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Export supply and import demand elasticities Lawrence, Denis Anthony 1987

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EXPORT SUPPLY AND IMPORT DEMAND ELASTICITIES By DENIS ANTHONY LAWRENCE B.Ec.(Hons . ) , Australian National University, 1977 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Department of Economics) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May 1987 (c) Denis Anthony Lawrence, 1987 A 6 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of E c o n o m i c s The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date 1 J u n e 1987 ABSTRACT The aim of this thesis is to extend the empirical research which has been undertaken using the GNP function approach to measuring export supply and import demand responsiveness. Exports and imports are divided into several components and detailed sets of e l a s t i c i t i e s produced. In the second part o£ the thesis imperfect adjustment is allowed for in the GNP function model. The GNP function framework treats imports as an input to the domestic technology while exports are an output. The aggregate technology can then be represented by a r e s t r i c t e d p r o f i t function f a c i l i t a t i n g the derivation of net output supply e l a s t i c i t i e s . In this study the aggregate net outputs are exports, imports, labour and domestic sales supply. Capital i s treated as a fixed input. Time-series of input-output data for Canada are used covering the period 1961 to 1980. In the f i r s t model estimated, four export and four import components are included by the use of aggregator functions and a two-stage estimation process. The recently developed Symmetric Generalised McFadden functional form which permits imposition of the correct curvature conditions while retaining f l e x i b i l i t y is used at both the aggregator and GNP function l e v e l s . The aggregate export own-price supply e l a s t i c i t y was found to be 1.67 in 1970 while the aggregate import own-price demand e l a s t i c i t y was -1.62. Increases in the prices of both imports and labour were found to decrease the supply of exports while exports were found to be complementary to the output of domestic sales supply. The demand for labour was found to be more e l a s t i c than in ( i i ) e a r l i e r studies and a general trend towards increasing price responsiveness ln the Canadian economy was observed. The own-price e l a s t i c i t i e s for the four export and four import components were stable and of reasonable magnitude. A l l the export and import components were found to be complementary. To remove the assumption of s e p a r a b i l i t y , modelling was extended to two larger disaggregated Generalised McFadden GNP function models containing four export (import) components, aggregate imports (exports), labour and domestic sales as net outputs. Using t h i s procedure more substitution between the export and import components was found. A planning price model whereby the producers' notional price adjusts gradually to actual price changes indicated that imperfect adjustment i s p a r t i c u l a r l y important in the traded goods sector. Exports f u l l y adjusted to price changes only over an extended period. F i n a l l y , an adjustment costs model was estimated which indicated that the main e f f e c t of allowing for imperfect adjustment was on input use. Differences between long-run and short-run export supply and import demand responsiveness were r e l a t i v e l y small. Considerable s u b s t i t u t a b i l i t y between labour and c a p i t a l in the long-run was observed and since labour was also variable in the short-run t h i s produced overshooting of labour demand. An increase in export prices thus caused a large short-run increase in labour demand but in the long-run the c a p i t a l stock was increased and substituted for much of the short-run labour increase. ( i i i ) TABLE OF CONTENTS A b s t r a c t i i L i s t of T a b l e s v L i s t of F i g u r e s v i i Acknowledgement v i i i Chapter 1. INTRODUCTION 1 Chapter 2. PREVIOUS STUDIES 5 Chapter 3. A FLEXIBLE AGGREGATOR FUNCTION MODEL 13 3.1 The GNP F u n c t i o n Framework 13 3.2 Aggregator F u n c t i o n s 20 3.3 E l a s t i c i t i e s Produced 26 3.4 R e s u l t s 27 3.5 C o n c l u s i o n s 35 Chapter 4. FLEXIBLE DISAGGREGATED MODELS 48 4.1 The G e n e r a l i s e d McFadden GNP F u n c t i o n 49 4.2 R e s u l t s 52 4.3 C o n c l u s i o n s 57 Chapter 5. A PLANNING PRICE MODEL 65 5.1 The P l a n n i n g P r i c e Approach 65 5.2 R e s u l t s 69 Chapter 6. AN ADJUSTMENT COSTS MODEL 80 6.1 A T h e o r e t i c a l E x t e r n a l Adjustment Cos t s Model 80 6.2 An E c o n o m e t r i c A d a p t a t i o n 84 6.3 R e s u l t s 90 6.4 C o n c l u s i o n s 96 Chapter 7. CONCLUSIONS AND FURTHER RESEARCH 105 7.1 F u r t h e r Research 107 B i b l i o g r a p h y 111 Appendix 1. DATA 116 Appendix 2. PRIMAL VERSUS DUAL ESTIMATION 129 ( i v ) LIST OF TABLES Table 3. 1 SGM Parameter Estimates 37 Table 3. 2 GNP Function E l a s t i c i t i e s of Transformation 38 Table 3. 3 Export Supply E l a s t i c i t i e s 39 Table 3. 4 Import Demand E l a s t i c i t i e s 40 Table 3. 5 Labour Demand E l a s t i c i t i e s 41 Table 3. 6 Domestic Sales Supply E l a s t i c i t i e s 42 Table 3. 7 1970 Export Aggregator E l a s t i c i t i e s 43 Table 3. 8 1970 Import Aggregator E l a s t i c i t i e s 43 Table 3. 9 Export Component Own Supply E l a s t i c i t i e s 44 Table 3. 10 1970 Export Component Cross Supply E l a s t i c i t i e s 45 Table 3. 11 Import Component Own Demand E l a s t i c i t i e s 46 Table 3. 12 1970 Import Component Cross Demand E l a s t i c i t i e s 47 Table 4. 1 GM Parameter Estimates 59 Table 4. 2 Export Model Own Price E l a s t i c i t i e s 61 Table 4. 3 1970 Cross E l a s t i c i t i e s - Export Model 62 Table 4 . 4 Import Model Own Price E l a s t i c i t i e s 63 Table 4. 5 1970 Cross E l a s t i c i t i e s - Import Model 64 Table 5. 1 Generalised Leontief Parameter Estimates 76 Table 5. 2 1970 Net Output Supply E l a s t i c i t i e s 77 Table 6. 1 Dynamic Parameter Estimates 99 Table 6. 2 1965 Net Output Price E l a s t i c i t i e s 100 Table 6 . 3 1970 Net Output Price E l a s t i c i t i e s 101 Table 6. 4 1978 Net Output Price E l a s t i c i t i e s 102 Table 6. 5 Capital-Net Output Cross E l a s t i c i t i e s 103 Table 6. 6 Scale and Technical Change E l a s t i c i t i e s 104 Table Al .1 Aggregate Price Indices 122 (v) Table A l . 2 Aggregate Quantities in M i l l i o n s of 1961 Dollars 123 Table A l . 3 Export Component Price Indices 124 Table A l . 4 Export Component Quantities in M i l l i o n s of 1961 Dollars 125 Table A l . 5 Import Component Price Indices 126 Table A l . 6 Import Component Quantities in M i l l i o n s of 1961 Dollars 127 Table A l . 7 Adjustment Costs Model Capital Data 128 Table A2 . 1 MACE Data 144 Table A2. 2 Cost Function C o e f f i c i e n t s 146 Table A2. 3 F i t s and Tests 147 Table A2 . 4 E l a s t i c i t i e s of Substitution 148 Table A2. 5 Own Price E l a s t i c i t i e s of Demand 150 (vi) LIST OF FIGURES Figure 5.1 Adjustment of Planning Prices 78 Figure 5.2 Adjustment of Quantities 79 ( v i i ) ACKNOWLEDGEMENT i n c o m p l e t i n g t h i s t h e s i s there are numerous people to whom I am i n d e b t e d . I would l i k e to thank my t h e s i s committee of E r w i n D i e w e r t , John H e l l i w e l l , T e r r y Wales and B r i a n Copeland for t h e i r h e l p and encouragement. I a l s o thank my w i f e , M i r i n d a , and d a u g h t e r , Amanda, for t h e i r su p p or t and p a t i e n c e . My parent s a l s o p r o v i d e d encouragement and s u p p or t and p a r t i c u l a r l y my mother who d i d not l i v e to see my s t u d i e s comple ted . F i n a l l y , I would l i k e to thank my employer , the A u s t r a l i a n P u b l i c S e r v i c e , and i n p a r t i c u l a r the I n d u s t r i e s A s s i s t a n c e Commiss ion, for generous f i n a n c i a l s u p p o r t d u r i n g the p e r i o d of my s t u d i e s . ( v i i i ) 1. INTRODUCTION T r a d i t i o n a l empirical trade models have t y p i c a l l y attempted to model export supply and import demand relations by the use of linear or log-linear functions of r e a l income and the price of traded goods r e l a t i v e to the price of domestic substitutes. These models have assumed that exports, imports and domestic goods can be aggregated and have ignored much of the information available on the i n d u s t r i a l structure of the economy. The use of single equation methods has further ignored much of the theoreti c a l knowledge available on the properties of demand systems. The objective of th i s thesis i s to extend the r e l a t i v e l y small amount of empirical trade work which has been undertaken using models which integrate the supply of exports and demand for imports with the i n d u s t r i a l structure of the economy and more c l o s e l y approximate the well developed l i t e r a t u r e on trade theory. The influence of the i n d u s t r i a l structure of the economy on export supply and import demand i s captured by using the GNP function framework f i r s t implemented by Kohli (1975, 1978). The GNP function framework treats imports as an input to the production technology and exports as an output of the technology thus enabling the derivation of an integrated system of supply and demand equations. The responsiveness of export supply and import demand in the Canadian economy is characterised by a detailed set of e l a s t i c i t y estimates. These e l a s t i c i t i e s provide information on the response of the economy to changes in traded and non-traded goods prices and factor endowments. As such, the e l a s t i c i t i e s may be thought 1 of as being analogous to the standard trade theory results except that they show a more complex set of responses as we move outside the standard 2x2x2 model and allow for j o i n t production. The e l a s t i c i t y estimates for exports and imports are l i k e l y to be of most interest in forecasting the effects of various exogenous changes. For instance, the effects of an across the board import t a r i f f or export subsidy on the supply of exports and domestic outputs and import demand can be calculated (subject to the fixed factor supply). S i m i l a r l y , the ef f e c t of such changes on the return to factors can be calculated. A l t e r n a t i v e l y , the e f f e c t of changes in factor prices (eg. due to favourable taxation treatment or increased unionisation) on the supply of the various outputs and exports, and import demand can be calculated. The e l a s t i c i t y estimates presented in t h i s study w i l l also be of interest to those constructing larger applied general equilibrium models of the Canadian economy. The GNP function framework of Kohli i s extended in a number of di r e c t i o n s in t h i s t h e s i s . F i r s t l y , exports and imports are each disaggregated into several components. While the usual GNP or r e s t r i c t e d p r o f i t function approach rapid l y becomes unmanageable as more output and input categories are allowed t h i s can be f a c i l i t a t e d by the use of aggregator functions as f i r s t applied by Fuss (1977). Furthermore, recently developed functional forms are used which have p o t e n t i a l l y superior curvature properties to the now t r a d i t i o n a l translog function. An alt e r n a t i v e means of allowing for several export and import components explored i s the use of larger disaggregated models 2 which overcome the r e s t r i c t i v e s e p a r a b i l i t y assumptions of the aggregator function approach but at the expense of not including the f u l l set of net outputs in the one model. The second avenue explored l s the allowance for Imperfect adjustment in the GNP function model. This i s f a c i l i t a t e d i n i t i a l l y by the use of planning prices as developed by Woodland (1976, 1977). Modelling is then extended to an e x p l i c i t costs of adjustment model as developed by Berndt, Fuss and Waverman (1977). The data used in the study are time-series of input-output data for Canada covering the period 1961 to 1980. The data are available for 37 d i f f e r e n t industries but are aggregated to five output groups and six input groups for estimation of the GNP function models. The output groups are sales to domestic end-users and four types of exports while the input groups consist of four categories of imports, labour and c a p i t a l . While th i s data set is limited to 20 observations ending in 1980 i t has the advantage of being detailed, well developed and i n t e r n a l l y consistent for the entire period. A b r i e f review of previous empirical studies of export supply and import demand is presented in the following chapter of this t h e s i s . The f l e x i b l e aggregator function model and i t s results are presented in Chapter 3 followed by the larger export and import disaggregated models in Chapter 4. Chapters 5 and 6 contain presentations of the planning price and adjustment costs models, respectively. F i n a l l y , conclusions are drawn and areas for future research i d e n t i f i e d in Chapter 7. The data used in the 3 s t u d y are d e s c r i b e d and l i s t e d i n Appendix 1 w h i l e Appendix 2 c o n t a i n s the r e s u l t s of a s t u d y comparing p r i m a l and d u a l e s t i m a t i o n r o u t e s . 4 2. PREVIOU S STUDIES A b r i e f r e v i e w of p r e v i o u s s t u d i e s of e x p o r t s u p p l y and import demand r e s p o n s i v e n e s s and t h e i r r e l a t i o n s h i p t o the u n d e r l y i n g t h e o r y of i n t e r n a t i o n a l t r a d e i s p r e s e n t e d i n t h i s c h a p t e r . In s p i t e of the w e l l d e v e l o p e d l i t e r a t u r e on t r a d e t h e o r y , i t i s o n l y over the l a s t decade and a h a l f t h a t both t h e o r e t i c a l and e m p i r i c a l developments have e n a b l e d a more i n t e g r a t e d approach t o m o d e l l i n g a c t u a l e x p o r t s u p p l y and import demand. A good r e v i e w of the l i n k between e m p i r i c a l s t u d i e s and u n d e r l y i n g t r a d e t h e o r y can be found i n Woodland (1982, Chapter 12) . Many t r a d i t i o n a l e m p i r i c a l s t u d i e s c o n c e n t r a t e d on import demand and m o d e l l e d i m p o r t s as f i n a l goods not e n t e r i n g the d o m e s t i c p r o d u c t i o n s e c t o r . Assuming t h a t i m p o r t s a r e s e p a r a b l e from o t h e r commodities demanded then import demand can be model l e d as a f u n c t i o n of import p r i c e s , the p r i c e s of o t h e r goods and d o m e s t i c income. Import demand was o f t e n m o d e l l e d as a l o g - l i n e a r r e l a t i o n s h i p of t h e s e v a r i a b l e s i n s p i t e of the f a c t t h a t t h i s cannot be d e r i v e d from u t i l i t y m a x i m i s i n g b e h a v i o u r e x c e p t under v e r y r e s t r i c t i v e c i r c u m s t a n c e s . E x p o r t demand can be mo d e l l e d i n an analogous manner u s i n g income and the p r i c e of oth e r goods from the r e s t of the w o r l d . T y p i c a l of t h e s e s t u d i e s was t h a t of Houthakker and Magee (1969) i n which demand f u n c t i o n s f o r b oth i m p o r t s and e x p o r t s f o r 26 c o u n t r i e s were e s t i m a t e d f o r the p e r i o d 1951-66. For Canada an import p r i c e e l a s t i c i t y of -1.46 and income e l a s t i c i t y of 1.20 were o b t a i n e d w h i l e the e x p o r t p r i c e e l a s t i c i t y was -0.59 and the e x p o r t income 5 e l a s t i c i t y 1.41. In another study Rhomberg (1964) found the Canadian export demand e l a s t i c i t y to be around -2 and the import demand e l a s t i c i t y to be around -1 using a linear version of the demand rel a t i o n s h i p . An alternative s p e c i f i c a t i o n of the consumer demand model for imports was used by Gregory (1971). By assuming a CES u t i l i t y function the logarithm of the r a t i o of import to domestic demand becomes a function of the logarithm of r e l a t i v e prices. An analogous procedure within a producer model was used by Alaouse, Marsden and Zeitsch (1977) to estimate the substitution between imported and domestic inputs to various Australian industries. The CES function was also used by Hickman and Lau (1973) within an import a l l o c a t i o n model. This type of model postulates that the quantity of a country's t o t a l Imports is a CES function of the quantities of imports from each country. The import price index is also assumed to be a CES function and imports are sourced from countries on the basis of the cost minimisation p r i n c i p l e s i m p l i c i t in the price index. The model is l i n e a r i s e d and factors such as trends, expectations and adjustment lags are allowed for. E l a s t i c i t i e s of substitution between imports from d i f f e r e n t countries in each import market are obtained and used in the derivation of aggregate export demand functions for each country. Using trade data for the period 1961-69 and an adaptive expectations dynamic model a short run e l a s t i c i t y of export demand for Canada of 0.59 was obtained. The corresponding long run e l a s t i c i t y was estimated to be 0.84. 6 The f i r s t empirical studies to model import demand within an integrated production sector model were those of Denny (1972) and Burgess (1974a, 1974b). These studies were also among the f i r s t to use f l e x i b l e functional forms. Burgess (1974a) assumes s e p a r a b i l i t y of the transformation function and models output as a function of the inputs of imports, c a p i t a l and labour. A set of translog share equations is estimated for the US for the period 1947-68. The e l a s t i c i t y of demand for imports ranges from -1.6 to -2.0. An increase in the price of imports was found to reduce the wage/rental price of c a p i t a l r a t i o . Burgess (1974b) models import demand by the use of a translog j o i n t cost function. Imports are assumed to be an input into the aggregate production process. This assumption is j u s t i f i e d by the argument that in many cases imports constitute intermediate inputs which have to undergo further processing before being supplied to the consumer. Even imports of consumer goods have to go through d i s t r i b u t i o n and commercial channels before reaching f i n a l demand. Burgess uses a two output (consumer and investment goods), three input (labour, c a p i t a l and imports) translog cost function for the U.S. for the period 1929-69 to model substitution p o s s i b i l i t i e s . Imports were found to be substitutable with labour and complementary to c a p i t a l . The own price e l a s t i c i t y of the demand for imports ranges from -0.51 to -0.66. Burgess (1976) uses a d i f f e r e n t functional form for the j o i n t cost function and d i f f e r e n t output groups (durables and non-durables, and non-governmental services and structures) for the US for the shorter period 1948-69. Import demand e l a s t i c i t i e s 7 range from -0.19 to -1.6 and imports were found to be substitutes for labour and complements to c a p i t a l . These substitution relationships, however, assume that output levels and input prices are exogenously given. An approach more in keeping with the neoclassical small country assumption in which the domestic country behaves as a price-taker in both export and import markets would have prices for outputs and imports and the quantities of factors exogenously given. Domestic export supply and import demand can then move in response to world prices subject to domestic factor endowments. This i s the basis of the GNP function approach used by Kohli (1975, 1978). Imports are again treated as an input to the production technology and exports are treated as an output of the technology, i e . domestic consumers have no demand for export goods. This assumption may be j u s t i f i e d by appealing to the fact that export goods t y p i c a l l y proceed through d i f f e r e n t channels to those destined for domestic consumption. Kohli models the technology by the use of a translog r e s t r i c t e d p r o f i t function which has consumption goods, investment goods, exports and imports as variable net outputs. Labour and c a p i t a l inputs are assumed to be fixed with th e i r prices adjusting endogenously. This is a s i m i l a r representation to Samuelson's (1953-4) GNP function in trade theory. Supply equations for consumption goods, investment goods and exports, a demand equation for imports and Inverse demand equations for labour and c a p i t a l are derived from the GNP function. These were among the f i r s t studies to model 8 domestic export supply subject to a given world price rather than modelling the rest o£ the world's demand for a country's exports, Kohli (1978) estimated his model for Canadian data for the period 1949-72 and found the own-price e l a s t i c i t y of demand for imports to vary between -0.9 and -1.0 and the own price e l a s t i c i t y of supply of exports to vary between 1.5 and 2.2. Exports, consumption and investment goods were found to be substitutes in production and the wage rate was found to f a l l in response to an increase in import prices and r i s e in response to an increase in export prices. Capital rental prices responded in the opposite d i r e c t i o n . Increases in investment goods and export prices increased the demand for imports while increases in consumption goods prices reduced import demand. Increases in c a p i t a l stocks reduced both exports and imports. It should be noted that a model such as this w i l l not necessarily produce results similar to the Rybczynski Theorem in t r a d i t i o n a l trade theory as jo i n t production i s allowed in the GNP function model. Also, the model is only p a r t i a l equilibrium in that no balance of payments or exchange rate adjustment mechanisms are included and no explanation of the c a p i t a l accumulation process is made. In the e a r l i e r study, Kohli (1975), an attempt was made to disaggregate imports and exports by the use of translog submodels but curvature conditions were not s a t i s f i e d and the submodels did not perform well. A recent application of the GNP function model is that of Diewert and Morrison (1986). In this study c a p i t a l is treated as a fixed input and constant returns to scale are imposed. The 9 economy's outputs are modelled as domestic sales and exports while i t s variable inputs are Imports excluding petroleum, imports of petroleum, and labour. The normalised quadratic p r o f i t function is used which permits the correct curvature conditions to be imposed on the model with minimal cost to f l e x i b i l i t y properties. The model i s applied to US data for the period 1967-82. Export supply e l a s t i c i t i e s range from 0.52 to 0.60 while non-petroleum import demand e l a s t i c i t i e s range from -0.74 to -1.12. Petroleum import demand e l a s t i c i t i e s range from -0.14 to -0.87. Exports were found to be highly substitutable with domestic sales and highly complementary with labour. Non-petroleum imports were substitutable with labour while petroleum imports were complementary with domestic sales and exports. A r e l a t i v e l y high own price e l a s t i c i t y of demand for labour of around -1.0 was obtained. A series of devaluation e l a s t i c i t i e s was also presented. In order to model both the production and consumption sectors and their influence on export supply and import demand one has to move into the realm of general equilibrium models. A small scale general equilibrium model in which the consumption as well as the production sector i s e x p l i c i t l y modelled as i s the balance of payments mechanism is that of Clements (1980). The model i s highly aggregated with only three goods (non-tradeables, importables and exportables). Unlike the Burgess and Kohli models, imports and exports are assumed to be perfect substitutes for domestic production. The model was estimated using U.S. data for the period 1952-71 but performed r e l a t i v e l y poorly. A 10 simulation of the ef f e c t of imposing a 10 per cent import t a r i f f indicated that r e a l exports would be 20 per cent lower in a l l periods and re a l imports would be 32 per cent lower after 12 years. Dynamics enter the model v i a intertemporal optimising behaviour by consumers. Applied general equilibrium models have often been used in simulations of the eff e c t s of d i f f e r e n t trade p o l i c i e s and exogenous shocks on the supply of exports and demand for imports. Most applied general equilibrium modelling, however, has been on a "large scale" basis with many goods and industries. The objective of these studies has been to assess the impact of exogenous changes on the economy once a l l the flow on effects of the change have been worked through. This is done by comparing the post-shock solution of the complete model with the base sol u t i o n . Typical of these larger scale models are those of Boadway and Treddenick (1978) of the Canadian economy and the ORANI model of Dixon, Parmenter, Ryland and Sutton (1977) of the Australian economy. Boadway and Treddenick find that the ef f e c t of reducing Canadian trade taxes to zero would be a small reduction in aggregate u t i l i t y due to the role of trade taxes in expl o i t i n g monopoly power. The t a r i f f was found to benefit t e r t i a r y industries and have an adverse impact on most manufacturing and primary industries while r a i s i n g the wage/rental r a t i o . The model of Harris (1984) represents the s t a r t of a new generation of general equilibrium models which incorporate recent developments in the f i e l d s of i n d u s t r i a l organisation and trade 11 theory. By allowing for internal economies of scale and product d i f f e r e n t i a t i o n Harris finds that the results of simulations can d i f f e r markedly from those of models based on the neoclassical assumptions of constant returns to scale and perfect competition. For instance, the e f f e c t of a move to m u l t i l a t e r a l free trade on the Canadian economy was estimated as an 8.6 per cent gain in aggregate welfare using the model based on scale economies and product d i f f e r e n t i a t i o n compared to only a 2.4 per cent welfare gain from the model based on neoclassical assumptions. While large scale general equilibrium models are capable of producing more detailed r e s u l t s than many smaller scale models they are t y p i c a l l y based on r e l a t i v e l y s i m p l i s t i c functional forms to enable t h e i r implementation. Export supply and import demand e l a s t i c i t i e s are also usually assumed rather than estimated within the models. Furthermore, while recent developments in i n d u s t r i a l organisation theory have opened up new areas of applied research, other recent developments in empirical techniques mean that many useful studies remain to be undertaken using models within the neoclassical framework. In p a r t i c u l a r , new means of incorporating many goods and factors using r e l a t i v e l y f l e x i b l e functional forms and models of imperfect adjustment w i l l enable modellers to produce more detailed e l a s t i c i t y estimates. It i s these avenues which are explored in this thesis within a neoclassical production sector model. Although the results w i l l be of interest ln the i r own r i g h t , they may also provide improved e l a s t i c i t y estimates for input to larger scale general equilibrium models. 