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Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research
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The Taylor rule
In the past years, the Taylor rule attracted the interest of many scholars, since it is a very simple but powerful tool on how to set monetary policy. A standard Taylor rule takes the following form: it = a + ß (p t p t ) + ? (yt yt ) + et (1)
where a is the stabilizing interest rate of an economy (when p t = p t and yt = yt ), (p t p t ) is the in‡ation gap between the actual values of the in‡ation (p t ) and a desired level (p t ), (yt yt ) is the output gap and et is the stochastic term.
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The Taylor rule
The interpretation of the above rule is very straightforward. It recommends that the interest rate should rise above the stabilizing one if the in‡ation is above the target level and should decrease if in‡ation is below the target. A second recommendation coming from equation (1) is that the interest rate should be set above the stabilizing one if the gap is positive (real GDP is above potential real GDP) and below if the gap is negative (real GDP is below potential real GDP). Moreover, Taylor (1993) claims that a conducive monetary requires that ß = ? = 0.5. This implies that equal weights should be posed on the impact of the in‡ation and output gap. Note that putting more weight on the in‡ation gap, for instance, implies that the monetary authority displays a more aggressive policy to target in‡ation.
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The Taylor rule
As we may see, although very simple, this rule o¤ers crucial information to the policymakers. Its power relies on the fact that it is grounded on the characteristics of an economy, as mentioned before. From the above elements, it can be concluded that the objectives of the Taylor rule are price stability and maximum employment. However, as we stressed earlier, more weight could be attached to one of the targets in the above equation.
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The Taylor rule
A standard Taylor rule is well speci…ed and, therefore, ß and ? can be correctly estimated if monetary authority do not target other variables than the ones speci…ed in equation (1). This is a very crucial point. As a matter of fact, there exists a large debate in the literature on whether other variables should be included into the regression model for a more appropriate analysis of the monetary policy. Scholars show opposite views with respect to whether asset price movements should be included into the model to be estimated. On one hand, they do not believe that asset price movements should be a key determinant for monetary policy (Bernanke and Gertler, 2000 and 2001; Vickery, 2000) On the other, some scholars argue that asset price movements do provide critical information for shaping monetary policy (Cecchetti et al., 2000; Cecchetti et. al., 2002)
Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research 21/01/2014 5 / 32
Bernanke and Gertler (2001)
Given the above opposite views, the …rst step is to understand which are the reasons in favor or against the role of asset price movements in shaping monetary policy. It is well know that a large boom-and-bust cycles in asset prices witnesses changes in the underlying economic fundamentals. Bust periods are usually associated with a signi…cant contraction in the real economy. The crucial question is whether and how a central bank should respond to asset price volatility within a more general strategy for monetary policy. Bernanke and Gertler (2001) recognize that monetary policy itself is not a su¢ cient tool to address the potential damages, which come from the boom and busts in an economy. Instead it should be associated to regulatory actions to prevent the risk of exposure to a large asset volatility.
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Bernanke and Gertler (2001)
However, they point out that the damages may be severe only if monetary policy remains unresponsive to the changes in the economy. Built on the previous assumption, Bernanke and Gertler (2001) claim that monetary policy should not respond to any to change in asset prices, unless they can be understood as a signal of a change in the fundamentals of the economy. More speci…cally, those signals should account for a potential change in the in‡ation level.
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Bernanke and Gertler (2001)
Bernanke and Gertler (2001) motivate their choice with a wide range of arguments, which evolve on the idea that stabilizing asset price may be very di¢ cult. This is because it is not always clear whether the asset price volatility stems from fundamental factors, non-fundamental ones or a combination of both. Instead, an in‡ation-targetting monetary policy by focusing on the in‡ationary/de‡ationary pressure generated by asset volatility can account for the negative e¤ects of boom and busts without asking which is the source (fundamental/non fundamental) of that volatility.
