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http://clevelandfed.org/research/workpaper/index.cfm Best available copy Working Paper 8401 ECONOMIC ESTIMATES OF URBAN INFRASTRUCTURE NEEDS by Paul Gary Wyckoff Laura Kuhn and Michael Dvorak provided research assistance for t h i s paper. I have benefited from comments made a t seminars here a t the Bank and a t Case Western Reserve University. Responsi bil i t y for any remaining errors i s , of course, my own. Working papers of the Federal Reserve Bank of Cl eve1and are prel imi nary materi a1 s, circulated t o stimulate d i scossion and c r i t i c a l comment. The views stated herein are the author's and not necessarily those of the Federal Reserve Bank of Cleveland or of the Board of Governors of the Federal Reserve System. June 1984 1- Federal Reserve Bank of Cleveland http://clevelandfed.org/research/workpaper/index.cfm Best available copy Abstract This paper c r i t i c i z e s commonly employed measures of capital-spending needs and offers an alternative method f o r constructing needs estimates. The usual technical estimate of needs compares an inventory of current conditions w i t h some "ideal" level of capital stock, and i s inadequate because of the arbitrary (and sometimes unrealistic) benchmarks t h a t are employed i n i t s construction. The a1 ternati ve economic measure proposed here i s based on a model of c i t y spending decisions. Using these estimated parameters, t h i s method provides a measure of the typical or average spending patterns of policymakers, and controls f o r the particular circumstances faced by each city. I t i s suggested t h a t t h i s standard f o r capital - spendi ng needs w i 11 be more re1 evant t o admi n i s t r a t o r s and decision-makers who must reconcile capital-stock deterioration w i t h t i g h t budgets. The empirical work i n the paper i s a pooled time-series cross-section analysi s of aggregate highway spending w i t h i n ten m i dwestern urban counties between 1965 and 1976. T h i s aggregated data i s shown t o be representative of the average c i t y w i t h i n each county. Final l y, actual and needed highway expenditures f o r each county a r e presented. I. Introduction Recently, a great deal of attention has been focused on the condition of the nation' s i nf rastructure--i t s pub1 i c capital stock of roads, http://clevelandfed.org/research/workpaper/index.cfm Best available copy bridges, sewers, t r a n s i t systems, and pub1i c buildings. Conventional studies o f t h i s problem have brought f o r t h alarming f i g u r e s about the extent o f i n f r a s t r u c t u r e deterioration. For example, t h e Congressional Budget O f f i c e (1983) has estimated that, nationwide, i t w i l l c o s t $53 b i l l i o n per year t o ensure t h a t the n a t i o n ' s highways, t r a n s i t systems, sewer and water f a c i l i t i e s , and a i r p o r t s are ( i n i t s words) "adequate". Another widely quoted study (Choate and Walter, 1981, p. 2) notes t h a t i n t h e 1980s, i t w i l l take $40 b i l l i o n t o service the i n f r a s t r u c t u r e needs o f New York City alone. 1 Typically, these technical estimates of i n f r a s t r u c t u r e needs are based upon a d e t a i l e d examination of t h e q u a n t i t y and qua1i t y o f e x i s t i n g public capital. This information i s then combined w i t h an assumption ( u s u a l l y imp1i c i t ) about the standard o r benchmark against which c u r r e n t conditions are t o be measured. When such standards a r e made e x p l i c i t , they are usually based upon one of two approaches: t h e author's subjective determination of t h e "proper' amount of p u b l i c c a p i t a l , o r the views o f technical experts, such as c i v i l engineers o r urban planners. The a r b i t r a r i n e s s o f these underlyi ng assumptions has dimi n i shed the useful ness of many o f the c a p i t a l -spending needs estimates i n these studies. For example, t h e federal government c l a s s i f i e s as "inadequate" bridges t h a t have " inappropriate deck geometry u --that is, the bridge i t s e l f i s narrower than the connecting highway. Estimates o f spending needs f o r bridges, then, w i l l include t h e c o s t of widening these bridges, even i f there i s n o t enough t r a f f i c on t h e bridge t o warrant a d d i t i o n a l investment. Lacking appropriate benchmarks f o r budgeting purposes, communities are i n danger o f abandoning c a p i t a l investment p l anni ng a1together, pursui ng instead a pay-as-you-go strategy. http://clevelandfed.org/research/workpaper/index.cfm Best available copy T h i s problem i n setting pol icy goal s i s most acute i n the 01der c i t i e s of the Midwest, where an aging infrastructure base is combined w i t h changing demands for publ i c services. Presumably, the reduced popul a t i on and slower rates of income growth i n these c i t i e s might affect the desired amount of capital spending i n these c i t i e s , b u t the technical approach offers no method for quantifying these changes. In t h i s paper, economic estimates of infrastructure needs are developed as a supplement t o the technical approach. Investment i n publ i c capital i s modeled a s the result of conscious choice on the part of publ i c authorities, given the resources avai 1able to them. The econometric estimates of t h i s model provide an answer t o the question, 'What would a community like ours i n terms of income, population, density, age, etc., normally spend on publ i c capital goods?" This, then, becomes the basis for capital -spendi ng need standards. The empirical analysi s i n the paper exami nes aggregate spending on highways ( i ncl udi ng roads, streets, and bridges) w i t h i n ten midwestern urban counties between 1965 and 1976. A demand function from the almost ideal demand system (AIDS) cost function i s employed, and i t i s demonstrated that aggregate spending for a geographic area corresponds t o that demanded by the average or typical c i t y i n that area--even when income i s adjusted by non-monetary factors such as population, area, and age of capital stock. Section I1 explains the basic model, beginning w i t h the notation employed. A static, one-period model i s f i r s t examined, and then the model i s amended t o incorporate the long-lived, many-period nature of capital goods. Finally, the specification of the mode1 i s examined under http://clevelandfed.org/research/workpaper/index.cfm Best available copy the case o f data t h a t are aggregated f o r a l l l o c a l governments w i t h i n a geographic area. Section I 1 1 presents an empirical t e s t o f the model, beginning w i t h the data used, the sources of e r r o r i n the model, and the estimation technique employed. A f t e r the estimated c o e f f i c i e n t s o f the model are analyzed, capital-needs estimates are d e t a i l e d f o r a l l ten urban counties i n the study. Section I V contains some b r i e f concluding comments. 