In this section, we present the regression results of the policy rules for the eight OECD Central Banks emphasizing the better performance of the semiparametric approach previously described. Four main specifications of the reaction function are investigated: an augmented semiparametric rule (ASP), a standard semiparametric rule (SP), an augmented parametric rule (AP) and a standard parametric rule (P):

ASP : it=c+s(ASPπ )(Etπt+1) +s(ASP)x (Etxt+1) +s(ASP)π,x (Etπt+1, Etxt+1) +(ASPt ) SP : it =c+s(SPπ )(Etπt+1) +s(SPx )(Etxt+1) +(SPt )

AP : it =β0(AP)+βπ(AP)Etπt+1+βx(AP)Etxt+1+βπ,x(AP)Etπt+1×Etxt+1+(AP)t P : it =β0(P)+βπ(P)Etπt+1+βx(P)Etxt+1+(Pt ),

where it is the policy interest rate, cis a constant term, Etπt+1 and Etxt+1 are the

3.3. Empirical evidence 99 inflation and real GDP growth forecasts for the current year respectively. s(y)(.) stands for a smooth function of its arguments for variable y and t is a stochastic disturbance term. The estimation results rely on the fact thatt are i.i.d. for all the Taylor Rules we consider. Our assumption is that Central Banks should only react to macroeconomic fundamentals. Some researchers claim that it−1 should be present in the set of explanatory variables in order to explain the moderation of Central Banks behavior. However, this reasoning does not necessarily imply moderation.

Moreover, our framework does not necessarily exclude this behavior either.

As the ASP policy rule is the most general specification considered, we discuss the estimation results of that policy rule. Importantly, the ASP policy rule generally displays a better fit than the other specifications among the Central Banks con-sidered in the analysis. Tables 3.2, 3.3, 3.4 and 3.5 in the appendix report the regression results of the semiparametric and parametric policy rules performed in this section.

The main purpose of the semiparametric specification is to show the presence of nonlinearities in the reaction function in order to better track the actual mone-tary policy decisions. In this paper, nonlinearities are defined as a different Central Bank’s responsiveness to macroeconomic fundamentals along their empirical sup-port. We include an interaction term of the inflation and output growth variables to account for a more complex policy rate decision process, for example in the event of a cost-push shock. The interest rate response to inflation, for instance, will depend on the level of output growth. Figures 3.1 to 3.32 in the appendix present the plots of the estimated smooth functions. The latter show clear evidence for nonlinearities of the policy reaction function for most countries.7 The degree of nonlinearities is measured by the estimated degrees of freedom of the smooth functions.8 More precisely, a linear policy rule would imply an estimated degree of freedom of one in the case of a univariate smooth term, while higher degrees of freedom point to

7As clear evidence for nonlinearities we refer to the estimated large degrees of freedom of the smooth terms.

8The degrees of freedom can be interpreted as the number of parameters needed to estimate the smooth terms.

increasing nonlinearities in the estimated functions.

3.3.1 Australia

Since the adoption of an inflation targeting strategy, the Reserve Bank of Australia (RBA) focuses on maintaining price stability in the medium term as an overriding monetary policy goal. The Statement on the conduct of monetary policy between the Governor and the Treasurer defines the inflation target as an average inflation rate between 2% and 3% in the medium term (over the cycle) without specifying it in terms of an inflation band or as a midpoint target level. The short term overnight lending rate (the cash rate) is used as the key policy rate. We first start the analysis of the Australian monetary policy by presenting the estimates of the smooth functions of inflation and real GDP growth forecasts in figures 3.1 to 3.4.9 First, it is important to emphasize that the estimated smooth functions are statisti-cally significant and the model features good explanatory power given that the fit is 64.8%. A first look at the graphs shows that both the inflation and output growth responsiveness of the RBA are close to linear as indicated by the estimated small degrees of freedom of the smooth functions. The latter score 1.36 and 1.22 for the inflation and the output growth functions respectively. However, the function of the interaction term seems clearly nonlinear showing 7.09 estimated degrees of freedom thus pointing to the presence of interaction between the inflation and output growth forecasts.

