RUHR
ECONOMIC PAPERS
Thomas K. Bauer
Stefan Bender
Jörg Heining
Christoph M. Schmidt
Brother Sun, Sister Moon:
The Lunar Cycle, Sunspots
and the Frequency of Births
#225
Imprint
Ruhr Economic Papers
Published by
Ruhr-Universität Bochum (RUB), Department of Economics
Universitätsstr. 150, 44801 Bochum, Germany
Technische Universität Dortmund, Department of Economic and Social Sciences
Vogelpothsweg 87, 44227 Dortmund, Germany
Universität Duisburg-Essen, Department of Economics
Universitätsstr. 12, 45117 Essen, Germany
Rheinisch-Westfälisches Institut für Wirtschaftsforschung (RWI)
Hohenzollernstr. 1-3, 45128 Essen, Germany
Editors
Prof. Dr. Thomas K. Bauer
RUB, Department of Economics, Empirical Economics
Phone: +49 (0) 234/3 22 83 41, e-mail: [email protected]
Prof. Dr. Wolfgang Leininger
Technische Universität Dortmund, Department of Economic and Social Sciences
Economics – Microeconomics
Phone: +49 (0) 231/7 55-3297, email: [email protected]
Prof. Dr. Volker Clausen
University of Duisburg-Essen, Department of Economics
International Economics
Phone: +49 (0) 201/1 83-3655, e-mail: [email protected]
Prof. Dr. Christoph M. Schmidt
RWI, Phone: +49 (0) 201/81 49 -227, e-mail: [email protected]
Editorial Office
Joachim Schmidt
RWI, Phone: +49 (0) 201/81 49 -292, e-mail: [email protected]
Ruhr Economic Papers #225
Responsible Editor: Thomas K. Bauer
All rights reserved. Bochum, Dortmund, Duisburg, Essen, Germany, 2010
ISSN 1864-4872 (online) – ISBN 978-3-86788-257-6
The working papers published in the Series constitute work in progress circulated to
stimulate discussion and critical comments. Views expressed represent exclusively the
authors’ own opinions and do not necessarily reflect those of the editors.
Ruhr Economic Papers #225
Thomas K. Bauer, Stefan Bender, Jörg Heining, and Christoph M. Schmidt
Brother Sun, Sister Moon:
The Lunar Cycle, Sunspots
and the Frequency of Births
Bibliografische Informationen
der Deutschen Nationalbibliothek
Die Deutsche Bibliothek verzeichnet diese Publikation in der deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über:
http://dnb.d-nb.de abrufbar.
ISSN 1864-4872 (online)
ISBN 978-3-86788-257-6
Thomas K. Bauer, Stefan Bender, Jörg Heining, and Christoph M. Schmidt 1
