UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Determinants of the long term interest rate in Canada Mouat, Robert Lawrence 1977

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1977_A4_6 M68.pdf [ 3.84MB ]
Metadata
JSON: 831-1.0093988.json
JSON-LD: 831-1.0093988-ld.json
RDF/XML (Pretty): 831-1.0093988-rdf.xml
RDF/JSON: 831-1.0093988-rdf.json
Turtle: 831-1.0093988-turtle.txt
N-Triples: 831-1.0093988-rdf-ntriples.txt
Original Record: 831-1.0093988-source.json
Full Text
831-1.0093988-fulltext.txt
Citation
831-1.0093988.ris

Full Text

DETERMINANTS OF THE LONG TERM INTEREST RATE IN CANADA by ROBERT LAWRENCE MOUAT B . S c , U n i v e r s i t y o f B r i t i s h Columbia, 1969 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF SCIENCE IN, BUSINESS ADMINISTRATION i n THE FACULTY OF GRADUATE STUDIES (Dept. o f B u s i n e s s A d m i n i s t r a t i o n ) We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA January 1977 (c) Robert Lawrence Kouat, 1977 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree l y ava i lab le for reference and study. I further agree that permission for extensive copying of th is thes is for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thes is fo r f i nanc ia l gain sha l l not be allowed without my written permission. Department of cSrc^c/ia./^ SiCc/ser The Univers i ty of B r i t i s h Columbia 2075 W e s b r o o k P l a c e V a n c o u v e r , C a n a d a V 6 T 1W5 Date / T l ^ V r 7 * / 9 7 7 ABSTRACT The purpose of t h i s t h e s i s was to d e v e l o p a model t h a t would demonstrate whether the government o f Canada can e f f e c t an independent, or p a r t i a l l y independent long-term i n t e r e s t r a t e p o l i c y w i t h r e s p e c t to the U n i t e d S t a t e s . The t h e o r e t i c a l a n a l y s i s of the economics r e s u l t e d i n f o u r d i s t i n c t e q u a t i o n s f o r long-term i n t e r e s t r a t e d e t e r m i n a t i o n ; two f o r each o f a c l o s e d economy model and an open economy model. The f i r s t e q u a t i o n f o r the c l o s e d model r e l a t e s long-term i n t e r e s t r a t e s to the r a t e of change of money supply, government e x p e n d i t u r e and i n f l a t i o n . The second e q u a t i o n r e p l a c e s government e x p e n d i t u r e w i t h unemployment, a l l o t h e r v a r i a b l e s r e m a i n i n g the same. The v a r i a b l e s o f the two e q u a t i o n s f o r the open economy were i d e n t i c a l with those of the c l o s e d model. However, the open economy had v a l u e s o f the dependent v a r i a b l e which were the d i f f e r e n c e between the Canadian and U.S. long-term i n t e r e s t r a t e s and v a l u e s f o r the independent v a r i a b l e s which were the d i f f e r e n c e s between the Canadian and U.S. v a l u e s of the r a t e of change o f ( f o r the f i r s t e q u a t i o n ) money s u p p l y , i n f l a t i o n and government spending and ( f o r the second e q u a t i o n ) money supply, i n f l a t i o n and unemployment. Q u a r t e r l y d a t a were used over 92 p e r i o d s from 1953 to 1975 i n c l u s i v e with money supply and government spending b e i n g c o r r e c t e d f o r i n f l a t i o n . The long-term i n t e r e s t r a t e were government bond y i e l d s of ten y e a r s and ov e r ; the money supply were the sum of demand d e p o s i t s p l u s c u r r e n c y h e l d o u t s i d e the banks; the government spending were t o t a l f e d e r a l government i i i e x p e n d i t u r e s a n d ; t h e i n f l a t i o n r a t e were t h e g r o s s n a t i o n a l e x p e n d i t u r e d e f l a t o r . The e q u a t i o n s were a n a l y s e d u s i n g a r o u t i n e w h i c h c o m b i n e d t h e Almon l a g t e c h n i q u e w i t h t h e C o c h r a n e - O r e u t t method o f r e g r e s s i o n . T h i s a l l o w e d a s e l e c t i o n o f t h e l a g l e n g t h and t h e d e g r e e o f t h e p o l y n o m i a l o f t h e e q u a t i o n . I n a l l o f t h e e q u a -t i o n s i n t h i s p a p e r t h e l a g l e n g t h i s f o u r p e r i o d s and t h e d e g r e e o f t h e p o l y n o m i a l i s two. F o r t h e c l o s e d economy model t h e r e s u l t s showed t h e e x p e c t e d s i g n s (money s u p p l y and unemployment n e g a t i v e l y r e l a t e d , and i n f l a t i o n and g o v e r n m e n t s p e n d i n g p o s i t i v e l y r e l a t e d ) , w i t h few e x c e p t i o n s , t h e most n o t a b l e b e i n g a n e g a t i v e g o v e r n m e n t e x p e n d i t u r e i n t h e f i r s t l a g p e r i o d . The v a l u e s o f t h e c o e f f i c i e n t s i n d i c a t e d t h a t i n f l a t i o n was t h e g r e a t e s t i n f l u e n c e on l o n g - t e r m i n t e r e s t r a t e s , money s u p p l y and u n e m p l o y -ment h a v i n g a much s m a l l e r i n f l u e n c e , a n d g o v e r n m e n t e x p e n d i t u r e h a v i n g a l m o s t no a f f e c t o v e r t h e f o u r l a g p e r i o d s . T h e open economy model r e s u l t s showed t h e e x p e c t e d s i g n s f o r t h e c o -e f f i c i e n t s w i t h a s i m i l a r e x c e p t i o n t o t h e c l o s e d m o d e l . The v a l u e o f t h e c o e f f i c i e n t s i n d i c a t e d t h a t t h e i n f l a t i o n d i f f e r e n t i a l o f t h e two c o u n t r i e s was t h e g r e a t e s t i n f l u e n c e on t h e l o n g - t e r m i n t e r e s t r a t e d i f f e r e n t i a l w i t h t h e money s u p p l y d i f f e r e n t i a l s e c o n d , unemployment d i f f e r e n t i a l t h i r d and g o v e r n m e n t e x p e n d i t u r e d i f f e r e n t i a l h a v i n g a l m o s t no e x p l a n a t o r y power. Money s u p p l y d i f f e r e n t i a l had f o u r s i g n i f i -c a n t l a g c o e f f i c i e n t s - - i n d i c a t i n g a d i v e r g e n c e b e t w e e n m o n e t a r y p o l i c y o f C a n a d a and t h e U.S. ( w h e t h e r i n t e n d e d o r n o t ) . I t a p p e a r s f r o m t h e r e s u l t s t h a t a l t h o u g h t h e U.S. l a r g e l y I v c o n t r o l s Canada's long-term i n t e r e s t r a t e , Canada has the a b i l i t y , whether i t i s used or not, to c o n t r o l part of i t s long-term i n t e r e s t r a t e . The d i f f e r e n t i a l of Canada and the U.S's rate of change of i n f l a t i o n , money supply'and unemploy-ment a l l influence the l e v e l of long-term i n t e r e s t r a t e s . The c o n t r o l of these va r i a b l e s i s the key to the government's c o n t r o l over the long-term i n t e r e s t r a t e . V TABLE OF CONTENTS Page INTRODUCTION 1 REVIEW OF CURRENT LITERATURE 3 THEORIES OF INTEREST RATE DETERMINATION 9 C l o s e d system . . . 9 Open system 16 MODELS 19 C l o s e d system 19 D i f f e r e n t i a l i n t e r e s t r a t e s 19 ANALYSIS 21 Method 21 Data 22 RESULTS 25 C l o s e d system 25 D i f f e r e n t i a l i n t e r e s t r a t e s 34 CONCLUSIONS 45 BIBLIOGRAPHY 49 v i LIST OF TABLES T a b l e Page I Summary of v a r i a b l e s 24 I I Computer r e s u l t s f o r E q u a t i o n 26 26 I I I S t a t i s t i c a l r e s u l t s f o r Eq u a t i o n 26 . . . . 27 IV Computer r e s u l t s f o r Eq u a t i o n 27 31 V S t a t i s t i c a l r e s u l t s f o r E q u a t i o n 27 . . . . 32 VI Computer r e s u l t s f o r E q u a t i o n 28 36 V I I S t a t i s t i c a l r e s u l t s f o r E q u a t i o n 28 . . . . 37 V I I I Computer r e s u l t s f o r E q u a t i o n 29 . . . . . . 40 IX S t a t i s t i c a l r e s u l t s f o r E q u a t i o n 29 . . . . 41 X C o r r e l a t i o n matrix . . . . . 44 v i i LIST OF FIGURES F i g u r e Page 1 Graph of Equation 26 28 2 Graph o f E q u a t i o n 27 33 3 Graph o f Canada and U.S. long term i n t e r e s t r a t e s . . . . . 35 4 Graph o f Eq u a t i o n 28 38 5 Graph o f Eq u a t i o n 29 42 INTRODUCTION 1 T h i s t h e s i s a t t e m p t s t o d e v e l o p a model t o d e m o n s t r a t e w h e t h e r t h e Government o f C a n a d a c a n e f f e c t an i n d e p e n d e n t , o r p a r t i a l l y i n d e p e n d e n t l o n g - t e r m i n t e r e s t r a t e p o l i c y w i t h r e s -p e c t t o t h e U n i t e d S t a t e s . The p a p e r a d d r e s s e s two r e l a t e d i s s u e s : C a n a d a ' s l o n g -t e r m i n t e r e s t r a t e i n a c l o s e d economy s e t t i n g ; and, an a n a l y s i s o f t h e d i f f e r e n c e b e t w e e n C a n a d a ' s l o n g - t e r m i n t e r e s t r a t e and t h a t o f t h e U.S.A. i n an open economy s e t t i n g . The c l o s e d economy model assumes C a n a d i a n i n t e r e s t r a t e s a r e i n f l u e n c e d o n l y by f a c t o r s i n d i g e n o u s t o t h e C a n a d i a n economy. A l t h o u g h t h i s v i e w i s u n r e a l i s t i c , i t e n a b l e s us t o a n a l y s e t h o s e d o m e s t i c f a c t o r s w h i c h c h a n g e w i t h , a r e a f f e c t e d b y, and i n f l u e n c e , t h e l o n g - t e r m i n t e r e s t r a t e . T h i s s e c t i o n i n t r o d u c e s t h e v a r i a b l e s ; money s u p p l y , i n f l a t i o n , u n e m p l o y -ment, and g o v e r n m e n t e x p e n d i t u r e . T h e y a r e b o t h d e t e r m i n a n t s o f i n t e r e s t r a t e s and t o o l s o f g o v e r n m e n t p o l i c y . The s e c o n d a r e a o f a t t e n t i o n , ( u n l i k e t h e f o r m e r w h i c h h a s b e e n w i d e l y i n v e s t i g a t e d ) , i s a new a p p r o a c h i n a s s e s s i n g C a n a d a ' s a b i l i t y t o d e t e r m i n e i t s l o n g - t e r m i n t e r e s t r a t e . I n t h i s s e c t i o n , t h e d i f f e r e n c e between t h e C a n a d i a n l o n g - t e r m i n t e r e s t r a t e and t h e U.S. l o n g - t e r m i n t e r e s t r a t e i s e x p l o r e d . The i n d e p e n d e n t v a r i a b l e s c o n s i s t o f t h e d i f f e r e n c e b e t w e e n C a n a d i a n and U.S. v a l u e s f o r t h o s e v a r i a b l e s i n t r o -d u c e d i n t h e c l o s e d economy m o d e l . T h i s c h a p t e r a t t e m p t s t o g i v e an i n s i g h t i n t o t h e p o s s i b i l i t y o f g o v e r n m e n t c o n t r o l o v e r d o m e s t i c l o n g - t e r m i n t e r e s t r a t e s t h r o u g h t h e u s e o f m o n e t a r y and f i s c a l t o o l s . 2 F o l l o w i n g t h e p a p e r ' s i n t r o d u c t i o n , t h e r e a r e s i x c h a p t e r s : t h e f i r s t c h a p t e r i s a r e v i e w o f t h e c u r r e n t l i t e r a t u r e ; t h e s e c o n d i s an e x p l a n a t i o n o f t h e e c o n o m i c s o f a c l o s e d s y s t e m and o f an o p en s y s t e m ; t h e t h i r d c h a p t e r i s a d e s c r i p t i o n o f t h e m o d e l s u s e d ; t h e f o u r t h c h a p t e r i s a d e s c r i p t i o n o f t h e method o f a n a l y s i s ; t h e f i f t h c h a p t e r h i g h l i g h t s t h e r e s u l t s ; and, t h e s i x t h c o n t a i n s t h e c o n c l u s i o n s . 