Department of Economics Professorship of Macroeconomics Christian Albrechts University of Kiel Monetary Reaction Function Forward looking and Non linear Behaviours Master’s thesis in Master of Science[.]
Department of Economics Professorship of Macroeconomics Christian-Albrechts-University of Kiel Monetary Reaction Function: Forward-looking and Non-linear Behaviours Master’s thesis in Master of Science Economics Supervisor: Prof Dr Kai Carstensen WS 2016/2017 Abstract This paper investigates forward-looking and non-linear characteristics of monetary reaction funciton using Fed’s data By employing hybrid New Keynesian with non-linear Phillips curve and asymmetric preferences of Fed, a “hybrid-type” non-linear reaction function is derived The estimation results provide more empirical evidence for a non-linear monetary policy rule in the period between 1983 and 2008, as well as a notable role of forwardlooking behavior of the policy rule toward output gap Name: Nguyen Thi Truc Ngan Field of study: Economics Semester: E-mail: trucngan.19@gmai.com Deadline: 01.06.2017 Matriculation Number: 1020472 Contents List of Abbreviation II Introduction Literature Review 2.1 Instrument rule and Targeting rule 2.2 Forward-looking behaviours 2.3 Non-linearity of the Reaction Function 2.3.1 Convex Aggregate Supply curve 2.3.2 Asymmetric Preferences 2.4 Zero Lower Bound 2 8 Monetary Reaction Function model 3.1 Case I: Linear Aggregate Supply (τ = 0) 3.2 Case II: Quadratic Loss fucntion (γ → 0) 3.3 Case III: Linear Rule 3.4 With Zero Lower Bound 13 13 14 14 Estimation 4.1 Preliminary analysis 4.1.1 Generated regressor 4.1.2 Measurement error 4.1.3 Multicollinearity 4.1.4 Inflation Target in the U.S 4.2 Estimation 4.3 Estimation results 14 14 15 16 17 18 18 19 Conclusion 21 Appendix III A Monetary Reaction Function III B Data appendix VII References VIII Affirmation XIII I List of Abbreviations AS ECB FED IPI NAIRU NKPC ZLB Aggregate Supply European Central Bank Federal Reserve (U.S Central bank) Industrial Production Index Non-accelerating inflation rate of unemployment New Keynesian Phillips Curve Zero Lower Bound II Introduction Literatures on monetary reaction function provide us learnings about characteristics of policy as well as the priority target of the central bank With the introducting of New Keynesian model as the monetary transmission mechanism (Clarida, Gali, and Gertler 1999) and inflation targeting (Svensson 1997, Svensson 2003), the most used derivations of optimal rules is base on a linearquadratic framework This framework involves the central bank minimizing its quadratic-form objectives function subject to a linear structure of the economy Derivations of this framework produce a linear reaction function, or targeting rule (Svensson 1997, Svensson 2003).1 This linear reaction function means the Federal Reserve of the United States’s adjustment of Federal fund rate is a straight line of inflation and output However, in recent literatures, this linear-quadratic framework has been challenged, either by considering a non-linear Phillips curve (Orphanides and Wieland 2000; Dolado, Marıa-Dolores, and Naveira 2005); or by abandoning the quadratic loss function assumption and adopting asymmetric preferences instead (Dolado and Pedrero 2002; Cukierman et al 1999); or both (Surico 2003; Surico 2007; Dolado, Pedrero, and Ruge-Murcia 2004) This paper studies the non-linearity of monetary reaction function combining both channels: non-linear Phillips curve and asymmetric loss function of central bank as conducted by Dolado, Pedrero, and Ruge-Murcia (2004) We would like to engage in a quasi-convex Phillip curve as in Dolado et al (2004) Next, our asymmetric objective function suggested biased preference in inflation only, output gap is also included, but in a quadratic form2 This setup will be discussed more in Section Several literatures using forward monetary policy rule augmenting purely New Keynesian model have been conducted (Surico 2003; Clarida, Gali, and Gertler 1999) Some of them have showed that a purely-forward looking model may sometime misspecified due to the lack of history dependence (Gal´ı, Gertler, and Lopez-Salido 2005) Thus, in this paper, the hybrid New Keynesian model, which covers both backward and forward-looking variables, is employed instead In most papers, including this study, the term monetary policy rule, monetary reaction function or Taylor rule are used interchargeable This asymmetric loss function with the entering of output gap has also been mentioned by Dolado, Pedrero, and Ruge-Murcia (2004), section 2.6, and a reaction function has been derived Nonetheless, in their studies, an empirical application based on this function was not done For empirical studies, estimation of the non-linear rule is done using the U.S data According to Belke and Klose (2013), some evidence for a structural break in the time of 2008-financial-crisis has been found Thus, we would employ two periods of time: the first period is after Volcker and Greenspan became the chairman of Fed excluding the period when Fed