The role of oil prices on the Russian business cycle

We study the role of oil prices in forecasting Russian recession periods with probit models. Our ndings suggest that uctuations in nominal oil prices are useful predictors of the Russian business cycle, even when controlling for a number of classic recession predictors. However, in line with international ndings, the term spread turns out to be the most powerful predictor of future recessions. Overall, the best in-sample t is found using a model including the term spread and the oil price variable as predictors. The pseudo out-ofsample forecasts con rm the ndings.


Introduction
Russia is the second largest producer of natural gas and the third largest producer of oil in the world, with over 106 billion barrels of oil reserves at the end of 2017. Furthermore, it is the largest exporter of oil in the world (BP, 2018). Exports of mineral products (consisting mainly of oil and natural gas) accounted for 59.2% of total Russian exports in 2016 (Rosstat, 2017). Given these gures, it is undeniable that changes in oil and gas prices have a large impact on the economic uctuations in Russia. In this article, we will analyze the impact of oil price changes on Russian business cycle uctuations by means of probit models.
The role of oil prices as a source of business cycle uctuations has been a topic of wide interest, and was sparked by the two oil crises in the 1970's. Early contributions in the literature include Hamilton (1983), who found statistical evidence of increases in oil prices leading recessions in the U.S., and since then, the topic has received wide attention (see, e.g., Serletis and Elder, 2011 and references therein). Extensions to the literature have suggested that the relationship may be asymmetric (Mork, 1989;Hamilton, 2011), as well as dependent on whether the shock in oil price is demand or supply driven (Brown and Yucel, 2002;Kilian, 2009). Furthermore, the eects of oil price shocks vary between oil producing and importing countries (see, e.g., Mork et al., 1994), where increases of oil prices have found to have signicant positive eects on output in oil exporting countries (see, e.g., Berument et al., 2010).
In the literature on business cycle uctuations, binary dependent variable models, such as probit and logit models, have been a standard tool in modelling the probability of recessions since the seminal paper of Estrella and Hardouvelis (1991). The ndings based on these models have identied the term spread and stock market returns as useful predictors of U.S. recessions (see, e.g., Estrella and Mishkin, 1998;Chauvet and Potter, 2005;Nyberg, 2010;Ng, 2012). Later research has suggested that also sentiment (Christiansen et al., 2014) and credit (Pönkä, 2017) variables have predictive ability for future recession periods.
We contribute to the literature by studying oil price business cycle relationship in Russia. Although the Russian economy is in many ways dependent on oil production, making it an ideal candidate for research on the topic, the relationship between oil prices uctuations and recession periods in Russia has not been studied widely in a formal econometric setting. The existing literature has examined the relationship between oil prices and real GDP growth in Russia in a structural vector autoregressive (SVAR) framework (see, e.g., Rautava, 2004;Ji et al., 2015;Alekhina and Yoshino, 2018). This diers from our approach, since we are more explicitly interested in the role of oil price uctuations as a leading indicator of recessions and expansions. Nevertheless, the ndings of the SVAR literature have documented that real GDP in Russia exhibits a positive response to oil price increases.
Further motivation for analysing the relationship is given in Figure 1, indicating that three latest recession periods in Russia (as dened in Section 3.1) have coincided with decreases in oil prices. Obviously, there are also other contributing factors to these recessions, discussed e.g. in Smirnov et al. (2017), but the relationship implied by the gure calls for a formal investigation between oil prices and Russian recession periods. The ndings of our study suggest that changes in oil prices have predictive ability on future recession periods. Furthermore, models combining the oil price variable with classic recession predictors improve the in-sample performance, as measured with the area under the receiver operating characteristic curve (AUC). However, our ndings point out that the term spread is the most powerful predictor of future recessions in Russia, which is in line with ndings from previous literature on other countries (see, e.g., Estrella and Mishkin, 1998;Nyberg, 2010) that have highlighted the role of the term spread as a leading indicator. The best in-sample t is obtained with a model using the term spread and the oil price variable as predictors. The out-ofsample ndings are in line with the in-sample results, as models including the term spread and change in oil prices yield the highest AUC:s.
The rest of this paper is organised in the following way. In Section 2, we describe the employed model and goodness-of-t measures. In Section 3, we discuss the data, including the business cycle chronology and the explanatory variables. In Section 4, we present the empirical ndings of the study. Finally, Section 5 concludes.

Empirical Approach
In this section we present the econometric framework and discuss goodnessof-t measures related to the probit model.

