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An economic analysis of public housing in Yellowknife, Northwest Territories Steele, Margaret Jean 1986

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AN ECONOMIC ANALYSIS OF PUBLIC HOUSING IN YELLOWKNIFE, NORTHWEST TERRITORIES by MARGARET JEAN STEELE B.Comm.(Urban Land Economics), The U n i v e r s i t y of B r i t i s h Columbia, 1974 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE (BUSINESS ADMINISTRATION) in THE FACULTY OF GRADUATE STUDIES Commerce and Business A d m i n i s t r a t i o n We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA J u l y 1986 © MARGARET JEAN STEELE, 1986 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6 (3/81) ABSTRACT For many years, s o c i a l housing p o l i c y i n Canada has r e l i e d upon s u p p l y - s i d e programs. Recently, these programs have come under c r i t i c i s m f o r f a i l i n g to serve the needs of poor households, p r e c i p i t a t i n g a p h i l o s o p h i c a l s h i f t toward income supplement programs. While e v a l u a t i o n s of past programs support t h i s s h i f t , most s t u d i e s have been done at the n a t i o n a l l e v e l and may not r e f l e c t the housing needs of s p e c i f i c r e g i o ns or communities in Canada. T h i s study e v a l u a t e s a s u p p l y - s i d e housing program for one community i n northern Canada - Y e l l o w k n i f e , Northwest T e r r i t o r i e s . Drawing upon the t o o l s of w e l f a r e economics, the study e v a l u a t e s the P u b l i c Housing Program in Y e l l o w k n i f e i n terms of economic e f f i c i e n c y and e q u i t y . The study analyses the program from the viewpoints of the Canadian p u b l i c and the r e s i d e n t s of the N.W.T. In both cases, the Net Present Value, c a l c u l a t e d from measurable c o s t s and b e n e f i t s , i s negative suggesting the program i s not economically e f f i c i e n t . Non-tenant b e n e f i t s of between $446,082 and $966,955 per year are r e q u i r e d to j u s t i f y the program from the n a t i o n a l p e r s p e c t i v e and between $123,724 and $320,304 from the t e r r i t o r i a l p e r s p e c t i v e . The a n a l y s i s suggests the program i s promoting a small degree of e q u i t y . B e n e f i t s from the program are g r e a t e r f o r households with lower incomes and d e c l i n e by approximately $11 f o r every $100 i n c r e a s e i n annual household income. The program supports h o r i z o n t a l e q u i t y with respect to age of i i household head, but there i s some i n e q u a l i t y with respect to sex as f e m a l e - l e d households r e c e i v e s i g n i f i c a n t l y g r e a t e r b e n e f i t s than t h e i r male c o u n t e r p a r t s . The r e s u l t s of the study are c o n s i s t e n t with the economics l i t e r a t u r e . As expected, j u s t i f i c a t i o n of the P u b l i c Housing Program i n Y e l l o w k n i f e must appeal to n o t i o n s other than economic e f f i c i e n c y . Advocates of the program may f i n d support i n the e q u i t y achievements of the program or i n recent r e s e a r c h suggesting that p u b l i c housing programs have smaller work d i s i n c e n t i v e e f f e c t s than programs of cash t r a n s f e r s . Table of Contents ABSTRACT i i LIST OF TABLES v i LIST OF FIGURES v i i ACKNOWLEDGEMENT v i i i 1 . INTRODUCTION 1 1 . 1 BACKGROUND 1 1.2 OBJECTIVES OF THE STUDY 3 1 .3 OUTLINE 4 2. SOCIAL HOUSING POLICY 7 2.1 INTRODUCTION 7 2.2 SOCIAL HOUSING POLICY AS A TOOL FOR INCOME REDISTRIBUTION 8 2.3 SOCIAL HOUSING POLICY IN CANADA 11 2.4 SOCIAL HOUSING POLICY IN THE NORTHWEST TERRITORIES 13 3. THE ANALYSIS OF HOUSING POLICY 16 3.1 INTRODUCTION 16 3.2 GOVERNMENT INTERVENTION IN THE HOUSING MARKET ...17 3.3 MEASURING WELFARE GAIN 19 3.3.1 MEASURING BENEFITS - THE DEMAND SIDE 20 3.3.2 MEASURING COSTS - THE SUPPLY SIDE 26 3.3.3 THE SOCIAL DISCOUNT RATE 28 4. LITERATURE REVIEW 30 4.1 ASSUMPTIONS 30 4.2 METHODOLOGY 31 4.3 RESULTS 34 5. METHODOLOGY AND DATA 37 5.1 STUDY AREA AND DATA 37 5.2 HYPOTHESES 39 5.3 ASSUMPTIONS 40 5.4 TESTING FOR EFFICIENCY 42 5 .4 .1 ESTIMATING TENANT BENEFITS 42 5 . 4 . 2 ESTIMATING NON-TENANT BENEFITS 46 5 . 4 . 3 ESTIMATING COSTS 46 5 . 4 . 4 CHOOSING A SOCIAL DISCOUNT RATE 47 5.5 TESTING FOR EQUITY 48 6. EMPIRICAL RESULTS 50 6.1 ECONOMIC EFFICIENCY 50 6 .1 .1 ESTIMATES OF TENANT BENEFITS 50 6 .1 .2 ESTIMATES OF COSTS 66 6 .1 .3 ESTIMATES OF NET PRESENT VALUE 68 6.2 EQUITY 69 6.3 COMPARISON OF PUBLIC HOUSING PROGRAMS TO SHELTER ALLOWANCES 73 7. IMPLICATIONS 83 7.1 POLICY OBJECTIVES 84 7.2 EVALUATION OF THE PUBLIC HOUSING PROGRAM IN YELLOWKNIFE 85 7.3 CONCLUSIONS 89 REFERENCES 94 APPENDIX 1 102 APPENDIX 2 1 08 APPENDIX 3 130 APPENDIX 4 • 134 APPENDIX 5 135 v L i s t of Tables I E f f i c i e n c y Results Reported in the L i t e r a t u r e . . . 34 II Yellowknife Rental Housing Stock, 1981 38 III Yellowknife Public Housing Projects, 1985 . . . . . 39 IV Comparison of Market Rent Equivalents and Market Rents 59 V Minimum Expenditure Levels by Household Size 61 VI Gross Rent-to-income Ratios, Yellowknife, 1980 63 VII Revised Minimum Housing Expenditure Levels . . . . 65 VIII Public Housing Project Costs 67 IX Estimates of Net Present Value 69 X Household Incomes, Yellowknife, 1980 71 XI Households With Rent-to-income Ratios in Excess of 25%, Yellowknife, 1980 77 XII Estimated Annual Cost of a Shelter Allowance Program 78 XIII Estimates of Net Present Value, N.W.T. Share . . . 87 XIV Regression Results from Linear Model Using Data Set 1 102 XV Hedonic Regression C o r r e l a t i o n Matrix 103 XVI Hedonic Regression C o l l i n e a r i t y Diagnostics . . . .104 v i o L i s t of F i g u r e s 1 D i r e c t Cash T r a n s f e r 9 2 P r i c e Subsidy Program 10 3 I n - K i n d Housing Program . 1 1 4 Compensation V a r i a t i o n Measure . . . 25 5 E q u i v a l e n t V a r i a t i o n Measure . . 25 6 Measuring EV i n a Demand Framework 27 7 P l o t of R e s i d u a l s A g a i n s t P r e d i c t e d V a l u e . .105 8 Normal P l o t of R e s i d u a l s 106 9 P l o t of YHAT A g a i n s t Rent 107 10 T r a d i t i o n a l Income-Leisure Model 110 11 Murray's Model 115 12 G e o m e t r i c a l Proof of Theorem 117 v i i ACKNOWLEDGEMENT I am indebted to many people f o r t h e i r a s s i s t a n c e i n completing t h i s study. I would l i k e to thank Clay Cederholme and h i s s t a f f at the Y e l l o w k n i f e Housing A u t h o r i t y f o r a l l o w i n g me access to p u b l i c housing records and a s s i s t i n g me i n c o l l e c t i n g data. I would a l s o l i k e t o thank employees of the Bureau of S t a t i s t i c s and the Assessment Department of the Government of the N.W.T. f o r data on the Y e l l o w k n i f e housing market. I acknowledge f i n a n c i a l a s s i s t a n c e from a C.M.H.C. U n i v e r s i t y S c h o l a r s h i p and a N.W.T. Post-Secondary Student I n c e n t i v e Grant. I am a l s o g r a t e f u l to the N.W.T. Housing C o r p o r a t i o n f o r purchasing data from S t a t i s t i c s Canada. Above a l l , I am indebted to my t h e s i s a d v i s o r , Robert H e l s l e y , f o r h i s u n f a i l i n g support, guidance and c l e a r v i s i o n . v i i i CHAPTER 1 INTRODUCTION ix 1. INTRODUCTION 1 . 1 BACKGROUND Canadian housing p o l i c y has changed s i g n i f i c a n t l y s i n c e the f i r s t housing l e g i s l a t i o n was enacted over f i f t y years ago. Government a c t i v i t y i n the housing market has expanded from i t s o r i g i n a l r o l e as banker to a more a c t i v e r o l e i n income r e d i s t r i b u t i o n i n recent decades. Today, the r o l e of government i n housing markets i s being questioned by many, i n c l u d i n g the government i t s e l f . In January, 1985, B i l l McKnight, M i n i s t e r Responsible f o r C.M.H.C., i n i t i a t e d a n a t i o n a l debate on housing p o l i c y w i t h the p r e s e n t a t i o n of h i s C o n s u l t a t i o n Paper on Housing. Among the many i s s u e s r a i s e d f o r d i s c u s s i o n i n t h i s document, i s the problem of " a f f o r d a b i l i t y " . In g e n e r a l , a household has an a f f o r d a b i l i t y problem i f i t cannot o b t a i n adequate, uncrowded accommodation f o r l e s s than a given percentage of i t s income. Over the years, t h i s percentage has been set at 20%, 25% and, more r e c e n t l y , at 30%. Using the f i g u r e of 30%, the C o n s u l t a t i o n Paper r e p o r t s over 700,000 households i n Canada (8.5% of t o t a l households, 1981 Census) with a f f o r d a b i l i t y problems. The C o n s u l t a t i o n Paper summarizes t h i s i s s u e as f o l l o w s : Few would d i s a g r e e that governments have a r e s p o n s i b i l i t y to a s s i s t these groups. Whether j u s t i f i e d through concepts of b a s i c human r i g h t s , s o c i a l j u s t i c e or the r e d i s t r i b u t i v e r o l e of government, there i s a c l e a r r a t i o n a l e f o r government involvement i n a l l e v i a t i n g the problems of p o v e r t y . The key q u e s t i o n s i n t h i s area are what i s the most a p p r o p r i a t e t o o l f o r a s s i s t i n g groups i n 1 2 need and at what l e v e l of government does t h i s r e s p o n s i b i l i t y r e s t ? ( C o n s u l t a t i o n Paper on Housing, p. 17) H i s t o r i c a l l y , the housing needs of the poor have been addressed through the s u p p l y - s i d e programs of P u b l i c Housing, N o n - P r o f i t Housing and C o - o p e r a t i v e Housing. These programs have a l l come under c r i t i c i s m i n recent y e a r s . The P u b l i c Housing Program has been accused of " g h e t t o i s i n g " the poor and d e t r a c t i n g from neighbourhood q u a l i t y . The N o n - P r o f i t and C o - o p e r a t i v e Housing Programs, designed to i n t e g r a t e poor households i n t o the community by o f f e r i n g accommodation to a broad range of income groups, have been c r i t i c i s e d f o r f a i l i n g to serve the poorest of the poor. The problem seems to be one of t a r g e t t i n g l i m i t e d d o l l a r s to households most in need without i s o l a t i n g those households from the community. Opponents of s u p p l y - s i d e programs suggest the way to do t h i s i s to interv e n e i n the demand s i d e of the market. They argue that the i n a b i l i t y of low income households to a f f o r d decent q u a l i t y housing i s an income problem r a t h e r than a housing problem and should be addressed through a program of income supplements. According to t h i s view, a d o l l a r i n cash improves the household's welfare more than a d o l l a r in k i n d . The present f e d e r a l government seems to support demand-side programs r a t h e r than the d i r e c t supply of s u b s i d i z e d housing. E v a l u a t i o n s of past housing programs support t h i s viewpoint. However, most s t u d i e s are done at the n a t i o n a l l e v e l and may not r e f l e c t the s p e c i a l housing 3 needs i n s p e c i f i c r e g i o n s or communities in Canada. T h i s study analyses a s u p p l y - s i d e program i n one community i n a remote region of Canada - Y e l l o w k n i f e , Northwest T e r r i t o r i e s . 1.2 OBJECTIVES OF THE STUDY A l l economic s t u d i e s of s u p p l y - s i d e housing programs conclude that they are not economically e f f i c i e n t . N e o - c l a s s i c a l economists are unanimous i n t h e i r support of d i r e c t cash t r a n s f e r s as an e f f i c i e n t method of housing the poor. However, economic e f f i c i e n c y i s not the only c r i t e r i o n f o r e v a l u a t i n g government programs. An e q u a l l y important c r i t e r i o n i s the concept of e q u i t y . In a study of p u b l i c housing p r o j e c t s i n small c i t i e s i n North C a r o l i n a , Sumka and Stegman (1978) conclude t h a t , while the program i s not eco n o m i c a l l y e f f i c i e n t , i t i s j u s t i f i e d on the grounds that i t serves the needs of a m i n o r i t y p o p u l a t i o n t h a t i s s y s t e m a t i c a l l y d i s c r i m i n a t e d a g a i n s t i n the market. Accor d i n g to Sumka and Stegman: The important p o l i c y q u e s t i o n i s not j u s t how e f f i c i e n t i s the p u b l i c housing program, but what i s the a d d i t i o n a l c o s t that must be borne to maintain a p u b l i c l y supported housing d e l i v e r y system that p a r t i a l l y serves the unmet needs of a m i n o r i t y p o p u l a t i o n ? In s e a r c h i n g f o r a t e c h n i c a l l y more e f f i c i e n t housing s t r a t e g y , one must c a r e f u l l y account f o r the r e a l i t i e s of the market p l a c e . In nonmetropolitan c i t i e s , p u b l i c housing a p p a r e n t l y f i l l s a l a r g e v o i d that the p r i v a t e s e c t o r cannot, or w i l l not, f i l l . U n t i l such time as we are prepared and a b l e to improve the o p e r a t i o n of the market per se, a program of p u b l i c c o n s t r u c t i o n may be the only way to assure the d e l i v e r y of adequate housing to the m i n o r i t y poor i n the nonmetropolitan c i t y . (Sumka and Stegman, pp. 409-410) 4 Although the race problems i d e n t i f i e d i n Sumka and Stegman's study are not a f a c t o r i n most Canadian c i t i e s , race i s an i s s u e i n northern Canada. In Y e l l o w k n i f e , n a t i v e people represent a m i n o r i t y of the p o p u l a t i o n (14% i n 1981, G.N.W.T. Bureau of S t a t i s t i c s , unpublished d a t a ) . P u b l i c housing may be s e r v i n g the same purpose for them as i t does f o r b lack people in small American c i t i e s . I t may a l s o be s e r v i n g the needs of other m i n o r i t y groups, such as s i n g l e parents or the e l d e r l y . T h i s study examines the P u b l i c Housing Program i n Y e l l o w k n i f e from the two p e r s p e c t i v e s of economic e f f i c i e n c y and e q u i t y . The s p e c i f i c o b j e c t i v e s a r e : 1. to determine i f the d i r e c t p r o v i s i o n of p u b l i c housing i n Y e l l o w k n i f e i s an economically e f f i c i e n t method of meeting the housing needs of poor households; and 2. to determine i f the P u b l i c Housing Program i n Y e l l o w k n i f e promotes h o r i z o n t a l and v e r t i c a l e q u i t y . 1.3 OUTLINE The t h e s i s c o n s i s t s of seven chapters i n c l u d i n g t h i s i n t r o d u c t o r y c hapter. Chapter 2 examines s o c i a l housing p o l i c y as a t o o l f o r r e d i s t r i b u t i n g income and t r a c e s the e v o l u t i o n of s o c i a l housing programs i n Canada and the Northwest T e r r i t o r i e s . Chapter 3 i n t r o d u c e s the economic framework f o r a n a l y s i n g housing p o l i c y . Chapter 4 examines the i s s u e s that a r i s e i n a p p l y i n g t h i s framework to s u b s i d i z e d housing programs and reviews s e v e r a l s t u d i e s appearing i n the recent l i t e r a t u r e . Chapter 5 d e s c r i b e s the 5 p u b l i c housing p r o j e c t s i n Y e l l o w k n i f e forming the sample for the study. I t a l s o s e t s out the four hypotheses and o u t l i n e s the study methodology. Chapter 6 p r e s e n t s the r e s u l t s of the a n a l y s i s and Chapter 7 concludes the t h e s i s by suggesting p o s s i b l e i m p l i c a t i o n s of the a n a l y s i s f o r policy-makers. 6 CHAPTER 2 SOCIAL HOUSING POLICY 2. SOCIAL HOUSING POLICY T h i s chapter focuses on s o c i a l housing p o l i c y as a t o o l f o r income r e d i s t r i b u t i o n . I t examines the three methods governments use to r e d i s t r i b u t e income: d i r e c t cash t r a n s f e r s , p r i c e s u b s i d i e s and i n - k i n d t r a n s f e r s . F i n a l l y , i t reviews s o c i a l housing p o l i c y i n Canada and the Northwest T e r r i t o r i e s . 2.1 INTRODUCTION Housing i s a m u l t i - f a c e t e d good. F i r s t and foremost, i t i s a b a s i c n e c e s s i t y of l i f e . I t i s a l s o a market commodity and an investment good r e p r e s e n t i n g the l a r g e s t s i n g l e investment made by Canadian f a m i l i e s ( F u l t o n , 1981). Furthermore, i t i s an important i n d u s t r y , a c c o u n t i n g f o r approximately 4% of the Gross N a t i o n a l Expenditure i n 1985 (N a t i o n a l Income and Expenditure Accounts, 1985). The m u l t i - d i m e n s i o n a l nature of housing r e s u l t s i n gr e a t e r government i n t e r v e n t i o n i n the market than would be expected i f housing were simply a market commodity. The government achieves a v a r i e t y of p u b l i c p o l i c y g o a l s through housing p o l i c y . Housing programs are designed to f a c i l i t a t e homeownership, to s t i m u l a t e the economy and to make housing more a f f o r d a b l e . T h i s study focuses on housing as a b a s i c need and the s o c i a l housing p o l i c y designed t o make housing more a f f o r d a b l e . 7 8 2.2 SOCIAL HOUSING POLICY AS A TOOL FOR INCOME  REDISTRIBUTION The f a c t that housing i s a b a s i c need does not a u t o m a t i c a l l y imply that the government should i n t e r v e n e i n the housing market. I n t e r v e n t i o n i s only necessary because some households have inadequate incomes to o b t a i n decent, uncrowded accommodation. As i n d i c a t e d i n Chapter 1, over 700,000 households i n Canada f a l l i n t o t h i s c a t e gory. P u b l i c p o l i c y to a s s i s t these households takes the form of income r e d i s t r i b u t i o n . Governments can r e d i s t r i b u t e income i n one of three ways: d i r e c t cash t r a n s f e r s (e.g., income supplements), p r i c e s u b s i d i e s (e.g., s h e l t e r allowances) or i n - k i n d t r a n s f e r s (e.g., p u b l i c housing programs). Each a l t e r n a t i v e has a d i f f e r e n t impact on the household's budget set and, consequently, a d i f f e r e n t e f f e c t on household behavior. In a program of d i r e c t cash t r a n s f e r s , the household's budget c o n s t r a i n t s h i f t s out by an amount equal to the cash gran t . T h i s i s i l l u s t r a t e d i n F i g u r e 1. Housing (h) i s on the h o r i z o n t a l a x i s and a composite commodity ( x ) , r e p r e s e n t i n g a l l other goods, i s on the v e r t i c a l a x i s . In the absence of the program, the household maximizes u t i l i t y by consuming that combination of h and x that c o i n c i d e s with the tangency p o i n t of an i n d i f f e r e n c e curve and the budget c o n s t r a i n t ( i . e . , ( h 1 , x^) i n t h i s c a s e ) . With a d i r e c t cash t r a n s f e r of G d o l l a r s , the budget c o n s t r a i n t s h i f t s out by a v e r t i c a l d i s t a n c e of G, i n c r e a s i n g the household budget 9 (Y+G)/Px \ U2 Y/Px x2 xi hi h.2 Y/Ph (Y+G)/Ph h 1 D i r e c t Cash T r a n s f e r space. The i n c r e a s e d income a l l o w s the household to reach a h i g h e r l e v e l of u t i l i t y 0 * 2 , where i t consumes commodity bundle (b^, x 2 ) . A p r i c e - s u b s i d y program i n v o l v e s a d i r e c t payment to the household to reduce monthly r e n t . The s u b s i d y a l t e r s the p r i c e r a t i o of h o u s i n g and o t h e r goods, r o t a t i n g the household budget c o n s t r a i n t upward as i n d i c a t e d i n F i g u r e 2 . The household i n c r e a s e s i t s consumption from ( h 1 , x ^ to ( h 2 , x 2 ) . An i n - k i n d t r a n s f e r program a s s i g n s a s p e c i f i c housing u n i t t o the household a t a s u b s i d i z e d r e n t (e.g. r e n t as a per c e n t a g e of income). As t h i s r e n t i s lower than the market p r i c e , the p r i c e r a t i o s f a c i n g the household change, but, as O l s e n and Barton (1983) p o i n t out, the budget c o n s t r a i n t does not r o t a t e outward. I n s t e a d , an i n - k i n d h o u s i n g program 10 V/Px h i Y / P h h2 V / P h ( 1 - s ) 2 P r i c e S u b s i d y Program adds one p o i n t to the budget s e t . T h i s i s i l l u s t r a t e d i n F i g u r e 3 where h 2 r e p r e s e n t s the s p e c i f i c q u a n t i t y of h o u s i n g p r o v i d e d by the program and ( h 2 , x 2 ) i s the p o i n t added to the household budget s e t . The household i s c o n s t r a i n e d t o consume t h i s commodity bundle even though i t may not c o i n c i d e w i t h the tangency p o i n t of the budget c o n s t r a i n t and an i n d i f f e r e n c e c u r v e . In t h i s c a s e , the t r a d e o f f between housing and o t h e r goods w i l l not be o p t i m a l . The s u b - 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 r e s u l t i n g from an i n - k i n d h ousing program g e n e r a l l y l e a d s economists to support d i r e c t cash t r a n s f e r s . U2 h i V/Po h2 h 3 In-Kind Housing Program 2.3 SOCIAL HOUSING POLICY IN CANADA In Canada, the r e s p o n s i b i l i t y for housing i s di v i d e d between the fed e r a l and p r o v i n c i a l governments. The Cons t i t u t i o n Act of 1982 confirms the d i v i s i o n of powers o r i g i n a l l y established in the B r i t i s h North America Act. The federal government i s responsible for economic a c t i v i t i e s at the n a t i o n a l l e v e l , including the regulation of the money supply, banking and i n t e r e s t rates. P r o v i n c i a l governments are responsible for municipal i n s t i t u t i o n s , property r i g h t s and public lands and natural resources (Goldberg and Mark, 1983). While the federal government influences the housing market through i t s f i s c a l and monetary powers, any d i r e c t involvement in the d e l i v e r y of housing programs must be in partnership with the provinces. 