Theory and Practice of International Trade Linkage Models

This book was mainly written while I stayed at the Catholic University of Louvain. Professor Anton P. Barten was the one who did not only give me a warm welcome in Louvain, but also supported my research with most valuable comments and constructive criticisms. In addition I benefitted from dis­ cussions with Erik Schokkaert, Denis de Crombrugghe and Jo Baras on various subjects, such as the small-sample correction of Chapter 9. The arduous task of transferring my neat handwriting into a readable typescript was excellently taken care of by Brs. E. Crabbe and notably Brs. F. Duij sens, even after working hours. Mrs. A. Molders prevented me of making serious abuse of the English language. My admiration for Carien, finally, is an exponential function of the patience and enthusiasm with which she sup­ ported my research. Chapter I is a general introduction to the subject of linkage models, and it contains few mathematical elaborations. Chapters 2 to 4 use more, but elementary, mathematics, and treat several aspects related to the deriva­ tion, interpretation and estimation of linkage models. Chapter 2 deals vii tll the theory of import allocation models, Chapter J treats the problem of defining and interpreting elasticities of substitution, while Chapter 4 is concerned with the econometric problems related to the estimation of mul­ tivariate models with linear restrictions, such as import allocation models.

Inhalt

1: The Linkage System.- 1.1 Introduction.- 1.2 Some Conventions.- 1.3 Elements of a World Trade Linkage Model.- 1.3.1 Data framework.- 1.3.2 Conceptual aspects.- 1.4 Methods of Trade Linkage.- 1.4.1 Global and bilateral linkage.- 1.4.2 Total and import-export allocation.- 1.4.3 Consistent and inconsistent linkage.- 1.4.4 Estimation-consistent linkage and simulation-consistent linkage.- 1.4.5 Methodological problems.- 1.4.6 The choice of a linkage model.- 1.5 A Sluice.- 1.5.1 Summary.- 1.5.2 Outline of the rest of the study.- 1.5.3 The hypotheses.- Footnotes to Chapter 1.- 2: Import Allocation Models.- 2.1 Introduction.- 2.2 Theoretical Considerations.- 2.2.1 The aggregator function.- 2.2.2 Separability.- 2.2.3 The aggregation problem.- 2.2.4 The adding-up condition.- 2.3 Empirical Models.- 2.3.1 The CES model.- 2.3.2 Other models.- 2.4 Summary and Concluding Remarks.- Footnotes to Chapter 2.- 3: On the Use of Elasticities of Substitution.- 3.1 Introduction.- 3.2 Basic Definitions.- 3.2.1 Notation.- 3.2.2 The two-factor case.- 3.2.3 Multifactor elasticities of substitution.- 3.3 The Nature of the Experiment.- 3.3.1 Constant output (constrained cost minimization).- 3.3.2 Constant cost (constrained output maximization).- 3.3.3 Constant marginal cost (profit maximization).- 3.4 A Framework for Elasticities.- 3.4.1 One-factor, one-price elasticities of substitution (OOES).- 3.4.2 Two-factor, one-price elasticities of substitution (TOES).- 3.4.3 Two-factor, two-price elasticities of substitution (TTES).- 3.5 A Generalisation of the Two-Factor Case ?.- 3.6 Short-Run Elasticities of Substitution.- 3.7 Constant Elasticities of Substitution.- 3.8 Summary and Concluding Remarks.- Footnotes to Chapter 3.- 4 Maximum Likelihood Estimation of Nonlinear Models with Linear Constraints on the Functional Form.- 4.1 Introduction.- 4.2 Constrained Model and Lopped Model.- 4.3 A Homoscedastic Covariance Matrix.- 4.3.1 The case k=l: one constraint.- 4.3.2 The case k?l: more than one constraint.- 4.4 A Special Case with a Heteroscedastic Covariance Matrix.- 4.5 Summary and Conclusions.- Footnotes to Chapter 4.- 5: A Model with Pairwise Differing Elasticities of Substitution.- 5.1 Introduction.- 5.2 The Cresh Model with Constant Returns to Scale.- 5.2.1 The choice for the CRESH function.- 5.2.2 Definition.- 5.2.3 First-order conditions.- 5.2.4 Elasticities of substitution.- 5.2.5 Second-order conditions.- 5.3 Three Approximations.- 5.3.1 A linearization in levels.- 5.3.2 A loglinear approximation.- 5.3.3 A differential approximation.- 5.4 An Interpretation as Total Allocation Model.- 5.5 Summary and Conclusions.- Footnotes to Chapter 5.- 6: Econometric Specification.- 6.1 Introduction.- 6.2 A Further Simplification.- 6.3 Stochastic Specification.- 6.4 Static Model Without Time Trend.- 6.5 Static Model With Time Trend.- 6.6 Dynamic Model Without Time Trend.- 6.7 Dynamic Model With Time Trend.- 6.8 Summary and Concluding Remarks.- Footnotes to Chapter 6.- 7: The Data.- 7.1 Introduction.- 7.2 Compatibility of Classifications.- 7.3 Price Indices; Current and Constant Prices.- 7.4 Anomalies.- 7.5 The Domestic Aggregate.- 7.6 Concluding Remarks.- Appendix 7.A Goods Classification.- Appendix 7.B Composition of the Zones.- Footnotes to Chapter 7.- 8: Estimation.- 8.1 Introduction.- 8.2 Model Characteristics.- 8.3 The Covariance Matrix.- 8.4 The Aggregate Trade Model.- 8.4.1 Estimation.- 8.4.2 Functional forms.- 8.5 Models Per Category of Goods.- 8.6 Summary and Concluding Remarks.- Appendix 8.A Detailed Estimation Results.- Footnotes to Chapter 8.- 9: Hypothesis Testing.- 9.1 Introduction.- 9.2 The General Test Procedure.- 9.3 Weak Separability.- 9.4 Classification of Partners.- 9.4.1 An analytical example.- 9.4.2 Test procedure.- 9.4.3 Test results.- 9.5 Classification of Goods.- 9.5.1 Test procedure.- 9.5.2 Test results.- 9.6 Summary and Concluding Remarks.- Appendix 9.A A Small-Sample Correction for the Likelihood Ratio Test.- Footnotes to Chapter 9.- 10: Conclusions.- 10.1 Theory.- 10.2 Practice.- 10.3 Suggestions for Further Research.- References.- Author Index.