“Risks and the influence of negative interest rates on economic activity: a case study of Sweden, Denmark, and Switzerland”

The purpose of this paper is to analyze the impact of negative interest rates on eco- nomic activity in a selected group of countries, in particular Sweden, Denmark, and Switzerland, for the period 2009–2018. The central banks of these countries were among the first to implement negative interest rates to revive the economic growth. Therefore, this study analyzed long- and short-term relationships between interest rates announced by central banks and gross domestic product and blue chip stock indices. Time series analysis was conducted using Engle-Granger cointegration analy- sis and Granger causality testing to identify long- and short-term relationship. The first step, using the Akaike criteria, was to determine the optimal delay of the entire time interval for the analyzed periods. Time series that seem to be stationary were excluded based on the results of the Dickey-Fuller test. Further testing continued with the Engle-Granger test if the conditions were met. It was designed to identify co-inte-gration relationships that would show correlation between the selected variables. These tests showed that at a significance level of 0.05, there is no co-integration between any time series in the countries analyzed. On the basis of these analyses, it was determined that there were no long-term relationships between interest rates and GDP or stock indices for these countries during the monitored time period. Using Granger causality, the study only confirmed short-term relationship between interest rates and GDP for all examined countries, though not between interest rates and the stock indices. or even negative interest rates should be used to revive the economy. The side effects of negative rates are greater than for more traditional monetary policy tools in areas such as asset price inflation. Negative interest rates can have some stimulating effect, but can also come with potentially significant downside risks. When conventional monetary policy instruments become ineffective, central banks resort to untraditional (unconvention-al) measures. Conventional monetary policy tools primarily began to fail in conjunction with the 2008 financial crisis, when many central banks reached near zero in setting monetary policy interest rates, and it was not possible to continue lowering the rates, thereby further easing monetary conditions. The central banks needed to resort to tools that they had no experience with. First of all, this led to setting negative rates, quantitative easing, and even forward guidance.


INTRODUCTION
For central banks, negative interest rates have become a more important monetary policy tool than anticipated before the financial crisis. Prior to the global financial crisis, many economists assumed that negative interest rates would be effective when combined with other unconventional monetary policy tools as they would provide sufficient incentives to revive economic growth. Low or even negative interest rates should be used to revive the economy. The side effects of negative rates are greater than for more traditional monetary policy tools in areas such as asset price inflation. Negative interest rates can have some stimulating effect, but can also come with potentially significant downside risks. When conventional monetary policy instruments become ineffective, central banks resort to untraditional (unconventional) measures. Conventional monetary policy tools primarily began to fail in conjunction with the 2008 financial crisis, when many central banks reached near zero in setting monetary policy interest rates, and it was not possible to continue lowering the rates, thereby further easing monetary conditions. The central banks needed to resort to tools that they had no experience with. First of all, this led to setting negative rates, quantitative easing, and even forward guidance.
Negative interest rates of the central bank occur when commercial banks pay the central bank for holding their excessive financial resources. The reason for applying negative interest rates is that banks do not allow their surplus funds to remain in their accounts at the central bank, but rather release them into the economy, e.g., in the form of loans for other economic entities. In conjunction with the financial crisis, central bank interest rates dropped to zero in 2008; in 2009, the central bank of Sweden was the first bank to use negative interest rates in practice. Shortly thereafter, Danish and Swiss banks followed the Swedish lead, and the ECB also joined the banks that apply negative interest rates in 2014.
The purpose of this paper is to find a relationship between negative interest rates and economic activity in the selected countries for the years 2009 to 2018 (specifically for countries that first implemented negative interest rates, i.e., Denmark, Sweden, and Switzerland), using statistical methods of cointegration analysis and Granger causality to identify long-term and short-term relationships.

THEORETICAL BACKGROUND
The subject of necessary changes to monetary policy in recent years has been explored by Mishkin (2017), who observed new trends in strategies and approaches to monetary policy in the wake of the financial crisis. Namely, it was demonstrated that the development of the financial sector has a much greater impact on a country's economic activity than before. He considers zero interest rates to be a serious problem, because conventional expansive monetary policy becomes ineffective when a negative shock impacts the economy. Low or even negative interest rates are thus necessary to revive the economy. In 2019, five central banks had negative interest rates -Japan and the Eurozone joined Swiss, Swedish, and Danish central banks. Negative interest rates, as we know them today, were also mentioned by the Swedish economist Svensson (2000), who dealt with the monetary policy transmission mechanism in open economies with zero interest rates. He concluded that this type of monetary policy is a reliable way to get out of the liquidity trap, consisting of a stable price level, currency depreciation, and temporary fluctuation of the exchange rate. Zero interest rates thus clearly result in jump-starting an economy, limiting the emergence of inflation and real depreciation of domestic currency, and increasing inflation expectations. Table 1 shows the actual amounts of the central bank interest rates.