1 2 E a r l y housing l e g i s l a t i o n was c a r e f u l l y s t r u c t u r e d to f i t w i t h i n the f e d e r a l mandate to r e g u l a t e and s t i m u l a t e the economy. Both the Dominion Housing Act of 1935 and the f i r s t N a t i o n a l Housing Act (N.H.A.) of 1938 were designed to st i m u l a t e the demand f o r homeownership. Except f o r the p r o v i s i o n of mortgage money, the government d i d not i n t e r f e r e with the a l l o c a t i o n of housing res o u r c e s p r o v i d e d by the p r i v a t e s e c t o r . In 1949, amendments to the N.H.A. a u t h o r i z e d the f e d e r a l government, through C.M.H.C., to enter i n t o p a r t n e r s h i p agreements with the p r o v i n c e s to pro v i d e low income housing. Under S e c t i o n 35 (now S e c t i o n 40), the c a p i t a l and o p e r a t i n g c o s t s of the p r o j e c t s were shared on a 75/25 b a s i s , with C.M.H.C. c o n t r i b u t i n g 75%. While the 1949 amendments were a major st e p forward i n the development of an i n - k i n d housing p o l i c y , i t was not u n t i l the N.H.A was amended i n 1964 that a cohesive p u b l i c housing p o l i c y emerged. The 1964 amendments b a s i c a l l y re-wrote the s o c i a l housing p r o v i s i o n s of the N.H.A. and intr o d u c e d the phrase " p u b l i c housing" i n t o the Act for the f i r s t time (Rose, 1980). These amendments a u t h o r i z e d C.M.H.C. to loan money to p r o v i n c i a l governments f o r the c o n s t r u c t i o n of p u b l i c housing p r o j e c t s i n a d d i t i o n to the p a r t n e r s h i p p r o v i s i o n s of S e c t i o n 35. Under t h i s new s e c t i o n ( S e c t i o n 35D, now S e c t i o n 43), 90% loans are a v a i l a b l e at below market i n t e r e s t r a t e s . Operating c o s t s , i n c l u d i n g a m o r t i z a t i o n , are shared e q u a l l y by the two l e v e l s of 13 government. Fu r t h e r amendments to the N.H.A. i n 1969 allowed C.M.H.C. to enter i n t o agreements with the p r o v i n c e s to provide p u b l i c housing through a Rent Supplement Program. Under t h i s program, up to 25% of the u n i t s i n an e x i s t i n g privately-owned b u i l d i n g are desig n a t e d as p u b l i c housing. Rents f o r p u b l i c housing u n i t s are based on income and range from a minimum of $32 per month to a maximum of 25% of adj u s t e d f a m i l y income (see Appendix 3 f o r f u r t h e r d e t a i l s ) . Some p r o v i n c e s and t e r r i t o r i e s have r e v i s e d the f e d e r a l s c a l e and charge higher or lower r e n t s to r e f l e c t r e g i o n a l c o n d i t i o n s . Since 1980, no p u b l i c housing p r o j e c t s have been c o n s t r u c t e d i n southern Canada. Only the Northwest T e r r i t o r i e s and the Yukon continue to c o n s t r u c t new housing under t h i s program. The p e r c e i v e d f a i l u r e of l a r g e s c a l e p u b l i c housing p r o j e c t s i n the p r o v i n c e s has turned a t t e n t i o n to n o n - p r o f i t and c o - o p e r a t i v e housing p r o j e c t s to serve the needs of low income households. 2.4 SOCIAL HOUSING POLICY IN THE NORTHWEST TERRITORIES The f i r s t housing program i n the N.W.T. was the Eskimo Housing Loan Program int r o d u c e d i n 1959 by the Department of Indian A f f a i r s and Northern Development (Thomas and Thompson, 1972). The program was intr o d u c e d t o combat the spread of t u b e r c u l o s i s among the I n u i t but was not s u c c e s s f u l as people were u n f a m i l i a r with concepts of loans 14 or homeownership and had l i t t l e access to cash f o r mortgage payments or u t i l i t y b i l l s . The program was r e p l a c e d i n 1965 by the Eskimo Rental Housing Program which p r o v i d e d low cos t s h e l t e r f o r monthly re n t s of between $2.00 and $67.00, depending on income and house s i z e (Thompson, 1969). In 1970, the P u b l i c Housing Program was o f f i c i a l l y i n t r o d u c e d i n the N.W.T. with the c o n s t r u c t i o n of housing p r o j e c t s i n Hay Ri v e r , Y e l l o w k n i f e and Inuvik and small s e n i o r c i t i z e n s p r o j e c t s i n s e v e r a l Mackenzie V a l l e y communities. The p r o j e c t s were f i n a n c e d under S e c t i o n 40 of the N.H.A. and were j o i n t l y funded by C.M.H.C. (75%), the Government of the N.W.T. (15%) and the m u n i c i p a l i t i e s (10%). The P u b l i c Housing Program i n the N.W.T. i s i d e n t i c a l to i t s southern c o u n t e r p a r t s w i t h one major e x c e p t i o n - the r e n t a l s c a l e . In r e c o g n i t i t o n of the high c o s t of l i v i n g i n remote, northern communities, the Housing C o r p o r a t i o n has designed a r e n t a l s c a l e that takes i n t o account the co s t of l i v i n g . D e t a i l s of the s c a l e are con t a i n e d i n Appendix 3. CHAPTER 3 THE ANALYSIS OF HOUSING POLICY 3. THE ANALYSIS OF HOUSING POLICY T h i s chapter d e s c r i b e s the economic framework for a n a l y s i n g housing p o l i c y . I t i n t r o d u c e s the key concepts of economic e f f i c i e n c y and e q u i t y which form the b u i l d i n g blocks of the a n a l y s i s and d e s c r i b e s how these c r i t e r i a are measured. 3. 1 INTRODUCTION The economic e v a l u a t i o n of p u b l i c p o l i c y f a l l s i n t o the area of welfare economics. Boadway and Bruce (1984) d e f i n e welfare economics as a means of ranking " a l t e r n a t i v e p o s s i b l e s t a t e s of the world" where the term " s t a t e of the world" d e s c r i b e s the a l l o c a t i o n and d i s t r i b u t i o n of r e s o u r c e s . The t o o l s of welfare economics measure the change in s o c i a l welfare i n moving from one s t a t e of the world to another. Using these t o o l s , a p o l i c y i s e v a l u a t e d by the change i n s o c i a l w e l f a r e i t produces. In order to rank a l t e r n a t i v e s t a t e s of the world, some value judgements must be made. In welfare economics, the concepts of e f f i c i e n c y and e q u i t y are used. A s t a t e of the world i s e f f i c i e n t i f i t meets the c r i t e r i o n of P a r e t o - e f f i c i e n c y . A P a r e t o - e f f i c i e n t a l l o c a t i o n i s one i n which " i t i s i m p o s s i b l e , through any change i n resource a l l o c a t i o n , to make some person or persons b e t t e r o f f without making someone e l s e worse o f f " (Browning and Browning, 1983). 16 17 The concept of P a r e t o - e f f i c i e n c y p r o v i d e s a c r i t e r i o n f o r comparing e f f i c i e n t a l l o c a t i o n s to i n e f f i c i e n t ones but i t does not permit a comparison of e f f i c i e n t a l l o c a t i o n s to each other. In order t o rank a l l p o s s i b l e s t a t e s of the world, i t i s necessary to compare household u t i l i t y l e v e l s under each a l l o c a t i o n of re s o u r c e s . In theory, t h i s i s accomplished by i n t r o d u c i n g a s o c i a l w e l f a r e f u n c t i o n to represent s o c i e t y ' s v a l u e s . However, i n p r a c t i c e i t i s d i f f i c u l t to s p e c i f y a s o c i a l welfare f u n c t i o n . As an a l t e r n a t i v e , w e l f a r e economics uses the two concepts of h o r i z o n t a l and v e r t i c a l e q u i t y . A p o l i c y promotes h o r i z o n t a l e q u i t y i f i t " t r e a t s equals e q u a l l y " . That i s , i f i t pro v i d e s e q u i v a l e n t b e n e f i t s to households with i d e n t i c a l c h a r a c t e r i s t i c s . A p o l i c y promotes v e r t i c a l e q u i t y i f i t " t r e a t s unequals unequally". That i s , i f i t pr o v i d e s d i f f e r e n t b e n e f i t s to households with d i f f e r e n t c h a r a c t e r i s t i c s . A p o l i c y p r o v i d i n g g r e a t e r b e n e f i t s to households with lower incomes promotes v e r t i c a l e q u i t y . The c r i t e r i a of h o r i z o n t a l and v e r t i c a l e q u i t y do not permit a complete ranking of s t a t e s of the world, but they are u s e f u l as they are widely accepted and r e l a t i v e l y simple to apply. 3.2 GOVERNMENT INTERVENTION IN THE HOUSING MARKET The economic e v a l u a t i o n of any government program begins from the premise that government i n t e r v e n t i o n i n the market must be j u s t i f i e d . L e g i t i m a t e grounds f o r 18 i n t e r v e n t i o n g e n e r a l l y r e l a t e to (1) market f a i l u r e , (2) r e d i s t r i b u t i o n of income and (3) s t a b i l i z a t i o n of the economy. Market f a i l u r e a r i s e s when a market i s not p e r f e c t l y c o m p e t i t i v e . A p e r f e c t l y c o m p e t i t i v e market has the f o l l o w i n g c h a r a c t e r i s t i c s : 1. a l l economic agents have p e r f e c t i n f o r m a t i o n ; 2. t h e r e are no monopolies or i n c r e a s i n g r e t u r n s to s c a l e ; and 3. markets are u n i v e r s a l ( i . e . , no p u b l i c goods or e x t e r n a l i t i e s and no t r a n s a c t i o n c o s t s ) . By the F i r s t Theorem of Welfare Economics, a p e r f e c t l y c o m p e t i t i v e market produces a P a r e t o - e f f i c i e n t a l l o c a t i o n of re s o u r c e s . Government i n t e r v e n t i o n i s not j u s t i f i e d as i t w i l l not i n c r e a s e the welf a r e of one person without making someone e l s e worse o f f . However, i f any one of these c o n d i t i o n s i s v i o l a t e d , government i n t e r v e n t i o n i s j u s t i f i e d i f i t can b r i n g about a Pareto-improvement. A second reason f o r government i n t e r v e n t i o n r e l a t e s to the d i s t r i b u t i o n of income. The p a t t e r n of income d i s t r i b u t i o n i n a market economy depends upon ownership of the f a c t o r s of p r o d u c t i o n and does not n e c e s s a r i l y r e f l e c t s o c i e t y ' s p r e f e r e n c e s . Government i n t e r v e n t i o n may be j u s t i f i e d t o change the income d i s t r i b u t i o n t o correspond to s o c i e t y ' s s o c i a l w e l f a r e f u n c t i o n . Governments may a l s o i n t e r v e n e i n the market to s t a b i l i z e the economy. A market economy does not 19 a u t o m a t i c a l l y guarantee f u l l employment and p r i c e s t a b i l i t y . Government p o l i c y may be r e q u i r e d to p r o t e c t the economy from s u s t a i n e d p e r i o d s of unemployment, s t a g n a t i o n and i n f l a t i o n . In Canada, government i n t e r v e n t i o n i n the housing market has been defended on the b a s i s of a l l three c r i t e r i a . Mortgage insurance programs have been designed to c o r r e c t market f a i l u r e , s o c i a l housing programs to r e d i s t r i b u t e incomes and employment programs such as the Canadian Home Ownership S t i m u l a t i o n Program t o s t a b i l i z e the economy. The a b i l i t y of housing p o l i c y to achieve these v a r i e d o b j e c t i v e s stems from the m u l t i - f a c e t e d nature of housing. 3.3 MEASURING WELFARE GAIN The a p p r o p r i a t e c r i t e r i o n f o r e v a l u a t i n g p u b l i c p o l i c y i s the change i n s o c i a l w e l f a r e i t produces. The t r a d i t i o n a l method f o r measuring w e l f a r e change i s c o s t - b e n e f i t a n a l y s i s . The a n a l y s i s proceeds i n two s t e p s . The f i r s t s t e p measures i n p u t s and outputs, v a l u i n g inputs at t h e i r s o c i a l o p p o r t u n i t y cost and outputs by the b e n e f i t s they produce for s o c i e t y . The second s t e p c a l c u l a t e s net present value (NPV) by aggregat i n g expected c o s t s and b e n e f i t s over the l i f e of the p r o j e c t and d i s c o u n t i n g them at the s o c i a l d i s c o u n t r a t e . The s i g n and magnitude of the NPV i n d i c a t e the net ga i n (or l o s s ) produced by the p o l i c y . 20 3.3.1 MEASURING BENEFITS - THE DEMAND SIDE B e n e f i t s from a housing p o l i c y may be t a n g i b l e or i n t a n g i b l e . While t a n g i b l e b e n e f i t s may be i n f e r r e d from the market, i n t a n g i b l e b e n e f i t s are more d i f f i c u l t to measure. Pearce (1971) suggests three approaches: su r v e y i n g households to determine "surrogate v a l u e s " of the b e n e f i t -that i s , the p r i c e they would be w i l l i n g t o pay i f there were a market f o r the i n t a n g i b l e good; i n f e r r i n g p r i c e s from consumer behavior; or using a r e s i d u a l approach. In the r e s i d u a l approach, measurable b e n e f i t s are estimated and s u b t r a c t e d from c o s t s and the decision-maker then determines i f i n t a n g i b l e b e n e f i t s can account f o r the d i f f e r e n c e . B e n e f i t s may a l s o be c l a s s i f i e d as d i r e c t or i n d i r e c t or, e q u i v a l e n t l y , as tenant b e n e f i t s and non-tenant benef i t s . Non-tenant b e n e f i t s Non-tenant b e n e f i t s may occur in s e v e r a l ways. If the housing c o n d i t i o n s of poor households enter i n t o the u t i l i t y f u n c t i o n s of other members of s o c i e t y , the p r o v i s i o n of s u b s i d i z e d housing not only i n c r e a s e s the u t i l i t y of program p a r t i c i p a n t s , i t a l s o adds to the u t i l i t y of n o n - p a r t i c i p a n t s . Non-tenant b e n e f i t s from s u b s i d i z e d housing may a l s o a r i s e i f low-cost housing i s a "merit good". Musgrave & Musgrave (1984) d e f i n e merit goods as goods which s o c i e t y , as d i s t i n c t from i n d i v i d u a l consumers, wishes to encourage. 21 If housing i s a merit good, then s o c i e t y i s b e t t e r o f f when the housing c o n d i t i o n s of people l i v i n g i n sub-standard housing improve. An a l t e r n a t i v e j u s t i f i c a t i o n f o r s u b s i d i z e d housing i s suggested by Tobin's theory of commodity e g a l i t a r i a n i s m (Tobin, 1970). While Tobin argues t h a t , i n most cases, the unequal d i s t r i b u t i o n of commodities can and should be r e c t i f i e d through income r e d i s t r i b u t i o n p o l i c i e s , he suggests there may be grounds f o r e n s u r i n g a " s p e c i f i c e g a l i t a r i a n " d i s t r i b u t i o n of some commodities. He p o i n t s out that " [ t ] h e s o c i a l conscience i s more offended by severe i n e q u a l i t y i n n u t r i t i o n and b a s i c s h e l t e r , or i n access to medical care or to l e g a l a s s i s t a n c e , than by i n e q u a l i t y i n automobiles, books, c l o t h e s , f u r n i t u r e , boats." (Tobin, 1970, p. 265). Tobin i d e n t i f i e s two s i t u a t i o n s c a l l i n g f o r s p e c i f i c e g a l i t a r i a n i s m : the f i r s t i s f o r those e s s e n t i a l s of l i f e t h a t are i n i n e l a s t i c supply (e.g., consumption goods d u r i n g wartime) and the second i s f o r merit goods. Tobin suggests food and housing may f a l l i n t o the second category. However, housing i s p a r t i c u l a r l y p r o b l e m a t i c a l f o r Tobin and, while he concludes that the f r e e o p e r a t i o n of the market, as p r e s e n t l y o r g a n i z e d , i s not o p t i m a l , he sees l i t t l e " c o n v i n c i n g j u s t i f i c a t i o n " i n the long run f o r commodity e g a l i t a r i a n i s m i n housing. Non-tenant b e n e f i t s from s u b s i d i z e d housing may a l s o a r i s e i f there are e x t e r n a l i t i e s a s s o c i a t e d with the program. I f p u b l i c housing p r o j e c t s improve the h e a l t h and 22 s a f e t y c o n d i t i o n s of the neighbourhood, the w e l f a r e of n o n - p a r t i c i p a n t s i n the neighbourhood i n c r e a s e s . Weicher (1979) c a t e g o r i z e s e x t e r n a l i t i e s from s u b s i d i z e d housing i n t o two groups: (1) e x t e r n a l i t i e s having an e f f e c t on p r o p e r t y values and (2) e x t e r n a l i t i e s due to reducing the " s o c i a l " c o s t s of slums. (1) Property V a l u e s . I t seems reasonable to suggest t h a t improved housing leads to improved neighbourhoods. In f a c t , F i s h e r (1959) r e p o r t s that one j u s t i f i c a t i o n f o r i n t r o d u c i n g the P u b l i c Housing Program i n the U n i t e d S t a t e s was the b e l i e f t h a t the program would i n c r e a s e the value of the surrounding housing. T h i s hypothesis has been t e s t e d in s e v e r a l recent s t u d i e s . In a study of the Chicago housing market, F e r r e r a (1969) f i n d s p r i c e i n c r e a s e s f o r p r o p e r t i e s l o c a t e d w i t h i n one block of one p u b l i c housing p r o j e c t i n h i s sample. However, p r o p e r t i e s adjacent to other housing p r o j e c t s i n the sample showed no i n c r e a s e s . In a s i m i l a r study i n New York C i t y , DeSalvo (1974) f i n d s average annual i n c r e a s e s of approximately 5% i n the assessed v a l u e s of p r o p e r t i e s adjacent to p r o j e c t s b u i l t under the Mitchell-Lama program. 1 A t h i r d study by Rabiega, L i n and Robinson (1984) of small p u b l i c housing p r o j e c t s i n P o r t l a n d , Oregon f i n d s i n c r e a s e s of between $400 and $2,400 i n s a l e s p r i c e s of surrounding p r o p e r t i e s . 1 The Mitchell-Lama Housing Program i s designed to f a c i l i t a t e the c o n s t r u c t i o n or r e h a b i l i t a t i o n of c o - o p e r a t i v e or r e n t a l housing f o r middle income f a m i l i e s . 23 Weicher (1979) argues a g a i n s t the r e s u l t s o b tained by F e r r e r a and DeSalvo. He suggests that the p r i c e i n c r e a s e s found by F e r r e r a were due to a zoning change and those found by DeSalvo were based on assessed values and do not n e c e s s a r i l y r e f l e c t a " t r u e " i n c r e a s e i n v a l u e . He concludes that there i s no stong evidence that e x t e r n a l i t i e s e x i s t . The study by Rabiega, L i n and Robinson (1984) appears to be an e x c e p t i o n to Weicher's c l a i m . T h i s may be due to the small s c a l e of p u b l i c housing p r o j e c t s c o n s t r u c t e d i n P o r t l a n d ( i . e . , small by n a t i o n a l standards) as the s i x p r o j e c t s under study range i n s i z e from 18 u n i t s to 118 u n i t s . A l t e r n a t i v e l y , i t c o u l d be due to the r a c i a l composition of the program r e c i p i e n t s . As the authors p o i n t out, most of the c l i e n t s f o r p u b l i c housing i n P o r t l a n d are white, suggesting the phenomenon of "white f l i g h t " sometimes a s s o c i a t e d with p u b l i c housing p r o j e c t s i n the U.S. should not be s i g n i f i c a n t . (2) " S o c i a l " Costs of Slums. T h i s term, c o i n e d by Rothenberg (1967), encompases a wide range of u n d e s i r a b l e s o c i a l e f f e c t s of slums. These i n c l u d e high crime and delinquency r a t e s , poor h e a l t h and s a f e t y c o n d i t i o n s and p s y c h o l o g i c a l problems r e s u l t i n g from a poor l i v i n g environment. Economists have conducted very l i t t l e r e s e a r c h i n t h i s area due to the d i f f i c u l t y of e m p i r i c a l l y t e s t i n g the h y p o t h e s i s . Weicher (1979) summarizes the c u r r e n t t h i n k i n g as f o l l o w s : Thus, Rothenberg s t r e s s e d the d i f f i c u l t y of e m p i r i c a l work, arguing that r e s e a r c h so f a r does 24 not show that e x t e r n a l i t i e s do not e x i s t , Aaron concluded that i t has not been shown that they do e x i s t , and M i l l s s t a t e d t h a t , "Undoubtedly, the important causes of these problems . . . [ s o c i a l c o s t s ] are poverty, r a c i a l c o n f l i c t , e t c . none of which represent housing market f a i l u r e s . " (Weicher, 1979, p. 492) Tenant b e n e f i t s Tenant b e n e f i t s accrue to program r e c i p i e n t s and are equal to the sum of the p r o j e c t rent ( i . e . , rent p a i d by the tenants) and the welfare gain enjoyed by the tenants from the program. Welfare gain i s measured by one of two money me t r i c s - the Compensation V a r i a t i o n (CV) or the E q u i v a l e n t V a r i a t i o n (EV). These two measures are d e f i n e d as f o l l o w s : CV - the amount of money that a household would r e q u i r e ( f o r f e i t ) to o f f s e t the l o s s (gain) i n u t i l i t y r e c e i v e d from the program - i . e . , to r e t u r n i t to i t s o r i g i n a l u t i l i t y l e v e l given the new p r i c e r a t i o s . EV - the amount of money that the household would r e q u i r e ( f o r f e i t ) t o make i t as w e l l o f f without the program as with i t - i . e . , to keep i t at i t s new u t i l i t y l e v e l given the o l d p r i c e r a t i o s . F i g u r e s 4 and 5 i l l u s t r a t e CV and EV i n a u t i l i t y schedule framework. Housing (h) i s measured along the h o r i z o n t a l a x i s and other goods (x) along the v e r t i c a l a x i s . The p r i c e of x i s normalized to 1, a l l o w i n g income (Y) to be read o f f the v e r t i c a l a x i s . In the absence of a s u b s i d i z e d housing program, the household purchases h Q u n i t s of housing and X Q u n i t s of other goods. With a s u b s i d i z e d housing program (with no q u a n t i t y c o n s t r a i n t ) the p r i c e of housing reduces to p 1 , the budget c o n s t r a i n t r o t a t e s outward and the household moves up to i n d i f f e r e n c e curve U 1, consuming commodity bundle X 4 Compensation V a r i a t i o n Measure X 5 E q u i v a l e n t V a r i a t i o n Measure ( h 1 , x ^ . CV i s the amount.of income t h a t the household c o u l d g i v e up at the new p r i c e l e v e l and s t i l l enjoy the 26 o r i g i n a l l e v e l of u t i l i t y ( U Q ) . I t equals Y - Y' i n F i g u r e 4. EV i s the a d d i t i o n a l income r e q u i r e d f o r the household to remain on U 1 at the o r i g i n a l p r i c e s . I t equals Y' - Y i n F i g u r e 5. The d i f f e r e n c e between CV and EV can a l s o be expressed i n terms of the expenditure f u n c t i o n [e(p,u)] as f o l l o w s : CV = Y 1 - e ( P l , u o ) EV = e ( p Q , u 1 ) - Y Q where Y Q r p Q and u Q are the o r i g i n a l income, p r i c e and u t i l i t y l e v e l s and Y 1, p 1 and are the income, p r i c e and u t i l i t y l e v e l s with the program. The expenditure f u n c t i o n d e s c r i b e s the minimum amount of expenditure r e q u i r e d to a t t a i n a given l e v e l of u t i l i t y at a given p r i c e l e v e l . Since EV uses o r i g i n a l p r i c e s , i t may be s u p e r i o r to CV. The CV measure produces ambiguous r e s u l t s i n comparing a l t e r n a t e p r o j e c t s as i t uses the p r i c e l e v e l of each p r o j e c t as the base. As the base d i f f e r s f o r d i f f e r e n t p r o j e c t s , the measures of CV are not d i r e c t l y comparable. EV can a l s o be d e r i v e d i n a demand framework as i l l u s t r a t e d i n F i g u r e 6. DD i s the compensated ( H i c k s i a n ) demand f o r housing. EV i s the i n c r e a s e i n consumer's s u r p l u s r e s u l t i n g from the p r i c e subsidy - i n t h i s case, area abed. T h i s area equals Y' - Y i n F i g u r e 5. 3.3.2 MEASURING COSTS - THE SUPPLY SIDE Most government p r o j e c t s i n c u r t a n g i b l e and i n t a n g i b l e c o s t s . I n t a n g i b l e c o s t s are d i f f i c u l t to measure and i n c l u d e any c o s t s due to the stigma of l i v i n g i n a s u b s i d i z e d 27 ho h i Quantity 6 Measuring EV i n a Demand Framework hou s i n g p r o j e c t or the p e r c e i v e d (or r e a l ) d e t e r i o r a t i o n of a neighbourhood due t o the p r o j e c t . T a n g i b l e c o s t s r e l a t e t o the l a n d , l a b o u r and c a p i t a l r e s o u r c e s used t o produce the p r o j e c t and are measured by o p p o r t u n i t y c o s t . O p p o r t u n i t y c o s t i s the v a l u e of the goods and s e r v i c e s foregone by s o c i e t y as a r e s u l t of u n d e r t a k i n g the p r o j e c t . I f a l l i n p u t markets a r e p e r f e c t l y c o m p e t i t i v e , i f the economy i s at f u l l employment and i f the government produces the output as e f f i c i e n t l y as the p r i v a t e s e c t o r , o p p o r t u n i t y c o s t s and market p r i c e s are e q u a l . However, i f any of these c o n d i t i o n s does not h o l d , market p r i c e s w i l l not r e f l e c t t r u e o p p o r t u n i t y c o s t s . 