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

These results could be intuitively explained, as financial stress stemming from the bank sector and stock market might be difficult to forecast and thus react to ex ante. Additionally, by loosening its policy during episodes of financial stress originating in the banking sector, the central bank adds liquidity to the bank market which in turn may reduce the likelihood of crisis that reach systemic proportions. The larger the stress to the financial sector, the higher the probability that the drainage of liquidity may spill over to the real economy and cause low inflation and weak economic growth.

Furthermore, Tables 1 and 2, as well as Tables A1 – A4 in Appendix A.1, show that an increase in the financial stress index yields an interest rate reduction. There are also similar results from applying different lags and leads to the financial stress index; suggesting that the central bank is more aggressive in its response toward financial stress ex post rather than ex ante.

Some of the specifications also yield somewhat counterintuitive results. First, the results show, in both tables, that for all but 9 leads on the exchange rate (k=9), for all other leads and lags in the output gap and the financial stress index, an increase in the variable leads to a decrease in the interest rate. This corresponds to the central bank lowering its interest rate if there is an expected depreciation of the exchange rate, thus further fueling the depreciation.

Second, in Table 1, with a specification of a one period lead on the financial stress index and a six period lead on the output gap, it is shown that an increase in the inflation rate today makes the central bank decrease its rate of interest. Hence, this result claims that the central bank fuels inflation by decreasing its interest rates in the case of growth in the inflation rate.

22 Moreover, the rather low values of the impact of the inflation rate on the interest rate, suggest that a unit increase in the inflation rate gives less than a unit increase in the real rate of interest, which in turn implies that the interest rate rule is destabilizing or accommodative to shocks to the economy. Table A1 also show similar results for a specification of 0 lags or leads on the inflation rate, different lag and lead structures of the output gap, as well as two leads on the financial stress index.

Third, from Table 2, if the central bank responds to an increase in the output gap this period as well as an expected increase in the inflation and exchange rate twelve periods into the future, it can be seen that the impact of an increase in the output gap brings about a reduction in the interest rates. That is, if the economy goes through a rough patch with a decrease in production, these results state that the central bank increases its interest rates.

Finally, from Table 1, it can be seen that for some specifications, the interest rate smoothing parameter yields a value above 1, which violates the assumptions of this coefficients being between 0 and 1.

For other specifications of different leads and lags, the tables show mixed results. The relationship between the inflation rate and the interest rate is positive and mostly significant.

As already stated, for nearly all specifications the results states that an increase in the expected exchange rate impacts the interest rate negatively, with some of the results being significant and others not. For all lead and lag structures, the estimates of the smoothing parameter yields significant results.

For other lead and lag structures of the monetary authority’s reaction towards the financial stress index, the results are similar to the ones described above. These results is presented in Tables A1 – A4 in appendix A.1, which show the estimation results for m=2, 0, -2, -3.

**Recursive estimation**

For further estimation, some of the lead specifications can thus easily be removed when estimating recursively. Immediately, an instant response to inflation rate and exchange rate may be removed from further estimation, as well as leads of -3, -1, 0, 3, 6, 9 and 12 for the output gap. For the exchange rate, leads of 6 and 12 can also be ruled out due to the insignificance of the coefficient for these lead lengths. That is, I will in the following assume that the central bank adjusts its interest rate in response to expected changes in the output gap 23 one period ahead and expected changes in the inflation rate and exchange rate 9 periods ahead. Specifically, as the lead structure in the estimation that follow I will use i= k= 9, j= 1 and m= -3, -2, -1, 0, 1, 2.

By recursively estimating the Taylor equation specified by eq. (4), I am able to find an estimated time path of the coefficients. The figures below show the recursive graphics of different lead length specifications for the financial stress index.

24 Figure 3: Recursive graphics, panels a- c. The plots show the time paths of the coefficients in the Taylor-type rule. In each panel, the top left graph is inflation, top right graph is the output gap, the bottom left graph is the exchange rate and the bottom right graph is the financial stress index.

26 The figures show that the different coefficients all vary somewhat across time. However, the jumps in the beginning of all the plots might be attributed to the initialization. Thus, the inflation rate, output gap and exchange rate seem to demonstrate a steady convergence in all panels. For the financial stress index, the coefficient drops around 2008, seemingly giving a negative effect on the interest rate setting. This abrupt fall in the stress indicator fits well with the latest financial turmoil where it was seen that interest rates were reduced in the wake of the increased stress to the financial sector.

**Time- varying coefficients estimation**

In employing the varying coefficients method, I will therefore keep all the coefficients but the financial stress index parameter constant in order to isolate the time-varying effect of financial instability on the interest rate. The exchange rate coefficient could also have been included as a time-varying parameter. However, as my previous results have shown that the effect of the exchange rate on monetary policy is minimal, I will therefore treat it as time-invariant.

**Thus, the time-varying model that is to be estimated is:**

(18) (19) In the estimating the equation above, I have once more used different lags and leads for the financial stress index, with m= -3, -2, -1, 0, 1, 2.

The time-varying impact of changes in the financial stress index on the interest rate for the different lags and leads are showed in the figures below.

Figure 5 above show the time-varying effect of financial stress on the interest rate for m=2, 1, 0, -1, -2, -3, and demonstrates that there is an abrupt drop in the impact of financial stress on the interest rate in late 2008. The effect is especially evident when estimating using lagged data, i.e. the time-paths dubbed δ_-1, δ_-2 and δ_-3. The effect also seems to become smaller when assuming that the central bank acts less sluggish to the increased stress in the financial sector. That is, the negative interest rate response is largest for δ_-3, and it can be seen that the effect diminishes as m increases. Moreover, the effect is smaller when the model specification assumes that the central bank acts to counteract the effects of financial stress.

