Economics of Forest Resources Gregory S. Amacher Markku Ollikainen Erkki Koskela The MIT Press Cambridge, Massachusetts London, England
( 2009 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. For information about special quantity discounts, please email special_sales@mitpress.mit.edu This book was set in Palatino on 3B2 by Asco Typesetters, Hong Kong. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Amacher, Gregory S., 1962 Economics of forest resources / Gregory S. Amacher, Markku Ollikainen, and Erkki Koskela. p. cm. Includes bibliographical references and index. ISBN 978-0-262-01248-5 (hardcover : alk. paper) 1. Forests and forestry Economic aspects. I. Ollikainen, Markku, 1952 II. Koskela, Erkki, 1946 III. Title. SD393.A46 2009 338.1 0 349 dc22 2008032762 10 9 8 7 6 5 4 3 2 1
Contents Preface xiii Organization of the Book xv I Basic Models 1 1 A Brief History of Forest Economics Thought 3 1.1 Prehistory of Economic Analysis of the Optimal Rotation Period 4 1.2 The Birth of the Optimal Rotation Framework 5 1.3 The Faustmann Revival 7 1.4 Revival of Age Class Models 8 2 The Faustmann Rotation Model 11 2.1 Forest Growth Technology 12 2.1.1 Properties 13 Box 2.1 Stand Growth and Its Properties 15 2.1.2 Landowner Preferences and Assumptions 18 2.2 Computing the Optimal Rotation Period 19 2.2.1 Developing the Faustmann Formula 19 Box 2.2 Rotation Ages and Comparative Statics 22 2.2.2 Comparison of Alternative Solutions 23 2.2.3 Comparative Statics 26 2.2.4 From Optimal Rotation Period to Timber Supply 28 2.3 Forest Taxation in the Faustmann Model 30 2.3.1 Harvest Taxes 31 2.3.2 Property Taxes 31 2.4 Modifications 33 2.4.1 Timber Management Effort 34 2.4.2 Duality 35
viii Contents 2.4.3 Competing Land Uses 38 2.4.4 A Life-Cycle Interpretation 41 2.5 Summary 42 3 Hartman Models of Timber and Amenity Production 43 3.1 Amenity Services 45 3.2 Landowner Preferences over Amenity Services 46 3.3 Determination of the Optimal Rotation Period 48 3.3.1 Optimal Hartman Rotation Period 48 Box 3.1 Joint Production of Timber and Amenities 49 Box 3.2 Optimal Rotation Age in the Hartman Model 54 3.3.2 Comparative Statics of the Hartman Model 56 3.3.3 Timber Supply in the Hartman Model 58 3.4 Effects of Forest Taxation 59 3.4.1 Harvest Taxes 60 3.4.2 Property Taxes 61 3.5 Amenities from Interdependent Stands 62 3.5.1 Spatial and Temporal Interdependence 63 3.5.2 Optimal Rotation Age and Stand Interdependence 66 3.6 Modifications 68 3.6.1 Competing Land Uses 69 3.6.2 Life-Cycle Models 70 3.6.3 Forests and Carbon Sinks 72 3.7 Summary 75 4 Two-Period Life-Cycle Models 77 4.1 Two-Period Timber Production Model 78 4.1.1 Harvesting Possibilities 78 Box 4.1 Short-Term Harvest Volumes in a Two-Period Model 80 4.1.2 Landowner Preferences and Consumption 81 4.1.3 Short-Term Harvesting Behavior 83 4.1.4 Forest Taxation and Timber Supply 86 Box 4.2 Short-Term Harvesting Behavior 87 4.2 Two-Period Amenity Production Model 90 4.2.1 Joint Production of Timber and Amenity Services 90 4.2.2 Landowner Preferences 91 4.2.3 Harvesting and Amenity Production 91 4.2.4 Forest Taxation 94 Box 4.3 Two-Period Amenity Model: Short-Term Harvest Volumes 95
Contents ix 4.3 Overlapping Generations Models 97 4.3.1 General Features 98 4.3.2 Bequests 99 4.4 Modifications 105 4.4.1 Some Extensions of Two-Period Models 105 4.4.2 Incidence of Forest Taxation 106 4.5 Summary 109 II Policy Problems 111 5 Design of Forest Policy Instruments 113 5.1 Optimal Taxation Faustmann Interpretations 115 5.1.1 First-Best Taxation Absence of Government Revenue Constraint 116 5.1.2 First-Best Taxation Presence of Neutral Tax and Revenue Constraint 116 5.1.3 Second-Best Taxation Distortionary Tax and Revenue Constraint 119 5.2 Optimal Taxation Hartman Interpretations 120 5.2.1 First-Best Taxation Absence of Government Revenue Constraint 120 5.2.2 First-Best Taxation Presence of Neutral Tax and Revenue Constraint 123 5.2.3 Optimal Forest Taxation Absence of Neutral Tax 124 Box 5.1 Socially Optimal Forest Tax Rates 125 5.3 Optimal Taxation Life-Cycle Interpretations 127 5.3.1 Timber Production 127 5.3.2 Joint Production of Timber and Amenity Services 128 5.4 Optimal Taxation Overlapping Generations Interpretations 130 5.4.1 Amenities as Private Goods 131 5.4.2 Amenities as Public Goods 133 5.5 Modifications 136 5.5.1 Progressive Taxation 136 5.5.2 Optimality of Progressive Forest Taxation 140 5.6 Summary 141 Appendix 5.1 Derivation of Tax Formulas in Section 5.3 142 6 Deforestation: Models and Policy Instruments 145 6.1 Basic Forms of Deforestation 146 6.1.1 Conversion to Agricultural Land 147 6.1.2 Commercial Harvesting through Concessions 147 6.1.3 Illegal Logging 148 6.1.4 Fuel Collection 149 6.2 Causes of Deforestation 149
