structural breaks in potential gdp of four major economies: just
TRANSCRIPT
Structural Breaks in Potential GDP of Four Major Economies: just
impaired credit or the «New Normal»?1
A. Apokin, I. Ipatova
This paper investigates the factors behind the recent growth slowdown (so-called «the
Secular Stagnation») in the US, euro area, China, and Japan using the metrics of potential output
growth. Specifically, our results offer limited support for a supply slowdown hypothesis
(Gordon, 2012), while not supporting an impaired credit transmission channel hypothesis
(Reinhardt and Rogoff, 2009a). We estimate potential output growth with a variety of
multivariate Kalman filters accounting for inflation, unemployment, and private credit dynamics
(«finance-neutral» estimates) and subject our estimates to structural breaks tests. We detect
structural breaks between 2008 and 2010 for all countries with Bai-Perron search procedure, the
result being robust to the filter, specification and sample choices, with no significant difference
between ordinary and «finance-neutral» estimates. We proceed with Chen-Liu test to detect
negative level shift outliers in The Great Recession for euro area and Japan. Moreover, Chen and
Liu test finds scarce evidence of temporary change outliers during The Great Recession if
estimates account for labour market indicators.
Keywords: New Normal, Secular Stagnation, Great Slump, potential GDP, Kalman filter, Bai-
Perron test, Chen-Liu test
JEL classification: C53, E17, F44, O57.
1 Apokin: Head, Global Research Unit, CMASF (Moscow), Senior Research Fellow, NRU-HSE, (Moscow),
[email protected]. Ipatova: Expert, CMASF (Moscow), NRU-HSE, (Moscow), [email protected]
The study was implemented in the framework of the Basic Research Program at the National Research University Higher
School of Economics (HSE) in 2014
1. Introduction
World GDP has grown at 3.9% on average between 2010 and 2014 against 4.5% between
2002 and 2008. According to IMF, the global economy is set to grow even slower in 2014,
prediction being 3.8%. This underperformance after the global economic crisis is often
considered a sign of transition to the new trend of economic growth.
Academics and practitioners offer different names for this new trend. B. Gross (former
PIMCO) coined in the term «New Normal» in 2009, forecasting a period of sluggish economic
growth for a period between 2010 and 2015. Since then, terms «The Second Great Contraction»
(Reinhardt and Rogoff, 2009b), «The Great Slump» (Hall, 2011), and, finally, «Secular
Stagnation» (Summers, 2014) were offered along with several interpretations of growth
slowdown. Fischer (2014) points out the absence of a single opinion on the nature of a current
slowdown, despite plenty of post-crisis data available, and emphasizes the point of
distinguishing cyclical slowdown from a structural one as a key to successful macroeconomic
policy.
The literature distinguishes between cyclical and structural slowdown using the concept
of potential (or trend) output2. In line with the literature we treat structural slowdown as a
decrease in potential GDP growth rate, ceteris paribus (e.g. at a constant unemployment rate
etc.). The rest of GDP dynamics is cyclical and can be explained by relationships between
potential output, unemployment and other fundamentals.
In this paper we test whether the recent global growth slowdown is structural. We
estimate potential output for major economies with a variety of methods typically used in the
literature, taking into account dynamics of «neutral» unemployment rate and other fundamentals.
Specifically, we try to isolate the effects of impaired credit transmission channel on potential
output noted by Reinhardt and Rogoff (2009a) by using «finance-neutral» potential output
estimates. We then subject obtained estimates of potential output to a barrage of structural break
tests to determine whether we can find and date structural slowdowns taking place and whether
the results change in case of «finance-neutral» potential output estimates.
We find that much of the post-crisis slowdown in major economies is of structural nature.
We identify post-crisis structural breaks around 2009. This result is robust across samples, most
model specifications, and estimation methods. In all four major economies, there is a significant
difference between potential output estimates and their «finance-neutral» versions. We find that
ongoing growth slowdown has other structural reasons beyond the impaired credit transmission
2 2
See Lazear, Spletzer (2012) for extensive discussion on what the term «potential output» might mean in
the literature.
channel: structural breaks in potential output persist even after financial cycle is taken into
account. Outcome of Chen and Liu tests partly confirms this result.
This paper is organized as follows. Section 2 provides a review of literature bordering
research questions of this article. Section 3 contains brief review and interpretation of statistical
methods we use to provide potential GDP estimates. Section 4 contains description and
comparison of potential GDP estimates. In section 5 we test our data for structural breaks.
Section 6 concludes. Appendix 1 contains descriptions of structural break and outlier tests we
use. Appendix 2 lists Kalman filters specifications for potential output estimates. Appendix 3
contains charts of potential output and output gap estimates, and Appendix 4 provides results of
Chen-Liu test.
2. Literature review
The literature on the subject of this paper can roughly be separated into two avenues. The
first deals with the economic policy debate on «secular stagnation» in the US and globally. The
second is dedicated to detecting structural breaks in economic growth data.
2.1 Growth slowdown and «secular stagnation» debate
There are two main lines of the so-called «secular stagnation debate» (CEPR, 2014) on
post-Great Recession slowdown in GDP growth rates, namely demand-side and supply-side
causes of the growth slowdown.
The first line is the original demand-side «secular stagnation» hypothesis reiterated by
Summers (2014), that focuses on the implications of zero interest rate constraint in developed
economies. Some authors like Paul Krugman (CEPR, 2014) and Hall (2011) find it to be a
variant of a liquidity trap.
Impaired credit transmission channel could be the cause of this phenomenon, as noted by
Lo and Rogoff (2015). If that is the case, Reinhardt and Rogoff (2009a) imply potential output-
unemployment-inflation relationship should be back to normal as financial sector recovers and
credit again starts to flow. In our paper we test this hypothesis from the potential output aspect,
contributing to the literature including Reinhardt and Rogoff (2009a) that mostly limits itself to
historical financial crises case studies. Impaired credit transmission channel hypothesis implies
that the shift in dynamics of potential output should fall in «temporary change» category rather
then «level shift» category (in terms of Chen and Liu (1993) outlier test here). Furceri and
Mourogane (2012) find that financial crises have a permanent effect on potential GDP, but not
on the growth rates.
Another method to model impaired credit transmission channel is offered by Borio et al.
(2013). They assume potential output is materially affected by financial cycles and thus the latter
have to be taken into account in potential output estimations. Using Borio’s «finance-neutral»
potential output, we test whether the break in potential output-unemployment-inflation
relationship disappears once we isolate financial cycles impact.
The second line is the supply-side restrictions debate that include argument on long-term
stability of relationship between GDP, unemployment and inflation.
