Download Leading indicators of the business cycle: dynamic

Anna Pestova1
Leading indicators of the business cycle: dynamic logit models
for OECD countries and Russia2
This paper develops leading indicators of the business cycle phase change for a wide range of
countries, including Russia, over the 1980-2013 period. I use dynamic binary choice models with the
dependent variable of the state of economy: recession, no recession. These models allow the estimation
of how likely a change of macroeconomic dynamics from positive to negative, and vice versa, is. The
empirical analysis suggests that taking into account financial sector variables can significantly improve
the predictive power of the models. The study also demonstrates that the larger the time lag between
the dependent and explanatory variables, the worse the results in terms of the predictive power of the
models. However, despite the quality of prediction for a one-year lag is the least precise, this model is
still useful as it correctly predicts more than 80% of recessions.
Keywords: business cycles, leading indicators, turning points, binary response models,
macroeconomic crisis.
JEL Classification: E32, E37.
1
Center for Macroeconomic Analysis and Short-Term Forecasting (CMASF), Senior Expert and National
Research University Higher School of Economics (NRU-HSE), Research fellow. Email: [email protected].
2
This study was implemented in the framework of the Basic Research Program at the National Research
University Higher School of Economics in 2013-2014. Thanks to the participants of XV April International Academic
Conference on Economic and Social Development, NRU-HSE, Moscow, April 2014, 34th Annual International
Symposium on Forecasting, Rotterdam, Netherlands, June 2014 and International conference “Modern
econometric tools and applications”, NRU-HSE, Nizhny Novgorod, September 2014 for valuable comments and
suggestions.
1
1. Introduction
The problem of early identification of the business cycle turning points is of great practical
interest to both the business community and policymakers. Since the 1946 study by W. Mitchell and A.
Burns, in which first serious statistical analysis of business cycles was conducted, the issue of "predicting
the future" has been holding an important place in macroeconomic analysis.
At the end of 1990s – in the mid-2000s following prolonged period of smooth macroeconomic
dynamics in most OECD countries analysts and researchers proclaimed the «end of the business cycle» Weber (1997). In the academic literature Stock, Watson (2002) paper provided strong evidence in favor
of what they called «great moderation» of the business cycle. The main factors behind moderated
volatility of macroeconomic indicators supposed to be the growth of the service sector, technological
shifts, financial innovations, improved monetary policy and «good luck» (decrease in the volatility of
exogenous shocks).
However, some factors that previously led to a decrease in amplitude of macroeconomic
fluctuations could contribute to an increase of vulnerability of economies to the recent global economic
crisis. For instance, excessive liberality in regulating the financial sector resulted in "bubbles" inflated at
different markets (dot-coms, real estate, commodity markets, etc.). This formed and led to sustaining of
positive expectations for a long period. A reduction of policy interest rate in USA to smooth out the
recession of 2001 translated into increased aggregate demand including demand for loans. This led to
steady imbalance between revenue and expenditures of the economic agents resulting in dramatic
increase of the debt burden of households and corporations in developed countries. The period of low
interest rates in most OECD countries pushed capital flows towards emerging markets where
overheating of financial markets was observed. Artificial increase in demand in developed and
developing countries has finally led to serious consequences: increase in loan defaults in the private
sector and tight situation in the government finance sector. Stress in the financial markets spilled over
into the real sector and brought most of the countries into the prolonged recession. This global crisis at
the end of 2000s was called «great recession» and was known as the most severe recession in the
postwar period.
In the post-crisis period, economists still have not come to the agreement whether the great
moderation ended. A return of it as it is stated in Clark (2009) is a very controversial issue (see Taylor,
2013). In any case after the global crisis of 2000s the problem of predicting recessions and foresee its
end got additional attention of policymakers and academia. Indeed, nowadays there is a high risk that
recession will re-emerge (or will continue for many OECD countries).
In this study, I develop leading indicators of the business cycle phase change. The methodology
relies on dynamic discrete dependent variable panel data models. As a dependent variable discrete
variable reflecting the state of the business cycle («1» - recession, «0» - otherwise) is used.
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The primary research question of this paper is whether it is possible to predict the state of the
business cycle (particularly, recessions) in advance. Despite much of the research has been aimed at
predicting business cycle turning points, none of them claim to be a comprehensive. First, existing
studies use data for only one country – USA, refusing to test whether their results would be relevant for
other, say, OECD countries. Second, most of the research use severely limited list of variables that
potentially could be the leading indicators of the business cycle. In particular, they omit credit market
variables as possible predictors, which in the light of growing macro-financial linkages could account for
considerable part of macroeconomic fluctuations. Third, in the relating works predominantly short lags
are used (from one to several months), thus missing an opportunity to predict recessions in advance.
Fourth, existing studies use exogenously determined cut-off thresholds in the discrete dependent
variable framework (either 0.5 or unconditional probability of recession), that could worsen model
predictive power.
This paper contributes to the literature in the four ways. First, in contrast to the previous studies,
dynamic panel data models for OECD countries and Russia are developed. Second, I test credit market
variables as potential leading indicators of the business cycle. Third, longer forecasting horizon (up to 1
year) when predicting turning points is studies. Fourth, I apply advanced analysis of cut-off thresholds
based on the optimization of regulator loss function. This method is widely used in the literature on
financial crises, and for the first time is applied to leading indicators models of the business cycle phase
change.
The main results of the paper can be summarized as follows. I found that leading indicators of the
business cycle could be uniformly developed for a panel of countries, and the quality of prediction of
these models would be comparable to analogues of single-country models. I show that financial sector
variables and, in particular, credit market ones, are extremely important when studying leading
indicators of the business cycle at long horizons (1 year) as their use leads to a reduction of noise-tosignal ratio of the model threefold. When testing different forecasting horizons I demonstrate that the
larger the time lag between dependent and explanatory variables, the worse the results in terms of
predictive power of models. However, despite prediction results with one-year lag are less precise, this
model is still useful as it correctly predicts more than 80% of recessions. I also try to convince the reader
that the use of the “optimal” cut-off threshold (selected by minimizing regulator loss function arising
from different types of false signals) improves model forecasting ability.
The rest of the paper is organized as follows. Section 2 presents relevant literature review.
Section 3 describes the model, the estimation methodology and data used. In Section 4 estimation
results are presented and discussed. Finally, Section 5 concludes the paper.
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2. Literature review
In the existing literature, two main approaches of constructing leading indicators of
macroeconomic dynamics could be identified. First, models with continuous dependent variable that
predict output level or its growth rates. These models are mostly represented by static and dynamic
factor models (see Stock, Watson, 1989, 2006; Forni et al. 2001, etc.) and non-model approach
developed by OECD (OECD, 2008). Second, models with discrete dependent variable that aim at
forecasting the state of the economy. These models say how likely is a change of regime from expansion
to recession and vice versa. This study belongs to the second strand of the literature as we aim to
forecast business cycle phase, not the entire dynamics of GDP or some other variables.
The majority of relevant empirical studies on leading indicators of recessions use a discrete
dependent variable (Stock, Watson, 1992; Estrella, Mishkin, 1998; Moneta, 2005; Kauppi, Saikkonen,
2008; Ng, 2012, etc.). Most of these studies analyze the predictive power of the slope of government
bond yield curve in anticipation of recessions in the US and in other developed countries. In most cases,
these papers use time series data for one or several countries.
In Estrella, Mishkin (1998) work the predictive power of financial sector variables for recessions
forecasting in the US is studied. The authors use interest rates and spreads between them, stock
indexes, monetary aggregates, macroeconomic indicators and composite leading index of
macroeconomic dynamics as leading indicators. Estrella and Mishkin found a high predictive power of
the two financial indicators: the slope of US government bond yield curve and stock index.
