Review of Business and Economics Studies, 2014, том 2, № 4
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Review of Business and Economics Studies EDITOR-IN-CHIEF Prof. Alexander Ilyinsky Dean, International Finance Faculty, Financial University, Moscow, Russia ailyinsky@fa.ru EXECUTIVE EDITOR Dr. Alexander Kaffka EDITORIAL BOARD Dr. Mark Aleksanyan Adam Smith Business School, The Business School, University of Glasgow, UK Prof. Edoardo Croci Research Director, IEFE Centre for Research on Energy and Environmental Economics and Policy, Università Bocconi, Italy Prof. Moorad Choudhry Dept.of Mathematical Sciences, Brunel University, UK Prof. David Dickinson Department of Economics, Birmingham Business School, University of Birmingham, UK Prof. Chien-Te Fan Institute of Law for Science and Technology, National Tsing Hua University, Taiwan Prof. Wing M. Fok Director, Asia Business Studies, College of Business, Loyola University New Orleans, USA Prof. Konstantin P. Gluschenko Faculty of Economics, Novosibirsk State University, Russia Prof. George E. Halkos Associate Editor in Environment and Development Economics, Cambridge University Press; Director of Operations Research Laboratory, University of Thessaly, Greece Dr. Christopher A. Hartwell President, CASE - Center for Social and Economic Research, Warsaw, Poland Prof. S. Jaimungal Associate Chair of Graduate Studies, Dept. Statistical Sciences & Mathematical Finance Program, University of Toronto, Canada Prof. Bartlomiej Kaminski University of Maryland, USA; Rzeszow University of Information Technology and Management, Poland Prof. Vladimir Kvint Chair of Financial Strategy, Moscow School of Economics, Moscow State University, Russia Prof. Alexander Melnikov Department of Mathematical and Statistical Sciences, University of Alberta, Canada Prof. George Kleiner Deputy Director, Central Economics and Mathematics Institute, Russian Academy of Sciences, Russia Prof. Kwok Kwong Director, Asian Pacific Business Institute, California State University, Los Angeles, USA Prof. Dimitrios Mavrakis Director, Energy Policy and Development Centre, National and Kapodistrian University of Athens, Greece Prof. Steve McGuire Director, Entrepreneurship Institute, California State University, Los Angeles, USA Prof. Rustem Nureev Head of the Department of Macroeconomics, Financial University, Russia Dr. Oleg V. Pavlov Associate Professor of Economics and System Dynamics, Department of Social Science and Policy Studies, Worcester Polytechnic Institute, USA Prof. Boris Porfiriev Deputy Director, Institute of Economic Forecasting, Russian Academy of Sciences, Russia Prof. Svetlozar T. Rachev Professor of Finance, College of Business, Stony Brook University, USA Prof. Boris Rubtsov Chair of Financial Markets and Financial Engineering, Financial University, Russia Dr. Minghao Shen Dean, Center for Cantonese Merchants Research, Guangdong University of Foreign Studies, China Prof. Dmitry Sorokin Deputy Rector for Research, Financial University, Russia Prof. Robert L. Tang Vice Chancellor for Academic, De La Salle College of Saint Benilde, Manila, The Philippines Dr. Dimitrios Tsomocos Saïd Business School, Fellow in Management, University of Oxford; Senior Research Associate, Financial Markets Group, London School of Economics, UK Prof. Sun Xiaoqin Dean, Graduate School of Business, Guangdong University of Foreign Studies, China REVIEW OF BUSINESS AND ECONOMICS STUDIES (ROBES) is the quarterly peerreviewed scholarly journal published by the Financial University under the Government of Russian Federation, Moscow. Journal’s mission is to provide scientific perspective on wide range of topical economic and business subjects. CONTACT INFORMATION Financial University Leningradskiy Av. 51 Building 3, 125993 Moscow Russian Federation Telephone: +7(499) 943-95-23 Website: www.robes.fa.ru AUTHOR INQUIRIES Inquiries relating to the submission of articles can be sent by electronic mail to robes@fa.ru. COPYRIGHT AND PHOTOCOPYING © 2014 Review of Business and Economics Studies. All rights reserved. No part of this publication may be reproduced, stored or transmitted in any form or by any means without the prior permission in writing from the copyright holder. Single photocopies of articles may be made for personal use as allowed by national copyright laws. ISSN 2308-944X
Вестник исследований бизнеса и экономики ГЛАВНЫЙ РЕДАКТОР А.И. Ильинский, профессор, декан Международного финансо вого факультета Финансового университета ВЫПУСКАЮЩИЙ РЕДАКТОР А.В. Каффка РЕДАКЦИОННЫЙ СОВЕТ М. М. Алексанян, профессор Бизнесшколы им. Адама Смита, Университет Глазго (Великобритания) К. Вонг, профессор, директор Института азиатско-тихоокеанского бизнеса Университета штата Калифорния, Лос-Анджелес (США) К. П. Глущенко, профессор Экономического факультета Новосибирского госуниверситета С. Джеимангал, профессор Департамента статистики и математических финансов Университета Торонто (Канада) Д. Дикинсон, профессор Департамента экономики Бирмингемской бизнесшколы, Бирмингемский университет (Великобритания) Б. Каминский, профессор, Мэрилендский университет (США); Университет информационных технологий и менеджмента в Жешове (Польша) В. Л. Квинт, заведующий кафедрой финансовой стратегии Московской школы экономики МГУ, профессор Школы бизнеса Лассальского университета (США) Г. Б. Клейнер, профессор, член-корреспондент РАН, заместитель директора Центрального экономико-математического института РАН Э. Крочи, профессор, директор по научной работе Центра исследований в области энергетики и экономики окружающей среды Университета Боккони (Италия) Д. Мавракис, профессор, директор Центра политики и развития энергетики Национального университета Афин (Греция) С. Макгвайр, профессор, директор Института предпринимательства Университета штата Калифорния, Лос-Анджелес (США) А. Мельников, профессор Депар та мента математических и ста тистических исследований Университета провинции Альберта (Канада) Р. М. Нуреев, профессор, заведующий кафедрой “Макроэкономика” Финансового университета