ANALYZING SPATIAL VARIATIONS IN FARM INCOME DISTRIBUTIONS-A MULTIVARIATE APPROACH Gary H . E l s n e r and Irving Hoch 1

Abstract Many studies have explored the size distribution of income, but e m p i r i c a l analysis has usually involved the examination of s t a t i s t i c s which, in effect, s u m m a r i z e c h a r a c t e r i s t i c s of the distribution, or the relation of a statistic (usually av er ag e income) to a set of explanatory v a r i a b l e s . The p r e s e n t study differs f r o m previous e m p i r i c a l work by relating observations in specified income i n t er v al s to a set of explanatory v a r i a b l e s . This multiple equation model appears to be an innovation in income distribution studies. Census data on family unit income distributions by county w e r e taken as observations on a set of dependent v a r i a b l e s . Each income cl as s interval is a s s o c i a t e d with a corresponding dependent v ari ab l e . The dependent v a r i a b l e consists of the proportionate number or frequency of income units m e a s u r e d in percentage t e r m s . F o r each dependent v a r i a b l e , then, there will be as many o b s e r v a tions as counties r e p o r t e d . Each of the dependent v a r i a b l e s is r e l a t e d to a given set of independent v a r i a b l e s using m u l t i v a r i a t e analysis. Observations on these v a r i a b l e s are the same for all c a s e s ; that is, each dependent v a r i a b l e is r e l a t e d to the same set of independent v a r i a b l e s . The m u l t i v a r i a t e approach employed h e r e allows an i n v e s t i g a tion of the b e h a v i o r of a coefficient in each income cl ass in turn. A good deal of additional information (relative to work with income c l a s s a v e r a g e s and economic development) is thereby generated. The model was e s t i m a t e d for two time points on California data. The paper includes an interpretation of the r e s u l t s for s e v e r a l independent v a r i a b l e s including education and location, and also some c o m p a r i s o n s of the r e s u l t s o v e r time. Introduction The income of f a r m e r s , like other occupations, v a r i e s widely with the c h a r a c t e r i s t i c s of the people and the a r e a . Many studies have analyzed the vari at i o n in av era g e f a r m income; but the c r i t i c a l problem, p a r t i c u l a r l y for

1The authors are r e s p e c t i v e l y , P r o j e c t L e a d e r of F o r e s t R e c r e a t i o n and Landscape Management R e s e a r c h , Pacific Southwest F o r e s t and Range E x p e r i ment Station, F o r e s t S e r v i c e , B e r k e l e y , California; and R e s e a r c h A s s o c i a t e , R e s o u r c e s for the Future, I n c . , Washington, D. C.

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underdeveloped countries, is understanding the variation in f a r m income d i s t r i butions. This paper suggests and r e p o r t s on a relatively simple method of attacking this problem. The key element of this approach is studying the income distribution in its most basic f o r m - - n a m e l y , as a set of frequencies or proportions for income c l a s s e s . Variables which are important in explaining the proportion of families in income c l a s s e s will often include m e a s u r e s of education, distance to u r b a n a r e a s , and availability of i r r i g a t i o n water. I n t e r pretations of analytical r e s u l t s may have direct implications for investment p r o g r a m s for roads, education and other items as they may relate to changing the existing shape of income distributions. The approach is seen as having general applicability. The p r e s e n t application is for income distributions of California farm families with counties being the spatial observation unit. Census data on family unit income d i s t r i b u tions by county were taken as observations on a set of dependent v a r i a b l e s . Each income class interval defined a corresponding dependent variable. Each dependent variable consisted of the proportionate frequency of income units m e a s u r e d in percentage t e r m s for a specific income class. F o r each dependent variable, then, there were as many observations as counties reported. Each of the dependent v a r i a b l e s was related to a given set of independent v a r i a b l e s using c r o s s - s e c t i o n m u l t i v a r i a t e analysis at two points in time (1950 and 1960). Observations on these v a r i a b l e s are the same for all cases; that is, each dependent variable is related to the same set of independent v a r i a b l e s . The multivariate approach 2, 3 employed here allows an investigation of the behavior of a coefficient in each income class in turn. Additional details on the specification of the model can be found in (3, pp. 34-41).