Kauppi, Saikkonen (2008) introduced dynamic binary models that allowed analyzing the impact of
the previous states of the business cycle to the next ones (dynamic nature of the cycle was accounted
for). The Ng (2012) paper introduced more variables in the dynamic binary business cycle models
compared with a standard set (stock indexes, slope of the yield curve). These variables characterize
interest rates at the interbank market (TED-spread) and price stability at the housing market. в
The Castro (2010) paper, although may seem as irrelevant to this study as it is focused on the
models of the duration of business cycle phases, in fact is very appealing. First, it studies the
determinants of the phases duration on the panel data of 13 developed countries. It contrasts to the
existing literature on predicting recessions dealing with one country data (mostly – USA). Second, Castro
(2010) proposes additional variables that are likely to affect the duration of the business cycle phases:
OECD leading indicators, calculated for most OECD countries in a unified methodology, dynamics of
private investment and US business cycle phase.
Considering leading indicators of the business cycle developed for the Russian economy it should
be noted that models with continuous dependent variable are largely presented: DFM models in Styrin,
Potapova (2009), Demidov (2008) and nonmodel based leading indicators constructed by OECD (2008)
and Smirnov (2001, 2006, 2011). As concerning the models that are oriented towards recession
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prediction only the author’s previous paper exist – Pestova (2013), where the preliminary analysis of
recession determinants was made on the basis of OECD countries yearly data.
3. Methodology and data
Dating the business cycle significantly depends on the choice of the concept of cycle. In the
literature, there three main approaches exist: (1) classical business cycle; (2) deviation or growth cycle;
(3) growth rate cycle.
The National Bureau of Economic Research (NBER) has been used classical business cycle
approach since the postwar period. Classic business cycle implies the identification of local minimum
and maximum points of the index variable ("peak" and "trough» - Pbc and Tbc – see Chart 1). On this
basis, it the state economy is determined whether it is in a recession or expansion (recession is defined
as period between the peak and the trough, expansion - between the trough and the next peak).
NBER has been published the announcements about changing phases of the business cycle of US
economy since 1980s (earlier data is also available, up to the mid-19th century) in line with the concept
of the classical cycle. As for the other countries, CEPR Business Cycle Dating Committee date recessions
and expansions in the euro area as a whole from 1999 onwards. The Economic Cycle Research Institute
(ECRI) dates recessions in line with US methodology in a number of developed and developing countries
(totally 22 countries of which eight are European ones).
Chart 1. Classical business cycle and growth rate cycle
Source: Banerji, Dua (2011)
Under the deviation cycle approach, the deviation of the economic activity from its long-term
trend is considered. This way of thinking about business cycle was introduced during the Great
Moderation, when the frequency of recessions in terms of absolute volume of output contraction
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decreased. The deviation cycle methodology is used in the OECD studies for dating and forecasting
business cycles in its member countries – see OECD (2008).
Third – alternative – approach relies on the analysis of the growth rates of economic activity
instead of its levels. As the limitation of that method, one can mention a significant noisy component in
the growth rates over the short period (month, quarter). This problem could be addressed by, for
example, taking year-over-year growth rates. In this case, change of the sign of the growth rates from
positive to negative can mark the onset of recession and a comeback to the positive values – as its end.
As the key indicator determining business cycle phases I use real GDP annual growth rate as the
most general and available for all countries economic activity indicator. Other types of variables, which
reflect cyclical fluctuations are industrial production index, previously used by OECD, see OECD (2008),
synchronous indicators used by NBER and in most of the research on the US business cycles - Estrella
Mishkin (1998), Kauppi, Saikkonen (2008), Ng (2012), other composite synchronous indices - Conference
Board (2000), Stock, Watson (1989).
The dating of the phases of business cycles in this study relies on the growth rate cycle approach.
The explanation of that choice splits into two main arguments: unavailability or low validity of
alternative dating and simplicity of methodology and clear identification of turning points. As we
previously noted, dating in the classical business cycle framework is not available for a representative
sample of countries (the largest dataset is available on the ECRI website, however it has a very limited
number of countries). The only available dating of the business cycles for a large sample of countries is
the OECD one made in the deviation cycle approach. However, it seems unreasonable because a large
number of “false” recessions were identified (when growth rates declined but stayed positive) – see
Chart 2.
The simplicity and tractability of growth rate cycle dating methodology arises from the easy rule
of classifying the data: the times when GDP experienced a steady decline (GDP growth rate was
negative) could be classified as a recession, when it grows - as an expansion, respectively, so that the
binary dependent variable could be defined as follows:
1 𝑖𝑓 𝐺𝐷𝑃𝑔𝑟 < 0 (𝑟𝑒𝑐𝑒𝑠𝑠𝑖𝑜𝑛)
𝑦𝑖𝑡 = {
0 𝑖𝑓 𝐺𝐷𝑃𝑔𝑟 > 0 (𝑒𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛)
To avoid noise in the dependent variable (flashing business cycle phases) I adopted more complex
definition of the recession than technical one described above. In particular, I did not classify onequarter GDP decline as a recession. Instead of it, at least two negative quarters of GDP should be
recorded to be qualified as a recession. The same logic was applied in case of one quarter of slight
positive growth was surrounded by recessionary quarters: this “positive” quarter was deliberately
marked as a recession.
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Chart 2. OECD recession dates and actual real GDP growth rates (y-o-y) for USA (on the left)
and UK (on the right)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
8.0
6.0
4.0
2.0
0.0
-2.0
-4.0
-6.0
-8.0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1980 Q1
1982 Q4
1985 Q3
1988 Q2
1991 Q1
1993 Q4
1996 Q3
1999 Q2
2002 Q1
2004 Q4
2007 Q3
2010 Q2
2013 Q1
1980 Q1
1982 Q4
1985 Q3
1988 Q2
1991 Q1
1993 Q4
1996 Q3
1999 Q2
2002 Q1
2004 Q4
2007 Q3
2010 Q2
2013 Q1
10.0
8.0
6.0
4.0
2.0
0.0
-2.0
-4.0
-6.0
OECD recessions dates
OECD recessions dates
Real GDP growth rates
Real GDP growth rates
The specification of the dynamic panel binary choice model is defined as:
′
𝑃𝑟{𝑦𝑖𝑡 = 1|𝛼𝑖 , 𝑥𝑖𝑡−𝑘 , 𝑦𝑖𝑡−𝑘 } = 𝐹(𝑦𝑖𝑡−𝑘 𝛾 + 𝑥𝑖𝑡−𝑘
𝛽 + 𝛼𝑖 ), where
𝑃𝑟{. } is a conditional probability of recession, 𝐹(. ) is a logistic distribution function (logit model),
𝑥𝑖𝑡−𝑘 is a set of explanatory variables for country 𝑖 in year (𝑡 − 1), 𝛽 is a vector of parameters
associated with 𝑥, 𝛾 is a state dependence parameter, 𝑘 is a quarter lag.
The dynamic specification of a model (previously used in Kauppi, Saikkonen, 2008; Nyberg, 2010
and Ng, 2012) implies that previous state of the business cycle influences the current one (lagged
dependent variable is included). I also include the component of unobservable country-specific
heterogeneity into the model that stands for exogenous differences between countries in the
probability of recession. Accounting for unobservable country-specific effects is necessary to distinguish
between true state dependence (coefficient 𝛾) from spurious one (driven by the persistence of countryspecific effect).
I use quarterly data set on 22 OECD countries including Russia3 over the period 1980-20134.
