The NBER’s Business Cycle Committee decides on the turning points (trough and peak) in the US business cycle several quarters after the passing of the turning points. The Committee waits until a sufficient amount of data is available to avoid the need for major ex-post revisions. The idea is to infer from these data on real GDP (and real Gross Domestic Income, GDI), which the Committee regards as the best single measure of aggregate economic activity. By combining monthly data with GDP data, it is not only possible to better assess lasting turning points of GDP, but also to time these turning points more precisely.
For instance, in September 2010, based on real GDP and GDI, which reached their lows in the second quarter of 2009, the Committee concluded that the trough occurred in mid-2009. With the help of several monthly indicators (estimated monthly GDP, manufacturing and trade sales, industrial production, real personal income less transfers and labor market indicators), the Committee then was able to identify June as the month of the trough. Similarly, for the previous turning points the NBER announced in April 1991 that a peak in the US cycle occurred in July 1990, and in December 1992 that there was a trough in March 1991. The most recent announcement was an exception to the rule. On June 8, 2020, the Committee determined that a peak in monthly economic activity in the USA occurred only four months earlier, in February 2020, marking the end of the 128-months long expansion—the longest in the history of US business cycles dating.Footnote 10
Following the NBER’s approach, we analyze a wide range of economic indicators to better capture the overall development of the German economy. However, we depart from their approach in two important respects. First, we avoid looking at quarterly GDP or GDI data, and instead look at a broader list of monthly indicators, also with data covering only a part of the economy. Second, based on these monthly indicators, we use principal component analysis (PCA) to derive a single and reliable Business Cycle Indicator for Germany to capture swings of the business cycle. These methodological innovations with respect to the NBER’s approach are important as they allow us to avoid the issue of repeated data revisions, which is typical for GDP figures. Indeed, as new available surveys come in and methodological improvements are integrated, GDP series need to be revised. This causes sometimes substantial delays in announcing the turning points of the business cycle.Footnote 11 Accordingly, using other economic indicators than GDP should reduce the problems caused by the delay (Anas et al., 2007). Moreover, by applying PCA and deriving the single BCI, we base our judgement concerning the turning points on a more transparent and comprehensive procedure.
PCA, and more generally, factor models are used in frameworks with a large number of closely related variables where multicollinearity is a risk. The aim is to reduce dimensionality of the system by identifying the most important influences from these variables. This is achieved by exploiting the correlations among the regressors to reduce their number, but at the same time retaining as much of the information in the original predictors as possible (Stock & Watson, 2020). Accordingly, the principal components maximize the variance of the linear combination of the variables.
Analytically, if there are n explanatory, closely related variables in the regression model, PCA transforms them into n uncorrelated new variables (principal components), of the form:
$$\begin{array}{*{20}c} {p_{1} = \alpha _{{11}} x_{1} + \alpha _{{12}} x_{2} + \cdots + \alpha _{{1n}} x_{n} } \\ {p_{2} = \alpha _{{21}} x_{1} + \alpha _{{22}} x_{2} + \cdots + \alpha _{{2n}} x_{n} } \\ \cdots \\ {p_{n} = \alpha _{{n1}} x_{1} + \alpha _{{n2}} x_{2} + \cdots + \alpha _{{nn}} x_{n} } \\ \end{array}$$
(1)
where xj, and pi (with i, j = 1, …, n) are the original explanatory variables and the newly estimated principal components, respectively, and αij are estimation coefficients (so called factor loadings) on the jth explanatory variable in the ith principal component. It is required that the sum of the squares of the coefficients for each component is one:
$$\mathop \sum \limits_{j = 1}^{n} \alpha_{ij}^{2} = 1\quad \forall i = 1, \ldots ,n$$
(2)
The principal components are derived in descending order of importance. Moreover, in the case of collinearity of the original variables, the first components will account for much of the variation, whereas the last few principal components will account for little variation and can be discarded. The stronger the correlation between the original variables, the higher is the explanatory power of the first principal components.
