Analysis of Business Activity Indicators in Russia

Another important critique is that this indicator does not depict the depth of the upcoming changes in the business activity, as it only shows the direction of change (Dasgupta and Lahiri 1993).

A very huge critique of the survey methodology was established quite recently byBroughton and Lobo (2017), who claim that there are multiple biases present, which could lead to major errors in forecasting. These biases come from "anti-herd" and "anti-anchor". The authors explain that: "Anti-herding supports a reputation-based notion that forecasters are rewarded not only for forecast accuracy but also for being the best forecast at a single point in time; whereas anti-anchoring is consistent with forecasters overreacting to private information". They also say that empirical tests have showed a high positive correlation between the biases, and it means that, possibly, there is some common cause for both anti-herding and anti-anchor.

Moreover, some economists suggest that the current methodology can be sufficiently improved if the weights of the PMI's components would be changed. For example, Pelaez (2003a) has come to a conclusion that instead of using fixed weights, one should be using time-varying weights. This author proposed that it can lead to a possible case when some components, which turn out to be unnecessary, will receive a zero weight, and hence, they will not mislead the final results. A further research on that issue from the other economist has revealed the following valuable remark - the weights for the index components should not be fixed when international PMIs are computed, each country should proceed with its own pack of components and its own weights for them (Siliverstovs, 2018). The reason for that is because the efficiency of the current fixed weights was only tested and confirmed for the USA, but not for other countries. When the weights and components are universal for each country, it is easy to compare the figures of the PMIs. However, implementing of universal weights and components can lead to a case when some important variable, that reflects the fluctuations of GDP a lot, is omitted or is underestimated.

Overall, a major part of the literature dedicated to the study of the PMI proves that it has close relationship with important economic parameters, such as GDP and Industrial Production. Also, this index indeed captures the forthcoming change in these variables, as its implementation in forecasting models improves their results.

2.4 Review of the papers regarding the BCI

The Business Confidence Indicator (BCI), established by the OECD, and its relationship with the macroeconomic variables are also being discussed in the scientific literature for a few decades. However, there is much less papers focused on the study of the BCI, than quantity of papers about the PMI.

One of the classic papers on the relationship between the BCI and economic variables was performed by Santero and Westerlund (1996). They have studied consumer and business confidence indicators of the OECD for 11 European countries. These economists applied graphical examination, correlation analysis and Granger causality tests to investigate this relationship. And they have found that for the BCI there is a statistically significant relationship with GDP and industrial production (which were used as proxies for output). So, the authors concluded that “sentiment measures obtained from business surveys provide valuable information for the assessment of the economic situation and forecasting”.

Other literature focuses more on the forecasting abilities of the BCI. For instance, one study has shown evidence that “the relationship between the confidence index and GDP may be exploited in relatively peaceful times while the relationship may be quite distorted when an economy is hit by unexpected shocks” (Poљta and Pikhart, 2012). It means that despite the fact that this index has added some predictive power to the ARMAX model, used by the authors to forecast GDP, the quality of the predictive power was deteriorating in 2007-2008, so, the relationship between the BCI and GDP in those years was quite weak.

Analysis of the BCI regarding South Africa has also showed that there is a positive relationship between the index and real GDP and that the BCI can be used for short-term forecasting of GDP growth (Coetzee, 2014). The author tried several model specifications and came to a conclusion that the model of two-way error component fixed effect regression is the best so far, taking into account that there is a limited data for the research.

In case of Chile the BCI has proven to be a leading indicator of economic activity because it improves backcasts, nowcasts and forecasts of that activity (Alabarce, 2016). It was concluded using the results of out-of-sample and in-sample exercises, where the usage of the BCI have shown that it improves prediction of economic activity. Moreover, there has been found evidence that the BCI can be used for forecasting of aggregate as weel as sectorial employment (Pincheira, 2014).

One of the other papers on Europe has showed that the BCI explains a huge part of the aggregate index of industrial production and that the exploitation of this index in conjunction with the US industrial production indicator in a conditional error-correction model would give the most accurate and reliable forecasting for the European aggregate index of industrial production (Parigi et al., 2000).

