MSc in Economics
Track: Monetary Policy, Banking and Regulation
Master Thesis
All those expectations: Measuring
central bank’s credibility using
inflation expectations heuristics.
by
Micha l Nauman
(11087501)
Supervisor:
Prof. Aerdt Houben
ABSTRACT
In this dissertation I study the issue of central bank’s credibility. I propose a model of inflation expectations heuristics that allows for calculating credibility with-out the assumption of the system steady state. In the model, agents are generating inflation expectations based either on the policy target or on the available informa-tion about actual inflainforma-tion. The model is augmented to account for inflainforma-tion risk and liquidity premium. To find whether the European Central Bank is credible, I run the model on the Eurozone data. The findings are that the ECB has suffered a 10% decline in credibility (based on the market expectations) since 2008. Moreover, the sum of liquidity and inflation risk premium is estimated to be negative from July 2015 onwards.
Contents
1 Introduction 4
2 Literature Review 6
2.1 Credibility and inflation expectations . . . 6
2.1.1 Inflation expectations . . . 6
2.1.2 Central bank credibility . . . 7
2.2 Measurement problem . . . 8
2.2.1 Measuring inflation expectations . . . 8
2.2.2 Measuring central bank credibility . . . 9
3 Model 11 3.1 Credibility model . . . 11
3.1.1 Heuristic expectations model . . . 11
3.1.2 Pure expectations model . . . 12
3.1.3 Distorted expectations model . . . 13
3.1.4 Solution to the model . . . 14
3.1.5 Model shortcomings . . . 15
4 Database and estimation technique 16 4.1 Database . . . 16
4.1.1 Survey of Professional Forecasters . . . 16
4.1.2 5Y5Y inflation expectations . . . 18
4.2 Estimation techniques . . . 19
4.2.1 Rolling ordinary least squares . . . 19
4.2.2 Maximum likelihood state-space model . . . 21
4.3 Summary of hypotheses . . . 21
5 Results 23 5.1 Experts expectations estimation . . . 23
5.1.1 Rational expectation hypothesis . . . 23
5.1.2 Experts-implied ECB credibility . . . 25
5.2 Market-implied inflation expectations . . . 26
5.2.1 Rational expectations hypothesis . . . 26
5.2.2 Market-implied inflation expectations . . . 27
5.2.3 ECB market-implied credibility . . . 28
5.3 Robustness analysis . . . 29
6 Conclusions 32
Appendices 39
I would like to thank professor Sweder van Wijnbergen for discussions that inspired this dissertation. I would also like to thank professor Aerdt Houben for very helpful comments and for providing me with the data crucial to run this experiment.
1
Introduction
Since the start of the global financial crisis inflation has become more volatile than in the previous years (Yellen (2016)). Central banks, in order to stabilize price developments, have used a variety of policies: from quantitative and qualitative easing, to crossing the zero lower bound and extending forward guidance. These policy measures have not, as yet, resulted in a return of inflation to the target of below, but close to 2%. The constantly effectiveness of policies can be explained by two theories:
1. Central bank’s credibility - Market does not find central bank’s policies credible, thus accommodates their short to long-run expectations above or below the target (Kydland & Prescott (1977); Barro & Gordon (1983)).
2. Central bank’s ability - Market does not believe that the policy will deliver the de-sired effect, given the fundamental economic environment (Williams (2009); Draghi (2016)). This can be due to lower future consumption or production path (Phelps (1967)).
Therefore, establishing whether the central bank is credible might be the essential input in design of an optimal monetary policy for the future.
Since credibility is not directly measurable, various estimators have been proposed. Most of them assume that, if the inflation objective is well known and the central bank is credible, the objective will be reflected in the long-term inflation expectations. This is so, because under a credible monetary regime the public would assess any inflationary shock as temporary. Many quantitative experiments have shown that, indeed, central banks labeled as credible tend to have anchored inflation expectations (Demertzis et al. (2010)). However, the inflation expectations are hardly measurable themselves. Market long-term inflation expectation, the so-called “break-even inflation rate”, has been an important index for both academics and central bankers alike (Draghi (2015)). But the break-even inflation rate measured as a spread between nominal and inflation indexed bond is contaminated by a variety of premiums.
The contribution of this dissertation is twofold. Firstly, I propose an alternative mea-sure for central bank’s credibility - an estimator based on microeconomic considerations that does not assume system equilibrium (steady state). Basing my considerations on behavioural economics drift-diffusion model, I assume a falsifiable inflation expectations heuristics function as defined by Brazier et al. (2008). The first heuristic, implied by the rational expectations hypothesis (Galati et al. (2011)) is connected to perfect credibility of the central bank. Under such choice, agent assumes that inflation will converge to the
inflation target over the long horizon. The second heuristic is consistent with the adap-tive expectations hypothesis (Roberts (1998)), and corresponds with the zero credibility. Under such heuristic agent’s expectations converge to actual inflation, but are also dis-torted in the short-term by changes in perceived inflation - therefore it is represented by an error-correction process. Secondly, by assuming that my model is complete1, I use the
model to disaggregate the break-even inflation rate into estimated market expectations and estimated total premium - a sum of liquidity and inflation risk premium.
The empirical experiment is divided into two sections: the estimation of the model of the surveyed expectations and the estimation of the model of the break-even inflation rate, both for the Euro Area. Firstly, I conduct a rolling OLS regression on both samples. After concluding that the rolling OLS estimator is not efficient, I proceed with the maximum-likelihood (ML) Kalman filter regression – as proposed by Stock & Watson (1996) and Nakajima (2011). Investigation of the results suggests that the European Central Bank (ECB) was highly credible in the sample period – with credibility averaging on 97% based on surveyed expectations, and 95% based on estimated market expectations. For both samples, however, there is a visible decline in credibility. Moreover, the model suggests that the sum of liquidity and inflation risk premium was negative from July 2015 onwards. The remainder of this paper is organized as follows: In the first chapter, I briefly discuss the theoretical concepts that are related to this dissertation and show some of the existing credibility measures. In the second chapter, I derive the estimated model and discuss the assumptions behind the framework. I discuss under what conditions premiums can be defined. Furthermore I investigate the set of solutions for the model. In the third chapter, I describe the database used in my thesis. I discuss the regression methods – rolling ordinary least squares (rOLS) and maximum-likelihood (ML) Kalman filter estimator. Moreover, I summarize the hypotheses tested in my dissertation. In the fourth chapter, I show the results of the estimation. I discuss the credibility of the European Central Bank (ECB), as estimated based on the Survey of Professional Forecasters expectations and suggested market inflation expectations. I show the estimated total premium - sum of liquidity and inflation risk premium, as derived from the model. Chapter six concludes.
