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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. 2 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. 3 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 4 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 5 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. 6 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 – 9 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 10 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). 11 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%). 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Chicago, London: The University of Chicago Press 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