A further research on that question of obtaining short-term forecasts of the industrial production for several European countries has highlighted that addition of the BCI data to country-specific, indicator-based and regression models for the industrial indices of France, Germany, Italy and of the whole euro area - is highly successful and these models give qualitative predictions (Zizza, 2002).

Moreover, in one of the papers, whose goal was to compare nowcasting abilities of many various business cycle indicators in Europe, there was found an evidence that the manufacturing PMI and the BCI are the strongest in prediction of European GDP compared to many other business indicators (R. Basselier et al., 2018). To prove it, the authors have proceeded with “state-space representation for a dynamic factor model” applied to a 34 monthly and quarterly series data. The authors used the data for the whole Eurozone as a whole and separately for Germany. In case of Germany, the researchers have concluded that the manufacturing PMI would be the second best business indicator.

Also, Mourougane and Roma (2003), who examined usefulness of the BCI in predicting real GDP growth in the short run. They also studied different Eurozone countries. As a result, a positive linear relationship between the BCI and real GDP was detected using Granger causality test and construction of Ordinary Least Squares regression of real GDP on this confidence index. Forecasting abilities of the estimated model were tested by ARIMA model and appeared to be useful.

All in all, most of the existing literature suggests that the BCI has strong positive association with GDP and Industrial Production. Moreover, models that include this indicator show more accurate predictions of turning points of the economic activity.

2.3. Research of the business activity indicators regarding Russian economy

There is much less existing literature, especially empirical one, regarding business activity indicators in Russia. One of the reasons for it, is that concept of such indicators has been applied not for so long. There is just a couple of studies for the PMI, ECI and BCI, whereas in case of the RSBI, no existing literature was found, as this index was introduced quite recently.

One of the papers regarding this topic is by Korte (2012), where the author had studied several confidence and composite indicators, which are applied in Russia, in terms of their efficiency in predicting of economic activity from 1996 to 2011.This scientist has used two models -- autoregressive model (AR) and autoregressive exogenous input (ARX). A combination of output of the 5 biggest sectors, which are industry, agriculture, construction, transportation and trade, has served as a proxy for economic activity. He examined many various indicators -- tendency ones, as well as composite indicators, and came to the conclusion that among them, the PMI, the BCI by the OECD and the Composite Leading Indicator by the OECD are the best ones in terms of forecasting power. That is because addiction of them into the model improves forecasting results and also decreases forecasting error, which occur due to the changes in the data generating process.

Pestova (2015) has carried out a study about various leading indicators, among whom were tendency indicators as well, of economic activity employed in the OECD states and Russia for period from 1980 to 2013. Four groups of variables were tested in this research, namely, macroeconomic variables, external sector variables, financial sector variables, and consumer and business expectations. The latter parameter was represented by the BCI and it turned out to have low predictive power in comparison with other variables, for instance, consumer confidence index, so, it was not included in forecasting model.

Another Russian study was devoted to investigation of which tendency and leading indicators were efficient at predicting the 2008-2009 crisis. The author reviewed thoroughly around 10 different indicators that existed in Russia at that time and discussed why only a few of them can be used for an empirical research (Smirnov, 2010). For instance, the ECI by Rosstat was one of such indices, because its methodology had been frequently changed, and hence, there were no wholesome time series for it. However, the PMI by IHS Markit was considered a good indicator for empirical purposes. Later, the author has compared how efficient were these various indicators in forecasting the turning points of economic activity in Russia, which was proxied by the output of 5 main brunches of the economy. The PMI was one of the studied indices, however, it did not show precise predictions of turning points, because it only had determined the turning point in October of 2008, but it failed to detect 2 next turning points in February and July of 2009.

Researchers Savin and Winker (2011) have conducted an examination about whether business tendency indicators in Russia and Germany can be considered leading indicators of economic activity. Their conclusion regarding Russian indicators is rather dismal - " While there are many studies providing evidence that leading indicators improve univariate time series models forecasting real output, this is by far not the case for developing countries like Russia, as business tendency surveys do not provide (or only to a minor extent) additional in-

formation for forecasting…". Regarding Russia, the authors study the ECI and the business confidence index by the Institute for the Economy in Transition, and the IFO index -- for Germany. There are several explanations of such a weak performance of Russian indices that were outlined in the paper. First of all, shorter time period of expectations, which is requested in the surveys, as the questionnaire for the German index asks for a 6-month horizon and Russian indices' methodology only solicits a 3-month period. Secondly, there might be a "poor calibration" of Russian surveys. And lastly, this problem might arise due to the limited data that was used in that research, as this fact could possibly lead to an over-estimated variance.

