Ebook Export and import price index manual: Theory and practice

Ebook Export and import price index manual: Theory and practice cover many topics; they elaborate on the different practices currently in use, propose alternatives whenever possible, and discuss the advantages and disadvantages of each alternative. Given its comprehensive nature, the manual is expected to satisfy the needs of many users in addition to national statistical offices and international organizations, particularly businesses,... Đề tài Hoàn thiện công tác quản trị nhân sự tại Công ty TNHH Mộc Khải Tuyên được nghiên cứu nhằm giúp công ty TNHH Mộc Khải Tuyên làm rõ được thực trạng công tác quản trị nhân sự trong công ty như thế nào từ đó đề ra các giải pháp giúp công ty hoàn thiện công tác quản trị nhân sự tốt hơn trong thời gian tới.

INTERNATIONAL MONETARY FUND Export and Import Price Index Manual Theory and Practice International Labour Office International Monetary Fund Organisation for Economic Co-operation and Development Statistical Office of the European Communities (Eurostat) United Nations Economic Commission for Europe The World Bank d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d INTERNATIONAL MONETARY FUND Export and Import Price Index Manual Theory and Practice International Labour Office International Monetary Fund Organisation for Economic Co-operation and Development Statistical Office of the European Communities (Eurostat) United Nations Economic Commission for Europe The World Bank 2009 d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d Copyright © 2009 International Labour Organization International Monetary Fund Organisation for Economic Co-operation and Development Statistical Office of the European Commission (Eurostat) United Nations Economic Commission for Europe The World Bank Production: IMF Multimedia Services Section All rights reserved Manufactured in the United States of America ISBN 978-1-58906-780-6 Cataloging-in-Publication Data Export and import price index manual : theory and practice – [Washington, D.C.] : International Monetary Fund, 2009 p ; cm “International Labour Organization ; International Monetary Fund ; Organisation for Economic Co-operation and Development ; Statistical Office of the European Communities (Eurostat) ; United Nations Economic Commission for Europe ; World Bank.” Includes bibliographical references and index ISBN 978-1-58906-780-6 Price indexes – Statistics – Handbooks, manuals, etc Imports – Prices – Statistics – Handbooks, manuals, etc Exports – Prices – Statistics – Handbooks, manuals, etc I Title II International Monetary Fund HB225.E976 2009 Please send orders to: International Monetary Fund, Publication Services 700 19th Street, N.W., Washington, DC 20431, U.S.A Tel.: (202) 623-7430 Fax: (202) 623-7201 E-mail: publications@imf.org Internet: www.imfbookstore.org d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d Contents Foreword xi Preface xiii A Export and Import Price Indices and Unit Value Indices B The Export and Import Price Index Manual C Background to the Present Revision D Organization of the Revision E Acknowledgments xiii xiv xv xxi xxii Reader’s Guide xxv A An Overview of the Sequence of Chapters xxv B Alternative Reading Plans xxviii C A Note on the Bibliography xxix A Summary of Export and Import Price Index Methodology A Introduction B Unit Value Indices and Price Indices C The Uses of XMPIs D Concepts, Scope, and Classifications E Source Data: Weights F Source Data: Prices G Transfer Prices H Missing Prices and Adjusting Prices for Quality Change I Commodity Substitution and New Goods J Basic Index Number Formulas and the Axiomatic and Economic Approaches to XMPIs K Elementary Price Indices L Basic Index Calculations M Organization and Management N Publication and Dissemination O Terms of Trade Appendix 1.1: An Overview of the Steps Necessary for Developing XMPIs 10 13 17 21 21 27 28 48 54 57 57 58 59 Unit Value Indices 71 A Introduction B International Recommendations C Unit Value Indices and Their Potential Bias D Evidence of Unit Value Bias E Strategic Options: Compilation of Hybrid Indices F Strategic Options: Improve Unit Value Indices G Strategic Options: Move to Establishment-Based Price Surveys H Summary Appendix 2.1: On Limitations to the Benefits of Stratification 71 73 74 80 81 85 87 88 90 The Price and Volume of International Trade: Background, Purpose, and Uses of Export and Import Price Indices 91 A Background and Origins of Price Indices B Official Price Indices C International Standards for Price Indices D Purpose of Export and Import Price Indices E Family of XMPIs 91 92 94 96 99 iii d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d EXPORT AND IMPORT PRICE INDEX MANUAL: THEORY AND PRACTICE iv Coverage, Valuation, and Classifications 101 A Introduction B Coverage C Valuation D Classifications 101 101 104 113 Data Sources 116 A Administrative Sources B Survey Sources C Summary 116 120 123 Sampling Issues in Price Collection 124 A Introduction B Starting Position C Goods: Testing Customs Elementary Aggregates for Multiple Elementary Items D Goods and Services: Surveying Enterprises to Identify Elementary Items E Common Problems in Price Survey Sampling F Sample Design G An Example of Sample Selection and Recruitment of Establishments H Sample Maintenance and Rotation I Summary of Sampling Strategies for the XMPI 124 126 127 129 131 134 140 144 146 Price Collection 148 A Introduction B Timing and Frequency of Price Collection C Commodity Specification D Collection Procedures E Respondent Relations F Verification G Related Price Issues 148 148 151 153 162 162 163 Treatment of Quality Change 164 A Introduction B What Is Meant by Quality Change C An Introduction to Methods of Quality Adjustment When Matched Items Are Unavailable D Implicit Methods E Explicit Methods F Choosing a Quality-Adjustment Method G High-Technology and Other Sectors with Rapid Turnover of Models H Long-Run and Short-Run Comparisons Appendix 8.1: Data for Hedonic Regression Illustration 164 168 174 177 185 195 198 205 210 Commodity Substitution, Sample Space, and New Goods 212 A Introduction B Sampling Issues and Matching C Information Requirements for a Strategy for Quality Adjustment D The Incorporation of New Goods E Summary Appendix 9.1: Appearance and Disappearance of Goods and Establishments Appendix 9.2: New Goods and Substitution 212 213 216 217 223 224 228 10 XMPI Calculation in Practice 230 A Introduction 230 CONTENTS B Calculation of Price Indices for Elementary Aggregates C Calculation of Higher-Level Indices D Data Editing 231 248 263 11 Treatment of Specific Products and Issues 269 A Introduction B Agriculture, SITC C Clothing, SITC 84 D Crude Petroleum and Gasoline, SITC 33 E Metals, SITC 68 F Electronic Computers, SITC 75 G Motor Vehicles, SITC 78 H Services I Pricing Issues of Importance in International Trade 269 270 274 275 276 276 278 280 282 12 Errors and Bias in XMPIs 287 A Introduction B Errors and Bias C Use, Coverage, and Valuation D Sampling Error and Bias on Initiation E Sampling Error and Bias: The Dynamic Universe F Price Measurement: Response Error and Bias, Quality Change, and New Goods G Substitution Bias H Administrative Data I World Commodity Prices 287 289 291 292 293 293 295 296 297 13 Organization and Management 298 A Introduction B Organizational Structure and Resource Management C The Sampling Process D The Initiation Process E The Repricing Process F The Estimation Process G The Publication and Documentation Process H Quality Assurance 298 299 303 303 304 307 308 309 14 Publication, Dissemination, and User Relations 311 A Introduction B Types of Presentation C Dissemination Issues D User Consultation E Press Release Example 311 311 317 319 320 15 The System of Price Statistics 322 A Introduction B Major Goods and Services Price Statistics and National Accounts C International Comparisons of Expenditure on Goods and Services 322 323 357 16 Basic Index Number Theory 358 A Introduction B Decomposition of Value Aggregates into Price and Quantity Components C Symmetric Averages of Fixed-Basket Price Indices D Annual Weights and Monthly Price Indices E Divisia Index and Discrete Approximations 358 359 362 366 376 d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d v d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d EXPORT AND IMPORT PRICE INDEX MANUAL: THEORY AND PRACTICE vi F Fixed-Base Versus Chain Indices Appendix 16.1: Relationship Between Paasche and Laspeyres Indices Appendix 16.2: Relationship Between Lowe and Laspeyres Indices Appendix 16.3: Relationship Between Young Index and Its Time Antithesis 379 383 383 384 17 Axiomatic and Stochastic Approaches to Index Number Theory 386 A Introduction B The Levels Approach to Index Number Theory C First Axiomatic Approach to Bilateral Price Indices D Stochastic Approach to Price Indices E Second Axiomatic Approach to Bilateral Price Indices F Test Properties of Young and Lowe Indices Appendix 17.1: Proof of Optimality of Törnqvist Theil Price Index in Second Bilateral Test Approach 386 388 390 398 403 410 18 Economic Approach 413 A Introduction B Economic Theory and the Resident’s and Nonresident’s Approach C Setting the Stage D The Export Price Index for a Single Establishment E Superlative Export Output Price Indices F Import Price Indices 413 414 415 419 425 439 19 Transfer Prices 444 A The Transfer Price Problem B Alternative Transfer Pricing Concepts C Transfer Price Concepts When There Are No Trade or Income Taxes D Transfer Pricing When There Are Trade or Profits Taxes and No External Market E Which Transfer Prices Can Be Usefully Collected by Statistical Agencies? F