11. An Econometric Model o f Local Pub1i c Capital Spending Notation. Let: xi j,k represent real per capita spending a t time i by c i t y j i n urban county k.2 The 1, j, and k subscripts represent these same dimensions f o r a l l variables i n the paper. However, f o r the sake of simp1i c i t y , not a11 o f these l e t t e r s w i l l be used i n every instance. Let: pi = the real opportunity cost of owni ng the c a p i t a l stock each year, including both the foregone i n t e r e s t and depreciation costs. Following Gramlich and Galper (1973, p. 26), http://clevelandfed.org/research/workpaper/index.cfm Best available copy Let: pi, (ri + 6) o ~ I ~ ~ , where: ri = the real municipal bond rate. In this study, the real r a t e i s proxied by the nominal bond r a t e m i n u s the current i nfl ation r a t e 6 = the rate of depreciation oi = an index which reflects the cost of constructing new capital hi = the GNP deflator = the real per capita income of the c i t y = the share of expenditures on the capital good as a J let: Yj wi j si j fraction o f total income--w i - x i./ y ij j= J = the per capita quantity of the capital good http://clevelandfed.org/research/workpaper/index.cfm Best available copy qJ = the per capita flow of services from the capital good each year. Units of services are defined so that each u n i t of capital yields one u n i t of service--qi = j i S j. In addition, define: X; -1 Xk = the sum of x across a l l j i n k: = the mean of x across all j i n k : This notation will be used consistently across a l l variables i n this paper. A simple spending model. The residents of each c i t y are assumed t o be interested i n q and m, where m represents real income l e f t over from capital spending, available for use on a1 1 other goods. In addition, previous studies have shown that a c i t y ' s expenditure decisions (and therefore presumably i t s u t i l i t y function) are affected by the composition of i t s effective income between 1ocal l y generated revenues http://clevelandfed.org/research/workpaper/index.cfm Best available copy and grants-in-aid. In this paper, this e f f e c t i s modeled by including t, the share of effective income provided by grants-in-aid, a s a parameter i n the c i t y ' s u t i l i t y function. T h i s parameter i s not a choice.variable f o r the c i t y , b u t rather, enters the u t i l i t y function exogenously. Several explanations f o r this composition of income e f f e c t have been given i n the l i t e r a t u r e . One approach i s to argue t h a t the voter m i stakes his average tax r a t e f o r h i s marginal tax rate, and t o note t h a t lump-sum grants lower t h i s average tax rate. In our model, this would mean t h a t u t i l i t y would be positively related t o this share of income variable, since more aid means a 1ower perceived tax price and a higher perceived level of satisfaction. A1 ternatively, i t has been a r b e d t h a t composition e f f e c t s occur because of differences i n the tax bases of national, s t a t e , and local government, so that, even though grants-in-aid must be financed through taxes a t the higher level of government, the pivotal voter may find his total taxes changed by a shift i n composition of effective income. In this case, u t i l i t y might be positively or negatively related t o t, depending upon the nature of the pivotal voter's tax l i a b i l i t i e s . The c i t y ' s political process maximizes u ( q , m , t ) subject t o pq + m = y. T h i s maximization process r e s u l t s i n choices q* = f ( p , y , t ) and m* = t g(p,y,t). No particular assumption about the nature of t h i s pub1 i c choice mechanism i s made i n this paper. The c i t y ' s decisions may follow the d i c t a t e s of the median voter or some dominant political party. The political process m a y be biased toward certain i n t e r e s t groups o r dominated by the wishes of bureaucrats and municipal employees. All t h a t i s required i s t h a t these decisions correspond t o the wishes of some individual or group w i t h i n the c i t y , and t h a t these two goods are important t o t h a t party. http://clevelandfed.org/research/workpaper/index.cfm Best available copy I n order t o estimate q* and m*, a functional form f o r t h e u t i l i t y f u n c t i o n o f the community must be assumed. For reasons which w i l l become apparent l a t e r , t h e AIDS demand f u n c t i o n was chosen f o r t h i s study. 3 ' This s p e c i f i c a t i o n represents u t i l i t y not by a d i r e c t u t i l i t y function, b u t by a c o s t f u n c t i o n which q u a n t i f i e s the c o s t o f achieving a p a r t i c u l a r l e v e l o f u t i l i t y given the p r i c e l e v e l o f each o f the goods i n question. I n t h i s case, t h e AIDS c o s t f u n c t i o n may be w r i t t e n : (1) In(C(u,p)/O) = a + b l n p + c(lnp12/2 + udpe - ft where a through f are parameters t o be estimated and C(u,p) i s the c o s t o f achieving a given l e v e l o f u t i l i t y . The r e s u l t i n g demand f u n c t i o n s are most o f t e n given i n budget share form: (2) w = b + c i n p + e i n ( y / ~ p V )+ e f t where v i s a weight determined by t h e average proportion o f spending on t h e good access a l l c i t i e s , counties, and time periods: v = ( m! )In, and y = per c a p i t a p r i v a t e income p l u s per c a p i t a J ,k 4 grants- in- aid. The parameter 0 i s a weighting f a c t o r which adjusts t h e necessary expenditure i n each c i t y by expenditure "needs". I t s purpose i s t o i d e