What Does Federal Reserve Target? Current or Expected Inflation

Transcription

1 Journal of Business and Policy Research Vol. 7. No. 2. July Issue. Pp What Does Federal Reserve Target? Current or Expected Inflation Charbel Bassil 1 This paper examines the transmission of monetary policy in USA between 1960 and We use a structural vector autoregressive model (SVAR) that includes federal funds rate, inflation rate (current or expected inflation) and output gap as endogenous variables. The contribution of this paper is to determine endogenously the number of structural changes in this multivariate system using Qu and Perron (2007) test. When we use expected inflation rate, we find two structural shifts, in October 1982 and December With current inflation rate we also find two breaks, in April 1979 and June We also found a significant increase in the influence of federal funds rate on variations in current inflation rate after We conclude that monetary policy was more efficient during Volcker and Greenspan chairmanships. We also conclude that Federal Reserve was more concerned by inflationary expectations between 1980 and We gave quantitative support to the fact that the goal of the domestic monetary policy during Volcker era was inflationary expectations rather than current inflation. Unfortunately our results do not support this for Greenspan era. JEL Codes: C12, C13, C32, E52, E58 1. Introduction A variety of rules have been proposed in the literature to explain the optimal interest rate policy. One of these monetary policy reaction rules was suggested by Taylor (1993). Many versions have been developped and used to model monetary policy in the context of both closed and open economies. See Taylor (1999) and references therein, Orphanides (2001, 2003), Gamber and Hakes (2006) and Molodtsova et al. (2008). Taylor and Wieland (2010) summarize much of the empirical research with large multicountry models. Some empirical papers treat monetary policy in multivariate models such as Bernanke and Mihov (1998), Favero and Rovelli (2003) and Bagliano and Favero (1998). Other papers consider a simple reaction function for the Federal Reserve such as Strongin (1995), Thornton (2001) and Clarida et al. (2000). Most of these papers rely on the transcripts of the Federal Open Market Committee, or the declarations of the chairman to determine the shift dates in the monetary policy. Nevertheless, there is a large literature on monetary policy estimation with endogenously determined break dates. The empirical findings depend on the methodoloy that is used to model changes in the coefficients and/or the variance of monetary policy shocks. The questions raised in this paper are: what type of monetary policy rule the Federal Reserve used to guide its decisions? In particular if the Fed relied on Taylor s rule, how responsive, if responsive at all, the federal funds rate was to output gap, the inflation rate itself and their lags. For this purpose we consider a structural VAR model, where the third equation comes very close to the fully optimal rule that reacts to current and 1 Notre Dame University Louaize, 72 Zouk Mosbeh Lebanon, cbassil@ndu.edu.lb.

2 lagged variables of the system. What does Federal Reserve target: current inflation rate or expected inflation rate? To answer this question, we estimate the identified structural VAR model using different measures of inflation. Since the empirical model is estimated over sample including shifts in U.S. monetary policy regimes, parameter instability is a potential problem. We suppose that these shift dates are endogenous and dependent on data. What is the number and the location of the break dates? We test formally the number of structural changes and we try to identify endogenously the break points in the VAR model. For this purpose, we apply the recent test proposed by Qu and Perron (2007). To our knowledge this is the most general test that considers multiple structural changes in multivariate regressions. We consider three cases. In the first one, we allow for changes in the conditional mean. In the second one, we only allow changes in the constant. In the third one, we only allow changes in the propagation mechanism. Once the break dates identified, we estimate a structural VAR model for each sub-period. By doing this, we can evaluate the impact of any change in the Federal Reserve s operating procedure on inflation rate and output gap during the period from January 1960 to December This allows us to examine the efficiency of the monetary policy for different sub-period. We are aware that a change in the variance of most of the macroeconomic variables has been dated in the early eighties. Major economic variables have become less volatile in the so-called "Great Moderation" period. Empirical investigation concludes for a structural break in the volatility of U.S. real GDP in early 1980's. Other studies like Kang et al. (2009) find that U.S. inflation underwent two regime shifts, both of which corresponded to changes in persistence. The first regime shift occured at the beginning of the seventies and the second in the early eighties. In our paper we only allow changes in the conditional mean but one of the break dates is found in the early eighties. Thus, the analysis will be resumed considering different sub-samples; i.e allowing different variance-covariance matrices for each sub-sample. As a result, the potential break in the variance-covariance matrix will be accounted in the empirical analysis. Our contribution to the litterature is three-fold: i. To our knowledge testing and dating the number of structural changes in a multivariate model using the recent econometric tool developped by Qu and Perron (2007) has not been yet done for the U.S. monetary policy. ii. We consider a structural VAR model to explore the role of monetary policy. We evaluate to what extend monetary policy differed between different policy regimes. iii. We give quantitative support to the fact that the goal of the domestic monetary policy during Volcker era was inflationary expectations rather than current inflation. To our knowledge this idea has not yet been quantified. Our results do not support the declaration of Greenspan that the priority of the Federal Reserve is the inflationary expectations. The paper is organized as follows. The second section reviews the literature. Section 3 develops the methodology and the data used for estimation. Section 4 details the empirical findings. In this section we comment and discuss in details the results for different models estimated. The last section stands for conclusion. 148