Stock and Watson (2012) argue that the Great Recession is fully explained by the
information contained in the historical macroeconomic relationships with an exception of
negative expected interest rates, which amounts to impaired credit transmission channel
hypothesis. Lazear and Spletzer (2012) assert that no significant cross-industry labour mismatch
remains, thus the problem of high unemployment is mostly cyclical and GDP-unemployment
relationship (Okun’s Law) holds. We test those findings directly in our paper with respect to
potential output-unemployment-inflation relationships.
There is a vast body of evidence on productivity growth slowdowns during the post-Great
Recession period, starting with the US economy, documented among others by Fernald (2012),
Gordon (2012, 2014). Those are mainly explained by the lack of innovation, with IT boom
productivity acceleration of the last 20 years slowly receding. However, the macroeconomic and
policy effects of that slowdown have long been on the periphery of the research. Gordon (2014)
is among the first who posed the «conundrum» for new potential GDP forecast implying
significant supply-side (labour market) restrictions. However, he uses growth accounting
techniques and assumes relationship between potential output and unemployment to be the same
over the previous 60 years. In our paper we test whether there is a break in the relationship
between potential output, unemployment and inflation on a smaller sample, and test if the break
persists after correcting for impaired transmission channel effects.
If the recent productivity slowdown pointed at by Fernald (2012), Gordon (2014) and
others has significantly affected supply-side performance (namely, potential output), the break in
output-production factors relationship should be resilient to the impaired credit transmission
channel impact. Moreover, structural break dates should roughly correspond to the productivity
slowdowns indicated and not to the financial crisis.
2.2 Structural breaks in GDP data
Macroeconomic modelling of growth shifts is usually done with regime-switching
models after Hamilton (1989) more often associated with business cycle fluctuations. Detecting
structural breaks in economic growth is not a widespread procedure, although the method is
widely used for developing economies (e.g. Kar et al. (2013)). Papell and Prodan (2012) propose
an approach to growth regime changes using structural break analysis. They develop a two-break
detection procedure for detecting both entrance and exit to the contraction in the same test based
on Bai (1999). In contrast to our paper, they ignore dynamics of other important variables
including unemployment and financial variables. Also, they search for consecutive pairs of
breaks instead of a single break while considering only GDP and not the potential output.
In recent years there emerged a vast body of literature on whether the Great Recession
interrupted the Great Moderation (a decrease in growth volatility since 80-s). However, most
research on this topic tests for the breaks in mean GDP growth rate along with its volatility. For
instance, Gadea et al. (2013) dismiss the possibility of any structural breaks in mean GDP
growth in 2008-2009 by visual analysis of the series for 1878-2012 US GDP growth. On the
contrary, Charles et al. (2014) used data for 1970-2011 to find breaks in GDP growth associated
with Great Recession for 10 OECD countries including the US, Japan and euro area economies.
The break type they detected using Chen-Liu test is «temporary change» rather than «level
shift», which indicates those breaks are transitory rather than permanent. Our results are closer to
Charles et al. (2014), though we test potential output rather than actual data, and we find the
breaks around the Great Recession date with both Chen-Liu test and Bai-Perron test.
3. Statistical methods to estimate potential GDP
Potential GDP is perceived as some long-term GDP trend3 that differs from actual GDP
by the output gap. The latter usually perceived to be the cyclical component of GDP growth:
potentialGDP GDP Output gap Equation 1
3.1 Methods overview
There is a barrage of methods and model specifications (most of them production
function or filter-based) to estimate potential GDP, extensively covered in a number of sources,
including Andrle (2013), Gerlach (2011) and Johnson (2013). Here we provide a short coverage.
Methods to estimate potential GDP can be divided into three groups:
structural – usually production function-based (Cobb, Douglas, 1928; Artus, 1977;
De Masi, 1997);
univariate nonstructural – series smoothing, including filtering:
• Hodrick, Prescott (1997);
• Baxter, King (1999);
3 The actual definitions could differ, but, as Borio (2013) sums up, «A common thread tying together the various
concepts of potential output is that of sustainability: potential output is seen as representing a level of output that is
sustainable given the underlying structure of the economy». As noted above, Lazear and Spletzer (2012) also give
an extensive discussion to the differing concepts of potential GDP.
• Kalman (1960);
multivariate nonstructural – allow for structural restrictions in smoothing, but do not
necessarily require production factors data which are scarce and unreliable for
developing economies (Hamilton, 1995; Laxton, Tetlow, 1992; Kuttner, 1994).
Production Function (PF) is usually log Cobb-Douglas with constant returns to scale.
Potential output is based on least-squares-calibration, actual capital stock series and smoothed
(usually HP-filtered) labour stock series (or vice versa).
HP-filtering is smoothing for actual series of output to this rule:
12 2
1
1 2
,T T
t t t t
t t
L y y y y Equation 2
where ty – actual output, ty – smoothed series (aka potential output), – smoothing degree,
for yearly data 100 .
Band-pass (BP) filtering is treating cyclical component (aka output gap) as a high-
frequency component.
Univariate Kalman filter is decomposing actual data into two series:
,p
t t ty y z
1 1,p p
t t ty y
1 ,t t t
1 1 2 2 ,t t t tz z z
Equation 3
where p
ty is potential output (trend), tz is a cyclical component (output gap), t and t are
white noise.
Multivariate Kalman filter allows for additional relationships on top of GDP. For Okun’s
law this works by adding labour market indicators.
,t t tur nairu g
1 ,t t tnairu nairu
1 1 2 1 2 2 ,t t t t tg g z z
Equation 4
where tur is unemployment rate, tnairu is NAIRU, tg is a cyclical component of
unemployment, ,t ,t ,t ,t and t are white noise.
3.2 The choice of methods and specifications
We use HP filter and multivariate Kalman filter methods to estimate potential output.
Along with the output trend equation, for each specification we include the following additional
structural relationships:
inflation dynamics to account for possible Lucas-Friedman AS (or Phillips curve)
relationship (a bivariate filter notated GDP+CPI);
unemployment/labour force particiration rate, akin to Okun’s law relationship. Along
with inflation dynamics this forms trivariate filters notated GDP+CPI+UR and
GDP+CPI+LFRP, respectively;
versions of the above filters with private credit ratio in the output gap equation, to
include financial cycles and credit transmission channel impairment after Borio et al
(2013).
Filtering procedure (identification requirement) does not allow for too many structural
relationships given a sample of 13-17 observations for each economy.
We do not use PF estimators in our paper. For China production function approach was
unavailable due to the lack of internationally comparable data on capital and labour, while for
other countries our estimates for production function were unstable. Thus, we concentrate more
on the variety of multivariate filter estimates.
Our yearly frequency dataset includes GDP, inflation, unemployment rate, labour force
participation rate and the private credit to GDP ratio for the US, euro area, Japan and China,
collected conditional on data availability. The sample covers 1986-2014 for US, 1998-2013 for
euro area, 1991-2013 for Japan and 1991-2014 for China. We estimate potential output for
overlapping samples starting at full sample available and then omitting the beginning years one
by one. This is expected to give us a better understanding of stability of our results.