3 C h a p t e r 1 REVIEW OF CURRENT LITERATURE W h i l e r e s e a r c h i n g t h e t o p i c o f t h i s p a p e r , s e v e r a l a r t i c l e s were f o u n d w h i c h d e a l t d i r e c t l y w i t h t h e a r e a o f i n t e r e s t . F o r t h e c l o s e d s y s t e m t h r e e m o d e l s were i n v e s t i g a t e d . The f i r s t was d e v e l o p e d by t h e F e d e r a l 1 R e s e r v e Bank o f S t . L o u i s t o p r o v i d e i n f o r m a t i o n on t h e most l i k e l y c o u r s e o f movement o f c e r t a i n s t r a t e g i c e c o n o m i c v a r i a b l e s i n r e s p o n s e t o m o n e t a r y and f i s c a l a c t i o n . The i n v e s t i g a t i o n o f bond y i e l d s i s b a s e d on t h e p r e m i s e t h a t c h a n g e s i n o u t p u t , c h a n g e s i n p r i c e s and a n t i c i p a t e d p r i c e s and c h a n g e s i n t h e money s t o c k d e t e r m i n e m a r k e t i n t e r e s t r a t e s . The e q u a t i o n i n v e s t i g a t e s l o n g - t e r m i n t e r e s t r a t e s a s a f u n c t i o n o f r a t e o f c h a n g e o f money s u p p l y , g r o s s n a t i o n a l e x p e n d i t u r e , i n f l a t i o n and unemployment. The F e d e r a l R e s e r v e Bank model was a c o n s i d e r a b l e i n f l u e n c e on t h e p a p e r b e i n g p r e s e n t e d h e r e as t h e two m o d e l s a r e c o n c e r n e d w i t h g o v e r n m e n t i n f l u e n c e ; b o t h m o n e t a r y and f i s c a l ; on l o n g - t e r m i n t e r e s t r a t e s . The s e c o n d p a p e r w h i c h l o o k e d a t a c l o s e d economy s y s t e m L e o n a l l C. A n d e r s e n , and K e i t h M. C a r l s o n , "A M o n e t a r i s t M o d e l f o r E c o n o m i c S t a b i l i z a t i o n " , F e d e r a l R e s e r v e Bank o f S t . L o u i s , R e v i e w , A p r i l 1970. 4 2 i s by F e l s t e i n and E c k s t e i n . I t i n v e s t i g a t e d the fundamental determinants of changes i n the long-term i n t e r e s t r a t e u s i n g Keynes' theory o f l i q u i d i t y p r e f e r e n c e and F i s h e r ' s model of the r o l e of a n t i c i p a t e d i n f l a t i o n . I t found t h a t : i n the long run, the r e a l r a t e of i n t e r e s t f a l l s as the r a t e of i n f l a t i o n r i s e s ; a per cent i n c r e a s e i n the i n f l a t i o n r a t e r a i s e s the i n t e r e s t r a t e by o n l y 66 b a s i s p o i n t s ; a l t h o u g h i n f l a t i o n has a v e r y important e f f e c t on i n t e r e s t r a t e s , i t s impact can o n l y be e s t i m a t e d w i t h a model t h a t r e c o g n i s e s the e q u a l l y important r o l e of l i q u i d i t y . As both l i q u i d i t y p r e f e r e n c e and i n f l a t i o n are important to t h i s paper, Keynes' th e o r y and F i s h e r ' s model g r e a t l y i n f l u e n c e d the development of t h i s paper's model. I t was a l s o hoped to t e s t the change of i n t e r e s t r a t e s due to i n f l a t i o n , as p r e s e n t e d i n the paper by F e l s t e i n and E c k s t e i n . The t h i r d paper which examined a c l o s e d economy system 3 was by D o b e l l and Sargent. I t i s important because one of i t s c o n c l u s i o n s s t a t e s t h a t t h e r e i s doubt about the e f f e c t i v e -ness with which the Bank of Canada's i n f l u e n c e can be communicated from the money market to the v e r y long end o f the m a t u r i t y s t r u c t u r e of y i e l d s . T h i s c o n c l u s i o n w i l l be i n v e s t i g a t e d . ""Martin F e l s t e i n , and G t t o E c k s t e i n , "The Fundamental Determinants of the I n t e r e s t Rate", The Review of Economics  and S t a t i s t i c s , V o l . I l l , F e bruary 1970, pp. 363-375. 3 Rodney D o b e l l , and Thomas Sargent, "The Term S t r u c t u r e of I n t e r e s t Rates i n Canada", The Canadian J o u r n a l o f Economics, V o l . I I , Feb.-Nov., 1969. 5 The open economy system has been w i d e l y r e s e a r c h e d ; f o u r papers w i l l be d i s c u s s e d here. The f i r s t two papers came up with some s i m i l a r c o n c l u s i o n s . 4 The f i r s t was by Nold. T h i s paper i n v e s t i g a t e d the l i n e a r r e l a t i o n s h i p between nominal i n t e r e s t r a t e s i n Canada and the U.S. and between these i n t e r e s t r a t e s and the i n t r a c o u n t r y i n f l a t i o n . The most important f i n d i n g of the paper was t h a t the Canadian i n t e r e s t r a t e s are l a r g e l y determined by s i m i l a r U.S. bonds. 5 The second paper was by H e r r i n g and-Marston. T h i s paper s t u d i e d the c h a n n e l s through which f o r e i g n monetary c o n d i t i o n s i n f l u e n c e the domestic money market by e s t i m a t i n g a model which e x p l a i n e d s i m u l t a n e o u s l y the demand and supply of bank money, i n t e r n a t i o n a l c a p i t a l movements, and the supply of bank r e s e r v e s i n such a way t h a t i t d e s c r i b e d the c h a n n e l s through which f o r e i g n i n t e r e s t r a t e s a f f e c t domestic i n t e r e s t r a t e s . Although some of the parameters of the equations were d i f f i c u l t t o e s t i m a t e , the r e s u l t s i n d i c a t e d t h a t the U.S. has a s i g n i f i c a n t i n f l u e n c e over the Canadian long-term i n t e r e s t r a t e , and t h a t a 1% r i s e i n the U.S. r a t e would r e s u l t i n about a .7% r i s e i n the Canadian r a t e . The papers by Nold, and by H e r r i n g and Marston i n d i c a t e d t h a t any i n v e s t i g a t i o n o f the open economy system i n v o l v i n g i n t e r e s t r a t e s must i n c l u d e the i n t e r e s t r a t e s "*F. Nold,- J.L.- C a r r , and J.W. Winder, Essays on Monetary  A s p e c t s of I n f l a t i o n , Ottawa, I n f o r m a t i o n Canada, 1973. 5 R . J . H e r r i n g , and R i c h a r d Marston, "The Monetary S e c t o r i n an Open Economy: An E m p i r i c a l A n a l y s i s f o r Canada and Germany", P r e l i m i n a r y D r a f t , U n i v e r s i t y of P e n n s y l v a n i a , 1973. 6 on s i m i l a r U.S. bonds. The most comprehensive study to date was by the Bank of Canada, 6 c a l l e d "The Structure of RDX2". RDX2 i s a new quarterly model of the Canadian economy. I t i s intended to be used for r e a l i s t i c short and medium-term simulation of a l t e r n a t i v e p o l i c y choices open to the Government; hence p a r t i c u l a r attention has been paid to the s p e c i f i c a t i o n of the Government and monetary sectors. Of primary concern to the monetary sector i s the determination of i n t e r e s t r a t e s . The equation for intermediate and long-term i n t e r e s t rates are based on the Modigliani-Sutch version of the expectation theory, which postulates that y i e l d d i f f e r e n t i a l s between short-term bonds, and those of other maturity classes depend on expecta-tions regarding future l e v e l s of i n t e r e s t r a t e s . A d d i t i o n a l v a r i a b l e s were included i n the regression to r e f l e c t f a c t o r s other than past experience that might influence expectation. F i r s t , the spread between U.S. and Canadian short-rates was entered to allow for the f a c t that a large spread i s l i k e l y to generate expectation of changes i n the Canadian rate given the close r e l a t i o n s h i p between the two c a p i t a l markets. Second, the spread between the long and short rate i n the U.S. i s included to act as a measure of expected future movement i n U.S. rates. T h i r d , the expected rate of increase of the price l e v e l i s used to r e f l e c t the interconnection between expected J.F. H e l l i w e l l , H.L. Shapiro, G. Sparkes, I.A. Stuart, F. Gorbert, and D. Stephenson, The Structure of RDX2. Part I, and I I : Bank of Canada S t a f f Research Studies, Issued by the Publications Committee of the Bank of Canada, 1971. 7 r a t e s o f i n f l a t i o n and e x p e c t e d f u t u r e n o m i n a l i n t e r e s t r a t e s . The r e s u l t s showed t h a t t h e l o n g - t e r m r a t e was a f u n c t i o n o f : t h e s h o r t - t e r m r a t e ; t h e d i f f e r e n c e b e t w e e n t h e U.S. t r e a s u r y b i l l s , and t h e s h o r t - t e r m r a t e ; t h e d i f f e r e n c e b e t w e e n t h e U.S. c o r p o r a t e r a t e and t h e U.S. t r e a s u r y b i l l r a t e ; t h e e x p e c t e d a n n u a l r a t e o f c h a n g e o f t h e c o n s u m e r p r i c e i n d e x ; and t h e r a t i o o f l o n g - t e r m Government b o n d s t o s h o r t - t e r m G overnment b o n d s . The most i m p o r t a n t a s p e c t o f RDX2 t o t h i s p a p e r i s t h a t i t i n t r o d u c e s t h e i d e a o f u s i n g t h e s p r e a d between U.S. and C a n a d i a n i n t e r e s t r a t e s a s a v a r i a b l e . 7 J e n k i n s a n d L i m i n v e s t i g a t e d t h e r e a c t i o n o f i n t e r e s t r a t e s t o c h a n g e s i n d o m e s t i c and f o r e i g n m o n e t a r y p o l i c y , c h a n g e s i n Government b o r r o w i n g and t h e e x p e c t a t i o n s o f c h a n g e s i n t h e p r i c e l e v e l . T h e r e s u l t s i n d i c a t e d : t h a t a c h a n g e i n m o n e t a r y p o l i c y l e a d s t o c h a n g e s i n t h e l e v e l o f i n t e r e s t r a t e s ; t h a t t h e g r o w t h o f r e a l G overnment d e b t p l a y s an i m p o r t a n t r o l e i n d e t e r m i n i n g n o m i n a l i n t e r e s t r a t e s ; and t h a t C a n a d i a n m o n e t a r y a u t h o r i t i e s a c t s o t h a t C a n a d i a n m o n e t a r y p o l i c y w i l l f o l l o w t h a t o f t h e U.S. T h i s s u g g e s t s t h a t a s p r e a d i n C a n a d i a n and U.S. m o n e t a r y p o l i c y may be r e f l e c t e d i n t h e i n t e r e s t r a t e s and o t h e r e c o n o m i c v a r i a b l e s . W i t h t h e s e p a p e r s i n m i n d , t h e n e x t c h a p t e r d e v e l o p s an e c o n o m i c a l l y s o u n d model f o r b o t h t h e c l o s e d and o p en s y s t e m s . T h i s p a p e r u t i l i z e s s e v e r a l o f t h e i d e a s f r o m t h e a b o v e p a p e r s G l e n n J e n k i n s , and H e n r y L i m , "The R o l e o f C a n a d i a n and U n i t e d S t a t e s M o n e t a r y P o l i c y i n t h e D e t e r m i n a t i o n o f I n t e r e s t R a t e s i n C a n a d a " , D i s c u s s i o n P a p e r , H a r v a r d I n s t i t u t e o f E c o n o m i c R e s e a r c h , O c t o b e r , 1973. 8 to s t r u c t u r e the models of the c l o s e d and open economies. The approach o f u s i n g the d i f f e r e n c e between Canadian and U.S. v a r i a b l e s r e s u l t e d l a r g e l y out of the above-mentioned papers and w i l l be the method of i n v e s t i g a t i o n employed i n the open economy model. 