Dykstra, K 2016, Cross-market correlation coefficient analysis of contagion d...
LH Becker Tesis
1. Business Cycles: Is the Concept of a Recovery Phase
Applicable Internationally?
by
Louis H. Becker
15832015
Dissertation presented in fullment of the requirements
for the degree of Masters of Commerce in
Economics in the Faculty of Economic and Management Sciences at
Stellenbosch University
Department of Economics
Stellenbosch University
Private Bag X1, Matieland 7602
South Africa
Supervisor: Dr. Willem Bosho
March 2017
4. 2
1 Introduction
Research on the “co-movements of aggregative time series (Lucas, 1977),” also known as the business cycle, has de-
veloped into a rich body of literature over the past 70 years. It is the Burns and Mitchell (1946:6) conceptualisation of
this “consensus among expansions in many economic activities followed by similarly general recessions, contractions
and revivals” that spawned the multi-faceted framework within which the business cycle is commonly studied. Busi-
ness cycle analysis is employed widely as a medium for macroeconomic research and comprises one of the central
constituents of economic theory. Burns and Mitchell (1946) sought to date periods of contraction and expansion in
output, and then proceeded to break up these segments into sub-phases, splitting the initial expansion into a revival
and a subsequent expansion followed by a contraction and a recession separated within the general contraction.
In addition to providing some form of economic bearing that assists in assessing the position of the economy and
the trajectory of output, these phases lend themselves to different definitions and quantitative characterisations that
provide insight into the macroeconomic tendencies of any particular economy.
Besides the technical and statistical research concerned with dating and characterising the business cycle and its
respective phases, the literature showcases a number of useful implementations of business cycle analysis. Probably
the most salient analytical feature of the business cycle is the ongoing endeavour to attach a thorough economic
understanding to the behaviour of output as it evolves through time and its link with economic welfare and stability.
Indeed, this materialises in the writings of such as Mitchell (1923), Hayek (1933), Keynes (1936) and Lucas (1977), to
name a few, who have shaped much of the contemporary thought on business cycles and their policy implications.
More recent empirical examples of business cycle analysis is found in, for example, Male (2011) who observes more
pronounced fluctuations – sharper expansion and contraction phases – in the output of emerging market economies
than in advanced economies. Other business cycle applications, as found in Diebold and Rudebusch (1990), Filardo
(1994), Layton and Smith (2007) and Castro (2010) focus on the transitional dynamics between business cycle phases,
such as duration dependence. Finally, one of the most important contributions of business cycle analysis is that it
has provided the means for studying economic recessions and economic recoveries (Burns Mitchell, 1946:116).
Historical accounts the world over show these phenomena as recurrent events in the evolution of output for which
a starting and an ending point can be identified, hence Burns and Mitchell’s description of the business cycle in
terms of phases. It is easy to see the intuitive appeal in using a phase-based framework, as it implies distinct and
recurring stages of macroeconomic progression that give an indication of the immediate general growth path of an
economy. The recovery phase, often referred to but less often defined, is of particular interest. It marks the period
immediately after a recession, making it a crucial point of analysis when trying to determine what is to be expected
moving forward.
Two approaches emerge in the literature when thinking of the international application of a recover phase defini-
tion. One hones in on the recovery experience of a few industrialised countries to extract the stylised facts that are
now associated with recoveries in general. The other assumes a recovery for a fixed period and classifies whatever
“recovery” seem to evolve. If it can be assumed that recoveries are not the same across countries, then it can prob-
ably be asked whether recoveries can be defined for some countries at all. This dissertation aims to investigate this
matter with a simple statistical enquiry. The aim is to see for how many countries an actual recovery phases is stat-
istically distinguishable. A stylised fact often quoted of recoveries is that of bounce-back growth. The hypothesis
tested, therefore, is whether countries in general exhibit bounce-back growth. This is found not to be the case. In
fact very few countries seem to possess this trait of accelerated growth. This dissertation dates the classical cycle for
a large sample of countries and then marks recoveries using a fixed duration definition and a more flexible defini-
tion of recoveries. Statistical tests are then performed on the growth rates within the expansion phase, comparing
5. 3
recoveries and post-recoveries. Section 2 looks at what the literature sees as a recovery and how these recoveries are
demarcated. The general characteristics of recoveries are also discussed, and then the motivation behind a recovery
phases is examined. Section 3 looks at the methodology used for dating the business cycle and then discusses the
identification strategy used for defining the recoveries that will be tested. Section 4 describes the data after which
the results are discussed in section 5. Section 6 concludes.
2 Understanding the Recovery Phase
2.1 Defining and Dating a Recovery
Following an economic crisis, discussions on recessions and recoveries emerge frequently in academic, business and
policy circles. While there exist widely accepted definitions for the former, exactly what is meant by the latter is
often unclear. Burns and Mitchell (1946) distinguish a revival, or recovery, phase in the general expansion, but do
not offer a more detailed characterisation of this phase beyond its position in the business cycle and its initiation
based on their turning points and monthly timing series. Schultze (1964) provides a slightly more telling description
of a recovery, speaking of the first phase of the general expansion as a recovery of Gross National Product (GNP) to
normal. The second phase he describes as a period of slower growth after normal capacity utilisation is surpassed.
The literature commonly defines this “normal” as a the pre-recession peak of output. Kannan, Scott and Terrones
(2009) and Claessens, Kose and Terrones (2009) mark the end of a recovery when GDP reaches the peak point just
before the start of the preceding contraction. Fatas and Mihov (2013), however, argue firstly that this definition fails
to take account for the fact that trend growth also occurs in a recession, and secondly that it also ignores phase length.
The length of a particular phase, whether it be a recession or a recovery, influences magnitude of its deviation from
the trend.
Another approach to dating a recovery is to mark a it when output returns to long-run equilibrium or aligns with
the natural rate of employment. Measuring potential output and natural employment, however, is a dubious exercise
(Fatás Mihov, 2013). There is also the possibility of using an econometric model for dating a recovery, as is done
in Fatas and Mihov (2013) who specify a regime switching, non-linear autoregressive model that uses 3 states of the
economy to date recoveries explicitly. Analysis of a large dataset of countries using this type of approach, however, is
likely to be tedious since replicating such a methodology for more than just a few countries can be time consuming.
The most popular option for dating recoveries seems to be setting a fixed duration for the recovery and then observing
the cumulative growth and behaviour of output over this period. Kim, Morley and Piger (2005), for instance, consider
a recovery phase assumed to span four quarters in their investigation of the permanent effect of a recession on
an economy. Morley and Piger (2012) use a six quarter recovery phase in their examination of the general shapes
of recession and recovery combinations. In comparing recoveries across different types of crises Claessens, Kose
and Terrones (2012) use both four and six quarter durations. Iqbal and Vitner (2011) launch in an enquiry into the
relationship between recessions and recoveries, using an implicit four quarter recovery specification when calculating
the percentage change one year after the preceding trough. The same question is asked by Balke and Wynne (1996),
who opt for marking recoveries by dividing the expansion equally into three distinct periods, and then assume the
first period to be the recovery.
One of the advantages of the duration-based approach is that a fixed specification is easily understood. Another
benefit is that a fixed recovery specification allows for the creation of a window that simply examines the behaviour
6. 2.2 General Characteristics of a Recovery 4
of an economy within that time frame. This is easily compared with the behaviour of another economy. The limitation
on a recovery with a fixed duration is that it implicitly assumes that all recoveries last for a fixed number of quarters
and that the recovery duration for all countries are the same. This assumption is unrealistic given the heterogeneous
nature of the economic factors contributing to GDP across countries. Nevertheless, a fixed recovery definition does
provide some useful insight into post-trough behaviour.
2.2 General Characteristics of a Recovery
Schultze’s (1964) definition also implies that a recovery be distinguished by accelerated growth. That is, an economy
tends to experience a stage of high initial growth following the end of a recession. This “bounce-back” growth effect
has been investigated empirically by Sichel (1994), who observes that post-war recessions tend to have been followed
by initial stages of high growth that quickly returned output to its pre-recession level. He subsequently brands these
initial stages as recoveries and argues that contractions and these types of recoveries should be viewed as temporary
interruptions of normal growth. Balke and Wynne (1996) observe the cumulative output loss from peak to trough
for the G-7 countries and report a negative correlation with the post-trough period and interpret these findings as
consistent with the bounce-back effect. The evidence is further strengthened by Morley and Piger (2012) who find
that empirics support a model that captures high growth recoveries following deep recessions. Iqbal and Vitner
(2011), on the other hand, find that deep recoveries in the U.S. are not necessarily followed by recoveries of equal
magnitude, arguing that what they define as deep recessions do not share a statistically significant relationship with
a strong recovery. This agreed with Friedman’s (1964; 1993) view that there is no systematic relationship between
a recession and a recovery, but despite this still finds that a particular recession tends to be followed by an equally
strong recovery. Friedman’s hypothesis of business cycle dynamics finds empirical support in the work done by Kim
and Nelson (1999) and Howard, Martin and Wilson (2011).