We choose specifications as follows4. First, we add inflation to univariate filter for
bivariate Kalman filter with Phillips curve-type relationship. Then, to account for labour market
dynamics, we estimate two versions of the multivariate Kalman filter using inflation together
unemployment rate and labour force participation ratio.
In his series of papers, Borio et al (2013) points at the importance of accounting for
financial cycles when estimating potential GDP. This approach seems consistent with our idea to
estimate potential GDP while isolating impaired credit transmission channel. Borio et al (2013)
test the impact of three financial variables on potential GDP, namely real interest rate, private
credit ratio and house prices and finds that real interest rate has negligible impact for potential
GDP while both private credit ratio and house prices matter.
4 The exact specified systems are listed in Appendix.
We build on that foundation to include private credit ratio as a proxy for the impaired
credit transmission channel on potential GDP. Unfortunately, because of degrees of freedom
constraints we can only use first lag of dependent variable (potential output) together with
independent factors, thus for this version of Kalman filter we use only a first autoregressive lag
for the output gap equation.
We use GLS estimates on HP-filtered data as our starting values for Kalman filter. For all
the estimates we used a code for Eviews 8 statistical package.
The variety of methods we use is typical for the literature, as both Cotis et al. (2004) and
Andrle (2013) stress there is no single formal criterion or test to choose between potential GDP
estimators, although Cotis et al. propose «consistency with priors» and the «difference between
real-time and final estimates» comparison criteria. In this paper we are interested in testing
whether our results are robust to the choice of the method, sample and specification. We list the
results for all methods, samples and specifications we tested in the Appendix 3 and compare
them in Section 4.
We do not use procedures integrating different estimators like the methodology of «thick
modelling» proposed by Granger and Leon (2004), as the forecasting exercises are not the
primary focus of our paper. However, we employ Cotis et. al (2004) logic of preference of
economic intuition over statistical procedures when choosing our filter specifications.
4. Potential GDP estimates
In this section we present the estimates for potential GDP and the output gap in the
largest economies (US, euro area, Japan and China).
For comparison purposes we list the dynamics of potential output estimator +CPI+LFPR
along with dynamics of capacity utilization and IMF potential output estimates for respective
economies (unavailable for China). Selected method-wise, specification-wise and sample-wise
results for potential output estimation are listed in Appendix 3. We plan to elaborate on
comparing properties of different potential output and output gap estimates and forecasting these
indicators in a separate paper.
We provide estimates for potential output and output gap based on current-vintage data in
figures 1-7.
The dynamics of capacity utilization closely correlate with output gap estimates: for the
US, the value of correlation coefficient is 0.76, for euro area – 0.82, for Japan – 0.92. In fig. 9-14
we compare obtained estimates to potential GDP dynamics inferred from IMF WEO October
2014. It follows that our estimates of potential output growth are highly correlated with IMF for
the US (0.85), for euro area (0.81) and somewhat worse for Japan (0.53).
Figures 8-13 also contain estimates of output gap calculated by IMF (except for China).
Our estimates of output gap are larger than the IMF estimates for US, euro area and lower for
Japan.
Equation 3 defines the output gap as a stationary autoregressive process of either the first
or the second order. Thus the filtering structure implies the economy converges to the steady
state as the output gap closes. This is a common assumption in the absence of external shocks.
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GDP (actual), % GDP (potential), % Output gap, % GDP (right scale)
Figure 1-2 – Kalman filter results (+CPI+LFPR) for US and euro area
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85
90
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Kalman filter (CPI+LFPR) IMF Capacity utilization (right scale), %
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Kalman filter (CPI+LFPR) IMF Capacity utilization (right scale), %
Figure 3-4 – Output gap measures for US and euro area
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GDP (actual), % GDP (potential), % Output gap, % GDP (right scale)
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GDP (actual), % GDP (potential), % Output gap, % GDP (right scale)
Figure 5-6 – Kalman filter results (+CPI+LF) for Japan and China
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100
110
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Kalman filter (CPI+LFPR) IMF Capacity utilization (right scale), %
Figure 7 – Output gap measures for Japan
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Figure 8-9 – IMF results for US and euro area
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GDP (actual), % IMF, GDP (potential), % GDP (potential), %
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Figure 10-11 – Potential GDP measures for US and euro area
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GDP (actual), % IMF, GDP (potential), % IMF, output gap, % GDP (right scale)
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GDP (actual), % IMF, GDP (potential), % GDP (potential), %
Figure 12-13 – IMF results and potential GDP measures for Japan
The analysis leads us to conclude that the most of the output gaps created in 2008-2009
were closed through world economy slowdown in 2011-2014. The remaining part of the negative
output gaps smaller for the US and Japan, and significantly larger for euro area.
For the most of the pre-crisis decade, there has been a decline in a potential output growth
rate in all considered economies, most pronouncedly in China (which probably corresponds to
advancement to the next development stage).
Table 1 displays average annual growth rates of actual and potential GDP for pre-crisis
and post-crisis periods. Our estimates for US, euro area, Japan and China show the potential
GDP slowed considerably post-crisis in line with actual GDP.
Table 1 – Actual vs Potential GDP growth, % and output gap, % potential GDP5
Region
2000-2007 2010-2013
Potential
output
Actual
GDP
Output
gap
Potential
output
Actual
GDP
Output
gap
US 3.1 2.7 -0.7 1.2 2.0 -3.2
Euro
area 1.6 2.2 1.5 -0.3 0.2 -1.4
Japan 1.0 1.5 -1.1 0.3 0.8 -2.6
China6 9.6 10.5 -3.9 8.8 8.2 -1.4
While we witnessed a sharp slowdown both in actual and in potential output, it is unclear
whether this change is permanent or transitory. To distinguish between temporary corrections
and permanent trend growth changes, we perform tests for structural breaks in the series.
5. Testing for structural breaks
In this section we perform several structural break tests on potential output growth rate
estimates discussed in the previous section. The concept of the Secular Stagnation implies lower
growth rates, so we do not test estimates of potential output level.
The logic of the New Normal or Secular Stagnation implies that post-crisis slowdown is
not explained by macroeconomic relationships between potential output, employment and
inflation. The concept of a structural break in the series implies a change in the properties of the
data-generating process, possibly induced by the change in relationships underlying it. Thus, one
should expect to detect a structural break in potential output series, estimated while taking into
account those relationships.
