p u r c h a s e d used. I n c r e a s e d maintenance c o s t s would reduce the e x p e c t e d e a r n i n g s from the machine and hence lower i t s v a l u e o r . r e s a l e p r i c e . Thus, a s i g n i f i c a n t d i f f e r e n c e i n maintenance c o s t s between machines p u r c h a s e d new and ones purchased used would be taken as s u p p o r t f o r the "lemons" h y p o t h e s i s . Bond [1982] conducted such a s t u d y f o r t r u c k s and found no s i g n i f i c a n t d i f f e r e n c e between the two groups i n terms of maintenance c o s t s . Because t r u c k s and farm machinery are f a i r l y s i m i l a r a s s e t s the study c o u l d be t a k e n as e v i d e n c e f o r r e j e c t i n g the "lemons" h y p o t h e s i s i n farm machinery a l s o . However, s i n c e some doubt may s t i l l l i n g e r , a c o r r e c t i o n w i l l be made f o r t h i s "lemons p o t e n t i a l " . One s o l u t i o n would be t o omit new p r i c e s from the sample. T h i s i s e f f e c t i v e because, t o the e x t e n t t h a t "lemons" c o n s i d e r a t i o n s do d e p r e s s the used p r i c e s , t h ey do so u n i f o r m l y - d e p r e s s i n g a l l used p r i c e s by t h e same amount. The o n l y p r i c e s which would be u n a f f e c t e d would be new p r i c e s and, t h u s , o n l y new p r i c e s are "out of l i n e " (Deleeuw [ 1 9 8 2 ] ) . "Lemons" would o n l y b i a s e s t i m a t e s of d e p r e c i a t i o n which u t i l i z e c omparisons of u n b i a s e d new 54 p r i c e s t o t h e o r e t i c a l l y downward b i a s e d p r i c e s of used machines. I f o n l y ' u s e d machines were c o n s i d e r e d and d e p r e c i a t i o n r a t e s were gleaned from comparisons of two and t h r e e y e a r - o l d , and three, and f o u r - y e a r - o l d machines e t c . , then d e p r e c i a t i o n r a t e s would not be b i a s e d . In o t h e r words, the d i f f e r e n c e between two e q u a l l y b i a s e d numbers.is not i t s e l f b i a s e d . . T h e r e f o r e , t o account f o r the p o s s i b i l i t y of "lemons" b i a s i n the sample (even though i t has been argued t h a t none may e x i s t ) new p r i c e s have been o m i t t e d from the samples t h r o u g h o u t t h i s r e s e a r c h . 4.2 TAX CREDITS AND FIRST YEAR DEPRECIATION There i s a n o t h e r problem w i t h the used market approach t o e s t i m a t i n g d e p r e c i a t i o n which may be r e l a t e d t o the 'lemons' problem. T h i s i s the phennomenon of extreme f i r s t y e a r , o r , "as soon as you d r i v e i t o f f the l o t " d e p r e c i a t i o n . P a r t of t h i s may be p s y c h o l o g i c a l , or i t may have t o do w i t h "lemons" r i s k , or as J o r g e n s o n [1973] and o t h e r s have argued the problem may be p a r t l y i l l u s o r y s i n c e d e p r e c i a t i o n s t u d i e s o f t e n compare t r a n s a c t i o n s p r i c e s i n the used market t o suggested r e t a i l p r i c e s which a r e seldom p a i d . However, t h e r e i s a t l e a s t one v e r y r e a l reason why such a gap s h o u l d e x i s t and t h a t has t o do w i t h b u s i n e s s investment t a x c r e d i t (BITC) schemes. In Canada the BITC a l l o w s f a r m e r s t o reduce t h e i r t a x a b l e income by c l a i m i n g a p e r c e n t a g e of the c a p i t a l 55 c o s t i n v e s t e d i n new machine. Because t h i s tax c r e d i t can o n l y be used on new machinery i t makes new machinery "worth" more t o the farmer than machinery which i s o n l y a few weeks o l d . Given t h i s , t h e r e s h o u l d e x i s t a wedge between new and used equipment p r i c e s which i s g r e a t e r than the pure age e f f e c t . L o o k i n g a t a sample which i n c l u d e s b oth new and used p r i c e s would b i a s the d e p r e c i a t i o n e s t i m a t e upwards. F o r t u n a t e l y , the c o r r e c t i o n made f o r "lemons" problems a l s o c o r r e c t s f o r t h i s . By l e a v i n g new p r i c e s out of the sample extreme " f i r s t - y e a r " d e p r e c i a t i o n i s not a l l o w e d t o b i a s the r e s u l t s . 4.3 CENSORED SAMPLE BIAS The approach of u s i n g average p r i c e d ata t o d e v e l o p a g e - p r i c e p r o f i l e s from which d e p r e c i a t i o n can be i n f e r r e d i s , as H-W [1981] p o i n t o u t , i s s l i g h t l y f l a w e d . The problem a r i s e s from the f a c t t h a t average p r i c e s of a c o h o r t , of a g i v e n age, do not account f o r the f a c t t h a t some (perhaps many) machines d i s a p p e a r from the market b e f o r e the sample i s t a k e n and t h e s e have low or z e r o v a l u e . That i s , the average p r i c e sample i s t r u n c a t e d and y i e l d s an o v e r e s t i m a t e of the r e m a i n i n g v a l u e of the c o h o r t . There a r e s e v e r a l ways of d e a l i n g w i t h t h i s b i a s . One way i s t o c a l c u l a t e the average r a t e of r e t i r e m e n t ( i . e . the number of machines t h a t drop out of the market) over a c e r t a i n p e r i o d . The e a s i e s t p e r i o d t o c o n s i d e r i n Canada 56 would be the f i v e y e a r census p e r i o d . From the number of machines a t the b e g i n n i n g of the p e r i o d , t h e number at the end and the number c o n s t r u c t e d i n the i n t e r i m , an average r e t i r e m e n t r a t e c o u l d e a s i l y be c o n s t r u c t e d . W e i g h t i n g average p r i c e s i n t h i s manner, w i t h o u t any f u r t h e r a d j u s t m e n t s would, however, be i m p l i c i t l y assuming a c o n s t a n t r e t i r e m e n t r a t e a c r o s s a l l ages. In c o n t r a s t t o t h i s i t i s g e n e r a l l y a c c e p t e d t h a t v e r y few machines r e t i r e i n the e a r l y ages, but t h a t the number of r e t i r e e s i n c r e a s e s as the average age i n c r e a s e s . The maximum number of r e t i r e m e n t s occur near the mean l i f e of the machine and d e c l i n e s t h e r e a f t e r w i t h some machines s u r v i v i n g a v e r y l o n g t i m e . In o t h e r words, some s o r t of r e t i r e m e n t d i s t r i b u t i o n s h o u l d be used r a t h e r than assuming a c o n s t a n t r a t e of r e t i r e m e n t . The problem i s , however, t h a t no r e c e n t , a c c u r a t e i n f o r m a t i o n on r e t i r e m e n t d i s t r i b u t i o n s of farm machinery i s a v a i l a b l e . The commonly used W i n f r e y '[ 1 935] d a t a a r e somewhat d a t e d and g e n e r a l . In s p i t e of t h i s they a r e f r e q u e n t l y used (eg. H-W [ 1 9 8 1 ] , T e r b o r g h [1954] ( e t c . ) ) because v e r y l i t t l e e l s e i s a v a i l a b l e . H-W weight r e m a i n i n g v a l u e ( i e . t r a n s a c t i o n s p r i c e i n the used market) i n the f o l l o w i n g manner: (9) RV = RV,(PS) - SVO-PS) Where RV, i s the o b s e r v e d r e m a i n i n g v a l u e , RV i s the 57 t h e o r e t i c a l r e m a i n i n g v a l u e , PS i s the p r o b a b i l i t y of s u r v i v a l and SV i s the s a l v a g e v a l u e of the s c r a p p e d machine i f i t does not s u r v i v e . Assuming t h i s s a l v a g e v a l u e i s z e r o ( f o r example the r e t i r e e may j u s t be worth the towing charges) then the second term above d i s a p p e a r s and a weig h t e d e s t i m a t e t h a t c o r r e c t s f o r t h i s c e n s o r e d sample b i a s i s s i m p l y : (10) RV = RV!(PS) That i s , H-W weight the dependent v a r i a b l e b e f o r e r u n n i n g t h e i r r e g r e s i o n s . T h i s i s perhaps v a l i d because i n t h e i r c a s e , average p r i c e d a t a was used as n o t e d above. F a i l u r e t o make t h i s adjustment would l e a d t o an o v e r e s t i m a t e of the v a l u e of the whole v i n t a g e due t o the d i s a p p e a r a n c e of the lower v a l u e d (some w i t h z e r o v a l u e ) machines from the market. T h i s would g i v e an u n d e r e s t i m a t e of a c t u a l d e p r e c i a t i o n . However, i n the p r e s e n t s t u d y t h e r e a r e some s e r i o u s problems i n v o l v e d w i t h such an app r o a c h . F i r s t of a l l the d a t a f o r the 1980 c r o s s - s e c t i o n a r e a c t u a l l y r e p o r t e d t r a n s a c t i o n s p r i c e d a t a . W h i l e i t i s t r u e t h a t t h e s e p r i c e s a r e , i n r e a l i t y , the p r i c e s of machines of a c e r t a i n v i n t a g e c o n d i t i o n a l upon t h e i r s u r v i v a l u n t i l t h a t age, i t would not be honest t o modi f y t h e s e p r i c e s and s t i l l c a l l them a c t u a l r e p o r t e d p r i c e s . A d j u s t i n g the average p r i c e i s p e r m i s s i b l e because i t i s an a r t i f i c i a l p r i c e g e n e r a t e d s t a t i s t i c a l l y i n an e f f o r t t o " r e p r e s e n t " 58 what i s g o i n g on i n the market more c o n c i s e l y . There i s no problem w i t h a d j u s t i n g i n o r d e r t o r e c t i f y some s t a t i s t i c a l " m a l f u n c t i o n " e n c o u n t e r e d d u r i n g the c r e a t i o n of t h i s " r e p r e s e n t a t i v e " p r i c e . On the o t h e r hand, t h e r e i s a problem w i t h a d j u s t i n g the a c t u a l p r i c e observed i n the market and s t i l l c a l l i n g i t the a c t u a l p r i c e . A second and more c o m p e l l i n g reason f o r not a l t e r i n g the dependent v a r i a b l e i s t h a t i n t h i s case i t does not work. When the dependent v a r i a b l e s were a d j u s t e d f o r c e s o r e d sample b i a s u s i n g . t h e W i n f r e y S 3 d i s t r i b u t i o n the (H-W used an a s y m m e t r i c a l L d i s t r i b u t i o n , but i n the i n t e r e s t of s i m p l i c i t y and because o t h e r s i n c l u d i n g the B.E.A. and Terbough [1954] have done l i k e w i s e , the s y m m e t r i c a l S 3 was used) r e s i d u a l s p i c k e d up a p a t t e r n which l o o k e d r e m a r k a b l y l i k e the S 3 d i s t r i b u t i o n . On r e f l e c t i o n t h i s may not seem so r e m a r k a b l e . R e t i r e m e n t s based on any d i s t r i b u t i o n are a f u n c t i o n of age. They a r e few a t young ages, i n c r e a s e t o a maximum near the mean l i f e s p a n and d e c l i n e t h e r e a f t e r . M u l t i p l y i n g the dependent v a r i a b l e by t h i s r e n d e r s the dependent v a r i a b l e a l s o a f u n c t i o n of age. Now AGE a l s o appears on the r i g h t - h a n d s i d e of the e q u a t i o n . Thus, u s i n g the H-W t e c h n i q u e r e s u l t s i n a r e g r e s s i o n i n which the dependent v a r i a b l e i s by c o n s t r u c t i o n , a f u n c t i o n of the most s i g n i f i c a n t independent v a r i a b l e . T h i s i s bound t o l e a d t o problems. The reason t h a t t h i s p a t t e r n i n the r e s i d u a l s i s so e v i d e n t here i s perhaps because the r e g r e s s i o n r e s u l t s a r e 59 so s t r o n g . S uperimposing a b e l l - s h a p e d c u r v e ( t h e S 3 d i s t r i b u t i o n f o r example) over a c l o s e l y c l u s t e r e d s t r a i g h t l i n e w i l l r e s u l t i n a b e l l - s h a p e d p a t t e r n i n the r e s i d u a l s . On the o t h e r hand the same super i m p o s i t i o n over a more l o o s e l y c l u s t e r e d r e g r e s s i o n l i n e may r e v e a l no p a t t e r n . E v i d e n c e to s u p p o r t t h i s e x p l a n a t i o n i s drawn from the f a c t t h a t when the same r e t i r e m e n t d i s t r i b u t i o n was f i t t e d t o the smoother average p r i c e d a t a i n the l a t e r c r o s s - s e c t i o n s the t r e n d became more pronounced. Because of t h e s e problems w i t h H-W t e c h n i q u e f o r d e a l i n g w i t h c e n s o r e d sample b i a s the approach was abandoned. However, t h e r e i s a n o t h e r way t o d e a l w i t h the c e n s o r e d sample problem and t h a t i s t o c o n s i d e r a c t u a l t r a n s a c t i o n s and the average p r i c e as the c o r r e c t p r i c e s and o n l y make a d j u s t m e n t s a f t e r the r e g r e s s i o n s have been run. T h i s i n v o l v e s c a l c u l a t i n g the r e t i r e m e n t s as a f u n c t i o n of age and from t h i s the s u r v i v a l p r o b a b i l i t i e s . These a r e th e n used, i n a manner s i m i l a r t o the H-W t e c h n i q u e , t o c o r r e c t the r e m a i n i n g v a l u e s so as not t o u n d e r e s t i m a t e the d e p r e c i a t i o n r a t e . T h i s i s e s s e n t i a l l y t a k i n g a w e i g h t e d average of the d e p r e c i a t i o n c o n d i t i o n a l upon i t s u r v i v i n g and the d e p r e c i a t i o n c o n d i t i o n a l upon i t not s u r v i v i n g , f o l l o w i n g H-W's assumption t h a t n o n s u r v i v o r s have zer o s a l v a g e v a l u e . Not making such an adjustment i n v o l v e s some problems. However, making the adjustment a l s o i n v o l v e s p roblems. F i r s t of a l l t h e W i n f r e y d a t a a r e e x t r e m e l y o l d and 6 0 g e n e r a l . To a p p l y them t o any p a r t i c u l a r a s s e t today r e q u i r e s making a v e r y s t r o n g , but u n t e s t e d assumption t h a t a s s e t s a r e homogeneous. A second though perhaps b e t t e r grounded, assumption i s r e q u i r e d when an average l i f e s p a n i s chosen f o r the a s s e t . Very l i t t l e i n f o r m a t i o n on t h i s s u b j e c t i s a v a i l a b l e f o r Canadian a s s e t s . F i n a l l y , most s t u d i e s mentioned have not made c o r r e c t i o n s f o r c e n s o r e d sample b i a s ( H-W and t h e BEA be i n g the e x c e p t i o n s ) , so c o r r e c t e d r e s u l t s would not be g e n e r a l l y comparable. T h e r e f o r e , because t h e s e problems e x i s t , no adjustment w i l l be made i n t h i s s t u d y f o r c e n s o r e d sample b i a s . More work i n t h i s a r e a i s r e q u i r e d b e f o r e r e l i a b l e c o r r e c t i o n s can be made. 5. DATA AND PRELIMINARY MODEL The d a t a used i n t h i s s t u d y came from M a r s h a l l ' s  Canadian Farm Equipment Guide . T h i s t w i c e y e a r l y p u b l i c a t i o n , p u b l i s h e d i n W i n n i p e g , i s the " o n l y Canadian sour c e of comprehensive p r i c e d a t a on used farm equipment." M a r s h a l l ' s p r i c e i n f o r m a t i o n i s d e r i v e d from a c t u a l farm equipment t r a n s a c t i o n s and u n t i l 1982 t h i s p r i c e i n f o r m a t i o n was not a v e r a g e d , but r e p o r t e d i n i n d i v i d u a l form complete w i t h c o n d i t i o n , hours of use, and o p t i o n a l equipment. T h i s f a c t a l o n e makes M a r s h a l l ' s u n i q u e . Most 'blue books', r e p o r t o n l y average p r i c e s of a ' t y p i c a l ' machine of a g i v e n age. T h e r e f o r e , t h e s e o t h e r s o u r c e s , by d e f i n i t i o n , cannot i n c l u d e i n f o r m a t i o n on the c o n d i t i o n of a s p e c i f i c machine, or the number of hours i t has .been used. M a r s h a l l ' s g i v e s p r i c e i n f o r m a t i o n f o r two and f o u r wheel d r i v e t r a c t o r s , s e l f - p r o p e l l e d and p u l l - t y p e combines and s w a t h e r s , and f o r b a l e r s . T h i s i n f o r m a t i o n i s g a t h e r e d i n the market f o r a p e r i o d of f o u r months p r i o r t o each p u b l i c a t i o n . I t i s g a t h e r e d from b o t h p r i v a t e and d e a l e r s a l e s and no attempt i s made t o s c r e e n i t e xcept t o the e x t e n t t h a t o b v i o u s d i s t r e s s s a l e s a r e o m i t t e d . T h i s i s done because d i s t r e s s s a l e s , such as b a n k r u p t c y s a l e s , a r e t y p i c a l l y a t p r i c e s which a r e l e s s than t h e i r ' r e a l v a l u e ' hence t h e i r i n c l u s i o n would t e n d t o b i a s d e p r e c i a t i o n e s t i m a t e s upwards. 