Empirical evidence also suggests that the strength of a recovery depend on the type of crisis that causes the recession.
Kannan (2012) uses industry level data to show that recoveries from recessions related to financial crises are much
more tepid than recoveries from other types of recessions, emphasising the cost incurred in financial crises. Claessens,
Kose and Terrones (2012) use quarterly aggregate data to delineate recoveries and find that recoveries from recessions
associated with house price crises tend to be more subdued than a credit or asset price bust. Howard, Martin and
Wilson’s (2011) results agree with this, also showing that recessions resulting from large house price declines tend
to be followed by slower recessions than otherwise. Cerra and Saxena (2008) document the behaviour of output
following political and financial crises and reveal some pessimistic findings. Their results show that less than 1
percentage point of the deepest output loss is regained by the end of the decade following either a political or financial
crisis.
The recovery phase is likely to be affected by asymmetry in the business cycle. Asymmetry is not a general charac-
teristic of a recovery per se, but the shape of the recovery phase is likely to depend on whether the business cycle
identification strategy is able to capture this phenomenon. Although the concept of asymmetric cycles has been
around since Keynes (1936:314), a formal model was first provided by Neftci (1984). Harding and Pagan (2002a) ob-
serve that cycle asymmetry regularly features in the literature, and Morley and Piger (2012) pick up asymmetrical
patterns in their model-averaged measure of the business cycle. Asymmetry in the business cycle materialises in the
form of non-linearities that result in sharper and deeper contractions relative to expansions (Sichel, 1993). Or to look
at it another way, expansions tend to be longer and less steep than contractions. In fact, Romer (1994) finds that
post-war period expansions have become much longer than their preceding contractions. A business cycle identi-
fication strategy that fails to account for asymmetry might end up misidentifying the expansion, which would have
7. 2.3 Motivating a Recovery Phase 5
an affect on the parameters of the recovery phase. Accounting for asymmetry is partly the reason for the accuracy
of Friedman’s plucking model, and incorporating this into the business cycle identification strategy has become a
common practice.
2.3 Motivating a Recovery Phase
Despite Burns and Mitchell’s exposition of four sub-phases in the business cycle, these authors only explicitly date
the overall contraction and expansion. Dating two-phase specifications like this has formed the basis of a number of
studies such as Hamilton (1989) and Diebold and Rudebusch (1990) when dating and studying business cycles such as
Hamilton (1989) and Diebold and Rudebusch (1990). Sichel (1994), however, drew a lot of attention to a period of high
growth early in the expansion, explicitly dating a third phase the U.S business cycle and pulling the recovery phase
out of its theoretic dormancy. This three-phase approach depicts a business cycle as having a contraction/recession
followed a recovery and then by an expansion/post-recovery. This approach has gained traction in the more recent
literature, with the likes of Layton and Smith (2000) showing that a three-phase business cycle captures business cycle
dynamics much better than a two-phase specification, and Bodman and Crosby (2000) finding it useful to define an
explicit recovery phase for Canada.
The recoveries literature in general seems to centre on the experience of handful of industrialised countries of which
the United States receives the bulk of the analytical attention. This is understandable given its well-documented turn-
ing points and data availability, which have made U.S. time series a mecca for business cycle researchers. However,
this raises the question as to whether the experience of a handful of countries can be extrapolated to the rest of the
world. There are studies that utilise richer datasets. Claessens, Kose and Terrones (2012) use a dataset of 44 countries
comprising both industrialised and developing countries, but focus on relationships between business cycles and fin-
ancial cycles. Howard, Martin and Wilson (2011) examine 59 countries, but opt for using a fixed recovery duration,
subjecting it to the disadvantages discussed earlier. Cerra and Saxena (2008) use a panel of 190 countries, but do not
explicitly date a recovery phase. These studies leave room for research on two aspects. The first is the application
of a more flexible, data-driven recovery dating approach that allows the time series to give an indication of where
in a recovery should be dated. Second, it seems appropriate to determine whether the stylised bounce-back growth
experience of the U.S. and the few countries for which it is shown to exist can also be found in general.
Examining whether there is recovery that is meaningful across countries is as much a statistical endeavour as it is
an economic one. From an economic point of view, the consider the premise of DeLong and Summers (1988) that
business cycle fluctuations are to be seen as temporary lapses in production beneath it sustainable levels. Friedman’s
(1964) “plucking” hypothesis argues along the same lines, picturing output as “bumping along the ceiling of maximum
feasible output” that is plucked downwards by a contraction. What can be concluded from these descriptions is that
fluctuations in the business cycle are transitive components that return output to some maximum level of growth.
A transitory component view could reasonably be assumed to hold across countries if it could be accepted that
economies that exhibit slower recovery, or the absence of bounce-back growth, simply experience a longer transition
back to maximum output. Another argument as to why accelerated growth occurs just after the trough is that excess
pent up capital and labour capacities are now available for utilisation in the expansion (Howard et al., 2011). Without
capital and labour as inputs there cannot be output. This holds in any economy, making it reasonable to assume that
the capacity and the behaviour of capital and labour markets affect the recovery. This means that for an economy
that does not show bounce-back growth is that there may be factors in labour and capital markets holding back
the re-utilisation of excess capacity after a recession. The conclusion drawn here is that, even if the bounce-back
8. 6
component is absent from what is marked as the recovery phase for a particular country, the general underlying
economic relationships need not necessarily be disqualified.
The statistical point of view, as taken by this paper, assumes nothing about the nature or existence of the economic
relationships underlying business cycle fluctuations. Rather, the approach taken here should be seen as more of a
descriptive analysis that merely looks at whether a bounce-back type recovery is discernible for countries in general
or not. If this bounce-back phenomenon is indeed limited to only a few countries, then two specific implications
materialise. First, an approach that delineates a business cycle with an explicit recovery phase would need to consider
carefully what should be counted as a recovery, or whether a recovery should be counted at all. Second, scope then
exists for research on recovery specifications other than that of bounce-back growth. These implications, though,
are left as future potential a avenues of research.
3 Methodology
In order to compare the recovery experience across multiple countries, it is necessary to formulate an identification
strategy that is able to clearly delineate business cycles, consistently identify a “recovery” phase and measure the
relevant attributes of these constructs in a quantitative manner. More specifically, it is necessary to decide on how
the expansion and contraction phases of the business cycle are to be determined, which definitions or descriptive
features are to be used to distinguish the recovery phase and what statistical features are to be used as measurements
for comparison. Each of these measurement factors are discussed in turn.
3.1 Delineating Business Cycles
Studying economic recovery requires scrutinising it within the context of the business cycle, which inevitably neces-
sitates careful consideration of the definition and the characterisation of the business cycle itself. Both the definition
and the characterisation of the business cycle are important because they constitute the underlying theoretical struc-
ture within which the business cycle is delineated, and ultimately affect the composition of the observed cycle phases.
Accordingly, it is also important to consider the type of approach that will be used to discern the business cycle since
it will affect in particular what is determined to be an economic recovery and how inference is conducted. The aim
here is not to reinvent the wheel with the construction of a business cycle model for dating turning points, but rather
to rely on a proven set of business cycle chronologies or a simple, reproducible method for dating turning points.
Careful evaluation of any chronology or dating method is necessary, however, since the resulting business cycle
delineations are not always the same.
3.1.1 Parametric and Non-Parametric Approaches
The configuration of the modern-day business cycle used in academia, business and policy finds its origin in the sem-
inal work done by Burns and Mitchell (1946). They essentially defined what is known as the classical business cycle
as patterns of movement in aggregate economic activity (Harding Pagan, 2002:366). These patterns of movement
over time were understood to evolve in the form of recurrent, but alternating, “periods of activity and sluggishness”
(Mitchell, 1923:6), which came to be known as expansions and contractions. Since Burns and Mitchell (1946), there
has developed an extensive body of literature offering a wide array of methodologies for discerning and character-
ising business cycles. Some of the most notable efforts in business cycle identification include Friedman’s (1964; 1993)
9. 3.1 Delineating Business Cycles 7
Plucking Model, Burns and Mitchell’s (1946) business cycle dating methodology, still used by the National Bureau for
Economic Research (NBER), and Hamilton’s (1989) Markov-Switching (MS) model.