3 2. Literature Review Bassil There is mainly two methods to identify structural changes in a simple equation or a system of equations. In this paper we are only interested in those that deal with multivariate models. The first one is a time-varying models with changes in the mean or the variance estimated by Bayesian approach. Hereafter are some studies that model changes in monetary policy endogenously. Cogley and Sargent (2001) estimate a Bayesian VAR model with drifting coefficients for inflation, unemployment and short term interest rate. They find evidence of significant changes in the degree of monetary policy activism over time. According to the authors, the monetary policy was activist in the early 1960's, became neutral in the early 1970's, stayed passive for the remainder of the 1970's and was activist from the early 1980's onward. Sims (2001) argues that Cogley and Sargent (2001) may exaggerate time variation of VAR's coefficients if the variance of the VAR innovations changes over time. Thus, Cogley and Sargent (2005) extend their model to allow heteroskedasticity in the VAR disturbances. They obtain similar results as those in Cogley and Sargent (2001). Primiceri (2005) estimates over the period 1953Q1 to 2001Q3 a structural VAR model with time-varying coefficients and variance-covariance matrix of the innovations. Three variables are included in the model: GDP inflation rate, unemployment rate and three-month Treasury bills. He finds both systematic and non-systematic changes in monetary policy during the last forty years. He finds evidence of higher volatility of monetary policy shocks before Kim and Nelson (2006) apply a time-varying parameter model to estimate a forward-looking Taylor rule. They find that the Fed's response to inflation drastically increased in the early 1980's and stayed at the high level throughout 1980's and 1990's. The literature provide evidence on the efficiency of the monetary policy in USA but do not give an answer to whether the Federal Reserve was targeting expected inflation as chairman Volcker s and Greenspan s speeches suggest. In this paper we will try to fill this gap. The Bayesian method consists in drawing the evolution of the movements in the variables and the covariance matrix of the residuals. These are estimated from local linear approximations to the means and evaluated at the posterior mean. Spiegelhalter and Rice (2009) and Yitzhaki (1991) briefly describe the advantages and disadvantages of the Bayesian estimation. The Bayesian analysis is a process for obtaining posterior distributions or predictions based on a range of assumptions about both prior distributions and likelihoods. Therefore, the prior distribution is central to Bayesian statistics. Prior distributions can be totally objective or fully subjective and remains controversial. In both cases, sensitivity analysis and reasoned justification for prior and likelihood become vital to show the accuracy of the results. The above examples, apart Primiceri (2005), do not test the robustness of their results. Nevertheless, in many cases, estimates, intervals, and other decisions will be extremely similar for Bayesian and frequentist analyses. A notable exception is in hypothesis testing, where default Bayesian and frequentist methods can give strongly discordant conclusions. We think that it will be interesting to check the robustness of the previous results using a formal test statistics that determines the number and the exact timing of structural breaks. For this reason we will use Qu and Perron (2007) test to investigate the presence of structural changes in our SVAR model. The second method used to identify structural changes in a simple equation or a system of equations is based on tests statistics. The latter formally test the presence and the number of structural changes. This method is less explored than the first one. Bai et al. (1998) propose a procedure to test the presence of a single break in multivariate time 149