О. В. Павлов, профессор Депар та мента по литологии и полити ческих исследований Ворчестерского политехнического института (США) Б. Н. Порфирьев, профессор, член-корреспондент РАН, заместитель директора Института народнохозяйственного прогнозирования РАН С. Рачев, профессор Бизнес-колледжа Университета Стони Брук (США) Б. Б. Рубцов, профессор, заведующий кафедрой “Финансовые рынки и финансовый инжиниринг” Финансового университета Д. Е. Сорокин, профессор, членкорреспондент РАН, проректор Финансового университета по научной работе Р. Тан, профессор, проректор Колледжа Де Ла Саль Св. Бенильды (Филиппины) Д. Тсомокос, Оксфордский университет, старший научный сотрудник Лондонской школы экономики (Великобритания) Ч. Т. Фан, профессор, Институт права в области науки и технологии, национальный университет Цин Хуа (Тайвань) В. Фок, профессор, директор по исследованиям азиатского бизнеса Бизнес-колледжа Университета Лойола (США) Д. Е. Халкос, профессор, Университет Фессалии (Греция) К. А. Хартвелл, президент Центра социальных и экономических исследований CASE (Польша) М. Чудри, профессор, Университет Брунеля (Великобритания) Сун Цяокин, профессор, декан Высшей школы бизнеса Гуандунского университета зарубежных исследований (КНР) М. Шен, декан Центра кантонских рыночных исследований Гуандунского университета (КНР) Издательство Финансового университета 125993, Москва, ГСП-3, Ленинградский проспект, 51, корп. 3, к. 104. Тел. 8 (499) 943-95-23. Интернет: www.robes.fa.ru. Журнал “Review of Business and Economics Studies” (“Вест ник исследований бизнеса и экономики”) зарегистрирован в Федеральной службе по надзору в сфере связи, информационных технологий и массовых коммуникаций 9 июля 2013 г. Свидетельство о регистрации ПИ № ФС77-54658. Подписано в печать: 25.12.2014. Формат 60 × 84 1/8. Заказ № 713 от 26.12.2014. Отпечатано в ООП Издательства Финуниверситета (Ленинградский проспект, д. 49). 16+
CONTENTS Post Reunification Economic Fluctuations in Germany: A Real Business Cycle Interpretation Michael A. Flor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The Informal Economy and the Constraints That It Imposes On Pension Contributions in Latin America David Tuesta Cárdenas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Study of Informational Requirements to Identify Reputational Risks Taisiya Iznova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Stakeholder Approach to Identification and Analysis of Value Creation Drivers Olga Efimova. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 National Intellectual Capital (NIC) — New Metrics Piotr Wiśniewski, Anna Wildowicz-Giegiel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Key Insurers Indicators in the Reports of Insurance Companies: Russian and Italian Experience Nadezda Kirillova, Andrea Bellucci . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Default Risk and Its Effect for a Bond Required Yield and Volatility Pavel Zhukov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Review of Business and Economics Studies Volume 2, Number 4, 2014
CОДЕРЖАНИЕ Флуктуации германской экономики после воссоединения с точки зрения теории реального цикла деловой активности Михаэль А. Флор . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 Теневая экономика и пенсионные взносы: опыт стран Латинской Америки Давид Туэста Карденас . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18 Исследование информационных требований в целях идентификации репутационных рисков Таисия Изнова . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51 Стейкхолдерский подход к выявлению и анализу факторов создания стоимости Ольга Ефимова, Вероника Самохина . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 Новые параметры измерения национального интеллектуального капитала Петр Вишневский, Анна Вилдович-Гегел . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71 Основные показатели финансового состояния в отчетах страховых компаний: российский и итальянский опыт Надежда Кириллова, Андреа Беллуччи . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80 Риск дефолта и его влияние на требуемую доходность облигаций и волатильность Павел Жуков . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87 Вестник исследований бизнеса и экономики № 4, 2014
Review of Business and Economics Studies Volume 2, Number 4, 2014 Post Reunification Economic Fluctuations in Germany: A Real Business Cycle Interpretation* Michael A. Flor University of Augsburg, Department of Economics, Germany michael.flor@wiwi.uni-augsburg.de Abstract. We consider the cyclical properties of the German economy prior and after reunification in 1990 from the perspective of a real business cycle model. The model provides the framework for the selection and consistent measurement of the variables whose time series properties characterize the cycle. Simulations of the calibrated model reveal the model’s potential to interpret the data. Major findings are that: i) the volatility of most aggregate time series has not changed significantly between the two time periods, ii) despite many conceptual differences between the European and the U.S. accounting systems, the calibrated parameter values for the German economy are within the range of values usually employed in the real business cycle literature, iii) the model is closer to the data for the time period prior to reunification. Aннотация. В статье рассматривается цикличность германской экономики до и после воссоединения 1990 года с точки зрения модели реального цикла деловой активности. Модель обеспечивает рамки для выбора и последовательного измерения переменных, характеризующих цикл. Использование калиброванной модели раскрывает ее потенциал для интерпретации данных. Основные выводы заключаются в следующем: i) неустойчивость большинства статистических временных рядов существенно не изменилось по сравнению с периодом до воссоединения, ii) Несмотря на многие концептуальные различия между европейской и американской системами бухгалтерской отчетности, калиброванные значения параметров немецкой экономики находятся в диапазоне значений, которые обычно используются в литературе по реальному циклу деловой активности, iii) модель ближе к данным периода до воссоединения. Key words: Macroeconomic data, measurement and data on national income and product accounts, economic fluctuations, real business cycles. * Флуктуации германской экономики после воссоединения с точки зрения теории реального цикла деловой активности. 