Brother Sun, Sister Moon: The Lunar
Cycle, Sunspots and the Frequency of
Births
Abstract
Based on multivariate linear regression models, we analyze the effect of the lunar cycle
and the number of sunspots occurring on a particular day on the number of births
using social security data and controlling for a number of other potential confounders.
The daily number of births between 1920 and 1989 have been calculated from the full
sample of individuals who have been registered at least once in the German social
security system. While the lunar cycle does not affect the number of births, the number
of sunspots has a positive, albeit small effect on the number of births which is decreasing
over time. The empirical results may be explained by medical technological progress
making natural influences on births less important over time. This interpretation is
supported by the results on the intertemporal influence of weekends and holidays on
the frequency of daily births.
JEL Classification: I12, J13
Keywords: Daily frequency of births; lunar cycle; sunspots
November 2010
1 Thomas K. Bauer, RWI, Ruhr-Universität Bochum and IZA, Bonn; Stefan Bender, IAB Nürnberg;
Jörg Heining, IAB Nürnberg; Christoph M. Schmidt, RWI, Ruhr-Universität Bochum, IZA, Bonn, and
CEPR London. – We thank Christina Grabinger at the IAB for her support in the preparation of the
data. – All correspondence to Thomas K. Bauer, RWI, Hohenzollernstr. 1-3, 45128 Essen, Germany,
E-Mail: [email protected].
Introduction
ƒ› ’‡‘’Ž‡ǡ —‡†—…ƒ–‡† ‘” ‡†—…ƒ–‡†ǡ „‡Ž‹‡˜‡ –Šƒ– –Š‡”‡ ‹• •‘‡–Š‹‰ •‹‹•–‡” ƒ„‘—– –Š‡ ˆ—ŽŽ
‘‘ǤƒŽ‡•ƒ„‘—–‘•–‡”•ǡ™‡”‡™‘Ž˜‡•ǡƒ†˜ƒ’‹”‡•”ƒ‹•‡†„›–Š‡ˆ—ŽŽ‘‘–‘’—”•—‡–Š‡‹”
‡˜‹Ž †‡‡†• •–‹ŽŽ „‡Ž‘‰ –‘ –”ƒ†‹–‹‘ƒŽ ˆ‘ŽŽ‘”‡ǡ ‘– ‘Ž› ‹ ”ƒ•›Ž˜ƒ‹ƒǤ ˜‡ ‘–Š‡”™‹•‡ “—‹–‡
•‘„‡”’‡‘’Ž‡•‘‡–‹‡•„Žƒ‡–Š‡ˆ—ŽŽ‘‘ˆ‘”–Š‡„ƒ†„‡Šƒ˜‹‘”‘ˆ‹†•‘”ˆ‘”•Ž‡‡’Ž‡••‹‰Š–•Ǥ
‡’‘’—Žƒ”ƒ†’‡”•‹•–‡–•—’‡”•–‹–‹‘‡˜‡ƒ‘‰—”•‡•‹‘„•–‡–”‹…•™ƒ”†•Š‘Ž†•–Šƒ––Š‡
Ž—ƒ”…›…Ž‡ƒˆˆ‡…–•–Š‡‘•‡–‘ˆŽƒ„‘”ƒ†–Šƒ–ǡ…‘•‡“—‡–Ž›ǡ–Š‡ˆ—ŽŽ‘‘”ƒ‹•‡•–Š‡—„‡”‘ˆ
„‹”–Š•Ǥ ˆ –Š‹• ™‡”‡ ‹†‡‡† –Š‡ …ƒ•‡ǡ ‹– •Š‘—Ž† „‡ ‘ˆ …‘•‹†‡”ƒ„Ž‡ ‹–‡”‡•– ˆ‘” –Š‡ ƒƒ‰‡”• ‘ˆ
Š‘•’‹–ƒŽ•ǡ•‹…‡–Š‡–Š‡›…‘—Ž†‡ƒ•‹Ž›ƒ†Œ—•––Š‡•–ƒˆˆ‹‰–‘–Š‡˜ƒ”‹ƒ„Ž‡™‘”Ž‘ƒ†‘……—””‹‰‹
†‹ˆˆ‡”‡–’Šƒ•‡•‘ˆ–Š‡Ž—ƒ”…›…Ž‡Ǥ
‘‰‘–Š‡”‘–‹˜‡•ǡ–Š‹•‹–‡”‡•–Šƒ•‹•’‹”‡†”‡•‡ƒ”…Š‡”•–‘‹˜‡•–‹‰ƒ–‡–Š‡‡ˆˆ‡…–‘ˆ–Š‡Ž—ƒ”