61 62 In mid-1981 M a r s h a l l ' s s w i t c h e d t o an average p r i c e f o r m a t . P r i o r t o t h i s they r e p o r t e d a c t u a l p r i c e s and averaged p r i c e d a t a were r e p o r t e d i n a supplementary s e c t i o n . T h i s p r a c t i c e was.stopped, however, because i t was f e l t t h a t r e a d e r s wanted the more r e a d i l y , a c c e s s i b l e average p r i c e d a t a . A s p e c i a l n o t e , however, accompanied the Spring/Summer 1982 e d i t i o n e l a b o r a t i n g on what they meant by average p r i c e d a t a . What M a r s h a l l ' s c a l l s average p r i c e i s a c t u a l l y 80% of the r e c o r d e d r e t a i l average. The 20% adjustment i s i n t e n d e d t o r e f l e c t what a d e a l e r would be w i l l i n g t o pay f o r a machine as opposed t o what he would s e l l i t f o r . T h i s "average p r i c e " i s thought t o be more r e l e v a n t t o farmers who can o n l y e x p e c t t h i s lower p r i c e when t r a d i n g i n t h e i r o l d machine. T h i s s h o u l d be kept i n mind when e s t i m a t e s based on average p r i c e a r e compared t o t h o s e based on i n d i v i d u a l ' p r i c e d a t a . A u s e f u l p r o p e r t y of M a r s h a l l ' s i n d i v i d u a l p r i c e d a t a i s t h a t the c o n d i t i o n of the machine i s g i v e n as of ' h i g h ' , 'average', or 'low'. H i g h c o n d i t i o n , i n t h i s c a s e , i m p l i e s t h a t the machine would l i k e l y have had l e s s than 1500 hours of use, have e v e r y t h i n g i n p r o p e r working o r d e r , and have t i r e s on which 80% of the t r e a d remains. Machines i n t h i s c a t e g o r y are t y p i c a l l y l e s s than 3 y e a r s o l d . Low c o n d i t i o n , on the o t h e r hand, i n d i c a t e s a machine w i t h poor appearance ( i . e . damaged sheet m e t a l , guards and s h i e l d s m i s s i n g and i n need of a p a i n t j o b ) , an engine 63 which i s i n need of r e p a i r and t i r e s which have l e s s than 50% of t h e i r t r e a d r e m a i n i n g . For most c a t e g o r i e s of machines i n t h i s s t u d y , both h i g h and low c o n d i t i o n dummy v a r i a b l e s were i n c l u d e d s i n c e c o n d i t i o n i s r e c o g n i z e d as b e i n g an i m p o r t a n t i n f l u e n c e on p r i c e . The e x c e p t i o n t o t h i s i s t r a c t o r s . In t h i s i n s t a n c e , t h e r e were not enough low c o n d i t i o n machines to, be a , f a c t o r so o n l y h i g h c o n d i t i o n machines were d i s t i n g u i s h e d from the a v e r a g e . Data from M a r s h a l l ' s Farm Equipment Guide were used i n t h i s s tudy t o c r e a t e d a t a b a s e s f o r 2-wheel d r i v e t r a c t o r s , s e l f - p r o p e l l e d combines, square b a l e r s and l a r g e round b a l e r s . These gave samples, of s i z e 136, 60", 131 and 55, r e s p e c t i v e l y . I n d i v i d u a l c r o s s - s e c t i o n models were run f o r each of t h e s e machine g r o u p i n g s f o r the y e a r 1980. Machines i n each group were as o l d as 1965. To v e r i f y the r e s u l t s o b t a i n e d i n t h i s c r o s s - s e c t i o n , a s e r i e s of c r o s s - s e c t i o n s f o r t r a c t o r s f o r the y e a r s 1981, 1982 and 1984 were a l s o run. As w e l l , an attempt t o i n c o r p o r a t e " s t a t e of the economy " v a r i a b l e s was made by p o o l i n g t h e s e c r o s s - s e c t i o n s w i t h 1980. T h i s p o o l i n g , however, does r e i n t r o d u c e the i s s u e of i n f l a t i o n which was s i d e s t e p p e d by d o i n g c r o s s - s e c t i o n a l models. T h i s had t o be d e a l t w i t h , t h e r e f o r e , by d e f l a t i n g the dependent v a r i a b l e u s i n g the consumer p r i c e i n d e x . U s i n g t h i s Canadian d a t a the f o l l o w i n g v a r i a b l e s were c r e a t e d : AGE r e p r e s e n t s the age of each machine i n y e a r s from the y e a r i t was b u i l t t o the date of the r e l e v a n t 64 c r o s s - s e c t i o n , HOURS g i v e s the cumhjulative hours of use f o r the p a r t i c u l a r t r a c t o r ( t h i s i n f o r m a t i o n was not a v a i l a b l e the o t h e r machines) and PTO-HP g i v e s the horsepower of the p a r t i c u l a r model model of t r a c t o r as measured a t the power t a k e - o f f i n the Nebraska farm t e s t s . NFI and INTERE g i v e farm cash income i n d o l l a r s and i n t e r e s t r a t e s i n each year f o r the y e a r s which c o n c e r n the p o o l e d c r o s s - s e c t i o n times s e r i e s model. These " s t a t e of the economy" v a r i a b l e s were i n c l u d e d t o c a p t u r e i n f l u e n c e s on p r i c e which were not r e l a t e d t o the s p e c i f i c c h a r a c t e r i s t i c s of the machines i n q u e s t i o n . As w e l l as t h e s e , dummy v a r i a b l e s were c r e a t e d f o r the f o l l o w i n g : 1. HICOND = 1 i f c o n d i t i o n i s h i g h and e q u a l s z e r o i f o t h e r w i se, 2. LCOND = 1 i f machine was c o n s i d e r e d t o be v e r y poor c o n d i t i o n by M a r s h a l l ' s , and z e r o i f o t h e r w i s e ( t h i s v a r i a b l e was o n l y a f a c t o r i n the case of combines, 3. AIR = 1 i f the machine has a i r c o n d i t i o n i n g and e q u a l s z e r o o t h e r w i s e , 4. CAB = 1 i f the machine has a cab and z e r o i f o t h e r w i s e , 5. COOLER = 1 i f t r a c t o r has a cab c o o l e r and z e r o i f o t h e r w i s e , 6. DUALS = 1 i f t r a c t o r has d u a l r e a r wheels and z e r o i f o t h e r w i s e , 7. P-ST = 1 i f the t r a c t o r has power s h i f t t r a n s m i s s i o n and z e r o i f o t h e r w i s e , 65 8. FEL = 1 i f the t r a c t o r has f r o n t - e n d - l o a d e r and z e r o i f o t h e r w i s e , 9. HTR = 1 i f the t r a c t o r has a cab h e a t e r and z e r o i f o t h e r w i s e , 10. AF = 1 i f the combine i n q u e s t i o n i s an a x i a l f l o w type and z e r o i f o t h e r w i s e , 11... HYDRO = 1 i f the combine has a h y d r o s t a t i c t r a n s m i s s i o n and z e r o i f o t h e r w i s e , 12. TYPE = 1 i f the square b a l e r i n q u e s t i o n used w i r e and ze r o i f i t used twine t o t i e b a l e s 13. In o r d e r t o d i s t i n g u i s h between the d i f f e r e n t makes (Case, John Deere, I n t e r n a t i o n a l H a r v e s t e r , Massey Ferguson and New H o l l a n d were the o n l y makes c o n s i d e r e d ) f o u r dummy v a r i a b l e s were c r e a t e d : 14. MF = 1 i f Massey F e r g u s o n , z e r o i f o t h e r w i s e , 15. DEER = 1 i f John Deere, z e r o i f o t h e r w i s e , 16. IH = 1 i f I n t e r n a t i o n a l H a r v e s t o r , z e r o i f o t h e r w i s e 17. NH = 1 i f S p e r r y New H o l l a n d , z e r o i f o t h e r w i s e . As w e l l , a number of m u l t i p l i c a t i v e terms were i n c l u d e d t o c a p t u r e any i n t e r a c t i o n between age and t h e p a r t i c u l a r v a r i a b l e . Such i n t e r a c t i o n s change the r a t e of d e p r e c i a t i o n and p e r m i t the t e s t i n g of s e v e r a l h y p o t h e s e s r e g a r d i n g the r e l a t i v e d e p r e c i a t i o n r a t e s of machines equipped w i t h v a r i o u s o p t i o n s , horsepower, or made i n d i f f e r e n t y e a r s . 6. TRACTORS 6.1 LINEAR MODEL I n i t i a l l y the model ( e q u a t i o n 8) was run w i t h a l l t h e s e dummy v a r i a b l e s i n c l u d e d : (11) p = 7786 - 1080AGE + 2867.8CAB + 32.3COOLER (4.4) (-7.7) (2.9) (0 .032) + 6 31.1DUALS + 10 75AIR + 32.7 3PH (1.53) (1.79) (0.078) + 423.9P-ST + 1584FEL + 125.5PTO-HP (0.9) (1.53) (10.7) -.9997HOURS + 958.2HICOND - 1378.5MF (-2.6) (1.52) (-2.5) + 410 2.8DEERE + 106 8.6IH (7.6) (2.06) R 2 = 0.8831 R 2 = 0.8696 n = 136 but COOLER, 3-PH and P-ST proved q u i t e i n s i g n i f i c a n t h a v i n g ' t ' s t a t i s t i c s l e s s than one i n a b s o l u t e v a l u e . These were dropped and the model was r e r u n : (12) P = 7897 .7 - 1074 .9AGE + 2777.6CAB + 605DUALS + 1203.3AIR (4.6) (-7.75) (2.997) (1.49) (2.3) + 1559FEL + 125.3PTO-HP - 0.99Hours + 1128.4HICOND (1.52) (10.77) (-2.6) (1.89) - 1264.7MF + 4316.7DEERE + 1190IH (-2.4) (9.22) (2.4) R 2 = .8824 R 2 = .8719 n = 136 66 67 This, t ime t h r e e v a r i a b l e s were s t i l l . n o t s i g n i f i c a n t (DUALS, FEL and HICOND), but a l l were much c l o s e r t o b e i n g so. They were r e t a i n e d because they were thought t o be e c o n o m i c a l l y s i g n i f i c a n t . That i s , d u a l , w h e e l s , f r o n t - e n d l o a d e r s a r e t y p i c a l l y e x p e n s i v e o p t i o n s which s h o u l d i n f l u e n c e the p r i c e . The c o n d i t i o n s h o u l d a l s o be i m p o r t a n t . T h i s l i n e a r model had an a d j u s t e d R-square of .8719 . 6.2 SEMI-LOG FUNCTIONAL FORM The l i n e a r model imposes a s p e c i f i c form on the p a t t e r n of d e p r e c i a t i o n . In t h i s case the p a t t e r n which c o r r e s p o n d s t o a l i n e a r r e g r e s s i o n model i s s t r a i g h t - l i n e d e p r e c i a t i o n . However, many b e l i e v e t he p a t t e r n of d e p r e c i a t i o n t o be d e c l i n i n g b a l a n c e . For example, G r i l i c h e s [1960 and 1974] found t h i s t o be the case and o t h e r s have used the the d e c l i n i n g b a l a n c e model e x t e n s i v e l y . T h i s i m p l i e s t h a t t he dependent v a r i a b l e i n the r e g r e s s i o n be " l o g g e d " , t h a t i s , the r e g r e s s i o n be of the s e m i - l o g form. T h e r e f o r e , PRICE was t r a n s f o r m e d t o become LOGPRICE (LOGP) (13) LOG P = 9.32 - 0.67AGE + 0.1724CAB + 0.0253DUALS + .0714AIR (114.9 ) ( - 1 0 . 4 4 ) (3.9) (1.34) (2.8) + .001643-PH + .0133P-ST + .0974FEL + .0063PTO-HP (.08) (.62) (2.05) (11.72) - .000056HOURS + .00575HICOND - .0815MF + .19 5 2DEERE (-3.201) (.199) (-3.22) (7.87) - .0496IH (2.09) R 2 = .9147 R 2 = .9057 n = 136 68 The r e s i d u a l s f o r t h e s e m i - l o g model d i s p l a y e d h o m o s c e d a s t i c e r r o r s . The e r r o r s w e r e . a l s o a p p r o x i m a t e l y normal and t h e r e was no p r oblem w i t h skewness or k u r t o s i s . T h i s s u g g e s t s t h a t the form of d e p r e c i a t i o n may indeed be g e o m e t r i c . T h i s w a s . v e r i f i e d u s i n g the B o x - T i d w e l l p r o c e d u r e . The maximum l i k e l i h o o d v a l u e e s t i m a t e d f o r the l i n e a r form (X=(1,1.,1)) was -1273.725, The s e m i - l o g form (X=0,1,1) was -12.67.06 and f o r the u n r e s t r i c t e d form (which here was X= .16,1,1) the v a l u e i s -1266.75. T e s t i n g the h y p o t h e s i s t h a t the, form i s a p p r o x i m a t e l y l i n e a r y i e l d s a v a l u e of 6.975 ( i . e . 1273.725 - 1266.75) which i s g r e a t e r than 1.96. T h e r e f o r e , the h y p o t h e s i s t h a t the form i s l i n e a r i s r e j e c t e d a t the 95% l e v e l of c o n f i d e n c e . On the o t h e r hand, a t e s t o f the h y p o t h e s i s t h a t the form i s s e m i - l o g y i e l d s a v a l u e of 0.31 ( i . e . 1267.06 - 1266.75) which i s l e s s than 1.96, t h e r e f o r e , the s e m i - l o g h y p o t h e s i s i s a c c e p t e d a t the 95% l e v e l of s i g n i f i c a n c e . T h i s , i s f u r t h e r e v i d e n c e s u p p o r t i n g the h y p o t h e s i s of g e o m e t r i c d e p r e c i a t i o n a t l e a s t f o r t r a c t o r s . (These t e s t s a p p l y t o the 1980 c r o s s - s e c t i o n f o r t r a c t o r s ) . A r e s u l t of t h i s s e m i - l o g f u n c t i o n a l form was t h a t HICOND became c l e a r l y v e r y i n s i g n i f i c a n t and DUAL, P-ST and 3-PH remained so. T h e r e f o r e , these v a r i a b l e s were dropped. T h i s change had l i t t l e e f f e c t e x cept t o render FEL l e s s s i g n i f i c a n t and r a i s e the a d j u s t e d R-square m a r g i n a l l y . An F t e s t on Ho : / 3 3 = j3 5 = 0 6 = 0, 0 = 0 d i d not 69 r e j e c t the h y p o t h e s i s (where the be t a s r e f e r t o DUAL, 3-PH and P-ST r e s p e c t i v e l y ) . ,This i m p l i e s t h a t t h e s e j o i n t l y add n o t h i n g t o the r e g r e s s i o n and may be dropped, ( c a l c u l a t e d F = 0.054 < c r i t i c a l F 0 5 ( 4 , 123 d . f . = 2.68) The r e s u l t i n g model i s ( 1 4 ) L O G P = 9 . 3 2 - . 0 6 5 8 A G E + . 1 7 2 1 C A B + . 0 0 7 8 A I R + . 0 8 7 F E L , (143 .5-6) ( - 1 0 . 4 6 ) ( 4 . 0 5 ) ( 3 . 2 9 ) ( 1 . 8 7 ) + . 0 0 6 6 P T O - H P - . 0 0 0 0 6 H O U R S - . 0 8 2 5 M F + . 2 0 5 9 D E E R E ( 1 3 . 5 2 ) (-4 . 9 2 ) ( - 3 . 4 6 ) ( 9 . 7 ) + . 0 5 3 3 1 1 1 ( 2 . 3 5 ) R 2 = . 9 1 3 2 R 2 = . 9 0 7 0 n = 1 3 6 G i v e n t h a t the c r i t i c a l t s t a t i s t i c i s a p p r o x i m a t e l y 1.97 a t the 95% l e v e l , a l l the r e m a i n i n g v a r i a b l e s a r e s i g n i f i c a n t a t the 95% p e r c e n t l e v e l of c o n f i d e n c e , ( e x c e pt FEL which was r e t a i n e d because a f r o n t - e n d l o a d e r s h o u l d e x e r t an i n f l u e n c e on p r i c e ) . F i n a l l y , the o v e r a l l r e g r e s s i o n was s i g n i f i c a n t . The c r i t i c a l v a l u e f o r F ( w i t h 8 and 127 degrees of freedom) was 4.96 a t the 99 % l e v e l and the v a l u e c a l c u l a t e d i s F = 143.71. Thus, the r a t e of d e p r e c i a t i o n f o r t r a c t o r s , g i v e n t h a t t he e f f e c t of hours use and c o n d i t i o n a r e s e p a r a t e d o u t , i s a p p r o x i m a t e l y 6.6% per year i n Canada. A g a i n r e c a l l t h a t t h i s i s the pure age e f f e c t of d e p r e c i a t i o n and assumes t h a t the machine i s not used. 70 6.3 ANALYZING THE STABILITY, OF THE ESTIMATES In t h e p r e v i o u s s e c t i o n an e s t i m a t e of d e p r e c i a t i o n has been g i v e n f o r t r a c t o r s i n the year 1980. The year 1980 may n o t , however, be r e p r e s e n t a t i v e of a l l y e a r s . There may be something unusual or unique about t h i s year which would l e a d t o a r e s u l t which does not a p p l y w e l l t o o t h e r y e a r s . To t e s t t h e g e n e r a l a p p l i c a b i l i t y of the 1980 r e s u l t s f o r t r a c t o r s , two d i f f e r e n t p a t h s were f o l l o w e d . The f i r s t approach was t o s i m p l y r e r u n t h e same model ( e q u a t i o n 14) f o r t h r e e o t h e r y e a r s : 1981, 1982 and 1984 (da t a was a v a i l a b l e f o r these y e a r s o n l y ) . A l t h o u g h the dat a f o r t h e y e a r s o t h e r than 1980 were average p r i c e d a t a , and so not d i r e c t l y comparable , t h i s s t i l l p r o v i d e d a q u i c k check and would show i f the 1980 r e s u l t s were s e r i o u s l y out of l i n e . In s p i t e of t h e use of a c t u a l p r i c e d a t a i n one case and average p r i c e d a t a i n t h e o t h e r , the r e s u l t s do show a h i g h degree of s t a b i l i t y : (15) 1980 A v g. P r i c e LOG P = 9.49 - .1071AGE + .042CAB + .0349AIR (124.57) (-30 .32) (.005) (.004) + .00897PTO-HP + . 