A general anatomic distinction that seems to have emerged within literature concerned with identifying business
cycles appears to be between parametric and non-parametric approaches (Harding Pagan, 2002:1862). The para-
metric framework encompasses the well known trend-cycle approach, popularised by Beveridge and Nelson (1981),
of which MS models are a typical example. Other examples in the form of neoclassical and stochastic growth models
can be found in Cooley (1995). The parametric approach partly owes its existence to a migration away from the
Burns-Mitchell methodology which has been argued to lack theoretical and statistical substance (Koopmans, 1947;
Kydland Prescott, 1990; Blanchard Fischer, 1989).
The non-parametric framework stems directly from the Burns-Mitchell methodology, which identifies turning points
using a dating algorithm applied to a composite of monthly time series considered to adequately measure aggregate
economic activity and thereby distinguishes the expansions and contractions of the business cycle. Harding and
Pagan1 have recently revisited this approach, arguing that it is more simplistic, robust, transparent and replicable than
its parametric counterparts (Harding Pagan, 2002:1689). Moreover, in response to the statistical criticism mentioned
earlier, they contend that if a turning point can be identified it can be seen as an event to which a probability can be
attached, which makes it possible to conduct an appropriate statistical analysis (Harding Pagan, 2002a:369). Basing
their work on Bry and Boschan’s (1971) computerised method for locating turning points at a monthly frequency,
Harding and Pagan propose an algorithm suitable for use on a univariate quarterly time series. Referred to as the
Bry-Boschan Quarterly (BBQ) algorithm, this identification strategy has been shown to replicate to a high degree the
turning points in the official business cycle chronologies for the likes of the United States, the United Kingdom, and
Australia (Harding Pagan, 2002a).
Another non-parametric approach is that of the Economic Cycle Research Institute (ECRI). This approach relies on
a composite leading indicator for the prediction of business cycle turning points, and uses a dating methodology
similar to that of the NBER (Achuthan Banerji, 2004). ECRI documents business cycle turning points on monthly
data for a group of 22 countries. An advantage of such collection of chronologies is that, if these turning points can
be assumed to be valid, a dataset of turning points then exist for delineating business cycles that have been generated
from one consistent methodology. ECRI’s turning points have been used in business cycle studies such as, Basistha
(2007) and Moersch and Pohl (2011).
Castro (2010) dissents from the practice of using a single series to date the business cycle, arguing that the original
approach of the NBER and the approach of ECRI that both rely a committee of experts to date the business cycle
based on a collection of economic indicators is better suited for business cycle analysis. This criticism of using a
single series to represent the “complexity that is the business cycle” is also echoed by De Venuto and Layton (2005).
While this argument does carry some merit, it immediately runs into issues of data availability and replicability if one
is to consider a broad range of countries, or countries other than those analysed by ECRI. This is exactly the problem
Castro (2010:363) runs into, consequently resorting to a univariate dating method for GDP for which chronologies
were not available, and implicitly assuming GDP as an appropriate measure of the business cycle. The ECRI turning
points for the United States match up almost exactly with that of the NBER, indicating its potential as an accurate
dating process. As many countries do not officially release turning point chronologies, this is a convenient alternative
for an analysis involving multiple countries if one is willing to assume that these turning points are valid.
1 See their work in Harding and Pagan (2001; 2002; 2002a; 2003; 2005) and Harding (2002).
10. 3.1 Delineating Business Cycles 8
3.1.2 The Turning Point Identification Strategy
This paper examines recoveries that originate within the classical business cycle. Its turning points are applied to
real GDP, and are obtained through two approaches. The first is the use of a combination either official or ECRI
determined business cycle turning points, collectively referred to as predetermined turning points or chronologies
from here on, to delineate the business cycle. The second is the application of the BBQ algorithm on the real GDP
of a larger dataset of countries in order to investigate their recovery experience. The ideal would to be able to use
either only predetermined chronologies or just a simple dating rule such as the BBQ algorithm to date business cycles.
However, for reasons that are discussed later on in section 5, the results from these two approaches are considered
in tandem. Naturally, the implementation of the BBQ algorithm takes a more hands-on approach, requiring a review
of its mechanics.
The purpose of the BBQ algorithm is to locate the local maxima or a local minima within the appropriate time series
based on a simple calculus rule over a specified time window. The maxima and minima are taken to be synonymous
with the peaks and troughs, or the turning points, in the underlying series. Formally, a point Yt at time t in a
univariate, quarterly time series {Y } can be defined as a peak point YP
t if
{Yt−k , ...,Yt−1 YP
t Yt+1, ...,Yt+k } (1)
where k is the number of quarters preceding Yt and also the number of quarters following Yt . k essentially specifies
the time window considered when determining the peak point. Similarly, Yt is defined as a trough point YT
t if
{Yt−k , ...,Yt−1 YT
t Yt+1, ...,Yt+k } (2)
An implication of scalar k is that a set of censoring rules can be applied to the potential turning points identified in
the series. These rules become especially useful if the series is volatile and, more importantly, they set the minimum
duration of the observed cycle which influences the duration of each of the cycle’s phases. As of yet there is no
formal method for determining k, and consequently no optimal value for k (du Plessis, 2006). Harding and Pagan
(2001), however, do translate a value of k = 2 quarters from Bry and Boschan’s (1971) arbitrarily chosen k = 5 months
and recommend a minimum duration of two quarters per cycle phase. The outcome is a cycle specification with a
minimum duration of five quarters, and cycle phases that avoid unrealistically short durations by disallowing peaks
and troughs to occur in direct succession. Delineating business cycles in this way offers two additional benefits.
Firstly, the way in which turning points are dated enables us to allow for asymmetries in the business cycle, which
have been shown to be a salient feature. Secondly, the BBQ method, due to its transparency, is quite intuitive and is
therefore easily grasped by the non-academic viewer.
Up to now, the focus has only been on the mechanics of the BBQ algorithm with no specific attention devoted to the
underlying time series. Originally Burns and Mitchell (1946) resorted to dating a collection of series they perceived
to portray aggregate economic activity since an appropriate single time series incorporating the factors they wished
to measure did not yet exist. Harding and Pagan (2002a:367) take the stance that these series were merely surrogates
for GDP, which was unavailable to Burns and Mitchell at the time and make the case that these authors sought to
date a univariate series as a single measure of the business cycle2. Therefore, if it can be assumed that aggregate
economic activity can be measured by a single time series, a case can be made for using quarterly real GDP as the
underlying time series for delineating business cycles.
2 Burns and Mitchell (1946:72-73) did advocate for the use of Gross National Product, but noted that the compilation of this series was still in its
experimental stage.
11. 3.2 Defining a Recovery Phase 9
If GDP is to be used as the series within which to identify turning points, it becomes important to consider the
functional form of GDP to which the BBQ algorithm will be applied. Three functional forms that offer meaningful
application can be distinguished from the literature (Harding Pagan, 2005). The first of these has been the choice of
the NBER since Burns and Mitchell (1946), and is simply the use of the level of GDP or some monotonic transformation
thereof, such as the log. The resulting turning points delineate what is often referred to as the classical cycle. The
second involves removing a simple deterministic trend3 from the series and then using the algorithm to date the
residual. This can be seen as identifying turning points in the growth cycle4 of a series. Finally, the BBQ algorithm
can be applied meaningfully to the growth rates of a series to delineate cycles within these growth rates, or growth
rate cycles. Growth rate cycles constitute an important part of the recovery identification strategy, and a detailed
discussion of this is deferred to section 3.2.
The business cycle identification strategy used in this analysis, then, can formally described as follows. If GDP is
represented by {Y }, then the log transformation of Yt is shown as
yt = ln (Yt ) (3)
which is the series to which the BBQ algorithm is applied. This results in calculus rules (4) and (5) for dating the
growth cycle peaks and troughs respectively.
{yt−k , ...,yt−1 yP
t yt+1, ...,yt+k } (4)
{yt − k, ...,yt−1 yT
t yt+1, ...,yt+k } (5)
This paper follows Harding and Pagan in settingk = 2 and also keeps to the censoring rules previously discussed. The
log transformation is convenient to work with and can be applied without loss of generality since the data pattern is
invariant to this transformation (Harding Pagan, 2002a). The classical cycle turning points identified according to
this approach allow us to proceed with characterising recoveries.
3.2 Defining a Recovery Phase
Having identified business cycle turning points, a distinction needs to be made between the functional forms of the
series used for dating turning points and the series used for inference. This becomes important when thinking about
how recoveries are to be defined and tested. Business cycle turning points are identified in yt to mark the expansion
and contraction phases, but inference will be done on the quarterly growth rates of the log of GDP, ∆yt , which are
obtained through the first difference of yt :
∆yt = yt − yt−1 (6)
The quarterly growth rates are used in two different capacities. The first is that they provide the means for construct-
ing a possible definition of the recovery phase. The second is that ∆yt can be used for hypothesis tests and inference.