9 Chapter 2 THEORIES OF INTEREST DETERMINATION CLOSED SYSTEM The c l o s e d system model d e s c r i b e s an economy a f f e c t e d o n l y by domestic v a r i a b l e s . Although Canada i s not i n t h i s c a t e g o r y , i t i s i n s t r u c t i v e i n i t i a l l y to i n v e s t i g a t e the c l o s e d system economy. The c l o s e d system model presented here i s i n e q u i l i b r i u m which i m p l i e s t h a t i t s component p a r t s , namely the money market, the pro d u c t market and the f a c t o r market, must be i n e q u i l i b r i u m w i t h each o t h e r . E q u a t i n g the money and pro d u c t markets and the money and f a c t o r markets r e s u l t s i n the p r o d u c t i o n of two d i s t i n c t e q u a t i o n s to d e s c r i b e the c l o s e d economy i n e q u i l i b r i u m . T h e r e f o r e , the a n a l y s i s o f the c l o s e d system i s d i v i d e d i n t o t h r e e p a r t s : the Money Market; the Product Market; and the F a c t o r Market to g e t h e r w i t h t h e i r r e s p e c t i v e i n t e r a c t i o n . THE MONEY MARKET The t r a d i t i o n a l theory on the demand f o r money h e l d t h a t the demand f o r money was p r o p o r t i o n a l o n l y to the l e v e l o f income: the g r e a t e r the income, the g r e a t e r the demand f o r money. However, Keynes h y p o t h e s i s e d i n h i s "General Theory of Employment, I n t e r e s t and Money", t h a t the demand f o r money was a c t u a l l y t h r e e s e p a r a t e demands: t r a n s a c t i o n demand, money h e l d t o make day-to-day t r a n s a c t i o n s ; p r e c a u t i o n a r y demand, money h e l d f o r unforeseen c o n t i n g e n c i e s ; and, s p e c u l a t i v e or 10 l i q u i d i t y demand, money h e l d a s an a s s e t . T h e t r a n s a c t i o n demand f o r money i s a d e c r e a s i n g f u n c t i o n o f t h e r a t e o f i n t e r e s t . T he e x p l a n a t i o n o f t h i s i s , a s i n t e r e s t r a t e s r i s e , t h e number o f t i m e s t h a t w e a l t h h o l d e r s f i n d i t p r o f i t a b l e t o e n t e r t h e bond m a r k e t i n c r e a s e s , and t h i s c a u s e s a r e d u c t i o n i n t h e i r a v e r a g e l e v e l o f money h o l d i n g s . The h i g h e r t h e r a t e o f i n t e r e s t , t h e more c o s t l y i t i s t o h o l d money r e l a t i v e t o o t h e r a s s e t s , and a r i s e i n t h e r a t e o f i n t e r e s t t h e r e f o r e p r o d u c e s an i n c e n t i v e t o e c o n o m i z e money b a l a n c e s and t o s u b -s t i t u t e e a r n i n g a s s e t s i n t h e i r p l a c e . L i k e t r a n s a c t i o n demand, p r e c a u t i o n a r y demand i s r e s p o n s i v e t o c h a n g e s i n t h e i n t e r e s t r a t e . As t h e r a t e o f i n t e r e s t i n c r e a s e s , t h e w e a l t h h o l d e r s w i l l y i e l d t o h i g h e r r i s k s o f s m a l l e r p r e c a u t i o n a r y b a l a n c e s i n r e t u r n f o r h i g h e a r n i n g a s s e t s . The s p e c u l a t i v e o r l i q u i d i t y demand f o r money r e s u l t s when w e a l t h h o l d e r s i n c l u d e money a s an a s s e t i n t h e i r p o r t f o l i o s . The r e a s o n f o r h o l d i n g t h i s n on-r e t u r n i n g s e c u r i t y as an a s s e t i s f r o m f e a r o f a c a p i t a l l o s s on h o l d i n g b o n d s . I f t h e b o n d p r i c e s a r e h i g h , and i n t e r e s t r a t e s a r e low, b u t e x p e c t e d t o r i s e , t h e n w e a l t h h o l d e r s w i l l h o l d money as an a s s e t b e c a u s e i f i n t e r e s t r a t e s do r i s e t h e n b o n d h o l d e r s w i l l t a k e a c a p i t a l l o s s . T h e r e f o r e i n t e r e s t r a t e s a r e i n v e r s e l y r e l a t e d t o l i q u i d i t y demand, p r e c a u t i o n a r y demand, and t r a n s a c t i o n demand, and t h e s e demands a r e d i r e c t l y r e l a t e d t o t h e l e v e l o f i n c o m e : Md = mY - n r ( 1 ) Md = money demand Y = in c o m e r = r e a l r a t e o f i n t e r e s t m, n = a r e c o e f f i c i e n t s 11 At equilibrium money supply (Ms ) equals money demand: Ms = Md (2) Ms = mY - nr ( 3 ) r = mY - Ms ( 4 ) n Equation ( 4 ) i s the money market equation and says that the r e a l rate of i n t e r e s t i s p o s i t i v e l y r e l a t e d to income and negatively r e l a t e d to money supply. That i s i f incomes increase then the r e a l i n t e r e s t rates w i l l increase but i f the money supply increases then the r e a l i n t e r e s t rate w i l l decrease. THE PRODUCT MARKET The rate of return on a new investment may be p l o t t e d as a negatively sloped curve r e l a t i n g investment and i n t e r e s t r a t e . I t i s negatively sloped because as the i n t e r e s t rate f a l l s , firms' cost of c a p i t a l decreases thus making previously unprofitable ventures p r o f i t a b l e : I = Io - wr (5) I - Investment Io = i n i t i a l investment r = r e a l i n t e r e s t rate w = c o e f f i c i e n t National income s t a t i s t i c s suggest that there i s a close r e l a t i o n s h i p between aggregate consumption expenditure and the l e v e l of disposable income. There i s also evidence to indicate that out of each additional d o l l a r of disposable income (Yd), the community w i l l increase i t s consumption (C) by a f r a c t i o n of the ad d i t i o n a l d o l l a r : C = Co + v Yd (6) C = Consumption Co = constant Yd = disposable income v - c o e f f i c i e n t 12 In a c l o s e d economy a t e q u i l i b r i u m , w i t h no Government involvement, the net n a t i o n a l product ( g r o s s n a t i o n a l p r o d u c t , minus d e p r e c i a t i o n , equals net n a t i o n a l p r o d u c t ) (Y) i s equal t o consumption (C) p l u s net r e a l i z e d investment ( I ) . However, t h e r e i s Government involvement i n the form of Government purchases of goods and s e r v i c e s (G), and these have the same a f f e c t on the l e v e l of income as investment e x p e n d i t u r e s . U n l i k e I, however, the l e v e l o f G i s assumed to be exogeneously determined. The e q u a t i o n f o r net n a t i o n a l product becomes: Y = C + I + G (7) S u b s t i t u t i n g e q u a t i o n (5) and e q u a t i o n (6) i n t o e q u a t i o n ( 7 ) : Y = Co + vYd + l o - wr + G (8) where d i s p o s a b l e income (Yd) e q u a l s income (Y) minus taxes ( T ) : Y = Co + v(Y-T) + l o - wr + G (9) S o l v i n g f o r Y: Y = Co - vT + l o - wr + G (10) 1 - v E q u a t i o n (10) shows the product market at e q u i l i b r i u m . E q u a t i o n (4) shows the money market a t e q u i l i b r i u m . The e q u i l i b r i u m of the product market and the money market must o c c u r a t the same i n t e r e s t r a t e and l e v e l of income, which are the two i d e n t i c a l v a r i a b l e s i n both markets. S u b s t i t u t i n g e q u a t i o n (10) i n t o e q u a t i o n (4) ( i n o r d e r to s o l v e the two e q u a t i o n s with two unknowns): r = m Co - vT + l o - wr + G - MR. (11) n 1 - v n r = m (Co - vT + l o + G) - Ms (12) n (1 - v) + mw n + mw 1-v 13 However, m, n, v, are a l l c o e f f i c i e n t s , Co and Io are c o n s t a n t s and T can be s a i d to be h e l d c o n s t a n t , then the e q u a t i o n becomes: r = X a + X 2 G - X 3 Ms (13) where X- = m (Co - vT + Io), Xp = rn X- = n(1-v)+mw n(l-v)+mw ) n-f mw 1-v However, t h i s paper i s i n t e r e s t e d i n nominal i n t e r e s t r a t e s . U s i n g F i s h e r ' s e q u a t i o n f o r i n t e r e s t r a t e s , nominal i n t e r e s t r a t e ( i ) can be expressed as the sum of the r e a l i n t e r e s t r a t e ( r ) and the expected r a t e o f change of p r i c e l e v e l (f>) : i = r + p (14) S u b s t i t u t i n g e q u a t i o n (13) i n t o e q u a t i o n ( 1 4 ) : i = X1 + X 2 G - X 3. Ms + X 4 p (15) E q u a t i o n (15) i s the e q u i l i b r i u m e q u a t i o n of the prod u c t market and the money market, r e l a t i n g nominal i n t e r e s t r a t e t o govern-ment spending, money supply and i n f l a t i o n . THE FACTOR MARKET The aggregate p r o d u c t i o n f u n c t i o n r e l a t i n g t o t a l i n p u t s t o t o t a l outputs show income (Y) as a f u n c t i o n o f the l e v e l o f employment (N), and the s i z e of c a p i t a l s t o c k (K): Y » St N + S 2 K (16) T h e r e f o r e , as a s u b s t i t u t e f o r income (Y) employment c o u l d be used i n e q u a t i o n ( 4 ) : r = ra I ( S 1 N) + ( S p K)~| - Ms (17) n L * J n 14 Now s u b s t i t u t i n g t h i s i n t o the F i s h e r e q u a t i o n (14): 1 = m n ( S 1 N) + ( S 2 K ) J - Ms + f> (18) n However, c a p i t a l s t o c k , which i s the a v a i l a b l e stock o f p r o d u c t i v e f a c i l i t i e s , can be c o n s i d e r e d to be h e l d c o n s t a n t and m, n, a r e c o e f f i c i e n t s , so the e q u a t i o n can be r e -w r i t t e n as: i = X a + X 2 N - X 3 Ms + X 4 p (19) where X1 = m S 2 K , X 2 = m } X 3 = 1 n n n E q u a t i o n (19) i s the e q u i l i b r i u m e q u a t i o n o f the f a c t o r market and money market, r e l a t i n g nominal i n t e r e s t r a t e s to employment, money supply and i n f l a t i o n . The" e q u a t i o n r e s u l t i n g from the e q u i l i b r i u m between the money market and the product market: i = X a + X 2 G - X 3 Ms + X 4 f> (15) and between the money market and the f a c t o r market: i = X 1 + X 2 N - X 3 Ms + X 4 f> (19) d i f f e r o n l y i n one v a r i a b l e . T h i s paper i s concerned w i t h government c o n t r o l o f long-term i n t e r e s t r a t e s . E q u a t i o n (15) c o n t a i n s government spending which i s a s u p e r i o r v a r i a b l e to employment, as employment i s l e s s c o n t r o l l a b l e by the govern-ment. Employment r e p l a c e s government spending i n e q u a t i o n (19). One might expect t h a t a change i n an independent v a r i a b l e would i n f l u e n c e the i n t e r e s t r a t e over a p e r i o d of time. To i n v e s t i g a t e t h i s , lagged forms of e q u a t i o n s (15) and (19) were used. 15 a b c i j . = X„ + > X 0 G, - < X. Ms. + 5 i X. pt-n (20) t 1 ^~ 2n t-n 3n t-n - _ _ 4n n=o n=o n=o a b c io. = X. + ? X„ N. - < X- Ms. + < X. pt-n (21) t 1 „ ^ 2n t-n <— ~ 3n t-n -F- 4n ^ n=o n=o n=o F u r t h e r , t h e r e are s e v e r a l reasons why one should e x p l o r e g the changes i n these v a r i a b l e s as J e n k i n s and Lim d i d . I f the v a l u e of an independent v a r i a b l e remains unchanged from p e r i o d to p e r i o d t h e r e s h o u l d be no e f f e c t by t h i s v a r i a b l e on the dependent v a r i a b l e . I f the r a t e o f change of a v a r i a b l e i s used, a s t a t i c v a r i a b l e w i l l have a v a l u e o f zer o i n the equa-t i o n . Secondly i t i s much e a s i e r to compare the impact t h a t each v a r i a b l e has on the i n t e r e s t r a t e i f a l l v a r i a b l e s are i n the same u n i t s . I f the r a t e o f change i s used then a l l v a r i a b l e s are i n the same u n i t s , they are d i m e n s i o n l e s s . T h i r d l y , owing to the s i z e d i f f e r e n t i a l o f the Canadian and U.S. economies, v a l u e s of the independent v a r i a b l e s of these two c o u n t r i e s are comparable o n l y i f r a t e of change v a r i a b l e s are used. The two e q u a t i o n s then become: f o r the money-product market e q u i l i b r i u m : b c i t = X a + £ X 2 n fc - - £ X 3 n / M s n - M s A + £ X 4 n (22) n=o ir—£ -J n=o \ — ^ n=o n - l t-n x n s n - l / t - n p n - fin-l) V $ n-l / t-n Glenn J e n k i n s and Henry Lim, "The Role of Canadian and U n i t e d S t a t e s Monetary P o l i c y i n the D e t e r m i n a t i o n of I n t e r e s t Rates i n Canada", D i s c u s s i o n Paper, Harvard I n s t i t u t e o f Economic Research, October 1973. 