Overall, due to a deficit of papers devoted to the examination of business tendency indices in Russia, very limited conclusion about efficiency of these indicators can be made. All the found studies show that inclusion of the PMI in the forecasting models gives more precise results and its implementation is useful to predict turning points. Regarding the ECI, no evidence of its usefulness was found in the literature yet. Whereas application of the BCI shows mixed results in the existing papers about its efficiency.



3. Empirical research

3.1 Variables description

The goal of this study is to analyze the relationship between the Russian economic activity, measured by real GDP growth, and 4 business activity indicatorsnamely, the manufacturing PMI, the BCI, the manufacturing ECI and the RSBI, and then to estimate how good these indicators identifyfluctuations of economic activity, or so-called, turning points, which are basically points in time when economic activity changes its direction from expansion to contraction, and vice versa. It is believed by many economists that business activity indices are able to foresee the change in economic activity beforehand in a few quarters. Therefore, in this research paper, abilities of business tendency indicators to detect changes in economic activity from different points in time will be studied. In particular, probability to correctly detect turning points from current time period and also 1, 2 and 3 quarters beforehandwill be tested.

The data for the first index was collected from the IHS Markit organization. Then, for the second indicator and the growth rate of real GDP the data was obtained from the OECD. For the ECI the data was sourced from publications of the Rosstat. And for the last indicator, the data was collected from the Opora Rossii organization.

All the first 3 variables were gathered for the period from the 3rd quarter of 2012 to the 4th quarter of 2018, which constitutes 26 quarters. Such a period was chosen due to the unavailability of some data before the 3rd quarter of 2012. All that business tendency indices' primary data was at the monthly frequency, due to the fact that these indicators are released monthly. However, growth rate of GDP is published quarterly. So, to perform any calculations, the frequency of all the variables should be matched. To do so, the data for indicators was transformed into a quarterly oneby taking the average of 3 months. Regarding the RSBI, a shorter time span will be considered because this indicator has only been established since the 3rd quarter of 2014.Therefore, a period which starts from that date and ends at the last quarter of 2018 will be used in the research. All the descriptive statistics for the variablescan be seen at the Appendix (see Appendix 1).

All of the indicators except the ECI by Rosstat were already seasonally adjusted by their publishers. So, seasonality in the ECI data had to be adjusted because, as suggested by Rosstat, it can over- or underestimate the true data for some months and hence, the degree of association between the ECI and the other variables would not be correct. So, seasonal adjustment was performed by applying the Difference of Moving Averageprocedure before the transformation of the data into quarters.

Below are the graphs,whichshow comparison of trend of each indicator with the corresponding figures of real GDP growth:

Picture 1. Comparison of trends of economic growth and the PMI. Source: calculations of the author.

It can be seen that all the indices except the BCI follow a similar trend with the real GDP growth. So far, only the graph of the BCI shows the most amount of contradiction, as it demonstrates a lot of discrepancies between the 2 variables. It seems that there is an incompatibility, in general, between values of this index and the growth rate. Other indicators of business confidence demonstrate much better correspondence with the growth throughout the whole time span, including the recession of 2014-2015.



Picture 2.Comparison of trends of economic growth and the ECI. Source: calculations of the author.

Picture 3. Comparison of trends of economic growth and the BCI.Source: calculations of the author.

Picture 4. Comparison of trends of economic growth and the RSBI. Source: calculations of the author.



The RSBI seems to have the least amount of discrepancy with the direction of economic growth, whereas the first 2 pictures indicate more variation. One common fact that all the 4 indicators share is that they all follow a declining trend starting around the 1st - 2nd quarters of 2018, indicating pessimistic sentiment in the business environment and bad expectations about future,while in reality, economic growth tends to increase gradually at that time.That negative spirit is caused by the forthcoming introduction of the VAT increase in 2019 and the following inflation rise, that is expected to harm all the firms a lot as well as their customers wellbeing. However, until economic growth figure for 2019 is not available, it cannot be stated for sure, whether these negative values are just foreseeing the future bad consequences or these indices fail to predict direction of economic growth.