Beyond testing for the break, we aim at sorting out its nature. As discussed earlier (see
section 2), literature on Secular Stagnation places special emphasis on credit transmission
channel impairment. The «broken transmission channel» literature points out that the main cause
5 Here we use «finance-neutral» multivariate Kalman filter potential GDP estimates +CPI+ LFPR for the longest
sample used. 6 Estimates for China using the sample 1991-2013 might be inappropriate because of huge transformation of the
economy. While using only latest 15 years of data one can see potential output falling from 12% to 6%.
of the Great Recession (and, probably, Secular Stagnation) is the damage done to the financial
system. Consequently, faster growth will be back as the financial system repairs itself. If this is
true, we expect to see a «temporary change» outlier (break) in the growth data. For example,
Charles et. al (2014) find a temporary change outlier (break) in mean for 2009 but no evidence of
a level shift in GDP growth rates for ten advanced countries. Conversely, Gadea et al. (2014)
using Bai-Perron test report no evidence of structural break in the mean US GDP growth rate on
a sample of 1878-2012.
It is important to bear in mind three important issues related to the structural break tests.
First, there are front end sample restrictions: minimum three data points required for a
regression. This currently does not allow us to parsimoniously test for structural breaks that
might have occurred after 2011. Second, break dates determination is problematic. Third, tests
need to be able to distinguish transitory breaks (which are in place if we heed the transmission
channel damage literature) from permanent ones (which are consistent with the New Normal
hypothesis).
We can address second problem by applying Bai and Perron (2003) test, which offers
automatic break selection procedure that requires just the maximum number of breaks. We can
address the third problem using Chen and Liu (1993) break detection procedure that allows for
distinction in the type of breaks, including level shifts and transitory changes. Absence of a
sound statistical remedy for the first problem (other than going to quarterly level and having to
deal with seasonality) is partly compensated by the absence of anecdotal evidence of significant
structural shifts (on a scale of a global crisis) in the world economy apart from the Great
Recession.
We provide Bai-Perron test results for selected samples in Table 2. Procedure clearly
detects a break in the potential GDP growth series, with exact timing ranging from 2007 to 2012
dependent on the region, sample and version of the test. Recent break dates, though, are mostly
clustered in 2009 and 2011.
Results are quite robust across different filters, samples and specifications. We can infer
from the data that there was a notable breakdown in fundamental macroeconomic relationships
in all major economies in 2009-2010, during the global crisis and the Great Recession. In Table
2 a structural break between pre- and post-crisis dynamics is evident. This supports analogous
findings of Huang and Luo (2014) for the US and contrast findings of Stock and Watson (2012),
who assume the underlying relationships are stable.
Table 2 – Bai-Perron test results for potential GDP7
HP gap=AR(2) gap=AR(1) +CPI +CPI+UR +CPI+LFPR
gap=AR(1)+dCR_Y
+CPI+LFPR, gap=AR(1)
+dCR_Y
+CPI+UR, gap=AR(1)
+dCR_Y
+CPI, gap=AR(1)
+dCR_Y
+CPI, gap=AR(1)
+CPI+UR, gap=AR(1)
+CPI+LFPR, gap=AR(1)
US (1998-2014)
1991-2014 2003, 2007 2007, 2011 2002, 2009 2002, 2009 2002, 2009 2002, 2009 2002, 2008 2004, 2009 -
2003, 2008 - 2002, 2009 2002, 2009
1996-2014 2002, 2006 2002, 2009 2007, 2011 2002, 2009 2002, 2009 2005, 2009 - 2005, 2009 -
2002, 2009 2002, 2009 2002, 2009 2004, 2009
1997-2014 2002, 2006 2002, 2009 2007, 2011 2002, 2009 2002, 2009 2002, 2009 - 2005, 2009 -
2002, 2009 2002, 2009 2002, 2009 2004, 2009
Euro area (2000-2013)
1998-2013 2004, 2008 2007, 2010 2010 2005, 2009 2003, 2010 2003, 2009 2009 2004, 2011 -
2005, 2009 2005, 2009 2004, 2011 2003, 2011
2001-2013 2006, 2009 2010 2010 2005, 2009 2007, 2010 - - 2005, 2010 -
2005, 2009 2005, 2009 2011 2005, 2011
Japan (2000-2013)
1991-2013 2005, 2008 - - 2006, 2009 2005, 2009 2006, 2009 - 2006, 2009 -
2006, 2009 2006, 2009 2005, 2009 2006, 2009
1996-2013 2005, 2008 - - 2005, 2009 2005, 2009 2005, 2009 - 2005, 2009 -
2005, 2009 2005, 2009 2005, 2009 2005, 2009
2000-2013 2005, 2008 - - 2004, 2009 2005, 2009 - 2010 2004, 2009 -
2004, 2009 2004, 2009 2004, 2009 2004, 2009
China (2001-2014)
1991-2013 2009, 2012 - - - - 2006 - - -
- - - -
1996-2013 2009, 2012 - - 2004, 2011 2005 - 2006, 2009 - -
- - - 2007, 2012
2001-2013 2004, 2009 2005, 2009 2006, 2009 2005, 2008 2005, 2008 2005, 2012 2006, 2009 2005, 2008 -
2005, 2008 2005, 2008 2005, 2008 2005, 2008
7 Filter specification abbreviations are listed in Appendix 2.
Another important finding is that using «finance-neutral» versions of the estimates
(notated +dCR_Y) does not seem to change the break instance and break date much. The
structural break date and instance persist even after we account for the financial cycle. This can
be interpreted in two ways. Firstly, the persistence of a break could indicate that the impact of
financial crisis on potential output growth extends far beyond the flow of credit, which contrasts
Reinhardt and Rogoff’s hypothesis. Or, secondly, the persistence of the break could indicate
there are other strong factors affecting potential output even after we account for credit ratio
dynamics, such as supply restrictions like productivity slowdown pointed at by Fernald (2014)
and Gordon (2014).
There is another way to test for structural breaks that accounts for the nature of the break,
namely distinguishes between permanent (level shift) and transitory (i.e. temporary change)
breaks. Charles et al (2014) approached this question with a Chen and Liu (1993) test realized in
the «tsoutliers» package of R. We follow suit with a distinction between additive-outlier, level-
shift and temporary-change types of breaks, and test whether some (or all) of them are the case
for the break dates selected by Bai-Perron test.
Two hypotheses for the cause of the Secular Stagnation we surveyed before are not
mutually exclusive: indeed, both demand-side and supply side factors might be at work. In terms
of Chen and Liu (1993) test, impaired credit transmission channel hypothesis of Reinhardt and
Rogoff implies a temporary change outlier: a significant but transitory reduction in GDP growth
rates. Permanent supply-side changes hypothesis advocated by Robert Gordon, on the other
hand, should be supported by a level shift outlier (a permanent reduction in potential output
growth rate) in the results of the test.
Appendix 5 contains resume of results for Chen and Liu (1993) test. As the size of full
results for all samples makes them inconvenient to display, we list results for all filters, but limit
ourselves to several relevant samples in including the longest used.