16 f o r money-factor market e q u i l i b r i u m : t-n c n=o t-n OPEN SYSTEM The open economy d i f f e r s from the c l o s e d economy i n t h a t i t c o n t a i n s f o r e i g n v a r i a b l e s which a f f e c t domestic i n t e r e s t r a t e s . Because the Canadian and U.S. money markets are so c l o s e l y a l l i e d , and because Canada's and the U.S's debt i n s t r u -ments are e a s i l y i n t e r c h a n g e a b l e , bond p o r t f o l i o s c o u l d c o n t a i n e i t h e r Canadian o r U.S. bonds, whichever y i e l d the h i g h e s t r e t u r n . T h e r e f o r e the U.S. i n t e r e s t r a t e becomes a f a c t o r i n the d e t e r m i n a t i o n of the Canadian i n t e r e s t r a t e . I t s h o u l d be> noted t h a t the European C a p i t a l Market i s a l s o an i n f l u e n c e on the Canadian C a p i t a l Market. However, o n l y U.S. i n f l u e n c e w i l l be assumed i n t h i s paper. There i s some ev i d e n c e to suggest t h a t the Canadian monetary a u t h o r i t i e s a c t so t h a t Canadian 9 monetary p o l i c y w i l l f o l l o w t h a t of the U.S. I t c o u l d be expected t h a t the Canadian i n t e r e s t r a t e w i l l approach the U.S. i n t e r e s t r a t e , the nearness o f the two b e i n g determined by: how i n t e r c h a n g e a b l e the debt i n s t r u m e n t s r e a l l y are and; how Glenn J e n k i n s , and Henry Lim, "The Role of Canadian and U n i t e d S t a t e s Monetary P o l i c y i n the D e t e r m i n a t i o n of I n t e r e s t Rates i n Canada", D i s c u s s i o n Paper, Harvard I n s t i t u t e of Economic Research, October 1973. 17 c l o s e l y t h e C a n a d i a n m o n e t a r y a u t h o r i t i e s a c t u a l l y f o l l o w t h e U.S. m o n e t a r y p o l i c y . The C a n a d i a n l o n g - t e r m i n t e r e s t r a t e c a n t h e r e f o r e b e s t be i n v e s t i g a t e d u s i n g t h e d i f f e r e n c e o f t h e C a n a d i a n and U.S. l o n g - t e r m i n t e r e s t r a t e s as t h e d e p e n d e n t v a r i a b l e and t h e d i f f e r e n c e b e t w e e n t h e C a n a d i a n and U.S. v a l u e s o f v a r i a b l e s t h a t r e f l e c t g o v e r n m e n t p o l i c y as t h e i n d e p e n d e n t v a r i a b l e s . T h e r e a r e t h r e e p o s s i b l e o u t c o m e s t o t h i s d i f f e r e n -t i a l m o d e l . F i r s t l y i f C a n a d i a n and U.S. l o n g - t e r m i n t e r e s t r a t e s f o l l o w i d e n t i c a l p a t h s b u t g o v e r n m e n t p o l i c i e s d i f f e r t h e n C a n a d i a n a c t i o n s must h a v e l i t t l e e f f e c t on C a n a d i a n c r e d i t c o n d i t i o n s . S e c o n d l y , i f t h e C a n a d i a n and U.S. l o n g - t e r m i n t e r e s t r a t e s d i s p l a y some i n d e p e n d e n t movement b u t g o v e r n m e n t p o l i c i e s a r e i d e n t i c a l t h e n t h e r e must be f o r c e s a t work o t h e r t h a n t h e g o v e r n m e n t p o l i c i e s p r e s e n t e d h e r e . T h i r d l y , i f i n t e r e s t r a t e d i f f e r e n t i a l s a p p e a r and C a n a d i a n p o l i c y i n s t r u -ments d i s p l a y some i n d e p e n d e n t movement o v e r t i m e t h e n t h i s may i n d i c a t e e f f e c t i v e i n d e p e n d e n t p o l i c y a c t i o n . The v a r i a b l e s u s e d i n t h i s m o d e l a r e t h e same as t h o s e o f t h e c l o s e d economy m o d e l . The e q u a t i o n s f o r t h e o p e n economy become: i n t h e m o n e y - p r o d u c t m a r k e t e q u i l i b r i u m : a i (CAN ), - i ( U S ) , .«= X^ + JT X0 IG(CAN) - G(CAN) ' - G(US) - G ( U S ) t z x d.n\ n n—1 n n— n = ° t G(CAN) , G T D S 7 ~ n - l n-1 J t - n b " n o X 3 n =o Ms (CAN) -Ms (CAN) „ - Ms(US) - Ms(US) * n n— l n n — l Ms(CAN) . M s(US) . n - l n-1 4 t - n c ' £ ( C A N ) n - p ( C A N ) n _ a - £ ( U S ) n - M U S ) n _ a i ( 2 4 ) : £ ( C A N ) n - 1 P ( U S J n - l n=o t - n 18 i n the money-factor market e q u i l i b r i u m a i ( C A N ) f c - i ( U S ) t = X a + £ X 2 n f N ( C A N ) n " N ( C A N ) n - l ~ N ( u s ) n - N(US> n ^ n - l N ( U S ) n-1 t-n b - ^ X n=o 3n Ms(CAN) -Ms(CAN) „ - MS(US) - M S ( U S ) " ' n n-1 n n-1 M s ( U S ) Ms(CAN) n-1 n-1 t-n c n=o + ^ . X 4 n P ( C A N ) n " ^ ( C A N ) n - l ~ ^ ( U S 3 ' n ~ g > ( U S ) n - l it r M C A N ) n _ a pTusT n-1 (25) t-n 1 9 C h a p t e r 3 MODELS CLOSED ECONOMY MODEL T h i s p a p e r p r e s e n t s two d i f f e r e n t m o d e l s o f t h e economy. The c l o s e d economy model v i e w s C a n a d a as an e n t i t y , w i t h no e x t e r n a l i n f l u e n c e s . However, b e c a u s e o f t h e i n f l u e n c e o f t h e U n i t e d S t a t e s , C a n a d a d o e s n o t b e h a v e as a c l o s e d s y s t e m . The v a l u e o f t h i s m o d e l i s t h a t i t shows t h e r e l a t i o n s h i p b e t w e e n d o m e s t i c v a r i a b l e s and t h e i n t e r e s t r a t e , d i s r e g a r d i n g t h e i n f l u e n c e o f t h e U.S. T h i s c l o s e d s y s t e m i s a l s o n e c e s s a r y i n t h e u n d e r s t a n d i n g o f t h e d o m i n a n c e t h a t t h e U n i t e d S t a t e s h a s , n o t o n l y on t h e C a n a d i a n l o n g - t e r m i n t e r e s t r a t e s , b u t on a l l e c o n o m i c v a r i a b l e s . I n a p r e c e d i n g s e c t i o n , an e c o n o m i c model o f t h e c l o s e d s y s t e m was p r e s e n t e d . I t made r e f e r e n c e t o s e v e r a l e c o n o m i c v a r i a b l e s a s b e i n g d e t e r m i n a n t s o f t h e i n t e r e s t r a t e . T h i s p a p e r d e a l s m a i n l y w i t h t h e d e t e r m i n a n t s o f l o n g -t e r m i n t e r e s t r a t e s t h a t t h e Government c o u l d ( i f i t w i s h e d ) i n f l u e n c e . The c l o s e d economy m o d e l , t h e r e f o r e , w i l l i n v e s t i g a t e i n t e r e s t r a t e s a s a f u n c t i o n o f t h e r a t e o f c h a n g e o f money s u p p l y , i n f l a t i o n and unemployment, o r g o v e r n m e n t e x p e n d i t u r e . DIFFERENCE IN CANADIAN AND U.S. LONG-TERM INTEREST RATE MODEL The s e c o n d model p r e s e n t e d i n t h i s p a p e r i s an o p e n economy model w h i c h i s u s e d i n o r d e r t o u n d e r s t a n d C a n a d a ' s a b i l i t y t o i n f l u e n c e i t s own l o n g - t e r m i n t e r e s t r a t e w i t h r e s p e c t t o t h e U.S. I t s h o u l d g i v e a p i c t u r e o f how t h e 20 d o m e s t i c and U.S. l o n g - t e r m i n t e r e s t r a t e s v a r y as a f u n c t i o n o f t h e d i f f e r e n c e i n g o v e r n m e n t p o l i c y o f t h e two c o u n t r i e s . I n d o i n g t h i s , t h e model i n h e r e n t l y assumes t h r e e t h i n g s : t h a t t h e C a n a d i a n g o v e r n m e n t h a s c o n t r o l o v e r t h e i n d e p e n d e n t v a r i a b l e s ; t h a t t h e U.S. i s t h e m a j o r i n f l u e n c e , and p r o b a b l e , c o n t r o l l i n g i n f l u e n c e o f t h e C a n a d i a n l o n g - t e r m i n t e r e s t r a t e ; and, t h a t t h e e f f i c i e n t m a r k e t h y p o t h e s i s , w h i c h s u g g e s t s t h a t t h e two r a t e s o f i n t e r e s t s h o u l d be t h e same w i t h i n s i m i l a r r i s k c a t e g o r i e s , i s n o t c o m p l e t e l y c o r r e c t and t h a t t h i s i s a l e s s t h a n e f f i c i e n t m a r k e t . T h i s model i n c o r p o r a t e s t h e e c o n o m i c s o f t h e c l o s e d m o d e l w i t h t h e i n f l u e n c e o f t h e U.S. on C a n a d a and p r o d u c e s a m o d e l where t h e d i f f e r e n c e b e t w e e n t h e C a n a d i a n and U.S. r a t e s a r e a f u n c t i o n o f t h e d i f f e r e n c e o f t h e r a t e o f c h a n g e o f : t h e money s u p p l y o f C a n a d a and t h e U.S.; t h e i n f l a t i o n o f C a n a d a and t h e U.S.; and t h e unemployment o f C a n a d a and t h e U.S.; o r t h e g o v e r n m e n t e x p e n d i t u r e o f C a n a d a and t h e U.S. 21 Chapter 4 ANALYSIS METHOD The data was analyzed u s i n g the computer program U.B.C. 10 TSP (time s e r i e s p r o c e s s o r ) , which i s a 'canned* program. TSP i s a computer language f o r the s t a t i s t i c a l a n a l y s i s of time s e r i e s by o r d i n a r y l e a s t squares and two stage l e a s t squares. I t i s designed to c a r r y out a l l the computational steps that occur r o u t i n e l y i n econometric r e s e a r c h . In t h i s paper, the subprograms used were: CORREL, which computes a c o r r e l a t i o n m a t r i x on any v a r i a b l e s d e s i r e d ; CORC, the Coch-rane-Oreutt method of combining o r d i n a r y l e a s t squares and the e s t i m a t i o n of the f i r s t order s e r i a l c o e f f i c i e n t of the di s t u r b a n c e ; PDL, which c a l c u l a t e s estimates of polynomial d i s t r i b u t e d l a g s u s i n g the Almon l a g technique; PDLCORC, i s tantamount to running a CORC t r a n s f o r m a t i o n on the PDL r e g r e s -s i o n . This means that the r o u t i n e w i l l perform polynomial d i s t r i b u t e d l a g e s t i m a t i o n w i t h f i r s t order s e r i a l l y c o r r e l a t e d e r r o r by combining PDL and CORC. In both the PDL and PDLCORC there i s the o p p o r t u n i t y to use some freedom w i t h r e s p e c t t o the d i s t r i b u t e d l a g v a r i a b l e . With t h i s o p t i o n , one can choose the degree of the polynomial w i t h which one wishes to f i t the data; the number of peri o d s TSP was adapted f o r the U.B.C. computer by Malcolm Greig and Robin Morley, from P r i n c e t o n U n i v e r s i t y ' s Department of Economic Documentation and Programming. 