28 3.3.3 THE SOCIAL DISCOUNT RATE The b e n e f i t s and c o s t s of s u b s i d i z e d housing are spread over the l i f e of the p r o j e c t . As s o c i e t y i s not i n d i f f e r e n t between b e n e f i t s r e c e i v e d today and b e n e f i t s r e c e i v e d in the f u t u r e , the net b e n e f i t stream from the p r o j e c t must be d i s c o u n t e d at the s o c i a l d i s c o u n t r a t e . Two i n t e r p r e t a t i o n s of the s o c i a l d i s c o u n t r a t e appear i n the l i t e r a t u r e . Some economists, f o l l o w i n g Harberger (1972), b e l i e v e the r a t e should represent s o c i e t y ' s time p r e f e r e n c e s ( i . e . , the r a t e at which s o c i e t y i s w i l l i n g to s u b s t i t u t e present f o r f u t u r e consumption). Others, f o l l o w i n g F e l d s t e i n (1972) and M a r g l i n (1963), b e l i e v e i t should r e f l e c t the o p p o r t u n i t y c o s t of government funds. These two i n t e r p r e t a t i o n s r e s u l t i n d i f f e r e n t e stimates of the s o c i a l d i s c o u n t r a t e , with the former view producing a lower r a t e (Treasury Board, 1976). Recent l i t e r a t u r e has attempted to i n t e g r a t e the two approaches with most economists agreeing that the NPV of p u b l i c p r o j e c t s depends upon both the o p p o r t u n i t y c o s t of government funds and s o c i e t y ' s r a t e of time p r e f e r e n c e . CHAPTER 4 LITERATURE REVIEW 4. LITERATURE REVIEW The recent economics l i t e r a t u r e c o n t a i n s s e v e r a l s t u d i e s of s u b s i d i z e d housing programs i n North America and Europe. A l l s t u d i e s use the welfare economics framework to eval u a t e the program although the e s t i m a t i o n techniques and approach d i f f e r s l i g h t l y . T h i s chapter reviews the recent l i t e r a t u r e and examines the i s s u e s i n v o l v e d i n a p p l y i n g the welfare economics framework to housing p o l i c y . 4.1 ASSUMPTIONS A l l s t u d i e s assume a two good economy c o n s i s t i n g of housing and a composite commodity r e p r e s e n t i n g a l l other goods. F o l l o w i n g Muth (1960), the consumption of housing i s measured i n u n i t s of housing s e r v i c e s . T h i s concept i s u s e f u l as i t reduces the household's consumption d e c i s i o n to the t r a d i t i o n a l u t i l i t y maximization problem. The household s e l e c t s i t s commodity bundle of housing and other goods to maximize u t i l i t y s u b j e c t to i t s budget c o n s t r a i n t . Housing markets are assumed to be p e r f e c t l y c o m p e t i t i v e , r u l i n g out market f a i l u r e caused by monopoly power, e x t e r n a l i t i e s or imperfect i n f o r m a t i o n . T h i s assumption ensures market p r i c e s represent e q u i l i b r i u m l e v e l s . The long-run supply curve f o r housing i s assumed to be p e r f e c t l y e l a s t i c , i m p l y i n g a constant c o s t housing i n d u s t r y . T h i s assumption i s g e n e r a l l y supported by e m p i r i c a l f i n d i n g s (e.g., Muth, 1960). 30 31 A l l s t u d i e s assume the housing program has no e f f e c t on the p r i c e of non-subsidized housing or other goods. T h i s i s v a l i d p r o v i d i n g the amount of s u b s i d i z e d housing represents a small percentage of the housing stock i n the study area. F u r t h e r assumptions i n c l u d e p e r f e c t s u b s t i t u t a b i l i t y of s u b s i d i z e d and non-subsidized housing; exogenous deter m i n a t i o n of household income and market e q u i l i b r i u m . 4.2 METHODOLOGY A l l s t u d i e s estimate welf a r e gain using the EV measure. Some s t u d i e s measure EV w i t h i n a u t i l i t y schedule framework, while others use the demand framework. To measure EV using u t i l i t y f u n c t i o n s , c e r t a i n assumptions are made about the form of household p r e f e r e n c e s . DeSalvo (1975) assumes pr e f e r e n c e s can be represented by a Cobb-Douglas u t i l i t y f u n c t i o n . The Cobb-Douglas f u n c t i o n i m p l i e s u n i t a r y p r i c e and income e l a s t i c i t i e s f o r housing and other goods and a u n i t a r y e l a s t i c i t y of s u b s t i t u t i o n . Aaron and von Furstenberg (1971), Murray (1975) and P i g g o t t (1984) q u e s t i o n the assumption of u n i t a r y e l a s t i c i t i e s and recommend a l e s s r i g i d u t i l i t y f u n c t i o n such as the CES (Constant E l a s t i c i t y of S u b s t i t u t i o n ) or the g e n e r a l i z e d CES. While the CES imposes u n i t a r y income e l a s t i c i t y , no r e s t r i c t i o n s are imposed on p r i c e e l a s t i c i t y or the e l a s t i c i t y of s u b s t i t u t i o n . The g e n e r a l i z e d CES allows f l e x i b i l i t y f o r a l l three e l a s t i c i t i e s . 32 Murray (1975) f i n d s the Cobb-Douglas u t i l i t y f u n c t i o n p r o v i d e s d i s t o r t e d r e s u l t s f o r e s t i m a t i n g the d i s t r i b u t i o n of program b e n e f i t s although i t pr o v i d e s s i m i l a r r e s u l t s to the CES f u n c t i o n f o r e s t i m a t i n g average b e n e f i t s . The mean b e n e f i t estimates f o r the sample h a r d l y d i f f e r from one s p e c i f i c a t i o n to the oth e r , but examination of the f a m i l y composition means shows c o n s i d e r a b l y g r e a t e r d i s c r e p a n c i e s . T h i s suggests the Cobb-Douglas may be u s e f u l f o r computing aggregate b e n e f i t s but should be used with c a u t i o n i f o n l y one u t i l i t y f u n c t i o n i s to be es t i m a t e d . Our r e s u l t s should a l s o serve to make r e s e a r c h e r s c a u t i o u s i n e s t i m a t i n g the d i s t r i b u t i o n of b e n e f i t s with the Cobb-Douglas s p e c i f i c a t i o n . . . Since s t r u c t u r a l c h a r a c t e r i s t i c s such as the c o r r e l a t i o n s of income or age with b e n e f i t s are of s u b s t a n t i v e i n t e r e s t to p o l i c y makers, we encourage the use of f u n c t i o n a l forms l e s s r e s t r i c t i v e than the Cobb-Douglas. (Murray, p. 787) U n f o r t u n a t e l y , as Murray notes, the CES f u n c t i o n presents some disadvantages f o r r e s e a r c h e r s as i t r e q u i r e s o b s e r v a t i o n s on p r i c e s and q u a n t i t i e s . The Cobb-Douglas f u n c t i o n , on the other hand, has onl y one parameter (0, the tenant's rent-to-income r a t i o ) and i t can be estimated from data on budget shares and income. A second disadvantage of the g e n e r a l i z e d CES f u n c t i o n i s that i t r e q u i r e s an i t e r a t i v e r e g r e s s i o n program to estimate EV to the d e s i r e d degree of accuracy. The Cobb-Douglas f u n c t i o n , on the other hand, y i e l d s an e x p l i c i t formula f o r the c a l c u l a t i o n of EV. The ease of e s t i m a t i o n of EV per m i t t e d by the Cobb-Douglas f u n c t i o n makes i t h i g h l y d e s i r a b l e i n cases where the assumptions of u n i t a r y e l a s t i c i t i e s are t e n a b l e . At the time of DeSalvo's study, most e m p i r i c a l evidence on the demand f o r housing supported u n i t a r y p r i c e and income 33 e l a s t i c i t i e s . In a survey of the l i t e r a t u r e , DeLeeuw (1971) found income e l a s t i c i t y of r e n t a l housing i n the United S t a t e s to be between 0.8 and 1.0 and p r i c e e l a s t i c i t y to be between -0.7 and -1.5. However, recent evidence supports much lower e l a s t i c i t i e s . S t u d i e s by P o l i n s k y (1977), Mayo (1981) and P o l i n s k y and Ellwood (1977) suggest t h a t , i n the aggregate, housing demand i s s l i g h t l y i n e l a s t i c with respect to both p r i c e and income. More s i g n i f i c a n t l y , s t u d i e s at the micro l e v e l suggest that income e l a s t i c i t i e s may be very low fo r an i n d i v i d u a l household. In response to the recent evidence, economists have s e l e c t e d more f l e x i b i l e u t i l i t y f u n c t i o n s than the Cobb-Douglas. Olsen and Barton (1983), Cronin (1983) and DeBorger (1985) experimented with the Stone-Geary or d i s p l a c e d Cobb-Douglas f u n c t i o n . T h i s f u n c t i o n takes the form: U = (h - h Q ) ^ (x - x Q ) 1 ^ + M where h and x are housing and non-housing; h Q and X q are minimum consumption l e v e l s ; 0 i s the rent-to-income r a t i o ; and M i s the u t i l i t y enjoyed by a household consuming the minimum l e v e l s . The Stone-Geary f u n c t i o n o f f e r s the advantage of f l e x i b l e income and p r i c e e l a s t i c i t i e s . E l a s t i c i t i e s are not r e s t r i c t e d to u n i t y , although they m o n o t o n i c a l l y approach u n i t y as income i n c r e a s e s . T h i s f l e x i b i l i t y , combined with the r e l a t i v e ease of e s t i m a t i n g EV makes the Stone-Geary f u n c t i o n h i g h l y d e s i r a b l e . Other economists choose to estimate EV from demand f u n c t i o n s . A c c o r d i n g to Clemmer (1984), t h i s approach i s 34 s u p e r i o r to the u t i l i t y framework as i t does not impose a p r i o r i assumptions on household p r e f e r e n c e s . However, estimates of p r i c e s and q u a n t i t i e s are necessary, adding to the c o s t of r e s e a r c h . 4.3 RESULTS A l l s t u d i e s conclude the c o s t of the housing program exceeds measurable b e n e f i t s . Estimates of e f f i c i e n c y (EV/Subsidy) range from a low of 25% r e p o r t e d by Sumka and Stegman (1978) i n t h e i r study of p u b l i c housing in non-metropolitan c i t i e s to a high of 85% r e p o r t e d by Walden (1981) in h i s study of s e n i o r c i t i z e n p r o j e c t s (see Table I ) . S u b s t a n t i a l non-tenant b e n e f i t s are r e q u i r e d to j u s t i f y the programs i n terms of economic e f f i c i e n c y . Table I E f f i c i e n c y R e s u l t s Reported i n the L i t e r a t u r e DeBorger (1985) 70% DeSalvo (1975) 55% K r a f t and K r a f t (1979) 67.5% Olsen and Barton (1983) 63% Sumka and Stegman (1978) 25% Walden (1981) 45%/85% NOTE: 1. Walden's study c o n s i s t s of two samples: (1) p u b l i c housing p r o j e c t s f o r middle income groups and (2) p u b l i c housing p r o j e c t s f o r o l d e r people. 2. E f f i c i e n c y i s estimated by the r a t i o of EV t o the subsidy amount. 35 The e q u i t y r e s u l t s are mixed. DeSalvo (1975), K r a f t and K r a f t (1979) and Murray (1975) f i n d b e n e f i t s decrease with income, while DeBorger (1985) f i n d s no s i g n i f i c a n t r e l a t i o n s h i p and Sumka and Stegman (1978) and Olsen and Barton (1983) both f i n d b e n e f i t s t o f i r s t r i s e and then f a l l with i n c r e a s i n g income. Most s t u d i e s f i n d l i t t l e evidence of h o r i z o n t a l e q u i t y . DeSalvo (1975) f i n d s b e n e f i t s are lower for f emale-led households and K r a f t and K r a f t (1979) f i n d b e n e f i t s higher f o r white households. CHAPTER 5 METHODOLOGY AND DATA 5. METHODOLOGY AND DATA T h i s chapter d e s c r i b e s the p u b l i c housing p r o j e c t s i n Y e l l o w k n i f e that form the data base f o r the study. I t s e t s out the four hypotheses and d e s c r i b e s the t e s t i n g p r o c e s s . I t a l s o e x p l a i n s the e s t i m a t i n g techniques used to measure the program c o s t s and b e n e f i t s and to c a l c u l a t e net present v a l u e . 5.1 STUDY AREA AND DATA The C i t y of Y e l l o w k n i f e i s l o c a t e d on the n o r t h shore of Great Slave Lake, over 600 a i r m i l e s from Edmonton. O r i g i n a l l y a remote mining town, the c i t y grew r a p i d l y over the past twenty years to a c u r r e n t p o p u l a t i o n of approximately 10,500 (Bureau of S t a t i s t i c s , unpublished data, 1984). The 1981 Census recorded a t o t a l of 3,185 occupied d w e l l i n g u n i t s i n Y e l l o w k n i f e , of which 2,250 or 71% were r e n t a l and the balance were owner-occupied. Of the 2,250 r e n t a l u n i t s , 179 or 8% are p u b l i c housing. Table II compares the composition of the p u b l i c housing stock to the t o t a l r e n t a l s tock. 37 38 Table II Y e l l o w k n i f e Rental Housinq Stock, 1981 P u b l i c Housinq T o t a l Stock S i n g l e Detached 18 565 Rowhousing 1 24 335 Apartment (5 or more s t o r e y s ) n i l 205 Apartment (under 5 s t o r e y s ) 20 890 Double House n i l 60 Duplex n i l 55 House a t t a c h e d to commercial n i l 5 Movable D w e l l i n g n i l 135 S u b - t o t a l 1 62 Senior C i t i z e n s Home* 1 7 T o t a l 179 2,250 * Senior C i t i z e n s Home i s i n c l u d e d data as "rowhousing" i n census SOURCE: 1. S t a t i s t i c s Canada, 1981 Census. 2. N.W.T. Housing C o r p o r a t i o n , unpublished data. The study excludes households i n s i n g l e detached d w e l l i n g s and r e s i d e n t s of the Senior C i t i z e n s Home. The former are excluded because market re n t s of s i n g l e detached d w e l l i n g s are not a v a i l a b l e . Without t h i s data, i t i s impossible to estimate the market rent e q u i v a l e n t s of the p u b l i c housing u n i t s and imp o s s i b l e to c a l c u l a t e EV. The Senior C i t i z e n s Home i s excluded because there are no comparable u n i t s in the p r i v a t e market. These e x c l u s i o n s 39 reduce the sample s i z e to 144 p u b l i c housing u n i t s . A l l p r o j e c t s are fi n a n c e d through S e c t i o n s 40, 43 or 44.1(a) of the N.H.A., as i n d i c a t e d i n Table I I I . Table III Y e l l o w k n i f e P u b l i c Housing P r o j e c t s , 1985 P r o j e c t Name Type U n i t s NHA Sec t i o n "Condominium P r o j e c t " Fourplex 52 40 F o r r e s t D r i v e Apartments 6 44. K a ) H i l l t o p Rowhousing 24 40 Lanky Court Apartments 14 44. 1 (a) Siss o n s Court Rowhousing 48 43 T o t a l 144 SOURCE: Y e l l o w k n i f e Housing A u t h o r i t y r e c o r d s . 5.2 HYPOTHESES The study p o s t u l a t e s four hypotheses about the e f f i c i e n c y and e q u i t y achievements of the program: E f f i c i e n c y Hypothesis 1: P r o j e c t s c o n s t r u c t e d under the P u b l i c Housing Program i n Y e l l o w k n i f e have a neg a t i v e net present v a l u e . E q u i t y Hypothesis 1: P u b l i c housing tenants i n Y e l l o w k n i f e have incomes i n the lowest q u a r t i l e of the t o t a l p o p u l a t i o n . Hypothesis 2: The P u b l i c Housing Program i n Ye l l o w k n i f e i s a c h i e v i n g v e r t i c a l e q u i t y , that i s , b e n e f i t s d e c l i n e with income. Hypothesis 3: The P u b l i c Housing Program i n Ye l l o w k n i f e i s a c h i e v i n g h o r i z o n t a l e q u i t y , t h a t i s , 40 "equals are t r e a t e d e q u a l l y " . 5.3 ASSUMPTIONS The t h e s i s adopts the t r a d i t i o n a l assumptions of the l i t e r a t u r e : a two good economy (housing and non-housing); r a t i o n a l u t i l i t y - m a x i m i z i n g households; p e r f e c t l y c o m p e t i t i v e markets; a constant c o s t housing i n d u s t r y ; a s u b s i d i z e d housing program that has no e f f e c t on p r i c e s i n other markets; p e r f e c t s u b s t i t u t a b i l i t y of s u b s i d i z e d and n o n - s u b s i d i z e d housing; exogenous d e t e r m i n a t i o n of household income; and market e q u i l i b r i u m . Most of these assumptions are r e a d i l y j u s t i f i a b l e . Some, however, are adopted f o r ease of a n a l y s i s and must be r e l a x e d at some p o i n t to produce more r e a l i s t i c r e s u l t s . S p e c i f i c a l l y , three assumptions are q u e s t i o n a b l e : (1) r a t i o n a l u t i l i t y maximizing households, (2) exogenous de t e r m i n a t i o n of household income and (3) market e q u i l i b r i u m . Each of these i s d i s c u s s e d b r i e f l y i n t u r n . (1) R a t i o n a l U t i l i t y Maximizing Households. N e o - c l a s s i c a l economists assume that households are the best judges of t h e i r own welfare and a c t to maximize t h e i r u t i l i t y . Some groups of s o c i e t y - r e f e r r e d to as " p a t e r n a l i s t i c a l t r u i s t s " i n the economics l i t e r a t u r e -th i n k that poor households tend to value some goods too l i g h t l y and, i n s e l e c t i n g t h e i r bundles of goods, they f a i l to maximize t h e i r w e l f a r e . Others b e l i e v e that while an i n d i v i d u a l may behave i n a u t i l i t y - m a x i m i z i n g manner, 41 households may not. In a household with c h i l d r e n , the a d u l t decision-makers may not behave i n a manner c o n s i s t e n t with the best i n t e r e s t s of the c h i l d r e n . These viewpoints l e a d some economists to oppose u n r e s t r i c t e d cash g r a n t s . Olsen (1971) supports the p r o v i s i o n of rent c e r t i f i c a t e s on the grounds that "there are many p a t e r n a l i s t i c a l t r u i s t s i n t h i s country and . . . housing i s one of the goods that these people t h i n k the poor value too l i g h t l y " (Olsen, 1971, p. 224). T h i s study accepts the premise that there are s o - c a l l e d p a t e r n a l i s t i c a l t r u i s t s i n Canada who b e l i e v e some poor households tend to undervalue housing. Consequently, the former d e r i v e a non-tenant b e n e f i t from the d i r e c t p r o v i s i o n of p u b l i c housing that would not be d e r i v e d from a cash t r a n s f e r to the poor. (2) Exogenous Determination of Household Income. The study assumes that people l i v i n g i n p u b l i c housing would choose the same job and work the same number of hours i n the absence of the program. U n f o r t u n a t e l y , the very nature of the rent s c a l e i n p u b l i c housing i n Canada may i n v a l i d a t e t h i s assumption. As d e s c r i b e d i n Chapter 2, ren t s f o r p u b l i c housing u n i t s are c a l c u l a t e d based on the income l e v e l and fam i l y composition of the household. T h i s r e s u l t s i n higher income households paying higher r e n t s than lower income households f o r the i d e n t i c a l u n i t . Consequently, some households may choose to work l e s s hours or to remain unemployed r a t h e r than seek higher paying jobs and pay 42 higher r e n t s . In an a n a l y s i s of t h i s h y p o t h e s i s , Murray (1980) estimates that p u b l i c housing induces tenants to reduce t h e i r work e f f o r t by about 4 percent i n the U.S. A p p l i c a t i o n of Murray's model to the Y e l l o w k n i f e data p r e d i c t s a r e d u c t i o n i n work e f f o r t of between 2% and 8% (see Appendix 2 f o r f u r t h e r d e t a i l s ) . (3) Market E q u i l i b r i u m . Market e q u i l i b r i u m i s a c r i t i c a l assumption f o r any economic a n a l y s i s . U n f o r t u n a t e l y , t h i s assumption d i d not h o l d i n the Y e l l o w k n i f e housing market d u r i n g the study p e r i o d . The apartment vacancy r a t e i n Y e l l o w k n i f e i n 1985 approached zero percent and there were long w a i t i n g l i s t s f o r accommodation. T h e o r e t i c a l l y , t h i s s i t u a t i o n should have c o r r e c t e d i t s e l f by an i n c r e a s e i n the supply of housing. However, as economic f o r e c a s t s f o r Y e l l o w k n i f e were u n c e r t a i n i n the e a r l y 1980's, mortgage c r e d i t f o r r e n t a l c o n s t r u c t i o n was r e s t r i c t e d and no new apartment b u i l d i n g s were c o n s t r u c t e d . Consequently, market r e n t s i n 1985 may not represent e q u i l i b r i u m l e v e l s . 5.4 TESTING FOR EFFICIENCY 5.4.1 ESTIMATING TENANT BENEFITS Tenant b e n e f i t s are c a l c u l a t e d by the E q u i v a l e n t V a r i a t i o n measure of welfare gain using a Stone-Geary u t i l i t y f u n c t i o n . The f i r s t order c o n d i t i o n s of the u t i l i t y maximization problem y i e l d M a r s h a l l i a n demand equations f o r 43 housing and non-housing that are l i n e a r i n income and p r i c e s . These " l i n e a r expenditure" f u n c t i o n s are given by equations [1] and [ 2 ] : [1] housing: P h h Q + 0(Y- p h h Q - P x x Q ) [2] non-housing: p x x o + (1-0)(Y- P h h Q - P x x Q ) where P, li and p x are the expenditures on the minimum h o x o consumption l e v e l s of housing and non-housing; Y i s income; and /3 i s the rent-to-income r a t i o f o r purchases of housing i n excess of the minimum l e v e l . I n t u i t i v e l y , the equations can be i n t e r p r e t e d as f o l l o w s : the committed e x p e n d i t u r e s ( P n h 0 and P x x Q ) are purchased f i r s t l e a v i n g a r e s i d u a l (Y -p,h - p x ) which i s a l l o c a t e d between housing and h o x o non-housing i n f i x e d p r o p o r t i o n s 0 and (1 - /3) . The l i n e a r expenditure f u n c t i o n s are a p p e a l i n g from a t h e o r e t i c a l p e r s p e c t i v e as they s a t i s f y the requirements of demand f u n c t i o n s - namely, the p r o p e r t i e s of adding up, homogeneity and n e g a t i v e t y of the d i r e c t s u b s t i t u t i o n e f f e c t (Mayo, p. 105). However, the l i n e a r expenditure system i s not always a p p r o p r i a t e as i t has some l i m i t a t i o n s . I t cannot be used i f one of the goods i s i n f e r i o r or i f any two goods are complementary. In both cases, the l i n e a r expenditure system produces a non-concave expenditure f u n c t i o n . F o r t u n a t e l y , these two r e s t r i c t i o n s do not pose a problem f o r t h i s study as the two good economy r e p r e s e n t s goods which are n e i t h e r i n f e r i o r nor complementary. The expenditure f u n c t i o n c o r r e s p o n d i n g to the Stone-Geary u t i l i t y f u n c t i o n i s given by equation [3]: 44 [3] e(p,u) = u C p j / p J " * 3 ) + ( p h h D + p x x o ) . The l a s t term represents expenditure on the minimum consumption l e v e l s . The f i r s t term i n d i c a t e s that u t i l i t y can be "bought" at a constant p r i c e per u n i t of ( P n ^ P x 1 T h i s term i s a weighted geometric mean of p r i c e s f o r the two goods and re p r e s e n t s the marginal c o s t of l i v i n g (Deaton and Muellbauer ( 1 9 8 0 ) , p. 6 5 ) . S e t t i n g u t i l i t y at that l e v e l enjoyed by a household with the housing program (commodity bundle ( h 1 , x ^ ) , the expenditure f u n c t i o n becomes: [4] e(p,u) = [ ( h 1 - h 0 ) p h ] ^ ( Y 0 - a p h h 1 - p x x 0 ) d - p ' > + p h h 0 + p x x c 0 ( 1 - 0 ) L e t t i n g P n h 1 = R m (market rent of p u b l i c housing u n i t ) and a p ^ h 1 = Rp ( p r o j e c t r e n t ) , the formula f o r E V i s given by equation [ 5 ] : [ 5 ] E V = [<R m - p h h o ) / / 3 ] 0 [ ( Y o - R p - P X X O ) / ( 1 - / ? ) ] ( 1 - ^ + Ph ho + Px Xo " Y o Observations or estimates of s i x v a r i a b l e s are r e q u i r e d to c a l c u l a t e E V from equation [ 5 ] : Y Q - c u r r e n t household income Rp - p r o j e c t rent R m - market rent e q u i v a l e n t of p u b l i c housing u n i t /3 - household's rent-to-income r a t i o without the program ( f o r housing i n excess of minimum l e v e l ) Ph no ~ minimum expenditure on housing p x x Q - minimum expenditure on non-housing. Of these s i x v a r i a b l e s , only the f i r s t two are observable: household income and p r o j e c t r e n t . Data f o r these v a r i a b l e s are o b t ained from Y e l l o w k n i f e Housing A u t h o r i t y records and represent 1 9 8 5 f i g u r e s . The remaining v a r i a b l e s are estimated. 