3.2 Correlation testing

To measure empirically the degree of association between the variables,cross-correlation between the real GDP growth rate and each of the indicators was computed. Cross-correlation is used to measure the extent of association between two time-series, as it computes their correlation on different levels of lag. In particular, for that research, for each index 4 cross-correlations were computed:

cross-correlation of economic growth with current values of the index

cross-correlation of economic growth with values of the indexof lag 1

cross-correlation of economic growth with values of the indexof lag 2

cross-correlation of economic growth with values of the indexof lag 3

Values of cross-correlation for each 4 of the indicators can be seen below:



Table 1.Cross-correlation matrix. Source: calculations of the author.

	Correlation of economic growth with the PMI	Correlation of economic growth with the ECI	Correlation of economic growth with the BCI	Correlation of economic growth with the RSBI
lag 0	0,49	0,56	0,02	0,61
lag 1	0,40	0,47	0,16	0,54
lag 2	0,46	0,40	0,17	0,44
lag 3	0,38	0,19	0,21	0,27

All the indicators except the BCI show pretty decent correlation, while the latter shows no correlation at all. So, it means that the BCI is not related to the economic growth. The PMI and the ECI have a moderate correlation with the real GDP growth, whereas the RSBI shows the strongest correlation. Cross-correlation for the ECI and RSBI with economic growth tends to be the highest when there is no lag in the values of these indicators, and then, correlation gradually decreases, so that the values of 3 quarter lag have almost no correlation with economic growth. In case of the PMI, its correlation with the real GDP growth is pretty moderate for all the values of the index at any lag., however, the values of 3 quarter lag also show the weakest relationship with the economic growth.

3.3Rolling correlations

With the time series data, it can be the case that the correlation figure between 2 variables, like the one obtained above, is skewed, because the relationship between them was changing during the given period. Their correlation might be high for some time and then become low due to some circumstances. So, application of rolling correlation is necessary to reveal the truth, as this method would assist to reveal the correlation level between the dependent and independent variables over time. It is a useful method because it allows to see if the relationship between the variables is stable over time or not, and also, to measure all the changes in the level of correlation between the variables at different moments in time. In the case of business tendency indicators, rolling correlation might help to detect, if there is some new source of information about economic activity, that these indicators are missing and which they would have to identify and include.

Rolling correlation is calculated as a moving average using a rolling window. The size of the window used in the study is 4 as the data is at the quarter frequency. Four different rolling correlations would be run in the study:

the 1st one, correlation between the current quarter value of index and current value of growth

the 2nd one, correlation between the past quarter value of index and current value of growth

then, correlation between the index value, which was two quarters before, and current value of growth

and lastly, correlation between the index value, which was three quarters before, and current value of growth

If the value of rolling correlation is greater than 0, it indicates a positive correlation. In the opposite case, if this value is less than 0, then there is a negative correlation. The closer is the obtained figure to 1 or -1, the stronger is the relationship, whereas 0 indicates no correlation.



Picture 5. Comparison of rolling correlations between current economic growth and different values of thePMI. Source: calculations of the author.



By looking at the graphs of rolling correlation of the PMI, it can be seen that the weakest correlation is in the situation, when the index value from 3 quarters before is used to predict current growth, as there are a lot of values that are negative or near zero.



Picture 6. Comparison of rolling correlations between current economic growth and different values of the ECI. Source: calculations of the author.

Other graphs show much more positive correlation, however, this relationship is rather unstable because there are few drastic decreases. It is hard to say which picture of these 3 shows the largest amount of positive or at least stable correlation. It can be seen, that correlation can change substantially every few quarters. It may be also noticed that the graph that pictures rolling correlation of 2 quarter lag values of the PMI highlights quite high positive correlation during the whole period of recession in 2014-2015. The nearby graph that corresponds to correlation of last quarter values of the PMI shows similar pattern on that period, but with a slight decrease around the end of 2014, that will be also reflected further in the paper when probability of prediction of economic growth will be estimated.