Conclusion 444 446 447 449 454 459 20 Exports and Imports from Production and Expenditure Approaches and Associated Price Indices Using a Simplified Example and an Artificial Data Set 460 A Introduction B Expanded Production Accounts for the Treatment of International Trade Flows C The Artificial Data Set D The Artificial Data Set for Domestic Final Demand E National Producer Price Indices F Value-Added Price Deflators G Two-Stage Value-Added Price Deflators H Final Demand Price Indices I Conclusion 460 462 474 483 490 492 495 497 500 21 Elementary Indices 501 A Introduction B Ideal Elementary Indices C Elementary Indices Used in Practice D Numerical Relationships Between the Frequently Used Elementary Indices E The Axiomatic Approach to Elementary Indices F The Economic Approach to Elementary Indices G Sampling Approach to Elementary Indices H A Simple Stochastic Approach to Elementary Indices I Conclusion 501 503 506 507 509 511 512 517 518 411 CONTENTS 22 Quality Change and Hedonics 519 A New and Disappearing Items and Quality Change: Introduction B Hedonic Prices and Implicit Markets C Hedonic Indices D New Goods and Services Appendix 22.1: Some Econometric Issues 519 521 531 538 538 23 Treatment of Seasonal Products 546 A Problem of Seasonal Products B A Seasonal Product Data Set C Year-over-Year Monthly Indices D Year-over-Year Annual Indices E Rolling-Year Annual Indices F Predicting Rolling-Year Index Using Current-Period Year-over-Year Monthly Index G Maximum Overlap Month-to-Month Price Indices H Annual Basket Indices with Carryforward of Unavailable Prices I Annual Basket Indices with Imputation of Unavailable Prices J Bean and Stine Type C or Rothwell Indices K Forecasting Rolling-Year Indices Using Month-to-Month Annual Basket Indices L Conclusions 546 548 548 556 558 561 564 569 571 572 574 579 24 Measuring the Effects of Changes in the Terms of Trade 581 A Introduction B The Effects of Changes in the Real Price of Exports C The Effects of Changes in the Real Price of Imports D The Combined Effects of Changes in the Real Prices of Exports and Imports E The Effects on Household Cost-of-Living Indices of Changes in the Prices of Directly Imported Goods and Services F Conclusion 581 584 591 594 Glossary 603 Bibliography 629 Index 644 Illustration of Unit Value Bias Example of Assigning Weights Data Sources for Export and Import Price Indices Unit Values and Product Mix Using Price Surveys and Customs Unit Values in the Same “Hybrid” Index Step for Establishment Sample Selection Step for Establishment Sample Selection Selection of Products Using the Ranking Method Price-Determining Characteristics Estimating a Quality-Adjusted Price Example of Overlap Method of Quality Adjustment Example of the Bias from Implicit Quality Adjustment for r2  1.00 Hedonic Regression Results for Dell and Compaq PCs Example of Long-Run and Short-Run Comparisons Sample Augmentation Example Calculation of Price Indices for an Elementary Aggregate Properties of Main Elementary Aggregate Index Formulas Imputation of Temporarily Missing Prices Disappearing Commodities and Their Replacements with No Overlap 75 121 123 130 132 141 141 143 152 176 177 182 190 206 221 233 235 241 242 d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d 597 602 Tables 2.1 5.1 5.2 6.1 6.2 6.3 6.4 6.5 7.1 8.1 8.2 8.3 8.4 8.5 9.1 10.1 10.2 10.3 10.4 vii d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d EXPORT AND IMPORT PRICE INDEX MANUAL: THEORY AND PRACTICE 10.5 10.6 10.7 10.8 10.9 10.10 10.11 10.12 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 15.10 15.11 15.12 15.13 15.14 15.15 15.16 18.1 20.1 20.2 20.3 20.4 20.5 20.6 20.7 20.8 20.9 20.10 20.11 20.12 20.13 20.14 20.15 20.16 20.17 20.18 20.19 20.20 20.21 20.22 20.23 20.24 20.25 20.26 20.27 viii Disappearing and Replacement Commodities with Overlapping Prices Calculation of a Weighted Elementary Index Calculation of Unit Value Index for Sample Commodity Category The Aggregation of the Elementary Price Indices Price Updating of Weights Between Weight and Price Reference Periods Calculation of a Chained Index Calculation of a Chained Index Using Linking Coefficients Decomposition of Index Change from January 2002 to January 2003 Production Account for an Establishment, Institutional Unit, or Institutional Sector Production Account with Product Detail for an Establishment or Local Kind of Activity Unit Industry/Activity Production Account with Detail for Products and Market/Nonmarket Use of Income Account for Institutional Units and Sectors Use of Income Account with Product Detail for Institutional Units and Sectors Use of Income Account with Product Detail for the Total Economy Capital Account Capital Account with Product Detail External Account of Goods and Services External Account of Goods and Services with Product Detail The Supply and Use Table (SUT) Location and Coverage of the Major Price Indices in the Supply and Use Table Definition of Scope, Price Relatives, Coverage, and Weights for Major Price Indices Generation of Income Account for Establishment, Institutional Unit, or Institutional Sector Generation of Income Account for Establishment and Industry with Labor Services (Occupational) Detail A Framework for Price Statistics Behavioral Assumptions for Resident’s and Nonresident’s Approaches Domestic Supply Matrix in Current Period Values Domestic Use Matrix in Current Period Values Export or ROW Supply Matrix in Current Period Values Import or ROW Use Matrix in Current Period Values Domestic Supply Matrix in Current Period Values with Commodity Taxes Export or ROW Supply Matrix in Current Period Values with Export Taxes Import or ROW Use Matrix in Current Period Values with Import Taxes Constant Dollar Domestic Supply Matrix Volume Domestic Use Matrix Volume ROW Supply or Export by Industry and Commodity Matrix Volume ROW Use or Import by Industry and Commodity Matrix Real Domestic Supply Matrix Real Domestic Use Matrix Real ROW Supply or Export by Industry and Commodity Matrix Real ROW Use or Import by Industry and Commodity Matrix Nominal Value Domestic Supply Matrix with Commodity Taxes Nominal Value Domestic Use Matrix Value ROW Supply or Export by Industry and Commodity Matrix Value ROW Use or Import by Industry and Commodity Matrix Industry G Final Demand Prices for All Transactions Industry G Commodity Taxes Industry G Quantities of Outputs and Intermediate Inputs Industry S Final Demand Prices Industry S Commodity Taxes Industry S Quantities of Outputs and Inputs Industry T Final Demand Prices Industry T Commodity Taxes 244 245 247 251 253 256 257 262 327 328 329 332 334 335 337 338 339 339 342 348 349 352 352 353 415 463 464 464 464 469 469 469 470 470 470 470 474 475 475 475 476 477 477 477 478 478 479 479 481 481 482 482 CONTENTS 20.28 20.29 20.30 20.31 20.32 20.33 20.34 20.35 20.36 20.37 20.38 20.39 20.40 20.41 20.42 20.43 20.44 20.45 20.46 20.47 20.48 20.49 20.50 20.51 20.52 20.53 20.54 20.55 20.56 20.57 20.58 20.59 20.60 20.61 20.62 20.63 20.64 20.65 20.66 20.67 23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8 23.9 23.10 Industry T Quantities of Outputs and Inputs Prices for Six Domestic Final Demand Commodities Quantities for Six Domestic Final Demand Commodities Total Expenditures and Expenditure Shares for Six Domestic Final Demand Commodities Fixed-Base Laspeyres, Paasche, Carli, and Jevons Indices Chained Laspeyres, Paasche, Carli, and Jevons Indices Asymmetrically Weighted Fixed-Base Indices Asymmetrically Weighted Chained Indices Symmetrically Weighted Fixed-Base Indices Symmetrically Weighted Chained Indices Single-Stage and Two-Stage Fixed-Base Superlative Indices Single-Stage and Two-Stage Chained Superlative Indices Diewert Additive Percentage Change Decomposition of the Fisher Index Van Ijzeren Additive Percentage Change Decomposition of the Fisher Index Fixed-Base National Domestic Gross Output Price Indices at Producer Prices Chained National Domestic Gross Output Price Indices at Producer Prices National Fixed-Base Export Price Indices at Producer Prices National Chained Export Price Indices at Producer Prices Fixed-Base National Domestic Intermediate Input Price Indices at Producer Prices Chained National Domestic Intermediate Input Price Indices at Producer Prices Fixed-Base National Import Price Indices at Producer Prices Chained National Import Price Indices at Producer Prices Fixed-Base Value-Added Price Deflators for Industry G Chained Value-Added Price Deflators for Industry G Fixed-Base Value-Added Price Deflators for Industry S Chained Value-Added Price Deflators for Industry S Fixed-Base Value-Added Price Deflators for Industry T Chained Value-Added Price Deflators for Industry T Fixed-Base National Value-Added Deflators Chained National Value-Added Deflators Fixed-Base Single-Stage and Two-Stage National Value-Added Deflators: Aggregation over Industries Method Chained Single-Stage and Two-Stage National Value-Added Deflators: Aggregation over Industries Method Fixed-Base Single-Stage and Two-Stage National Value-Added Deflators: Aggregation over Commodities Method Chained Single-Stage and Two-Stage National Value-Added Deflators: Aggregation over Commodities Method Fixed-Base and Chained Domestic Final Demand Deflators Fixed-Base and Chained Export Price Indices at Final Demand Prices Fixed-Base and Chained Import Price Indices at Final Demand Prices Fixed-Base and Chained GDP Deflators Fixed-Base GDP Deflators Calculated in Two Stages Chained GDP Deflators Calculated in Two Stages Artificial Seasonal Data Set: Prices Artificial Seasonal Data Set: Quantities Year-over-Year Monthly Fixed-Base Laspeyres Indices Year-over-Year Monthly Fixed-Base