The advantage of using a series of quarterly growth rates for inference is that each growth rate can be treated as
an observation. This greatly increases the sample size as a collection of growth rates within the recovery phase can
3 Harding and Pagan (2005:152) vehemently argue that this should rather be seen as “removing a permanent component” in the series instead of
“detrending” it. While there may be some philosophical weight behind this argument, there is no conceptual difference in the technique applied
to the underlying series.
4 Mintz (1972) provides a more detailed discussion on growth cycles specifically.
12. 3.3 Examining Recoveries Statistically 10
be tested statistically instead of just the recovery as a whole. Accordingly, it is appropriate to proceed first with the
definitions considered for the recovery phase and then discuss how these recoveries will be tested.
Two different approaches are taken to demarcate the recovery phase. The first is to define a recovery as occurring
over a fixed period of time. Consequently, a four-quarter specification for the fixed recovery is chosen where yt
constitutes a recovery if it coincides with the interval set out in equation 7
{yt : yT
yt ≤ yt+4} (7)
In other words, yt forms part of the recovery phase if it occurs within the first four quarters following the trough
of the classical cycle. This definition will principally be used as a comparison to the second, more flexible recovery
definition, namely that of the growth rate peak.
Proposed by Boshoff and Du Plessis (2015), the growth rate peak (GRP) definition implies a recovery spanning the
number of quarters following the business cycle trough up to the quarter containing the first peak in the quarterly5
growth rate cycle of output. This captures the notion that a recovery is a period in which accelerated growth occurs.
The GRP definition is operationally characterised through the application of the BBQ algorithm to ∆yt for each
country. Finding the turning points in the growth rate cycle requires rules (8) and (9) in order to identify growth rate
peak ∆yP
t and growth rate trough ∆yT
t respectively:
{∆yt−k , ..., ∆yt−1 ∆yP
t ∆yt+1, ..., ∆yt+k } (8)
{∆yt−k , ..., ∆yt−1 ∆yT
t ∆yt+1, ..., ∆yt+k } (9)
As before, k = 2 and the censoring rules discussed in section 3.1.2 apply. We are specifically interested in the trough-
to-peak specification in the growth rate cycle coinciding with the trough of the business cycle. Formally,yt constitutes
a GRP-defined recovery if
{yt : yT
yt , ≤ ∆yP
} (10)
In other words, quarters that occur after the business cycle trough, yT , up to the first succeeding growth rate cycle
peak, ∆yP , are taken to constitute the recovery phase of that particular cycle. The GRP recovery phase is now fully
identified. The fixed and GRP definitions both render a recovery phase that can be compared across countries and
and that can be statistically tested.
3.3 Examining Recoveries Statistically
The turning point-based approach allows for the use of the quarterly growth rates in each phase to be used for
statistical inference. One of the aims of this paper is to ascertain whether a recovery can be distinctly defined within
the expansion phase in the first place. Since the position is taken that a recovery phase is characterised by accelerated
growth, a two-sample, one-tailed T-test can be used to test whether the mean growth in the recovery phase is higher
than that of the post-recovery phase. This would be the case if the null that there is no difference between the two
means is rejected.
5 Using a quarter-on-quarter growth rate is also a possibility, but its use in this particular setting yielded higher average growth in the post-
recovery phase for all countries, including the U.S., which goes against intuition and the literature, and was therefore disregarded.
13. 11
Another useful approach is to test whether recovery growth rates and post-recovery growth rates in a particular ex-
pansion were generated from the same probability distributions. This can be done using a two-sample Kolmogorov-
Smirnov (KS) test (Conover, 1971:295-314). The null hypothesis that the distributions of growth rates of the two
phases are the same. Rejection of the null implies that a distributional distinction can be made between the recovery
and post-recovery phases. This means that there is significant statistical evidence that a third phase can be mean-
ingfully motivated in the business cycle. It should be noted that for samples smaller than n = 10000, asymptotic
distributions have to be used in the computation of the KS test statistic which leads to approximated p-values instead
of their exact values. This necessitates scrutinising each result in relation to its sample size and considering it along
with other tests such as the T-test described earlier to see whether the result fits the broader narrative.
In addition to the hypotheses tests above, there are two cycle phase descriptives that are of interest, namely the
duration of each cycle or phase and the amplitude of each phase (Harding Pagan, 2001). Phase statistics give a
better idea of the characteristics of a particular phases, and can themselves be used for inference. Harding and Pagan
(2001) suggest the following sample mean estimators for these phase measures.
Define St as an indicator variable that equals unity for the period that the business cycle transits a particular phase.
The sample average duration is then given by
ˆD =
1
nT P
T
t=1
St (11)
where nT P is the number of turning points which in essence represents the sample size of phases. The average
amplitude can be calculated as
ˆA =
1
nT P
T
t=1
St ∆yt (12)
These statistics can possibly be used to support the recovery definitions through comparison between recoveries and
post-recoveries in general, before using them to describe the characteristics of each phase. One shortcoming of these
averages is that it does not capture the effect of varying lengths of recoveries within the cycles that are identified,
and longer recoveries carry more weight. Nevertheless, they are still useful for gaining a ball-park perspective under
the assumption that recoveries of reasonable length have been identified. These metrics, along with the statistical
tests should provide useful insight into whether it is appropriate to define recoveries for any particular country in
the first place.
4 Data
For this analysis, a dataset is compiled from international sources through Quantec’s (2016) EasyData portal. GDP
data is obtained from the International Monetary Fund’s (IMF) International Financial Statistics (IFS, 2016) database
and from the Organisation for Economic Co-operation and Development’s (OECD) Main Economic Indicators (MEI,
2016) database. Real GDP series from IFS are denoted by an indexed GDP volume measure, and from MEI the series
were downloaded as stock figures at constant prices. Visual comparison for countries with a reputation for well
documented GDP data such as the United States, Australia the United Kingdom and South Africa confirm that these
series are, in fact, analogous. For other countries that overlap between the two databases and that needed seasonal
adjustment the post-adjustment series were not exact replicas of each other, but did show a high enough degree of
concordance to justify a substitution if needed.
14. 12
The IFS database covers a group of 88 countries while the MEI database includes series for its 34 members and 7
other non-member countries. The time series are of different lengths, with the longest GDP series for such as Japan,
Canada and the U.S. available as far back as 1958. These series span 234 quarters, or just under 60 years. The cut-off
for the shortest series is set at 15 years, or 60 quarters. All series have data up to late 2015 or early 2016 with the
exception of a small combination of Latin American and African countries who, along with Russia, terminate at the
end of 2014. One of the advantages of the classical cycle and the way in which it is dated is that the non-parametric
turning points are not affected by the overall length of the series as is the case with parametric models that use a
trend. In addition, the recovery growth rates are pooled for each individual country and then tested which allows for
a country-specific evaluation of the recovery phase. As result, this approach makes it possible to use time series of
different lengths, which strengthens the preference for the non-parametric predetermined chronologies. What the
length of a particular series does affect is the number of recoveries identified for a particular country, which affects
the end result. This must be kept in mind when examining the test statistics.
IFS boasts a bigger group of countries and series that are mostly longer than that of MEI, making it the preferred
database for this analysis. However, some issues emerge when taking a closer look at its series. Firstly, only 17 of
the 88 IFS countries report seasonally adjusted GDP whereas all the series in MEI have been seasonally adjusted.
This is easily overcome, and the IFS series are adjusted where appropriate using the U.S. Census Bureau’s adjustment
procedure in Eviews. The X-12 Auto procedure is selected with the ARIMA model left to the default specifications,
namely a multiplicative ARIMA(1,1,0) model. After seasonal adjustment, the real GDP series for most countries
appear well behaved save for Denmark and Norway, whose series still appear slightly suspect in certain periods.
This is the second issue. Consider Figure 1 which shows Denmark’s GDP series from both databases plotted against
each other. In Denmark’s case, a U-like formation appears in the IFS series that stretches from 1994 to 1998 before
returning to concordance with the MEI series. This is more likely to have been a result of the seasonal adjustment
process than an economic event. The the rest of the IFS series agrees closely with that of MEI, which shows no sign
any type of drop or accelerated growth over that specific period. This “U” is likely to cause the dating algorithm to
identify a different set of turning points than it otherwise would had this formation not been there, which would
affect the statistical tests. We therefore opt for the shorter MEI series. Norway6 simply exhibits a volatility in the IFS
series slightly different to the index in MEI which would result in different turning points. Despite being shorter, the
MEI series spans 154 quarters and starts from 1978, making this substitution a reasonable one.