Picture 7. Comparison of rolling correlations between current economic growth and different values of the BCI. Source: calculations of the author.

Rolling correlation in case of the ECI is also quite unstable throughout all the time. The first two graphs depict the largest amount of positive and substantialassociation, as, due to the author's calculation, they report correlation higher than 0,5 at approximately 45% of all cases. It suggests that these values of the index have closer relationship with the real GDP growth and hence, and they are more useful for prediction purposes. All the graphs show a huge opposite association around the last quarter of 2015, as this index reported very pessimistic climate in the business activity and even a presence of recession (as will be identified further in research), when in reality, economy was already recovering from recession period.



Picture 8. Comparison of rolling correlations between current economic growth and different values of the RSBI. Source: calculations of the author.

Rolling correlation for the BCI reveals that there is very unsustained association between the variables over time, as sometimes it shows strong positive results and sometimes -- that there is abundance of negative or zero correlation. In general, it can be suggested, that positive close relationship is the most frequently observedin case of the BCI with values from 1 quarter ago (around 33% of cases show correlation above 0,5), comparing to the other surrounding rolling correlations. Nevertheless, relationship for that values of the BCI and economic growth is still very volatile and unpredictable. Overall, it can be concluded that the BCI struggles to capture the fluctuations of real GDP growth and that values of this index totally lack credibility towards estimation of economic climate fluctuations.

There is a similar situation regarding the instability of relationship between the variables. The graphs with current and last quarter values of the RSBI seem to show the greatest amount of positive and quite strong correlation than the others, but there is still a plenty of negative values. Considering the situation of relationship between the RSBI with current values and economic growth, correlation value of 0,5 or greater is only present at one third of all cases, which is rather insufficient, but the other variables of the RSBI are a much worse position. A whole large interval of weak and negative correlation for current and past quarter values of the RSBI starts around the ending of 2017, and it constitutes around a third of all the time period, however, the PMI and ECI also exhibit such a pattern at that time, so it appeared to be a hard period for estimation for any business indicator. However, there is an 8 quarters shorter time span, than in the case of other business indices, so, again, if there had been a time interval, which is as long as for the other indicators, it would have become more apparent, whether there is always so little positive strong correlation or it is just an inclusion of such a hard and quite lengthy period that makes the whole picture look very unsatisfying.

So, overall, most of the results from performing of rolling correlation coincide with the conclusions from cross-correlation, but it became evident that relationship between the indices and economic growth is not stable over time, as it can change from strong and positive to very negative really quickly. The PMI and ECI values at 0 and 1 time-lag showquite decent amount of positive correlation with economic growth and their values at 3 quarter lag show the least amount of close relationship with the economic growth. The rolling correlation for the BCI confirms results from cross-correlation that there the relationship of this indicator with real GDP growth is not really compatible. In case of the RSBI, conclusions are a bit different from the previous ones obtained by cross-correlation, which established quite strong relationship with the economic growth. The rolling correlation for this index shows a lot of negative and weak relationship, with just few values of close positive association.

3.4 Methodology of estimation of turning points

One of the aims of this paper is to examine how useful are business tendency indicators in identifying the change in economic activity, which is also referred to as a turning points. So, turning point denotes that economic activity is changing its direction from expansion (contraction) to contraction (expansion), where contractions mean that there is basically a recession in the economy. So, capability of these indicators to detect turning points from different moments in time will be tested. In particular, the study is aimed to compute the likelihood to identify turning point with the use of current values of the business activity indices, as well as the use of past quarter values of the indices, namely, values from 1, 2 and 3 quarters ago. Then, this estimated likelihood will be compared with the realization of the event (i.e. whether this turning point indeed occurred in real life or not).

To measure the extent at which business tendency indicators can identify turning points, logit model will be used to compute such a probability. In particular, estimation of logistic regression will show the probability that economy is in a recession according to the data of a particular business activity index.

Logistic models are widely used to determine whether a particular indicator is successful in reporting of turning points of economic activity. For instance,the following papers have applied logit models for that purpose: Layton and Katsuura, (2001);Camacho, (2004); Bodart et al., 2005; Hamberg and Verstandig, (2009); Comelli, (2014)).