22 of l a g , and a j z e r o r e s t r i c t i o n . The j z e r o r e s t r i c t i o n a l l o w s t h r e e o p t i o n s : t o f o r c e the l a g c o e f f i c i e n t s t o approach z e r o as the time approaches the l a s t p e r i o d ; to f o r c e the l a g co-e f f i c i e n t to approach zero a t the f i r s t time p e r i o d ; o r to put no r e s t r i c t i o n on the l a g c o e f f i c i e n t . F o r each e q u a t i o n t h a t i s r e p o r t e d i n t h i s paper the PDLCORC r o u t i n e was used. (Other r o u t i n e s were t r i e d but none were as s a t i s f a c t o r y ) . T h i s r o u t i n e a l l o w s one to choose the degree of the p o l y n o m i a l w i t h which to f i t the d a t a . Second, t h i r d , f o u r t h and f i f t h degree p o l y n o m i a l s were t r i e d w i t h the second degree p o l y n o m i a l b e i n g s e l e c t e d . The r e s u l t s v a r i e d l i t t l e between a l l degrees of p o l y n o m i a l s but the second degree po l y n o m i a l proved b e s t mainly as i t p r o v i d e d the s i m p l e s t o u t p u t . I t was d e c i d e d not to r e s t r i c t the l a g c o e f f i c i e n t s so each e q u a t i o n p r e s e n t e d i n t h i s paper has no j z e r o r e s t r i c t i o n . DATA The d a t a used i n t h i s paper were o b t a i n e d from f o u r s o u r c e s : The Cansim Tapes; The Canadian S t a t i s t i c a l Review; The Bank of Canada Review; and, the F e d e r a l Reserve B u l l e t i n . The Cansim tapes are the computerized d a t a s t o r a g e of S t a t i s t i c s Canada, which u n f o r t u n a t e l y a r e not kept u p - t o - d a t e . The r e m a i n i n g d a t a from about 1974 (second q u a r t e r ) to the end of 1975, were o b t a i n e d from the Canadian S t a t i s t i c a l - Review, or the Bank of Canada Review. T h i s paper uses q u a r t e r l y d a t a from 1953 to 1975 i n c l u s i v e , or 92 q u a r t e r l y p e r i o d s . Much o f the d a t a had to be a l t e r e d b e f o r e b e i n g i n c l u d e d i n the model. The a l t e r a t i o n s took the form of one or more o f : a v e r a g i n g 23 m o n t h l y d a t a t o q u a r t e r l y d a t a ; c o m b i n i n g two o r more d a t a t a b l e s t o f o r m one v a r i a b l e ; o r f i n d i n g a r a t e o f c h a n g e v a r i a b l e . The l o n g - t e r m i n t e r e s t r a t e s (INTR ( C a n a d a ) ) and (USAR ( U S ) ) u s e d a r e t h e l o n g - t e r m bond y i e l d f o r Government i s s u e d b o n d s , t e n y e a r s and o v e r . The money s u p p l y v a r i a b l e s (MONY ( C a n a d a ) ) and (UMON ( U S ) ) were f o r m e d by a d d i n g t h e m o n t h l y demand d e p o s i t s t o t h e m o n t h l y amount o f c u r r e n c y h e l d o u t s i d e t h e bank, a v e r a g e d o v e r a t h r e e month p e r i o d t o g e t q u a r t e r l y d a t a . T h e n t h e r a t e o f c h a n g e o f t h e r e s u l t i n g d a t a was f o u n d and c o r r e c t e d f o r i n f l a t i o n and t h i s c o n s t i t u t e d t h e v a r i a b l e s . The i n f l a t i o n v a r i a b l e s (PRIC ( C a n a d a ) ) and (UPRI ( U S ) ) were f o r m e d by u s i n g t h e r a t e o f c h a n g e o f t h e q u a r t e r l y i m p l i c i t p r i c e i n d e x d a t a f o r g r o s s n a t i o n a l e x p e n d i t u r e . A l l d a t a were i n c o n s t a n t d o l l a r s . The unemployment v a r i a b l e s (UNEM ( C a n a d a ) ) and (UUNE ( U S ) ) u s e d were t h e r a t e o f c h a n g e o f q u a r t e r l y d a t a w h i c h had been o b t a i n e d by a v e r a g i n g m o n t h l y d a t a o v e r a t h r e e month p e r i o d . The g o v e r n m e n t e x p e n d i t u r e v a r i a b l e s (GOVT ( C a n a d a ) ) and (UGOV ( U S ) ) were c a l c u l a t e d f r o m t o t a l f e d e r a l g o v e r n m e n t e x p e n d i t u r e s , q u a r t e r l y d a t a , w h i c h were c o n v e r t e d t o r a t e o f c h a n g e o f g o v e r n m e n t e x p e n d i t u r e and c o r r e c t e d f o r i n f l a t i o n . 24 T a b l e I Summary o f V a r i a b l e s C a n a d a US D i f -f e r e n c e INTR USAR DINT l o n g - t e r m b o n d y i e l d , 1 0 y e a r s and o v e r MONY UMON DMON money s u p p l y , demand d e p o s i t s p l u s c u r r e n c y h e l d o u t s i d e t h e bank, r a t e o f c h a n g e PRIC UPRI DPRI i n f l a t i o n , i m p l i c i t p r i c e d e f l a t o r i n c o n s t a n t d o l l a r s , r a t e o f c h a n g e UNEM UUNE DUNE unemployment r a t e , r a t e o f ch a n g e GOVT UGOV DGOV t o t a l f e d e r a l g o v e r n m e n t e x p e n d i t u r e s , r a t e o f ch a n g e 25 Chapter 5 RESULTS CLOSED ECONOMY MODEL The c l o s e d economy model suggested t h a t t h e r e were two s l i g h t l y d i f f e r e n t e quations t h a t c o u l d be used i n the d e t e r -m i n a t i o n of i n t e r e s t r a t e s . The f i r s t e q u a t i o n was: 3 3 3 INTR, =C + £ a. GOVT. . - < b. MONY, . + . ^ C , PRIC. , (26) t . 1 t - l . 1 t - X 1 = 0 1 t - i 1 = 0 1 = 0 The e q u a t i o n had a r e s p e c t a b l e Durbin-Watson s t a t i s t i c and a good R-squared v a l u e (see T a b l e I I I ) . A l l o f the independent v a r i a b l e s are r a t e of change v a r i a b l e s w i t h both GOVT and MONY having been c o r r e c t e d f o r i n f l a t i o n . The Theory suggests that government e x p e n d i t u r e (GOVT) and i n f l a t i o n (PRIC) s h o u l d be p o s i t i v e l y r e l a t e d to long-term i n t e r e s t r a t e s (INTR) and th a t money supply (MONY) should be n e g a t i v e l y r e l a t e d to INTR. The r e s u l t s f o r t h i s e q u a t i o n (shown i n T a b l e I I ) show t h a t MONY i s n e g a t i v e l y r e l a t e d to INTR as expected, except i n the t h i r d l a g q u a r t e r where a very small c o e f f i c i e n t becomes p o s i t i v e , p o s s i b l y t h i s c o u l d be e x p l a i n e d by the i n s i g n i f i c a n c e o f t h i s c o e f f i c i e n t as i n d i c a t e d by i t s t - v a l u e . The v a r i a b l e PRIC i s shown to be p o s i t i v e l y r e l a t e d over a l l f o u r l a g q u a r t e r s but the v a r i a b l e GOVT i s f i r s t n e g a t i v e l y r e l a t e d f o r one l a g q u a r t e r then p o s i t i v e l y r e l a t e d (as was expected) f o r the next t h r e e l a g q u a r t e r s . T h i s i n d i c a t e s t h a t the government expendi-t u r e s i n i t i a l l y i n c r e a s e the money supply perhaps caused by the method of government f i n a n c i n g . Only i n the second to f o u r t h 26 T a b l e I I Computer R e s u l t s f o r E q u a t i o n 26 Independent E s t i m a t e d Standard V a r i a b l e Lag C o e f f i c i e n t E r r o r t - S t a t i s t i c C • 7.731 1.177 6.564 GOVT 1 -1.274 0.752 -1.693 2 0.404 0.972 0.415 3 0.729 0.978 0.950 4 0.301 0.782 0.385 MONY 1 -0.423 0.224 -1.797 2 -0.045 0.242 -0.188 3 0.031 0.241 0.128 4 -0.173 0.219 -0.788 PRIC 1 14.310 4.777 2.997 2 16.750 5.827 2.910 3 12.370 5.886 2.101 4 0.549 4.920 0.111 27 T a b l e I I I S t a t i s t i c a l R e s u l t s f o r E q u a t i o n 26 R-Squared = 0.976 Durbin-Watson S t a t i s t i c = 1.867 Va l u e o f Rho = 0.976 Number of O b s e r v a t i o n s = 86 Sum o f Squared R e s i d u a l s = 5.773 Standard E r r o r o f the R e g r e s s i o n = 0.275 F i g u r e 1 Graph o f Equa t i o n 26 28 P L O T nt= " : T I I M . I '• ) V J O F I T T c r ) ! * ! v"LUrS P L O T OF o . r s i O U S L SI Hr.Tt.i4L P r S ! D U « l 7 9 9 io 1 1 l? 1 3 1 4 1 5 1 6 1 7 H 19 2 0 2 1 2 T 23 2 4 2 5 2 6 2 7 2 8 2 9 3 0 3 1 3 2 33 3 4 3 5 1 6 3 7 3 8 3 9 4 0 4 I 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 5 0 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 6 0 6 1 6 2 6-> 6 4 6 5 6 6 6 7 6 3 6 9 / 0 71 I? 7 ? 74 7.5 76 7 T 7 3 7 9 •JO av A 2 3 ' 3'-8'-3 7 3 3 9 •»1 >! 3 . 0 9 0 2 . 9 8 1 ft* 0. 1 0 9 3 . 1 2 0 3 . 179 » - 0 . 5 3 9 C - 0 ! 3 . 0 7 0 3 . 1 9 0 *• - 0 . 1 2 0 3 . 0 5 0 3 . 274 '« * - 0 . 2 2 4 3 . 1 0 0 3 . 0 3 0 »* 0 . 7 0 5 = - 0 ! 3 . 3 2 0 3 . 3 1 7 • 0 . 2 7 4 f - 0 2 3 . 3 2 0 3 . 5 9 7 *» - 0 . 2 6 7 3 ^ 4 5 0 3 . 4 3 7 • - 0 . 7 1 0 ' - 0 2 3 . 7 5 0 3 . 7 8 0 . + - 0 . 3 0 4 F - 0 1 3 . 9 2 0 3 . 9 1 4 • O . S 9 2 F - 0 2 4 . 0 ' 0 3 . 7 3 5 * * , 0.2.9 5 4 . 1 3 0 4 . 045 • * 0 . 1 3 5 4 . 3 50 4 . ' 4 9 • 0 . 5 1 3 F - 0 2 3 . 8 9 0 4 . 4 7 6 * » - 0 . 5 8 6 3 . 8 4 0 3 . 7 3 0 0 . 1 1 0 3 . 7 1 0 4 . 1 5 7 * ft - 0 . 4 4 7 4 . 2 1 0 3 . 8 4 8 • * 0 . 3 6 2 4 . 5 0 0 4 . 0 9 5 0 . 4 0 5 4 . 7 4 0 4 . 700 ft 0 . 4 0 2 c - 0 1 4 . 9 4 0 4 ; 3 2 0 • ft 0 . 1 1 0 5 . 2 6 0 5 . 0 2 5 ft * 0 . 2 3 5 5 . 3 5 0 5 . 2 1 8 ++ 0 . 1 3 2 5 . 4 * 0 5 . 4 2 6 * 0 . 3 7 4 * - 0 2 5 . 1 7 0 5. 565 * ft - 0 . 3 9 5 4 . 9 0 0 5 . 0 1 5 *• - 0 . 1 1 5 5 . 2 3 0 5 . 0 2 3 ft* 0 . 2 0 7 5 . 1 6 C 5. 3 1 7 *» - 0 . 1 5 7 5 .1 .10 5 . 1 4 5 ft -0. 34 7= - 0 1 4 . 9 3 0 5 . 0 9 4 ft - 0 . 114 4 . 9 2 0 5 . 1 8 7 « * - 0 . 2 6 7 4 . 9 2 0 4 . 9 4 3 * - 0 . 2 3 2 c - 0 1 5 . 0 2 0 5 . 0 6 3 • - 0 . 4 3 1 F - 0 1 5 . 4 0 0 5 . 1 8 6 «• * 0 . 2 1 4 5 . 0 9 0 5 . 4 5 0 * + - 0 . 3 6 0 5 . 0 80 5 . 0 7 3 ft 0 . 7 1 9 F - 0 2 4 . 9 6 0 5 . 158 * ft - 0 . 1 9 8 5 . 1 7 0 5 . 0 1 1 ft* 0 . 159 5 . 1 3 0 5 . 3 6 2 *ft - 0 . 2 3 2 5 . 1 9 0 5 . 0 6 9 ft* 0 . 1 2 1 5 . 2 1 0 5 . 3 6 1 *• - Q . 1 5 1 5 . 2 2 0 3 . 3 3 5 *• - 0 . 1 * 5 5.1 O C 5 . 2 8 4 * » T O . 1 8 4 5 . 0 1 0 5 . 0 9 2 ft . -6 . 3 ! 3 = - 0 1 5 . 1 1 C 5 . 2 0 0 • - 0 . 9 0 4 F - 0 1 5 . 3 1 0 5 . 2 1 2 ft* 0 . 9 3 4 = - 0 1 5 . 3 9 0 5 . 3 3 7 ft* 0. 5 2 7 T - 0 1 5 . 5 2 C 5 . 544 ft - 0 . 1 4 Z C - 0 1 5 . 6 2 0 5 . 5 7 8 ft 0 . 4 1 6 - - 0 1 5 . 8 1 0 5 . B 4 6 ft -0. 3 5 3 F - 0 1 5 . 7 9 0 5 . 6 6 7 * 0 . 1 2 3 5 . 5 7 0 f . 0 0 0 * * - 0 . 4 7 0 5 . 7 1 0 5 . 4 9 6 • * 0 . 2 1 4 6 . 0 2 0 5 . 7 7 7 ft •« 0 . 2 4 3 6 . 4 3 0 6 . 1 3 2 ft 0 . 2 9 3 6 . 7 2 0 6 . 7 6 0 ft * 0 . 3 6 0 6 . 7 3 0 6 . 6 3 7 ft 0. 4 2 7 * - 0 l 6 . 5 0 0 6 . 8 2 9 * * - 0 . 3 2 9 7 . 0 < 0 6 . 5 1 6 ft * 0 . 4 9 4 7 . 190 7 . 032 0 . 1 0 3 7 . 4 2 0 7 . 4 6 4 *«• - 0 . 4 3 5 ^ - 0 1 7 . 6 2 0 7 . 3 ' 7 » * 0 . 3 0 3 8 . 1 0 0 7 . 6 ' 6 • ft ft 0 . 4 3 4 S . 1 2 C 3. C39 ft 0 . 3 1 0 * - 0 1 « . * 2 0 . « . 1 5 4 *ft - 1 . 3 3 6 * - 0 ! 7 . 6 9 0 " . 1 7 7 -* ft -0. ' , 37 7 . 4 7 0 7. 701 * ft - 0 . 22*. 6 . 7 * . 0 7 .1 - .5 * ft' - 0 . 4 0 5 7 . 21 C 6 . 374 » * 0. * 3 6 7 . 2 0 0 7 . ?55 ft - 0 . 5 5 2 * - 0 > 6 . 6 1 0 7 . 2 6 5 » ft - 0 . 6 5 5 6 . unri 6 . 6 * 9 I * 0 . 1 9 * 7 . 3 * 0 6 . ° * 9 ft * 0 . 3 5 1 7 . 4 6 C 7 . 5 1 8 ft - 0 . 5 3 4 R - 0 1 7 . 1 5 0 7 . 4 * 3 • * ft - . 0 . 31 3 7 . 2 2 0 7 . 0 2 9 • • 0. I T . 7 . M O 7. 4 * 4 ft* 0 . 11 6 7 . 7->0 0*8 f -0. 23"< 7.6-.C-- 7. 6^7 f 0. 1 2 ' - r - 0 1 7 . ">91 7. r- »0 ft ft o. 3 :o 9 . 0f,0 •<. 5 ' 9 ft * 0. S41 " . 7 1 0 « * 0.'.'r. 3 . 94 f) * . 4 ' * * ft - :1. 4 •> 1 8 . 3 * C 3. 4 * 9 - 0 . 1 ?9 3 . "70 3. • * ^ . 2 2 7 *. "0 3 . 339 * * 0. ,;,">? '•>.••• C:0 '•». 401 » o.srir-o? 29 l a g q u a r t e r s do they a c t as one would e x p e c t . I t sho u l d be noted t h a t t h e r e i s q u i t e a high n e g a t i v e c o r r e l a t i o n between GOVT and MONY of 0.7887 ( T a b l e X) which means as GOVT i n c r e a s e s MONY decrea s e s , t h e r e f o r e one would not expect the n e g a t i v e f i r s t q u a r t e r l a g of GOVT. The e s t i m a t e d c o e f f i c i e n t s and t h e i r t - s t a t i s t i c s g i v e v a l u a b l e i n f o r m a t i o n on the c o n t r i b u t i o n o f each v a r i a b l e t o the t o t a l e q u a t i o n , and because the v a r i a b l e s are a l l r a t e o f change, the s i z e o f the c o e f f i c i e n t s o f a l l v a r i a b l e s a re comparable. The v a r i a b l e GOVT has o n l y one c o e f f i c i e n t which approaches s i g n i f i c a n c e , i t s f i r s t l a g c o e f f i c i e n t . I n i t i a l l y a GOVT i n c r e a s e o f 1% would decrease the long-term i n t e r e s t r a t e by .012 f o r the f i r s t q u a r t e r but by the end of the year t h a t 1% i n c r e a s e would have i n c r e a s e d long-term i n t e r e s t r a t e s by .0016. The money supply v a r i a b l e has o n l y one s i g n i f i c a n t l a g c o e f f i c i e n t , i n d i c a t i n g t h a t an i n c r e a s e i n the money supp l y i n f l u e n c e s long-term i n t e r e s t r a t e s almost immediately a f t e r the i n c r e a s e o c c u r s . An i n c r e a s e of 1% i n the money sup p l y would decrease the i n t e r e s t r a t e .004 i n the f i r s t q u a r t e r and .0059 over the e n t i r e y e a r . The i n f l a t i o n v a r i a b l e (PRIC) has by f a r the g r e a t e s t i n f l u e n c e on the i n t e r e s t r a t e and has th r e e s i g n i f i c a n t l a g c o e f f i c i e n t s . An i n c r e a s e of 1% i n i n f l a t i o n i n the f i r s t l a g p e r i o d w i l l have an immediate e f f e c t on long-term i n t e r e s t r a t e s o f .143. The e f f e c t of t h i s 1% i n c r e a s e i n the f i r s t q u a r t e r w i l l r e s u l t i n an i n c r e a s e i n the second, t h i r d and f o u r t h q u a r t e r s as w e l l as with the r e s u l t i n g t o t a l i n c r e a s e i n long-term i n t e r e s t r a t e s o f .440. 