Results of the Chen and Liu test do not appear very stable with respect to method,
specification and sample, unlike Bai-Perron test results. Especially stark differences are observed
between the countries results. Test results change once credit dynamics are accounted for. Some
results, however, are stable over sample and filter choice.
Overall, Chen-Liu test results support supply-side slowdown hypothesis for Japan and
euro area, but not for the US. For the US just a handful of samples detect level shift breaks, but
they are never at the years preceding the crisis8. It looks quite different for the euro area and
Japan, where level shift breaks in potential output growth rate for 2009 are detected quite often.
8 The only level-shift break detected in the US during pre-crisis years, namely in 2006, is for specification with
inflation, LFPR and credit dynamics estimated on a sample of 1997-2013.
It is worth noting, though, that all level-shift breaks for euro area were detected for multivariate
estimates accounting for labour market dynamics, while for Japan level-shift breaks are present
for all multivariate estimates (and absent for univariate ones). For China, it is quite hard to form
a coherent picture. Estimates accounting for labour market factors alone have level shift breaks
in 2005, 2008 and 2009, and estimates accounting for credit dynamics alone have level shift
breaks in 2009. However, if credit dynamics and labour market factors are taken into account
simultaneously, all outliers disappear.
Based on Chen-Liu test we conclude that the changes in potential output growth rates in
some instances did not occur and in other instances were permanent rather than temporary. This,
as well as the absence of contrast between results for estimators and their «finance-neutral»
versions, resembles the results of Bai-Perron test.
Chen-Liu test detects plenty of temporary change breaks in potential output growth rates
in 2009 and 2010 in euro area for estimates that account for inflation (alone and with credit
dynamics), and for inflation and unemployment rate in case of the US. However, these breaks
disappear once we factor in labour market indicators (unemployment rate or, in case of the US,
LFPR). For Japan, the temporary change breaks in 2009-2010 are present only for univariate
estimates and for multivariate estimates that account for labour force participation rate. For
China, temporary change breaks (in 2009 and 2010) are detected only for univariate filters.
These findings are quite similar to the insights Bai-Perron test results offer, and contradict
impaired credit transmission channel hypothesis, as potential output growth does not appear to
heal itself as financial system would. We can again conclude that either the impaired credit
transmission channel hypothesis should imply a permanent reduction in potential output growth
rates, or there are other factors at work besides credit-driven factors, like supply-side factors.
6. Conclusions and discussion
In this paper we try to infer whether there is a structural slowdown of the major
economies in the post-crisis period. We find structural breaks in estimated potential output
growth rates between 2007 and 2010. The results are robust to the choice of the sample, method,
specification and they hold for all countries surveyed. This indicates that Secular Stagnation
materially and negatively affected potential output growth rate of all major economies.
Further examination leads us to conclude this reduction might be permanent rather than
transitory. Presence of pre-crisis negative level shifts for euro area and Japan gives some
evidence in favour of the productivity slowdown affecting the macroeconomic relationships.
We provide two arguments why impaired credit transmission channel factors likely play a
secondary role in potential output growth slowdown. Firstly, breaks are present whether we
account for private credit dynamics or not. Secondly, most changes detected in potential output
growth are classified as permanent rather than transitory, which contradicts the expectation that
financial sector heals itself and returns to normal. Same results hold for the «finance-neutral»
version of the estimates.
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Appendix 1. Testing for structural breaks in the series
Testing for structural breaks can be done in several ways:
1) exact dates of probable structural breaks are known; researches test did they happen
or not in each point (for example, Chow, 1960);
2) the maximum number of structural breaks is only known; researches find exact
dates, but there is still the possibility of no structural breaks in the series (Bai, Perron, 2003);
3) there is no information about dates and number of structural breaks in the series
(Chen, Liu, 1993, Gómez, Maravall, 1997).
Bai and Perron test
In this paper the second way is presented by Bai and Perron (2003) test. It is assumed that
the series have the maximum possible number of breaks. The test is based on the multiple linear
regression with m breaks including parameters which are constant in each 1m regimes:
1, 1,..., , 1,..., 1,t t t j t j jy x z u t T T j m Equation 5
where ty is the dependent variable at time t , ( 1)tx p and ( 1)tz q are vectors of
independent variables at time t , and ( 1,..., 1)j j m are corresponding vectors of
parameters, tu is the disturbance at time t . It is also assumed that there is no break in variance.
Equation 5 is estimated for each m-partition using least-squares method:
1 1
1 122
1, ,1 1 1 1
,..., .min mini i
j ji i
T Tm m
T m t t t t j
i t T i t T
S T T u y x z Equation 6
Derived estimates of coefficients are substituted in the objective function 1,...,T mS T T
which depends only on break points. Then this function is minimized over all partitions
1,..., mT T . Thus final dates of structural breaks are global minimizers of the objective function:
11 ,..., 1ˆ ˆ,..., argmin ,..., .
mm T T T mT T S T T Equation 7
However when 2m this statistic becomes difficult to compute. Therefore several
alternative methods exist to determine optimum estimates of break points. All calculations have
been made in Eviews8.
Chen and Liu test
In case of no information about dates and number of structural breaks in the series Chen
and Liu (1993) have offered test for outliers and determination their types. There are three main
types of outliers: additive outlier (AO), level shift (LS) and temporary change (TC). It is
assumed that the testing series is composed of two parts:
( ), 1,..., .t ty z f t t n Equation 8
The first part tz is an ARMA process: 2( ) ( ) , (0, ),t t t aL z L a a N where L is lag
operator. The second part ( )f t contains structural breaks. However in practice estimation ty as
ARMA model gives not pure white noise ta but noise combined with structural breaks effects:
2
1 2ˆ ( ) , ( ) ( ) ( ) / ( ) 1 ...t ta L z L L L L L L Equation 9
This equation can be written in another way for each type of breaks:
(AO) ˆ ( ) ( ),t t AO ta a L I
(LS) ˆ ( ) / (1 ) ( ),t t LS ta a L L I
(TC) ˆ ( ) / (1 ) ( ).t t TC ta a L L I
Commonly the parameter equals 0.7. In the simplest form these regressions are as
follows:
,ˆ , , , ,t i i t ta x a i AO LS TC Equation 10
where for all i :
, 0i tx for t ,
, 1i tx for t ,
for t and 1k (with 1,...,k T ) ,AO t k kx (AO),
, 1
1k
LS t k jjx (LS),
1
, 1
kk k j
TC t k j kjx (TC).
The next general t-statistics (with ( 1)t n distribution) for an OLS-estimate of the
parameter i is used for detection outliers:
1/2
2
,ˆˆ ˆ( ) ( ) / / , , , ,
n
i i a i t
t
x i AO LS TC Equation 11
where ˆa is an estimate of the standard deviation of white noise ta from Equation 10.
These statistics are calculated for each type of break and for each probable date of break.