Taking these data, I treat cross-country heterogeneity component 𝛼𝑖 as fixed effects because the sample
appears to be restricted. Initially it consisted of more than 30 OECD countries and Russia, but after
checking for data availability on explanatory variables it decreased significantly.
Under the fixed effects methodology the so called “incidental parameter problem” is unlikely to
arise because in case of this study the number of countries (𝑁) do not grow to infinity, it is fixed as well
3
Complete list of countries: Australia, Austria, Belgium, Canada, Czech Republic, Denmark, Finland,
France, Germany, Ireland, Italy, Japan, Mexico, Netherlands, New Zealand, Portugal, Russia, Slovak Republic, Spain,
Switzerland, UK, USA.
4
A period of the transition crisis (recession) experienced by the post-soviet countries after abandoning
planned economy and transition to the market economy was excluded from the analysis.
7
as the number of quarters (𝑇) does. Besides, taking into account the specificity of models I develop –
leading indicator models – one can see that explanatory variables taken with lags would be exogenous
to the dependent variable. That is why using ordinary logistic regression with country-specific dummy
variables and fixed effects conditional maximum likelihood estimator yields unbiased estimates. Fixed
effects regressions are run only if the test on joint significance of the country-specific dummy variables
shows that these variables are significant.
In line with the empirical and theoretical literature, I study the following set of indicators, which
could predict business cycle phase changes: (1) macroeconomic variables; (2) consumer and business
expectations; (3) external sector variables; (4) financial sector variables.
Macroeconomic variables include lagged GDP growth (previously used in Estrella, Mishkin, 1998)
and investment expenditures (Stock, Watson, 1993; Birchenhall et al., 1999; Ozildirim et al., 2010,
Castro, 2010). I also separately examine the predictive power of country GDP leading indicator in OECD
methodology (other papers where composite leading indices were used are Stock, Watson, 1989, 1992;
Birchenhall et al., 1999; Ng, 2012; Castro, 2010).
Consumer and business expectation variables are often used in this literature, see Estrella,
Mishkin (1998), Birchenhall et al. (1999) and Ozildirim et al. (2010) works. In this study I use OECD
standardised confidence indicators database where these indicators are available for the most member
countries.
External sector variables list consists of US business cycle phase (previously used in Castro, 2010),
current account balance to GDP ratio and real effective exchange rate index (NEER was included in
recession equation in Estrella, Mishkin, 1998 work). The last two variables measure the external trade
and currency balance, which, if violated, could provoke the recession.
Financial sector variables include those previously used in the literature: interest rates and
spreads5 (Estrella, Mishkin, 1998; Kauppi, Saikkonen, 2008; Ng, 2012; Ozildirim et al., 2010; Castro,
2010), stock market indices (Estrella, Mishkin, 1998; Stock, Watson, 1992; Birchenhall et al., 1999; Ng,
2012; Ozildirim et al., 2010; Castro, 2010), as well as those proposed in this paper: bank lending and
interest rates on loans. The omission of these variables in the modern empirical studies is remarkable in
the light of early business cycle theories by Hawtrey and Hayek, who say that bank lending instability is a
source of cyclical fluctuations in the economy (Zarnowitz, 1996). In these theories, interest rate on loans
is considered as a transmission link that connected financial and real sector variables through the
availability of financial resources to investment.
5
The most widespread used leading indicator of the recessions – the slope of the government bond yield
curve – is not used in this study because it is not available for a wide range of countries.
8
4. Estimation results
I start estimation of the dynamic recession models from the analysis of the predictive power of
the individual indicators. To do that, I run pairwise regressions of the dependent variables on each
indicator separately. The quality of prediction is assessed by the difference between pseudo-R2 in the
model and the corresponding indicator in the simple autoregressive business cycle model (if only lag of
the dependent variable is included), as well as the significance of corresponding coefficients. The results
are presented in the Table A2 in the Appendix. Descriptive statistics for dependent and explanatory
variables are given in the Table A1 in the Appendix.
The analysis suggests that country GDP leading indicators in the OECD methodology is the most
informative individual predictor (with the exception of three- and four-quarter lag). In addition to this,
an extremely high level of the explanatory power was demonstrated by consumer and business
confidence indicators (except for deep lags too). Investment dynamics is also an important predictor of
switching between business cycle phases but only for the one-quarter lag. Slowdown of real GDP growth
is a good predictor of recession for the same lag. US GDP leading indicator makes sense for one to three
quarter lags. Current account balance to GDP ratio and REER significantly influence in all lag models.
Stock price index is extremely valuable for one to four lags. Spreads between interest rates are also
important while loans to GDP ratio predictive power increases with lag growth. Based on the
preliminary analysis of individual indicators I then estimate multivariate models with most informative
individual predictors as explanatory variables.
The estimation of multivariate recession models was carried out in four steps. First, I estimated
dynamic models where the only explanatory variable was country GDP leading indicator in the OECD
methodology. I was interested, would this single indicator predict the state of an economy most
precisely (if it turned out to be the best predictor, then constructing and using other models would be
useless). Secondly, I estimated dynamic models, which used only the real sector variables, without OECD
GDP leading indicator. The following indicators were included to the block of real sector variables (only
those indicators are mentioned that showed themselves in the best way in the pairwise models):
consumer confidence indicator, investment dynamics, GDP growth rates, US GDP leading indicators in
OECD methodology, REER index and current account balance to GDP ratio. Third, I added financial sector
variables to the models with the real sector variables, in order to estimate whether considering them
would lead to an increase in the predictive power of models. The block of financial sector variables
included stock market indices, spreads between interest rates and bank loans to GDP ratio. At the fourth
step I dropped lagged dependent variable from the models with real and financial sector variables to
learn whether accounting for inertia in the business cycle phases makes sense. These four types of
models were estimated for one, two and four quarter lag of all of the explanatory variables.
Additionally, not to restrict the models by rigid lag selection, I also estimated models with “best” lags –
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for which the predictive power was largest in the pairwise models. Totally sixteen models are presented
in the Appendix in the Tables A3-A6.
Discussion of the results. Most of the variables are significant in the estimated equations with
expected coefficient signs. Lag of the dependent variable is significant in one and two-quarter lag
specifications and becomes insignificant at longer horizons. This can indicate damping of inertia with
increasing lag.
The estimated coefficients are robust to the change of specification (addition of variables) and
variation of the quarter lags. This indicates that the obtained results seem to reveal the underlying
relationships between business cycle phases and its leading indicators.
I obtained negative sign at country GDP leading indicator in the OECD methodology meaning that
an increase of the value of this indicator lowers the probability of recession with a lag. An increase in the
consumer confidence indicate an increased propensity to consume thus preventing an economy from a
recession. The US leading indicator measuring the state of the major economy in the globe significantly
influences business cycle phase of the other countries, however the significance disappears for more
than two-quarter lag. The risk of recession increases during the slowdown of GDP growth rates that are
important for short lags (up to two quarters). Weakening of the country’s external balance (decrease of
the current account surplus or its shift to the negative values) is a factor increasing the probability of a
negative output growth rates with only four-quarter lag. An increase in the interbank market rate
spread anticipates crisis with one and two quarter lag (via credit crunch mechanism) while rise of the
interest rate on loans predicts recession with a year lag (due to borrowers adverse selection and
possible rise of defaults on loans). Substantial growth of loans to GDP ratio up to an excessively high
level may imply that significant credit risks have accumulated, which are not compatible with the
continuation of expansion. This indicator is significant with a four-quarter lag only meaning that credit
overheating peak occurs one year before the recession.