Paasche Indices Year-over-Year Monthly Fixed-Base Fisher Indices Year-over-Year Approximate Monthly Fixed-Base Paasche Indices Year-over-Year Approximate Monthly Fixed-Base Fisher Indices Year-over-Year Monthly Chained Laspeyres Indices Year-over-Year Monthly Chained Paasche Indices Year-over-Year Monthly Chained Fisher Indices d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d 483 483 483 484 484 485 485 486 487 487 488 488 489 490 490 490 491 491 491 491 492 492 493 493 493 493 494 494 494 495 496 496 496 497 497 498 498 498 499 499 549 550 553 553 553 554 554 554 554 554 ix EXPORT AND IMPORT PRICE INDEX MANUAL: THEORY AND PRACTICE 22.101 There is a situation in which an unweighted OLS estimator is preferred This is when markets are in perfect hedonic equilibrium Observations with unusual characteristics, say old or new models, would take values that were particularly dispersed from their means and thus increase the variation of the sample for the same underlying model Such increased variation leads to an increase in the efficiency of the estimates However, theory and empirical observation (see Silver and Heravi, 2005) find that such outliers not have the same structural relationships as other models If the sales shares of these new and old models are low relative to the number of models they represent in the market, then an OLS regression would give them undue weight Multicollinearity 22.102 There are a priori reasons to expect for some commodities that the variation in the values of one characteristic will not be independent of one or a linear combination of other z characteristics As a result, parameter estimates will be unbiased yet imprecise To illustrate this, a plot of the confidence interval for one parameter estimate against another collinear one is often described as elliptical, because the combinations of possible values they may take can easily drift from, say, high values of 1 and low 2 to higher values of 2 and lower values of 1 Because the sample size for the estimates is effectively reduced, relatively small additions to and deletions from the sample may affect the parameter estimates more than would be expected These are standard statistical issues, and the reader is referred to Maddala (1988) and Kennedy (2003) In a hedonic regression, multicollinearity might be expected because some characteristics may be technologically tied to others Producers including one characteristic may need to include others for it all to work, whereas for the consumer side, purchasers buying, for example, an up-market brand may expect a certain bundle of features to come with it Triplett (2004) argued strongly for the researcher to be aware of the features of the product and consumer market There are standard, though not completely reliable, indicators of multicollinearity (such as variance inflation factors), but an exploration of its nature is greatly aided by an understanding of the market along with exploration of the effects of including and excluding individual variables on the signs and coefficients and on other diagnostic test statistics (see Maddala, 1988).41 41Triplett (2004) stressed the point that R2 alone is insufficient for this purpose 544 22.103 If a subset of the estimated coefficients from a hedonic regression is to be used to quality adjust a noncomparable replacement price, and if there is multicollinearity between variables in this subset and other independent variables, then the estimates of the coefficients to be used for the adjustment will be imprecise The multicollinearity effectively reduces the sample size, and some of the effects of the variables in the subset may be wrongly ascribed to the other independent variables The extent of this error will be determined by the strength of the multiple-correlation coefficient between all such “independent” variables (the multicollinearity), the standard error or “fit” of the regression, the dispersion of the independent variable concerned, and the sample size These all affect the precision of the estimates, because they are components in the standard error of the t-statistics Even if multicollinearity is expected to be quite high, large sample sizes and a well-fitting model may reduce the standard errors on the t-statistics to acceptable levels If multicollinearity is expected to be severe, the predicted value for an item’s price may be computed using the whole regression and an adjustment made using the predicted value, as explained in Chapter 8, Section E.4, because there is a sense in which it would not matter whether the variation was wrongly attributed to either 1 or 2 If dummy variable hedonic indices are being calculated (Section B.3 above), the time trend will be collinear with an included variable if a new feature appears in a new month for the vast majority of the items, so that the data are not rich enough to allow the separate effects of the coefficient on the time dummy to be precisely identified The extent of the imprecision of the coefficient on the time dummy will be determined by the aforementioned factors A similar argument holds for omitted variable bias Omitted variable bias 22.104 The exclusion of tastes and technology and community characteristics has already been discussed The concern here is with product characteristics Consider again the use of a subset of the estimated coefficients from a hedonic regression to quality adjust a noncomparable replacement price It is well established that multicollinearity of omitted variables with included variables leads to bias in the estimates of the coefficients of included ones If omitted variables are independent of the included variables, then the estimates of the coefficients on the included variables are unbiased This is acceptable in this instance; the only caveat is that the quality adjustment for the replacement item may also require an adjustment for these d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d 22 QUALITY CHANGE AND HEDONICS omitted variables, and this adjustment, as noted by Triplett (2004), has to be undertaken using a separate method and data But what if the omitted variable is multicollinear with a subset of included ones, and these included ones are to be used to quality adjust a noncomparable item? In this case, the coefficient on the subset of the included variables may be wrongly picking up some of the omitted variables’ effects The coefficients will be used to quality adjust prices for items that differ only with regard to this subset of included variables, and the price comparison will be biased if the characteristics of both included and omitted variables have different price changes For hedonic indices using a dummy time trend, the estimates of quality-adjusted price changes will suffer from a d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d similar bias if omitted variables multicollinear with the time change are excluded from the regression What are picked up as quality-adjusted price changes over time may, in part, be changes due to the prices of these excluded variables This requires that the prices on the omitted characteristics follow a different trend Such effects are most likely when there are gradual improvements in the quality of items, such as the reliability and safety of consumer durables,42 which are difficult to measure, at least for the sample of items in real time The quality-adjusted price changes will thus overstate price changes in such instances 42There are some commodity areas, such as airline comfort, that have been argued to have overall patterns of decreasing quality 545 d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d 23 Treatment of Seasonal Products A Problem of Seasonal Products 23.1 The existence of seasonal products poses some significant challenges for price statisticians Seasonal commodities are products that are either (1) not available in the marketplace during certain seasons of the year or (2) available throughout the year but there are regular fluctuations in prices or quantities that are synchronized with the season or the time of the year.1 A commodity that satisfies (1) is termed a strongly seasonal commodity, whereas a commodity that satisfies (2) is called a weakly seasonal commodity Strongly seasonal products create the biggest problems for price statisticians in the context of producing monthly or quarterly export and import price indices (XMPIs) If a product price is available in only one of the two months (or quarters) being compared, then it is not possible to calculate a relative price for the product, and traditional bilateral index number theory breaks down In other words, if a product is present in one month but not the next, how can the month-to-month amount of price change for that product be computed?2 In this chapter, a solution to this problem is presented that works even if the products produced are entirely different for each month of the year.3 23.2 There are two main sources of seasonal fluctuations in prices and quantities: (1) climate and (2) custom.4 In the first category, fluctuations in temperature, 1This classification of seasonal commodities corresponds to Balk’s narrow and wide sense seasonal commodities; see Balk (1980a, p 7; 1980b, p 110; and 1980c, p 68) Diewert (1998b, p 457) used the terms “type 1” and “type 2” seasonality Zarnowitz was perhaps the first to note the importance of this problem: “But the main problem introduced by the seasonal change is precisely that the market basket is different in the consecutive months (seasons), not only in weights but presumably often also in its very composition by commodities This is a general and complex problem which will