targeted nonborrowed reserves, until the financial crisis in 2008 (1983Q1 to 2008Q2); and the second period is after the crisis until recent time (2008Q3 to 2016Q4) The rest of the paper is structured as follows In section 2, we will discuss some theories regardings monetary policy rules as well as reasons for considering a non-linear reaction function Section is the derivation of a non-linear reaction funciton under asymmetric preferences and hybrid non-linear Keynesian model, with the consideration of some linear cases and zero lower bound Section concludes estimation methodology and results using two subsamples Conclusion of this studies is covered in section Two appendices are derivation of the general reaction rule and description of the data Literature Review 2.1 Instrument rule and Targeting rule First introduced by John Taylor (1993), Taylor rule (instrument rule) has been widely used to monitor the policy rule of central banks because of its simpliness yet effectiveness At the time, this simple rule can well explained responds of instrument rates to the “price stability” target of central banks it = f + fπ (πt − π ∗ ) + fx xt , (2.1) Ever since, several studies have been done to examined this simple instrument rules, which included some variations of the Taylor rules Levin, Wieland, and Williams (1999) has empirically proven the relatively robustness of the simple Taylor reaction function with a combination of smoothing interest rate Belke and Klose (2013) modified Taylor rules using Fisher equation to estimate reaction functions in the presence of zero-lower bound (ZLB) from Taylor (1993), it is the instrument rate in period t, f is a constant, πt is inflation rate at time t, π* is inflation target and xt is the output gap In the original Taylor rule, fπ is 1.5 and fx is 0.5 Their empirical results provide more evidence for a structural break in reaction fucntion of ECB and Fed between before and after 2008 crisis.4 In another study, Kim and Nelson (2006) used a forward-looking Taylor rule with interest rate smoothing to estimate Fed’s monetary policy Their work focuses on the change of instrument rate over time and effectively find evidence for time-varying response of Fed toward future macroeconomic conditions Not only for US data, this simple rule is also applied in differrent macro models.5 In the context of policy design, for the monetary policy rule to work and stimulate the economy, a highly-creditable announcement from central banks is desirable In other words, central bank’s commitmet must be trustworthy In our study, data from the United States is used, so we believe we can safely assume that creditibility from FED is relatively high Following the minimizing the objective function approach, the matter related to creditibility of policy design is the distinctions between discretion and commitment policy There are several reasons that commitment is more preferable in recent studies As stated in Svensson (1997), discretion policy could lead to too much inflation variability and too little output variability Clarida, Gali, and Gertler (1999) argue that monetary policy under commitment could be used to manipulate private sector expectation about the future Morever, in the presence of Zero lower bound, commitment optimal monetary policy rule has been proven to be effective to stimulate the economy (Nakov, 2005) Problems related to ZLB would be further discussed in section 2.4 With the expansion of rational-expectation and development of macroeconomics theory, the idea that central banks’ decision making process is more focused on optimization and forward-looking behaviors starts to gain more supports Stated that credibility of central bank should highly relevant to expectation of pivate sector, Clarida, Gali, and Gertler (1999) combined New Keynesian perspective with “instrument rule” of monetary policy and derive an optimal instrument rule which emphasizes targeting objects of central banks Belke and Klose (2013) estimated ECB and Fed’s reaction function using real interest rate rather the nominal one In their model, even when nominal rate is close to zero, central banks still have power to stimulate the economy via quantitative easing Bră uggemann and Riedel (2011) use a non-linear Taylor rule to estimate the United Kingdom’s monetary reaction funtion; Cukierman, Muscatelli, et al (2008) also use nonlinear instrument rule for the U.K data but with asymmetric preference; Salgado, Garcia, and Medeiros (2005) examined Brazil’s instrument rule with both linear and non-linear Taylor rule; Even being heavily examined in various studies, this simple instrument rule was intepreted in a very narrow view of “policy rule” (Svensson, 2003) From the definition of Taylor (2003) about monetary policy rule, the instrument rule should not be followed strictly but be seen as a “guidelines” and should be viewed looser Following the ideas of inflation targeting rule , he then propose to broaden the approach of monetary policy rule as “a precribed guide for monetary-policy conduct” that include both “instrument