4 series including (0), (1) and deterministically trending regressors. They find that a 90% confidence interval for the break in U.S. output growth is centered around the first quarter of Bai (2000) considers the consistency, rate of convergence and limiting distribution of estimated break dates in a segmented stationary VAR model estimated by quasi maximum likelihood. He considers breaks in the parameters of the conditional mean, the covariance matrix of the error term or both. Hansen (2000) considers multiple structural changes in a cointegrated system, though his analysis is restricted to the case of known break dates. To our knowledge, the most general framework is that of Qu and Perron (2007). Qu and Perron (2007) test allows for breaks in the condiational mean and/or the variance-covariance matrix. The breaks can be globaly or locally ordered. In other words, the breaks can be common to all the equations or not. They provide critical values for up to ten changing coefficients. In order to compute critical values when the total number of changing parameters exceeds ten, we introduce some modifications to the Gauss code provided by Perron and Qu (2006). 3. The Methodology and Model 3.1 Monetary Policy Analysis in SVARs We consider the following three dimensional structural VAR model for vector of endogenous variables for. We consider two measures for inflation rate, is current inflation rate and is expected inflation rate, is the output gap and is the federal funds rate. The general SVAR is given by: for where is a vector of deterministic variable, an intercept. is an vector of structural disturbances. are serially uncorrelated errors distributed independently of with a zero mean and a constant positive definite diagonal variance-covariance matrix. Matrix describes the contemporaneous relations among the variables and allows some shocks to affect directly more than one endogenous variable in the system. The reduced form of the structural model (1) is given by: (1) (2) where is a column vector, for are matrices of coefficients and is the vector of errors. The errors of the system are interpreted as linear combination of exogenous shocks from which we can derive the relation between the variance-covariance matrices of and as follows: where is a symetric diagonal matrix and is an identity matrix. This identification of assumes orthogonality of structural disturbances. This assumption is required to consider the dynamic impact of an isolated shock. can be written as: This is a nonlinear system of equations. We use a maximum likelihood estimation to (3) (4) 150

5 estimate and matrices. Because no closed form solution is available, this has to be done by employing numerical optimization methods. Sometimes the optimization turns out to be difficult in practice, and the choice of appropriate starting values is crucial. The resulting ML estimator is asymptotically efficient and normally distributed. Moreover, a ML estimator for is given by: (5) where and are estimators of and, respectively. For more technical details see Hamilton (1994). To identify the assumptions, we consider that monetary authority, in order to control inflation, needs to set interest rates systematically, reacting to the state of the economy. Thus, we allow for responses by the monetary authorities to current or expected inflation and output gap. This is Taylor's rule that permits, via the inclusion of lags of, for central bank interest rate smoothing. Using current inflation rate we have a backward version of Talor's rule, while using expected inflation we have the forward version. Unless there exist an objective of output smoothing, the output gap variable has no reason to be considered because its role in forecasting the inflation evolution is already implicitly taken into account by the variable expected inflation. We interpret the estimated constant term as composed of the sum of the steady state real interest rate and an inflation target. We also suppose that macroeconomic variables (, and ) are directly affected by an interest rate shock. This is consistent with a wide spectrum of applied studies. This model is geared to deliver monetary policy shocks, so the identification of shocks to inflation and output gap is not crucial for the subsequent analysis. We consider that neither an output gap shock has an instantaneous effect on inflation rate, nor an increase in prices has an instantaneous effect on production. Matrix and can be written as: ( ) and ( ) and provide information about how much the Federal Reserve should adjust its interest rate each month in response to an increase in inflation rate or output gap. Thus, the third line of matrix is Taylor rule. and suggest that a monetary policy shock has a direct effect on inflation rate and output gap. The third equation of the VAR is interpreted as a policy reaction function: it gives a description of how the federal funds rate is adjusted in response to lagged values of output and inflation rate. Impulse response functions and variance decompositions for structural disturbances will be performed using Sims-Bernanke decomposition. 3.2 Suitability of VAR VAR models have several advantages. The researcher does not need to specify which variables are endogenous or exogenous - all are endogenous. VARs allow the value of a variable to depend on more than just its own lags or combinations of white noise terms. The forecasts generated by VARs are often better than traditional structural models. VAR models of course also have drawbacks and limitations relative to other model classes. VARs are a-theoretical since they use little theoretical information about 151