45 The market rent e q u i v a l e n t s of p u b l i c housing u n i t s are estimated u s i n g hedonic r e g r e s s i o n . Market r e n t s of non-public housing u n i t s are regressed on housing and neighbourhood c h a r a c t e r i s t i c s . The r e s u l t i n g parameter est i m a t e s are a p p l i e d to the c h a r a c t e r i s t i c s of the p u b l i c housing stock to estimate market rent e q u i v a l e n t s . T h i s assumes that the c o n d i t i o n a l d i s t r i b u t i o n of rent given the s p e c i f i e d housing and neighbourhood c h a r a c t e r i s t i c s i s the same f o r p u b l i c housing and market housing. I f p u b l i c housing i s s y s t e m a t i c a l l y d i f f e r e n t from market housing, the r e s u l t i n g estimates w i l l be b i a s e d . However, there i s no reason to b e l i e v e there are such systematic d i f f e r e n c e s i n the housing stock i n Y e l l o w k n i f e . P u b l i c housing p r o j e c t s are w e l l i n t e g r a t e d i n t o the community and are almost i n d i s t i n g u i s h a b l e from market housing. The p r e f e r r e d method of c a l c u l a t i n g |3 i s to regress rent-to-income r a t i o s on household c h a r a c t e r i s t i c s of the non-public housing p o p u l a t i o n and use these c o e f f i c i e n t s to p r e d i c t j3 f o r the p u b l i c housing tenants. U n f o r t u n a t e l y , d e t a i l e d data on household c h a r a c t e r i s t i c s of the non-public housing s e c t o r i s not a v a i l a b l e f o r Y e l l o w k n i f e . In the absence of t h i s data, 0 i s estimated from c r o s s t a b u l a t i o n s of rent-to-income r a t i o s by household income from 1981 census d a t a . T h e o r e t i c a l y , estimates of minimum expenditure l e v e l s should represent a c t u a l minimum expenditures observed from a sample of the p o p u l a t i o n . Olsen and Barton (1983) and 46 DeBorger (1985) estimate these l e v e l s from data c o n t a i n e d i n a sample of u n s u b s i d i z e d households. They assume the a c t u a l minimum expenditures i n c u r r e d by households of v a r i o u s c h a r a c t e r i s t i c s (e.g., s i z e , race, m a r i t a l s t a t u s , age of head) represent the s u b s i s t e n c e l e v e l s f o r households with s i m i l a r c h a r a c t e r i s t i c s . U n f o r t u n a t e l y , no comparable data i s a v a i l a b l e f o r Y e l l o w k n i f e households l i v i n g i n uns u b s i d i z e d housing. In the absence of hard data on minimum su b s i s t e n c e expenditures, t h i s study r e l i e s on estimates prepared by government ag e n c i e s . 5.4.2 ESTIMATING NON-TENANT BENEFITS In view of the i n c o n c l u s i v e evidence on the non-tenant b e n e f i t s of p u b l i c housing p r o j e c t s , a common approach i n c o s t - b e n e f i t s t u d i e s i s to c a l c u l a t e the net present value based on d i r e c t b e n e f i t s o n l y , compare t h i s f i g u r e with the d i r e c t c o s t s of the p r o j e c t and judge whether non-tenant b e n e f i t s can reasonably j u s t i f y the d i f f e r e n c e . T h i s study f o l l o w s t h i s approach. 5.4.3 ESTIMATING COSTS P u b l i c housing p r o j e c t s i n c u r both t a n g i b l e and i n t a n g i b l e c o s t s . Most economic s t u d i e s ignore i n t a n g i b l e c o s t s as does t h i s study. F o l l o w i n g K r a f t and K r a f t (1979) and Sumka and Stegman (1978), t h i s study uses a c t u a l c a p i t a l and o p e r a t i n g c o s t data to estimate t a n g i b l e c o s t s . 47 5.4.4 CHOOSING A SOCIAL DISCOUNT RATE F e d e r a l department submissions to the Treasury Board of Canada use a range of s o c i a l d i s c o u n t r a t e s . The Treasury Board B e n e f i t - C o s t A n a l y s i s Guide recommends the use of 5%, 10% and 15%. The r a t i o n a l e f o r the c h o i c e of these f i g u r e s i s e x p l a i n e d as f o l l o w s : J e n k i n s has estimated the weighted s o c i a l r a t e of r e t u r n on c a p i t a l i n Canada d u r i n g the p e r i o d 1965 -1969 to be approximately 9.5 per cent. He a l s o found that the s o c i a l r a t e of r e t u r n of 15.1 per cent f o r manufacturing in t h i s p e r i o d was the h i g h e s t of any s e c t o r i n the economy . . . One might a c c o r d i n g l y s e l e c t 10 and 15 per cent as median and upper bounds fo r our s e n s i t i v i t y a n a l y s i s . The upper bound f i g u r e c o u l d be j u s t i f i e d by the argument of Mishan that the use of a discount r a t e r e f l e c t i n g a commercial r a t e of r e t u r n on c a p i t a l w i l l s a t i s f y the decision-maker that "only those p u b l i c p r o j e c t s having expected r e t u r n s g r e a t e r than those of the h i g h e s t - y i e l d i n g p r i v a t e investments are accepted". . . . A lower bound s o c i a l d i s c o u n t r a t e of f i v e per cent might be j u s t i f i e d on the b a s i s that H e l l i w e l l et a l . found t h i s to be approximately the r e a l supply p r i c e of c a p i t a l i n Canada i n the p e r i o d 1955 - 72. ( B e n e f i t - C o s t A n a l y s i s Guide, p. 26) Correspondence from the S e c r e t a r y of the Treasury Board confirms that f e d e r a l departments c u r r e n t l y use a number of d i s c o u n t r a t e s i n the range 5% - 15%. F o l l o w i n g the Treasury Board g u i d e l i n e s , the study uses a range of s o c i a l d i s c o u n t r a t e s . However, as the c o s t s and b e n e f i t s are t r a n s l a t e d to 1985 d o l l a r s , r e a l r a t e s rather than nominal r a t e s are used. The range of r e a l r a t e s i s determined from estimates of r e a l r a t e s over the past ten year p e r i o d . 48 5.5 TESTING FOR EQUITY The three e q u i t y hypotheses are s t a t e d i n S e c t i o n 5.2. As a reminder, they a r e : 1. P u b l i c housing tenants in Y e l l o w k n i f e have incomes in the lowest q u a r t i l e of the t o t a l p o p u l a t i o n . 2. The P u b l i c Housing Program i n Y e l l o w k n i f e i s a c h i e v i n g v e r t i c a l e q u i t y , that i s , b e n e f i t s d e c l i n e with income. 3. The P u b l i c Housing Program i n Y e l l o w k n i f e i s a c h i e v i n g h o r i z o n t a l e q u i t y , that i s , "equals are t r e a t e d e q u a l l y " . The f i r s t h ypothesis i s t e s t e d simply by comparing the income d i s t r i b u t i o n s of the p u b l i c housing tenants to that of the t o t a l p o p u l a t i o n i n Y e l l o w k n i f e . Households with lower incomes are expected to be d i s p r o p o r t i o n a t e l y represented i n the p u b l i c housing stock. The second and t h i r d hypotheses are t e s t e d by r e g r e s s i n g the EV measure of w e l f a r e gain f o r each household a g a i n s t household income and c h a r a c t e r i s t i c s . CHAPTER 6 EMPIRICAL RESULTS 6. EMPIRICAL RESULTS T h i s chapter presents the r e s u l t s of the c o s t - b e n e f i t a n a l y s i s . S e c t i o n s 6.1 and 6.2 d e s c r i b e the r e s u l t s from t e s t i n g the four hypotheses of e f f i c i e n c y and e q u i t y . The f i n a l s e c t i o n compares the net annual c o s t of the P u b l i c Housing Program to the estimated c o s t of a s h e l t e r allowance program. 6.1 ECONOMIC EFFICIENCY E a r l i e r chapters r e p o r t that a l l economic e v a l u a t i o n s of s u b s i d i z e d housing f i n d the programs to be i n e f f i c i e n t . There i s no reason to b e l i e v e , a p r i o r i , that the program i n Y e l l o w k n i f e w i l l be i n c o n s i s t e n t with these r e s u l t s . T h i s e x p e c t a t i o n i s f o r m a l i z e d i n Hypothesis 1. Hypothesis 1: P r o j e c t s c o n s t r u c t e d under the P u b l i c Housing Program i n Y e l l o w k n i f e have a negative net present v a l u e . The r e s u l t s of the a n a l y s i s support t h i s h y p o t h e s i s . The net present value of the f i v e p r o j e c t s i s estimated to be between - $13,345 m i l l i o n and - $17,485 m i l l i o n depending on the s o c i a l d i s c o u n t r a t e . T h i s s e c t i o n d e s c r i b e s the e s t i m a t i o n process l e a d i n g to these r e s u l t s . 6.1.1 ESTIMATES OF TENANT BENEFITS Tenant b e n e f i t s are estimated by c a l c u l a t i n g the EV measure f o r each i n d i v i d u a l household and adding t h i s amount to p r o j e c t rent as i n d i c a t e d i n equation [ 6 ] : 50 51 [6] TENANT BENEFIT = (Rm - Ph ho>^ (Yp - Rp - P X X Q ) 1 ' * 3 + Phh 0 + Px xo " Y o + R p where: Y c = c u r r e n t household income Rp = p r o j e c t rent R m = market rent e q u i v a l e n t of p u b l i c housing u n i t 0 = household rent-to-income r a t i o without the program ( f o r housing i n excess of minimum l e v e l ) Phh Q = minimum expenditure on housing p x x Q = minimum expenditure on non-housing. The f i r s t two v a r i a b l e s ( c u r r e n t household income and p r o j e c t rent) are obtained from the Y e l l o w k n i f e Housing A u t h o r i t y r e c o r d s . The remaining four v a r i a b l e s are estimated. E s t i m a t e s o f M a r k e t Rent E q u i v a l e n t s The market rents of p u b l i c housing u n i t s are estimated using hedonic r e g r e s s i o n . Market ren t s are assumed to be a f u n c t i o n of the v a r i a b l e s l i s t e d i n equation [7] p l u s an independent e r r o r term. [7] RENT = f(STOR, YEAR, BED, COND, TYPE, FURN, UTIL, DIST2, DIST3) The f i r s t three v a r i a b l e s are q u a n t i t a t i v e , the remainder are dummy v a r i a b l e s . STOR i s the number of s t o r e y s i n the b u i l d i n g ; YEAR i s the year of c o n s t r u c t i o n ; and BED i s the number of bedrooms i n the u n i t . COND i s a dummy v a r i a b l e f o r c o n d i t i o n r a t i n g (0 = F a i r , 1 = Good) TYPE f o r s t r u c t u r a l type (0 = apartment, 1 = rowhousing); FURN f o r f u r n i t u r e p r o v i d e d (0 = no, 1 = yes) and UTIL f o r u t i l i t i e s i n c l u d e d 52 i n the rent (0 = none, 1 = e l e c t r i c i t y ) . DIST2 and DIST3 are dummy v a r i a b l e s f o r l o c a t i o n . Three l o c a t i o n s are i d e n t i f i e d based on walking d i s t a n c e from the downtown c o r e . The base l o c a t i o n i s the downtown c o r e . DIST2 =1 i f u n i t i s l o c a t e d w i t h i n "easy walking d i s t a n c e " from the downtown core and 0 otherwise. DIST3 = 1 i f u n i t i s l o c a t e d at more than 15 minutes walking d i s t a n c e from the downtown core and 0 otherwise. The base case i s an u n f u r n i s h e d apartment i n f a i r c o n d i t i o n l o c a t e d i n the downtown core of the c i t y . U t i l i t i e s are not i n c l u d e d i n r e n t . The sample c o n s i s t s of 921 housing u n i t s . Of these, 881 are p r i v a t e l y owned and r e n t e d . The balance are l e a s e d by the t e r r i t o r i a l government and are rented as s t a f f housing u n i t s . Rents f o r s t a f f u n i t s are based on p r e v a i l i n g market l e v e l s a c c o r d i n g to government p o l i c y . Observations f o r a l l independent v a r i a b l e s are obtained from the assessment records of the t e r r i t o r i a l government. Market rents f o r p r i v a t e l y owned u n i t s are obtained from the March 1985 Y e l l o w k n i f e Rental Survey conducted by the t e r r i t o r i a l Bureau of S t a t i s t i c s . Rents f o r s t a f f housing are p r o v i d e d by the Government of the N.W.T. On the s u r f a c e , i t seems reasonable to expect that housing a t t r i b u t e s have an a d d i t i v e e f f e c t on r e n t . However, a review of the l i t e r a t u r e r e v e a l s a wide v a r i e t y of forms used i n hedonic r e g r e s s i o n s . In the c o s t - b e n e f i t a n a l y s i s l i t e r a t u r e , Murray (1975) and Olsen (1972) use the l i n e a r model while Sumka and Stegman (1978) use the l o g l i n e a r 53 form. As Quigley (1979) observes "most authors have chosen the l i n e a r , semi-log, or l o g a r i t h m i c form f o r a n a l y s i s , presumably on the grounds of convenience and without r i g o r o u s s t a t i s t i c a l e xperimentation" (Quigley, p. 400). In the absence of any agreement i n the l i t e r a t u r e , Box-Cox t e s t s are run on the Y e l l o w k n i f e data to determine an a p p r o p r i a t e model. The r e s u l t s suggest a l i n e a r model w i l l f i t the data q u i t e w e l l . The r e g r e s s i o n s are run using Ordinary Least Squares. An a n a l y s i s of the r e s i d u a l s i n d i c a t e s the data comply with the c r i t i c a l assumptions of constant v a r i a n c e and u n c o r r e l a t e d e r r o r s (see F i g u r e 7 i n Appendix 1). However, the normal p l o t of r e s i d u a l s suggests the e r r o r term may not be normally d i s t r i b u t e d (see F i g u r e 8 i n Appendix 1). T h i s means that the model may not provide a c c u r a t e r e s u l t s f o r hypothesis t e s t i n g . F o r t u n a t e l y , the model i s only r e q u i r e d f o r p r e d i c t i o n purposes. The estimates r e s u l t i n g from the r e g r e s s i o n are presented i n equation [ 8 ] , T - s t a t i s t i c s are i n parentheses and s i g n i f i c a n c e l e v e l s i n square b r a c k e t s . [8] R m = 5860.242 - 259.968 STOR + 174.750 YEAR (110.597) (-29.304) (37.359) [.0001] [.0001] [.0001] + 1124.991 BED -618.612 COND +937.311 TYPE +261.032 FURN (54.058) (-14.674) C12.065) (5.288) [.0001] [.0001] [.0001] [.001] + 261.286 DIST2 - 441.560 DIST3 - 313.820 UTIL (8.308) (-5.854) (-10.943) [.0001] [.0001] [.0001] R i s the "market rent e q u i v a l e n t " of the p u b l i c housing 54 u n i t , a l l other v a r i a b l e s are as p r e v i o u s l y d e f i n e d . A l l parameter estimates are s i g n i f i c a n t at the . 0 1 % l e v e l . The 2 model produces an R of .93 i n d i c a t i n g a good f i t . In g e n e r a l , the parameter estimates have the c o r r e c t s i g n s and c o n f i r m the e x p e c t a t i o n that r e n t s i n c r e a s e with number of bedrooms, with type of s t r u c t u r e ( i . e . , rowhousing i s more expensive than apartment u n i t s ) , and with f u r n i t u r e p r o v i d e d . The parameter estimate f o r number of s t o r e y s has a negative s i g n , suggesting r e n t s decrease with b u i l d i n g height p o s s i b l y r e f l e c t i n g a g r e a t e r demand f o r ground-oriented accommodation. Rents a l s o decrease with age of b u i l d i n g ( i . e . , i n c r e a s e with year of c o n s t r u c t i o n ) . The parameter estimates f o r d i s t a n c e c o n f i r m e x p e c t a t i o n s t h a t u n i t s w i t h i n "easy walking d i s t a n c e " from downtown are more d e s i r a b l e than those l o c a t e d e i t h e r i n the heart of the downtown core or at a more remote l o c a t i o n . Two parameter estimates r e s u l t i n g from the r e g r e s s i o n do not conform to e x p e c t a t i o n s . The c o e f f i c i e n t s f o r COND ( c o n d i t i o n ) and UTIL ( u t i l i t i e s ) both have negative s i g n s suggesting r e n t s are lower f o r u n i t s i n b e t t e r c o n d i t i o n and for u n i t s with u t i l i t i e s i n c l u d e d i n the r e n t . In e q u i l i b r i u m , one would expect r e n t s to i n c r e a s e with q u a l i t y ( i . e . , c o n d i t i o n ) and with amenities p r o v i d e d (e.g., u t i l i t i e s ) . In g e n e r a l , there are s e v e r a l p o s s i b l e e x p l a n a t i o n s f o r an " i n c o r r e c t " s i g n : 1. m u l t i c o l l i n e a r i t y among independent v a r i a b l e s ; 55 2. m i s s p e c i f i e d f u n c t i o n a l form (e.g., i n t e r a c t i o n terms or higher order terms o m i t t e d ) ; 3. omitted v a r i a b l e ; or 4. inadequate data. Of these four p o s s i b i l i t i e s , o n l y the l a s t two seem p l a u s i b l e f o r t h i s model. M u l t i c o l l i n e a r i t y i s r u l e d out by an examination of the c o r r e l a t i o n matrix and the c o l l i n e a r i t y d i a g n o s t i c s produced by SAS (see Appendix 1). M i s s p e c i f i e d f u n c t i o n a l form i s r u l e d out by Box-Cox t e s t s and by t r i a l and e r r o r . Box-Cox t e s t s produce a value of .94 f o r lambda, suggesting a l i n e a r model should f i t the data q u i t e w e l l . I n t e r a c t i o n terms such as AGE x COND were added to the model and found to be i n s i g n i f i c a n t , suggesting c r o s s product terms are not causing the problem. However, m i s s p e c i f i c a t i o n due to o m i t t i n g an independent v a r i a b l e i s a p o s s i b i l i t y . The model does not i n c l u d e a v a r i a b l e r e p r e s e n t i n g tenant c h a r a c t e r i s t i c s . U n i t s i n poorer c o n d i t i o n may be commanding a higher rent than comparable u n i t s i n good c o n d i t i o n because they are rented by q u a l i t a t i v e l y d i f f e r e n t groups. Tenants in the poorer u n i t s may be g r e a t e r r i s k s (lower income, more rowdy e t c . ) and l a n d l o r d s may be c h a r g i n g higher r e n t s to compensate f o r the i n c r e a s e d r i s k . T h i s l a t t e r behavior draws some support from economic theory. For example, Henderson (1985) suggests there i s a " r e n t a l e x t e r n a l i t y " a s s o c i a t e d with r e n t i n g that makes i t an i n h e r e n t l y more expensive form of tenure than owning. 56 A ccording to Henderson, because owners are d i r e c t l y r e s p o n s i b l e f o r a l l o p e r a t i n g and maintenance c o s t s , they u t i l i z e t h e i r housing at an optimal r a t e . Conversely, r e n t e r s tend to o v e r u t i l i z e t h e i r housing as they are not d i r e c t l y r e s p o n s i b l e f o r the f u l l c o s t s of t h e i r occupancy. T h e r e f o r e , l a n d l o r d s set r e n t s at a higher l e v e l to compensate f o r the expected c o s t of o v e r u t i l i z a t i o n . Henderson a t t r i b u t e s the d i f f e r e n c e i n user c o s t between r e n t i n g and owning to t h i s r e n t a l e x t e r n a l i t y . A n a t u r a l extension of Henderson's theory suggests that l a n d l o r d s r e n t i n g to tenants who are c o n s i d e r e d prime candidates to o v e r u t i l i z e the prop e r t y w i l l charge higher r e n t s than l a n d l o r d s r e n t i n g to other groups. S i m i l a r reasoning c o u l d be used to e x p l a i n a negative s i g n on UTIL. A second e x p l a n a t i o n f o r the " i n c o r r e c t " s i g n s c o u l d be an i n a c c u r a t e data base, p a r t i c u l a r l y i n the case of COND. The c o n d i t i o n r a t i n g s were obtained from the assessment records of the T e r r i t o r i a l Government. Each b u i l d i n g i s assi g n e d a c o n d i t i o n r a t i n g of POOR, FAIR, GOOD or EXCELLENT based on the s u b j e c t i v e judgement of the a s s e s s o r . A l l the b u i l d i n g s used i n t h i s study were assig n e d r a t i n g s of FAIR or GOOD. As the r a t i n g s were done at d i f f e r e n t times by d i f f e r e n t a s s e s s o r s , i t i s p o s s i b l e that some i n c o n s i s t e n c i e s may be pr e s e n t . A few such i n c o n s i s t e n c i e s c o u l d produce the wrong s i g n on COND. A s i m i l a r e x p l a n a t i o n c o u l d be c o n s t r u c t e d f o r the " i n c o r r e c t " s i g n on UTIL. 57 An a l t e r n a t e e x p l a n a t i o n f o r the perverse r e s u l t s c o u l d be that the r e n t a l market i n Y e l l o w k n i f e i s not i n e q u i l i b r i u m . At the time of the study, there were long w a i t i n g l i s t s f o r accommodation suggesting demand exceeds supply. Landlords may be c a p i t a l i z i n g on t h i s s i t u a t i o n by c h a r g i n g higher r e n t s f o r poorer u n i t s than the market would t o l e r a t e i n e q u i l i b r i u m . T h e o r e t i c a l l y , t h i s s i t u a t i o n should c o r r e c t i t s e l f by an i n c r e a s e i n r e n t s f o l l o w e d by an i n c r e a s e i n supply. However, as economic f o r e c a s t s f o r Y e l l o w k n i f e were u n c e r t a i n i n the e a r l y 1980's, mortgage c r e d i t f o r r e n t a l c o n s t r u c t i o n was r e s t r i c t e d and no new apartment b u i l d i n g s were c o n s t r u c t e d u n t i l 1985/86. While none of these e x p l a n a t i o n s i s as s a t i s f y i n g as o b t a i n i n g the " c o r r e c t " s i g n s would be, there appears to be no a l t e r n a t i v e but to use equation [8] f o r e s t i m a t i n g the market rent e q u i v a l e n t s f o r the p u b l i c housing u n i t s . On the p o s i t i v e s i d e , there are two reasons to suggest that the model i s v a l i d f o r f o r e c a s t i n g purposes. F i r s t , v e r i f i c a t i o n of the model by " h a l f and h a l f " techniques produces estimates of market rent t h a t very c l o s e l y approximate the true r e n t . The model i s v e r i f i e d by s p l i t t i n g the data i n t o two data s e t s using the random number generator i n SAS. The model i s f i t using the f i r s t data set and the c o e f f i c i e n t s r e s u l t i n g from the r e g r e s s i o n are used to f i t the second data s e t . The r e s u l t s of t h i s r e g r e s s i o n are reproduced i n Appendix 1. The estimated rent (YHAT) r e s u l t i n g from the a p p l i c a t i o n of the parameter estimates to the second data 58 set i s then regressed on RENT producing the r e s u l t s i n equation [ 9 ] . T - s t a t i s t i c s are i n parentheses and s i g n i f i c a n c e l e v e l s i n square b r a c k e t s . [9] YHAT = 600.815 + .925 RENT (4.978) (63.162) [.0001] [.0001] The t - s t a t i s t i c s f o r the parameter estimates are s i g n i f i c a n t 2 at the .01% l e v e l . The R i s .90 suggesting the model produces a good f i t . The p l o t of YHAT a g a i n s t RENT, shown i n Fi g u r e 9 i n Appendix 1, confirms t h i s . A second reason to have c o n f i d e n c e i n the model i s provided by examining the market rent e q u i v a l e n t s obtained f o r p u b l i c housing u n i t s l o c a t e d i n "mixed use" b u i l d i n g s . Included i n the stock of p u b l i c housing are two b u i l d i n g s ( F o r r e s t D r i v e Apartments and Lanky Court Apartments) that o f f e r a mix of p u b l i c housing u n i t s and market apartments i n the same b u i l d i n g . Presumably, the market rent e q u i v a l e n t of the p u b l i c housing u n i t s i n these b u i l d i n g s would equal the a c t u a l rent of the market u n i t s . Table IV compares the market rent e q u i v a l e n t s o b t a i n e d from the model i n equation [8] to the a c t u a l market r e n t s . The estimates f o r the u n i t s in Lanky Court are very c l o s e to the a c t u a l rent (only 2.3 -4.7% above), while the esti m a t e s f o r the F o r r e s t D r i v e apartments are somewhat l e s s a c c u r a t e (10.6 - 13.0% above). 