METHODOLOGY AND DATA
The concept of cointegration is a good choice to investigate the links between two variables. Among the first important authors to deal with cointegration were Granger and Engle (1987), who pointed out that time series may behave differently over the short term, whereas the values have a tendency to return to a certain state of equilibrium over the long term, thereby demonstrating mutual ties between the two variables. The analyses conducted here involve observing the relationships between the primary interest rate of the respective central bank and the value of both stock indices and GDP in the selected countries.
The input data for 2009-2018 for interest rates were obtained from the official websites of the respective central banks (Danmarks Nationalbank, 2019; The Swiss National Bank, 2019; Sveriges Riksbank, 2019); GDP values were obtained from the OECD database (2019), and the performance of the blue chip stock indices was obtained from investment websites (Investing.com, 2019). All calculations were conducted using the Gretl 1.9.4 program. Table 2 contains abbreviations and descriptions of variables that were selected for use in the time series analysis.
To determine the causal relationship between the variables under examination, it was necessary to first test the time series for optimal lag length, next to verify the existence of a unit root (i.e., the stationarity or non-stationarity of the time series), and then to conduct cointegration analysis using the Engle-Granger cointegration test. The following authors have described the individual tests in more detail in their studies: Kočišová (2018), Gerlach and Svensson (2003), and Černohorský (2017).
Testing time series for the optimal lag length is one of the prerequisites for Granger testing.
When analyzing time series, the goal is to find the lowest value for the selected information criterion. The lag length is determined by locating where the lowest value occurs for the information criterion. Lag lengths that have been established in this way are then used in subsequent testing. The choice of the appropriate criterion depends on the number of observations. According to Liew (2004) and Gottschalk et al. (2000), it is appropriate to use the Akaike information criterion to determine optimal lag length when the number of observations is small (less than 60). This can be expressed as follows (Akaike, 1981): where RSS -the residual sum of squares, k -the number of parameters, n -the number of measurements, and RSS/n -the residual variance.
Next, an analysis to determine the existence of a unit root was conducted; this determines the stationarity or non-stationarity of the time series being examined. Time series' stationarity or non-stationarity was determined using the Augmented Dickey-Fuller test (ADF test), in which all three types of test were conducted, i.e., with a constant, without a constant, and with a constant and a trend. When testing, it is assumed that the process listed below, i.e., (2), which tests whether Ø = 0 (the variable contains a unit root), takes the form (Dickey and Fuller, 1979): where again expresses the dependent variable, p -lag, and -the residual component.
The determination whether the time series are stationary or non-stationary is made by evaluating the p-value at a 0.05 level of significance, which thus establishes whether the null hypothesis should be rejected or not with 95% confidence. The null hypothesis is set as follows: If the time series achieve integration at the same level, it is then possible to proceed to the third step, cointegration analysis, which is conducted through the Engle-Granger cointegration test. Accordingly, error terms are also checked using the ADF test to determine if there is a unit root (Engle & Granger, 1987): Time series ratios were determined using the p-value, which was identified with the Engle-Granger cointegration test. When the null hypothesis is not rejected (p > 0.05), the time series are not cointegrated, that is, they have a unit root. The opposite situation (p < 0.05) indicates that the time series should be identified as cointegrated. The results of the Engle-Granger test were then used to decide whether to continue using the error correction model -if the time series were cointegrated, or to test for Granger causality -if we were working with non-cointegrated time series. Error correction models have dynamic specification, because they contain lagged values for the explained and explanatory variables. At the same time, they make it possible to interpret short-term changes in the model's dependent variable regarding its past equilibrium as well as changes in the explanatory independent variables.
When the time series are non-cointegrated, one can proceed to the Granger causality test, using the following hypotheses: H 0 : The X t variable does not Granger-cause the Y t variable.
H 1 : The X t variable does Granger-cause the Y t variable.

EMPIRICAL RESULTS
As already presented in Section 3, it is necessary to test the time series for optimal lag length before using the Engle-Granger tests. The interest rate was established as the independent variable in this relationship; the dependent variables were GDP and the behavior of the stock indices.

Testing for optimal lag length
Mankiw (2014) states that within the economic theory, the optimal lag length for time series is between 12 and 18 months, which corresponds to six lags for quarterly data established. In Table 3, AIC values were recorded for 6 lag lengths for tests with a constant, with a trend, and with a constant and a trend depending on which type of test exhibited the minimum AIC value. Table 3 shows that the lag length for GDP in Denmark is three quarters, using the test with a constant and a trend. For Swedish GDP, the lag is four quarters for the test with a constant. Swiss GDP has a resulting lag length of four quarters using the test with a constant and a trend.
The optimal lag length test (see Table 4) determined a lag of one quarter for the Danish and Swedish stock indices using the test with a constant. The Swiss stock index also had a resulting lag of one quarter, though using the test with a constant and with a trend. These results were considered when testing for time series stationarity (the ADF tests) and cointegration.