The third and final issue is the occurrence of anomalies in the series that are unrelated to the data generating process
for Portugal and Greece. Figure 2 plots both the IFS and MEI versions of GDP for Portugal. The IFS version shows a
sharp plunge from the last quarter of 1998 to the first quarter of 1999 which is rather large and unnatural. The MEI
version does not show this at all even though full concordance with the IFS version can be observed for the rest of
the series. Also, the literature does not give any indication of a significant event affecting Portuguese GDP in this
way at this point in time. A possible explanation of this drop is the fact that Portugal was part of the first countries
that adopted the Euro in the first quarter of 1999, which could have affected the way in which GDP was recorded.
Nevertheless, it seems appropriate to proceed with the series from MEI. The final substitution occurs for Greece for
which the IFS series has missing data from the second quarter of 1991 up to the last quarter of 1998.
In summary, the final dataset consists of 67 countries of which 29 are developed countries and 38 are emerging market
economies. IFS is used as the main database, with substitutions made for MEI series for four countries. A complete
list of the countries in this dataset along with their sources is provided in Appendix A. For convenience, an arbitrary
distinction is made between a “long” dataset that contains countries whose series span 100 quarters or more, and
6 See Figure 4 in Appendix B
16. 14
a “short” dataset that contains countries whose series are shorter than a 100 quarters. This distinction splits the
broad dataset roughly in half with the long dataset containing 33 countries and the short dataset 34. The reason for
this is that countries with longer series typically deliver more recoveries on average which increases the accuracy
of the tests. Unsurprisingly, the majority of the countries in the long data set are industrialised countries, with 6
industrialised countries forming part of the short dataset. The long and short datasets with their respective lengths
and the number of recoveries identified for each country are shown in Tables 4 and 5 in Appendix C. A total of 299
recoveries are identified for which the results are discussed in the next section.
5 Results
5.1 Business Cycle Identification: A Turning Point Problem
In section 3.1 it was argued that business cycle specification plays a big role in demarcating recoveries. The spe-
cification influences the turning points identified, and the turning points influence the recovery properties. This is
exactly what is encountered the in the business cycle identification stage of this analysis. The application of the
BBQ algorithm to U.S. real GDP identifies a set of turning points different to that of the NBER. This is important
for a number of reasons. The first is that, as already alluded to, U.S. data and consequently the U.S business cycle
is considered to be a type of gold standard for business cycle models. Due to the quality of the data and the well
documented turning points of the NBER, the U.S. business cycle chronology is often used as a reference across the
literature to test the accuracy of dating methodologies. This is the case with Hamilton (1989), and this is also done
with the BBQ algorithm in Harding and Pagan (2002a) who, as mentioned earlier, find that chronology dated by the
BBQ corresponds with that of the NBER. A visual inspection comparing the NBER and BBQ turning points in Figure
3 reveals that the BBQ turning points, although relatively close to their NBER counterparts, differ from the NBER
turning points in multiple cycles. BBQ cycles appear to occur just before that of the NBER for the first two, and dates
a recession too early in the 1980s. The BBQ also fails to date the 2001 recession. In 2008, it dates the recession too
late. This misalignment between the algorithm and a recognised authority leads us to the next reason, namely its
affect on the statistical tests.
A comparison between the statistical test results from the two chronology sets also shows that their results are quite
sensitive to the above-mentioned disparity. Under the NBER chronology, both the T-test and the KS test reject the null
at a 10% level of significance across both definitions, indicating compelling evidence for the presence of a separate
recovery phase. Under the BBQ chronology, however, not even one of the tests rejected the null. The third reason
for why this difference is so important is that it brings into doubt the dependability of the results for the tests of all
the other countries to which the BBQ algorithm was a applied is used, which brings us to a turning point problem.
One alternative is to date the growth cycle of real GDP instead of just the log. Du Plessis (2006) does this for the
South African business cycle and replicates the South African Reserve Bank’s (SARB) turning points with a high
measure of success. The application of the BBQ algorithm to the growth cycles in the dataset at hand delivers quite
a few more recoveries and line up with the earlier NBER cycles for the U.S. The biggest problem, though, is that it
fails to date the Great Recession in 2008 for countries such as the U.S. and Korea and South Africa, which brings us
back to the original turning point problem. Another alternative is to opt for using officially determined turning point
chronologies that are released by the likes of the NBER and the SARB. However, the fact that very few countries
actually officially report turning point chronologies that are readily available. This is the very reason that the BBQ
17. 5.1 Business Cycle Identification: A Turning Point Problem 15
Figure 3: Comparison between BBQ and NBER turning points
0
20
40
60
80
100
120
1958/03/31
1959/09/30
1961/03/31
1962/09/30
1964/03/31
1965/09/30
1967/03/31
1968/09/30
1970/03/31
1971/09/30
1973/03/31
1974/09/30
1976/03/31
1977/09/30
1979/03/31
1980/09/30
1982/03/31
1983/09/30
1985/03/31
1986/09/30
1988/03/31
1989/09/30
1991/03/31
1992/09/30
1994/03/31
1995/09/30
1997/03/31
1998/09/30
2000/03/31
2001/09/30
2003/03/31
2004/09/30
2006/03/31
2007/09/30
2009/03/31
2010/09/30
2012/03/31
2013/09/30
2015/03/31
IFSGDPVol.index(2010=100)
US GDP BBQ NBER
algorithm exists in the first place. It is at this point that it seems appropriate to use the business cycle chronologies
as set out by ECRI.
ECRI chronologies are readily available and its credibility can be argued based on the high similarity between its
chronology and that of the NBER’s turning points. It is by no means a perfect measure, however, as its chronology
for South Africa does not align with that of the SARB, hence the use of a combination of officially dated and ECRI
turning points. The OECD (2017) also documents business cycle turning points, but dates the growth cycle of a
composite leading indicator. Despite its misalignment with the U.S. and South Africa, it does not seem appropriate
to discard the BBQ algorithm based on the results of just two countries. The BBQ algorithm and its parent, the
monthly Bry-Boschan measure, are used quite widely in the literature and presumably without complication which
does say something about its credibility. Moreover, it is still the best alternative for dating countries for which
predetermined chronologies do not exist. Also, discarding the BBQ algorithm would severely limit the sample size
of the dataset, throwing out all developing countries except for the few for which ECRI dates business cycle turning
points. This would then focus the analysis almost exclusively on industrialised countries. Finally, it is not the aim
of this paper to participate in the debate surrounding the appropriate business cycle measure, or to critique any
particular methodology’s turning points. It seems best to recognise that the current set of chronologies is less than the
ideal, but to argue that something is better than nothing and proceed with the analysis under a stronger assumption
with regards to the legitimacy of the set of chronologies.
18. 5.2 Statistical Tests 16
5.2 Statistical Tests
Before discussing the test results it is necessary to institute some additional refinements to ensure some measure
of robustness for the outcomes at hand. Firstly, countries for which four or more recoveries could be identified
are considered as this number seems to provide a fair amount of observations for the T-test and KS test to provide
accurate results. Furthermore, a country is deemed to have a statistically significant recovery if any two or more of
the statistical tests across the two recovery definitions reject the null hypothesis. If, for example, both T-tests indicate
a significant recovery but the KS tests do not, it is still considered a significant recovery. The odd combination of
significance for a fixed duration KS test and a GRP T-test are also allowed for. The reasoning behind this is that if at
least two tests reject their respective null hypotheses, then there must be some indication of a bounce back growth
recovery.
Table 1 shows the countries for which statistically significant recoveries were identified and adhere to the above
criteria. The test statistics for the T-tests and KS tests and the business cycle turning point chronology used for
each country in the dataset are provided in Tables 4 and 5 in Appendix C. A couple of observations can be made
immediately. The first is that there is a clear indication of bounce-back growth in the recovery phases for the United
States which is consistent with the literature. The T-tests for both the fixed and the GRP definitions show that the
average growth is higher in the recovery phase than in the post-recovery. The same is true for the KS tests, which
indicate that U.S. growth rates in the recovery phase are generated from different distributions. These tests are all
significant at α = 0.1.
The second observation is that very few countries indicate statistically that a separate recovery phase can be dis-
tinguished in their respective business cycles. This leads to the conclusion that the bounce-back phenomenon is
probably not a feature of recoveries in general, but more importantly this result also points to the the possibility
that the concept of a recovery phase may not be internationally applicable. Only 11 countries, of which the U.S. and
Australia are the only developed countries, indicate the presence of bounce-back growth. Even if the the minimum
recovery criteria is relaxed to 3 recoveries, only Malaysia, Estonia and Turkey are added. This means that the original
Burns-Mitchell approach in dating only expansions and contractions might be more applicable in general, reserving
the recently popularised three-phase business cycle approach to for these select few countries.
Another observation that can be made is with regards to the geographical groupings of the countries for which
significant recoveries are found. A clear majority of the countries with significant bounce-back recoveries reside in
the Americas. North America is almost fully represented with Canada narrowly missing out on being included. In
fact, tests run on the OECD version of the data renders significant T-tests for both the fixed and GRP definitions.