To validate PCA, the so-called Kaiser-Mexer-Olkin’s (KMO) measure of sampling adequacy can be calculated. KMO takes values between 0 and 1, with relatively high values suggesting that variables have sufficient in common to warrant a PCA. Small KMO values suggest that the sample is insufficiently adequate to apply a PCA.
A potential issue within the framework of the PCA may occur when the underlying time series are affected by exogenous trends and have complex structures, resulting in non-stationary series (Schmitt et al., 2013; Zhao & Shang, 2016). The presence of non-stationarity, which may reflect a persistent trend in the series, could increase the value of the variance that is maximized for every principal component, but at the same time deliver poor information by the component (Zhao & Shang, 2016). Specifically, under non-stationarity, the PCA could result in a few components assigning similar factor loadings to all variables (Lansangan & Barrios, 2009).
We therefore analyse the time-series properties of our data first. If they are non-stationary, we perform the PCA analysis on first-differenced data and recalculate our Business Cycle Indicator, which we then compare with its baseline estimate. Given that a trend is the most important driver of non-stationarity, this exercise should easily reveal how much of a problem the PCA with non-stationary data is in our framework.
In our PCA exercise, we use 20 economic indicators for which we can rely on monthly observations and which together cover the entire breadth of activity in the economy (Table 1). Given that we use our BCI for the inspection of the past business cycle performance, we focus on hard data only, which deem to reflect the actual economic situation of the real economy. Accordingly, our data set does not include financial series, like the stock market index, interest rates or exchange rates, which undeniably might send important cyclical signals, but by their nature are rather volatile around the cycle. This could contribute to an undesired noisiness of the incoming signals. We also do not consider survey information, like the purchasing manager index or different sentiment or confidence indicators, given that they often send premature or exaggerated signals on the cyclical state of the economy.
Table 1 Monthly data used in the Principal Component Analysis Related to this, we use the largest possible set of hard-data indicators. Nevertheless, our data coverage remains narrow compared with analyses applying large-scale dynamic factor models, like the one by Galli (2018). However, more recent contributions in this field tend to indicate that smaller sets of indicators capture more reliably business cycle dynamics than larger sets do (Aastveit et al., 2016; Camacho & Martinez-Martin, 2015; Carstensen et al., 2020).
All raw series are calendar and seasonally adjusted. We additionally use smoothed data, which are calculated as centered moving averages over one-year periods. Since PCA is scale sensitive, we index all time series to January 2019 = 100.
The longest data series are available back to 1991, but some series are available only starting in 2008 (international trade data). For this reason, the workable version of our monthly BCI, which we will update on a regular basis, is available from January 2008. However, to validate our model prior to 2008 we compare the performance of the Indicator with quarterly real GDP data back to 1991.
The use of PCA in the field of business cycle analysis builds on the pioneering works of Stock and Watson (1988, 2002), Harvey (1990), Harvey and Jäger (1993), Harvey and Trimbur (2003), and Forni et al. (1999). These authors developed the formal approach for the derivation and estimation of common cycles, based on the idea that the business cycle is the common factor in the economy.Footnote 12 Specifically, the crucial contribution of Stock and Watson (1988) was to show that a common component is a fundamental aspect of the underlying dynamics in any economic system. The validity of their finding was confirmed subsequently, using other, more sophisticated methods, like unobserved components models (Harvey, 1990, Harvey and Jäger 1993, Harvey and Trimbur 2003) and large-scale dynamic factor models (Forni et al. 1999; Watson, 2003).
To our knowledge, PCA has so far not been applied to the German business cycle. Although we adopt the graphical inspection as our main approach, we make sure that the procedure is transparent and understandable. Moreover, we compare the results from our qualitative approach with the ones we obtain from a recognition pattern algorithm (Bry & Boschan, 1971).