The Rushin: An Index of Czech Economic Activity

We introduce a preliminary version of the Rushin, a weekly index of Czech economic activity. The index captures the common dynamics of four alternative high-frequency indicators and six standard macroeconomic monthly indicators of activity. It allows us to assess the current pace of economic growth and turning points in the business cycle in a timely way. In addition, it is valuable for nowcasting the current GDP growth rate. It is particularly useful in turbulent times, such as during lockdowns imposed due to the Covid-19 pandemic. It is currently signalling a slight decline in economic activity compared to the last quarter.

Time To Rush

The Covid-19 pandemic shock has given rise to several challenges for macroeconomic forecasters and policymakers. First, several countries imposed strict lockdowns to limit the spread of the virus, which led to abrupt and severe economic downturns. Time series and structural economic models calibrated to historical data were unable to assess the depth of these downturns, since no similar episode had occurred in history, and the standard relationships between the variables used in the models broke down. Second, the lockdowns were not due to economic forces, and some sectors had to shut down completely; this reaction was highly non-linear and had not been assumed by the economic models. Finally, the explanatory power of the leading indicators used in nowcasting models diminished significantly; these indicators are typically constructed based on surveys where the participants are asked whether the situation will improve or worsen, but not by how much.

To estimate the scale of the downturns following the lockdowns, economists started to look at alternative, often high-frequency, indicators of economic activity. These indicators, such as electricity consumption,^[1] air pollution, toll collection on highways and Google searches, have not usually been considered in economic modelling due to their noisiness or high volatility even in standard times (INSEE, etc.). To extract meaningful signals from these noisy high-frequency indicators, several central banks have introduced indices of economic activity (the Fed, the Bundesbank, the Bank of Italy, the Austrian Central Bank and the Banco de Portugal).

We follow this strand of the literature and introduce the Rushin, an index of Czech economic activity. To this end, we combine several high-frequency indicators and monthly macroeconomic indicators. The index is named in honour of Alois Rašín, a prominent economist and politician from the period of the establishment of the independent Czechoslovakia. His name is pronounced [Rasheen] in Czech; the modified term is an allusion to Mr Rašín and the timeliness (rush-) of the index (-in).

The index is still a work in progress. We aim to publish a paper describing the methodology of the index and testing its explanatory power. After the paper is published, we will regularly update the index on the CNB’s website. Please note that the index does not represent an official forecast of the Czech National Bank.

The Birth of the Rushin

Compared to larger economies such as Germany and the USA, high-frequency indicators (i.e. daily or weekly) are relatively scarce for the Czech economy. Still, we managed to collect more than ten high-frequency variables, including electricity consumption, atmospheric nitrogen dioxide concentration, several Google Trends searches, currency volumes, the Prague Stock Exchange Index and weekly indicators from Germany. Unfortunately, some of these variables remained very noisy or volatile even after thorough data pre-processing. Additionally, their correlation with the GDP growth rate was less significant than that for monthly indicators.

To reduce the noise in our dataset, we loosely follow the methodology of Eraslan and Götz (2020) by including monthly indicators in the index. For monthly data, we face the opposite problem: most of them capture changes in economic activity well, but there are too many of them.

Overall, we tested about 200 indicators. Including their lagged values, about 500 time series were eligible for the construction of the Rushin.

In the end, we managed to collect a balanced dataset of four weekly and six monthly indicators representing all crucial segments of the economy (see the table below). Each variable meets three criteria: 1) economic relevance, 2) reasonable correlation with the quarterly GDP growth rate, 3) significant comovement with other indicators, which is captured by the association with the first principal component extracted from the dataset. At the same time, we aimed to keep the dataset balanced to avoid over-representing some segments of the economy.

Table: The Rushin Index Composition

Source: CEPS, Google, Deutsche Bundesbank, CZSO, Road and Motorway Directorate, ifo Institute, Prague Stock Exchange

The Rushin is constructed as the comovement among the variables used to construct it (see the appendix below for the data transformation, imputation and index construction). By definition, it is a dimensionless variable. In order to obtain an economic interpretation, we scale it to have the same mean and standard deviation as the quarterly GDP growth rate. Subsequently, we interpret the value of the index as economic growth in the last 13 weeks relative to the preceding 13 weeks. As a result, to obtain an estimate of quarterly GDP growth, we can take the last observation of the index in the quarter.