14 3DEERE (17.7) (6.507) + .005IH - .166MF (.217) (-7.26) R 2 = .9781 R 2 = .9764 n = 95 ( c o n t i n u e d ) 7 0 a ( 1 6 ) 1 9 8 1 A v g . P r i c e L O G P = 9 . 4 7 8 - . 1 0 0 7 A G E + . 1 9 1 0 C A B + . 1 2 1 6 A I R ( 1 3 3 ) ( - 3 2 . 6 6 ) ( . 1 0 4 ) ( 4 . 5 3 ) + . 0 0 6 4 P T O - H P + . 2 0 4 5 D E E R E + . 1 1 3 7 I H - . 0 5 8 M F ( 1 0 . 1 3 ) ( 8 . 3 2 ) ( 4 . 4 7 ) ( - 2 . 3 6 2 ) R 2 = . 9 7 2 9 R 2 = . 9 7 1 1 n = 1 1 1 ( 1 7 ) 1 9 8 2 A v g . P r i c e L O G P = 9 . 5 6 - . 1 0 5 6 A G E + . 0 7 6 C A B ( 2 8 9 . 5 7 ) ( - 7 4 . 3 8 ) ( 5 . 0 8 1 ) - . 0 0 7 1 3 A I R + . 0 0 8 4 P T O - H P + . 0 0 2 6 D E E R E - . 0 6 5 I H ( - 4 . 9 3 ) ( 2 7 . 8 3 ) ( . 1 5 4 ) ( - 5 . 5 2 ) - . 2 7 9 M F ( - 1 8 . 1 8 ) R 2 = . 9 9 4 2 R 2 = . 9 9 3 8 n = 1 0 3 ( 1 8 ) 1 9 8 4 A v g . P r i c e L O G P = 9 . 7 4 - . 1 0 4 8 A G E ( 1 4 1 . 2 H 5 0 . 9 7 ) + . 0 6 9 P T O - H P + ( 1 5 . 4 3 ) + . 0 8 1 4 C A B ( 3 . 4 7 ) . 0 2 5 D E E R E - . 0 8 8 9 I H - . 2 9 7 M F ( 1 . 1 8 ) ( - 4 . 0 8 ) ( - 1 6 . 5 7 ) R 2 = . 9 8 3 7 R 2 = . 9 8 2 5 n = 1 0 6 71 The o n l y major changes over th e s e y e a r s were i n the c o e f f i c i e n t s of the make dummies. These, however, o n l y i n d i c a t e t h a t the new p r i c e s of t h e v a r i o u s makes were sometimes s i g n i f i c a n t l y d i f f e r e n t from Case (t h e o m i t t e d make) and sometimes were not . More i m p o r t a n t l y , the c o e f f i c i e n t on age, which has been shown t o c o r r e s p o n d t o d e p r e c i a t i o n , was found t o be s t a b l e a t about t e n p e r c e n t (.1071, .1007, .1056 and .1048 f o r 1980, 81, 82 and 84 r e s p e c t i v e l y . N o t i c e t h a t these e s t i m a t e s r e f e r t o r e g r e s s i o n s i n which HOURS was not i n c l u d e d because average p r i c e d a t a do not i n c l u d e i t . A l s o , i n f o r m a t i o n f o r a l l but the most major o p t i o n s was not a v a i l a b l e . These a r e the p e n a l t i e s a s s o c i a t e d w i t h u s i n g average p r i c e d a t a . In these average p r i c e e q u a t i o n s , CAB, AIR, DEERE and IH were sometimes i n s i g n i f i c a n t . However, as these were run o n l y f o r comparison p u r p o s e s , no changes were made t o the b a s i c model. I n s p e c t i o n of the r e s i d u a l s i n d i c a t e d a p a t t e r n c o r r e s p o n d i n g t o horsepower r a t i n g s . T h i s i s s i m i l a r t o ' s p a t i a l c o r r e l a t i o n ' which o f t e n o c c u r s i n c r o s s - s e c t i o n a l r e g r e s s i o n s i n which the d a t a a r e a r r a n g e d g e o g r a p h i c a l l y ( a c c o r d i n g t o c o u n t r y or p r o v i n c e e t c . ) and where b e h a v i o u r i s d i f f e r e n t i n each a r e a . I t o c c u r r e d here because the d a t a was e n t e r e d by model (as l i s t e d ) and each model i s a s s o c i a t e d w i t h a unique horsepower r a t i n g . W h i l e MAKE dummies were added t o account f o r "makes e f f e c t s " no dummies were added t o c a p t u r e the "model 72 e f f e c t " . In f a c t , the v a r i a b l e PTO-HP was used because i t was c o n s i d e r e d t o be a proxy f o r t r a c t o r model and was a l s o c o n t i n u o u s . The e f f e c t of the lum p i n e s s i n PTO-HP a c c o r d i n g t o make i s e x a c t l y t r a c e d out i n t h e p l o t of the r e s i d u a l s . a n d t h i s s u g g e s t s t h a t a dummy v a r i a b l e f o r each model would c u r e the problem. However, t h i s would i n v o l v e a n o t h e r t h i r t e e n dummy v a r i a b l e s and i s not d e s i r a b l e g i v e n the sample s i z e f o r the c r o s s - s e c t i o n s . 6.4 POOLED CROSS-SECTION TIME SERIES In the l a s t s e c t i o n a rough q u i d e t o the g e n e r a l a p p l i c a b i l i t y of the 1 9 8 0 . r e s u l t s was a c h i e v e d . However, i t was noted t h a t i t would be b e t t e r t o be a b l e t o s t a t i s t i c a l l y t e s t the h y p o t h e s i s t h a t 1980 was no d i f f e r e n t from the o t h e r y e a r s c o n s i d e r e d . Due t o l i m i t a t i o n s of the da t a - namely, the f a c t t h a t o n l y a veraged p r i c e d a t a i s a v a i l a b l e f o r y e a r s o t h e r than 1980 - the o n l y way t o a c h i e v e such a t e s t i s t o compare average p r i c e d a t a f o r a l l y e a r s i n c l u d i n g 1980. In t h i s way i t i s p o s s i b l e t o have one l a r g e model of f o u r d i f f e r e n t c r o s s - s e c t i o n s over time which can be r e s t r i c t e d i n s e v e r a l ways and those r e s t r i c t i o n s t e s t e d . T h i s does n o t , however, r e p r e s e n t a b a c k i n g away from t h e b e l i e f t h a t the i n d i v i d u a l t r a n s a c t i o n s d a t a a r e the most i n t e r e s t i n g p o i n t of view from which t o appr o a c h the q u e s t i o n of d e p r e c i a t i o n . The average p r i c e d a t a w i l l never p e r m i t the s e p a r a t i o n of the age e f f e c t from the use 73 and o t h e r e f f e c t s , f o r example. However, the average p r i c e d a t a a r e the o n l y d a t a a v a i l a b l e which span the e n t i r e p e r i o d i n v o l v e d and so a r e used f o r the purposes of compar i s o n . The p o o l e d r e g r e s s i o n was f i r s t run w i t h the same v a r i a b l e s as i n the 1980 c r o s s - s e c t i o n . In t h i s case a l l c o e f f i c i e n t s were of the e x p e c t e d s i g n and a l l were s i g n i f i c a n t except f o r IH which was not s t a t i s t i c a l l y s i g n i f i c a n t . A gain IH was r e t a i n e d i n o r d e r t o f a c i l i t a t e c o mparisons of makes e f f e c t s ( n o t i c e t h a t t h i s a l s o i s average p r i c e d a t a which does not i n c l u d e i n f o r m a t i o n on hours of use or c o n d i t i o n ) . (19) LOG P = 9.52 - .1028AGE + .0082PTO-HP + .069CAB + .065AIR (298.8)(-75.22) (29.92) (4.93) (6.36) + .09 8DEERE - .014IH - .19 7MF (7 .87) (-1.07) (-16 .59) R 2 = .312h R 2 = .9720 n= 4 l7 In o r d e r t o see i f 1980 was a unique y e a r , dummies were then added f o r 1980, 1981 and 1982. In t h i s way i t was p o s s i b l e t o t e s t the h y p o t h e s i s t h a t p r i c e s i n 1980 ,1981 and 1982 were no d i f f e r e n t i n t h e i r e f f e c t than i n the 1984 r e g r e s s i o n . These a r e summed up i n the f o l l o w i n g manner: 74 Ho:/38 = 0, Ho:/39 = 0, Ho:0 1 o= 0, Here 0 B , 0 9 and (3, 0 r e f e r t o dummies f o r 1980, 81, 82 r e s p e c t i v e l y . The v a r i a b l e "84" was o m i t t e d h e r e , so t h a t 1984 was the year t o which a l l o t h e r s were compared. (20) L O G P = 9 . 6 0 9 - . 1 0 5 0 A G E + . 0 6 2 6 C A B + . 0 5 8 A I R + . 0 9 9 7 D E E R E ( 2 9 3 . 8 2 ) ( - 7 8 . 7 4 ) ( 4 . 7 4 ) ( 5 . 2 9 ) ( 8 . 5 ) - . 0 1 7 6 I H - . 2 0 M F - . 0 5 9 ( 1 9 8 0 ) - . 0 5 8 ( 1 9 8 1 ) - . 0 9 2 ( 1 9 8 2 ) ( 1 . 4 9 ) ( - 1 8 . 1 ) ( - 4 . 8 6 ) ( - 4 . 9 2 ) ( - 8 . 3 6 ) R 2 = . 9 7 6 6 R 2 = . 9 7 6 0 n - 4 1 7 On the b a s i s of thes e t - s t a t i s t i c s t h e s e t h r e e h y potheses were r e j e c t e d . T h i s i m p l i e s t h a t t h e r e i s a d i s t i n c t d i f f e r e n c e between the y e a r s i n terms of t h e i r e f f e c t on p r i c e . T h i s s t i l l does not r e v e a l a n y t h i n g about the e f f e c t s of the v a r i o u s year dummies on d e p r e c i a t i o n . In o r d e r t o see i f the d e p r e c i a t i o n r a t e s were d i f f e r e n t i n the d i f f e r e n t y e a r s i t i s n e c e s s a r y t o employ i n t e r a c t i v e v a r i a b l e s . T h e r e f o r e , i n t e r a c t i v e dummies were c r e a t e d : 80AGE,81 AGE and 82AGE c o r r e s p o n d i n g t o the r e s p e c t i v e y e a r s compared. When the r e g r e s s i o n was run , none of the s e had s i g n i f i c a n t t - s t a t i s t i c s ( t ' s e q u a l e d 0.1, 75 -0.526 and -1.183 r e s p e c t i v e l y ) . ( 2 1 ) L O G P = 9.6 - . 1 0 3 8 A G E + . 0 0 8 P T O - H P + . 0 6 2 C A B + . 0 5 9 5 A I R ( 2 6 5 . 6 ) ( - 4 7 . 7 ) ( 3 1 . 0 3 ) ( 4 . 6 2 ) ( 5 . 3 5 ) + . 1 0 D E E R E - . 0 6 8 I H - . 0 2 M F - . 0 5 8 9 ( 1 9 8 0 ) - . 0 4 1 4 ( 1 9 8 1 ) ( 8 . 4 5 ) ( - 1 . 4 1 5 ) ( - 1 8 . 0 4 ) ( - 2 . 0 ) ( - 1 . 4 5 ) - . 0 5 9 6 ( 1 9 8 2 ) + . 0 0 0 3 3 ( 1 9 8 0 A G E ) - . 0 0 1 5 9 ( 1 9 8 1 A G E ) ( - 2 . 0 2 ) ( . 1 ) ( - . 5 2 6 ) - . 0 0 3 6 ( 1 9 8 2 A G E ) ( - 1 . 1 8 3 ) R 2 = . 9 7 6 7 R 2 = . 9 7 5 9 n = 417 A l s o , an F t e s t d r o p p i n g a l l t h r e e j o i n t l y c o n f i r m e d the h y p o t h e s i s : Ho: 80AGE = 81 AGE = 82AGE = 0 • The c a l c u l a t e d F v a l u e was 0.5729 and the c r i t i c a l F f o r 3 and 404 degrees of freedom was 2.62 a t the 95% l e v e l of s i g n i f i c a n c e . T h i s i m p l i e s t h a t t he n u l l h y p o t h e s i s cannot be r e j e c t e d and t h i s , i n t u r n , i m p l i e s t h a t no year i s d i f f e r e n t from 1984 i n i t s e f f e c t on d e p r e c i a t i o n . In p a r t i c u l a r , 1980 appears t o be the same as a l l the o t h e r y e a r s i n t h i s r e s p e c t , so t h a t d e p r e c i a t i o n e s t i m a t e s from the 1980 model a r e g e n e r a l l y a p p l i c a b l e t o t h e s e o t h e r y e a r s . Another purpose of c o n d u c t i n g p o o l e d a n a l y s i s i s t h a t i t p e r m i t s the i n c l u s i o n of s t a t e - o f - t h e - e c o n o m y v a r i a b l e s such as i n t e r e s t r a t e s and y e a r l y farm incomes. A c c o r d i n g t o t h e o r y , t h e s e may have i m p o r t a n t e f f e c t s on the 76 d e c i s i o n t o r e p l a c e farm equipment. T h i s may a f f e c t the number of used machines on the market and, t h e r e f o r e , the p r i c e s of used machines. However, a t e s t of th e s e two v a r i a b l e s ( I n t e r and FCI f o r the i n t e r e s t r a t e and farm c a s h income r e s p e c t i v e l y ) , were n e i t h e r i n d i v i d u a l l y nor j o i n t l y s i g n i f i c a n t . The t - s t a t s were .044 and -.062 f o r I n t e r and FCI, which are c l e a r l y i n s i g n i f i c a n t . The s c a l c u l a t e d F s t a t i s t i c was z e r o s i n c e the R-square d i d not change. (22) LOG P = 11.2 - 0.105AGE + 0.0081PTO-HP (0 . 438) (-98 .55) ( 31.2) + 0.0 6 3CAB + 0.0 5 8AIR + 0.099 7DEERE (4.7) (5.3) (8.4) - 0.0176IH - 0.20MF - 0.35(1980) (1 .5) (-18.05) (-0 .07) - 0.1(1981) - 0.158(1982) - 0.00008FCI (-.08) (-0.13) (-0.062) - 0.00 73INTERE (-0 .044) R 2 = 0.9766 R 2 = 0.9759 n - 417 T h i s means t h a t Ho: /3 1 t = /5 1 2 = 0 , where the b e t a s are the c o e f f i c i e n t s on INTER and F C I , cannot be r e j e c t e d . One i n t e r p r e t a t i o n of t h i s i s t h a t w i t h i n the s h o r t p e r i o d 77 c o n s i d e r e d here, these v a r i a b l e s were approximately c o n s t a n t . The stronger i n t e r p r e t a t i o n would be that these v a r i a b l e s do not i n f l u e n c e d e c i s i o n s to buy or s e l l machinery and t h e r e f o r e , do not a f f e c t demand or p r i c e . However, n e i t h e r of these s c e n a r i o s seems l i k e l y . T h i s i s because these s t a t e of the economy v a r i a b l e s reduced the s i g n i f i c a n c e of the year dummies suggesting that much of the d i f f e r e n c e between years may be a t t r i b u t a b l e to these f a c t o r s . The n o n i n t e r a c t i v e terms (1980, 81, etc.) terms were s i g n i f i c a n t i n d i c a t i n g that the p r i c e s of new machines d i d d i f f e r from year to year. One p o s s i b l e e x p l a n a t i o n i s that i n t e r e s t r a t e s or farm cash incomes were d i f f e r e n t i n these y e a r s . The reason that i n t e r e s t r a t e s and net farm income d i d not turn out to be s i g n i f i c a n t c o u l d be because t h e i r e f f e c t was swamped by the year dummies. T h i s view was r e i n f o r c e d when the r e g r e s s i o n was rerun without the year dummies. (23) LOG P = 9.5 - 0.105AGE + 0.0797PTO-HP + 0.0698CAB (123.3) (-74.7) (29 .3) (5.03) + 0.063AIR + 0.103DEERE - 1.98MF + 0.0000FCI (5 . 47) (8 .31) (-17 .00) (2.4) - 0.062INTERE (-3.24) R 2 - .9740 R 2 = .9734 n = 417 78 In t h i s r e g r e s s i o n FCI and INTER were s i g n i f i c a n t ( t - s t a t s of 2.44 and 3.235 r e s p e c t i v e l y . T h i s i n d i c a t e s t h a t farm incomes and the i n t e r e s t -rate do p l a y some r o l e i n d e t e r m i n i n g t r a c t o r p r i c e s . A f i n a l note t o t h i s s e c t i o n i s t h a t an F t e s t on the h y p o t h e s i s t h a t the j o i n t c o n t r i b u t i o n of the n o n i n t e r a c t i v e year dummies was z e r o was r e j e c t e d ( c a l c u l a t e d F g r e a t e r than c r i t i c a l F ( 3, 402 d . f . ) = 3.68 a t the 5% l e v e l of s i g n i f i c a n c e ) . In o t h e r words, i t i s not c o r r e c t t o drop the n o n i n t e r a c t i v e y e a r dummy v a r i a b l e s a l t o g e t h e r . T h e r e f o r e , t h e r e must be more t o the d i f f e r e n c e between y e a r s than i s c a p t u r e d by FCI and INTER. Thus, t o c o n c l u d e t h i s s e c t i o n , i t can be s a i d t h a t w h i l e t h e s e s t a t e - o f - t h e - e c o n o m y v a r i a b l e s a r e i m p o r t a n t , t h ey do not account f o r a l l the d i f f e r e n c e between y e a r s . 