2

Some useful r e f e r e n c e s are:

T. W. Anderson, An Introduction to Multivariate Statistical Analysis (New York: John Wiley and Sons, I n c . , 1958), 374 p; Arthur S. Goldberger, Econometric Theory (New York: John Wiley and Sons, I n c . , 1964), 399 p; J. W. Hooper and Arnold Zellner, "The E r r o r of F o r e c a s t for Multivariate Reg r e s s i o n Models," Econometrica, Vol. 29, No. 4 (October 1961), pp. 544-555; Harold Hotelling, "A Generalized T Test and Measure of Multivariate D i s p e r s i o n , " Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (Berkeley and Los Angeles: University of California P r e s s , 1951), pp. 23-42; William Gerard O'Regan, "An Experimental Approach to the Determination of Demand for Orange Concentrate" (Unpublished Ph.D. d i s s e r tation, Department of Agriculture Economics, University of California, B e r k e ley, 1962), 74 p; Martin Schatzoff, "Sensitivity Comparisons Among Tests of the General Linear Hypothesis," Journal of the A m e r i c a n Statistical A s s o c i a tion, Vol. 61, P a r t 1 {June 1966), pp. 415-435. 3See especially pages 207-212 of Goldberger, A. S., Econometric Theory, John Wiley and Sons, 1964, 399 pps. 14

A__pplication of the Model and Variables Employed In order to compare underlying changes in rural farm income distributions over time--the model was estimated on both 1950 and 1960 data. 4 For 1950 there were 14 income classes, and for 1960 there were ii income classes. Thus, by treating the county observation on a specific dependent variable, 14 equations were developed for the 1950 data. Each of the 14 different dependent variables were related to the same set of (1950) explanatory variables. In similar fashion, ii equations were developed for 1960. In both cases, the number of observations, N, is equal to 52. Six counties were eliminated because of lack of comparable data over the decade. 5 The explanatory variables might be characterized as of two types: (i) measures of characteristics of farm entrepreneurs (for example, education and age) and (2) measures of characteristics of the spatial unit (for example, index of urbanization, availability of irrigation water, etc. ). In particular, the explanatory variables included the following measures~ 6

1.

2.

Real estate - - average value of land and buildings per farm. (Values are expressed for $1,000. ) This may be a useful proxy for total capital. Education-- the recorded average education of farm operators in the county. (Values are expressed in average y e a r s of schooling completed. )

4Data on county income distributions for the year 1949 appear in the 1950 Census of Population and for the year 1959, in the 1960 Census of Population. For simplicity, these sets of data are referred to as the 1950 and 1960 data, respectively. The following data sources were used: U.S. Bureau of the Census, U.S. Census of Population: 1950. Vol. II, Characteristics of the Population, Part 5, California, 1952, 5-438 p. Idem, U.S. Census of Population: 1960. Vol. i~ Characteristics of the Population, Part 6, California, 1963, 6-990 p. The 1960 Census data differ from the 1950 data in several characteristics. The 1950 Census income data are generally based upon a 20 percent sample while the 1960 data are based upon a 25-percent sample. For both years, Census income data include only dollars of income received and do not record imputed income, for example, rental value of owned housing.

5The counties eliminated were: Trinity, Sierra, Alpine, Mono, San :Francisco, and Inyo. 6The Census of Agriculture (1950 and 1959) was the b a s i c source of data for these v a r i a b l e s . U.S. Bureau of Census, U.S. Census of Agriculture: 1950~ Vol. I, Counties and State Economic Areas, Part 33, California, 1952, 296 p. ; and idem U.S. Census of Agriculture: 1959. Vol. I, Counties, Part 48, California 1961, 287 p.

15

3. 4.

F a r m s i z e - - a v e r a g e a c r e a g e p e r f a r m in the county. (Original v a l u e s w e r e divided by 1 , 0 0 0 . ) I s a r d index - - a m e a s u r e of f a r m - t y p e s p e c i a l i z a t i o n . T h i s is a m o d i f i e d I s a r d c o e f f i c i e n t of s p e c i a l i z a t i o n , defined as follows: N

c*:~

1

IPi-~[

i=1 w h e r e C* = index Pi = p r o p o r t i o n of county f a r m s which a r e c l a s s i f i e d in f a r m - t y p e i, N = n u m b e r of f a r m - t y p e c l a s s e s . 7 5. 6. 7. 8. 9. 10.