n t i f y the most important h i s t o r i c a l and demographic f a c t o r s which necessitate d i f f e r e n t l e v e l s o f spending i n d i f f e r e n t c i t i e s . To http://clevelandfed.org/research/workpaper/index.cfm Best available copy construct t h i s measure, two sources o f information were used. First, the 1it e r a t u r e on intergovernmental grants was exami ned t o a s c e r t a i n which v a r i a b l e s are used t o i n d i c a t e t h e "need" f o r a d d i t i o n a l money from the federal government. Two o f the most frequently used f a c t o r s i n formulas f o r d i s t r i b u t i n g federal do11a r s are population and 1and area. Therefore, a l l income and expenditure terms were p u t i n per c a p i t a terms, and 1and area and population were included as need variables. Next, t h e l i t e r a t u r e on technical analysis of c a p i t a l needs was reviewed, t o see i f any exogenous f a c t o r s not already included i n t h e model might a f f e c t spending. A r e c u r r i n g theme i n t h i s 1i t e r a t u r e i s t h a t the average age o f the c a p i t a l stock i s very important i n determining t h e c o s t o f maintaining it, so t h i s v a r i a b l e was a l s o included i n the need index. Since the l i t e r a t u r e on l o c a l p u b l i c spending i n d i c a t e s t h a t these variables often affect expenditures i n a log-1 i n e a r way, our assumption about expenditure needs takes the f o l l o w i n g form: (3) 0 = -exp (gl population + g2 area + g3 age) where the g' s are parameters t o be estimated. I n t e g r a t i n g these f a c t o r s i n t o equation 2 r e s u l t s i n t h e f o l l o w i n g functional form f o r t h i s simple spending model: (4) w = b + c i n p + e ln(y/pV) + e f t + e(gl population + g2 area + g3 age). http://clevelandfed.org/research/workpaper/index.cfm Best available copy A more complex model. The preceding model, of course, t o t a l l y ignores the 1ong-1 ived nature of capital goods; i t i s constructed as i f these goods are built and consumed w i t h i n a single time period. A real i s t i c model of the publ i c spending process must recognize the benefit spillover of expenditures from one time period to the next, as well a s the slow manner i n which gaps i n the supply of publ ic capital are f i l led. To deal with this difficulty, the preceding model i s amended so t h a t capital spending by each c i t y i s equal t o the cost of maintaining the previous year's capital stock (6si-I ) plus some portion of the gap between the previous year' s capital stock and "desired" capital stock (s i* . Formally t h i s flexible accelerator model i s given by: where Y i s a parameter to be determined by the data. The model can be p u t into budget share form by d i v i d i n g through by income: By definition, si * i s the steady-state capital stock; i t i s the capital stock the city would choose i f , as i n the preceding simplier model, stock levels could be completely adjusted i n one year. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Since si*/yi (7) = qi*/yi = wi* /y i, we have t h a t : i wi= ~ [ +b c l n p + e ln(yi/pi)v)+ e f t + egl popi i i-1 i + eg2 area + eg3 agei~/pi + (6-Y 1s /y . Aggregation i n the model. Those doing econometric research i n 1ocal pub1i c finance have long been faced w i t h a dilemma about the use o f data t h a t are aggregated over a l l governments w i t h i n a geographic area. If researchers used aggregate data, they could never be sure t h a t these data were representative o f i n d i v i d u a l units. If, instead, they used data f o r i n d i v i d u a l j u r i sdictions, they avoided t h i s aggregation problem b u t r i sked a d d i t i o n a l e r r o r due t o non- uniformity i n t h e type and l e v e l o f services o f f e r e d by i n d i v i d u a l governments. To c i t e some concrete examples: Baltimore and St. Louis have i n t e g r a t e d c i t y and county governments, so t h a t these governments have greater r e s p o n s i b i l i t i e s than t h e c i t y governments o f D e t r o i t o r C l evel and. Thus, by using j u r i s d i c t i o n s w i t h d i f f e r e n t l e v e l s o f responsibil i t y i n a cross- section estimation procedure, t h e researcher r isks confusi ng expenditure d i fferences due t o varying 1evel s o f responsi b i 1ity w i t h a d d i t i o n a l expenditures made by one j u r i s d i c t i o n due t o changing circumstances w i t h i n t h a t c i t y . Fortunately, innovation i n modern demand theory has l e d t o the development o f functional forms t h a t f i t the data well and aggregate p e r f e c t l y - - t h a t i s , aggregate demand can be shown t o be determined by the economic c o n d i t i o n s o f the average c i t y i n the sample. The AIDS demand http://clevelandfed.org/research/workpaper/index.cfm Best available copy f u n c t i o n s are generally o f t h i s type. Thus, aggregate data can be u t i l i z e d w i t h o u t concern about t h e i r representativeness. However, t h i s property has never been demonstrated over a l l possible f u n c t i o n s f o r 0, the needs variable; t y p i c a l l y , 0 i s assumed t o equal u n i t y f o r a1 1 observations. Hence, i t seems worthwhile t o examine t h i s p e r f e c t aggregation property i n the context o f the present model. We begin by making two assumptions (A.l and A.2) d i s t r i b u t i o n of c h a r a c t e r i s t i c s across c i t i e s : (A.1) about t h e Across time and across counties, the intracounty d i s t r i b u t i o n s of c i t y per c a p i t a income are approximately proportional. That is, f o r any two counties (kl and k2) and time periods ( t l and t 2 ) f o r c i t i e s w i t h equivalent p o s i t i o n s i n t h e income d i s t r i b u t i o n ( o r more precisely, f o r c i t i e s a t the same p e r c e n t i l e i n the frequency d i s t r i b u t i o n of c i t y incomes), there e x i s t s a parameter i1si2 T kl, k2 such t h a t : (A.2) Across c i t i e s w i t h i n each county, age, area, and population are independent of income. 