6.5 INTERPRETING THE BETA COEFFICIENTS The advantage of h a v i n g the model se t up i n t h i s a d d i t i v e manner i s t h a t the s e p a r a t e e f f e c t s of age and the o t h e r dependent v a r i a b l e s can be d i s t i n g u i s h e d . S i n c e the p r i c e s of used machines a r e of i n t e r e s t , c h a r a c t e r i s t i c s such as age and the number of hours which the machine has been used are a l s o i n c l u d e d . For farm machinery i t i s b e l i e v e d t h a t t h e s e two c h a r a c t e r i s t i c s , a t l e a s t , w i l l have n e g a t i v e c o e f f i c i e n t s . Another way of i n t e r p r e t i n g t h e s e c o e f f i c i e n t s would be the i m p l i c i t p r i c e of age (or the n e g a t i v e p r i c e of newness) and the 79 i m p l i c i t p r i c e of use. However, one d i f f i c u l t y w i t h such,a f o r m u l a t i o n i s t h a t i t imposes independence among the r i g h t - h a n d - s i d e v a r i a b l e s . That i s , the pure age e f f e c t , or economic d e p r e c i a t i o n i n t h i s c o n t e x t , cannot i n t e r a c t w i t h the o t h e r c h a r a c t e r i s t i c s , such as the make of the machine, a i r c o n d i t i o n i n g , or even w i t h the number of hours the machine has been used. T h i s s e p a r a t i o n i s somewhat u n r e a l i s t i c . As n o t e d , f o r example, the c o e f f i c i e n t on age w i l l y i e l d a measure of d e p r e c i a t i o n which assumes t h a t the machine has no hours on i t . That i s , i t i s as i f the machine had been l e f t i n a shed f o r i t s whole l i f e up u n t i l t h e sample was t a k e n . W h i l e t h i s i s perhaps s t r i c t l y c o r r e c t , t h i s type of i n f o r m a t i o n may not be a l l t h a t u s e f u l . As t h e model s t a n d s t h e r e i s no way f o r the make of the machine, nor the o p t i o n s i t has, t o a l t e r the r a t e of d e p r e c i a t i o n . To get t h e s e changes i n d e p r e c i a t i o n r a t e s i t i s n e c e s s a r y t o i n t r o d u c e m u l t i p l i c a t i v e or i n t e r a c t i v e terms as was done above i n the p o o l e d c r o s s - s e c t i o n time s e r i e s r e g r e s s i o n . In t h a t i n s t a n c e , terms l i k e 80AGE were added t o see i f the year the sample was t a k e n had any e f f e c t on the d e p r e c i a t i o n r a t e . C u r r e n t l y , i n t h i s c r o s s - s e c t i o n model, v a r i a b l e s can o n l y s h i f t the i n t e r c e p t or the p r i c e a t age z e r o . They cannot a f f e c t the r a t e of d e c l i n e i n p r i c e . However, some makes of machine t e n d t o d e p r e c i a t e more q u i c k l y than o t h e r s and i t i s 80 p o s s i b l e t o t e s t f o r t h i s d i f f e r e n c e among makes. By a d d i n g i n t e r a c t i v e between o p t i o n s ( l i k e Cab and a i r c o n d i t i o n i n g ) and age, i t i s a l s o p o s s i b l e t o t e s t the e f f e c t s t h a t d i f f e r e n t o p t i o n s have on the pure d e p r e c i a t i o n r a t e t o see i f they d e p r e c i a t e more q u i c k l y or more s l o w l y than ones w i t h o u t such o p t i o n s . To answer these t y p e s of q u e s t i o n s , i n t e r a c t i v e terms were added as f o l l o w s : HPAGE (PTO-HP*AGE), MFAGE(MASSEY FERGUSON*AGE), IHAGE(INTERNATIONAL HARVESTER*AGE), JDAGE(JOHN DEERE *AGE), CABAGE(CAB*AGE) and AlRAGE(AIRCONDITIONING*AGE). These p a r t i c u l a r i n t e r a c t i o n terms were added because t h e s e v a r i a b l e s were thought t o i n f l u e n c e d e p r e c i a t i o n and, t h e r e f o r e , s h o u l d be a l l o w e d t o i n t e r a c t w i t h age. The n u l l h y p o t h e s i s , however, was t h a t n o t h i n g would i n f l u e n c e the r a t e of d e p r e c i a t i o n so none were i n c l u d e d o r i g i n a l l y . The c o e f f i c i e n t on age i n t h i s model i s of p a r t i c u l a r i m p o r t a n c e . S i n c e the model i s of the s e m i - l o g form i t can be shown t h a t the c o e f f i c i e n t on age or 0, i s the r a t e of d e p r e c i a t i o n as d e f i n e d above (the pure age e f f e c t h o l d i n g a l l e l s e c o n s t a n t ) . In o t h e r words, we can f i n d d e p r e c i a t i o n ( s t r i c t l y i n terms of the age e f f e c t ) by t a k i n g the p a r t i a l d e r i v a t i v e of p r i c e w i t h r e s p e c t t o age. Assuming t h a t AGE and a l l o t h e r v a r i a b l e s a r e independent (not a v e r y r e a s o n a b l e assumption) then e v e r y t h i n g o t h e r than B, d rops o u t . 81 S e c o n d l y , t h e s e c o e f f i c i e n t s can be i n t e r p r e t e d as pecentages s i n c e the s e m i - l o g form i s b e i n g used. T h e r e f o r e , B,= 0.0658 i m p l i e s t h a t the r a t e of d e p r e c i a t i o n i s a p p r o x i m a t e l y 7 %. To f i n d the e f f e c t s of the o t h e r i n d e p e n d e n t . v a r i a b l e s t h e p a r t i a l d e r i v a t i v e s a r e t a k e n w i t h r e s p e c t t o each. M a i n t a i n i n g the independence a s s u m p t i o n , these p a r t i a l s w i l l show the e f f e c t each has on the dependent v a r i a b l e , but none w i l l i n t e r a c t w i t h AGE ( u n l e s s i t i s s p e c i f i c a l l y an i n t e r a c t i v e term) so the r a t e of d e p r e c i a t i o n i s u n a f f e c t e d . R a t h e r , t h e s e v a r i a b l e s w i l l a c t as cur v e s h i f t e r s a l t e r i n g the new p r i c e o n l y . T h i s , f o r example, h o l d s i f HOURS i s assumed t o be c o n s t a n t or i f t h e r e i s no i n t e r a c t i o n between HOURS and AGE. In the p r e s e n t example t h i s pure age i n t e r p r e t a t i o n of d e p r e c i a t i o n i s as though a farmer purchased a t r a c t o r and l e f t i t i n the barn unused. Each year the t r a c t o r would be worth 7% l e s s than the year b e f o r e . 6.6 AGE VERSUS USE DEPRECIATION As noted above, most s t u d i e s , based on average p r i c e d a t a , cannot d i s e n t a n g l e the e f f e c t s of age and hours because i n f o r m a t i o n on the number of hours a s p e c i f i c machine has been used i s t y p i c a l l y ' : ' not a v a i l a b l e i n average p r i c e d a t a . F o r the same reason the v a r i a b l e r e p r e s e n t i n g hours of use was a l s o m i s s i n g from the average p r i c e r e g r e s s i o n s shown h e r e . W h i l e t h e s e 82 average p r i c e models may be mere r e l e v a n t f o r comparison t o the r e s t of the l i t e r a t u r e , they a r e not the best models t o use. Age and hours of use are not independent. Removing hours from the r i g h t hand s i d e f o r c e s age t o do more work i n the r e g r e s s i o n , l e a d i n g t o a l a r g e r c o e f f i c i e n t on age. As shown, t h i s i m p l i e s a h i g h e r r a t e of d e p r e c i a t i o n i n t h i s type of model. That i s , average p r i c e models w i l l t y p i c a l l y , i n d i c a t e a h i g h e r r a t e of d e p r e c i a t i o n than a c t u a l p r i c e models. F u r t h e r m o r e , t h e r e i s a r i s k i n v o l v e d i n o m i t t i n g a p o t e n t i a l l y s i g n i f i c a n t v a r i a b l e such as h o u r s . T h i s i s the danger of s p e c i f i c a t i o n s b i a s . In o r d e r t o see the importance of t h i s b i a s the model was run f i r s t w i t h , and l a t e r w i t h o u t hours i n c l u d e d . C a l c u l a t i n g t he c o e f f i c i e n t on age from a r e g r e s s i o n of hours on age, and then c a l c u l a t i n g t he reduced form of the p r i c e r e g r e s s i o n i n d i c a t e d t h a t the e f f e c t s of d r o p p i n g hours a r e not se v e r e . (24) LOG P = 9.2 - 0.0 6 7AGE + 0.17 2CAB (140 .2) (-10.59) (4.0) + 0.076AIR + 0.086FEL + 0.0065PTO-HP (3.17) (1.84) (13.2) - 0.00006HOURS - 0.084MF + 0.20DEERE (-4.2) (-3.5) (9.39) + 0.053IH (2.33) R 2 = .8990 R 2 = .8930 n = 136 (25) LOG P = 9.26 - 0.89AGE + 0.14CAB (13 6 . 8 ) ( - 2 2 . 6 ) (3.1) + 0.083AIR + 0.09FEL + 0.006PTO-HP (3.5) (1.8) (11.94) - 0.09MF + 0.18DEERE + 0.041IH (-3.55) (8.12) (1.1) 2 -2 R = .8990 R = .8930 n = 136 83 The e f f e c t i s t o make the ; c o e f f i c i e n t of age much l a r g e r . The o t h e r c o e f f i c i e n t s , the F s t a t i s t i c and the R-square remain f a i r l y c o n s t a n t . P r e v i o u s s t u d i e s have not t y p i c a l l y had d a t a on h o u r s of use, but o n l y on age, so t h e i r e s t i m a t e s of d e p r e c i a t i o n may w e l l be g r e a t e r than any e s t i m a t e s r e p o r t e d h e r e from r e g r e s s i o n s t h a t i n c l u d e d HOURS. A l s o what the s e s t u d i e s have r e p o r t e d i s not s t r i c t l y the pure age v a r i e t y of d e p r e c i a t i o n . I t i s r a t h e r some c o m b i n a t i o n of the pure age e f f e c t and the pure use e f f e c t . I t s h o u l d a l s o be p o i n t e d out t h a t i n c r o s s - s e c t i o n a l s t u d i e s which i n c o r p o r a t e a c o n d i t i o n v a r i a b l e , a s i m i l a r s i t u a t i o n may a r i s e . T h i s i s because c o n d i t i o n i s a f u n c t i o n of hours which i s i t s e l f a f u n c t i o n of age. Thus, i t s h o u l d be e x p e c t e d t h a t models which i n c l u d e a c o n d i t i o n v a r i a b l e on t h e l e f t - h a n d s i d e w i l l a l s o y i e l d d e p r e c i a t i o n e s t i m a t e s t h a t a r e lower than t h o s e which p l a c e c o n d i t i o n under the age " u m b r e l l a " . T h i s i s r e l e v e n t when comparing s t u d i e s such as M c N e i l l ' s and t h i s one (which c o n t a i n a c o n d i t i o n v a r i a b l e ) t o o t h e r s t u d i e s of deprec i a t i o n . 6.7 RESULTS OF ADDING INTERACTIVE TERMS TO MODEL S e v e r a l i n t e r e s t i n g h y p o t h e s e s r e g a r d i n g the s i x a d d i t i o n a l i n t e r a c t i v e terms remain t o be t e s t e d . As was noted above terms l i k e horsepower, the v a r i o u s makes and some i m p o r t a n t o p t i o n s , may e x e r t an i n f l u e n c e on the r a t e 84 of d e p r e c i a t i o n . To t e s t t h e s e , the 1980 i n d i v i d u a l t r a n s a c t i o n s p r i c e model w i t h HOURS i n c l u d e d was used ( e q u a t i o n 14) and a number of i n t e r a c t i v e v a r i a b l e s were added ( r e c a l l t h a t the o n l y i n t e r a c t i v e terms used so f a r were tho s e d e s i g n e d t o c a p t u r e the e f f e c t t he d i f f e r e n t y e a r s had on d e p r e c i a t i o n i n the p o o l e d c r o s s - s e c t i o n time s e r i e s m o del). 6.7.1 THE EFFECT OF HORSEPOWER ON DEPRECIATION The v a r i a b l e HPAGE a l l o w s t e s t i n g of the • h y p o t h e s i s t h a t horsepower a f f e c t s the r a t e of d e p r e c i a t i o n . T h i s c o u l d be the case i f i t were supposed t h a t l a r g e r , more p o w e r f u l t r a c t o r s d e p r e c i a t e more r a p i d l y because they a r e pu r c h a s e d t o be used more i n t e n s i v e l y . C o n v e r s e l y , i t might be t h a t s m a l l e r t r a c t o r s d e p r e c i a t e more q u i c k l y because they a r e o v e r s t r e s s e d and r e q u i r e d t o do the same work as the l a r g e r ones. In o r d e r t o answer t h i s type of q u e s t i o n the f o l l o w i n g n u l l h y p o t h e s i s was t e s t e d : H o : 0 1 3 = 0, where B,3 i s the c o e f f i c i e n t on horsepower t i m e s age (HPAGE). The ' t ' s t a t i s t i c a s s o c i a t e d w i t h B,3, the c o e f f i c i e n t on HPAGE was 0.694 and the c r i t i c a l v a l u e of t h i s ' t ' s t a t i s t i c ( a t 95% and 127 degrees of freedom) was about 1.98. (26) LOG P = 9 .29 - 6 .048AGE + .343CAB + .057AIR + . 13FEL (53.4) (-1.88) (3.36) (.717) (2.302) + .00PTO-HP - .000062HOURS + .061MF + .25DEERE (3.45) (-3.98) (.927) (4.29) + .151IH - .00 45MFAGE - .00 6 7JDAGE - .017IHAGE (2 .24) (-. 34) (-.73) (-1.51) + .00019HPAGE - .0 25CABAGE + .000945AIRAGE (.694) (-2.03) (.94) 85 T h e r e f o r e , the n u l l h y p o t h e s i s was a c c e p t e d and i t was c o n c l u d e d t h a t the horsepower of t h e t r a c t o r has no i n f l u e n c e on the r a t e of d e p r e c i a t i o n . A c c o r d i n g l y , HPAGE was not i n c l u d e d i n the b a s i c model. On the o t h e r hand, n o t i c e t h a t horsepower (PTO-HP) a l o n e does have a s i g n i f i c a n t c o e f f i c i e n t ( t = 3.45). T h i s s i g n i f i c a n c e , however, does not i n f l u e n c e the r a t e of d e p r e c i a t i o n , j u s t the i n t e r c e p t on t h e . p r i c e a x i s . In o t h e r words, the p r i c e of a new machine i s dependent on i t s horsepower, but h i g h e r horsepower machines do not d e p r e c i a t e more s l o w l y or more q u i c k l y than lower horsepower machines. 6.7.2 MAKES EFFECTS AND DEPRECIATION As shown above (see e q u a t i o n 14 f o r example), the makes dummies have s i g n i f i c a n t e f f e c t s on the p r i c e of new t r a c t o r s * . A d i f f e r e n t h y p o t h e s i s t h a t can be t e s t e d u s i n g i n t e r a c t i v e terms, i s t h a t d i f f e r e n t makes d e p r e c i a t e a t d i f f e r e n t r a t e s . In o t h e r words, t h e i n c l u s i o n of MFAGE, JDAGE AND IHAGE p e r m i t the t e s t i n g of what G r i l i c h e s [1974] has c a l l e d "makes e f f e c t s " . He uses t h i s term i n the c o n t e x t of Hedonic f u n c t i o n s t o r e f e r t o d i f f e r e n c e s i n p r i c e s a c r o s s makes which cannot be a d e q u a t e l y r e l a t e d t o any p a r t i c u l a r c h a r a c t e r i s t i c o r q u a l i t y of the p r o d u c t . As used h e r e , the term i s meant t o c a p t u r e any s i g n i f i c a n t d i f f e r e n c e s i n the r a t e of d e p r e c i a t i o n among the v a r i o u s makes of t r a c t o r s w h i c h i s not a t t r i b u t a b l e t o 86 any of the independent v a r i a b l e s i n c l u d e d i n the model. I t was e x p e c t e d t h a t no d i f f e r e n c e s i n d e p r e c i a t i o n a c r o s s makes would show up which were not r e l a t e d t o some q u a n t i f i a b l e d i f f e r e n c e i n the machine. In t h i s c a s e , t h e h y p o t h e s i s i s t h a t d e p r e c i a t i o n i s the same f o r a l l makes. To v a l i d a t e t h i s the f o l l o w i n g n u l l h y p o t h e s i s was proposed: Ho: 0 1 2 = 0i3 = /3i« = 0, where the b e t a s r e f e r t o MFAGE, IHAGE and JDAGE r e s p e c t i v e l y . R e f e r r i n g back t o e q u a t i o n 25, i t can be seen t h a t none of these had s i g n i f i c a n t t - s t a t i s t i c s . T h i s i n d i c a t e s t h a t no make d e p r e c i a t e s a t a r a t e s i g n i f i c a n t l y d i f f e r e n t from the o m i t t e d brand Case. To check t h e i r j o i n t s i g n i f i c a n c e , the f o l l o w i n g r e g r e s s i o n was run. (27) LOG P = 9.16 - 0.061AGE + 0.31CAB (76.1) (-2.8) (3.1) + 0.066AIR + 0.106FEL + 0.0058PTO-HP (0 . 