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Cecchetti et al. (2002)
Cecchetti et al. (2002) o¤er a divergent view on the topic. Right from the beginning it is important to note that they do not invoke for the asset prices being a target of monetary policy. On the contrary, they claim that the central bank could improve macroeconomic performance by reacting systematically to asset price misalignments over and above their reaction to in‡ation and output gap. In other words, provided that the central banks’objective is to smooth in‡ation and output gap, Cecchetti et al. (2002) suggest that monetary policy should account for asset price volatility in order to ameliorate macroeconomic performance. The main reason of this view relies on the fact that asset price bubbles may create distortions in individuals’consumption and investments, this impacting on the real output and in‡ation.
Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research 21/01/2014 9 / 32
Cecchetti et al. (2002)
Moreover, raising/lowering interest rates when asset prices raise/decrease may also reduce the probability of bubbles arising. It is critical to note that Cecchetti et al. (2002) do not suggest that monetary policy should always act as a “lean against the wind”, but this should be the case only if asset price movements are determined by a disturbance in the demand and/or supply of the assets. This implies that, although asset price volatility o¤ers critical information to shape monetary policy, the latter should not react automatically to the former.
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Monetary Policy and Stock Market: Augmented Taylor rule
Following the above literature, we can reformulate the standard Taylor rule in order to encompass the e¤ect of asset price movements: it = a + ß (p t p t ) + ? ( yt yt ) + ? di st
i =1 n k
+ et
where n is the number of lags of s (asset price volatility) to be introduced to model the monetary e¤ect. Note that failing to reject the null hypothesis that the estimated ds are equal to zero implies acceptance of the Bernanke and Gertler (2001) theory about the e¤ect of asset prices on monetary policy. However, we may note that the impact of asset price volatility may be only indirect, through its impact on in‡ation and output gap. This is why it is sometimes more convenient to use an IV approach to model that indirect e¤ect.
Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research 21/01/2014 11 / 32
Monetary Policy and Stock Market: Extending research
While the above contrasting views are the basis to understand how central banks (should) set monetary policy, there exist a large amount of works, which extended the analysis to disclose the mechanism of monetary policy. In the following slides we will consider three possible extensions to study the relationship between monetary policy and stock market. You should note that in some cases, the analysis o¤ers a view on how the Taylor rule can be better speci…ed in order to capture in a more appropriate way how monetary policy should be set. We extend our analysis by considering:
1 2 3
Forward-looking models; Non-linearity in the monetary policy; Reverse causality in the relationship between monetary policy and stock market.
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Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research
Monetary Policy and Stock Market: Forward-looking models
As Furher and Tootell (2008) point out, using ex-post data may have a misleading impact in the interpretation of monetary policy. Their view is also accepted by Gorter et al. (2008), who claim that it is more appropriate that monetary policy should have a forward-looking view about in‡ation and output gaps. Moreover, Further and Tootell (2008) make use of that forward-looking model in order to evaluate whether asset volatility a¤ects monetary policy directly or indirectly.
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Monetary Policy and Stock Market: Forward-looking models
Furher and Tootell (2008)
They propose to estimate a model like the following: it = a + ßEt (p t +1 p t +1 ) + ?Et (yt +1 yt +1 ) +
k =1
? d k st
n
k
+ et
(2)
where Et denotes expected values conditional to the information available at time t . Monetary policy should take into account the expectation about the in‡ation and output gap. In order to create expected values, we estimate the following auxiliary regression for in‡ation: p t +1 = ?1 p t + ? 1 (yt yt ) + ? 1 st
1
+ µt
(3)
Using the residuals from equation (3), we generate the one-step-ahead in‡ation by subtracting them from the actual in‡ation series.
Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research 21/01/2014 14 / 32
Monetary Policy and Stock Market: Forward-looking models
Furher and Tootell (2008)
In the same vein, we can generate the expected values of output gap by estimating the following auxiliary equation:
(yt +1
yt +1 ) = ?2 p t + ? 2 (yt
yt ) + ? 2 st
1
+ ?t
(4)
Using the residuals from equation (4), we generate the one-step-ahead output gap by subtracting them from the actual output gap series.
Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research
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Monetary Policy and Stock Market: Forward-looking models
Furher and Tootell (2008)
As Furher and Tootell (2008) point out, if asset price volatility a¤ect directly monetary policy, di in equation (2) should be signi…cantly di¤erent from zero. Instead, if it does a¤ect monetary policy indirectly, ? 1 and ? 2 should be statistically di¤erent from zero in equation (3) and(4). Clearly there is no a priori possibility to exclude that asset price volatility a¤ects monetary policy both directly and indirectly.
Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research
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Monetary Policy and Stock Market: Forward-looking models
Furher and Tootell (2008)
Furher and Tootell (2008) test their null hypothesis by using di¤erent measures of stock price volatility and a di¤erent number of lags, k , to be included in their estimation. They use a GMM estimator to carry out their IV procedure. The results are summarized in the table in the next slide. The results indicate that in more that one third of the regressions carried out, it can be rejected the hypothesis that the lagged values of s enter only as an instrument for the expected output and in‡ation gap. This is an evidence of the importance of asset price volatility as an information driver for monetary policy. Note that a similar approach to model monetary policy has been developed by Castelnuovo (2007) and Gorter (2008).
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Monetary Policy and Stock Market: Forward-looking models
Furher and Tootell (2008)
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Monetary Policy and Stock Market: Non linear Taylor rule
Petersen (2007)
The Taylor rule is a linear function, where (in its simple version) the interest rate depends on the in‡ation and output gap. However, Petersen (2007) points out that there exist both theoretical and empirical reasons to think that Federal Reserve may follow a non-linear Taylor rule, instead. For instance, suppose that the Federal Reserve is following a rule, which postulates di¤erent weights for negative and positive in‡ation and output gaps. If this is the case, then the FED is following a non-linear rule.
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Monetary Policy and Stock Market: Non linear Taylor rule
Petersen (2007)
Moreover, both in‡ation and output gap are themselves non-linear processes with asymmetric adjustment mechanisms. This is a further explanation on why FED should follow a non-linear rule. Among all possible approach to non-linear time series, Petersen (2007) opts for the use of a smooth transition regression (STR) model, to capture non-linearity in the Taylor rule. The choice is motivated by the fact that the STR model allows for a smooth change from one regime – low in‡ation – to another – high in‡ation.
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Monetary Policy and Stock Market: Non linear Taylor rule
Petersen (2007)
Petersen (2007)’ s empirical strategy takes the following steps:
1
2 3
Preliminarily, he suggests to apply the Ng-Perron unit root tests to the variables employed in the analysis. If the series are non-stationary, the researcher should check for the existence of a cointegration relationship among the variables. Test the linear Taylor rule as a benchmark Apply the STR model in order to capture for any non-linearity in the rule used by the FED.
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Monetary Policy and Stock Market: Non linear Taylor rule
Petersen (2007)
The analysis is carried out on the period 1960-2005 with a particular emphasis on the periods 1985-2005 and 1960-1979. The research o¤ers interesting insight. The …rst result comes from the comparison of the linear and non-linear approach:
Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research
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Monetary Policy and Stock Market: Non linear Taylor rule
Petersen (2007)
We may easily note that the non-linear approach performs better than the linear one. The Schwarz information criterion improves by about 5%, as well as the Adjusted R 2 , while the standard errors of the residuals are smaller. Moreover, Petersen (2007) shows that using the non-linear approach we may clearly assess how the change from a low in‡ation regime to a high in‡ation one may generate a more severe response from the central bank. More speci…cally, he shows that the more the in‡ation approach the 3.55% threshold, the more the central bank responds to the in‡ation. Moreover, the higher the in‡ation rate, the most severe is central bank reply.
Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research
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Monetary Policy and Stock Market: Non linear Taylor rule
Petersen (2007)
While this analysis focuses on the estimation of simple Taylor rule, an interesting extension would check whether such a non-linearity exists in the impact of the asset price volatility on monetary policy. It might be the case that central bank replies to asset price only when volatility is considerably high.
Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research
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Monetary Policy and Stock Market: Reverse causality
So far we have been focusing on the possibility that asset price volatility a¤ects monetary policy. In other words, we assumed that the following relationship holds: it = f (st ) (5)
However there is also a large literature, such as Patelis (1997) and Rigobon and Sack (2002), which argues that asset price responds to monetary policy. In other words such a literature envisage a relationship like the following: st = f (it ) For instance Rigobon and Sack (2002) …nd that an increase in the short-term interest rate generates a decline in the stock price. Similarly Patelis (1997) shows that monetary policy variables are signi…cant predictors of future asset returns, although they cannot fully account for observed stock returns.
Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research 21/01/2014 25 / 32
(6)
Monetary Policy and Stock Market: Reverse causality
The existence of this literature posits some questions on the direction of causality between the main variables of interest. The question, which we may pose, is whether asset price volatility a¤ects monetary policy or whether the opposite holds. Although we do not review all the large literature on the e¤ect of monetary policy on stock market, we o¤er some information about how we can check for reverse causality. In order to answer the above question, we can set a Granger (1969) causality test to check the correct direction of causality between st and it .
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Monetary Policy and Stock Market: Reverse causality
The Granger causality test works in the following way. Suppose that we have the following equation: it = a + ? fi it
i =1 k i
+ ? ? j st
j =1
m
j
+ ?t
(7)
The objective of the test is to check whether the ?s are jointly di¤erent from zero. Therefore we set the following null hypothesis: H0 : ?j = 0 8j 2 f1..m g which implies that the sum of the coe¢ cients associated to the terms st j are statistically not di¤erent from zero (this hypothesis may be tested via a Wald test) Rejection of the null hypothesis implies that the terms ?m j = 1 ? j st improve our ability to predict it .
Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research 21/01/2014
j
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Monetary Policy and Stock Market: Reverse causality
We may repeat the same analysis by testing the e¤ect of it on the asset volatility, i.e.: s t = a + ? ? i st
i =1 k i
+ ? ?j it
j =1
m
j
+ ?t
(8)
The objective of the test is to check whether the ?s are jointly di¤erent from zero. Therefore we set the following null hypothesis: H0 : ?j = 0 8j 2 f1..m g Acceptance of the null hypothesis implies that the terms ?m j =1 ?j it do not improve our ability to predict it .
j
Based on those results we may safely claim that st Granger-cause it , while it does not Granger-cause st . The direction of causality goes from st to it .
Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research 21/01/2014 28 / 32
Monetary Policy and Stock Market: Reverse causality
From the analysis above we may have the following results:
1
2
3
m ?m j =1 ?j is statistically di¤erent from 0, while ?j =1 ?j is statistically not di¤erent from zero: in this case we have enough evidence to claim that changes in the stock market do help us in explaining interest rate movements (7), while changes in the interest rate do not help us in explaining stock market movements (8) (in this case we may claim that stock market movements Granger cause interest rate); m ?m j =1 ?j is statistically not di¤erent from 0, while ?j =1 ?j is statistically di¤erent from zero: in this case we have enough evidence to claim that changes in the stock market do not help us in explaining interest rate movements (7), while changes in the interest rate do help us in explaining stock market movements (8) (in this case we may claim that interest rate Granger causes stock market movements); m Both ?m j =1 ?j and ?j =1 ?j are statistically di¤erent from 0: we have enough evidence to claim that the direction of causality is twofold.
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References
Taylor, J. B. (1993). Discretion versus policy rules in practice. Carnegie-Rochester Conference Series on Public Policy 39, pp. 195-214. Bernanke, B. S. and Gertler, M. (2001). Should central banks respond to movements in asset prices? American Economic Review, 91(2): 253-257. Bernanke, B. S. and Gertler, M. (2000). Monetary policy and asset price volatility. NBER WP n. 7559. Castelnuovo, E. (2007). Taylor Rules and Interest Rate Smoothing in the Euro Area, The Manchester School, 75(1): 1-16. Cecchetti, S., Genberg, H. and Wadhwani, S. (2002). Asset prices in a ‡exible in‡ation targetting framework. NBER WP n. 8970.