have to be dealt with separately at later stages of our analysis” (1961, p 238) However, the same products must reappear each year for each separate month! This classification dates back to Mitchell at least: “Two types of seasons produce annually recurring variations in economic 546 precipitation, and hours of daylight cause fluctuations in the demand or supply for many products; for example, think of summer versus winter clothing, the demand for light and heat, vacations, and so on With respect to custom and convention as a cause of seasonal fluctuations, consider the following quotation: Conventional seasons have many origins—ancient religious observances, folk customs, fashions, business practices, statute law Many of the conventional seasons have considerable effects on economic behaviour We can count on active retail buying before Christmas, on the Thanksgiving demand for turkeys, on the first of July demand for fireworks, on the preparations for June weddings, on heavy dividend and interest payments at the beginning of each quarter, on an increase in bankruptcies in January, and so on (Mitchell, 1927, p 237) 23.3 Examples of important seasonal products are the following: many food items; alcoholic beverages; many clothing and footwear items; water, heating oil, and electricity; flowers and garden supplies; vehicle purchases, vehicle operation; many entertainment and recreation expenditures; books; insurance expenditures; wedding expenditures; recreational equipment; toys and games; software; air travel; and tourism purchases For a typical country, seasonal purchases will often amount to one-fifth to one-third of all consumer purchases.5 23.4 In the context of producing monthly or quarterly XMPIs, it must be recognized that there is no completely satisfactory way of dealing with strongly seasonal products If a product is present in one month but missing in the next month, then none of the index number theories that were considered in Chapters 16 activity—those which are due to climates and those which are due to conventions” (1927, p 236) 5Alterman, Diewert, and Feenstra (1999, p 151) found that over the 40 months between September 1993 and December 1996, somewhere between 23 and 40 percent of U.S imports and exports exhibited seasonal variations in quantities, whereas only about percent of U.S export and import prices exhibited seasonal fluctuations 23 TREATMENT OF SEASONAL PRODUCTS through 21 can be applied because all of these theories assumed that the dimensionality of the product space was constant for the two periods being compared However, if seasonal products are present in the market during each season, then, in theory, traditional index number theory can be applied in order to construct month-to-month or quarter-to-quarter price indices This traditional approach to the treatment of seasonal products is followed in Sections H, I, and J of this chapter The reason why this straightforward approach is deferred to the end of the chapter is twofold: • The approach that restricts the index to products that are present in every period often does not work well in the sense that systematic biases can occur; and • The approach is not fully representative; that is, it does not make use of information on products that are not present in every month or quarter 23.5 In Section B, a modified version of Turvey’s (1979) artificial data set is introduced This data set is used to numerically evaluate all of the index number formula that are suggested in this chapter It will be seen in Section G that large seasonal fluctuations in volumes combined with systematic seasonal changes in price can make month-to-month or quarter-to-quarter price indices behave rather poorly d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d year-over-year indices and they are found to work very well on this data set 23.8 The rolling-year indices can provide an accurate gauge of the movement of prices in the current rolling year compared to the base year However, this measure of price inflation can be regarded as a measure of inflation for a year that is centered around a month that is six months prior to the last month in the current rolling year As a result, for some policy purposes, this type of index is not as useful as an index that compares the prices of the current month to the previous month, so that more up-to-date information on the movement of prices can be obtained However, in Section F, it is shown that under certain conditions, the currentmonth year-over-year monthly index, along with last month’s year-over-year monthly index, can successfully predict or forecast a rolling-year index that is centered around the current month 23.6 Even though existing index number theory cannot deal satisfactorily with seasonal products in the context of constructing month-to-month indices of consumer and producer prices, it can deal satisfactorily with seasonal products if the focus is changed from month-to-month XMPIs to XMPIs that compare the prices of one month with the prices of the same month in a previous year Thus, in Section C, year-over-year monthly XMPIs are studied Turvey’s seasonal data set is used to evaluate the performance of these indices, and they are found to perform quite well 23.9 The year-over-year indices defined in Section C and their annual averages studied in Sections D and E offer a theoretically satisfactory method for dealing with strongly seasonal products, that is, products that are available only during certain seasons of the year However, these methods rely on the year-over-year comparison of prices; therefore, these methods cannot be used in the month-to-month or quarter-to-quarter type of index, which is typically the main focus of a consumer and a producer price program Thus, there is a need for another type of index, one that may not have strong theoretical foundations but can deal with seasonal products in the context of producing a month-tomonth index In Section G, such an index is introduced, and it is implemented using the artificial data set for the products that are available during each month of the year Unfortunately, owing to the seasonality in both prices and quantities in the always available products, this type of index can be systematically biased This bias is apparent in the modified Turvey data set 23.7 In Section D, the year-over-year monthly indices defined in Section C are aggregated into an annual index that compares all of the monthly prices in a given calendar year with the corresponding monthly prices in a base year In Section E, this idea of comparing the prices of a current calendar year with the corresponding prices in a base year is extended to annual indices that compare the prices of the last 12 months with the corresponding prices in the 12 months of a base year The resulting rolling-year indices can be regarded as seasonally adjusted price indices The modified Turvey data set is used to test out these 23.10 Because many XMPIs are month-to-month indices that use annual basket quantity weights, this type of index is studied in Section H For months when the product is not available in the marketplace, the last available price is carried forward and used in the index In Section I, an annual quantity basket is again used but instead of carrying forward the prices of seasonally unavailable items, an imputation method is used to fill in the missing prices The annual basket-type indices defined in Sections H and I are implemented using the artificial data set Unfortunately, the empirical results are not satisfactory because the indices show 547 EXPORT AND IMPORT PRICE INDEX MANUAL: THEORY AND PRACTICE tremendous seasonal fluctuations in prices This volatility makes them unsuitable for users who want up-todate information on trends in general inflation 23.11 In Section J, the artificial data set is used in order to evaluate another type of month-to-month index that is frequently suggested in the literature on how to deal with seasonal products: namely the Bean and Stine (1924) Type C or Rothwell (1958) index Again, this index does not get rid of the tremendous seasonal fluctuations that are present in the modified Turvey data set 23.12 Sections H and I showed that the annual basket-type indices with carryforward of missing prices (Section H) or imputation of missing prices (Section I) not get rid of seasonal fluctuations in prices However, in Section K, it is shown how seasonally adjusted versions of these annual basket indices can be used to successfully forecast rolling-year indices that are centered in the current month In addition, the results in Section K show how these annual basket-type indices can be seasonally adjusted (using information obtained from rolling-year indices from prior periods or by using traditional seasonal adjustment procedures) Hence, these seasonally adjusted annual basket indices could be used as successful indicators of general inflation on a timely basis 23.13 Section L concludes with several suggestions for dealing with seasonal products B A Seasonal Product Data Set 23.14 It will be useful to illustrate the index number formulas that are defined in subsequent sections by computing them for an actual data set Turvey (1979) constructed an artificial data set for five seasonal products (apples, peaches, grapes, strawberries, and oranges) for four years by month, so that there are times times 12 observations, equal to 240 observations in all At certain times of the year, peaches and strawberries (products and 4) are unavailable, so in Tables 23.1 and 23.2, the prices and quantities for these products are entered as zeros.6 The data in Tables 23.1 and 23.2 are essentially