x Contents 6.3 Forest Concessions 152 6.3.1 Optimal Policy Design Absence of Corruption 152 6.3.2 Optimal Policy Design Presence of Corruption 154 6.4 Competing Land Uses and Deforestation 160 Box 6.1 An Example of Illegal Logging and Corruption 161 6.4.1 Insecure Property Rights 165 6.4.2 Land Allocation by the Private Market 171 6.4.3 Land-Use Results 174 6.5 Summary 179 Appendix 6.1 Comparative Statics of Land Allocation 181 7 Conservation of Biodiversity in Boreal and Temperate Forests 185 7.1 Conservation Networks 187 7.2 Auctions for Biodiversity Conservation 190 7.2.1 Basic Framework 190 7.2.2 Optimal Bidding 193 7.2.3 Parametric Solution 194 7.3 Green Tree Retention 196 Box 7.1 Comparison of Simulation with the Actual TNV Outcomes 197 7.3.1 Commercial Forests 198 7.3.2 Socially Optimal Biodiversity Management 200 7.3.3 First-Best Policy Instruments 202 7.3.4 Retention Tree Volumes and Instruments Example 205 7.4 Modifications 208 7.5 Summary 210 8 Forest Age Class Models 213 8.1 Basic Structure 215 8.2 A Model with No Competing Land Use 218 8.3 A Model with Competing Land Uses 222 8.4 Carbon Policies 224 8.5 Uneven-Aged Forest Management 228 8.5.1 Dynamic Problem 229 8.5.2 Static Problem 231 8.5.3 Timber Market Considerations 232 8.6 Summary 233 Appendix 8.1 Reduction of First-Order Conditions (8.13i) (8.13v) 234 Appendix 8.2 Proof of Normality as an Optimal Stable Steady State 235
Contents xi III Advanced Topics 237 9 Uncertainty in Life-Cycle Models 239 9.1 Uncertainties and Risk Preferences 240 9.1.1 Types of Uncertainties 241 9.1.2 Risk-Bearing Behavior 243 9.2 Timber Production under Uncertainty 244 9.2.1 Timber Prices 244 9.2.2 Real Interest Rates 247 9.2.3 Forest Growth 250 9.2.4 Forest Stock 251 9.3 Amenity Production under Uncertainty 253 9.3.1 Timber Prices 253 9.3.2 Real Interest Rates 254 9.3.3 Forest Growth 255 9.3.4 Forest Stock 256 9.4 Modifications 258 9.4.1 Idiosyncratic Timber Price Risk 259 9.4.2 Aggregate Risk 260 9.5 Summary 262 Appendix 9.1 Disentangling Risk and Time 263 Appendix 9.2 Taylor Approximations and Distributions of Functions of Random Variables 264 10 Risk of Catastrophic Events 267 10.1 Stochastic Processes 268 10.2 Faustmann Interpretations 270 10.2.1 Arrival Rate Independent of Stand Age 270 10.2.2 Arrival Rate Dependent on Stand Age 275 10.3 Amenity Services 278 10.3.1 Arrival Rate Independent of Stand Age 278 10.3.2 Arrival Rate Dependent on Stand Age 282 Box 10.1 Risk of Fire Loss 284 10.4 Modifications 285 10.4.1 Partial Destruction of a Stand 286 10.4.2 Costly Protection 288 10.5 Summary 291
xii Contents 11 Stochastic Rotation Models 293 11.1 Preliminaries Stochastic Processes and Ito s Lemma 294 11.1.1 Stochastic Processes 295 11.1.2 Ito s Lemma 298 11.2 Continuous-Time Stochastic Optimal Stopping 300 11.3 Harvesting Thresholds 305 11.3.1 Single-Rotation Problem 306 11.3.2 Ongoing-Rotations Problem 310 11.4 Modifications 315 11.4.1 Stochastic Interest Rates 315 11.4.2 Stochastic Amenity Services 316 11.4.3 Catastrophic Risks 318 11.5 Summary 318 Appendix 11.1 Derivation of Equation (11.16) 320 Appendix 11.2 A Heuristic Proof of Equation (11.15) 320 12 Dynamic Models of Forest Resources 323 12.1 Dynamic Optimization 324 12.1.1 Optimal Control 324 12.1.2 Dynamic Programming and the Bellman Equation 326 12.2 Applications of Optimal Control Theory 328 12.2.1 Faustmann Interpretations 328 12.2.2 Hartman Interpretations 331 12.2.3 Old-Growth Forests: Mining, Amenity Benefits, and Deforestation 334 12.2.4 Land-Use Interpretations 339 12.2.5 A Note on the Stability of Steady States in Dynamic Models 343 12.3 Applications of Dynamic Programming 343 12.3.1 Perfect Foresight Interpretations 343 12.3.2 A Note on Stochastic Interpretations 348 12.4 Summary 349 Appendix: Mathematics Review 351 References 359 Author Index 387 Subject Index 393