rules” and “targeting rule” Accordingly, the endogenous variables that enter the central bank’s loss function are “target variables”, and “targeting” means minimizing this loss function From latest studies, this “targeting rule” seem to be better fit to modern theory (Dolado et al 2003, 2004; Gal´ı 2015; Cacciatore, Ghironi, Turnovsky, et al 2015) Inherit the ideas of “targeting rule” and the optimal monetary policy under commitment, Svensson (2003) argues that commiting to follow even a simple transmission mechanism under direct optimal-control approach7 will be impracticable and hardly verifiable.8 While committing to a direct optimal monetary policy is not practical, committing to a simple instrument rule or a simple Taylor-rule type is not optimal either9 Instead, in his study, Svensson (2003) has proven the superiority of “targeting rule” over instrument rule Accordingly, inflation targeting rule could be understood as commiment to a targeting rule10 and he stated, “ Targeting rules have the important advantage that they allow the use of judgment and extra-model information They are also more robust and easier to verify than optimal instrument rules, but they can nevertheless bring the economy close to the socially optimal equilibrium ” Thereafter, the idea of interpreting monetary policy rule as inflation targeting has gained more attention and have been adopted by various countries It is also widely applied to estimate the reaction function (Svensson and Wood6 from Svensson, 1997, 1999; Rudebusch and Svensson, 1999 Clarida, Gali and Getler (1999) use New-Keynesian model and follow Woodford (1998) to minimize the objective function using Lagrange with with forward-looking aggregate supply and aggregate demand relations contraints From their model, they stated that under commitment, a global optimal monetary policy could be attained see Svensson (2003), section for more details e.g Even the instrument rule is robust, it may not be optimal in some case (e.g Zero lower bound), there is no room for extra-model information or adjustments, lack of history dependence, no improvement of instrument rule is allowed if new information arrives, (Svensson, 2003, section 4) 10 this could be a general targeting rule (commit to minimizing a specific central bank’s objective function) or a specific targeting rule In his paper, Svensson also stated that specific targeting rule could be more helpful and most literature, both support and againts targeting rule, focused this rule ford, 2004; Dolado, Pedredo and Ruge-Murcia, 2004) It is not until 2012 that the U.S started adopting this approach, however, some empirical studies have also proven that the inflation targeting rule could also well describe the behavior of central bank in the period prior-2012 (Dolado et al, 2004; Dolado, Maria-Dolores and Naveira, 2005; Goodfriend, 2004) 2.2 Forward-looking behaviours By definition, a variable is referred as forward-looking if it depends on expectation of future values From the 90s of last century, the importance of forward-looking dimension toward economic policy (or monetary policy) was highly admitted, as Donald Kohn (1995) stated: “Policymakers cannot avoid looking into future” Several empirical studies has been conducted and prove that monetary policy is driven more by future values rather than by lagged variables (Clarida et al., 1999; Belke and Klose, 2013) Using a simple forecast-based rule with inflation forecasts as intermediate targets in the operation of forward-looking behavior, Batini and Haldane (1999) theoretically and empirically have debated benefits of including this aspect Accordingly, this rule can express: • Transmission lags Transmission lags are the most straightforward reason for the need of forward-looking behaviors There are some lags needed for the monetary policy start to affect inflation and output Without demonstrating this characteristic, as Batini and Haldane said, policymakers will always be behind its target • Information encompassing Expected inflation is an indicator “most closely related with future value of interest variables”, therefore, it should contains all information that could have effect on future path of inflation • Output encompassing Ouput actually does not enter this rule, but they argue that with a wise choice of targeting horizon, inflation forecastbased rules can secure the output stabilizing Another method to implement the forward-looking dimension is by modifying the economic model that describes practices of private sectors (a.k.a New Keynesian model) (Clarida, Gali, and Gertler 1999, Clarida, Gali, and Gertler 2000) or by letting expectation of future values enter the central bank’s objective function (Dolado, Pedrero, and Ruge-Murcia 2004) or both (Surico 2007, Surico 2003) Applying advances from methodology of macroeconomic modelling, Clarida, Gali and Getler (1999) adopted the New Keynesian perspectives implying the forward-looking dimension into their reaction function Furthermore, in another study, they11 applied forward-looking model to estimate response of