2
Literature Review
In this chapter I review the key theoretical concepts linked to this dissertation. I explain the importance of inflation expectations for central bankers and discuss how inflation expectations are linked to central bank’s credibility. I show why maintaining credibility is crucial for anchoring of inflation expectations, thus for central bank’s mission. Finally, I show existing estimators for central bank’s credibility – and describe crucial assumptions behind them.
2.1
Credibility and inflation expectations
“The self-fulfilling prophecy is, in the beginning, a false definition of the situation evoking a new behaviour which makes the original false conception come true. This specious validity of the self-fulfilling prophecy perpetuates a reign of error. For the prophet will cite the actual course of events as proof that he was right from the very beginning.” -Robert K. Merton
2.1.1 Inflation expectations
Expectations play a crucial role in contemporary macroeconomics. Indeed, expectations define the level of activity in the economy - and policies seek to shape these expectations in line with the policy target. As the European Central Bank states in its bulletin: “Mon-etary policy involves anticipating future developments, monitoring and shaping private sector inflation expectations over the cycle, and providing a long-term nominal anchor for the economy”. Forward guidance is one of the core elements in conducting the monetary policy (Filardo & Hofmann (2014)). It is so, because inflation expectations are crucial to the real price changing process (Bernanke (2007)). The effect can be categorized into three channels:
1. Staggered price/competition effect - according to Taylor (1979; 1998) and Calvo (1983), producers tend to keep staggered prices. In such situation, considering competition, suppliers set an optimal price for few periods a priori. Thus creating a self-fulfilling prophecy of inflation.
2. Wage/demand feedback effect - Most labour contracts have a fixed wage (Taylor (1979; 1998)). This implies that inflation expectations, through wage negotiations, have a direct effect on the wage level in the economy. The level of income in households defines both the cost structure for producers but also the level of demand in the economy (Keynes (1936)).
3. Intertemporal optimalization effect – Aggregate demand is not only defined by wages, but also by the real interest rate (Koopmans (1961)). Households might postpone their consumption if deflation is expected. Postponing consumption re-duces aggregate demand and further lowers the price level.
It is unclear how inflation expectations are formed over different horizons. Roberts (1998) shows that, in developed economies, some agents are backward looking. Such expectations, also called the “adaptive expectations”, are formed based on the available information on past inflation. Another theory explaining how expectations are formed is the rational expectations hypothesis (REH). It implies that, given well-known policy target and policy function2, long-term inflation expectations are not affected by any new
information (Galati et al. (2011)) - it is called rational, because it assumess that CB will be successful in its mission. Brazier et al. (2008) argues that agents use heuristics to form the inflation expectation - ”optimal policy” heuristic (inflation target) and ”lagged inflation” heuristic. Each term, the agent would assess (basing on imperfect information) which heuristic will be better. This theory implies that agents have at least two ways of constructing expectations. King (1995) and Demertzis et al. (2008; 2010) show that, under credible monetary regimes, long-term inflation expectations converge to the central bank’s inflation target.
It is crucial to understand that, assuming perfect information, every inflation expecta-tion heuristic is raexpecta-tional. Raexpecta-tional in the sense that, it is following the rule of maximizing utility - and being right about the future inflation always grants the biggest utility. There-fore, if agent believes that the central bank will provide with the announced policy, it is rational to anchor inflation expectations on the policy target. On the other hand, if the central bank will not3 provide with the announced target, it is rational to use any other information while assessing possible future states.
On the other hand, optimality of inflation expectations can be interpreted in a co-ordination game framework. Because actual inflation is determined by expectations, it is optimal to have the same expectations as others4. Therefore central bank has to
cre-ate a nominal anchor for the future inflation. Moreover, to ensure price stabilization, achieving this anchor has to be highly probable.
2.1.2 Central bank credibility
King (1995) defines credibility in the context of monetary economics – “a monetary strat-egy (. . . ) is credible if the public believes that the central bank will actually carry out its plans”. The concept of a credible central bank is directly linked to the time-inconsistency problem. Time-inconsistency in monetary policy describes the inconsistency of the ex
2 REH is implied by general equilibrium framework.
3 Either because of inconsistency or because of lack of suitable policy. 4 This mechanism creates the contagion in expectations.
ante and ex post optimal policy. The announced policy becomes suboptimal, when the agents actually believe it and act upon it. After the wages and prices are set, the central bank has incentives to change the policy and increase the output or decrease the un-employment. Because agents in the economy are rational, they are able to foresight this hazard. Then they accommodate their expectations below or above the announced policy. The problem highlighted by Kydland & Prescott (1977) and Barro & Gordon (1983) has changed how monetary policy is conducted. A monetary authority needs to tie its hands to its objective in order to be credible. Indeed: “following the start of Stage 3 of Economic and Monetary Union, a crucial objective for the European System of Central Banks is the rapid acquisition and maintenance of credibility for achieving price stability”5.
Ac-cording to the ECB, credibility is crucial factor determining whether forward guidance will be effective. According to Blinder (1999) a credible central bank can arrange a less costly disinflation – by having a stronger influence on forward-looking variables like long-term interest rates and inflation expectations (thus lowering the output and employment cost of lowering inflation). Moreover, Mishkin & Schmidt-Hebbel (2007) have shown that credibly committed monetary regimes have lower output volatility. Thus, central bank’s credibility is directly connected to the social welfare.
2.2
Measurement problem
“Science may be described as the art of systematic oversimplification.” - Karl Popper. 2.2.1 Measuring inflation expectations
Since inflation expectations cannot be directly measured, various estimators have been proposed. The existing measures can be divided into survey-based and market-based expectations. Survey-based measures are subject to various problems. Experts based surveys can be subject to non-representative sample issue. That means that an expert’s knowledge of both the economy and central bank policies grant them “better than usual” judgement. Consumer based surveys can be subject to memory-bias issue, as shown by Bruin et al. (2011). Also, survey-based methods are always subject to incentive biases. Market based expectations - derived from financial instruments – are widely used by both central bankers, and academics (Draghi (2015)). As they are subject to forces of the market, they should reflect the public’s perception of the future inflation. The two major sources for market inflation expectations are inflation-linked swaps (short to medium-term) and inflation-linked bonds (long-medium-term) (ECB Bulletin (Feb 2011)). As they are derived from financial market, they can be contaminated with variety of premiums. The most commonly mentioned are inflation-risk and liquidity premium (Garcia & Werner (2010)). There is only a limited amount of methodologies used to derive such premiums.