85) (2 .2) (4 .67) - 0.00006HOURS - 0.087MF + 0.21DEERE (-4.0) (-3.6) (9.6) + 0.055IH + 0 .000096HPAGE (2.4) (0.45) - 0.021CABAGE - 0.00043AIRAGE (-1.74) (-0.04) R 2 = .9148 R 2 = .9065 n = 417 Comparing the model w i t h and w i t h o u t t h e s e t h r e e v a r i a b l e s t o g e t h e r y i e l d s an F s t a t i s t i c of 0.435. S i n c e the c r i t i c a l F 99% ( a t 3 and 124 degrees of freedom) i s about 2.68 and F a t 99% (3 and 124 d . f . ) i s about 1.83, 87 the n u l l h y p o t h e s i s was not r e j e c t e d a t e i t h e r the 1% or 5% l e v e l . T h i s i m p l i e s t h a t , t aken j o i n t l y , t h e s e makes do not d e p r e c i a t e a t a d i f f e r e n t r a t e than Case t r a c t o r s . T h i s i n d i c a t e s t h a t d e p r e c i a t i o n r a t e s a re the same r e g a r d l e s s of make. 6.8 THE EFFECT OF OPTIONS ON DEPRECIATION The f i n a l s e t of hypotheses h a v i n g t o do w i t h i n t e r a c t i v e v a r i a b l e s c o n c e r n s the o p t i o n s cab and a i r c o n d i t i o n i n g . From the e a r l i e r r e g r e s s i o n s which have been run (eg. e q u a t i o n 14) i t i s e v i d e n t t h a t t h e s e e x e r t a s i g n i f i c a n t i n f l u e n c e on p r i c e i n the secondhand market. T h i s does not i n d i c a t e whether machines w i t h t h e s e p a r t i c u l a r o p t i o n s caused the t r a c t o r t o d e p r e c i a t e more s l o w l y than t r a c t o r s not h a v i n g t h e s e o p t i o n s . The decade of the s e v e n t i e s i s g e n e r a l l y c h a r a c t e r i z e d by an improvement i n o p e r a t o r c o m f o r t and s a f e t y i n the a r e a of t r a c t o r d e s i g n (see h i s t o r i c a l s e c t i o n 2.1). Thus, i f the t r e n d has been towards more t r a c t o r s w i t h cabs and a i r c o n d i t i o n i n g , examples p r e s e n t l y i n the second hand market s o - e q u i p p e d might be p e r c e i v e d as s t i l l b e i n g v e r y u p - t o - d a t e . On the o t h e r hand, o l d a i r c o n d i t i o n i n g s ystems, i n p a r t i c u l a r , might be p e r c e i v e d as b e i n g v e r y e x p e n s i v e and c o m p l i c a t e d systems t o m a i n t a i n and t h u s , would do n o t h i n g t o a l t e r the d e p r e c i a t i o n r a t e o r even t e n d t o i n c r e a s e d e p r e c i a t i o n . The n u l l h y p o t h e s i s t h a t d e p r e c i a t i o n i s u n a f f e c t e d by the f a c t t h a t the t r a c t o r 88 has a cab (Ho: Bg = 0) was not a c c e p t e d ( t = - 2 . 0 5 l compared t o c r i t i c a l f=1.98). A i r c o n d i t i o n i n g was found t o have no e f f e c t on d e p r e c i a t i o n ( a c c e p t Ho: B,0 = 0 g i v e n t s t a t i s t i c 0.094 i s l e s s than t c r i t i c a l = 1 . 9 8 ) . W i t h C A B A G E & A I R A G E (28) L O G P = 9 . 2 4 - . 0 5 1 A G E + 0 . 3 1 3 C A B + 0 . 0 5 2 6 A I R + 0 . 1 0 5 F E L ( 1 2 6 ) ( - 5 . 5 ) ( 3 . 1 5 ) ( . 7 0 5 ) ( 2 . 2 ) + 0 . 0 0 6 3 7 P T O - H P - 0 . 0 0 0 0 6 H O U R S - 0 . 0 8 7 M F + 0 . 2 l D E E R E ( 1 2 . 9 6 ) ( - 4 . 3 ) ( - 3 . 6 6 ) ( 9 . 8 8 ) + 0 . 0 5 5 I H - 0 . 0 2 C A B A G E + 0 . 0 0 1 6 A I R A G E ( 2 . 4 3 ) ( - 1 . 7 ) ( . 1 6 8 ) R 2 = . 9 1 6 4 R 2 = . 9 0 9 0 n = 4 1 7 A g a i n , the d i s t i n c t i o n between t h e s e i n t e r a c t i v e terms and the n o n i n t e r a c t i v e o p t i o n v a r i a b l e s s h o u l d be no t e d . A l l these v a r i a b l e s e x e r t a s i g n i f i c a n t e f f e c t on the p r i c e of a t r a c t o r . The n o n s i g n i f i c a n c e of AIRAGE, f o r example, o n l y i m p l i e s t h a t t r a c t o r s w i t h a i r c o n d i t i o n i n g d e p r e c i a t e a t the same r a t e as thos e t h a t do n o t . I f the i n t e r a c t i v e term a p p l i e s t o an o p t i o n then i t s i n s i g n i f i c a n t e f f e c t on p r i c e s i n the used market might be 89 taken t o imply t h a t such an o p t i o n was not "worth p u r c h a s i n g " , i f r e s a l e v a l u e i s an im p o r t a n t c o n s i d e r a t i o n . Assuming t h a t the o p t i o n d i d a f f e c t the new p r i c e ( o p t i o n s are not t y p i c a l l y g i v e n away f r e e of c h a r g e ) , then the f a c t t h a t the o p t i o n does not a f f e c t the used p r i c e would mean t h a t the p r e s e n t owner t r y i n g t o r e s e l l h i s t r a c t o r would be unable t o recoup h i s e x t r a i n vestment o u t l a y made f o r the o p t i o n . In t h i s sense t h e n , the o p t i o n was not worth the e x t r a c o s t t o the farmer. Of c o u r s e , t h i s says n o t h i n g about the v a l u e or u t i l i t y of o p t i o n t o a farmer i n the p e r i o d between purchase and r e s a l e . In t h i s sense such an o p t i o n might w e l l be "worth" p u r c h a s i n g even i f i t had a s i g n i f i c a n t n e g a t i v e e f f e c t on r e s a l e p r i c e . To c o n c l u d e , i t appears t h a t the r a t e of d e p r e c i a t i o n of farm t r a c t o r s i s u n a f f e c t e d by horsepower, the presence of a i r c o n d i t i o n i n g , or the make of the t r a c t o r . A cab i s the o n l y v a r i a b l e which seems a l t e r the r a t e of d e p r e c i a t i o n . . 7. COMBINES AND BALERS Hav i n g d e r i v e d a f i n a l model f o r t r a c t o r d e p r e c i a t i o n (14) i t remains t o a p p l y t h i s i n o r d e r t o e s t i m a t e the d e p r e c i a t i o n r a t e f o r s e l f - p r o p e l l e d combines and b a l e r s . As d i s c u s s e d i n the h i s t o r i c a l s e c t i o n of t h i s paper t h e r e i s good reason t o expect t h a t , f o r combines a t l e a s t , the r a t e of d e p r e c i a t i o n w i l l be s i g n i f i c a n t l y h i g h e r than t h a t of t r a c t o r s . T h i s i s e s p e c i a l l y t r u e of the o l d e r r e c i p r o c a t i n g t y pe combine, as opposed t o the newer a x i a l - f l o w type combines. Due t o the l a t t e r s ' fewer r e c i p r o c a t i n g p a r t s and lower l e v e l s of v i b r a t i o n t hey s h o u l d wear out l e s s q u i c k l y . Thus, t h e r e a r e a t l e a s t two h y p o t h e s e s worth t e s t i n g . One i s the h y p o t h e s i s t h a t the r a t e of d e p r e c i a t i o n i s d i f f e r e n t from th e r a t e of t r a c t o r d e p r e c i a t i o n and the second i s t h a t the r a t e i s d i f f e r e n t f o r t h e two t y p e s of combines mentioned. The r e s u l t s of t h e s e t e s t s s h o u l d j u s t i f y or r e j e c t t h e i r t r e a t m e n t i n t h e t a x s c h e d u l e s . R e g a r d l e s s of the a b s o l u t e magnitudes of the r a t e s of d e p r e c i a t i o n t h i s i n f o r m a t i o n on the r e l a t i v e r a t e s s h o u l d be of i n t e r e s t t o p o l i c y makers. 7.1 COMBINES I t would be p r e f e r a b l e i f the same model t h a t was used f o r t r a c t o r s c o u l d be used a g a i n f o r b oth combines and b a l e r s . However, due t o the d i f f e r e n t n a t u r e s of the machines the model had t o be amended. 90 91 The f i r s t change i n v o l v e d t h e f a c t t h a t no d a t a were a v a i l a b l e f o r Case. T h e r e f o r e , S p e r r y New H o l l a n d was s u b s t i t u t e d f o r Case. S e c o n d l y , h y d r o s t a t i c t r a n s m i s s i o n s a r e a more imp o r t a n t f e a t u r e than they were f o r t r a c t o r s and so a v a r i a b l e was i n c l u d e d f o r t h e s e . A l s o i n f o r m a t i o n on horsepower was not a v a i l a b l e f o r combines. T h i s l a c k of dat a i s i m p o r t a n t s i n c e PTO-HP was such a s i g n i f i c a n t v a r i a b l e f o r t r a c t o r s . A l s o a f u e l dummy t o account f o r d i e s e l and g a s o l i n e power _ was i n c l u d e d . T h i s was abandoned i n the work on t r a c t o r s s i n c e i t p r o v e d t o be a c o n s t a n t , i m p l y i n g t h a t a l l t r a c t o r s i n the sample were d i e s e l powered. In the combine d a t a , however, t h e r e were a s u f f i c i e n t number of g a s o l i n e combines t o i n c l u d e t he v a r i a b l e i n i t i a l l y . F i n a l l y , because the d i f f e r e n c e i n d e p r e c i a t i o n r a t e s between a x i a l - f l o w and r e g u l a r combines was of i n t e r e s t the dummy v a r i a b l e AF was i n c l u d e d f o r a x i a l f l o w t y p e combines. (29) LOG P = 1 1 . 0 6 - . 1 0 9 A G E + .104HYDRO + . 2 1 6 A F - . 1 7 I H ( 1 5 3 . 9 ) ( - 9 . 6 9 ) ( 2 . 2 3 ) ( 3 . 7 ) ( - 2 . 5 6 ) - .1656MF - .36NH (-3.11) (6.0) R 2 = . 7947 R 2 = .7714 n = 60 Where HYDRO i s h y d r o s t a t i c t r a n s m i s s i o n , AF r e p r e s e n t s a x i a l f l o w t y p e combines, IH i s I n t e r n a t i o n a l H a r v e s t e r , MF i s Massey Ferguson and NH i s New H o l l a n d . The v a r i a b l e s were a l l s i g n i f i c a n t a t the 95% l e v e l . The d e p r e c i a t i o n r a t e was found t o be a p p r o x i m a t e l y 10.9 % f o r combines which i s c l o s e t o the r a t e f o r t r a c t o r s . T h i s r e s u l t i s 92 i n t e r e s t i n g s i n c e combines were e x p e c t e d t o d e p r e c i a t e more r a p i d l y than t r a c t o r s . On the o t h e r hand, n o n i n t e r a c t i v e make and t ype dummy v a r i a b l e s were i n c l u d e d and from t h e s e i t was seen t h a t "makes e f f e c t s " seem t o e x e r t a s i g n i f i c a n t i n f l u e n c e on the p r i c e s of new machines i n t h e market. The dummy v a r i a b l e f o r a x i a l - f l o w a l s o d e monstrated a s i g n i f i c a n t e f f e c t on the p r i c e of combines ( t - s t a t . of 3.713) i n d i c a t i n g t h a t t h e newer, a x i a l - f l o w t y p e combines a r e more e x p e n s i v e . To t e s t whether or not make or t y p e a f f e c t d e p r e c i a t i o n the f o l l o w i n g i n t e r a c t i v e dummy v a r i a b l e s were i n c l u d e d : MFAGE, NHAGE, JDAGE and AXIAGE. The o n l y s i g n i f i c a n t a d d i t i o n was NHAGE i n d i c a t i n g t h a t New H o l l a n d combines do not d e p r e c i a t e a t t h e same r a t e as the o t h e r makes. The i n s i g n i f i c a n c e of AXIAGE, t h e term f o r the i n t e r a c t i o n of the d e p r e c i a t i o n r a t e and a x i a l - f l o w type combines, i n d i c a t e s t h a t t h e s e t y p e s do not d e p r e c i a t e a t a s l o w e r r a t e as was e x p e c t e d . T h i s may, a t l e a s t i n p a r t , be due t o t h e i r r e l a t i v e n o v e l t y and a c e r t a i n c a u t i o n on the p a r t of used combine buyers w a i t i n g f o r t h e new t e c h n o l o g y t o prove i t s e l f b e f o r e o f f e r i n g a premium on the market. Another f a c t o r may s i m p l y be t h a t any new t ype of a n y t h i n g has "bugs" i n i t i n i t i a l l y , r e d u c i n g t h e r e l i a b i l i t y of the e a r l y examples. 7.2 BALERS In t h i s study both the l a r g e round type and the s m a l l square t y p e b a l e r s a r e c o n s i d e r e d . S i n c e t h e r e a r e two 93 ( 3 0 ) L O G P = 1 1 . 2 7 - . 1 3 7 A G E - . 1 6 A I R - . 0 4 F U E L + . 1 6 5 H Y D R O ( 7 8 ) ( - 6 . 7 5 ) ( - 1 . 5 7 1 ) ( - . 7 1 4 ) ( 3 . 0 8 6 ) + . 2 2 A F - . 1 6 I H - . 2 8 M F - . 6 2 7 N H - . 0 0 1 9 6 I H A G E ( 1 . 0 8 ) ( - . 8 3 2 ) ( - 2 . 4 ) ( - 3 . 9 5 ) ( - . 0 4 ) + . 0 4 9 M F A G E + . 1 1 8 N H A G E - . 0 4 l A X I A G E ( 1 . 2 0 4 ) ( 1 , 9 9 ) ( - . 5 8 9 ) R 2 = . 8 1 9 9 R 2 = . 7 7 3 5 n = 6 0 d i s t i n c t l y d i f f e r e n t t y p e s of b a l e r s i t would be i n t e r e s t i n g t o compare d e p r e c i a t i o n r a t e s between them i n the same model. However, because square b a l e r s o f t e n have d i s t i n c t a p p l i c a t i o n s ( f o r example, square b a l e r s w i l l be used i n o p e r a t i o n s which r e q u i r e t he t r a n s p o r t a t i o n of b a l e s because square b a l e s t r a v e l b e t t e r ) i t was d e c i d e d t o run two s e p a r a t e r e g r e s s i o n s : one f o r square and one f o r round. The models, i n both c a s e s , a r e d i f f e r e n t from e i t h e r t he t r a c t o r or the combine models. In n e i t h e r model were v a r i a b l e s f o r engine type o r horspower i n c l u d e d s i n c e o n l y p u l l - t y p e combines were c o n s i d e r e d . I n the model f o r square type b a l e r s a v a r i a b l e was a l s o i n c l u d e d t o ac c o u n t f o r t he d i f f e r e n c e between t w i n e and w i r e t y p e s . T h i s i n f o r m a t i o n i s not r e l e v a n t f o r round b a l e r s so i f round b a l e r s and square b a l e r s were p l a c e d i n the same model any d i f f e r e n c e between t w i n e and w i r e square b a l e r s would be confounded w i t h the d i f f e r e n c e between round and square b a l e r s . F o r thes e r e a s o n s , s e p a r a t e models s h o u l d be run f o r each. 94 7.3 SQUARE BALERS The model was i n i t i a l l y : ( 3 1 ) L O G P = 8 . 9 - . 1 3 3 A G E + . 2 2 T Y P E - . 1 9 D E E R E - . 4 6 I H - . 3 5 M F ( 1 3 0 . 8 ) ( - 1 7 . 1 ) ( 4 . 1 8 ) ( - 1 . 7 ) ( - 2 . 7 8 ) ( - 3 . 0 7 ) + . 0 0 1 4 J D A G E + . 0 3 3 I H A G E + . 0 0 0 9 7 9 M F A G E ( . 1 0 4 ) ( 2 . 0 2 1 ) ( . 0 5 4 ) R 2 = . 8 4 1 5 R 2 = . 8 3 1 1 n = 1 3 1 T h i s model y i e l d e d a d e p r e c i a t i o n r a t e of a p p r o x i m a t e l y 13.34%. Compared t o both t r a c t o r s and combines, t h i s r a t e i s q u i t e h i g h . W h i l e the make of the b a l e r a f f e c t s the new p r i c e of the machine (except Deere, p e r h a p s ) , the make does not seem t o i n f l u e n c e the r a t e of d e p r e c i a t i o n of Deere and Massey Ferguson r e l a t i v e t o New H o l l a n d . The i n t e r a c t i o n terms JDAGE and MFAGE were i n s i g n i f i c a n t , h a v i n g t - s t a t i s t i c s of 0.104, and 0.054 r e p e c t i v e l y which i n d i c a t e s t h a t John Deere and Massey Ferguson b a l e r s do not have any i n f l u e n c e on the d e p r e c i a t i o n r a t e w h i c h i s s i g n i f i c a n t l y d i f f e r e n t from t h a t of New H o l l a n d ( w hich i s the o m i t t e d dummy v a r i a b l e i n t h i s i n s t a n c e ) . I t i s " s i g n i f i c a n t " t o n o t e , however, 95 t h a t I n t e r n a t i o n a l H a r v e s t e r does d e p r e c i a t e a t a d i f f e r e n t r a t e from New H o l l a n d ( t - s t a t i s t i c = 2.021). In f a c t d r o p p i n g JDAGE and MFAGE from the model and t e s t i n g t h e h y p o t h e s i s : Ho: JDAGE =MFAGE = 0 , i t i s p o s s i b l e t o s t a t e t h a t I n t e r n a t i o n a l b a l e r s d e p r e c i a t e a t a d i f f e r e n t r a t e from a l l o t h e r s . The c a l c u l a t e d F - s t a t i s t i c was 0.0385 (F c r i t i c a l = 3.07 a t 95% w i t h 2 and 123 d . f . ) . T h e r e f o r e , the above h y p o t h e s i s was a c c e p t e d and i n the f i n a l model t h e s e were dropped.The f i n a l d e p r e c i a t i o n r a t e f o r square b a l e r s was a p p r o x i m a t e l y 13.285 %. Given t h a t t r a c t o r s and combines had d e p r e c i a t i o n r a t e s c l o s e r t o 10%, i t may be s a i d t h a t square type b a l e r s l o s e t h e i r v a l u e r e l a t i v e l y q u i c k l y . (32) LOG P = 8.93 - .0133AGE - .2175TYPE - .18DEERE - .45IH (161.89) (-22 .4) (-4 .2) (-3 .66) (-2.87) - .35MF - .0 32IHAGE (-6.08) (-2.11) R 2 = .'8414 R 2 = .8338 n = 60 96 H a v i n g removed the i n s i g n i f i c a n t i n t e r a c t i v e make terms, a l l the n o n i n t e r a c t i v e make terms became s i g n i f i c a n t , i n c l u d i n g Deere. On the b a s i s of i t s t - s t a t i s t i c (4.22) the h y p o t h e s i s t h a t " t y p e " ( i e . whether t w i n e or w i r e ) a f f e c t s p r i c e would a l s o be a c c e p t e d . T h i s i m p l i e s t h a t w i r e type b a l e r s g e n e r a l l y command a h i g h e r new p r i c e i n the market than s t r i n g ( t w i n e ) type b a l e r s . 