The inflation univariate term indicates that the RBA’s responsiveness is increasing in the level of the forecasts ranging from around 0% to slightly above 5%. For higher inflation forecasts, the RBA’s reaction softens substantially and becomes even neg-ative. However, the estimated smooth term is statistically insignificant. For modest levels of inflation, the Central Bank seeks to achieve its price stability commitment

9On each figure we display an asymptotic 95% confidence interval for the estimated smooth terms and the dots correspond to partial residuals. The reported covariates are intended for the forecasts of inflation and real output growth rates.

3.3. Empirical evidence 101 and offsets the inflationary pressures by raising the policy rate to maintain inflation expectations anchored with the inflation target. The reversal of the policy behavior that appears above a certain level for inflation indicates that the RBA is actually more concerned about pursuing other policy goals such as boosting output growth or offsetting currency appreciation rather than containing inflationary pressures. As the very high inflationary expectations are clearly at odds with the price stability objective of the RBA, the latter suffers from an eroded inflation aversion credibility.

This in turn reflects an inflation destabilizing policy which can sustain a self-fulfilling increase in inflation.

The univariate real output growth function is insignificant as well. The former in-dicates that the Central Bank further accommodates real GDP growth increases by cutting its policy rate especially for negative and very low output growth levels.

Finally, the estimated interaction term features a strongly positive and linear infla-tion reacinfla-tion of the RBA for levels up to 10%. The Central Bank’s responsiveness to output growth is asymmetric around a level of 2%. For a negative and close to 2% level for output growth the RBA accommodates the output expansion by fur-ther cutting the cash rate. However, for GDP growth above 2% the Central Bank strongly counteracts an increase in output growth by raising the policy rate which exerts a stabilizing effect on the economy by containing future inflationary pressures.

The threshold level of 2% is broadly in line with the growth level of potential output in Australia. Thereof, as output growth exceeds the growth rate of potential, the Central Bank implements a speed limit policy in the words of [Walsh, 2003] and swiftly increases the policy rate to prevent the build-up of inflationary pressures in the economy in line with its price stability mandate.

3.3.2 Japan

The monetary policy framework of the Bank of Japan (BoJ) is based on an explicit definition of price stability as the overriding goal: the Central Bank is “... aimed at achieving price stability, thereby contributing to the sound development of the

national economy” thus resembling inflation targeting Central Banks. Since April 2013 the BoJ has clarified that it aims at achieving a 2% inflation target in a horizon of two years using an explicit target for the monetary base. In order to achieve this goal the Central Bank sets an operating target for the uncollateralized overnight market interest rate (the call rate). Figures 3.5, 3.6, 3.7 and 3.8 display the estimated smooth functions of inflation, real output growth and the interaction term for the BoJ. The model performs well as it explains 82.6% of the policy rate.

The inflation smooth function reveals that BoJ reacts positively and linearly to inflation along the entire empirical support. However, there is no evidence that the Central Bank does react to output growth as the estimated function is flat and insignificant.

Importantly, there is a nonlinear reaction to both inflation and output growth as reflected in the estimated interaction term pointing to the presence of dependence between macroeconomic fundamentals. This dependence scores 12.37 estimated degrees of freedom, revealing a highly nonlinear relationship. This evidence suggests that the BoJ possibly takes into account the trade-off between inflation and output growth stabilization when setting the policy rate. The estimated interaction term reveals that the BoJ reacts positively to inflation along the entire support. In addition, above a 5% inflation rate the responsiveness becomes slightly stronger.

The behavior of the Central Bank is consistent with its mandate of preserving price stability as the BoJ counteracts increases in inflation expectations. Regarding output growth there is a nearly flat reaction (for a given level of inflation) which becomes strongly positive for GDP growth above 5%. The latter implies a stabilizing effect on the economy above that threshold. Finally, there is a highly nonlinear interaction between inflation and output growth as reflected in the curvature of the plot, particularly for large inflation rates.

An interesting result from the model fit is the prediction of negative nominal policy rates for periods of very low and subdued output growth and deflationary expec-tations. Indeed, Japan has experienced a prolonged period of particularly subdued

3.3. Empirical evidence 103 economic growth in the 1990’s and during the last decade which accounts for the very low actual policy rate. Thereof, the estimated model captures remarkably well the Zero Lower Bound (ZLB) issue the Japanese monetary authorities have been facing during most of the last two decades.