The most popular are the so-called term structure models (H¨ordahl (2008)). That class of no-arbitrage models assume that bond yieds are constant+linear functions of state vector X. However, an ambiguous price of risk has to be assumed.
2.2.2 Measuring central bank credibility
Bomfin & Rudebusch (2000) proposed an intuitive definition for the central bank’s cred-ibility. In their proposition, the CB announces the long-term inflation target for each period. Subsequently, the private sector has to evaluate whether the announced policy is achievable under the existing constraints, and if this is indeed the true goal of the CB. The extent to which the public believes the central bank can be defined as credibility. Such a setting implies the following equation:
πte= λtπ target
t + (1 − λt)πth (1)
Where inflation history is calculated as a mean of inflation over n periods. The model implies that, under positive credibility (λt > 0), agents will consider the CB inflation
target while forming expectations. If there is no credibility, that is when λt = 0, agents
will ignore the inflation target. Demertzis et al. (2008; 2010) assume this specification of expectations. They have based their considerations on VAR(1) model:
πt= α0+ α1πt−1+ α2πt−1e + e1t πte= β0+ β1πt−1+ β2πet−1+ e2t (2)
They show that both the implicit inflation target and central bank credibility can be calculated using the assumption of long-term system equilibrium . Combining the equilibrium condition with credibility function yields:
λ = 1 − β1 1−β2 πtarget = β0 (1−β2)λ (3)
Thus credibility is negatively correlated with the elasticity of inflation expectations with respect to actual inflation. There are few problems with such setting. Firstly, they assume similar estimator distribution for inflation history during times with credibility and without credibility. Secondly, assuming a steady state can be suitable for a wide, long-term sample. However, it is not suitable for intra-business cycle experiment – especially if the variables have large variation over the sample . Such variation has an unpredictable effect on the credibility estimator. Finally, such a model cannot be used on market expectations that contain risk premiums. Nevertheless, they have shown that their measure fits the data well - matching times when the credibility was known to be high or low. Moreover,
they have shown that the ECB was almost perfectly credible6 in the period 19992009
-averaging at 0,99.
Bomfin & Rudebusch inspired more measures for the central bank credibility. De Mendonca (2007) has proposed an index based on the difference between the long-term inflation expectations and the inflation target:
CREDDeM endonca =
1 if πet = πmidt 1 − πte−πmidt πx t−πmidt if π(xlow)t < πe t < π (xhigh) t 0 if πe t < π (xlow) t or πte> π (xhigh) t (4)
Such an estimator assumes that there is a ceiling and a floor for inflation expectations. Such a formula implies that ∂CRED∂πe
t = constant - credibility loss flows linearly with respect
to expectations deviation from the target.
A second credibility index, proposed by Levieuge et al. (2015) assumes a nonlinear relationship between deviations from the inflation target and credibility. They assume the following estimator:
CREDLevieuge= 1 eπe t−π target t − (πe t − π target t ) (5) The authors assume a LINEX function for the credibility. Such a setting implies that
∂CRED ∂πe t = f (π e t− π target
t ) - the bigger the difference between the inflation expectations and
the inflation target the higher the loss in credibility.
Both of mentioned estimators can be used only on survey data – with assumption that one is measuring credibility basing on the survey. The indices would interpret market deviations like liquidity and inflation risk premium as changes in central banks credibility. While the inflation risk premium might be connected to credibility, liquidity premium most certainly is not. Moreover, the indices proposed by Levieuge et al (2015) and De Mendonca (2007), cannot be directly interpreted (besides the ambiguous statement that credibility is “high” or “low”). It is so, because those indices have no theoretical microeconomic base. They do not account for any form of expectations beside rational, anchored on the target. Moreover, they assume an ambiguous credibility loss function. Therefore, those indices should be carefully interpreted. Both measures suggest that the ECB was almost perfectly credible in the sample period7.
6 Calculations were based on the Survey of Professional Forecasters. 7 Calculations were based on the SPF. Appendix.
3
Model
In this chapter I propose a new heuristics model describing inflation expectations. I show how such model can be used to estimate central bank’s credibility. I describe assumptions needed to derive the empiric model. Secondly, I show how such model can be augmented to account for inflation risk and liquidity premium and describe the solution to the model. Finally, I assess shortcomings of my model.
3.1
Credibility model
I base my considerations on Bomfin & Rudebusch (2000) heuristic specification of inflation expectations. They state that credibility is crucial when long-term inflation expectations are defined. Under full credibility, an agent’s long-term expectations are anchored on the inflation target. The rationale is that a credible central bank sets a policy that will stabilize inflation over the long-term in line with the stated target. With no credibility, agent’s use other available information to assess the possible future states of inflation. 3.1.1 Heuristic expectations model
I start my consideration from a single agent perspective. Following Brazier et al. (2008) I am assuming that a single agent forms his inflation expectations based on “a rule of thumb”. • Assumption 1: πe t = Xπ e+ t + (1 − X)π e− t
Where I define X as random variable from a Bernoulli distribution with a certain probability of success p that tells if the agent finds the central bank fully credible. The definition above implies that agent follows a heuristic function, as defined by Brazier et al. (2008). Under probability p the agent forms “inflation expectations under full credibil-ity”, under probability (1-p) agent forms “inflation expectations under zero credibility”. Inflation expectations under full credibility are grounded in rational expectations hypoth-esis (Galati et al. (2011)), it implies that agent’s long-term inflation expectations are independent of any new information about inflation. As such, are equal to the central bank’s inflation target - πte+ = πttarget - as stated by both Cukierman & Meltzer (1986) and Bomfin & Rudebusch (2000). The inflation expectations under zero credibility follow an adaptive process (independent of the inflation target) – as shown in Roberts (1998). Thus, I assume that in the long-term πe−= π. However, I also assume that agents would
accommodate their expectations on arrival of any new information about inflation. Probability p can be defined in various ways. To be consistent with my estimation technique, I propose p to be determined by a drift-diffusion process (Fechner (1889);
Camerer et al. (2012); Caplin & Martin (2014)). This implies that agents get noisy information pointing towards various choices. After gathering enough evidence in favour of one, agent will choose his heuristic. Moreover, probability p can be linked to an information game as in Demertzis (2005) or heterogenous preferences, as proposed by Levieuge et al. (2015).
After aggregating expectations over entire the population, credibility is defined as mean probability of success p and can be interpreted as percentage of population that finds central bank fully credible. Thus, my definition is very close to Cukierman & Meltzer (1986) theoretical model definition. They define credibility as the absolute value of the difference between the central bank’s planned monetary policy and the private sectors beliefs about these plans. Thus, they define it as the “average credibility of announcements”.