6 the relationships between the variables to guide the specification of the model. In our case some of the restrictions that we impose are based on economic theory. There are several approaches available for determining the lags number and may lead to different results. For relatively small sample sizes with a big number of endogenous variables, the degrees of freedom will rapidly be used up, implying large standard errors and therefore wide confidence intervals for model coefficients. Our estimation covers a large sample thus we are not worry about this problem. All of the components in the VAR should be stationary. However, many proponents of the VAR approach recommend that differencing to induce stationarity should not be done. They would argue that the purpose of VAR estimation is purely to examine the relationships between the variables, and that differencing will throw information on any long-run relationships between the series away. For this reason we will test the possibility that the variables are stationary around a break and include them in level instead of first difference in the VAR. 3.3 Data Federal funds rate, current inflation rate and output gap are monthy series from January 1960 until December 2008 and seasonally adjusted, except the federal funds rate. Expected inflation rate is a monthly series from January 1980 until December It is the real inflation forcasts constructed from household survey data by the University of Michigan Surveys of Consumers. The procedure to estimate price expectations is well described in Curtin (1996). The graphs of these series are plot in the appendix. The variables are available on the web site of the Federal Reserve of Saint Louis. Current inflation rate is the CPI inflation over the previous twelve months. 1 It is measured by the CPI for all urban consumers. Output gap is defined as the deviation of the actual output from the potential output. Since GDP is a quarterly series, we measure the actual output by the industrial production index taken in log (LIPI). 2 Potential output is unobserved and must be estimated. It is estimated as a quadratic trend with a structural change. Thus, we use Lee and Strazicich (2001) unit root test to test the stationarity of LIPI with one break under the null and the alternative. We consider the two models proposed by Lee and Strazicich (2001). Model A only allows a change in the mean and model C allows a change in the mean and the slope. To do this test we choose the minimum lags number that eliminates the residuals autocorrelation. Thus, we consider 11 lags. The test statistics are respectively - and - for model A and C. We reject the null hypothesis of unit root with one break only for model A. Thus, we conclude that Industrial Production Index taken in log is stationary with a break in November The break occurs in the mean of the series. Hereafter, we measure output gap as the gap between Industrial Production Index taken in Log and a quadratic trend with a mean change in 1970: Results 4.1 The Data Order Integration Since models with unit root regressors such as models with cointegration are not permitted in Qu and Perron (2007) according to assumption (A1) p.6-7 therein, we begin the analysis by checking the data order integration. For this purpose we perform Eliott et al. (1996) test, noted hereafter and Kwiatkowski et al. (1992) noted hereafter. In order to treat under the stationary hypothesis the relevant deterministic component we simply visualize the graphs. We consider that, in level, federal funds rate ( ), inflation rates (, ) and output gap present only a constant. In first 152

7 difference we retain the same models. We choose the lags number that minimizes the Modified Akaike Information Critira proposed by Ng and Perron (2001) with. 4 According to table (1), test rejects the null hypothesis of unit root for at 10% and for and at 5% but does not reject it for. test does not reject the null hypothesis of stationarity for, and at 1% but it rejects it for. In the presence of a break in the series, standard unit root tests loose in power. To check this possibility, we use Lee and Strazicich (2001) stationarity test with one break under the null and the alternative. We represent and by model C (break in the mean and the slope) and and by model A (break in the mean). We find respectively (15), (16), (9) and (12). Between parentheses are the selected lags number. We reject the null hypothesis of unit root with one break for at 10%, at 1% and at 5%. Table 1: and tests Series Series Series Series Level First difference Level First difference - - (15) (17) (18) (09) - - (13) (15) (18) (10) - (16) (13) (15) (20) - - (5) (5) (18) (13) NB: *, ** and *** present respectively the rejection of the null assumption at 1% 5% and 10% levels. Between parenthesis are the lags number for the and the bandwidth (Bartlett kernel) for the. Since we investigated the nature of the non stationarity, using different types of test, we difference the non stationary variables and we consider two VAR models. The endogenous variables for the first VAR are, and. These variables are taken in level. We name this VAR model 1. The endogenous variables for the second one are, and. Only is taken in first difference. We name this VAR model 2. In the next paragraph, we search for structural breaks in these two stationary VARs. 4.2 Testing and estimating structural changes To test for unknown structural changes, we use Qu and Perron (2007) likelihood ratio test. The test statistic considered is the highest value of the likelihood ratio test over all admissible partitions in the set. We suppose that the break date such as and with. We do not allow consecutive breaks that is why we impose that with. We consider that the break dates are simultaneous in the three equations. is the smallest lags number that eliminates autocorrelation from the residuals from order one to at 1%. We set, this means that we only allow a shift of half a year. is calculated before considering break dates. For the full sample, it is set to, see the first part of tables (2) and (3) below. 153