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References
Cecchetti, S., Genberg, H., Lipski, J., and Wadhwani, S. (2000). Asset price and central bank policy. The Geneva Report on the World Economy. Fuhrer, J. and Tootell G. (2008). Eyes on the prize: How did the fed respond to the stock market? Journal of Monetary Economics, 55: 796-805. Gorter, J., Jacobs, J. and de Haan, J. (2008). Taylor rule for the ECB using expectation data. Scandinavian Journal of Economics, 110(3): 473-488. Patelis, A. D. (1997). Stock return predictability and the role of monetary economics. Journal of Finance 52(5): 1951-1972.
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References
Petersen, K. B. (2007). Does the Federal Reserve follow a non-linear Taylor rule?. University of Connecticut, Department of Economics Working Paper Series, n. 37. Rigobon, R. and Sack, B. (2002). The impact of monetary policy on asset price. NBER WP n. 8794. Vickers, J. (2000). Monetary policy and asset prices. The Manchester School, 68 (1): 1-22.
Dario Maimone Ansaldo Patti (Queen Mary University Data of London) Analysis for Research
Estimating the simple Taylor rule
In this exercise, we want to test whether there exists a relationship between the way in which monetary policy is detemined and stock market volatility. We use the Taylor rule as the estimation framework and make use of UK data ranging from 1990:1Q to 2010:4Q. The variables contained in the dataset are: RGDP, which is the UK real GDP, CPI, which is the consumer price index, ftse, i.e. the stock market index, and interest is the interest rate, set by the Bank of England. We start our analysis by estimating the following simple Taylor rule: it = a + ß (p t p t ) + ? (yt yt ) + et (1)
where it is the log of interest rate, p t is the actual in‡ation, p t is the desired level of in‡ation, yt is the actual output and yt is the potential one. Note that for convenience, we set p t = 0. Therefore the interest rate depends on the actual in‡ation level and output gap only.
(Queen Mary University of London) Data Analysis for Research 21/01/2014 2 / 19
Estimating the simple Taylor rule
Note that the variables, which we need for our analysis have been already calculated and included in the dataset. More speci…cally, we generated it , the log of interest rate, p t , the year-on-year in‡ation percentage rate and the output gap (yt yt ). In all cases we used the command Quck/Generate Series. Remember that:
1
The year-on-year in‡ation percentage requires …rst that you take the log CPI (pt ) and, secondly, that you generate in‡ation using the following formula (to be written in EViews): in‡ation = 100 ((pt p (t 4))
2
In order to generate the ouput gap, we need to calculate the potential output, yt . First, we take the log of RGDP (the variable y in the dataset). Double click on this variable and when the spreadsheet opens, click Proc/Hodrick-Prescott. Generate the potential output (yt ) and, …nally, the output gap as (yt yt ).
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(Queen Mary University of London)
Estimating the simple Taylor rule – Visual inspection
Our …rst step consists of a graphical inspection of our data. Plotting the variables of interest yields:
In‡ation and output gaps show a similar behavior. The interest rate remains stable over the period until the 2008, when we may assist to a large decrease in it. It could be the consequence of the …nancial crisis.
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Estimating the simple Taylor rule – OLS analysis
The further step consists of estimating equation (1) employing the OLS estimator. Remember that we expect that both ß and ? be positive. Results are reported in the following table:
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Estimating the simple Taylor rule – OLS analysis
As expected, the coe¢ cients associated to in‡ation and output are positive and signi…cant. A 1% increase in in‡ation leads to a 0.15% increase in the interest rate. Moreover a unitary increase in the output gap raises the interest rate by 0.17%. Overall we may note that the R 2 indicates that our model can explain about the 24% of the variability of dependent variable. Moreover the F-statistic argues in favor of the correctness of our model, since its associated probability is smaller than 0.05. Finally, the DW statistics is about 0.06. This indicates that our speci…cation may su¤er from a problem of serial correlation. Taylor (1993) suggests that a conducive monetary policy should set both ß and ? equal to 0.5. This implies that the output and the in‡ation gap weight equally in shaping monetary policy. A more severe in‡ation-targetting monetary policy is such that the weight for in‡ation is considerably larger compared to the one for output gap.