1. IntRoduCtIon And MotIvAtIon Since the seminal papers of Kydland and Prescott (1982), Long and Plosser (1983), and Prescott (1986), among others, it has become standard praxis to consider business cycles (BC’s) within the framework of dynamic stochastic general equilibrium (DSGE) models. This class of models shares the basic ingredients of the first-generation models, namely intertemporal optimization and rational expectations, but also allows for many frictions as, e. g., real or nominal price stickiness, limited participation in financial markets, or obstacles in the allocation of labor.1 Recent models, e. g. the model of Smets and Wouters (2003), a replacement of the Area Wide Model (AWM) 1 Such models are known as New Keynesian (NK) models, which were widely established by Mankiw (1989), Mankiw and Romer (1991), as well as Cho and Cooley (1995), among others. of the European Central Bank (ECB), can replicate NK effects in the short-run (determined by aggregate demand) and neoclassical effects in the long-run (determined by aggregate supply). Medium scale DSGE models are useful for economic policy evaluation. Their increased complexity vis-a-vis the first-generation models, however, makes them less suited for studying elementary driving forces of the BC. However, as has been widely documented in the empirical literature, the stylized facts of the BC have remained relatively stable over time and region.2 This suggests that elementary economic mechanisms shape the cycle more than many institutional details. For this reason we will employ a first-generation real business cycle (RBC) model to organize ideas about eco 2 See for instance Cooley and Prescott (1995), pp. 29–33, for a description of the U.S. BC facts.
Review of Business and Economics Studies
Volume 2, Number 4, 2014
nomic fluctuations prior and after the territorial status
of the Federal Republic of Germany of October 03, 1990,
where the entire considered time period covers the first
quarter of 1970 until the last quarter of 2012.
The motivation is twofold. First, we want to ask
whether the nature of the German BC has changed. As a
reference we take the West German economy, West Berlin included, over the period 1970: I-1991: IV. The split
of the period 1970: I-2012: IV into two subsamples is not
only marked by the German reunification but also by a
major change in the German National Income and Product Accounts (GNIPA). As a data base we employ data
provided by the German Federal Statistical Office (GFSO),
which rests on the European System of Accounts (ESA).
Only recently the GFSO finished the revision of data prior to 1991 on the occasion of the great revision in 2005,
so that a set of comparable data is available.3 The second
motivation is to explore to what extend the new GNIPA data allows to consistently calibrate an RBC model
that can be used to interpret the data. This endeavor is
similar to the work of Cooley and Prescott (1995) and
Gomme and Rupert (2007) for the U.S. economy. There
are, however, conceptual differences between the NIPA
System in the U.S. and in Europe that necessitate deviations from the work of these authors. As a result of this
work, we have gathered a data base suitable for calibrating DSGE models to German data.4
The main findings are: i) with respect to the volatility of major macroeconomic aggregates the BC has not
changed significantly,5 ii) despite several differences in
data and methodology we find parameter values within
the range of those estimated for the U.S. economy, and
iii) taking into account the uncertainty in the estimated
second moments, the model is closer to the data for the
period 1970: I-1991: IV.
The next section describes the theoretical model.
This model provides the framework for the selection and
definition of variables employed to calibrate the model
and to characterize the BC in section 3. Section 4 provides the results, and section 5 concludes.
2. thEoREtICAl FRAMEwoRK
As a framework for ( )1 the selection of data that characterize the BC, ( )
2 the consistent calibration, and ( )
3
the interpretation of the empirical findings we employ
the RBC model of Heer and Maußner (2009), chapter 1.5.
This model abstracts from population growth, but is oth
3 See Braakmann et al. (2005) and also the Subject-matter series
18, S.27. For the comparability of time series between the period
1970–1991 and 1991–2004, see also Räth et al. (2006).
4 An Excel sheet with the regarding pre-adjusted time series is
available upon request.
5 As it is also reported by Buch et al. (2004).
erwise similar to the model of Cooley and Prescott (1995).
Thus, we exclude home production and investment-specific shocks as in Gomme and Rupert (2007), because
these authors already argue on p. 489 that “removing
home production from the model has little effect on the
model’s predicted business cycle moments” and because
their results indicate that adding such an investmentspecific shock only leads to more volatility of almost
every considered macroeconomic series and brings the
model more at odds with the real data.
The economy is populated by a representative firm
and a representative household. Time t is discrete.
The Firm. A representative firm produces output,
Yt , according to the constant returns to scale production function
Y
Z F A N K
t
t
t
t
t
(
,
),
(2.1)
where the firm employs labor and capital services, Nt
and Kt . Total factor productivity (TFP), Z t , is governed
by the covariance-stationary, stochastic process
ln
ln
Z
Z
t
t
t
1
,
t
0 1
0 1
,
,
( , )
. (2.2)
Labor augmenting technical progress, At , grows deterministically at the gross rate a
1:
A
aA
t
t
1
.