59 Table IV Comparison of Market Rent E q u i v a l e n t s and Market Rents B u i l d i n g S i z e A c t u a l Market E r r o r Rent Equiv. Lanky 2 BR $8,400 $8,793 $393 (4.7%) Court 3 BR 9,600 9,918 318 (3.3%) 4 BR 10,800 11,043 243 (2.3%) F o r r e s t 2 BR 8,400 9,496 1 ,096 (13.0%) Driv e 3 BR 9,600 10,621 1 ,021 (10.6%) In c o n c l u s i o n , the l i n e a r model presented i n equation [8] seems to be a good p r e d i c t o r f o r market r e n t s i n Y e l l o w k n i f e and i s used to estimate the market rent e q u i v a l e n t s of p u b l i c housing u n i t s . Estimates of Minimum Expenditure L e v e l s The t e r r i t o r i a l Department of S o c i a l S e r v i c e s c a l c u l a t e s minimum expenditure l e v e l s f o r non-housing by household s i z e i n order to e s t a b l i s h welfare r a t e s f o r the Northwest T e r r i t o r i e s . These l e v e l s r e f l e c t the " b a s i c l i v i n g allowance" component of we l f a r e e x c l u s i v e of housing c o s t s . A housing component i s not i n c l u d e d as i t i s government p o l i c y to pay the a c t u a l cost of s h e l t e r f o r a l l w e l f a r e r e c i p i e n t s . S t a t i s t i c s Canada c a l c u l a t e s "low income c u t - o f f l e v e l s " by household s i z e and p l a c e of r e s i d e n c e . Although these l e v e l s are not designed to represent o f f i c i a l poverty l i n e s , they are i n t e r p r e t e d as such by the N a t i o n a l C o u n c i l of Welfare. These l e v e l s are set at the amount of income 60 r e q u i r e d by a household so that i t spends 58.5 percent of i t s income on the basic n e c e s s i t i e s of food, s h e l t e r and c l o t h i n g . 2 Thus, 58.5 percent of the "low income c u t - o f f " l e v e l s can be i n t e r p r e t e d as minimum expenditures f o r  s u b s i s t e n c e . T h i s study uses these l a t t e r f i g u r e s as minimum expenditure l e v e l s . Minimum expenditures on housing are c a l c u l a t e d by s u b t r a c t i n g the "b a s i c l i v i n g allowances" from the minimum expenditures f o r s u b s i s t e n c e . The estimates of minimum expenditures r e s u l t i n g from t h i s process are prov i d e d i n Table V. 2 The 1978 Survey of Family Expenditures found t h a t , on average, Canadian f a m i l i e s spent 38.5% of t h e i r income on food, c l o t h i n g and s h e l t e r . Since the p o r t i o n of income spent on the b a s i c n e c e s s i t i e s d e c l i n e s with income, poor f a m i l i e s are expected to spend d i s p r o p o r t i o n a t e l y more on food, c l o t h i n g and s h e l t e r than the average f a m i l y . In c a l c u l a t i n g the low income c u t - o f f s , S t a t i s t i c s Canada set t h i s l e v e l at 58.5%, 20 percentage p o i n t s above the n a t i o n a l l e v e l . 61 Table V Minimum Expenditure L e v e l s by Household S i z e Poverty* Minimum Exp.** Basic L i v i n g Minimum Exp. S i z e L e v e l For Subsi s t e n c e Allowance On Housinq 1 $8,432 $4,933 $1,812 3,121 2 1 1 ,098 6,492 3, 156 3,336 3 14,886 8,708 4,392 4,316 4 17,206 10,066 5,520 4,546 5 19,960 11,677 6,552 5, 125 6 21,767 12,734 7,452 5,282 7 24,004 14,042 8,256 5,786 24,004 14,042 8,940 5,786 * S t a t i s t i c s Canada "low income c u t - o f f " l e v e l s ** F i g u r e s represent 58.5% of poverty l e v e l *** While the poverty l e v e l remains constant at $24,004 f o r households of 7 or more people, the b a s i c l i v i n g allowance i s i n c r e a s e d f o r each a d d i t i o n a l household member. Th e r e f o r e , to prevent the estimate of "Minimum Expenditure on Housing" from d e c l i n i n g f o r a household of 8, i t i s set at the same l e v e l as that c a l c u l a t e d f o r a household of 7 ($5,786). SOURCE: 1. Department Of S o c i a l S e r v i c e s , Government of the N.W.T., unpublished data. 2. "1985 Poverty L i n e s " - estimates by the N a t i o n a l C o u n c i l of Welfare, March, 1985. There are some problems with t h i s method. The low income c u t - o f f l e v e l s e s t a b l i s h e d by S t a t i s t i c s Canada are not prepared s p e c i f i c a l l y f o r Y e l l o w k n i f e but are determined a c c o r d i n g t o c i t y s i z e . The l e v e l s f o r Y e l l o w k n i f e are taken from the category " p o p u l a t i o n of l e s s than 30,000". Given the higher c o s t of l i v i n g i n Y e l l o w k n i f e than i n c i t i e s of 62 comparable s i z e i n s o u t h e r n Canada, the e s t i m a t e s of minimum e x p e n d i t u r e s may be u n d e r s t a t e d . E s t i m a t e s o f /3 The parameter |3 r e p r e s e n t s the h o u s e h o l d net r e n t - t o - i n c o m e r a t i o i n the absence of the program. I t i s c a l c u l a t e d e x c l u s i v e of the minimum e x p e n d i t u r e l e v e l s as i n d i c a t e d i n e q u a t i o n [ 1 0 ] : [10] 0 = (RENT - p.ri ) / (INCOME - p,h - p x ). h o  rh o x o In o r d e r t o c a l c u l a t e 0, the v a r i a b l e RENT must f i r s t be e s t i m a t e d . A l l o t h e r v a r i a b l e s are e i t h e r o b s e r v a b l e (INCOME) or p r e v i o u s l y e s t i m a t e d ( P j 1 b Q , P X X Q ) - E s t i m a t e s of RENT ar e o b t a i n e d i n two s t e p s . In the f i r s t s t e p , g r o s s r e n t - t o - i n c o m e r a t i o s f o r t e n a n t s i n Y e l l o w k n i f e a r e c a l c u l a t e d by income group from 1981 Census d a t a . 3 In the second s t e p , these r a t i o s a r e m u l t i p l i e d by h o u s e h o l d income to e s t i m a t e the v a r i a b l e RENT f o r each h o u s e h o l d i n p u b l i c h o u s i n g . In s t e p one, e s t i m a t e s of the average g r o s s r e n t - t o - i n c o m e r a t i o s a r e o b t a i n e d by r e g r e s s i n g r e n t - t o - i n c o m e r a t i o s of a l l r e n t a l h o u s e h o l d s i n Y e l l o w k n i f e on h o u s e h o l d income. The r e g r e s s i o n t a k e s the form g i v e n by e q u a t i o n [ 1 1 ] : [11] RENT/INCOME = ^ I N C I + /32INC2 + 0 3INC3 + j3 4 INC4 + 0 5INC5 + 0 6INC6 + 07INC7 + 0 8INC8 + 0O.INC9 + u where INC1 t o INC9 a r e dummy v a r i a b l e s r e p r e s e n t i n g annual 3 I am i n d e b t e d t o the N.W.T. Housing C o r p o r a t i o n f o r f i n a n c i a l a s s i s t a n c e i n p u r c h a s i n g t h i s d a t a from S t a t i s t i c s Canada. 63 household income i n $5,000 increments. The r e g r e s s i o n i s run using O r d i n a r y Least Squares, suppressing the i n t e r c e p t . The c o e f f i c i e n t s r e s u l t i n g from the r e g r e s s i o n represent the mean values of the gross rent-to-income r a t i o f o r each income group. They are presented i n Table VI. Table VI Gross Rent-to-income R a t i o s , Y e l l o w k n i f e , 1980 Income Ranqe R a t i o under $5000 42% $5,000 - $9,999 35% $10,000 - $14,999 28% $15,000 - $19,999 24% $20,000 - $24,999 19% $25,000 - $29,999 1 7% $30,000 - $34,999 1 5% $35,000 - $39,999 15% $40,000 + 1 3% In s t e p two, estimates of RENT are obtained by a p p l y i n g the a p p r o p r i a t e r a t i o to household income f o r a l l households i n p u b l i c housing. These estimates are s u b s t i t u t e d i n equation [10] to produce estimates of /3 f o r each household. Before d e s c r i b i n g the r e s u l t s of t h i s p r o c e s s , a note should be made about the sample s i z e . The sample of p u b l i c housing stock used i n t h i s study c o n s i s t s of 144 u n i t s . When the data were c o l l e c t e d , 7 u n i t s were vacant, reducing the number of households to 137 and, of these, 27 households 64 r e p o r t e d zero income. T h e r e f o r e , the net sample c o n s i s t s of 110 households. In theory, 0 rep r e s e n t s the percentage of household income, over and above the minimum expenditure l e v e l , t h a t would be spent on o b t a i n i n g housing i n excess of the minimum l e v e l . By c o n s t r u c t i o n , a l l estimates of 0 should be non-negative s i n c e both the numerator and denominator of equation [10] should be g r e a t e r than or equal to zero. The numerator should be non-negative s i n c e the v a r i a b l e RENT, by d e f i n i t i o n , must be g r e a t e r than or equal to the s u b s i s t e n c e s h e l t e r l e v e l and the denominator must be non-negative s i n c e household income, a l s o by d e f i n i t i o n , cannot be l e s s than the minimum expenditure l e v e l s . However, i n i t i a l a p p l i c a t i o n of the data to equation [10] r e s u l t s i n negative /3's f o r 54 of the 110 households i n the sample. T h i s suggests one of two t h i n g s : 1. the average rent-to-income r a t i o s d e r i v e d from the Y e l l o w k n i f e p o p u l a t i o n are "too low"; or 2. the minimum expenditure l e v e l s are "too h i g h " . In f a c t , both of these f a c t o r s c o u l d be c o n t r i b u t i n g to the problem as the e s t i m a t i o n techniques i n both cases are q u i t e crude. However, as the estimates of average rent-to-income r a t i o s are d e r i v e d from a c t u a l market data, there i s more reason f o r co n f i d e n c e i n these f i g u r e s than i n the minimum expenditure l e v e l s f o r s h e l t e r . Hence, minimum housing e x p e n d i t u r e s are r e - d e f i n e d as the minimum estimates of RENT ( i . e . , rent-to-income r a t i o m u l t i p l i e d by household income) 65 fo r each category of household s i z e . The r e v i s e d minimum s h e l t e r l e v e l s are presented i n Table V I I . Table VII Revised Minimum Housing Expenditure L e v e l s Household S i z e Basic L i v i n g Allowance Minimum S h e l t e r * Revised S h e l t e r 1 1,812 3,121 2,738 2 3,1 56 3,336 2,738 3 4,392 4,316 3,023 4 5,520 4,546 3,023 5 6,552 5, 125 3,628 6 7,452 5,282 4,445 7 8,256 5,786 4,869 8 8,940 5,786 4,895 * from Table V SOURCE: Department Of S o c i a l S e r v i c e s , Government of the N.W.T., unpublished data. T h i s adjustment s t i l l l e a v e s 7 households with incomes l e s s than the minimum s u b s i s t e n c e l e v e l s . Incomes f o r 2 of the households are l e s s than the Basic L i v i n g Allowance suggesting income i s under-reported. These two o b s e r v a t i o n s are d e l e t e d . The remaining 5 o b s e r v a t i o n s have incomes i n excess of the B a s i c L i v i n g Allowance but have inadequate income to purchase housing i n the market. They are only able to s u b s i s t on t h e i r incomes because they are l i v i n g i n p u b l i c housing and t h e i r rent i s l i m i t e d to 25% of t h e i r income. These 5 o b s e r v a t i o n s are a l s o d e l e t e d , reducing the 66 sample s i z e to 103 households. With these r e v i s i o n s , estmates of /3 are obtained f o r each household in the sample. These values are s u b s t i t u t e d in equation [6] along with estimates of the other v a r i a b l e s to produce an estimate of tenant b e n e f i t s f o r each household. The estimates range from $2744.45 to $8064.63 with a median value of $6,519.25 and a mean of $6276.16. T o t a l tenant b e n e f i t s are estimated to be $903,767 ( i . e . , 144 x $6276.16) . 6.1.2 ESTIMATES OF COSTS Only t a n g i b l e c o s t s are measured at t h i s p o i n t . A c t u a l c a p i t a l c o s t s are obtained from C.M.H.C. and are presented in Table V I I I . A c t u a l o p e r a t i n g c o s t s were u n a v a i l a b l e f o r 1985, but o p e r a t i n g budgets f o r the 1985 calendar year have been p r o v i d e d by the Y e l l o w k n i f e Housing A u t h o r i t y as w e l l as a c t u a l c o s t s f o r 1984. These are a l s o presented i n Table V I I I . 67 Table VIII P u b l i c Housing P r o j e c t Costs 1. C a p i t a l Cost ( a c t u a l ) $ 6,972,987 2. C a p i t a l Cost (1985 d o l l a r s ) 11,094,893 3. Operating Costs (1984 a c t u a l ) 927,634 4. Operating Costs (1985 budget) 882,900 SOURCE: 1. Correspondence from C.M.H.C., Y e l l o w k n i f e O f f i c e . 2. Y e l l o w k n i f e Housing A u t h o r i t y . The use of a c t u a l c a p i t a l c o s t s and o p e r a t i n g c o s t s assumes that the input markets are p e r f e c t l y c o m p e t i t i v e and that the p r i c e s p a i d f o r the land, labour and c a p i t a l resources represent t h e i r value i n the best a l t e r n a t i v e use. A c t u a l o p e r a t i n g c o s t s may understate resource c o s t as they do not i n c l u d e the a d m i n i s t r a t i o n c o s t s of the N.W.T. Housing C o r p o r a t i o n or C.M.H.C. To the extent that the resources used t o admi n i s t e r the housing p r o j e c t s c o u l d be used to produce other goods, they represent a tr u e cost to s o c i e t y . However, i n t h i s study, i t i s assumed t h a t the a d m i n i s t r a t i o n c o s t s of the N.W.T. Housing C o r p o r a t i o n and C.M.H.C. are not i n c r e a s e d by the e x i s t e n c e of the P u b l i c Housing Program i n Y e l l o w k n i f e . T h i s may not be a l l that u n r e a l i s t i c as the 144 p u b l i c housing u n i t s i n Y e l l o w k n i f e represent a n e g l i g i b l e p o r t i o n of the p u b l i c housing stock in the N.W.T. and i n Canada. 68 6.1.3 ESTIMATES OF NET PRESENT VALUE Net p r e s e n t v a l u e (NPV) i s c a l c u l a t e d i n the t r a d i t i o n a l manner by s u b t r a c t i n g the c a p i t a l c o s t from the d i s c o u n t e d net income stream as i n e q u a t i o n [ 1 2 ] : [12] NPV = - C a p i t a l Cost + Z ( B e n e f i t s - C o s t s ) (1 + r ) n where r i s the s o c i a l d i s c o u n t r a t e and n i s the number of y e a r s . B e f o r e c a l c u l a t i n g NPV, the c a p i t a l c o s t s of t h e p r o j e c t s a r e i n f l a t e d t o 1985 d o l l a r s u s i n g the r e s i d e n t i a l c o n s t r u c t i o n p r i c e i n d e x . O p e r a t i n g c o s t s f o r 1985 a r e not a v a i l a b l e but the 1985 budgets i n d i c a t e c o s t s a r e e x p e c t e d t o be l e s s than 1984 a c t u a l c o s t s (see Table V I I I ) . To r e t a i n c o n s i s t e n c y i n u s i n g a c t u a l c o s t s , the 1984 f i g u r e s a r e used t o r e p r e s e n t 1985 o p e r a t i n g c o s t s . A l l p r o j e c t s a r e f i n a n c e d o ver a f i f t y y e a r p e r i o d and a r e assumed t o have an e x p e c t e d l i f e of f i f t y y e a r s . The income streams a r e d i s c o u n t e d a t r e a l r a t e s of 1%, 3%, 5% and 7%. These r a t e s r e f l e c t the range of r e a l r a t e s over the p a s t 10 year p e r i o d , 1975 - 1985 (see Appendix 5 f o r c a l c u l a t i o n s ) . As t h r e e of the p r o j e c t s a r e f i n a n c e d by l o a n s a t s u b s i d i z e d i n t e r e s t r a t e s , the e s t i m a t e s of NPV a r e a d j u s t e d upward t o r e f l e c t the o p p o r t u n i t y c o s t of c a p i t a l . The e s t i m a t e s of NPV range from -$13,345 t o -$17,485 m i l l i o n , as i n d i c a t e d i n T a b l e IX. 69 Table IX Estimates of Net Present Value I I 2 1 5% 2 % -$17,484,684 -15,289,385 -14,070,992 -13,344,704 In order to j u s t i f y the program on e f f i c i e n c y grounds, these f i g u r e s suggest that the p r o j e c t s must generate non-tenant b e n e f i t s of between $13,345 and $17,485 m i l l i o n over 50 y e a r s . At i n t e r e s t r a t e s of 1% to 7%, t h i s t r a n s l a t e s to annual b e n e f i t s of between $446,082 and $966,955. As i n d i c a t e d i n Chapter 3 ( s u b - s e c t i o n 3.2.1), the j u r y i s s t i l l out on the e x i s t e n c e of non-tenant b e n e f i t s , but, i n any case, i t i s not l i k e l y that that they would approach the f i g u r e s necessary to j u s t i f y the program on e f f i c i e n c y grounds. As expected, the j u s t f i c a t i o n of the P u b l i c Housing Program must appeal to n o t i o n s of e q u i t y . 6.2 EQUITY The f i r s t e q u i t y hypothesis i s t e s t e d by comparing the income d i s t r i b u t i o n of the p u b l i c housing tenants to that of the t o t a l p o p u l a t i o n i n Y e l l o w k n i f e . Table X summarizes the most recent i n f o r m a t i o n on household incomes. U n f o r t u n a t e l y , the data are not d i r e c t l y comparable as the income data f o r the c i t y i s taken from the 1981 Census and r e p r e s e n t s 1980 income l e v e l s while the data f o r the p u b l i c housing tenants r e p r e s e n t s 1985 income. To make the data more comparable, the income f i g u r e s f o r the p u b l i c housing tenants are 70 d e f l a t e d by the Consumer P r i c e Index to t r a n s l a t e them to 1980 d o l l a r s . The data i n d i c a t e that households i n the lowest q u a r t i l e of the Y e l l o w k n i f e p o p u l a t i o n have household incomes of under $20,000 per year. Eleven p u b l i c housing tenants out of 130 (8.5%) have annual incomes i n excess of t h i s amount l e a d i n g to a r e j e c t i o n of the h y p o t h e s i s . However, i t should be noted that the average household income of p u b l i c housing tenants i s $11,632, 35.1% of that of the t o t a l p o p u l a t i o n . A l s o , a l l households l i v i n g i n p u b l i c housing have incomes below the median c i t y income of $31,325. These s t a t i s t i c s suggest that the program i s s e r v i n g low income groups. The hypothesis would not be r e j e c t e d i f i t were re - f o r m u l a t e d to read: The m a j o r i t y of p u b l i c housing tenants i n Y e l l o w k n i f e have incomes i n the lowest q u a r t i l e of the p o p u l a t i o n . or A l l p u b l i c housing tenants i n Y e l l o w k n i f e have incomes below the median c i t y income. Table X Household Income, Yellowknife, 1980 A11 Households Income Total Households Under $5000 5,000 - 9,999 10,000 - 14,999 15,000 - 19,999 20,000 - 24,999 25,000 - 29,999 30,000 - 39,999 40,000 and over Average Income Median income Number 3,200 155 155 190 325 330 345 680 1 ,020 $33,133 $31,325 Percent 100.0 4.8 4.8 5.9 10.2 10.3 10.8 21 .3 31.9 * 1985 incomes delfated to 1980 dollars SOURCE: 1. S t a t i s t i c s Canada, 1981 Census. 2. Yellowknife Housing Authority, unpublished data. 71 Public Housing Tenants 1985 Pollars 1980 P o l l a r s * Number Percent Number Percent 130 100.0 130 100.0 13 10.0 24 18.5 22 16.9 28 21.5 23 17.7 43 33.1 23 17.7 24 18.5 26 20.0 10 7.7 18 13.8 1 0.8 5 3.8 0 0 0 * 0 0 0 $16,645 $11,632 $16,800 $11,740 72 The second and t h i r d e q u i t y hypotheses ( v e r t i c a l and h o r i z o n t a l e q u i t y ) are t e s t e d by r e g r e s s i n g the estimate of tenant w e l f a r e gain (EV) a g a i n s t household c h a r a c t e r i s t i c s . The r e g r e s s i o n takes the form of equation [13]: [13] EV = f(INCOME, AGE, SIZE, SEX). INCOME, AGE and SIZE are q u a n t i t a t i v e v a r i a b l e s r e p r e s e n t i n g household income, age of household head and s i z e of household, r e s p e c t i v e l y . SEX i s a dummy v a r i a b l e f o r sex of household head (0 = male, 1 = female). Observations f o r a l l independent v a r i a b l e s are obtained from the Y e l l o w k n i f e Housing A u t h o r i t y and are coded to preserve c o n f i d e n t i a l i t y . The r e g r e s s i o n i s run us i n g Ordinary Least Squares and produces the f o l l o w i n g r e s u l t s ( t - s t a t i s t i c s are i n parentheses and s i g n i f i c a n c e l e v e l s i n square b r a c k e t s ) : EV = 2782.523 - 0.108 INCOME + 10.362 AGE + 36.669 SIZE (3.188) (-5.432) (0.782) (0.254) [.0022] [.0001] [.4369] [.7999] + 602.510 SEX ( 1 .844) [.0698] 2 . 2 The model produces an R of .3642 and an a d j u s t e d R of .3245. The r e s i d u a l p l o t s suggest the e r r o r term i s homoskedastic, u n c o r r e l a t e d and normally d i s t r i b u t e d . The r e g r e s s i o n r e s u l t s suggest the P u b l i c Housing Program may be a c h i e v i n g some v e r t i c a l and h o r i z o n t a l e q u i t y . V e r t i c a l e q u i t y i s supported by the negative sign on the INCOME c o e f f i c i e n t , suggesting b e n e f i t s decrease with income. For every $100 i n c r e a s e i n annual household income, b e n e f i t s d e c l i n e by $10.80. However, the r e s u l t s do not 73 suggest households of d i f f e r e n t s i z e s are t r e a t e d e q u i t a b l y . I d e a l l y , one would expect b e n e f i t s to i n c r e a s e with household s i z e . The parameter estimate f o r SIZE i s not s i g n i f i c a n t l y d i f f e r e n t from zero, suggesting b e n e f i t s are u n a f f e c t e d by s i z e . The r e g r e s s i o n r e s u l t s support h o r i z o n t a l e q u i t y with r e s p e c t to age. The parameter estimate f o r AGE i s not s i g n i f i c a n t l y d i f f e r e n t from zero, suggesting "equals" are t r e a t e d e q u a l l y by the program. However, there appears to be some i n e q u a l i t y with respect to sex. The parameter estimate of 602.510 f o r SEX i s s i g n i f i c a n t at the 7% l e v e l and suggests t h a t female-led households r e c e i v e an e x t r a $602.51 of b e n e f i t s per year compared to t h e i r male c o u n t e r p a r t s . In c o n c l u s i o n , the data p r o v i d e some evidence that the P u b l i c Housing Program promotes e q u i t y i n Y e l l o w k n i f e . Hypothesis 2 ( v e r t i c a l e q u i t y ) cannot be r e j e c t e d by the data and Hypothesis 3 ( h o r i z o n t a l e q u i t y ) i s p a r t l y supported, at l e a s t with r e s p e c t to age of household head. While Hypothesis 1 i s r e j e c t e d by the data, a reasonable m o d i f i c a t i o n to the hypothesis cannot be r e j e c t e d , suggesting the program i s s e r v i n g low income groups. 