6 Armed w i t h these assumptions, we can now proceed w i t h t h e aggregation. Note t h a t : - 'Yj,kwj,k /yi. k Using 7 and the d e f i n i t i o n o f t: http://clevelandfed.org/research/workpaper/index.cfm Best available copy Each one- or two-line group on the right-hand side of 8 can now be addressed separately. Notice, f i r s t of a l l , that the f i r s t 1ine consists of constants and a variable ( p i ) that does not vary across u n i t s . 1 Therefore, these variables can be pulled outside the sumnation operation; a s a resul t the y s d i sappear, si nce cy I /yi = 1. The second two-1 ine group i s a1so straightforward, since when the summation i s j,k k carried out, the 1i t t l e ys disappear, leaving the fol lowing: The t h i r d two-line group requires the use of the independence assumption A. 2. Consider f i r s t the population term i n t h a t line. Under independence, and letting N equal the number of c i t i e s i n the county: http://clevelandfed.org/research/workpaper/index.cfm Best available copy S i m i l a r r e s u l t s apply t o area and age. F i n a l l y , t h e l a s t 1i n e o f 8 employs t h e p r o p o r t i o n a l i t y assumption. I g n o r i n g t h e Y, e, and pi terms, which are constant under aggregation, the l i n e consists of: Now, consider a hypothetical county w i t h an income d i s t r i b u t i o n proportional t o each o f t h e sample c i t i e s and a mean c i t y income o f one. T h i s county i s denoted by t h e index to. Under p r o p o r t i o n a l i t y : 4 = Tk,k~;o = T k,ko f o r any county k. Therefore, i t f o l l ows t h a t : i Yj,k .. --11 - Ykyj,ko and t h a t : f o r any c i t y j http://clevelandfed.org/research/workpaper/index.cfm Best available copy where 2 inequality. =Lyji,kOln y ij, k0 i s a constant index of The effect of the proportional i ty assumption A.1, a s shown by the kO subscripts, i s to make this index invariant across counties, removing i t s i nfl uence on the coefficients of the regression. , Using a l l of these results, and rearranging the equation somewhat, 8 become s: + Ye (In 7: where T: = i form, t h i s becomes: i - v in pi)/pi +Y ef T : / ~ ~ Y j Y k = In i t s unrestricted, estimatable http://clevelandfed.org/research/workpaper/index.cfm Best available copy where: b ' = y b + Yez c' = YC e' = f' = Ye ref 111. An Appl ication t o Urban Highways: The data and specification of variables. 1965-1976 The data used f o r this study and the source for each variable are l i s t e d i n table 1. Ten urban counties were chosen for investigation, each of which has been designated by the Census Bureau as the central portion of a midwestern standard metropol itan s t a t i s t i c a l area (SMSA) : Allegheny County, Pennsylvania http://clevelandfed.org/research/workpaper/index.cfm Best available copy ( p i t t s b u r g h ); Cook County, I 11i n o i s (Chicago) ; Cuyahoga County, 0 h i o (Cl eve1and) ; E r i e County, Mew York ( B u f f a l o ) ; Hamil t o n County, Ohio ( C i n c i n n a t i ) ; Hennepi n County, Minnesota (Minneapol is-St. Paul ) ; Jefferson County, Kentucky (Loui s v i l l e) ; Milwaukee County, Wisconsin (Milwaukee) ; and Monroe County9 New York (Rochester). 7 It should be noted t h a t some , o f the variables employed are proxies f o r t h e t r u e variables i n the preceding model. Instead o f t h e average per c a p i t a income across c i t i e s i n each county, the per c a p i t a income f o r the e n t i r e county i s employed. The age o f t h e highway c a p i t a l stock i s approximated by the r a t i o of t h e number o f bridges b u i l t before 1930 t o the number o f bridges b u i l t between 1930 and 1955 f o r t h e c e n t r a l c i t y i n each county. The r e a l r a t e o f i n t e r e s t i s proxied by t h e Bond Buyer's 20-bond index of y i e l d s on municipal bonds minus t h e average i n f l a t i o n r a t e (as measured by t h e GNP d e f l a t o r ) over the previous three years. The c a p i t a l stock measure employed i n t h i s study i s only an estimator o f t h e t r u e l e v e l of c a p i t a l stock. Unfortunately, data on the highway expenditures t h a t are aggregated over a11 j u r i s d i c t i o n s i n an urban county are n o t a v a i l a b l e before 1965, except f o r the Census o f government c a r r i e d by t h e Census Bureau i n 1957 arid i n 1962. However, there i s information about t h e expenditures, o f t h e l a r g e s t few c i t i e s i n each o f these counties as f a r back as 1941; these constitute, on average, about 50 percent o f the t o t a l . Accordingly, we estimated the expenditures f o r each year back t o 1941 by mu1t i p l y i n g t h e sum o f these l a r g e c i t y expenditures by t h e r a t i o of t o t a l expenditures t o l a r g e c i t y expenditures i n the nearest census year. This measure i s n e i t h e r complete (many bridges i n http://clevelandfed.org/research/workpaper/index.cfm Best available copy use, f o r example, were doubtless b u i l t before 1941 ) nor exact, b u t i t should capture the l i o n ' s share of variations i n capital stock across urban counties. Because the data do not go back further than 1941, the age of capital -stock proxy was retained t o pick up differences i n expenditures prior to that date. In testing the model, intergovernmental grants were simply added to the income of the community. The Advisory Commission on Intergovernmental Relations (ACIR) reports that (1977, p. 20) a s of 1972, 96 percent of all grants received by local governments came from the state, not the federal . 