(2.3)
The firm takes the real wage, Wt , and the rental rate
of capital, rt , as given and maximizes its current-period
profits
t
t
t
t
t
t
Y
W N
r K
.
(2.4)
This provides two conditions that will hold in the
equilibrium of the labor market and the market for capital services:6
W
A
Z F
A N K
t
t
t
N
t
t
t
,
,
(2.5a)
r
Z F
A N K
t
t
K
t
t
t
(
,
).
(2.5b)
The Household. A representative household supplies labor and capital services to the firm, consumes,
and accumulates capital. Capital depreciates at a rate
( , ]
0 1 , so that
6 We denote the partial derivatives of a function F with respect to
its argument x
N K
{
,
} by a subscript.
Review of Business and Economics Studies
Volume 2, Number 4, 2014
K
K
I
t
t
t
1
1
(2.6)
is the law of motion of the capital stock, where It
denotes gross fixed investments. The household’s period-to-period budget constraint, thus, reads:
W N
r K
C
I
t
t
t
t
t
t
.
(2.7)
The household values consumption, Ct , and leisure,
1
Nt , according to the current-period utility function
u C
N
t
t
(
,
)
1
. This function is strictly increasing in consumption and leisure and strictly concave. The household discounts future utility t
s
at the rate s , ( , )
0 1 ,
and maximizes his expected life-time utility
U
u C
N
t
t
s
s
t s
t s
0
1
(
,
),
subject to the budget constraint (2.7) and a given
stock of capital, Kt
0. Expectations, t , are conditional on information available at time t .7
In addition to the budget constraint, which holds at
equality in equilibrium, and the law of motion of the
capital stock two further equations characterize the
household’s optimal plan:8
W
u
C
N
u
C
N
t
N
t
t
C
t
t
1
1
1
(
,
)
(
,
) ,
(2.8a)
u
C
N
u
C
N
r
C
t
t
t
C
t
t
t
t
,
(
,
)(
)
1
1
1
1
1
1
.
(2.8b)
The first condition determines the household’s labor supply. It equates the real wage to the marginal rate
of substitution between leisure and consumption. The
second condition is the Euler equation for capital accumulation. It equates the disutility from savings with the
discounted expected future reward.
Equilibrium. In equilibrium factor markets clear so
that the household’s budget constraint reduces to
Y
C
I
t
t
t
.
(2.9)
Equations (2.1), (2.5), (2.6), (2.8a), (2.8b), (2.9), and
(2.2) fully describe the dynamics of the model. Due to
(2.3) the economy will grow over time and exhibit fluctuations around its balanced-growth path which are driven
by the covariance-stationary shocks to TFP, Z t .
Parameterization. Except for a few special cases, DSGE models as the one presented in the previous
7 For this, see also Maußner (2013b), pp. 59–60.
8 We denote the partial derivatives of a function u with respect to
its argument x
C
N
{ ,
}
1
by a subscript.
paragraphs do not have an analytical solution. The rules
describing the household’s choice of consumption and
leisure must be approximated with the help of numerical
methods. Among the most popular methods are perturbation methods that yield a polynomial approximation
at the stationary solution of the non-stochastic version
of the model. To apply these methods the researcher
must specify the functional form of the production
function F and the utility function u and transform
the model to a stationary one.
On the firms side we follow Heer and Maußner (2009)
as well as Cooley and Prescott (1995) and employ a
Cobb-Douglas production function
F A N K
A N
K
t
t
t
t
t
t
,
(
)
1
, ( , )
0 1
(2.10)
with capital share parameter .
Since the model depicts a growing economy, the
household’s preferences must be chosen so that conditions (2.8) are consistent with a constant supply of hours
and a constant growth rate of consumption. The function
u C
N
C
N
t
t
t
t
,
[
]
1
1
1
1
1
1
1
,
1
(2.11)
has this property and is strictly concave in consumption and leisure, as mentioned before. The parameter
equals the coefficient of relative risk aversion and its
inverse is the elasticity of intertemporal substitution.
is the share parameter for leisure in the composite commodity.
Given these parameterizations it is easy to see that
scaling all growing variables by the level of labor augmenting technical progress, At , transforms the model to
a stationary one. We will use lower case letters to refer to
these scaled variables.
Stationary Solution. The stationary solution of the
non-stochastic model can be computed in the following
steps: ( )1 set Z
t
t
1
. This is the long-run value of
Z t implied by the process (2.2) if 0. ( )
2 scale growing variables by At . ( )
3 assume that the dynamics has
ceased so that x
x
x
t
t
1
for all variables of the model.