8 Table 2: VAR Residual Serial Correlation LM Tests, model : M: : : : : : :12 VAR(5) VAR(3) VAR(3) VAR(5) -Stat Prob -Stat Prob -Stat Prob -Stat Prob Note: is a Lagrange multiplier test for order serial correlation. Probs from chi-square with 9 df. The endogenous variables are, and. The residuals of the three dimensional VAR with ( ) are not autocorrelated to order 6 only with 46 lags. This high number of lags is not meaningful and could be due to a misspecification issue. It could stem from an omitted break in the model s parameters. Table 3: VAR Residual Serial Correlation LM Tests, model M1 2008M M M M M12 VAR(5) VAR(3) VAR(5) -Stat Prob -Stat Prob -Stat Prob Note: is a Lagrange multiplier test for order serial correlation. Probs from chi-square with 9 df. For the full sample adding more than 5 lags may worsen the results. The endogenous variables are, and. As will be seen later, accounting for structural breaks seems to solve this serial correlation problem. For that reason, hereafter, we retain 5 lags. Note that the subsamples given in these tables are those found according to Qu-Perron test presented below. To determine the number of structural breaks we use the following procedure. First we use to test whether at least one break is present. If the test rejects the null of no breaks, then we apply a sequential testing procedure based on the estimates of the break dates obtained from the maximization of the likelihood function. We apply the test sequentially, for until the test fails to reject the null hypothesis of no additional structural break. The limiting distribution of the test depends only on the breaks number, the total number of coefficients that are subject to change and the trimming parameter. It has the same form as the one developped in Proposition 6 of Bai and Perron (1998). Critical values if the total number of coefficients that are subject to change is less than 10 can be found in Bai and Perron (1998, 2003a,b). In the pure structural change model 48 coefficients are allowed to change. In the two partial structural change models 3 and 45 coefficients are allowed to change. In order to compute critical values, we introduce 154

9 some modifications to the Gauss code provided by Perron and Qu (2006). To compute the critical values for the test we use theorem 6 of Qu and Perron (2007). The tests for a pure structural change or a partial structural change, are reported in table (4). There is no evidence for breaks in the constant, neither in model one nor in model two. Whether we use current or expected inflation rate we conclude that there is two breaks in the propagation mechanism (lags). For model one, the sequential test concludes in favor of two breaks. The break points that maximize the likelihood function are 1979:04 and 1987:06. These break dates seem plausible. The first one coincides with the second oil price shock and the changes in the Federal Reserve operating procedures conducted by Paul Volcker. Once appointed as chairman of the Fed, Paul Volcker initiated a strong disinflationary policy. He switches the focus of monetary policy to tighter control of the monetary base in order to bring down the high inflation rate. The second one coincides with the stock market crash. It also corresponds to the time Alan Greenspan took over the helm. It is also interesting that we do not find evidence of changes in policy at peaks and troughs of the business cylce or across different Fed chairmanships. When we replace current inflation by expected inflation we also find two breaks over the period The estimated break dates are 1982:10 and 1987:12. This break date is very close to the one found in model one. The results of the pure structural change model in the conditional mean conclude that there is two breaks. The break dates are the same as the ones described above. Our results can be related to other findings in the literature. Duffy and Engle-Warnick (2006) test the stability of the original Taylor rule over the period They use the sequential test of Bai and Perron (1998) and found three breaks: the first quarter of 1968, the third quarter of 1979 and the fourth quarter of The last two breaks come very close to our findings. Note that our data is monthly while their data is quarterly. Boivin (2006) estimates a forward-looking Taylor rules with drifting coefficients. The estimation is based on real-time data and accounts for the presence of heteroskedasticity in the policy shock. He finds that Fed's response to the real-time forecast of inflation regained strength from the early 1980's onward. Using Qu and Perron (2007) we also find a break beginning Boivin and Giannoni (2006) use an heteroskedasticity robust version of the Bai et al. (1998) multivariate stability test, to investigate the stability of the parameters in a four dimensional VAR. The VAR's regressors are detrended output, inflation rate, commodity price measure and federal funds rate. They found a break in 1982:1. 155