1eve1 ( T h i s remained true even when federal money that i s passed through s t a t e highway departments on i t s way to local governments was included i n the federal total. Of t h i s money, only 3 percent was i n the form of project grants; the rest was revenue-sharing grants based on some measure of need such as area, mileage, motor vehicle registration fees, and license fees (ACIR, 1977, p. 31 1. Since local governments have l i t t l e control over these factors, i t seemed reasonable t o model these grants as having an income effect b u t not a price effect on the decisions of local 1eaders. A1 so included i n t h i s grants total (and a1so modeled a s a noncategorical grant) was the direct expenditure of state highway departments on local roads and streets i n each county. Sources of error and estimation technique. An error term, E i , must be added to equation 10 because of several factors, including: a) differences i n tastes among c i t y residents b) geographical and cl imate difference among c i t i e s c) perceptual errors made by pol icymakers resulting i n the actual values of the independent variables differing from thei r perceived values http://clevelandfed.org/research/workpaper/index.cfm Best available copy d) differences i n revenue structures and pub1 i c deci sion-making mechani sms among c i t i e s e) ommi tted variables f) errors due to the aggregation assumptions A.l and A. 2, which are only approximations to actual conditions Because of the widespread usebof incremental budgeting techniques--the use of the previous year's budget a s a starting point f o r consideration of the current budget--these errors are expected to be autocorrelated. Since pooled cross-section and time-series data are used, the estimation technique should account for the possi bil i ty of differences i n error variance and degree of autocorrelation across units. I t i s also conceivable that some national event, such as a winter w i t h heavy snowfall or a change i n the provisions of federal grants-in-aid, might affect a l l cross-sectional units a t the same period of time, so the estimation technique must a1 so account for t h i s contemporaneous correlation. One approach t o dealing w i t h these three difficulties- heteroskedastici ty, autocorrel a t i on, and contemporaneous correl a t i on--was proposed by Parks (1967) and i s out1 ined i n the textbook by Kmenta (1971, pp. 512-14). I t consists of three steps. In the f i r s t step, an ordinary l e a s t squares regression i s r u n on the model and the residual s of t h i s regression are used to calculate autocorrel ation coefficients for each separate cross-section. The second step consi s t s of partially f i r s t differencing all of the variables i n the model, using the coefficients estimated above, and running a second ordinary l e a s t squares regression on these transformed variables. In the final step, the residuals from the second regression are used to estimate heteroskedasticity and http://clevelandfed.org/research/workpaper/index.cfm Best available copy contemporaneous correlation i n the model's error term, and a t h i r d generalized l e a s t squares regression i s used on the transformed variables to get final parameter estimates. The result of a l l these manipulations i s estimates which are consistent, asymptotically normal, and have the same asymptotic d i s t r i bution a s A i tken' s general ized 1east squares T h i s i s the method01ogy employed f o r t h i s paper. estimator. Empirical results. Table 2 presents the results for t h i s model. In addition t o t h i s regression for the entire sample, a sensitivity analysis was performed i n which each urban county was separately excluded from the sample and the Parks procedure was r u n on the remaining nine counties. The results of these regressions, while not enumerated here, were used i n interpreting the coefficients of table 2. First, a word about the depreciation rate used i n t h i s study. We began by using the straightline depreciation rates implied by the useful 1i fe assumptions employed by the Federal Highway Administration' s, estimates of highway capital stock. However, since t h i s figure may be inaccurate, we investigated whether the f i t of the regression ( i n terms of the sum of squared residual s ) coul d be improved by searchi ng over various values of a. 0.085 for years. This procedure resulted i n an unexpectedly h i g h value of a, which corresponds to a useful l i f e of approximately 12 T h i s i s the value used for the final regression. All of this suggests that local governments are primarily concerned w i t h maintaining capital (such as pavement) w i t h a relatively short l i f e span, rather than w i t h repairing the 1onger-1 ived assets, such as bridges and roadbeds, which are also under their control. We begin w i t h the most important results. Table 2 shows t h a t adjustment coefficient between actual and desired capital stock i s the http://clevelandfed.org/research/workpaper/index.cfm Best available copy positive and significant, b u t extremely 1ow. On average, 1ocal governments make up only about 2 percent of the difference between their actual and desired level s per year. This suggests t h a t local admi n i s t r a t o r s are primarily concerned w i t h repairing and rep1aci ng 01d capital stock, rather than meeting the new investment needs of the community. Table 2 also shows that, consistent w i t h most studies of public goods expenditure, i t matters whether community resources come from private income or grants-in-aid. - The positive value for f ' means that the greater the proportion of a city resources coming from higher level s of government, the more the city will spend on highways. The need variables i n the regression (population, area, and age) are a l l positive and have interesting interpretations. The area coefficient, which i s highly significant i n every regression t h a t was run, suggests that greater highway spending i s necessary for more dispersed populations. The population coefficient, gl ', impl i e s d i seconomies of scale i n highway production: the larger the city i n terms of population, the greater the share of the income of the entire c i t y (and of each< individual citizen) that must be devoted to highways. Upon closer inspection, however, this result appears to be due to the high spending of the second largest u n i t i n the sample--Wayne County i n Michigan. When t h i s u n i t is removed from the sample, t h i s coefficient becomes negative and insignificantly different from zero. A coefficient of zero impl i e s constant returns t o scale i n the production of highways: each person has t o spend the same share of his income on the good, regardless of the size of the city he l i v e s i n . The age coefficient, g3', suggests that the http://clevelandfed.org/research/workpaper/index.cfm Best available copy older the capital stock, the more i t c o s t s t o repair and replace. However, most of the variation i n this variable i s due t o the very high age figure recorded f o r Hennepin County, Minnesota, so the r e s u l t s are sensi t i ve t o t h i s high i nfl uence point. When Hennepi n County