U r b a n index - - p r o p o r t i o n of the c o u n t y ' s population c l a s s i f i e d as urban. I r r i g a t e d f a r m s - - p r o p o r t i o n of all f a r m s using i r r i g a t i o n w a t e r . Road C l a s s 1 - - p r o p o r t i o n of all f a r m s on h a r d s u r f a c e r o a d s . 8 T e n u r e - - p r o p o r t i o n of t o t a l f a r m s o p e r a t e d by m a n a g e r s . T r a d i n g c e n t e r - - a m e a s u r e of a v e r a g e d i s t a n c e in m i l e s to an u r b a n settlement. Age l e v e l - - a v e r a g e age of f a r m o p e r a t o r s . (Original v a l u e s w e r e divided by 10. )

7The o r i g i n a l f o r m of the index a p p e a r s in W a l t e r I s a r d in a s s o c i a t i o n with David F. B r a m h a l l et a l . , Methods of R e g i o n a l A n a l y s i s : An Introduction to R e g i o n a l Science (Regional S c i e n c e Studies S e r i e s 4, Vol. II; C a m b r i d g e , M a s s a c h u s e t t s : The MIT P r e s s , 1960, Chap. 7, pp. 232-308. The f a r m type c l a s s i f i c a t i o n s y s t e m u s e d h e r e is that defined by the C e n s u s of A g r i c u l t u r e . The following eight m a j o r types of f a r m s a r e defined: c o m m e r c i a l , v e g e t a b l e , f r u i t and nut, p o u l t r y , d a i r y , l i v e s t o c k , g e n e r a l , and m i s c e l l a n e o u s . The o b j e c t i v e was to m e a s u r e the d e g r e e of f a r m - t y p e s p e c i a l i z a t i o n . If the county had the s a m e n u m b e r of f a r m s in e a c h of the eight c l a s s e s , the index v a l u e would be z e r o . The o t h e r l i m i t f o r the index would o c c u r , if all the c o u n t y ' s f a r m s w e r e of one type. In this l a t t e r c a s e , the index v a l u e would be 1 . 7 5 . T h e s e a r e the l o w e r and u p p e r l i m i t s of the index f o r eight f a r m types. The value of 1.75 e q u a l s [ 1 - 1/8 I + 7 I 0 - i/8 I = 7/8 + 7 (1/8)

14/8.

An index with m i n i m u m v a l u e equal to z e r o and m a x i m u m v a l u e equal to 1 would be c o n s t r u c t e d by dividing all of t h e s e c a l c u l a t e d v a l u e s by 1.75. 8Other road classes defined by the Census of Agriculture are: Road Class 2--gravel, shell or shale; and Road Class 3--dirt or unimproved.