Applying this procedure to equations (2.1), (2.5), (2.6),
(2.8a), (2.8b), and (2.9) yields the following equations:
y
k
a
(
)
1
,
(2.12a)
y
N
k
1 ,
(2.12b)
y
c i
,
(2.12c)
Review of Business and Economics Studies Volume 2, Number 4, 2014 c y N N ( ) 1 1 . (2.12d) Equation (2.12a) follows from equation (2.5b) and the Euler condition (2.8b). Equation (2.12b) is the production function for Z 1, written in stationary variables y Y A / and k K A / . Equation (2.12c) is the resource constraint (2.9), also written in stationary variables c C A / and i I A / . And equation (2.12d) follows from (2.5a) and the labor supply condition (2.8a). We will return to these equations when we discuss the results from the calibration procedure for the simulation of the model in subsection 4.1. 3 EMPIRICAl FRAMEwoRK 3.1 tREnd And CyClE The model laid out in the previous section predicts the short- and long-run behavior of the observable variables • output Y , • consumption C, • investments I, • hours N, and • real wage W . We will use this set of variables to characterize the BC. Seasonal Adjustment. Quarterly economic data contains a seasonal and a calendar component, which are not explained by the model. Thus, the researcher must use seasonal- and calendar-adjusted time series. The GFSO employs an indirect approach to remove the seasonal and calendar component from a time series. It computes seasonal- and calendar-adjusted aggregates as the sum of seasonal- and calendar-adjusted subaggregates.9 For the adjustment either the Berlin Method (currently Version 4.1) or the Census X-12-ARIMA method is employed.10 Since more time series adjusted with the latter method are available, we will use the Census X-12-ARIMA method throughout. Trend Removal. To achieve stationarity of the time series, its trend must be removed. To isolate the cyclical component in a time series, the popular filter by Hodrick and Prescott (1997), the HP-Filter, is used.11 In detail, detrending occurs by filtering the log of the time series. For quarterly data it is customary to choose the smoothing parameter by 1600, because of the normally as 9 For example, see the Subject-matter series 18, S.23 and especially for the time period 1970 till 1991 the Subject-matter series 18, S.28 10 See https://www.destatis.de/DE/Methoden/Zeitreihen/Zeitreihenanalyse.html for a detailed description and the regarding differences of these two methods. See also http://www.census.gov/srd/ www/x13as/ for the X-13ARIMA-SEATS Seasonal Adjustment Program, which is the successor of the Census X-12-ARIMA. 11 For different methods concerning detrending in general and their different implications on the considered time series, see Canova (1998). sumed BC fluctuation frequencies from about three to five years.12 Second Moments. A standard tool to evaluate DSGE models is to compare the second moments of simulated time series with those of the respective macroeconomic aggregates. Therefore the set of the following second moments of the variables introduced above will be used to uncover the properties of the RBC model and to characterize the cycle: • standard deviation, • standard deviation relative to standard deviation of output, • cross-correlation with output, • cross-correlation with hours, and • first-order autocorrelation. 3.2 PRICE AdjustMEnt The variables output, consumption, investments, and the real wage are measured in units of the final good. The data collected in the GNIPA is based on nominal aggregates and need to be deflated by some measure of the price level. Before the revision in 2005, real variables were defined with respect to the price system of a particular base year. The advantage of this concept is that real magnitudes, such as consumption, investments, and net exports add up to GDP. The disadvantage is that changes in relative prices, which induce changes in the composition of subaggregates, cannot be taken into account. Thus, constant price aggregates are intertemporally not really comparable. Since 2005, the real time series of the GFSO are reported as chain indices, which include a kind of non-linearity and therefore face the problematic characteristic of non-additivity.13 The deflators of the main aggregates, such as GDP, consumption expenditures, and gross investments, are meanwhile also constructed from chained indices, so that the real aggregates are intertemporally comparable, but the subaggregates do no longer add up without a residual. This residual is greater, the greater the relative prices have changed, and this effect is known as “substitution bias”.14 12 See for instance Cooley and Prescott (1995), pp. 27–29. 13 See Mayer (2001), Braakmann et al. (2005), and also the Subjectmatter series 18, S.24. For a more sophisticated contemplation of the properties of chain indices and the possibilities for the computation of chained and unchained real aggregates, see the Appendix, which is available upon request. See also von der Lippe (2000) for critical comments on chain indices in general. And for a detailed dispute with U.S. chain aggregated NIPA data, see Whelan (2002). 14 Between 1991 and 2004 the GDP residual (difference between the directly determined chained real GDP and the sum of the chained real GDP components) differ at most 0.4% in relation to real GDP, as Nierhaus (2005) mentions. Residuals arise naturally also in spatial units, such as between real GDP at the federal level and the accumulated GDP of the 16 states in Germany. For this, see Nierhaus (2001), Nierhaus (2004a), Nierhaus (2004b), and again
Review of Business and Economics Studies Volume 2, Number 4, 2014 To tackle the problem of structural inconsistency of the computable chained real aggregates in a certain frame, we follow Gomme and Rupert (2007) in line with Greenwood et. al. (1997). The former authors mention on p. 484 that “a common price deflator should be used when converting nominal NIPA data into real terms and that a natural choice is the price deflator for nondurable goods and nonhousing services”, and designate their weighted average deflator out of the two just mentioned price deflators simply as the consumption deflator. Greenwood et. al. (1997), pp. 347–348, mention that such a choice is natural because they want “to avoid the issue of the accounting for quality improvement in consumer durables”. In our context such a weighted price index (PI) corresponds with the consumer PI (CPI) for Germany, since this is also the average price development of all goods and services purchased by households for consumption by purpose.15 But since the above described model framework and the data pre-adjustments for a consistent measurement also include the net exports, the GDP-deflator is the corresponding or rather adequate PI, following Reich (2003) and Balk and Reich (2008) as well, who argue that a GDP-deflator should be used because this implies a measure of inflation and growth. Therefore all four nominal main aggregates will be deflated by one common PI, which is the GDPdeflator, to guarantee a data and model consistent fashion. Since the chain indices for the subsample 1991: I till 2012: IV are reported with the reference year 2005, where the average of this year is set to 100, first there has to be made a rebasing to the year 1991, to achieve that the two subsamples are comparable.16 3.3 ConsIstEnt MEAsuREMEnt Definitions and Constructions. Given that the data availability in Germany is different to the data availability in the U.S.,17 the following considerations focus on the German case.18 Nierhaus (2005). Gomme and Rupert (2007) also mention that already in the late 1990s the U.S. BEA pointed out that it is not appropriate to add real magnitudes. For this, see also Braakmann et al. (2005), and Räth et al. (2006). There are also difficulties with values reached by balances, as net exports or inventory investments, if they are zero. See, among others, Nierhaus (2005), Nierhaus (2007), and Tödter (2005) 15 This price deflator is also available over the entire period, however, the PI, which refers to the former Federal Territory of Germany, is reported as the PI for living of all households. 16 Note, that for the second subperiod hedonic PI’s are used, which also include a quality aspect. 