…›…Ž‡ƒ†‘–Š‡”ƒ–—”ƒŽ’Š‡‘‡ƒ•—…Šƒ•ǡˆ‘”‡šƒ’Ž‡ǡ’”‡…‹’‹–ƒ–‹‘ǡ–‡’‡”ƒ–—”‡˜ƒ”‹ƒ–‹‘•ǡ
ƒ† „ƒ”‘‡–”‹… ’”‡••—”‡ ‘ ’”‡‰ƒ…› ƒ† Žƒ„‘”Ǥ ȋͳȌ ȋʹȌ ȋ͵Ȍ ȋͶȌ ȋͷȌ ȋ͸Ȍ ȋ͹Ȍ ȋͺȌ Ž‘•‡Ž› ”‡Žƒ–‡† ’ƒ’‡”•
ƒƒŽ›œ‡†‘–Š‡”’‘–‡–‹ƒŽ‡ˆˆ‡…–•‘ˆ–Š‡Ž—ƒ”…›…Ž‡ǡ•—…Šƒ•–Š‡‡ˆˆ‡…–‘ˆ–Š‡ˆ—ŽŽ‘‘‘ƒ‹ƒŽ
„‹–‡•ȋͻȌȋͳͲȌǡ…”‹‡ȋͳͳȌǡƒ†—”‹ƒ”›”‡–‡–‹‘ȋͳʹȌǤŽŽ–Š‡•‡•–—†‹‡•ǡŠ‘™‡˜‡”ǡ‡‹–Š‡””‡Ž›‘”ƒ–Š‡”
•ƒŽŽ•ƒ’Ž‡•ǡƒ”‡”‡Žƒ–‡†–‘ƒ•‹‰Ž‡Š‘•’‹–ƒŽ‘”ƒ•‹‰Ž‡”‡‰‹‘‘Ž›ǡ‡”‡Ž›…‘˜‡”ƒ•Š‘”––‹‡
’‡”‹‘†‘”‡’Ž‘›‘˜‡”Ž›•‹’Ž‡„‹˜ƒ”‹ƒ–‡•–ƒ–‹•–‹…ƒŽ–‡•–•™Š‹…Šƒ”‡’”‘‡–‘‰‡‡”ƒ–‡•’—”‹‘—•
”‡•—Ž–•ǤŠ‡‘˜‡”ƒŽŽ‡˜‹†‡…‡ƒ’’‡ƒ”•–‘„‡‹š‡†ǡ™‹–Š‘•–•–—†‹‡•ˆ‹†‹‰‘‘”ƒ–„‡•–ƒ™‡ƒ
ƒ••‘…‹ƒ–‹‘„‡–™‡‡–Š‡Ž—ƒ”…›…Ž‡ƒ†–Š‡ˆ”‡“—‡…›‘ˆ„‹”–Š•Ǥ
ƒ–—”ƒŽ ’Š‡‘‡ƒ –Šƒ– Šƒ˜‡ „‡‡ ‹˜‡•–‹‰ƒ–‡† Ž‡•• ‡š–‡•‹˜‡Ž› ƒ”‡ –Š‡ ”‘Ž‡ ‘ˆ ‰‡‘ƒ‰‡–‹…
†‹•–—”„ƒ…‡•ƒ†”ƒ†‹ƒ–‹‘‘Š—ƒŠ‡ƒŽ–Š‘—–…‘‡•Ǥš‹•–‹‰‡˜‹†‡…‡‹†‹…ƒ–‡•ǡˆ‘”‡šƒ’Ž‡ǡ
–Šƒ–•‘Žƒ”ƒ…–‹˜‹–›‹•…‘””‡Žƒ–‡†™‹–ŠŠ—ƒ…‘…‡’–‹‘•ȋͳ͵ȌȋͳͶȌȋͳͷȌȋͳ͸ȌǡŠ—ƒŽ‹ˆ‡•’ƒȋͳ͹ȌȋͳͺȌƒ†
‘–Š‡”Š‡ƒŽ–Š‘—–…‘‡˜ƒ”‹ƒ„Ž‡•ȋ•‡‡ȋͳ͵Ȍˆ‘”ƒ”‡˜‹‡™ȌǤ
Š‹• ’ƒ’‡” ‡šƒ‹‡• –Š‡ ‡ˆˆ‡…– ‘ˆ –Š‡ Ž—ƒ” ƒ† •‘Žƒ” …›…Ž‡ ‘ –Š‡ †ƒ‹Ž› ˆ”‡“—‡…› ‘ˆ „‹”–Š• ‹
‡”ƒ› —•‹‰ ƒ Žƒ”‰‡ †ƒ–ƒ •‘—”…‡ …‘˜‡”‹‰ –Š‡ „‹”–Š ›‡ƒ”• ˆ”‘ ͳͻʹͲ –‘ ͳͻͻͲǤ ‡ ‡’Ž‘›
—Ž–‹˜ƒ”‹ƒ–‡ ”‡‰”‡••‹‘ ƒƒŽ›•‹• ‹ ‘”†‡” –‘ ƒ……‘—– ˆ‘” …‘ˆ‘—†‹‰ ˆƒ…–‘”•ǡ •—…Š ƒ• •‡ƒ•‘ƒŽ
ƒ†™‡‡Ž›„‹”–Š’ƒ––‡”•ƒ•™‡ŽŽƒ•–Š‡‡ˆˆ‡…–‘ˆ’—„Ž‹…Š‘Ž‹†ƒ›•Ǥ
Data and Methods
‡—•‡–Š‡ˆ—ŽŽ•ƒ’Ž‡‘ˆ–Š‡
‡”ƒ‡’Ž‘›‡–”‡‰‹•–‡”Ȃƒƒ†‹‹•–”ƒ–‹˜‡†ƒ–ƒ•‡–…‘˜‡”‹‰
ƒŽŽ’‡”•‘•™‹–Š
‡”ƒƒ–‹‘ƒŽ‹–›™Š‘Šƒ˜‡’ƒ‹†•‘…‹ƒŽ•‡…—”‹–›…‘–”‹„—–‹‘•ˆ‘”ƒ–Ž‡ƒ•–‘‡
†ƒ› †—”‹‰ –Š‡ ’‡”‹‘† ˆ”‘ ͳͻ͹ͷ –‘ ʹͲͲͺ ƒ† †‡•…”‹„‡† ‹ †‡–ƒ‹Ž „› ȋͳͻȌǤ ‡ ‡š…Ž—†‡†
ˆ‘”‡‹‰‡”•ˆ”‘–Š‡ƒƒŽ›•‹•„‡…ƒ—•‡–Š‡›•Š‘™ƒ—ƒ–—”ƒŽ…Ž—•–‡”‹‰‘ˆ„‹”–Š†ƒ›•ƒ–•’‡…‹ˆ‹…
†ƒ›•ǡ•—…Šƒ•–Š‡ˆ‹”•–†ƒ›‘ˆ‡ƒ…Š‘–ŠǤ”‘–Š‹••ƒ’Ž‡™‡—•‡–Š‡‡šƒ…–„‹”–Š†ƒ›•ˆ‘”‘”‡
–Šƒ ͸ͳǤͶ ‹ŽŽ‹‘ ‹†‹˜‹†—ƒŽ• –‘ …ƒŽ…—Žƒ–‡ –Š‡ —„‡” ‘ˆ „‹”–Š• ‘ ‡ƒ…Š †ƒ› ‹ –Š‡ ’‡”‹‘† ˆ”‘
ͳͻʹͲ –‘ ͳͻͺͻǡ ’”‘˜‹†‹‰ —• ™‹–Š ƒ –‘–ƒŽ ‘ˆ ʹͷǡͷ͸ͺ ‘„•‡”˜ƒ–‹‘•Ǥ ‡ ‡”‰‡† –Š‹• †ƒ–ƒ ™‹–Š –Š‡
†ƒ‹Ž› —„‡” ‘ˆ •—•’‘–•ǡ ‘„–ƒ‹‡† ˆ”‘ –Š‡ ™‡„’ƒ‰‡ ‘ˆ –Š‡ ‘Žƒ” ˆŽ—‡…‡• ƒ–ƒ ƒŽ›•‹•
‡–‡” ȋŠ––’ǣȀȀ•‹†…Ǥ‘ƒǤ„‡Ȁ•—•’‘–Ǧ†ƒ–ƒȀ†ƒ‹Ž›••Ǥ’Š’Ȍǡ ƒ† ™‹–Š ‹ˆ‘”ƒ–‹‘ ‘ –Š‡ Ž—ƒ”
…›…Ž‡ǡ
‘„–ƒ‹‡†
ˆ”‘
–Š‡
Š‡
—‹…Š
•–”‘
”…Š‹˜‡
ȋŠ––’ǣȀȀ™™™ǤƒƒǤŠǤ†‡Ȁ–ƒ”ƒ–‡Ȁ‘†’Šƒ•‡ǤŠ–ŽȌǤ  –‘–ƒŽǡ ‘—” •ƒ’Ž‡ ’‡”‹‘† …‘˜‡”•
ƒ„‘—–ͺ͸͸”‡’‡–‹–‹‘•‘ˆ–Š‡Ž—ƒ”…›…Ž‡Ǥ
4
01/01/1960
01/01/1970
01/01/1980
01/01/1990
01/01/1960
01/01/1970
01/01/1980
01/01/1990
01/01/1950
01/01/1940
01/01/1930
01/01/1920
0
100
200
