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Temi di discussione del Servizio Studi (Fractional) Beta Convergence by C. Michelacci and P. Zaffaroni Number 383 - October 2000
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Page 1: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

Temididiscussionedel Servizio Studi

(Fractional) Beta Convergence

by C. Michelacci and P. Zaffaroni

Number 383 - October 2000

Page 2: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

Thepurposeof the“Temididiscussione”series is topromote the circulationofworkingpapers prepared within the Bank of Italy or presented in Bank seminars by outsideeconomists with the aim of stimulating comments and suggestions.

The views expressed in the articles are those of the authors and do not involve theresponsibility of the Bank.

Editorial Board:ANDREA BRANDOLINI, FABRIZIO BALASSONE, MATTEO BUGAMELLI, FABIO BUSETTI, RICCARDOCRISTADORO, LUCA DEDOLA, PATRIZIO PAGANO, PAOLO ZAFFARONI; RAFFAELA BISCEGLIA(Editorial Assistant).

Page 3: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

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**Bank of Italy, Research Department.* CEMFI.

JEL classification: C22, C43, E10, O40.

Keywords: growth model, convergence, long memory, aggregation.

Page 4: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

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��W?|hL_�U|�L?���������������������������������������������������������������������������������������������b2�Empirics of the Solow growth model and unit roots �����������������������������������2��Theory of long memory and the Barro regression���������������������������������������.

���.Theory of long memory processes......�������������������������������������������������H��2.Robustness of the Barro regression........����������������������������������������������2�

e�The Solow model augmented by cross sectional heterogeneity�������������������2eD�Generalizing the concept of q�UL?�ih}i?Ui�����������������������������������������������2bS�,4T�h�U@* resu*|t������������������������������..................................���������������������������f.��L?U*�t�L?t�����������������������������������������������������������������������������������������������eH�Appendix: the log-periodogram estimator......�������������������������������������������������D6�}�hit����������������������������������������������������������������������������������������������������������e�+iuihi?Uit����������������������������������������������������������������������������������������������������eD

Page 5: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

� Introduction 1

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Reprinted from Journal of Monetary Economics, vol. 45 (1), C. Michelacci and P. Zaffaroni,

"(Fractional) Beta Convergence", pages 129-53, copyright (2000), with permission from

Elsevier Science.

Page 6: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

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Page 7: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

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Page 8: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

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Page 9: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

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Page 14: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

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Page 36: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

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Page 37: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

Figure 1: The dashed and bold lines represent the country-speci�c (OLS)

and common (GLS) trends, respectively. The solid line represents logged

GDP.

Page 38: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

Figure 2: The left hand side column displays the periodogram of the logged

GDP (1865-1994) for the 16 OECD countries considered here. The right

hand side column displays three lines versus the logged frequency: the solid

line represents the logged periodogram ordinates, the bold line represents

the OLS interpolating line (cf. Table 2) while the dashed line represents the

unit root case (slope ��=4). An interpolating line atter than the bisector

corresponds to a value of the long memory parameter d smaller than one.

Page 39: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking
Page 40: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

Figure 3: The test statistic for the null H0 di � d0; i = 1; : : : 16 is plotted

for di�erent values of d0. The horizontal line represents the critical value fora 10% signi�cance level.

Page 41: by C. Michelacci and P. Zaffaroni - Banca D'Italia · by C. Michelacci and P. Zaffaroni Number 383 - October 2000. Thepurposeofthe“Temididiscussione”seriesistopromote the circulationofworking

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RECENTLY PUBLISHED “TEMI” (*)

No. 359 — Does Market Transparency Matter? a Case Study, by A. SCALIA and V. VACCA(October 1999).

No. 360 — Costoedisponibilitàdel creditoper le impreseneidistretti industriali,byP.FINALDIRUSSO and P. ROSSI (December 1999).

No. 361 — Why Do Banks Merge?, by D. FOCARELLI, F. PANETTA and C. SALLEO (December1999).

No. 362 — Markup and the Business Cycle: Evidence from Italian Manufacturing Branches,by D. J. MARCHETTI (December 1999).

No. 363 — The Transmission of Monetary Policy Shocks in Italy, 1967-1997, by E. GAIOTTI(December 1999).

No. 364 — Rigidità nel mercato del lavoro, disoccupazione e crescita, by F. SCHIVARDI(December 1999).

No. 365 — Labor Markets and Monetary Union: A Strategic Analysis, by A. CUKIERMAN andF. LIPPI (February 2000).

No. 366 — On the Mechanics of Migration Decisions: Skill Complementarities andEndogenous Price Differentials, by M. GIANNETTI (February 2000).

No. 367 — An Investment-Function-Based Measure of Capacity Utilisation. Potential Outputand Utilised Capacity in the Bank of Italy’s Quarterly Model, by G. PARIGI andS. SIVIERO (February 2000).

No. 368 — Information Spillovers and Factor Adjustment, by L. GUISO and F. SCHIVARDI(February 2000).

No. 369 — Banking System, International Investors and Central Bank Policy in EmergingMarkets, by M. GIANNETTI (March 2000).

No. 370 — Forecasting Industrial Production in the Euro Area, by G. BODO, R. GOLINELLIand G. PARIGI (March 2000).

No. 371 — The Seasonal Adjustment of the Harmonised Index of Consumer Prices for the EuroArea: a Comparison of Direct and Indirect Methods, by R. CRISTADORO andR. SABBATINI (March 2000).

No. 372 — Investment and Growth in Europe and in the United States in the Nineties, byP. CASELLI, P. PAGANO and F. SCHIVARDI (March 2000).

No. 373 — Tassazione e costo del lavoro nei paesi industriali, by M. R. MARINO andR. RINALDI (June 2000).

No. 374 — Strategic Monetary Policy with Non-Atomistic Wage-Setters, by F. LIPPI (June2000).

No. 375 — Emu Fiscal Rules: is There a Gap?, by F. BALASSONE and D. MONACELLI (June2000).

No. 376 — Do Better Institutions Mitigate Agency Problems? Evidence from CorporateFinance Choices, by M. GIANNETTI (June 2000).

No. 377 — The Italian Business Cycle: Coincident and Leading Indicators and Some StylizedFacts, by F. ALTISSIMO, D. J. MARCHETTI and G. P. ONETO (October 2000).

No. 378 — Stock Values and Fundamentals: Link or Irrationality?, by F. FORNARI and M.PERICOLI (October 2000).

No. 379 — Promise and Pitfalls in the Use of “Secondary” Data-Sets: Income Inequality inOECD Countries, by A. B. ATKINSON and A. BRANDOLINI (October 2000).

No. 380 — Bank Competition and Regulatory Reform: The Case of the Italian BankingIndustry, by P. ANGELINI and N. CETORELLI (October 2000).

No. 381 — The Determinants of Cross-Border Bank Shareholdings: an Analysis withBank-Level Data from OECD Countries, by D. FOCARELLI and A. F. POZZOLO(October 2000).

No. 382 — Endogenous Growth with Intertemporally Dependent Preferences, by G.FERRAGUTO and P. PAGANO (October 2000).

(*) Requests for copies should be sent to:Banca d’Italia -- Servizio Studi -- Divisione Biblioteca e pubblicazioni -- Via Nazionale, 91 -- 00184 Rome(fax 0039 06 47922059). They are available on the Internet at www.bancaditalia.it


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