• Assumption 2: πe
t = λtπte++ (1 − λt)πte−
Considering assumptions made on the “inflation expectations under zero credibility” – the specific form of adaptive expectations (Roberts (1998)), such expectations can be described by an error correction process, with long-term convergence parameter equal to (−γt) and short-term inflation innovation parameter equal to α3,t:
• Assumption 3: ∆πe−
t = α3t∆πt− γt(πt−1e− − πt−1) + et
Adding πe−t−1 to both sides of the equation yields:
πte−= (1 − γt)πt−1e− + (γt− α3,t)πt−1+ α3,tπt+ et (6)
3.1.2 Pure expectations model
Expectations under zero credibility are purely a hypothetical concept8, thus cannot be
measured. However, by inputing transformed Bomfin & Rudebusch equation, expecta-tions under zero credibility can be estimated as a function of expectaexpecta-tions under full credibility, real inflation expectations and credibility:
πte−= π
e
t − λtπe+t
1 − λt
(7) It is worth noting that expectations under zero credibility are undefined when λt= 1,
because we have no information about the zero credibility state. Thus, by combining equations (7) and (6) we can show that:
πe t − λtπte+ 1 − λt = (1 − γt) πt−1e − λt−1πt−1e+ 1 − λt−1 + (γt− α3,t)πt−1+ α3,tπt+ et (8)
8 Because it represents expectations under an assumption that nobody believes in the central bank’s
Recombining above equation yields: πte = (1 − γt)( 1 − λt 1 − λt−1 )πt−1e + (γt− α3,t)(1 − λt)πt−1+ α3,t(1 − λt)πt+ δt+ et (9) With: δt= λtπte+− (1 − γt)( 1 − λt 1 − λt−1 )λt−1πe+t−1 (10)
And (King (1995); Bomfin & Rudebusch (2000)):
πe+= πtarget (11)
The presented equation has a corresponding regression equation:
πet = β1,tπet−1+ β2,tπt−1+ β3,tπt+ δt+ ut (12) Where: β1,t = (1 − γt)(1−λ1−λt−1t ) β2,t = (γt− α3,t)(1 − λt) β3,t = α3,t(1 − λt) (13)
However, such model can only be estimated only on surveyed expectations9. Market
expectations can be distorted by different premiums. Liquidity premium is connected to the size of the market; inflation risk premium is connected to the expected variation of future inflation (Imakubo & Nakajima (2015); Grishchenko & Huang (2012)).
3.1.3 Distorted expectations model
The model I have derived can be augmented to include different premiums. Such an augmented version could be used to estimate credibility from market-implied expectations, as well as estimate liquidity and inflation risk premium. I assume following behaviour of the premiums:
• Assumption 4:
1. Inflation risk premium is dependant on central bank’s credibility. The rationale behind such assumption is that, if the entire population believes in the central bank’s policy, agents will not expect any variation in inflation. Thus, under perfect credibility the inflation risk premium would be equal to zero. If CBs credibility is
low, the expected variation of inflation will be higher – thus increasing the inflation risk premium (Garcia & Lowenkron (2007)).
2. Liquidity premium is, in principal, independent of CBs credibility. It is dependant on the liquidity of the specific financial market (Hilbert (2007)).
Taking above assumptions under consideration, I propose: • Assumption 5: πmarket
t = λtπ(e+)t + (1 − λt)(πt(e−)+ ρt) + σt
Where πmarket
t is a market implied inflation expectation proxy (for example 5y5y
in-flation expectations), ρt corresponds with inflation risk premium and σt is the liquidity
premium. It can be rigorously shown that such equation has a corresponding autoregres-sive model: πet = β1,tπet−1+ β2,tπt−1+ β3,tπt+ δt+ ut (14) Where: δt= λtπe+t − (1 − γt)( 1 − λt 1 − λt−1 )(λt−1πe+t−1+ σt−1+ (1 − λt−1)ρt−1) + σt+ (1 − λt)ρt (15)
3.1.4 Solution to the model
The model links unobserved, theoretical parameters to observed, real data. It can be shown that for any assumed pair of λ0 and τ0 one can estimate the model from following
set of equations:
λt= 1 − β2,t− β3,t− β1,t(1 − λt−1) (16)
Equation (16) can be interpreted as a law of motion for the central bank’s credibility. It depicts that credibility converges to 1, but is distorted in the short term by elasticity of expectations with respect to the recent inflation and (during times of lower credibility) the autoregressive component. Such prediction is consistent with rational expectations hypothesis, as well as findings of Demertzis et al. (2008; 2010) – under perfectly cred-ible monetary regime expectations will be disconnected from the inflation and previous expectations (β1,t = β2,t = β3,t = 0) → λt= 1
γt=
β2,t + β3,t
1 − λt
(17) Equation (17) shows the dynamic of expectations under zero credibility convergence parameter. The higher credibility is, the higher is the estimated convergence rate. Under full credibility this parameter is undefined, because we have no information about the zero
credibility state. The estimated convergence ratio is positively correlated with estimated elasticity of expectations in regard to recent inflation.
α3,t =
β3,t
1 − λt
(18) Equation (18) shows the equilibrium rate for error-correction component of expecta-tions under zero credibility. Again, it is undefined for the state of perfect credibility. It is positively correlated with estimated elasticity of expectations in respect to inflation.
τt= σt+ (1 − λt)ρt= δt+ β1,t(λtπte++ σt−1+ (1 − λt−1)ρt−1) − λtπte+ (19)
Where (1 − λt)ρt can be interpreted as effective inflation risk premium, τt as total
effective premium. The equation (19) shows the law of motion for total effective premium, as estimated from the model. As the value of total effective premium is completely dependent on the constant, it is important to mention that I assume that my model perfectly explains the underlying dynamic of the system. That is, there is no missing explanatory variable bias.
3.1.5 Model shortcomings
As shown above, both credibility and total premium can be estimated based on the presented model. Robustness of these results is, however, dependant on the consistency of the assumptions. Both the credibility, and the total premium estimator is derived using the assumption of completeness of the functional specification. Thus, I assume that my heuristic function completely describes the inflation generating process. That has far reaching implications, which can affect the validity of the model. Consider, for example, a situation in which there exists a third heuristic: memory-bias heuristic (as proposed by Bruin et al. (2011)). In such situation, all of the proposed estimators would become inefficient. Moreover, assuming correlation, omitted variable bias can occur. The degree of this ineffectiveness is, however, to be discussed. The mentioned memory-bias would eventually be normally distributed, thus stabilizing the estimators. Moreover, the estimated total premium has to be carefully interpreted. As it is derived from the time-varying intercept in the model, it is particularly vulnerable to the problem of omitted variable or wrong specification. In the time-varying setting the intercept is very likely to be correlated with a missing variable. As such, the estimated premium can be biased by variables exogenous to the model.