Testing for data stationarity
To verify whether the time series were stationary or not, the ADF test was used. The models with a constant or a trend were introduced into the ADF test depending on the results of optimal lag testing, i.e., the minimum AIC value. Table 5 depicts the resulting p-values and shows that all p-values are greater than the 0.05 level of significance, which means that the time series are non-stationary; therefore, the null hypotheses were not rejected. To achieve time series stationarity, it was necessary to conduct differencing using the first difference.
The results of the ADF tests for the differenced time series are shown in Table 6. Time series were tested for stationarity or non-stationarity at the same lag length using the same type of test (with a constant or a trend) as for the original time series.
Even after conducting the first difference, certain time series remained non-stationary. These were   Conducting the ADF test for the second difference of the selected time series resulted in all the time series becoming stationary (Table 7). This fact can also be verified via the graphic path of the time series' second difference (Figure 1).
The time series modified in this way were stationary at the level of significance (p < 0.05), i.e., they have a unit root. All of the stationary time series were subsequently included in the Engle-Granger cointegration test.

Determining interdependence of the time series using the Engle-Granger cointegration test
The previous test determined that the original time series were non-stationary, and after modification by differencing, it was then found that some of the time series have the same order of stationarity. For these time series, it was possible to proceed to the Engle-Granger cointegration test, which assumes that the original time series are non-stationary (Table 5). Table 8 shows the relationship between the given pairs of time series, which were specified as fixed).
The determined p-value, which had values higher than the set level of significance (p > 0.05), show that the time series under examination are not cointegrated, i.e., there are no long-term relationships between them for any of the three countries being studied. In terms of determining the results of the ADF and Engle-Granger cointegration tests, causal relationships were determined by Granger causality -not with the error correction model that assumes the time series are cointegrated.

Granger causality for interest rates and other variables studied
When testing for Granger causality, as with cointegration, variables were tested for their effect in both directions. Based on the calculations, one can conclude that all the countries showed only a one-directional effect, which was always the interest rate's impact on GDP (Table 9). For relevant results, this study is interested in the p-values at 0.05 (**) and 0.01 (***) levels of significance, rather than p-values at a 0.1 (*) level of significance.
For Denmark, it was determined that the interest rate variable Granger-causes GDP at a lag length of two quarters; for Sweden, this caused a lag of three and five quarters; and there were lags of two and four quarters for Switzerland. It can thus be stated that interest rates in Denmark, Sweden, and Switzerland influenced GDP of their countries between 2009 and 2018 at the above lag lengths. This means that the accuracy of GDP forecasting can be improved by using the evolution of interest rates in the given country.
Similarly, the paper further tested Granger causality for the variables being studied. Based on these tests, no effect was found for Danish, Swedish, or Swiss interest rates and their corresponding blue chip stock indices. The p-value was greater than 0.05 for all the lag lengths tested, and it was, therefore, not possible to reject the null hypothesis in any of the cases. From this, one can conclude that there are no short-term causal relationships (Table 10).
On the basis of the analyses, it was found that there were no long-term correlations between interest rates and GDP or stock indices in the countries studied for the examined period. Other authors, Khatkhate (1988), Arestis and Sawyer (2003), and Wu and Xia (2016), also came to the same conclusion, i.e., they could not find a relationship between interest rate and GDP. The use of Granger causality allowed proving short-term correlation between interest rates and GDP for all the countries studied, though not between interest rates  Denmark has its own currency, but it is pegged to the euro, which essentially forces it to copy the European Central Bank's interest rates. Even the situation in Switzerland is linked to the global economy. The franc limit was dropped due to expectations of quantitative easing by the European Central Bank; without a significant reversal in developments in the Eurozone, the Swiss Central Bank has no room for maneuver. Therefore, it is currently forced fight against deflation using only negative interest rates. It first tried to avoid deflationary pressures by appreciating the Swiss franc by applying an exchange rate peg that plunged global financial markets into chaos. Investors did not expect this step at all, and the situation was not even helped by eliminating the peg in 2015, when the franc began to appreciate once more. Eventually abolishing the negative rates will subsequently cause enormous appreciation pressures.
When the basic interest rates of the given central banks are lowered, the transmission mechanism's interest rate channel, which affects the economy, should result in lowering interest rates on the interbank market, which can lead to lowered interest rates announced by banks. The outcome should be a revival of aggregate demand and its related economic activity. At the beginning of the period examined before the onset of the financial crisis, these central banks pursued a conventional monetary policy using changes in interest rates. Naturally, during the financial crisis, it turned out that all the central banks examined here decided to use unconventional monetary policy of negative interest rates as one of their tools, which did not naturally result in supporting the growth of economic activity. There are many negative impacts of negative interest rates, e.g. taking liquidity risk, especially when investors' capital is at risk in ways, which may not seem obvious to retail investors. Negative interest rates can distort financial markets and increase the risk of financial instability for a long time. These findings certainly do not preclude the possibility that negative interest rates could have long-or short-term impact on other economic variables in the selected countries or in others (such as, the price level or exports), which is a topic that may be the subject of future research.

ACKNOWLEDGMENT
The paper has been created with the financial support of The Czech Science Foundation GACR 18-05244S -Innovative Approaches to Credit Risk Management.