12 3 . A. FLEXIBLE AGGREGATOR FUNCTION MODEL. In t h i s C h a p t e r t h e GNP f u n c t i o n f r a m e w o r k i s e l a b o r a t e d and u s e d t o p r o v i d e e s t i m a t e s o f t h e r e s p o n s i v e n e s s o f e x p o r t s u p p l y a n d i m p o r t demand i n C a n a d a . By u s i n g a g g r e g a t o r f u n c t i o n s s e v e r a l e x p o r t a n d i m p o r t c o m p o n e n t s a r e i n c l u d e d t h u s p r o d u c i n g d e t a i l e d s e t s o f e l a s t i c i t i e s . F i n a l l y , t h e i m p l i c a t i o n s o f t h e s e e l a s t i c i t y e s t i m a t e s f o r t h e e f f e c t s o f v a r i o u s p o l i c y c h a n g e s a n d e x o g e n o u s s h o c k s a r e d i s c u s s e d . 3 .1 The GNP F u n c t i o n F r a m e w o r k The GNP f u n c t i o n m o d e l a s s u m e s t h a t t h e e c o n o m y i s made up o f p r o f i t m a x i m i s i n g f i r m s o p e r a t i n g u n d e r c o n d i t i o n s o f p e r f e c t c o m p e t i t i o n i n g o o d s a n d f a c t o r s m a r k e t s . O u t p u t l e v e l s a n d m i x e s a n d i m p o r t demands a r e c h o s e n t o m a x i m i s e p r o f i t s g i v e n o u t p u t a n d i m p o r t p r i c e s a n d a v a i l a b l e f a c t o r q u a n t i t i e s . F a c t o r s a r e a s s u m e d t o be m o b i l e b e t w e e n f i r m s w i t h t h e i r m a r k e t p r i c e s e q u a l t o t h e i r s h a d o w p r i c e s . The a g g r e g a t e t e c h n o l o g y i s a s s u m e d t o be c h a r a c t e r i s e d b y c o n s t a n t r e t u r n s t o s c a l e , f r e e d i s p o s a l , n o n - i n c r e a s i n g m a r g i n a l r a t e s o f s u b s t i t u t i o n a n d t r a n s f o r m a t i o n , a n d t o be b o u n d e d f r o m a b o v e f o r g i v e n f i n i t e f a c t o r e n d o w m e n t s . The c o m p e t i t i v e e q u i l i b r i u m c a n t h e n be r e p r e s e n t e d a s t h e s o l u t i o n t o t h e p r o b l e m o f m a x i m i s i n g GNP s u b j e c t t o t h e a v a i l a b l e t e c h n o l o g y , f a c t o r endowments and g i v e n o u t p u t and i m p o r t p r i c e s . E x p o r t s a r e t r e a t e d a s a n o u t p u t o f t h e p r o d u c t i o n s e c t o r w h i l e i m p o r t s a r e t r e a t e d a s a n i n p u t . As n o t e d i n t h e p r e c e d i n g C h a p t e r , t r e a t i n g i m p o r t s a s i n p u t s t o p r o d u c t i o n may be 13 j u s t i f i e d b y a p p e a l i n g t o t h e f a c t t h a t m a n y i m p o r t s a r e i n t e r m e d i a t e i n p u t s a n d e v e n t h o s e i m p o r t s w h i c h a r e " f i n a l " c o n s u m e r g o o d s s t i l l h a v e t o g o t h r o u g h d i s t r i b u t i o n a n d r e t a i l c h a n n e l s b e f o r e r e a c h i n g t h e c o n s u m e r . T r e a t i n g e x p o r t s a s s e p a r a t e g o o d s f o r w h i c h t h e r e i s n o d o m e s t i c d e m a n d i s n o t n e c e s s a r i l y r e s t r i c t i v e a s d o m e s t i c c o n s u m e r s m a y d e m a n d o t h e r g o o d s f r o m t h e p r o d u c t i o n s e c t o r w h i c h a r e h i g h l y o r e v e n p e r f e c t l y s u b s t i t u t a b l e w i t h t h e g o o d s c l a s s i f i e d a s e x p o r t s . W h i l e t h i s a p p r o a c h e n a b l e s u s t o m o d e l e x p o r t s u p p l y a n d i m p o r t d e m a n d b y c o n c e n t r a t i n g o n t h e p r o d u c t i o n s e c t o r a n d n o t e x p l i c i t l y i n c l u d i n g t h e c o n s u m p t i o n s e c t o r w h i c h i s u s u a l l y d i f f i c u l t t o m o d e l , t h e c o s t o f t h i s p r o c e d u r e i s t h a t t h e r e s u l t i n g m o d e l i s p a r t i a l e q u i l i b r i u m i n n a t u r e . B y h o l d i n g a l l p r i c e s f i x e d , t h e m o d e l w i l l b e p a r t l y m i s s p e c i f i e d a s n o t a l l t h e e f f e c t s o f e x o g e n o u s c h a n g e s w i l l b e c a p t u r e d . F o r i n s t a n c e , t h e p r i c e o f d o m e s t i c s a l e s i s t a k e n a s b e i n g e x o g e n o u s a n d i t i s a s s u m e d t h a t f i r m s c a n s e l l a n y a m o u n t o f d o m e s t i c s a l e s o u t p u t a t t h e e x i s t i n g p r i c e . N o t a l l o f t h e c o n s u m e r i n c o m e e f f e c t r e s p o n s e t o a n e x o g e n o u s p r i c e c h a n g e w i l l b e c a p t u r e d a s n o a l l o w a n c e i s m a d e f o r t h e e f f e c t o f c h a n g e s i n f a c t o r r e w a r d s o n t h e p r i c e o f d o m e s t i c s a l e s o u t p u t . A l s o , n o a l l o w a n c e i s m a d e f o r f o r c e s w h i c h w o u l d t e n d t o e l i m i n a t e d i s e q u i l i b r i u m i n t h e b a l a n c e o f p a y m e n t s a n d n o a t t e m p t i s m a d e a t t h i s s t a g e t o e x p l a i n t h e p r o c e s s o f c a p i t a l a c c u m u l a t i o n . D e n o t i n g t h e N v a r i a b l e n e t o u t p u t q u a n t i t i e s b y t h e v e c t o r x ( e n t r i e s p o s i t i v e f o r o u t p u t s , n e g a t i v e f o r i n p u t s ) , n e t o u t p u t p r i c e s b y t h e v e c t o r p>>0, t h e M f i x e d i n p u t q u a n t i t i e s b y t h e 14 vector z, fixed input shadow prices by the vector w and the production p o s s i b i l i t y set by T, the technology can be represented by the following r e s t r i c t e d p r o f i t (GNP) function: (3.1) G(p;z) = max. { p'x : (z;x) belongs to T, p>>0 }. x The r e s t r i c t e d p r o f i t function (3.1) w i l l be l i n e a r l y homogeneous and convex in net output prices and monotonically increasing (decreasing) in the prices of variable outputs (inputs). It w i l l be l i n e a r l y homogeneous, concave and monotonically increasing in fixed input quantities. The properties of r e s t r i c t e d p r o f i t functions are discussed in d e t a i l in Diewert (1973, 1974) while the GNP function in the trade theory context i s described by Woodland (1982). The model i s also based on the small country assumption; I.e., that the home country is a price taker in both i t s import and export markets. The quantity of imports i s then determined by domestic industry demand conditions while the quantity of exports is determined by domestic supply conditions. The small country assumption for Canada was tested by Appelbaum and Kohli (1979) who found they could not reject the price taking assumption for imports but found that i t was rejected for Canadian exports. If the r e s t r i c t e d p r o f i t function is d i f f e r e n t i a b l e with respect to p then the net output supply functions can be derived by applying Hotelling's (1932) Lemma: (3.2) x(p,z) = v p G ( p ; z ) Furthermore, i f the r e s t r i c t e d p r o f i t function i s d i f f e r e n t i a b l e with respect to the fixed input quantities, z, then the inverse demand functions for the fixed inputs may be obtained by: 15 (3.3) w(p,z) = V 2G(p;z) In t h i s study the aggregate c a p i t a l stock i s treated as the only fixed input. P r o f i t is maximised each period subject to the c a p i t a l stock available and so the process of c a p i t a l accumulation is not modelled. Labour is treated as a variable input; i . e . , producers choose how much labour they wish to employ at the given exogenous wage rate. With the existence of unemployment, t h i s treatment of labour appears more plausible than the a l t e r n a t i v e of assuming that the labour stock is f u l l y employed with the wage rate becoming an endogenous variable. Constant returns to scale are also assumed with respect to the c a p i t a l stock. The r e s t r i c t e d p r o f i t function (3.1) can then be represented by a unit p r o f i t function which represents the maximum amount of revenue the economy can produce from one unit of c a p i t a l . If the c a p i t a l stock were increased by a given proportion then the economy's net revenue would increase by the same proportion. The assumption of constant returns to scale helps avoid the conceptual problems which can occur when aggregating over producers. However, as Blackorby and Schworm (1984) point out, the requirements for consistent aggregation and the existence of an aggregate technology are highly r e s t r i c t i v e . E s s e n t i a l l y there remains a trade-off between the requirements for consistent aggregation and the use of models s u f f i c i e n t l y f l e x i b l e to capture substitution p o s s i b i l i t i e s . The data used in t h i s study are time-series of input-output data for the Canadian economy made available by S t a t i s t i c s Canada 16 and covering the period 1961 to 1980. I n i t i a l l y four variable net outputs for the economy as a whole are i d e n t i f i e d ; - the quantity of domestic sales; - the quantity of aggregate exports; - (minus) the quantity of aggregate imports; and - (minus) the quantity of labour. Corresponding price indices are set equal to 1.0 in 1961 and the i m p l i c i t quantities derived by d i v i d i n g the value of the net output by the relevant price index. An aggregate c a p i t a l price index is derived as a residual to equate the value of t o t a l outputs and t o t a l inputs under constant returns and the quantity of the c a p i t a l stock rescaled so that the price index assumes the value of 1.0 in 1961. The e l a s t i c i t y estimates presented are invariant to t h i s c a p i t a l r e s c a l i n g . The data are described in d e t a i l and l i s t e d in Appendix 1. To implement the model empirically a functional form for the r e s t r i c t e d p r o f i t function must be s p e c i f i e d and estimation of the system of derived net output supply functions undertaken. The c h a r a c t e r i s t i c s of the production technology and export and import responses are obtained from the c a l c u l a t i o n of various e l a s t i c i t i e s derived from the estimated p r o f i t function. These e l a s t i c i t i e s and t h e i r interpretation are discussed in Section 3.3 below. Desirable c h a r a c t e r i s t i c s of a functional form for the r e s t r i c t e d p r o f i t function are that i t be f l e x i b l e (able to provide a second order approximation to an a r b i t r a r y twice continuously d i f f e r e n t i a b l e p r o f i t function), parsimonious (have 17 t h e m i n i m a l number o f f r e e p a r a m e t e r s r e q u i r e d f o r f l e x i b i l i t y ) , a n d c o n s i s t e n t w i t h t h e r e q u i r e d t h e o r e t i c a l p r o p e r t i e s o f a p r o f i t f u n c t i o n . W h i l e t h e t r a n s l o g a n d G e n e r a l i s e d L e o n t i e f f o r m s h a v e become p o p u l a r b e c a u s e o f t h e i r f l e x i b i l i t y a n d r e l a t i v e e a s e o f i m p l e m e n t a t i o n , t h e y o f t e n s u f f e r i n e m p i r i c a l a p p l i c a t i o n s f r o m f a i l u r e t o s a t i s f y t h e r e q u i r e d c u r v a t u r e p r o p e r t i e s a t a l l ( o r a n y ) o f t h e o b s e r v a t i o n p o i n t s . I n r e s p o n s e t o t h i s p r o b l e m , r e c e n t d e v e l o p m e n t s i n f u n c t i o n a l f o r m s h a v e l e d t o t h e d e v e l o p m e n t o f f u n c t i o n s w h i c h a r e f l e x i b l e a n d e a s i l y v e r i f i e d a s s a t i s f y i n g c u r v a t u r e c o n d i t i o n s g l o b a l l y . I f t h e c u r v a t u r e c o n d i t i o n s a r e n o t s a t i s f i e d t h e y c a n be i m p o s e d w i t h m i n i m a l c o s t t o f l e x i b i l i t y p r o p e r t i e s a l t h o u g h n o n - l i n e a r r e g r e s s i o n t e c h n i q u e s t h e n h a v e t o be u s e d . The f u n c t i o n a l f o r m f o r t h e u n i t p r o f i t f u n c t i o n a d o p t e d i n t h i s s t u d y i s t h e S y m m e t r i c G e n e r a l i s e d M c F a d d e n (SGM) f u n c t i o n o f D i e w e r t a n d W a l e s ( 1 9 8 7 ) . The 4 - v a r i a b l e n e t o u t p u t SGM u n i t p r o f i t f u n c t i o n i s g i v e n b y ; ( 3 . 4 ) G ( p , K ) / K = (1/2)1^?.^ s i j P i P j / ( Z k 4 1 T R p k ) + b i i P i + Ziii * > l t P i t + b t t ( ^ i = l c i P i ) t 2 w h e r e t i m e s u p e r s c r i p t s h a v e b e e n d e l e t e d a n d t h e s-xj' ^ i i ' ^ i t a n d b t t a r e p a r a m e t e r s t o be e s t i m a t e d s u b j e c t t o ; ( 3 . 5 ) s i j = s j i f o r a l l i , j ; a n d , ( 3 . 6 ) ZLti s i j = 0 f o r J = l / . - / 4 . The v a r i a b l e t i s a t i m e t r e n d r e p r e s e n t i n g t e c h n i c a l p r o g r e s s a n d t h e e x o g e n o u s p a r a m e t e r s T k a n d C^^ a r e s e t e q u a l t o t h e a v e r a g e n e t o u t p u t q u a n t i t y p e r u n i t o f c a p i t a l i n p u t q u a n t i t y f o r k , 1 = 1 , . . , 4 . 18 Diewert and Wales (1987) show that the SGM form is f l e x i b l e for a price vector p~ s a t i s f y i n g Sp~=0N. While the non- symmetric Generalised McFadden function (analogous to the normalised quadratic form used by Diewert and Morrison (1986)) has superior f l e x i b i l i t y properties in that i t is not r e s t r i c t e d to being f l e x i b l e at just one point, the r e s u l t s obtained are sensitive to the choice of the numeraire good which plays an asymmetric r o l e . This s e n s i t i v i t y i s eliminated by use of the SGM form. D i f f e r e n t i a t i n g the GNP function (3 . 4 ) with respect to the net output prices y i e l d s a domestic supply function, an export supply function, (minus) an import demand function and (minus) a labour demand function. The form of these net output supply functions i s ; (3.7) X i / K = Zj=i SijPj/fZk 4:! T kp k) - T R ( Z k f i Z j i i s k j p k P j ) / 4 2 2 2(Zk = i TkPk^ + b i i + t ) i t t + b t t c i * : + u i ' 1 = 1,.. ,4. The variable net output quantity is divided by the quantity of the c a p i t a l input to reduce heteroskedasticity problems and an error term is appended to each equation. The vectors of error terms for the observations are assumed to be independently d i s t r i b u t e d with a multivariate normal d i s t r i b u t i o n with zero means and covariance matrix The estimating system consists of (3.7) subject to the r e s t r i c t i o n s (3.5) and (3.6). The p r o f i t function (3 . 4 ) is not included in the estimating system as i t adds no new information. Maximum l i k e l i h o o d estimates of the system of equations (3.7) can be obtained by using the Iterative Zellner technique available in the SYSTEMS command of SHAZAM (White 1978). If the matrix of 19 e s t i m a t e d c o e f f i c i e n t s S i s p o s i t i v e s e m i - d e f i n i t e t h e n t h e r e s t r i c t e d p r o f i t f u n c t i o n c a n be shown t o be g l o b a l l y c o n v e x i n p r i c e s p . I f t h e e s t i m a t e d S m a t r i x i s n o t p o s i t i v e s e m i - d e f i n i t e t h e n i t c a n be r e p a r a m e t e r i s e d u s i n g a t e c h n i q u e due t o W i l e y , S c h m i d t a n d B r a m b l e (1973) t o e n s u r e g l o b a l c o n v e x i t y . T h i s t e c h n i q u e r e p l a c e s t h e m a t r i x S = [ s i j ] b y t h e p r o d u c t o f a l o w e r t r i a n g u l a r m a t r i x a n d i t s t r a n s p o s e : ( 3 . 8 ) S = A A ' where A = ta^.. ] / i / J = l * « » / 4 ; a n d 3 ^ = 0 f o r i < j . U s i n g a r e s u l t due t o L a u ( 1 9 7 8 ) , D i e w e r t a n d W a l e s (1987) show t h a t t h i s i s a g e n e r a l way o f i m p o s i n g p o s i t i v e s e m i -d e f i n i t e n e s s . U s i n g t h i s p r o c e d u r e t h e c o e f f i c i e n t s i n t h e f i r s t t h r e e rows a n d c o l u m n s o f S b e c o m e ; 2 a l l a l l a 2 1 a l l a 3 1 ( 3 . 9 ) [ s i : j ] = 2 2 a 1 1 a 2 1 a 2 1 + a 2 2 a 2 1 a 3 1 + a 3 2 a 2 2 2 2 2 a l l a 3 1 a 2 1 a 3 1 + a 3 2 a 2 2 a 3 1 + a 3 2 + a 3 3 ; i , j = l , 2 , 3 The f o u r t h row a n d c o l u m n o f S a r e o b t a i n e d f r o m t h e summing r e s t r i c t i o n s ( 3 . 6 ) . The r e p a r a m e t e r i s e d s y s t e m i m p o s i n g c u r v a t u r e c a n be e s t i m a t e d b y u s i n g t h e n o n - l i n e a r r e g r e s s i o n a l g o r i t h m i n SHAZAM. 3 . 2 A g g r e g a t o r F u n c t i o n s A g g r e g a t i o n o f i n p u t a n d o u t p u t c o m p o n e n t s i s a n e c e s s a r y p a r t o f a n y e m p i r i c a l s t u d y t o e n s u r e t r a c t a b i l i t y b u t t h e c o s t o f t h i s p r o c e d u r e i s u s u a l l y a l o s s o f i n f o r m a t i o n . T h e r e a r e t h r e e c o n d i t i o n s u n d e r w h i c h a g g r e g a t i o n w i l l be c o n s i s t e n t o r n o t l o s e a n y o f t h e a v a i l a b l e i n f o r m a t i o n . The f i r s t o f t h e s e i s H i c k s a g g r e g a t i o n where t h e p r i c e s o f a g r o u p o f g o o d s a l w a y s 20 move i n e x a c t p r o p o r t i o n . A g g r e g a t e p r i c e a nd q u a n t i t y i n d i c e s c a n t h e n be f o r m e d w h i c h w i l l b e h a v e a s f o r a s i n g l e g o o d . S e c o n d l y , L e o n t i e f a g g r e g a t i o n p r o v i d e s c o n s i s t e n t a g g r e g a t e q u a n t i t y a n d p r i c e i n d i c e s when t h e q u a n t i t i e s o f a g r o u p o f g o o d s a l w a y s move i n e x a c t p r o p o r t i o n . C l e a r l y , H i c k s and L e o n t i e f a g g r e g a t i o n a r e b a s e d on s t r i c t c o n d i t i o n s w h i c h a r e u n l i k e l y t o be met i n p r a c t i c e . The t h i r d b a s i s f o r a g g r e g a t i o n p r o v i d e s a more g e n e r a l c a s e b y i m p l y i n g c e r t a i n p r o p e r t i e s f o r t h e f u n c t i o n a l s t r u c t u r e . T h i s i s t h e c o n d i t i o n o f homogeneous weak s e p a r a b i l i t y , o r i g i n a l l y due t o S h e p h a r d ( 1 9 5 3 ) , w h i c h assumes t h e GNP f u n c t i o n c a n be w r i t t e n a s : ( 3 . 1 0 ) G ( p , z ) = G~(R,V) w h e r e R = ( R 1 Rn'"-)' V = ( V 1 V - - > ' R n = R n ( P n >< Vm= Vm ( zm > and p n , z m b e l o n g t o p , z , r e s p e c t i v e l y . R n ( P n ) i s a p r i c e i n d e x f o r t h e g o o d s i n g r o u p n w h i l e v m ( z m ) i s a q u a n t i t y i n d e x f o r t h e f i x e d i n p u t s i n g r o u p m. The c o r r e s p o n d i n g t r a n s f o r m a t i o n f u n c t i o n i s : ( 3 . 1 1 ) T ( x , z ) = T~(Y,V) = 0 where Y= ( Y^, . . ., Y , . . ) and Y^ ( x n ) *-s ^ n e c o r r e s p o n d i n g q u a n t i t y i n d e x w h i c h i s assumed t o be l i n e a r l y homogeneous. We t h e n h a v e : ( 3 . 1 2 ) max. i p n x n : Y n ( x n ) = Y n } x n = Y n max. { p x / Y n : Y n ( x / Y n ) = l } = Y R (p ) n ,,, *n n n n n n n n n X n / Y n where R n ( P n ) i s a r e v e n u e o r a g g r e g a t o r f u n c t i o n . T h u s , ( 3 . 1 3 ) G ( p , z ) = max. p R x n : T ~ ( Y 1 ( x n ) , . . . , V ) = 0 } = max. R n ( P n ) Y n : T~(Y,V)=0 } 21 = G~(R,V) which i s a v a l i d GNP function in the aggregates to which Hotelling's Lemma and the standard GNP function properties can be applied (Woodland 1982, p.368). The important implication of weak s e p a r a b i l i t y i s that optimisation proceeds by a two-stage process. F i r s t , the optimal quantity of the aggregate i s chosen and then the optimal mix of that aggregate quantity is chosen. The marginal rate of substitution between two components of one aggregate is independent of the quantities of the other aggregates. Thus, the mix of that aggregate i s independent of both the l e v e l and the mix of the other aggregates. It is th i s aspect of weak s e p a r a b i l i t y which forms the basis of the use of aggregator functions as proposed by Fuss (1977) to accommodate many input (and output) components. With the use of f l e x i b l e functional forms the e x p l i c i t incorporation of many inputs and outputs r a p i d l y exhausts the available degrees of freedom and creates s i g n i f i c a n t m u l t i c o l l i n e a r i t y problems which are d i f f i c u l t , i f not impossible, to overcome. The increased computational burden i s also an important consideration. The use of aggregator functions permits the use of f l e x i b l e functional forms for the GNP function at the aggregate l e v e l along with f l e x i b l e aggregator functions. The response at the most disaggregated l e v e l can be obtained by: (3.14) X n = 9G/9p n = OG~/3R n.9R n/9p n wm = 8G/8z m = 9G~ /av m.9V m/8z m. 22 The cost of t h i s procedure i s , of course, acceptance of the property o£ weak s e p a r a b i l i t y . An unfortunate implication of weak s e p a r a b i l i t y i s that the s u b s t i t u t a b i l i t y of any two components within one aggregate with another aggregate is equal. Thus, imports of, say, tractors and hairpins might be assumed to be equally substitutable with the domestic sales aggregate. In t h i s study the aggregator function procedure i s used to disaggregate t o t a l exports and t o t a l imports each into four components. The four export components are; Group 1 : A g r i c u l t u r a l and Forestry Products; Group 2 : Minerals and Energy Products; Group 3 : Motor Vehicles, Textiles and E l e c t r i c a l Products; and Group 4 : Heavy Industrial and Service Products. The four import components are; Group 1 : A g r i c u l t u r a l , Forestry and Service Products; Group 2 : Metals and Energy Products; Group 3 : Machinery, E l e c t r i c a l and Textile Products; and Group 4 : Motor Vehicles, Chemicals and Other Products. The four export and import groups were formed by aggregating input-output industries according to s i m i l a r i t y of price movements over the 20 year period, the basis of Hicks aggregation. The composition of each of the components is explained and prices and quantities l i s t e d in Appendix 1. Making use of the assumption that the Y n ( x n ) functions are l i n e a r l y homogeneous the following Symmetric Generalised McFadden 23 u n i t revenue f u n c t i o n s are used f o r the export and import a g g r e g a t e s ; (3.15) R ( p , X ) / X = d / 2 ) Z " i i 1 Z j i 1 S i j P i P j / ( 2 7 k i i T k p k ) + Z - 4 i b , . p . + F . 4 , b . . p . t + b..(>~- 4-. C p . ) t 2 ^1=1 i 1 ^ 1 ^ i = l i t F i t t v < c i - l where t ime s u p e r s c r i p t s have a g a i n been d e l e t e d , X r e p r e s e n t s t o t a l e x p o r t s ( import s ) and the s ^ , b . ^ , b i t and b f c t are parameters to be e s t i m a t e d s u b j e c t t o ; (3.16) S j ^ j = S j j ^ f or a l l i , j ; a n d , (3.17) Ziii s i j = 0 for j = l , . . , 4 . The v a r i a b l e t i s a time t r e n d r e p r e s e n t i n g t e c h n i c a l p r o g r e s s and the exogenous parameters T k and C\ are s e t e q u a l to the average expor t ( import ) component q u a n t i t y per u n i t of t o t a l expor t ( import ) q u a n t i t y f o r k , i = l , . . , 4 . P r o f i t maximis ing behav iour i m p l i e s t h a t the export ( import ) component q u a n t i t i e s per u n i t of t o t a l e x p o r t s ( imports ) are g i v e n by; (3 .18) X . / X = Z.i± 8 , ^ / ( 2 ^ T R p k ) - TAZ^ Z.i± s k j P k P j ) / 2 ( C i V k ) 2 + b i i + b i t f c + b t t c i t 2 + u i ' l s l - ' 4 -The q u a n t i t y of t o t a l e x p o r t s ( import s ) X i s d e r i v e d as a D i v i s i a index of the c o r r e s p o n d i n g expor t ( import ) component q u a n t i t i e s . C o n v e x i t y i n p r i c e s can be imposed on the aggregator f u n c t i o n s by r e p a r a m e t e r i s i n g the S m a t r i x a l o n g the same l i n e s as (3 .8) and ( 3 . 9 ) . The v e c t o r s of e r r o r terms are a g a i n assumed to be i n d e p e n d e n t l y d i s t r i b u t e d w i t h a m u l t i v a r i a t e normal d i s t r i b u t i o n w i t h zero means and c o v a r i a n c e m a t r i x SL-By e s t i m a t i n g the system (3.18) and s u b s t i t u t i n g the e s t i m a t e d parameters i n ( 3 . 1 5 ) , an e s t imate of the aggregate u n i t 24 price i s obtained. A property of the two-stage optimisation procedure ls that although the prices of the Individual components of the aggregate are exogenous, the price of the aggregate i t s e l f i s not exogenous because the choice of input and output mix w i l l determine the aggregate price. Thus, to implement the procedure empirically an instrumental variable for the aggregate price i s required. Fuss proposes the use of the estimated price of the aggregate obtained by substituting the parameters estimated in equations similar to (3.18) into the aggregator function. This is used as an instrumental variable for the aggregate price in the second stage of the estimation process. Fuss j u s t i f i e s the use of the estimated aggregate price as an instrumental variable in his case by appealing to the fact that the translog aggregator function is exact for the D i v i s i a price index of the components as established by Diewert (1976). The estimation procedure is thus to f i r s t estimate the unit quantity equations (3.18) for the export and import components. Next, the parameter estimates obtained in the f i r s t stage are substituted in (3.15) to obtain instrumental variables for the aggregate export and import prices. The second stage of the estimation procedure is the estimation of the net output supply equations (3.7) derived from the SGM r e s t r i c t e d p r o f i t function using the instrumental variables for aggregate export and import prices . Application of thi s conditional estimation procedure produces estimates which are f u l l information maximum l i k e l i h o o d (Fuss 1977). The role of weak s e p a r a b i l i t y can be seen from (3.15) where the instrument for each aggregate depends only on 25 the prices of the components of that aggregate. In the absence of weak s e p a r a b i l i t y the prices of the other aggregates would also enter (3.15) and the above estimation procedure would not be consistent. 