Then the largest absolute value of a statistic over all types of breaks is chosen to define the most
probable type of break at each point. If the value of a corresponding statistic at time t is higher
than the critical value, the test indicates the presence of a structural break of a given type at time
t .
Appendix 2. Kalman filter specifications
1. Univariate Kalman filter with AR(1) part (gap=AR(1)):
,p
t t ty y z
1 1,p p
t t ty y
1 ,t t t
1 1 ,t t tz z
where p
ty is potential output (trend), tz is a cyclical component (output gap), t and t are
white noise.
2. Univariate Kalman filter with AR(2) part (gap=AR(2):
,p
t t ty y z
1 1,p p
t t ty y
1 ,t t t
1 1 2 2 ,t t t tz z z
where p
ty is potential output (trend), tz is a cyclical component (output gap), t and t are
white noise.
3. Univariate Kalman filter with AR(1) part and private credit to GDP (gap=AR(1)+dCR):
,p
t t ty y z
1 1,p p
t t ty y
1 ,t t t
1 1 ,t t t tz z cr
where p
ty is potential output (trend), tz is a cyclical component (output gap), tcr is change of
private credit to GDP, t and t are white noise.
4. Bivariate Kalman filter with AR(1) part and Phillips curve-type relationship (+CPI,
gap=AR(1)):
,p
t t ty y z
1 1,p p
t t ty y
1 ,t t t
1 1 ,t t tz z
0 1 1 2 ,t t t tcpi cpi z
where p
ty is potential output (trend), tz is a cyclical component (output gap), tcpi is CPI, ,t
,t and t are white noise.
5. Bivariate Kalman filter with AR(2) part and Phillips curve-type relationship (+CPI,
gap=AR(2)):
,p
t t ty y z
1 1,p p
t t ty y
1 ,t t t
1 1 2 2 ,t t t tz z z
0 1 1 2 ,t t t tcpi cpi z
where p
ty is potential output (trend), tz is a cyclical component (output gap), tcpi is CPI, ,t
,t and t are white noise.
6. Bivariate Kalman filter with AR(1) part, private credit to GDP, and Phillips curve-type
relationship (+CPI, gap=AR(1)+dCR):
,p
t t ty y z
1 1,p p
t t ty y
1 ,t t t
1 1 ,t t t tz z cr
0 1 1 2 ,t t t tcpi cpi z
where p
ty is potential output (trend), tz is a cyclical component (output gap), tcr is change of
private credit to GDP, tcpi is CPI, ,t ,t and t are white noise.
7. Trivariate Kalman filter with AR(1) part, Phillips curve-type and Okun’s law
(unemployment rate) relationships (+CPI+UR, gap=AR(1)):
,p
t t ty y z
1 1,p p
t t ty y
1 ,t t t
1 1 ,t t tz z
0 1 1 2 ,t t t tcpi cpi z
,t t tur nairu g
1 ,t t tnairu nairu
1 1 2 1 ,t t t tg g z
where p
ty is potential output (trend), tz is a cyclical component (output gap), tcpi is CPI, tur is
unemployment rate, tnairu is NAIRU, tg is a cyclical component of unemployment, ,t ,t
,t ,t and t are white noise.
8. Trivariate Kalman filter with AR(2) part, Phillips curve-type and Okun’s law
(unemployment rate) relationships (+CPI+UR, gap=AR(2)):
,p
t t ty y z
1 1,p p
t t ty y
1 ,t t t
1 1 2 2 ,t t t tz z z
0 1 1 2 ,t t t tcpi cpi z
,t t tur nairu g
1 ,t t tnairu nairu
1 1 2 1 2 2 ,t t t t tg g z z
where p
ty is potential output (trend), tz is a cyclical component (output gap), tcpi is CPI, tur is
unemployment rate, tnairu is NAIRU, tg is a cyclical component of unemployment, ,t ,t
,t ,t and t are white noise.
9. Trivariate Kalman filter with AR(1) part, private credit to GDP, Phillips curve-type and
Okun’s law (unemployment rate) relationships (ss08):
,p
t t ty y z
1 1,p p
t t ty y
1 ,t t t
1 1 ,t t t tz z cr
0 1 1 2 ,t t t tcpi cpi z
,t t tur nairu g
1 ,t t tnairu nairu
1 1 2 1 ,t t t t tg g z cr
where p
ty is potential output (trend), tz is a cyclical component (output gap), tcr is change of
private credit to GDP, tcpi is CPI, tur is unemployment rate, tnairu is NAIRU, tg is a cyclical
component of unemployment, ,t ,t ,t ,t and t are white noise.
10. Trivariate Kalman filter with AR(1) part, Phillips curve-type and Okun’s law (labour
force participation rate) relationships (+CPI+LFPR, gap=AR(1)):
,p
t t ty y z
1 1,p p
t t ty y
1 ,t t t
1 1 ,t t tz z
0 1 1 2 ,t t t tcpi cpi z
,p
t t tlfpr lfpr g
1 ,p p
t t tlfpr lfpr
1 1 2 1 ,t t t tg g z
where p
ty is potential output (trend), tz is a cyclical component (output gap), tcpi is CPI, tlfpr
is labour force participation rate, p
tlfpr is trend of labour force, tg is a cyclical component of
labour force, ,t ,t ,t ,t and t are white noise.
11. Trivariate Kalman filter with AR(2) part, Phillips curve-type and Okun’s law (labour
force participation rate) relationships (+CPI+LFPR, gap=AR(2)):
,p
t t ty y z
1 1,p p
t t ty y
1 ,t t t
1 1 2 2 ,t t t tz z z
0 1 1 2 ,t t t tcpi cpi z
,p
t t tlfpr lfpr g
1 ,p p
t t tlfpr lfpr
1 1 2 1 2 2 ,t t t t tg g z z
where p
ty is potential output (trend), tz is a cyclical component (output gap), tcpi is CPI, tlfpr
is labour force participation rate, p
tlfpr is trend of labour force, tg is a cyclical component of
labour force, ,t ,t ,t ,t and t are white noise.
12. Trivariate Kalman filter with AR(1) part, private credit to GDP, Phillips curve-type and
Okun’s law (labour force participation rate) relationships (+CPI+LFPR,
gap=AR(1)+dCR):
,p
t t ty y z
1 1,p p
t t ty y
1 ,t t t
1 1 ,t t t tz z cr
0 1 1 2 ,t t t tcpi cpi z
,p
t t tlfpr lfpr g
1 ,p p
t t tlfpr lfpr
1 1 2 1 ,t t t t tg g z cr
where p
ty is potential output (trend), tz is a cyclical component (output gap), tcr is change of
private credit to GDP, tcpi is CPI, tlfpr is labour force participation rate, p
tlfpr is trend of
labour force, tg is a cyclical component of labour force, ,t ,t ,t ,t and t are white
noise.