In general, the logit modellooks as follows:



where:

- probability that an event occurs

Xi - explanatory variable

and - logistic coefficients, that need to be estimated

This formula represents the natural logarithm of the odds that the dependent variable equals to one of the two states. In particular, dependent variable has a Bernoulli distribution, so it takes only two values, namely, 1 and 0.

Then, due to mathematical rearrangements and conversion of the natural logarithm to the base e, the following formula is obtained:

This formula denotes probability that dependent variable equals to one of the states, 1 or 0. So, in application for the given paper, logit model will derive probability that there is a state1 (recession) according to the subjective data of a business tendency index.

So, turning points of economic activity serve as dependent variable Y for this paper. As there are no sources of information about the dating of turning points for Russia, they would have to be specially computed. Approach for detection of a recession that will be used in the model, which will transform the real GDP growth data into binary series, is the growth rate cycle approach. It is a simple method that is widely used in research literature and business community. It was firstly published in The “New York Times” magazine by Shiskin (1974). This method of identification of turning points consists in the following - when GDP growth is negative, there is a recession, and when it is positive - there is an expansion. However, "to prevent the noise due to the flashingbusiness cycle phases, not one quarter of negative values of economic growth, but at least two should be recognized as a recession; and the same concept is applied to a one quarter of positive growth surrounded by recessionary quarters both before and after it: this “positive” quarter should by design be marked as a recession" (Bodart et al., 2005; Rudebusch and Williams, 2009; Цsterholm, 2012; Mazzi et al, 2014;Pestova, 2015). Therefore,dependent variable will be manually created on the basis of the above stated methodology:

For the time span used in the study, there is only one, but huge recession period depicted by the aforementioned methodology, this recession took place from the 2nd quarter of 2014 to the 4th quarter of 2015. So, values of dependent variable Y are equal to 1 for this interval and the rest of the values are 0.

As the paper aims to estimate ability of the indices to detect turning point with the use of current values of the business activity indices, as well as the use of values from 1, 2 and 3 quarters ago, then for each of the business tendency indicators 4 model specifications will be tested, based on different lag of the values (0, 1, 2 or 3 quarter lag). So, it will be highlighted which exactly data -- current, from 1 quarter ago, 2 quarters ago, or 3 quarters ago -- is the most useful for identification of turning points and which data is insignificant.

To test whether the model is correct in its fit quadratic probability score (QPS) will be used.Method of QPS has been established by Diebold and Rudebusch (1989), and it is a measure that compares estimated probability of a prediction withrealization of event in real life, so technically, it is a measure of mean square error. Examples of studies thatemployed QPS measure in predictions of recessions are: Layton and Katsuura, (2001); Lahiri and Wang (2005); Bodart et al., 2005; Laytonand Smith (2007).

The formula for QPS is the following:



Where:

t is number of observations

is forecasted probability

is observedprobability

This indicator of fit has a range from 0 to 1. The closer the obtained value to 0, the more correct is the model. So, implementation of such measure will help to estimate goodness of fit of the model, i.e. whether the computed specification of a model is indeed correct.

Further, 2 methods of estimation of prediction accuracy will be used. The first one is calculation of share of probabilities captured true. It is a measure that shows which portion of estimated probabilities matches with the realization of event. Realization of event, in case of this study, is whether or not there is indeed a recession in real life. The greater this measure, the better is a prediction accuracy, which means that indicator of business activity has a successful ability to capture economic activity changes. The second method is computation of share of false recessions reported. So it denotes a share of mistakenly estimated recessions. The larger is this measure, the worse is the prediction accuracy, because it would mean that index frequently reports a fake recession.

3.5 Granger causality test

It can be the case, that two variables are interdependent and they are being calculated simultaneously, this fact can sufficiently influence empirical results and make them invalid.So it is important to confirm that there is no such situation between the dependent and independent variables before any empirical analysis. To reveal whether there is an endogeneity problem between the current values of indices and the dependent variable Y, Granger causality test will be performed:



Table 2.Output for Granger causality test. Source: calculations of the author.