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Estimating the simple Taylor rule – OLS analysis
To test the aforementioned restriction, we set a Wald test (from the ouput window, click on View/Coe¢ cient diagnostics/Wald Test Coe¢ cient restriction). The null is: H0 : ß = 0.5 and ? = 0.5 HA : ß 6= 0.5 and ? 6= 0.5 The result of the Wald test is reported below:
We may note that the Wald test is extremely sign…cant. Therefore we should reject the null hypothesis stated above. This implies that in‡ation and output gap weight di¤erently in shaping monetary policy.
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Estimating the simple Taylor rule – OLS analysis
To have a visual impression regarding our model, we may consider how it performs in predicting the variability of the dependent variable. To accomplish this objective, we plot the actual values along with the …tted ones (from the ouput window, click on View/Actual, Fitted, Residuals/Actual, Fitted, Residuals Graph):
The immediate impression is that our model (green line) underestimate the actual data (red line) at the beginning of our series while consistently overestimate it from the 2008 onwards.
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Estimating the simple Taylor rule – OLS analysis
According to the above graph, we may conclude that our model may be misspeci…ed and/or a¤ected by a problem of omitted variables. However, before addressing the above issues, we may want to check the stability of the relationship under investigation. More speci…cally, the presence of some shocks may a¤ect it. For instance, the dotcom bubble at the beginning of 2001 may had some consequences on the way in which the monetary authority shaped monetary policy. In order to disclose the presence of a structural break, we set up a Chow break test (from the window output, select View/Stability Diagnostics/Chow Break test. In the window, which appears, write 2001 : 1, to underline that you suspect that a break occurred at that point).
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Estimating the simple Taylor rule – OLS analysis
The null hypothesis for this test is the following: H0 : there is not a break HA : thre is a break at 2001:Q1
The result of the test is the following:
We may note that all the reported statistics argue against the acceptance of the null hypothesis. Therefore, we should conclude that the dotcom bubble played a role in the way in which the monetary policy was set.
(Queen Mary University of London) Data Analysis for Research 21/01/2014 10 / 19
Estimating the augmented Taylor rule – OLS analysis
According to the main literature, there exists the possibility that asset price volatility a¤ects the monetary policy by bringing more information to the monetary authority. If we want to test this possibility, we need to slightly change the equation to be estimated as follows: it = a + ß (p t p t ) + ? (yt yt ) +
k =1
? d k st
n
k
+ et
(2)
where st k is the year-to-year ftse index change for stock market volatility (to calculate s : take the log of ftse – you may call it asset and then write in Eviews s = 100 (asset asset ( 4))). The hurdle of this estimation is to set k , i.e. the number of lagged values for s .We adopt a speci…c to general approach. We start by including the …rst lag. If it is signi…cant, we include the second lag. If both the …rst and the second lags are signi…cant, we include the third lags and so on. We stop when some of the included lags are not signi…cant.
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Estimating the augmented Taylor rule – OLS analysis
The results from our …rst estimations are the following:
The inclusion of the …rst lag of s improves the goodness of …t of our model. Instead of focusing on the R 2 , we look at the adjusted R 2 , since the latter is sensitive only to the inclusion of meaningful regressors. We may note that it slightly increased from 0.21 to 0.22, this suggesting that our model can explain better the variability of the dependent variable.