3.3 E l a s t i c i t i e s Produced The e l a s t i c i t i e s may be presented in either a scale invariant normalised form analogous to the Allen-Uzawa e l a s t i c i t i e s of substitution or in the standard net output price e l a s t i c i t y form. The scale invariant e l a s t i c i t i e s are a symmetric matrix of e l a s t i c i t i e s of transformation between net outputs (normalisations of 3xn/"2>pn) given by: (3.19) ET = G.Gpp/(Gp.Gp) where G p = diag. ^ 7 p G ( p ; z ) . The diagonal elements of ET are a l l non-negative. The more familiar net output price e l a s t i c i t i e s represent the response of net output i ' s quantity to changes in net output j's p r i c e : (3.20) E- . = din x./dln p. = s.ET. . where s.. is the share of net output j in r e s t r i c t e d p r o f i t and the e l a s t i c i t i e s s a t i s f y the following adding up r e s t r i c t i o n s ; (3.21) . Z}ii E.j = 0. Due to the maintained hypothesis of constant returns to scale the net output supply e l a s t i c i t i e s with respect to c a p i t a l a l l take the value 1.0. This also means that the e l a s t i c i t i e s of complementarity and i n t e n s i t y normally obtained in p r o f i t function studies are not presented. These e l a s t i c i t i e s and various summation r e s t r i c t i o n s which apply to them are presented 26 in Diewert (1974). For empirical applications of the translog r e s t r i c t e d p r o f i t function and interpretations of the associated e l a s t i c i t i e s not in the trade model context see McKay, Lawrence and Vlastuin (1982, 1983). While the e l a s t i c i t i e s above refer to aggregate exports and imports, and the second stage of the estimation procedure, two sets of e l a s t i c i t i e s are obtained for the individual components of exports and imports. In the case of cross-price e l a s t i c i t i e s between export components, for instance, from the f i r s t stage of estimation (equation (3.18)) we obtain cross-price supply e l a s t i c i t i e s given a fixed l e v e l of aggregate exports. By extending equation (3.14) we obtain cross-price supply e l a s t i c i t i e s between export components i and j subject to the constant fixed c a p i t a l input quantity as follows: (3.22) E i j K = E i j X + s j E x x K where E^j is the cross-price e l a s t i c i t y between i and j given a constant l e v e l of aggregate exports, S j is the share of export j if in t o t a l exports and E X x i s the own-price e l a s t i c i t y of aggregate exports for a given fixed c a p i t a l input l e v e l . By extending (3.22) to the import components price e l a s t i c i t i e s for a l l the export and import components are obtained which are d i r e c t l y comparable with the price e l a s t i c i t i e s for the other net output categories obtained from the second stage of estimation. 3.4 Results I n i t i a l estimation of the linear systems in (3.18) and (3.7) produced c o e f f i c i e n t matrices S which were not positive semi-d e f i n i t e for the export and import aggregators and the GNP 27 function. In each case one eigenvalue of the S matrix was negative. Subsequent estimation was, therefore, undertaken using the non-linear reparameterised model imposing curvature. The results of these non-linear regressions and the corresponding asymptotic t-values are presented in Table 3.1. In each case the Davidson-Fletcher-Powell algorithm in the SHAZAM package was used and the systems converged from the default c o e f f i c i e n t s t a r t i n g values of 1.0 within 200 i t e r a t i o n s . Limited experimentation with d i f f e r e n t s t a r t i n g values produced the same parameter estimates. The low R-square value for the Group 3 equation in the import aggregator model is due to lack of v a r i a t i o n in the dependent variable with the quantity r a t i o being almost constant for the entire period. The scale invariant e l a s t i c i t i e s of transformation derived from the GNP function, the second stage of the estimation process, are presented in Table 3.2. The e l a s t i c i t i e s of transformation for import own demand are largest in magnitude followed by those for export own supply. The transformation e l a s t i c i t i e s for domestic sales own supply are p a r t i c u l a r l y small indicating l i t t l e price responsiveness for t h i s output. The largest cross transformation e l a s t i c i t i e s are those between exports and imports indicating r e l a t i v e price s e n s i t i v i t y between these items. Of more intere s t , however, are the more e a s i l y interpreted conventional price e l a s t i c i t i e s . These price e l a s t i c i t i e s w i l l now be discussed in turn for each of the four net output categories. 28 Export supply e l a s t i c i t i e s are presented in Table 3.3. The own-price e l a s t i c i t y of aggregate export supply increases from 1.26 to 2.29 over the period. In 1970 an export price increase of of 1 per cent would have brought forth an increase in t o t a l exports of 1.67 per cent. These findings are consistent with the r e l a t i v e l y e l a s t i c export supply e l a s t i c i t i e s found by Kohli (1978) for Canada but larger than the comparable U.S. export supply e l a s t i c i t i e s of Diewert and Morrison (1986). A one per cent increase in the price of the inputs labour and imports would reduce export supply by 1.09 and 1.57 per cent, respectively, in 1970. An increase in the price of domestic sales of 1 per cent, on the other hand, would increase exports by approximately 1 per cent. In the p r o f i t function context, two goods are Hicks (1946)-Allen (1938) substitutes i f the cross p a r t i a l derivative of the p r o f i t function with respect to the i r two prices i s negative. Complementary goods have a positive second order price d e r i v a t i v e . The e l a s t i c i t i e s presented in Table 3.3 are a second order price derivative of the p r o f i t function multiplied by the r a t i o of a price and a positive quantity. They w i l l hence have the same sign pattern as the corresponding second order deri v a t i v e s . Exports are thus substitutes for both imports and labour and complements for domestic sales. From the import e l a s t i c i t e s of demand presented in Table 3.4 i t can be seen that the aggregate import own-price e l a s t i c i t i e s range from -0.98 to -2.40. In 1970 a 1 per cent increase in import prices due to, say, an across-the-board t a r i f f would have 29 reduced t o t a l import demand by 1.62 per cent. This e l a s t i c response of import demand to changes in the t o t a l import price is considerably higher than the e a r l i e r Canadian results of Kohli (where labour was treated as a fixed input) and also the U.S. results of Diewert and Morrison where the e l a s t i c i t y has a value closer to one. Import demand f a l l s when labour prices increase. In 1970, 1 per cent increases in export and domestic sales prices would have increased import demand by 1.67 and 0.72 per cent, respectively. Import demand would have f a l l e n by 0.78 per cent in response to a 1 per cent increase in labour prices. Since these e l a s t i c i t i e s are a second order price derivative multiplied by the r a t i o of a price to a negative quantity they w i l l have the opposite sign to the corresponding second order price d e r i v a t i v e . Consequently, imports are substitutes with domestic sales and complementary to labour. A noticeable trend of increasing price responsiveness is apparent in the labour demand e l a s t i c i t i e s presented in Table 3.5. The own-price e l a s t i c i t y of labour demand increases from -0.21 in 1962 to -2.23 in 1980. If this r e s u l t accurately r e f l e c t s actual price responsiveness in the economy then there is a growing role for wage moderation in overcoming current unemployment problems. In 1970 a 1 per cent reduction in wages would have increased labour demand by 0.88 per cent. By 1980 the re s u l t i n g increase in labour demand from a 1 per cent wage cut had more than doubled to 2.23 per cent. It is possible that the Canadian economy has become more price responsive and f l e x i b l e in recent decades due to increasing openness in international trade 30 and deregulation. The cross labour demand e l a s t i c i t i e s also show a pattern of increasing responsiveness highlighting the importance of other prices on labour demand as well. In 1970 a 1 per cent increase in export and domestic sales prices would have increased labour demand by 0.66 and 0.46 per cent, respectively. The positive value of the e l a s t i c i t y of labour demand with respect to the domestic sales price indicates that labour and domestic sales are substitutes. The price responsiveness of domestic sales has also increased markedly over the period although t h i s started from very low l e v e l s . As can be seen from Table 3.6, in 1962 a 1 per cent increase in the price of domestic sales would have had a negl i g i b l e impact on the output of domestic sales but by 1980 such a price increase would have increased the quantity of domestic sales supply by 0.50 per cent. In 1970 domestic sales supply would have f a l l e n by 0.12 and 0.31 per cent in response to 1 per cent increases in the prices of imports and labour, respectively. An increase in the export price would have increased domestic sales supply by 0.26 per cent r e f l e c t i n g the complementarity between exports and domestic sales. Having derived these price e l a s t i c i t i e s i t is of interest to examine the i r implications for the effects of various exogenous price changes on the economy. If import prices were to decrease by 10 per cent due to, say, a substantial trade barrier l i b e r a l i s a t i o n or move to free trade then, using mid-point e l a s t i c i t i e s , imports would increase by 16 per cent, exports would increase by 11 per cent and labour demand would increase by 31 2 per c e n t . Domestic s a l e s s u p p l y would f a l l s l i g h t l y i n response to the l o w e r i n g of import p r i c e s . I f Canadian expor t p r i c e s were to i n c r e a s e by 10 per cent due t o , s a y , a s u b s t a n t i a l r e d u c t i o n i n f o r e i g n t rade b a r r i e r s or an i n c r e a s e i n wor ld demand for Canadian p r o d u c t s then e x p o r t s would i n c r e a s e by 16 per c e n t , imports would a l s o i n c r e a s e by 16 per cent and labour demand would i n c r e a s e by 6 per c e n t . Domestic s a l e s s u p p l y would i n c r e a s e by about 2.5 per c e n t . I t s h o u l d be n o t e d , however, t h a t p o l i c y a n a l y s i s s h o u l d not be based too h e a v i l y on any one se t of e l a s t i c i t y e s t i m a t e s due to l i k e l y s e n s i t i v i t y to the s p e c i f i -c a t i o n and d a t a used and the f a i l u r e to take account of a l l g e n e r a l e q u i l i b r i u m i n f l u e n c e s . The p r i c e e l a s t i c i t i e s of s u p p l y for the four expor t components s u b j e c t to a f i x e d aggregate expor t q u a n t i t y are p r e s e n t e d i n T a b l e 3.7 f o r the year 1970. These e l a s t i c i t i e s are d e r i v e d from the aggregator f u n c t i o n used i n the f i r s t s tage of the e s t i m a t i o n proces s and so are not d i r e c t l y comparable w i t h the GNP f u n c t i o n e l a s t i c i t i e s which show the response of net outputs s u b j e c t to the f i x e d c a p i t a l input a v a i l a b l e . The expor t aggrega tor e l a s t i c i t i e s show t h a t i f the p r i c e of A g r i c u l t u r a l and F o r e s t r y P r o d u c t s i n c r e a s e d by 1 per cent t h e n , to m a i n t a i n a c o n s t a n t t o t a l e x p o r t q u a n t i t y , the q u a n t i t y of A g r i c u l t u r a l and F o r e s t r y P r o d u c t e x p o r t s would have to i n c r e a s e by 0.23 per cent and t h a t of M i n e r a l s and Energy expor t s by 0.08 per c e n t . The q u a n t i t i e s of Heavy I n d u s t r i a l and S e r v i c e e x p o r t s and Motor V e h i c l e , T e x t i l e and E l e c t r i c a l e x p o r t s would f a l l by 0.23 and 0.16 per c e n t , r e s p e c t i v e l y . In a l l cases the q u a n t i t i e s of 32 A g r i c u l t u r a l and Forestry exports and Minerals and Energy exports move together and in the opposite d i r e c t i o n to those of Motor Vehicle, T e x t i l e and E l e c t r i c a l exports and Heavy Industrial and Service exports. The corresponding import aggregator e l a s t i c i t i e s for 1970 are presented in Table 3.8. These e l a s t i c i t i e s show very l i t t l e price responsiveness among import components to maintain a constant t o t a l quantity of imports but are also not comparable to the other e l a s t i c i t i e s presented nor r e a d i l y interpreted. The e l a s t i c i t i e s show that i f the price of A g r i c u l t u r a l , Forestry and Service imports increased by 1 per cent there would be neg l i g i b l e f a l l s in A g r i c u l t u r a l , Forestry and Service imports and Vehicles, Chemical and Other imports to maintain a constant t o t a l import l e v e l . There would be o f f s e t t i n g n e g l i g i b l e increases in Metals and Energy imports and Machinery, E l e c t r i c a l and Textile imports. Of most interest are the export and import component e l a s t i c i t i e s derived from equation (3.22). These e l a s t i c i t i e s show the component response subject to a fixed aggregate c a p i t a l input and are thus d i r e c t l y comparable with the other net output e l a s t i c i t i e s derived from the second stage of estimation. The export component own-price e l a s t i c i t i e s appear in Table 3.9 while the cross e l a s t i c i t i e s for 1970 are presented in Table 3.10. The price e l a s t i c i t i e s of supply for A g r i c u l t u r a l and Forestry exports range from 0.62 to 0.86. Those for Motor Vehicle, Textile and E l e c t r i c a l exports range from 0.53 to 0.76. Minerals and Energy exports and Heavy Industrial and Service exports each exhibit s l i g h t l y less price responsiveness with e l a s t i c i t i e s 33 ranging from 0.40 to 0.77 and 0.41 to 0.64, respectively. The interesting r e s u l t evident in the table of cross e l a s t i c i t i e s i s that a l l the cross e l a s t i c i t i e s are p o s i t i v e . Hence, the four export components can be considered complementary in supply as an Increase in the price of any one component w i l l lead to increases in the quantities of a l l four export components subject to the fixed c a p i t a l stock. This explains why the own-price e l a s t i c i t i e s of the components are a l l less than the e l a s t i c i t y of supply for t o t a l exports obtained from the GNP function. When the aggregate export price increases the prices of a l l four components e f f e c t i v e l y increase and hence compounding cross price e f f e c t s come into play. If the price of just one component is increased then these compounding cross e f f e c t s are not present. The other implication of these results is that i f the price of one export component, say, A g r i c u l t u r a l and Forestry Products, i s reduced due to foreign trade barriers or dumping then the other export components w i l l also be adversely affected. F i n a l l y , import component own-price demand e l a s t i c i t i e s are presented in Table 3.11 and cross e l a s t i c i t i e s in Table 3.12. A g r i c u l t u r a l , Forestry and Service imports exhibit the most price responsiveness with e l a s t i c i t i e s ranging from -0.36 to -0.75 while Machinery, E l e c t r i c a l and Tex t i l e imports exhibit the least responsiveness with a range of -0.27 to -0.41. Metals and Energy imports and Vehicle, Chemicals and Other imports exhibit intermediate responsiveness with ranges of -0.21 to -0.80 and -0.42 to -0.67, respectively. Again a l l cross import component e l a s t i c i t i e s are negative indicating a complementarity among the 34 import groups. Hence, i f a 10 per cent t a r i f f had been placed on Machinery, E l e c t r i c a l and Tex t i l e imports in 1970 the imports of Machinery, E l e c t r i c a l and Tex t i l e Products would have f a l l e n by 3.7 per cent, A g r i c u l t u r a l , Forestry and Service imports would have f a l l e n by 2.6 per cent and Metals and Energy imports and Vehicle, Chemicals and Other imports would have f a l l e n by 3.1 per cent and 1.7 per cent, respectively. 3.5 Conclusions These results i l l u s t r a t e the usefulness of the aggregator function approach in allowing the incorporation of several output and input categories within a GNP function model. They also i l l u s t r a t e the importance of recently developed functional forms such as the Symmetric Generalised McFadden in implementing the aggregator function model with the correct curvature requirements imposed. While the e l a s t i c i t i e s obtained from the model at the aggregate or second stage l e v e l are generally similar to comparable e l a s t i c i t i e s in other studies (eg. Kohli(1978)), they do exhibit some troublesome tendencies. The major anomaly present is the general trend towards rapid l y increasing price responsiveness over time. This is p a r t i c u l a r l y apparent for the labour demand e l a s t i c i t y . This tendency may be the consequence of shortcomings in the data, the imposition of curvature requirements on the model, or, of course, might be an accurate r e f l e c t i o n of actual substitution p o s s i b i l i t i e s . It may also be related to the f a i l u r e to take account of declining c a p i t a l capacity u t i l i s a t i o n rates towards the end of the period. Another 35 potential anomaly in the results is the complementarity observed between a l l export components and import components when responses are measured r e l a t i v e to a fixed c a p i t a l input. To further examine the potential cause of these features of the results and in p a r t i c u l a r to ascertain the role of the s e p a r a b i l i t y assumption i m p l i c i t in the aggregator function approach, the following Chapter of th i s thesis presents results for two f l e x i b l e disaggregated models which do not use the aggregator approach. 36 TABLE 3.1 SGM PARAMETER ESTIMATES Co e f f i c l e n t Export Aggregator a l l a12 a13 a22 a23 a33 b l l b l t b t t b22 b 2 t b33 b 3 t b44 b 4 t R 2 Values Equation 1 Equation 2 Equation 3 Equation 4 Log Likelihood -0.2652 (-3.62) •0.0796 (-1.40) 0.1826 (2.66) •0.1057 (-1.58) 0.1926 (1.42) •0.0095 (-0.00) 0.4095 (27.37) -0.1246 (-9.99 ) 0.0094 (1.61) 0.2999 (58.29) -0.0691 (-10.06) 0.1270 (5.45) 0.1693 (8.15) 0.1692 (36.05) 0.0269 (3.76) 0.7650 0.8977 0.7701 0.7085 261.38 Import Aggregator -0.0052 (-0.17) 0.0523 (1.85) 0.1318 (0.93) -0.0350 (-25.5) -0.0890 (-92.8) -0.0000 (-0.00) -0.3486 (-28.78) 0.0104 (0.80) 0.0174 (12.51) -0.2394 (-62.93) 0.0480 (14.78) -0.2054 (-31.2) 0.0131 (2.47) -0.2277 (-21.08) -0.0489 (-4.66) 0.4052 0.9007 0.0166 0.5948 275.25 GNP Function 0.9169 (5.31) -0.5440 (-6.86) -0.4119 (-4.88) 0.4221 (4.70) -0.4512 (-2.67) -0.0000 (-0.00) 0.5432 (18.19) 0.3497 (7.74) -0.0633 (-3.36) -0.3325 (-26.9) -0.1280 (-5.81) -1.4233 (-68.3) 0.0473 (0.70) 2.3446 (46.1) 0.1341 (1.51) 0.7605 0.9121 0.9859 0.4890 182.55 't Values in parentheses are assymptotic t-values. The c o e f f i c i e n t subscripts and equation numbers 1,..,4 refer to Groups 1,..,4, respectively. 3 The c o e f f i c i e n t subscripts and equation numbers 1,..,4 refer to Exports, Imports, Labour and Domestic Sales, respectively. 37 TABLE 3.2 GNP FUNCTION ELASTICITIES OF TRANSFORMATION Year ETXX ETXM E TXL ETXD ETMM 1962 2.5643 2.8611 0.4974 0.1297 4.8283 1964 2.6340 3.0708 0.5896 0.2015 5.3129 1966 2.4235 2.7104 0.6382 0.2249 4.5329 1968 2.4597 2.5911 0.7703 0.2931 4.0931 1970 2.7651 2.7867 1.0177 0.4248 4.1704 1972 2.2500 1.9265 1.0549 0.3910 2.5755 1974 2.1969 2.0809 1.0900 0.4098 3.0177 1976 2.8083 2.4428 1.6868 0.6799 3.1997 1978 2.7395 2.6139 1.7616 0.7050 3.7070 1980 3.0694 3.4598 2.0327 0.8596 5.5805 Year ETML ETMD ET L L E TLD ' E T D D 1962 0.2177 0.1841 0.1660 0.0171 0.0075 1964 0.3209 0.2741 0.2095 0.0368 0.0163 1966 0.3224 0.2432 0.2701 0.0614 0.0209 1968 0.3702 0.2440 0.3840 0.1128 0.0380 1970 0.5060 0.3116 0.5729 0.2008 0.0752 1972 0.3429 0.1218 0.8337 0.3122 0.1169 1974 0.4371 0.1965 0.8794 0.3123 0.1115 1976 0.7022 0.3064 1.5577 0.6113 0.2402 1978 0.8485 0.4009 1.7039 0 .6399 0.2424 1980 1.3446 0.7533 1.8792 0.6907 0.2684 1 The subscripts X,M,L and D refer to Exports, Imports, Labour and Domestic Sales, respectively. 38 TABLE 3.3  EXPORT SUPPLY ELASTICITIES 1 Year EXX EXM EXL EXD 1962 1.2666 -0.9014 -0.6381 0.2730 1964 1.3415 -0.9977 -0.7719 0.4281 1966 1.3406 -0.9465 -0.8850 0.4909 1968 1.4569 -0.9731 -1.1515 0.6677 1970 1.6657 -1.0852 -1.5704 0.9898 1972 1.4404 -0.7445 -1.5694 0.8736 1974 1.5666 -0.8813 -1.5647 0.8794 1976 1.9560 -1.0483 -2.3551 1.4475 1978 2.0125 -1.1460 -2.2722 1.4056 1980 2.2967 -1.4871 -2.4181 1.6085 1 The subscripts X,M,L and D refer to Exports, Imports, Labour and Domestic Sales, respectively. 39 TABLE 3 . 4  IMPORT DEMAND ELASTICITIES Year EMX EMM E M L EMD 1962 1 .4132 - 1 . 5 2 1 2 - 0 .2794 0 . 3 8 7 4 1964 1 . 5 6 3 9 - 1 . 7 2 6 2 - 0 . 4 2 0 1 0 . 5 8 2 4 1966 1 . 4 9 9 3 - 1 . 5 8 3 0 - 0 . 4 4 7 1 0 . 5 3 0 8 1968 1 . 5 3 4 7 - 1 . 5 3 7 1 - 0 . 5 5 3 4 0 . 5 5 5 8 1970 1 . 6 7 8 7 - 1 . 6 2 4 0 - 0 . 7 8 0 8 0 . 7 2 6 1 1972 1 . 2 3 3 3 - 0 . 9 9 5 4 - 0 . 5 1 0 1 0 . 2 7 2 2 1974 1 .4839 - 1 . 2 7 8 1 - 0 . 6 2 7 4 0 . 4 2 1 7 1976 1 . 7 0 1 4 - 1 . 3 7 3 2 - 0 . 9 8 0 4 0 . 6 5 2 2 1978 1 . 9 2 0 3 - 1 . 6 2 5 2 - 1 . 0 9 4 4 0 . 7 9 9 3 1980 2 . 5 8 8 8 - 2 . 3 9 8 7 - 1 . 5 9 9 6 1 . 4 0 9 5 1 The s u b s c r i p t s X , M , L and D r e f e r to E x p o r t s , Imports , Labour and Domest ic S a l e s , r e s p e c t i v e l y . 40 TABLE 3.5  LABOUR DEMAND ELASTICITIES 1 Year ELX ELM E L L ELD 1962 0.2457 -0.0686 -0.2129 0.0359 1964 0.3003 -0.1043 -0.2743 0.0782 1966 0.3531 -0.1126 -0.3745 0.1341 1968 0.4562 -0.1390 -0.5741 0.2569 1970 0.6131 -0.1970 -0.8839 0.4679 1972 0.6753 -0.1325 -1.2403 0.6974 1974 0.7773 -0.1851 -1.2624 0.6702 1976 1.1748 -0.3013 -2.1748 1.3013 1978 1.2941 -0.3720 -2.1978 1.2757 1980 1.5210 -0.5780 -2.2355 1.2925 1 The subscripts X,M,L and D refer to Exports, Imports, Labour and Domestic Sales, respectively. 41 TABLE 3.6 DOMESTIC SALES SUPPLY ELASTICITIES 1 Year EDX EDM EDL EDD 1962 0.0641 -0.0580 -0.0219 0.0158 1964 0.1026 -0.0891 -0.0482 0.0346 1966 0.1244 -0.0849 -0.0852 0.0457 1968 0.1736 -0.0916 -0.1686 0.0866 1970 0.2559 -0.1213 -0.3099 0.1753 1972 0.2503 -0.0471 -0.4645 0.2612 1974 0.2922 -0.0832 -0.4483 0.2393 1976 0.4736 -0.1315 -0.8535 0.5114 1978 0.5180 -0.1758 -0.8254 0.4832 1980 0.6432 -0.3238 -0.8217 0.5023 1 The subscripts X,M,L and D refer to Exports, Imports, Labour and Domestic Sales, respectively. 42 TABLE 3.7 1970 EXPORT AGGREGATOR ELASTICITIES 1' With Respect to Price of AF ME VTE HIS AF 0 .2238 0.0610 -0 .1383 -0 .1465 Chanqe ln ME 0 .0743 0.0646 -0 .1220 -0 .0169 Quantity of VTE -0 .1675 -0.1213 0 .2335 0 .0553 HIS -0 .2282 -0.0217 0 .0711 0 .1788 x Export component response subject to a fixed quantity of aggregate exports. 2 Export components are A g r i c u l t u r a l and Forestry Products (AF), Minerals and Energy Products (ME), Motor Vehicles, T e x t i l e and E l e c t r i c a l Products (VTE), and Heavy Industrial and Service Products (HIS). TABLE 3.8 1970 IMPORT AGGREGATOR ELASTICITIES ' With Respect to Price of AFS MN MET VCO AFS -0 .0000 0 .0002 0.0004 -0 .0006 Chanqe in MN 0 .0004 -0 .0203 -0.0429 0 .0629 Quantity of MET 0 .0010 -0 .0505 -0.1066 0 .1561 VCO -0 .0009 0 .0462 0.0975 -0 .1428 1 Import component response subject to a fixed quantity of aggregate imports. 2 Import components are A g r i c u l t u r a l , Forestry and Service Products (AFS), Metals and Energy Products (MN), Machinery, E l e c t r i c a l and Tex t i l e Products (MET), and Vehicles, Chemicals and Other Products (VCO). 43 TABLE 3.9 EXPORT COMPONENT OWN SUPPLY ELASTICITIES 1' Year EAF EME EVTE EHIS 1962 0.6955 0.4377 0.5837 0.4122 1964 0.7395 0.4270 0.5344 0.4364 1966 0.6949 0.3997 0.5585 0.4392 1968 0.6147 0.4316 0.6888 0.4437 1970 0.6556 0.4966 0.7262 0.4881 1972 0.6399 0.3937 0.6425 0.4630 1974 0.6864 0.4815 0.5876 0.4693 1976 0.7630 0.5692 0.7312 0.5387 1978 0.7892 0.5582 0.7554 0.5492 1980 0.8594 0.7655 0.6631 0.6369 Export component response subject to fixed c a p i t a l input a v a i l a b l e . 2 Export components are A g r i c u l t u r a l and Forestry Products (AF), Minerals and Energy Products (ME), Motor Vehicles, T e x t i l e and E l e c t r i c a l Products (VTE), and Heavy Industrial and Service Products (HIS). 44 TABLE 3.10 1970 EXPORT COMPONENT CROSS SUPPLY ELASTICITIES 1' With Respect to Price of AF ME VTE HIS AF 0.6556 0.4930 0.3544 0.1628 Chanqe in ME 0.5061 0.4966 0.3707 0.2924 Quantity of VTE 0.2643 0.3106 0.7262 0.3646 HIS 0.2036 0.4103 0.5638 0.4881 1 Export component response subject to fixed c a p i t a l input a v a i l a b l e . 2 Export components are A g r i c u l t u r a l and Forestry Products (AF), Minerals and Energy Products (ME), Motor Vehicles, T e x t i l e and E l e c t r i c a l Products (VTE), and Heavy Industrial and Service Products (HIS). 45 TABLE 3.11 IMPORT COMPONENT OWN DEMAND ELASTICITIES 1/ 2 Year EAFS EMN EMET EVCO 1962 -0.6287 -0.3410 -0.3789 -0.4765 1964 -0.7009 -0.3822 -0.4113 -0.5186 1966 -0.6191 -0.3287 -0.3911 -0.5255 1968 -0.5530 -0.3069 -0.3593 -0.5973 1970 -0.5977 -0.3348 -0.3715 -0.5900 1972 -0.3631 -0.2070 -0.2851 -0.4300 1974 -0.4374 -0.3613 -0.2789 -0.4569 1976 -0.4528 -0.3831 -0.2766 -0.5150 1978 -0.5304 -0.4153 -0.3114 -0.6240 1980 -0.7551 -0.8013 -0.3978 -0.6777 x Import component response subject to fixed c a p i t a l input a v a i l a b l e . 2 Import components are A g r i c u l t u r a l , Forestry and Service Products (AFS), Metals and Energy Products (MN), Machinery, E l e c t r i c a l and Tex t i l e Products (MET), and Vehicles, Chemicals and Other Products (VCO). 46 TABLE 3.12 1,2 1970 IMPORT COMPONENT CROSS DEMAND ELASTICITIES With Respect to P r i c e of AFS MN MET VCO AFS -0 .5977 -0 .3142 -0 . 2645 -0 . 4476 Chanqe in... MN -0 .5973 -0 .3348 -0 .3078 -0 .3842 Q u a n t i t y of MET -0 .5967 -0 . 3649 -0 . 3715 -0 . 2909 VCO -0 .5986 -0 .2682 -0 .1674 -0 .5900 1 Import component response s u b j e c t to f i x e d c a p i t a l i n p u t a v a i l a b l e . 2 Import components are A g r i c u l t u r a l , F o r e s t r y and S e r v i c e P r o d u c t s ( A F S ) , Meta l s and Energy P r o d u c t s (MN), M a c h i n e r y , E l e c t r i c a l and T e x t i l e P r o d u c t s (MET), and V e h i c l e s , Chemica l s and Other P r o d u c t s (VCO). 47 4 . FLEXIBLE DISAGGREGATED MODELS In order to compare the results obtained from the aggregator function model with those of a model not making use of the s e p a r a b i l i t y assumption, several f l e x i b l e disaggregated models were investigated. I n i t i a l attempts to estimate a f u l l model with the four export components, the four import components, domestic sales and labour as variable net outputs in the one model proved unsuccessful as the estimating system of ten equations would not converge. Attempts to economise on the number of parameters in the system by the use of semi-flexible functional forms as proposed by Diewert and Wales (1986) also proved to be unsuccessful. Semi-flexible functional forms, by reducing the size of the triangular matrices multiplied together to form the quadratic price c o e f f i c i e n t matrix, reduce the t o t a l number of parameters in the system but at the expense of achieving less than f u l l f l e x i b i l i t y . In t h i s case, however, even a four-column semi-flexible system would not converge. This would appear to further reinforce the t r a c t a b i l i t y of the aggregator function procedure when dealing with many output and input categories, p a r t i c u l a r l y when there is a limited number of observations a v a i l a b l e . To further investigate the relationships between the export and import components and the other aggregate net outputs, two smaller disaggregated models were estimated. In the f i r s t of these the four export components were treated as net outputs along with aggregate imports, domestic sales and labour. In the second, the four import components, aggregate exports, domestic 48 sales and labour were taken to be the net outputs. By examining these two disaggregated models i t w i l l be possible to gain more information on the relationships between the export components and the import components and on the s t a b i l i t y of the estimated e l a s t i c i t i e s to changes in s p e c i f i c a t i o n of the model. 