i s removed from the sample, this coefficient i s not significantly different from zero. Interpretation of the coefficients c ' and e ' i s complicated by the f a c t t h a t the dependent variable i s i n share-of-income form. A negative value f o r e l , f o r example, means t h a t the share of income spent on highways declines a s effective income r i s e s ; i n other words, highways a r e necessities and not normal goods or luxuries. As shown a t the bottom of 1 the table, the value f o r e implies a long-run income e l a s t i c i t y of 0.1 772. Interestingly, when the highest income c i t y , Chicago, is excluded from the sample, the income e l a s t i c i t y figure jumps t o 1.647. indicate a nonlinearity i n the response of spending t o income. T h i s may A t low 1eve1 s of i ncome, extra income might a1 1ow considerable extra highway spending by the community, b u t a t some point the c i t y ' s needs are f i l l e d , and i t devotes 1ittl e of i t s extra income t o highways when per capita income r i s e s above t h a t point. The positive value f o r c ' indicates t h a t demands are price inelastic. As prices r i s e , total expenditure and the share of income spent on the goods also rise. Notice, however, t h a t the estimated standard error i s quite large, and therefore this coefficient i s insignificantly different from zero. The estimated 1ong-run price e l a s t i c i t y i s -0.2689. Unfortunately, the Parks procedure does not provide R-squared--the coefficient of determination--because the final regression uses variables t h a t are extensively transformed from those of the original model. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Nevertheless, i t i s possible to get a reasonable measure of goodness of f i t by examining the in-sample predictive power of the estimated - coefficients. Equivalently, one could examine the R-squared that would have resulted i f these parameter values were the result of a simple ordinary 1east squares regression on the dependent variable of i nterest. This might be called a "rebuilt" R-squared measure of goodness of f i t . In equation 10, we take t h i s approach by multiplying both sides of the equation by income, moving the 6S term to the right-hand side, and then examining the R-squared of the resulting model of gross real per capita spending. As shown a t the bottom of tab1e 2, the resulting rebuil t R-squared i s 0.81 36. Highway needs estimates for ten urban counties. Every capital -spendi ng needs estimate contains w i t h i n i t an element of subjectivity. The analyst i s really presenting a particular s e t of spending preferences as being better than other spending plans. The best the positivist can hope for here i s t o tap into a widely shared s e t of be1 ief s about what circumstances necessitate extra capital spendi ng, and to base his estimates on these. The goal i s simply a benchmark from which local authorities can begin debate on capital spending plans, rather t h a n a mathematical formula that determines the final and optimal allocation of resources i n any city. A1 1 b u t two of the independent variables i n the preceding model would seem t o pass muster as "1egi timate determinants" of capital -spendi ng needs. In other words, most people would agree t h a t effective income, the price of capital goods, the stock of capital goods a1 ready on hand, http://clevelandfed.org/research/workpaper/index.cfm Best available copy population, area, and the age of the capital stock all ought t o be considered i n determining highway needs. More controversial woul d be the inclusion of the share of resources coming from grants-in-aid i n a capital-spending needs estimate. I t might easily be argued t h a t the need for highways i s simply independent of the source of financing available to the community. Does a city need more roads simply because Washington or the s t a t e capitol i s willing to pay for them? I t would a1 so be d i f f i c u l t to refute the argument that, apart from i t s effects on the current capital stock, the previous year's spending levels shouldn't dictate current capital spending needs. Are a c i t y Is needs reduced one year j u s t because i t refused to spend enough on roads the year before? To develop estimates of capital-spending needs, then, we f i r s t multiplied both sides of equation 10 by income and moved the sS term to the right-hand side to derive a model of gross real per capita highway spending. Using the values given i n table 2, the needs estimate was s e t equal to the predicted values of the resulting equation, except f o r two adjustments. First, the influence of aid was neutralized by g i v i n g every county the average per capita real aid f o r the entire sample. Second, t h i s equation was not corrected for autocorrel ation, heteroskedastici ty, or contemporaneous correlation, a s would have been done w i t h the Parks procedure. The equation was not partially f i r s t differenced, so 1a s t y e a r ' s spending does not appear a s a determinant of this year's capital -spending needs. The resulting estimates are shown i n figure 1. For each urban county, the average actual and needed real per capital highway spending http://clevelandfed.org/research/workpaper/index.cfm Best available copy are depicted. The gaps between actual and needed expenditures look small on the chart, b u t i n some cases they represent s i g n i f i c a n t sums o f money. I t t u r n s o u t t h a t the two most western areas i n our sample--Hennepin County i n Minnesota and Milwaukee County i n W i sconsin--are f a r t h e s t above t h e i r needs estimates, while two old, i n d u s t r i a l , more eastern counties- E r i e County i n New York and Cuyahoga County i n Ohio--have the l a r g e s t capital- spending d e f i c i t s . To put these f i g u r e s i n t o perspective, the Cuyahoga County d e f i c i t amounts t o about 3 percent o f actual expenditures o r approximately $2 m i l l i o n per year. The Milwaukee County surplus, on t h e other hand, comprises 6 percent o f actual expenditures o r approximately $3 m i l 1i o n annually. As t a b l e 3 shows, these differences can only p a r t l y be explained by d i f f e r e n c e s i n aid. Milwaukee and Hennepin counties do have t h e second and t h i