# «MICHAEL W. MADSEN THESIS FOR THE DEGREE MASTER OF ECONOMIC THEORY AND ECONOMETRICS DEPARTMENT OF ECONOMICS UNIVERSITY OF OSLO MAY 2012 © Michael W. ...»

Stock market volatility is measured as the six-month backward-looking moving average of the squared monthly returns of the stock market. An increase in the time-varying volatility measure corresponds to increased uncertainty in the stock market. Source: Oslo Børs.

The foreign-exchange market volatility is measured as the six-month backward-looking moving average of the squared monthly growth rate of the nominal effective exchange rate and captures the amount of stress in the foreign exchange rate market. Source: IMF.

Figure 1 below shows the evolution of the financial stress index, as well as bank related stress, stock market stress and instability in the exchange rate market. As seen from the figure, financial stress caused by negative shocks to the bank sector was the biggest contributor to the massive increase in the FSI in 2008. Moreover, it is clear that the stress was great during the latest financial crisis of 2008- 2009, for all the financial sectors covered by the index.

However, it is evident that the biggest shocks to the index came through the stock market, as well as the banking sector. There are two large shocks to the banking sector, resulting in a small, second shock to the index around 2010. The massive increase in the banking sector and stock market sub indexes illustrates the nature of the last financial crisis, which was initiated in the banking sector before it spilled over to the real economy. Furthermore, it is clear from looking at the figure that during what might be dubbed normal times, the index fluctuates around 0, in the interval of -1 to 1.

13 Figure 1: The evolution of the financial stress index (FSI) and its sub indexes. In the top left corner is the FSI, in the top right corner is the FSI for the bank sector, in the bottom left corner is the FSI for the stock market, and finally, in the bottom right corner is the FSI for the exchange rate. The bank sector FSI is defined as the sum of the banking beta, the TED spread proxy and the inverted term spread variables, the stock market FSI is defined as the sum of the stock market returns and stock market volatility variables, and the exchange rate market FSI is simply the exchange rate volatility variable. The sub indexes are demeaned and standardized.

Moreover, by having a glance at Figure 2 below, in which the evolution of the variables included in the stress index are depicted, it is easily seen that stress caused by shocks to the banking beta is the largest contributor to the stress seen in the most recent financial turmoil.

This increase represents an amplification of the banking sector risk. Furthermore, the graph representing the TED spread, which is proxied by the spread between the overnight lending rate and the three month NIBOR, suggests that the increase in the interbank rate over the overnight lending rate in 2007 has been persistent. Together with the inverted term spread, the evolution of the interest rates suggests that short-term borrowing has been relatively harder to 14 receive and long-term borrowing relatively easier for the banks after 2007 than in the period up until 2007. That is, it seems as though the risk premium the banks charge each other in the interbank market has been persistent, even though the central bank has kept its interest rates low, ultimately resulting in a tougher climate in the interbank market. The graphs also show that the volatility in the stock market increased abruptly in 2008. Around the same time, the stock market returns measure increased heavily. Keeping in mind that this corresponds to a decrease in the actual returns, it is clear that these three graphs capture the increased risk and uncertainty in the securities market. Additionally, the volatility of the exchange rate increased rapidly in the same period, implying a higher degree of uncertainty in the exchange rate market.

Figure 2: The evolution of the variables measuring financial stress in which the FSI is constructed from. In the upper left corner is the Banking beta, the upper right corner the TED spread proxy, to the left in the middle is the inverted term spread, to the right in the middle is the stock market returns, in the bottom left corner is the stock market volatility, and finally, in the bottom right corner is the exchange rate volatility.

15 5 Econometric Analysis Based on the theoretical model, I anticipate that an increase in the expected rate of inflation results in an increase in the interest rate, due to the inflation target embedded in the Taylor rule. As Norway has had an inflation targeting regime the last decade, the effect of inflation on interest rates should be stable or even slightly decreasing, if the central bank is able to anchor inflation expectations, which in turn might diminish the central bank’s need to act aggressively towards changes in the inflation rate. Moreover, the time horizon at which the central bank wants the inflation rate to approach its target has increased since the introduction of the inflation targeting regime. This effect might give results corresponding to a decrease in the aggressiveness towards inflation from the earlier parts of the inflation targeting regime to the more recent parts of the sample.

Through the effects that an increase in the output gap has on the inflation rate, one would expect an increase in the output gap to be followed by an increase in the interest rate. When using the deviation of the unemployment rate from its natural rate, it is expected that an increase in this measure will tend to have an expansionary effect on monetary authority.

As an increase in the exchange rate variable corresponds to a depreciation of the Norwegian Krone, one would expect that this would lead to an increase in the interest rate. Moreover, the response of an exchange rate depreciation should be larger during the period with a stable exchange rate regime than during the inflation targeting regime, when the exchange rate has been floating.

Moreover, by implementing a model with time-varying parameters, I am able to see whether the emphasis put on inflation and the exchange rate actually varies across time.

An interesting question in this study is how the financial stress index affects the interest rate.

This variable is likely to have a negative effect on the interest rate. That is, as the degree of financial distress increases, I anticipate the central bank to decrease the interest rate in order stabilize the financial side of the economy. As the degree of financial instability is likely to vary across time, the utilization of a time-varying parameter model will help capture the differing in the effect this variable has on the interest rate. Additionally, by employing this type of model, one could also explore if the central bank adjusts its interest rate in the buildup of financial instability. That is, the model exposition can be used to check whether the 16 interest rate is adjusted solely ex post or if there is an ex ante component in the interest rate adjustment to financial stress.

