Global Recessions and Booms: What do Probit models tell us?

We present non-linear binary Probit models to capture the turning points in global economic activity as well as in advanced and emerging economies from 1980 to 2016. For that purpose, we use four different business cycle dating methods to identify the regimes (upswings, downswings). We find that especially activity-driven variables are important indicators for the turning points. Moreover, we identify similarities and differences between the different regions in this respect. Deutsche Zusammenfassung: Das Papier analysiert nicht-lineare binäre Probit-Modelle, um Wendepunkte der Weltkonjunktur sowie in fortgeschrittenen und aufstrebenden Volkswirtschaften von 1980 bis 2016 zu bestimmen. Zur Identifikation der Regime (Aufund Abschwung), verwenden wir vier verschiedene Konjunkturzyklusbestimmungsmethoden. Als Ergebnis ergibt sich, dass vor allem aktivitätsgetriebene Variablen wichtige Indikatoren der Wendepunkte sind. Die Determinanten der Wendepunkte lassen Unterschiede und Gemeinsamkeiten in den unterschiedlichen Regionen erkennen.


Introduction
One of the greatest challenges of empirical business cycle research is the timely detection and modelling of business cycle turning points. In the US and the euro area, there are the Business Cycle Dating Committees of the NBER and the CEPR, respectively, which date the turning points in the dynamics of economic activity. However, at a global level -be it worldwide, advanced economies, emerging market economies -such dating does not exist and the business cycle analysis is quite limited. To detect as well as model the turning points in a global context, we make use of the dynamic and non-linear bivariate Probit models.
Dynamic Probit models estimate a multi-regime variable directly with the help of one or more economic variables (e.g. Haltmaier 2008, Christiansen et al. 2014  There are only few papers on turning points in global economic activity. Ferrara & Marsilli's (2014) approach builds on a Factor-Augmented Mixed Data Sampling model of various countries and sectors worldwide. Ravazzolo & Vespignani (2015) also concentrate on growth rates and evaluate the quality of world steel production compared to Kilian's index of global economic activity and the index of OECD world industrial production. Stratford (2013) uses linear models to investigate several global indicators' ability to nowcast world trade and world GDP. He finds that the indicators are most helpful during periods of large swings in world growth. However, their usefulness fluctuates greatly over time. The only paper which addresses turning points directly and on a global level within a non-linear framework is Camacho & Martinez-Martin (2015). They propose a two-state Markov-switching dynamic factor model to produce short-term forecasts of world GDP and to compute business cycle probabilities.
Our analysis differs in several aspects from these papers. First, and in contrast to Ferrara & Marsilli (2014), Ravazzolo & Vespignani (2015) and Stratford (2013), we concentrate solely and directly on turning points of global GDP growth. Second, we use Probit models to capture the turning points on a global level. So far, these methods have been predominantly applied to a national level. Third, we use several business cycle turning point dating methods to evaluate the models. Fourth, the indicator variables are included individually, not as factors as in Camacho & Martinez-Martin (2015) and Ferrara & Marsilli (2014).
Our results reveal that lagged GDP growth rates and activity-based variables are the best indicators of upswing and downswing periods. The emerging market economies are the hardest to model. The remainder of the paper is structured as follows. Section 2 describes the independent and dependent variables used. Following this, section 3 introduces the Probit models and presents their results. Section 4 summarises and concludes.