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Estimation and Hypothesis Testing Coefficient e s t i m a t e s w e r e obtained and r e s i d u a l c o r r e l a t i o n m a t r i c e s w e r e calculated for each application of the model, with r e l a t i v e l y high values o c c u r r i n g for off-diagonal e l e m e n t s in all c a s e s . The null hypothesis of z e r o off-diagonal e l e m e n t s was tested for both 1950 and 1960 using a test developed by O'Regan [ 3, pp 26 and 27] . In each case, the hypothesis was r e j e c t e d and the m u l t i v a r i a t e approach was justified. A test of the hypothesis that all coefficients equalled z e r o was c a r r i e d out for both 1950 and 1960, using the U s t a t i s t i c s , as developed by Anderson, [1, chapter 8 ] . In both c a s e s , the hypothesis was c l e a r l y r e j e c t e d . Hotelling's T2 statistic was employed to test the hypothesis that the coefficients of a given independent v a r i a b l e a r e z e r o in all equations. 9 This test was c a r r i e d out for each of the v a r i a b l e s in turn. F o r both 1950 and 1960, education, trading c e n t e r and r e a l estate w e r e significant at the one per cent level. Road c l a s s 1 was significant at the five per cent l ev el in both periods. At the other e x t r e m e , age level and i r r i g a t e d f a r m s w e r e not significant in e i t h e r period. The r e m a i n i n g four independent v a r i a b l e s were significant at the five p er cent level in one period, but not in the other. Interpretations of Results Obtained As graphic e x a m p l e s , e s t i m a t e d coefficients obtained for education and trading c e n t e r are plotted against the mid-points of t h ei r corresponding income c l as s intervals in F i g u r e s 1 and 2, r e s p e c t i v e l y . The r e l a t i o n is shown for both 1950 and 1960. Coefficients a r e indicated as points. Straight-line approximations are drawn between s u c c e s s i v e points; 1960 coefficients a r e plotted against appropriately deflated values. Since 1950 had 14 c l a s s e s and 1960 has 11 c l a s s e s , t h ere will be some lack of c o r r e s p o n d e n c e in the c o m p a r i s o n s . F u r ther, the plot r e s u l t s a r e not adjusted for different cl ass s i z e s . This lack of adjustment for cl a s s size is useful in t e r m s of exhibiting coefficient values actually obtained. However, for a c o m p a r i s o n between c l a s s e s of the impact of a unit change in an independent v a r i a b l e , it would be n e c e s s a r y to take differing cl as s s i zes into account. In interpreting r e s u l t s , the following g e n e r a l considerations apply. A v a r i a b l e with a positive coefficient i n c r e a s e s the frequency of o c c u r r e n c e in the given income c l a s s , and a negative coefficient d e c r e a s e s the frequency of o c c u r rence. If a v a r i a b l e exhibits an increasing coefficient as income i n c r e a s e s , moving f r o m negative to positive v a l u e s , then this indicates that i n c r e a s i n g the value of the explanatory v a r i a b l e will d e c r e a s e the number of low-income r e c i pients and i n c r e a s e the number of h ig h - i n c o m e r e c i p i e n t s . The r e v e r s e r e l a tion o c c u r s , of co u r s e , if the coefficient d e c r e a s e s as income i n c r e a s e s . Other

9For explicit definition of Hotelling's T2 statistic in matrix terms, see Henry Scheffe, The Analysis of Variance (NewYork: John Wiley & Sons, Inc., 1959), p. 418. 17

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Plot of E s t i m a t e d C o e f f i c i e n t s for T r a d i n g C e n te r ( D i s t a n c e to U r b a n S e t t l e m e n t ) on MLdpoints of I n c o m e C l a s s e s , 1 9 5 0 and 1 9 6 0