3.3.3 New Zealand

The Reserve Bank of New Zealand (RBNZ) is at the forefront of inflation targeting being the first Central Bank to adopt this strategy as an explicit monetary policy framework. The Policy Targets Agreement (PTA) between the RBNZ’s Governor and the Minister of Finance defines the inflation target as an average rate of inflation between 1% and 3% that has to be achieved in the medium term. Moreover, the Central Bank Act stipulates that “...in pursuing its price stability objective, the Bank shall implement monetary policy in a sustainable, consistent and transparent manner and shall seek to avoid unnecessary instability in output, interest rates and the exchange rate”. In order to meet the policy objectives the RBNZ has specified an operating target for the short term overnight market lending rate (the cash rate).

The augmented semiparametric model explains 57.1% of the variability of the cash rate. On the one hand, the univariate function points to an increasing and nonlinear reaction of the RBNZ to inflation with 3.22 estimated degrees of freedom. For infla-tion forecasts ranging from 0% to close to 10% the Central Bank strongly increases the cash rate in the event of an increase in inflation. For higher inflation prints the reaction becomes softer. This evidence suggests that the Central Bank might have assigned different weights to the inflation and output growth stabilization goals depending on the state of the economy.

On the other hand, there is clearly a positive and linear responsiveness to the eco-nomic outlook. The Central Bank offsets increases in the GDP growth rate by raising the cash rate aiming to contain the build-up of inflationary pressures. Finally, the estimated interaction term does not show evidence for dependence between inflation

and output growth and the relationship is not statistically significant. However, the RBNZ seems to respond exclusively to inflation as the output growth function is not statistically significant. In this setting, adding an interaction term to the reaction function does not help to explain the RBNZ’s cash rate decisions.

3.3.4 Norway

The Bank of Norway (Norges Bank) implements monetary policy within a flexible inflation targeting framework. The government has defined an operational target for inflation at 2.5% over the medium term. In addition, monetary policy should contribute to stabilizing output and employment. The Central Bank sets as a policy rate the sight deposit rate on bank reserves.10 Figures 3.13, 3.14, 3.15 and 3.16 displayed in the appendix present the estimated smooth functions of the inflation, output growth forecasts and the interaction term. The augmented semiparametric model explains 39.5% of the policy rate which is a substantial improvement from 16.7% reported for the augmented parametric model.

At a first look, the inflation smooth function points to a significant and linear policy response of the Bank of Norway with an estimated degree of freedom of 1.00. The output growth reaction is linear as well, with 1.00 estimated degrees of freedom of the smooth function, although it is not significant. Importantly, the estimated interaction term is highly nonlinear and significant thus implying a large degree of dependence between macroeconomic fundamentals. The smooth function features 8.10 degrees of freedom. The estimated surface indicates a strongly increasing inflation responsiveness for high levels of inflation and for a given level of output growth. The responsiveness flattens for very high inflation rates (around 10% and above). The output growth reaction is gradually increasing along the empirical support for a given level of inflation and becomes weaker for high output growth rates (above 4%). Overall, Norges Bank’s responsiveness becomes stronger

10However, given that the overnight lending rate is commonly used as a policy rate for most Central Banks we have decided to use the latter in the empirical analysis. This ensures a better comparability of the results with those obtained for the remaining Central Banks.

3.3. Empirical evidence 105 for high inflation rates given a relatively slow pace of output growth. To sum up, the evidence shows that the Central Bank’s behavior changes along the level of inflation and output growth depending on the prioritized policy objectives and on macroeconomic shocks. The parametric specification displays a very limited explanatory power and shows a quite muted inflation responsiveness.

3.3.5 Sweden

The Riksbank implements monetary policy within a formal inflation targeting frame-work. The Central Bank Act does not assign other policy objectives except to pro-mote a safe and efficient payments system. The operational target for inflation is specified as a point target of 2%. The Riksbank sets the repo rate as an operational instrument for the one-week interbank market lending rate. The estimated smooth functions are displayed in figures from 3.17 to 3.20 in the appendix.