6.3 COMPARISON OF PUBLIC HOUSING PROGRAMS TO SHELTER  ALLOWANCES The r e s u l t s of t h i s study c o n f i r m e x p e c t a t i o n s that p u b l i c housing i s not an economically e f f i c i e n t method of improving the welfare of poor households. J u s t i f i c a t i o n of 74 the P u b l i c Housing Program i n Y e l l o w k n i f e must appeal to other c r i t e r i a such as commodity e g a l i t a r i a n i s m , i r r a t i o n a l behavior of households, p a t e r n a l i s m or the e x i s t e n c e of e x t e r n a l i t i e s . C r i t i c s of s u p p l y - s i d e housing programs argue th a t these l a t t e r c r i t e r i a are not s u f f i c i e n t j u s t i f i c a t i o n f o r the d i r e c t p r o v i s i o n of s u b s i d i z e d housing. They advocate government i n t e r v e n t i o n on the demand s i d e of the market through the p r o v i s i o n of income supplements or s h e l t e r allowances. The purpose of t h i s f i n a l s e c t i o n i s to compare the c o s t s of the p u b l i c housing p r o j e c t s i n Y e l l o w k n i f e with a s h e l t e r allowance program. A s h e l t e r allowance i s a s p e c i a l type of income supplement designed to reduce the c o s t of housing f o r s p e c i f i c groups in s o c i e t y . The Canadian C o u n c i l on S o c i a l Development d e f i n e s a s h e l t e r allowance as f o l l o w s : A d i r e c t cash t r a n s f e r made r e g u l a r l y to f a m i l i e s or i n d i v i d u a l s to enable them to a f f o r d adequate housing of t h e i r own c h o i c e from e x i s t i n g stock; the amount of the allowance i s based on income and housing c o s t s . . . (C.C.S.D., 1979, p. 2) In g e n e r a l , there are three b a s i c types of s h e l t e r allowance p l a n s : 1. an income gap p l a n where s u b s i d i e s are c a l c u l a t e d based on the d i f f e r e n c e between a c t u a l rent and a f i x e d percentage of r e c i p i e n t ' s income (e.g., a 75/30 income gap plan would p r o v i d e a subsidy based on 75% of the gap between the a c t u a l rent and 30% of income); 2. a percent of rent p l a n where s u b s i d i e s are c a l c u l a t e d based on rent o n l y ; and 75 3. an income t r a n s f e r plan where s u b s i d i e s are c a l c u l a t e d based on income c r i t e r i a o n l y . In Canada, four p r o v i n c e s p r e s e n t l y have s h e l t e r allowance programs: B r i t i s h Columbia, Quebec and New Brunswick f o r s e n i o r c i t i z e n s and Manitoba f o r f a m i l i e s and s e n i o r c i t i z e n s . A l l four programs are income gap p l a n s . The program p a r t i c i p a n t s r e c e i v e an allowance given by the f o l l o w i n g formula: [14] A = 0(R - 6Y) where A i s the s h e l t e r allowance, R i s a c t u a l r e n t , Y i s household income and 6 and 8 are program parameters and are set between 0 and 1. The e x p r e s s i o n i n parentheses re p r e s e n t s the amount by which rent exceeds a given percentage of income and i s r e f e r r e d to as the " a f f o r d a b i l i t y gap". The parameter 6 i n d i c a t e s the percentage of the a f f o r d a b i l i t y gap that i s c l o s e d by the s h e l t e r allowance program. S h e l t e r allowance programs are g e n e r a l l y t a r g e t t e d to s p e c i f i c groups, that i s , those with a f f o r d a b i l i t y problems. To l i m i t the a v a i l a b i l i t y of the program, most plans impose one or a l l of the f o l l o w i n g c o n s t r a i n t s : maximum income f o r p a r t i c i p a t i n g i n the program, maximum subsidy amount a v a i l a b l e and maximum rent t h r e s h o l d . With these c o n s t r a i n t s , equation [14] can be r e - w r i t t e n as f o l l o w s : [15] A = 0(R - 8Y) p r o v i d i n g : 1. Y < Y*; 2. A < A*; 76 3. R < R*; where Y*, A* and R* are maximums imposed by the program. In a re p o r t f o r the Canadian Homebuilders' A s s o c i a t i o n , S t e e l e (1985) estimates the c o s t s of a n a t i o n a l s h e l t e r allowance program using equation [14]. Her c a l c u l a t i o n s are based on program parameters of 75% for 0, 30% f o r 5 and the p r o v i n c i a l median ren t s f o r R*. There are no maximums imposed on household income or the amount of the allowance other than those i m p l i c i t i n the formula. T h i s study uses the same methodology as S t e e l e (1985) to estimate the c o s t of a s h e l t e r allowance program f o r Y e l l o w k n i f e . In the 1981 Census, 445 households i n Y e l l o w k n i f e r e p o r t e d annual rent payments i n excess of 25% of t h e i r incomes ( S t a t i s t i c s Canada, 1985). Table XI i n d i c a t e s the breakdown of these households by rent-to-income r a t i o and household income. 77 Table XI Households With Rent-to-income Ratios in Excess of 25%, Yellowknife, 1980  Household Income Rat io 25-29 30-34 35-39 40-44 45-49 50+ Total < $5,000 0 0 0 5 5 70 80 $5,000 - 9,999 15 15 5 5 5 50 95 $10,000 - 14,999 10 15 5 20 15 15 80 $15,000 - 19,999 25 40 25 10 5 5 110 $20,000 - 24,999 30 10 10 0 0 5 55 $25,000 - 29,999 10 0 0 0 0 5 15 $30,000 - 34,999 5 0 0 0 0 0 5 $35,000 - 39,999 5 0 0 0 0 0 5 Total 100 80 45 40 30 150 445 SOURCE: S t a t i s t i c s Canada, Private Households in Tenant-Occupied Non-Farm Dwellings Showing Gross Rent As A Percentage of 1980 Household Income By Income Categories For Yellowknife, N.W.T. , unpublished data, Nov. 1985. •^4 ~-4 78 T h i s study assumes that household incomes and r e n t s i n c r e a s e d a t the same r a t e over the p e r i o d 1980 - 1985. If the income c a t e g o r i e s i n Table XI are i n f l a t e d by the i n c r e a s e i n the C.P.I, over the f i v e - y e a r p e r i o d , the d i s t r i b u t i o n of households with rent-to-income r a t i o s i n excess of 25% remains co n s t a n t . The c o s t s of a s h e l t e r allowance program are estimated assuming the program i s an income gap p l a n . F o l l o w i n g S t e e l e (1985), the t h r e s h o l d rent (R*) i s set at the median market rent (1985) of $8,112 per year. The r e s u l t s of the c a l c u l a t i o n s are p r o v i d e d i n Table X I I . Table XII Estimated Annual Cost of a S h e l t e r Allowance  Program ( a l l f i g u r e s i n 1985 d o l l a r s ) 6 THRESHOLD RENT 5 ANNUAL COST .75 $8,112 .25 $1,191,011 .75 $8,112 .30 $985,081 .50 $8,112 .25 $794,008 .50 $8,112 .30 $656,721 NOTE: 6 i s the percentage of the a f f o r d a b i l i t y gap c l o s e d by the program and 5 i s the rent-to-income r a t i o set by the program (see equation [ 1 4 ] ) . SOURCE: Author's c a l c u l a t i o n s Estimated annual c o s t s range from $656,721 f o r a 50/30 income gap p l a n to $1,191,011 f o r a 75/25 p l a n . These f i g u r e s compare to estimated net annual c o s t s of between $848,213 and $1,369,086 f o r the p u b l i c housing p r o j e c t s 79 (assuming a 1% - 7% discount r a t e ) . These f i g u r e s are not d i r e c t l y comparable as the s h e l t e r allowance program would pr o v i d e b e n e f i t s to an estimated 365 households compared to the 144 households r e c e i v i n g b e n e f i t s from p u b l i c housing. R e c a l c u l a t i n g the program c o s t s on a per household b a s i s makes the s h e l t e r allowance program more a t t r a c t i v e . Annual c o s t s are estimated between $1,799 and $3,263 per household compared to $5,890 to $9,508 f o r each household i n p u b l i c housing. Based on these estimates, a s h e l t e r allowance program would appear to be more co s t e f f e c t i v e than a continued program of s u b s i d i z e d housing. However, s h e l t e r allowances do present some disadvantages to policymakers: (1) they may be i n e f f e c t i v e i n a housing market with a low vacancy r a t e as the amount of the allowance may be swallowed up by rent i n c r e a s e s ; (2) they cannot ensure households have access to decent q u a l i t y housing; (3) they do not n e c e s s a r i l y achieve h o r i z o n t a l e q u i t y as the amount of the allowance depends on the amount of rent p a i d by the household - two households with i d e n t i c a l c h a r a c t e r i s t i c s l i v i n g i n d i f f e r e n t q u a l i t y housing, paying d i f f e r e n t r e n t s would r e c e i v e d i f f e r e n t b e n e f i t s from the program; and (4) they cannot a s s i s t people with s p e c i a l housing needs. In a d d i t i o n to these disadvantages, s h e l t e r allowance programs may a l s o have an adverse impact on the w o r k / l e i s u r e d e c i s i o n of the household. In a recent paper, Murray (1980) compares the work d i s i n c e n t i v e s a s s o c i a t e d with cash grants 80 t o those of commodity s u b s i d y programs. A r e v i e w of h i s model w i t h a p p l i c a t i o n t o p u b l i c h o u s i n g i n Y e l l o w k n i f e i s p r e s e n t e d i n Appendix 2. The i n t e r e s t i n g r e s u l t from Murray's r e s e a r c h i s t h a t , under c e r t a i n c o n d i t i o n s , i n - k i n d s u b s i d i e s such as p u b l i c h o u s i n g , can a c t u a l l y have a s t i m u l a t i v e e f f e c t on work e f f o r t compared t o e q u i v a l e n t c a s h g r a n t s . T h i s r e s u l t s u g g g e s t s t h a t i n - k i n d t r a n s f e r s may be a p p r o p r i a t e p o l i c y i n i t i a t i v e s i n some c a s e s , d e s p i t e t h e i r economic i n e f f i c i e n c y . U l t i m a t e l y , the r e l a t i v e e f f e c t i v e n e s s of s h e l t e r a l l o w a n c e s and p u b l i c h o u s i n g programs depends upon s u p p l y and demand e l a s t i c i t i e s . As Weicher (1979) p o i n t s o u t , s u p p l y - s i d e programs a r e most e f f e c t i v e i n markets where s u p p l y i s i n e l a s t i c and demand i s i n e l a s t i c w i t h r e s p e c t t o income and e l a s t i c w i t h r e s p e c t t o p r i c e . The p r o v i s i o n of p u b l i c h o u s i n g i n such a market w i l l i n c r e a s e the t o t a l s u p p l y of h o u s i n g as l a n d l o r d s and b u i l d e r s w i l l not r e a c t by r e d u c i n g the s u p p l y . However, i f the s u p p l y of h o u s i n g i s e l a s t i c , the p r o v i s i o n of p u b l i c h o u s i n g w i l l d i s p l a c e p r i v a t e c o n s t r u c t i o n . Under t h e s e c i r c u m s t a n c e s , a demand-side s u b s i d y w i l l be more e f f e c t i v e i n i m p r o v i n g the h o u s i n g c o n d i t i o n s of low-income h o u s e h o l d s . The s u p p l y and demand e l a s t i c i t i e s f o r h o u s i n g i n Y e l l o w k n i f e l e a d t o i n c o n c l u s i v e r e s u l t s about the r e l a t i v e e f f e c t i v e n e s s of s h e l t e r a l l o w a n c e s and p u b l i c h o u s i n g . As argued p r e v i o u s l y , the s u p p l y of r e n t a l h o u s i n g appears t o be r e l a t i v e l y i n e l a s t i c , as e v i d e n c e d by the z e r o vacancy 81 ra t e and long w a i t i n g l i s t s f o r e x i s t i n g apartments. Income and p r i c e e l a s t i c i t i e s of the t o t a l p o p u l a t i o n i n Y e l l o w k n i f e are not known, but esti m a t e s obtained from the p o p u l a t i o n of p u b l i c housing tenants i n d i c a t e the demand f o r housing i s i n e l a s t i c with r e s p e c t to both c u r r e n t income and p r i c e . The estimates of income e l a s t i c i t y cover a wide range from .00007 to .64 and tend to i n c r e a s e with income, as expected. Estimates of p r i c e e l a s t i c i t y span a s i m i l a r range from - .00005 to - . 5 6 with an upward d r i f t i n ab s o l u t e value as income i n c r e a s e s . The demand e l a s t i c i t i e s do not pr o v i d e d e c i s i v e evidence on the r e l a t i v e e f f e c t i v e n e s s of demand-side versus s u p p l y - s i d e s u b s i d i e s . The i n e l a s t i c supply of housing tends to favour s u p p l y - s i d e programs but without f u r t h e r r e s e a r c h , no d e f i n i t e c o n c l u s i o n s can be drawn. CHAPTER 7 IMPLICATIONS 7. IMPLICATIONS Chapter 1 i d e n t i f i e d two o b j e c t i v e s f o r t h i s study: 1. to determine i f the d i r e c t p r o v i s i o n of p u b l i c housing i n Y e l l o w k n i f e i s an economically e f f i c i e n t method of meeting the housing needs of poor households; and 2. to determine i f the P u b l i c Housing Program i n Ye l l o w k n i f e promotes h o r i z o n t a l and v e r t i c a l e q u i t y . The i m p l i c i t q u e s t i o n s posed by these o b j e c t i v e s were answered i n Chapter 6. As expected, the P u b l i c Housing Program i s not economically e f f i c i e n t and has a negative net present value ranging from -$13,345 m i l l i o n to -$17,485 depending on the s o c i a l d i s c o u n t r a t e . The q u e s t i o n u n d e r l y i n g the second o b j e c t i v e i s more d i f f i c u l t to answer, although the a n a l y s i s suggests the program achieves a small degree of v e r t i c a l e q u i t y and some h o r i z o n t a l e q u i t y . In any case, the message d e l i v e r e d by t h i s a n a l y s i s i s c l e a r : the j u s t i f i c a t i o n of the P u b l i c Housing Program i n Y e l l o w k n i f e must appeal to not i o n s other than economic e f f i c i e n c y . T h i s chapter analyses the i m p l i c a t i o n s of t h i s message f o r policy-makers. The a n a l y s i s begins i n S e c t i o n 7.1 with a statement of o b j e c t i v e s of the two agents i n v o l v e d i n fo r m u l a t i n g housing p o l i c y i n the N.W.T. - the N.W.T. Housing C o r p o r a t i o n and C.M.H.C. S e c t i o n 7.2 ana l y s e s the r e s u l t s of t h i s study from the separate p e r s p e c t i v e s of these two agen c i e s . S e c t i o n 7.3 concludes the chapter and the t h e s i s with a summary of the major f i n d i n g s of the study and some suggestions f o r f u r t h e r r e s e a r c h . 83 84 7.1 POLICY OBJECTIVES The o b j e c t i v e s of the f e d e r a l housing agency, C.M.H.C., are taken d i r e c t l y from the preamble to the N a t i o n a l Housing A c t : to promote the c o n s t r u c t i o n of new houses, the r e p a i r and modernization of e x i s t i n g houses, and the improvement of housing and l i v i n g c o n d i t i o n s . (N.H.A. 1953-54, p. 1) Within t h i s broad mandate, C.M.H.C. has d e f i n e d four s p e c i f i c s u b - o b j e c t i v e s : 1. S o c i a l Housing - to a s s i s t those whose income i s i n s u f f i c i e n t to gain access to adequate housing by supp o r t i n g i n c o n j u n c t i o n with p r o v i n c e s , m u n i c i p a l i t i e s and t h e i r agencies low and moderate income p u b l i c housing and the establishment of n o n - p r o f i t and co - o p e r a t i v e housing c o r p o r a t i o n s . 2. R e h a b i l i t a t i o n and Conservation - to promote and support the r e h a b i l i t a t i o n of substandard housing and the improvement of e x i s t i n g housing. 3. Market Housing - to promote the e f f e c t i v e o p e r a t i o n of mortgage and housing markets. 4. Community S e r v i c e s - to a s s i s t i n the achievement and maintenance of sound community environment by sup p o r t i n g the p r o v i s i o n of ba s i c community s e r v i c e . ( C o n s u l t a t i o n  Paper, 1985, pp. 13-15). The o v e r a l l o b j e c t i v e of the N.W.T. Housing C o r p o r a t i o n , as s t a t e d i n the 1983/84 Annual Report, i s : to develop, c o - o r d i n a t e and d i r e c t s o c i a l housing programs to ensure that an adequate standard of housing i s a v a i l a b l e to r e s i d e n t s i n need, i n the 85 Northwest T e r r i t o r i e s . (Annual Report, 1983/84, p.3) The next s e c t i o n e v a l u a t e s the P u b l i c Housing Program in Y e l l o w k n i f e i n terms of i t s success i n promoting the s t a t e d o b j e c t i v e s of the two housing a g e n c i e s . 7.2 EVALUATION OF THE PUBLIC HOUSING PROGRAM IN YELLOWKNIFE The c o s t - b e n e f i t a n a l y s i s i n t h i s study adopts the p e r s p e c t i v e of the Canadian p u b l i c . As the f e d e r a l agency r e s p o n s i b l e f o r housing, C.M.H.C.'s p o l i c y o b j e c t i v e s should r e f l e c t the i n t e r e s t s of the p u b l i c and, t h e r e f o r e , the r e s u l t s of t h i s study w i l l d i r e c t l y a p p l y . The N.W.T. Housing C o r p o r a t i o n , on the other hand, has a mandate t o serve the p u b l i c i n t e r e s t of the N.W.T. on l y . The c r i t e r i a f o r e v a l u a t i n g housing p o l i c y from the t e r r i t o r i a l p e r s p e c t i v e w i l l not d i f f e r - i s s u e s of e f f i c i e n c y and eq u i t y are s t i l l r e l e v a n t . However, the measurement of c o s t s and b e n e f i t s , p a r t i c u l a r l y non-tenant b e n e f i t s w i l l d i f f e r and c o u l d l e a d to d i f f e r e n t assessments of the e f f i c i e n c y of the program. From C.M.H.C.'s p e r s p e c t i v e , the P u b l i c Housing Program in Y e l l o w k n i f e i s promoting one of the C o r p o r a t i o n ' s s t a t e d o b j e c t i v e s . I t i s " a s s i s t [ i n g ] those whose income i s i n s u f f i c i e n t to gain access to adequate housing." As rep o r t e d i n the l a s t c hapter, the program i s s e r v i n g low income households. However, as i n d i c a t e d by the negative net present v a l u e , i t i s not doing so e f f i c i e n t l y . From the f e d e r a l p e r s p e c t i v e , i t i s d o u b t f u l that the program i s 86 ge n e r a t i n g non-tenant b e n e f i t s to the Canadian p u b l i c of the order r e q u i r e d to j u s t i f y the program on the grounds of economic e f f i c i e n c y . Furthermore, the N.W.T., i n g e n e r a l , and Y e l l o w k n i f e , i n p a r t i c u l a r , i s so remote from southern Canada that i t i s u n l i k e l y t h a t the median v o t e r would support the program on the grounds of a merit good argument, commodity e g a l i t a r i a n i s m or p a t e r n a l i s m . However, before c o n c l u d i n g that the P u b l i c Housing Program i n Y e l l o w k n i f e cannot be supported from a f e d e r a l p e r s p e c t i v e , some c o n s i d e r a t i o n should be given to Murray's r e s e a r c h on work d i s i n c e n t i v e s (Murray, 1980). In a n a l y s i n g s u b s i d i z e d housing programs and income maintenance experiments i n the Unit e d S t a t e s and comparing the impact of the two programs on the work e f f o r t of the household, Murray f i n d s that s u b s i d i z e d housing programs can a c t u a l l y have a s t i m u l a t i v e e f f e c t on work e f f o r t compared to u n r e s t r i c t e d e q u i v a l e n t cash g r a n t s . H i s a n a l y s i s suggests the P u b l i c Housing Program i n the U.S. reduces work e f f o r t by approximately 4% compared to estimates of approximately 13% f o r the income maintenance experiments. A p p l y i n g Murray's model to the Ye l l o w k n i f e data suggests the P u b l i c Housing Program i n Ye l l o w k n i f e reduces work e f f o r t by between 2% and 8% per week (see Appendix 2 f o r complete r e s u l t s ) . U n f o r t u n a t e l y , there are no comparable f i g u r e s f o r the d e c l i n e i n work e f f o r t from income maintenance or s h e l t e r allowance programs i n the N.W.T., but i f the f i g u r e of 13% obtained i n the U.S. i s a p p l i c a b l e , there seems to be some support f o r p r o v i d i n g 87 low-income households with s u b s i d i z e d housing r a t h e r than income supplements. In order to examine the program from the t e r r i t o r i a l p e r s p e c t i v e , two adjustments are made to the a n a l y s i s conducted i n Chapter 6. F i r s t , the NPV i s r e v i s e d to i n c l u d e only the N.W.T. Housing C o r p o r a t i o n ' s share of the c a p i t a l and o p e r a t i n g c o s t s . Secondly, arguments are presented f o r su p p o r t i n g the program on the f o l l o w i n g grounds: p o s i t i v e e x t e r n a l i t i e s from good housing, housing as a merit good and commodity e g a l i t a r i a n i s m . Revised Net Present Value R e c a l c u l a t i n g the c a p i t a l and o p e r a t i n g c o s t s to r e f l e c t the N.W.T. share of the investments y i e l d s r e v i s e d net present values ranging between -$4,420 m i l l i o n and -$4 ,850 m i l l i o n as i n d i c a t e d i n Table X I I I . Table XIII Estimates of Net Present Value, N.W.T. Share J_% 3% 5% 7% -$4 ,849 ,514 -4 ,621 ,986 -4 ,495 ,708 -4 ,420 ,433 In order to j u s t i f y the program on e f f i c i e n c y grounds, the p r o j e c t s must generate non-tenant b e n e f i t s of between $4,420 and $4,850 m i l l i o n over 50 y e a r s . At d i s c o u n t r a t e s of 1% to 7%, t h i s t r a n s l a t e s to annual b e n e f i t s of between $123,724 and $320,304 or approximately $12 to $31 per c a p i t a of the Y e l l o w k n i f e p o p u l a t i o n . The remainder of t h i s s e c t i o n 88 examines the p o s s i b i l i t y t h a t non-tenant b e n e f i t s of t h i s magnitude may be a t t r i b u t a b l e to the p r o j e c t s . Positive E x t e r n a l i t i e s In Chapter 3, two p o s s i b l e e x t e r n a l i t i e s a s s o c i a t e d with s u b s i d i z e d housing p r o j e c t s were i d e n t i f i e d : (1) a net i n c r e a s e i n the value of surrounding p r o p e r t i e s and (2) a r e d u c t i o n i n the " s o c i a l " c o s t s of sub-standard housing. As no e m p i r i c a l work has been undertaken to determine the impact of p u b l i c housing p r o j e c t s on house p r i c e s i n Y e l l o w k n i f e , no d e f i n i t e c o n c l u s i o n s can be reached at t h i s time. S i m i l a r l y , there i s no e m p i r i c a l evidence to t e s t the hy p o t h e s i s that the p u b l i c housing p r o j e c t s have reduced the " s o c i a l " c o s t s of sub-standard housing. Housing as a Merit Good/Commodity Egalitarianism In Chapter 3, Musgrave's n o t i o n of "merit goods" and Tobin's theory of commodity e g a l i t a r i a n i s m were int r o d u c e d (see S e c t i o n 3.2.1). To r e i t e r a t e , a merit good i s a good that s o c i e t y wishes to encourage i t s members to consume. The concept of merit goods i s r e l a t e d to Tobin's theory that some goods, such as the n e c e s s i t i e s of l i f e and h e a l t h , should be d i s t r i b u t e d e q u a l l y . In t h i s sense, a b a s i c minimum standard of housing f o r a l l members of s o c i e t y can be c o n s i d e r e d e i t h e r as a merit good or as a good q u a l i f y i n g f o r "commodity e g a l i t a r i a n i s m " . 89 While i t may be d i f f i c u l t to j u s t i f y the P u b l i c Housing Program i n Y e l l o w k n i f e on the grounds of commodity e g a l i t a r i a n i s m or merit good arguments from the p e r s p e c t i v e of the Canadian p u b l i c , i t may be f e a s i b l e to do so from the p e r s p e c t i v e of the r e s i d e n t s of the N.W.T., or at l e a s t from the p e r s p e c t i v e of the r e s i d e n t s of Y e l l o w k n i f e . Y e l l o w k n i f e i s a small community of under 11,000 people. The welfare of i t s poorer c i t i z e n s i s not as easy to mask as i t may be i n l a r g e c i t i e s i n southern Canada. The median v o t e r i n Y e l l o w k n i f e i s unable to a v o i d the e x t e r n a l i t i e s of poor q u a l i t y housing by l i v i n g i n remote, e x c l u s i v e s u b d i v i s i o n s of the c i t y . T h e r e f o r e , i t seems l i k e l y that the welfare of poorer households w i l l enter the u t i l i t y schedule of other r e s i d e n t s of the c i t y . By improving the housing c o n d i t i o n s of the poor, through programs such as the P u b l i c Housing Program, s o c i e t y i n Y e l l o w k n i f e may move up to a higher l e v e l of u t i l i t y . The u n d e r l y i n g q u e s t i o n that must be addressed by policy-makers i n the N.W.T. i s whether t h i s i n c r e a s e i n welfar e i s worth the $123,724 to $320,304 necessary to j u s t i f y the program on e f f i c i e n c y grounds. 