17 For example, GDP is reported in the GNIPA within the production and the use approach, but not within the distribution approach, because of missing data. This is in contrast to the reported GDP in the U.S. 18 See the Appendix for a more detailed description of the following steps, wherein all computations are made with the nominal magnitudes. Note, that for convenience the time subscripts are repressed. Starting from the use approach perspective of the new GNIPA data and keeping in mind that the theoretical framework does not distinguish between government and private consumption (Cgov and Cpr ) as well as investments, the private consumption expenditures in the data can be decomposed into long-lived durables, shortlived durables, non-durables, and services.19 Only longlived durables are included as I prdur in the composite gross fixed investments, I , since these can be regarded as a kind of investment goods. For total consumption, C , therefore follows: C C C I gov pr prdur , which is consistent in the model context. Cooley and Prescott (1995), p. 38, argue that when “there is no foreign sector in this economy, net exports are viewed as representing additions to or claims on the domestic capital stock, depending on whether they are positive or negative”. We follow this argumentation and add the whole net exports as I NE to the total gross investments, I , which also include government and private gross fixed capital formation or rather gross fixed investments (GI gov and GI pr ) as well as changes in inventories (CI gov and CI pr ). Thus I can be written as: I GI GI CI CI I I GI I I gov pr gov pr prdur NE prdur NE . Therefore output reads:20 Y C I , where Y stands consistently for GDP in data, which is valued at market prices.21 But since the model framework assumes Y at factor prices, Y has to be adjusted in the sense of a subtraction of net taxes to get a valued GDP at factor prices. Then Y is consistent to the model. The labor measure, N, is calculated as the average quarterly fraction of total hours worked and the real wage, W , is calculated as the nominal wage divided by the GDP-deflator.22 For the construction of a quarterly composite capital stock time series, the annual net fixed capital plus the 19 It should also be mentioned that the time series of consumption expenditures used here also include home-based services. See Braakmann et al. (2005) and Burghardt (2006). 20 This is also the resource constraint for the whole economy (2.9). 21 In this paper the conceptually appropriate measure of output is GDP rather than GNP, also because of deflation problems. See Brümmerhoff and Lützel (2002), pp. 59 f. and 62 f. For this, see also Gomme and Rupert (2007). 22 With this PI the main focus is on firms perspective, unlike the PI for final domestic use or the CPI, where the main focus is on households perspective. See the Appendix for a description of the different calculation opportunities of PI’s in the GNIPA.
Review of Business and Economics Studies Volume 2, Number 4, 2014 annual net stock of durable goods of the households can be combined with the calculated quarterly total gross investments with the “Perpetual Inventory Method” (PIM) to obtain such an adequate capital stock measurement.23 For this purpose an interpolation method is conceivable: Let Kt denote the capital stock in year t . The GFSO provides capital stock data for each year and data on gross investments, Itq , for each year and quarter. Therefore, we can interpolate between two years, t and t 1, in the following way: K I I I I K t t t t t t t t t t 1 4 3 2 2 3 1 4 1 1 1 1 ( ) ( ) ( ) . The variable t is the implicit rate of depreciation of the capital stock in the year t . Given K K I q t t tq 1 1 2 3 4 , , , , , , , we can solve for the unique t ( , ) 0 1 . The time variant or rather variable quarterly depreciation rate, t , is the solution of this method to achieve that the capital stock at the end of period t is the same as the capital stock at the beginning of period t 1.24 The average of this depreciation rate, , is used in subsection 4.1 for the calibration in each subsample. Cooley and Prescott (1995) calibrate the Solow residual without fixed capital, arguing that the quarterly variations in the aggregate capital stock are approximately zero and so the omission of the capital stock has only little effect on the Solow residual at BC frequencies, which are typically between 6 and 32 quarters. They argue further in line with Prescott (1986) that any interpolation method for constructing a quarterly capital stock will be arbitrary and will bring some noise into the measures, because the capital stock series are only reported annually in the U.S. and in Germany. However it poses some difficulties as well to avoid the whole time series, also in consideration of the fact that the statistical offices, e. g. the GFSO, as well use extra- and interpolation methods for the construction of some time series.25 For this argumentation, see also Gomme and Rupert (2007), who compute the Solow residual with and without a capital stock (aggregated as well as separated for market structures and equipment and software).26 They find similar results of these three different methods, so that the parameter estimates of the Solow residual are not 23 See also Heer and Maußner (2009), Gomme and Rupert (2007), and the Appendix for the construction of the capital stock. The latter also includes a briefly contemplation of the PIM used by the GFSO for the construction of the capital stock. 24 An advantage of such a depreciation rate is that it is delimited equal as the composite capital stock and the total gross fixed investments. 25 E.g. durables in the period 1970: I-1991: IV. See for instance Räth et al. (2006). 26 They derive a quarterly series of the capital stock with a method based on Greenwood et al. (1997), who derived admittedly annual capital stocks. too sensitive between these different calculations. We further compute the Solow residual without a capital stock and with a composite capital stock, where net fixed assets and the net stock of household durables are included, so that the Solow residuals can be computed as z y eh t t t 1 1 and z y eh k t t t t 2 1 1 , where eht denotes effi cient working hours. The deviations from balanced growth are therefore ˆz z z z t t t t 1 1 1 1 and ˆz z z z t t t t 2 2 2 2 , respectively. Used Variables. The following list crudely enumerates the used variables for the pre and post reunification in the periods 1970: I-1991: IV and 1991: I-2012: IV: 1. Output measure Yt : GDP at factor prices 2. Consumption measure Ct : Private and public consumption of non-durables 3. Investment measure It : i. Private and public gross fixed investments ii. Private and public gross fixed investments plus changes in inventories plus private consumption of consumer durables plus net exports27 4. Capital measure Kt : Private and public net fixed assets (structures, equipment, and inventories) plus net stock of consumer durables28 5. Labor measure Nt : Average quarterly fraction of total hours worked 6. Real wage measure Wt : Nominal wage divided by the GDP-deflator 7. Labor share 1: Average mean over the sum of total real wage of the dependent employees plus a share of self-employed divided by the GDP at factor prices 8. TFP measure Z : i. Based on labor variations only ii. Based on labor and capital variations using the adequate capital measure 4. REsults 4.1. CAlIBRAtIon In consideration with the outlay of estimation methods and that in the “literature on intertemporally optimized models has shown a clear preference for calibrating rather than estimating parameters of interest”, as Favero (2001), p. 248, mentions, in this paper the decision falls also to classical or rather traditional calibration. Accordingly calibration simply means “to standardize as a measuring instrument”, as Cooley and Prescott (1995), 27 As in Cooley and Prescott (1995). 28 To that Cooley and Prescott (1995) also add land. They argue that this should as well integrated into the production function, but the data on the stock of land is inadequate and is omitted here.