4
Database and estimation technique
In this chapter I describe the database used to verify my hypotheses. Firstly, I discuss the recent innovations in both SPF and 5Y5Y inflation expectations, as well as changes in HICP index. Secondly, I describe estimation techniques used to test my model and assess CB credibility. Finally, I summarize the hypotheses tested in this paper.
4.1
Database
The dataset used in my dissertation consists of two units with different frequency and horizon. The Survey of Professional Forecasters (SPF) unit consists of two variables in quarterly frequency: SPF inflation expectation at 5 years horizon (as reported by the European Central Bank) and HICP price index (for the Eurozone; as reported by Eurostat). The 62 observations cover a period from the first quarter of 2001 to the first quarter of 2016. The 5Y5Y unit consists of two variables at a monthly frequency: 5 year/5 year inflation expectations (for the Eurozone; as reported by Bloomberg) and HICP price index (for the Eurozone; seasonally adjusted; percentage of price change over last year; as reported by Eurostat). The 146 observations cover the period from April 2004 to May 2016.
4.1.1 Survey of Professional Forecasters
The ECB Survey of Professional Forecasters is conducted quarterly. The SPF participants are experts affiliated with both financial and non-financial institutions within the EU. The questionnaire consists of questions regarding future inflation, unemployment and real GDP over different time horizons. Experts are not only asked to give a mean point of their expectations, but also specific probabilities that the variable would fall in a certain bracket. That allows for calculation of higher moments of the distribution, as well as the perceived probability of deflation. Experts mean expectations are often generated from various models, but perceived probabilities are subject to judgement around 80% of the time (ECB bulletin Feb/2011).
Figure I: Survey of Proffesional forecasters expectations and implied credibility
Note: Authors calculations. SPF corresponds with mean 5-year inflation expectations de-rived from the SPF. HICP corresponds with the harmonized index of consumer prices. deflprob corresponds with estimated 5 years deflation probability as derived from the SPF. CredDeMendonca corresponds with De Mendonca (2007) credibility index. The y-axis cor-responds with percentage points and real numbers. The x-axis corcor-responds with the sample period. The data was provided by the ECB. 2001 - Q1; 2006 - Q1; 2011 - Q1; 2016 - Q1.
The financial crisis has impacted the distribution of SPF expectations. From 2009 onwards the perceived probability of deflation10 has been steadily growing, reaching as
high as 1,5% in 2016. The mean of expert’s expectations seems to be stable, implying that the variance of distribution has changed. It is worth pointing out that higher variance of distribution implies both higher inflation risk premium11, as well as some loses in credibility. For measures that are dependent only on the mean that is not the case – credibility remains stable as long as mean is close to the inflation target. Eurozone HICP inflation index has reached sample minimum in July 2009. The sample maximum took place in July 2008.
10 As implied by the SPF. Author’s calculations based on the ECB data. Sample questionnaire is in
the appendix.
4.1.2 5Y5Y inflation expectations
The 5Y5Y inflation expectations, sometimes called the “break-even” inflation rate, are an important indicator for market inflation expectations. The rate is calculated as the spread between a regular bond, and an inflation-indexed bond – thus it can be contaminated with variety of financial premiums. Such expectations can be interpreted as the average expected inflation over a period of five years, five years from now. The rate has attracted great attention from policymakers and bankers (Draghi (2015); Yellen (2015)), because it is generated from the market. Thus, after subtracting premiums, the rate can be interpreted as an efficient estimate of inflation expectations.
Figure II: Raw 5Y5Y inflation expectations and HICP index
Note: The y-axis corresponds with percentage points of price change. The x-axis corresponds with the sample period. Data was provided by the ECB and Bloomberg. 2004 -March; 2008 - May; 2012 - July; 2016 - September.
As we can see on the graph above, 5Y5Y inflation expectations were remarkably stable during the financial crisis. The small rise in the perceived expectations during 2009 could be explained by bigger inflation risk and liquidity premium (Garcia & Werner (2010)).
4.2
Estimation techniques
In my model, central bank’s credibility is linked to the elasticity of inflation expectations in respect to inflation and inflation target. That implies that changes in credibility are generated through time-variation of parameters in the model. This is consistent with both theory and practice of policy making. The first one to stress the importance of time-variation was Robert Lucas in his famous critique (1976).In practice, time-time-variation im-plies that the preferences of the agents are changing over time (Ericsson & Irons (1995)). Following Bomfin & Rudebusch (2000): if agents assess the CB as credible, they will generate expectations based on the inflation target; but if agents assess CB as not cred-ible, they will increase the importance of actual inflation in the generating process. As set out earlier, I assume an error-correction model for inflation expectations under zero credibility. By implication, for both regressions, inflation expectations are the explained variable. Lagged inflation expectations, inflation as measured by the HICP index, and lagged inflation are explanatory variables.
4.2.1 Rolling ordinary least squares
To induce time-variability in the regression, I conduct a rolling ordinary least squares (Stock & Watson (2011)) regression on both SPF and 5Y5Y inflation expectations. The rolling regression model consists of two parts: assessing the rolling samples; and per-forming the regression (Stock & Watson (2011)). Choosing the rolling sample determines the degree of time-variability and robustness of the estimators, because the regression is performed on a sample created by 1. . . n observations; then on a sample created by 2. . . (n+1); etc. Thus, the rolling OLS regression has the following shortcomings:
1. Probability of type-1 or type-2 errors due to limited sample. 2. Ambiguous choice of rolling sample size and tests.
3. Each observation contain errors created by neighbour observations.
I choose a bracket of 8 quarters for surveyed expectations, and a bracket of 12 months for market expectations. Due to the relatively small sample, standard errors are large. The problem of choosing the rolling sample size is related to the time-variability/robustness trade-off. By choosing a smaller sample I induce more variation by assuming independence between smaller brackets of time. Because my SPF sample consists of 62 observations, I assume 7 independent time brackets. 5Y5Y database consists of 146 observations, thus I have 12 independent brackets. The third problem is connected to the fact that each estimator is biased. Because at each point in time I use n observations, the estimators that are recorded are neither efficient nor unbiased. However, if one assumes normality of the errors, Hodrick-Prescott filter can be used (Favero (2001)). In this paper, normality
of such errors is assumed. Following Hodrick & Prescott (1997) and Ravn & Uhlig (2002), I select the smoothing factor equal to 1600 for quarterly data and 129600 for monthly data. Finally, in the OLS regression, there is the risk of spurious regressions (Entorf (1997)). The time-series regressions are especially liable to the problem. It is so, because many variables are trending – either deterministically or stochastically. If the variables share common trend – we will get a spurious correlation. Unfortunately, due to assumed functional form, as well as rolling estimation technique, I cannot perform unit root tests – like augmented Dickey-Fuller test. Due to our a-posteriori knowledge of ECB credibility (Demertzis et al. (2010)), we can state that the expectations will have a strong intercept equal to λtπtarget.
