Structural Breaks in Potential GDP of Four Major Economies: just ...

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)

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Figure 1-2 – Kalman filter results (+CPI+LFPR) for US and euro area

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Kalman filter (CPI+LFPR) IMF Capacity utilization (right scale), %

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Figure 3-4 – Output gap measures for US and euro area

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Figure 5-6 – Kalman filter results (+CPI+LF) for Japan and China

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Figure 7 – Output gap measures for Japan

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GDP (actual), % IMF, GDP (potential), % IMF, output gap, % GDP (right scale)

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Figure 8-9 – IMF results for US and euro area

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Figure 10-11 – Potential GDP measures for US and euro area

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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.

References

1. Andrle M. What is in Your Output Gap? Unified Framework & Decomposition into

Observables. IMF Working Paper, WP/13/105, 2013.

2. Baxter M., King R. Measuring Business Cycles: Approximate Band-Pass Filters for

Economic Time Series. Review of Economics and Statistics, 1999, 81, pp. 575–593.

3. Borio C., Disyatat P. and M. Juselius. Rethinking potential output: Embedding

information about the financial cycle. BIS Working Papers No 404 February 2013

4. Cahn C., Saint-Guilhem A. Issues on Potential Growth Measurement and Comparison:

How Structural Is the Production Function Approach? Federal Reserve Bank of St. Louis

Review, July/August 2009, 91(4), pp. 221-40.

5. Camba-Mendez G., Rodriguez-Palenzuela D. Assessment criteria for output gap

estimates. Economic Modelling Volume 20, Issue 3, May 2003, Pages 529–562

6. Charles A., Darné O., Ferrara L. Does the Great Recession imply the end of the Great

Moderation? International evidence Economix Working Paper 2014-21

7. CEPR (2014): Secular Stagnation: Facts, Causes and Cures. Coen Teulings and Richard

Baldwin, Eds. ISBN: 978-1-907142-77-2 CEPR Press, 2014

8. Chinn M., Ferrara L., Mignon V. (2013): Post-recession US employment through the lens

of a non-linear Okun’s law NBER Working Paper No.w19047

9. Cobb C.W., Douglas P.H. A Theory of Production. American Economic Review

(Supplement), 1928, 18, pp. 139–165.

10. Cotis, J.P., Elmeskov J., Mourougane A. (2004), ‘Estimates of potential output: benefits

and pitfalls from a policy perspective’, in L. Reichlin (ed.) The Euro Area Business

Cycle: Stylized Facts and Measurement Issues, CEPR, London.

11. De Masi P.R. IMF Estimates of Potential Output: Theory and Practice. IMF Working

Paper, WP 97/177, 1997.

12. Fernald J. Productivity and Potential Output before, during, and after the Great

Recession. NBER Working Paper 20248, June 2014

13. Fischer S. Speech at the "The Great Recession--Moving Ahead," a Conference Sponsored

by the Swedish Ministry of Finance, Stockholm, Sweden, 11.08.2014

http://www.federalreserve.gov/newsevents/speech/fischer20140811a.htm

14. Furceri D., Mourougane A., The effect of financial crises on potential output: New

empirical evidence from OECD countries. Journal of Macroeconomics Volume 34, Issue

3, September 2012, Pages 822–832

15. Gadea-Rivas M., Gómez-Loscos A., Perez-Quiros G. The Two Greatest. Great Recession

vs. Great Moderation (September 17, 2014). Banco de Espana Working Paper No. 1423

16. Gerlach P. The global output gap: measurement issues and regional disparities. BIS

Quarterly Review, June 2011.

17. Granger, C and Y Jeon (2004) Thick Modelling. Economic Modelling, 21, pp 323-343.

18. Gordon R. Is US economic growth over? Faltering innovation confronts the six

headwinds. NBER Working Paper, no 18315, August 2012.

19. Gordon R. A New Method of Estimating Potential Real GDP Growth: Implications for

the Labor Market and the Debt/GDP Ratio. NBER Working Paper No. 20423, August

2014

20. Hall, R. The Long Slump American Economic Review 101 (April 2011): 431–469

21. Hamilton, J A New Approach to the Economic Analysis of Nonstationary Time Series

and the Business Cycle Econometrica Vol. 57, No. 2 (Mar., 1989), pp. 357-384

22. Hamilton, J (1995), “State-space models” in Engle, R F and D Mc Fadden (eds)

Handbook of Econometrics Volume 4, 3041-3077

23. Hodrick R.J., Prescott E.C. Post-War U.S. Business Cycles: An Empirical Investigation.

Journal of Money, Credit, and Banking, 1997, 29, pp. 1–16.

24. Huang, Yu-Fan and Luo, Sui, How Different Is This Time? Investigating the Declines of

the U.S. Real GDP During the Great Recession (January 16, 2014). Available at SSRN:

http://ssrn.com/abstract=2426023 or http://dx.doi.org/10.2139/ssrn.2426023

25. Johnson C.A. Potential Output and Output Gap in Central America, Panama and

Dominican Republic. IMF Working Paper, WP/13/145, 2013.

26. Kalman R.E. A New Approach to Linear Filtering and Prediction Problems. Transaction

of the ASME—Journal of Basic Engineering, March 1960, pp. 35–45.

27. Kar S., Pritchett L., Raihan S., Sen K. Looking for a break: Identifying transitions in

growth regimes Journal of Macroeconomics 38 (2013) 151–166

28. Kuttner K.N. Estimating potential output as a latent variable, Journal of Business and

Economic Statistics, 1994, 12, pp. 361–368.

29. Laxton D., Tetlow R. A Simple Multivariate Filter for the Measurement of the Potential

Output. Technical Report, Bank of Canada, June 1992, 59.

30. Lazear E., Spletzer J. The United States Labor Market: Status Quo or A New Normal?

NBER Working Paper No. 18386. September 2012

31. Lo, S. and Rogoff K. Secular Stagnation, Debt Overhang and Other Rationales for

Sluggish Growth, Six Years On (January 2015). BIS Working Paper No. 482

32. Papell D.H., Prodan R. The Statistical Behavior of GDP after Financial Crises and Severe

Recessions // The B.E. journal of macroeconomics.- De Gruyter, ISSN 1935-1690, ZDB-

ID 22666771. - Vol. 12.2012, 3, p. 1-29

33. Reinhart C. and Rogoff K. (2009a): “The aftermath of financial crises”, American

Economic Review, no 99, May, pp 466–72.

34. Reinhart C. and Rogoff K. (2009b), This Time Is Different: Eight Centuries of Financial

Folly, Princeton University Press, Princeton.

35. Stock, J. H., and M. W. Watson (2012): Disentangling the Channels of the 2007-2009

Recession," Brookings Papers on Economic Activity, 1, 81–135.

36. Summers L. U.S. Economic Prospects: Secular Stagnation, Hysteresis, and the Zero

Lower Bound, Business Economics, Vol. 49:2 (April 2014), pp. 65–73.

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


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


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


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


where p


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


,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


,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


,t t tur nairu g

1 ,t t tnairu nairu

1 1 2 1 ,t t t t tg g z cr

where p


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


,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


,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


,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


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



gap measure for the euro area (sample 1999-2013)

0

20

40

60

80

100

120

-8

-6

-4

-2

0

2

4

6



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)


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


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


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)

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