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p a t t e r n s a r e of i n t e r e s t . T h u s , a c o e f f i c i e n t m a y b e n e g a t i v e a t the e x t r e m e s of t h e i n c o m e d i s t r i b u t i o n and p o s i t i v e in t h e m i d d l e i n c o m e c l a s s e s . An i n c r e a s e in t h e a s s o c i a t e d i n d e p e n d e n t v a r i a b l e y i e l d s g r e a t e r i n c o m e e q u a l i t y , t h o u g h it m a y h a v e l i t t l e i m p a c t on t h e a v e r a g e l e v e l of i n c o m e . C o e f f i c i e n t s f o r a s u b s e t of i n c o m e i n t e r v a l s c a n b e a g g r e g a t e d so t h e i m p a c t of a c h a n g e in a n i n d e p e n d e n t v a r i a b l e c a n b e v i e w e d in b r o a d t e r m s . F o r e x a m p l e , in the 1950 c a s e , a n i n c r e a s e of one y e a r in t h e e d u c a t i o n l e v e l h a s t h e f o l l o w i n g i m p a c t , b a s e d on t a b l e 1 d a t a . T h e r e is a d r o p of 4 . 8 p e r c e n t in i n c o m e r e c i p i e n t s r e c e i v i n g $ 2 , 0 0 0 o r l e s s ; a n i n c r e a s e of 2 . 5 p e r c e n t in t h e $ 2 , 0 0 0 - $ 5 , 0 0 0 c l a s s ; and a n i n c r e a s e of 2 . 3 p e r c e n t in t h e o v e r $ 5 , 0 0 0 class. T h e c o e f f i c i e n t p a t t e r n s f o r t h e u r b a n index, r e a l e s t a t e a n d e d u c a t i o n v a r i a b l e s s e e m to e m e r g e r a t h e r c l e a r l y and f i t e x p e c t a t i o n s r a t h e r w e l l . F o r t h e s e v a r i a b l e s t h e r e is a g e n e r a l u p w a r d m o v e m e n t in c o e f f i c i e n t v a l u e a s i n c o m e i n c r e a s e s , i n d i c a t i n g a p o s i t i v e s h i f t in i n c o m e d i s t r i b u t i o n s a s t h e s e v a r i a b l e s i n c r e a s e . C o e f f i c i e n t s f o r t h e d i s t a n c e to t r a d i n g c e n t e r v a r i a b l e d e c l i n e a s i n c o m e i n c r e a s e s . T h i s is r e a s o n a b l e , f o r an i n c r e a s e in d i s t a n c e to t r a d i n g c e n t e r l e a d s to a n i n c r e a s e in l o w - i n c o m e r e c i p i e n t s , a d e c r e a s e in h i g h - i n c o m e r e c i p i e n t s , a n d h e n c e , a d e c l i n e in i n c o m e o v e r a l l . T h e i m p a c t of u r b a n i z a t i o n a n d d i s t a n c e to t h e n e a r e s t t r a d i n g c e n t e r add s u p p o r t to t h e l o c a t i o n h y p o t h e s i s of T. W. S c h u l t z , w h i c h i n v o l v e s t h e a r g u m e n t t h a t f a r m i n c o m e is a f u n c t i o n of p r o x i m i t y to m e t r o p o l i t a n m a r k e t s , w i t h i n c r e a s i n g i n c o m e w i t h i n c r e a s i n g a c c e s s [ 4, c h a p t e r s IX, X, XVII and XVIII ]. T h e e d u c a t i o n c o e f f i c i e n t s s h o w a c l e a r l y i n c r e a s i n g p a t t e r n in b o t h 1950 and 1960. H o w e v e r , s o m e s h i f t in p a t t e r n a p p e a r s i n v o l v e d , w i t h t h e 1960 e d u c a t i o n i m p a c t s e e m i n g s o m e w h a t m o r e p r o n o u n c e d . Such r e s u l t s a p p e a r m e a n i n g f u l in c o n s i d e r i n g e d u c a t i o n a s a n i n c o m e s h i f t e r . A g e n e r a l d i f f i c u l t y w i t h m e a s u r e s of t h e i m p a c t of e d u c a t i o n is t h a t t h e r e is no g u a r a n t e e t h a t t h e u n d e r l y i n g p o p u l a t i o n is h o m o g e n e o u s , s o t h a t b o t h i n c o m e and e d u c a t i o n m a y v a r y w i t h l e v e l of i n n a t e a b i l i t y . B u t it s e e m s p l a u s i b l e t h a t t h e r e is l i t t l e o r no v a r i a b i l i t y in i n n a t e a b i l i t y b e t w e e n c o u n t i e s . (Some i m p r o v e m e n t f o r b o t h a n a l y s i s anal p o l i c y p u r p o s e s m i g h t o c c u r b y d i s a g g r e g a t i o n to a s e t of e d u c a t i o n a c t i v i t i e s , e . g . , p r i m a r y , s e c o h d a r y , and c o l l e g e e d u c a t i o n ; l e v e l of e x t e n s i o n w o r k ; and m e a s u r e s of ,,quality,, of e d u c a t i o n . ) T h e r e a l e s t a t e c o e f f i c i e n t s e x h i b i t an u p w a r d m o v e m e n t w i t h i n c o m e , t h o u g h t h e 1950 e s t i m a t e s show r a t h e r p r o n o u n c e d v a r i a b i l i t y . Results for f a r m s i z e s h o w a d i f f e r e n t p a t t e r n . T h e r e is l i t t l e t r e n d in v a l u e of c o e f f i c i e n t as income increases. T h i s is the c a s e f o r b o t h 1950 a n d 1960, w i t h one e x c e p t i o n o c c u r r i n g in t h e 1960 r e s u l t s ; h e r e , t h e r e is a p r o n o u n c e d d r o p in c o e f f i c i e n t v a l u e f o r t h e h i g h e s t i n c o m e c l a s s . It t u r n s out t h e r e is l i t t l e c o r r e l a t i o n b e t w e e n r e a l e s t a t e , m e a s u r e d in d o l l a r s p e r f a r m , and f a r m s i z e , m e a s u r e d in a c r e s p e r f a r m . ( T h i s c o r r e l a t i o n w a s . 13 f o r 1950 and . 15 f o r 1960). It is l i k e l y t h a t v e r y l a r g e a c r e a g e s a r e a s s o c i a t e d w i t h g r a z i n g o p e r a t i o n s so t h a t t h e f a r m s i z e v a r i a b l e m a y b e a n i n d e x of g r a z i n g ; s u c h a n a r g u m e n t m i g h t b e a p p l i c a b l e in e x p l a i n i n g r e s u l t s f o r t h i s v a r i a b l e . R e s u l t s f o r R o a d C l a s s 1 i m p l y t h a t goods l e a d to g r e a t e r e q u a l i t y of i n c o m e . T h u s , f o r b o t h 1950 a n d 1960, i n c r e a s i n g t h e l e v e l of t h i s v a r i a b l e