Figure III: Coefficients from the model and their respective Wald statistics
(a) Coefficients from the rOLS model (b) Wald statistics
Note: Authors calculations based on the model presented in this dissertation. 5Y5Y cor-responds with the autoregressive component. C corcor-responds with the constant. HICP and LHICP correspond with the inflation and the first lag of inflation. The y-axis corresponds with real numbers and Wald statistic value. The x-axis corresponds with the sample period. The data used in the calculations was provided by the ECB and Bloomberg. 2004 - March; 2008 - May; 2012 - July; 2016 - September.
As stated earlier, the rolling OLS estimator is not efficient. It is not efficient be-cause, through rolling the sample, information12 is lost. Moreover it exhibits statisti-cally significant autoregressive component - which in fact is aa intercept. Moreover, the HP filter procedure can actually filter out the crucial variation - leaving noise (Petersen (2001); Cogley & Nason (1995)). Due to limited availability of robustness tests, I per-form additional regression with different estimation technique. I choose the time-varying Maximum-Likelihood estimator. Maximum likelihood estimator is proven to be asymp-totically effective (Hamilton (1994)) if errors are following the Gaussian distribution.
4.2.2 Maximum likelihood state-space model
State-space model is any model that consists of observation process and a state process. First version of the model was proposed by Hurst in 1952. Dynamic state-space models can be described by a simple set of equations (Petris (2010)):
yt= Ftθt+ w1,t θt = Gtθt−1+ w2,t (20) Where: w1,t ∼ N1(0, W1) w2,t ∼ N2(0, W2) (21)
And W1, W2, Ft and Gt are appropriate size matrices. Both space and state errors are
assumed to be independent of the starting state, and independent between each-other. To complete the experiment, one has to assign values for the θ0 state. Moreover, one
has to assume either constant or stochastic volatility. That is, assume if the variance of the evolutions is constant or random itself. The most celebrated way of estimating posterior distribution in stochastic models is the so-called, Markov-Chain Monte Carlo (MCMC) simulation (Primiceri (2005)). I am assuming constant variance of innovations, as proposed by Zivot & Yollin (2012) and Nakajima (2011). To avoid ambiguity, I assume standard errors achieved through Maximum-Likelihood estimation over the entire sample. Maximum Likelihood estimator finds the most likely values for parameters, conditional on the sample. Moreover, I assume Gaussian distribution of the errors and that each coeffi-cient follows an independent random walk. Finally, I use the Kalman filter to retrieve the most likely values for the time-varying coefficients (Gardner et al. (1980)). Kalman filter (Kalman (1960)) is a recursive state-space model, that allows for retrieving true states of a system that is subject to white noise perturbations. The estimators obtained through this experiment are more robust. It is because, through more rigorous assumptions, we can assess theoretical states based on the complete set of information. That means that, while estimating values at t0, we are using information from tT.
4.3
Summary of hypotheses
In sum, I estimate an autoregressive model of the following form:
πet = β1,tπet−1+ β2,tπt−1+ β3,tπt+ δt+ ut (22)
By estimating such model, I indirectly estimate the theoretical values I am interested in – that is, central bank credibility λt and total effective premium τt. The hypotheses
inflation expectation test in spirit of Demertzis et al. (2008; 2010).
First, I test if my inflation expectation specification is consistent. I do so by conduct of an a posteriori test of the model predictions:
1. Because the credibility was specified as a percentage of population, its value should statistically fall in the bracket between [0,1].
2. Because the credibility measure rationale is similar to the one presented by De Mendonca (2007), its values should resemble De Mendonca’s index values.
3. Estimated premium should resemble the values generated from other models (for example, Garcia & Werner (2010)).
As I have stated earlier, the credibility estimator proposed in this thesis is a linear combination of model’s coefficient and credibility from the previous term. Therefore, stan-dard deviation of the credibility is not simply the square root of the sample variance. To calculate the confidence intervals one should use the augmented Bienayme formula. Be-cause of time-varying framework, the coefficients standard errors are changing over time. Thus, to simplify the calculations greatly, I assume that covariance of model’s coefficients is zero13. Moreover, because credibility at t
0 is not a random variable, V ar(λt0) = 0.
Secondly, assuming correctness of the specification, I test the rational expectations hypothesis. King (1995), Bomfin & Rudebusch (2000) and Demertzis et al. (2008; 2010) find that, during times of relatively high credibility, inflation expectations are disconnected from the inflation. That implies that the model coefficients connected to inflation and lagged inflation should be statistically equal to zero. Moreover, as stated by Demertzis et al. (2008; 2010), the autoregressive component should be insignificant during periods of high credibility. This hypothesis can be tested with three independent Wald tests with corresponding hypotheses H0: βj,t = 0 for j = 1, 2, 3.
13 Obviously this assumption is false - model’s coefficients are almost always correlated. However, the
5
Results
In this chapter I describe the results of my estimations for both datasets. Firstly, I discuss the SPF dataset. I test the rational expectations hypothesis as stated by Demertzis et al. (2008; 2009) and calculate the ECB credibility, as implied by De Mendonca (2007) as well as the model presented in this dissertation. Secondly, I test the augmented model on the Eurozone break-even inflation rate. I repeat the procedure described for the SPF database. Moreover, I describe estimated premiums generated by the model. Finally, I prove that the model is relatively robust to initial values of credibility and premium.
5.1
Experts expectations estimation
For all calculations in this subsection, I am assuming 2% as the long-term inflation target. Moreover, I am assuming 95% credibility14,15 in the starting period. After calculating the model using the maximum-likelihood estimator, I will analyse the model’s output. 5.1.1 Rational expectation hypothesis
As stated by Demertzis et al. (2008; 2010), in times of high credibility, inflation expec-tations would be explained solely by the intercept. It should be so, because in times of high credibility, market expectations become rational. As such, they are firmly anchored on the inflation target. Moreover, any new information about inflation is ignored in the expectations forming process. That implies that coefficients corresponding with inflation, lagged inflation and lagged inflation expectations should be statistically insignificant. I test this hypothesis using three separate Wald tests with hypothesis H0: βj,t = 0. I
use the level of confidence 95% - therefore statistic equal to t > |1.96| rejects the initial hypothesis.