The preliminary analysis of predictive power of models using the pseudo-R2 measure shows that
models with the real sector indicators only are worse compared to the model with real and financial
sector variables. This shows that it is important to account for the latter. However, when the model with
GDP leading indicators in OECD methodology only is compared to the model with real and financial
sector variables by pseudo-R2 measure the result is less evident. Though, for one-quarter lag the latter
outperform the former, for two-quarter the relationship is reversed. Thus, an additional analysis of
models predictive power is needed.
According to the tests on the significance of individual effects (country dummy variables), for two
and four-quarter lag models, country-specific constants are jointly significant (Tables A4-A5 in the
Appendix). For one-quarter lag model, pooled specification is more preferable. For model with various
lags, the result depends on the specification. For the specification with real and financial sector
variables, individual effects are significant at 10% level (Table A6 in the Appendix). Taking into account
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these results, I reestimated those specifications where the presence of individual effects were shown.
The method I used is the conditional fixed-effects logit estimator. The obtained results revealed no
sharp differences between dummy variable and fixed effects estimator (Table A7 in the Appendix). The
values of the most of the coefficients remained almost unchanged; they also preserved their signs and
significance. Thus, if the estimation on the pooled sample gives almost the same results, it will unlikely
be biased compared to the fixed effects model.
Next, in order to assess the predictive power of models, I discuss and implement the method of
choosing a cut-off threshold that separates “crisis” values of the models from the normal state. This
raises a question about the rule, according to which a continuous series of model-based recession
probability values should be converted to a discrete scale (to compare with the actual values). A naive
cut-off threshold could be chosen at the value of 0.5 (equally distances from “0” and “1”), however,
there are modifications of this rule in the existing studies.
A work of Birchenhall et al. (1999) considers an issue of choosing a threshold for recession
probability models, exceeding which is treated as a “signal” of recession. The authors suggest that the
unconditional probability of an analyzed event should be used as threshold. They consider the
probability range between 0.5 to the unconditional probability as an ambiguous area.
In the literature on financial crisis leading indicators (e.g. Bussiere, Fratzscher, 2006) it is
suggested to choose the optimal threshold based on the minimization of the regulator loss function,
which is obtained from balancing between type 1 errors (missed event) and type 2 (false signal):
𝐿(𝜃) = 𝜃
𝐶
𝐵
+ (1 − 𝜃)
,
𝐴+𝐶
𝐵+𝐷
where 𝐴, 𝐵, 𝐶 and 𝐷 are calculated according to the classification presented in the Table below.
Table 1. Classification of the events of interest and their signals
𝑌=1
The event occurs in the
following k quarters
𝑌=0
The event does not occur in
the following k quarters
𝐴
𝐵
(type 2 error)
𝐶
(type 1 error)
𝐷
𝑆=1
indicator issues a signal
(exceed threshold)
𝑆=0
indicator does not issue a signal
(do not exceed threshold)
As the threshold increases, so does the type 1 error, while the type 2 error decreases. This means
that there is an optimum, where the weighted sum of these errors is minimal. These weights (𝛩, 1 − 𝛩)
depend on a parameter of regulator sensitivity to type 1 errors compared to type 2 errors (𝛩).
With any values of parameter 𝛩, the function 𝐿(𝜃) will have a minimum point, since the ratio of
type 1 errors C/(A+C) grows with an increase in threshold values, while the ratio of type 2 errors
B/(B+D) drops (Chart 2Error! Reference source not found.а).
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However, the result of the optimization depends on a choice of parameter 𝛩. That is why I
considered several values of parameter 𝛩: 0.5, 0.3, and 0.7. As seen from Chart 2b, the choice of
optimal threshold depends on the parameter 𝛩: the higher the parameter (regulator sensitivity with
respect to missing events), the lower the optimal threshold.
Chart 3. Choosing optimal threshold for the business cycle phase model with OECD GDP leading
indicator (lag - 1 quarter)6
а) Type 1 and type 2 errors and their weighted sum
b) The choise of optimal threshold depending on a
as a functions of cut-off threshold
parameter of regulator loss function
16%
20%
18%
16%
14%
12%
10%
8%
6%
4%
2%
0%
14%
12%
10%
8%
6%
4%
2%
0.01
0.03
0.05
0.07
0.09
0.11
0.13
0.15
0.17
0.19
0.21
0.23
0.25
0.27
0.29
0.01
0.03
0.05
0.07
0.09
0.11
0.13
0.15
0.17
0.19
0.21
0.23
0.25
0.27
0.29
0%
Optimal threshold (Θ=0.5)
Optimal threshold (Θ=0.3)
Optimal threshold (Θ=0.7)
0.5*C/(A+C)+0.5*B/(B+D)
0.3*C/(A+C)+0.7*B/(B+D)
0.7*C/(A+C)+0.3*B/(B+D)
Optimal threshold (Θ=0.5)
C/(A+C)
B/(B+D)
0.5*C/(A+C)+0.5*B/(B+D)
Table 2, based on a business cycle phase model with OECD leading indicators only, presents the
main indicators, upon which we assess the predictive power of models depending on parameter Θ. We
also show for comparison the model quality characteristics for the thresholds used in reviewed works,
which are equal to the unconditional probability of the event (in our case 0.11) and the value of 0.5.
As it is shown in the Table 2, the threshold of 0.5 leads to a drop in a noise-to-signal ratio to
negligibly low levels (2.5%). However, in this case the quality of prediction also decreases: the ratio of
correctly predicted events drops below 80% (see last column of the Table 2). At the same time, the
threshold, which is equal to the unconditional probability of the event, lies close to its "optimal" value
calculated with 𝛩 = 0.5, This means that the unconditional threshold could be taken into consideration.
However, I, when comparing models, will use another rule of choosing a threshold based on a regulator
loss function with a 0.5 sensitivity value to missed crises, since this threshold is both lies close to the
unconditional probability of the recession (and thus could be considered as reasonable) and at the same
6
Estimation results are given in the Table A3 in the Appendix, first column.
12
time, this value is obtained through the optimization of loss function calculated in a specific way. The
value of 0.5 is taken as an exogenous value as it is unknown what actually this value is.
Table 2. Indicators of the quality of business cycle phase model with OECD leading indicators only (lag - 1
quarter), depending on the cut-off threshold, %
Parameter of regulator loss function
Θ = 0.7
Θ = 0.5
Θ = 0.3
Optimal threshold
0.07
0.15
Noise-to-signal ratio
13.0%
Recessions correctly predicted
Absence of recessions correctly
predicted
0.29
P (Y = 1) =
= 0.16
0.5
7.1%
3.7%
7.0%
2.5%
95.9%
92.9%
86.8%
92.5%
78.6%
87.6%
93.4%
96.8%
93.5%
98.0%
0.0%
0.0%
0.0%
0.0%
0.0%
100.0%
100.0%
100.0%
100.0%
100.0%
100.0%
100.0%
100.0%
100.0%
100.0%
Full Sample (22 countries)
Russia
Noise-to-signal ratio
Recessions correctly predicted
Absence of recessions correctly
predicted
Table 3 shows values of the predictive power for four estimated business cycle phase models with
one-quarter lag of all of the explanatory variables and regulator loss function parameter Θ = 0.5. The
results of the calculations show that model with real sector indicator gives way to the model with OECD
GDP leading indicator only, namely, that it predicts worse with a higher noise-to-signal ratio. At the
same time, the model with real and financial indicators predicts recession more precisely, than the
model with OECD GDP leading indicator only with equal noise-to-signal ratio (Table 3). For two-quarter
lag model the optimal threshold gives ambiguous result when model with OECD GDP leading indicator
only is compared to the model with real and financial indicators (Table A8): for the latter both the ratio
of correctly predicted recessions and noise-to-signal is lower. However, if additional analysis of weighted
type one and type two errors is performed, one can see that for most of the thresholds regulator loss
function is lower for the model with real and financial sector variables when compared to the model
with OECD GDP leading indicator only (Chart 4). As concerns four-quarter lag models, the proposed
model with real and financial sector variables clearly outperforms model with OECD GDP leading
indicator only as the latter becomes too noisy at long horizons. These findings confirms the usefulness of
models based not only on the existing leading indicators (OECD GDP leading indicator), but also on a
selected set of predictors of both real and financial sector variables.