Review of Business and Economics Studies Volume 2, Number 4, 2014 p. 22, or Cooley (1997), p. 58, argue, and this meaning applies to the idea behind calibration of the stochastic growth model considered here.29 Table 4.1 reports the calibrated parameter values at the steady state equations (2.12a), (2.12b), (2.12c), and (2.12d) for the two different subsamples.30 For a comparison of these two subsamples one should hold in mind, that the territorial status is different in these two time periods. Accordingly it comes as no surprise that changes occur in all variables, apart from and which were set.31 The time preference parameter cannot be calculated by the steady state equations, because this violates the restriction 1 in representative agent models. To simply bypass this problematic value, the time preference parameter is set to 0 994 . , as in Heer and Maußner (2009).32 Firstly, the growth rate ( ) a 1 is inferred from fitting a linear trend to the log of GDP at factor prices per capita. It is a little bit lower for the new time period. This also emphasizes the observed reduction in the growth rate of GDP. These two derived values are in line with the values typically used in such models, see for example Cooley and Prescott (1995), who use a 1 00156 . , or Gomme 29 For a more detailed representation of the calibration methodology, see the Appendix. 30 See Stock and Watson (1996) and Ireland (2004) for a discussion of parameter instability per se. 31 Hall (1988) shows that a high value of implies an insensitive consumption growth. For a survey of microeconomic estimates of the coefficient of relative risk aversion, see Mehra and Prescott (1985), who find, “that the bulk of the evidence places its value between 1 and 2”, as Gomme and Rupert (2007) on p. 487 mention. The value of 2 is an evidence for a greater consumption smoothing over the life cycle of the households and so this value is set to 2, as in Heer and Maußner (2009). Furthermore, a larger elasticity of the marginal utility of consumption “reduces the variability of output, working hours, and investments, and thus this choice provides a better match between the model and the respective German macroeconomic variables”, as Heer and Maußner (2009), p. 51, argue. 32 Prescott (1986), Cooley and Prescott (1995), and Gomme and Rupert (2007) calculate this parameter as 0 99 0 987 . , . , and 0 9860 . , respectively, so that this value is toward the high end of values typically used in the literature considered here. and Rupert (2007), who use an average a of 1 005 . . Secondly, the capital income parameter , increased from 0 32 . to 0 34 . or inversely the labor income reduced from 0 68 . to 0 66 . , which suggests a now more capital-intensive economy. In other words, the economy was more labor-intensive in the first time period. This argumentation also corresponds to the statement by Schmalwasser and Schidlowski (2006), who argue that production becomes more capital-intensive, because labor is increasingly replaced by capital and therefore the capital stock grows faster than production. These different values also suggest that a TFP shock affects the labor income share.33 Further, related to the decline in the growth rates of investments and the capital stock over time, the degree of modernity of the capital stock is reduced.34 For example, Cooley and Prescott (1995) calibrate the parameter as 0 40 . , which is greater than the usually used value of 0 40 . by, e. g., Kydland and Prescott (1982), Hansen (1985), Prescott (1986) or Maußner (1994), because they included the imputed income of governmental capital. This suggests a more capital-intensive U.S. economy than the German economy. Gomme and Rupert (2007) calibrate the share of capital income as 0.283 and mention on p. 493 that their value “is toward the low end of values typically used in the “RBC/DSGE” literature”, such as the value in Heer and Maußner (2009). The values derived above are between these ranges. Furthermore, the U.S. NIPA data is more accurate for determining the income of the capital side, the GNIPA data is more accurate for determining the income of the labor supply side, because the data is very detailed, extensive, and more reliable, and so 1 is specified here, which equals the average wage share 33 For this, see Cantore et al. (2013), who examine inter alia this relationship within an RBC and a NK framework. 34 This is the ratio of net to gross fixed assets, where this characteristic variable also provides information about the aging process of investment goods and indicates how much percentage of the assets are not impaired by wear or depreciated in value. See Schmalwasser and Schidlowski (2006). table 4.1. Calibration of the parameters for the GNIPA data set of the GFSO. 1970: I-1991: Iv 1991: I-2012: Iv Production Preferences Production Preferences a 1 006 . 0 994 . a 1 003 . 0 994 . 0 32 . 2 0. 0 34 . 2 0. 0 015 . N 0 14 . 0 017 . N 0 12 . . 1 0 98 . 5 80 . 1 0 97 . 6 13 . 2 0 92 . 2 0 83 . 1 0 0089 . 1 0 0086 . 2 0 0081 . 2 0 0082 .