7.4 ROUND BALERS F i n a l l y , a model f o r the l a r g e round t y p e of b a l e r s was i n c l u d e d . However, because v e r y l i t t l e i n f o r m a t i o n was a v a i l a b l e f o r round b a l e r s , the c h o i c e of independent v a r i a b l e s was l i m i t e d t o age and make v a r i a b l e s . (33) LOG P = 9 .73 - .085AGE - .506DEERE - .408IH + .34MF - .0794JDAGE (28) (-1.16) (-1. 54) M . 27) (1.03) (-1.003) - .699IHAGE - .088MFAGE (-.902) (-1.097) R 2 = .7325 R 2 = .6926 n - 55 Becuase the i n t e r a c t i v e terms were a l l i n s i g n i f i c a n t , t he l a s t t h r e e terms were dropped. A j o i n t F t e s t on t h i s c o n f i r m e d the h y p o t h e s i s : JDAGE = IHAGE = MFAGE = 0 97 ( c a l c u l a t e d F s t a t i s t i c 0.4302 compared t o the c r i t i c a l v a l u e of 4.22 a t 95% and 3 and 48 d . f . , t h e r e f o r e , t h e h y p o t h e s i s was a c c e p t e d ) . T h i s i m p l i e s t h a t a l l makes of l a r g e round b a l e r t e s t e d d e p r e c i a t e a t t h e same r a t e . T h i s l e a v e s a f i n a l e s t i m a t e of d e p r e c i a t i o n f o r round b a l e r s of 15.937 %. T h i s r e s u l t i s somewhat unexpected s i n c e i t was b e l i e v e d Round b a l e r s d e p r e c i a t e more s l o w l y than square ones. (34) LOG P = 9.03 - 1.59AGE + 0.18DEERE + 0.17IH - 0.02MF (115.26)(-10.44) (3.29) (2.011) (-0.26) R 2 = .7253 R 2 = .7033 n = 55 8. SUMMARY AND IMPLICATIONS FOR POLICY In the p r e v i o u s s e c t i o n the r a t e s of d e p r e c i a t i o n f o r t r a c t o r s , combines, and round and square b a l e r s have been e s t i m a t e d u s i n g Canadian d a t a . The g e r e r a l c o n c l u s i o n i s t h a t t h e s e r a t e s of d e p r e c i a t i o n are l e s s than the Canadian t a x system a l l o w s f o r . That i s , the t a x system seems t o be generous t o the owners of Canadian farm machinery. For example, the most q u i c k l y d e p r e c i a t i n g machine i n t h i s study was found t o l o s e l e s s than 16% of i t s v a l u e each y e a r , and on average the r a t e s were found t o be lower than t h i s . To summarize, i t was found t h a t t r a c t o r s l o s e about 9% of t h e i r v a l u e each year ( e q u a t i o n 22b). T h i s r a t e was d e r i v e d u s i n g unaveraged i n d i v i d u a l p r i c e d a t a f o r the year 1980, and when compared t o averaged p r i c e d a t a f o r o t h e r y e a r s was found t o be s t a b l e . W h i l e t h i s r a t e i s s u i t a b l e f o r comparison t o p r e v i o u s s t u d i e s i t was argued t h a t t h i s i s not pure age d e p r e c a i t i o n i n s t r i c t e s t sense of the term. Because the d a t a used i n t h i s t h e s i s i n c l u d e d a c c u m u l a t e d hours of use, i t was p o s s i b l e t o s e p a r a t e the 'pure age' from the 'pure use' e f f e c t of d e p r e c i a t i o n . Doing t h i s , i t was found t h a t the l o s s i n v a l u e s t r i c t l y a t t r i b u t a b l e t o age was a p p r o x i m a t e l y 6.6% per y e a r (eq. 14). A nother g e n e r a l c o n c l u s i o n from t h i s s t u d y i s t h a t w i t h the e x c e p t i o n of a cab, o p t i o n s do not i n f l u e n c e the r a t e a t which a t r a c t o r l o s e s v a l u e i n Canada. F u r t h e r m o r e , the r a t e of d e p r e c i a t i o n was a l s o not c 98 99 a f f e c t e d by the make or the horsepower r a t i n g of the t r a c t o r . S i m i l a r r e s u l t s were found f o r the o t h e r machines. S e l f - p r o p e l l e d combines l o s e a p p r o x i m a t e l y 11% of t h e i r v a l u e per year (eq. 25) f o r example, but t h i s r a t e i s u n a f f e c t e d by the o p t i o n s the combine was e q u i p p e d w i t h . In f a c t the r a t e of d e p r e c i a t i o n was not s i g n i f i c a n t l y d i f f e r e n t f o r the newer a x i a l - f l o w t ype combines. However, t h i s r e s u l t may change as the a x i a l - f l o w combines become more common. F i n a l l y , when the r a t e of d e p r e c i a t i o n was e s t i m a t e d f o r b a l e r s i t was found t h a t square b a l e r s l o s e 13.3% of t h e i r v a l u e each year and t h a t round b a l e r s l o s e 15.5% (see eq. 28 and 29b r e s p e c t i v e l y . ) 8.1 DEPRECIATION FOR TAXATION The p r e v a i l i n g t a x system t a x e s income i n c l u d i n g income d e r i v e d from d e p r e c i a b l e a s s e t s . However, i t i s r e c o g n i z e d t h a t d e p r e c i a t i o n or the l o s s i n v a l u e of the i n c o m e - g e n e r a t i n g a s s e t i s a l e g i t i m a t e c o s t t h a t s h o u l d be d e ducted from t a x a b l e income. The c u r r e n t method f o r d o i n g so i s v i a c a p i t a l c o s t a l l o w a n c e s . The q u e s t i o n i m m e d i a t e l y a r i s e s : do t h e s e a l l o w a n c e s a d e q u a t e l y compensate (or over compensate) the farmer f o r t h i s l o s s i n v a l u e ? Without a c c u r a t e e s t i m a t i o n s of t h e a c t u a l r a t e of d e p r e c i a t i o n t h e r e i s no way of knowing. The i s s u e of adequate compensation f o r a c t u a l d e p r e c i a t i o n has come 100 i n t o the s p o t l i g h t of l a t e , due t o the h i g h r a t e s of i n f l a t i o n e x p e r i e n c e d i n the p a s t decade, combined w i t h the low r a t e s of p r o d u c t i v i t y i n c r e a s e i n N o r t h America. I t i s g e n e r a l l y r e c o g n i z e d t h a t , i n an i n f l a t i o n a r y p e r i o d , p u r c h a s i n g a d e p r e c i a b l e a s s e t now and a c c e p t i n g a s e r i e s of y e a r l y t a x a l l o w a n c e s as compensation i s , i n essence, ' t r a d i n g good d o l l a r s f o r bad'. That i s t o say, the p u r c h a s i n g power of those f u t u r e t a x a l l o w a n c e s w i l l be eroded i n an i n f l a t i o n a r y p e r i o d . F u r t h e r m o r e , some have l i n k e d t h i s t o poor p r o d u c t i v i t y . By p o s t u l a t i n g a c o n n e c t i o n between inadequate d e p r e c i a t i o n a l l o w a n c e s and lower i n v e s t m e n t i n d e p r e c i a b l e a s s e t s , and a l s o a c o n n e c t i o n between t h i s lower investment and s l o w e r p r o d u c t i v i t y growth, the importance of a c c u r a t e d a t a on a c t u a l d e p r e c i a t i o n r a t e s can be seen i m m e d i a t e l y (whether such c o n n e c t i o n s a c t u a l l y e x i s t or not i s d e b a t a b l e , the i s s u e s a r e beyond the the scope of the p r e s e n t r e s e a r c h . See H u l t e n [ 1 9 8 4 ] , f o r example, f o r f u r t h e r d i s c u s s i o n ) . Inadequate d e p r e c i a t i o n a l l o w a n c e s w i l l d i s c o u r a g e investment and t h i s may, the argument goes, reduce the r a t e of p r o d u c t i v i t y growth. The f r e q u e n t l y mentioned s o l u t i o n i s a c c e l e r a t e d d e p r e c i a t i o n . However, i f the government i s t o a c c e l e r a t e d e p r e c i a t i o n a l l o w a n c e s t o s o l v e t h i s problem i t needs t o know by how much i n each s e c t o r and f o r each a s s e t group. T h i s l e a d s t o the i s s u e of n o n - n e u t r a l i t i e s i n the tax system. I t has been argued (and i s p r e s e n t l y b e i n g 101 argued both i n the U n i t e d S t a t e s and Canada by those s e e k i n g t a x l i b e r a l i z a t i o n ) t h a t s p e c i f i c d a t a on d e p r e c i a t i o n a r e . n o t what i s needed s i n c e d e p r e c i a t i o n a l l o w a n c e s a r e d e l i b e r a t e l y used by the t a x a t i o n a u t h o r i t i e s as an i n c e n t i v e . That i s , i t i s r e c o g n i z e d t h a t d e p r e c i a t i o n a l l o w a n c e s don't conform t o the a c t u a l d e p r e c i a t i o n , but are p u r p o s e l y l a r g e r t o encourage new i n v e s t m e n t . Y e t , even i f i n c e n t i v e i s the p urpose, the a c t u a l d e p r e c i a t i o n r a t e s a c r o s s a s s e t s must be known so as not t o i n t r o d u c e b i a s e s or n o n - n e u t r a l i t i e s i n t o the t a x system. W h i l e the i s s u e of the p r e c e d i n g p aragraph might have been l a b e l e d " t o a c c e l e r a t e or not a c c e l e r a t e i n the f a c e of i n f l a t i o n ? " , t h i s i s s u e i s b e t t e r l a b e l e d " i f a c c e l e r a t i o n - h o w much and i n and i n which s e c t o r s ? " W i t h o u t i n f o r m a t i o n on d e p r e c i a t i o n , the t a x a u t h o r i t y might o v e r s t i m u l a t e some s e c t o r s and u n d e r s t i m u l a t e o t h e r s , l e a d i n g t o n o n - o p t i m a l a l l o c a t i o n of r e s o u r c e s . T h i s p o i n t has been r a i s e d by Coen [1975] "To a c h i e v e t a x e q u i t y and n e u t r a l i t y , the t r e a s u r y s h o u l d s t r i v e t o keep, t a x d e p r e c i a t i o n i n l i n e w i t h economic d e p r e c i a t i o n ; even i f T r e a s u r y p o l i c y s h o u l d seek t o s t i m u l a t e c a p i t a l e x p e n d i t u r e s by r e d u c i n g e f f e c t i v e t a x r a t e s t h r o u g h l i b e r a l i z a t i o n of t a x d e p r e c i a t i o n , a r e a s o n a b l e o b j e c t i v e might be t o reduce e f f e c t i v e t a x r a t e s e q u a l l y i n a l l i n d u s t r i e s which might r e q u i r e d i f f e r e n t degrees of l i b e r a l i z a t i o n i n d i f f e r e n t i n d u s t r i e s . E f f o r t s a l o n g t h e s e l i n e s a r e g r e a t l y c o m p l i c a t e d , however, by the l a c k of adequate i n f o r m a t i o n r e g a r d i n g s e r v i c e l i v e s and p a t t e r n s of economic d e p r e c i a t i o n of c a p i t a l goods i n v a r i o u s i n d u s t r i e s . " T h i s i s s u e of n e u t r a l i t y and the market's a b i l i t y t o a l l o c a t e r e s o u r c e s e f f i c i e n t l y i s an i n t e r e s t i n g one. Many 1 02 of those who espouse b l a n k e t a c c e l e r a t i o n schemes (such as the American "10-5-3" p r o p o s a l ) b e l i e v e they a r e e q u a l i z i n g t a x burdens and a l l o w i n g t h e 'market f o r c e s ' t o a l l o c a t e r e s o u r c e s o p t i m a l l y . E i t h e r t hey a r e f o r g e t t i n g the i s s u e of e f f e c t i v e t a x r a t e s , which depend t o a g r e a t e x t e n t on d e p r e c i a t i o n , or they do not f e e l t h a t d e p r e c i a t i o n r a t e s can be a c c u r a t e l y measured and hence s h o u l d be i g n o r e d . In r e a l i t y a t r u l y n e u t r a l and e q u i t a b l e a c c e l e r a t i o n p o l i c y r e q u i r e s v a r y i n g degrees of t a x a c c e l e r a t i o n f o r v a r i o u s a s s e t s , each a c c o r d i n g t o i t s r a t e of d e p r e c i a t i o n . Thus, t h e r e i s a need f o r a c c u r a t e measures. These i s s u e s are r e f l e c t e d i n the debate over proposed changes t o the U.S. t a x system, which would see d e p r e c i a b l e a s s e t s d i v i d e d i n t o o n l y t h r e e comprehensive c a t e g o r i e s [ S u n l e y ,1981]. These broad c a t e g o r i e s would s i m p l y be n o n r e s i d e n t i a l b u i l d i n g s , , machinery and equipment, and a l i m i t e d c a t e g o r y f o r l i g h t t r u c k s and a u t o m o b i l e s . T h i s i s the "10-5-3" p r o p o s a l which i s , b a s i c a l l y , an a c c e l e r a t e d d e p r e c i a t i o n p l a n t h a t would s h o r t e n the p e r i o d over which a s s e t s , i n t h e s e a l l i n c l u s i v e c a t e g o r i e s c o u l d be w r i t t e n o f f t o t e n y e a r s , f i v e y e a r s , and t h r e e y e a r s r e s p e c t i v e l y . I t s h o u l d be noted a l s o t h a t the t a x laws ».applying t o farm machinery i n the U n i t e d S t a t e s were changed i n 1981 under the Economic Recovery Tax A c t (ERTA) and t h e a s s o c i a t e d A c c e l e r a t e d Tax Recovery System (ACRS). These changes 103 r e f l e c t the same b e l i e f s t h a t l e d t o the "10-5-3" p r o p o s a l . The m o t i v a t i o n b e h i n d such schemes i s the b e l i e f a) t h a t d e p r e c i a t i o n a l l o w a n c e s need t o be l i b e r a l i z e d i n the f a c e of i n f l a t i o n , b) t h a t such s i m p l i f i c a t i o n s would g e n e r a l l y enhance the e q u a l i t y and n e u t r a l i t y of the t a x system, and c) t h a t a c t u a l d e p r e c i a t i o n r a t e s a r e i m p o s s i b l e t o measure a t any r a t e . The l a s t i s s u e i s one which r e q u i r e s e m p i r i c a l i n v e s t i g a t i o n and t h i s t h e s i s r e p r e s e n t s an attempt t o show how t h i s i n v e s t i g a t i o n c o u l d be c a r r i e d out f o r a s s e t s f o r which t h e r e e x i s t s r e l a t i v e l y complete second-hand markets. T h i s i n f o r m a t i o n or i n f o r m a t i o n l i k e i t , must be used by the t a x a u t h o r i t y , i f i t w ishes t o p r e s e r v e the n e u t r a l and o p t i m a l a l l o c a t i o n of r e s o u r c e s which the market t h e o r e t i c a l l y y i e l d s . In t h i s s tudy of t h r e e c a t e g o r i e s of Canadian farm machinery d e p r e c i a t i o n r a t e s were found t o v a r y between c l a s s and, i n one i n s t a n c e , t o v a r y depending on the o p t i o n s t h a t the machine was e quipped w i t h . In a l l c a s e s , the r a t e of d e p r e c i a t i o n was found t o be l e s s than s i x t e e n p e r c e n t per y e a r . I t was a l s o found t h a t t h e p a t t e r n of t h i s d e p r e c i a t i o n does conform t o c o n s t a n t g e o m e t r i c form. T h i s r e s u l t s i n immediate, c o n c l u s i o n s f o r t a x p o l i c y . The p o s i t i v e r e s u l t i s t h a t the g e o m e t r i c p a t t e r n i n c u r r e n t use i n the t a x laws seems t o j u s t i f i e d . On the n e g a t i v e s i d e , r a t e s found i n t h i s s tudy a r e not n e a r l y as h i g h as the d e p r e c i a t i o n a l l o w a n c e s g r a n t e d 1 04 by t h i s same t a x system. I f a l l r a t e s e s t i m a t e d had been the same, t h i s " g e n e r o s i t y " c o u l d not be seen i n a n e g a t i v e l i g h t (except perhaps t o the e x t e n t t h a t i t promotes the s u b s t i t u t i o n of c a p i t a l f o r l a b o u r on the f a r m ) . However, from t h i s s m a l l sample i t i s e v i d e n t t h a t a c t u a l economic d e p r e c i a t i o n r a t e s v a r y a g r e a t d e a l . T h e r e f o r e , such " g e n e r o s i t y " can cause d i s t o r t i o n s , f a v o u r i n g some machines more than o t h e r s , u n l e s s i t i s t a i l o r e d t o the p a r t i c u l a r machine. On the b a s i s of t h i s s t u d y , i t can be s a i d t h a t t h i s p r e c i s e i n f o r m a t i o n needed t o p e r f o r m t h i s t a i l o r i n g , i s o b t a i n a b l e f o r Canadian machines, from Canadian s o u r c e s . By u s i n g such i n f o r m a t i o n t a x p o l i c y can be made much l e s s of a b l u n t i n s t r u m e n t than i t i s now. The g e n e r a l i m p l i c a t i o n f o r p o l i c y , t h e n , i s t h a t a c t u a l d e p r e c i a t i o n r a t e s , f o r s p e c i f i c t y p e s of Canadian machines, can and s h o u l d be e s t i m a t e d i n o r d e r c r e a t e a more n e u t r a l t a x system. F u r t h e r m o r e , t h i s i n f o r m a t i o n which i s a v a i l a b l e from Canadian s o u r c e s , s h o u l d p l a y a r o l e i n making farm management d e c i s i o n s more r e l e v e n t t o Canadian farm c o n d i t i o n s . O p t i m a l replacement d e c i s i o n s , f o r example, r e q u i r e a c c u r a t e e s t i m a t e s of d e p r e c i a t i o n , but i n the p a s t farm o p e r a t o r s have had t o r e l y on American d a t a . The r e s u l t s o f f e r e d here may h e l p Canadians manage t h e i r o p e r a t i o n s more e f f e c t i v e l y . 