4.1 The Generalised McFadden GNP Function The GNP function framework outlined in the previous Chapter is again used in the models presented here. The same assumptions regarding p r o f i t maximising firms, perfect competition in goods and factor markets, and the c h a r a c t e r i s t i c s of the aggregate technology set are made. Imports are again assumed to be an input to the production sector while exports are an output of the production sector not consumed domestically. Aggregate c a p i t a l is again assumed to be the only fixed input and constant returns to scale are imposed with respect to aggregate c a p i t a l . Seven net outputs are included in each model. In the f i r s t (second) model these are the 4 export (import) components, aggregate imports (exports), domestic sales and labour. Imports and labour quantities are again negative and the same data set as that of Chapter 3 is used. On the basis of these assumptions the aggregate technology is represented by the following Generalised McFadden GNP function; (4.1) G(p,K)/K = (1/2) I j f i b i j p i p j / p 7 + l i l x b i P i + Z i l i b i t P i t + b ^ C Z i l ! C i P i ) t 2 where time superscripts have again been deleted and the b ^ parameters s a t i s f y the following symmetry r e s t r i c t i o n s ; 49 (4.2) bj^j = b j j for a l l i , j = 1,..,6. The variable t i s a time trend representing technical progress and the exogenous parameters are set equal to the average net output quantity per unit of c a p i t a l input quantity for 1=1,..,7. As noted in the preceding Chapter, the Generalised McFadden (GM) r e s t r i c t e d p r o f i t function i s sensitive to the choice of the numeraire good (good 7 as sp e c i f i e d in (4.1)). While the Symmetric Generalised McFadden (SGM) form used in Chapter 3 overcomes this s e n s i t i v i t y the non-symmetric GM form is more tractable when estimating a large model. In fact, in the present context estimation of an SGM model of thi s size with curvature imposed is precluded by the equation size constraint in the non-linear algorithm of the SHAZAM package. Domestic sales supply was used as the numeraire good in both the GM models estimated here. The GM form has the further s l i g h t advantage over the SGM form of not being limited to being f l e x i b l e at just one price vector. By applying Hotelling's Lemma the following set of net output supply equations is obtained; (4.3) X j / K = Zjli b i j P j / P 7 + b i + D i t t + b t t c i t 2 + u i ' i=l/./6; (4.4) x ?/K = - ( l / 2 ) Z i ! 1 Z j = 1 b i j P i P j / P 7 + b ? + b ? t t + b t f c C 7 t 2 + u ? The vectors of error terms for the observations are again assumed to be independently d i s t r i b u t e d with a multivariate normal d i s t r i b u t i o n with zero means and covariance • matrix The estimating system thus consists of (4.3) and (4.4) subject to the symmetry r e s t r i c t i o n s (4.2). 50 If the matrix of estimated quadratic terms B=[b ij ] is posi t i v e semi-definite then the r e s t r i c t e d p r o f i t function i s gl o b a l l y convex in prices (Diewert 1985). If B is not positive semi-definite then It can again be reparameterised using the Wiley, Schmidt and Bramble technique of replacing B by the product of a lower triangular matrix and i t s transpose; (4.5) B = AA' where A = ta^jJ ; i,j=l,..,6 ; and a ij=0 for i<j. Estimation of the r e s u l t i n g system requires the use of non-linear regression techniques. For s i m p l i c i t y of presentation, only the conventional net output supply e l a s t i c i t i e s derived from the estimated system are discussed in the following section. The conventional price e l a s t i c i t i e s are given by; (4.6) E i ; J = din X j / din p^ = DP^p^ / X j ^ ; i , j = l , . . , 7 , where DP^j is the second order price derivative of the r e s t r i c t e d p r o f i t function and X i i s the estimated quantity of net output i obtained from the system of net output supply equations ( 4 . 3 ) and (4.4). In the GM case the second order price derivatives are given by; (4.7) DPi:j = b i ; j/p 7 for i,j = l , . . , 6 ; (4.8) DP i ? = -Z-j^! b i j P j / P 7 2 f o r i = l / . . , 6 ; and (4.9) DP 7 ? = 1 ^ b i j P i P j / p 7 3 . 51 4.2 Results I n i t i a l estimation of both the f i r s t (export) and second (import) models without curvature imposed produced systems which did not s a t i s f y the convexity in prices property. In a l l cases the non-linear algorithm of SHAZAM was used with s t a r t i n g values of zero for the quadratic terms, and the constant and technology parameters set equal to values obtained from regressing these variables against the dependent variables. These s t a r t i n g values represent the polar Leontief case where there i s no substitution between net outputs. The linear export model converged r e l a t i v e l y quickly but three out of the six eigenvalues of the estimated B matrix were negative, indicating that the B matrix f a i l e d to be positive semi-definite. In the linear export model case three out of the seven estimated own-price e l a s t i c i t i e s had the wrong sign. Subsequent imposition of curvature requirements by reparameterising the B matrix produced slower convergence, a r e f l e c t i o n of the degree to which curvature i n i t i a l l y f a i l e d to be met. The log l i k e l i h o o d of the non-linear system was 423.48 compared to 443.74 for the linear system without curvature imposed. The import model had two out of the six B matrix eigenvalues negative and two of the estimated own-price e l a s t i c i t i e s had the wrong sign. Imposition of curvature again led to slower convergence of the non-linear model from the Leontief s t a r t i n g values. The log l i k e l i h o o d of the non-linear system was 497.75 compared to 510.05 for the linear system without curvature imposed. The fact that the non-linear import model's log 52 l i k e l i h o o d i s c l o s e r to t h a t of the l i n e a r model than i s the case for the c o r r e s p o n d i n g e x p o r t model v a l u e s r e f l e c t s the f a c t t h a t the import model came c l o s e r to meet ing the c u r v a t u r e r e q u i r e m e n t s and so i m p o s i t i o n of c u r v a t u r e r e p r e s e n t s l e s s of a r e s t r i c t i o n i n the case of the import model . The n o n - l i n e a r parameter e s t i m a t e s for both models are p r e s e n t e d i n Tab le 4 . 1 . A g a i n some low e q u a t i o n R-square v a l u e s are observed due to l a c k of v a r i a t i o n i n the q u a n t i t y r a t i o dependent v a r i a b l e s . Own-pr ice e l a s t i c i t y e s t i m a t e s for the expor t model are p r e s e n t e d i n T a b l e 4 .2 . The own s u p p l y e l a s t i c i t i e s for e x p o r t s of A g r i c u l t u r a l and F o r e s t r y P r o d u c t s c o r r e s p o n d c l o s e l y to those o b t a i n e d from the aggrega tor model of Chapter 3. The expor t model e l a s t i c i t i e s range from 0.70 to 0.90 compared to 0.63 to 0.85 for the c o r r e s p o n d i n g aggrega tor e l a s t i c i t i e s . The e l a s t i c i t i e s of s u p p l y f o r e x p o r t s of M i n e r a l s and Energy P r o d u c t s a l s o c o r r e s p o n d c l o s e l y between the two models , r a n g i n g from 0.39 to 0.72 i n the expor t model compared to 0.39 to 0.76 i n the aggrega tor model . The resemblance of the r e s u l t s breaks down, however, i n the case of e x p o r t s of V e h i c l e s , T e x t i l e and E l e c t r i c a l P r o d u c t s . In the aggrega tor model these e l a s t i c i t i e s were s t a b l e and ranged from 0.53 to 0 .76 . In the e x p o r t model , however, these e l a s t i c i t i e s are u n s t a b l e and of unreasonable magnitude r a n g i n g from 1.84 to 10 .58 . These r e s u l t s are the major cause for concern i n the expor t model ' s performance and are not a r e s u l t of the i m p o s i t i o n of c u r v a t u r e as e l a s t i c i t i e s of s i m i l a r s i g n and magnitude were o b t a i n e d i n the l i n e a r model . Use of a d i f f e r e n t 53 numeraire good i n the model had l i t t l e e f f e c t on these e l a s t i c i t i e s . T h i s r e s u l t may, i n p a r t , be due to the f a i l u r e to take account of the i n f l u e n c e of the Auto Pact which r a i s e d v e h i c l e e x p o r t s manyfold for g i v e n p r i c e s and t e c h n o l o g y . The e x p o r t model a l s o i n d i c a t e s more r e s p o n s i v e n e s s f o r e x p o r t s of Heavy I n d u s t r i a l and S e r v i c e P r o d u c t s a l t h o u g h the e l a s t i c i t i e s are of a r e a s o n a b l e order of magnitude r a n g i n g from 0.85 to 1.81 compared to 0.41 to 0.64 for the aggregator model . The export model i n d i c a t e s a t r e n d of d e c r e a s i n g r e s p o n s i v e n e s s for t h i s e x p o r t component whereas the aggregator model i n d i c a t e s a s l i g h t i n c r e a s e i n r e s p o n s i v e n e s s over the p e r i o d . The e x p o r t model i n d i c a t e s a t r e n d of i n c r e a s i n g r e s p o n s i v e n e s s f o r both domest ic s a l e s s u p p l y and labour demand. In the case of domest i c s a l e s s u p p l y , the expor t model i n d i c a t e s much g r e a t e r r e s p o n s i v e n e s s than the aggrega tor model w i t h an e l a s t i c i t y range of 1.15 to 1.60 compared to 0.02 to 0.51 for the aggrega tor model . Labour demand e l a s t i c i t i e s are of s i m i l a r magnitude between the two models a t the end of the p e r i o d a l t h o u g h the expor t model i n d i c a t e s g r e a t e r r e s p o n s i v e n e s s a t the b e g i n n i n g of the p e r i o d . The expor t model ' s aggregate import demand e l a s t i c i t i e s f o l l o w a s i m i l a r p a t t e r n to those of the a g g r e g a t o r model a l t h o u g h they are on average somewhat h i g h e r than those of the a g g r e g a t o r model . O v e r a l l , t h e n , the own-pr ice e l a s t i c i t i e s f o r the e x p o r t and aggrega tor models are l a r g e l y i n agreement w i t h the e x c e p t i o n of the t h i r d and f o u r t h export components. 54 The important difference between the export and aggregator models becomes apparent in Table 4.3 where cross e l a s t i c i t i e s for the year 1970 are presented. Whereas the aggregator model indicated that a l l 4 export components were complementary, the export model indicates that exports of A g r i c u l t u r a l and Forestry Products are substitutable with exports of Vehicles, Textile and E l e c t r i c a l Products which are in turn substitutable with exports of Minerals and Energy Products. Exports of Minerals and Energy Products are also substitutable with exports of Heavy Industrial and Service Products. The disaggregated export model thus gives a quite d i f f e r e n t impression of the relationships between the export components than does the r e s t r i c t i v e aggregator model. This difference c a r r i e s over to the relationships between the export components and the other aggregate net outputs. Exports of Vehicles, T e x t i l e and E l e c t r i c a l Products display the opposite re l a t i o n s h i p to aggregate imports, labour and domestic sales than do the other 3 export components in the export model and aggregate exports in the aggregator model.The relationships between aggregate imports, labour and domestic sales are the same in the export model as in the aggregator model. Turning now to the import model, own net output price e l a s t i c i t i e s are presented in Table 4.4. The import model indicates greater price responsiveness for imports of A g r i c u l t u r a l , Forestry and Service Products than does the aggregator model with a range of -0.71 to -1.89 compared to -0.36 to -0.76 for the aggregator model. Imports of Metals and Energy Products, on the other hand, exhibit less price responsiveness in 5 5 the import model w i th e l a s t i c i t i e s r a n g i n g from -0 .08 to -0 .30 compared to - 0 . 2 1 to -0 .80 i n the aggrega t or model . Imports of M a c h i n e r y , E l e c t r i c a l and T e x t i l e P r o d u c t s and V e h i c l e s , Chemica l s and Other P r o d u c t s both e x h i b i t c o n s i d e r a b l y more p r i c e r e s p o n s i v e n e s s i n the import model than i n the aggregator model but the e l a s t i c i t i e s are w i t h i n r e a s o n a b l e bounds. The import model does , however, i n d i c a t e c o n s i d e r a b l y l e s s p r i c e r e s p o n s i v e n e s s f o r aggregate e x p o r t s than does the aggregator model w i t h e l a s t i c i t i e s l e s s than h a l f the s i z e on a v e r a g e . The import model does i n d i c a t e i n c r e a s i n g p r i c e r e s p o n s i v e n e s s f o r both domest i c s a l e s s u p p l y and labour demand as do both the e x p o r t and aggr e ga tor models . The import mode l ' s l a b o u r demand e l a s t i c i t i e s c o i n c i d e c l o s e l y w i th those of the e x p o r t model wh i l e i t s domest ic s a l e s s u p p l y e l a s t i c i t i e s l i e a p p r o x i m a t e l y h a l f way between those of the expor t and aggrega t or models . The import model c r o s s e l a s t i c i t i e s f o r the year 1970 are p r e s e n t e d i n T a b l e 4 . 5 . The c r o s s e l a s t i c i t i e s i n d i c a t e t h a t a l l 4 import components are complementary wi th the e x c e p t i o n of V e h i c l e s , Chemica l s and Other P r o d u c t s and M a c h i n e r y , E l e c t r i c a l and T e x t i l e P r o d u c t s which are s u b s t i t u t a b l e . These r e s u l t s are thus l a r g e l y c o n s i s t e n t w i th the aggregator model f i n d i n g t h a t a l l import components are complementary. The c r o s s e l a s t i c i t i e s between the import components and the o ther aggregates as w e l l as between aggregate e x p o r t s , domest ic s a l e s and labour a l l i n d i c a t e the same r e l a t i o n s h i p s as found i n the aggregator model . 56 4.3 Conclusions Examination of the disaggregated export and import models which do not make use of the s e p a r a b i l i t y assumption reveals some apparent advantages and disadvantages r e l a t i v e to the aggregator function model. The aggregator function model produces more stable estimates of the own-price e l a s t i c i t i e s for the export and import components, but less stable estimates of the price e l a s t i c i t i e s for domestic sales supply and labour demand. With the exception of the export model e l a s t i c i t y estimates for the t h i r d export component which are implausibly large and unstable, i t is d i f f i c u l t to judge which s p e c i f i c a t i o n produces the "best" or most accurate e l a s t i c i t y estimates. One feature which a l l three models agree upon, however, is that there has been a marked trend towards increasing price responsiveness of domestic sales supply and labour demand. In fact, the models indicate that wage rate p o l i c i e s would now have a major impact on the l e v e l of labour demand and, hence, on employment. Another feature which the three models i l l u s t r a t e is that r e l a t i v e l y small changes in s p e c i f i c a t i o n can produce r e l a t i v e l y large changes in the magnitude of various e l a s t i c i t i e s . This is best i l l u s t r a t e d by the domestic sales supply e l a s t i c i t i e s in the three models. The conclusion one must draw from t h i s i s that not too much weight should be placed on any one set of estimates. Rather, a range of s p e c i f i c a t i o n s should be t r i e d to determine the s t a b i l i t y of the r e s u l t s . As expected, the major difference between the models comes in the area of cross e l a s t i c i t i e s . In p a r t i c u l a r , the export 57 model res u l t s do not indicate complementarity between a l l the export components as found in the aggregator model. On the basis of these re u l t s then, i t would appear that the aggregator model has advantages in producing stable component own-price e l a s t i c i t y estimates over the larger disaggregated models which have d i f f i c u l t y producing stable estimates for a l l net outputs. On the other hand, the larger disaggregated models appear to have an advantage In detecting the relationships between the individual components. Which of the two approaches is used should take these considerations Into account. If the main interest i s in detecting the cross relationships then the larger disaggregated model would appear to be more suitable. 58 TABLE 4.1 GM PARAMETER ESTIMATES Export Import Export Import C o e f f i c i e n t Model 1 Model 2 C o e f f i c i e n t Model 1 Model 2 a 1 1 0.3784 0.6077 a55 0.0360 -0.1328 a21 0.1884 -0.2257 a65 0.1165 -0.1268 a31 -0.3349 -0.0543 a66 0.0123 0.1616 a41 0.0774 -0.1761 b l 0.6301 1.0301 a51 -0.4376 -0.1101 b2 0.5588 -0.2915 a61 -0.8882 -0.9145 b3 -1.1873 -0.1006 a22 -0.1849 0.2669 b4 0.0765 -0.2559 a32 0.7611 0.0119 b5 -0.8355 -0.1322 a42 0.1562 -0.1131 b6 -2.8092 -2.3840 a52 0.1212 -0.0286 b7 3.4573 2.6636 a62 0.2803 -0.2785 b l t 0.1038 0.5178 a33 -0.2829 -0.0681 b 2 t 0.0680 -0.0929 a43 -0.0820 -0.0622 b 3 t 0.2045 -0.0272 a53 0.5151 -0.1998 b 4 t 0.1827 -0.0605 a63 -0.1768 0.5283 b 5 t -0.2679 -0.0983 a44 -0.3573 -0.3628 b 6 t -0.3094 -0. 4292 a54 0.0385 0.2103 b 7 t 0.8264 1.0296 a64 0.6002 0.0484 b t t -0.1439 -0.1583 R 2 Values Equation 1 0.1190 0.8147 Equation 5 0.9349 0.9550 Equation 2 0.1243 0.9316 Equation 6 0.9795 0.9802 Equation 3 0.9322 0.6754 Equation 7 0.7499 0.6070 Equation 4 0.9475 0.7721 59 TABLE 4.1 (CONTINUED) x The subscripts and equation numbers 1,..,7 refer to A r i c u l t u r a l and Forestry Product Exports, Minerals and Energy Product Exports, Vehicles, T e x t i l e and E l e c t r i c a l Product Exports, Heavy Industrial and Service Product Exports, Aggregate Imports, Labour and Domestic Sales, respectively. 2 The subscripts and equation numbers 1,..,7 refer to Aggregate Exports, A g r i c u l t u r a l , Forestry and Service Product Imports, Metals and Energy Product Imports, Machinery, E l e c t r i c a l and Tex t i l e Product Imports, Vehicles, Chemical and Other Product Imports, Labour and Domestic Sales, respectively. 60 TABLE 4.2 EXPORT MODEL OWN PRICE ELASTICITIES 1 Year EAF EME EVTE EHIS EM E L ED 1962 0 .7147 0. 4636 10 .5813 1. 8161 -2. 6624 -0 .9502 1. 0416 1964 0 .7087 0. 4414 6 .9753 1. 5493 -2. 5862 -0 .9960 1. 1553 1966 0 .6961 0. 4204 4 .9657 1. 3808 -2. 0776 -1 .0908 1. 1460 1968 0 .7255 0. 4267 3 .2552 1. 2787 -1. 8132 -1 .2627 1. 2462 1970 0 .7557 0. 4459 2 .5020 1. 2045 -1. 6876 -1 .4554 1. 3646 1972 0 .7176 0. 3913 2 .0495 1. 0465 -1. 0762 -1 .6191 1. 3573 1974 0 .7559 0. 4240 2 .4006 1. 0000 -1. 2253 -1 .5926 1. 2052 1976 0 .8024 0. 5132 1 .9087 1. 0106 -1. 2115 -1 .9671 1. 4234 1978 0 .8466 0. 6023 1 .8459 0. 8972 -1. 3623 -2 .1072 1. 5198 1980 0 .9023 0. 7216 1 .9225 0. 8451 -1. 7266 -2 .2312 1. 6016 1 The subscripts AF ME, VTE, HIS, M, L and D refer to A r i c u l t u r a l and Forestry Product Exports, Minerals and Energy Product Exports, Vehicles, T e x t i l e and E l e c t r i c a l Product Exports, Heavy Industrial and Service Product Exports, Aggregate Imports, Labour and Domestic Sales, respectively. 61 TABLE 4.3 1970 CROSS ELASTICITIES - EXPORT MODEL1 Change in With Respect to Price of: Quantity AF ME VTE HIS M L D of: AF 0.756 0.384 -0.570 0.151 -0.988 -2.439 2.701 ME 0.447 0.446 -1.089 -0.088 -0.743 -1.887 2.914 VTE -0.482 -0.661 2.502 0.432 0.400 2.930 -4.990 HIS 0.219 -0.109 0.741 1.205 -0.600 -2.312 0.856 M 0.522 0.337 -0.250 0.218 -1.688 -1.551 2.410 L 0.280 0.186 -0.398 0.183 -0.338 -1.455 1.542 D 0.204 0.189 -0.445 0.045 -0.345 -1.012 1.365 1 The labels AF, ME, VTE, HIS, M, L and D refer to A r i c u l t u r a l and Forestry Product Exports, Minerals and Energy Product Exports, Vehicles, T e x t i l e and E l e c t r i c a l Product Exports, Heavy Industrial and Service Product Exports, Aggregate Imports, Labour and Domestic Sales, respectively. 62 TABLE 4 . 4 IMPORT MODEL OWN PRICE ELASTICITIES 1 Year EX E AFS EMN EMET EVCO E L ED 1962 0 .7115 -1. 6126 -0 .1332 -3 .4082 -1 .8418 -0 .9207 0 .4987 1964 0 .6448 -1. 8946 -0 .1296 -3 .0592 -1 .5716 -0 .9680 0 .5511 1966 0 .5795 -1. 5893 -0 .1170 -2 .5197 -1 .2522 -1 .0612 0 .5891 1968 0 .5418 -1. 3762 -0 . 1084 -2 .3039 -1 .0780 -1 .2217 0 . 6746 1970 0 .5146 -1. 3613 -0 .1055 -2 .1502 -0 .9290 -1 .3998 0 .7818 1972 0 .4517 -0. 7099 -0 .0824 -1 .6090 -0 .7101 -1 . 5604 0 .8015 1974 0 .4688 -0. 8012 -0 .1447 -1 .7685 -0 .6626 -1 .6089 0 .8227 1976 0 . 4716 -0. 7293 -0 .1529 -1 .6312 -0 .6549 -1 .9516 0 .9877 1978 0 .4842 -0. 7921 -0 .1758 -1 .6337 -0 .7798 -2 .0249 1 .0130 1980 0 .5059 -0. 8581 -0 . 3010 -1 .6102 -0 .9053 -2 . 0682 1 .0286 1 The subscripts X, AFS, MN, MET, VCO, L and D refer to Aggregate Exports, A g r i c u l t u r a l , Forestry and Service Product Imports, Metals and Energy Product Imports, Machinery, E l e c t r i c a l and Text i l e Product Imports, Vehicles, Chemical and Other Product Imports, Labour and Domestic Sales, respectively. 63 TABLE 4.5 1970 CROSS ELASTICITIES - IMPORT MODEL1 Change in With Respect to Price of; Quantity X AFS MN MET VCO L D of; X 0.515 -0.264 -0.050 -0.139 -0.095 -1.088 1.122 AFS 1.107 -1.361 -0.137 -0.072 -0.142 -1.497 2.102 MN 0.412 -0.211 -0.106 -0.145 -0.245 -0.181 0.531 MET 1.377 -0.170 -0.176 -2.150 0.542 -2.568 3.145 VCO 0.530 -0.188 -0.167 0.305 -0.929 -0.335 0.785 L 0.448 -0.147 -0.009 -0.107 -0.025 -1.400 1.240 D 0.301 -0.134 -0.018 -0.085 -0.038 -0.808 0.782 1 The labels X, AFS, MN, MET, VCO, L and D refer to Aggregate Exports, A g r i c u l t u r a l , Forestry and Service Product Imports, Metals and Energy Product Imports, Machinery, E l e c t r i c a l and Text i l e Product Imports, Vehicles, Chemical and Other Product Imports, Labour and Domestic Sales, respectively. 64 5. A PLANNING PR I CE MODEL. As In other areas o£ economics It is important to allow for imperfect adjustment in the GNP function model. In fact, imperfect adjustment is l i k e l y to be p a r t i c u l a r l y important in regard to traded goods due to the r e l a t i v e l y long lags involved between the decision to buy or s e l l a good i n t e r n a t i o n a l l y and i t s ultimate d e l ivery to the end-user. The J-curve ef f e c t whereby a devaluation leads to an i n i t i a l worsening of the trade balance but then to a longer-term improvement is an important example of the role of slow adjustment in the traded goods sector. Its explanation, however, requires a more sophisticated model than those presented here. Many Canadian exports are also of primary products which have long lead times between the decision to increase supply of, say, a p a r t i c u l a r mineral and the time when that supply i s available for sale. As a r e s u l t , GNP function models which assume instantaneous adjustment are l i k e l y to miss much of the underlying dynamics at work in the economy's traded goods sector. This Chapter and the following one of this thesis present the r e s u l t s of models which attempt to include dynamics and imperfect adjustment within the GNP function framework. 5.1 The Planning Price Approach An approach to modelling imperfect adjustment which has received l i t t l e attention i s the use of "planning prices" as developed by Woodland (1976,1977). Under t h i s approach producers do not adjust f u l l y to current prices within the observation period. Instead they adjust f u l l y within the period to planning prices which in turn adjust gradually to actual prices. This 65 behaviour may be interpreted in one of two ways. F i r s t l y , firms may have to commit themselves to input decisions before current prices are known or even i f current prices are known the firm may wish to wait and see i f price changes are permanent before f u l l y adjusting to a new current p r i c e . This may be likened to a p a r t i a l adjustment process whereby producers adjust only part-way towards a new price in the current period depending on their expectations of future price movements. Either way, planning prices w i l l adjust to actual prices only gradually. An a l t e r n a t i v e interpretation i s that the use of planning prices is a dual representation of a quantity adjustment path. For instance, i f input prices change to a new l e v e l and then remain at that l e v e l then producers faced with adjustment costs and quasi-fixed inputs w i l l gradually change the i r input mix to approach the new optimal quantities i f the adjustment path is stable. Thus, i t may not be possible or p r o f i t a b l e to f u l l y adjust c a p i t a l , p a r t i c u l a r l y that in the form of buildings, in the current period. Rather, c a p i t a l would be increased towards i t s new optimal l e v e l over a number of periods. If producers are t e c h n i c a l l y e f f i c i e n t then the quantity adjustment path w i l l follow the boundary of the transformation f r o n t i e r . However, corresponding to each point on the boundary of the transformation f r o n t i e r there w i l l be a normal vector of prices for which that quantity decision i s optimal. Hence, a planning price path which approaches the new price vector w i l l be a dual representation of, and observationally equivalent to, an optimal quantity adjustment path. 66 The planning price approach has the advantage, over early attempts to model quantity adjustment paths, of automatically ensuring technical e f f i c i e n c y at each point. It has the disadvantage though that an adjustment r e l a t i o n s h i p of planning to actual prices must be sp e c i f i e d to make the approach operational. This introduces a degree of a r b i t r a r i n e s s . In t h i s a p p l i c a t i o n the following adaptive price adjustment model is used: (5.1) q l t - q ^ t ^ = D i ( p i t - q ^ t ^ ) where the q i t are planning prices and p i t actual prices. If D ^=1 then adjustment of planning to actual prices i s instantaneous. For the adjustment process to be stable the adjustment parameters , m u s t l i e in the i n t e r v a l (0,2). If DL i s in the range (0,1) then adjustment to the new price is monotonic while i t is c y c l i c a l i f Di i s in the range (1,2). To make t h i s mechanism implementable the following version is estimated: (5.2) q i t = DiZ5 = 0 ( l - D i ) j p t - j + ( l - D i J ^ n where the base period planning price q i Q is treated as a parameter and estimated along with the adjustment c o e f f i c i e n t Dj. Embedding th i s price r e l a t i o n s h i p within a standard functional form for the GNP function means that non-linear regression techniques must be used. The Davidson-Fletcher-Powell non-linear algorithm in the SHAZAM package was again used. The planning price model estimated uses a unit Generalised Leontief r e s t r i c t e d p r o f i t function. Given the computational complexity of the estimation procedure, use of the SGM or Generalised McFadden forms would be p r o h i b i t i v e , p a r t i c u l a r l y 67 g i v e n the s i z e c o n s t r a i n t on each e q u a t i o n i n the n o n - l i n e a r SHAZAM f a c i l i t y . The t r a n s l o g form i s not s u i t e d to the p l a n n i n g p r i c e procedure because the dependent v a r i a b l e s of the share e q u a t i o n s c o n t a i n the p l a n n i n g p r i c e terms which are not known b e f o r e e s t i m a t i o n . E s t i m a t i o n of a f o u r - v a r i a b l e net output model analogous to the second s tage GNP f u n c t i o n model i n Chapter 3 imposing c o n s t a n t r e t u r n s to s c a l e w i t h r e s p e c t to the aggregate c a p i t a l input was not p o s s i b l e u s i n g the SHAZAM package due to the non-l i n e a r e q u a t i o n s i z e r e s t r i c t i o n . C o n s e q u e n t l y , l a b o u r and c a p i t a l were aggregated i n t o a s i n g l e f i x e d Input and c o n s t a n t r e t u r n s to s c a l e Imposed w i t h r e s p e c t to t h i s aggregate f i x e d i n p u t . The r e m a i n i n g 3 v a r i a b l e net output c a t e g o r i e s were, t h u s , the q u a n t i t y of e x p o r t s , (minus) the q u a n t i t y of imports and the q u a n t i t y of domest i c s a l e s . The 3 v a r i a b l e net output u n i t G e n e r a l i s e d L e o n t i e f r e s t r i c t e d p r o f i t f u n c t i o n i s g i v e n by: (5 .3) G ( p , Z ) / Z = Z i ^ E j ^ b ^ q ^ ' V ' 2 + b i i * i + ^1 = 1 b i t < 3 i t + £ i = l b i t t ( 3 i t 2 where t ime s u b s c r i p t s have been d e l e t e d , Z i s the aggregate f i x e d i n p u t and the are p l a n n i n g p r i c e s as g i v e n by ( 5 . 