equal to that constructed by Turvey except that a number of adjustments 6The corresponding prices are not necessarily equal to zero (the commodities may be offered for sale at certain prices but there are no purchasers at those prices), but they are entered as zeros for convenience in programming the various indices 548 were made in order to illustrate various points The two most important adjustments were as follows: • The data for product (grapes) were adjusted, so that the annual Laspeyres and Paasche indices (which are defined in Section D below) would differ more than in the original data set;7 and • After the aforementioned adjustments were made, each price in the last year of data was escalated by the monthly inflation factor 1.008, so that monthto-month inflation for the last year of data would be at an approximate monthly rate of 1.6 percent per month, compared with about 0.8 percent per month for the first three years of data.8 23.15 Turvey sent his artificial data set to statistical agencies around the world, asking them to use their normal techniques to construct monthly and annual average price indices About 20 countries replied; Turvey summarized the responses as follows: It will be seen that the monthly indices display very large differences, for example, a range of 129.12–169.50 in June, while the range of simple annual means is much smaller It will also be seen that the indices vary as to the peak month or year (Turvey, 1979, p 13) The (modified) data below are used to test out various index number formulas in subsequent sections C Year-over-Year Monthly Indices 23.16 It can be seen that the existence of seasonal products that are present in the marketplace in one month but absent the next causes the accuracy of a month-to-month index to fall.9 A way of dealing with 7After the first year, the price data for grapes were adjusted downward by 30 percent each year and the corresponding volume was adjusted upward by 40 percent each year In addition, the quantity of oranges (product 5) for November 1971 was changed from 3,548 to 8,548 so that the seasonal pattern of change for this product would be similar to that of other years For similar reasons, the price of oranges in December 1970 was changed from 1.31 to1.41 and in January 1971 from 1.35 to 1.45 8Pierre Duguay of the Bank of Canada, while commenting on a preliminary version of this chapter, observed that rolling-year indices would not be able to detect the magnitude of systematic changes in the month-to-month inflation rate The original Turvey data set was roughly consistent with a month-to-month inflation rate of 0.8 percent per month; that is, prices grew roughly at the rate 1.008 each month over the four years of data Hence this second major adjustment of the Turvey data was introduced to illustrate Duguay’s observation, which is quite correct: The centered rolling-year indices pick up the correct magnitude of the new inflation rate only after a lag of half a year or so However, they quickly pick up the direction of change in the inflation rate 9In the limit, if each product appeared in only one month of the year, then a month-to-month index would break down completely d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d 23 TREATMENT OF SEASONAL PRODUCTS d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d Table 23.1 Artificial Seasonal Data Set: Prices Year t Month m p t,m p t,m p t,m p t,m p t,m 1970 1.14 2.48 1.30 1.17 2.75 1.25 1.17 5.07 1.21 1.40 5.00 1.22 1.64 4.98 5.13 1.28 1.75 3.15 4.78 3.48 1.33 1.83 2.53 3.48 3.27 1.45 1.92 1.76 2.01 1.54 1.38 1.73 1.42 1.57 10 1.10 1.94 1.39 1.61 11 1.09 1.75 1.59 12 1.10 2.02 1.41 1.25 2.15 1.45 1.36 2.55 1.36 1.38 4.22 1.37 1.57 4.36 1.44 1.77 4.18 5.68 1.51 1.86 3.77 4.08 3.72 1.56 1.94 2.85 2.61 3.78 1.66 2.02 1.98 1.79 1.74 1.55 1.80 1.28 1.76 10 1.34 1.95 1.26 1.77 11 1.33 1.62 1.76 1971 1972 1973 12 1.30 1.81 1.50 1.43 1.89 1.56 1.53 2.38 1.53 1.59 3.59 1.55 1.73 3.90 1.62 1.89 3.56 6.21 1.70 1.98 4.69 3.51 3.98 1.78 2.07 3.32 2.73 4.30 1.89 2.12 2.29 1.65 1.91 1.73 1.90 1.15 1.92 10 1.56 1.97 1.15 1.95 11 1.56 1.46 1.94 12 1.49 1.73 1.64 1.68 1.62 1.69 1.82 2.16 1.69 1.89 3.02 1.74 2.00 3.45 1.91 2.14 3.08 7.17 2.03 2.23 6.40 3.07 4.53 2.13 2.35 4.31 2.41 5.19 2.22 2.40 2.98 1.49 2.26 2.09 2.21 1.08 2.22 10 2.03 2.18 1.08 2.31 11 2.05 1.36 2.34 12 1.90 1.57 1.97 549 d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d EXPORT AND IMPORT PRICE INDEX MANUAL: THEORY AND PRACTICE Table 23.2 Artificial Seasonal Data Set: Quantities Year t Month m qt,m 1970 3,086 82 10,266 3,765 35 9,656 4,363 7,940 4,842 5,110 4,439 26 700 4,089 5,323 91 75 2,709 3,362 4,165 498 82 1,970 3,396 3,224 6,504 1,490 2,406 4,025 4,923 2,937 2,486 10 5,784 865 2,826 3,222 11 6,949 1,290 6,958 12 3,924 338 9,762 3,415 119 10,888 4,127 45 10,314 4,771 14 8,797 5,290 11 5,590 4,986 74 806 4,377 5,869 98 112 3,166 3,681 4,671 548 132 2,153 3,748 3,534 6,964 2,216 2,649 4,509 5,370 4,229 2,726 10 6,299 932 4,178 3,477 11 7,753 1,831 8,548 12 4,285 496 10,727 3,742 172 11,569 4,518 67 10,993 5,134 22 9,621 5,738 16 6,063 5,498 137 931 4,625 6,420 104 171 3,642 3,970 5,157 604 202 2,533 4,078 3,881 7,378 3,269 2,883 4,917 5,839 6,111 2,957 10 6,872 1,006 5,964 3,759 11 8,490 2,824 8,238 12 5,211 731 11,827 4,051 250 12,206 4,909 102 11,698 5,567 30 10,438 6,253 25 6,593 6,101 220 1,033 4,926 7,023 111 252 4,085 4,307 5,671 653 266 2,877 4,418 4,187 7,856 4,813 3,165 5,446 6,291 8,803 3,211 10 7,377 1,073 8,778 4,007 11 9,283 4,517 8,833 12 4,955 1,073 12,558 1971 1972 1973 550 qt,m qt,m qt,m qt,m 23 TREATMENT OF SEASONAL PRODUCTS these strongly seasonal products is to change the focus from short-term month-to-month price indices to yearover-year price comparisons for each month of the year In the latter type of comparison, there is a good chance that seasonal products that appear in February, for example, will also appear in subsequent Februarys, so that the overlap of products will be maximized in these year-over-year monthly indices 23.17 For more than a century, it has been recognized that making year-over-year comparisons10 provides the simplest method for making comparisons that are free from the contaminating effects of seasonal fluctuations: In the daily market reports, and other statistical publications, we continually find comparisons between numbers referring to the week, month, or other parts of the year, and those for the corresponding parts of a previous year The comparison is given in this way in order to avoid any variation due to the time of the year And it is obvious to everyone that this precaution is necessary Every branch of industry and commerce must be affected more or less by the revolution of the seasons, and we must allow for what is due to this cause before we can learn what is due to other causes (Jevons, 1863 reprinted 1884, p 3) 23.18 The economist Flux and the statistician Yule also endorsed the idea of making year-over-year comparisons to minimize the effects of seasonal fluctuations: Each month the average price change compared with the corresponding month of the previous year is to be computed The determination of the proper seasonal variations of weights, especially in view of the liability of seasons to vary from year to year, is a task from which, I imagine, most of us would be tempted to recoil (Flux, 1921, pp 184–85) My own inclination would be to form the index number for any month by taking ratios to the corresponding month of the year being used for reference, the year before presumably, as this would avoid any difficulties with seasonal commodities I should then form the annual average by the geometric mean of the monthly figures (Yule, 1921, p 199) In more recent times, Zarnowitz also endorsed the use of year-over-year monthly indices: d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d years, if a month is our unit “season”, and if a constant seasonal market basket can be used, for traditional methods of price index construction can be applied in such comparisons (Zarnowitz, 1961, p 266) 23.19 In the remainder of this section, it is shown how year-over-year Fisher indices and approximations to them can be constructed.11 For each month m  1, 2, , 12, let S(m) denote the set of products that are available for purchase in each year t  0, 1, , T For t  0, 1, , T and m  1, 2, , 12, let pt,m n and qt,m denote the price and quantity of product n that is n available in month m of year t for n belongs to S(m) Let pt,m and qt,m denote the month m and year t price and quantity vectors, respectively Then the year-overyear monthly Laspeyres, Paasche, and Fisher indices going from month m of year t to month m of year t  can be defined as follows: pt,m, PL pt1,m, qt,m   pt1,m qnt,m n n苸S(m) ; pnt,m qnt,m n苸S(m)  m  1, 2, , 12; (23.1)  pt1,m qt1,m n n n苸S(m) PPpt,m, pt1,m, qt1,m  ; t1,m  pt,m n qn n苸S(m) m  1, 2, , 12; (23.2) PF pt,m, pt1,m, qt,m, qt1,m  PL pt,m, pt1,m, qt,mPPpt,m, pt1,m, qt1,m ; m  1, 2, , 12 (23.3) 23.20 The above formulas can be rewritten in price relative and monthly value share form as follows: t1,m t,m PLpt,m, pt1,m, st,m   st,m pn ; n pn n苸S(m) m  1, 2, , 12; (23.4) PP pt,m, pt1,m, st1,m  [ n苸S(m) 1 st1,m pt,m pt1,m n n n  ] 1 ; m  1, 2, , 12; (23.5) There is of course no difficulty in measuring the average price change between the same months of successive 10In the seasonal price index context, this type of index corresponds to Bean and Stine’s (1924, p 31) Type D index 11Diewert (1996b, pp 17–19; 1999a, p 50) noted various separability restrictions on purchaser preferences that would justify these year-over-year monthly indices from the viewpoint of the economic approach