Number of sunspots
300
400
Figure 1:ƒ‹Ž›—„‡”‘ˆ•—•’‘–•ǡͳͻʹͲȂͳͻͺͻ
Year
01/01/1950
01/01/1940
01/01/1930
01/01/1920
1000
2000
3000
Number of births
4000
5000
Figure 2:ƒ‹Ž›—„‡”‘ˆ„‹”–Š•
Year
‹‰—”‡ͳ•Š‘™•–Š‡—„‡”‘ˆ•—•’‘–•ˆ‘”‡˜‡”›†ƒ›…‘˜‡”‡†„›–Š‡†ƒ–ƒǤ–…Ž‡ƒ”Ž›•Š‘™•–Š‡
™‡ŽŽ†‘…—‡–‡†ͳͳǦ›‡ƒ”…›…Ž‡‘ˆ•—•’‘–•ǡ†‘—„Ž‡Ǧ’‡ƒ‹‰ˆ‘”ƒ„‘—––Š”‡‡›‡ƒ”•‹‡˜‡”›…›…Ž‡Ǥ
ȋʹͲȌŠ‡ƒ˜‡”ƒ‰‡†ƒ‹Ž›—„‡”‘ˆ•—•’‘–•‹‘—”†ƒ–ƒ‹•͸͸ǡ”ƒ‰‹‰ˆ”‘‘•—•’‘–•‘ʹͷͺͻ
5
†ƒ›•–‘ƒƒš‹—‘ˆ͵ͷͷ•—•’‘–•‘……—””‹‰‘–Š‡ʹͶ–Šƒ†ʹͷ–Š‘ˆ‡…‡„‡”ͳͻͷ͹Ǥ‹‰—”‡ʹ
†‡’‹…–• –Š‡ †‡˜‡Ž‘’‡– ‘ˆ –Š‡ —„‡” ‘ˆ †ƒ‹Ž› „‹”–Š• ‹ ‘—” •ƒ’Ž‡ ’‡”‹‘†Ǥ – •Š‘™• –Š‡
‹…”‡ƒ•‹‰ —„‡” ‘ˆ „‹”–Š• —–‹Ž ͳͻͶͲǡ –Š‡ †”‘’ ‹ „‹”–Š• ƒ– –Š‡ ‡† ‘ˆ ‘”Ž† ƒ” ǡ –Š‡
‹…”‡ƒ•‹‰ˆ‡”–‹Ž‹–›–Š‡”‡ƒˆ–‡”ǡ…—Ž‹ƒ–‹‰‹–Š‡„ƒ„›„‘‘‹–Š‡ͳͻ͸Ͳ•ǡƒ†ˆ‹ƒŽŽ›–Š‡†”‘’‹
–Š‡—„‡”‘ˆ„‹”–Š•ƒ••‘…‹ƒ–‡†ǡƒ‘‰‘–Š‡”•ǡ™‹–Š–Š‡‹˜‡–‹‘‘ˆ–Š‡‘”ƒŽ…‘–”ƒ…‡’–‹˜‡’‹ŽŽǤ
Š‡‡ƒ—„‡”‘ˆ†ƒ‹Ž›„‹”–Š•‹‘—”•ƒ’Ž‡‹•ʹͶͲͲǡ”ƒ‰‹‰ˆ”‘ƒ‹‹——„‡”‘ˆͺʹ͵
–‘ƒƒš‹——„‡”‘ˆͷʹͷͲǤ
‘†‡–‡”‹‡–Š‡‡ˆˆ‡…–‘ˆ–Š‡Ž—ƒ”ƒ†•‘Žƒ”…›…Ž‡‘–Š‡ˆ”‡“—‡…›‘ˆ„‹”–Š•ǡ™‡‡•–‹ƒ–‡Ž‹‡ƒ”
—Ž–‹˜ƒ”‹ƒ–‡ ”‡‰”‡••‹‘ ‘†‡Ž• „› ‘”†‹ƒ”› Ž‡ƒ•– •“—ƒ”‡• —•‹‰ –Š‡ Ž‘‰ƒ”‹–Š ‘ˆ –Š‡ †ƒ‹Ž›
—„‡”‘ˆ„‹”–Š•ƒ•†‡’‡†‡–˜ƒ”‹ƒ„Ž‡ƒ†–Š‡Ž‘‰ƒ”‹–Š‘ˆ–Š‡—„‡”‘ˆ•—•’‘–•ƒ•™‡ŽŽƒ•ƒ
•‡”‹‡•‘ˆ†‹…Š‘–‘‘—•˜ƒ”‹ƒ„Ž‡•‹†‹…ƒ–‹‰–Š”‡‡‘ˆ–Š‡ˆ‘—”•–ƒ–‡•‘ˆ–Š‡Ž—ƒ”…›…Ž‡ȋ‡™‘‘ǡ
ˆ‹”•–“—ƒ”–‡”ƒ†ˆ—ŽŽ‘‘ǡ™‹–ŠŽƒ•–“—ƒ”–‡”ƒ…–‹‰ƒ•”‡ˆ‡”‡…‡‰”‘—’Ȍƒ•‡š’Žƒƒ–‘”›˜ƒ”‹ƒ„Ž‡•Ǥ
 –Š‡ —Ž–‹˜ƒ”‹ƒ–‡ ”‡‰”‡••‹‘ ‘†‡Ž• ™‡ ƒŽ•‘ …‘–”‘Ž ˆ‘” ƒ —„‡” ‘ˆ ’‘–‡–‹ƒŽ …‘ˆ‘—†‹‰
ˆƒ…–‘”•Ǥ–ƒ’’‡ƒ”•–‘„‡‹’‘”–ƒ–ǡˆ‘”‡šƒ’Ž‡ǡ–‘–ƒ‡’‘–‡–‹ƒŽ‡ˆˆ‡…–•†—‡–‘–Š‡…Ž—•–‡”‹‰‘ˆ
‹†—…‡† Žƒ„‘”• ƒ† ‡Ž‡…–‹˜‡ Ǧ•‡…–‹‘• ‘ ’ƒ”–‹…—Žƒ” †ƒ›• ‘” ™‡‡‡† ‡ˆˆ‡…–• ‹–‘ ƒ……‘—–Ǥ ȋʹͳȌ
Š‡‘†‡Ž–Š‡”‡ˆ‘”‡‹…Ž—†‡•ƒ•‡”‹‡•‘ˆ†‹…Š‘–‘‘—•˜ƒ”‹ƒ„Ž‡•‹†‹…ƒ–‹‰–Š‡†ƒ›‘ˆ–Š‡™‡‡ǡ
™‹–Š ‡†‡•†ƒ› „‡‹‰ –Š‡ ”‡ˆ‡”‡…‡ ‰”‘—’ǡ ƒ• ™‡ŽŽ ƒ• †‹…Š‘–‘‘—• ˜ƒ”‹ƒ„Ž‡• ˆ‘” –Š‡ ‘•–
‹’‘”–ƒ–
‡”ƒŠ‘Ž‹†ƒ›•Ǥ‡ˆ—”–Š‡”‹…Ž—†‡ƒ•‡”‹‡•‘ˆ‹†‹…ƒ–‘”˜ƒ”‹ƒ„Ž‡•ˆ‘”–Š‡‘–Š‘ˆ
„‹”–Š ƒ• ™‡ŽŽ ƒ• ͸ͻ †—‹‡• ˆ‘” –Š‡ ”‡•’‡…–‹˜‡ ›‡ƒ”• ‘ˆ „‹”–Šǡ–‘ …‘–”‘Ž ˆ‘” ’‘–‡–‹ƒŽ •‡ƒ•‘ƒŽ
’ƒ––‡”•™‹–Š‹ƒ’ƒ”–‹…—Žƒ”›‡ƒ”ƒ•™‡ŽŽƒ•–Š‡Ž‘‰Ǧ–‡”†‡˜‡Ž‘’‡–‘ˆˆ‡”–‹Ž‹–›‹‘—”•ƒ’Ž‡
’‡”‹‘†Ǥ
Results
‘šǦŽ‘–• ȋʹʹȌ ‘ˆ –Š‡ ”‡Žƒ–‹‘•Š‹’ „‡–™‡‡ –Š‡ Ž‘‰ƒ”‹–Š ‘ˆ †ƒ‹Ž› „‹”–Š• ƒ† –Š‡ Ž—ƒ” …›…Ž‡
ȋˆ‹‰—”‡͵Ȍ ‹†‹…ƒ–‡ –Šƒ– –Š‡”‡ ‹• ‘ ‡˜‹†‡– ”‡Žƒ–‹‘•Š‹’ „‡–™‡‡ –Š‡ ‘‘’Šƒ•‡• ƒ† –Š‡
—„‡”‘ˆ„‹”–Š•ǤŠ‡’”‡†‹…–‡†”‡Žƒ–‹‘•Š‹’ȋƒ†ƒͻͷΨ…‘ˆ‹†‡…‡‹–‡”˜ƒŽȌ„‡–™‡‡–Š‡†ƒ‹Ž›
—„‡” ‘ˆ „‹”–Š• ƒ† –Š‡ †ƒ‹Ž› —„‡” ‘ˆ •—•’‘–• ”‡•—Ž–‹‰ ˆ”‘ ƒ „‹˜ƒ”‹ƒ–‡ ”‡‰”‡••‹‘