2 ) . The parameters b^j s a t i s f y the f o l l o w i n g symmetry r e s t r i c t i o n ; (5 .4) _ b i ; J = b j i f o r a l l i , j = 1 , 2 , 3 . The net output s u p p l y e q u a t i o n s d e r i v e d from (5 .3) by d i f f e r e n t i a t i n g w i t h r e s p e c t to p r i c e s a r e ; (5 .5) X j i / Z = ZTj = i bi5(q6/qi)1/2 + b u + b i t t + b i t t t 2 ; i = l , 2 , 3 . 6 8 The estimating system thus consists o£ (5.5) where the planning prices are given by (5.2). The parameters of the net output supply equations (b — , D i i . / b i t a n < * b i t t '' **ne P l a n n i n 9 price adjustment c o e f f i c i e n t s (D^) and the base period planning prices (q^ Q) are a l l chosen simultaneously to maximise the concentrated l i k e l i h o o d function of (5.5). Estimation of t h i s model enables tests to be carried out of the v a l i d i t y of the instantaneous adjustment model normally used by t e s t i n g whether 0^=1 for 1=1,2,3. The rel a t i o n s h i p between planning and actual prices, and instantaneous and imperfect quantity adjustment paths, w i l l be plotted by tracking the effe c t s of simulated price increases. One would expect the planning prices for exports and Imports to lag behind actual prices ( i e . 0<Di <1) due to the lags involved between producer decisions and del i v e r y dates. 5.2 Results The maximum l i k e l i h o o d parameter estimates for the Generalised Leontief models using actual prices and planning prices are both presented in Table 5.1. Both estimated p r o f i t functions are positive at a l l observation points and s a t i s f y the curvature requirements of being convex in prices at a l l observation points. The gradients with respect to prices have the correct signs and so both estimated p r o f i t functions are well behaved. The non-linear model was estimated using the linear estimates of the Instantaneous adjustment model as st a r t i n g values for the price and technology parameters in the planning 69 price model along with values of 0.8 and 1.0 for the adjustment c o e f f i c i e n t s and base period planning prices, respectively. The f i r s t r e s u l t of interest to be examined is whether the two models are s i g n i f i c a n t l y d i f f e r e n t ; i . e . , are the adjustment c o e f f i c i e n t s in the planning price model s i g n i f i c a n t l y d i f f e r e n t from 1.0 indicating that imperfect adjustment i s of importance. The hypothesis that a l l adjustment c o e f f i c i e n t s are equal to unity (subject to the base period planning prices being unrestricted) may be tested by use of the l i k e l i h o o d r a t i o t e s t . The test s t a t i s t i c has a value of 43.58 (twice the difference between the two log l i k e l i h o o d values) compared to a 1 per cent c r i t i c a l Chi-square value of 11.34 with 3 degrees of freedom. Consequently, the hypothesis of instantaneous adjustment i s strongly rejected by the model. This indicates that i t is important to allow for imperfect adjustment when modelling production sector a c t i v i t i e s . This r e s u l t i s not unexpected but i t remains to est a b l i s h whether the planning price model provides reasonable estimates of the imperfect adjustment process. As the base period planning prices are estimated in t h i s model examination of the estimated base period values and the rela t i o n s h i p between actual prices and the estimated planning price series provides one method of checking the reasonableness of the model. In the estimated model the base period planning price refers to the planning price for the year 1960. While the input-output data are only available from 1961 onwards i t is reasonable to assume that the actual prices p r e v a i l i n g in 1960 would be close to and probably s l i g h t l y below the 1961 price 70 index values of 1.0. The base period planning price estimated for imports i s indeed 0.95 which seems very close to what might be expected a p r i o r i . The estimate of 0.64 for the base period domestic sales planning price i s somewhat below what might be expected. The estimate of 1.89 for the export base period planning price appears to be unreasonable, being considerably higher than the actual export prices l i k e l y to have prevailed prior to 1961. Comparisons of the actual price and estimated planning price series for the observation period tend to confirm these impressions. The planning price series for domestic sales c l o s e l y follows but lags s l i g h t l y behind the actual price s e r i e s , ranging from 0.92 to 2.85 compared to the actual price range of 1.00 to 2.94. Import planning prices also follow but lag further behind actual import prices, ranging from 0.97 to 2.94 compared to the actual price range of 1.00 to 3.74. Export planning prices, however, bear less resemblance to actual export prices, being higher than actual prices for the f i r s t half of the period and lower than actual prices for the second half of the period. These comparisons would appear to indicate that less reliance can be placed on the model's r e s u l t s with regard to exports than i t s predictions for both imports and domestic sales. The parameter estimates of most interest in the model are those of the planning price adjustment c o e f f i c i e n t s . Using one int e r p r e t a t i o n , these parameters Indicate how quickly planning prices change when there is a change in the actual p r i c e . The three estimated parameters a l l l i e in the range (0,2) required 71 for s t a b i l i t y of the adjustment process. Furthermore, they a l l l i e in the range (0,1) indicating that adjustment in a l l three cases i s monotonic rather than c y c l i c a l . As expected, the adjustment c o e f f i c i e n t for domestic sales is closer to unity than those for the two traded goods indicating that domestic sales supply is quicker to respond to actual price changes than is export supply and import use. Indeed, s t a r t i n g from a position of long run equilibrium where the i n i t i a l actual and planning prices are equal, an increase in the actual price of domestic sales of ten per cent would lead to an increase in the planning price of 7.7 per cent in the f i r s t period. The adjustment of the planning prices to the actual price changes under these conditions i s graphed in Figure 5.1. In the case of domestic sales the planning price approaches the new actual price r e l a t i v e l y quickly with the adjustment e f f e c t i v e l y being complete within 5 years. In the case of imports the import planning price would increase 3.4 per cent in the f i r s t year in response to a 10 per cent increase in the actual price of imports. This slower adjustment i s l i k e l y due to the longer order and delivery lags associated with imported purchases. The time elapsed between the i n i t i a l price increase and the e f f e c t i v e adjustment of the import planning price is 10 years. The export price adjustment c o e f f i c i e n t i s r e l a t i v e l y small indicating that adjustment of the planning price to the actual price is very sluggish indeed. In fact, the planning price would only increase 0.7 per cent the f i r s t year in response to a 10 per cent increase in the actual export price. Even afte r 15 years only two-thirds of the 72 adjustment would have taken place. While t h i s very sluggish adjustment of exports may be r e a l i s t i c for ventures such as bringing a new mine on stream or expanding cropping into v i r g i n , uncleared land, i t seems less plausible for the output of manufacturing exports and increasing production from exi s t i n g mines and a g r i c u l t u r a l land. The alternative interpretation of the model i s that the planning prices are simply part of the dual representation of a quantity adjustment path. The adjustment path w i l l depend on the i n i t i a l prices, the magnitude of the price changes and the c h a r a c t e r i s t i c s of the GNP function. Within t h i s context i t is d i f f i c u l t to interpret the individual adjustment c o e f f i c i e n t s d i r e c t l y in terms of th e i r implications for the quantity adjustment paths. To gain a better understanding of the quantity adjustment process a series of simulations were carried out. The price of each net output was in turn assumed to increase by 10 per cent and then remain at t h i s higher l e v e l . The effects of these price changes on net output supply were simulated subject to the i n i t i a l period technology l e v e l and a constant l e v e l of the aggregate fixed input. The results of these simulations are presented in Figure 5.2. The quantity adjustment paths are monotonic in each case which follows from the monotonic rather than c y c l i c a l adjustment of the three planning prices. An increase In the price of domestic sales leads to increases in domestic sales supply and import use and to a decrease in exports. Adjustment is e f f e c t i v e l y complete in five years with most of the adjustment occurring in the f i r s t three 73 t years. An increase in import prices leads to a large f a l l in import demand and f a l l s in supply of the two outputs. Adjustment is e f f e c t i v e l y complete in ten years with most of the adjustment having taken place in the f i r s t f i v e years. An increase in export prices leads to increases in export supply and import demand and a f a l l in domestic sales supply. Adjustment is very sluggish, however, with the process s t i l l being incomplete after f i f t e e n years. F i n a l l y , the net output supply e l a s t i c i t i e s obtained from the two models are presented in Table 5.2. It should be noted that the instantaneous adjustment model e l a s t i c i t i e s represent the one period response to a change in actual prices while the planning price model e l a s t i c i t i e s represent the response to a change in the planning price, not the actual p r i c e . Accordingly, the planning price model own e l a s t i c i t i e s are a l l s u b s t a n t i a l l y larger than the corresponding instantaneous adjustment e l a s t i c i t i e s because more adjustment is allowed for in the planning price case. The cross e l a s t i c i t i e s are also larger in the planning price case with the exception of that between exports and imports which remains approximately constant. Exports and domestic sales supply are substitutes in the planning price case but s l i g h t complements in the instantaneous adjustment case. The instantaneous adjustment e l a s t i c i t i e s sign pattern corresponds to that of the instantaneous adjustment GNP function of Chapter 3 although the two sets of e l a s t i c i t i e s show responses subject to d i f f e r e n t conditions being held fixed. 74 In conclusion, then, the planning price model has served to demonstrate the importance o£ allowing for Imperfect adjustment when modelling production sector response. It appears that imperfect adjustment i s more important for traded goods sectors than for those supplying domestic sales. The model appears to present plausible r e s u l t s for import demand and domestic sales supply but may overstate the importance of imperfect adjustment in the case of export supply. To further investigate the role of imperfect adjustment in export supply and import demand a more sophisticated model of imperfect adjustment i s presented in the following chapter. 75 T A B L E 5 . 1 G E N E R A L I S E D L E O N T I E F P A R A M E T E R E S T I M A T E S 1 ' 2 C o e f f i c i e n t bDD bDM bDX kMM bMX b X X b D t b M t b X t b D t t b M t t b X t t ^ D O <3M0 ^ X O D D D M D X R 2 V a l u e s E q u a t i o n D E q u a t i o n M E q u a t i o n X L o g L i k e l i h o o d I n s t a n t a n e o u s  A d j u s t m e n t 1 . 0 3 2 0 ( 2 . 1 0 ) - 0 . 1 2 8 7 ( - 0 . 9 6 ) 0 . 0 2 4 1 ( 0 . 0 4 ) 0 . 2 8 0 7 ( 5 . 7 0 ) - 0 . 2 8 2 5 ( - 1 . 7 0 ) 0 . 4 4 6 8 ( 0 . 6 2 ) 0 . 2 4 1 7 ( 3 . 7 2 ) - 0 . 0 8 3 6 ( - 4 . 2 4 ) 0 . 2 0 8 1 ( 2 . 9 0 ) - 0 . 0 6 0 9 ( - 1 . 7 6 ) 0 . 0 1 2 3 ( 1 . 2 1 ) - 0 . 0 4 6 6 ( - 1 . 1 8 ) P l a n n i n g  P r i c e M o d e l 0 . 9 2 1 6 0 . 8 4 9 4 0 . 9 2 1 6 1 8 6 . 2 8 2 . 1 9 3 7 ( 8 . 3 7 ) - 0 . 1 6 6 8 ( - 1 . 4 4 ) - 0 . 7 6 8 1 ( - 4 . 6 8 ) 0 . 4 8 4 3 ( 3 . 9 5 ) - 0 . 3 1 5 9 ( - 2 . 1 5 ) 0 . 9 3 8 6 ( 4 . 9 5 ) - 0 . 0 5 3 0 ( - 0 . 5 6 ) - 0 . 1 9 0 8 ( - 2 . 3 1 ) 0 . 3 9 7 1 ( 4 . 9 3 ) - 0 . 0 4 1 4 ( - 1 . 7 9 ) 0 . 0 2 4 1 ( 1 . 1 8 ) 0 . 0 1 0 1 ( 0 . 3 1 ) 0 . 6 3 9 7 ( 2 . 2 3 ) 0 . 9 5 9 5 ( 6 . 3 3 ) 1 . 8 8 9 7 ( 4 . 4 8 ) 0 . 7 6 8 3 ( 1 . 3 5 ) 0 . 3 4 0 3 ( 6 . 3 3 ) 0 . 0 6 6 6 ( 5 9 . 7 1 ) 0 . 9 5 6 5 0 . 9 8 1 9 0 . 9 8 8 4 2 0 8 . 0 7 7 6 TABLE 5.2 (CONTINUED) The subscripts and equation labels D, M and X refer to Domestic Sales, Imports and Exports, respectively. 2 Values in parentheses are asymptotic t-values. TABLE 5.2 1970 NET OUTPUT SUPPLY ELASTICITIES" Instantaneous Adjustment Model With Respect to Price of : X M D Chanqe in X 0. 4236 -0.4613 0.0377 Quantity of: M 0. 7445 -1.0934 0.3488 D 0. 0106 -0.0610 0.0504 Planning Price Model Chanqe in  Quantity of With Respect to Planning Price of X M D X 1.4674 -0.4362 -1.0312 M 0.9342 -1.3874 0.4531 D -0.3832 -0.0786 0.4619 1 The l e t t e r s X, M and D refer to Exports, Imports and Domestic Sales, respectively. 77 FIGURE 5.1  ADJUSTMENT OF PLANNING PRICES a) 10% Increase in Domestic Sales Price Price 1.101 Actual Price Planning Price Yrs 1 2 3 4 5 6 7 b) 10% Increase in Import Price 10 11 12 13 14 15 Yrs 1 2 3 4 5 6 7 c) 10% Increase in Export Price 10 11 12 13 14 15 Yrs 10 11 12 13 14 15 78 FIGURE 5.2  ADJUSTMENT OF QUANTITIES a) 10% Increase-in -Domestic Sales Price Quantity Index 1.10 1.00 0.90 _Domest i c .1 mports Instant. Adjustment Imperfect Adjustment _Exports Yrs 8 9 10 11 12 13 14 15 b) 10% Increase in Import Price Quantity Index 1.00 _Domest i c _Exports x _I mports Yrs 8 9 10 11 12 13 14 15 c) 10% Increase in Export Price Quantity Index 1.20 1.10 1.00 0.90 .Imports "Exports Domestic Yrs 9 10 11 12 13 14 15 79 6- AN ADJUSTMENT COSTS MODEL An approach to modelling Imperfect adjustment which has proven to be more popular than the planning price model outlined in the previous Chapter is the development of models which e x p l i c i t l y allow for costs of adjustment within an optimising framework. The aim of these models can be described as modelling short and long run factor demands within a un i f i e d framework where the (costly) rate of adjustment of quasi-fixed factors i s an endogenous choice variable and factor demands are int e r r e l a t e d . Shocks which r e s u l t in a l l factor demands being out of long-run equilibrium are consistent with the models although short-run equilibrium is maintained at a l l times, i e . the phenomenon of "overshooting" of short-run demands for variable factors is allowed for. At the same time output f e a s i b i l i t y i s maintained and the Le Chatelier p r i n c i p l e i s s a t i s f i e d whereby long-run own-price e l a s t i c i t i e s are greater in absolute value than the corresponding short-run own-price e l a s t i c i t i e s . By using an empirical model derived from such an adjustment costs model i t should be possible to gain a better understanding of the role of imperfect adjustment in the GNP function framework. A th e o r e t i c a l adjustment costs model i s b r i e f l y outlined in the following section and an econometric adaptation is then presented. 6.1 A Theoretical External Adjustment Costs Model The t h e o r e t i c a l model used in t h i s a p p l i c a t i o n is similar to that of Berndt, Fuss and Waverman (1977, Chapter 4) and thi s section draws on their presentation. The Berndt, Fuss and Waverman model i s in turn derived from Lucas' (1967) model of 80 external adjustment costs where quasi-fixed factors (denoted by z) are fixed in the stort-run but can be varied over time subject to p o s i t i v e , increasing marginal costs of adjustment. The marginal adjustment costs are denoted by C m (z m) where z m dz m/dt and where; (6.1) C m(0) = 0 , C m ' ( z m ) > 0 , C m»(z m) > 0 ; m=l,..,M. Firms are assumed to know the prices of variable net outputs with cer t a i n t y and have s t a t i c expectations regarding those prices. Adjustment costs are external in the sense that current production is unaffected by changes in the quasi-fixed factors although future production is affected. Time paths for variable net outputs and fixed inputs are chosen to maximise the present value of net receipts given the i n i t i a l stock of quasi-fixed inputs. The present value of net receipts i s ; (6.2) V(0) = / 0 ° ° e " r t R ( t ) dt where r i s the appropriate discount rate and R(t) is the value of net receipts. Using a r e s t r i c t e d p r o f i t function which s a t i s f i e s the standard properties of Hotelling's Lemma, convexity in p and concavity in z and denoting the r e s t r i c t e d p r o f i t function by H(p,z), the revenue function (R(t)) can be written as; (6.3) R(t) = H(p(t),z(t)) - zjlx C m ( z m ( t ) ) . The f i r s t order condition with respect to the quasi-fixed inputs from the maximisation of the present value of net receipts is now given by; (6.4) H z - r C m ' ( z m ) + C m " ( z m ) z m = 0 ;rd = l,..,M. m 81 A stationary solution for the quasi-fixed inputs exists when ZjjfZnfO and hence s a t i s f i e s ; (6.5) H Z m(p,z) - rC m'(0) = 0. This condition can be shown to be equivalent to the requirement that in a steady state the marginal value product of the quasi-fixed input equals i t s marginal accumulation cost. The steady state net supplies of the variable net outputs can be obtained by substituting the steady state values of the quasi-fixed inputs into the r e s t r i c t e d p r o f i t function. Lucas shows that this model can be linked to the ad hoc p a r t i a l adjustment l i t e r a t u r e (where actual stocks are adjusted part-way towards some optimal l e v e l each period) by the short-run demand for quasi-fixed inputs derived from (6.4) and (6.5) being an approximate solution to a linear d i f f e r e n t i a l equation system. In the case of one quasi-fixed input the d i f f e r e n t i a l equation system to which (6.4) and (6.5) are an approximate solution reduces to; (6.6) z = B~(z~(t) - z ( t ) ) where z~ i s the steady state quasi-fixed input l e v e l and B~ i s an endogenous adjustment parameter given by; (6.7) B~ = -(1/2) [r - { r 2 - 4H"(z~)/C"(0)} 1 / 2]. Since H ls concave in z and C"(0)>0, B~ must l i e between zero and one so that the actual stock approaches the steady state stock monotonically. Further, as marginal adjustment costs increase r a p i d l y then B~ approaches zero and no adjustment occurs. The adjustment parameter i s also affected by the curvature of the r e s t r i c t e d p r o f i t function and the interest rate (a decrease in 82 I the interest rate acts to increase the adjustment speed). As a r e s u l t , the adjustment parameter i s determined within the economic model. Before t h i s model can be Implemented empirically the zero depreciation assumption has to be relaxed, the units of the cost of adjustment function must be s p e c i f i e d and functional forms have to be chosen for the r e s t r i c t e d p r o f i t and adjustment cost functions. To s i m p l i f y the presentation, i t w i l l be assumed that there is only one quasi-fixed input. To allow for non-zero depreciation i t w i l l be assumed that the quasi-fixed input depreciates exponentially at the rate d. We then have; (6.8) z = y - dz where y i s the gross addition to the stock of z. We now specify C(z) as; (6.9) C(z) = qy + qD(z) where q is the asset price of the quasi-fixed input. Using (6.9) the cost of not changing the l e v e l of the quasi-fixed input is now the cost of depreciation and adjustment costs are s p e c i f i e d in terms of the fixed input's asset p r i c e . The present value of net receipts function (6.2) now becomes; (6.10) V(0) = / Q 0 0 e _ r t { H ( t ) - qdz - qD(z) - qz} dt noting that y=z+dz. Integrating the l a s t term in (6.10) by parts produces; (6.11) y ^ 0 0 e" r tqz dt = / c ] C P e " r t r q z dt - qz(0). Substituting t h i s in (6.10) y i e l d s ; (6.12) qz(0) + V(0) = v/ u G 0 e~ r t{H(t)_ - uz - qD(z)} dt = Jo® W(0) dt 83 where u=q(r+d) i s the user cost of the quasi-fixed input. Maximising the present value of net receipts ls now equivalent to maximising the right hand side of (6.12) since qz(0) is an i n i t i a l condition. The f i r s t order condition for thi s maximisation problem now becomes; (6.13) dW(0)/dz - d{dW(0)/dz)/dt = 0 which i s ; (6.14) H z - u - rqD'(z) + qD"(z)z =0. The steady state solution must then s a t i s f y ; (6.15) H z(p,z) - u - rqD»(0) = 0. The adjustment parameter B~ is now given by; (6.16) B~ = -(1/2) [r - i r 2 - 4H z z(p,z)/(qD"(0))} 1 / 21. This completes the t h e o r e t i c a l external adjustment costs model and the next task i s to specify an implementable version of the model. 6.2 An Econometric Adaptation In t h i s a p p l i c a t i o n the external adjustment costs model i s used in conjunction with the four-net output, one-fixed input aggregate model of Chapter 3 to estimate short, intermediate and long-run responses of net outputs to changes in prices. The four net outputs are aggregate exports, aggregate imports, labour and domestic sales. Capital ls again treated as the sole fixed input. The same assumptions regarding p r o f i t maximising firms, perfect competition in goods and factor markets, and the c h a r a c t e r i s t i c s of the aggregate technology set are made. Imports are again assumed to be an input to the production sector while exports are an output of the production sector not consumed domestically. The 84 same data set i s used as in Chapter 3 except that the price of c a p i t a l i s now derived e x p l i c i t l y rather than as a r e s i d u a l . The c a p i t a l asset price, user cost and quantity are described and l i s t e d in Appendix 1 along with the discount rate. The aggregate technology i s now represented by the following Generalised McFadden or biquadratic r e s t r i c t e d p r o f i t function as s p e c i f i e d by Diewert (1985); (6.17) H(p,K) = a=l b i P i + d/2) Z i = l Z j i l b i j p i P j / p 4 + Z i=l b i K P i K + Z i=l b i t p i t + (1/2) b K K ( Z h=l Pn)K 2 + b K t ( Z n = l Pn)Kt + (1/2) b t t ( Z n = l Pn) t 2 where the bj_j parameters again s a t i s f y the following symmetry r e s t r i c t i o n s ; (6.18) b i : j = b j i for a l l i , j = 1,2,3. A time trend is again used to represent the technology index. It should be noted that t h i s s p e c i f i c a t i o n of the Generalised McFadden GNP function d i f f e r s from those used e a r l i e r in this thesis in that constant returns to scale are not imposed with respect to the fixed c a p i t a l input in order to obtain more information on the c a p i t a l adjustment process and, following Diewert's (1985, p.90) suggestion, the weights on the prices in the second order c a p i t a l and technology terms are set equal to the inverse of the base period p r i c e s . By applying Hotelling's Lemma the following set of net output supply equations is obtained; (6.19) X i = bi + Zj=i bijpj/p4 + b i KK + b i t t + (1/2) b K K K 2 + b K t K t + (1/2) b t t t 2 ; 1=1,2,3; 3 3 (6.20) X 4 = b 4 - (1/2) Z i = l l j = l bijpipj/p4 + b4KK + b4tt 85 + (1/2) b K K K 2 + b K t K t + (1/2) b t t t 2 . If the matrix of estimated quadratic terms B=tbjj ] Is positi v e semi-definite then the r e s t r i c t e d p r o f i t function is gl o b a l l y convex in prices (Diewert 1985). If B is not positive semi-definite then i t can again be reparameterised using the Wiley, Schmidt and Bramble technique of replacing B by the product of a lower triangular matrix A and i t s transpose; (6.21) B = AA1 where A = la^] ; i , j = l,2,3 ; and a i j = 0 for i<j. In t h i s s p e c i f i c a t i o n of the Generalised McFadden GNP function concavity in the quantity of the fixed c a p i t a l input requires that b K K be negative. If the estimated b K K parameter is non-negative then concavity in the c a p i t a l input quantity can be 2 imposed by replacing b^K by the term -aj(K where a^K i s a parameter to be estimated. To capture costs of adjustment a quadratic approximation i s used; (6.22) D(K) = (1/2) d K KK 2. Using (6.22) and the r e s t r i c t e d p r o f i t function (6.17) the f i r s t order condition with respect to the fixed input (6.14) i s ; 4 4 4 (6.23) Zi=l b i K P i + b K K ( Z i = i Pi)K + b K t ( £ i = 1 P i ) t - u K " r<3K(dKKK) + <3KdKKK = n-From (6.15) the steady state l e v e l of the c a p i t a l input i s now; (6.24) K~ = -(ZIi = i b i K P i + b K t ( Z i = i Pi>t - uK>/(b K KZi=i P i ) -It i s further assumed that current period production a c t i v i t y i s affected by the c a p i t a l stock e x i s t i n g at the beginning of the period and that changes made to the c a p i t a l stock in the current period only a f f e c t next period's production. This enables the 86 following discrete approximation to the f l e x i b l e accelerator formulation to be used; (6.25) K t - Kt.! = B~(K~ t - K ^ ) where; (6.26) B~ = -(1/2) tr - { r 2 - 4 b K K r i = i Pi/(qR^KK)> 1 / 21• The complete estimating system i s now given by the four net output equations and the c a p i t a l adjustment equation; (6.27) X i = b i + Zjli b i j p j / p 4 + b i KK + b i t t + (1/2) b R K K 2 + b K t K t + (1/2) b t t t 2 + e i ; 1=1,2,3; (6.28) X 4 = b 4 - (1/2) Z i = l Z j=l bijPiPj/P4 + *>iRK + b i t t 2 2 + (1/2) bKRK + b KtKt + (1/2) b t t t + e 4 (6.29) K - K_± = -(1/2) [r - { r 2 - 4b K K 27 i = 1 Pi/(°. K dKK } } 1 / 2 ] [ (£i = l b i K P i + b K t ( ^ i = l P i ) i : " u K ) / ( b K K ^ i = l P i } - K_ 1J + e R. The vectors of error terms for the observations are again assumed to be independently d i s t r i b u t e d with a multivariate normal d i s t r i b u t i o n with zero means and covariance matrix Si-From the parameters of the estimating system a set of e l a s t i c i t i e s can be derived which completely describes the dynamic relationships within the estimated system. In the case of variable net outputs, e l a s t i c i t i e s which characterise the short, intermediate and long-run response of net output supply to the prices of net outputs are produced. The short-run response represents the response which occurs in less than one period to a price change when c a p i t a l input levels have not changed. The intermediate-run response represents the response aft e r one period has elapsed and the c a p i t a l input has p a r t i a l l y adjusted. 