Data
We use seasonally-adjusted quarterly data for the sample 1980Q1-2016Q4. World activity is measured by real quarterly world GDP, derived from a PPP-weighted aggregation of national GDP data based on national sources. We also distinguish between real quarterly GDP for advanced economies and emerging economies (see Appendix A for details).
The independent variables considered can be grouped as follows:  Activity data: industrial production in OECD countries and emerging market economies, world steel production (see Ravazzolo and Vespignani, 2015), the Kilian index of real world economic activity, the Goldman Sachs Global Leading Indicator, the Composite Leading Indicator by the OECD, a global factor derived by Delle Chiaie, Ferrara and Giannone (2017) and the Conference Board US Leading Economic Index.
 Survey data: consumer confidence in OECD countries and the US.
 Financial data: the US term spread (10years minus 3 month), the US BBB bond spread, S&P500, M1 and M3 for OECD countries.
 Commodity prices: oil prices in USD and indices of metal prices and non-oil commodity prices.
The results reported in section 3 concentrate, however, on those independent variables that turned out to be statistically significant in the various specifications selected and in line with economic reasoning.
Chart 1 plots quarterly world, advanced economy and emerging economy real GDP growth from 1980Q1 to 2016Q4. We distinguish two types of periods with different mean growth rates: (i) negative or slightly positive, but low growth rates; (ii) periods of robust growth (either briefly following recessions or on a more prolonged basis). The only common recession in all three country groupings is the great recession 2009 which affected global economies, AEs as well as EMEs, although the latter to a lesser extent.
In what follows, our aim is to use model-based techniques and judgmental approaches to detect these alternative episodes, and thereafter to estimate probabilities of staying in a regime or moving to a different one.

Methodology
One methodology commonly used to analyse turning points in economic activity is the Probit method. A textbook treatment may be found in Verbeek (2012). Recent business cycle applications are, inter alia, Chauvet & Potter (2010), Christiansen et al. (2014), Nyberg (2014, Fossati (2015), Hsu (2016), and Proaño (2017). In our case, a value of the binary variable of "0 signals a "downswing" whereas the value "1" indicates an "upswing". The objective of the analysis is to assess with what probability the variable changes its value at a specific date.
Formally, the probit method can be represented as follows: (1) where Pi represents the probability that a specific event (e.g. an upswing) will occur; (.) is the distribution function of the standard normal distribution (the so-called probit function); u stands for the normally distributed residuals. Xi is the vector of the independent variables, in our analysis specifically the potential variables that explain an upswing or a downswing or, more specifically, a turning point. The ß coefficients of the independent variables of this nonlinear estimation approach can only be determined by iteration. To estimate these coefficients, we use the Newton-Raphson method with Marquardt steps to obtain parameter estimates. The standard errors are estimated by the inverse of the estimated information matrix. The latter is computed with the help of the observed Hessian.
A precondition for the empirical application of probit models is the specification of the binary variable. As there is neither an official business cycle dating available at the global level nor for advanced or emerging economies as a whole (as, for example, for the US from the NBER), we rely on our own dating. For that purpose, we use four variants in what follows: -"Acceleration" is defined as 1 if there is an acceleration in year-on-year real GDP growth in at least three out of five quarters (measured on a centred rolling basis), and 0 otherwise (p_yoy), -"High growth" is 1 in any period if the centred five-quarter moving average quarterly growth rate in real GDP is above the 40 th (35 th ) percentile of the series, and 0 otherwise (p_pct40(35)), -5 --"Bry/Boschan" is a quarterly analogue to the Bry-Boschan algorithm to detect turning points in time series (bbq) (see Bry & Boschan, 1971;Harding & Pagan, 2002). This methodology identifies a turning point by using the definition that a peak happens at time t if y(t-k),..,y(t-k+1) < y(t) > y(t+1),…,y(t+k), where k is the so-called symmetric window parameter (turnphase). It needs to be set. For for quarterly data, usually k=2.
Chart 2  What is also evident is that the year-over-year growth rates in the advanced economies declined to a lesser extent compared to the emerging world in the Great Recession. In the former, growth rates declined to around -5%, while they did not turn into negative territory in the latter.
In what follows, we describe in detail the results for the best model(s) of one indicator and refer to similarities and differences of the others in footnotes and separate paragraphs. Our preferred indicator is the year-over-year procedure as it looks especially at turning points and yields in most of the cases-economically and statistically -the most promising results.

Chart 2: Global GDP growth and the binary variables
Note: quarterly: quarterly growth rate of real GDP; yoy: year-over-year growth rate of real GDP. p_yoy: 1 if there is an acceleration in year-on-year real GDP growth in at least three out of five quarters, and 0 otherwise; p_pct40(35): 1 in any period if the centred five-quarter moving average quarterly growth rate in real GDP is above the 40th (35th) percentile of the series, and 0 otherwise; bbq: quarterly analogue to the Bry-Boschan algorithm.