–‘‰‡–Š‡”™‹–Šƒ•…ƒ––‡”’Ž‘–‘ˆ–Š‡–™‘˜ƒ”‹ƒ„Ž‡•‹••Š‘™‹ˆ‹‰—”‡ͶǤ›…‘–”ƒ•––‘–Š‡Žƒ…‹‰
ƒ••‘…‹ƒ–‹‘ ™‹–Š –Š‡ Ž—ƒ” …›…Ž‡ –Š‡”‡ ‹• ƒ •–ƒ–‹•–‹…ƒŽŽ› •‹‰‹ˆ‹…ƒ– ’‘•‹–‹˜‡ ƒ••‘…‹ƒ–‹‘ „‡–™‡‡
–Š‡–™‘˜ƒ”‹ƒ„Ž‡•Ǥ
 ‘”†‡” –‘ ‡š’Ž‘”‡ ™Š‡–Š‡” –Š‡ ƒ••‘…‹ƒ–‹‘ „‡–™‡‡ –Š‡ —„‡” ‘ˆ „‹”–Š• ƒ† –Š‡ Ž—ƒ” ƒ†
•‘Žƒ” …›…Ž‡ †‘…—‡–‡† ‹ ˆ‹‰—”‡•͵ ƒ† Ͷ ƒ”‡ …‘ˆ‹”‡† ™Š‡ …‘–”‘ŽŽ‹‰ ˆ‘” ‘–Š‡” ’‘–‡–‹ƒŽ
…‘ˆ‘—†‹‰ ˆƒ…–‘”• ˆ‘” –Š‡ —„‡” ‘ˆ „‹”–Š•ǡ –ƒ„Ž‡ͳ •Š‘™• –Š‡ ”‡•—Ž–• ˆ”‘ —Ž–‹˜ƒ”‹ƒ–‡
”‡‰”‡••‹‘‘†‡Ž•ˆ‘”‘—”ˆ—ŽŽ•ƒ’Ž‡‘ˆ„‹”–Š•„‡–™‡‡ͳͻʹͲƒ†ͳͻͺͻȋ…‘Ž—ȋͳȌȌƒ•™‡ŽŽƒ•
–Š‡•—„•ƒ’Ž‡‘ˆ„‹”–Š•‘……—””‹‰„‡–™‡‡ͳͻʹͲƒ†ͳͻͶͻǡͳͻͷͲƒ†ͳͻ͸ͻǡƒ†ͳͻ͹Ͳƒ†ͳͻͺͻ
ȋ…‘Ž—•ȋʹȌ –‘ ȋͶȌȌǤ Š‡ ‡•–‹ƒ–‹‘ ”‡•—Ž–• …‘ˆ‹” –Š‡ ‡š’Ž‘”ƒ–‘”› •–ƒ–‹•–‹…ƒŽ ƒƒŽ›•‹• ‘ˆ
ˆ‹‰—”‡•͵ ƒ† ͶǤ Š‡ ‡•–‹ƒ–‡† …‘‡ˆˆ‹…‹‡–• ‘ˆ –Š‡ –Š”‡‡ †‹…Š‘–‘‘—• ˜ƒ”‹ƒ„Ž‡• †‡•…”‹„‹‰ –Š‡
Ž—ƒ” …›…Ž‡ ƒ”‡ ‘– •–ƒ–‹•–‹…ƒŽŽ› •‹‰‹ˆ‹…ƒ–Ž› †‹ˆˆ‡”‡– ˆ”‘ œ‡”‘ ˆ‘” ƒ› ’‡”‹‘† …‘•‹†‡”‡†Ǥ
……‘”†‹‰ –‘ –Š‡ ”‡•—Ž–• ‘ˆ –Š‡ ƒ’’”‘’”‹ƒ–‡ Ǧ–‡•–ǡ –Š‡ —ŽŽ Š›’‘–Š‡•‹• –Šƒ– –Š‡ ‡•–‹ƒ–‡†
…‘‡ˆˆ‹…‹‡–• ‘ˆ –Š‡•‡ –Š”‡‡ ˜ƒ”‹ƒ„Ž‡• ƒ”‡ Œ‘‹–Ž› œ‡”‘ ‹• ‘– ”‡Œ‡…–‡† ˆ‘” ƒ› ‘ˆ –Š‡•‡ •ƒ’Ž‡• ƒ–
…‘˜‡–‹‘ƒŽŽ‡˜‡Ž•‘ˆ•‹‰‹ˆ‹…ƒ…‡Ǥ
6
6.5
Logarithm of Number of Births
7
7.5
8
8.5
Figure 3:‘‰ƒ”‹–Š‘ˆƒ‹Ž›—„‡”‘ˆ‹”–Š•ƒ†‘‘’Šƒ•‡•
New Moon
First Quarter
Full Moon
Last Quarter
6.5
Logarithm of Number of Births
7
7.5
8
8.5
Figure 4:‘‰ƒ”‹–Š‘ˆƒ‹Ž›—„‡”‘ˆ‹”–Š•ƒ†—•’‘–•
0
1
2
Number of Sunspots (in 100)
3
4
7
Table 1: ‡‰”‡••‹‘‡•—Ž–•Ǣ‡’‡†‡–ƒ”‹ƒ„Ž‡ǣ‘‰ƒ”‹–Š‘ˆƒ‹Ž›—„‡”‘ˆ‹”–Š•
‘Ž—
ƒ’Ž‡
ȋͳȌ
ŽŽ‡ƒ”•
ȋʹȌ
ͳͻʹͲǦͳͻͶͻ
ȋ͵Ȍ
ͳͻͷͲǦͳͻ͸ͻ
ȋͶȌ
ͳͻ͹ͲǦͳͻͺͻ
—„‡”‘ˆ—•’‘–•
ͲǤͲͲ͵ͳȗȗ
ȋͲǤͲͲͳͷȌ
ͲǤͲͲ͸ͺȗȗȗ
ȋͲǤͲͲʹͶȌ
ͲǤͲͲͲͺ
ȋͲǤͲͲͳͷȌ
ͲǤͲͲͲͺ
ȋͲǤͲͲͳ͹Ȍ
ǦͲǤͲͲͲͷ
ȋͲǤͲͲͳ͵Ȍ
ǦͲǤͲͲͲͳ
ȋͲǤͲͲͳ͵Ȍ
ǦͲǤͲͲͳ͵
ȋͲǤͲͲͳ͵Ȍ
ǦͲǤͲͲͳͷ
ȋͲǤͲͲʹͲȌ
ǦͲǤͲͲͳ͹
ȋͲǤͲͲʹͲȌ
ǦͲǤͲͲͳͳ
ȋͲǤͲͲʹͲȌ
ǦͲǤͲͲͳͲ
ȋͲǤͲͲͳͷȌ
ǦͲǤͲͲͲͻ
ȋͲǤͲͲͳͷȌ
ǦͲǤͲͲʹͶȗ
ȋͲǤͲͲͳͷȌ
ͲǤͲͲͳ͵
ȋͲǤͲͲͳ͸Ȍ
ͲǤͲͲ͵Ͳȗ
ȋͲǤͲͲͳ͸Ȍ
ͲǤͲͲͲʹ
ȋͲǤͲͲͳ͸Ȍ
ǦͲǤͲͶͷͷȗȗȗ
ȋͲǤͲͲͳ͹Ȍ
ǦͲǤͲͲͺͺȗȗȗ
ȋͲǤͲͲͳ͹Ȍ
ǦͲǤͲͲͲͶ
ȋͲǤͲͲͳ͹Ȍ
ͲǤͲͳͲͲȗȗȗ
ȋͲǤͲͲͳ͹Ȍ
ͲǤͲͳ͸ͻȗȗȗ
ȋͲǤͲͲͳ͹Ȍ
ǦͲǤͲͳͺ͸ȗȗȗ
ȋͲǤͲͲͳ͹Ȍ
ͲǤͲͶ͹͸ȗȗȗ
ȋͲǤͲͲʹ͸Ȍ
ǦͲǤͲͳͳͶȗȗȗ
ȋͲǤͲͲʹ͸Ȍ
ǦͲǤͲͳ͹͵ȗȗȗ
ȋͲǤͲͲʹ͸Ȍ
ͲǤͲͳ͹͸ȗȗȗ
ȋͲǤͲͲʹ͸Ȍ
ͲǤͲͳ͸ͳȗȗȗ
ȋͲǤͲͲʹ͸Ȍ
ͲǤͲʹ͹͸ȗȗȗ
ȋͲǤͲͲʹ͸Ȍ
ǦͲǤͲʹ͵͵ȗȗȗ
ȋͲǤͲͲͳͻȌ
ǦͲǤͲͲʹ͸
ȋͲǤͲͲͳͻȌ
ǦͲǤͲͲʹ͸
ȋͲǤͲͲͳͻȌ
ͲǤͲͳͳͻȗȗȗ
ȋͲǤͲͲͳͻȌ
ͲǤͲͳͻͶȗȗȗ
ȋͲǤͲͲͳͻȌ
ͲǤͲͳͲͶȗȗȗ
ȋͲǤͲͲͳͻȌ
ǦͲǤʹͲ͹Ͷȗȗȗ
ȋͲǤͲͲʹͳȌ
ǦͲǤͲͳͳͳȗȗȗ
ȋͲǤͲͲʹͳȌ
ͲǤͲʹ͹ʹȗȗȗ
ȋͲǤͲͲʹͳȌ
ǦͲǤͲͲʹͺ
ȋͲǤͲͲʹͳȌ
ͲǤͲͳͷͺȗȗȗ
ȋͲǤͲͲʹͳȌ
ǦͲǤͳͳ͸͸ȗȗȗ
ȋͲǤͲͲʹͳȌ
ͲǤͳʹͳͲȗȗȗ
ȋͲǤͲͲͻͲȌ
ǦͲǤͲ͵ͷͶȗȗȗ
ȋͲǤͲͲͶ͹Ȍ
ǦͲǤͲʹ͸ͻȗȗȗ
ȋͲǤͲͲͷ͵Ȍ
ǦͲǤͲͶʹͲȗȗȗ