Appendix 3. Potential output and output gap estimates
40
45
50
55
60
65
70
75
80
85
90
-8
-6
-4
-2
0
2
4
6
HP-filter Kalman filterKalman filter (CPI) Kalman filter (CPI+UR)Kalman filter (CPI+LFPR) IMFCapacity utilization (right scale), %
Chart 3-1 Output gap estimates (% potential output), capacity utilization and IMF output
gap measure for the US (sample 1997-2014)
40
45
50
55
60
65
70
75
80
85
90
-7
-5
-3
-1
1
3
5
HP-filter Kalman filterKalman filter (CPI) Kalman filter (CPI+UR)Kalman filter (CPI+LFPR) IMFCapacity utilization (right scale), %
Chart 3-1 Output gap estimates (% potential output), capacity utilization and IMF output
gap measure for the euro area (sample 1999-2013)
0
20
40
60
80
100
120
-8
-6
-4
-2
0
2
4
6
HP-filter Kalman filterKalman filter (CPI) Kalman filter (CPI+UR)Kalman filter (CPI+LFPR) IMFCapacity utilization (right scale), %
Chart 3-3 Output gap estimates (% potential output), capacity utilization and IMF output
gap measure for Japan (sample 1999-2013)
-10
-5
0
5
10
15
20
25
30
35
40
45
HP-filter Kalman filter Kalman filter (CPI)
Kalman filter (CPI+UR) Kalman filter (CPI+LFPR)
Chart 3-4 Output gap estimates (% potential output), capacity utilization and IMF output
gap measure for China (sample 2001-2014)
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
1988-2013 1989-2013 1990-2013 1991-2013 1992-2013
1993-2013 1994-2013 1995-2013 1996-2013 1997-2013
Chart 3-5 Output gap estimates (+CPI+LFPR, gap=AR(1)+dCR) for the US (all
samples), % potential output
-7
-5
-3
-1
1
3
5
1998-2013 1999-2013 2000-2013 2001-2013
Chart 3-6 Output gap estimates (+CPI+LFPR, gap=AR(1)+dCR) for the euro area (all
samples), % potential output
-10
-8
-6
-4
-2
0
2
4
1991-2013 1992-2013 1993-2013 1994-2013 1995-2013
1996-2013 1997-2013 1998-2013 1999-2013 2000-2013
Chart 3-7 Output gap estimates (+CPI+LFPR, gap=AR(1)+dCR) for Japan (all samples),
% potential output
-10
-8
-6
-4
-2
0
2
4
6
8
1991-2013 1992-2013 1993-2013 1994-2013 1995-2013
1996-2013 1997-2013 1998-2013 1999-2013 2000-2013
Chart 3-8 Output gap estimates (+CPI+LFPR, gap=AR(1)+dCR) for China (all samples),
% potential output
Appendix 4. Results of Chen-Liu test9
Table 5-1 Chen-Liu test results for the US
year type coef tstat year type coef tstat year type coef tstat year type coef tstat year type coef tstat
2009 TC -2.29 -3.28 2008 TC -1.36 -2.81
2010 AO -3.26 -5.49 2009 TC -2.10 -4.27
2011 LS 3.114 4.59 2010 AO -2.75 -5.46
2009 TC -2.59 -3.13 2008 TC -1.62 -2.63 2011 TC 6.46 3.52 2009 TC -2.58 -2.79 2009 AO -2.22 -2.58
2010 AO -4.02 -5.84 2009 TC -2.80 -4.50
2011 LS 4.01 5.11 2010 AO -3.67 -5.81
2009 TC -2.58 -3.29 2008 TC -1.57 -2.70 2009 TC -2.60 -3.86 2009 AO -2.29 -2.66
2010 AO -3.84 -5.83 2009 TC -2.74 -4.68
2011 LS 3.71 4.95 2010 AO -3.58 -6.03
year type coef tstat year type coef tstat year type coef tstat year type coef tstat year type coef tstat
2009 TC -1.93 -2.50 2009 AO -1.50 -3.31 2009 AO -1.79 -2.62
2011 AO 1.75 2.33 2010 AO 1.19 2.63 2010 AO 1.50 2.21
2009 TC -1.95 -3.29 2009 TC -1.53 -2.72 2009 AO -1.62 -5.61 2009 AO -1.14 -2.30 2010 AO 1.261 2.84
2011 AO 1.55 2.97 2010 AO 1.47 5.10 2011 AO 1.64 3.30 2011 TC -1.00 -2.16
2011 TC -1.14 -2.94
2009 TC -1.99 -4.38 2009 TC -1.63 -3.14 2009 AO -1.18 -2.71 2008 AO 0.841 2.546 2006 LS -0.53 -2.89
2011 AO 1.381 2.843 2010 AO 1.435 3.279 2009 AO -1.21 -3.67 2007 AO -0.57 -3.25
2011 TC -1.49 -3.08 2010 TC 0.98 2.24 2008 AO 0.68 3.88
2009 AO -0.61 -3.45
*Kalman filter (+CPI, gap=AR(2)) has no outliers.
gap=AR(1) gap=AR(2) gap=AR(1)+dCR +CPI, gap=AR(1) +CPI, gap=AR(1)+dCR
+CPI+UR, gap=AR(1) +CPI+UR, gap=AR(2) +CPI+LFPR, gap=AR(1) +CPI+LFPR, gap=AR(2) +CPI+LFPR, gap=AR(1)+dCR