Also, ECRI identifies only 3 recoveries for this country. Central America is missing, from this set though, but South
America is well represented. Europe, Asia and Africa are, for all practical intents and purposes, absent. None of
the major European or Scandinavian countries feature at all despite a relatively large presence in the broad dataset.
Malta seems to be the only exception. The fact, that there are no Asian countries exhibiting this bounce-back growth
phenomena seems surprising given their patterns of growth in the past. There are 8 Asian countries in the data set
if Turkey is counted here. Turkey shows a stunning significance, which is also surprising, given its economic woes
in the past. Countries such as India and Thailand did not yield enough recoveries to warrant serious consideration,
and China couldn’t be included in the data set because of the short length of its series. What is also interesting is
that of the BRIC countries, only Brazil indicates a significant recovery. Only 3 African countries, Morocco, Botswana
and South Africa, had sufficient data to be included in the data set. South Africa’s results robustly show across SARB,
ECRI and BBQ chronologies that bounce-back growth is not characteristic of its business cycle.
20. 5.3 Phase Statistics 18
5.3 Phase Statistics
Because so few countries were found to have a significant, separate recovery phase, there is not too much to be
said about their phase statistics, shown in Table2. The average duration of recoveries in the Americas seem to be
longer than the rest, with Mexico having the longest average duration. The maximum duration of recoveries are
also more or less the same for all the countries except United States and Mexico both of whom have a maximum
recovery duration of 10. The maximum duration for Canada, shown in Table 6, is 9. This gives a slight indication of
the similarity between the business cycles of these economies. Furthermore, the average amplitude does not seem to
vary much across countries, except for Botswana, whose amplitude is quite high relative to the rest. If the average
amplitudes are considered for both definitions in the whole dataset, shown in Tables 6 and 5 in Appendix D regardless
of whether these dated recoveries are significant or not, there still is not much difference across this statistic.
Table 2: Recovery Phase Statistics for GRP(Fixeda) Definition
Country Recovery Quarters Recoveries Avg Duration Max Duration (GRP) Avg Amplitude
United States 32(32) 8 4(4) 10 0.05(0.04)
Mexico 34(24) 6 5.67(4) 10 0.07(0.05)
Brazil 16(20) 5 3.2(4) 5 0.04(0.06)
Chile 19(16) 4 4.75(4) 6 0.09(0.06)
Ecuador 20(20) 5 4(4) 5 0.06(0.06)
Paraguay 15(19) 5 3(3.8) 6 0.06(0.08)
Europe
Malta 15(18) 5 3(3.6) 6 0.05(0.07)
Asia-Pacific
Australia 8(16) 4 2(4) 4 0.03(0.06)
Turkey 13(24) 6 2.17(4) 3 0.07(0.11)
Africa
Morocco 19(22) 6 3.17(3.67) 5 0.07(0.1)
Botswana 11(14) 4 2.75(3.5) 5 0.1(0.13)
a Results for the fixed definition are shown in brackets.
One of the secondary aims of this dissertation was to evaluate a more flexible recovery definition, namely that of the
GDP, against the fixed duration definition. Looking again at Tables 6 and 5, it can be observed that GRP recoveries are
often longer than 4 quarters, but are almost as often not. The same then holds for the number of quarters identified
as part of the recovery. Across the two definitions, there is also no notable difference in the average amplitude. In
summary, while there are some differences, it does not appear that this definition performs differently than a fixed
duration specification.
6 Conclusion
The dissertation sought to test whether the concept of a recovery phase can be applied to business cycles in gen-
eral. The first step taken was to look at business cycle specification techniques, since the particular delineation of a
business cycle affects the parameters of a recovery phase. Using officially determined chronologies such as those of
21. 19
the NBER seemed the most obvious, but most countries do not report official chronologies. A simple rule, the BBQ
algorithm, was another candidate and can be used to date peaks and troughs in the GDP of each country. These
expansion-contraction chronologies were used to set the framework for marking recoveries according to two defin-
itions. The BBQ algorithm failed to date the U.S. business cycle according to the NBER’s turning points, resulting
in the use of a hybrid set of chronologies from external sources and the from the BBQ for countries for which chro-
nologies could not be found. The first is a simple four quarter duration phase and the second used the peak of the
quarterly growth rate to signal the end of a recovery. The aim was to see whether the bounce-back characteristic
often associated with industrialised countries such as the U.S. held for a broad data set. Two statistical tests, the T-test
and the Kolmogorov-Smirnov test, were used to see if the demarcated recovery’s growth rates behaved differently to
elsewhere in the expansion. Phases statistics were also examined for any information on whether a recovery phase
could be statistically defined in general.
The result was that very few countries provided statistically significant evidence of this third phase in the business
cycle, raising the question of whether recoveries can be defined for countries in general at all. Countries for which
recoveries came up significant are mostly concentrated in North and South America. The presence of a significant
bounce-back recovery is virtually non-existent in European and Scandinavian countries, in Asia but visible for two
countries in Africa. South Africa is not one of them. This paper also evaluated the GRP recovery definition against
a fixed duration definition and did not find any remarkably different results in terms of recovery outcomes between
the two. Given the evidence, this paper brings into question the general stigma associated with what is referred to
as a recovery phase, since it is not clear how recoveries should be defined in general. That is, if a recovery phase can
be appropriately defined at all.
22. REFERENCES 20
References
Achuthan, Lakshman, Banerji, Anirvan. 2004. Beating the business cycle: How to predict and profit from turning
points in the economy. Danvers: Crown Business.
Balke, Nathan S., Wynne, Mark A. 1996. Are deep recessions followed by strong recoveries? Economic Let-
ters, 39, 183–189. [Online]. Available: http://www.sciencedirect.com.ez.sun.ac.za/science/journal/01651765 [2016,
September 1].
Basistha, Arabinda. 2007. Trend-cycle correlationsm drift break and the estimation of trend and cycle in Canadian
GDP. Canadian Journal of Economics, 40(2), 584–606. [Online]. Availble: https://www.jstor.org/stable/4620621
[2017, January 11].
Beveridge, Stephen, Nelson, Charles R. 1981. A new approach to decomposition of economic time series
into permanent and transitory components with particular attention to measurement of the business cycle.
Journal of Monetary economics, 7, 151–174. [Online]. Available: http://www.sciencedirect.com/science/article/pii/
0304393281900404 [2016, September 5].
Blanchard, Olivier J, Fischer, Stanley. 1989. Lectures on Macroeconomics. Cambridge, Massechusetts: MIT
Press.
Bodman, Philip M., Crosby, Mark. 2000. Phases of the Canadian Business Cycle. Canadian Journal of Economics,
33(3), 618–633. [Online]. Available: https://www.jstor.org/stable/2667420?seq=1#page_scan_tab_contents [2017,
January 8].
Boshoff, Willem, du Plessis, S. A. 2015. Recovery phases in the South African business cycle. Unpublished paper
delivered at the ESSA 2015 Biennial Conference. 4 September, Cape Town. [Online]. Available: 2015.essa.org.za/
fullpaper/essa_2904.pdf [2017, January 15].
Bry, Gerhard, Boschan, Charlotte. 1971. Recession and Recovery Analysis. Cyclical Analysis of Time Series:
Selected Procedures and Computer Programs. New York: NBER. 151-216. [Online]. Available: http://www.nber.org/
chapters/c2150 [2016, Septemeber 1].
Burns, Arthur F., Mitchell, Wesley C. 1946. Measuring Business Cyclesf. New York: NBER. [Online]. Available:
http://www.jstor.org/stable/2280551 [2016, September 5].
Castro, Vítor. 2010. The duration of economic expansions and recessions: More than duration dependence. Journal
of Macroeconomics, 32, 347–365. [Online]. Available: 10.1016/j.jmacro.2009.06.006. [2016, December 29].
Cerra, Valerie, Saxena, Sweta Chaman. 2008. Growth dynamics: the myth of economic recovery. The American
Economic Review, 98(1), 439–457. [Online]. Available: :https://www.aeaweb.org/articles?id=10.1257/aer.98.1.439
[2016, December 7].
Claessens, Stijn, Kose, M. Ayhan, Terrones, Marco E. 2009. What Happens During Recessions, Crunches and
Busts? Working Paper No. WP/08/274 Washington D.C., Virginia: IMF. [Online]. Available: https://www.imf.org/
external/pubs/ft/wp/2008/wp08274.pdf [2017 January 15].
Claessens, Stijn, Kose, M. Ayhan, Terrones, Marco E. 2012. How do business and financial cycles interact?
Journal of International Economics, 87(1). [Online]. Available: http://dx.doi.org/10.1016/j.jinteco.2011.11.008 [2016,
September 1].