ȋͲǤͲͲͷͶȌ
ǦͲǤͲ͵ʹ͵ȗȗȗ
ȋͲǤͲͳͲʹȌ
ͲǤͲͲͳͶ
ȋͲǤͲͳͲͲȌ
ǦͲǤͲͲ͹ͻ
ȋͲǤͲͲ͹ͶȌ
͸Ǥͻ͹ͳͷȗȗȗ
ȋͲǤͲͲͶͶȌ
ͲǤ͵ͻ
ȏͲǤ͹͸ͳͲȐ
ʹͷǡͷ͸ͺ
ͲǤͻͷ͸ͻ
ͲǤͳͳͲͲȗȗȗ
ȋͲǤͲͳ͵ͷȌ
ǦͲǤͲͲͲͷ
ȋͲǤͲͲ͹ͳȌ
ǦͲǤͲͲͲʹ
ȋͲǤͲͲͺͲȌ
ͲǤͲʹͶͶȗȗȗ
ȋͲǤͲͲͺͳȌ
ͲǤͲ͵͵ͻȗ
ȋͲǤͲͳͻ͹Ȍ
ͲǤͲ͵ͳͻ
ȋͲǤͲʹʹͷȌ
ͲǤͲͲ͹Ͷ
ȋͲǤͲͳ͹ͺȌ
͸ǤͻͷͲͶȗȗȗ
ȋͲǤͲͲͷͲȌ
ͲǤʹͻ
ȏͲǤͺ͵͵ͺȐ
ͳͲǡͻͷͺ
ͲǤͻͷͷʹ
ͲǤʹͳ͹ͳȗȗȗ
ȋͲǤͲͳͲͲȌ
ǦͲǤͲʹͷͻȗȗȗ
ȋͲǤͲͲͷʹȌ
ǦͲǤͲͳͻʹȗȗȗ
ȋͲǤͲͲͷͻȌ
ǦͲǤͲʹͶͺȗȗȗ
ȋͲǤͲͲ͸ͲȌ
ǦͲǤͲͳͻʹȗ
ȋͲǤͲͳͲͳȌ
ͲǤͲʹ͸ͺȗȗȗ
ȋͲǤͲͳͲͲȌ
ͲǤͲͲ͸ͷ
ȋͲǤͲͲ͹ͶȌ
͹Ǥͻͻ͹ͳȗȗȗ
ȋͲǤͲͲ͵͵Ȍ
ͲǤͻ͵
ȏͲǤͶʹͷ͸Ȑ
͹ǡ͵Ͳͷ
ͲǤͺͺͷͶ
ͲǤͲͶʹ͹ȗȗȗ
ȋͲǤͲͳͲͺȌ
ǦͲǤͲͻ͸͸ȗȗȗ
ȋͲǤͲͲͷ͸Ȍ
ǦͲǤͲ͹ͷͳȗȗȗ
ȋͲǤͲͲ͸ͶȌ
ǦͲǤͳͷͻͶȗȗȗ
ȋͲǤͲͲ͸ͶȌ
ǦͲǤͳͲ͸͹ȗȗȗ
ȋͲǤͲͳͲͻȌ
ǦͲǤͲ͸ʹͳȗȗȗ
ȋͲǤͲͳͲͺȌ
ǦͲǤͲ͵͸ʹȗȗȗ
ȋͲǤͲͲ͹͸Ȍ
͹ǤͷʹͲʹȗȗȗ
ȋͲǤͲͲͶͶȌ
ͳǤͶͻ
ȏͲǤʹͳ͸ͶȐ
͹ǡ͵Ͳͷ
ͲǤͺͻ͵ͺ
Moonphases
‹”•–—ƒ”–‡”
—ŽŽ‘‘
ƒ•–—ƒ”–‡”
Weekdays
—†ƒ›
‘†ƒ›
—‡•†ƒ›
Š—”•†ƒ›
”‹†ƒ›
ƒ–—”†ƒ›
Holidays
‡™‡ƒ”
ƒ•–‡”
‘™—†ƒ›
Š”‹•–ƒ•
•…‡•‹‘ƒ›
ƒ„‘—”ƒ›
ƒ–‹‘ƒŽƒ›
‘•–ƒ–
ȋ‹”•–—ƒ”–‡”α—ŽŽ‘‘αƒ•–—ƒ”–‡”αͲȌ
ȏ”‘„δȐ
„•‡”˜ƒ–‹‘•
†Œ—•–‡†ʹ
‘–‡•ǣ–ƒ†ƒ”†‡””‘”•‹’ƒ”‡–Š‡•‡•Ǣȗȗȗǣ–ƒ–‹•–‹…ƒŽŽ›•‹‰‹ˆ‹…ƒ–†‹ˆˆ‡”‡–ˆ”‘œ‡”‘ƒ–ƒŽ‡˜‡Ž
‘ˆ•‹‰‹ˆ‹…ƒ…‡‘ˆͳΨǢȗȗǣ–ƒ–‹•–‹…ƒŽŽ›•‹‰‹ˆ‹…ƒ–†‹ˆˆ‡”‡–ˆ”‘œ‡”‘ƒ–ƒŽ‡˜‡Ž‘ˆ•‹‰‹ˆ‹…ƒ…‡‘ˆ
ͷΨǢȗǣ–ƒ–‹•–‹…ƒŽŽ›•‹‰‹ˆ‹…ƒ–†‹ˆˆ‡”‡–ˆ”‘œ‡”‘ƒ–ƒŽ‡˜‡Ž‘ˆ•‹‰‹ˆ‹…ƒ…‡‘ˆͳͲΨǤŽŽ”‡‰”‡••‹‘•
‹…Ž—†‡ ‡Ž‡˜‡ †‹…Š‘–‘‘—• ˜ƒ”‹ƒ„Ž‡• ‹†‹…ƒ–‹‰ –Š‡ ‘–Š ƒ† ƒ •‡”‹‡• ‘ˆ †‹…Š‘–‘‘—•
˜ƒ”‹ƒ„Ž‡•‹†‹…ƒ–‹‰–Š‡›‡ƒ”‘ˆ„‹”–ŠǤ
› …‘–”ƒ•– –‘ –Š‡ Ž—ƒ” …›…Ž‡ǡ –Š‡ •‘Žƒ” …›…Ž‡ •Š‘™• ƒ •–ƒ–‹•–‹…ƒŽŽ› •‹‰‹ˆ‹…ƒ– ’‘•‹–‹˜‡ǡ ƒŽ„‡‹–
•ƒŽŽ ‡ˆˆ‡…– ‘ –Š‡ —„‡” ‘ˆ „‹”–Š•Ǥ ……‘”†‹‰ –‘ –Š‡ ‡•–‹ƒ–‡† …‘‡ˆˆ‹…‹‡– ‹ …‘Ž—ȋͳȌ ‘ˆ
–ƒ„Ž‡ͳǡ–Š‡‘……—””‡…‡‘ˆ•‘‡͸Ͳƒ††‹–‹‘ƒŽ•—•’‘–•ǡƒ’’”‘š‹ƒ–‡Ž›‘‡•–ƒ†ƒ”††‡˜‹ƒ–‹‘‹
–Š‡†‹•–”‹„—–‹‘‘ˆ•—•’‘–•ǡ‹…”‡ƒ•‡•–Š‡—„‡”‘ˆ„‹”–Š•„›ƒ„‘—–ͲǤͲͲʹΨ‘”Ȃ‡˜ƒŽ—ƒ–‡†ƒ–
–Š‡ƒ˜‡”ƒ‰‡†ƒ‹Ž›—„‡”‘ˆ„‹”–Š•Ȃ„›ƒŽ‘•–ͷ„‹”–Š•Ǥ‘•–‹’‘”–ƒ–Ž›ǡ–Š‹•‡ˆˆ‡…–ƒ’’‡ƒ”•–‘
8
†‡…”‡ƒ•‡‘˜‡”–‹‡ǤŠ‹Ž‡ƒ‘‡Ǧ•–ƒ†ƒ”†Ǧ†‡˜‹ƒ–‹‘‹…”‡ƒ•‡ ‹ –Š‡—„‡”‘ˆ•—•’‘–•”ƒ‹•‡†
–Š‡†ƒ‹Ž›—„‡”‘ˆ„‹”–Š•‘ƒ˜‡”ƒ‰‡„›‘”‡–ŠƒͲǤͲͲͶΨ„‡ˆ‘”‡ͳͻͷͲǡ–Š‡‡ˆˆ‡…–†‡…”‡ƒ•‡†–‘
Ž‡••–ŠƒͲǤͲͲͲͷΨƒˆ–‡”ͳͻͷͲǡ‘–‡˜‡„‡‹‰•–ƒ–‹•–‹…ƒŽŽ›•‹‰‹ˆ‹…ƒ–†‹ˆˆ‡”‡–ˆ”‘œ‡”‘‹–Š‡
Žƒ–‡”’‡”‹‘†ǤŠ‡•‡”‡•—Ž–••—‰‰‡•––Šƒ––Š‡”‡‹•ƒƒ–—”ƒŽ‹ˆŽ—‡…‡‘ˆ–Š‡•—‘–Š‡ˆ”‡“—‡…›‘ˆ
„‹”–Š•ǡ „—– –Šƒ– –Š‹• ‡ˆˆ‡…– Šƒ• †‹•ƒ’’‡ƒ”‡† ƒ• ‡†‹…ƒŽ –‡…Š‘Ž‘‰‹…ƒŽ ’”‘‰”‡•• ‹…”‡ƒ•‹‰Ž›
™‹†‡‡†–Š‡‰›‡…‘Ž‘‰‹…ƒŽ’‘••‹„‹Ž‹–‹‡•–‘…‘–”‘Ž–Š‡–‹‹‰‘ˆ„‹”–Š•Ǥ
Š‹•‹–‡”’”‡–ƒ–‹‘‹••—’’‘”–‡†„›–Š‡”‡•—Ž–•ˆ‘”–Š‡‘–Š‡”ˆƒ…–‘”•†‡–‡”‹‹‰–Š‡ˆ”‡“—‡…›‘ˆ
„‹”–Š•Ǥ ˜‡”ƒŽŽǡ „‹”–Š• ƒ’’‡ƒ” –‘ „‡ Ž‡•• Ž‹‡Ž› ‘ ™‡‡‡†• ƒ• ™‡ŽŽ ƒ• Š‘Ž‹†ƒ›• ȋ…‘Ž—ȋͳȌ ‘ˆ