r d highest a i d per capita, b u t Cuyahoga County receives more than the average amount o f a i d ( s i x t h highest) and E r i e County gets only t h e t h i r d lowest l e v e l o f aid. Clearly, some o f these differences remain t o be explained by f a c t o r s such as the p o l i t i c a l c u l t u r e o f each area. More surprising, perhaps, i s the wide range o f c a p i t a l needs l e v e l s allowed under t h i s procedure. Since t h e highway spending process i s dominated by r e p a i r and rep1acement considerations, these l e v e l s are determined, t o a l a r g e extent, by the size of the c a p i t a l stock which must be maintained. Thus, Jefferson County i n Kentucky has the smallest c a p i t a l -spendi ng need of $11.75 per person ( 1972 do11a r s ) because o f i t s low per c a p i t a income and i t s ma11, and re1a t i v e l y new, c a p i t a l stock. Milwaukee County, on the other hand, despite having t h e smallest 1and area http://clevelandfed.org/research/workpaper/index.cfm Best available copy i n t h e sample and a r e l a t i v e l y new c a p i t a l stock, has t h e l a r g e s t c a p i t a l - stock need ($46.30 per person), because o f t h e sheer s i z e o f t h e c a p i t a l stock t h a t must be maintained there. This l a r g e v a r i a t i o n i n highway-spending needs a1 so p o i n t s up how m i s l eadi ng a simp1e average expenditure f i g u r e would be as a measure of capital- spending needs. Such an approach (which i s sometimes employed f o r t h i s purpose) would g i v e seriously d i s t o r t e d estimates f o r many o f these c i t i e s . IV. Conclusion This paper has attempted two r e l a t e d tasks. F i r s t , a p o s i t i v e model o f p u b l i c c a p i t a l spending was developed and tested using highway spending data f o r t e n midwestern urban counties. The most s i g n i f i c a n t determinants o f highway spending were found t o be population, the value o f t h e e x i s t i n g c a p i t a l stock, t h e 1and area o f t h e c i t y , and t h e amount o f a i d received from higher l e v e l s o f government. Weaker and l e s s c o n s i s t e n t r e l a t i o n s h i p s were found between highway spending and income, t h e p r i c e o f c a p i t a l goods, and t h e age o f the c a p i t a l stock. Second, t h e estimated c o e f f i c i e n t s from t h i s model were used t o generate c a p i t a l -spendi ng needs estimates f o r these counties, on t h e premise t h a t t h e predicted values o f t h e model provide t h e responses o f a t y p i c a l c i t y i n t h e sample t o changes i n i t s characteristics. It was found t h a t Hennepin and Milwaukee counties spend considerably more than t h e needed amount on highways, while E r i e and Cuyahoga counties had l a r g e s h o r t f a l l s i n spending r e l a t i v e t o t h e i r need http://clevelandfed.org/research/workpaper/index.cfm Best available copy levels. Moreover, not all of the differences between these c i t i e s can be accounted for by differences i n aid, so some of these discrepancies must be due t o factors such as the political environment i n each urban area. The economic method of estimating capital-stock needs has two principal advantages over previous methods. F i r s t , i t requires considerably l e s s staff time to prepare, since no exhaustive inventory of physical units i s needed. Second, this method may be more useful t o pol icymakers, since i t avoids arbitrariness i n the calculation of capital-spending needs by using as i t s benchmark the typical response of similar c i t i e s . Given these advantages, it would be highly desirable t o continue research i n t h i s area, both t o check results and t o provide more information for pol icymakers. I t would be useful to see how these results vary across time, across regions of the country, and across types of pub1 i c capital . http://clevelandfed.org/research/workpaper/index.cfm Best available copy Notes 1. Here Choate and Walter are summarizing the r e s u l t s of a government study. 2. Throughout t h i s paper, I use the term c i t y i n a generic sense, t o refer t o any local jurisdiction such a s a c i t y , village, township, o r county. 3. The seminal reference on the AIDS demand system i s Angus Deaton and John Muellbauer, "An Almost Ideal Demand System," Review, 4. vol . 70, American Economic no. 3 (June 1980), pp. 312-26. Actually, the term ln p V i s only a l i n e a r approximation t o the t r u e * , which price index p + c ( I n p ) 2/2. * i s determined by the formula In p = a + b In p T h i s substitution allows the use of l e a s t squares rather than maximum 1i kel i hood techniques. Deaton and Muel 1bauer (1980, p. 31 6) find t h a t this technique y i e l d s a close approximation f o r more than one price, when those prices are closely collinear. Presumably then, the same technique ought t o work well for only one price. , 5. The f i r s t application of the concept of proportionality of income distributions t o the study of deci sion-maki ng i n local government, appears t o have been i n Bergstrom and Goodman (1973, pp. 287-90). For a discussion of the meaning and plausibil i t y of this assumption, see Robert P. Inman, "Testing Political Economy's 'As I f ' Proposition: I s the Median Voter Really Decisive?" Pub1 i c Choice, vol. 33, no. 4 (1978), p. 48. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Following Inman (p. 481, t h i s hypothesis was tested by examining the moments o f t h e d i s t r i b u t i o n of intracounty, c i t y , per c a p i t a income i n seven o f t h e urban counties i n our sample. (Three o f the sample counties had too few c i t i e s t o be useful f o r t h i s purpose. ) I f income d i s t r i b u t i o n s are proportional, the r a t i o s o f median t o mean and the c o e f f i c i e n t s o f v a r i a t i o n ( standard deviation/mean) w i l l be equal. According t o t h e 1980 Census o f Populatic 1, t h e r a t i o o f median t o mean f o r a l l incorporated places w i t h populations greater than 2,500 i n these urban counties ranged from 0.87 t o 0.92 w i t h a mean o f 0.90. The c o e f f i c i e n t o f v a r i a t i o n ranged from 0.25 t o 0.45 w i t h a mean o f 0.34. Some o f t h e d i f f e r e n c e i n c o e f f i c i e n t s o f v a r i a t i o n appears t o be due t o differences i n t h e number o f j u r i s d i c t i o n s i n each county; the greater t h e number o f j u r i s d i c t i o n s , the l a r g e r the d i spersion o f per c a p i t a incomes. As long as t h i s effect i s independent of t h e o v e r a l l l e v e l o f income i n the county, i t should create no problems f o r t h e analysis. I n an e f f o r t t o t e s t t h i s assumption, data were gathered f o r 46 6. j u r i sdications i n Cuyahoga County ( i n c l u d i n g the county i t s e l f ) from t h e Census Bureau. For t h i s sample, the c o r r e l a t i o n between 1980 population 1979 per c a p i t a income was -0.1 7264, and the c o r r e l a t i o n between area and 1979 per c a p i t a income was -0.11663. Neither o f these f i g u r e s i s s t a t i s t i c a l l y s i g n i f i c a n t ; t h e data do n o t r e j e c t the hypothesis t h a t these c h a r a c t e r i s t i c s are uncorrel ated. Unfortunately, data concerni ng the age o f pub1i c c a p i t a l were n o t a v a i l a b l e a t the i n d i v i d u a l community . 1eve1 http://clevelandfed.org/research/workpaper/index.cfm Best available copy 7. Actually, both Hennepin and Ramsey counties are considered part of the central portion of the Minneapol is-St. Paul SMSA. only because i t was more populous. Hennepin was chosen http://clevelandfed.org/research/workpaper/index.cfm Best available copy - 31 - Figure 1 REAL PER CAPITA EXPENDITURES ON HIGHWAYS A N N U A L AVERAGES, 1965-1976 COOK C O . , I L (CHI CAGO) ERIE C O . , NY (BUFFALO) JEFFERSON C O . , KY (LOUISV I LLE) MILWAUKEE C O . , W I (MILWAUKEE) Legend I actual DItneeded" ( predicted value of the adjusted model) HAMILTON C O . , O H (C1,NCINNATI) HENNEPIN CO., M N (MINNEAPOLIS) CUYAHOGA CO., O H (CLEVELAND) ALLEGHENY C O . , PA (PITTS B U R G H) WAYNE C O . , M I (DETROIT) MONROE CO., NY (ROCHESTER) http://clevelandfed.org/research/workpaper/index.cfm Best available copy Table 1 Sources of Data Age of bridges Area of county The Urban I n s t i t u t e , via special release from U.S. De~artmentof Transportation, ~ e d e r a lHighway Admi n i stration, Bureau of Bridges. U.S. Department of Commerce, Census Bureau, 1977 City and County Data Book. Capital stock estimates Devel oped u si ng expendi ture data from U.S. Department of Commerce, Census Bureau, c i t y finances annual s, 1 941 -45 and compendi um of c i t y government finances annual s, 1946-64. Cost index, highways U. S. Department of Transportation, Federal Highway Administration, composite index of prices f o r federal -aid highway construction. GNP deflator U.S. Deparmtment of Commerce, Bureau of Economic Analysis. Highway expenditures and revenue sharing Department of Commerce, Census Bureau, Local Government Finances i n Sel ected Metropol i tan Areas and Large t o u n t i e s (annual I. Highway grants U.S. Department of Commerce, Bureau of Publ i c Roads, special re1 ease. Municipal i n t e r e s t rate Bond Buyer 20-bond index of yields on domestic municipal bonds. Number of highway jurisdictions U.S. Department of Commerce, Census Bureau, 1967, 1972, and 1977 Census of Governments. Per capita income Department of Commerce, Bureau of Economic Analysi s, Regional Economic Measurement D i v i sion. Popul ation Department of Commerce, Census Bureau. State highway department d i rect expenditure on local roads and streets U.S. Department of Transportation, Bureau of Publ i c Roads, special re1 ease. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Table 2 Regression Results Parameter Variable Estimated coefficient Estimated standard error t-Stat estimated : 0.085 estimated income el astici ty: 0.1 772 estimated price el astici ty: -0.2689 "Rebuilt" ~ 2 for , regression on real per capita highway spending using these coefficients: 0.81 36 http://clevelandfed.org/research/workpaper/index.cfm Best available copy Table 3 Average Real Per Capita Aid, 1965-76 (1972 dollars) County Average All counties, a l l years 18.24 (Buffalo) Erie County, New York 13.10 (Chicago) Cook County, I l l i n o i s 20.69 (Cincinnati ) Hamil ton County, Ohio 19.66 (Cl eve1and) Cuyahoga County, Ohio 19.48 (Detroit) Wayne County, Michigan 28.75 (Loui svill e ) Jefferson County, Kentucky 9.76 ( M i 1waukee) Milwaukee County, Wisconsin ( M i nneapol i s ) Hennepi n County, Minnesota (Pittsburgh) A1 1egheny County, Pennsyl vania (Rochester) Monroe County, New York 14.37 http://clevelandfed.org/research/workpaper/index.cfm Best available copy References Bergstrom, Theodore C., Goods," and Robert P. Goodman. American Economic Review, Borcherding, Thomas E., 62, no. 4 (December vol. 63, no. 3 (June 1973), pp. 280-96. and Robert T. Deacon. Services o f Non-Federal Governments, " P r i v a t e Demands f o r Public " "The Demand f o r t h e American Economic Review, vol . 1972), pp. 801-901. Choate, Pat, and Susan Ma1ter. America i n Ruins: Beyond the Publ i c Works . Pork ~ a r r e l Washington, DC: The Council o f State Planning Agencies, Congressional Budget Office. Publ i c Works I n f r a s t r u c t u r e : Washington, DC: U.S. Considerations f o r t h e 1980s. Pol i c y Government P r i n t i n g Office, A p r i l 1983. Deaton, Angus, and John Muellbauer. "An Almost Ideal Demand System," American Economic Review, vol. 70, no. 3 (June 19801, pp. 312-26. Gramlich, Edward M. "Intergovernmental Grants: A Review o f t h e Empirical Literature," i n Wallace E. Oates, ed. The Pol i t i c a l Economy o f F i scal Federal ism. Lexington, MA: Lexington Books, 1 977. http://clevelandfed.org/research/workpaper/index.cfm Best available copy , and Harvey Gal per. Federal Grant Pol icy," "State and Local Fiscal Behavior and Brooki ngs Papers on Economic Activity, 1:1973, pp. 15-58. Inman, Robert P. "Testing Political Economy's 'As I f ' Proposition: I s the Median Voter Really Decisive?" Public Choice, vol. 33, no. 4 (1978)) p. 4. Kmenta, Jan. Elements of Econometrics. New York, NY: Macmill an . Company, 1 971 Parks, Richard W. "Efficient Estimation of a System of Regression Equations when Disturbances are Both Serially and Contemporaneously Correlated," Journal of the American S t a t i s t i c a l Association, vol. 62, no. 31 7 (June 1967), pp. 500-09.
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