Global GDP
The explanatory variables in the best Probit model include the contemporaneous and lagged Goldman Sachs Global Leading Indicator. 2 This is also true for the other binary variables.
The equation reads as   These conclusions are underscored by Table 2. Here, an assessment based on the model is correct if the predicted probability is below the cut-off value of C = 0.5 in the case of y = 0 or above 0.5 in the case of y = 1. It is obvious that in 76.2 % of the cases the model prediction is correct (the specificity, i.e. the correct y = 0 observations, is 81.7 %; the sensitivity, i.e. the correct y = 1 observations, is 69.1 %). For comparative purposes, the right part of Table 2 shows the results of a model with a constant probability, which arises when one estimates the model only with a constant. It reveals that our preferred model is over 49 % better (calculated as the percent of incorrect predictions corrected by the equation, i.e. (0.778-0.563)/(1-0.563)) than the model with constant probability, which generates 56.3% correct values. predicted probability  C = 0.5 and act. y=0 or predicted probability > C = 0.5 and act. y=1.
For the other classification schemes of upswings and downswings, the statistical properties and the economic interpretation are not as good as for p-yoy. 4 However, they all lead to an improvement compared to a model with constant probability.    Table 3 compares the fitted expected to the actual values by group (ten deciles) and calculates the Hosmer-Lemeshow test statistic. This test of goodness-of-fit shows that, in general, the model behaviour is quite good. There are some problems in the 5 th decile in which the accuracy is only slightly above 50 %. In general, however, differences between "actual" and "expected" are not too large. Therefore, we do not reject the model as providing a sufficient fit to the data.   predicted probability  C = 0.5 and act. y=0 or predicted probability > C = 0.5 and act. y=1.

Advanced economies
The model with the binary variable specified by "High growth (40)" performs slightly better in discriminating between regimes and with regard to the overall fit of the model. In contrast, the results of all others binary variable specifications are worse than the one presented.

Emerging markets
All in all, the emerging market economies were the hardest to model. As with the advanced economies, the best model includes lagged quarterly GDP growth rates, but in the emerging market case together with industrial production in emerging markets (see Equation 4). This result is in line with Baumann et al. (2018) who use a three regime classification to analyse emerging market economies with a Markov Switching framework. Overall, we have 140 -12 -observations, of which 77 belong to regime 0 and 63 to regime 1. The model has the lowest R² and the highest standard error of all the regional models considered.

Summary, conclusions
In this paper, we tried to shed light on the question what determines the turning points of world GDP on the one side and advanced as well as emerging economies on the other from the beginning of the 1980s onwards. For that purpose, we constructed different binary variables to capture upswings and downswings to integrate and explain them with the help of Probit models. It seems that world and advanced economy activity can be captured better than that in emerging markets. This could be due to the poor data quality. The most important variables in these exercises are lagged GDP growth rates and activity-based indicators.
Interestingly, the yield spread does not yield significant results in detecting turning points.
However, against the background that we neither have yield data on a global level nor for advanced and emerging economies as a whole, this is not too surprising.
It might be interesting to combine our approach with the Markov-Switching methodology to identify the turning points. These models might also be helpful to decide whether the tworegime case is really the correct one or whether we should take more than two regimes into account. This is left to a separate paper, see Baumann et al. (2018).

Appendix A: Data used
Activity data: -real GDP growth, national accounts at country level weighted using PPP shares of world total, ECB and WEO databases -the EME GDP aggregate is based on ECB data after 1995, which are linked up to IMF International Financial Statistics data (in year-on-year growth rates) before 1995 -industrial production in OECD countries, index excluding construction, OECD -industrial production in emerging market economies (EMEs) excluding construction weighted using PPP shares of EMEs total, country statistical offices -world crude steel production in thousand tonnes, World Steel Association Note: quarterly: quarterly growth rate of real GDP; yoy: year-over-year growth rate of real GDP. ee: emerging economies; p_yoy: 1 if there is an acceleration in year-on-year real GDP growth in at least three out of five quarters, and 0 otherwise; p_pct40 (35): 1 in any period if the centred five-quarter moving average quarterly growth rate in real GDP is above the 40th (35th) percentile of the series, and 0 otherwise; bbq: quarterly analogue to the Bry-Boschan algorithm.