20

r e d u c e s i n c o m e r e c i p i e n t s in b o t h t h e l o w e s t t h r e e and t h e h i g h e s t t h r e e i n c o m e c l a s s e s . In 1950 t h e r e d u c t i o n s a r e 11 a n d 6 p e r c e n t , r e s p e c t i v e l y ; w h i l e in 1960, t h e r e s p e c t i v e r e d u c t i o n s a r e 7 and 15 p e r c e n t . B e f o r e r o a d b u i l d i n g i s r e c o m m e n d e d s e r i o u s l y a s a n e g a l i t a r i a n d e v i c e , h o w e v e r , it i s w o r t h n o t i n g t h a t t h i s v a r i a b l e s h o w s s o m e n e g a t i v e c o r r e l a t i o n w i t h d i s t a n c e to t r a d i n g c e n t e r , w h i c h s e e m s r e a s o n a b l e , b o t h in t e r m s of o v e r - t h e - r o a d m i l e a g e a n d b y p o s s i b l e g e n e r a t i o n of n e w t r a d i n g c e n t e r s . The c o r r e l a t i o n b e t w e e n t h e s e v a r i a b l e s w a s - . 5 in 1950 a n d -. 6 in 1960. R e s u l t s f o r t h e r e m a i n i n g f o u r v a r i a b l e s a r e not p a r t i c u l a r l y e n l i g h t e n i n g . T h e v a r i a b l e l a b e l e d " t e n u r e ' , is a m e a s u r e of t h e p r o p o r t i o n of h i r e d m a n a g e r s . F o r 1950 t h e c o e f f i c i e n t s e x h i b i t s o m e d e c l i n e a s i n c o m e i n c r e a s e s , b u t l i t t l e p a t t e r n a p p e a r s f o r 1960. T h e I s a r d index, w h i c h m e a s u r e s s p e c i a l i z a t i o n , s h o w s a g r e a t d e a l of v a r i a b i l i t y a n d l i t t l e p a t t e r n in e i t h e r 1950 o r 1960. T h e age v a r i a b l e s h o w s l i t t l e p a t t e r n f o r 1950 b u t in 1960 e x h i b i t s a m a r k e d d e c l i n ing t r e n d f o r u p p e r i n c o m e g r o u p s , i n d i c a t i n g s o m e i n c o m e d e c l i n e with i n c r e a s i n g age. F u t u r e w o r k m i g h t allow f o r a p o s s i b l e n o n l i n e a r r e l a t i o n b e tween age and income. Finally, the irrigated farm variable, measured as a f r a c t i o n of a l l f a r m s , s h o w s l i t t l e in t h e way of p a t t e r n f o r b o t h 1950 a n d 1960. Future work might experiment with alternative measures, such as irrigated a c r e a g e a s a f r a c t i o n of a l l a c r e a g e . O v e r - a l l , t h e r e is a good d e a l of s i m i l a r i t y in t h e p a t t e r n of b e h a v i o r of a g i v e n c o e f f i c i e n t f o r 1950 a n d 1960. M o s t of the v a r i a b l e s e x h i b i t r o u g h l y the s a m e g r a p h i c r e l a t i o n s h i p s in the two p e r i o d s , t h o u g h - - a s in the c a s e of e d u c a t i o n - - t h e r e a r e s o m e s i g n s of u n d e r l y i n g c h a n g e s in s t r u c t u r e .