The probit model
We are interested in understanding the drivers of business cycle uctuations in Russia, and especially on the role of oil price changes as an explanatory variable. Therefore, throughout the analysis, the dependent variable is the status of the Russian business cycle. In practice, this variable is a binary indicator given by: , if the economy is in a recession, 0, if the economy is in an expansion. (1) As the methodology we employ probit models using lagged potential predictors, such as changes in oil prices, as explanatory variables. To determine the conditional probability of a recession (p t ), a univariate probit model is specied as where Φ(·) is the cumulative distribution function of the standard normal distribution and π t is a linear function of the variables in the information set Ω t−1 . In a standard static probit model, π t is specied as where ω is a constant term and x t−k includes the k:th lagged values of the explanatory variables. We estimate the parameters of the model using maximum likelihood and compute robust standard errors, similarly to Kauppi and Saikkonen (2008).
We also consider an extension to the conventional static probit model. More explicitly, we employ the rst-order autoregressive probit model of Kauppi and Saikkonen (2008) An autoregressive structure is introduced into the model by including the lagged value of the linear function π t . The autoregressive specication of the probit model has been found by Nyberg (2010Nyberg ( , 2014 to outperform static models in predicting U.S. and German recessions.

Goodness-of-t Measures
There are several possible measures for evaluating the goodness-of-t of binary dependent variable models. The most obvious one is the percentage of correct predictions, typically referred to as the success ratio (SR). Formally, a signal forecast for the state of the economy y t may be dened aŝ where the conditional probability of recession p t is obtained from a probit model, dened in equation (2). If p t is larger than a threshold ξ, we get a signal forecastŷ t = 1 (i.e. recession), and vice versaŷ t = 0 if p t ≤ ξ.
In this paper, we employ the threshold ξ = 0.5 for SR, which can be seen as natural threshold in (5). However, this is not a fully objective selection, and in some previous studies lower values for ξ have also been used (see, e.g. Nyberg, 2010). In practice, the assigned threshold involves a tradeo between type I and II errors, i.e. the false positive and negative rates. The success ratio is important from the practical forecasters' point of view, especially if decisions are based on signals given by the model. However, as recession periods are uncommon compared to expansion periods, the success ratios of relatively uninformative models might turn out to be high. To test whether the value of the success ratio is higher than that obtained when the realized values y t and the forecastsŷ t are independent, we employ the predictability test (PT) of Pesaran and Timmermann (2009).
Another way to measure the goodness-of-t of binary dependent variable models is the Receiver Operating Characteristic (ROC) curve, which has become a commonly used method in economic applications in the recent years (see, e.g., Schularick and Taylor, 2012;Christiansen et al., 2014;Pönkä, 2016). The ROC curve is a mapping of the true positive rate and the false positive rate for all possible thresholds 0 ≤ ξ ≤ 1, described as an increasing function in [0, 1] × [0, 1] space, with T P (ξ) plotted on the Y -axis and F P (ξ) on the X-axis. A ROC curve above the 45-degree line indicates forecast accuracy superior to a coin toss. Given that it takes into account all possible thresholds ξ, the ROC curve is a more robust method to evaluate the goodness-of-t of a model than the success ratio. The information in the ROC curve is typically summarized by the area under the ROC curve (AUC), which is the integral of the ROC curve between zero and one. Therefore, the AUC also gets values between 0 and 1, with the value of 0.5 corresponding a coin toss and the value 1 to a perfect forecast. Any improvement over the AUC=0.5 indicates statistical predictability. We test the null hypothesis of AUC= 0.5 implying no predictability using standard techniques (see Hanley and McNeil, 1982).
A commonly used measure-of-t for binary dependent variable models is the pseudo-R 2 of Estrella (1998). The measure is dened as where logL u and logL c are the maximum values of the unconstrained and constrained log-likelihood functions respectively, and T is the sample size. The pseudo-R 2 takes on values between 0 and 1, and can be interpreted in the same way as the coecient of determination (R 2 ) in the usual linear predictive regression model. In Section 4, we report the adjusted form of (8) (see Estrella, 1998) that takes into account the trade-o between improvement in model t and the use of additional estimated parameters.

Data
In this section, we discuss the data employed in this study. The sample used in the study is 19972017 and the data is quarterly.

The Russian Business Cycle
One of the key issues in terms of data is the selection of the business cycle chronology, as dened in equation (1). Unlike in the U.S., where the Business Cycle Dating Committee of the National Bureau of Economic Research (NBER) 2 determines the ocial turning points, in Russia there is no such ocial chronology of recessions and expansions. However, there are a number of ways to determine the turning points based on data. Smirnov et al. (2017) recently established a monthly reference chronology for the Russian economic cycle from the early 1980s to mid-2015, using various seasonal adjustment methods and dating methods. In this paper, we dene the turning points for business cycles using the Bry-Boschan (BB) algorithm (Bry and Boschan, 1971), which is a commonly used method in the literature. The dating is based on the algorithm used for seasonally adjusted quarterly real GDP data for the period 1997Q12017Q4. The sample length is determined by the availability of the predictive variables, described in the following Section. The resulting chronology is presented in Table 1 and was plotted with the Brent oil price in Figure 1. The BB algorithm nds three recession periods in the period 1997Q1 2017Q4. These ndings are in line with those of Smirnov et al. (2017), who use monthly data in their reference chronology.