That is, the evidence suggests that the central bank decreases its interest rate more ex post than ex ante as a result of an increase in financial stress. In the most recent period of financial turmoil, the central bank lowered the interest rate by roughly 0.7 basis points three months after a unit increase in the financial stress index, whereas the decrease in the interest rate was 28 about 0.4 percentage points as a response to an expected unit increase in the stress index two periods ahead.

These results are comparable to those found by Baxa et al. (2011), who estimate the impact of financial stress on interest rates for five countries. They find that there was in fact a reduction in interest rates when financial instability increased, especially during the last period of financial distress, in 2008. Moreover, the results are supported by Borio and Lowe (2004), in that the central bank is asymmetric in its response towards financial instability.

Moreover, it can be seen that interest rate increases also exist as an effect of increased financial stress. Specifically, the plot named δ_1in Figure 5 shows a large increase for the estimation with m= 1, i.e. when the central bank responds to an expectation of a change one period ahead. Depending on the nature of the expected increase in financial stress, i.e. from which sector the shock is initiated, an interest rate increase may serve to amplify a situation with financial distress. That is, if there is a shock to the financial sector through an increase in the risk premium in the interbank market, this effect may be propagated if the central bank increases its interest rates. Furthermore, as financial instability may cause reduced output and inflation, increasing the interest rates might make matters worse by further amplifying a potential economic decline. The time-path of the δ_1 plot in Figure 5, that there is an increase in the interest rate as a result of increased financial stress, can also be seen as a lowering of the interest rates by the central bank as it anticipates a decrease in the financial stress index.

5.2.2 Estimating using unemployment as an output gap proxy In what follows, I will turn to the case where the output gap is being proxied by the deviation of the unemployment rate from its natural rate. The inflation rate, the exchange rate and financial stress index are all defined as before. I have gone through the same steps of estimation as above, i.e. estimation of (4) by estimation through the use of the two-stage least squares method, recursively estimating (4) and finally estimating (18) – (19) by utilizing the varying coefficients method.

Two stage least squares estimation In the first estimation process, I once more estimate the augmented Taylor rule using different lags and leads for the inflation rate, exchange rate, output gap proxied by unemployment rate

The results apprehended through the two-stage least squares estimations procedure can be seen in Tables 3 and 4 below, as well as in Tables A5 – A8 in appendix A.1. In Tables 3 and 4, the estimation results using m=1, -1 are depicted, the estimation results using m=2, 0, -2, -3 are found in the tables in the appendix.

30 Table 3: Results from two-stage least squares estimation, with a lead of 1 period on the financial stress index.

32 The results in Tables 3 – 4 above show similar results as the ones obtained when using the output gap instead of the deviation of the unemployment rate from its natural rate. That is, for a structure using nine leads on the inflation and exchange rate, as well as a lag of one period on the output gap proxy, the 2SLS estimation again yields the most reasonable results. To be precise, the results show that an expected increase in the inflation rate or exchange rate nine periods ahead yields an interest rate increase. For the inflation rate, a target horizon of six months also gives results that state that the central bank increases its interest rate when the inflation increases. Unsurprisingly, an increase in the unemployment rate also leads the central bank to a lower the interest rate. Hence, if the unemployment gap is to increase through an increase in the level of unemployment, the central bank wants to counteract a possible economic downturn by reducing the interest rate. This relationship holds for all lead and lag specifications of the model, both the estimation results shown in Tables 3 and 4 above and Tables A5 – A8 in appendix A.1. The interest rate smoothing parameter is positive and significant in both tables above.

Moreover, an increase in financial stress leads to a monetary expansion, through a decrease in the interest rates. This result applies for all lead and lag structures imposed on the financial stress index. In general, the results also show that an increase in the financial stress index has a bigger impact on the interest rate setting decision when it is assumed that the monetary authority adjusts its interest rates in the same period as or after the increase in the stress index has occurred, rather than due to an expected increase. Specifically, the impact of financial stress is greater when the model is estimated using a lag structure rather than a lead structure on the financial stress index. This can, once more, be interpreted as the central bank being more aggressive towards financial stress ex post rather than ex ante.

For the more counterintuitive results, it can once again be seen from Table 3 that if the monetary authority adjusts the interest rate according to an increase in inflation rate and exchange rate today, as well as an increase in the unemployment rate gap 12 periods ahead;

the interest rate smoothing parameter is above 1, which, as already noted, violates the assumption that this parameter should take a value between 0 and 1. Moreover, from Table 3 it can be seen that, for a 0 lead on the inflation rate and for all lags and leads on the output gap proxy, an increase in the inflation rate yields a reduction of the interest rate. This is quite counterintuitive, as this means that the central bank fuels inflation, as cutting the interest rates in the case of an inflation rate increase in turn leads to an increase of the inflation rate. Hence,

Recursive estimation In the next step, I will estimate the augmented Taylor rule through recursive estimation. The object of this procedure is once again to identify the coefficients that seem to exhibit somewhat unstable time-paths. Moreover, I will remove some of the leads and lags used when estimating by the means of the two-stage least squares method. Specifically, I assume that the central bank’s target horizon for the inflation rate and exchange rate is nine months, whereas the target horizon for the output gap is one period, giving i= k = 9 and j= 1. For the financial stress index, I will use all the different leads and lags as above, with m= -3, -2, -1, 0, 1, 2.