When models with real and financial sector variables are compared to the models with real sector
variables only, the choice would be not in favor of the latter (Table 3 and Tables A8-A10 in the
Appendix). This gap is especially pronounced at the long horizons (four-quarter lad models) where the
financial sector variables improves the accuracy of the model reducing its noise-to-signal ratio threefold.
Thus, our calculations show that if financial sector variables are considered, the periods of recession
could be better predicted.
13
Table 3. Quality of prediction of the business cycle models, lag=1 quarter
Optimal threshold
Full Sample (22 countries)
Noise-to-signal ratio
Recessions correctly
predicted
Absence of recessions
correctly predicted
Russia
Noise-to-signal ratio
Recessions correctly
predicted
Absence of recessions
correctly predicted
Dynamic model
with OECD GDP
leading indicator
only
0.15
Dynamic
model with
real sector
variables only
0.12
Dynamic model
with real and
financial sector
variables
0.15
Static model
with real and
financial sector
variables
0.15
7.1%
8.6%
7.1%
8.7%
92.9%
94.7%
94.7%
94.0%
93.4%
91.9%
93.2%
91.9%
0.0%
15.6%
7.8%
7.8%
100.0%
80.0%
80.0%
80.0%
100.0%
87.5%
93.8%
93.8%
Note. Optimal threshold is chosen on the basis of regulator loss function minimization with 𝛩 = 0.5.
Chart 4. Regulator loss function depending on the threshold of the business cycle models, lag=2 quarters
0.3
0.25
0.2
0.15
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.20
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.30
0.1
CLI
Real
Real+Fin
In different lag specifications, the dynamic models were more accurate than the static ones: they
yielded both higher quality of recession prediction and lower noise rate - see Table 3 and Tables A8- A10
in the Appendix. It means that accounting for the dynamic nature of the business cycle not just helps to
avoid misspecification of the business cycle phase model but also improves its forecasting accuracy.
14
Testing uniform specification (with real and financial sector variables) among different forecasting
horizons demonstrated that the larger the time lag between dependent and explanatory variables, the
worse the results in terms of predictive power of models (Table 4). Therefore, there is a trade-off
between forecasting accuracy and earliness of recession signal. With the precision increase, the leadtime of the models drops and vice versa. However, despite prediction results with four-quarter lag were
the least precise, this model is still could be viewed as useful as it correctly predicts more than 80% of
recessions with the noise-to-signal ratio equals to one quarter.
Table 4. Quality of prediction of business cycle models, dynamic models with real and financial sector
variables
Optimal threshold
Full Sample (22 countries)
Noise-to-signal ratio
Recessions correctly
predicted
Absence of recessions
correctly predicted
Russia
Noise-to-signal ratio
Recessions correctly
predicted
Absence of recessions
correctly predicted
1Q lag
2Q lag
4Q lag
Various lag
0.15
0.19
0.15
0.15
7.1%
10.8%
25.1%
6.9%
94.7%
89.8%
81.2%
94.4%
93.2%
90.3%
79.6%
93.5%
7.8%
15.6%
23.4%
7.8%
80.0%
80.0%
80.0%
80.0%
93.8%
87.5%
81.3%
93.8%
Note. Optimal threshold is chosen on the basis of regulator loss function minimization with 𝛩 = 0.5.
The analysis of the predictive power of models suggests that the model with various lags turns out
to be the best among models with the restricted time lag of the explanatory variables (Table 4, last
column). In particular, this model slightly overrides the one-quarter lag model. The estimated variouslag model mostly consist of one-quarter lags of the explanatory variables (that recommended
themselves better compared to other lags in the pairwise models, see Table A2 in the Appendix) and
also includes some financial sector variables, which performed better at the deeper lags (the estimation
results are given in the Table A6 in the Appendix). The latter obviously increases various-lag model
predictive power when it is compared to the one-quarter lag analogue.
Chart 5 once again demonstrates a trade-off between the precision of forecasting the recessions
and the lead time when the signal of forthcoming crisis is issued. For the one-quarter lag model (first
column of the Chart), the predicted probability of recession clearly gets actual dating. For two-quarter
lag model, the rate of noise is higher, however the predicted probability rises more early than for the
one-quarter lag model. When the four-quarter lag model is considered, one can see that the model
becomes quite noisy but at the same timing lag turns out to be long enough to implement some policy
measures.
15
Chart 5. Actual and predicted probabilities of recession in USA, Germany and France in the models with
real and financial sector variables with different lags
1Q lag model
USA
2Q lag model
USA
4Q lag model
USA
1.2
100% 1.2
100%0.6
100%
1.0
80%
1.0
80% 0.5
80%
0.8
0.4
0.8
60%
0.6
60%
0.6
40%
0.4
60%
0.3
40%
0.4
40%
0.2
20% 0.1
20%
0.0
0%
0.0
0% 0.0
0%
BC phase ("1" - recession, "0" - expansion)
Prob. (recession), lag = 1 q
Unconditional threshold
1980 Q1
1982 Q3
1985 Q1
1987 Q3
1990 Q1
1992 Q3
1995 Q1
1997 Q3
2000 Q1
2002 Q3
2005 Q1
2007 Q3
2010 Q1
2012 Q3
0.2
1980 Q1
1982 Q3
1985 Q1
1987 Q3
1990 Q1
1992 Q3
1995 Q1
1997 Q3
2000 Q1
2002 Q3
2005 Q1
2007 Q3
2010 Q1
2012 Q3
20%
1980 Q1
1982 Q3
1985 Q1
1987 Q3
1990 Q1
1992 Q3
1995 Q1
1997 Q3
2000 Q1
2002 Q3
2005 Q1
2007 Q3
2010 Q1
2012 Q3
0.2
BC phase ("1" - recession, "0" - expansion)
Prob. (recession), lag = 2 q
Unconditional threshold
Germany
Germany
BC phase ("1" - recession, "0" - expansion)
Prob. (recession), lag = 4 q
Unconditional threshold
Germany
1.2
100% 1.2
100%1.0
100%
1.0
80%
1.0
80% 0.8
80%
60% 0.6
60%
40% 0.4
40%
0.8
60%
0.6
0.8
0.6
40%
0.4
0.4
20% 0.2
20%
0.0
0%
0.0
0% 0.0
0%
BC phase ("1" - recession, "0" - expansion)
Prob. (recession), lag = 1 q
Unconditional threshold
1980 Q1
1982 Q3
1985 Q1
1987 Q3
1990 Q1
1992 Q3
1995 Q1
1997 Q3
2000 Q1
2002 Q3
2005 Q1
2007 Q3
2010 Q1
2012 Q3
0.2
1980 Q1
1982 Q3
1985 Q1
1987 Q3
1990 Q1
1992 Q3
1995 Q1
1997 Q3
2000 Q1
2002 Q3
2005 Q1
2007 Q3
2010 Q1
2012 Q3
20%
1980 Q1
1982 Q3
1985 Q1
1987 Q3
1990 Q1
1992 Q3
1995 Q1
1997 Q3
2000 Q1
2002 Q3
2005 Q1
2007 Q3
2010 Q1
2012 Q3
0.2
BC phase ("1" - recession, "0" - expansion)
Prob. (recession), lag = 2 q
Unconditional threshold
France
France
BC phase ("1" - recession, "0" - expansion)
Prob. (recession), lag = 4 q
Unconditional threshold
France
1.2
100% 1.2
100%1.0
100%
1.0
1.0
80% 0.8
80%
60% 0.6
60%
40% 0.4
40%
80%
0.8
60%
0.6
0.8
0.6
40%
0.4
0.4
20% 0.2
20%
0.0
0%
0.0
0% 0.0
0%
BC phase ("1" - recession, "0" - expansion)
Prob. (recession), lag = 1 q
Unconditional threshold
BC phase ("1" - recession, "0" - expansion)
Prob. (recession), lag = 2 q
Unconditional threshold
16
1980 Q1
1982 Q3
1985 Q1
1987 Q3
1990 Q1
1992 Q3
1995 Q1
1997 Q3
2000 Q1
2002 Q3
2005 Q1
2007 Q3
2010 Q1
2012 Q3
0.2
1980 Q1
1982 Q3
1985 Q1
1987 Q3
1990 Q1
1992 Q3
1995 Q1
1997 Q3
2000 Q1
2002 Q3
2005 Q1
2007 Q3
2010 Q1
2012 Q3
20%
1980 Q1
1982 Q3
1985 Q1
1987 Q3
1990 Q1
1992 Q3
1995 Q1
1997 Q3
2000 Q1
2002 Q3
2005 Q1
2007 Q3
2010 Q1
2012 Q3
0.2
BC phase ("1" - recession, "0" - expansion)
Prob. (recession), lag = 4 q
Unconditional threshold
5. Conclusion
In this paper, leading indicators of the business cycle phases were first in the known empirical
literature constructed on the quarterly panel data set of OECD countries and Russia over 30 years.