Xi:	Probability that Y do not granger cause X	Probability that X do not granger cause Y
PMI	0,1479	0,2285
ECI	0,0481	0,714
BCI	0,5608	0,78
RSBI	0,0892	0,981

Results of this test suggest that there is an endogeneity problem between the current values of ECI and dependent variable Y.It means that variables are interdependent, and the current values of ECI are not exogenous, which is unacceptable. So, it will be excluded from the further research, as it would have given biased results.

3.6 Results of regression

Due to the output of logit regression,the BCI or various lagged values of it appeared to be insignificant at any percentage level. So, regression analysis has confirmed previous conclusions that there is no relationship between this index and economic growth, and it is useless for forecasting.

Considering the PMI, it turned out that all 4 tested specifications -- models that include current value of the PMI, and its values with 1, 2 and 3 quarter lag-- are all significant at 5% level, as it can be seen below:

Table 3.Regression output. Source: calculations of the author.

PMI values from:	p value	z-statistics	McFadden R Squared	log likelihood
current quarter	0,0253	-2,236	0,2547	-11,29
1 quarter lag	0,019	-2,346	0,338	-9,81
2 quarter lag	0,0294	-2,179	0,245	-10,93
3 quarter lag	0,0486	-1,97	0,1852	-11,52



Significance of the index deteriorates with time starting from the values of lag 2, so, values of the PMI with 3 quarter lag show the lowest significance, which almost reaches 5%. The highest significance is for the past quarter values of the PMI, also McFaddenR Squared and log likelihood both suggest that this specification is the most correct among all of them.

Forecasting results and accuracy can be seen at the table below:

Table 4. Measures of prediction accuracy. Source: calculations of the author.

PMI values from:	QPS	% of probabilities captured true	% false recessions reported
current quarter	0,145	81%	8%
1 quarter lag	0,154	84%	8%
2 quarter lag	0,145	79%	8%
3 quarter lag	0,149	70%	13%

As QPS numbers are quite close to 0, then it can be concluded that these models have a good fit. However, it can be noticed that again goodness of fit slightly decreases with time starting from the 2 quarter lag. Hence, again a model that uses past quarter values of the PMI shows the best QPS output and a model with 3 quarter lag values shows the lowest results among all the models (but it is still a good fit). By looking at the percentage of probabilities captured true, similar conclusions can be drawn, that in general, all the specified models show high enough share of probabilities estimated correctly. But once again, regression with past quarter PMI values outperforms the others. Share of so-called, "false alarms", which is simply a share of falsly reported recessions, is low among all the regression specifications, as all of them, except the last one, have only mistaken twice, which consists 8% of all the estimations. And the last specification model has recorded 3 false alarms, which constitute 13% of all the cases.

Overall, a conclusion can be made that logit model that uses last quarter values of the PMI as an explanatory variable has better characteristics than other specifications of model with the PMI figures. Below, a graph that depicts the volume of discrepancy between the realization of eventof recession and the estimated probabilities by this model can be observed:

Picture 9. Comparison of estimated probabilities of recession with thethe realization of this event for the PMI. Source: calculations of the author.

As a value of estimated probability that exceeds 0,5 denotes that there is a forecasted recession, one can note that for the period of huge recession in 2014-2015, lagged values of PMI were able to catch almost all of it, except for two quarters. However, as was previously said, this index also gives 2 false recession alarms. So, in general, it can be concluded that this index gives not perfect, but quite credible results in detecting recessions.

Regarding the results for regression output of the ECI, it was found that only model with 1 quarter lag values of the ECI has statistically significant coefficients:

Table 5.Regression output. Source: calculations of the author.

ECI values from:	p value	z-statistics	McFadden R Squared	log likelihood
1 quarter lag	0,0172	-2,3817	0,325	-10,003



So, variable of past values of the ECI is significant at 5% level.

Below the accuracy of predictions and goodness of fit are reported:

Table 6.Measures of prediction accuracy. Source: calculations of the author.

ECI values from:	QPS	% of probabilities captured true	% false recessions reported
past quarter	0,095	84%	4%

Goodness of fit measure, QPS, is really close to 0, which corresponds to correct fit. Also, the ECI has estimated precisely around 84% of economic fluctuations, which is quite a successful result. Regarding the false recessions -- this indicator had only 1 false alarm, what constituted around 4% of all the estimated values.

