Elasticity diagram
An elasticity diagram is a graphic illustration that relates the development of two economic variables over time. From this, conclusions can be drawn about a cause-and-effect relationship. The elasticity diagram is formed from a scatter diagram ( scatter diagram , XY diagram) with the special feature that the individual data points are linked to one another in chronological order. The resulting line courses can have typical patterns with which certain dynamic reaction patterns can be identified. On the one hand, the elasticity diagram can be used as an instrument for time series analysis . On the other hand, it is suitable for controlling economic variables, for example in the context of pricing policy .
background
Elasticities can generally be defined as the cause-and-effect relationship between two economic variables in the sense of a sensitivity analysis. Most often, relative changes are put into a relationship, for example in the case of price-sales functions . However, it is also possible to form difference quotients that relate absolute quantities. The term appeared for the first time in the context of the so-called elasticity concept in connection with the analysis of interest rate risks . This corresponds more to the price perception from the customer's point of view, for example for banking products.
Often the focus is on the price reactions of companies (banks, mineral oil companies, etc.) to changes in market prices (crude oil price, interest on the money and capital markets). An elasticity of 0.6 means, for example, that a company reacts to a market price increase or a market price decrease of one percentage point with a 0.6 percent price increase or a 0.6 percent price decrease. The linear equation thus has the following functional relationship:
Price = 0.6 * market price + constant
In contrast to the classic elasticity term, interest rate elasticity does not relate relative changes in the dependent and explanatory variables, but rather absolute changes in interest rates .
description
Since difference quotients and elasticities can be interpreted as the slope of a straight line, they can be read off directly from the linear regression line equation:
- xi: economic cause size
- yi: economic impact quantity
- b0: intercept
- b1: slope, responsiveness or elasticity of the causal relationship
The analysis of causal dependencies with the help of elasticities will be demonstrated using an example. For this use of the credit line on a current account, the bank charges interest, the amount of which depends on the short-term interest rates ( i.e. interest rates with a fixed interest rate that can be fixed each day) on the money and capital markets (see revolving credit ). There is therefore a causal relationship between the development of interest rates on the financial markets and the interest rates that the banks apply to their customers. The figure shows the interest rates for overdrafts and the EURIBOR money market interest rate since 2003.
The relationship is to be analyzed using simple linear regression . "Simple" in this context means that the variable to be explained (the overdraft interest) is related to only one reference value (money market interest). Multiple linear regression would exist if, for example, a money market interest rate and the consumer climate were used to explain the current account interest rate.
The time series from Figure 1 is transferred to a Cartesian coordinate system in such a way that the independent variable (market interest rate) is shown on the x-axis and the dependent variable (position interest rate) on the y-axis. For each point in time there is a corresponding combination of the two quantities, which is made visible as a point in the diagram. If you transfer all the observation values of the time series, a point cloud is created from which you can already see the form of the dependency.
The upper graphic (Figure 2) shows such a coordinate system, also known as a scatter diagram. Such an arrangement of the points indicates a positive regression of the variables, that is, with rising money market interest rates as the causative variable, customer interest rates also increase.
In the regression analysis using the least squares method, a straight line is drawn through the point cloud, the slope of which corresponds to the elasticity sought. The elasticity diagram differs from the “traditional” scatter diagram or point diagram only in that the combination points of the following points in time are connected by lines. The original time series is therefore not changed or falsified in any way.
The great advantage is that the connecting lines form adjustment paths in the diagram from month to month , with which statements about the dynamic behavior of the variables can be made. The result is a more differentiated analysis of elasticity, which not only provides consistent values for the past, but also allows a variety of interpretations of the cause-effect relationship.
Delay effects in the elasticity diagram
Purely proportional behavior is rarely found in operational practice, since in economic systems the effect of the cause often lags behind at a sometimes considerable time interval. Rather, there are a large number of adaptation mechanisms that describe the system's response over time to a change in the input variable. Such dynamic behavior is called delay or time lag.
In the following consideration, this delay effect should be demonstrated using idealized price time series in the form of sine waves. They have the advantage that they only contain systematic time series components, i.e. are free of stochastic influences. In addition, they can be represented with just a few parameters. The market price is represented as a sine curve in such a way that price increases and decreases are passed through. The time series of the product price is realized with exactly the same sine function (same amplitude), but this is shifted by two or four days on the x-axis in order to simulate the delay in the price adjustment (see Fig. 3) .
The time series from Fig. 3 are now transferred to a Cartesian coordinate system with the x-axis as the independent variable (market price) and on the y-axis as the dependent variable (product price). For each point in time there is a corresponding combination of the two quantities, which is made visible as a point in the diagram. The adaptation paths in loop shapes that are more pronounced with increasing delay are typical for delays (see Fig. 3). The elliptical arrangement of the price combinations increases the distance and with it the measure for explaining the regression line. A problematic (side) effect arises from the fact that the slope of the regression line and thus the elasticity no longer correctly reflects the economic relationship due to systematic distortion. With a time lag of only two days, the elasticity is no longer 1.00, but 0.91 (0.68 for four days), although the series are identical, but time-shifted.
Individual evidence
- ↑ Bernd Rolfes (1985): The control of interest rate risks in credit institutions . Frankfurt am Main
- ↑ Rolfes, B. / Schwanitz, J. (1992): The “stability” of interest rate elasticities, in: Die Bank, No. 6, pp. 334–337
- ^ Johannes Schwanitz: Elasticity-Oriented Interest Rate Risk Control in Credit Institutions , p. 62, series of publications by the Center for Yield-Oriented Bank Management, Münster; founded and edited by H. Schierenbeck and B. Rolfes, Frankfurt am Main 1996
- ↑ Schween, Olaf (1998): Interest rate risks in commercial banking: A value at risk-based analysis for balance sheet structure management , p. 71, Gabler Verlag
- ↑ Schwanitz, Johannes (1995): "Analysis of the current account interest rate with the help of the elasticity diagram", p. 166 in: Die Bank 3/95
- ↑ Rümmele, Andreas (2009): Interest rate adjustment behavior of banks when setting interest rates in retail banking , Volume 34, p. 64
- ↑ Johannes Schwanitz: Elasticity- oriented interest rate risk control in credit institutions , p. 82, series of publications by the Center for Yield-Oriented Bank Management, Münster; founded and edited by H. Schierenbeck and B. Rolfes, Frankfurt am Main 1996
- ↑ Schierenbeck, Henner (2001): Earnings-Oriented Bank Management , p. 138, Volume 2: Risk Controlling and Integrated Return / Risk Management, 7th Edition, Gabler Verlag