Accounting for the business cycle historical data on a wide range of countries significantly increases the
quality and the validity of models and conclusions derived from them.
Using a dynamic specification of the business cycle model, I show that the existing leading
indicators in the OECD methodology are less precise in the recession forecasting that the models
developed in the paper. In particular, two types of models are studied: with real sector variables only
and with real and financial sector variables. The analysis suggests that adding financial sector variables
allows for significant increase in the quality of the constructed models; it results in substantial predictive
power growth and significant noise-to-signal ratio decline, as compared to the models with real sector
variables only.
I apply advance analysis of cut-off thresholds for leading indicator models based on the
optimization of regulator loss function. This method is widely used in the literature on financial crises,
was for the first time applied to leading indicators models of business cycle phase change.
I estimated business cycle leading indicator models at different forecasting horizons (from one to
four quarters). The obtained results demonstrated that there is a trade-off between forecasting
accuracy and earliness of recession signal. Best predictions were achieved for one-quarter lag model
(approximately 94% of the observations were correctly classified with the noise-to-signal ratio equaled
to 7%). Prediction results of the four-quarter lag model were the least precise (about 80% of recessions
were caught with the three times higher noise-to-signal ratio). However, this model still was viewed as
useful.
17
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19
Appendix – Additional empirical results
Table A1 – Descriptive statistics of indicators used in the business cycle phase change models
Variable name
Phase of the business cycle (1 - recession, 0 - absence of
recession*)
GDP growth rates, over corresponding quarter of the
previous year
Consumption, growth rate over corresponding quarter
of the previous year
Investment in fixed capital, growth rate over
corresponding quarter of the previous year
Inventories to GDP ratio, growth over corresponding
quarter of the previous year
Country GDP leading indicator, in OECD methodology, in
annual terms
Consumer confidence indicator, in OECD methodology,
growth rate over corresponding quarter of the previous
year
Business confidence indicator, in OECD methodology,
growth rate over corresponding quarter of the previous
year
US GDP leading indicator, in OECD methodology, in
annual terms
Current account balance to GDP ratio
REER index, 2005=100
Stock price index, growth rate per quarter
Spread between interest rate on loans and government
bonds interest rate
Spread between money market interest rate and
government bonds interest rate
Bank loans to GDP ratio
Number of obs.
Mean
Stand. dev.
Min.
Max
2621
0.15
0.36
0
1
3034
2.6
3.2
-18.6
34.6
3002
2.7
3.9
-27.9
42.0
2986
2.3
9.8
-55.0
87.9
3135
0.0
1.8
-9.0
8.4
2492
2.3
2.6
-12.8
16.4
2226
0.0
1.5
-11.3
9.0
2075
0.0
1.9
-8.3
8.3
3135
2.7
2.3
-6.0
9.0
2848
3135
2789
-0.8
101.0
2.4
5.6
13.6
10.1
-27.0
59.9
-57.2
17.5
176.2
54.3
3135
1.9
2.6
-5.8
14.6
3053
-1.1
2.3
-12.6
33.8
3036
81.4
57.6
5.7
346.2
*
Note: – 1 corresponds to the quarters of recession (at least 2 quarters of negative GDP growth rates, over corresponding quarter of the previous
year), 0 - all remaining observations
20
Table A2 – The predictive power of individual leading indicators of the business cycle phase change
Lag = 1 quarter
Lag =2 quarters
Lag =3 quarters
Dependent variable: phase of the business cycle
(1 - recession, 0 - absence of recession)
Coef-t
Pseudo R2
Coef-t
Pseudo R2
Coef-t
Pseudo R2
Macroeconomic variables
GDP growth rates, over corresponding quarter of
-0.560***
0.046
-0.047
0.001
0.074***
0.004
the previous year
Investment in fixed capital, growth rate over
-0.084***
0.017
-0.013
-0.001
0.021***
-0.002
corresponding quarter of the previous year
Country GDP leading indicator, in OECD
-1.028***
0.171
-0.837***
0.107
-0.348***
0.022
methodology, in annual terms
Consumer and business expectations
Consumer confidence indicator, in OECD
methodology, growth rate over corresponding
-0.984***
0.083
-0.813***
0.048
-0.527***
0.011
quarter of the previous year
Business confidence indicator, in OECD
methodology, growth rate over corresponding
-0.765***
0.065
-0.468***
0.012
-0.122**
-0.020
quarter of the previous year
External sector variables
US GDP leading indicator, in OECD methodology, in
-0.571***
0.076
-0.366***
0.036
-0.145***
0.007
annual terms
-0.098***
0.001
-0.103***
0.004
-0.120***
0.004
Current account balance to GDP ratio
REER index, 2005=100
0.040***
0.009
0.037***
0.008
0.033***
0.006
Financial sector variables
Stock price index, growth rate per quarter
-0.086***
0.049
-0.072***
0.039
-0.083***
0.049
Spread between interest rate on loans and
0.119***
0.008
0.150***
0.011
0.157***
0.009
government bonds interest rate
Spread between money market interest rate and
0.170***
0.013
0.208***
0.015
0.211***
0.015
government bonds interest rate
0.009***
0.003
0.010***
0.006
0.011***
0.007
Bank loans to GDP ratio
2
Lag =4 quarters
Coef-t
Pseudo R2
0.118***
0.010
0.026***
0.003
-0.067
-0.003
-0.190**
-0.008
0.080
-0.019
-0.002
0.000
-0.131***
0.034***
0.003
0.007
-0.037***
0.017
0.112**
0.008
0.085
0.004
0.012***
0.010
Notes. * – significant at 10%; ** – significant at 5%; *** – significant at 1%. Pseudo R is provided in differences from the corresponding indicator in the simple autoregressive
2
2
business cycle model (only lag of the dependent variable is included). Negative values in Pseudo R column mean that R in autoregressive model is larger than in the model with
additional explanatory variable.