7.3 CONCLUSIONS T h i s study has eva l u a t e d the P u b l i c Housing Program i n Y e l l o w k n i f e a c c o r d i n g to the two c r i t e r i a of economic e f f i c i e n c y and e q u i t y . The program has been analysed from the p e r s p e c t i v e of the Canadian p u b l i c , as r e f l e c t e d i n C.M.H.C.'s p o l i c y o b j e c t i v e s , and from the p e r s p e c t i v e of 90 the r e s i d e n t s of the N.W.T., as r e f l e c t e d i n the o b j e c t i v e s of the N.W.T. Housing C o r p o r a t i o n . In both cases, the NPV, c a l c u l a t e d from measurable c o s t s and b e n e f i t s , i s negative, suggesting that the program i s not economically e f f i c i e n t . Non-tenant b e n e f i t s of between $446,082 and $966,955 per year are r e q u i r e d to j u s t i f y the program from the n a t i o n a l p e r s p e c t i v e . Arguments presented here suggest that non-tenant b e n e f i t s to the Canadian p u b l i c of t h i s magnitude are not l i k e l y , l e a d i n g to the c o n c l u s i o n that the program cannot be j u s t i f i e d on grounds of e f f i c i e n c y . From the t e r r i t o r i a l p e r s p e c t i v e , r e q u i r e d non-tenant b e n e f i t s to support economic e f f i c i e n c y are much lower at $123,724 to $320,304 or $12 to $31 per c a p i t a of the Y e l l o w k n i f e p o p u l a t i o n , suggesting i t may be p o s s i b l e to appeal to notions of merit goods, p o s i t i v e e x t e r n a l i t i e s or commodity e g a l i t a r i a n i s m to j u s t i f y the program. The a n a l y s i s of Chapter 6 p r o v i d e s some evidence that the P u b l i c Housing Program i s promoting e q u i t y i n Y e l l o w k n i f e . The r e g r e s s i o n r e s u l t s support the hypothesis of v e r t i c a l e q u i t y with respect to income. The r e s u l t s from t e s t i n g the hyp o t h e s i s of h o r i z o n t a l e q u i t y are s l i g h t l y ambiguous. While there i s some support f o r h o r i z o n t a l e q u i t y with respect to age of household head, the a n a l y s i s suggests that male- and female - l e d households are not t r e a t e d e q u a l l y . The r e g r e s s i o n r e s u l t s i n d i c a t e that female-led households r e c e i v e much l a r g e r annual b e n e f i t s from the program than t h e i r male c o u n t e r p a r t s . 91 A comparison of the r e s u l t s of t h i s study with other s t u d i e s i n the l i t e r a t u r e suggest the P u b l i c Housing Program i n Y e l l o w k n i f e i s performing at approximately the same l e v e l as s i m i l a r programs i n the U n i t e d S t a t e s and Europe. The estimates of e f f i c i e n c y r e p o r t e d i n the l i t e r a t u r e range from a low of 25% r e p o r t e d by Sumka and Stegman (1978) i n t h e i r study of p u b l i c housing i n non-metropolitan c i t i e s i n the U.S. to a high of 85% r e p o r t e d by Walden (1981) i n h i s study of s e n i o r c i t i z e n p r o j e c t s i n Rochester, New York. Estimates of e f f i c i e n c y f o r the Y e l l o w k n i f e p r o j e c t s f a l l w i t h i n t h i s range and vary between 29% and 47% depending on the d i s c o u n t r a t e . The e q u i t y r e s u l t s r e p o r t e d i n the l i t e r a t u r e vary, although most s t u d i e s f i n d the s u b s i d i z e d housing program under study a c h i e v e s v e r t i c a l but not h o r i z o n t a l e q u i t y . A comparison of the P u b l i c Housing Program i n Y e l l o w k n i f e to a s h e l t e r allowance program suggests that the l a t t e r would be much more e f f i c i e n t . Estimated annual c o s t s of a s h e l t e r allowance program range from $1,799 f o r a 50/30 pla n to $3,263 f o r a 75/25 p l a n . A l l f i g u r e s r epresent annual c o s t s per r e c i p i e n t . In comparison, annual c o s t s of the P u b l i c Housing Program, a f t e r deducting rent revenues, range from $5,890 to $9,508 per household. However, as p o i n t e d out i n Chapter 6, s h e l t e r allowance programs present some disadvantages to policy-makers as they cannot ensure the housing c o n d i t i o n s of the program r e c i p i e n t s are improved. A l s o , as i n d i c a t e d i n Murray's re s e a r c h , p u b l i c 92 housing programs may be p r e f e r r e d to cash grants as they have l e s s of an impact on the work e f f o r t decisons of the household (Murray, 1980). In c o n c l u s i o n , the r e s u l t s of t h i s study are c o n s i s t e n t with the recent l i t e r a t u r e . From an e f f i c i e n c y viewpoint, i t i s very d i f f i c u l t to j u s t i f y i n - k i n d housing programs such as p u b l i c housing from the n a t i o n a l p e r s p e c t i v e . S u b s t a n t i a l non-tenant b e n e f i t s are r e q u i r e d to produce a p r o j e c t with a non-negative net present v a l u e . 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Mieszkowski and M. Strasheim, ( e d s . ) , Current Issues i n Urban  Economics, (Ba l t i m o r e : Johns Hopkins U n i v e r s i t y Press, 1979). Wilner, D a n i e l M., Walkley, R. P., Pin k e r t o n , T . C and Tayback, M. The Housing Environment and Family L i f e : A  L o n g i t u d i n a l Study of the E f f e c t s of Housing on  M o r b i d i t y and Mental Health~ ( B a l t i m o r e : The Johns Hopkins Press, 1962). 101 APPENDICES APPENDIX 1 HEDONIC REGRESSION RESULTS 1. Market Rent E q u i v a l e n t Model RENT = 0n + |3,STOR + 0-YEAR + /3-BED + 0.COND + j3cTYPE + /3gFURN + 0 7DIST2 + 0gDIST3 + /3QUTIL + u 2. V e r i f i c a t i o n Model YHAT = aQ + a 1RENT + u Data Set 1 = 462 o b s e r v a t i o n s Data Set 2 = 464 o b s e r v a t i o n s Table XIV Regression R e s u l t s from L i n e a r Model Using Data Set 1 V a r i a b l e Parameter Est imate t - S t a t i s t i c S i g n i f i c a n c e L e v e l INTERCEPT 5866.174 77.504 .0001 STOR -227.065 -18.508 .0001 AGE 168.618 25.384 .0001 BED 1 1 71.447 38.932 .0001 COND -601.083 -10.167 .0001 TYPE 935.039 7.819 .0001 FURN 309.028 4.439 .0001 DIST2 296.786 6.542 .0001 DIST3 -436.318 -3.769 .0002 UTIL -375.666 -9.242 .0001 R 2 = .9227 2 R (adjusted) = .9212 F s t a t i s t i c = 599.437 102 1 03 Table XV Hedonic Regression C o r r e l a t i o n M a t r i x INT STOR YEAR BED COND TYPE FURN DIST2 DIST3 UTIL INT 1.0 .06 -.21 -.52 -.64 .21 -.53 .08 .31 -.26 STOR 1.0 -.35 .52 -.01 -.02 .10 .20 .00 -.24 YEAR 1 .0 -.21 -.27 .40 .24 -.04 .02 -.14 BED 1.0 .24 -.38 .20 -.04 -.38 -.05 COND 1 .0 -.31 .30 -.27 -.20 .01 TYPE 1.0 .07 .20 .26 -.23 FURN 1 .0 .06 -.05 .00 DIST2 1 .0 .20 -.01 DIST3 1 .0 -.15 UTIL 1 .0 104 Table XVI Hedonic Regression C o l l i n e a r i t y D i a g n o s t i c s Number Eigenvalue C o n d i t i o n Index 1 4.848 1 .000 2 1 .326 1.912 3 1 .043 2.1 56 4 1 .003 2. 1 98 5 0.839 2.404 6 0.427 3.370 7 0.234 4.550 8 0. 1 35 5.986 9 0. 1 06 6.753 10 0.037 11.427 NOTE: Eigenvalues r e p o r t e d here are f o r the matrix (X'X). The c o n d i t i o n index i s the square root of the r a t i o of the l a r g e s t eigenvalue to each i n d i v i d u a l e i g e n v a l u e . A c o n d i t i o n index of 30 or more i n d i c a t e s moderate to strong c o l l i n e a r i t y . 1800 + 1500 + 1200 + 900 + E 600 + S I D U 300 + A L S 0 + * -300 + -600 + -900 + 1200 + 1500 + -- + --5000 + 5500 FIGURE 7 PLOT OF RESIDUALS AGAINST PREDICTED VALUES 105 * * * * * * * * * * * * * * * * * * 6000 +--6500 + - -7000 + - -7500 + _. 8000 +- -8500 + __ 9000 + --9500 10000 — + 10500 o PREDICTED VALUE FIGURE 8 NORMAL PLOT OF RESIDUALS 106 4 + 3 + S T U D 2 + E N T I Z 1 + E D R E 0 + S I D U A -1 + L * * t . ****** * * *** * *** * * * » * * -2 + t * -3 + -4 + 4 0 " 3 5 "3-0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 & EXPECTED VALUES FROM STANDARDIZED NORMAL DISTRIBUTION FIGURE 9 PLOT OF YHAT AGAINST RENT 107 YHAT 11000 + 10000 + 9000 + 8000 + 7000 + 6000 + 5000 + 4000 + 5000 M D N EB C D 0 B C C F H A U L K B HC B CB W B C KM C D D G B D B 5500 6000 6500 7000 7500 8000 RENT 8500 9000 9500 10000 10500 o LEGEND: A = 1 OBSERVATION. B = 2 OBSERVATIONS. ETC. APPENDIX 2 A MODEL FOR ESTIMATING WORK DISINCENTIVES ASSOCIATED WITH  IN-KIND SUBSIDIES WITH SPECIFIC APPLICATION TO PUBLIC  HOUSING IN YELLOWKNIFE, N.W.T. Government p o l i c y to r e d i s t r i b u t e income can take one of three forms: d i r e c t cash t r a n s f e r s ( i . e . , income supplements), p r i c e s u b s i d i e s ( i . e . s h e l t e r allowances) or i n - k i n d t r a n s f e r s (e.g., p u b l i c housing programs). Each of these a l t e r n a t i v e s has a d i f f e r e n t impact on the household's budget set and, consequently, a d i f f e r e n t e f f e c t on household behavior. From an e f f i c i e n c y viewpoint, an optimal p o l i c y i s one that minimizes the d i s t o r t i o n i n household behavior. T r a d i t i o n a l l y , i n Canada, the housing needs of the poor have been addressed through i n - k i n d t r a n s f e r s from programs such as P u b l i c Housing, Co-operative Housing and No n - P r o f i t Housing. In a l l these programs, a s p e c i f i c q u a n t i t y of housing i s provided to the household at a rent based on income. As t h i s rent l e v e l i s l e s s than the market rent, i n - k i n d s u b s i d i e s i n d i r e c t l y i n c r e a s e household income. I f l e i s u r e i s a normal good, then any incr e a s e i n income w i l l induce a u t i l i t y - m a x i m i z i n g household to consume more l e i s u r e . In other words, i n - k i n d s u b s i d i e s w i l l reduce work e f f o r t . An i n t e r e s t i n g q u e s t i o n f o r p u b l i c p o l i c y i s whether the work d i s i n c e n t i v e a s s o c i a t e d with an i n - k i n d t r a n s f e r i s gr e a t e r than or l e s s than that of other income r e d i s t r i b u t i o n mechanisms. 108 109 T h i s appendix d e s c r i b e s the t r a d i t i o n a l economic model f o r a s s e s s i n g work d i s i n c e n t i v e s and a l s o p r e s e n t s a new approach to the problem developed by Michael Murray (1980). The model i s a p p l i e d to the P u b l i c Housing Program i n Y e l l o w k n i f e to determine the extent of the work d i s i n c e n t i v e . 1. THE TRADITIONAL INCOME-LEISURE MODEL The t r a d i t i o n a l i n c o m e - l e i s u r e model t r e a t s the work e f f o r t d e c i s i o n of a household as a consumer maximization problem. The household d e r i v e s u t i l i t y from consumption of l e i s u r e and n o n - l e i s u r e goods and chooses i t s bundle of goods to maximize u t i l i t y s u b j e c t to a budget c o n s t r a i n t . The household u t i l i t y f u n c t i o n takes the form U = u(L, x 1 , . . . x n ) where L r e p r e s e n t s l e i s u r e and x^ re p r e s e n t s consumption of the i n o n - l e i s u r e good. The v e c t o r of n o n - l e i s u r e goods, ( x ^ . . . x n ) i s r e p l a c e d with a composite commodity, Y, which re p r e s e n t s t o t a l income (earned and unearned). It i s assumed that the household has a f i x e d number of hours, T, to a l l o c a t e between work and l e i s u r e . T h i s i m p l i e s the household faces the f o l l o w i n g budget c o n s t r a i n t : Y = w(T - L) + y where w i s the wage r a t e and y i s unearned income. Fo r m a l l y , the household's o p t i m i z a t i o n problem can be s t a t e d as: Max u(L, Y) s u b j e c t to Y = w(T - L) + y. 110 S o l v i n g t h i s m a x i m i z a t i o n problem y i e l d s the f o l l o w i n g f i r s t o r d e r c o n d i t i o n s : L: 3U/3L + Xw = 0 Y: 3U/3Y + X = 0 R e a r r a n g i n g the f i r s t o r d e r c o n d i t i o n s g i v e s the o p t i m i z a t i o n c o n d i t i o n t h a t the m a r g i n a l r a t e of s u b s t i t u t i o n between l e i s u r e and n o n - l e i s u r e goods e q u a l s the wage r a t e . D i a g r a m a t i c a l l y , the household o p t i m i z a t i o n problem can be r e p r e s e n t e d as i n F i g u r e 10. Income (Y) i s on the v e r t i c a l a x i s and w o r k / l e i s u r e on the h o r i z o n t a l . The h o r i z o n t a l d i s t a n c e 0T measures the t o t a l hours a v a i l a b l e . Work e f f o r t i s measured from p o i n t T and l e i s u r e i s measured from the o r i g i n 0. Y r e p r e s e n t s the maximum income max a v a i l a b l e i f the household devotes a l l i t s time to e a r n i n g V 0 A T L Le isure > Work 10 T r a d i t i o n a l Income-Leisure Model 111 income. I f unearned income i s assumed to be zero, then the budget c o n s t r a i n t f a c i n g the household i s Y T. If unearned 3 3 max income i s p o s i t i v e , the budget c o n s t r a i n t s h i f t s out by a v e r t i c a l d i s t a n c e equal to the amount of unearned income. Given a well-behaved u t i l i t y f u n c t i o n ( s t r i c t l y quasi-concave, twice c o n t i n u o u s l y d i f f e r e n t i a b l e ) , the household maximizes u t i l i t y at the tangency p o i n t of i n d i f f e r e n c e curve U and the budget c o n s t r a i n t (point E i n F i g u r e 10). At t h i s p o i n t , the household works TA hours and r e c e i v e s earned income Y.. A The assumptions u n d e r l y i n g t h i s model can be summarized as f o l l o w s : 1. the household may work as many hours as i t d e s i r e s , up to the maximum of T; 2. the wage ra t e per hour i s the same i r r e s p e c t i v e of the number of hours worked (a change in the wage rate due to overtime bonuses e t c . would not change the a n a l y s i s , i t would only introduce a "kink" i n the budget c o n s t r a i n t ) ; 3. the household u t i l i t y f u n c t i o n i s s t r i c t l y quasi-concave and twice c o n t i n u o u s l y d i f f e r e n t i a b l e ; and 4. the r e l a t i v e p r i c e s of n o n - l e i s u r e goods are constant. Assumptions 1, 2 and 3 are r e l a t i v e l y weak. Assumption 4 i s a stronger r e s t r i c t i o n and i s necessary i f n o n - l e i s u r e goods are to be t r e a t e d as a composite commodity. By the Hicks Aggregation Theorem, goods may be represented by a composite commodity i f the p r i c e s of a l l goods i n the composite move toge t h e r . The assumption of constant r e l a t i v e p r i c e s ensures 112 t h i s c o n d i t i o n i s s a t i s f i e d . While t h i s assumption may be a p p r o p r i a t e f o r modelling income supplement programs, i t i s not a p p r o p r i a t e when commodity s u b s i d i e s are i n v o l v e d because the p r i c e r a t i o s w i t h i n the composite are a l t e r e d . The usual method f o r d e a l i n g with commodity s u b s i d i e s i s to add a t h i r d dimension to the model and express the u t i l i t y f u n c t i o n as f o l l o w s : [ 1 ] U = u(L, H, Z) where L i s l e i s u r e , as before, H i s the s u b s i d i z e d good and Z i s a composite of un s u b s i d i z e d goods. As Murray (1980) p o i n t s out, t h i s method has some p r a c t i c a l disadvantages as i t r e q u i r e s c o l l e c t i o n of work e f f o r t data f o r each subsidy program i n order to estimate the parameters of the u t i l i t y f u n c t i o n . To av o i d the expense of data c o l l e c t i o n , Murray designs a new model that allows the work d i s i n c e n t i v e e f f e c t s of commodity subsidy programs to be i n f e r r e d from data c o l l e c t e d f o r income supplement programs. His mo t i v a t i o n i n developing t h i s model stems from the a v a i l a b i l i t y of a r i c h data base on work e f f o r t e f f e c t s of income maintenance programs i n the U.S. His model i s d e s c r i b e d i n S e c t i o n 2. 2. MURRAY'S MODEL The essence of Murray's approach i s to r e - d e f i n e the composite commodity, Y, i n the u t i l i t y schedule. Instead of t r e a t i n g Y as money income, Murray t r e a t s i t as the H i c k s i a n e q u i v a l e n t income. The r e l a t i o n s h i p between money income and 1 1 3 H i c k s i a n income can be expressed as f o l l o w s . H i c k s i a n income, f o r a given bundle (H, Z), i s d e f i n e d as the money income which would, at market p r i c e s , enable the household to achieve the same u t i l i t y l e v e l as with (H, Z). In the s p e c i a l case of constant commodity p r i c e s , H i c k s i a n income i s equal to money income. However, i f p r i c e r a t i o s change, as they do when a housing subsidy i s i n t r o d u c e d , the two measures w i l l d i f f e r . A housing subsidy a l l o w s the household to move up to a higher l e v e l of u t i l i t y . The H i c k s i a n income i s the amount of income that the household would r e q u i r e to enable i t to achieve t h i s new l e v e l of u t i l i t y at the o r i g i n a l p r i c e r a t i o s . Murray r e d e f i n e s the household u t i l i t y f u n c t i o n f o r l e i s u r e and n o n - l e i s u r e goods as f o l l o w s : [2] U = u(L, Y') T h i s r e p r e s e n t a t i o n assumes the u t i l i t y f u n c t i o n i s weakly separable with respect to l e i s u r e and n o n - l e i s u r e goods. T h i s i m p l i e s that the marginal r a t e s of s u b s t i t u t i o n among commodities are independent of the amount of l e i s u r e consumed. As Murray p o i n t s out, t h i s assumption i s not unreasonable f o r a n a l y s i n g housing s u b s i d i e s as the v e c t o r of n o n - l e i s u r e commodities would i n c l u d e housing and a composite of other goods. I t would be unreasonable f o r a n a l y s i n g programs such as v o c a t i o n a l t r a i n i n g as consumption of t h i s commodity would not be independent of the amount of l e i s u r e consumed. For our purposes, however, the assumption of weak s e p a r a b i l i t y seems p l a u s i b l e . 114 For ease of p r e s e n t a t i o n , i t i s a l s o assumed that unearned income, y, i s zero. The r e s u l t s of the a n a l y s i s do not change i f y i s p o s i t i v e , but the assumption of zero unearned income s i m p l i f i e s the n o t a t i o n i n the maximization problem that f o l l o w s . In the absence of a housing subsidy, the household maximizes u t i l i t y s u b j e c t to the c o n s t r a i n t that expenditures cannot exceed money income, Y. In t h i s case, Y' and Y are i d e n t i c a l and the model c o l l a p s e s to the t r a d i t i o n a l i n c o m e - l e i s u r e model. However, i n the presence of a housing subsidy, the household budget i s e f f e c t i v e l y c o n s t r a i n e d by the H i c k s i a n income, Y', i n s t e a d of money income. As Y' i s some f u n c t i o n of Y, the household maximization problem can be expressed as: Max u(L,Y') s u b j e c t to Y' = f(Y) where f(Y) = f(w/c), w = wage r a t e and K = hours of labour ( e q u i v a l e n t to T - L ) . The Lagrangian becomes: L(L,Y',X) = U(L,Y') + X[Y' - f(w- K ) ] S o l v i n g the maximization problem y i e l d s the f o l l o w i n g f i r s t order c o n d i t i o n s : L: 9u(L,Y')/3L - X3f(w->c)/3L = 0 = 3u(L,Y')/3L + Xw3Y'/3Y = 0 Y': 3u(L,Y')/3Y' + X = 0 X: Y' - f(w- K) = 0 Rearranging the f i r s t order c o n d i t i o n s g i v e s the o p t i m i z a t i o n c o n d i t i o n : [3] 3u/3L = w 3Y' 3u/3Y' 3Y 1 15 In words, e q u a t i o n [3] says t h a t the m a r g i n a l r a t e of s u b s t i t u t i o n between l e i s u r e and H i c k s i a n income must equal the e f f e c t i v e wage r a t e . In the absence of a housing s u b s i d y , dl'/dY = 1 and e q u a t i o n [3] reduces t o the t r a d i t i o n a l f i r s t o r d e r c o n d i t i o n t h a t the m a r g i n a l r a t e of s u b s t i t u t i o n between l e i s u r e and income e q u a l s the wage r a t e . Murray demonstrates t h a t , under c e r t a i n c o n d i t i o n s , i n - k i n d h o u s i n g s u b s i d i e s w i l l r e s u l t i n 3Y'/9Y be i n g g r e a t e r than 1, making Y' a concave f u n c t i o n of work e f f o r t . T h i s i s i l l u s t r a t e d i n F i g u r e 11. In the absence of a su b s i d y , the household maximizes a t p o i n t A i n F i g u r e 11. With an i n - k i n d h ousing s u b s i d y , r e q u i r i n g consumption of a f i x e d minimum q u a n t i t y of ho u s i n g , the household moves up to p o i n t B, r e d u c i n g work e f f o r t from V U2 ,U3 Y2 Y1 ' • ' LI L2 L3 T 0 L 11 Murrays Model 1 16 ( T - L 1 ) to ( T - L 2 ) hours. With an " e q u i v a l e n t " cash grant, equal to Y 2 - Y 1 , the household moves up to p o i n t C, f u r t h e r reducing i t s work hours from (T-L 2) to ( T - L ^ ) . The i n t e r e s t i n g r e s u l t emerging from t h i s a n a l y s i s i s that i n - k i n d t r a n s f e r s can a c t u a l l y s t i m u l a t e work e f f o r t compared to e q u i v a l e n t cash g r a n t s . The necessary c o n d i t i o n to o b t a i n t h i s r e s u l t i s that Y' be a concave f u n c t i o n of work e f f o r t , that i s , 9Y'/9Y be gr e a t e r than one. Murray summarizes the c o n d i t i o n s f o r c o n c a v i t y of Y' i n the f o l l o w i n g theorem. THEOREM. I f a s i n g l e s u b s i d i z e d good i s normal and i f the subsidy imposes or induces more consumption of the good than would an e q u i v a l e n t cash grant then 9Y'/9Y > 1. (Murray 1980, p.74) Two v e r s i o n s of the proof of t h i s theorem are presented here: a simple geometric proof and a more e l a b o r a t e mathematical p r o o f . G e o m e t r i c a l l y , the problem can be i l l u s t r a t e d as i n F i g u r e 12. Housing i s represented on the h o r i z o n t a l a x i s and a composite good, Z, ,,-on the v e r t i c a l a x i s . The p r i c e of Z i s normalized to 1, a l l o w i n g Y and Y' to be read o f f the v e r t i c a l a x i s . The household i s c o n s t r a i n e d to consume H 1 u n i t s of housing at a p r i c e R l e a v i n g a r e s i d u a l income of Y-R f o r the purchase of Z 1 u n i t s of the composite good. The household i s on i n d i f f e r e n c e curve U"1 with e q u i v a l e n t income Y' 1 . I f household income i n c r e a s e s by AY, Murray argues that the f u l l amount of the i n c r e a s e w i l l be spent on i n c r e a s e d consumption of Z as the household cannot change i t s consumption of housing. T h e r e f o r e , the household w i l l move 117 V , Z 12 Geometrical Proof of Theorem up to i n d i f f e r e n c e curve with equivalent income ^ ' 2 * I n r e a l i t y , however, while the household cannot change the quantity of housing consumed under the program, i t w i l l be assessed a higher rent as a r e s u l t of the increase in income. In general, public housing rents are based on 25% of income. Therefore, the increase in income w i l l be spent as follows: .25AY on housing and .75AY on other goods. Murray seems to overlook this- point. Points A and B in Figure 12 represent the commodity bundles that would be purchased i f cash grants of (Y^-Y) and (Y'2~Y) were given instead of a fix e d quantity of public housing. If a good i s normal, then measuring i t along the h o r i z o n t a l a x i s , as in Figure 12, w i l l r e s u l t in a decrease in the v e r t i c a l distance between any two i n d i f f e r e n c e curves as the quantity of that good increases (Murray, 1980). This 118 i s due to the f a c t t h a t , f o r a normal good, H, the marginal u t i l i t y of the other good, Z, i n c r e a s e s as Z decreases (see S e c t i o n 6 f o r p r o o f ) . T h e r e f o r e , as H i s h e l d f i x e d and Z i n c r e a s e s , the marginal u t i l i t y of Z w i l l decrease and the marginal r a t e of s u b s t i t u t i o n between H and Z w i l l i n c r e a s e , i n c r e a s i n g the v e r t i c a l d i s t a n c e s between any two i n d i f f e r e n c e curves." The v e r t i c a l d i s t a n c e between p o i n t B and Y" must be g r e a t e r than the d i s t a n c e between B and a p o i n t C on i n d i f f e r e n c e curve U 1. Since the subsidy i s assumed to impose more of H than would be taken with a cash grant (a c o n d i t i o n of the theorem), H 1 l i e s to the r i g h t of e i t h e r A or B. T h e r e f o r e , the v e r t i c a l d i s t a n c e between U 1 and U 2 at H 1 ( i . e . , AY) must be l e s s than the d i s t a n c e Y ^ - Y ^ ( i . e . , AY'). In other words, 9Y'/9Y > 1. However, i f we acknowledge that only .75AY i s a v a i l a b l e f o r i n c r e a s e d consumption of Z ( s i n c e .25AY i s spent on i n c r e a s e d r e n t ) , then the r e l a t i o n s h i p of 9Y'/9Y to 1 appears ambiguous. A l l we can say f o r c e r t a i n i s 9Y'/9(.75AY) > 1, i n which case, 3Y'/9Y may be g r e a t e r or l e s s than 1. T h i s i s s u e seems to warrant f u r t h e r study. The mathematical proof of the theorem proceeds as f o l l o w s : (1) Define B as the e q u i v a l e n t v a r i a t i o n measure of welfare gain a s s o c i a t e d with the program: a T h i s r e s u l t seems to run counter to c o n v e n t i o n a l economic wisdom and i s p r e s e n t l y being pursued. 