–ƒ„Ž‡ͳȌǤ Š‡”‡ ‹•ǡ Š‘™‡˜‡”ǡ ƒ ”‡ƒ”ƒ„Ž‡ ‹–‡”–‡’‘”ƒŽ ’ƒ––‡”Ǥ Š‡ ‡•–‹ƒ–‡† …‘‡ˆˆ‹…‹‡–•
•—‰‰‡•––Šƒ–„‹”–Š•ƒ–™‡‡‡†•„‡…ƒ‡•—„•‡“—‡–Ž›Ž‡••Ž‹‡Ž›‘˜‡”–‹‡Ǥ‘”‡šƒ’Ž‡ǡ„‡ˆ‘”‡
ͳͻͷͲ •‘‡ ͶǤ͸Ψ ‘”‡ „ƒ„‹‡• Šƒ˜‡ „‡‡ „‘” ‘ —†ƒ›• –Šƒ ‘ ‡†‡•†ƒ›•ǡ ™Š‹Ž‡ ‹ –Š‡
ͳͻ͹Ͳ•ƒ†ͳͻͺͲ••‘‡ʹͲǤ͹؈‡™‡”„ƒ„‹‡•Šƒ˜‡„‡‡„‘”‘—†ƒ›•–Šƒ‘‡†‡•†ƒ›•Ǥ
•‹‹Žƒ”’ƒ––‡”ƒ’’‡ƒ”•ˆ‘”ƒ–—”†ƒ›•ƒ†‘•–‘ˆ–Š‡Š‘Ž‹†ƒ›•ǤŠ‹Ž‡ʹǤͶ؏‘”‡„ƒ„‹‡•Šƒ˜‡
„‡‡ „‘” ‘ Š”‹•–ƒ• –Šƒ ‘ ƒ˜‡”ƒ‰‡ „‡–™‡‡ ͳͻʹͲ ƒ† ͳͻͶͻǡ ƒŽ‘•– ͳ͸Ψ ˆ‡™‡” „ƒ„‹‡•
Šƒ˜‡„‡‡„‘”‘Š”‹•–ƒ•–Šƒ‘ƒ˜‡”ƒ‰‡„‡–™‡‡ͳͻ͹Ͳƒ†ͳͻͺͻǤ‰ƒ‹–Š‹•†‡˜‡Ž‘’‡–
ƒ›„‡‡š’Žƒ‹‡†„›‹’”‘˜‡†’‘••‹„‹Ž‹–‹‡•‘ˆ‡†‹…ƒŽ–”‡ƒ–‡–ǡ‹…”‡ƒ•‹‰–Š‡‘’–‹‘•–‘ƒ˜‘‹†
„‹”–Š•ƒ–†ƒ›•™‹–Šƒ”‡Žƒ–‹˜‡Ž›Ž‘™•–ƒˆˆ‹‰ƒ–‘„•–‡–”‹…™ƒ”†•Ǥ
Š‡”‡•—Ž–•ˆ‘”–Š‡†‹…Š‘–‘‘—•˜ƒ”‹ƒ„Ž‡•†‡•…”‹„‹‰–Š‡‘–Šƒ†›‡ƒ”‘ˆ„‹”–Šǡ™Š‹…Šƒ”‡‘–
•Š‘™ ‹ –ƒ„Ž‡ͳ „—– ƒ”‡ ƒ˜ƒ‹Žƒ„Ž‡ ˆ”‘ –Š‡ ƒ—–Š‘”• —’‘ ”‡“—‡•–ǡ ƒ”‡ ‹ ƒ……‘”†ƒ…‡ ™‹–Š
‡š‹•–‹‰ ‡˜‹†‡…‡Ǥ ’‡…‹ˆ‹…ƒŽŽ›ǡ „‹”–Š ˆ”‡“—‡…‹‡• ‹ ‘—” †ƒ–ƒ •Š‘™ –Š‡ —•—ƒŽ •‡ƒ•‘ƒŽ ’ƒ––‡”ǡ
„‡‹‰‘”‡Ž‹‡Ž›ƒ––Š‡„‡‰‹‹‰‘ˆ–Š‡›‡ƒ”•–ƒ”–‹‰‹‡„”—ƒ”›ƒ†Ž‡••Ž‹‡Ž›‹‹†•—‡”
ƒ† ƒ– –Š‡ ‡† ‘ˆ –Š‡ ›‡ƒ”Ǥ —”–Š‡”‘”‡ –Š‡ ‡•–‹ƒ–‡† …‘‡ˆˆ‹…‹‡–• ‘ˆ †‹…Š‘–‘‘—• ˜ƒ”‹ƒ„Ž‡•
†‡•…”‹„‹‰–Š‡›‡ƒ”‘ˆ„‹”–Š”‡ˆŽ‡…––Š‡‘˜‡”ƒŽŽ†‡˜‡Ž‘’‡–‘ˆ„‹”–Š”ƒ–‡•‹
‡”ƒ›™‹–ŠŽ‘™‡”
”ƒ–‡•‹–Š‡‰”‡ƒ–†‡’”‡••‹‘‹–Š‡ͳͻʹͲ•ƒ†–Š‡„ƒ„›„‘‘‹–Š‡ͳͻ͸Ͳ•Ǥ
‹ƒŽŽ›ǡ –Š‡ ‡š’Žƒƒ–‘”› ’‘™‡” ‘ˆ ‘—” ”‡‰”‡••‹‘ ‘†‡Ž †‡…”‡ƒ•‡• ‘˜‡” –‹‡ ƒ† Š‡…‡ǡ ƒŽ•‘
•—’’‘”–• ‘—” ‹–‡”’”‡–ƒ–‹‘ –Šƒ– ‹’”‘˜‡† ‡†‹…ƒŽ –‡…Š‘Ž‘‰› †‡…”‡ƒ•‡ –Š‡ ‹’ƒ…– ‘ˆ ƒ–—”ƒŽ
ˆƒ…–‘”• †‡–‡”‹‹‰ –Š‡ —„‡” ‘ˆ „‹”–Š•Ǥ Š‹Ž‡ –Š‡ ƒ†Œ—•–‡† ʹ ‹†‹…ƒ–‡• –Šƒ– ™‡ ƒ”‡ ƒ„Ž‡ –‘
‡š’Žƒ‹‘”‡–ŠƒͻͷΨ‘ˆ–Š‡˜ƒ”‹ƒ–‹‘‘ˆ‘—”†‡’‡†‡–˜ƒ”‹ƒ„Ž‡ˆ‘”’‡”•‘•„‘”„‡ˆ‘”‡ͳͻͷͲǡ
–Š‡ •ƒ‡ ‘†‡Ž ‡š’Žƒ‹• ‘Ž› ƒ„‘—– ͺͻΨ ‘ˆ –Š‡ ˜ƒ”‹ƒ–‹‘ ‘ˆ –Š‡ —„‡” ‘ˆ †ƒ‹Ž› „‹”–Š• ‹ –Š‡
ͳͻ͹Ͳ•ƒ†ͳͻͺͲ•Ǥ
Discussion
‘ˆ‹”‹‰ ‡š‹•–‹‰ ‡˜‹†‡…‡ ˆ‘” ‘–Š‡” …‘—–”‹‡•ǡ –Š‡ ˆ”‡“—‡…› ‘ˆ „‹”–Š• ‹ ‡”ƒ› †‘‡• ‘–
•‡‡–‘„‡”‡Žƒ–‡†–‘–Š‡Ž—ƒ”…›…Ž‡Ǥ‘™‡˜‡”ǡ„‹”–Š•ƒ”‡ƒ’’ƒ”‡–Ž›”‡Žƒ–‡†•‹‰‹ˆ‹…ƒ–Ž›–‘–Š‡
—„‡”‘ˆ•—•’‘–•ǡ‡˜‡–Š‘—‰Š‹“—ƒ–‹–ƒ–‹˜‡–‡”•–Š‡‡ˆˆ‡…–‘ˆ–Š‡•‘Žƒ”…›…Ž‡‘„‹”–Š•‹•
•ƒŽŽǤ ‡…‡ǡ ™Š‹Ž‡ ‘—” ”‡•—Ž–• ƒ› Š‡Ž’ ™ƒ”†‹‰ ‘ˆˆ –Š‡ …‘‘ •—’‡”•–‹–‹‘• ”‡‰ƒ”†‹‰ –Š‡
‡ˆˆ‡…–• ‘ˆ –Š‡ Ž—ƒ” …›…Ž‡ǡ ‘—” ”‡•—Ž–• ƒ› •—’’‘”– ‘–Š‡”ǡ ƒŽ„‡‹– Ž‡•• …‘‘ „‡Ž‹‡ˆ• ƒ„‘—– –Š‡
‹ˆŽ—‡…‡‘ˆ–Š‡•—‘Š—ƒˆ‘”–—‡Ǥ
—”‡’‹”‹…ƒŽƒƒŽ›•‹•ƒ‡••–”‘‰‡ˆˆ‘”–•–‘ƒ˜‘‹†–Šƒ–™‡Œ—•–‡ƒ•—”‡ƒ•–ƒ–‹•–‹…ƒŽƒ”–‹ˆƒ…–Ǥ
‡ —•‡ ƒ Š—‰‡ •ƒ’Ž‡ …‘˜‡”‹‰ ƒŽ‘•– –Š‡ ‡–‹”‡ ‡”ƒ ’‘’—Žƒ–‹‘ „‘” „‡–™‡‡ ͳͻʹͲ ƒ†
ͳͻͺͻǤ‡…‡ǡ„‹ƒ•‡†‡•–‹ƒ–‹‘”‡•—Ž–•†—‡–‘•ƒ’Ž‡•‡Ž‡…–‹‘’”‘„Ž‡•†‘‘–ƒ’’‡ƒ”–‘„‡ƒ