10 Table 4: Estimated break dates, and tests Part one: Partial structural change model in the constant (23.23) Partial structural change model in the lags 1 (85.642) (75.266) ( ) 1979: :06 95% confidence interval [1979: :06] [1987: :07] Pure structural change model in the conditional mean 1 (90.54) (80.40) (233.01) 1979: :06 95% confidence interval [1979: :05] [1987: :07] Part two: Partial structural change model in the constant (23.23) Partial structural change model in the lags 1 (85.642) (72.118) ( ) 1982: :12 95% confidence interval [1982: :12] [1987: :10] Pure structural change model in the conditional mean 1 (90.54) (80.40) (233.01) 1982: :12 95% confidence interval [1982: :12] [1987: :10] Note: * and ** denote respectively rejection of the null at 5% and 10% level. Between parentheses are the critical values at 5% and 10%. The 90% confidence interval for the VAR parameters break date ranges from the fourth quarter of 1977 to the second quarter of This confidence interval is consistent with one of our break date. Contrary to Boivin and Giannoni (2006), we consider the possibility of the presence of multiple structural changes. Boivin and Giannoni (2002) check if there is a break in the coefficients of a VAR model using U.S. data from 1960 to The specific VAR that they consider contains four variables: detrended output, inflation rate, commodity price inflation, and federal funds rate. For each equation of the reduced-form VAR, they test jointly for the stability of all the coefficients on the lags of a given variable using Andrews (1993) stability test. They use a heteroskedasticity-robust version of the test. They report instability in 1979:3 and 1984:1. Some of these break dates coincide with our results. Qu and Perron (2007) test catches the most frequently cited date in the litterature examining changes in the U.S. monetary policy. This break date occured in early eighties. Since we do not have enough observations to estimate the SVAR over the sub-period 1980: :10, in the following sections we will limit our study to the two sub-periods 1982: :12 and 1988: : Dynamic Effect of Federal Funds Shock Now we estimate model 1 over the periods 1960: :04, 1979: :06 and 1987: :12. We choose the minimum lags order that eliminates the autocorrelation in the residuals. The results of the autocorrelation LM test are given in table (2). We estimate model 2 over the period 1982: :12 and 1988: :12. The results of the autocorrelation test are presented in table (3). In model 2, when we 156

11 take into consideration the presence of structural breaks and estimate the model over the two sub-samples the residuals' autocorrelation vanishes. To find a solution to the system of equations (4), we use a numerical maximization of the log-likelihood function. We use Broyden, Fletcher, Goldfarb and Shanno algorithm incorporated in RATS and we impose initial guess values for and. We took as the start values the coefficients of the simple benchmark rule proposed in Taylor (1993, 1999). is set equal to -1.5 and is set equal to The negative sign of the policy rule coefficients ( and ) in table (5) tells us that the federal funds rate rises if current inflation or expected inflation increases or if real output rises above potential output. The results show that the weight on current inflation and expected inflation is greater than the weight on output gap. This suggests that interest rate was adjusted more aggressively in reponse to changes in inflation rates. We also notice that the weight on the output gap increases during Volcker's chairmanship but decreases after This suggest that while the Fed responded to the rising inflation after the second oil price shock, it continued to give weight to output gap deviations. Sub-samples Table 5: Estimated A and B matrices 1960: : (0.109) -0.01(0.051) -0.39(0.033) 0.05(0.192) 1979: : (0.377) -1.03(0.216) -0.16(0.029) -0.30(0.075) 1987: : (0.042) -0.01(0.022) -1.01(0.060) 0.21(0.161) 1982: : (0.161) -0.19(0.110) -0.50(0.062) -0.28(0.199) 1988: : (0.038) -0.00(0.022) -1.06(0.064) 0.14(0.208) Note: Standard errors in parentheses. Since,,, and are stationary, the long run effects of innovations on these variables are zero. However, innovations may have permanent effects on the level of,. Hereafter, we plot the accumulated impulse response functions for the effects of the innovations on the level of expected inflation rate, based on the two VARs model for different sampling periods. The impulse response functions to a normalized shock and the two-standard error band are obtained from bootstrapped simulations. The evidence reported in the impulse response functions represents some stylized facts. They are fairly reasonable in that they confirm that monetary contractions identified as innovation in the federal funds rate lower prices at short term, see the third graph in the first line of figures (5) to (9). Rather than converging to zero, the response of expected inflation rate converges steadily to a long run non-zero value. This is because expected inflation rate is not stationary and the response presented here is the accumulated impulse response function. The response of output gap to an interest rate shock is not very clear. It depends on the sub-periods and the inflation measure, see the third graph in the second line of figures (5) to (9). Some figures present an output puzzle. For the period pre-1979 and post-1987, after a positive interest rate shock, output gap moves first above zero before becoming negative for some cases. This result is unexpected and does not fit the conventional theory. Uhlig (2005) and Rafiq and Mallik (2008) find the same result. They use an agnostic identification procedure to 157

12 estimate the effects of a contractionary monetary policy on real output. They find that monetary policy shocks have no clear effect on real output. The impulse response functions capture the two factors emphasized by Taylor rule. The first factor is the output gap adjustment factor. This factor recommends that Federal Reserve raises the federal funds rate if the gap is positive. This means that if real output is above potential real output, Federal Reserve raises the interest rate. A positive shock on output gap rises the federal funds rate at short and middle term then vanishes at long term. This is shown by the impulse reponse functions represented in the second graph of the third lines of figures (5) to (9). The second factor is an inflation adjustment factor. This factor recommends that Federal Reserve reacts to an increase in current or expected inflation by increasing the federal funds rate. A positive shock on inflation rate rises the federal funds rate. This is shown by the impulse reponse functions represented in the first graph of the third lines of figures (5) to (9). In the second graph of the first line and the second graph of the first column of figures (5) to (9) we can see the two restrictions that we imposed. A positive output gap shock does not have an instantaneous effect on inflation rate and an increase in prices does not affect instantaneously output gap. Output gap does not decrease simultaneously with an increase in prices. 158