5.1 Estimation I have estimated the model by utilizing different methods. The estimation procedures are repeated using both the output gap constructed from the production data and by using the deviation of the unemployment rate from its natural rate as an output gap proxy. The model is

**estimated in the three following ways:**

- First, the estimation is carried out by running the regression as a two-stage least squares. In the first stage, the endogenous regressors in the Taylor rule, equations (12) – (15), are estimated. In the second stage, the Taylor rule, equation (4), is estimated.

The estimation procedure has been implemented while applying different lags and leads for the right-hand-side variables in the final estimation step. That is, the interest rate was estimated by applying different lags and leads for the fitted values of the right-hand-side variables. Moreover, this procedure is executed using data from the official inflation targeting regime, i.e. from April 2001 until December 2011.

- Second, the process is repeated for the preferred lag-/lead structure by the means of recursive estimation so as to find the evolution of the coefficients in the final Taylor rule. This estimation is implemented using data from August 1998, using twelve observations for initialization.

- Finally, I estimate the Taylor rule by the means of the varying coefficients method, keeping the coefficients with a stable time path constant. That is, some of the coefficients in (17) are time-invariant, i.e. do not follow a random walk. Consistent estimates of the coefficients in (17) are provided by estimation in two steps. In the first, I estimate the endogenous right-hand side variables, given by eqs. (12) – (15), and store the standardized residuals,,,,. In the second step, I estimate the model with time-varying parameters, i.e. equations (17) and (6) – (11), using the fitted values of the regressors. Estimation using time-varying coefficients is carried out in order to isolate the effect of financial stress on the interest rate setting over time. The estimation is carried out using observations from August 1998, as the estimation process does not work with fewer observations.

17 I will to begin by turning to the case where the output gap is constructed as the deviation of the log production from its trend.

In estimating eq. (4) by employing the two-stage least squares method, I have chosen different lags and leads for the variables in order to find the structure that yields the best results. I estimated the model using 0, 6, 9 and 12 leads for the inflation rate and exchange rate variables, -3,-1, 0, 1, 3, 6, 9 and 12 leads for the output gap and finally -3, -2, -1, 0, 1 and 2 leads for the financial stress index, where -3, -2 and -1 leads refers to 1, 2 and 3 lags. That is, with reference to the model specification above, i=k= 0, 6, 9, 12, j= -3, -1, 0, 1, 3, 6, 9, 12 and m= -3, -2, -1, 0, 1, 2.

5.2 Estimation results 5.2.1 Estimating using output gap Two stage least squares estimation In the tables below, the results are presented, with the deviation of log production from its trend being used as the output gap. The rest of the right-hand side variables in the Taylor-type rule are the inflation rate, the per cent monthly growth in the nominal exchange rate and the financial stability index.

18 Table 1: Results from two-stage least squares estimation, with a lead of 1 period on the financial stress index.

20 Tables 1 and 2 above depict the cases where the central bank adjusts its interest rates in response to an expected increase in the financial stress index and in response to past shocks to the financial stress index, respectively. That is, Table 1 shows the effects on the different parameters in the Taylor-type rule when the central bank is assumed to have an ex ante approach toward adjusting its monetary policy following an increase in the financial stress index. Table 2 shows the results when the opposite is assumed – namely that the central bank has an ex post policy towards financial stress.

From Tables 1 and 2 above, it can be seen that the model specification which yields the most reasonable results is a structure where the inflation rate and exchange rate are led nine periods (i=k=9) ahead and the output gap is led one period (j=1); that is, when it is assumed that the central bank adjusts its interest rates in response to expected changes in the inflation rate and exchange rate nine periods ahead and the output gap one period ahead. Both for a one period lead (m=1; see Table 1) and a one period lag (m=-1; see Table 2) on the financial stress index, this yields significant results for the inflation rate, the exchange rate, the financial stress index and the interest rate smoothing parameter, and mostly significant results for the output gap.

For this specification, both Tables show that there is a positive relationship between the inflation rate and the interest rate, implying that a unit increase in the expected inflation rate results in an interest rate increase by the central bank. Conversely, a reduction in the expected inflation rate will cause the central bank to decrease its interest rates. Moreover, an increase in the expected exchange rate results in an increase in the interest rates. That is, an expected depreciation of the Norwegian Krone tends to yield a monetary contraction through increased interest rates. It can also be seen that there is a positive relationship between the expected output gap and interest rates. Thus, increased economic activity leads to higher interest rates.

The interest rate smoothing parameter, ϱ, is also positive and significant for all specifications.

Moreover, conferring Table 1, an increase in the financial stress index one period ahead yields a negative response by the central bank, in that it is found to reduce the interest rate when the financial stress index is expected to increase in the next period. That is, if the central bank expects the financial stress index to increase by one unit one period ahead, it decreases the interest rate by 0.148 percentage points. The same effect is evident when having a glance at Table 2, where it can be seen that an increase in the financial stress index last period results in a slashing of the interest rate by the central bank. Specifically, a unit increase in the stress 21 index one period ago brings about a decrease of the interest rate by the central bank of 0.197 percentage points in this period.

Hence, it can be seen that an ex ante policy towards financial stress yields a lower interest rate cut than with an ex post policy. That is, with reference to the tables above, if the central bank adjusts its interest rates to respond to past shocks to the financial stress index, it decreases interest rates by more than if it adjusts its interest rates due to an expected increase in the index. These results suggest that the central bank is more concerned with financial stress after it has occurred rather than being pre-emptive by adjusting its interest rates in order to minimize future financial stress.