Review of Business and Economics Studies Volume 2, Number 4, 2014 in GDP at factor prices.35 To that it should also be mentioned that this specification as well contemplates the governmental labor income, because the income time series include also public labor and so this approach is more or less identical to the approachy Cooley and Prescott (1995). Thirdly, the average quarterly depreciation rate, , has also increased, which suggests a higher depreciation rate for, e. g., communication systems and personal computers. Cooley and Prescott (1995) choose the average depreciation rate as 0 048 . yearly or 0 012 . quarterly and argue that, if the economy does not explicitly include growth, these values must be larger in order to match the investment-output ratio. Furthermore, Gomme and Rupert (2007) compute an average depreciation rate of 0 0271 . and so the above-derived values are also between these two ranges. The preference parameter also increases, suggesting that the households now appreciate leisure more. The observed demographic change in Germany can be explained by the parameter N , which is slightly lower for the period 1991: I till 2012: IV, because the population as a whole grows older. So more people are on pension and no longer participate in the working life, which leads to a reduction of labor supply.36 The parameters of the shock in the period 1970: I-1991: IV with 1 0 98 . and 1 0 0089 . , where only labor input is considered in the Solow residual, and 2 0 92 . and 2 0 0081 . , where labor and capital input are integrated in the Solow residual, are more or less in line with the values normally taken in the literature. For example, Cooley and Prescott (1995) choose, among others, the value 0 95 . and Gomme and Rupert (2007) choose the value 0 9641 . for the persistence parameter . For the volatility of the shock, , Cooley and Prescott (1995) take the value 0 007 . , Prescott (1986) chooses the value 0 00763 . , and Gomme and Rupert (2007), who also take consumer durables into account, choose the value 0 0082 . . This indicates that the derived values above are on the top of values typically used for this variable in this literature. Gomme and Rupert (2007) argue that the Solow residual is at best characterized by an autoregressive parameter of 0 9641 . and a standard deviation of 0 0082 . , compared to more standard values of 0 95 . and 0 00763 . , respectively. They further argue that their results are not sensitive, if no capital stock ( . , . ) 0 9697 0 0081 , one capital stock ( . , . ) 0 9643 0 0082 , or two capital stocks ( . , . ) 0 9641 0 0082 is (are) included, but here this 35 As in Heer and Maußner (2009). For this and the different calculation bases for GDP in Germany and the U.S., see again Schmalwasser and Schidlowski (2006) and further Schwarz (2008). 36 For a recent analysis of changes in the age composition of the labor force and the connection to BC volatility in the G7 countries, see Jaimovich and Siu (2009) as well as Heer et al. (2013). is not the case, as well as the different values demonstrate. For both subsamples this difference is conspicuous for the autoregressive parameter , which falls from 0 98 . to 0 92 . and from 0 97 . to 0 83 . , if additionally the capital input is included into the Solow residual.37 Also the volatility of the shock, , falls from 0 0089 . to 0 0081 . and from 0 0086 . to 0 0082 . in both subsamples, respectively. The finding that the shocks in the second subsample are smaller than in the first subsample emphasizes as well the argumentation by Buch et. al. (2004), who find the same result for the period till 2001: IV with a counterfactual VAR analysis and call this phenomenon “good luck”. In this respect it should also be mentioned that does not account for a differentiation of these results in the shock process, the working hours also do not matter (only is a little bit higher), and only GDP and the capital stock do matter slightly. Also Cooley and Prescott (1995) mention that Prescott (1986) already argues that the volatility of the innovations might be affected by measurement errors in the measured labor input and taking these into account would actually very slightly increase the standard deviation of the innovations to technology, as just mentioned. However, just as Cooley and Prescott (1995) too, we choose to ignore it here and leave it for future research. 4.2. PRoPERtIEs oF thE BusInEss CyClE The following table displays the results from the computation of the real economy, where the variables are as defined and constructed in subsection 3.3. A comparison between the two different subsamples reveals at first that the standard deviation of output is increased from 1 27 . to 1 51 . and the volatility of durables consumption is reduced by about a half. So it is apparent, on the one hand, that the decline of output volatility in Germany, as it is reported for the period 1970: I-2001: IV by Buch et. al. (2004) as well, is not detected for the whole time period.38 Thereto it should be mentioned that the reason is the financial crisis during the second subsample and thus, the output decline in Germany is only detected till 2008: IV, since both subsamples are compared with each other as point estimates as done in this paper solely. On the other hand, it is apparent that the reduction of durables volatility 37 In their model with all shocks, Gomme and Rupert (2007) set the autoregressive parameter on durables technological change even to 0 9999 . . 38 However it should be mentioned that Buch et al. (2004) use the Census X-11-ARIMA method for seasonal-adjusting and the HPFilter with a smoothing parameter of 1000 for detrending, following Pedersen (2001). They argue on p. 454 that their “results were not affected”, since they choose a smoothing parameter of 1600, as done in this paper. Admittedly, it is not at all clear what the authors mean by “real GDP”, because they do not refer to how they achieve the price-adjusting at all.