23. REFERENCES 21
Conover, William J. 1971. Practical Nonparametric Statistics. New York: John Wiley Sons.
Cooley, Thomas F. (ed). 1995. Economic Growth and Business Cycles. New Jersey:Princeton University Press.
de Long, J. Bradford, Summers, Lawrence H. 1988. How Does Macroeconomic Policy Affect Output? Brook-
ings Papers on Economic Acativity, 2, 433–494. [Online]. Available: http://www.jstor.org.ez.sun.ac.za/stable/pdf/
2534535.pdf [2014, January 15].
Diebold, Francis X, Rudebusch, Glenn D. 1990. A nonparametric investigation of duration dependence in the
American business cycle. Journal of political Economy, 98(3), 596–616. [Online]. Available: http://www.jstor.org.
ez.sun.ac.za/stable/pdf/2937701.pdf [2017, January 7].
du Plessis, S.A. 2006. Reconsidering the business cycle and stabilisation policies in South Africa. Economic Modelling,
23(5), 761–774. [Online]. Available: http://dx.doi.org/10.1016/j.econmod.2005.10.006 [2016, September 1].
Du Venuto, Nicholas, Layton, Allan P. 2005. Do the Phases of the Business Cycle Die of Old Age? Aus-
tralian Economic Papers, 44(3), 290–305. [Online]. Available: http://onlinelibrary.wiley.com.ez.sun.ac.za/doi/10.
1111/j.1467-8454.2005.00266.x/abstract [2017, January 15].
Fatás, Antonio, Mihov, Ilian. 2013. Recoveries. Discussion Paper Series No. 9551. London, England: Center for
Economic Policy Research. [Online]. Available: www.cepr.org/pubs/dps/DP9551.asp [2016, September 1].
Filardo, Andrew J. 1994. Business-Cycle Phases and their Transitional Dynamics. Journal of Business and Economic
Statistics, 12(3), 299–308. [Online]. Available: http://www.jstor.org/stable/1392086?seq=1cid=pdf-reference#
references_tab_contents [2016, December 30].
Friedman, Milton. 1964. Monetary Studies of the National Bureau. The National Bureau Enters Its 45th Year, 44,
7–25. [Online]. Available: http://www.nber.org/chapters/c4453.pdf [2016, November 3].
Friedman, Milton. 1993. The Plucking Model of Business Fluctuations Revisited. Economic Inquiry, 31(April), 171–
177. [Online]. Available: http://www.jstor.org/stable/2601114?seq=1#page_scan_tab_contents [2016, November 3].
Hamilton, James D. 1989. A new approach to the economic analysis of nonstationary time series and the business
cycle. Econometrica: Journal of the Econometric Society, 57(2), 357 – 384. [Online]. Available: http://www.jstor.org/
stable/1912559 [2016, September 7].
Harding, Don. 2002. The Australian Business Cycle: a New View. MPRA Paper No. 3698. Melbourne, Australia: Mel-
bourne Institute of Applied Economics and Social Research. [Online]. Available: https://mpra.ub.uni-muenchen.
de/3698/1/MPRA_paper_3698.pdf [2016, September].
Harding, Don, Pagan, Adrian. 2001. Extracting, analysing and using cyclical information. MPRA Paper No. 15.
Melbourne, Australia: Melbourne Institute of Applied Economics and Social Research.[Online]. Available: https:
//mpra.ub.uni-muenchen.de/15/1/MPRA_paper_15.pdf [2016, September 7].
Harding, Don, Pagan, Adrian. 2002. A comparison of two business cycle dating and methods. Journal of Economic
Dynamics Control, 49(2), 365 – 381. [Online]. Available: http://dx.doi.org.ez.sun.ac.za/10.1016/S0165-1889(02)
00076-3 [2016, September 5].
Harding, Don, Pagan, Adrian. 2002a. Dissecting the cycle and a methodological investigation. Journal of Monet-
ary Economics. [Online]. Available: http://dx.doi.org.ez.sun.ac.za/10.1016/S0304-3932(01)00108-8 [2016, September
5].
24. REFERENCES 22
Harding, Don, Pagan, Adrian. 2003. Rejoinder to James Hamilton. Journal of Economic Dynamics Control, 27,
1695 – 1698. [Online]. Available: http://www.sciencedirect.com.ez.sun.ac.za/science/article/pii/S0165188902000787
[2016, September 1].
Harding, Don, Pagan, Adrian. 2005. A Suggested Framework for Classifying the Modes of Business Cycle
Research. Journal of Applied Econometrics, 20, 151–159. [Online]. Available: http://onlinelibrary.wiley.com.ez.sun.
ac.za/doi/10.1002/jae.838/full [2016, September 7].
Hayek, Friedrich A. 1933. Monetary Theory and the Trade Cycle. New York: Sentry Press.
Howard, Greg, Martin, Robert, Wilson, Beth Anne. 2011. Are Recoveries from Banking and Financial Crises
Reallly So Different? International Finance Discussion Papers No. 1037. Washington D.C., Virginia Board of Gov-
ernors of the Federal Reserve System. [Online]. Available: http://www.hngzw.gov.cn/caijing/uploadfiles/201112/
201112/20111231100525416.pdf [2016, November 3].
IFS. 2016. International Statistics Database. Available: http://data.imf.org/?sk=5dabaff2-c5ad-4d27-a175-1253419c02d1
[2016, November 29].
Iqbal, Azhar, Vitner, Mark. 2011. The Deeper the Recession, the Stronger the Recovery: Is it Really That
Simple? Business Economics, 46(1), 22–31. [Online]. Available: http://link.springer.com/article/10.1057/be.2010.38
[2016, November 3].
Kannan, Prakash. 2012. Credit Conditions and Recoveries from Financial Crises. Journal of International Money
and Finance, 31, 930–947. [Online]. Availble: http://dx.doi.org/10.1016/j.jimonfin.2011.11.017 [2016, November 3].
Kannan, Prakash, Scott, Alasdair, Terrones, Marco E. 2009. From Recession to Recovery: How soon and
how strong?. World Economic Outlook, Washington D.C.: IMF. 109-138. [Online]. Available: https://www.imf.org/
external/pubs/ft/weo/2009/01/pdf/c3.pdf [2017, January 7].
Keynes, John M. 1936. The General Theory of Employment, Interest and Money. London: MacMillan.
Kim, Chang-Jin, Nelson, Charles R. 1999. Friedman’s plucking model of business fluctuations: tests and estimates
of permanent and transitory components. Journal of Money, Credit and Banking, 31(3), 317–334. [Online]. Available:
http://www.jstor.org.ez.sun.ac.za/stable/2601114?seq=1#page_scan_tab_contents [2017, January 7].
Kim, Chang-Jin, Morley, James, Piger, Jeremy. 2005. Nonlinearity and the permanent effects of recessions.
Journal of Applied Econometrics, 20(2), 291–309. [Online]. Available: http://doi.wiley.com/10.1002/jae.831 [2016,
September 1].
Koopmans, Tjalling C. 1947. Measurement without theory. The Review of Economics and Statistics, 29(3), 161–172.
[Online]. Available: http://www.jstor.org/stable/pdf/1928627.pdf [2016, September 7].
Kydland, Finn E, Prescott, Edward C. 1990. Business cycles: Real facts and a monetary myth. Quarterly Review,
14(2), 383–398. [Online]. Available: https://minneapolisfed.org/research/qr/qr1421.pdf [September 5].
Layton, Allan P., Smith, Daniel R. 2000. A further note on the three phases of the U.S. business cycle. Ap-
plied Economics, 32, 1133–1143. [Online]. Available: http://www-tandfonline-com.ez.sun.ac.za/doi/pdf/10.1080/
000368400404272?needAccess=true [2017, January 15].
25. REFERENCES 23
Layton, Allan P., Smith, Daniel R. 2007. Business cycle dynamics with duration dependence and leading indicat-
ors. Journal of Macroeconomics, 29, 855–875. [Online]. Available: doi:10.1016/j.jmacro.2006.02.003 [2016, December
30].
Lucas, Robert E. 1977. Understanding Business Cycles. North-Holland. Understanding Business Cycles, in Confer-
ence on Growth Without Inflation. Chicago: University of Chicago. 7-9 [Online]. Available: http://icm.clsbe.lisboa.
ucp.pt/docentes/url/jcn/MaBES/LucasUnderstanding.pdf [2016, September 5].
Male, Rachel. 2011. Developing Country Business Cycles: Characterizing the Business Cycle. Emerging Mar-
kets Finance and Trade, 47(2), 20–39. [Online]. Available: http://dx.doi.org/10.2753/REE1540-496X4703S202 [2016,
November 3].
MEI. 2016. Main Economic Indicators. Available: http://www.oecd.org/std/oecdmaineconomicindicatorsmei.htm
[2016, November 29].