to index number theory 551 d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d EXPORT AND IMPORT PRICE INDEX MANUAL: THEORY AND PRACTICE PF pt,m, pt1,m, st,m, st1,m  PAP pt,m, pt1,m, s0,m  _ PLpt,m, pt1,m, st,mPPpt,m, pt1,m, st1,m ; m  1, 2, , 12 (23.6)    [  n苸S(m) st,m n [ n苸S(m) t1,m t,m 1 s0,m pn  n pn m  1, 2, , 12; m  1, 2, , 12 ]  t,m pt,m n qn _ st,m  ; m  1, 2, , 12; n苸S(m); n t,m  pt,m i qi i苸S(m) t  0, 1, , T; (23.7) and st,m denotes the vector of month m value shares in year t, [st,m n ] for n苸S(m) 23.21 Current-period value shares snt1,m are not likely to be available As a consequence, it will be necessary to approximate these shares using the corresponding value shares from a base year 23.22 Use the base-period monthly value share vectors s0,m in place of the vector of month m and year t value shares st,m in equation (23.4) and use the baseperiod monthly value share vectors s0,m in place of the vector of month m and year t  value shares st1,m in equation (23.5) Similarly, replace the share vectors st,m and st1,m in equation (23.6) with the base-period value share vector for month m, s0,m The resulting approximate year-over-year monthly Laspeyres, Paasche, and Fisher indices are defined by equations (23.8) through (23.10):12  n苸S(m) [ t1,m t,m s0,m pn  n pn n苸S(m) t1,m t,m 1 s0,m pn  n pn ] 1 (23.10) 23.23 The approximate Fisher year-over-year monthly indices defined by equation (23.10) will provide adequate approximations to their true Fisher counterparts defined by equation (23.6) only if the monthly value shares for the base year are not too different from their currentyear t and t  counterparts Thus, it will be useful to construct the true Fisher indices on a delayed basis in order to check the adequacy of the approximate Fisher indices defined by equation (23.10) 23.24 The year-over-year monthly approximate Fisher indices defined by equation (23.10) will normally have a certain amount of upward bias, because these indices cannot reflect long-term substitution toward products that are becoming relatively cheaper over time This reinforces the case for computing true year-over-year monthly Fisher indices defined by equation (23.6) on a delayed basis, so that this substitution bias can be estimated 23.25 Note that the approximate year-over-year monthly Laspeyres and Paasche indices, PAL and PAP, defined by equations (23.8) and (23.9), satisfy the following inequalities: PALpt,m, pt1,m, s0,m PALpt1,m, pt,m, s0,m  1; m  1, 2, , 12; (23.11) t1,m t,m s0,m pn ; n pn m  1, 2, , 12; (23.8) 12If the monthly revenue shares for the base year, s 0,m, are all equal, n then the approximate Fisher index defined by (23.10) reduces to Fisher’s (1922, p 472) formula 101 Fisher (1922, p 211) observed that this index was empirically very close to the unweighted geometric mean of the price relatives, while Dalén (1992, p 143) and Diewert (1995a, p 29) showed analytically that these two indices approximated each other to the second order The equally weighted version of equation (23.10) was recommended as an elementary index by Carruthers, Sellwood, and Ward (1980, p 25) and Dalén (1992, p 140) 552 (23.9) PAF pt,m, pt1,m, s0,m, s0,m 1 where the monthly value share for product n苸S(m) for month m in year t is defined as n苸S(m) ;  PAL pt,m, pt1,m, s0,mPP pt,m, pt1,m, s0,m ; 1 st1,m pt,m pt1,m n n n  PALpt,m, pt1,m, s0,m   1 pt,m pt1,m n n  _ n苸S(m) ] PAPpt,m, pt1,m, s0,mPAPpt1,m, pt,m, s0,m  1; m  1, 2, , 12; (23.12) with strict inequalities if the monthly price vectors pt,m and pt1,m are not proportional to each other.13 Equation (23.11) says that the approximate year-over-year monthly Laspeyres index fails the time reversal test with an upward bias while equation (23.12) says that the approximate year-over-year monthly Paasche index fails 13For reasons given in Hardy, Littlewood, and Pólya (1934), p 26 23 TREATMENT OF SEASONAL PRODUCTS d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d there are substantial differences between the indices for the last five months of the year by the time the year 1973 is reached The largest percentage difference between the Laspeyres and Paasche indices is 12.5 percent for month 10 in 1973 (1.40601.2496  1.125) However, all of the year-over-year monthly series show a nice smooth year-over-year trend the time reversal test with a downward bias As a result, the fixed-weights approximate Laspeyres index PAL has a built-in upward bias whereas the fixed-weights approximate Paasche index PAP has a built-in downward bias Statistical agencies should avoid the use of these formulas However, they can be combined, as in the approximate Fisher formula in equation (23.10) The resulting index should be free from any systematic formula bias, although some substitution bias could still exist 23.28 Approximate fixed-base year-over-year Laspeyres, Paasche, and Fisher indices can be constructed by replacing current-month revenue shares for the five products with the corresponding baseyear monthly revenue shares for the same five products The resulting approximate Laspeyres indices are equal to the original fixed-base Laspeyres, so there is no need to table the approximate Laspeyres indices However, the approximate year-over-year Paasche and Fisher indices differ from the fixed-base Paasche and Fisher indices found in Tables 23.4 and 23.5, so these new approximate indices are listed in Tables 23.6 and 23.7 23.26 The year-over-year monthly indices defined in this section are illustrated using the artificial data set tabled in Section B Although fixed-base indices were not formally defined in this section, these indices have formulas similar to those of the year-over-year indices that were defined, with the exception that the variable-base year t is replaced by the fixed-base year The resulting 12 year-over-year monthly fixed-base Laspeyres, Paasche, and Fisher indices are listed in Tables 23.3 to 23.5 23.27 Comparing the entries in Tables 23.3 and 23.4, one can see that the year-over-year monthly fixed-base Laspeyres and Paasche price indices not differ substantially for the early months of the year However, 23.29 Comparing the entries in Table 23.4 with the corresponding entries in Table 23.6, it can be seen that Table 23.3 Year-over-Year Monthly Fixed-Base Laspeyres Indices Month 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1085 1.1068 1.1476 1.1488 1.1159 1.0844 1.1103 1.0783 1.0492 1.0901 1.1284 1.0849 1972 1.2060 1.2442 1.3062 1.2783 1.2184 1.1734 1.2364 1.1827 1.1049 1.1809 1.2550 1.1960 1973 1.3281 1.4028 1.4968 1.4917 1.4105 1.3461 1.4559 1.4290 1.2636 1.4060 1.5449 1.4505 Table 23.4 Year-over-Year Monthly Fixed-Base Paasche Indices Month 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1074 1.1070 1.1471 1.1486 1.1115 1.0827 1.1075 1.0699 1.0414 1.0762 1.1218 1.0824 1972 1.2023 1.2436 1.3038 1.2773 1.2024 1.1657 1.2307 1.1455 1.0695 1.1274 1.2218 1.1901 1973 1.3190 1.4009 1.4912 1.4882 1.3715 1.3266 1.4433 1.3122 1.1664 1.2496 1.4296 1.4152 Table 23.5 Year-over-Year Monthly Fixed-Base Fisher Indices Month 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1080 1.1069 1.1474 1.1487 1.1137 1.0835 1.1089 1.0741 1.0453 1.0831 1.1251 1.0837 1972 1.2041 1.2439 1.3050 1.2778 1.2104 1.1695 1.2336 1.1640 1.0870 1.1538 1.2383 1.1930 1973 1.3235 1.4019 1.4940 1.4900 1.3909 1.3363 1.4496 1.3694 1.2140 1.3255 1.4861 1.4327 553 d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d EXPORT AND IMPORT PRICE INDEX MANUAL: THEORY AND PRACTICE Table 23.6 Year-over-Year Approximate Monthly Fixed-Base Paasche Indices Month 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1077 1.1057 1.1468 1.1478 1.1135 1.0818 1.1062 1.0721 1.0426 1.0760 1.1209 1.0813 1972 1.2025 1.2421 1.3036 1.2757 1.2110 1.1640 1.2267 1.1567 1.0788 1.1309 1.2244 1.1862 1973 1.3165 1.3947 1.4880 1.4858 1.3926 1.3223 1.4297 1.3315 1.1920 1.2604 1.4461 1.4184 Table 23.7 Year-over-Year Approximate Monthly Fixed-Base Fisher Indices Month 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1081 1.1063 1.1472 1.1483 1.1147 1.0831 1.1082 1.0752 1.0459 1.0830 1.1247 1.0831 1972 1.2043 1.2432 1.3049 1.2770 1.2147 1.1687 1.2316 1.1696 1.0918 1.1557 1.2396 1.1911 1973 1.3223 1.3987 1.4924 1.4888 1.4015 1.3341 1.4428 1.3794 1.2273 1.3312 1.4947 1.4344 with few exceptions, the entries correspond fairly well One of the bigger differences is the 1973 entry for the fixed-base Paasche index for month 9, which is 1.1664, while the corresponding entry for the approximate fixed-base Paasche index is 1.1920 for a 2.2 percent difference (1.19201.1664  1.022) In general, the approximate fixed-base Paasche indices are a bit bigger than the true fixed-base Paasche indices, as one might expect because the approximate indices have some substitution bias built in This is due to the fact that their revenue shares are held fixed at the 1970 levels 23.30 Turning now to the chained year-over-year monthly indices using the artificial data set, the resultant 12 year-over-year monthly chained Laspeyres, Paasche, and Fisher indices, PL, PP, and PF, where the month-to-month links are defined by equations (23.4) through (23.6), are listed in Tables 23.8 to 23.10 Table 23.8 Year-over-Year Monthly Chained Laspeyres Indices Month 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1085 1.1068 1.1476 1.1488 1.1159 1.0844 1.1103 1.0783 1.0492 1.0901 1.1284 1.0849 1972 1.2058 1.2440 1.3058 1.2782 1.2154 1.1720 1.2357 1.1753 1.0975 1.1690 1.2491 1.1943 1973 1.3274 1.4030 1.4951 1.4911 1.4002 1.3410 1.4522 1.3927 1.2347 1.3593 1.5177 1.4432 Table 23.9 Year-over-Year Monthly Chained Paasche Indices Month 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1074 1.1070 1.1471 1.1486 