21
Table A3 - Estimation results of business cycle phase models (lag of all explanatory variables - 1 quarter)
Dependent variable: phase of the business cycle
(1 - recession, 0 - absence of recession)
Dynamic model with
OECD GDP leading
indicator only
Dynamic model with
real sector variables
only
Dynamic model with
real and financial sector
variables
Static model with
real and financial
sector variables
4.591***
(16.25)
-1.027***
(-10.52)
2.408***
(5.67)
2.683***
(5.74)
-0.087***
(-2.82)
-0.632***
(-4.44)
-0.080**
(-2.55)
-0.748***
(-5.02)
-0.104***
(-2.97)
-1.258***
(-8.31)
-0.780***
(-7.18)
-0.482***
(-5.42)
0.032***
(2.67)
-0.674***
(-5.62)
-0.418***
(-4.50)
0.028**
(2.20)
-0.070***
(-4.15)
0.242***
(2.96)
-4.582***
(-3.14)
1941
0.729
-218.7
317.5
0.000
22
0.462
-0.646***
(-5.19)
-0.365***
(-4.49)
0.028**
(2.23)
-0.053***
(-3.60)
0.256***
(3.44)
-3.608**
(-2.44)
1941
0.701
-241.2
254.3
0.000
22
0.097
Explanatory variables
Dependent variable (lag = 1 quarter)
Country GDP leading indicator, in OECD methodology,
in annual terms
Investment in fixed capital, growth rate over
corresponding quarter of the previous year
GDP growth rates, over corresponding quarter of the
previous year
Consumer confidence indicator, in OECD
methodology, growth rate over corresponding
quarter of the previous year
US GDP leading indicator, in OECD methodology, in
annual terms
REER index, 2005=100
Stock price index, growth rate per quarter
Spread between money market interest rate and
government bonds interest rate
Constant
Number of observations
Pseudo R-sq
Log pseudolikelihood
LR-test, significance of equation as a whole
(P-value)
Number of countries
LR-test, absence of fixed effects (P-value)
-1.692***
(-3.84)
1941
0.699
-242.4
365.5
0.000
22
0.286
-5.407***
(-3.96)
1941
0.710
-233.5
328.9
0.000
22
0.318
Notes. t-statistics are in parentheses. * – significant at 10%; ** – significant at 5%; *** – significant at 1%
22
Table A4 - Estimation results of business cycle phase models (lag of all explanatory variables - 2 quarters)
Dependent variable: phase of the business cycle
(1 - recession, 0 - absence of recession)
Dynamic model with
OECD GDP leading
indicator only
Dynamic model with
real sector variables
only
Dynamic model with
real and financial sector
variables
1.608***
(6.88)
-1.075***
(-14.72)
0.855**
(2.54)
0.931**
(2.55)
-0.132***
(-5.37)
-0.084
(-0.81)
-0.796***
(-7.82)
-0.404***
(-6.92)
0.041***
(4.48)
-0.136***
(-5.26)
-0.167
(-1.47)
-0.667***
(-6.05)
-0.317***
(-4.85)
0.032***
(3.03)
-0.059***
(-3.68)
0.326***
(5.26)
0.012***
(3.31)
-5.251***
(-4.48)
1881
0.543
-360.8
297.6
0.000
22
0.002
Static model with
real and financial
sector variables
Explanatory variables
Dependent variable (lag = 2 quarters)
Country GDP leading indicator, in OECD methodology, in
annual terms
Investment in fixed capital, growth rate over corresponding
quarter of the previous year
GDP growth rates, over corresponding quarter of the
previous year
Consumer confidence indicator, in OECD methodology,
growth rate over corresponding quarter of the previous year
US GDP leading indicator, in OECD methodology, in annual
terms
REER index, 2005=100
Stock price index, growth rate per quarter
Spread between money market interest rate and
government bonds interest rate
Bank loans to GDP ratio
Constant
Number of observations
Pseudo R-sq
Log pseudolikelihood
LR-test, significance of equation as a whole
(P-value)
Number of countries
LR-test, absence of fixed effects (P-value)
-0.885**
(-2.30)
1881
0.545
-359.6
399.2
0.000
22
0.042
Notes. t-statistics are in parentheses. * – significant at 10%; ** – significant at 5%; *** – significant at 1%
23
-6.503***
(-6.06)
1881
0.505
-390.5
303.0
0.000
22
0.007
-0.143***
(-5.52)
-0.305***
(-3.13)
-0.667***
(-6.14)
-0.307***
(-4.72)
0.032***
(3.00)
-0.056***
(-3.60)
0.343***
(5.31)
0.012***
(3.23)
-4.923***
(-4.21)
1881
0.538
-364.8
279.0
0.000
22
0.000
Table A5 - Estimation results of business cycle phase models (lag of all explanatory variables - 4 quarters)
Dependent variable: phase of the business cycle
(1 - recession, 0 - absence of recession)
Dynamic model with
OECD GDP leading
indicator only
Dynamic model with
real sector variables
only
Dynamic model with
real and financial sector
variables
Static model with
real and financial
sector variables
-1.211***
(-4.40)
-0.703***
(-11.13)
-0.315
(-1.13)
-0.476
(-1.46)
-0.033**
(-2.03)
-0.030*
(-1.74)
-0.014
(-1.05)
-0.716***
-0.511***
-0.490***
(-7.71)
0.037***
(5.00)
-0.126***
(-3.48)
(-6.18)
0.025***
(2.92)
-0.125***
(-3.22)
-0.077***
(-8.49)
0.356***
(4.82)
0.025***
(5.75)
-5.942***
(-6.37)
1690
0.323
-486.7
274.9
0.000
22
0.000
(-6.03)
0.024***
(2.85)
-0.126***
(-3.25)
-0.077***
(-8.47)
0.356***
(4.89)
0.024***
(5.79)
-5.923***
(-6.35)
1690
0.321
-488.1
265.0
0.000
22
0.000
Explanatory variables
Dependent variable (lag = 4 quarters)
Country GDP leading indicator, in OECD methodology,
in annual terms
Investment in fixed capital, growth rate over
corresponding quarter of the previous year
Consumer confidence indicator, in OECD
methodology, growth rate over corresponding
quarter of the previous year
REER index, 2005=100
Current account balance to GDP ratio
Stock price index, growth rate per quarter
Spread between interest rate on loans and
government bonds interest rate
Bank loans to GDP ratio
Constant
Number of observations
Pseudo R-sq
Log pseudolikelihood
LR-test, significance of equation as a whole
(P-value)
Number of countries
LR-test, absence of fixed effects (P-value)
-0.743**
(-2.01)
1690
0.285
-513.8
187.3
0.000
22
0.023
-6.253***
(-7.12)
1690
0.216
-563.4
189.4
0.000
22
0.000
Notes. t-statistics are in parentheses. * – significant at 10%; ** – significant at 5%; *** – significant at 1%
24
Table A6 - Estimation results of business cycle phase models (various lags of explanatory variables)
Dependent variable: phase of the business cycle
(1 - recession, 0 - absence of recession)
Explanatory variables
Dependent variable (lag = 1 quarter)
Country GDP leading indicator, in OECD methodology, in
annual terms (lag = 1 quarter)
Investment in fixed capital, growth rate over corresponding
quarter of the previous year (lag = 1 quarter)
GDP growth rates, over corresponding quarter of the