Mintz, Ilse. 1972. Dating American Growth Cycles, in Victor Zarnowitz(ed.). Economic Research: Ret-
rospect and Prospect, Volume 1, The Business Cycle Today. New York: NBER. 39-88.[Online]. Available:
http://www.nber.org/chapters/c4393.pdf [2016, September].
Mitchell, Wesley C. 1923. Business Cycles, in Committee of the President’s Conference on Unemployment, and
a Special Staff of the National Bureau (eds.). Business Cycles and Unemployment. New York, NBER. 7-20.[Online].
Available: http://www.nber.org/chapters/c4658. [2017, January 15].
Moersch, Mathias, Pohl, Armin. 2011. Predicting recessions with the term spread - recent evidence from seven
countries. Applied Economics Letters, 18, 1285–1288. [Online]. Availble: http://www.tandfonline.com/doi/abs/10.
1080/13504851.2010.534055 [2017, January 11].
Morley, James, Piger, Jeremy. 2012. The Asymmetric Business Cycle. The Review of Economics and Statistics.
[Online]. Available: http://www.mitpressjournals.org/doi/pdf/10.1162/REST_a_00169 [2016, September 10].
Neftci, Salih N. 1984. Are economic time series asymmetric over the business cycle? The Journal of Polit-
ical Economy, 92(2), 307–328. [Online]. Available: http://www.jstor.org.ez.sun.ac.za/action/showPublication?
journalCode=jpoliecon [2016, September 8].
OECD. 2017. OECD Composite Leading Indeicators: Turning Points of Reference Series and Component Series. [Online].
Available: http://www.oecd.org/std/leading-indicators/CLI-components-and-turning-points.pdf [2017, January
15].
Quantec. 2016. Easy Data. Available: http://www.easydata.co.za/ [2016, November 29].
Romer, Christina D. 1994. Remeasuring Business Cycles. The Journal of Economic History, 54(3), 573–609. [Online].
Available: http://www.jstor.org/stable/2123869 [2016, November 3].
Schultze, Charles. 1964. Short-Run Movements of Income Shares. The Behavior of Income Shares: Selec-
ted Theoretical and Empirical Issues. New Jersey: Princeton University Press. 143-188. [Online]. Available:
http://www.nber.org/chapters/c1845 [2017, January 7].
Sichel, Daniel E. 1993. Business Cycle Asymmetry: A Deeper Look. Economic Inquiry, 31, 224–236. [Online]. Avail-
able: http://onlinelibrary.wiley.com.ez.sun.ac.za/doi/10.1111/j.1465-7295.1993.tb00879.x/full [2016, September 1].
Sichel, Daniel E. 1994. Inventories and the First Three Phases of the Business Cycle. Journal of Business and Economic
Statistics, 12(3), 269–277. [Online]. Available: http://www.jstor.org.ez.sun.ac.za/stable/pdf/1392083.pdf [2017, 14].
26. 24
A Appendix: Sample Country Data Sources
Country IFS Identifier MEI Identifier Database Used
Argentina IFS-I21399BVPZFQ IFS
Australia IFS-I19399BVRZFQ MEI-AUS_NAEXKP01_STSAQ IFS
Austria IFS-I12299BVPZFQ MEI-AUT_NAEXKP01_STSAQ IFS
Belarus IFS-I91399BVPZFQ IFS
Belgium IFS-I12499BVPZFQ MEI-BEL_NAEXKP01_STSAQ IFS
Bolivia IFS-I21899BVPZFQ IFS
Botswana IFS-I61699BVPZFQ IFS
Brazil IFS-I22399BVPZFQ MEI-BRA_NAEXKP01_STSAQ IFS
Bulgaria IFS-I91899BVPZFQ IFS
Canada IFS-I15699BVRZFQ MEI-CAN_NAEXKP01_STSAQ IFS
Chile IFS-I22899BVPZFQ MEI-CHL_NAEXKP01_STSAQ IFS
Costa Rica IFS-I23899BVPZFQ MEI-CRI_NAEXKP01_STSAQ IFS
Croatia IFS-I96099BVPZFQ IFS
Cyprus IFS-I42399BVPZFQ IFS
Czech Rep IFS-I93599BVPZFQ MEI-CZE_NAEXKP01_STSAQ IFS
Denmark IFS-I12899BVPZFQ MEI-DNK_NAEXKP01_STSAQ MEI
Ecuador IFS-I24899BVPZFQ IFS
Estonia IFS-I93999BVPZFQ MEI-EST_NAEXKP01_STSAQ IFS
Finland IFS-I17299BVPZFQ MEI-FIN_NAEXKP01_STSAQ IFS
France IFS-I13299BVRZFQ MEI-FRA_NAEXKP01_STSAQ IFS
Georgia IFS-I91599BVPZFQ IFS
Germany IFS-I13499BVRZFQ MEI-DEU_NAEXKP01_STSAQ IFS
Greece IFS-I17499BVPZFQ MEI-GRC_NAEXKP01_STSAQ MEI
Guatemala IFS-I25899BVPZFQ IFS
Hong Kong IFS-I53299BVPZFQ IFS
Hungary IFS-I94499BVPZFQ MEI-HUN_NAEXKP01_STSAQ IFS
Iceland IFS-I17699BVPZFQ MEI-ISL_NAEXKP01_STSAQ IFS
India IFS-I53499BVPZFQ MEI-IND_NAEXKP01_STSAQ IFS
Indonesia IFS-I53699BVPZFQ MEI-IDN_NAEXKP01_STSAQ IFS
Ireland IFS-I17899BVPZFQ MEI-IRL_NAEXKP01_STSAQ IFS
Israel IFS-I43699BVPZFQ MEI-ISR_NAEXKP01_STSAQ IFS
Italy IFS-I13699BVRZFQ MEI-ITA_NAEXKP01_STSAQ IFS
Jamaica IFS-I34399BVPZFQ IFS
Japan IFS-I15899BVRZFQ MEI-JPN_NAEXKP01_STSAQ IFS
Korea IFS-I54299BVPZFQ MEI-KOR_NAEXKP01_STSAQ IFS
Kyrgyz Rep IFS-I91799BVPZFQ IFS
Latvia IFS-I94199BVPZFQ MEI-LVA_NAEXKP01_STSAQ IFS
Lithuania IFS-I94699BVPZFQ MEI-LTU_NAEXKP01_STSAQ IFS
Macao IFS-I54699BVPZFQ IFS
27. 25
Macedonia IFS-I96299BVPZFQ IFS
Malaysia IFS-I68499BVPZFQ IFS
Malta IFS-I55699BVPZFQ IFS
Mauritius IFS-I18199BVPZFQ IFS
Mexico IFS-I27399BVRZFQ MEI-MEX_NAEXKP01_STSAQ IFS
Morocco IFS-I68699BVPZFQ IFS
Netherlands IFS-I13899BVRZFQ MEI-NLD_NAEXKP01_STSAQ IFS
New Zealand IFS-I19699BVRZFQ MEI-NZL_NAEXKP01_STSAQ IFS
Norway IFS-I14299BVPZFQ MEI-NOR_NAEXKP01_STSAQ MEI
Paraguay IFS-I28899BVPZFQ IFS
Peru IFS-I29399BVPZFQ IFS
Philippines IFS-I56699BVPZFQ IFS
Poland IFS-I96499BVPZFQ MEI-POL_NAEXKP01_STSAQ IFS
Portugal IFS-I18299BVRZFQ MEI-PRT_NAEXKP01_STSAQ MEI
Romania IFS-I96899BVPZFQ IFS
Russia IFS-I92299BVPZFQ IFS
Serbia IFS-I94299BVPZFQ IFS
Singapore IFS-I57699BVPZFQ IFS
Slovak Rep IFS-I93699BVPZFQ MEI-SVK_NAEXKP01_STSAQ IFS
Slovenia IFS-I96199BVPZFQ MEI-SVN_NAEXKP01_STSAQ IFS
South Africa IFS-I19999BVRZFQ MEI-ZAF_NAEXKP01_STSAQ IFS
Spain IFS-I18499BVRZFQ MEI-ESP_NAEXKP01_STSAQ IFS
Sweden IFS-I14499BVPZFQ MEI-SWE_NAEXKP01_STSAQ IFS
Switzerland IFS-I14699BVRZFQ MEI-CHE_NAEXKP01_STSAQ IFS
Thailand IFS-I57899BVPZFQ IFS
Turkey IFS-I18699BVPZFQ MEI-TUR_NAEXKP01_STSAQ IFS
United Kingdom IFS-I11299BVRZFQ MEI-GBR_NAEXKP01_STSAQ IFS
United States IFS-I11199BVRZFQ MEI-USA_NAEXKP01_STSAQ IFS