Sample
Sample
1997-2014
1996-2014
1991-2014
1991-2014
1996-2014
1997-2014
9 Specification of the filters like «+CPI, gap=AR(1)» is provided in Appendix 3.
Table 5-2 Chen-Liu test results for the euro area
year type coef tstat year type coef tstat year type coef tstat year type coef tstat year type coef tstat year type coef tstat
2010 AO -3.95 -4.15 2010 AO -4.18 -2.56 2009 AO 1.51 2.84 2005 TC 3.50 4.63 2005 TC 3.18 3.70 2005 TC 3.53 4.80
2010 AO -2.80 -5.26 2007 TC 2.43 3.21 2007 TC 2.44 2.84 2007 TC 2.44 3.31
2008 AO 2.47 3.43 2008 AO 2.32 2.95 2008 AO 2.47 3.51
2009 TC -3.44 -4.54 2009 TC -3.38 -3.92 2009 TC -3.43 -4.65
2010 AO -3.76 -4.01 2010 AO -4.19 -2.89 2009 AO 1.43 2.75 2005 TC 3.65 3.12 2005 TC 3.23 3.60 2005 TC 3.64 3.13
2010 AO -2.48 -4.74 2007 AO 3.58 2.75 2007 TC 2.47 2.75 2007 AO 3.58 2.76
2009 TC -3.90 -3.32 2008 AO 2.40 2.78 2009 TC -3.90 -3.34
2009 TC -3.84 -4.28
2006 TC 1.03 2.23 2010 AO -2.91 -3.41 2009 AO 1.34 2.51 2005 TC 3.79 2.64 2005 TC 3.18 2.68 2005 TC 3.76 2.71
2007 TC 1.26 2.73 2010 AO -2.11 -3.92 2007 AO 3.60 2.17 2009 TC -3.30 -2.78 2007 AO 3.54 2.23
2008 AO 1.57 3.22 2009 AO -3.81 -2.30 2009 AO -3.84 -2.41
2009 TC -1.24 -2.66
2010 AO -3.26 -6.69
year type coef tstat year type coef tstat year type coef tstat year type coef tstat year type coef tstat
2009 LS -1.02 -2.40 2009 LS -1.21 -2.19
2011 AO 1.09 2.59
1999-2013 2009 AO -0.9 -3.4 2009 LS -0.9 -2.2 2008 AO 0.57 3.77611
2010 TC 1.27 3.78 2009 LS -0.97 -3.89
2010 AO -0.27 -2.24
1998-2013
2001-2013
Sample
Sample+CPI, gap=AR(1)+dCR
1998-2013
1999-2013
2001-2013
gap=AR(1) gap=AR(2) gap=AR(1)+dCR +CPI, gap=AR(1) +CPI, gap=AR(2)
+CPI+UR, gap=AR(2) +CPI+LFPR, gap=AR(1) +CPI+LFPR, gap=AR(2) +CPI+LFPR, gap=AR(1)+dCR+CPI+UR, gap=AR(1)
Table 5-3 Chen-Liu test results for Japan
Sample year type coef tstat year type coef tstat year type coef tstat year type coef tstat year type coef tstat year type coef tstat
2009 TC -1.22 -3.02 2009 TC -1.13 -2.90 2005 TC 0.83 3.08 2008 LS 0.46 2.30 2008 AO 0.84 3.67
2010 AO -2.73 -5.22 2010 AO -2.54 -4.99 2008 AO 1.16 3.67 2009 LS -0.80 -3.69
2009 TC -1.33 -4.83
2010 AO -2.79 -8.75
2009 TC -0.42 -2.23 2005 TC 0.32 2.65 2006 LS 0.38 2.72 2008 LS 0.38 2.25 2008 AO 0.94 3.88
2010 AO -1.02 -4.08 2008 AO 0.45 2.87 2008 LS 0.51 3.16 2009 LS -1.17 -3.75
2009 TC -0.44 -3.68
2010 AO -1.04 -6.61
2005 TC 0.70 3.27 2005 TC 0.68 3.26 2009 TC -0.94 -2.50 2010 AO -0.23 -2.42
2006 TC 0.55 2.57 2006 TC 0.54 2.58 2010 AO -2.04 -5.23
2008 AO 0.88 3.74 2008 AO 0.85 3.73
2009 TC -1.07 -4.86 2009 TC -1.03 -4.79
2010 AO -2.21 -9.37 2010 AO -2.13 -9.27
Sample year type coef tstat year type coef tstat year type coef tstat year type coef tstat year type coef tstat
2008 AO 0.76 2.14 2008 AO 0.83 3.29 2008 AO 0.87 3.54
2009 LS -0.88 -2.70 2009 LS -0.84 -3.12 2009 LS -0.85 -3.49
2010 AO -0.9 -2.4
2006 LS 0.26 2.22 2005 TC 0.58 2.25 2005 TC 0.39 5.05 2005 TC 0.52 2.24
2008 LS 0.36 2.63 2007 TC 0.55 2.12 2006 TC 0.38 4.88 2007 TC 0.50 2.16
2008 AO 0.91 3.65 2007 TC 0.43 5.56 2008 AO 1.14 5.41
2009 LS -0.82 -3.64 2008 AO 0.89 11.6 2009 LS -0.99 -4.73
2010 AO -0.7 -2.8 2009 LS -0.8 -11.4
2010 TC -0.38 -4.69
2008 AO 0.47 2.26 2009 LS -0.51 -2.13 2009 LS -0.54 -2.33
2009 LS -0.53 -2.84
+CPI, gap=AR(1)+dCRgap=AR(1) gap=AR(2) gap=AR(1)+dCR +CPI, gap=AR(1) +CPI, gap=AR(2)
+CPI+LFPR, gap=AR(1) +CPI+LFPR, gap=AR(2) +CPI+LFPR, gap=AR(1)+dCR+CPI+UR, gap=AR(1) +CPI+UR, gap=AR(2)
1991-2013
1996-2013
2000-2013
1991-2013
1996-2013
2000-2013
Table 5-4 Chen-Liu test results for China
Sample year type coef tstat year type coef tstat year type coef tstat year type coef tstat year type coef tstat year type coef tstat
2008 AO -2.77 -4.16 2010 TC -2.32 -2.23 2009 AO 2.97 3.28 2009 AO 4.12 2.60 2006 LS 1.72 2.28
2009 AO 5.37 8.05 2010 TC -5.10 -3.74 2007 TC 1.58 2.17
2010 TC -3.19 -3.92 2008 TC 2.19 3.00
2011 AO -2.54 -3.80 2009 AO 2.68 4.47
2010 TC -5.83 -7.88
2008 AO 4.98 2.54 2008 AO 2.66 2.56 2006 TC 5.30 3.95 2006 TC 5.40 2.21 2010 AO 4.07 2.59 2006 TC 6.94 2.62
2009 LS -6.28 -2.80 2009 LS -4.11 -2.82 2007 TC 3.33 2.48 2009 AO -6.42 -2.48 2011 TC -3.48 -2.13 2009 LS -6.71 -2.70
2008 AO 4.89 3.94
2009 LS -6.51 -5.10
2001-2014 2009 LS -5.67 -2.57
Sample year type coef tstat year type coef tstat year type coef tstat year type coef tstat year type coef tstat
2009 AO -6.33 -3.49 2006 AO -7.67 -2.45
2011 AO 7.13 2.27
2008 AO 2.82 2.45 2010 AO 0.73 2.42 2006 AO -3.90 -2.24
2009 LS -3.57 -2.27 2011 TC -1.44 -2.67 2011 AO 5.54 3.18
2005 LS -1.53 -2.33 2008 LS -1.03 -2.13 2010 AO -0.97 -2.19 2010 AO 1.71 2.11
2011 AO 1.10 2.48 2011 TC -2.74 -2.31
+CPI+LFPR, gap=AR(1)+dCR
1991-2014
1996-2014
2001-2014
1991-2014
1996-2014
+CPI+UR, gap=AR(1) +CPI+UR, gap=AR(2) +CPI+LFPR, gap=AR(1) +CPI+LFPR, gap=AR(2)
+CPI, gap=AR(1)+dCRgap=AR(1) gap=AR(2) gap=AR(1)+dCR +CPI, gap=AR(1) +CPI, gap=AR(2)