previous year (lag = 1 quarter)
Consumer confidence indicator, in OECD methodology,
growth rate over corresponding quarter of the previous
year (lag = 1 quarter)
US GDP leading indicator, in OECD methodology, in annual
terms (lag = 1 quarter)
Dynamic model with Dynamic model with Dynamic model with real
OECD GDP leading
real sector variables
and financial sector
indicator only
only
variables
4.566***
(15.14)
-1.048***
(-9.68)
2.307***
(5.12)
2.649***
(5.13)
-0.071**
(-2.37)
-0.705***
(-4.59)
-0.831***
-0.065**
(-2.04)
-0.803***
(-4.64)
-0.760***
-0.077**
(-2.14)
-1.322***
(-7.86)
-0.731***
(-6.83)
-0.496***
(-4.93)
(-5.81)
-0.366***
(-3.38)
-0.076***
(-4.46)
0.323***
(3.49)
0.012**
(2.50)
-2.353***
(-4.16)
1686
0.736
-189.4
238.6
0.000
22
0.096
(-5.28)
-0.323***
(-3.32)
-0.055***
(-3.58)
0.362***
(4.04)
0.014***
(2.93)
-1.437**
(-2.36)
1686
0.711
-207.7
192.1
0.000
22
0.004
Stock price index, growth rate per quarter (lag = 1 quarter)
Spread between money market interest rate and
government bonds interest rate (lag = 3 quarters)
Bank loans to GDP ratio (lag = 4 quarters)
Constant
Number of observations
Pseudo R-sq
Log pseudolikelihood
LR-test, significance of equation as a whole
(P-value)
Number of countries
LR-test, absence of fixed effects (P-value)
-1.625***
(-3.66)
1686
0.702
-213.7
324.4
0.000
22
0.266
-2.102***
(-3.73)
1686
0.713
-206.4
269.4
0.000
22
0.195
Notes. t-statistics are in parentheses. * – significant at 10%; ** – significant at 5%; *** – significant at 1%
25
Static model with real
and financial sector
variables
Table A7 – Dynamic business cycle phase models with real and financial sector variables, logit with dummy variables and fixed effects logit estimates
Dependent variable: phase of the business
cycle (1 - recession, 0 - absence of recession)
Explanatory variables
Dependent variable (lag = k quarters)
Investment in fixed capital, growth rate
over corresponding quarter of the previous
year
GDP growth rates, over corresponding
quarter of the previous year
Consumer confidence indicator, in OECD
methodology, growth rate over
corresponding quarter of the previous year
US GDP leading indicator, in OECD
methodology, in annual terms
REER index, 2005=100
Stock price index, growth rate per quarter
Spread between money market interest
rate and government bonds interest rate
Bank loans to GDP ratio
2 lags model
Logit with DV Logit with FE
4 lags model
Logit with DV Logit with FE
1.035***
(2.63)
0.906***
(2.78)
-0.489
(-1.51)
-0.468*
(-1.67)
1q
2.649***
(5.13)
2.550***
(5.64)
-0.138***
-0.131***
-0.031*
-0.030*
1q
-0.065**
-0.064*
(-4.86)
-0.150
(-1.23)
(-4.94)
-0.162*
(-1.80)
(-1.76)
(-1.86)
1q
(-2.04)
-0.803***
(-4.64)
(-1.90)
-0.751***
(-5.03)
-0.670***
-0.651***
-0.513***
-0.496***
1q
-0.760***
-0.722***
(-5.58)
-0.326***
(-4.64)
0.031***
(2.73)
-0.074***
(-5.74)
0.328***
(4.62)
0.015***
(3.99)
(-7.43)
-0.305***
(-5.46)
0.031***
(2.79)
-0.057***
(-5.11)
0.314***
(5.11)
0.011***
(3.52)
(-6.17)
(-7.33)
1q
(-5.81)
-0.366***
(-3.38)
(-5.89)
-0.346***
(-4.14)
-0.076***
(-4.46)
0.323***
(3.49)
0.012**
(2.50)
-0.073***
(-4.46)
0.308***
(3.40)
0.011**
(2.31)
-2.353***
(-4.16)
1686
0.736
-189.4
238.6
0.000
22
1686
0.749
-162.5
970.1
0.000
22
0.025***
(2.97)
-0.077***
(-8.43)
0.358***
(4.84)
0.025***
(5.76)
-0.126***
(-3.23)
-5.992***
(-6.40)
1686
0.323
-485.8
273.4
0.000
22
Current account balance to GDP ratio
Constant
Number of observations
Pseudo R-sq
Log (pseudo)likelihood
LR-test, significance of equation as a whole
(P-value)
Number of countries
lag
Various lags model
Logit with DV
Logit with FE
-5.231***
(-4.15)
1686
0.557
-317.8
270.6
0.000
22
1881
0.542
-326.4
772.4
0.000
22
Notes. t-statistics are in parentheses. * – significant at 10%; ** – significant at 5%; *** – significant at 1%
26
0.024***
(2.74)
-0.075***
(-8.30)
0.348***
(5.86)
0.024***
(7.29)
-0.123***
(-3.46)
1690
0.308
-448.7
398.9
0.000
22
1q
3q
4q
Table A8 - Quality of prediction of business cycle phase models, lag of all explanatory variables - 2 quarters
Optimal threshold
Full Sample
Noise-to-signal ratio
Recessions correctly
predicted
Absence of recessions
correctly predicted
Russia
Noise-to-signal ratio
Recessions correctly
predicted
Absence of recessions
correctly predicted
Dynamic model
with OECD GDP
leading indicator
only
0.13
Dynamic
model with
real sector
variables only
0.17
Dynamic model
with real and
financial sector
variables
0.19
Static model
with real and
financial sector
variables
0.16
13.8%
12.4%
10.8%
12.4%
91.4%
87.2%
89.8%
91.0%
87.4%
89.2%
90.3%
88.7%
6.3%
12.5%
15.6%
15.6%
100.0%
100.0%
80.0%
80.0%
93.8%
87.5%
87.5%
87.5%
Note. Optimal threshold is based on regulator loss function with Θ=0.5%.
Table A9 - Quality of prediction of business cycle phase models lag of all explanatory variables - 4 quarters
Optimal threshold
Full Sample
Noise-to-signal ratio
Recessions correctly
predicted
Absence of recessions
correctly predicted
Russia
Noise-to-signal ratio
Recessions correctly
predicted
Absence of recessions
correctly predicted
Dynamic model
with OECD GDP
leading indicator
only
0.19
Dynamic
model with
real sector
variables only
0.14
Dynamic model
with real and
financial sector
variables
0.19
Static model
with real and
financial sector
variables
0.15
21.8%
35.2%
10.8%
25.3%
73.7%
79.7%
89.8%
82.0%
83.9%
72.0%
90.3%
79.3%
31.3%
41.7%
15.6%
23.4%
60.0%
60.0%
80.0%
80.0%
81.3%
75.0%
87.5%
81.3%
Note. Optimal threshold is based on regulator loss function with Θ=0.5%.
27
Table A10 - Quality of prediction of recession models, various lags of explanatory variables
Optimal threshold
Full Sample
Noise-to-signal ratio
Recessions correctly
predicted
Absence of recessions
correctly predicted
Russia
Noise-to-signal ratio
Recessions correctly
predicted
Absence of recessions
correctly predicted
Dynamic model
with OECD GDP
leading indicator
only
Dynamic
model with
real sector
variables only
Dynamic model
with real and
financial sector
variables
Static model
with real and
financial sector
variables
0.15
0.09
0.15
0.19
7.1%
11.4%
6.9%
7.3%
92.9%
96.2%
94.4%
93.2%
93.4%
89.0%
93.5%
93.2%
0.0%
15.6%
7.8%
7.8%
100.0%
80.0%
80.0%
80.0%
100.0%
87.5%
93.8%
93.8%
Note. Optimal threshold is based on regulator loss function with Θ=0.5%.
28