Picture 10.Comparison of estimated probabilities of recession withthe realization of this event for the ECI.Source: calculations of the author.

This graph shows that the ECI has not detected the first three quarters of recessionand also overestimated the probability of recession in the first quarter of 2016. But in general, it has showed good results in identification of economic contractions. Compared to the PMI model, this indicator has more accurate results.

Results of regression for the RSBI reveal that only a model with current values of this index has significant coefficients (significant at 5% level). So, only such a specification model will be used for further research.

Table 7. Regression output. Source: calculations of the author.

RSBI values from:	p value	z-statistics	McFadden R Squared	log likelihood
current quarter	0,0411	-2,043	0,528	-5,413

Fit of the model can be considered as good because QPS figure is low (Table 8). Percentage of incorrectly predicted probabilities is 18%, whereas portion of false alarms is 6%, which is indeed just 1 case from all the estimations.The picture12 below, which shows the difference between the estimated probabilities of recession and the realization of such event, reflects that the model failed to detect 2 quarters of recession in 2014-2015, but in general it shows rather fine forecasting power.So, model with current values of the RSBI shows successful identification abilities of turning points. However, one should remember that this results are obtained from using a much shorter period of time than what was used for the other 3 indicators, and moreover, this time period lacks the first quarter of observed recession, hence, if the identical time period had been used, the results of the regression and predicting abilities could have been different.

Table8.Measures of prediction accuracy. Source: calculations of the author.

QPS	% of probabilities captured true	% false recessions reported
0,103	82%	6%



Picture 11. Comparison of estimated probabilities of recession with the realization of this event for the RSBI. Source: calculations of the author.

Overall, the empirical testing has pointed out that models with 1 quarter lag values of the ECI, current values of the RSBI and 1 quarter lag values of the PMI have the most efficient forecasting features. All of the above models can detect correctly above 80% of economic activity fluctuations, therefore, economic agents can have enough trust for values of these indicators and keep checking in with them to make business decisions. Also, the PMI values of different time lag has proven to be indeed significant and efficient for estimation of turning points, what coincides with the conclusions from empirical literature.



Conclusion

This paper has focused on examination of business activity indicators implemented in Russia from both theoretical and empirical point of view. Here, classic worldwide popular indicators such as the PMI and the BCI has been reviewed, as well as Russian indicators -- the ECI and the recently introduced RSBI. Methodology, history and practical usefulness of these indices has been deeply discussed. Then, in the empirical part, quality of their relationship with the economic activity, represented by real GDP growth, was tested using cross-correlations and rolling correlations, what has led to conclusion that all the indicators have rather unstable relationship with the growth. Also, the PMI and ECI have showed the greatest amount of close correlation with it, while the RSBI and BCI appeared to have very mixed and vague results. Then, ability of these indices to detect fluctuations in economic activity, or turning points, was assessed with the use of construction of logit model probability. The constructed probability represents subjective likelihood that there is a recession in the economy based on the data of business index. This derived likelihood is compared to the situation in real life, i.e. if there indeed was a recession at that point in time. Matching with the previous results, the BCI turned out to be insignificant for detecting of turning points, whereas the PMI has showed successful results, because its values of any lag are significant for estimation of economic activity and their application gives good predicting accuracy. In case of the RSBI, conclusions of regression state that only its current values are significant, and moreover, their implementation in forecasting of turning points gives thriving results. And lastly, studying of the ECI has revealed that only its values from 1 quarter ago are useful in identifying of turning points, and the model with this indicator points out quite high prediction power.

So, overall, among all the business activity indices that are used in Russia, the PMI and the ECI give the best results for the period from 2012 to 2018 in regard to relationship with economic activity and ability to determine its changes. So, economic agents can use information about these indices to make decisions. The RSBI, which has a much shorter existence, shows quite good results for detection of turning points, however, its contradictory results about relationship with the economic growth are a source of concern. Also, the BCI turned out to provide very unsatisfying results on the considered time period, what leads to a conclusion that it is impossible to use this index to make any decisions.

For a further research it can be suggested to try to assess quality of these indicators with some different models, what would provide the opportunity to compare results of the logit model with the other ones, to see if a type of regression model influences conclusions about the indicators.



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