’”‘„Ž‡Ǥ Ž•‘ǡ „› —•‹‰ —Ž–‹˜ƒ”‹ƒ–‡ ”‡‰”‡••‹‘ ƒƒŽ›•‹• –Šƒ– …‘–”‘Ž• ˆ‘” ƒ ˜ƒ•– —„‡” ‘ˆ
9
’‘–‡–‹ƒŽ…‘ˆ‘—†‹‰ˆƒ…–‘”•ǡ™‡–”›–‘ƒ˜‘‹†’”‘„Ž‡•‘ˆ•’—”‹‘—•”‡‰”‡••‹‘Ǥ‡˜‡”–Š‡Ž‡••ǡ™‡
ƒ› Šƒ˜‡ ‹••‡† •‘‡ ’‘–‡–‹ƒŽ ‘–Š‡” †‡–‡”‹ƒ–• ‘ˆ –Š‡ †ƒ‹Ž› ˆ”‡“—‡…› ‘ˆ –Š‡ —„‡” ‘ˆ
„‹”–Š•–Šƒ–‹‰Š–„‡…‘””‡Žƒ–‡†™‹–Š–Š‡—„‡”‘ˆ•—•’‘–•Ǥ˜‡–Š‘—‰Š…‘•‹•–‡–•…‹‡–‹ˆ‹…
”‡•—Ž–•ƒ”‡•–‹ŽŽ‹••‹‰ǡ‹–ƒ›„‡–Š‡…ƒ•‡–Šƒ–•—•’‘–•‹ˆŽ—‡…‡–Š‡…Ž‹ƒ–‡ǡ‹Ǥ‡Ǥ–‡’‡”ƒ–—”‡ǡ
Š—‹†‹–› ‘” „ƒ”‘‡–”‹… ’”‡••—”‡Ǥ ‘ –Š‡ ‡š–‡– –Šƒ– –Š‡•‡ ˜ƒ”‹ƒ„Ž‡• ƒŽ•‘ ƒˆˆ‡…– „‹”–Š•ǡ ‘—”
‡’‹”‹…ƒŽ”‡•—Ž–•ƒ›„‡„‹ƒ•‡†Ǥ˜‡”ƒŽŽǡ‘—””‡•—Ž–••—‰‰‡•––Šƒ–ˆ—”–Š‡”•–ƒ–‹•–‹…ƒŽƒ†‡†‹…ƒŽ
‹˜‡•–‹‰ƒ–‹‘•‘ˆ–Š‡†‡–‡”‹ƒ–•‘ˆ„‹”–Š••Š‘—Ž†…‘…‡–”ƒ–‡‘”‡‘–Š‡•‘Žƒ”ƒ†‘–‘–Š‡
Ž—ƒ”…›…Ž‡Ǥ
—” ”‡•—Ž–• …‘˜‡› –™‘ ‡••ƒ‰‡•ǡ ‘‡ ‹•–‹‰ƒ–‹‰ Š‘’‡ ‹ Š—ƒ ’”‘‰”‡•• ƒ† –Š‡ ‘–Š‡”
‡Žƒ…Š‘Ž›Ǥ‘•–‹’‘”–ƒ–Ž›ǡ™‡ˆ‹†ƒ’Ž‡”‡ƒ•‘–‘•–”‡‰–Š‡‘—”…‘ˆ‹†‡…‡‹‘†‡”‡”ƒ
Š‡ƒŽ–Š •›•–‡•Ǥ ƒ–—”ƒŽ ’Š‡‘‡ƒǡ ‹– ‹• –”—‡ǡ •Šƒ’‡ Š—ƒ ‡š’‡”‹‡…‡ ‹ ˆ—†ƒ‡–ƒŽ ™ƒ›•ǡ
‡˜‡ ‹ˆŽ—‡…‹‰ –Š‡ †ƒ› ‘ˆ „‹”–ŠǤ ‹…‡ ‹ ‘†‡” •‘…‹‡–‹‡• Š‡ƒŽ–Š …ƒ”‡ ‹• •›•–‡ƒ–‹…ƒŽŽ›
‘”‰ƒ‹œ‡† ƒ……‘”†‹‰ –‘ –Š‡ ™‘” ™‡‡ǡ ™‹–Š Ž‘™‡” •–ƒˆˆ‹‰ ‘ˆ Š‘•’‹–ƒŽ• ‘ ™‡‡‡†•ǡ –Š‡
†‹˜‡”‰‡…‡„‡–™‡‡ƒ–—”‡ƒ†Š—ƒ‘”‰ƒ‹œƒ–‹‘…‘—Ž†‰‡‡”ƒ–‡’”‘„Ž‡•Ǥ‘–Š‡”•™Š‘ƒ”‡
ˆ‘ŽŽ‘™‹‰ƒ–—”‡ǯ•…‘—”•‡™Š‹…Šƒ–Ž‡ƒ•––‘•‘‡‡š–‡–‹•‹ˆŽ—‡…‡†„›–Š‡•‘Žƒ”…›…Ž‡ǡƒ†‰‘
‹–‘ Žƒ„‘” ‘ ƒ ™‡‡‡†ǡ ‹‰Š– ”‡…‡‹˜‡ Ž‡•• ‘„•–‡–”‹… ƒ––‡–‹‘ǡ •‹…‡ Š‘•’‹–ƒŽ •–ƒˆˆ‹‰ ‹•
‰‘˜‡”‡†„›Š—ƒ”—Ž‡•‹•–‡ƒ†Ǥ—–ƒ––Š‡•ƒ‡–‹‡ƒ•–Š‡‘”‰ƒ‹œƒ–‹‘‘ˆŠ‡ƒŽ–Š•›•–‡•Šƒ•
ƒ†ƒ’–‡†–‘–Š‡†‡ƒ†•‘ˆƒ‘†‡”‡…‘‘›ǡ–‡…Š‘Ž‘‰‹…ƒŽ…ƒ’ƒ…‹–‹‡•Šƒ˜‡‹’”‘˜‡†‹•–‡’ǡ
ƒ†–Š‡‹ˆŽ—‡…‡‘ˆ–Š‡•‘Žƒ”…›…Ž‡‘–Š‡–‹‹‰‘ˆ„‹”–Š•Šƒ•‡ˆˆ‡…–‹˜‡Ž›„‡‡‡Ž‹‹ƒ–‡†Ǥ—–ƒ•
—…Šƒ•™‡‹‰Š–…‡Ž‡„”ƒ–‡–Š‡‡ˆˆ‡…–‹˜‡ƒ†‡“—‹–ƒ„Ž‡–”‡ƒ–‡–™Š‹…Š‘†‡”Š‡ƒŽ–Š•›•–‡•
‘ˆˆ‡”–Š‡‹”…Ž‹‡–•ǡ–Š‹•…‘…Ž—•‹‘†‘‡•‘–Œ—•–‹ˆ›ƒ—“—ƒŽ‹ˆ‹‡†ƒ’‘–Š‡‘•‹•‘ˆ’”‘‰”‡••Ǥ‡––‡”
Š‡ƒŽ–Š …ƒ”‡ †‡Ž‹˜‡”›ǡ ‹– •‡‡•ǡ ‹• —ƒ˜‘‹†ƒ„Ž› ƒ……‘’ƒ‹‡† „› Ž‘•‹‰ ›‡– ƒ‘–Š‡” ˆƒ…‡– ‘ˆ –Š‡
†‹˜‡”•‹–›‘ˆŠ—ƒ‡š‹•–‡…‡Ǥ
10
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11
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- opportunities for analysis provided by the anonymised subsample. ‘ǣǡʹͲͲͲǤ
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ʹͳǤMacFarlane, A.ƒ”‹ƒ–‹‘•‹—„‡”‘ˆ„‹”–Š•ƒ†’‡”‹ƒ–ƒŽ‘”–ƒŽ‹–›„›†ƒ›‘ˆ™‡‡‹
‰Žƒ†ƒ†ƒŽ‡•ǤBMJ. ͳͻ͹ͺǡ‘ŽǤʹǡ’’Ǥͳ͸͹ͲǦͳ͸͹͵Ǥ
ʹʹǤMitchell, Michael N.A Visual Guide to Stata Graphics. ʹ††‹–‹‘Ǥ‘ŽŽ‡‰‡–ƒ–‹‘ǡ‡šƒ•ǣ
–ƒ–ƒ”‡••ǡʹͲͲͺǤ
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