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Estimating the augmented Taylor rule – OLS analysis
As far as the coe¢ cient associated to s ( 1) is concerned , we may note that the associate t-statistic is equal to 1.84, with a p-value of 0.07. This means that we have only a mild evidence of signi…cance. Nonetheless, this is enough to claim that asset price volatility brings some more information into the model. Note that consistently with the theory, as the asset price volatility increases, the interest rate goes up as well. Given this result, we re-estimate our model by including the second lag of s . The results are the following:
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Estimating the augmented Taylor rule – OLS analysis
By including the second lag, we may note that s ( 1) loses its signi…cance. Moreover, it displays a change in the sign. Moreover, the coe¢ cient associated with s ( 2) is much more closer to the rejection region. Therefore, we may conclude that only the …rst lag should be included in our model. A second source of misspeci…cation may come from the fact that our model does not satisfy the man assumptions of the classical regression model. More speci…cally, it may su¤er from heteroskedasticity and serial correlation of the residuals and at a small extent from normality of the residuals. Therefore, we carry out some tests to check our model.
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Estimating the augmented Taylor rule – Diagnostic tests
The …rst test is the normality one (in the output window select View/Residual Diagnostic/Histogram – Normality test). Remember that the Jarque Bera test has the null of normality distribution in the residuals. The result is reported below:
We may easily note that the Jarque Bera test strongly reject the hypothesis of normality in the distribution of the residuals. Actually, we could reach the same result by looking at the graph reported along with the statistic.
(Queen Mary University of London) Data Analysis for Research 21/01/2014 15 / 19
Estimating the augmented Taylor rule – Diagnostic tests
The second test is the White test for heteroskedasticity (in the output window select View/Residual Diagnostic/Heteroskedasticity Tests/White). Remember that the test has the null of homoskedasticity in the residuals. The result is the following:
The reported statistics indicate a clear rejection of the null hypothesis. Therefore, our residuals are heteroskedastic.
(Queen Mary University of London)
Data Analysis for Research
21/01/2014
16 / 19
Estimating the augmented Taylor rule – Diagnostic tests
The third test, which we carry out, is the LM test for serial correlation (View/Residual Diagnostic/Serial correlation LM test. Remember to select 1 lag). The null hypothesis for this test is that the residuals are not serially correlated. The results are the following:
Also in this case, we have enough evidence to reject the null hypothesis. Actually, this result is consistent with the interpretation of the DW statistic reported in the estimation table. It is equal to 0.11, this denoting the existence of positive serial correlation.
(Queen Mary University of London)
Data Analysis for Research
21/01/2014
17 / 19
Estimating the augmented Taylor rule – Robust S. E.
We may conclude by saying that our model su¤ers from both serial correlation and heteroskedasticity. We may overcome this problem, by re-estimate our model using the Newey-West option to obtain robust standard errors:
We may note that after re-estimating our model by using robust standard errors, none of the variables enter the model signi…cantly, although they show the expected sign.
(Queen Mary University of London) Data Analysis for Research 21/01/2014 18 / 19
Estimating the augmented Taylor rule – GMM
However, the previous results may be determined by the fact that the asset price volatility a¤ects monetary policy indirectly. Someone argued that the asset price volatility may a¤ect both the output gap and the in‡ation rate. Therefore, we may consider the following auxiliary regressions:
(yt
= ?p t yt ) = fp t
pt
+ ? (yt 1 + ? (yt
1
1 1
+ µt yt 1 ) + ? st 1 + µt
yt
1 ) + ? st 1
The results from the above regressions are reported in the following slide.
Estimating the augmented Taylor rule – GMM
Estimating the augmented Taylor rule – GMM
As we may note, asset price volatility a¤ects both in‡ation and output gap. Therefore, there exists a problem of endogeneity that we need to address. We do so by implementing an IV procedure using a GMM estimator:
Right from the beginning, we may note that the probability associated with the J-statistic support the choice of our instruments. We may note that the coe¢ cient associated with s ( 1) is positive, although not statistically signi…cant. This may be an evidence that the asset price volatility a¤ects the interest rate only indirectly.
(Queen Mary University of London) Data Analysis for Research 21/01/2014 19 / 19
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