105 8.2 SUGGESTIONS FOR FURTHER RESEARCH More work needs t o be done t o i n c r e a s e the number of Canadian a s s e t s f o r which t h e r e a r e e s t i m a t e d d e p r e c i a t i o n r a t e s . There a r e many o t h e r t y p e s of farm machinery a l o n e , w hich need t o be s t u d i e d . S e c o n d l y , more work needs t o be done on the r e t i r e m e n t of farm machinery. R e t i r e m e n t d i s t r i b u t i o n s form an i m p o r t a n t p a r t of the e s t i m a t i o n of d e p r e c i a t i o n , y e t t h i s i n f o r m a t i o n i s weak and d a t e d . 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DATA APPENDIX 111 1980 C r o s s - S e c t i o n Data For T rac to r s M Y R A G E P R I C E C D C A B C L D A I R 3 P p F E L H T R H P H O U R S 1 7 2 8 1 1 0 0 0 2 , 0 0 1 , 0 0 0 9 4 3 7 7 0 1 7 3 7 1 5 0 0 0 2 1 0 1 1 1 1 0 0 9 4 2 5 5 0 1 7 5 5 1 8 5 0 0 1 1 0 0 1 1 1 0 0 9 4 1 1 5 0 1 7 6 4 1 9 7 0 0 1 1 0 0 1 1 1 0 0 9 4 1 3 0 0 1 7 7 3 2 1 0 0 0 1 1 0 0 1 1 1 0 0 9 4 1 0 0 0 1 7 8 2 2 4 0 0 0 1 1 0 0 1 1 0 1 0 9 4 3 4 0 1 7 0 1 0 1 1 0 0 0 2 1 1 0 0 0 0 0 1 0 7 4 0 0 0 1 7 0 1 0 1 3 0 0 0 2 1 0 1 0 1 0 0 1 1 0 7 3 5 0 0 1 7 1 9 1 2 0 0 0 2 1 0 0 0 0 0 0 1 0 7 3 8 8 0 1 7 2 8 1 5 0 0 0 2 1 0 1 1 1 0 0 0 1 0 7 2 7 5 0 1 7 2 8 1 6 0 0 0 2 1 0 1 1 1 1 0 0 1 0 7 3 1 3 5 1 7 4 6 1 7 5 0 0 2 1 0 1 1 0 0 0 1 0 7 2 0 0 0 1 7 4 6 1 8 0 0 0 2 1 0 1 1 1 0 0 0 1 0 7 1 8 5 0 1 7 5 5 1 9 5 0 0 2 1 0 0 1 1 0 0 0 1 0 7 1 7 0 0 1 7 6 4 1 8 9 0 0 2 1 0 0 1 1 1 0 0 1 0 7 2 1 0 0 1 7 6 4 2 0 0 0 0 1 1 0 1 1 1 1 0 0 1 0 7 1 2 0 0 1 7 6 4 2 1 9 0 0 1 ] 0 1 1 1 1 0 , - Q , - - K ) 7 - 6 9 0 1 7 6 4 2 2 8 0 0 1 1 0 0 1 1 1 0 0 1 0 7 1 0 0 0 1 7 7 3 2 2 0 0 0 ] 1 0 0 1 1 1 0 0 1 0 7 3 9 0 1 7 7 3 2 4 5 0 0 1 1 0 1 1 1 0 0 0 1 0 7 5 0 0 1 7 8 2 2 5 9 0 0 1 1 0 1 1 1 1 0 0 1 0 7 6 9 5 1 7 8 2 2 6 0 0 0 1 1 0 1 1 1 1 0 0 1 0 7 6 0 0 1 7 2 8 1 3 9 0 0 2 1 0 1 0 0 0 1 2 4 2 9 7 0 1 7 2 8 1 4 5 0 0 2 1 0 1 1 0 0 1 1 2 4 2 5 0 0 1 7 3 7 1 5 9 0 0 2 1 0 1 1 ' 1 0 0 0 1 2 4 2 9 0 0 1 7 5 5 1 7 0 0 0 2 1 0 1 0 0 1 1 2 4 2 0 0 0 1 7 5 5 1 7 5 0 0 2 1 0 1 1 1 0 0 0 1 2 4 2 2 0 0 1 7 7 3 2 3 0 0 0 1 1 0 1 1 1 0 0 0 1 2 4 1 2 0 0 1 7 7 3 2 5 0 0 0 1 1 0 1 1 1 0 0 0 1 2 4 1 3 0 0 1 7 8 2 2 7 9 0 0 1 1 0 1 1 1 0 0 0 1 2 4 6 7 5 1 7 2 8 1 6 5 0 0 2 1 0 1 1 1 0 0 1 3 2 3 3 0 0 1 7 2 8 1 8 5 0 0 2 1 0 1 1 0 0 0 1 3 2 2 6 6 0 1 7 3 7 1 6 9 0 0 2 1 0 0 1 1 0 0 0 1 3 2 2 0 0 0 1 7 3 7 1 6 9 5 0 2 1 0 0 1 0 0 1 1 3 2 2 8 0 0 1 7 6 4 1 8 5 0 0 2 1 0 1 1 1 0 0 0 1 3 2 2 1 0 0 1 7 6 4 2 3 5 0 0 1 1 0 1 1 1 1 0 0 1 3 2 1 7 8 0 1 7 7 3 2 4 0 0 0 1 1 0 0 0 1 0 1 1 3 2 1 3 1 5 1 7 7 3 2 7 0 0 0 1 1 0 1 1 1 1 0 0 1 3 2 6 6 0 2 7 5 5 1 6 5 0 0 2 0 0 0 0 1 1 1 0 7 4 2 1 8 0 2 7 6 4 1 6 9 9 5 1 0 0 0 0 1 1 0 0 7 4 4 5 0 2 7 7 3 1 5 5 0 0 1 0 0 0 0 1 1 0 0 7 4 3 7 5 2 7 8 2 1 6 9 0 0 1 0 0 0 0 1 1 0 0 7 4 3 2 5 2 7 8 2 1 7 5 0 0 1 0 0 0 0 1 1 1 0 7 4 3 1 0 2 6 5 1 5 7 7 5 0 2 0 0 1 0 0 1 0 0 9 5 4 1 2 0 2 6 5 1 5 8 7 5 0 2 1 0 1 0 0 1 0 0 9 5 4 4 0 0 2 6 9 1 1 8 9 7 5 2 1 0 0 0 0 1 0 0 9 5 3 7 5 0 2 6 9 1 1 1 0 9 9 5 2 1 0 0 1 0 1 0 0 9 5 4 6 0 0 2 7 0 1 0 1 1 5 0 0 2 1 0 1 1 0 1 0 0 9 5 3 6 6 0 2 7 0 1 0 1 2 5 0 0 2 1 1 1 0 0 1 0 0 9 5 3 9 0 0 2 7 0 1 0 1 3 5 0 0 2 1 0 0 0 1 0 0 0 9 5 2 7 7 0 M Y R A G E P R I C E C D C A B C L D A I R 3 P p F E L H T R H P H O U R S 2 7 2 8 1 2 0 0 0 2 1 0 0 1 0 0 0 9 5 3 8 0 0 2 7 2 8 1 5 5 0 0 2 1 0 1 1 1 1 0 0 9 5 2 2 8 0 2 7 3 7 1 6 5 0 0 2 1 0 1 1 1 1 0 0 8 0 2 5 8 0 2 7 3 7 1 8 0 0 0 2 1 0 0 1 0 1 0 0 8 0 3 1 0 0 2 7 4 6 1 8 6 0 0 2 1 0 0 1 1 1 0 0 8 0 3 0 0 0 2 7 4 6 1 9 0 0 0 2 1 0 1 1 0 1 0 0 8 0 2 5 0 0 2 7 5 5 2 0 9 0 0 2 1 0 1 1 0 1 0 0 8 0 2 8 6 0 2 7 6 4 2 1 9 9 5 2 1 0 0 1 0 1 0 0 8 0 2 2 0 0 2 7 6 4 2 2 5 0 0 1 1 0 1 1 1 1 0 0 8 0 1 6 8 0 2 7 7 3 2 5 0 0 0 1 1 0 1 1 1 1 0 0 9 1 5 8 0 2 7 8 2 2 7 5 0 0 1 i 0 1 1 0. 1 0 0 9 1 6 6 0 2 7 9 1 2 6 5 0 0 1 1 0 0 1 1 1 0 0 91 1 2 7 0 2 7 9 1 2 8 9 0 0 1 1 ' 0 0 1 0 1 0 0 9 1 2 7 0 2 7 2 8 1 8 0 0 0 2 1 1 1 0 0 1 0 0 1 2 8 4 1 0 0 2 7 2 8 1 8 5 0 0 2 1 0 1 1 0 1 0 0 1 2 8 2 1 2 0 2 7 3 7 2 0 5 0 0 2 1 0 1 0 0 0 1 1 2 8 3 2 5 5 2 7 3 7 2 2 5 0 0 2 1 0 0 1 1 1 0 0 1 2 8 3 9 0 0 2 7 3 7 2 4 0 0 0 2 1 0 1 1 0 1 0 0 1 2 8 3 3 5 0 2 7 4 6 2 1 0 0 0 2 1 0 1 1 0 1 0 0 1 2 8 3 0 5 0 2 7 4 6 2 3 5 0 0 2 1 0 1 1 1 1 0 0 1 2 8 2 4 0 0 2 7 4 6 2 5 5 0 0 2 1 0 1 1 0 0 0 1 2 8 2 6 5 0 2 7 4 6 2 7 0 0 0 2 1 0 1 1 1 1 0 0 1 2 8 1 9 5 0 2 7 4 6 2 7 5 0 0 2 1 0 1 1 0 1 0 0 1 2 8 2 5 0 0 2 7 5 5 2 2 0 0 0 2 1 0 1 1 1 0 0 1 2 8 3 0 0 0 2 7 5 5 2 4 0 0 0 2 1 0 1 1 0 1 0 0 1 2 8 2 7 7 0 2 7 5 5 2 5 9 0 0 2 1 0 1 1 1 1 0 0 1 2 8 2 3 0 0 2 7 5 5 2 7 0 0 0 2 1 0 0 1 0 1 0 0 1 2 8 2 3 0 0 2 7 5 5 3 0 0 0 0 1 1 0 1 1 1 1 0 0 1 2 8 1 0 8 0 2 7 6 4 2 5 0 0 0 2 1 . 0 1 . 1 0 1 0 0 1 2 8 2 1 0 0 2 7 6 • 4 2 6 0 0 0 2 ! 0 1 1 1 1 0 0 1 2 8 3 0 0 0 2 7 6 4 2 6 0 0 0 2 1 0 1 1 0 1 0 0 1 2 8 1 8 5 0 2 7 6 4 2 8 0 0 0 1 1 0 1 1 1 1 0 0 1 2 8 1 7 2 0 2 7 7 5 2 8 0 0 0 1 1 0 1 1 1 1 0 0 1 2 8 1 4 0 0 3 7 2 8 1 2 0 0 0 2 1 0 0 0 1 0 0 9 6 3 4 4 0 3 7 4 6 1 3 5 0 0 2 1 0 0 1 0 1 0 0 9 6 3 2 0 0 3 7 4 6 1 6 4 0 0 2 1 0 0 1 0 1 0 0 9 6 2 4 5 0 3 7 4 6 1 8 5 0 0 1 1 0 0 1 1 1 0 0 9 6 1 8 8 0 3 7 6 4 1 8 9 5 0 1 1 0 1 1 0 1 0 0 9 6 1 2 8 0 3 7 1 9 1 2 5 0 0 2 0 0 0 0 1 0 0 0 1 1 6 4 1 0 0 3 7 2 8 1 5 5 0 0 2 1 0 0 1 1 0 0 0 1 1 6 3 1 0 0 3 7 2 8 1 7 5 0 0 2 1 0 0 1 1 0 0 0 1 1 6 2 2 8 0 3 7 3 7 1 5 8 0 0 2 1 0 0 0 0 0 0 1 1 1 6 3 4 5 0 3 7 3 7 1 6 0 0 0 2 1 0 0 1 1 1 0 0 1 1 6 3 6 0 0 3 7 3 7 1 7 5 0 0 2 1 0 1 1 1 1 0 1 1 1 6 1 7 5 0 3 7 4 6 1 7 5 0 0 2 1 0 1 1 1 1 0 0 1 1 6 2 9 0 0 3 7 4 6 1 8 0 0 0 2 1 0 1 1 1 1 0 0 1 1 6 2 1 0 0 3 7 5 5 20000 1 1 0 1 1 0 1 0 0 1 1 6 9 7 5 3 7 5 5 2 1 0 0 0 2 1 0 1 1 1 0 0 1 1 6 2 3 0 0 3 7 6 4 2 0 0 0 0 1 1 0 1 1 1 1 0 0 1 1 6 1 8 3 0 3 7 6 4 2 3 5 0 0 1 1 0 1 1 1 1 0 0 1 1 6 9 0 0 3 7 6 4 2 4 5 0 0 1 1 0 1 1 1 1 0 0 1 1 6 . 1 1 0 0 3 7 7 3 3 0 0 0 0 1 1 0 ) 1 1 1 0 0 1 3 4 1 6 0 0 3 7 7 3 3 3 0 0 0 1 1 0 1 1 1 1 0 0 1 3 4 4 5 0 3 7 9 1 3 7 5 0 0 1 1 0 1 1 1 1 0 0 1 3 4 3 3 0 3 7 1 9 1 3 5 0 0 2 1 0 1 1 0 0 1 39 3800 3 7 3 7 1 8 7 0 0 2 1 1 1 0 1 0 0 0 1 3 9 2 7 0 0 3 7 4 6 1 9 5 0 0 2 1 0 1 1 1 0 0 0 1 3 9 4 0 4 0 3 7 4 6 2 2 0 0 0 2 1 1 1 0 1 0 0 0 1 3 9 2 3 0 0 3 7 5 5 2 1 5 0 0 2 1 0 1 1 1 1 0 0 1 3 9 2 0 0 0 M Y R A G E P R I C E C D C A B C L D A I R 3 P P F E L H T R H P H O U R S v 114 3 7 6 4 2 4 5 0 0 1 0 1 1 1 1 0 0 1 3 9 1 1 7 0 3 7 6 4 2 7 0 0 0 1 0 1 1 1 1 0 0 1 3 9 1 7 7 0 3 7 6 4 2 7 5 0 0 2 0 1 1 1 1 0 0 1 3 9 1 9 0 0 4 7 3 7 8 7 5 0 2 C ) 0 0 c ) 1 1 0 0 8 1 2 6 0 0 4 7 3 7 9 9 5 0 2 0 1 c ) 1 0 0 0 8 1 3 1 0 0 4 7 5 5 1 5 0 0 0 1 0 0 1 1 0 0 8 1 1 6 6 0 4 7 7 3 1 7 5 0 0 1 0 0 1 1 0 0 8 1 5 0 0 4 7 3 7 1 3 0 0 0 2 0 0 c ) 0 1 0 0 1 0 0 3 3 0 0 4 7 4 6 1 4 9 0 0 2 0 0 1 0 0 0 1 0 0 2 2 0 0 4 7 4 6 1 5 5 0 0 2 0 0 0 1 0 0 1 0 0 2 8 8 0 4 7 5 5 1 6 5 0 0 2 0 1 0 0 0 0 1 0 0 1 4 0 0 4 7 6 4 1 6 5 0 0 1 0 0 1 0 0 0 1 0 0 1 1 2 5 4 7 6 4 1 9 8 0 0 1 ( ) 0 0 ( ) 1 1 1 0 1 0 0 6 8 0 4 7 7 3 1 9 0 0 0 1 0 0 0 1 0 0 1 0 0 7 4 0 4 7 7 3 1 9 9 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 4 7 7 3 2 0 5 0 0 1 0 0 1 1 0 0 1 0 0 1 3 8 0 4 7 7 3 2 2 2 0 0 1 0 1 0 1 0 0 1 0 0 6 8 0 4 7 3 7 1 4 5 0 0 2 0 0 ( ) 0 1 0 0 1 2 2 2 7 5 0 4 7.4 6 1 6 2 0 0 2 0 0 1 1 0 0 1 2 2 1 8 0 0 4 7 4 6 1 7 9 0 0 2 0 1 ( ) 0 0 0 0 1 2 2 2 2 0 0 4 7 5 5 1 6 5 0 0 2 0 1 0 0 0 0 1 2 2 2 6 0 0 4 7 6 4 1 8 0 0 0 1 0 0 1 1 0 0 1 2 2 1 5 5 0 4 7 6 4 2 0 0 0 0 1 0 1 0 1 0 0 1 2 2 1 7 0 0 4 7 6 4 2 1 0 0 0 1 0 1 1 1 0 0 1 2 2 9 5 0 4 7 7 3 2 2 5 0 0 2 0 1 1 1 0 0 1 2 2 1 9 0 0 4 7 8 2 2 5 0 0 0 1 0 0 1 1 0 0 1 2 2 5 8 0 4 7 9 1 2 7 5 0 0 1 0 0 1 1 1 0 1 2 2 1 6 0 W h e r e : M = m a k e o f t r a c t o r , Y r = y e a r o f t r a c t o r , A G E = a g e o f t r a c t o r i n y e a r s , P R I C E = p r i c e o f t r a c t o r i n d o l l a r s , C D = c o n d i t i o n o f t r a c t o r , C = d u m m y f o r c a b , C L = d u m m y f o r c o o l e r , D = d u m m y f o r d u a l r e a r w h e e l s , A I R = d u m m y f o r a i r c o n d i t i o n i n g , 3 p = d u m m y f o r t h r e e - p o i n t - h i t c h , P = d u m m y f o r p o w e r s h i f t t r a n s m i s s i o n , F E L = d u m m y f o r f r o n t - e n d - l o a d e r , H T R = d u m m y h e a t e r , H P = h o r s e p o w e r o f t r a c t o r , H o u r = n u m b e r o f h o u r s t h e t r a c t o r h a s b e e n u s e d . 115 Pooled C r o s s - s e c t i o n Time Se r i es Data For T rac to r s M A K E Y E A R A G E 7 0 1 1 7 1 1 0 7 2 9 7 3 8 7 4 7 7 5 6 7 6 5 7 7 4 7 8 3 7 0 1 1 7 1 1 0 7 2 9 7 3 8 7 4 7 7 5 6 7 6 5 7 7 4 7 8 3 7 0 1 1 7 1 1 0 7 2 9 7 3 8 7 4 7 7 5 6 7 6 5 7 7 4 7 8 3 7 2 9 7 3 8 7 4 7 7 5 6 7 6 5 7 7 4 7 8 3 2 6 5 1 6 2 6 6 1 5 2 6 7 1 4 2 6 8 1 3 2 6 9 1 2 2 7 0 1 1 2 7 1 1 0 2 7 2 9 2 6 5 1 6 2 6 6 1 5 2 6 7 1 4 2 6 8 1 3 2 6 9 1 2 2 7 0 1 1 2 7 1 1 0 2 7 2 9 2 7 3 8 2 7 4 7 2 7 5 6 2 7 6 5 2 7 3 8 2 7 4 7 2 7 5 6 2 7 6 5 P R I C E H P 9 0 2 9 . 0 0 8 5 1 0 0 3 3 . 0 0 8 5 1 1 1 4 7 . 0 0 8 5 1 2 3 8 6 . 0 0 8 5 1 3 7 6 2 . 0 0 8 5 1 5 2 9 2 . 0 0 8 5 1 6 8 2 1 . 0 0 8 5 1 8 5 0 3 . 0 0 8 5 2 0 6 4 8 . 0 0 8 5 1 0 4 1 5 . 0 0 1 0 0 1 1 4 5 6 . 0 0 t o o 1 2 6 0 2 . 0 0 1 0 0 1 3 8 6 2 . 0 0 1 0 0 1 5 7 6 7 . 0 0 1 0 0 1 7 6 7 2 . 0 0 1 0 0 1 9 5 7 7 . 0 0 1 0 0 2 1 4 8 1 . 0 0 1 0 0 2 3 8 6 8 . 0 0 1 0 0 1 5 5 3 1 . 0 0 1 2 3 1 6 5 6 7 . 0 0 1 2 3 1 7 6 0 3 . 0 0 1 2 3 1 8 6 3 9 . 0 0 1 2 3 1 . 9 6 7 4 . 0 0 1 2 3 2 0 7 1 0 . 0 0 1 2 3 2 1 7 4 5 . 0 0 1 2 3 2 2 7 8 1 . 0 0 1 2 3 2 3 8 1 6 . 0 0 1 2 3 1 4 6 9 7 . 0 0 1 2 6 1 6 3 3 0 . 0 0 1 2 6 1 8 1 4 5 . 0 0 1 2 6 2 0 1 6 1 . 0 0 1 2 6 2 2 1 7 7 . 0 0 1 2 6 2 5 0 4 7 . 0 0 1 2 6 2 7 9 1 6 . 0 0 1 2 6 4 9 2 7 . 0 0 7 0 5 4 7 4 . 0 0 7 0 6 0 8 3 . 0 0 7 0 6 7 5 9 . 0 0 7 0 7 5 1 0 . 0 0 7 0 8 4 3 5 . 0 0 7 0 9 2 7 2 . 0 0 7 0 1 0 3 0 2 . 0 0 7 0 6 1 6 1 . 0 0 9 5 6 8 4 6 . 0 0 9 5 7 6 0 7 . 0 0 9 5 8 4 5 2 . 0 0 9 5 9 3 9 1 . 0 0 9 5 1 0 4 3 4 . 0 0 9 5 1 1 5 9 4 . 0 0 9 5 1 2 8 8 2 . 0 0 9 5 2 2 7 7 2 . 0 0 1 0 0 2 4 4 3 8 . 0 0 1 0 0 2 6 5 5 8 . 0 0 1 0 0 2 8 6 6 7 . 0 0 1 0 0 2 0 8 5 5 . 0 0 1 2 7 2 3 6 3 6 . 0 0 1 2 7 2 6 4 1 6 . 0 0 1 2 7 2 9 1 9 6 . 0 0 1 2 7 1 9 8 ? C A B A I R 1 1 0 . 1 1 0 . 1 1 0 . 1 1 0 . 1 1 0 . 1 1 0 . 1 1 0 . 1 1 0 . 1 1 0 . 1 1 0 . 1 1 0 . 1 1 0 . 1 1 0 . I 1 0 . I I 0 . 1 1 . 0 . 1 1 0 . 1 1 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 1 0 . 1 0 . 1 0 . 1 0 . 1 0 . 1 0 . 1 0 . I 0 . 1 . 1 . ; 1 . 1 . . 0 . 1 0 . 1 0 . 1 0 . M A K E Y E A R A G E 2 7 7 4 3 7 1 1 0 3 7 2 9 3 7 3 8 3 7 4 7 3 7 5 6 3 7 6 5 3 7 1 1 0 3 7 2 9 3 7 3 8 3 7 4 7 3 7 5 6 3 7 6 5 3 7 6 5 3 7 7 4 3 7 8 3 3 7 9 2 3 7 6 5 3 7 7 4 3 7 8 3 3 7 9 2 4 7 2 9 4 7 3 8 4 7 4 7 4 7 5 6 4 7 6 5 4 7 7 4 4 7 8 3 4 7 9 2 4 6 5 1 6 4 6 6 1 5 4 ' 6 7 1 4 4 6 8 1 3 4 6 9 1 2 4 7 0 1 1 4 7 1 1 0 4 7 2 9 4 7 2 9 4 7 3 8 4 7 4 7 4 7 5 6 4 7 6 5 4 7 7 4 4 7 8 3 4 7 9 2 4 7 2 9 4 7 3 8 4 7 4 7 4 7 5 6 4 7 6 5 4 7 7 4 4 7 8 3 4 7 9 2 1 7 0 1 2 1 7 1 1 1 1 7 2 1 0 1 7 3 9 1 7 4 8 1 7 5 7 1 7 6 6 P R I C E H P 3 1 9 7 6 . 0 0 1 2 7 1 1 0 8 1 . 0 0 9 6 1 2 3 1 3 . 0 0 9 6 1 3 6 8 0 . 0 0 9 6 1 5 2 0 1 . 0 0 9 6 1 6 8 9 0 . 0 0 9 6 1 8 7 6 7 . 0 0 9 6 1 4 6 6 7 . 0 0 1 1 6 1 6 2 9 7 . 0 0 116 1 8 1 0 8 . 0 0 116 2 0 1 2 0 . 0 0 1 1 6 2 2 1 3 2 . 0 0 1 1 6 2 4 3 4 5 . 0 0 1 1 6 2 7 3 4 2 . 0 0 1 3 3 3 0 3 8 0 . 0 0 1 3 3 3 3 7 5 6 . 0 0 1 3 3 3 7 1 3 2 . 0 0 1 3 3 3 1 3 5 6 . 0 0 1 4 5 3 4 8 3 9 . 0 0 1 4 5 3 8 7 1 0 . 0 0 1 4 5 4 3 0 1 2 . 0 0 1 4 5 1 1 3 1 6 . 0 0 8 1 1 2 0 1 2 . 0 0 8 1 1 2 7 0 7 . 0 0 8 1 1 4 1 1 9 . 0 0 81 1 5 5 3 1 . 0 0 8 1 1 6 2 2 7 . 0 0 8 1 1 6 9 9 2 . 0 0 8 1 1 8 6 1 4 . 0 0 8 1 4 4 6 2 . 0 0 9 3 4 9 5 9 . 0 0 9 3 5 5 1 0 . 0 0 ' 9 3 6 1 2 1 . 0 0 9 3 6 8 0 2 . 0 0 9 3 7 4 8 2 . 0 0 9 3 8 1 5 5 . 0 0 9 3 8 8 8 9 . 0 0 9 3 1 3 0 6 0 . 0 0 1 0 0 1 4 3 6 6 . 0 0 1 0 0 1 5 8 0 3 . 0 0 1 0 0 1 6 6 8 3 . 0 0 1 0 0 1 7 5 6 3 . 0 0 1 0 0 1 9 3 1 9 . 0 0 1 0 0 2 0 0 4 0 . 0 0 1 0 0 2 0 7 6 0 . 0 0 1 0 0 1 3 3 1 8 . 0 0 1 2 2 1 5 1 9 9 . 0 0 1 2 2 1 6 1 0 7 . 0 0 1 2 2 1 7 0 1 5 . 0 0 1 2 2 1 8 9 0 6 . 0 0 1 2 2 2 0 7 9 6 . 0 0 1 2 2 2 1 7 0 4 . 0 0 1 2 2 2 2 6 1 2 . 0 0 1 2 2 9 3 4 7 . 0 0 8 5 1 0 3 8 6 . 0 0 8 5 1 1 5 4 0 . 0 0 8 5 1 2 8 2 2 . 0 0 8 5 1 4 2 4 7 . 0 0 8 5 1 5 8 3 0 . 0 0 8 5 1 7 4 1 3 . 0 0 8 5 1 9 8 ? C A B A I R 0 . 0 . 0 . 0 . 0 . 0 . 0 . 0 . 0 . 0 . 0 . 0 . 0 . 1 0 . 1 0 . 1 0 . 1 0 . 1 0 . 1 0 . 1 0 . 1 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 1 0 . 1 0 . 1 0 . 1 0 . 1 0 . 1 0 . 1 0 . 1 0 . 1 0 . 1 — G - . 1 0 . 1 0 . 1 0 . 1 0 . 1 0 . 1 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . A K E Y E A R A G E P R I C E H P 1 9 8 ? C A B A I F , 7 7 5 1 9 1 5 4 0 0 8 5 2 0 0 . 1 7 8 4 2 1 0 6 9 0 0 8 5 2 0 0 . 1 7 0 1 2 1 0 9 0 6 0 0 1 0 0 2 1 1 . 1 7 1 1 1 1 2 1 7 3 0 0 1 0 0 2 1 1 . 1 7 2 1 0 1 3 0 2 5 0 0 1 0 0 2 1 1 . 1 7 3 9 1 5 0 2 9 0 0 1 0 0 2 1 1 . 1 7 4 8 1 6 6 9 8 0 0 1 0 0 2 1 1 . 1 7 5 7 1 8 5 5 4 0 0 1 0 0 2 1 1 . 1 7 6 6 2 0 5 9 5 0 0 1 0 0 2 1 1 . 1 7 7 5 2 2 8 6 0 0 0 1 0 0 2 1 1 . 1 7 8 4 2 5 1 4 6 0 0 1 0 0 2 1 1 . 1 7 0 1 2 1 3 3 9 7 0 0 1 2 3 2 1 1 . 1 7 1 1 1 1 4 8 1 1 0 0 1 2 3 2 1 1 . 1 7 2 ' 1 0 1 6 4 5 6 0 0 1 2 3 2 1 1 . 1 7 3 9 1 8 2 8 5 0 0 1 2 3 2 1 1 . 1 7 4 8 2 0 3 1 7 0 0 1 2 3 2 1 1 . 1 7 5 7 2 2 3 4 9 0 0 1 2 3 2 1 1 . 1 7 6 6 2 4 5 8 3 0 0 1 2 3 2 1 1 . 1 7 7 5 2 6 0 4 2 0 0 1 2 3 2 1 1 . 1 7 8 4 2 8 7 4 6 0 0 1 2 3 2 1 1 . 1 7 2 1 0 1 7 1 6 6 0 0 1 2 6 2 1 1 . 1 7 3 9 1 8 8 0 6 0 0 1 2 6 2 1 1 . 1 7 4 •8 2 0 8 0 6 0 0 1 2 6 2 1 1 . 1 7 5 7 2 2 9 1 6 0 0 1 2 6 2 1 1 . 1 7 6 6 2 4 8 7 7 0 0 1 2 6 2 1 1 . 1 7 7 5 2 7 3 6 4 0 0 1 2 6 2 1 1 . t 7 8 4 3 0 1 0 8 0 0 1 2 6 2 1 1 . 2 6 5 1 7 . 4 6 3 5 0 0 7 0 2 0 0 . 2 6 6 1 6 5 1 5 0 . 0 0 7 0 2 0 0 . 2 6 7 1 5 5 7 2 2 0 0 7 0 2 0 0 . 2 6 8 1 4 6 3 5 8 0 0 7 0 2 0 o ; 2 6 9 1 3 7 0 6 5 0 0 7 0 2 0 0 . 2 7 0 1 2 7 7 7 1 0 0 7 0 2 0 0 . 2 7 1 1 1 8 5 4 9 0 0 7 0 2 0 0 . 2 7 2 1 0 9 4 0 4 0 0 7 0 2 0 0 . 2 6 5 1 7 6 2 3 5 0 0 9 5 2 1 0 . 2 6 6 1 6 6 9 2 7 0 0 9 5 2 1 0 . 2 6 7 1 5 7 6 9 7 . 0 0 9 5 2 1 0 . 2 6 8 1 4 8 5 5 3 0 0 9 5 2 1 0 . 2 6 9 1 3 9 4 0 8 . 0 0 9 5 2 1 0 . 2 7 0 1 2 1 0 3 4 9 . 0 0 9 5 2 1 0 . 2 7 1 1 1 1 1 3 8 4 . 0 0 9 5 2 1 0 . 2 7 2 1 0 1 2 5 2 2 . 0 0 9 5 2 1 0 . 2 7 3 9 2 0 2 1 1 . 