Predictive Variables
The oil price variable selected for the study is the Brent Crude oil price in U.S. dollars, since it is a major global benchmark price for oil purchases. The main specication used is the quarterly change in prices (DOIL). 3 As we are interested in studying the predictive ability of oil prices over and above other predictors, we employ a number of commonly used predictors of recessions as control variables. Several studies on other countries have suggested that nancial variables are useful predictors of real activity and recessions (see, e.g., Stock and Watson, 2003). Among the most useful nancial leading indicators are the term spread (TS) and stock returns (RET) (see, e.g., Estrella and Mishkin, 1998;Nyberg, 2010). Therefore, these predictors are obvious choices as additional predictors. The term spread is dened as the dierence between the 10-year government bond yield and the 3-month interest rate 4 . The stock return is dened as the logarithmic rst dierence on the stock market index 5 .
Along with these variables, also the short term interest rate has been employed as an explanatory variable in a number of studies (see, e.g. Wright, 2006;Pönkä, 2017). The ndings of Wright (2006) suggest that a model including a short-term interest rate as a predictor alongside the term spread achieves a better in-sample t in predicting U.S. recession periods. Sentiment variables, such as consumer condence indices, are a particularly interesting group of variables, due to their forward-looking nature. Christiansen et al. (2014) nd that the consumer condence and purchasing managers' indices are useful predictors of US recession periods, even when combined with classic recession predictors and common factors based on a large panel of economic and nancial variables. Based on these ndings, we include the consumer condence index (CCI) in our set of potential predictors 6 .
In Table 2, the predictive variables have been listed, along with the abbreviations and the starting points of the sample for each variable. Altogether, some of the data are already available from the beginning of 1997, so we are able to include the rst recession period (1997Q41998Q3)   The correlations between the predictive variables are presented in Table  3. The highest correlations are found for the change in consumer condence (DCCI). It is positively correlated with the term spread and the change in oil prices (DOIL) and negatively correlated with the change in the short term interest rate (DTM). The correlation between the oil price and term spread variables are also close to 0.5. In this Section, we present the main ndings of our research. We rst study the performance of the individual explanatory variables as predictors of the Russian business cycle. We allow each predictor to have a lag length beween one to four quarters, as ndings from previous literature has suggested that dierent variables have predictive ability at dierent lag lengths. so high in the rst two years of the sample that using the data from that point onwards caused problems with the estimation of the model.  Kauppi and Saikkonen, 2008). The goodness-of-t measures are described in detail in Section 2. In the table, *, **, and *** denote the statistical signicance of the estimated coecients and the AUC at 10%, 5% and 1% signicance levels, respectively.
The ndings in Table 4 illustrate that changes in oil prices do have predictive ability on future recession periods (using rst and second lags). The coecient is of the expected negative sign, implying that a fall in oil prices is related to an increased recession risk. However, it is the term spread that performs clearly the best as a predictor. The model including the rst lag of the term spread yields an AUC of 0.969, whereas the one with the change in oil price yields an AUC of 0.743, which is also relatively high for a single predictor. The dierence in t is only partly explained by the shorter sample used for the term spread. In line with previous ndings in the literature, the term spread has predictive ability even using longer lag lengths. The AUC for the model including the fourth lag of the term spread is 0.829.
The ndings from the single predictor models were rather promising. Following the typical convention, we proceed by estimating multiple predictor models. Moreover, we estimate models including the oil price variable with each of the other predictors. We allow each variable to have a lag between one and four quarters, and report the best performing models in Table 5. In the case of the oil price variable, it turns out that either the second or the third lag of the variable is selected into the model. 0.797*** 0.812*** 0.812*** 0.974*** 0.973*** Notes: This table presents the ndings from probit models for Russian recessions. In the table, *, **, and *** denote the statistical signicance of the estimated coecients, the Pesaran and Timmermann (2009) (PT) predictability test for the success ratio, and the AUC at 10%, 5% and 1% signicance levels, respectively. See also notes to Table 4. In general, we nd that models combining the oil price variable with classic recession predictors (Table 5) yield stonger results than single-predictor models (Table 4). Model 21 includes the oil price variable and the short term interest rate as predictors. The AUC is 0.797, which is higher than for the individual predictors in Table 4, but lower than for the other two predictor models (Models 2224). In Models 2123, the coecient of the oil price variable is statistically signicant, indicating that the oil price variable has predictive ability over and above the interest rate, stock return, and consumer condence index variables. Model 24, including the term spread and the oil price, yields the highest AUC among the two-predictor models (0.974). This is higher than for the single-predictor model (Model 5) including the term spread. However, when used in combination with the term spread, the coecient for the oil price variable is no longer statistically signicant. The reason for this nding may lie in the relationship between these two variables. In Section 3.2, we noted that these variables are relatively highly correlated. The relationship between these two variables may be described as follows. A large reduction in oil prices leads to a weakening in the ruble 8 . This in turn increases import prices, leading to higher ination. As a reaction to higher ination, short-term interest rates are raised. In extreme cases, the short term rates exceed the long term government bond yields, as happened both in 2008 and 2014.
In the last column of Table 5, we present the ndings for the best performing three-variable model (Model 25). This model includes the short term interest rate in addition to the oil price and term spread variables. The ndings indicate that increasing the number of predictive variables from two to three does not improve the model t, as the AUC is lower than for the two-variable model (Model 24), and also the other goodness-of-t measures imply a lower t.