So here’s the Rushin (values above zero indicate positive q-o-q growth in economic activity):

What the Rushin Says

The overall evolution of the index captures the dynamics of GDP growth in a satisfactory way.

The peaks and troughs of the index and the GDP growth rate largely coincide, particularly in turbulent times (i.e. during the financial crisis and the Covid-19 crisis). Also, the value of the index is relatively close to the GDP growth rates.

The index has performed relatively well during the Covid-19 episode, too. The chart below demonstrates that putting too much emphasis on one particular standard indicator can be misleading. As an example, the quarterly decline in industrial production in 2020 Q3 was much deeper than that in retail sales, which had a similar value to the Rushin and the GDP growth rate. On the other hand, in 2020 Q4, retail sales signalled a decline in economic activity, while industrial production increased relatively strongly. The Rushin stood between these two variables and signalled a slight increase in overall GDP, which is what actually materialised in the said quarter. Currently, the Rushin is pointing to a slight economic downturn in 2021 Q1.

Appendix

The construction of the Rushin loosely follows the methodology of Eraslan and Götz (2020), who calculate the Weekly Activity Index (WAI) for the German economy using principal components analysis (PCA). Adopting this methodology makes the Rushin comparable to the German WAI, allowing us to compare domestic economic activity with the economic activity of our biggest trading partner. (Note that the following chart shows the normalised values of the indices – values above zero are interpreted as above-average growth rates).

Data transformation and imputation

Before aggregating the mixed-frequency indicators into the index, we transform them to the same scale and create a balanced dataset with weekly frequency.

In the initial step, we transform the variables so that the final index reflects the quarter-on-quarter dynamics of Czech economic activity. All indicators (in levels) are therefore first transformed into moving averages that span one quarter (for weekly indicators, one quarter spans 13 weeks for simplicity). The quarter-on-quarter growth rates of these averages are then constructed.

Next, we align the weekly and monthly data to the same frequency. To this end, we assign the values of each monthly indicator to the last week of the month. Other weekly observations of the indicator are denoted as missing. The resulting dataset contains two types of missing observations. One is due to the mixed-frequency nature of the dataset, while the second is due to the publication lag of most traditional monthly indicators. Both types of missing observations are imputed using a modified expectation-maximisation (EM) algorithm which takes into account information on the dynamics of single variables and information on the correlations between the variables. This approach converts the monthly indicators to weekly frequency, and the additional information from the other series allows us to nowcast the values of indicators that are usually published with a significant delay.

Index Construction

Having a full dataset with imputed observations, we can now apply the principal component analysis (PCA) technique to obtain the information needed to calculate the index. This method provides us with weights, which in turn are used to calculate the index as a standardised weighted average of all the variables in the dataset. Hence, each variable’s contribution to the index depends on how strongly it relates to the factor extracted by PCA.

In other words, let x_i,t be a single observation of variable i  in week t. Let λⁱ be a vector of factor loadings given by the PCA. The resulting Rushin is a linear combination of  n economic indicators weighted by the first vector factor of the factor loadings:

Since we want the index to relate to the quarterly GDP growth rate, in the last step, we scale it using the mean and variances of the quarterly GDP growth rate. As a result, the Rushin can be interpreted as a proxy for the quarterly dynamics of Czech economic activity.

References

Adam, T. and Michl, A. (2020, April 8). První odhad dopadu pandemie COVID-19 na ekonomiku CR [čnBlog]. Retrieved from https://www.cnb.cz/cs/o_cnb/cnblog/Prvni-odhad-dopadu-pandemie-COVID-19-na-ekonomiku-CR/

Eraslan, S. and T. Götz (2020). An unconventional weekly economic activity index for Germany, Deutsche Bundesbank Technical Paper, 02/2020. Data retrieved from www.bundesbank.de/wai.

^[1] Aleš Michl and Tomáš Adam started to publish a blog [https://www.cnb.cz/cs/o_cnb/cnblog/Prvni-odhad-dopadu-pandemie-COVID-19-na-ekonomiku-CR/] with estimates of economic downturn based on electricity consumption in the Czech Republic already in April 2020.