87 The long-run response represents the complete response after c a p i t a l input levels have f u l l y adjusted to their new steady state l e v e l s . The short-run net output price e l a s t i c i t i e s are given by; (6.30) E S i j = (d log X i/d log PJ ) IR=K_ 1 = < P j / X i > 0 * i / 9 p j ) • In the Generalised McFadden case t h i s produces; (6.31) E S i j = (Pj/xi) (bi j/p 4) ; i , j = l , 2 , 3 ; (6.32) E S i 4 = (p 4 / X i ) ( - Z j = l b j i p j / p 4 2 ) ; 1=1,2,3; (6.33) E S 4 4 = (p 4/x 4) (Zi=12Tjll b i j p i p j / p 4 3 ) . The long-run net output price e l a s t i c i t i e s are given by; (6.34) E L i j = (d log x^/d log Pj ) IK=K~ = (Pj/xi ) [ (9xi/9pj ) + Oxi/9K~) (9K~/9 P j ) ] This produces in the Generalised McFadden case; (6.35) EL i : J = E S i j + <<biK + bKK K ^ t ^ ^ l bnRPn " UK " b j K Zn=l Pn)Pj /<bK K Xi (Zn=l Pn>2 ; 1 ,j=l,. . , 4 . The intermediate-run e l a s t i c i t i e s after one period's c a p i t a l stock adjustment has taken place are given by; (6.36) E l i j = ESij + K b i K + bKKK +bK tt)(Zn=l b n K p n - u K " b j K Z n = l Pn)Pj/^b KKXi ( Z n = l Pn> 2HBl ; i,j= l , . . , 4 . where; (6.37) Bl = B ~ ( l + dB~/dpj) = B ~ [ l - b j ^ / U r 2 - 4 ^ , ^ ^ ^ 9 i / ( ^ K K ) ) 1 / 2 ^ K K } ^ It can be shown that the own-price e l a s t i c i t i e s s a t i s f y the Le Chatelier p r i n c i p l e i f the r e s t r i c t e d p r o f i t function i s well behaved and the absolute value of the long-run e l a s t i c i t y w i l l 88 exceed that of the Intermediate-run e l a s t i c i t y which ln turn exceeds that of the short-run e l a s t i c i t y . With regard to cross-price e l a s t i c i t i e s the phenomenon of "overshooting" is allowed whereby short or intermediate-run c r o s s - e l a s t i c i t i e s may exceed the magnitude of the corresponding long-run c r o s s - e l a s t i c i t y . This may arise due to an output price increase. The response to th i s w i l l be an increase in output supply but in the short-run t h i s w i l l have to be achieved by using some variable inputs more intensively due to the f i x i t y of c a p i t a l . In the long-run when the c a p i t a l input has been increased the variable inputs may be used less i n t e n s i v e l y and so the long-run c r o s s - e l a s t i c i t y may be less than the short-run c r o s s - e l a s t i c i t y . By d e f i n i t i o n a l l short-run e l a s t i c i t i e s involving either the price or quantity of c a p i t a l are zero. However, intermediate and long-run e l a s t i c i t i e s between net output quantities and the user cost of c a p i t a l can be obtained. The long-run e l a s t i c i t y between net output quantities and the user cost of c a p i t a l i s given by; (6.38) E L i u = ( u K / X i ) Caxi/'SUK) l K=K~ = ( u K / X i ) [ ( b i K + b K KK + b K t t ) / ( b K K r j i l Pj)] ;i=l,.,4. The corresponding intermediate-run e l a s t i c i t y i s given by; (6.39) E I i u = B~EL i u. The long and intermediate-run response of c a p i t a l input levels to changes in net output prices can also be obtained. The long-run c r o s s - e l a s t i c i t y i s given by; (6.40) E L K i = (Pi/K)(dK~/dpi) ; i=l,..,4; 89 = ( P i / K ) [ ( Z j 4 1 b j K P j - u K - b ^ 4 ! V^/.ib^T^ P j ) 2 } ] . The corresponding intermediate-run e l a s t i c i t y i s given by; (6.41) E I R i = B l . E L R i ; 1 = 1,.. ,4. F i n a l l y , e l a s t i c i t i e s can be derived which provide information on the response of p r o f i t s to changes in scale and technology. The e l a s t i c i t y for returns to scale i s ; (6.42) E R T S = [(dH(p,K)/dK).Kl/H(p,K). This e l a s t i c i t y shows the percentage change in p r o f i t s following a one percent change in the c a p i t a l input. If i t s value Is greater than one then there Is increasing returns to scale. The technical change e l a s t i c i t y is given by ; (6.43) E T C = (dH(p,K)/dt)/H(p,K) . If t h i s e l a s t i c i t y Is negative there is technical regress as an increase in technology acts to reduce p r o f i t s . From th i s set of e l a s t i c i t i e s i t should be possible to gain a better understanding of the importance of allowing for the dynamics of the adjustment process within the GNP function model. 6.3 Results I n i t i a l estimation of the system (6.27)-(6 . 29) produced results which f a i l e d to meet convexity of the r e s t r i c t e d p r o f i t function in prices but which were concave in the quantity of the c a p i t a l input. Subsequent estimation was therefore of the reparameterised model imposing price convexity using (6.21). The r e s u l t i n g maximum l i k e l i h o o d parameter estimates and their asymptotic t-values are presented in Table 6.1. Concavity of the r e s t r i c t e d p r o f i t function In the quantity of c a p i t a l input was 90 again s a t i s f i e d as indicated by the negative value of b K K which i s s i g n i f i c a n t l y d i f f e r e n t from zero. The adjustment costs function parameter dj<K i s positive and s i g n i f i c a n t l y d i f f e r e n t from zero as required by economic theory. The estimated dependent variables track the actual dependent variable values well in a l l cases and the equation R-square values are reported in Table 6.1. The values of B~, the p a r t i a l adjustment c o e f f i c i e n t for the c a p i t a l stock, produced by the estimated system are stable and range from 0.07 to 0.09, taking a value of 0.0727 in 1970. This means that the actual c a p i t a l stock adjusts only seven to nine per cent towards i t s steady state value in one year. This implies r e l a t i v e l y slow adjustment of the c a p i t a l stock. As a re s u l t one would expect substantial differences between the estimated short-run and long-run own-price e l a s t i c i t i e s for net outputs which are either strongly substitutable or strongly complementary to c a p i t a l . For net outputs which are r e l a t i v e l y independent of c a p i t a l ( i e . those which are either weakly substitutable or weakly complementary with c a p i t a l ) the slow adjustment of c a p i t a l need not imply substantial differences between short-run and long-run own-price e l a s t i c i t i e s . Due to the large volume of output produced by thi s model, detailed e l a s t i c i t y estimates are presented only for three of the nineteen years for which output is obtained. Net output price e l a s t i c i t i e s for the year 1965 near the beginning of the time-series are presented in Table 6.2. Those for the year 1970 near the middle of the time-series are presented in Table 6.3 while 91 those for 1978, a year near the end of the time-series, appear in Table 6.4. The estimated short-run export own-price e l a s t i c i t i e s are of sim i l a r magnitude to those obtained in the aggregate model of Chapter 3. The s i g n i f i c a n t difference i s that in t h i s case the export own-price e l a s t i c i t y tends to decrease over time. This is l i k e l y due to the fact that constant returns are not being imposed here and the dependent variable in the estimating equation i s the gross export quantity rather than export quantity per unit of c a p i t a l input quantity. This would appear to indicate that more confidence can be placed in mid-point estimates. The estimated long-run export own-price e l a s t i c i t i e s are somewhat larger than the short-run e l a s t i c i t i e s but not to the extent that may have been expected beforehand. For instance, in 1970 the long-run e l a s t i c i t y was 1.58 compared to a short-run e l a s t i c i t y of 1.51. This would appear to indicate that the relat i o n s h i p between export supply and c a p i t a l i s not strong. As expected from the small value of the estimated B~ adjustment c o e f f i c i e n t the intermediate-run e l a s t i c i t y i s close to the short-run e l a s t i c i t y value. The export c r o s s - e l a s t i c i t i e s produce a more interesting set of r e s u l t s . While exports f a l l in response to an increase in the price of imports the f a l l i s s l i g h t l y less in the long-run than i t i s in the short-run indicating that some substitution away from imports and towards c a p i t a l occurs in the long-run. This e f f e c t is most pronounced in the case of the labour cross-price e l a s t i c i t y . While exports f a l l in response to an increase in 92 l a b o u r p r i c e s t h e r e d u c t i o n i n t h e l o n g - r u n i s o n l y one f i f t h what i t i s i n t h e s h o r t - r u n i n d i c a t i n g s u b s t a n t i a l s u b s t i t u t i o n away f r o m l a b o u r a n d t o w a r d s c a p i t a l . T h i s t r e n d i s e v e n e v i d e n t i n t h e i n t e r m e d i a t e - r u n a n d r e p r e s e n t s a c l a s s i c c a s e o f " o v e r s h o o t i n g " . I t w o u l d a l s o a p p e a r t o i n d i c a t e t h a t t h e r e l a t i o n s h i p b e t w e e n l a b o u r a n d c a p i t a l i s r e l a t i v e l y s t r o n g . C r o s s - p r i c e e l a s t i c i t i e s w i t h r e s p e c t t o t h e d o m e s t i c s a l e s p r i c e a r e s m a l l b u t n e g a t i v e ( b e i n g n e a r z e r o i n t h e s h o r t - r u n ) i n d i c a t i n g t h a t e x p o r t s a r e r e d u c e d s l i g h t l y f o l l o w i n g a n i n c r e a s e i n t h e d o m e s t i c s a l e s p r i c e . T h i s i s t h e o n l y c r o s s -p r i c e e l a s t i c i t y w h i c h d i f f e r s i n s i g n f r o m t h e c o r r e s p o n d i n g e l a s t i c i t i e s o b t a i n e d i n C h a p t e r 3. I m p o r t s h o r t - r u n o w n - p r i c e e l a s t i c i t i e s a r e a l s o o f s i m i l a r m a g n i t u d e t o t h o s e o b t a i n e d i n C h a p t e r 3. The e l a s t i c i t i e s t e n d t o d e c l i n e i n m a g n i t u d e d u r i n g t h e f i r s t h a l f o f t h e p e r i o d a n d t h e n s t a b i l i s e d u r i n g t h e s e c o n d h a l f . T h e r e i s v e r y l i t t l e d i f f e r e n c e b e t w e e n t h e e s t i m a t e d l o n g - r u n a n d s h o r t - r u n i m p o r t o w n - p r i c e e l a s t i c i t i e s i n d i c a t i n g t h a t i m p o r t s a n d c a p i t a l a r e a l m o s t i n d e p e n d e n t . A g a i n a l a r g e r d i f f e r e n c e b e t w e e n s h o r t - r u n a n d l o n g - r u n e l a s t i c i t i e s i s e v i d e n t i n t h e i m p o r t c r o s s - p r i c e e l a s t i c i t i e s . Some o v e r s h o o t i n g o c c u r s i n r e s p o n s e t o a n e x p o r t p r i c e i n c r e a s e w i t h i m p o r t u s a g e i n c r e a s i n g l e s s i n t h e i n t e r m e d i a t e a n d l o n g - r u n t h a n i t d o e s i n t h e s h o r t - r u n . F o l l o w i n g a n i n c r e a s e i n l a b o u r p r i c e s , h o w e v e r , i m p o r t u s a g e d r o p s more i n t h e l o n g - r u n t h a n i t d o e s i n t h e s h o r t - r u n i n d i c a t i n g f u r t h e r s u b s t i t u t i o n away f r o m i m p o r t s a s t h e c a p i t a l s t o c k i n c r e a s e s . I m p o r t u s a g e i s i n c r e a s e d more i n t h e l o n g - r u n 93 than i t i s i n the s h o r t - r u n f o l l o w i n g an i n c r e a s e i n the domest ic s a l e s p r i c e . The e s t i m a t e d s h o r t - r u n l a b o u r own-pr ice e l a s t i c i t i e s are a l l r e l a t i v e l y s t a b l e around the v a l u e of - 1 . 0 which i s near the m i d - p o i n t va lue o b t a i n e d i n Chapter 3. As expected from the r e s u l t s above , the l o n g - r u n labour o w n - p r i c e e l a s t i c i t y i s s u b s t a n t i a l l y l a r g e r than the s h o r t - r u n e l a s t i c i t y , a v e r a g i n g around - 1 . 5 0 . T h i s i n d i c a t e s t h a t l a b o u r and c a p i t a l are s t r o n g l y s u b s t i t u t a b l e w i th the usage of l a b o u r d e c l i n i n g c o n s i d e r a b l y more i n the l o n g - r u n f o l l o w i n g an i n c r e a s e i n l a b o u r p r i c e s once the c a p i t a l s tock has been i n c r e a s e d . A g a i n c o n s i d e r a b l e o v e r s h o o t i n g i s e v i d e n t i n the usage of l a b o u r f o l l o w i n g an i n c r e a s e i n e x p o r t p r i c e s w i t h the i n c r e a s e i n l a b o u r use b e i n g a p p r o x i m a t e l y h a l f i n the l o n g - r u n what i t i s i n the s h o r t - r u n . Labour usage d e c l i n e s s l i g h t l y more i n the l o n g - run than i n the s h o r t - r u n f o l l o w i n g an Increase i n import p r i c e s . Labour usage i n c r e a s e s c o n s i d e r a b l y more i n the l o n g - r u n than i t does i n the s h o r t - r u n , however, f o l l o w i n g an i n c r e a s e i n the domest ic s a l e s p r i c e . T h i s would appear to i n d i c a t e t h a t domest ic s a l e s p r o d u c t i o n i s r e l a t i v e l y i n t e n s i v e i n i t s use of l a b o u r , a p l a u s i b l e r e s u l t g i v e n the importance of s e r v i c e i n d u s t r i e s i n domest i c s a l e s p r o d u c t i o n . The e s t i m a t e d domest ic s a l e s s h o r t - r u n own-pr i ce e l a s t i c i t y i s somewhat h i g h e r than t h a t o b t a i n e d i n Chapter 3 and s t a b l e around the v a l u e of 0 .85 . The l o n g - r u n own-pr i ce e l a s t i c i t y i s o n l y s l i g h t l y l a r g e r , a g a i n i n d i c a t i n g a r e l a t i v e l y weak r e l a t i o n s h i p between domest i c s a l e s s u p p l y and c a p i t a l . Domest ic 94 sales supply drops s l i g h t l y following an increase in export prices but the cross e l a s t i c i t y values are close to zero in both the short and long-run. Domestic sales supply also f a l l s to a small degree following an increase ln import prices with the short and long-run cross e l a s t i c i t i e s being approximately equal. Larger f a l l s in domestic sales supply occur following an increase in labour prices with the f a l l being larger in the long-run. Intermediate and long-run cross-price e l a s t i c i t i e s between net output and c a p i t a l prices and quantities are presented in Table 6.5. As expected from the small value of B~, an increase in the user cost of c a p i t a l has a n e g l i g i b l e impact on net output supply in the intermediate-run. In the long-run, however, an increase in the user cost of c a p i t a l acts to decrease the supply of exports and s l i g h t l y increase the supply of domestic sales output, thus confirming that domestic sales output i s r e l a t i v e l y labour intensive while export supply is r e l a t i v e l y c a p i t a l intensive. Increases in the user cost act to increase the usage of the other two inputs, labour and imports. The e f f e c t on the quantity of the c a p i t a l stock of an increase in net output prices i s also near zero in the intermediate-run due to the small value of the p a r t i a l adjustment c o e f f i c i e n t B~. In the long-run, however, an increase in export prices increases the c a p i t a l stock while an increase in the domestic sales price a c t u a l l y decreases the c a p i t a l stock. As expected an increase in import prices has a n e g l i g i b l e e f f e c t on the c a p i t a l stock even in the long-run indicating that c a p i t a l and imports are almost independent. The strongest rel a t i o n s h i p i s 95 between c a p i t a l and labour with an increase in labour prices leading to a substantial Increase ln the c a p i t a l stock ln the long-run. F i n a l l y , the returns to scale and technical change e l a s t i c i t i e s are presented in Table 6.6. The returns to scale e l a s t i c i t i e s are calculated in the neighbourhood of exis t i n g c a p i t a l stock levels and indicate that there are increasing returns to scale and increase in value over time. The technical change e l a s t i c i t e s , however, indicate that there is i n i t i a l l y technical progress but then technical regress towards the end of the period. There, hence, appears to be some d i f f i c u l t y d i s t inguishing the influences of returns to scale and technical change with the increasing value of the returns to scale e l a s t i c i t i e s capturing some of the effects l i k e l y due to technical change. This would account for the declining and negative values of the technical change e l a s t i c i t i e s towards the end of the period and the high values of the returns to scale e l a s t i c i t i e s . To the extent that there are increasing returns to scale, however, th i s represents a contradiction of the neoclassical assumptions of the model as a competitive equilibrium w i l l not exist with increasing returns to scale. 6.4 Conclusions The adjustment costs model presented in t h i s Chapter has the advantage of incorporating the adjustment process of the quasi-fixed input c a p i t a l as the solution to an e x p l i c i t . dynamic optimisation problem where the rate of adjustment of the quasi-fixed input i s endogenously determined. Output f e a s i b i l i t y i s 96 m a i n t a i n e d w h i l e o v e r s h o o t i n g o f v a r i a b l e i n p u t demands i s a l l o w e d . The s h o r t , i n t e r m e d i a t e a n d l o n g - r u n e l a s t i c i t i e s p r o d u c e d b y t h e m o d e l h e l p t o i n c r e a s e o u r u n d e r s t a n d i n g o f t h e d y n a m i c a d j u s t m e n t p r o c e s s w i t h i n t h e GNP f u n c t i o n m o d e l . W h i l e t h e r e s u l t s may I n d i c a t e l e s s d i v e r g e n c e b e t w e e n s h o r t a n d l o n g - r u n e l a s t i c i t i e s f o r t h e e x p o r t s a n d i m p o r t s o f t h e t r a d e d s e c t o r t h e y do p o i n t t o o t h e r i m p o r t a n t a r e a s o f a d j u s t m e n t i n t h e d y n a m i c p r o c e s s . E x p o r t s t u r n o u t t o be o n l y w e a k l y r e l a t e d t o c a p i t a l a s i s d o m e s t i c s a l e s s u p p l y w h i l e i m p o r t demand l s a l m o s t i n d e p e n d e n t o f c a p i t a l . As a r e s u l t t h e d i f f e r e n c e b e t w e e n s h o r t a n d l o n g - r u n o w n - p r i c e e l a s t i c i t i e s i s n e g l i g i b l e f o r i m p o r t s a n d s m a l l f o r e x p o r t s a n d d o m e s t i c s a l e s s u p p l y . T h e i m p o r t a n t e f f e c t o f a l l o w i n g f o r d y n a m i c s i n t h i s m o d e l i s on i n p u t u s a g e , p a r t i c u l a r l y t h a t o f l a b o u r . W h i l e a s h o r t - r u n i n c r e a s e i n e x p o r t s u p p l y i s b r o u g h t a b o u t b y u s i n g more l a b o u r i n c o n j u n c t i o n w i t h t h e f i x e d c a p i t a l i n p u t , i n t h e l o n g - r u n t h e c a p i t a l s t o c k i s i n c r e a s e d a n d s u b s t i t u t e d f o r t h e i n c r e a s e d l a b o u r u s a g e . T h i s a l s o h a p p e n s t o a l e s s e r e x t e n t w i t h i m p o r t u s a g e f o l l o w i n g a n e x p o r t p r i c e , i n c r e a s e . H e n c e , w h i l e a l l o w i n g f o r i m p e r f e c t a d j u s t m e n t a p p e a r s t o make l i t t l e d i f f e r e n c e t o a c t u a l e x p o r t s u p p l y i t d o e s make a s i g n i f i c a n t d i f f e r e n c e t o t h e i n p u t u s a g e w h i c h g o e s i n t o p r o d u c i n g t h a t e x p o r t s u p p l y . A n o t h e r a s p e c t o f t h e a d j u s t m e n t p r o c e s s h i g h l i g h t e d b y t h e d y n a m i c m o d e l i s t h e i m p o r t a n c e o f t h e l a b o u r i n t e n s i v e n e s s o f d o m e s t i c s a l e s s u p p l y . An i n c r e a s e i n d o m e s t i c s a l e s p r i c e s a c t u a l l y a c t s t o 97 decrease the steady state c a p i t a l stock and hence reduces export supply. While the adjustment costs model may appear to downplay the importance of allowing for imperfect adjustment on export supply and import demand r e l a t i v e to the results of the planning price model of the preceding Chapter, i t must be remembered that the two models have quite d i f f e r e n t assumptions and hence the results are not d i r e c t l y comparable. In the planning price model c a p i t a l and labour are aggregated together and treated as a fixed input. Hence the major avenue of dynamic adjustment indicated by the adjustment costs model, namely the adjustment of labour input usage as the c a p i t a l stock is increased, is precluded in the planning price model. The e f f e c t of t h i s in the planning price model is highlighted by the much greater increase in import use following an export price increase, given that both labour and c a p i t a l inputs are fixed for the duration of the simulation. Furthermore, the adjustment costs model views the s h i f t of the production f r o n t i e r as the only source of dynamics, while the planning price model considers adjustment along the production f r o n t i e r following changes in net output price s . In p r i n c i p l e , both forms of adjustment could be considered simultaneously. As a res u l t more experimentation with d i f f e r e n t dynamic models and sets of assumptions w i l l be necessary before the dynamic process is f u l l y understood. To f u l l y understand phenomena such as the J-curve e f f e c t i t w i l l be necessary to model imperfect adjustment on the demand side within a general equilibrium context and to allow for endogeneity with respect to import and export prices. 98 TABLE 6.1  DYNAMIC PARAMETER ESTIMATES Coeff i c l e n t Estimate t-value C o e f f i c i e n t Estimate t-value bX -0.1251 -0.1440 aML -1.3082 -4.7518 a x x -1.4685 -4.7798 bMK 0 .0527 1.4400 aXM 0.8951 5.7610 bMt -1.0516 -4.7532 aXL 0.3249 0.7640 b L -4.2531 -4.4495 bXK 0.0758 1.2022 aLL -0.0000 -0.0000 b x t 0.4740 0.8415 bLK 0.1486 4.3780 bKK -0.0034 -2.1381 b L t -2.0457 -8.2437 b K t 0.0334 2.2309 bD 4.1866 4.2798 b t t -0.4001 -2.4949 bDK -0.0175 -0.2227 bM -0.9898 -2.5164 bDt 3.0128 5.0193 aMM -0.2811 -0.8718 dKK 1.6831 2.3937 R 2 Values Equation X 0. 9795 Equation D 0 .9842 Equation M 0. 9851 Equation K 0 . 4667 Equation L 0. 9701 Log Likelihood 141.80 x The subscripts and equation labels X, M, L, D, K and t refer to aggregate exports, aggregate imports, labour, domestic sales, c a p i t a l and technology, respectively. 99 TABLE 6.2 1965 NET OUTPUT PRICE ELASTICITIES 1 s t i c i t y Short-run Intermediate-run Lonq-run EXX 2.2607 2.2692 2.3737 EXM -1.6610 -1.6584 -1.6265 EXL -0.5535 -0.5221 -0.1342 EXD -0.0462 -0.0634 -0.2752 EMX 2.5377 2.5291 2.4236 EMM -2.0484 -2.0511 -2.0833 EML -1.4070 -1.4387 -1.8306 EMD 0.9177 0.9351 1.1491 ELX 0.2206 0.2115 0.0998 ELM -0.3670 -0.3698 -0.4039 E L L -0.9296 -0.9632 -1.3778 ELD 1.0760 1.0944 1.3208 EDX -0.0114 -0.0132 -0.0346 EDM -0.1487 -0.1492 -0.1557 EDL -0.6682 -0.6746 -0.7542 EDD 0.8282 0.8318 0.8752 1 The subscripts X, M, L and D refer to aggregate exports, aggregate imports, labour and domestic sales, respectively. 100 TABLE 6.3 1970 NET OUTPUT PRICE ELASTICITIES 1 E l a s t i c i t y Short-run Intermediate-run Long-run EXX 1.5052 1.5105 1.5779 EXM -1.0609 -1.0600 -1.0479 EXL -0.4678 -0 .4404 -0.0934 E X D 0.0236 0.0099 -0.1625 EMX 1.6559 1.6502 1.5779 EMM -1.2823 -1.2833 -1.2962 EML -1.1654 -1.1948 -1.5666 E M D 0.7918 0.8064 0.9911 ELX 0.1955 0.1884 0.0981 ELM -0.3121 -0.3134 -0.3296 E L L -1.0459 -1.0826 -1.5473 ELD 1.1624 1.1807 1.4116 EDX 0.0063 0.0053 -0.0069 E D M -0.1357 -0.1359 -0.1381 EDL -0.7441 -0.7491 -0.8122 E D D 0.8735 0. 8760 0.9073 1 The subscripts X, M, L and D refer to aggregate exports, aggregate imports, labour and domestic sales, respectively. 101 TABLE 6.4 1978 NET OUTPUT PRICE ELASTICITIES 1 E l a s t i c i t y Short-run Intermediate-run Lonq-run EXX 0.9846 0.9873 1.0238 EXM -0.6372 -0.6371 -0.6366 EXL -0.3216 -0.3051 -0.0840 E X D -0.0258 -0.0336 -0.1382 EMX 1.0752 1.0722 1.0327 EMM -0.7644 -0.7645 -0.7651 EML -0.7953 -0.8132 -1.0531 E M D 0.4845 0.4930 0.6065 ELX 0.1823 0.1771 0.1087 ELM -0.2671 -0.2672 -0.2682 E L L -1.0247 -1.0557 -1.4707 ELD 1.1095 1.1242 1.3205 EDX -0.0096 -0.0101 -0.0179 E D M -0.1064 -0.1064 -0.1065 EDL -0.7255 -0.7290 -0.7758 E D D 0.8414 0.8431 0.8652 1 The subscripts X, M, L and D refer to aggregate exports, aggregate imports, labour and domestic sales, respectively. 102 TABLE 6.5 CAPITAL - NET OUTPUT CROSS ELASTICITIES 1 Year 1965 1970 1978 1965 1970 1978 1965 1970 1978 1965 1970 1978 E l a s t i c i t y EI XU EI MU EI LU EI DU -0.0251 -0.0199 -0.0114 E LXU -0.3378 -0.2742 -0.1650 E IKX 0.0130 0.0083 0.0047 E L R X 0.1728 0.1127 0.0671 0.0254 0.0214 0.0124 E LMU 0.3413 0.2938 0.1791 E IKM 0.0040 0.0015 0.0001 E LKM 0.0528 0.0202 0.0010 0.0268 0.0267 0.0215 E L L U 0.3611 0.3672 0.3097 E I K L 0.0481 0.0425 0.0283 E L K L 0.6413 0.5798 0.4072 0.0051 0.0036 0.0024 E LDU 0.0693 0.0499 0.0349 E IKD -0.0263 -0.0211 -0.0134 E LKD -0.3502 -0.2881 -0.1926 1 The subscripts X, M, L, D, U and K refer to aggregate exports, aggregate imports, labour, domestic sales, the user cost of c a p i t a l and c a p i t a l input quantity, respectively. 