119 B = e(P m,g(H, Z)) - Y where Y i s money income as before and e(«) i s the expenditure f u n c t i o n . (2) Define R as the p r o j e c t rent charged f o r the s u b s i d i z e d housing u n i t (R may vary with income). (3) I f a household p a r t i c i p a t e s i n the program, expenditures on Z can be c a l c u l a t e d as: Z s = Y - R Pz where P„ i s the market p r i c e of one u n i t of Z and Z i s the 7. c s amount of Z consumed with the program. (4) D i f f e r e n t i a t i n g B with respect to income g i v e s 9B/9Y = U e ( . ) / 9 g ) • (3g/3Z) • (9Z g /9Y) - 1 where 9e(»)/3g i s the r a t e of change of income that would allow a n o n - p a r t i c i p a t i n g household to a t t a i n the l e v e l of u t i l i t y achieved with the program (at constant p r i c e s ) . (5) D i f f e r e n t i a t i n g Zs with respect to Y g i v e s 9Z /9Y = (1/P )[1 - (9R/9Y)]. (6) S u b s t i t u t i n g f o r 9Z s/9Y in (4) g i v e s 3B/9Y = ( 9 e ( • ) / 9 g ) • [ ( 3 g / 9 Z ) ( 1 / P ) ] [ 1 - ( 9 R / 9 Y ) ] - 1 where the second term i n p a r e n t h e s i s on the r i g h t hand s i d e 120 i s the marginal u t i l i t y of income (MtLy) ev a l u a t e d at ( H g , zs>-(7) The p a r t i a l d e r i v a t i v e of e ( p m r g(H, Z)) with r e s p e c t to g(H, Z) i s p o s i t i v e and, t h e r e f o r e , the s i g n of 9B/9Y w i l l depend upon the s i g n of {[(9g/9Z)(1/p )][1 - OR/ 9Y)] - 1}. In the absence of income c o n d i t i o n i n g ( i . e . , i f 9R/9Y = 0), the s i g n of 9B/9Y w i l l depend only upon MUy over the range (H, Z) to (H , Z g ) . I f MUy r i s e s , ( i . e . , i f 9MUy/9Z > 1) 9B/9Y w i l l be p o s i t i v e . (8) MUy w i l l r i s e over the r e l e v a n t range i f the marginal u t i l i t y of Z r i s e s over the range. That i s , (9g/9Z • 1/P ) > 1 i f and only i f 9g/9Z > 1 as P z > 0 by assumption. (9) The marginal u t i l i t y of Z w i l l i n c r e a s e from (H, Z) to (H , Z g) as long as H i s a normal good and Z > Z g (see S e c t i o n 6 f o r p r o o f ) . (10) From ( 1), B = Y' - Y , so 9B/9Y = (9Y'/9Y) - 1 i f 9B/9Y > 0, then 9Y'/9Y > 1 The r e f o r e , i f housing i s a normal good, 9Y'/9Y > 1, q.e.d. Again, while i n i t i a l l y acknowledging the r e l a t i o n s h i p between rent and income i n s u b s i d i z e d housing, Murray seems 121 to ignore t h i s r e l a t i o n s h i p i n h i s formal p r o o f . In step (7) above, i f 3R/3Y * 0, then the s i g n of 3B/3Y appears to be ambiguous. That i s , i f 3R/3Y = .25, then 3B/3Y = (3e(-)/3g) •[(3g/3Z)•(1/P,] (1 - .25) - 1. Since 3e(«)/3g > 0, the s i g n of 3B/3Y depends on the magnitude of MUV. I f .75 MUy > 1, then 3B/3Y > 0 and v i c e v e r s a . However, Murray's r e s u l t s do co n f i r m t h a t , i n the absence of income c o n d i t i o n i n g , 3Y'/3Y > 1. I n t u i t i v e l y , he e x p l a i n s t h i s r e s u l t as f o l l o w s : Since the subsidy imposes "too much" of the good and the good i s normal, i n c r e a s e s i n income reduce the degree to which the c o n s t r a i n t i s b i n d i n g ( i f income r i s e s enough, the c o n s t r a i n t might no longer b i n d at a l l ) and the d i s c o u n t i n g i s reduced. Thus i n c r e a s e s in money income are themselves worth d o l l a r s , but they a l s o i n c r e a s e the value of the p r e v i o u s l y r e c e i v e d subsidy and d r i v e r e a l income up by s t i l l more. (Murray, 1980, pp. 75-76) In other words, i f a s u b s i d i z e d program imposes, too much housing, an i n c r e a s e i n money income w i l l i n c r e a s e the b e n e f i t s of the program by reducing the extent of the c o n s t r a i n t . T h i s i n c r e a s e i n marginal b e n e f i t s i m p l i e s an in c r e a s e i n the marginal u t i l i t y of money. Supply-side housing programs such as p u b l i c housing are f r e q u e n t l y defended on the grounds that housing i s a "merit good". As such, s o c i e t y p r e f e r s to pr o v i d e i n - k i n d s u b s i d i e s to ensure poor households consume a b a s i c minimum l e v e l of housing. The assumption i s that a household would not consume t h i s l e v e l of housing with an e q u i v a l e n t cash t r a n s f e r . That i s , s u p p l y - s i d e housing programs are designed 122 to impose a higher l e v e l of housing consumption than households would s e l e c t with cash g r a n t s . T h i s assumption, along with the assumption that housing i s a normal good, suggests that p u b l i c housing programs meet the c o n d i t i o n s necessary f o r Murray's theorem to h o l d . As a consequence, p u b l i c housing may not reduce work e f f o r t as much as a program of guaranteed annual incomes. As an a s i d e , i t should be noted that Murray's theorem and subsequent p r o o f s r e f e r to marginal ( i . e . , small) changes i n income. The r e s u l t s do not a u t o m a t i c a l l y extend to cases where income i s i n c r e a s e d by more than a marginal amount. As income maintenance programs are g e n e r a l l y designed to e f f e c t d i s c r e t e i n c r e a s e s i n incomes, some f u r t h e r study of Murray's model may be warranted. 3. EMPIRICAL RESULTS FROM MURRAY'S MODEL Murray developed h i s model i n order to i n f e r work i n c e n t i v e e f f e c t s of i n - k i n d t r a n s f e r programs from data c o l l e c t e d f o r income maintenance programs. In the U.S., the I n s t i t u t e f o r Research on Poverty c o l l e c t e d data on work i n c e n t i v e e f f e c t s f o r a s e r i e s of income maintenance experiments. The evidence suggests that cash t r a n s f e r programs would not induce major r e d u c t i o n s i n work e f f o r t . Murray was i n t e r e s t e d i n comparing these r e s u l t s to the work e f f o r t e f f e c t s of i n - k i n d programs. Murray i d e n t i f i e s f i v e b a s i c steps f o r e s t i m a t i n g the work i n c e n t i v e e f f e c t s of a program f o r which no work e f f o r t 123 data i s a v a i l a b l e : 1. s p e c i f y and estimate the parameters of the household u t i l i t y f u n c t i o n u(H,Z) 2. s p e c i f y and estimate the parameters of the household u t i l i t y f u n c t i o n u(L,Y') 3. estimate L m , the amount of l e i s u r e consumed without the program 4. estimate L s , the amount of l e i s u r e consumed with the program 5. estimate the decrease i n work e f f o r t as ( L s -L m ) . As b e f o r e , Murray assumes that the u t i l i t y f u n c t i o n u(L,Y') i s weakly separable with r e s p e c t to l e i s u r e and n o n - l e i s u r e goods. He a l s o assumes that the p o p u l a t i o n r e c e i v i n g income maintenance i s not q u a l i t a t i v e l y d i f f e r e n t from the p o p u l a t i o n r e c e i v i n g housing s u b s i d i e s . T h i s assumption a l l o w s the parameter estimates from the income maintenance experiments to be used i n c a l c u l a t i n g changes to work e f f o r t i n the subsidy program. With these assumptions, Murray estimates the work i n c e n t i v e e f f e c t s of p u b l i c housing i n the U.S. Step 1 E s t i m a t i o n of U t i l i t y F u n c t i o n u(H,Z) Murray s p e c i f i e s a Cobb-Douglas u t i l i t y f u n c t i o n of the form [5] U(H,Z) = H / 3 Z ( 1 _ < 3 ) where /3 i s the rent-to-income r a t i o i n the absence of the subsidy, H and Z are as p r e v i o u s l y d e f i n e d . From p r e v i o u s s t u d i e s , Murray estimates /3s ranging between .26 and.34 f o r v a r i o u s f a m i l y compositions. Step 2 E s t i m a t i o n of U t i l i t y F u n c t i o n u(L,Y') Murray assumes that the household's l e i s u r e / n o n - l e i s u r e p r e f e r e n c e s can be represented by a Stone-Geary u t i l i t y 124 f u n c t i o n of the form: [6] W = (L - 5 ) 3 [Eh{]-^]{]-a) where W i s u t i l i t y , L i s l e i s u r e , 5 i s some minimum l e v e l of l e i s u r e , a i s the e l a s t i c i t y of s u b s t i t u t i o n of l e i s u r e f o r l a b o u r , 5 a l l other v a r i a b l e s are p r e v i o u s l y d e f i n e d . S u b s t i t u t i n g the H i c k s i a n e q u i v a l e n t income i n equation [6] y i e l d s [7] U = (L - 6 ) a ( Y ' ) ( L _ A ) In a separate study, Abbot and A s h e n f e l t e r (1976) o b t a i n estimates of 6,403 f o r 5 and .12 f o r a. In other words, the minimum amount of l e i s u r e consumed by a l l f a m i l i e s i n the U.S. i s 6,403 hours or 17.5 hours per day. T h i s equates with a 45.5 hour work week. Murray uses these estimates f o r h i s a n a l y s i s . Step 3 E s t i m a t i o n of Lm, L e i s u r e Without the Program By c o n s t r u c t i o n , the amount of l e i s u r e without the program i s d e f i n e d as: [8] L m = a(T - 5) + 6 where T i s the t o t a l number of hours a v a i l a b l e or 365 x 24 = 8,760. S u b s t i t u t i n g the parameter estimates of .12 f o r a, 6,403 f o r 5 and 8,760 f o r T, Murray o b t a i n s an estimate f o r L m of 6,686 hours of l e i s u r e per year or 39.9 hours of work per week. 5 The e l a s t i c i t y of s u b s t i t u t i o n of l e i s u r e f o r labour i s the r a t e of change i n the r a t i o of work (K) and l e i s u r e (L) when the r a t e of s u b s t i t u t i o n i s i n c r e a s e d at the r a t e of 1%, h o l d i n g u t i l i t y constant ( R u s s e l l and W i l k i n s o n , 1979). It can be expressed as the d i f f e r e n c e between the wage e l a s t i c i t y and t o t a l income e l a s t i c i t y (Cain and Watts, 1973): 9K/9W - 9K/9Y(K 0) where KQ i s the e q u i l i b r i u m l e v e l of labour supply. 125 Step 4 E s t i m a t i o n of Ls, L e i s u r e With the Program An e x p r e s s i o n f o r L g i s obtained by maximizing u t i l i t y with the program (U ) with r e s p e c t to l e i s u r e . U i s c a l c u l a t e d i n three steps as f o l l o w s : 1 . Minimize household expenditure with r e s p e c t to u*s to ob t a i n the f o l l o w i n g expenditure f u n c t i o n : Y' = [(p hH ) / 0 ] 0 [ ( p z Z ) / ( 1-/3) ] < 2. Modify the expenditure f u n c t i o n to r e f l e c t the f a c t that r e n t s i n p u b l i c housing are l i m i t e d to 25 percent of household income. The r e v i s e d e x p r e s s i o n i s : Y' = [(pjH)//*]- 5 [(.75w(T - D ) / ( l - / 3 ) ] ( 1 _ / 3 ) where w(T - L) r e p r e s e n t s income. 3. S u b s t i t u t e t h i s e x p r e s s i o n f o r Y' i n t o equation [7] to g i v e : [8] U s = (L - 6 ) a • [(p hH)//3] P • [{[.75w(T - L ) ] / ( l - / 3 ) } ( ( l _ a ) Maximizing equation [8] with respect to L, Murray o b t a i n s the f o l l o w i n g e x p r e s s i o n f o r L g : [9] L s = aT + (1 - a) (1 - 0)6 a + (1 - a) ( 1 - / 3 ) Step 5 E s t i m a t i o n of the Decrease in Work E f f o r t The change i n work e f f o r t as a r e s u l t of the p u b l i c housing program i s estimated as the d i f f e r e n c e between equations [8] and [ 9 ] . For the nine f a m i l y compositions i n Murray's study, the d e c l i n e i n work e f f o r t ranges from 1.4 to 1.7 hours per week per household, r e p r e s e n t i n g approximately a 4 percent r e d u c t i o n . 1 26 4 APPLICATION OF MURRAY'S MODEL TO YELLOWKNIFE DATA In t h i s s e c t i o n , Murray's model i s a p p l i e d to the f i v e p u b l i c housing p r o j e c t s i n Y e l l o w k n i f e to determine the impact of the program on work e f f o r t . As d e s c r i b e d i n the pre v i o u s s e c t i o n , estimates of 4 v a r i a b l e s are r e q u i r e d to estimate changes i n work e f f o r t : T - the t o t a l hours a v a i l a b l e = 8,760 by d e f i n i t i o n (24 x 365) . 5 - the minimum l e v e l of l e i s u r e . a - the e l a s t i c i t y of s u b s t i t u t i o n of l e i s u r e f o r work. 0 - the rent-to-income r a t i o i n the absence of the program. In Murray's study, estimates of 5 and a were obtained from a previous study i n the U.S. U n f o r t u n a t e l y , no comparable s t u d i e s e x i s t i n Canada. E s t i m a t i o n of the parameters from Canadian data using Abbott and A s h e n f e l t e r ' s (1976) approach would r e q u i r e e s t i m a t i o n of a system of 8 simultaneous equations, a task beyond the scope of t h i s a n a l y s i s . T h e r e f o r e , f o r the purposes of t h i s study, the parameter estimates from the U.S. data are used. That i s , 5 = 6,403 and a = .12. Estimates of the parameter 0 d e r i v e d i n Chapter 5 f o r nine income groups i n Y e l l o w k n i f e range from .13 to .42. Reduction i n work e f f o r t due to the program i s estimated f o r 110 households. Estimates range from 0.8 to 3.2 hours per week per household, or approximately 2% - 8% of the pre-subsidy work e f f o r t (39.9 hours per week). In 1 27 comparison to Murray's r e s u l t s , the Y e l l o w k n i f e data produce a much wider range of e s t i m a t e s . Murray's estimates f a l l w i t h i n a range of 1.4 to 1.7 hours per week or approximately 4% of pre-subsidy work e f f o r t . The d i f f e r e n c e stems from the wider range of rent-to-income r a t i o s used i n the Y e l l o w k n i f e sample: .13 to .42 compared to .26 to .34. The rent-to-income r a t i o s have a d i r e c t i n f l u e n c e on the d e c l i n e in work e f f o r t with higher r a t i o s producing g r e a t e r r e d u c t i o n s . As hig h r a t i o s are a s s o c i a t e d with low income households, the model p r e d i c t s a g r e a t e r r e d u c t i o n i n work e f f o r t among poorer households. These r e s u l t s should be i n t e r p r e t e d as very rough approximations of the d e c l i n e i n work e f f o r t a s s o c i a t e d with the P u b l i c Housing Program i n Y e l l o w k n i f e . B e t t e r approximations c o u l d be obtained by e s t i m a t i n g the parameters 5 (minimum l e v e l of l e i s u r e ) and a ( e l a s t i c i t y of s u b s t i t u t i o n ) from Canadian data or, i d e a l l y , from N.W.T. data. A l s o , the f u l l p o l i c y i m p l i c a t i o n s of the r e s u l t s are not c l e a r without comparative estimates of the d e c l i n e i n work e f f o r t from income maintenance or p r i c e subsidy programs. 5. SUMMARY AND IMPLICATIONS The work d i s i n c e n t i v e e f f e c t s of government r e d i s t r i b u t i o n programs are u s u a l l y analysed w i t h i n the t r a d i t i o n a l i n c o m e - l e i s u r e economic framework. While t h i s approach i s u s e f u l f o r stu d y i n g income maintenance programs, 1 28 i t i s not a p p r o p r i a t e f o r a n a l y s i n g commodity s u b s i d i e s as the p r i c e r a t i o s w i t h i n the n o n - l e i s u r e composite change. In response to t h i s o b s e r v a t i o n , and i n an attempt to u t i l i z e a r i c h data base of work d i s i n c e n t i v e e f f e c t s of income maintenance programs in the U.S., Murray (1980) designed a model f o r a n a l y s i n g work d i s i n c e n t i v e s of commodity subsidy programs. The i n t e r e s t i n g r e s u l t from Murray's work i s t h a t , under c e r t a i n c o n d i t i o n s , i n - k i n d s u b s i d i e s can a c t u a l l y have a s t i m u l a t i v e e f f e c t compared to e q u i v a l e n t cash g r a n t s . The necessary c o n d i t i o n s f o r t h i s r e s u l t to h o l d are (1) the s u b s i d i z e d good must be normal and (2) the program must impose "too much" consumption of the s u b s i d i z e d good. As both these c o n d i t i o n s are u s u a l l y met i n p u b l i c housing programs, the model p r e d i c t s t h a t the work d i s i n c e n t i v e a s s o c i a t e d with a p u b l i c housing program w i l l a c t u a l l y be l e s s than t h a t with a program of u n r e s t r i c t e d , " e q u i v a l e n t " cash g r a n t s . T h i s r e s u l t suggests that i n - k i n d t r a n s f e r s may be a p p r o p r i a t e p o l i c y i n i t i a t i v e s i n some cases, d e s p i t e t h e i r economic i n e f f i c i e n c y . 6. PROOF OF THEOREM Theorem: For two goods H and Z, the marginal u t i l i t y of Z i n c r e a s e s as Z decreases over the i n t e r v a l (H, Z) to (H , s Z g) i f H i s a normal good. P r o o f ; 6 1. n o t a t i o n : l e t g(H, Z) be the household u t i l i t y f u n c t i o n l e t g^ be the p a r t i a l d e r i v a t i v e of g(«) with r e s p e c t to i , i = H, Z l e t g ^ be the second p a r t i a l of g(«) with respect to i 2. along an i n d i f f e r e n c e curve, u t i l i t y i s c o n s t a n t : i . e . , g dZ + g udH = 0 Z ri or dH = - ( g z / g H ) d Z 3. t o t a l d i f f e r e n t i a l of g : z a g z = g z z d z + g z H d H 4. s u b s t i t u t i n g for dH: dg z= g z z d z - g z H (g z/g H ) d z 5. r e a r r a n g i n g : d 9 z " [ 9 z z " 9zH <VV]dZ 6. as Z f a l l s , d g z > 0 i f and only i f [ 9 Z Z " g 2 H ( 9 2 / g H ) ] < 0 7 . dH/dY = f g z H ( g z / g H ) ~ g z z ] l D l ~ 1 w h e r e l°l i s the determinant of the bordered Hessian matrix. As g i s quasi-concave, |D| > 0. 8. i f dH/dY > 0, then [g„„(g /g„) - g ] > 0 and Zn Z ri Z Z [ 9 z z " 9 Z H ( 9 Z / 9 H ) 1 K 0 9. dH/dY > 0 f o r a normal good 10. as Z f a l l s , g i n c r e a s e s i f H i s a normal good, q.e.d. 6 f r o m Murray APPENDIX 3 PUBLIC HOUSING RENT-TO-INCOME SCALES I c. M.H.C. RENTAL SCALE Income Rent (%) Income Rent (%) under 200 16.7 303 - 31 1 22.5 201 - 209 17.4 312 - 320 22.9 210 - 219 18.1 321 - 329 23. 1 220 - 228 18.6 330 - 339 23.4 229 - 237 19.2 340 - 348 23.5 238 - 246 19.7 349 - 357 23.9 247 - 255 20.2 358 - 366 24.0 256 - 265 20.7 367 - 375 24.2 266 - 274 21.2 376 - 385 24.5 275 - 283 21.6 386 - 394 24.6 284 - 292 22.0 395 - 403 24.8 293 - 302 22.3 403 + 25.0 NOTES: 1. Income f i g u r e s represent monthly fa m i l y income as de f i n e d on the f o l l o w i n g page. 2. The rent percentages apply to f a m i l i e s or i n d i v i d u a l s with no c h i l d r e n . Monthly rent i s reduced by $2.00 f o r each c h i l d t o a minimum of $32. SOURCE: C.M.H.C, N a t i o n a l O f f i c e . 1 30 131 DEFINITION OF INCOME For the purposes of c a l c u l a t i n g monthly r e n t , "income" i s d e f i n e d as aggregate gross income of a l l members of the f a m i l y or i n d i v i d u a l e x c l u d i n g the f o l l o w i n g : 1. Earnings of c h i l d r e n i n r e g u l a r attendance at recognized i n s t i t u t i o n s of l e a r n i n g ; 2. L i v i n g out or t r a v e l l i n g allowances of a f a m i l y head; . 3. Earnings of a working spouse of up to $900.00 per annun; 4. Income from any source other than s o c i a l a s s i s t a n c e payments of a one-parent f a m i l y up to $900.00 per annum; 5. Earnings i n excess of $75.00 per month of a l l members of the f a m i l y other than the f a m i l y head or spouse. ( T h i s w i l l i n c l u d e persons r e l a t e d by blood, marriage or adoption or other persons who may reasonably be assumed to form p a r t of the f a m i l y . ) ; 6. C a p i t a l gains, such as insurance s e t t l e m e n t s , i n h e r i t a n c e s , d i s a b i l i t y awards, s a l e of e f f e c t s ; 7. Family allowance. SOURCE: C.M.H.C, N a t i o n a l O f f i c e . 1 32 II N.W.T. HOUSING CORPORATION RENT SCALE By agreement, C.M.H.C. c o n t r i b u t e s e i t h e r 50% (Se c t i o n 43 and 44.1(a) p r o j e c t s ) or 75% (S e c t i o n 40 p r o j e c t s ) of the "net o p e r a t i n g l o s s " of the p u b l i c housing p r o j e c t s . In order to c a l c u l a t e "net o p e r a t i n g l o s s " , revenue i s c a l c u l a t e d based on e i t h e r the f e d e r a l r e n t a l s c a l e or the t e r r i t o r i a l s c a l e , whichever produces the g r e a t e s t revenue. During the e a r l y years of the P u b l i c Housing Program i n the N.W.T., the N.W.T. Housing C o r p o r a t i o n used the f e d e r a l r e n t a l s c a l e to assess rents f o r a l l i t s p u b l i c housing p r o j e c t s . However, in 1978, i n response to r e s o l u t i o n s from dele g a t e s at the B a f f i n Housing Conference, the Housing C o r p o r a t i o n i n t r o d u c e d a new r e n t a l s c a l e to r e f l e c t northern l i v i n g c o n d i t i o n s . The s c a l e r e s u l t e d i n lower rent assessments f o r many households but, because of the agreement with C.M.H.C, the new s c a l e s h i f t e d the f i n a n c i a l burden of the program from C.M.H.C. to the Housing C o r p o r a t i o n . In 1983, the Housing C o r p o r a t i o n r e v i s e d i t s s c a l e to reduce t h i s burden, but, at the same time acknowledge the higher c o s t of l i v i n g i n remote communities. T h i s s c a l e i s c u r r e n t l y i n use and d i f f e r s from the f e d e r a l s c a l e i n the f o l l o w i n g ways: 1. In the nineteen communities designated as "homeownership" communities ( i . e . , communities where homeownership i s a r e a l i s t i c o p t i o n ) , monthly rent i s l i m i t e d by the economic rent or market rent of the u n i t , whichever i s g r e a t e r . 133 2. In the remaining communities, monthly rent i s l i m i t e d by the rent l e v e l s of comparable G.N.W.T. s t a f f housing u n i t s . 3. Monthly rent i n remote communities i s a d j u s t e d to r e f l e c t the higher cost of l i v i n g . co > T3 •X) Dd as a n APPENDIX 5 ESTIMATION OF REAL INTEREST RATES, 1976 - 1985 Year Average Bond (10 years & Y i e l d over) Annual Average I n f l a t i o n Real Rate 1976 8.47 7.52 .95 1 977 8.77 7.95 .82 1 978 9.68 8.84 .84 1 979 1 1 .32 9.20 2.12 1980 12.67 10.16 2.51 1981 15.27 12.49 2.78 1 982 1 1 .69 10.80 .89 1983 1 2.02 5.78 6.24 1 984 1 1 .66 4.35 7.31 1985 1 0.06 4.00 6.06 SOURCE: 1. Bank of Canada Review, v a r i o u s y e a r s . 2. The Consumer P r i c e Index, June 1985. 135 

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