14 That implies that 95% of population had found the inflation target to be an optimal estimate of the
future inflation.
15 Because the model relies on the recursive input, λ
Figure IV: Coefficients from the model and their respective Wald statistics
(a) Coefficients from the ML estimation (b) Wald statistic
Note: Authors calculations based on the model presented in this dissertation. SPF corre-sponds with the autoregressive component. C correcorre-sponds with the constant. HICP and LHICP correspond with the inflation and the first lag of inflation. The y-axis corresponds with real numbers (regression estimates) and Wald statistic value. The x-axis corresponds with the sample period. The data used in the calculations was provided by the ECB. 2001 - Q1; 2006 - Q1; 2011 - Q1; 2016 - Q1.
As can be noted from the graph above, inflation has relatively small positive effects on inflation expectations. The lagged inflation coefficient, however, is statistically significant from Q3/2010 onwards. Thus, the hypothesis of perfect credibility in SPF sample is rejected at the level of 95% confidence. That estimate can be explained by the fact that, in the period sample, inflation value was relatively close to the inflation target. Thus, it is hard to say, at least not ambiguously, if expectations were adaptive or rational in nature. Moreover, as mentioned earlier, I have assumed inflation target to be equal to 2% - which is an approximation. In fact, the European Central Bank targets inflation, as measured by the HICP index, to be below, but close to the level of 2%.
5.1.2 Experts-implied ECB credibility
To verify if my model’s estimates are plausible, I shall compare my credibility measure to the one proposed by De Mendonca (2007). I assume credibility at t0 to be equal to
95%16,17. Moreover, I calculate my measure by assuming the mean values for estimators.
De Mendonca’s (2007) credibility index is calculated assuming 2% inflation target. Figure V: Experts-implied ECB credibility
(a) ECB credibility (b) Confidence interval
Note: Author’s calculations based on De Mendonca (2007) and presented model. mlCRED-DeMendonca corresponds with credibility index calculated upon estimated market inflation expectations. mlCRED corresponds with credibility measure proposed in this thesis. The y-axis corresponds with percentage points. The x-axis corresponds with the sample period. The data used in the calculations was provided by the ECB. 2001 Q1; 2006 Q1; 2011 -Q1; 2016 - Q1.
The graph shows the credibility of the European Central Bank, as calculated by index proposed by De Mendonca (2007) and me. As can be noted my measure not only statisti-cally falls into the desired bracket, but also closely follows the other credibility estimators. As follows from the indices, the ECB was very credible in the sample period. According to all estimators, ECB credibility fell between values of 0.9 to 1. As noted earlier, my measure can be interpreted as a percentage of the population that has expectations equal to the policy target18. Thus, in the first quarter of 2016, around 95% of SPF participants
found the ECB perfectly credible - which implies a 5% decline in credibility during the sample period.
16 That implies that 95% of population had found the inflation target to be an optimal estimate of the
future inflation.
17 Because the model relies on the recursive input, λ
0 has to be assumed.
18 Thus it can be interpreted as ”effective credibility” - percentage of expectations that is formed based
5.2
Market-implied inflation expectations
For all calculations in this subchapter, I am assuming 2% as the long-term policy target. Moreover, I am assuming V (λ0, τ0) = (0.95, 0.5). As mentioned in chapter one, standard
credibility indices cannot be used on raw market inflation expectations data. Thus, I will start my analysis by disaggregating raw inflation expectations into estimated market inflation expectations and estimated total effective premium.
5.2.1 Rational expectations hypothesis
To test the Demertzis et al. (2008; 2010) hypothesis corresponding with my thesis, I look into statistical significance of the inflation, lagged inflation and lagged inflation expecta-tions coefficients. I test this hypothesis using three separate Wald tests with hypothesis H0: βj,t = 0 (Demertzis et al. (2008; 2010)). I am interested in the confidence level of
95%. Such level corresponds with statistic equal to t > |1.96|. Moreover, the rational ex-pectations hypothesis (Galati et al. (2011)) implies that the time-varying constant should be the only statistically significant predictor of the inflation expectations.
Figure VI: Coefficients from the model and their respective Wald statistics
(a) Coefficients from the ML estimation (b) Wald statistic
Note: Authors calculations based on the model presented in this dissertation. 5Y5Y cor-responds with the autoregressive component. C corcor-responds with the constant. HICP and LHICP correspond with the inflation and the first lag of inflation. The y-axis corresponds with real numbers (regression estimates) and Wald statistic value. The x-axis corresponds with the sample period. The data used in the calculations was provided by the ECB and Bloomberg. 2004 - March; 2008 - May; 2012 - July; 2016 - September.
Inflation, lagged inflation and lagged inflation expectations coefficients remained in-significant over the entire sample. Thus the rational expectations hypothesis, as defined in Demertzis et al. (2008; 2010), is failed to be rejected. This implies that, based on the
estimated market inflation expectations, the European Central Bank was highly credible in the sample period.
5.2.2 Market-implied inflation expectations
As mentioned earlier, the break-even inflation rate is contaminated with variety of pre-miums. Thus, to calculate credibility from market inflation expectations rate, one has to substract the assumed premiums. Using the model presented in this dissertation, and an assumed inflation target of 2%, I will disaggregate the break-even inflation rate into estimated market-implied inflation expectations and total premium (inflation risk and liquidity).
Figure VII: Estimated market inflation expectations and total premium
Note: Author’s calculations based on the model presented in this dissertation. ml-PREMIUM corresponds with the estimated total premium. mlEXPECTATIONS corre-sponds with the mean estimated market inflation expectations. The y-axis correcorre-sponds with percentage points. The x-axis corresponds with the sample period. The data used in the calculations was provided by the ECB and Bloomberg. 2004 - March; 2008 - May; 2012 - July; 2016 - September.
According to model’s estimates, market inflation expectations were remarkably stable during the sample period – reaching minimum of 1,76% in March 2015. Interestingly,
March 2015 was the month when Public Sector Purchase Programme was implemented. Moreover, it was March 2015 when the ECB has positively revised its growth and infla-tion forecasts19. The estimated premiums resemble dynamics generated within different
models20. It is falling steadily from 2004 to the end of 2005. Then it has reached its
maximum of 0,85% in September 2009 – just month before Greece’s sovereign debt crisis has started. The premium minimum of -0,4% has been reached in February 2016. The negative premium is sometimes explained by a perceived risk of deflation. Moreover, the quantitative easing programme might have affected the liquidity of the bond market - decreasing the liquidity premium. The model suggests that the premiums are much more volatile than expectations. Because premiums estimated through my model can be distorted by missing variables, volatility hypothesis is left to be verified.