103 TABLE 6.6 SCALE AND TECHNICAL CHANGE ELASTICITIES Year 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 RTS 1.1229 1.1866 1.2817 1.4217 1.5936 1.6490 1.8280 1.9710 1.9361 1.9495 TC 0.0926 0.0593 0.0380 0.0193 0.0044 -0.0032 -0.0123 -0.0193 -0.0192 -0.0216 104 7 . CONCLUSIONS AND FURTHER RESEARCH The results presented in t h i s thesis have extended our understanding of the roles of disaggregation and Imperfect adjustment in the GNP function approach to measuring the responsiveness of export supply and import demand to price changes. They have also pointed to a number of directions in which further research needs to be undertaken. Combination of the aggregator function method of including several export and import categories with the use of the recently developed Generalised McFadden functional form which allows imposition of the correct curvature conditions has proved to be an e f f e c t i v e means of obtaining detailed sets of e l a s t i c i t i e s characterising export supply and import demand responsiveness. At the aggregate l e v e l export supply responsiveness was found to be of a si m i l a r magnitude to that found by Kohli (1978) in an e a r l i e r Canadian study, while import responsiveness was found to be somewhat higher in t h i s study. Increases in the prices of both imports and labour were found to decrease the supply of exports while exports were found to be complementary with the output of domestic sales supply. The demand for labour was found to be more e l a s t i c than in most e a r l i e r studies and a general trend towards increasing price responsiveness within the Canadian economy was observed. At the disaggregated l e v e l the own-price e l a s t i c i t i e s produced for the export and import components were generally stable and of reasonable magnitude. The disadvantage of the 105 aggregator function approach, however, is that i t r e l i e s on the r e s t r i c t i v e assumption of s e p a r a b i l i t y of the production structure and a l l export and import components, respectively, were found to be complementary with each other subject to the fixed c a p i t a l input av a i l a b l e . Extension of modelling to larger disaggregated models which contained four export (import) components along with aggregate imports (exports) produced a d i f f e r e n t impression of the cross relationships between export (import) components with some substitution becoming evident. The larger disaggregated models tended, however, to produce less stable estimates of the component own-price e l a s t i c i t i e s in some instances. The major conclusion, then, regarding disaggregation i s that the aggregator function approach, when combined with f l e x i b l e functional forms which permit curvature imposition, is an ef f e c t i v e means of obtaining information on the responsiveness of export and import components to own-price changes. The aggregator function approach appears to be less suited to providing information on cross relationships among components. Larger disaggregated models, on the other hand, appear to have a r e l a t i v e advantage in providing information on , cross re l a t i o n s h i p s . Combining the planning price method of allowing for imperfect adjustment with the GNP function framework produced res u l t s which indicated that imperfect adjustment was p a r t i c u l a r l y important in the traded goods sector with exports in par t i c u l a r taking an extended period to f u l l y adjust to price 106 changes. Extension of modelling to a more sophisticated adjustment costs model, however, produced a d i f f e r e n t impression of the adjustment process. Both export supply and import demand responses were found to be l i t t l e d i f f e r e n t in the long-run to those of the short-run. Important differences were found, however, in the composition of input usage over time with a strong s u b s t i t u t a b i l i t y between c a p i t a l and labour in the long-run. Since c a p i t a l was fixed in the short-run but variable in the long-run, while labour was variable in the short-run, the adjustment costs model indicated considerable overshooting with respect to labour demand. This avenue of adjustment was not available in the planning price model where both labour and c a p i t a l were treated as fixed in both the short and long-run. The major conclusions, then, from these re s u l t s are that i t is important to allow for imperfect adjustment to gain a f u l l e r understanding of export supply and import demand response but that the r e s u l t s obtained are l i k e l y to be sensitive to the assumptions made. Consequently, more experimentation with d i f f e r e n t models and sets of assumptions w i l l be necessary before the dynamic process is f u l l y understood. 7.1 Further Research At the most general l e v e l , an Important area which warrants further research is extension of the GNP function framework to make i t more general equilibrium in nature. This would involve e x p l i c i t modelling of the domestic consumption sector and allowance for exchange rate adjustment to maintain balance of 107 payments equilibrium. The work of Clements (1980) represents a promising s t a r t in t h i s d i r e c t i o n . With regard to the s p e c i f i c r e s u l t s of t h i s thesis an obvious area for further research is experimentation with d i f f e r e n t functional forms to assess the robustness of the r e s u l t s . This would be p a r t i c u l a r l y interesting In examining whether the trend towards increasing price responsiveness found in the aggregator function and disaggregated models is replicated with other f l e x i b l e forms permitting curvature imposition such as the Generalised Barnett (Diewert and Wales 1987). Extension of the work to d i f f e r e n t data sets may permit successful estimation of semi-flexible functional forms as proposed by Diewert and Wales (1986). This procedure would have the advantage of including a l l the variable net output components while not r e l y i n g on the s e p a r a b i l i t y assumption. An important area of input adjustment which has received l i t t l e attention i s allowance for variable capacity u t i l i s a t i o n rates of the fixed inputs. In a l l the models presented here the c a p i t a l stock i s assumed to be u t i l i s e d at a constant rate. Although the adjustment costs model attempts to allow for adjustment of the c a p i t a l stock over time within an optimising framework no allowance is made for changes in capacity u t i l i s a t i o n . In r e a l i t y changes in capacity u t i l i s a t i o n of c a p i t a l and other quasi-fixed inputs such as some labour types w i l l represent an important response to output fluctuations and i t i s correspondingly important that they be modelled in applied work. One approach to allowing for q u a s i - f i x i t y and variable 108 u t i l i s a t i o n i s that of H e l l i w e l l and Chung (1986). Epstein and Denny (1980) attempt to endogenise u t i l i s a t i o n and depreciation decisions as solutions to optimising problems. Recent advances in Industrial organisation theory have increased interest in relaxing the perfect competition assumption present in most applied work. A r e l a t i v e l y straight-forward extension of the material in t h i s thesis would involve testing the v a l i d i t y of the perfect competition price-taking assumption along the l i n e s of Appelbaum (1979). Many avenues exi s t for extending the material presented in th i s thesis on imperfect adjustment. A simple f i r s t step might be extension of the planning price model to include labour as a variable net output, leaving c a p i t a l as the sole fixed input. This would go some way towards making the model more comparable to the adjustment costs model although as currently s p e c i f i e d the fixed input remains fixed in the long-run ln the planning price model. More information on the fixed input could be obtained by e x p l i c i t l y estimating a "planning shadow pr i c e " equation for the fixed input. A number of variations can be made to the adjustment costs model presented in Chapter 6. Adjustment costs can be made intern a l in the sense that a change in the stock of the quasi-fixed input a f f e c t s current production as well as future production. The model could be extended along the lines of Morrison and Berndt (1981) to include two quasi-fixed factors. The assumption of s t a t i c price expectations could be relaxed and 109 a version consistent with r a t i o n a l expectations estimated along the l i n e s of Morrison (1985). There are also a l t e r n a t i v e models of the dynamic adjustment process which should be investigated. A framework for testing r e s t r i c t i o n s within a f l e x i b l e dynamic system i s developed by Anderson and Blundell (1983). 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Vlastuin (1982), "Production F l e x i b i l i t y and Technical Change in Australia's Wheat/Sheep Zone", Review of Marketing and A g r i c u l t u r a l Economics 50, 9-26. McKay, L., D. Lawrence and C. Vlastuin (1983), " P r o f i t , Output Supply, and Input Demand Functions for Multiproduct Firms: The Case of Australian Agriculture", International Economic  Review 24, 323-39 . Morrison, C.J. (1985), "On the Economic Interpretation and Measurement of Optimal Capacity U t i l i s a t i o n with Anticipatory Expectations", Review of Economic Studies 52, 295-310 . Morrison, C.J. and E.R. Berndt (1981), "Short-run Labour Productivity in a Dynamic Model", Journal of Econometrics 16, 339-65. Ostensoe, L.A. (1986), 'Production Analysis for Applied General Equilibrium Modelling*, B.A.(Hons) thesis, University of B r i t i s h Columbia. Pindyck, R.S. and J.J. Rotemberg (1983a), "Dynamic Factor Demands and the Effects of Energy Price Shocks", American Economic  Review 73, 1066-79. Pindyck, R.S. and J.J. Rotemberg (1983b), "Dynamic Factor Demands under Rational Expectations", Scandinavian Journal of  Economics 85, 223-38. Rhomberg, R.R. (1964), "A Model of the Canadian Economy under Fixed and Fluctuating Exchange Rates", Journal of P o l i t i c a l  Economy 72, 1-31. Samuelson, P.A. (1953-4), "Prices of Factors and Goods in General Equilibrium", Review of Economic Studies 21, 1-20. Shephard, R.W. (1953), Cost and Production Functions, Princeton University Press, Princeton. 114 S t a t i s t i c s Canada (1983), "The Input-Output Structure of the Canadian Economy in Constant Prices 1971-79", Catalogue No. 15-202E, Minister of Supply and Services, Ottawa. Wiley, D.E., W.H. Schmidt and W.J. Bramble (1973), "Studies of a Class of Covariance Structure Models", Journal of the  American S t a t i s t i c a l Association 68, 317-23. White, K.J. (1978), "A General Computer Program for Econometric Methods - SHAZAM", Econometrica 46, 239-40. Woodland, A.D. (1976), 'Modelling the Production Sector of an Economy: A Selective Survey and Analysis', Department of Economics Working Paper No. 76-21, University of B r i t i s h Columbia. Woodland, A.D. (1977), "Estimation of a Variable P r o f i t and of Planning Price Functions for Canadian Manufacturing, 1947-70", Canadian Journal of Economics 10, 355-77. Woodland, A.D. (1982), International Trade and Resource  A l l o c a t i o n , North-Holland, Amsterdam. 115 AP PENDI yC 1  DATA The data used in t h i s study are derived from a 20 year time series of annual input-output data made available by S t a t i s t i c s Canada to UBC in 1984. The data consist of current and constant d o l l a r series for 37 i n d u s t r i a l c l a s s i f i c a t i o n s . The methodology used by S t a t i s t i c s Canada in preparing i t s input-output data is described in d e t a i l in Dominion Bureau of S t a t i s t i c s (1969) and S t a t i s t i c s Canada (1983). Lai (1982) reviews some of the methodological problems encountered in r e c o n c i l i n g input-output data with the National Accounts data and compares the Canadian input-output tables to those of other countries. For each industry data is available for 8 primary inputs, 36 interindustry inputs and 2 outputs. The primary inputs consist of competitive and non-competitive imports, inputs purchased from Crown corporations and government bodies, and 5 durable inputs; inventories of raw materials, inventories of finished goods, machinery and equipment c a p i t a l , construction c a p i t a l and land. Outputs of each industry are c l a s s i f i e d according to end use, either domestic sales or exports. In addition to these variables, several f i n a n c i a l variables are also available for each i n d u s t r i a l c l a s s i f i c a t i o n . To more c l o s e l y approximate the actual prices faced by producers these f i n a n c i a l variables were di s t r i b u t e d to other input and output categories. Given the lack of d e t a i l available on the f i n a n c i a l variables t h i s procedure often involved r e l a t i v e l y ad hoc methods. For instance, commodity in d i r e c t taxes were di s t r i b u t e d across the 36 intermediates and 2 116 import components proportionate to each commodity's share of t o t a l intermediate input value, other i n d i r e c t taxes were analogously d i s t r i b u t e d across construction c a p i t a l and land while subsidies and r o y a l t i e s were, respectively, added to and subtracted from domestic output. The constant d o l l a r series are available for the periods 1961 to 1971 using 1961 as the base year and 1971 to 1980 using 1971 as the base year. The two series were sp l i c e d using the overlapping year 1971 and based in 1961. A price series was obtained by d i v i d i n g the nominal d o l l a r series by the constant d o l l a r s e r i e s . The constant d o l l a r series then serves as an i m p l i c i t quantity index. The r e s u l t i n g industry data is l i s t e d and i t s construction described in Ostensoe (1986). Other recent applications using the data set are Cas, Diewert and Ostensoe (1986) and Diewert and Ostensoe (1986). In t h i s study the data were aggregated over the 37 industries by the use of D i v i s i a indices in the SHAZAM package. The discrete D i v i s i a index procedure has the advantage that i t is superlative, being exact for the f l e x i b l e translog aggregator function (Diewert 1976). The domestic sales, aggregate export and labour hours variables were taken d i r e c t l y from the input-output data aggregated to the economy l e v e l . The aggregate import variable was obtained by aggregating the competitive and non-competitive import categories, the d i s t i n c t i o n being considered neither r e l i a b l e nor useful. F i n a l l y , an aggregate c a p i t a l stock quantity series was obtained by aggregating the 5 durable input categories l i s t e d e a r l i e r for the 37 industries using c a p i t a l 117 stock prices as weights. Since constant returns to scale are imposed in this study the user cost of c a p i t a l was derived as a residual to equate the values of outputs and inputs. After adding the values of domestic sales and exports and subtracting the values of labour and imports, the r e s u l t i n g residual value was divided by the c a p i t a l quantity series to obtain a price index for the user cost of c a p i t a l . Subsequent rescallng made the value of the price index 1.0 in 1961 and price times quantity equal to the residual value. The price and quantity series used for the four net outputs (aggregate exports, aggregate imports, domestic sales and labour) and the fixed input c a p i t a l are l i s t e d in Tables A l . l and Al.2, respectively. The technology index used throughout t h i s thesis was a time trend ranging from a value of 0.1 in 1961 to 2.0 in 1980. This sc a l i n g was chosen so that the squared value of the index was of the same maximum order of magnitude as the price index s e r i e s . The four export and import component categories were obtained by aggregating the exports and imports of industries which had sim i l a r export and import price patterns over the 20 year period. Some e f f o r t was also made to keep sim i l a r industries together. The composition of the four export component groups by input-output industries (and corresponding 1-0 industry numbers) is as follows; Export Group 1 : A g r i c u l t u r a l and Forestry Products 1) Agriculture and Fishing 7) Leather 2) Forestry 11) Woods 4) Food and Beverages 13) Paper and A l l i e d 118 Export Group 2 : Minerals and Energy Products 3) Mines, Quarries and O i l Wells 21) Petroleum and Coal 15) Primary Metals 33) E l e c t r i c Power Export Group 3 ; Motor Vehicles, T e x t i l e and E l e c t r i c a l Products 5) Tobacco 6) Rubber and P l a s t i c 8) T e x t i l e s 9) K n i t t i n g M i l l s 10) Clothing 12) Furniture and Fixtures 14) P r i n t i n g and Publishing 18) Transport Equipment 19) E l e c t r i c a l Equipment 26) Railway Transport 32) Telephones 34) Gas D i s t r i b u t i o n Export Group 4 : Heavy Industrial and Service Products 16) Metal Fabricating 17) Machinery 20) Non-metallic Minerals 22) Chemicals 23) Miscellaneous Manufacturing 25) Air Transport 27) Water transport 28) Motor Transport 29) Urban Transport 30) Storage 31) Broadcasting 35) Trade 36) Finance, Insur. & Realty 37) Commercial Services. The price and i m p l i c i t quantity series for the four export components are l i s t e d in Tables Al.3 and A1.4, respectively. The 1-0 Industrial composition of the four import components i s as follows; Import Group 1 : A g r i c u l t u r a l , Forestry and Service Products 1) Agriculture and Fishing 2) Forestry 4) Food and Beverages 7) Leather 26) R a i l Transport 27) Water Transport 28) Motor Transport 29) Urban Transport 119 11) Woods 30) Storage 13) Paper and A l l i e d 35) Trade 14) P r i n t i n g and Publishing 36) Finance, Insur. & Realty 24) Construction 37) Commercial Services 25) Air Transport Import Group 2 ; Metals and Energy Products 3) Mines, Quarries and O i l Wells 21) Petroleum and Coal 15) Primary Metals 33) E l e c t r i c Power 16) Metal Fabricating 34) Gas D i s t r i b u t i o n Import Group 3 : Machinery, E l e c t r i c a l and T e x t i l e Products 5) Tobacco 12) Furniture and Fixtures 6) Rubber and P l a s t i c s 17) Machinery 8) Textiles 19) E l e c t r i c a l Equipment 9) K n i t t i n g M i l l s 31) Broadcasting 10) Clothing 32) Telephones Import Group 4 : Vehicles, Chemicals and Other Products 18) Transport Equipment 22) Chemicals 20) Non-metallic Minerals 23) Misc. Manufacturing The price and i m p l i c i t quantity series for the four import components are l i s t e d in Tables A1.5 and A1.6, respectively. In the adjustment costs model of Chapter 6 constant returns to scale with respect to c a p i t a l are not imposed. As a r e s u l t an e x p l i c i t asset price and user cost for c a p i t a l have to be derived. In t h i s case the asset price of c a p i t a l was derived d i r e c t l y from the input-output data. The asset prices for the f i v e durable inputs were aggregated using a D i v i s i a index to form an aggregate c a p i t a l asset pr i c e . 120 Derivation of a user cost for c a p i t a l presents more problems. Using a nominal discount rate tends to produce rapid l y increasing user cost series when c a p i t a l gains are not allowed for while using a r e a l discount rate produces negative user costs in more recent years. To overcome t h i s problem the same ad hoc approach as used by Ostensoe (1986) was used whereby a weighted average of the nominal and real discount rates is used along with appropriate depreciation rates to produce a r e l a t i v e l y stable, non-negative user cost s e r i e s . The nominal interest rate was taken as the unweighted average of the 90 day corporate paper rate taken at monthly i n t e r v a l s . The rea l interest rate was constructed by subtracting the percentage change in the consumer price index from the nominal interest rate. The discount rate used in deriving the user cost of c a p i t a l was obtained by placing a weight of 0.68 on the real Interest rate and 0.32 on the nominal interest rate. The disaggregated data from which the user cost series was obtained are l i s t e d in d e t a i l in Ostensoe (1986). For consistency, the same weighted average discount rate was used in the estimating system of Chapter 6. The asset price, user cost and quantity series for c a p i t a l are presented in Table A1.7 along with the weighted average discount rate. 121 TABLE A l . l AGGREGATE PRICE INDICES Year Exports Imports Dom. Sales Labour Capital 1961 1.0000 1.0000 1.0000 1.0000 1.0000 1962 1.0204 1.1960 1.0071 1.0350 1.0667 1963 1.0239 1.2399 1.0250 1.0747 1.1129 1964 1.0340 1.2723 1.0370 1.1101 1.1654 1965 1.0559 1.2728 1.0603 1.1684 1.2191 1966 1.0853 1.2957 1.1054 1.2664 1.2711 1967 1.1078 1.3132 1.1437 1.3564 1.2405 1968 1.1319 1.3150 1.1730 1.4581 1.3114 1969 1.1653 1.3447 1.2216 1.5748 1.3680 1970 1.2053 1.3939 1.2759 1.6931 1.3510 1971 1.2230 1.2108 1.3343 1.8360 1.4353 1972 1.2751 1.2494 1.3961 1.9738 1.5392 1973 1.4167 1.3670 1.5140 2.1892 1.7841 1974 1.7102 1.8005 1.7390 2.4937 1.9934 1975 1.9456 2.0591 1.9653 2.8539 2.1016 1976 2.0819 2.1346 2.1110 3.2378 2.2778 1977 2.2671 2.3861 2.2532 3.4999 2.3690 1978 2.5106 2.6657 2.4130 3.7063 2.5881 1979 2.8651 3.0923 2.6024 3.9336 2.9382 1980 3.2431 3.7384 2.9404 4.4886 3.1815 122 TABLE A1.2 AGGREGATE QUANTITIES IN MILLIONS OF 1961 DOLLARS Y e a r E x p o r t s I m p o r t s Dom. S a l e s L a b o u r C a p i t a l 1961 6445 .8 4272 . 8 29988. 3 18747. 4 13414.0 1962 6840 .8 3929 .6 32298. 7 19403. 0 13806.3 1963 7550 .8 4117 .6 33783. 9 19811. 5 14345.1 1964 8664 .6 4581 .1 35865. 0 20604 . 1 14971.4 1965 8989 .3 5038 .3 39067. 5 21721. 4 15686.2 1966 10251 . 3 5607 .1 41243. 2 22439 . 1 16547.3 1967 11047 .8 5777 .0 41578. 5 22568. 9 17407.0 1968 12866 .7 6416 . 4 42976. 8 22459. 5 18139.0 1969 13743 .4 7097 .8 45548. 1 22984. 0 18943.8 1970 14960 .6 6939 .6 44712. 8 22782. 9 19862.8 1971 15672 .1 8923 .1 47519. 2 23056. 7 20507.3 1972 16891 .3 10010 .0 50745. 1 23808. 4 21365.4 1973 19083 .3 11191 .2 54886. 0 25095. 6 22360.1 1974 19287 .3 11883 .3 57993. 5 26230. 5 23591.0 1975 17699 .2 11169 .1 58963. 9 26236. 0 24954.1 1976 19292 .2 11688 .1 61903. 0 26563. 6 26291.6 1977 20802 .9 11825 .6 62552. 0 26848. 2 27827.7 1978 22603 .7 12499 .1 64277. 8 27685. 4 29333.9 1979 23949 .6 13296 .2 67519. 4 28674. 0 30773.8 1980 25055 .1 12613 .9 67671. 5 29153. 3 32132.0 123 TABLE Al.3  EXPORT COMPONENT PRICE INDICES Year 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 A g r i c u l t u r a l  & Forestry  Products 1.0000 1.0347 1.0458 1.0548 1.0764 1.1200 1.1420 1.1718 1.2218 1.2336 1.2518 1.3629 1.6445 1.9986 2.1906 2.2353 2.3731 2.6363 3.0640 3.3090 Minerals  & Energy  Products 1.0000 1.0212 1.0228 1.0356 1.0685 1.1013 1.1275 1.1480 1.1759 1.2583 1.2418 1.2697 1.4499 1.9430 2.3470 2.6105 2.9656 3.3414 3.9620 4.7162 MVs. Textiles  & E l e c t r i c a l  Products 1.0000 0.9821 0.9683 0.9613 0.9645 0.9750 0.9852 1.0006 1.0236 1.0509 1.0764 1.0996 1.1361 1.2625 1.4058 1.5081 1.6420 1.8140 2.0077 2.2520 Heavy Ind. & Services  Products 1.0000 1.0099 1.0111 1.0324 1.0526 1.0667 1.0989 1.1308 1.1623 1.2042 1.2482 1.2950 1.3765 1.6014 1.8181 1.9618 2.0917 2.2630 2.5050 2.8385 124 TABLE A1.4 EXPORT COMPONENT QUANTITIES IN MILLIONS OF 1961 DOLLARS Aqr i c u l t u r a l M i n e r a l s MVs. T e x t i l e s Heavy Ind . Year & F o r e s t r y & Enerqy & E l e c t r i c a l & S e r v i c e s P r o d u c t s P r o d u c t s P r o d u c t s P r o d u c t s 1961 2763.9 1853.1 687.8 1141.0 1962 2767.9 2053.5 831.1 1191.3 1963 3074.8 2130.5 968.5 1383.2 1964 3502.0 2379.5 1215.0 1582.2 1965 3455.6 2477.3 1376.4 1707.4 1966 3700.7 2567.8 2127.4 1948.9 1967 3320.9 2802.2 3037.9 2087.3 1968 3448.6 3227.6 4230.8 2285.3 1969 3471.1 3129.7 4983.0 2575.4 1970 3788.9 3716.3 5075.1 2780.7 1971 4072,4 3617.7 5490.1 2938.4 1972 4306.0 3880.6 5914.6 3273.0 1973 4748.4 4572.1 6803.6 3536.2 1974 4834.7 4615.0 6594.8 3765.5 1975 4187.7 4034.8 6607.2 3577.6 1976 4789 .9 3980.2 7614.8 3864.9 1977 5343.8 4025.5 8365.9 4209.8 1978 5726 . 4 4135.5 9267.5 4870.5 1979 5955.1 4642.0 8836.5 5684.3 1980 6385.3 5209 .8 8126.7 6079 .3 125 TABLE A1.5 IMPORT COMPONENT PRICE INDICES Year 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 Ag., Forestry  & Service  Products 1.0000 1.3568 1.4575 1.5280 1.5174 1.5504 1.5516 1.5457 1.5768 1.6638 1.2443 1.3027 1.4509 1.7726 1.9386 1.9853 2.2172 2.4396 2.7455 3.0906 Metals &  Energy Products 1.0000 1.1344 1.1375 1.1587 1.1678 1.1940 1.2223 1.2270 1.2563 1.3221 1.2147 1.2526 1.3997 2.5983 3.1224 3.2792 3.6450 3.9983 5.0706 7.2636 Machinery,Elec,  & T e x t i l e  Products 1.0000 1.0708 1.0836 1.0834 1.0835 1.0837 1.0915 1.0903 1.1103 1.1235 1.0643 1.0754 1.1803 1.3946 1.5062 1.5800 1.7327 1.9135 2.1486 2.3489 Vehicles,  Chem. &Other  Products 1.0000 1.0642 1.0872 1.1017 1.1093 1.1332 1.1685 1.1783 1.2102 1.2316 1.1901 1.2208 1.2847 1.4764 1.7539 1.8102 2.0544 2.3807 2.6856 3.0792 126 TABLE A1.6 IMPORT COMPONENT Q U A N T I T I E S IN M I L L I O N S OF 1961 DOLLARS A q . , F o r e s t r y M e t a l s & M a c h i n e r y , E l e c V e h i c l e s , Y e a r & S e r v i c e E n e r q y & T e x t i l e C h e m . &Othe: P r o d u c t s P r o d u c t s P r o d u c t s P r o d u c t s 1961 1 8 2 1 . 8 9 2 3 . 9 7 7 3 . 7 7 5 3 . 5 1962 1 4 3 1 . 3 8 8 5 . 4 7 7 7 . 0 8 6 5 . 9 1963 1 4 2 6 . 1 9 5 8 . 0 8 3 2 . 5 9 5 2 . 1 1964 1 5 4 8 . 8 1 0 6 6 . 3 9 4 8 . 9 1 0 8 7 . 9 1965 1 6 5 5 . 8 1 1 4 0 . 5 1 0 3 9 . 1 1 3 0 0 . 7 1966 1 8 3 2 . 5 1 1 9 6 . 0 1 2 0 2 . 2 1 4 9 4 . 5 1967 1 9 1 5 . 7 1 1 5 8 . 8 1 2 1 4 . 4 1 6 0 2 . 3 1968 1 9 6 3 . 7 1 2 8 6 . 9 1 2 6 0 . 4 2 0 7 8 . 5 1969 2 1 7 5 . 4 1 3 5 2 . 4 1 4 4 8 . 2 2 3 1 9 . 4 1970 2139 .7 1 4 1 6 . 5 1 4 0 4 . 3 2 1 6 2 . 0 1971 3 1 4 7 . 8 1 7 0 7 . 7 1 6 4 9 . 9 2 5 6 8 . 4 1972 3 5 0 1 . 9 1839 .6 1 9 5 4 . 3 2 8 9 8 . 7 1973 3 8 3 1 . 3 2 1 0 0 . 7 2 1 1 8 . 8 3 3 4 5 . 5 1974 4 1 2 4 . 6 2 1 6 2 . 1 2 2 6 2 . 1 3 5 9 8 . 3 1975 3 9 0 1 . 7 2 0 5 8 . 1 2 0 5 3 . 7 3 3 7 2 . 7 1976 4 1 3 9 . 1 1 9 5 8 . 6 2 1 6 5 . 8 3 8 0 4 . 6 1977 4 1 9 3 . 2 1 8 9 9 . 6 2 1 5 4 . 3 4 0 2 2 . 4 1978 4 4 5 5 . 7 1 9 5 6 . 5 2 3 6 4 . 8 4 2 4 2 . 8 1979 4 7 7 3 . 7 2 1 6 0 . 2 2 7 5 5 . 9 4 1 4 6 . 1 1980 4 7 9 8 . 2 2 0 6 9 . 4 2 7 3 6 . 8 3528 .8 127 TABLE A1.7 ADJUSTMENT COSTS MODEL CAPITAL DATA  Year Asset Price User Cost Capital Quantity 1 Discount Rate 1961 1.0000 0.0998 10.3960 0.0510 1962 1.0152 0.1012 10.7000 0.0501 1963 1.0395 0.0956 11.1176 0.0414 1964 1.0731 0.0977 11.6030 0.0405 1965 1.1250 0.0975 12.1570 0.0361 1966 1.1858 0.0977 12.8243 0.0321 1967 1.2299 0.1009 13.4906 0.0320 1968 1.2478 0.1186 14.0579 0.0458 1969 1.3084 0.1278 14.6816 0.0486 1970 1.3582 0.1240 15.3939 0.0414 1971 1.4393 0.1073 15.8934 0.0240 1972 1.5330 0.1033 16.5584 0.0170 1973 1.7104 0.1039 17.3293 0.0126 1974 2.0089 0.0950 18.2833 0.0011 1975 2.2797 0.1171 19.3397 0.0059 1976 2.5141 0.1747 20 . 3762 0.0264 1977 2.7302 0.1853 21.5668 0.0245 1978 2.9436 0.2474 22.7341 0.0427 1979 3.2096 0.2902 23.8500 0.0507 1980 3.4800 0.3251 24.9026 0.0540 1 In tens of b i l l i o n s of 1961 d o l l a r s . 