0 0 1 2 7 2 1 0 . 2 7 4 8 2 2 4 5 7 . 0 0 1 2 7 2 1 0 . 2 7 5 7 2 4 9 0 2 . 0 0 1 2 7 2 1 0 . 2 7 6 6 2 7 7 2 5 . 0 0 1 2 7 2 1 0 . 2 7 7 5 3 0 4 9 7 . 0 0 1 2 7 2 1 0 . 3 7 6 6 1 9 0 3 7 . 0 0 1 0 5 2 1 1 . 3 7 7 5 2 1 1 5 2 . 0 0 1 0 5 2 1 1 . 3 7 8 4 2 3 5 0 2 . 0 0 1 0 5 2 1 1 . 3 7 9 3 2 6 1 1 4 . 0 0 1 0 5 2 1 1 . 3 8 0 2 2 9 0 1 6 . 0 0 1 0 5 2 1 1 . 3 7 1 1 1 1 4 5 0 6 . 0 0 1 1 6 2 1 1 . 3 7 2 1 0 1 5 6 1 8 . 0 0 1 1 6 2 1 1 . 3 7 3 9 1 7 3 5 8 . 0 0 1 1 6 2 1 1 . 3 7 4 8 1 9 2 8 2 . 0 0 1 1 6 2 1 1 . 3 7 5 7 2 1 4 2 5 . 0 0 1 1 6 2 1 1 . 3 7 6 6 2 3 8 0 6 . 0 0 1 1 6 2 1 1 . 3 7 6 6 2 6 1 8 6 . 0 0 1 3 3 2 r 1 . M A K E Y E A R A G E 3 7 7 5 3 7 8 4 3 7 9 3 3 8 0 2 3 7 1 1 1 3 7 2 1 0 3 7 3 9 3 7 4 8 3 7 5 7 3 7 6 6 4 7 3 9 4 7 4 8 4 7 5 7 4 7 6 6 4 7 7 5 4 7 8 4 4 6 5 1 7 4 6 6 1 6 4 6 7 1 5 4 6 8 1 4 4 6 8 1 4 4 6 9 1 3 4 7 0 1 2 4 7 1 1 1 4 7 2 1 0 4 7 3 9 4 7 4 8 4 7 5 7 4 7 6 6 4 7 7 5 4 7 8 4 4 • 7 3 9 4 7 4 8 4 7 5 7 4 7 6 6 4 7 7 5 4 7 8 4 1 7 0 1 4 1 7 1 1 3 1 7 2 1 2 1 7 3 1 1 1 7 4 1 0 1 7 5 9 1 7 6 8 1 7 7 7 1 7 8 6 1 7 0 1 4 1 7 1 1 3 1 7 2 1 4 1 7 3 1 3 1 7 4 1 2 1 7 5 1 1 1 7 6 1 0 1 7 7 9 1 7 8 8 1 7 0 1 4 1 7 1 1 3 1 7 2 1 2 1 7 3 1 1 1 7 4 1 0 P R I C E H P 2 8 8 0 5 . 0 0 1 3 3 3 1 6 8 5 . 0 0 1 3 3 3 4 8 5 3 . 0 0 1 3 3 3 8 3 3 9 . 0 0 1 3 3 1 6 3 8 9 . 0 0 1 4 5 1 8 0 1 0 . 0 0 1 4 5 1 9 8 0 4 . 0 0 1 4 5 2 1 7 8 4 . 0 0 1 4 5 2 3 9 6 2 . 0 0 1 4 5 2 6 3 5 9 . 0 0 1 4 5 9 9 5 2 . 0 0 8 1 1 0 9 4 6 . 0 0 8 1 1 2 0 4 1 . 0 0 8 1 1 3 2 4 5 . 0 0 8 1 1 4 5 7 0 . 0 0 8 1 1 6 0 2 7 . 0 0 8 1 4 0 1 0 . 0 0 9 3 4 4 5 6 . 0 0 9 3 4 9 5 1 . 0 0 9 3 5 5 0 1 . 0 0 9 3 6 1 1 3 . 0 0 9 3 6 7 9 2 . 0 0 9 3 7 5 4 6 . 0 0 9 3 8 3 8 5 . 0 0 9 3 9 3 1 7 . 0 0 9 3 1 1 8 8 6 . 0 0 1 0 0 1 3 2 0 7 . 0 0 1 0 0 1 4 6 2 8 . 0 0 1 0 0 1 6 2 9 1 . 0 0 1 0 0 1 8 1 1 9 . 0 0 1 0 0 2 0 1 3 1 . 0 0 1 0 0 1 3 6 9 1 . 0 0 1 2 2 1 5 2 1 2 . 0 0 1 2 2 1 6 9 0 3 . 0 0 1 2 2 1 8 5 9 0 . 0 0 1 2 2 2 0 4 4 9 . 0 0 1 2 2 2 2 4 9 4 . 0 0 1 2 2 8 5 7 5 . 0 0 8 5 9 4 2 3 . 0 0 8 5 1 0 3 5 5 . 0 0 8 5 1 1 3 7 8 . 0 0 8 5 1 2 5 0 4 . 0 0 8 5 1 3 7 4 1 . 0 0 8 5 1 5 0 9 9 . 0 0 8 5 1 6 5 9 2 . 0 0 8 5 1 8 2 3 4 . 0 0 8 5 9 8 7 6 . 0 0 1 0 0 1 0 8 5 3 . 0 0 1 0 0 1 1 9 2 6 . 0 0 1 0 0 1 3 1 0 5 . 0 0 1 0 0 1 4 4 0 2 . 0 0 1 0 0 1 5 8 2 6 . 0 0 1 0 0 1 7 3 9 1 . 0 0 1 0 0 1 9 1 1 1 . 0 0 1 0 0 2 1 0 0 1 . 0 0 1 0 0 1 2 1 0 5 . 0 0 1 2 3 1 3 3 0 3 . 0 0 1 2 3 1 4 6 1 9 . 0 0 1 2 3 1 6 0 6 5 . 0 0 1 2 3 1 7 6 5 4 . 0 0 1 2 3 1 9 8 ? C A B A I R 2 1 1 . 2 1 1 . 2 1 1 . 2 1 1 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 2 1 0 . 4 0 0 . 4 0 0 . 4 0 0 . 4 0 0 . 4 0 0 . 4 0 0 . 4 0 0 . 4 0 0 . 4 0 0 . 4 1 1 . 4 1 1 . 4 1 1 . 4 4 4 4 4 4 4 4 4 4 A K E Y E A R A G E P R I C E H P 1 9 8 ? C A B A l F , 7 5 9 1 9 4 0 1 0 0 1 2 3 4 , , , 1 7 6 8 2 1 3 1 8 0 0 1 2 3 4 1 1 . 1 7 7 7 2 3 4 2 7 0 0 1 2 3 4 1 1 . 1 7 8 6 2 5 7 4 4 0 0 1 2 3 4 1 1 . 1 7 2 1 2 1 5 8 3 3 0 0 1 2 6 4 1 1 . 1 7 3 1 1 1 7 3 9 9 0 0 1 2 6 4 1 1 . 1 7 4 1 0 1 9 1 2 0 0 0 1 2 6 4 1 1 . 1 7 5 9 2 1 0 1 1 0 0 1 2 6 4 1 1 . 1 7 6 8 2 3 0 8 9 0 0 1 2 6 4 1 1 . 1 7 7 7 2 5 3 7 2 0 0 1 2 6 4 1 1 . 1 7 8 6 2 7 8 8 2 0 0 1 2 6 4 1 1 . 2 7 6 8 1 5 1 7 6 0 0 7 4 4 0 0 . 2 7 7 7 1 6 6 7 8 0 0 7 4 4 0 0 . 2 7 8 6 1 8 3 2 7 0 0 7 4 4 0 0 . 2 7 9 5 2 0 1 4 0 0 0 7 4 4 0 0 . 2 6 5 1 9 5 4 3 9 . 0 0 9 5 4 1 0 . 2 6 6 1 8 5 9 7 7 0 0 9 5 4 1 0 . 2 6 7 1 7 6 5 6 8 . 0 0 9 5 4 1 0 . 2 6 8 1 6 7 2 1 8 . 0 0 9 5 4 1 0 . 2 6 9 1 5 7 9 3 1 . 0 0 9 5 4 1 0 . 2 7 0 1 4 8 7 1 6 . 0 0 9 5 4 1 0 . 2 7 1 1 3 9 5 7 8 . 0 0 9 5 4 1 0 . 2 7 2 1 2 1 0 5 2 6 0 0 9 5 4 1 0 . 2 7 3 1 1 1 5 4 8 7 . 0 0 1 0 0 4 1 0 . 2 7 4 1 0 1 7 0 1 8 . 0 0 1 0 0 4 1 0 . 2 7 5 9 1 8 7 0 2 . 0 0 1 0 0 4 1 0 . 2 7 6 8 2 0 5 5 1 . 0 0 1 0 0 4 1 0 . 2 7 7 7 2 2 5 8 4 . 0 0 1 0 0 4 1 0 . 2 7 3 1 1 1 8 4 7 0 . 0 0 1 2 7 4 1 1 . 2 . 7 4 1 0 2 0 2 9 7 . 0 0 1 2 7 4 1 1 . 2 ' 7 5 9 2 2 3 0 5 . 0 0 1 2 7 4 1 1 . 2 7 6 ; 8 2 4 5 1 0 0 0 1 2 7 4 1 1 . 2 7 7 7 2 6 9 3 5 . 0 0 1 2 7 4 1 1 . 3 7 6 8 1 8 0 9 2 . 0 0 1 0 5 4 1 1 . 3 7 7 7 1 9 8 8 2 . 0 0 1 0 5 4 1 1 . 3 7 8 6 2 1 8 4 8 . 0 0 1 0 5 4 1 1 . 3 7 9 5 2 4 0 0 9 . 0 0 1 0 5 4 1 1 . 3 8 0 4 2 6 3 8 3 . 0 0 1 0 5 4 1 1 . 3 8 1 3 2 8 9 9 2 . 0 0 1 0 5 4 1 1 . 3 7 1 1 3 1 2 3 0 4 . 0 0 1 1 6 4 1 0 . 3 7 2 1 2 1 3 5 2 0 . 0 0 1 1 6 4 1 0 . 3 7 3 1 1 1 4 8 5 8 . 0 0 1 1 6 4 1 0 . 3 7 4 1 0 1 6 3 2 7 . 0 0 1 1 6 4 1 0 . 3 7 5 9 1 7 9 4 2 . 0 0 1 1 6 4 1 0 . 3 7 6 8 1 9 7 1 6 . 0 0 1 1 6 . 4 1 0 . 3 7 6 8 2 0 4 2 0 . 0 0 1 3 3 4 1 0 . 3 7 7 7 2 2 4 3 9 . 0 0 1 3 3 4 1 0 . 3 7 8 6 2 4 6 5 9 . 0 0 1 3 3 4 1 0 . 3 7 9 5 2 7 0 9 8 . 0 0 1 3 3 4 1 0 . 3 8 0 4 2 9 7 7 8 . 0 0 1 3 3 4 1 0 . 3 8 1 3 3 2 7 2 3 . 0 0 1 3 3 4 1 0 . 3 7 6 8 2 6 9 4 1 . 0 0 1 4 5 4 1 1 . 3 7 7 7 2 9 6 0 6 . 0 0 1 4 5 4 1 1 . 3 7 8 6 3 2 5 3 4 . 0 0 1 4 5 4 1 1 . 3 7 9 5 3 5 7 5 1 . 0 0 1 4 5 4 1 1 . 3 8 0 4 3 9 2 8 6 . 0 0 1 4 5 4 1 1 . 3 8 1 3 4 3 1 7 3 . 0 0 1 4 5 4 1 1 . 4 7 3 11 9 2 3 1 . 0 0 8 1 4 1 -.1 . •4 7 4 1 0 1 0 1 4 4 . 0 0 8 1 4 1 1 . 4 7 5 9 1 1 1 4 7 . 0 0 8 1 4 1 1 . ik-p V P 1 D DDT r p WD 1 QR? a T 4 7 6 8 1 2 2 4 9 . 0 0 8 1 4 1 1 4 7 7 7 1 3 4 6 1 . 0 0 8 1 4 1 1 4 7 8 6 1 4 7 9 7 . 0 0 8 1 4 1 1 4 7 9 5 1 6 2 5 0 . 0 0 8 1 4 1 1 4 6 5 1 9 3 7 7 2 . 0 0 9 3 4 0 0 4 6 6 18 4 1 4 6 . 0 0 9 3 4 0 0 4 6 7 1 7 4 5 5 5 . 0 0 9 3 4 0 0 4 6 8 1 6 5 0 0 6 " . 0 0 9 3 4 0 0 4 6 9 1 5 5 5 0 1 . 0 0 9 3 4 0 0 4 7 0 1 4 6 0 4 5 . 0 0 9 3 4 0 0 4 7 1 1 3 6 6 4 3 . 0 0 9 3 4 0 0 4 7 2 1 2 7 2 2 9 . 0 0 9 3 4 0 0 4 7 3 1 1 1 1 6 7 7 . 0 0 1 0 0 4 1 1 4 7 4 1 0 1 2 8 3 2 . 0 0 1 0 0 4 1 1 4 7 5 9 1 4 1 0 2 . 0 0 1 0 0 4 1 1 4 7 6 8 1 5 4 9 6 . 0 0 1 0 0 4 1 1 4 7 7 7 1 7 0 2 9 . 0 0 1 0 0 4 1 1 4 7 8 6 1 8 7 1 3 . 0 0 1 0 0 4 1 1 4 7 3 1 1 1 2 3 4 5 . 0 0 1 2 2 4 1 0 4 7 4 1 0 1 3 5 6 6 . 0 0 1 2 2 4 1 0 4 7 5 9 1 4 9 0 8 . 0 0 1 2 2 4 1 0 4 7 6 8 1 6 3 8 2 . 0 0 1 2 2 4 1 0 4 7 7 7 1 8 0 0 3 . 0 0 1 2 2 4 1 0 4 7 8 6 1 9 7 8 4 . 0 0 1 2 2 4 1 0 1 7 0 1 0 9 3 1 8 . 0 0 8 5 0 1 1 1 7 1 9 1 0 3 5 3 . 0 0 8 5 0 1 1 1 7 2 8 1 1 5 0 3 . 0 0 8 5 0 1 1 1 7 3 7 1 2 7 8 2 . 0 0 8 5 0 1 . 1 1 7 4 6 1 4 2 0 2 . 0 0 8 5 0 1 1 1 7 5 5 1 5 6 2 0 . 0 0 8 5 0 1 1 1 7 6 4 1 7 1 8 2 . 0 0 8 5 0 1 1 1 7 7 3 1 8 9 0 0 . 0 0 8 5 . 0 1 1 1 7 8 2 2 0 7 9 0 . 0 0 8 5 0 1 1 1 7 0 1 0 1 1 6 3 6 . 0 0 1 0 0 0 1 1 1 7 1 9 1 3 0 8 8 . 0 0 1 0 0 0 1 1 1 7 2 8 1 4 4 8 7 . 0 0 1 0 0 0 1 1 1 7 3 7 1 6 1 0 5 . 0 0 1 0 0 0 1 1 1 7 4 6 1 7 7 1 0 . 0 0 1 0 0 0 1 1 1 7 5 5 1 9 5 5 1 . 0 0 1 0 0 0 1 1 1 7 6 4 2 1 4 3 3 . 0 0 1 0 0 0 1 1 1 7 7 3 2 3 5 7 1 . 0 0 1 0 0 0 1 1 1 7 8 2 2 5 9 3 0 . 0 0 1 0 0 0 1 1 1 7 0 1 0 1 3 2 8 8 . 0 0 1 2 3 0 1 1 1 7 1 9 1 4 3 6 0 . 0 0 1 2 3 0 1 1 1 7 2 8 1 5 7 5 7 . 0 0 1 2 3 0 1 1 1 7 3 7 1 7 7 3 0 . 0 0 1 2 3 . 0 1 1 1 7 4 6 1 9 7 1 3 . 0 0 1 2 3 0 1 1 1 7 5 5 2 1 4 3 3 . 0 0 1 2 3 0 1 1 1 7 6 4 2 3 8 5 0 . 0 0 1 2 3 0 1 1 1 7 7 3 2 5 9 3 0 . 0 0 1 2 3 0 1 1 1 7 2 8 1 6 3 9 4 . 0 0 1 2 6 0 1 1 1 7 3 7 1 8 2 1 6 . 0 0 1 2 6 0 1 1 1 7 4 6 2 0 2 4 2 . 0 0 1 2 6 0 1 1 1 7 5 5 2 2 2 6 4 . 0 0 1 2 6 0 1 1 1 7 6 4 2 4 6 8 4 . 0 0 1 2 6 0 1 1 1 7 7 3 2 7 2 2 0 . 0 0 1 2 6 0 1 1 1 7 8 2 2 9 9 4 0 . 0 0 1 2 6 •0 1 1 2 6 5 1 5 5 1 5 9 . 0 0 7 0 0 0 0 2 6 6 1 4 5 7 3 2 . 0 0 7 0 0 0 0 2 6 7 1 3 6 3 6 9 . 0 0 7 0 0 0 0 M A K E Y E A R A G E 2 6 8 1 2 2 • 6 9 1 1 2 7 0 1 0 2 7 1 9 2 7 2 8 2 6 5 1 5 2 6 6 1 4 2 6 7 1 3 2 6 8 1 2 2 6 9 1 1 2 7 0 1 0 2 7 1 9 2 7 2 8 2 7 2 8 2 7 3 7 2 7 4 6 2 7 5 5 2 7 6 4 2 7 2 8 2 7 3 7 2 7 4 6 2 7 5 5 2 7 6 4 3 7 2 8 3 7 3 7 3 7 4 6 3 7 5 5 3 7 6 4 3 7 1 9 3 7 2 8 3 7 3 7 3 7 4 6 3 7 5 5 3 7 6 4 3 7 7 3 3 7 8 2 3 7 7 3 3 7 8 2 4 7 3 7 4 7 4 6 4 7 5 5 4 7 6 4 4 7 7 3 4 7 8 2 4 6 5 1 5 4 6 6 1 4 4 6 7 1 3 4 6 8 1 2 4 6 9 1 1 4 7 0 1 0 4 7 1 9 4 7 2 8 4 7 3 7 4 7 4 6 4 7 5 5 4 7 6 4 4 7 7 3 4 7 8 2 4 7 3 7 P R I C E H P 7 0 7 7 . 0 0 7 0 7 8 6 3 . 0 0 7 0 8 5 7 1 . 0 0 7 0 9 3 4 2 . 0 0 7 0 1 0 1 8 1 . 0 0 7 0 6 4 2 2 . 0 0 9 5 7 1 3 5 . 0 0 9 5 7 9 7 8 . 0 0 9 5 8 8 0 9 . 0 0 9 5 9 7 8 8 . 0 0 9 5 1 0 7 6 7 . 0 0 9 5 1 1 8 4 3 . 0 0 9 5 1 3 0 2 8 . 0 0 9 5 1 8 1 7 6 . 0 0 1 0 0 2 0 1 9 6 . 0 0 1 0 0 2 2 4 4 1 . 0 0 1 0 0 2 4 2 3 5 . 0 0 1 0 0 2 6 1 7 4 . 0 0 1 0 0 1 8 8 6 5 . 0 0 1 2 7 2 0 9 6 1 . 0 0 1 2 7 2 3 2 9 0 . 0 0 1 2 7 2 5 6 1 9 . 0 0 1 2 7 2 8 1 8 0 . 0 0 1 2 7 1 2 2 2 1 . 0 0 9 6 1 3 5 7 9 . 0 0 9 6 1 5 0 8 8 . 0 0 9 6 1 6 5 9 6 . 0 0 9 6 1 8 2 5 6 . 0 0 9 6 1 5 1 9 6 . 0 0 1 1 6 1 6 8 8 4 . 0 0 1 1 6 1 8 7 6 4 . 0 0 1 1 6 2 0 6 3 6 . 0 0 1 1 6 2 2 6 9 9 . 0 0 1 1 6 2 4 6 7 0 . 0 0 1 1 6 2 6 2 9 5 . 0 0 1 3 3 2 8 7 0 6 . 0 0 1 3 3 3 2 3 6 1 . 0 0 1 3 3 3 5 9 5 7 . 0 0 1 3 3 1 0 6 0 2 . 0 0 8 1 1 1 8 0 8 . 0 0 8 1 1 3 1 2 2 . 0 0 8 1 1 4 5 8 0 . 0 0 8 1 1 6 0 3 8 . 0 0 8 1 1 7 6 4 2 . 0 0 8 1 4 4 4 5 . 0 0 9 0 4 9 4 1 . 0 0 9 0 5 4 9 0 . 0 0 9 0 6 1 0 8 . 0 0 9 0 6 7 1 8 . 0 0 9 0 7 3 9 1 . 0 0 9 0 8 1 3 0 . 0 0 9 0 8 9 4 2 . 0 0 9 0 1 2 4 8 0 . 0 0 9 3 1 3 8 6 7 . 0 0 9 3 1 5 4 0 8 . 0 0 9 3 1 6 9 4 9 . 0 0 9 3 1 8 6 4 4 . 0 0 9 3 2 0 5 0 8 . 0 0 9 3 1 3 4 0 5 . 0 0 9 4 1 9 8 ? C A B A I R 0 0 0 . 0 0 0 . 0 1 1 . 0 1 1 . 0 1 1 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 ' 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 0 1 1 . 1980 C r o s s - Sec t i on Data For Combines M YR A G E P R I C E H O U R S 1 7 4 6 2 9 0 0 0 0 0 1 0 7 0 0 0 1 7 6 4 3 7 5 0 0 1 • 1 1 1 3 1 0 0 1 7 7 3 4 1 5 0 0 1 1 1 1 3 6 0 0 1 7 7 3 4 2 0 0 0 1 1 1 3 7 5 0 1 7 8 2 4 4 5 0 0 1 1 1 1 1 3 0 1 1 7 8 2 5 7 5 0 0 1 1 1 1 3 0 0 1 1 7 8 2 5 8 5 0 0 1 1 1 1 3 0 0 1 1 7 9 1 5 4 0 0 0 1 1 1 1 1 6 0 1 1 7 9 1 5 7 5 0 0 1 1 1 1 2 7 0 1 1 7 9 1 5 7 5 0 0 1 1 1 1 3 0 0 1 1 7 9 1 7 2 5 0 0 1 1 1 1 9 0 1 1 7 9 1 7 2 5 0 0 1 1 1 1 1 1 7 0 1 1 7 9 1 7 7 9 0 0 1 1 1 1 1 2 8 0 1 1 7 9 1 8 0 5 0 0 1 1 1 1 1 1 0 0 1 1 7 9 1 8 4 5 0 0 1 1 1 1 1 2 5 0 1 2 7 2 8 2 5 8 0 0 0 1 0 0 1 1 0 0 0 2 7 2 8 2 6 0 0 0 0 1 0 0 8 0 0 0 2 7 3 7 2 7 5 0 0 0 1 1 0 1 7 0 0 0 - . 2 7 4 6 2 7 5 0 0 0 1 1 0 9 0 0 0 2 7 8 2 4 4 0 0 0 1 1 1 1 1 2 2 0 0 2 7 8 2 4 7 5 0 0 1 1 1 1 0 1 0 0 0 2 7 9 1 5 8 5 0 0 1 1 1 1 0 2 0 0 0 2 7 9 1 5 9 9 9 5 1 1 1 1 1 2 0 0 0 2 7 3 7 3 6 5 0 0 0 1 0 0 1 1 0 0 0 2 7 4 6 3 8 0 0 0 0 1 0 0 1 2 0 0 0 2 7 6 4 4 7 5 0 0 1 1 1 1 1 2 7 5 0 2 7 7 3 4 6 5 0 0 1 1 1 0 0 4 4 0 0 2 7 7 3 4 8 9 0 0 1 1 1 1 1 5 6 0 0 2 7 7 3 5 2 0 0 0 1 1 1 1 1 5 0 0 0 2 7 8 2 5 6 5 0 0 1 1 1 1 1 2 0 0 0 2 7 9 1 7 0 0 0 0 1 1 1 1 1 1 5 0 0 2 7 9 . 1 8 0 8 0 0 1 1 1 1 1 1 0 0 0 3 7 8 2 3 5 5 0 0 0 1 1 1 0 2 8 0 0 3 7 9 1 3 9 5 0 0 1 1 1 1 0 2 1 0 0 3 7 5 5 3 2 5 0 0 0 1 1 1 0 6 7 5 0 3 7 7 3 3 6 0 0 0 0 1 1 1 0 6 7 5 0 3 7 7 3 3 8 0 0 0 1 1 1 1 1 4 2 0 0 3 7 8 2 4 1 0 0 0 1 1 1 1 1 2 0 0 0 3 7 9 1 5 2 7 0 0 1 1 1 1 1 1 1 0 0 3 7 6 4 3 7 9 0 0 0 1 1 0 0 8 0 0 0 3 7 7 3 3 9 5 0 0 1 1 1 0 1 3 2 0 0 3 7 7 3 3 9 9 0 0 1 1 1 1 0 3 9 0 0 3 7 7 3 4 0 9 0 0 1 1 1 0 0 3 0 5 0 3 7 8 2 5 2 5 0 0 1 1 1 0 1 2 0 0 0 3 7 8 2 5 9 0 0 0 1 1 1 0 1 1 0 0 0 3 7 8 2 5 9 5 0 0 1 1 1 1 1 2 7 5 0 3 7 9 1 6 0 0 0 0 1 1 1 1 1 1 9 0 0 4 7 7 3 3 0 0 0 0 0 1 1 1 0 4 0 0 0 4 7 8 2 3 8 5 0 0 1 1 1 1 1 3 5 0 0 4 7 8 2 3 9 0 0 0 1 1 1 1 1 2 0 0 0 4 7 5 2 2 7 0 0 0 0 1 1 0 0 9 0 0 0 4 7 6 4 3 5 5 0 0 0 1 1 0 0 2 7 0 0 4 7 7 3 3 8 5 0 0 1 1 1 1 1 3 2 0 0 4 7 9 1 • 5 0 0 0 0 1 1 1 1 1 2 2 0 0 4 7 6 4 3 6 9 0 0 0 1 0 0 5 5 0 1 4 7 6 4 4 0 0 0 0 0 1 1 1 1 9 0 0 1 4 7 6 4 4 4 5 0 0 1 1 1 1 0 2 8 0 1 4 7 7 3 3 8 5 0 0 0 1 1 1 1 3 9 5 1 4 7 7 3 4 0 0 0 0 0 1 1 0 1 6 0 0 1 4 7 8 2 4 6 6 0 0 1 1 1 1 1 1 0 0 1 1980 C r o s s - S e c t i o n Data For Large Round Ba le r s M YR A G E P R I C E H I C O N D LOWC 1 7 6 4 4 9 5 0 0 0 1 7 7 3 5 5 0 0 1 0 1 7 7 3 5 7 5 0 0 0 1 7 8 2 6 3 5 0 1 0 1 7 8 2 7 0 0 0 ! 0 t 7 5 5 3 8 5 0 0 1 1 7 5 5 4 0 0 0 0 0 1 7 5 5 4 2 5 0 0 0 1 7 5 5 4 4 5 0 0 0 1 7 5 5 4 9 9 5 0 0 1 7 5 5 5 0 0 0 0 0 1 7 6 4 4 8 5 0 0 0 1 7 6 4 5 1 5 0 0 0 1 7 6 4 5 5 0 0 0 0 1 7 6 4 . 4 9 9 5 0 0 1 7 6 4 6 7 5 0 1 0 1 7 7 3 7 0 0 0 0 0 1 7 7 3 7 2 5 0 1 0 1 7 7 3 7 8 0 0 1 0 4 7 5 5 3 4 5 0 0 1 4 7 5 5 3 5 0 0 0 0 4 7 5 5 4 2 9 5 0 0 4 7 5 5 4 6 5 0 0 0 4 7 5 5 5 0 0 0 0 0 4 7 6 4 4 7 5 0 ' 0 0 4 7 6 4 5 3 0 0 0 0 4 7 6 4 6 0 0 0 1 0 4 7 7 3 5 7 5 0 0 0 4 7 7 3 6 1 5 0 1 0 4 . 7 8 2 6 7 0 0 1 0 4 7 9 1 7 5 0 0 .1 0 4 ' 7 9 1 7 9 5 0 1 0 2 7 6 4 3 5 0 0 0 1 2 7 6 4 3 9 5 0 0 0 2 7 6 4 4 2 0 0 0 0 2 7 7 3 4 7 5 0 0 0 2 7 7 3 4 9 0 0 0 0 2 7 8 • 2 5 1 0 0 1 0 2 7 5 5 3 1 5 0 0 1 2 7 5 5 3 7 5 0 0 0 2 7 5 5 4 5 0 0 0 0 2 7 6 4 4 7 5 0 0 0 2 7 7 3 5 2 0 0 0 0 2 7 7 3 5 2 5 0 0 0 2 7 7 3 5 6 0 0 0 0 2 7 7 3 6 5 0 0 0 0 2 7 8 2 6 4 0 0 1 0 2 7 8 2 6 6 5 0 1 0 3 7 6 4 3 9 9 5 0 0 3 7 6 4 4 4 5 0 0 0 3 7 6 4 4 9 9 5 0 0 3 7 7 3 5 0 0 0 0 0 3 7 5 5 3 9 9 5 0 0 3 7 5 5 4 2 5 0 0 0 3 7 6 4 3 8 0 0 0 0 1980 C r o s s - s e c t i o n Data For Square Ba le r s YR A G E P R I C E T Y P E HCOND L C O N D 6 5 1 5 9 5 0 0 0 0 6 8 1 2 . 1 1 0 0 0 0 0 7 0 1 0 1 4 9 5 0 0 0 7 1 9 2 0 0 0 0 0 1 6 5 1 5 9 0 0 0. 1 0 6 7 1 3 1 0 9 5 0 1 0 6 8 1 2 1 3 5 0 0 0 0 7 0 1 0 1 6 5 0 0 0 0 7 2 8 2 4 0 . 0 0 0 1 7 2 ' 8 2 5 0 0 0 0 1 7 2 8 2 0 0 0 0 0 0 7 2 8 2 5 0 0 0 0 0 7 3 7 2 9 5 . 0 0 0 1 7 3 7 3 0 0 0 0 0 0 7 4 6 3 0 0 0 0 0 1 7 4 6 3 2 5 0 0 0 0 7 5 5 2 5 0 0 0 0 0 7 6 4 3 3 5 0 1 0 0 7 6 4 3 8 0 0 1 0 0 7 6 4 4 5 0 0 1 0 1 7 7 3 3 7 5 0 1 0 0 7 8 2 4 0 0 0 1 0 0 7 7 3 3 9 5 0 0 0 0 7 2 8 3 1 5 0 0 0 0 7 5 5 4 2 0 0 0 0 0 7 6 4 4 6 5 0 0 0 0 7 6 4 6 5 0 0 0 0 1 6 5 1 5 8 9 5 0 1 0 6 5 1 5 1 5 0 0 0 1 1 6 8 1 2 1 2 5 0 . 0 0 0 6 8 1 2 1 5 0 0 0 0 0 6 5 1 5 9 0 0 0 0 0 6 8 1 2 1 4 5 0 0 0 0 6 8 1 2 1 7 5 0 0 0 0 6 9 1 1 1 5 0 0 0 0 0 6 9 1 1 1 7 9 5 0 0 0 7 0 1 0 1 6 5 0 0 0 0 7 1 9 2 0 0 0 0 0 0 7 2 8 2 4 5 0 0 0 0 7 3 7 2 5 0 0 0 0 0 7 4 6 2 8 9 5 0 0 0 6 9 1 1 1 6 5 0 0 0 0 6 9 1 1 1 7 5 0 0 0 0 7 0 1 0 1 7 5 0 0 0 0 7 0 1 0 1 8 9 5 0 0 0 7 1 9 1 9 9 5 0 0 0 7 2 8 2 6 7 5 0 0 1 7 3 7 2 2 5 0 0 0 0 7 5 5 2 7 7 5 0 0 1 7 7 3 3 5 0 0 1 0 0 6 9 1 1 1 4 0 0 0 0 0 6 9 1 1 1 7 5 0 0 0 0 7 0 1 0 2 4 5 0 0 0 1 7 1 9 2 0 0 0 0 0 0 6 7 1 3 1 0 0 0 0 1 0 7 2 8 1 9 5 0 0 0 0 7 3 7 1 8 0 0 0 0 0 7 5 5 2 0 0 0 0 0 0 7 6 4 2 5 0 0 0 0 0 7 2 8 1 8 5 0 0 0 0 J 2 8 M Y R A G E P R I C E T Y P E HCOND L C O f 3 7 2 8 2 0 0 0 0 0 0 3 7 4 6 2 5 0 0 0 0 0 3 7 4 6 2 6 5 0 0 0 0 3 7 5 5 2 8 5 0 0 0 0 3 7 5 5 3 6 0 0 0 0 0 3 7 6 4 3 2 0 0 0 0 0 3 7 8 2 4 0 0 0 1 0 0 3 7 8 2 4 2 0 0 1 0 0 3 7 9 1 4 9 5 0 1 0 0 3 7 4 6 2 7 5 0 0 0 1 3 7 7 3 3 6 0 0 0 0 0 3 7 7 3 3 8 0 0 0 0 0 3 7 8 2 4 2 0 0 1 0 0 3 7 9 1 5 0 0 0 1 0 0 4 6 7 1 3 7 5 0 0 1 0 4 6 8 1 2 1 1 5 0 0 0 0 4 6 5 1 5 7 5 0 0 1 0 4 6 6 1 4 7 5 0 0 1 0 4 6 7 1 3 1 2 5 0 0 0 0 4 6 7 1 3 1 4 0 0 0 0 0 4 6 8 1 2 1 5 5 0 0 0 0 4 6 9 1 1 1 6 9 5 0 0 0 4 6 8 1 2 1 3 5 0 0 0 0 4 6 9 1 1 1 7 5 0 0 0 0 4 7 0 1 1 1 7 5 0 0 0 0 4 7 0 1 0 2 0 0 0 0 0 0 4 7 1 9 2 9 5 0 0 0 0 4 7 2 8 3 5 0 0 0 0 1 4 7 3 7 3 2 0 0 0 0 0 4 7 3 7 . 3 6 0 0 0 0 0 4 7 4 6 3 5 0 0 0 0 0 4 7 4 6 3 8 9 5 • 0 0 1 4 7 5 5 3 7 5 0 0 0 0 4 7 6 4 4 1 5 0 1 0 0 4 6 9 1 1 1 4 5 0 0 0 0 4 7 0 1 0 1 9 9 5 0 0 1 4 7 2 8 2 2 0 0 0 0 0 4 7 3 7 2 1 5 0 0 0 0 4 7 3 7 2 7 9 5 0 0 1 4 7 4 6 2 4 0 0 0 0 0 4 7 5 5 2 6 0 0 0 0 0 4 7 5 5 2 7 5 0 0 0 0 4 7 6 4 2 8 9 5 1 0 0 4 7 6 4 4 2 0 0 0 0 1 4 6 9 1 1 2 0 0 0 0 0 0 4 7 1 9 2 4 0 0 0 0 0 4 7 1 9 2 8 5 0 0 0 0 4 7 1 9 3 0 0 0 0 0 0 4 7 1 9 3 7 5 0 0 0 0 4 7 2 8 3 5 0 0 0 0 0 4 7 3 7 4 4 5 0 0 0 0 4 7 4 6 3 7 5 0 0 0 0 4 7 4 6 4 5 0 0 0 0 0 4 7 5 5 4 6 5 0 0 0 0 4 7 6 4 4 7 5 0 0 0 0 4 7 7 3 5 1 5 0 0 0 0 4 6 5 1 5 1 0 0 0 0 1 0 4 6 9 1 1 1 3 7 5 0 0 0 4 7 0 1 0 2 9 9 5 0 0 0 4 7 3 7 4 5 0 0 0 0 1 129 » 

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