13 Figure 1: Impulse Response Functions from model 1: 1960M01 to 1979:04 159

14 Figure 2: Impulse Response Functions from model 1: 1979:05 to 1987:12 160

15 Figure 3: Impulse Response Functions from model 1: 1988:01 to 2008M12 161

16 Figure 4: Impulse Response Functions from model 2: 1982:10 to 1987:12 162

17 Figure 5: Impulse Response Functions from model 2: 1988:01 to 2008:12 163

18 4.4 Relative Contribution of Federal Funds Rate Disturbances The variance decomposition for forecasts of, and are obtained from the structural VAR model represented in equation (1) and estimated for the different sub samples. Here we are only interested in the federal funds rate shock since it represents a monetary policy shock. This decomposition provides insight regarding to what extent, the monetary policy results from discretionary measures from the monetary authorities. In tables (6) to (7) we have the results for the SVAR with current inflation rate and in tables (8) to (9) we have the results for the SVAR with expected inflation rate. Table 6: Forecast error variance decomposition of. Model 1 Decomposition of 1960: : : : : :12 Step According to table (6), between January 1960 and April 1979 monetary policy shock accounts for less than 10% of the variations in current inflation rate at long term. Monetary policy shock has an important instantaneous effect on current inflation rate but this effect diminishes with time. The effects of a contractionary monetary policy on current inflation dissipates after 3 months. After 3 months, monetary policy shock explains around 20% of the forecast error variance of current inflation rate at all horizons. It seems that monetary policy was not very efficient before This result is not surprising. Many economists agree that monetary policy in the United States was not so well managed in the fifteen or so years prior to Paul Volcker. During Carter, Burns and Miller eras, monetary policy had for priority the responsibility to manage a low unemployment rate. During this period there has been a consensus that inflation originated in cost push pressures rather than in a monetary phenomenon (Hetzel (2008)). After 1980, the results become more relevant. We see from the second part of this table that the effect of monetary policy on current inflation increases with time. It accounts for the third of the variations in current inflation rate at short term, and more than 65% of the variations at long horizon. According to the third part of this table, after 1987, the year Alan Greenspan was nominated as chairman of the Board of Governors of the Federal Reserve, monetary contraction explains around 60% of the forecast error variance of current inflation rate at short term. The effect of this shock diminishes with time but remains significant. It accounts for the third of the current inflation rate's variations at long term. It turns out that the effect of a monetary policy contraction was more aggressive during Volcker's chairmanship. 164

19 Table 7: Forecast error variance decomposition of. Model 1 Decomposition of 1960: : : : : :12 Step The results in table (7) suggest that before 1980 federal funds rate has an insignificant effect on output gap. Monetary contraction explains around 10% of the forecast error variance of output gap in the long-run. This suggests that monetary contraction does not have a real effect on output gap. This is not at odd with some empirical studies such as the ones by Uhlig (2005) and Boivin and Giannoni (2006). The latter, finds that changes in the Fed funds rate have been followed by a smaller and unclear response of output. Here, we use output gap in place of real GDP but we find the same results. It seems that monetary policy during Volcker and Greenspan eras put more weight on ouput gap. The latter result reverses the one of Duffy and Engle-Warnick (2006). By estimating a simple Taylor equation, they conclude that the weight on output gap decreases after 1979:3. This is not the case in our multivariate model. Table 8: Forecast error variance decomposition of. Model 2 Decomposition of 1982: : : :12 Step From the results of the first sub-period in table (8), we see that federal funds rate shock acounts for around 55% of the forecast error variance decomposition of expected inflation at short term. The effect of federal funds rate shock on expected inflation decreases at short term then increases at long term. It acounts for 80% of the forecast error variance decomposition of expected inflation at the end of the year. For the second sub-period, the effect of federal funds rate shock decreases with time but never falls below 30%. The contribution of the federal funds rate shock to the forecast error variance decomposition of output gap is given in table (9). We clearly see that monetary policy during the two subperiods does not have an important real effect on the economy. This contribution increases with time but does not exceed 10%. 165