instrument rates to expected inflation They found that after Volker-Greespan era, the interest rate is highly sensitive to expected inflation, again confirm that the Federal Reserve did focus more on controlling inflation after Volker time This conclusion is highly recognized, their model as well as method is also further applied in various studies The method of combining the forward-looking model with commitment to targeting rule is explained by Svensson (2003) and was followed by several reseachers (Surico, 2003, 2007; Svensson and Woodford, 2004).This forwardlooking monetary reaction function seems to be the most used among researchers (Svensson, 2003; Surico, 2003, 2007; Dolado et al., 2005) However, while forward looking behaviours is dominant in most researches, some recent tests for backward and forward-looking Taylor-based rule have been conducted and it seems that the there is no strong evidence supports a purely-forward-looking behaviors (Sooreea 2008; Dolado, Pedrero, and RugeMurcia 2004; Svensson and Woodford 2004) The reason for it could be the lack of “history dependence”, even using interest rate smoothing is also a popular way to account for this matter, the role of backward-looking in the model may be underestimated Thus, in our setup, we would like to use a hybrid New Keynesian model which includes both forward and backwardlooking variables 2.3 Non-linearity of the Reaction Function Traditionally, combination between quadratic loss function and a linear dynamic system has been used to acquire a linear reaction function12 , or to develop an optimal monetary policy rule The dynamic system could be forwardlooking or backward-looking as we discussed above, but in this framework, the nominal interest rate will be a linear function of current or expectation of inflation and output gap This straight-forward traditional rule could also provide a resonably good description of the monetary policy Nonetheless, it is desirable to enable non-linearity in the setup of optimal monetary policy rule due to some reasons (Dolado et al., 2005) 11 12 Clarida, Gali, and Gertler 2000 Svensson, 1997; Clarida et al., 1999 • Nonlinear trade-off between inflation and output gap Under traditional Keynesian assumption, nominal wages are elastic upward but rigorous downward, leading to a quasi-convex aggregate supply curve13 • Central bank’s asymmetric preferences From recent literarutes, there are more evidences for the belief that central bank’s preference should be non-linear This asymmetry means that the central bank not only care about the level of deviation of inflation/output from its target but also the sign of deviations • Uncertainty about the NAIRU As mentioned in Meyer et al (2001), high uncertainty about the NAIRU would leads to a non-linear interest-rate policy, which implies cautions of policy-makers when adjusting interest rate in response to small output gaps To the extent of this paper, achieving non-linearity of monetary reaction function through a quasi-convex aggregate supply curve and asymmetry of central bank’s preference is the main focus Furthermore, following Dolado et al., (2004), a general model combining both non-linear Phillips curve and central bank’s asymmetric preferences is preferable in this study 2.3.1 Convex Aggregate Supply curve As mentioned above, by tranditional Keynesian assumption, inflation is implied to be a decreasing and convex function of employment rate Which means inflation will be driven down much more by an increase of unemployment rate when this unemployment rate is high than when it is low14 Then by Okun’s law, the co-movement between output gap and unemployment rate leads to the convex relationship between output gap and inflation (Schaling,1999; Nobay and Peel, 2000; Dolado et al., 2005) In particular, Dolado, Mar´ıa-Dolores and Naveira (2005) studied the asymmetry of monetary policy reaction function through a non-linear Phillips curve They found empirical support for asymmetric reaction function that, the weights for positive inflation deviation or output gap is larger than negative ones This non-linear behavior is spotted from European central banks but not from the Federal reserve 13 Orphanides and Wieland 2000 also considered this convex function in the derivation of ´ reaction functions, Gerlach (2000), Alvarez-Lois (2000) also provide some emprirical supports to this approach 14 see Layard et al., 2005, Unemployment: macroeconomic performance and the labour marketfor details ... a non- linear reaction function Section is the derivation of a non- linear reaction funciton under asymmetric preferences and hybrid non- linear Keynesian model, with the consideration of some linear. .. model which includes both forward and backwardlooking variables 2.3 Non- linearity of the Reaction Function Traditionally, combination between quadratic loss function and a linear dynamic system has... Introduction Literature Review 2.1 Instrument rule and Targeting rule 2.2 Forward- looking behaviours 2.3 Non- linearity of the Reaction Function 2.3.1 Convex Aggregate Supply curve 2.3.2