30 The second c l o s e d economy model has the f o l l o w i n g form: I NTR.=C- £ a i UNEMfc^i - ^ 3 b ± M O N Y ^ + . J C ± P R I C ^ (27) i=o ~ i=o ~ i=o From T a b l e V i t i s e v i d e n t t h a t t h i s e q u a t i o n i s v e r y m a r g i n a l l y poorer at e x p l a i n i n g long-term i n t e r e s t r a t e s than the f i r s t e q u a t i o n . F or i n s t a n c e , t h i s e q u a t i o n has a lower R-squared v a l u e , a hi g h e r sum of squared r e s i d u a l s and a h i g h e r standard e r r o r of the r e g r e s s i o n . However as f a r as the o r y i s concerned t h i s e q u a t i o n does a s u p e r i o r job o f e x p l a i n i n g as a l l v a r i a b l e s a c t as they s h o u l d . T h i s e q u a t i o n d i f f e r s o n l y i n one v a r i a b l e from the f i r s t e q u a t i o n ; the r a t e of change of unemployment (UNEM) has been s u b s t i t u t e d f o r the r a t e of change of government e x p e n d i t u r e s (GOVT). I t sho u l d be noted t h a t t h e r e i s a high c o r r e l a t i o n between these two v a r i a b l e s of 0.8248 (see T a b l e X ) . As one would expect , when unemployment i s hi g h , the government e x p e n d i t u r e w i l l be up, spending money on w e l f a r e , unemployment i n s u r a n c e , make work p r o j e c t s , e t c . One would expect, from t h e o r y , t h a t both UNEM and MONY c o e f f i c i e n t s would be n e g a t i v e l y r e l a t e d and PRIC would be p o s i t i v e l y r e l a t e d to long-term i n t e r e s t r a t e s , and the r e s u l t s from t h i s e q u a t i o n show t h i s t o be the c a s e . Both UNEM and MONY have o n l y one s i g n i f i c a n t l a g c o e f f i c i e n t , the f i r s t c o -e f f i c i e n t . The i n f l u e n c e o f UNEM on INTR i s g r e a t e r than the i n f l u e n c e GOVT had on INTR as shown by the sum of the l a g c o e f f i c i e n t which f o r UNEM was -1.126 and f o r GOVT was 0.16. The i n f l u e n c e o f PRIC decreased s l i g h t l y from the f i r s t e q u a t i o n with o n l y the f i r s t two l a g c o e f f i c i e n t s now s i g n i f i -31 T a b l e IV Computer R e s u l t s f o r E q u a t i o n 27 Independent V a r i a b l e Lag E s t i m a t e d C o e f f i c i e n t Standard E r r o r t - S t a t i s t i c 7.844 1.296 6.049 UNEM 1 2 3 4 -0.522 • 0.300 -0.171 -0.133 0.243 0.278 0.276 0.217 •2.144 •1.082 •0.619 •0.616 MONY 1 2 3 4 •0.601 •0.346 •0.214 •0.203 0.275 0.316 0.321 0.258 •2.184 •1.097 •0.667 • 0.790 PRIC 1 2 3 4 15.600 14.170 9.182 0.644 4.976 6.106 6.198 5.173 3.135 2.320 1.482 0.124 32 T a b l e V S t a t i s t i c a l R e s u l t s f o r E q u a t i o n 27 R-Squared = 0.9740 Durbin-Watson S t a t i s t i c = 1.818 Valu e o f Rho = 0.977 Number of O b s e r v a t i o n s = 86 Sum of Squared R e s i d u a l s = 6.315 Standard E r r o r o f the R e g r e s s i o n = 0.288 F i g u r e 2 3 3 G r a p h o f E q u a t i o n 27 P 1 1 T 0 e A C T U M . ( * l ftN0 F ! T T ? 0 ( O V A L U F S " L O T OF R F S T O U & L ' 0 A C T U S ! T T r Q " 5 T 0 U A L 0 . 0 7 1 . 0 9 0 3 . 2 6 9 * • - 0 . 1 7 9 0 . a 3 . 1 2 0 3.20<? - 0 . 3 3 1 ^ - 0 1 0 . 9 3 . 0 7 0 3 . 1 9 0 *• - 0 . 1 2 0 0 . 1 0 3 . 0 5 0 3 . 1 0 1 • - 0 . 5 0 8 f - 0 1 0 . 1 1 3 . I O C 3 . 193 •* - 0 . 9 3 0 ^ - 0 1 0 . . 1 2 3 . P 2 0 3 . 1 8 1 0 . 1 3 9 . 0 . 1 3 3 . 3 3 0 3 . 6 0 5 • - 0 . 2 7 5 ) . . 1 4 3 . 4 8 0 3 . 4 8 0 • - 0 . 7 0 6 c - 0 4 1 5 3 . 7 5 0 3 . 7 9 7 - 0 . 4 7 4 = - 0 1 0 . 1 6 3 . 9 2 0 3 . 7 4 4 0 . 1 7 6 . 0 . 1 7 4 . 0 7 0 • » . 4 6 8 • * 0 . 5 6 2 1 8 4 . 1 1 0 4 . 3 2 5 ** - 0 . 1 4 5 0 . . 1 9 4 . 3 5 0 4 . 510 - 0 . 1 6 0 0 . 2 0 3 . 8 9 0 4 . 2 1 5 * • - 0 . 3 2 5 ) . . 21 3 . 8 4 0 3 . 8 5 1 - 0 . I 1 4 c - 0 1 0 . 2 2 3 . 7 1 0 4 . 1 5 0 * • - 0 . 4 7 0 0 . 2 3 4 . 2 1 0 3 . 7 7 4 0 . 4 3 6 2 4 4 . 5 0 0 4 . 2 8 8 0 . 2 1 2 . 0 . 2 5 4 . 7 4 0 4 . 6 7 5 • 0 . 6 4 7 C - 0 ! . 0 . 2 6 4 . 9 4 0 4 . 7 6 3 0 . 1 7 7 . 0 . 2 7 5 . 2 6 0 5 . 0 9 6 0 . 1 6 4 . 0 . 2 8 5 . 3 5 0 5 . 2 1 5 0 . 1 3 5 . 0 . 2 9 5 . 4 3 C 5 . 3 4 5 0 . 8 4 5 c - 0 l . 0 . 3 0 5 . 1 7 0 5 . 5 0 7 * • - 0 . 3 3 7 0 31 4 . - J 0 0 5 . 1 4 5 *+ - 0 . 2 4 5 0 . 3 2 5 . 2 3 0 4 . 9 4 8 • * 0 . 2 8 2 • c 3 3 5 . 1 6 C 5 . 3 6 0 - 0 . 2 0 0 0 . . 3 ' . . 5 . 1 7 . 0 ' 5 . 1 5 9 *» - 0 . 4 9 0 C - 0 1 0 . 3 5 4 . 9 9 0 5 . 0 9 6 *+ - 0 . 1 1 6 . 0 . 3 6 4 . 9 2 0 5 . 1 5 1 *»• - 0 . 2 3 1 0 3 7 4 . 9 2 0 5 . 0 1 7 •f - 0 . 9 6 8 c - 0 1 0 . 3 8 5 . 0 2 0 4 . 9 7 7 + 0 . 4 2 9 c - 0 1 3 9 5 . 4 0 0 5 . 1 7 4 + * 0 . 2 2 6 . 0 . 4 0 5 . 0 9 0 5 . 4 7 3 * • - 0 . 3 8 ? 0 . 41. 5 . 0 8 0 5 . 0 9 7 - 0 . 1 7 1 F - 0 1 0 . 4 2 4 . 9 6 0 5 . 1 5 1 * + - 0 . 2 0 1 0 . 4 3 5 . 1 7 0 4 . 9 4 7 0 . 2 2 3 . 0 . 4 4 5 . 1 3 0 5 . 3 9 4 - 0 . 2 6 4 . 0 4 5 5 . 1 9 0 5 . 145 0 . 4 5 5 c - 0 l 4 6 5 . 2 1 . 0 5 . 2 9 8 - Q . 8 7 5 F - 0 1 . 0 . . 4 7 5 . 2 2 0 5 . 2 7 3 - 0 . 5 3 3 S - 0 1 0 . 4 8 5 . 1 0 0 5 . 3 5 2 * • - 0 . 2 5 2 0 4 9 5 . 0 1 0 5 . 0 9 3 ** - 0 . 3 3 4 F - 0 1 0 . . 5 0 5 . 1 1 0 5 . 156 + - 0 . 4 6 2 E - 0 1 0 . 51 5 . 2 7 . 0 5 . 2 4 3 0 . 6 6 9 = - 0 1 . 0 . 5 2 5 . 3 9 0 5 . 3 2 4 0 . 6 6 3 F - O 1 . 0 , 5 3 5 . 5 3 0 5 . 5 2 8 + 0 5 4 5 . * 2 0 5 . 5 7 5 0 . 4 4 8 c - 0 1 • 0 5 5 5 . R I O 5 . 7 8 9 0 . 2 O 9 = - 0 1 0 5 6 5 . 7 9 0 5 . 7 4 0 ~ * 0 . 5 0 4 F - 0 1 . 0 5 7 5 . 5 7 C 5 . 8 3 6 - 0 . 2 6 6 ) . 5 8 5 . 7 1 0 5 . 6 9 3 ** 0 . 1 T 4 C - 0 1 0 5 9 6 . 0 2 0 5 . 6 7 5 «• * 0 . 3 4 5 6 0 6 . 4 2 0 6 . 0 3 9 * 0 . 3 9 ! 6? . 6 . 7 2 C 6 . 4 2 6 »• « 0 . 29 4 6 2 6 . 7 3 0 6 . 8 1 2 - 0 . 8 2 0 F - 0 1 . 0 . 6 3 6 . 5 C 0 6 . 772 * * - 0 . 2 2 2 . 0 6 4 7 . 0 1 0 . 6 . 5 2 7 + * 0 . 4 3 3 6 5 7 . 1 9 0 7 . 1 3 9 • 0 . 5 1 3 r - 0 1 6 6 7 . 4 2 0 7 . 4 5 6 - 0 . 3 5 6 c - 0 1 0 . 6 7 7 . 6 2 0 7 . 2 1 2 * 0 . 3 0 8 > • 6 R 3 . 1 0 0 7 . 5 4 4 • * 0 . 5 5 6 6 9 8 . 1 2 0 • 8 . 1 7 7 - 0 . 5 7 1 C - 0 1 0 . 7 0 S . 1 2 0 8 . 1 2 7 - 0 . 6 9 9 ^ - 0 2 7 1 7 . 6 9 9 8 . 0 9 2 - 0 . 4 0 2 0 7 2 7 . 4 7 0 7 . 7 2 2 ** - 0 . 2 5 2 . 0 7 1 6 . 7 6 0 7 . 2 3 9 * *• - 0 . 5 2 9 0 7 4 7.no 6 . 3 5 9 • * 0 . 3 5 1 7 5 7 . 2 0 0 7 . 2 1 9 - 0 . I 9 3 l ! - 0 l 0 . 7 6 6.61 0 7 . 2 3 7 * - 0 . 6 7 7 0 7 7 . 6 . 3 9 0 6 . 7 1 3 0 . 1 7 7 . 0 7 8 7 . 3 5 0 6 . 9 4 3 «• * 0 . 4 0 7 • • 7 9 7 . 4 6 0 7 . 4 7 7 * • - 0 . I 6 9 r - 0 1 0 . 8 0 7 . 1 5 C 7 . 4 7 6 * - 0 . 3 2 6 ) . 8 1 7 . 2 2 0 7 . 2 0 4 + 0 . 1 6 4 c - 0 1 3 2 7 . 6 1 0 7 . 3 6 2 * 0 . 2 4 3 8 3 7 . 7 2 0 7 . 3 1 0 * f - 0 . 1 7 0 . 0 . 8 4 7 . 6 4 0 7 . 742 - 0 . 1 0 2 . 0 . 8 5 7 . 8 9 0 7 . 722 • » 0 . 168 . 0 3 6 9 . 0 * 0 8 . 2 1 6 * 0 . B 4 4 , m 8 7 9 . 7 1 0 9 . 2 2 2 • •* 0 . 4 3 8 • * 8 8 S . 9 4 0 9 . 5 2 3 • * - 0 . 5 8 3 0 0 9 a. 3 1 0 3 . 4 2 5 - 0 . 1 1 5 • 0 . 9 0 8 . 3 7 0 8 . 5 2 2 • * 0 . 3 4 8 91 9 . 4 3 0 9 . 0 36 • * 0 . 4 4 4 9 2 9 . 4 6 0 9 . 5 6 0 * • - 0 . 1 0 0 . 0 . 34 c a n t and the sum o f the l a g c o e f f i c i e n t s decreased from 43.98 t o 39.60 CANADA-U.S. DIFFERENCE MODEL The Canadian and U.S. long-term i n t e r e s t r a t e s do not d i f f e r g r e a t l y over time. The c o r r e l a t i o n c o e f f i c i e n t i s hig h a t 0.9661 ( T a b l e X) with the mean d i f f e r e n c e between the r a t e s o f 1.125 (Canada minus U.S. long-term i n t e r e s t r a t e ) . (A p l o t o f the Canada and U.S. long-term i n t e r e s t r a t e s i s shown i n F i g u r e 3 ) . S t i l l t h ere s h o u l d be an e x p l a n a t i o n f o r a mean d i f f e r e n c e o f 1.125 and a d i f f e r e n c e t h a t has reached 2.79. The Canada - U.S. d i f f e r e n c e model suggested t h a t t h e r e were two s l i g h t l y d i f f e r e n t e q u a t i o n s t h a t c o u l d be used i n the examination o f the r e s i d u a l between the long-term i n t e r e s t r a t e s of these c o u n t r i e s . The f i r s t e q u a t i o n was: DINT, =C + J a. DGOV, b. DMON. .+ ^ C . D P R I , . (28) z i=o 1 r " 1 i=o 1 c _ 1 i=o 1 t " 1 The e q u a t i o n examined the d i f f e r e n c e i n Canadian and U.S. l o n g -term i n t e r e s t r a t e s i n terms o f the d i f f e r e n c e o f t h e i r r a t e o f charge o f government e x p e n d i t u r e , money su p p l y and i n f l a t i o n r a t e . The e q u a t i o n had a r e s p e c t a b l e Durbin-Watson s t a t i s t i c (see T a b l e V I I ) and an R-squared of 0.637 i n d i c a t i n g t h a t a good d e a l of the v a r i a n c e o f the long-term i n t e r e s t d i f f e r e n t i a l can be e x p l a i n e d i n t h i s manner. The DMON and DPRI v a r i a b l e s had the expected s i g n s but the DGOV began n e g a t i v e l y f o r the f i r s t two l a g s and then became p o s i t i v e (see T a b l e V I ) . T h i s i s s i m i l a r to the p a t t e r n encountered i n the c l o s e d economy model and may be e x p l a i n a b l e f o r the same r e a s o n s . F i g u r e 3 35 U.S. v s C a n a d a l o n g - t e r m i n t e r e s t r a t e s PLOT 0* A C T I j a K * ) ANO F I T T ^ O U ) V&II1TS PLOT OF R C S I0'J4L! U.S. C a n a d a 0 ACTUAL F ITTED 6 2 .490 3. 130 * • 7 2 . 5 1 0 3 .090 * • a 2 . 6 0 0 3.120 9 2 . 8 5 0 3.070 « * 10 2 .890 3 .050 t l 2.760 3.100 * • 1? 2 -690 3 .320 * • 13 3 .290 3 .330 *• 14 3 .10C 3.4 80 * . » 15 2 .960 3 .750 * * 16 2 .860 3 .920 * • 17 3 .530 4 .030 * • 18 3 .63C 4 . 180 * * 19 3 . 4 3 0 4 .350 * 20 3 .27C 3.890 * » 21 ' . 7 5 0 3 .840 * 22 3 .570 3.710 2 3 3 .500 4 . 210 * •• 24 3 .250 4 .500 * 25 4 .160 4 . 740 ft 26 4 .150 4 .940 * 27 4 . C 6 0 5.260 28 2 . 9 1 0 5 .350 * 29 3 . 9 1 0 5.430 * 30 2 .320 5 .170 ft 3 ! 4 .100 4 .900 ft 3? 4 .2 00 5 .230 ft 33 4 . C I O 5. 160 * 3 4 3 . 9 7 0 5 .110 ft 35 3 .800 4 .980 * 36 2 . 8 2 0 4 .920 ft 3 7 3 .880 4 .920 ft 39 3 .980 5 .020 ft 39 3 .890 5.400 ft 40 4 .060 5 . 0 ° 0 * 41 4 . 100 5.080 ft 42 4 . 0 1 0 4 .960 ft 43 3 .980 5. 170 ft 44 3 .910 5 .130 ft 45 4 . 1 4 0 5.190 ft 46 4 . 1 4 0 5.210 ft 47 4 . 1 6 0 5.220 ft 48 4 -160 5.100 ft 49 4 .340 5w010 50 4 . 1 9 0 5. 110 -v 51 4 . 1 4 0 5.310 ft 52 4 . 1 5 0 5.390 ft 53 4 . 6 9 0 5.530 54 4 .770 5.620 "5 5 4 .580 5 .810 56 4 . 6 2 0 5 .790 57 5 .32C 5.570 53 4 . 9 ? 0 5.710 59 4 . 710 6 .020 60 4 .440 6.430 61 5 .410 6 .720 62 5 .070 6.730 6? 5 .300 6 .500 64 5 .24C 7.010 65 6 .530 7 . 190 66 6 . 1 3 C 7.420 67 5 .910 7.620 68 5- BSC 8. 100 69 6 .260 8.120 70 6 .650 8.120 71 6.8'>0 7.690 72 6 .560 7.470 73 5 .500 6 .760 74 5 .75C 7.210 75 5 .830 7.200 76 5 .820 6 .610 77 5 .60C 6 .890 78 5 .600 7.350 79 5 .65C 7.460 30 5. 650 7.150 81 6 .300 7 .220 82 6 .580 7.610 83 6 .21C 7.720 34 6 .090 7.640 85 6 . 9 7 0 7.890 86 7 .270 9 .060 87 7 .040 9 .710 sa 6 .63C 8.940 89 7 .220 8 .310 V 0 7 .0RC 8.870 91 6 .960 9 .480 92 6 . 6 7 0 9-460 SI DUAL -0.640 0 -0.5B0 . 0 -0.520 0 - 0 . 2 2 0 -0.160 - 0 . 3 4 0 - 0 . 6 3 0 0 - 0 . 4 0 0 5 - 0 1 - 0 . 3 8 0 c - 0 . 7 9 0 . 0 - 1 . 0 6 . 0 - 0 . 5 0 0 c - 0 . 5 5 0 0 - 0 . 9 2 0 . 0 -0.620 0 -0.900=-01 ' 0 . 1 4 0 - 0 - 7 1 0 . 0 - 1 . 2 5 0 - 0 . 5 8 0 0 -0.790 . 0 • - 1 . 2 0 0 -1.44 0 . - 1 . 5 2 0 . * - 1 - 3 5 0 - 0 . 8 0 0 . 0 ft - 1 . 0 3 . 0 - 1 . 1 5 . 0 - 1 - 1 4 . 0 - 1 . 1 8 . 0 - 1 . 1 0 . 