128 A P P E N D I X 2  P R I M A L V E R S U S D U A L E S T I M A T I O N  A2.1. Introduction Applied researchers are interested in modelling the production structure of industries and economies as an input to larger econometric models and to simple p o l i c y analyses. The c h a r a c t e r i s t i c s of the production structure are usually summarised by estimates of the e l a s t i c i t i e s of substitution and price e l a s t i c i t i e s of demand between the various inputs. Advances in the f i e l d of f l e x i b l e functional forms have made available f l e x i b l e forms such as the translog and Generalised Leontief (GL) which are able to model the substitution p o s s i b i l i t i e s between inputs much more accurately than tr a d i d i o n a l forms such as the Cobb-Douglas and Constant E l a s t i c i t i e s of Substitution models. In the case of the Cobb-Douglas form a l l e l a s t i c i t i e s of substitution are r e s t r i c t e d to the value one. The CES form r e s t r i c t s the e l a s t i c i t i e s between a l l pairs of factors to be equal - a s i g n i f i c a n t disadvantage when there are more than two inputs. The f l e x i b l e functional forms, on the other hand, are able to approximate an a r b i t r a r y cost function up to the second-order terms and hence to approximate an a r b i t r a r y matrix of substitution e l a s t i c i t i e s . The Cobb-Douglas and CES forms are, however, s e l f - d u a l which means that both the production function and the cost function are members of the same family of functional forms. Hence the choice of whether to model the production structure by the primal (production function) or dual (cost function) route is in theory 129 of no s i g n i f i c a n c e . In practice, however, differences in estimated e l a s t i c i t i e s would be observed due to differences in the behavioural implications of the stochastic s p e c i f i c a t i o n (Burgess 1 9 7 5 ) . In the case of the f l e x i b l e functional forms mentioned, however, the choice between primal and dual estimation routes i s no longer t r i v i a l since these functional forms are not s e l f - d u a l , i e . a translog cost function does not have as i t s equivalent in the primal representation a translog production function. Hence the choice between primal and dual forms w i l l not only imply differences in the e l a s t i c i t y estimates due to d i f f e r e n t stochastic s p e c i f i c a t i o n s but also due to d i f f e r e n t underlying production structures being modelled. In spite of the d i f f e r e n t implications of choosing to derive e l a s t i c i t y estimates from the primal or dual form, which approach is adopted appears to depend primarily on the biases of the in d i v i d u a l researcher. Some authors consistently use the dual approach while others remain with the t r a d i t i o n a l primal approach. L i t t l e work has been done to compare the performance and magnitude of e l a s t i c i t y estimates from primal and dual f l e x i b l e functional forms. One exception i s that of Burgess (1975) where translog production and cost function e l a s t i c i t i e s were derived for the same data and found to give s i g n i f i c a n t l y d i f f e r e n t information regarding substitution p o s s i b i l i t i e s . Fisher and Chung (1986) have recently calculated e l a s t i c i t y estimates from translog and Generalised Leontief production functions for three inputs ( c a p i t a l , labour and energy) using aggregate Canadian data for the period 1954 to 1982. The data is 130 that used in the MACE macro econometric model ( H e l l i w e l l , MacGregor and Padmore, 1984). This work is extended in this Appendix where e l a s t i c i t y estimates are derived from translog and GL cost function models using the same data and compared with those derived by Fisher and Chung from the primal s p e c i f i c a t i o n . The cost function estimation is extended to the recently developed Symmetric Generalised McFadden (SGM) functional form developed by Diewert and Wales (1987). This form has s i g n i f i c a n t advantages over e a r l i e r f l e x i b l e functional forms in regard to s a t i s f y i n g global curvature conditions. E l a s t i c i t y estimates are found to be quite sensitive to the s p e c i f i c a t i o n used. The methodology used in the comparison of primal and dual estimation is outlined in the following section while the results are presented in the t h i r d section. F i n a l l y , conclusions are drawn in the fourth section. A2.2. Methodology The translog and GL production function estimation is summarised below. More d e t a i l s can be found in Fisher and Chung (1986) . A detailed discussion of the properties of the translog, GL and SGM cost functions can be found in Diewert and Wales (1987) . A2.2.1 The Translog Form The 3-factor [ c a p i t a l (K), labour (L) and energy (E)] translog production function is given by; 131 InQ = a Q + a KlnK + a L l n L + a E l n E + a t t + ( 1 / 2 ) a K K ( I n K ) 2 (A2.1) + ( l / 2 ) a K L l n K l n L + a K E l n K l n E + ( 1 / 2 ) a L L ( I n L ) 2 + a L E l n L l n E + ( 1 / 2 ) a E E ( I n E ) 2 + (1/2)a t tfe 2 + a K t t l n K + a L t t l n L + a E t t l n E where Q is output, T is a time trend and symmetry has been imposed. The translog production function exhibits constant returns to scale i f : aK + a L + a E = 1 aKK + aKL + aKE = 0 (A2.2) a K L + a L L + a L E = 0 aKE + a L E + aEE = 0 a K t + a L t + a E t = 0 If the test for constant returns to scale (A2.2) is accepted and p r o f i t maximisation i s assumed then the production function (A2.1) can be estimated along with the following cost share equations: (A2.3) S K = a K + a K K l n K + a K L l n L + a K E l n E + a K t t S L = a L + a K L l n K + a L L l n L + a L E l n E + a L t f c The t h i r d share equation i s excluded since the three factor shares must sum to unity. The test for neutral technical change i s : (A2 .4) a K t + a L t + a E t = 0 E l a s t i c i t i e s of substitution are derived from the bordered Hessian of the production function, G, as follows: (A2.5) ES i ;j = IGij|/|G| where IGjjl is the i , j cofactor of G. Own price e l a s t i c i t i e s of demand are derived as follows: 132 (A2.6) ED - . = S -ES . . ID D ID The translog cost function may be represented as follows: 3 2 lnC(p,Q,t) = a 0 + Zi=i a i l n P i + a QlnQ + a t t + ( l / 2 ) a t t t + where a i j = a j i for a l l i , j ; Zi=l a i = l , Zj=l aij=0 for i=l,2,3; 3 3 Zi=l a i Q=0 and Zi=l a i t=0. By applying Shephard's Lemma cost share equations are obtained: Again the t h i r d share equation i s excluded so that the estimating system consists of (A2.7) and (A2.8). The following test for constant returns to scale can be made; (A2.9) a Q = 1; a i Q = 0, 1=1,2,; a Q Q = 0; a Q t = 0. The test for neutral technical change i s ; (A2.10) at = 0; a i t = 0, 1=1,2; a Q t = 0; a t t = °-For the estimated cost function to s a t i s f y the requirements of economic theory i t must be concave in prices at a l l the observation points. In the translog case t h i s requires the following matrix to be negative semi-definite at each observation point (Diewert and Wales 1987); (A2 . 7 ) (A2.8 ) Si(p,Q,t) = a i + Zj=i a i j l n p j + aiQlnQ + a i t t ; 1=1,2,3. (A2.ll) ^ K K - S R + S K ^ K L + S R S L ^ K L + S R S L ^ L L - S L + S L a L E + s L s E a E E - s E + s E E A K E + S K S E A K E + S K S E A L E + S L S E Allen-Uzawa e l a s t i c i t i e s of substitution are given by: (A2.12) E S i i = ( a n + S i 2 - S i ) / S i 2 133 E s i j = a i j / ( S i S j ) + 1 P a r t i a l price e l a s t i c i t i e s are given by: (A2.13) EDii = S i E S i i ; ED^ j = SjES i :j. A2.2.2 The Generalised Leontief Form The primal GL system estimated by Fisher and Chung i s : Q = aQ + aKK 1 / 2 + a L L 1 / 2 + a E E 1 / 2 + a t t + aKKK + 2aKL(KL) 1 / 2 + 2aKE(KE) 1 / 2 + aLLL + a L E ( L E ) 1 / 2 + (A2.14) aEEE + ( l / 2 ) a t t t 2 + aKttK + aLttL + aEttE PK/PQ = aKK + l/2aKK" 1 / 2 + a K L ( L / K ) 1 / 2 + aKE(E/K) 1 / 2 + aKtt PL/PQ = aLL + l / 2 a L L _ 1 / 2 + a K L ( K / L ) 1 / 2 + a L E ( E / L ) 1 / 2 + aLtt PE/PQ = aEE + l / 2 a E E - 1 / 2 + aKE(K/E) 1 / 2 + a L E ( L / E ) 1 / 2 + aEtt The test for constant returns to scale i s : (A2.15) a Q = a K = a L = a E = a t = a t t = 0 The GL cost function as sp e c i f i e d by Diewert and Wales can be represented as: C(p,Q,t) = Z i = l Z j i l a i j ( p i p j ) 1 / 2 Q + Zi=l a i P i + (A2.16) Zlll a i t P l t Q + a t ( Z i = l A 1 P i ) t + aQQ<Zi=l B i P i ) Q 2 + a t t ( Z i ! l C 1 P i ) Q t 2 where a ^ s a ^ , for i,j=l,2,3 and A i 7 B^, and Cj^  are exogenously s p e c i f i e d constants. Since a l l the c o e f f i c i e n t s of the cost function would appear in the Input demand functions derived by the use of Shephard's Lemma, the cost function and input demand functions cannot be estimated as a t o t a l system. Consequently, in this a p p l i c a t i o n the following set of input-output c o e f f i c i e n t equations was estimated: 134 (A2.17) x ^ p ^ t J / Q = X j l i a i j t p j / p i ) 1 / 2 + a^1 + a i t t + a^-A^/Q + a^B i Q + a ^ t 2 Input-output c o e f f i c i e n t equations were estimated rather than input demand equations to reduce the problem of heteroskedasticity. The test for constant returns to scale i s : (A2.18) a-x = 0, 1=1,2,3; a t = 0; a Q Q = 0. The test for the cost function not being dependent on time i s : (A2.19) a i t = 0, 1=1,2,3; a t = 0; a f c t = 0. Concavity of the cost function was examined by determining whether the matrix of second order price derivatives was negative semi-definite at each observation point. E l a s t i c i t i e s of substitution were calculated using the o r i g i n a l d e f i n i t i o n : (A2.20) E S i j = CCij/(CiCj) where Ci and C i j are, respectively, the f i r s t and second order price derivatives of the cost function. P a r t i a l price e l a s t i c i t i e s were then computed using equation (A2.13). A2 .2.3 The Symmetric Generalised McFadden Form A problem often encountered by empirical studies using the dual s p e c i f i c a t i o n is that the estimated cost function is not concave in prices. This renders the estimated e l a s t i c i t i e s suspect as they are not derived from a cost function which s a t i s f i e s the basic requirements of economic theory. While i t i s possible to force the translog form to be concave this destroys the translog's f l e x i b i l i t y properties. The SGM form developed by 135 Diewert and Wales allows us to ensure global concavity in prices with minimal loss of f l e x i b i l i t y properties. The SGM cost function i s given by: C(p,Q,t) = g(p)Q + Zi = i a ^ P i Q + Zi = i a ^ i + (A2.21) Zi = i a ^ p ^ O + a t (Z i = i A ^ J t + aQQ (£i=l B i P i ) Q 2 + a t t ( Z i = l C i P i ) Q t 2 where g(p) = (1/2) p'Sp/(T fp) and the A^, and are exogenously given. Again t h i s cost function cannot be estimated along with i t s input demand equations so the following set of input-output c o e f f i c i e n t equations was used for estimation: xi/Q = X j=iSijPj / ( r k=lTkPk) " Ti ( r k = i F j=iSkjPkPj>/2 ( E k=l T k P k ) 2 -1 2 (A2.22) + a i i +aiQ + a i t t + Ait/Q + BiQ + Ci t + u i ; 1=1,2,3. 3 where s i j = s j i and Zi=l s i j = 0 for i,j=l,2,3. Using the s p e c i f i c a t i o n (A2.22) the at/ aQQ and a t t i n (A2.21) are set to unity to produce a more f l e x i b l e form. The T i in (A2.22) are set equal to the sample midpoint quantities for the relevant inputs. The tests for constants returns to scale and the cost function not being dependent on time are again given by (A2.18) and (A2.19), respectively. If the [Sjj ] matrix i s negative semi-definite then the cost function is g l o b a l l y concave. If i t i s not, the S matrix can be made negative semi-definite without losing the function's f l e x i b i l i t y properties. 136 The e l a s t i c i t i e s of substitution were again calculated using equation (A2.20) while the price e l a s t i c i t i e s of demand were in turn derived using equation (A2.13). A2.3. Results Detailed r e s u l t s for the translog and GL production function estimation can be found in Fisher and Chung. Only the results for the cost function estimation are presented in d e t a i l in t h i s Appendix. In undertaking the cost function estimation the data were converted to price indices having a value of 1.0 for the f i r s t observation and corresponding i m p l i c i t quantities for each of the inputs obtained by d i v i d i n g the input value by the relevant price index. In the case of output the quantity was normalised to have a value of 1.0 for the f i r s t observation. The translog form was found to be invariant in terms of f i t and e l a s t i c i t i e s obtained to the sca l i n g of the data but the GL form was found to be quite sensitive to s c a l i n g . The data used are l i s t e d in Table A2.1. Fisher and Chung report results for two c a p i t a l price s p e c i f i c a t i o n s . One has a constant r e a l opportunity cost component in deriving the user cost while the other has a r e a l opportunity cost component which varies over time. Since there appears to be no th e o r e t i c a l j u s t i f i c a t i o n for imposing a constant r e a l opportunity cost of c a p i t a l the res u l t s reported here are those for the time-varying c a p i t a l p r i c e . Conclusive evidence of autocorrelation was found in a l l three dual estimating systems. In the case of the translog cost function t h i s was corrected for by use of the AUTO option which 137 imposes a constant value of the autocorrelation c o e f f i c i e n t across equations. In the GL and SGM cases autocorrelation could not e a s i l y be corrected for but did not appear to be a serious problem with the scatter of residuals showing no marked pattern with the exception of the c a p i t a l equations where a c y c l i c a l trend in the residuals could be discerned. This is not surprising given the l i k e l y misspecification of the c a p i t a l equation due to the f a i l u r e to take account of inventory, u t i l i s a t i o n rate, and other considerations which a f f e c t the most durable input. The estimated c o e f f i c i e n t s for the translog, GL and SGM cost functions and corresponding asymmtotic t-values are presented in Table A2.2 for the time-varying c a p i t a l price data. Details of the f i t of the functions and the tests for constant returns to scale (CRTS) and neutral technical change (NTC) are presented in Table A2.3. The translog cost function appears to give the best f i t to the data, having a log l i k e l i h o o d value of 421. In terms of f i t the SGM system appears to perform better than the GL. In comparing the results of the tests for CRTS the f i r s t major difference between the primal and dual systems becomes apparent. In a l l three dual systems the assumption of CRTS is very strongly rejected whereas i t i s accepted in the translog production function t e s t s . It should be noted, however, that the translog production function test for CRTS i s a r e l a t i v e l y weak one as i t is conducted on the OLS estimate of the production function alone whereas the other tests are conducted within the complete estimating systems. The assumption of NTC i s accepted for both 138 primal systems but is d e c i s i v e l y rejected for a l l three dual systems. Fisher and Chung find the translog and GL primal systems to s a t i s f y the necessary curvature conditions at a l l observation points. S i m i l a r l y , the translog dual system i s concave in input prices at a l l observation points with the matrix (A2.ll) being negative semi-definite at each point. The GL , dual system, however, does not s a t i s f y concavity at a l l observation points with the matrix of second-order price derivatives not being negative semi-definite for 12 of the 29 observations. In contrast the S matrix in the SGM case was found to be negative semi-definite and hence the estimated cost function is gl o b a l l y concave. Given the f a i l u r e of the GL system to s a t i s f y concavity at a l l the observation points the derived e l a s t i c i t i e s must be treated with suspicion. The Allen-Uzawa e l a s t i c i t i e s of substitution between each pair of the three inputs are presented in Table A2.4 for 8 of the 29 observations. In the case of capital-labour and capital-energy substitution the translog cost function e l a s t i c i t i e s generally indicate much less scope for substitution than does the translog production function. The capital-labour e l a s t i c i t i e s from the cost function are only one f i f t h the magnitude of those from the production function. Labour-energy e l a s t i c i t i e s are approximately the same for both the primal and dual sources but while t h i s i s the highest of the translog cost function e l a s t i c i t i e s , the greatest scope for substitution as indicated by the translog production function is between c a p i t a l and labour. Hence the 139 d e t a i l s of the technology conveyed by the primal and dual translog estimates d i f f e r greatly. The GL dual estimates again generally Indicate less scope for s u b s t i t u t i o n between inputs than do the primal GL estimates. The capital-labour e l a s t i c i t i e s for the dual GL system indicate that there i s almost n e g l i g i b l e scope for s u b s t i t u t i o n . The GL cost function indicates the most scope for substitution between labour and energy. The GL primal estimates indicate that c a p i t a l and energy are complements and this finding is reinforced by the dual GL estimates, contrary to the translog r e s u l t s . While the dual GL s u b s t i t u t i o n e l a s t i c i t i e s are r e l a t i v e l y stable they must be treated with suspicion due to the f a i l u r e of the concavity requirement. The dual SGM e l a s t i c i t i e s are of s i m i l a r magnitude to the translog dual estimates for capital-labour substitution and indicate the greatest scope for substitution between labour and energy as did the dual translog estimates. In the case of capital-energy substitution, however, the SGM indicates a change through time from s l i g h t s u b s t i t u t a b i l i t y to no relationship to one of increasing complementarity. From the substitution e l a s t i c i t i e s , then, one must conclude that the impression of the technology c h a r a c t e r i s t i c s conveyed i s very sen s i t i v e not only to the choice between primal and dual estimation routes but also to the choice of functional form. With the exception of the dual GL estimates which can be ruled out due to concavity v i o l a t i o n s there is l i t t l e to indicate which set of estimates (translog or SGM, primal or dual) should be preferred. 140 Moving to Table A2.5 own price e l a s t i c i t i e s of demand for each of the three Inputs are presented for the same observations. As indicated by the substitution e l a s t i c i t i e s the dual translog and GL price e l a s t i c i t i e s generally indicate much less price responsiveness. The dual translog c a p i t a l and labour e l a s t i c i t i e s indicate minimal response of input demand to own price changes. The energy own price e l a s t i c i t i e s from the primal and dual translog sources are approximately equal. The dual GL c a p i t a l price e l a s t i c i t i e s are implausibly small and s t a r t off being p o s i t i v e , further evidence that t h i s set of e l a s t i c i t i e s must be treated with suspicion. Labour own price e l a s t i c i t i e s from the GL cost function are so small as to indicate huge wage reductions being necessary to a l l e v i a t e even small unemployment l e v e l s . The dual SGM own price e l a s t i c i t y estimates are extremely close to the dual translog estimates in a l l three cases. This r e s u l t i s reassuring as the two dual forms which perform best in terms of f i t and curvature requirements produce similar own price e l a s t i c i t i e s . The only major difference between the dual translog and SGM results is the SGM finding that c a p i t a l and energy are increasingly complementary whereas the translog finds them to be substitutes. There is c o n f l i c t i n g evidence from other empirical studies as to whether c a p i t a l and energy are in fact complementary or substitutable. A2 .4. Conclusions The findings .. of t h i s study support the e a r l i e r findings of Burgess which indicate that the choice between primal and dual estimation routes i s not a t r i v i a l one. Rather, quite d i f f e r e n t 141 i m p r e s s i o n s o f t h e p r o d u c t i o n t e c h n o l o g y w i l l be o b t a i n e d d e p e n d i n g on w h i c h e s t i m a t i o n r o u t e i s a d o p t e d . F u r t h e r m o r e , t h e i n f o r m a t i o n o b t a i n e d on t h e t e c h n o l o g y a p p e a r s t o be q u i t e s e n s i t i v e t o t h e p a r t i c u l a r f u n c t i o n a l f o r m c h o s e n . W h i l e some s e t s o f r e s u l t s c a n be d i s c a r d e d b e c a u s e t h e y f a i l t o s a t i s f y c u r v a t u r e c o n d i t i o n s t h e c h o i c e be tween r e m a i n i n g o p t i o n s i s l a r g e l y a r b i t r a r y . F o r i n s t a n c e , w h i l e t h e t r a n s l o g and SGM c o s t f u n c t i o n s p r o d u c e s i m i l a r e l a s t l c l t l y e s t i m a t e s f o r most i n p u t s and b o t h s a t i s f y c u r v a t u r e c o n d i t i o n s , t h e y p r e d i c t v e r y d i f f e r e n t r e l a t i o n s h i p s be tween c a p i t a l and e n e r g y . The t r a n s l o g c o s t f u n c t i o n has t h i s p a i r a s s u b s t i t u t e s w h i l e t h e SGM c o s t f u n c t i o n has t hem as c o m p l e m e n t s . T h i s s e r v e s t o h i g h l i g h t t h e s e n s i t i v i t y o f r e s u l t s t o t h e e s t i m a t i o n c h o i c e s made . F u r t h e r m o r e , i t h i g h l i g h t s t h e r e l a t i v e l a c k o f r o b u s t n e s s o f e l a s t i c i t y e s t i m a t e s u s e d a s i n p u t t o l a r g e r e c o n o m e t r i c m o d e l s . F i n a l l y , i t may be u s e f u l t o c o n s i d e r c r i t e r i a w h i c h s h o u l d be u s e d when d e c i d i n g t o mode l t h e p r o d u c t i o n s e c t o r by p r i m a l o r d u a l m e a n s . A t t h e most b a s i c l e v e l t h e c h o i c e s h o u l d d e p e n d on o n e ' s v i e w o f w h i c h v a r i a b l e s a r e t r u l y e x o g e n o u s t o t h e f i r m . I f p r i c e s f a c e d a r e b e y o n d t h e f i r m ' s c o n t r o l b u t t h e f i r m has c o n t r o l o f _ i t s i n p u t and o u t p u t d e c i s i o n s t h e n t h e d u a l mode l wou ld seem t o be more a p p r o p r i a t e . I f , on t h e o t h e r h a n d , t h e f i r m i s c o m m i t t e d t o c e r t a i n q u a n t i t y l e v e l s and i s p r e p a r e d t o a c c e p t w h a t e v e r p r i c e c l e a r s t h e m a r k e t g i v e n i t s q u a n t i t y l e v e l s t h e n t h e p r i m a l mode l may be more a p p r o p r i a t e . A t a more p r a c t i c a l l e v e l , h o w e v e r , i t s h o u l d a l s o be r e c o g n i s e d t h a t t h e p r i m a l and d u a l m o d e l s have d i f f e r e n t 142 comparative advantages in modelling and predicting c e r t a i n vari a b l e s . For instance, i f one i s interested mainly in forecasts of output levels then the primal model i s l i k e l y to give more accurate r e s u l t s . If one i s interested in cost l e v e l s , however, the dual model i s l i k e l y to be more accurate and, hence, appropriate. Whichever choice is made and for whatever reasons the important point to bear in mind i s that the r e s u l t s obtained w i l l be sensitive to the method of estimation (primal or dual, choice of functional form, etc.) and that some experimentation with d i f f e r e n t estimation methods may be appropriate to determine the robustness of the r e s u l t s obtained. 143 TABLE A2.1 MACE DATA  Output C a p i t a l C a p i t a l Labour Year Q u a n t i t y P r i c e Q u a n t i t y P r i c e 1954 1 .0000 1 .0000 5 .8912 1 .0000 1955 1 .0945 1 .0481 6 .1646 1 .0253 1956 1 .1864 1 .1287 6 .4954 1 • 093_6 1957 1 .2137 1 .1950 6 .8532 1 .1440 1958 1 .2447 1 .2468 7 .1946 1 .1727 1959 1 .2892 1 .2767 7 .5389 1 .2087 1960 1 .3233 1 .3157 7 .8683 1 .2464 1961 1 .3555 1 .3546 8 .1408 1 .2802 1962 1 .4357 1 .4112 8 .3940 1 .3228 1963 1 .5168 1 . 4630 8 .6693 1 .3692 1964 1 .6099 1 .5026 9 .0063 1 .4312 1965 1 .7143 1 .5377 9 .4273 1 .5165 1966 1 .8328 1 .5859 9 .9122 1 .6248 1967 1 .8860 1 .6306 10 .4008 1 .7459 1968 1 .9953 1 .6838 10 .8410 1 .8373 1969 2 .0953 1 .7787 11 .2888 2 .0112 1970 2 .1458 1 .8797 11 .7445 2 .1442 1971 2 .2950 1 .9572 12 .2232 2 .2969 1972 2 . 4190 2 .0465 12 .7750 2 .4786 1973 2 .6089 2 .1812 13 . 4246 2 .7204 1974 2 .7222 2 .4083 14 .1568 3 .1314 1975 2 .7996 2 .5916 14 .8831 3 .5865 1976 2 .9713 2 .6789 15 .6112 4 .1175 Labour Energy Energy Q u a n t i t y P r i c e Q u a n t i t y 15 . 3590 1 .0000 2 .1269 15 .7400 0 .9951 2 .4860 16 .3890 0 .9604 2 .7820 16 .8338 0 .9825 3 .0051 16 .7562 0 .9857 3 .1070 17 .2674 0 .9050 3 . 4664 17 .5751 0 .8753 3 .7356 17 .8565 0 .8755 3 .9108 18 .3813 0 .8681 4 .1749 18 .8528 0 .8608 4 . 4541 19 .5810 0 .8848 4 .8503 20 .3785 0 . 8707 5 .2459 21 .2819 0 .8747 5 .6338 21 .9057 0 .8888 6 .0376 22 .3240 0 .9091 6 .5599 23 .0340 0 .8969 6 .9819 23 .2874 0 .9079 7 .4121 23 .8680 0 .9503 7 .7892 24 .5353 0 .9571 8 .4472 25 .7767 1 .0223 8 .7976 26 .8543 1 .2509 9 .3174 27 .3125 1 .4768 9 .2115 27 .8397 1 .6554 9 .7194 144 TABLE A2.1 (CONTINUED) Output Capital Capital Labour Labour Enerqy Enerqy Year Quantity Pr ice Quantity Price Quantity Pr ice Quantity 1977 3.0418 2.7352 16.3232 4.4615 28.3814 1.8997 10.1380 1978 3.1701 2.8898 16.9430 4.7199 29 .3694 2.0830 10.4261 1979 3.2782 3.2439 17.5675 5.1023 30.5767 2.3172 10.7488 1980 3.3104 3.8424 18.2553 5.5827 31.5144 2.6869 11.0033 1981 3.4178 4.7141 18.9659 6.2671 32.3699 3.4063 10.8558 1982 3.2756 5.4384 19.5231 6.9630 31.2575 3.9482 10.9788 145 TABLE A2.2  COST FUNCTION COEFFICIENTS Transloq Gen. Leontief Sym. Gen. McFadden ao 3.14 (248.3) aRK 1 .22 (2.1) SKK -2.45 (-0.4) aK 0.26 (120.2) aKL 0 .35 (1.3) SKL 19.77 (1.3) aL 0 .64 * aKE -0 . 37 (-2.6) S K E 3.68 * aE 0.10 (50.9) aLL 5 .86 (7.7) SLL -78.88 (-3.5) aQ 0.16 (1.3) aLE 1 .67 . (9.9) SLE 59 .12 * at 0.03 (4.8) aEE 1 .09 (1.6) S E E -62.80 * aKK 0.16 (36.4) aK 4 .80 (8.9) aKK 0.25 (0.2) aKL -0.14 * aL 7 .29 (8.9) aK 5.24 (9.2) aKE -0.02 (-7.4) a E -0 .15 (-0.3) aKt -0.12 (-0.2) a L L 0.17 * aKt 0 .001 (0.03) AK 0.41 (1.9) a L E -0.03 * aLt -0 .11 (-2.8) BK 0 .12 (0.2) aEE 0.05 (14.1) aEt -0 .09 (-2.9) C K 0.004 (3.5) aKQ -0.11 (-6.9) at 0 .66 (7.3) aLL 6.31 (1.0) aLQ 0.12 * aQQ -0 .80 (-1.6) aL 9.40 (1.6) a£Q -0.01 (-1.1) at t 0 .007 (4.5) aLt 0 .20 (0.6) 3Rt 0.006 (10.0) AL .-0.04 (-0.3) a L t -0.008 * BL -0.61 (-0.9) a E t 0.002 (4.4) CL -0.003 (-0.4) aQQ 0.82 (2.9) aEE 4 .27 (2.0) aQt -0.03 (-1.9) aE -1.11 (-0.5) at t O.001 (1.1) aEt A E -0.01 0.04 (-0.1) (0.4) RHO 0.56 B E C E -1.04 0.002 (-2.7) (0.7) Asymptotic t-values ln parentheses * C o e f f i c i e n t derived from summation r e s t r i c t i o n s 1 A r\ TABLE A2.3 FITS AND TESTS Translog GL SGM Primal Dual P r i m a l 1 Dual Dual Log Likelihood 310.99 421.55 128.30 120.83 134.60 Test for CRTS 5.402 114.342 32.083 129.362 126.OO3 Test for NTC 3.184 75.502 . 3.805 78.462 112.603 Concavity Violations 0 0 0 12 0 !A11 GL primal results are not corrected for autocorrelation 2 C r i t i c a l Chi-square (0.99) = 15.09 3 C r i t i c a l Chi-square (0.99) = 16.81 4 C r i t i c a l Chi-square (0.99) = 9.21 5 C r i t i c a l Chi-square (0.99) = 11.34 147 TABLE A2.4 ELASTICITIES OF SUBSTITUTION Translog Pr imai Dual Gen. Leontief  Pr imai Dual SGMcFadden Dual 1954 1958 1962 1966 1970 1974 1978 1982 1954 1958 1962 1966 1970 1974 1978 1982 Capital-Labour 1.00 0.16 1.50 0.05 0.99 0.19 1.66 0.05 0.99 0.22 1.74 0.05 0.99 0.21 1.82 0.05 0.99 0.21 1.91 0.05 0.99 0.17 1.99 0.06 0.99 0.09 2.08 0.06 1.00 0.18 2.17 0.06 Capital-Energy 0.46 0.28 -0.36 -0.34 0.42 0.29 -0.60 -0.30 0.39 0.27 -0.82 -0.27 0.38 0.21 -0.94 -0.28 0.36 0.16 -1.12 -0.28 0.36 0.14 -1.21 -0.29 0.38 0.17 -1.34 -0.28 0.41 0.41 -1.52 -0.23 0.13 0.16 0.19 0.21 0.22 0.23 0.21 0.20 0.17 0.04 •0.08 •0.16 •0.24 •0.28 -0.27 •0.14 148 TABLE A2.4 (CONTINUED) Translog  Primal Dual Gen. Leontief  Primal Dual SGMcFadden  Dual 1954 1958 1962 1966 1970 1974 1978 1982 L a b o u r - E n e r g y 0.56 0.56 0.99 0.61 0.54 0.52 1.04 0.57 0.53 0.48 1.09 0.57 0.53 0.47 1.10 0.59 0.52 0.45 1.14 0.60 0.53 0.49 1.19 0.61 0.56 0.57 1.31 0.57 0.59 0.58 1.44 0.55 1.06 0.88 0.72 0.64 0.54 0.55 0.60 0.67 149 TABLE A2.5  OWN PRICE ELASTICITIES OF DEMAND Translog  Primal Dual Gen. Leontief Pr imal Dual SGMcFadden Dual 1954 1958 1962 1966 1970 1974 1978 1982 1954 1958 1962 1966 1970 1974 1978 1982 •0.57 -0.61 -0.68 -0.70 -0.67 -0.68 -0.62 -0.68 -0.38 •0.35 -0.32 •0.31 -0.32 •0.32 -0.33 -0.32 •0.13 -0.14 -0.16 -0.15 •0.15 -0.12 •0.08 -0.15 -0.10 •0.10 -0.11 0.10 -0.10 •0.09 •0.08 •0.12 Capital -0.91 -0.99 -1.05 -1.06 -1.07 -1.09 -1.18 -1.33 Labour -0.52 -0.56 -0.57 -0.60 -0.64 -0.67 -0.68 -0.66 0.002 -0.000 -0.004 -0.007 •0.011 -0.013 •0 . 012 -0.007 -0.07 •0.07 -0.07 •0.07 -0.07 •0.07 -0.07 •0.08 •0 .10 •0.11 •0.11 •0.12 •0.12 •0.13 •0.11 •0.10 -0.13 •0.13 •0.12 •0.12 -0.11 •0.11 -0.11 -0.14 150 T A B L E A 2 . 5 ( C O N T I N U E D ) Translog Gen. Leontief SGMcFadden Primal Dual Primal Dual Dual Energy 1 9 5 4 - 0 . 3 6 - 0 . 42 - 0 . 4 6 - 0 . 3 1 - 0 . 7 3 1 9 5 8 - 0 . 4 4 - 0 . 4 0 - 0 . 4 9 - 0 . 2 8 - 0 . 6 3 1 9 6 2 - 0 . 4 4 - 0 . 3 7 - 0 . 47 - 0 . 2 7 - 0 . 5 2 1 9 6 6 - 0 . 4 6 - 0 . 3 6 - 0 . 4 4 - 0 . 2 9 - 0 . 4 7 1 9 7 0 - 0 . 4 6 - 0 . 3 3 - 0 . 4 2 - 0 . 3 0 - 0 . 3 9 1 9 7 4 - 0 . 4 1 - 0 . 3 5 - 0 . 4 3 - 0 . 3 2 - 0 . 4 1 1 9 7 8 - 0 . 4 2 - 0 . 4 2 - 0 . 4 7 - 0 . 3 2 - 0 . 4 7 1 9 8 2 - 0 . 4 4 - 0 . 4 6 - 0 . 5 9 - 0 . 2 7 - 0 . 4 7 1 5 1 

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