Sweden scores noticeably better in terms of model fit than Norway given that the model fit amounts to 79.3%. The augmented semiparametric policy rule thus better fits it than the parametric specification which accounts for 62.6% of the variation in the policy rate. On the one hand, the univariate smooth functions of inflation and output growth show evidence for a linear policy behavior, thus mirroring the evidence for Norges Bank, although the inflation smooth term is statistically in-significant for Sweden. On the other hand, the estimated interaction term is highly nonlinear and significant, scoring 19.84 degrees of freedom. The interaction between inflation and output growth is therefore an important factor that helps to explain the policy rate setting. The interaction term shows that the Riksbank’s respon-siveness strongly increases along the inflation support and becomes flat for high inflation rates (close and above 10%). The output growth reaction is increasing for most of the empirical support while it becomes flatter for high output growth rates.

The high degree of interaction between macroeconomic fundamentals is observed over the entire inflation support along with large output growth rates. All in all, as Norges Bank the Riksbank reacts linearly to inflation and output growth, and

the higher degree of nonlinearities in the policy reaction function is related to an important interaction between macroeconomic fundamentals, as found in the case of the Norwegian Central Bank.

3.3.6 Switzerland

The Swiss National Bank (SNB) conducts monetary policy in the general interests of the country. The SNB’s monetary policy strategy embeds an explicit definition of price stability (annual increase of CPI inflation of less than 2%), a medium term inflation forecast and a target range for the three-month Libor rate on the Swiss franc as the key policy interest rate. In line with its price stability goal, the SNB should also take due account of the economic outlook as outlined in the Central Bank Act. Even though the monetary policy framework closely resembles that of inflation targeting Central Banks, the SNB is not an explicit inflation targeter. Nevertheless, the Central Bank considers the inflation forecast as the main indicator for its policy rate decisions, as well as an important communication tool with market participants.

The augmented semiparametric policy rule shows evidence for a linear SNB’s in-flation responsiveness while its reaction to output growth is clearly nonlinear. The estimated smooth terms feature 1.00 and 2.56 degrees of freedom respectively, al-though the output growth function is not statistically significant. The inflation smooth function points to a positive linear reaction to inflation along the entire em-pirical support, while the output growth function is nearly flat for negative and close to zero output growth rates. As output growth becomes positive, the SNB raises the Libor target rate to contain future inflationary pressures, thereby exerting a stabilizing effect on the economy. Finally, the estimated interaction term shows dependence between fundamentals albeit the estimated surface is not statistically significant. The bivariate smooth term reveals a strongly positive inflation reaction, while the output growth responsiveness is nearly flat for small output growth rates, though it becomes strongly positive for output growth above the 4% level. Overall, the Swiss policy reaction function is the closest to a linear parametric specification

3.3. Empirical evidence 107 among the Central Banks studied. The SNB’s monetary policy strategy has been particularly successful during the entire period investigated since the country has not experienced high inflation rates, even during the 1980’s, and contrarily to the inflation experience of most other industrialized economies.

3.3.7 USA

The U.S. Federal Reserve (Fed) is assigned with a dual mandate of price stability and maximum employment which is embedded in the Humphrey-Hawkins Act: the Fed “...shall maintain long run growth of the monetary and credit aggregates com-mensurate with the economy’s long run potential to increase production, so as to promote effectively the goals of maximum employment, stable prices, and moderate long-term interest rates”. In addition, the Federal Reserve specifies a numerical value of 2% for the definition of price stability consistently with most inflation tar-geting Central Banks. Without being an explicit inflation targeter, the Fed uses as operational instrument a target for the overnight federal funds rate in order to achieve the policy objectives it has been assigned with by the Central Bank Act.

On the one hand, the estimated univariate functions show evidence for a linear reaction to inflation and output growth, although they are significant at the 10%

level. The Fed reacts positively to inflation and output growth along the entire empirical support. The semiparametric model scores 71.6% in terms of model fit which is a substantial improvement over both parametric policy rules. In terms of information criterion, the former outperforms the SP policy rule. On the other hand, the estimated interaction term shows strong evidence for nonlinearities as it features 13.25 degrees of freedom. The interaction is particularly pronounced for high inflation and output growth rates whereas the Fed’s inflation reaction is relatively flat for negative and close to zero inflation rates. The inflation function becomes steeper for high inflation rates close to 5% and turns flatter again for very high inflation rates which are close to and above 10%. Along the same lines, the Fed’s responsiveness is nearly flat for negative and close to zero output growth while

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