1.1115 1.0827 1.1075 1.0699 1.0414 1.0762 1.1218 1.0824 1972 1.2039 1.2437 1.3047 1.2777 1.2074 1.1682 1.2328 1.1569 1.0798 1.1421 1.2321 1.1908 1973 1.3243 1.4024 1.4934 1.4901 1.3872 1.3346 1.4478 1.3531 1.2018 1.3059 1.4781 1.4305 Table 23.10 Year-over-Year Monthly Chained Fisher Indices Month 554 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1080 1.1069 1.1474 1.1487 1.1137 1.0835 1.1089 1.0741 1.0453 1.0831 1.1251 1.0837 1972 1.2048 1.2438 1.3052 1.2780 1.2114 1.1701 1.2343 1.1660 1.0886 1.1555 1.2405 1.1926 1973 1.3258 1.4027 1.4942 1.4906 1.3937 1.3378 1.4500 1.3728 1.2181 1.3323 1.4978 1.4368 23 TREATMENT OF SEASONAL PRODUCTS d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d be approximated by replacing current-period product revenue shares for each month with the corresponding base-year monthly revenue shares The resultant 12 year-over-year monthly approximate chained Laspeyres, Paasche, and Fisher indices (PAL , PAP, and PAF), where the monthly links are defined by equations (23.8) through (23.10), are listed in Tables 23.11 through 23.13 23.31 Comparing the entries in Tables 23.8 and 23.9, it can be seen that the year-over-year monthly chained Laspeyres and Paasche price indices have smaller differences than the corresponding fixed-base Laspeyres and Paasche price indices in Tables 23.3 and 23.4 This is a typical pattern that was found in Chapter 20: The use of chained indices tends to reduce the spread between Paasche and Laspeyres indices compared to their fixed-base counterparts The largest percentage difference between corresponding entries for the chained Laspeyres and Paasche indices in Tables 23.8 and 23.9 is 4.1 percent for month 10 in 1973 (1.3593/1.3059  1.041) Recall that the fixed-base Laspeyres and Paasche indices differed by 12.5 percent for the same month so that chaining does tend to reduce the spread between these two equally plausible indices 23.34 The year-over-year chained indices listed in Tables 23.11 through 23.13 approximate their true chained counterparts listed in Tables 23.8 through 23.10 closely For 1973, the largest discrepancies are for the Paasche and Fisher indices for month 9: The chained Paasche is 1.2018, while the corresponding approximate chained Paasche is 1.2183, for a difference of 1.4 percent The chained Fisher is 1.2181, while the corresponding approximate chained Fisher is 1.2305, for a difference of 1.0 percent It can be seen that for the modified Turvey data set, the approximate yearover-year monthly Fisher indices listed in Table 23.13 approximate the theoretically preferred (but practically unfeasible) Fisher chained indices listed in Table 23.10 23.32 The chained year-over-year Fisher indices listed in Table 23.10 are regarded as the best estimates of yearover-year inflation using the artificial data set 23.33 The year-over-year chained Laspeyres, Paasche, and Fisher indices listed in Tables 23.8 to 23.10 can Table 23.11 Year-over-Year Monthly Approximate Chained Laspeyres Indices Month 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1085 1.1068 1.1476 1.1488 1.1159 1.0844 1.1103 1.0783 1.0492 1.0901 1.1284 1.0849 1972 1.2056 1.2440 1.3057 1.2778 1.2168 1.1712 1.2346 1.1770 1.0989 1.1692 1.2482 1.1939 1973 1.3255 1.4007 1.4945 1.4902 1.4054 1.3390 1.4491 1.4021 1.2429 1.3611 1.5173 1.4417 Table 23.12 Year-over-Year Monthly Approximate Chained Paasche Indices Month 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1077 1.1057 1.1468 1.1478 1.1135 1.0818 1.1062 1.0721 1.0426 1.0760 1.1209 1.0813 1972 1.2033 1.2424 1.3043 1.2764 1.2130 1.1664 1.2287 1.1638 1.0858 1.1438 1.2328 1.1886 1973 1.3206 1.3971 1.4914 1.4880 1.3993 1.3309 1.4386 1.3674 1.2183 1.3111 1.4839 1.4300 Table 23.13 Year-over-Year Monthly Approximate Chained Fisher Indices Month 10 11 12 1970 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1971 1.1081 1.1063 1.1472 1.1483 1.1147 1.0831 1.1082 1.0752 1.0459 1.0830 1.1247 1.0831 1972 1.2044 1.2432 1.3050 1.2771 1.2149 1.1688 1.2317 1.1704 1.0923 1.1565 1.2405 1.1912 1973 1.3231 1.3989 1.4929 1.4891 1.4024 1.3349 1.4438 1.3847 1.2305 1.3358 1.5005 1.4358 555 d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d EXPORT AND IMPORT PRICE INDEX MANUAL: THEORY AND PRACTICE quite satisfactorily Because the approximate Fisher indices are just as easy to compute as the approximate Laspeyres and Paasche indices, it may be useful to ask statistical agencies to make available to the public these approximate Fisher indices, along with the approximate Laspeyres and Paasche indices D Year-over-Year Annual Indices 23.35 Assuming that each product in each season of the year is a separate annual product is the simplest and theoretically most satisfactory method for dealing with seasonal products when the goal is to construct annual price and quantity indices This idea can be traced back to Mudgett in the consumer price context and to Stone in the producer price context: The basic index is a yearly index and as a price or quantity index is of the same sort as those about which books and pamphlets have been written in quantity over the years (Mudgett, 1955, p 97) The existence of a regular seasonal pattern in prices which more or less repeats itself year after year suggests very strongly that the varieties of a commodity available at different seasons cannot be transformed into one another without cost and that, accordingly, in all cases where seasonal variations in price are significant, the varieties available at different times of the year should be treated, in principle, as separate commodities (Stone, 1956, p 74–75) 23.36 Using the notation introduced in the previous section, the Laspeyres, Paasche, and Fisher annual (chain link) indices comparing the prices of year t with those of year t  can be defined as follows: 23.37 The above formulas can be rewritten in price relative and monthly value share form as follows: t t,12 PL( pt,1, , pt,12; pt1,1, , pt1,12; t1st,1, , 12 s ) 12   t1,m t,m tmst,m pn ; n pn m1 n苸S(m) (23.16) PP( pt,1, , pt,12; pt1,1, , pt1,12; t1 t1,12 t1 st1,1, , 12 s )   [ [ 12   m1 n苸S(m) 12 m1  [ t1 m t1,m 1 t1 pt,m pt1,m m sn n n   n苸s(m) 1 st1,m pt,m pt1,m n n n  12 ] ] 1 1 t,m t1,m, st1,m ] 1  t1 m [ PP p , p m1 ] 1 ; (23.17) PF pt,1, , pt,12; pt1,1, , pt1,12; t1 st,1, , t12st,12; t1 st1,1, , t1 st1,12 12 _   12   m1 n苸S(m) [  t1,m t,m tmst,m pn  n pn 12  m1 n苸S(m) t1,m 1 t1 pt,m pt1,m m sn n n  _   [ pt1,m qt,m n n n苸S(m)  ; 12 t,m t,m p q   n n (23.13) tm m1 n苸S(m) PP ( pt,1, , pt,12; pt1,1, , pt1,12; qt1,1, , qt1,12) 12      12 t,m t1,m, st1,m ] 1  t1 m [ PP p , p m1   t,m pt,m n qn n苸S(m) ; 12 t,i pt,i j qj i1 j苸S(i)  t  0, 1, , T; ; (23.14) PF( pt,1, , pt,12; pt1,1, , pt1,12; qt,1, , qt,12; qt1,1, , qt1,12)  PL( pt,1, , pt,12; pt1,1, , pt1,12; qt,1, , qt,12) _  PP( pt,1, , pt,12; pt1,1, , pt1,12; qt1,1, , qt1,12) (23.15) 556 ] 1 , (23.18) where the value share for month m in year t is defined as   m1 pt1,m qt1,m n n m1 n苸S(m) 12 t1,m pt,m n qn m1 n苸S(m) 1 12  tm [ PL pt,m, pt1,m, st,m ] m1 PL( pt,1, , pt,12; pt1,1, , pt1,12; qt,1, , qt,12) 12 ] m  1, 2, , 12; (23.19) and the year-over-year monthly Laspeyres and Paasche (chain link) price indices PL ( pt,m , pt1,m , st,m) and PP ( pt,m, pt1,m, st1,m) were defined in the previous section by equations (23.4) and (23.5), respectively As usual, the annual chain link Fisher index PF defined by equation (23.18), which compares the prices in every month of year t with the corresponding prices in year t  1, is the geometric mean of the annual chain link Laspeyres and Paasche indices, PL and PP, defined 23 TREATMENT OF SEASONAL PRODUCTS by equations (23.16) and (23.17) The last equation in equations (23.16), (23.17), and (23.18) shows that these annual indices can be defined as (monthly) shareweighted averages of the year-over-year monthly chain link Laspeyres and Paasche indices, PL ( pt,m , pt1,m , st,m) and PP ( pt,m, pt1,m, st1,m), defined earlier by equations (23.4) and (23.5) Hence, once the year-over-year monthly indices defined in the previous section have been numerically calculated, it is easy to calculate the corresponding annual indices 23.38 Fixed-base counterparts to the formulas defined by equations (23.16) through (23.18) can readily be defined: Simply replace the data pertaining to period t with the corresponding data pertaining to the base period 23.39 Using the data from the artificial data set in Table 23.1 of Section B, the annual fixed-base Laspeyres, Paasche, and Fisher indices are listed in Table 23.14 Table 23.14 shows that by 1973, the annual fixedbase Laspeyres index exceeds its Paasche counterpart by 4.5 percent Note that each series increases steadily 23.40 The annual fixed-base Laspeyres, Paasche, and Fisher indices can be approximated by replacing any current shares with the corresponding base-year shares The resulting annual approximate fixed-base Laspeyres, Paasche, and Fisher indices are listed in Table 23.15 Also listed in the last column of Table 23.15 is the fixedbase geometric Laspeyres annual index, PGL It is the weighted geometric mean counterpart to the fixed-base Laspeyres index, which is equal to a base-period weighted arithmetic average of the long-term price relative (see Table 23.14 Annual Fixed-Base Laspeyres, Paasche, and Fisher Price Indices Year PL PP PF 1970 1.0000 1.0000 1.0000 1971 1.1008 1.0961 1.0984 1972 1.2091 1.1884 1.1987 1973 1.4144 1.3536 1.3837 Table 23.15 Annual Approximate Fixed-Base Laspeyres, Paasche, Fisher, and Geometric Laspeyres Indices Year PAL PAP PAF PGL 1970 1.0000 1.0000 1.0000 1.0000 1971 1.1008 1.0956 1.0982 1.0983 1972 1.2091 1.1903 1.1996 1.2003 1973 1.4144 1.3596 1.3867 1.3898 