20 Table 9: Forecast error variance decomposition of. Model 2 Decomposition of 1982: : : :12 Step If we compare the forecast error variance decomposition of current and expected inflation for the post-1980 period we would lean to say that, during Volcker's chairmanship, Federal Reserve's goal was to prevent a surge in inflation from permanently raising inflationary expectations. Since the sub-samples in question are not exactly the same this interpretation could be biased but we believe that the results would not significantly change. We believe that this result arises from the emphasis placed on expected inflation. On October 9, 1979, Volcker told the American Bankers Association that "the immediate challenge is to avoid embedding the current rate of inflation in expectations and wage and pricing decisions, before the current bulge in prices subsides". Chairman Greenspan testified on May, 1994 that "the challenge of monetary policy is to interpret current data on the economy and the financial markets, with an eye to anticipating future inflationary or contractionary forces and to countering them by taking action in advance". Unfortunately our results cannot empirically prove Greenspan's speech. We do not find a big difference between the forecast error variance decomposition of federal funds rate due to current and expected inflation rate. Thus, we can not say that Federal Reserve was forwardlooking during Greenspan's chairmanship. Maybe if we make Taylor rule completely forward-looking we will find evidence in favor of this declaration. This line of research is interesting to be explored. 5. Conclusion The main contribution of this paper is to test formally for a structural shift in the mean and the dynamic structure of the VAR. We used different measure of inflation: expected inflation rate and CPI inflation rate. When we used CPI inflation rate we found two break dates in 1979:4 and 1987:6. With expected inflation rate we also found two break dates; 1982:10 and 1987:12, which are quite close to the other ones. We find that federal funds rate targeting has been more efficient after After this date, monetary policy contraction has a more important effect on current inflation rate. Hence there is a significant difference in the way monetary policy was conducted pre- and post-1980, the year Paul Volcker was nominated Chairman of the Board of Governors of the Federal Reserve System. This result is very important for those who want to evaluate the effects of monetary policy shocks. We also conclude that Federal Reserve was more responsive to inflationary expectations during Volcker chairmanship. More than three quarters of the variation in expected inflation rate are explained by Fed funds rate shock at long term. As some other studies 166

21 found, we conclude that monetary policy had a small effect on output gap before What we do not find is also interesting. Our results do not support the idea that chairman Greenspan was specially worry about inflationary pressures as his declarations claim. Checking the robustness of our results using real time data is an interesting question. We can also include output gap forecasts and make the Taylor rule completely forwardlooking. Proxying Real GDP by the Industrial Production Index is a limitation for this study. Finally, testing for conditional mean structural change while allowing for regime shifts in the conditional variance as well, would also be a natural extension of our work. We leave these questions for future research. Endnotes 1 2 Following Bec and Bastien (2007), the logarithm of industrial production index is also multiplied by We tried other measures for potential output, such as a linear trend with a break in 1970:11 in the mean; we considered other break date like the first and the second oil price shock, a linear trend without a break, a quadratic trend without a break. We did the Qu- Perron test with these measures and we found almost the same break dates. The SVAR analysis does not present significant differences neither in the IRFs nor in the variances decomposition. We choose this measure for output gap because it gives the most reasonable results, as it will be shown in the next sections, in terms of the chosen lags, the residuals autocorrelation and the stationarity analysis. 4 We tested the sensitivity of the test's results to another lag selection method, such as Akaike Information Criteria with. We found the same results. The statistics of the test found for,, and are respectively (16), (18), (4), and 0.001(16). Between parentheses is the selected lags number. Thus, is stationary at 1%, is stationary at 5%, is stationary at 10%, and is not stationary. References Andrews, D 1993, Tests for Parameter Instability and Structural Change with Unknown Change Point, Econometrica, vol. 61, pp Bagliano, CF & Favero, CA 1998, Measuring Monetary Policy with VAR Models: An Evaluation, European Economic Review, vol. 42, pp Bai, J 2000, Vector Autoregressive Models With Structural Changes in Regression Coefficients and in Variance-Covariance Matrices, Annals of Economics and Finance, vol.1, pp Bai, J, Lumsdaine, RL & Stock, JH 1998, Testing for and Dating Common Breaks in Multivariate Time Series, The Review of Economic and Studies, Vol. 65, no. 3, pp Bai, J & Perron, P 1998, Estimating and Testing Linear Models With Multiple Structural Changes, Econometrica, vol. 66, pp Bai, J & Perron, P 2003a, Computation and Analysis of Multiple Structural Change Models, Journal of Applied Econometrics, vol. 18, pp Bai, J & Perron, P 2003b, Critical Values for Multiple Structural Change Tests, Econometrics Journal, vol. 6, pp

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