Conclusion, Suggestions for Future Research~

and Potential Applications

T h i s w o r k c a n b e v i e w e d a s a n a t t e m p t to u n c o v e r s o m e of the u n d e r l y i n g c a u s a t i v e f a c t o r s e x p l a i n i n g i n c o m e d i f f e r e n t i a l s . R e s u l t s f o r v a r i a b l e s of m a j o r i n t e r e s t - - e d u c a t i o n , r e a l e s t a t e , u r b a n i z a t i o n , and t r a d i n g c e n t e r - s e e m e d r e a s o n a b l e and in line w i t h e x p e c t a t i o n s . A n o t e w o r t h y a s p e c t of t h e e s t i m a t e s is t h a t , f o r e a c h i n d e p e n d e n t v a r i a b l e , the c o e f f i c i e n t s u m o v e r i n c o m e c l a s s e s t o t a l s z e r o , w h i l e the s u m s of c o n s t a n t s t o t a l s 100. A s a c o n s e q u e n c e , a n y c h a n g e in the l e v e l s of e x p l a n a t o r y v a r i a b l e s l e a v e s t o t a l f r e q u e n c y u n a f f e c t e d . T h i s is a u s e f u l f e a t u r e b o t h in t e r m s of v i e w i n g the i m p a c t of a u n i t c h a n g e in one i n d e p e n d e n t v a r i a b l e a n d in t e r m s of o b t a i n i n g n e w d i s t r i b u t i o n s b y c h a n g i n g l e v e l s of all i n d e p e n d e n t v a r i a b l e s , g i v e n e s t i m a t e s of t h o s e variables. E s t i m a t e d l e v e l s of i n d e p e n d e n t v a r i a b l e s c a n b e u s e d to e s t i m a t e income distributions for areas not coterminous with counties. Some a v e n u e s of f u t u r e w o r k m a y b e n o t e d . F i r s t , a n u m b e r of n e w i n d e p e n d e n t v a r i a b l e s m i g h t b e i n t r o d u c e d . In p a r t i c u l a r , s o m e s u g g e s t e d v a r i a t i o n s f o r e d u c a t i o n , age, and i r r i g a t i o n w e r e n o t e d a b o v e . Second, a t t e m p t s c a n b e m a d e to i n v e s t i g a t e the u n d e r l y i n g s t r u c t u r a l r e l a t i o n s h i p s w h i c h a r e roughly indicated by the figures plotting estimated coefficients against income c l a s s m i d p o i n t s . An a t t e m p t m i g h t b e m a d e to d e v e l o p s m o o t h c u r v e s f o r t h e r e l a t i o n s h i p s and, a l o n g w i t h t h i s , to t e s t t h e h y p o t h e s i s t h a t a c h a n g e in structure has occurred between time periods. Finally, there are intimations, 21

at l e a s t , that the a n a l y s i s developed here can be developed further for use as a policy tool, with explanatory v a r i a b l e s viewed as policy instruments.

REFERENCES

1.

Anderson, T. W. An Introduction to Multivariate Statistical Analysis. New York: John Wiley and Sons, I n c . , 1958. 374 p. 2. E l s n e r , Gary and Irving Hoch. Analyses of California F a r m Income R e l a tionships. Giannini Foundation R e s e a r c h Report No. 297, Giannini Foundation of A g r i c u l t u r a l Economics, B e r k e l e y , California, August 1968, 100 p. 3. O'Regan, W i l l i a m G e r a r d . "An E x p e r i m e n t a l Approach to the D e t e r m i n a tion of Demand for Orange Concentrate. " (Unpublished Ph.D. d i s s e r t a t i o n , Department of A g r i c u l t u r a l Economics, University of California, B e r k e l e y , 1962, 74 p.) 4. Schultz, Theodore. The.Economic Organization of A g r i c u l t u r e . New York: M c G r a w - H i l l Book Co., I n c . , 1953.

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