0 - 1 . 0 4 . 0 - 1 . 0 4 .0. - 1 . 5 1 0-- 1 . 0 3 . 0 • - 0 . 9 8 0 . 0 - 0 . 9 5 0 . 0 » - 1 . 1 9 0 * - 1 - 2 2 0 • - 1 . 0 5 . 0 - 1 . 0 7 .0 + - 1 . 0 6 . 0 • - 0 . 9 4 0 . 0 - 0 . 6 7 0 0 -0.920 . 0 ft - 1 . 1 7 .0 • - 1 . 2 4 0 + - 0 . 8 4 0 . 0 - 0 . 8 5 0 ' . 0 ft - 1 . 2 3 0 * - 1 . 1 7 .0 ft + - 0 . 2 5 0 . - 0 . 7 8 0 . 0 - 1 . 3 1 0 • - 1 . 9 9 0 ft • -1.31 0 * * - 1 . 6 6 0 . - 1 . 2 0 0 ft «• - 1 . 7 7 0 . ft + -0.660 . 0 ft *• - 1 . 2 9 0 ft •f- - 1 . 7 1 0 . ft * - 2 . 2 2 0 ft ft - 1 . 8 6 0 . ft • - 1 . 4 7 0 . ft -0. 360 - 0 ft • -0.910 . 0 * • - 1 . 2 6 0 ft • - 1 . 4 6 0. ft ¥ -1.2 2 0 ft • - 0 . 7 9 0 . 0 ft * - 1 . 2 9 0 ft ¥ - 1 . 7 5 0 . ft • - 1 . 8 1 0 . ft ¥ - 1 . 5 0 0 . ft - 0 . 9 2 0 . 0 ft • - 1 . 0 3 . 0 * • • - 1 . 5 1 0 . • - 1 . 5 5 0 . ft ¥ -0.920 . 0 ft • - 1 . 7 9 0 . ft • - 2 . 6 7 0 • ¥ - 2 . 3 1 0 ft • - 1 . 0 9 . 0 ft • - 1 . 7 9 0 . ft • - 2 . 5 2 0 ft • - 2 . 7 9 0 , . 36 T a b l e VI Computer R e s u l t s f o r E q u a t i o n 28 Independent V a r i a b l e Lag E s t i m a t e d C o e f f i c i e n t Standard E r r o r t - S t a t i s t i c 1.248 1.443 0.864 DGOV 1 2 3 4 •0.703 •0.092 0.300 0.474 0.412 0.423 0.429 0.406 •1.705 •0.217 0.698 1.166 DMON 1 2 3 4 • 0.750 •0.595 •0.611 -0.800 0.267 0.266 0.262 0.254 •2.803 •2.235 •2.330 •3.144 DPRI 1 2 3 4 6.931 14.880 12.570 -0.012 6.157 7.944 8.079 7.047 1.126 1.874 1.556 • 0.001 T a b l e V I I S t a t i s t i c a l R e s u l t s f o r E q u a t i o n 28 R-Squared = 0.637 Durbin-Watson S t a t i s t i c = 1.888 Va l u e o f Rho = .695 Number of O b s e r v a t i o n s = 86 Sum of the Squared R e s i d u a l s = 9.430 Standard E r r o r o f the R e g r e s s i o n = 0.352 '• F i g u r e 4 G r a p h o f E q u a t i o n 28 38 PLOT OF ACTUAL!*) ANP FI T TEO(fr) VALUFS PLOT OF P.FSIOUALM < ACTUAL F ! T T r : 0 "CSIOUAL 0 . 0 7 0.5300 1.018 * • -0.438 0 . . fl 0.5200 0.7066 * • -0.187 . 0 . 9 0.2200 0.2881 -0.681 c -01 0 . 1 0 0.1600 0.44 04 * t - 0 . 280 . 0 1 1 0. 3400 0.47BI * • -0.138 . 0 . . 12 0.6300 0.4772 • * 0.153 . . 0 . m 0.4000^ -01 0. 2328 * •. -0.243 . 0 1 4 0.3800 0.3223 • * 0.577 c-01 . 0 i s 0. 7900 0.8742 * • -0.8426-01 0 . 16 1.060 0.3] 16 • * 0.248 0 . 17 0.5000 0.6005 * • -0.101 0 . 13 C. 5? CC 0.7198 » f • - 0 . 170 . o . • . 19 0.9200 1.191 * * -0.271 . 0 . . 20 C.6200 1. 156 * • -0.536 0 . . . 27 C.9CC0- -01 0.3575 * + -0.268 . 0 . 22 0.'410 0.5666 -0.427 0 • 23 0.7100 0.8336 -0.129 . 0 . 24 1.250 0.8603 * * 0.390 25 0.5800 0.8671 * • -0.287 . 0 . 26 0.7900 0.6622 * * 0. 128 . 0 . 27 1.200 1 .12 6 ** n.640«-01 . . 0 2" 1.440 0.9349 * 0.505 . . 29 1 . 5 2 C 1. 292 0.228 0 . 30 1 .350 1.584 * f -0.234 . 0 . 31 0. 3000 1.393 * -0.593 0 . . • 32 1.030 0.9022 0.128 . 0 . 3? 1.150 0.9417 * * 0. 203 . 0 34 1.140 1. 161 *• -0.208P-01 0 . 35 1.180 1 . 086 + * 0.943F-01 . 0 36 1.100 1.000 0.999^-01 . 0 37 1.040 0.9543 0.857r-01 . 0 . 33 1 .040 0.9593 0.907^-01 . 0 39 1.510 1.341 * * 0.169 . 0 . 40 1.030 1.460 * -0.430 0 . . 47 0.9300 C.9070 • * 0. 730^-01 . 0 42 0.9500 1.093 -0.148 . 0 . 43 1.190 0.9733 + * 0. 217 . 0 44 1.220 1.219 0.863^-03 45 1 .050 0.9122 • * 0.138 . . 0 46 1.070 1.035 -0.151 c-01 04 47 1 .060 1.293 * + -0.233 . 0 48 0.9400 1.222 * • -0.282 . 0 49 C.67C0 0.6936 -0 .236P-01 0 . 50 0.9200 0.8306 • * 0.394^-01 . 0 51 1.170 1.242 -0.7175T-01 0 . 52 1.240 1. 181 0. 586 I I-01 . 0 53 C. 34CC 1.027 * • - 0 . 187 . 0 . 54 0.8500 0.7327 • * 0. 117 . 0 55 1.230 1.361 * f- -0.131 . 0 . 56 1.170 7.337 - * • -0.167 . 0 " . " 57 0.2500 0.9357 * + -0.736 0 5 3 0.7800 0.5751 0.205 . 0 . 59 1 .310 0.9823 » * 0.323 c 60 1.990 1.490 0. 500 6' 1 .370 1.469 * -0.159 . 0 . 62 1.660 1.173 0. 487 63 1.200 1.625 * -0.42 5 0 64 1 .770 1.163 * 0.607 65 C.fcfcOO I. 299 * • -0.639 0 66 1.290 0.9437 • * 0. 346 67 1 .710 1.273 + * 0. 437 68 2.220 1. 693 * 0.52 7 6 9 1 .860 1.66 4 • * 0. 196 . 0 70 1.4 70 1.668 -0.198 . 0 7'. . 0.8600 7 .435 * * -0.625 0 7 2 0.9100 1.473 * *• -0.568 0 73 1.260 0.6704 *• * 0.590 7 4 1 .460 1.095 «• * 0. 365 75 1.220 .405 - 0 . 351T-01 0 . 76 0.7900 1.538 * *• -0.748 0 77 1.290 0.7186 * * 0 . 571 78 1.750 1.353 * 0.397 7 9 1.310 1.353 - 0 . 427P-01 0 . 80 1.500 1.664 • -0.164 . 0 . 81 0.9200 1.162 * t -0.242 . 0 8? 1 .C3 0 0.8333 * * 0.146 . 0 . 83 1.510 1.27 3 + * 0.292 84 1 .550 1.390 * * 0. 16 0 . 0 . 85 0.9200 1.061 * • -0.141 . 0 . 8 6 1 .790 1.213 * 0.577 87 2.670 2.001 * 0.66 9 88 2.310 2. 516 * -0.206 . 0 39 1.090 1.543 + -0.453 0 • • II 90 i.7<;o 1. 463 * 0 . 327 91 2.530 2.415 > * o. ios .0 92 2 .700 2.326 »• * 0.454 39 An i n t e r e s t i n g r e s u l t shows the C = 1.248. I f the r a t e of change f o r the Canadian and U.S. v a r i a b l e s were i d e n t i c a l , o r i f Canadian p o l i c y was i d e n t i c a l w i t h U.S. p o l i c y , then the Canadian long-term i n t e r e s t r a t e would be 1.248 h i g h e r than the U.S. which i s c l o s e t o the mean d i f f e r e n c e between the two c o u n t r i e s . The s i z e o f the c o e f f i c i e n t s i n d i c a t e the r e l a t i v e importance of each of the v a r i a b l e s . I t i s obvious t h a t the d i f f e r e n c e i n the r a t e s of change of the i n f l a t i o n r a t e s (DPRI) i s the most s i g n i f i c a n t v a r i a b l e i n e x p l a i n i n g the d i f f e r e n c e between the two i n t e r e s t r a t e s . The d i f f e r e n c e i n the r a t e s o f change of money supply (DMON) i s a l s o a v a r i a b l e w i t h good e x p l a n a t o r y powers. I t appears from T a b l e VI th a t the l a g of DMON probably i s lo n g e r than f o u r q u a r t e r s as shown by the t - s t a t i s t i c s . However, DMON was lagged e i g h t p e r i o d s but -was not s i g n i f i c a n t beyond the f o u r t h l a g p e r i o d . The v a r i a b l e DGOV which i s the d i f f e r e n c e o f the r a t e o f change o f expen d i -t u r e s o f the two governments i s not a v e r y s i g n i f i c a n t v a r i a b l e . T h i s can be born out by summing the e s t i m a t e d c o e f f i c i e n t s which f o r DGOV i s -0.021, f o r DMON i s -2.856 and f o r DPRI i s 34.37. The second Canada-U.S. d i f f e r e n c i n g model had the form: DINT, = C - J a. DUNE . - J b. DMON. .+ £ c. DPRI, . (29) z i=o 1 c _ 1 i=o 1 c ~ 1 i=o 1 t " 1 From T a b l e IX i t i s e v i d e n t t h a t t h i s e q u a t i o n i s m a r g i n a l l y p oorer a t e x p l a i n i n g d i f f e r e n c e s i n the long-term i n t e r e s t r a t e s than the l a s t e q u a t i o n . F o r i n s t a n c e , t h i s e q u a t i o n has a lower R-squared v a l u e , a h i g h e r sum of squared 40 T a b l e V I I I Computer R e s u l t s f o r E q u a t i o n 29 Independent E s t i m a t e d Standard V a r i a b l e Lag C o e f f i c i e n t E r r o r t - S t a t i s t i c C 1.393 0.141 9.855 DUNE 1 -0.633 0.288 -2.194 2 -0.527 0.325 -1.621 3 -0.409 0.316 -1.293 4 -0.277 0.253 -1.097 DMON 1 -0.815 0.275 -2.956 2 -0.653 0.297 -2.194 3 -0.649 0.313 -2.072 4 -0.803 0.321 -2.498 DPRI 1 8.926 6.334 1.409 2 13.530 7.543 1.794 3 8.223 7.910 1.040 4 -6.993 7.576 -0.923 41 T a b l e IX S t a t i s t i c a l R e s u l t s f o r E q u a t i o n 29 R-Squared = 0.621 Durbin-Watson S t a t i s t i c = 1.729 Valu e o f Rho = 0.618 Number of O b s e r v a t i o n s = 86 Sum of the Squared R e s i d u a l s = 9.853 Standard E r r o r of the R e g r e s s i o n = 0.360 ...... Figure 5 Graph of Equation 29 P10 T OF A C T U A l ( * i ANO FITTFn(ft ) VALUES ro ACTUAL F I T T = 0 7 0.5300 0.8200 ft 3 0.5200 C.7636 * ft 9 0.2200 0.6019 * • 10 C.16CC 0.7 269 *• 1 t 0.3400 0.4984 * • 12 0.6300 0.4985 * 13 C . 4 0 C C " - 01 0.5135 * ft 14 0.7800 0.3191 t* 15 0.7900 0.7964 ft 16 1.060 0.8775 ft * 1 7 O.50O0 0.1993 • * 18 0. 5500 0.5661 10 0.9200 1.133 * ft 20 0.6200 1 .1 56 ft 21 c 9 o c o r -01 0.6093 » ft 2 7 0 . 1 4 0 0 0.6757 * ft 23 0. 7! 00 0.3255 * ft 24 1 .250 0.9191 ft * 25 0.5800 0.7027 * ft 26 C.75C0 0.7C39 ft* 27 1.200 1. 267 *t 23 1 .440 0.9754 ft ft 29 1.570 1.023 ft ft 30 1 .3 5.0 1. 50S * ft 31 C.8000 1.319 * ft 32 1 .030 1.074 ft 33 1 .150 0.9789 ft * 34 1 .1 'iO I. 189 ft 35 1 .180 1.101 ft* 36 1.100 1.033 ft* 37 1.040 0.3586 ft * 38 1 .040 0.9257 ft * 39 1.51C 1.337 ft * 40 1.070 1.444 * ft 4! 0.53C0 0.8493 ft * 42 0.9500 1 .073 * ft 43 1.190 1.070 ft * 44 1.270 1. 327 * ft 45 1 .050 0.9455 ft * 46 1 .070 1.121 *• 47 1.060 1.205 * + 48 0.9400 1.230 * ft 49 C.67C0 C.6 514 ft 50 0.9200 0.9256 ft 51 1 .170 1.168 ft 52 1.240 1. 196 ft 53 0.8400 0.9177 * ft 54 C.85CO 0.B071 ft 55 1.230 1.227 * ft 5 6 1.170 1.302 * ft 57 0.2500 0.9242 ft ft 53 0.7900 0.7677 ft 59 1.310 1.014 ft * 60 J .990 1 . 1 35 ft 61 1.710 1.415 *• 6 2 1 .660 1.285 ft * 63 1 .200 1.531 * ft 64 1.770 1.177 ft ' * 65 0.6600 1 . 335 * ft 66 1 . 2^0 0.9706 t * 67 1.710 1 .447 ft * 6 3 2.220 1.471 ft 69 ' . 860 1.911 ft 70 1.470 1 .6*8 ft ft 7 1 0.8600 1.683 « ft 72 0.9100 1.239 * ft 7 2 1 .260 " 0.9622 ft * 74 1.4 60 1. 134 ft ' * 75 1 .7 20 1.569 ft ft J 76 C.79C0 1.496 ft ft 77 1 .290 0.3519 ft * 78 1.750 1.234 ft * 79 1.810 I. 762 ft* 30 1 .500 I. 666 * ft 81 C. 9700 1.197 * ft 32 1.0*0 0.8925 f * 33 1.510 1 .343 ft ft 84 l . ^ ' O 1.463 ft * 35 0.9200 1 . 1 ?. 9 * ft 36 1.790 1.179 ft * 37 2 .670 2.081 88 2.310 2.477 89 1.050 1. 607 * ft 90 1 . 7 " 0 1.377 ft ft 91 2.520 2.137 92 2.790 2 . 3 0 3 T S I O U A L - 0 . 2 4 0 - 0 . 2 4 9 - 0 . 3 8 2 - 0 . 6 6 9 F - 0 1 - 0 . 1 5 9 0. 132 - 0 . 4 7 8 0.609F-01 - 0 . 6 3 7 c - 0 2 0.182 0.301 - 0 . 161=-0l - 0 . 2 6 3 - 0 . 536 - 0 . 5 1 9 - 0 . 4 8 6 - 0 . 116 0.331 - 0 . 1 2 3 . 0. 361F-01 - 9 . 6 7 3 F - 0 ! 0.46 5 0. 497 - 0 . 1 5 5 - 0 . 5 1 9 - 0 . 4 3 9 F - 0 2 0. 171 - 0 . 4 8 9 5 - 0 1 0 . 7 8 9 c - 0 1 0. 6 7 2 c - 0 1 0.191 0 .114 0.173 - 0 . 4 1 4 0 . 131 -0 .734 " : -OJ 0. 160 - 0 . 107 0.104 - 0 . 508F-01 - 0 . 1 4 5 - 0 . 290 0 . 1 3 6 c - 0 1 - Q . 5 5 5 F - 0 2 0 .183E-02 0 . 4 ? 9 c - 0 ! - 0 . 7 7 7 F - 0 1 0 .429F-01 - 0 . 9 7 2 F - 0 1 - 0 . 1 3 2 - 0 . 6 7 4 0. 123^-01 0.296 0.805 - 0 . 1 0 5 0.375 -0 .331 0.593 - 0 . 7 2 5 0. 319 0.263 0. 74 9 0.437?-01 - 0 .228 - 0 . 823 - 0 . 3 2 9 0.398 0. 326 - 0 . 2 4 9 - 0 . 706 0.43 3 0. 516 0 . 4 8 2 F - 0 ! - 0 . 1 6 6 - 0 . 2 7 7 0.137 0. 162 0.371T-01 - 0 . 2 0 9 0.611 0 .589 - 0 . 167 - 0 . 5 1 7 0.453 0.383 0.397 43 r e s i d u a l s and a h i g h e r s t a n d a r d e r r o r o f the r e g r e s s i o n . However, as f a r as theory i s concerned t h i s e q u a t i o n does a s u p e r i o r job of e x p l a i n i n g , as a l l v a r i a b l e s a c t as they s h o u l d . T h i s e q u a t i o n d i f f e r s i n o n l y one v a r i a b l e from the l a s t e q u a t i o n ; the d i f f e r e n c e o f the r a t e s o f change o f Canadian and U.S. unemployment has been s u b s t i t u t e d f o r the d i f f e r e n c e of the r a t e of change of Canadian and U.S. govern-ment e x p e n d i t u r e . The two s i m i l a r v a r i a b l e s t o the l a s t e q u a t i o n changed v e r y l i t t l e w i t h the i n t r o d u c t i o n o f the new v a r i a b l e (see T a b l e V I I I ) . The v a r i a b l e DUNE i s n e g a t i v e l y r e l a t e d t o DINT as expected. The v a r i a b l e DGOV i n the l a s t e q u a t i o n was i n s i g n i f i c a n t i n i t s c o n t r i b u t i o n to long-term i n t e r e s t r a t e s as i t s sum of es t i m a t e d c o e f f i c i e n t s was ve r y s m a l l (-0.021). However, the v a r i a b l e DUNE i s a s i g n i f i c a n t c o n t r i b u t o r t o the d i f f e r e n c e i n long-term i n t e r e s t r a t e s as i t s sum of the es t i m a t e d c o e f f i c i e n t s shows (-1.846). The c o r r e l a t i o n matrix (Table X) has been i n c l u d e d to show the i n t e r r e l a t i o n between the v a r i a b l e s . T a b l e X' CORRELATION MATRIX COL ROW INTR USAR UMON MONY UGOV GOVT UPRI PRIC UUNE UNEM 10 1 2 3 4 5 K 7 8 9 10 1.0000 0.9661 0.0586 •0.1358 0.0838 0 .0390 0 .7064 0 .6504 0 .1070 -0 .0639 0.9661 1.0000 0.0196 -0 .1522 0 .0170 0.0772 0 .7577 0.6812 0.1596 -0 .0191 0.0586 0.0196 1.0000 -0 .0851 0.1672 0.1058 - 0 .1766 -0 .0922 - 0 . 