d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d Table 23.16 Annual Chained Laspeyres, Paasche, and Fisher Price Indices Year PL PP PF 1970 1.0000 1.0000 1.0000 1971 1.1008 1.0961 1.0984 1972 1.2052 1.1949 1.2001 1973 1.3994 1.3791 1.3892 Chapter 20) It can be shown that PGL approximates the approximate fixed-base Fisher index PAF to the second order around a point where all of the long-term price relatives are equal to unity.14 It is evident that the entries for the Laspeyres price indices are exactly the same in Tables 23.14 and 23.15 This is as it should be because the fixed-base Laspeyres price index uses only revenue shares from the base year 1970; consequently, the approximate fixed-base Laspeyres index is equal to the true fixedbase Laspeyres index Comparing the columns labeled PP and PF in Table 23.14 and PAP and PAF in Table 23.15 shows that the approximate Paasche and approximate Fisher indices are quite close to the corresponding annual Paasche and Fisher indices Thus, for the artificial data set, the true annual fixed-base Fisher can be closely approximated by the corresponding approximate Fisher index PAF (or the geometric Laspeyres index PGL ), which can be computed using the same information set that is normally available to statistical agencies 23.41 Using the data from the artificial data set in Table 23.1 of Section B, the annual chained Laspeyres, Paasche, and Fisher indices can readily be calculated using the equations (23.16) through (23.18) for the chain links The resulting indices are listed in Table 23.16 That table shows that the use of chained indices has substantially narrowed the gap between the Paasche and Laspeyres indices The difference between the chained annual Laspeyres and Paasche indices in 1973 is only 1.5 percent (1.3994 versus 1.3791), whereas in Table 23.14, the difference between the fixed-base annual Laspeyres and Paasche indices in 1973 is 4.5 percent (1.4144 versus 1.3536) Thus, the use of chained annual indices has substantially reduced the substitution (or representativity) bias of the Laspeyres and Paasche indices Comparing Tables 23.14 and 23.16, one can see that for this particular artificial data set, the annual fixed-base Fisher indices are very close to their annual chained Fisher counterparts However, the annual chained Fisher indices should normally be regarded as the more desirable target index to approximate, because this index will 14See footnote 12 557 EXPORT AND IMPORT PRICE INDEX MANUAL: THEORY AND PRACTICE Table 23.17 Annual Approximate Chained Laspeyres, Paasche, and Fisher Price Indices Year PAL PAP PAF 1970 1.0000 1.0000 1.0000 1971 1.1008 1.0956 1.0982 1972 1.2051 1.1952 1.2002 1973 1.3995 1.3794 1.3894 normally give better results if prices and revenue shares are changing substantially over time.15 23.42 The current-year weights, snt,m and σmt and st1,m and σt1 m , which appear in the chain link equan tions (23.16) through (23.18), can be approximated by the corresponding base-year weights, s0,m n and σm This leads to the annual approximate chained Laspeyres, Paasche, and Fisher indices listed in Table 23.17 23.43 Comparing the entries in Tables 23.16 and 23.17 shows that the approximate chained annual Laspeyres, Paasche, and Fisher indices are extremely close to the corresponding true chained annual Laspeyres, Paasche, and Fisher indices Therefore, for the artificial data set, the true annual chained Fisher can be closely approximated by the corresponding approximate Fisher index, which can be computed using the same information set that is normally available to statistical agencies 23.44 The approach to computing annual indices outlined in this section, which essentially involves taking monthly expenditure share-weighted averages of the 12 year-over-year monthly indices, should be contrasted with the approach that simply takes the arithmetic mean of the 12 monthly indices The problem with the latter approach is that months in which revenues are below the average (e.g., February) are given the same weight in the unweighted annual average as are months in which revenues are above the average (e.g., December) E Rolling-Year Annual Indices 23.45 In the previous section, the price and quantity data pertaining to the 12 months of a calendar year were compared to the 12 months of a base calendar year However, there is no need to restrict attention to calendar-year comparisons; any 12 consecutive months of price and quantity data could be compared to the 15 “Better” in the sense that the gap between the Laspeyres and Paasche indices will normally be reduced using chained indices under these circumstances Of course, if there are no substantial trends in prices so that prices are just randomly changing, then it will generally be preferable to use the fixed-base Fisher index 558 price and quantity data of the base year, provided that the January data in the noncalendar year are compared to the January data of the base year, the February data of the noncalendar year are compared to the February data of the base year, and so on.16 Alterman, Diewert, and Feenstra (1999, p 70) called the resulting indices rolling-year or moving-year indices.17 23.46 In order to theoretically justify the rolling-year indices from the viewpoint of the economic approach to index number theory, some restrictions on preferences are required The details of these assumptions can be found in Diewert (1996b, pp 32–34; and 1999a, pp 56–61) 23.47 The problems involved in constructing rollingyear indices for the artificial data set that was introduced in Section B are now considered For both fixed-base and chained rolling-year indices, the first 13 index number calculations are the same For the year that ends with the data for December 1970, the index is set equal to for the Laspeyres, Paasche, and Fisher moving-year indices The base-year data are the 44 nonzero price and quantity observations for the calendar year 1970 When the data for January 1971 become available, the three nonzero price and quantity entries for January of calendar year 1970 are dropped and replaced with the corresponding entries for January 1971 The data for the remaining months of the comparison year remain the same; that is, for February through December of the comparison year, the data for the rolling year are set equal to the corresponding entries for February through December 1970 Thus, the Laspeyres, Paasche, or Fisher rolling-year index value for January 1971 compares the prices and quantities of January 1971 with the corresponding prices and quantities of January 1970, and for the remaining months of this first moving year, the prices and quantities of February through December 1970 are simply compared with the exact same prices and quantities of February through December 1970 When the data for February 1971 become available, the three nonzero price and quantity entries for February for the last rolling year (which are equal to the three nonzero price and quantity entries for February 1970) are dropped and replaced with the corresponding entries for February 1971 The resulting data become the price and quantity data for the second rolling year The Laspeyres, Paasche, or Fisher rolling-year index value 16Diewert (1983b) suggested this type of comparison and termed the resulting index a “split year” comparison 17Crump (1924, p 185) and Mendershausen (1937, p 245), respectively, used these terms in the context of various seasonal adjustment procedures The term “rolling year” seems to be well established in the business literature in the United Kingdom d7ab8e b82e b25 f771a 671e2 2eac3a57c81ccf10fbf2d5a d39c42dd8acfcf3e7 a3b2006 1742 0fc1db577 d1b1e 93fbdd0ab7 1b01 01f9f1 e124 c788 9b01 4208 558 42862e5 73af62d1 1a070 e4a1e6 16adfc8 d9d6 bba8 6091 70bf95 cbe6e 88dc2a8 53cf07 f646 b8c7339 c9bc5 c2a893 9633 c98 d993 4af9e 93a61a 3f7 58e77 bf2 8ae b585e4 c6 fc5 82399 8ad43 d515 95ae0 84789 9c4 c83 f8e 59ac3 f93 b72 418e4 0958 1e13c27bbdbb623 39b4a 6c1a 92ab4 b087 b9 f43e1 9cbdd2ef1 8735 b0a4e2 6a80 f 3c3b9e00a5 254b89e c7d9 4e5c66c6b2 b82e b06a2 4f1 75a896 44b0 e9c5398 f3 f1 4b5bc6a22 5fdff0 41df597 5d8 7500 b5865a d81 f6 f4d0 cb27cf3 f1b3 bbcf5a 9e7 325654e 7f4 d3a0 0975 d005a7 b55 0ef9 8d3 b3b7 e6a628 2e6e3 c0a4 2567 faa9c1c 049647 51b2 64f206 c364 bd75 9c1 31d9 64a9fdd5 2ab2a8 3f0 8075 e9f4714 f777 7e6c0 572a75 8f0 0c0 7a568e 4eb5 bc2b5 be222 3a3b9 f6 c0e1 1c56 d0 f87d13b5 04 180ac9 edf0d3 650 cbcc91 885db0e0 74ca 61a4 f6502 4b3 d16b9e005 49e5 6d2dc3 c7952 d3 c8baa0 9c2a 1c4 c631 3e5 f1c1471 f3a72 7a695 064ca 57e6 d7b65b0 57b9 1e04e04a 8992 7f6a c78 c86 d1e0 c2d175ad4fca 1fb6e36 521a34 4c3 9b3 f08 c331 cfed 7dd2ab0 d8e55 82df302 29a2b9eb3 f47 bb0 b317a 5b0 67abf16dc1 d1465 8d4 6c0c3e2bb9d54fb002 ebc95b823a11a b1 c12d09d4 d76a8 e2c083 cc4e fee4e f12 14e34d3b80 c3 dd69 5f8 9f0 6c2fba4 b08a b177 7a0b9 ba719ff 6d41 649 c7c39f3 4a49356 cd1 504 b41ac6b5 09f5a55d7d1e 0f7 34bd01b9f9 b418 306b079aa1 4b58 76c8 c235 4c6 d472 b9ba 67e47 c60a 45fe 16681 e6ab5 fc709e3 42c7d0fbd3a5df7 d15bea d4fc82e c67 40f6981 520a4 c275 1ef9 c52 e2ff5a7d195a4 76e05 fe65 012 aec9cfb 6aa3fde90ab9502aa0 11aa6a5 b6 f324 b3c8b6e 9c8 d6bc66 f121 4f2 82f bd4 c4bb166 f2f402e 7b7 f5d4 1a62 f16ae b3c4b79 2eb d8404a 58fb7 c62 f4a3d0d 72fbd58 b8d3 da629 cd15aa34 f047 0bfc4 c9d8 88b5 c22 89ee b55d15aeb c0 f747 aa95d9 c7988 7230 749a6a d6a6 f14b06a00 51c86fe2 186 f0a12a 9e6c2a4ef6661 2cf8da07 0f2 2943a2 5f7 1a1c0a867 c8 cf3 02b1 f11 bde4a 23e7 86be be180 10d4f e408373 6a892 76022 74e7 0c3 7d9d50ee0 258e 23c4 44e8 1ee032 d32 c44 b595e bf 8b9e5 f7e1 78ef067da 3bc8ed 3c5 bfcfde 88109 87c4baaab25b5 f5 b2f3c7 f34e 1b3cfe83 06969 dcd424fb6 05c081bd42 b333 9a88e0 f93 b11ff4 6486a bec9 8e8d