In-sample Findings From Autoregressive Models
As an extension to the conventional static probit model, we employ the autoregressive specication described in Equation (4). The ndings from autoregressive probit models are presented in Table 6 and they indicate that the autoregressive extension is not particularly useful in our application. For some of the models, the autoregressive extension does improve the model performance (Models AR21 and AR22) compared to their static counterparts in Table 5. However, this is not the case for the other models (AR23AR25). The best performing autoregressive model is Model AR25, with an AUC of 0.965, which is lower compared to 0.973 of Model 25.

Out-of-sample Findings
As previous forecasting literature has shown, good in-sample t does not necessarily imply good out-of-sample performance. Therefore, in this section, we will examine the pseudo out-of-sample forecasting performance of our models. We use an expanding window forecasting approach with estimation samples ranging from 2001Q32009Q4 to 2001Q32017Q3, and report the results of one-and two-quarter-ahead forecasting horizons. 9 Therefore, in our forecasting sample (2010Q12017Q4), there is only one recession. This limitation is due to the small number of recessions in the full sample, as for each estimation sample we need at least one recession period. For this reason, the out-of-sample ndings should mainly be seen as illustrative.
The ndings indicate that the models including the term spread (TS and Model 24) perform best among the models in one-quarter-ahead forecasts, with out-of-sample AUC:s of 0.932 for both models. Model 23, including the oil price and consumer condence variables, also performs relatively well (AUC=0.918). In the case of two-quarter-ahead forecasts, the single predictor model including the oil price variable performs the best, yielding an AUC of 0.894. Overall, the ndings are in line with the in-sample ones, and conrm that oil prices and the term spread are valuable indicators of future recessions in Russia.

Conclusion
In this paper, we have studied the role of oil prices on Russian business cycle uctuations. The ndings indicate that changes in oil prices are a valuable indicator of future recession periods. However, the term spread, dened as the dierence between the ten-year government bond and the three-month interest rate, yields even stronger results based on the area under the ROC curve (AUC), which has been the main goodness-of-t measure in this paper. This result shows that the previous ndings highlighting the usefulness of the term spread as a leading indicator of recession periods also apply for Russia.
In our in-sample estimations, we follow the strategy used by Christiansen et al. (2014) and Pönkä (2017), and test the predictive ability of our variable of interest over and above classic recession predictors. Overall, we nd that models combining the changes in oil prices with classic recession predictors improve the in-sample performance of the models. This underscores the importance of oil prices for the Russian economy. Although, when used in combination with the term spread, the predictive ability of the oil price is no longer suggested by the ndings of our models, the relationship between these variables provides a logical explanation to this nding, as monetary policy reacts to shocks in oil prices.
Furthermore, we test the robustness of our in-sample ndings in a pseudo out-of-sample exercise, and nd that the in-sample ndings are generally conrmed by the out-of-sample forecasts. Moreover, models including the term spread perform the best in one-quarter-ahead forecasts, whereas a model including the change in oil prices, yields the highest AUC in two-quarterahead forecasts.
As an extension to our main analysis, we have experimented with an autoregressive extension to the conventional static probit model. It turns out that the more parsimonious static model generally outperforms the autoregressive model in our application.
The ndings of this paper could be extended in a number of ways. One possible extension would be the use of a larger set of variables and possibly also common factors based on a large panel of nancial and macroeconomic variables, in the lines of Christiansen et al. (2014) and Pönkä (2017). Another possible extension would be to study the issue using dierent denitions of oil price shocks,such as the nonlinear oil price index (NOPI) of Hamilton (1996). Finally, the ndings of this paper could be complemented by studying the predictive ability of oil prices on the direction of Russian stock market returns, in a similar way as Pönkä (2016) did for eleven developed countries.