0 2 5 6 -0 .0001 •0.1358 •0.1522 -0.0851 1.0000 0.1145 -0 .7887 -0 .0364 -0 .0630 -0.3798 -0 .9179 0.0838 0.0170 0.1672 0.1145 1.0000 -0.0878 -0.0765 0.0156 -0.2436 -0.2001 0.0390 0.0772 0.1058 -0 .7887 -0.0878 1.0000 0.0271 -0 .0129 0.3414 0.8248 0.7064 0.7577 -0 .1766 - 0 . 0 3 6 4 - 0 .0765 0.0271 1.0000 0.7182 0.1356 -O i0389 0.6504 0.6812 -0 .0922 -0 .0630 0.0156 -0 .0129 0.7182 1.0000 0.0690 -0 .0162 0.1070 0.1596 •0.0256 -0.3798 •0.2436 0.3414 0.1356 0.0690 1.0000 0.4044 -0 .0639 -0 .0191 -0 .0001 - 0 . 9 1 7 9 -0 .2001 0.8248 - 0 . 0 3 8 9 - 0 .0162 0 .4044 1.0000 •is. Chapter 6 45 CONCLUSIONS T h i s paper has attempted t o develop a model to demonstrate whether the government of Canada can e f f e c t an independent or p a r t i a l l y independent long-term i n t e r e s t r a t e p o l i c y w i t h r e s p e c t to the U n i t e d S t a t e s . Viewing the above i n the l i g h t 11 12 of papers by both Nold and C a r r and H e r r i n g and Marston which found t h a t the Canadian i n t e r e s t r a t e i s l a r g e l y d e t e r -mined by r a t e s o f s i m i l a r U.S. bonds, -t h i s seems r e a s o n a b l e c o n s i d e r i n g the h i g h c o r r e l a t i o n between the two r a t e s o f 0.9661 (Table X ) . Both the models i n d i c a t e d t h a t the i n f l a t i o n r a t e i s the most important f a c t o r i n changes i n the i n t e r e s t r a t e . In the c l o s e d economy model a change i n the i n f l a t i o n r a t e w i l l a f f e c t the i n t e r e s t r a t e s i g n i f i c a n t l y f o r the next three q u a r t e r s . The r e s u l t s show t h a t a change i n i n f l a t i o n o f 1% w i l l i n c r e a s e i n t e r e s t r a t e s between 39 to 44 b a s i s p o i n t s which d i f f e r s from 13 the 66 b a s i s p o i n t s t h a t F e l s t e i n and E c k s t e i n found i n t h e i r r e s e a r c h . Even though t h e r e i s q u i t e h i g h c o r r e l a t i o n between T.1 - F.N. Nold, J.L. C a r r , and John Winder, Essays on Mone- t a r y Aspects of I n f l a t i o n , Ottawa, I n f o r m a t i o n Canada, 1973. 1 ? R i c h a r d J . H e r r i n g , and Ri c h a r d C. Marston, "The Mone-t a r y S e c t o r i n an Open Economy: An E m p i r i c a l A n a l y s i s f o r Canada and Germany", P r e l i m i n a r y D r a f t , U n i v e r s i t y o f P e n n s y l v a n i a , 1973. 13 M a r t i n F e l s t e i n , and O t t o E c k s t e i n , "The Fundamental Determinants of the I n t e r e s t Rate", The Review of Economics  and S t a t i s t i c s , V o l . I l l , F e b r uary 1970, pp. 363-375. 46 the i n f l a t i o n r a t e of Canada and the U.S. (= 0.7182 T a b l e X) the most i n f l u e n t i a l v a r i a b l e on the d i f f e r e n c e between the long-term i n t e r e s t r a t e s i s the d i f f e r e n c e between the i n f l a -t i o n r a t e s . Of the d i f f e r e n c e i n the two long-term i n t e r e s t r a t e s between 26 per cent and 32 per cen t can be e x p l a i n e d by the d i f f e r e n c e i n the r a t e o f change of i n f l a t i o n o f the two c o u n t r i e s . Although the su c c e s s of the a n t i - i n f l a t i o n program i s i n doubt t h e r e i s evidence t h a t the government has had some success i n changing the r a t e of i n f l a t i o n . T h e r e f o r e the government has some a b i l i t y t o c o n t r o l i n t e r e s t r a t e s by t h i s means even i f t h i s i s an u n i n t e n t i o n a l consequence of a p r o -gram o f r i g i d a n t i - i n f l a t i o n c o n t r o l s . The government e x p e n d i t u r e v a r i a b l e i n the c l o s e d economy model tended to a c t i n i t i a l l y l i k e a monetary t o o l f o r the f i r s t l a g q u a r t e r and then l i k e a f i s c a l t o o l . However, over the f o u r l a g q u a r t e r s i t added l i t t l e to the t o t a l e q u a t i o n . In the d i f f e r e n t i a l i n t e r e s t r a t e model government e x p e n d i t u r e a c t e d much as i t had i n the c l o s e d economy model adding l i t t l e t o the t o t a l e q u a t i o n . The v a r i a b l e t h a t r e p l a c e d government e x p e n d i t u r e f o r the second e q u a t i o n i n both models was unemployment. T h i s v a r i a b l e f o r both models was found t o add much more to the e q u a t i o n than d i d the government spending v a r i a b l e , as shown by t h e i r r e s p e c -t i v e sum of l a g c o e f f i c i e n t s . The f a c t t h a t the c l o s e d economy model shows one s i g n i f i c a n t v a l u e f o r unemployment means t h a t changing unemployment a f f e c t s long-term i n t e r e s t r a t e s . But the f a c t t h a t the d i f f e r e n c e between the two c o u n t r i e s ' unemployment v a r i a b l e showed one s i g n i f i c a n t c o e f f i c i e n t i n d i c a t e s t h a t the i n t e r e s t r a t e d i f f e r e n t i a l can be p a r t i a l l y e x p l a i n e d i n terms of unemployment d i f f e r e n t i a l s . T h e r e f o r e , i f the government can a f f e c t the l e v e l of unemployment then i t w i l l be a f f e c t i n g i n t e r e s t r a t e s . In both c l o s e d economy e q u a t i o n s the money supply v a r i a b l e showed one s i g n i f i c a n t l a g c o e f f i c i e n t i n d i c a t i n g a change i n monetary p o l i c y appears to e f f e c t some change i n the l o n g e r - t e r m i n t e r e s t r a t e . There i s some evidence t h a t the Canadian Monetary a u t h o r i t i e s a c t so t h a t Canadian Monetary p o l i c y w i l l f o l l o w 14 t h a t of the U.S. I f the Canadian monetary a u t h o r i t i e s attempt and succeed i n f o l l o w i n g the U.S. p o l i c y , then one would expect the money supply v a r i a b l e to have l i t t l e s i g n i f i c a n c e i n e q u a t i o n 28 and 29. In f a c t the d i f f e r e n c e between the money sup p l y of Canada and the U.S. i s v e r y s i g n i f i c a n t over a l l f o u r l a g q u a r t e r s (but not over a g r e a t e r l a g l e n g t h , which was t e s t e d ) . T h i s would seem to i n d i c a t e e i t h e r the Canadian monetary a u t h o r i t y does not a c t so t h a t monetary p o l i c y f o l l o w s t h a t of the U.S. or they do not do a v e r y good job of f o l l o w i n g 15 the U.S. monetary p o l i c y . D o b e l l and Sargent b e l i e v e t h a t t h e r e i s doubt on the e f f e c t i v e n e s s with which the Bank o f """^Glenn B. J e n k i n s , and Henry Lim, "The Role of Canadian and U n i t e d S t a t e s Monetary P o l i c y i n the D e t e r m i n a t i o n of I n t e r e s t Rates i n Canada", D i s c u s s i o n Paper, Harvard I n s t i t u t e of Economic Research, October 1973. 1 5 Rodney D o b e l l , and Thomas Sargent, "The Term S t r u c t u r e of I n t e r e s t Rates i n Canada", The Canadian J o u r n a l of Economics, V o l . I I , Feb.-Nov., 1969. C a n a d a c a n i n f l u e n c e t h e v e r y l o n g end o f t h e m a t u r i t y s t r u c -t u r e o f y i e l d . However, i f t h e Bank o f C a n a d a i s a b l e t o m a i n t a i n c o n t r o l o v e r t h e money s u p p l y t h e n i t a p p e a r s t h a t t h e y c a n a f f e c t l o n g - t e r m i n t e r e s t r a t e s . 49 BIBLIOGRAPHY Anderson, L e o n a l l C., and C a r l s o n , K e i t h M., "A M o n e t a r i s t Model f o r Economic S t a b i l i z a t i o n " , F e d e r a l Reserve Bank of S t . L o u i s , Review, A p r i l 1970. Clower, R.W., ed. Monetary Theory, Harmondsworth, England : Penguin E d u c a t i o n , 1969. Dernburg, Thomas F., andMcDougall, Duncan M., Macroeconomics. The Measurement, A n a l y s i s , and C o n t r o l o f Aggregate  Economic A c t i v i t y , T o r o n t o : McGraw-Hill Book Company, Fou r t h e d i t i o n , 1972. D o b e l l , Rodney, and Sargent, Thomas, "The Term S t r u c t u r e of I n t e r e s t Rates i n Canada", The Canadian J o u r n a l of  Economics, Volume I I , Feb.-Nov., 1969. F e l d s t e i n , M a r t i n , and E c k s t e i n , Otto, "The Fundamental Determinants of the I n t e r e s t Rate", The Review o f  Economics and S t a t i s t i c s , Volume I I I (February 1970) : 363-375. Freedman, C h a r l e s ; Longworth, David, and Masson, P a u l , "The Role of U.S. I n t e r e s t Rates i n Canadian I n t e r e s t Rate E q u a t i o n s : An E x p l o r a t o r y A n a l y s i s " , Paper p r e s e n t e d at annual meetings of Canadian Economic A s s o c i a t i o n , Quebec C i t y , May 31, 1976. Gibson, W i l l i a m E., and Kaufman, George G., Monetary Economics :  Readings on C u r r e n t I s s u e s , New York : McGraw-Hill Book Co., 1971. H e l l i w e l l , John F.; S h a p i r o , H a r o l d L.; Sparks, Gordon R.; Stewart, Ian A.; Gorbet, F r e d e r i c k W.; and Stephenson, Donald R., The S t r u c t u r e o f RDX2, P a r t I and I I : Bank of Canada S t a f f Research S t u d i e s , Issued by the P u b l i c a t i o n s Committee o f the Bank of Canada, 1971. H e r r i n g , R i c h a r d J . , and Marston, R i c h a r d C , "The Monetary S e c t o r i n an Open Economy : An E m p i r i c a l A n a l y s i s f o r Canada and Germany", P r e l i m i n a r y D r a f t , U n i v e r s i t y of P e n n s y l v a n i a , 1973. J e n k i n s , Glenn, and Lim, Henry, "The Role of Canadian and United S t a t e s Monetary P o l i c y i n the D e t e r m i n a t i o n of I n t e r e s t Rates i n Canada", D i s c u s s i o n Paper, Harvard I n s t i t u t e of Economic Research, October 1973. Malinvaud, E., S t a t i s t i c a l Methods of Econometrics, C h i c a g o : Rand McNally and Co., 1966. Mundell, Robert A., Monetary Theory ; I n f l a t i o n , I n t e r e s t ,  and Growth i n the World Economy, P a c i f i c P a l i s a d e s , C a l i f o r n i a : Goodyear P u b l i s h i n g Co. Inc., 1971. 50 Nold, F.C.; Carr,. Jack L.; and Winder, John W.L., Ess a y s  on Monetary Aspects o f I n f l a t i o n , Ottawa : I n f o r m a t i o n Canada, 1973. S t a t i s t i c s Canada, Cansim - Canadian Socio-Economic I n f o r m a t i o n  Manaqement System, J u l y 1974. U.B.C. Time S e r i e s P r o c e s s o r , adapted by Malcolm G r i e g , and Robin Morley, Vancouver : Computing C e n t r e , The U n i v e r s i t y of B r i t i s h Columbia, Re v i s e d e d i t i o n , June 1974. Wonnacott, Thomas H., and Wonnacott, Ronald J . , I n t r o d u c t o r y  S t a t i s t i c s f o r Business and Economics, Toronto : John Wiley and Sons, Inc., 1972. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0093988/manifest

Comment

Related Items