5.2.3 ECB market-implied credibility
After disaggregating 5Y5Y spread into estimated inflation expectations and estimated total premium I analyse the European Central Bank’s credibility as implied by the market. To do so, I use a credibility measure estimated through my model, as well as the linear credibility index proposed by De Mendonca (2007).To calculate the linear credibility index I assume 2% inflation target. Moreover, I assume the inflation target floor to be equal to 0%, and the inflation target ceiling to be equal to 4%21. To calculate credibility measure
proposed in this dissertation, I am considering means of the estimated parameters22.
The credibility estimator proposed in this dissertation is a linear combination of four random variables. Thus, there exists a high probability that the actual value for credibility lies below unity for the first years in the sample. From 2007 onwards, my measure seems to follow the linear estimator proposed by De Mendonca (2007). The credibility series proposed in this thesis exhibit a local minimum of 91% in July 2011 – corresponding with the peek of debt crisis in Ireland. The sample minimum of 89% was reached in July 2014. Concluding, the ECB is found to be highly credible – model output suggests that (in 2016) over 90% of the market found the bank to be credible. The credibility series, however, seem to be following a negative trend. The ECB has lost around 10% credibility since the early 2009. The credibility index proposed by De Mendonca (2007) exhibits a sample minimum in February 2015, shortly after the ECB expanded the asset purchase programme. The difference between the credibility measure proposed in this dissertation and the one proposed by De Mendonca (2007) can be due to few reasons. Firstly, De Mendonca’s index does not account for any information about the actual inflation. Thus, basing only on this measure, it is impossible to say if the expectations are rational or adaptive. Secondly, I have assumed the inflation floor to be equal to 0%, and the ceiling
19 The Telegraph.
20 Bekaert & Wang (2010)
21 Therefore, I assume a symmetric target bracket.
Figure VIII: Market-implied ECB credibility
(a) ECB credibility (b) Confidence interval
Note: Author’s calculations based on De Mendonca (2007) and presented model. mlde-mendona corresponds with credibility index calculated upon estimated market inflation expectations. mlcred corresponds with credibility measure proposed in this thesis. The y-axis corresponds with percentage points. The x-axis corresponds with the sample period. The data used in the calculations was provided by the ECB and Bloomberg. 2004 - March; 2008 - May; 2012 - July; 2016 - September.
to be equal to 4%. If the bracket is set tighter, the variation of the index will be higher. Finally, the estimators predicted by my model can be biased - either by the omitted variable bias, wrongly assessed variation of the innovations in the ML estimation or by noisy measure of inflation. The findings are consistent with Galati et al. (2009) - the expectations became less anchored after the financial crisis.
5.3
Robustness analysis
As I have stated earlier, the model has a unique equilibrium for every assumed V (λ0, τ0).
Thus, the initial state of the system affects the future states. For both set of results I have chosen V (λ0, τ0) = (0.95, 0.5). This assumption, however consistent with literature,
Figure IX: Sensitivity to initial assumptions
(a) Credibility sensitivity (b) Premium sensitivity
Note: Author’s calculations. For credibility, I have chosen initial values equal to I(0.2, 0.4; 0.6, 0.8, 0.99). For premium, I have chosen initial values equal to I(0.1, 0.3, 0.5, 0.7, 0.9). The y-axis corresponds with percentage points. The x-axis cor-responds with the sample period. The data used in the calculations was provided by the ECB and Bloomberg.
As can be seen on the figure (IX), model is robust to initial assumption. Intuitively, this property can be explained by the fact that the model is defined by all states from t0
to tT - thus the bigger the sample, the smaller the impact of the initial state . Curiously,
defining such property in terms of mathematics brings an interesting implication.
For simplicity, consider a situation in which coefficients of the system are not changing (βx,t = βx) and that we have only three periods. Thus, by recursive input:
λ3 = 1 − β2− β3− β1(1 − (1 − β2− β3− β1(1 − (1 − β2− β3− β1(1 − λ0))))) (23)
It can be easily shown that:
λ3 = 1 − ... − β13(1 − λ0) (24)
Now, I define the marginal effect of initial state23 as the differential:
∂λt
∂λ0
= β1t (25)
Moreover, it can be easily shown that for the time-varying setting: ∂λt
∂λ0
= β1∗ β2∗ ... ∗ βt (26)
Now, considering that the autoregressive component in the model should not be bigger than unity it is obvious that:
lim
t→∞β1∗ β2∗ ... ∗ βt= 0 (27)
Thus, as long as the autoregressive component is close to zero, the estimator of credibility will be unbiased - even if the initial state value was chosen ambiguously. It is worth noting that the smaller the credibility, the bigger will be the autoregressive component (as pre-dicted by the theory). Thus, my model will be more sensitive to initial assumption when the overall credibility is low. Again, the maximal deviation of the credibility estimator in regard to the initial state assumptions can be defined from equation (25). By assuming β1,tt = 1 one can see that the maximal deviation is equal to 1 ∗ λ0.
Sensitivity of the premium estimator in regard to the initial values can be calculated the same way. Indeed:
lim
t→∞
∂τt
∂λ0∂τ0
6
Conclusions
This dissertation focuses on the issue of measuring central bank credibility. I propose an alternative estimator of central bank’s credibility – an estimator that does not assume a system steady state. I base my model on behavioural economics considerations, as well as inflation expectations heuristics function proposed by Bomfin & Rudebusch (2000). I show under what assumptions the model can be estimated on the real data. My model’s implications are consistent with those presented in Demertzis et al. (2010) – that is, if the inflation expectations are disconnected from real inflation as well as previous expectations (as implied by the rational expectations hypothesis), the central bank is fully credible. I find that my model creates a plausible output – with the credibility estimator quite closely following the linear index of De Mendonca (2007). I propose a distorted heuristics function, which allows for estimation of premiums distorting the break-even inflation rate. I estimate the model on two datasets concerning the Euro Area – inflation expectations of economic forecasters (SPF), as well as the break-even inflation rate (5Y5Y). After conducting calculations using two regression methods – rolling OLS and ML Kalman filter – I find that ML produces more robust estimators. Finally, I show that estimators produced by the model are independent of the initial state, provided the big sample.
The results suggest that the European Central Bank (ECB) remained highly credi-ble in the sample period. It is estimated that the average of 97% of surveyed experts have found the European Central Bank to be credible (during the sample period). Their expectations are, however, statistically influenced by changes in inflation from Q3/2010 onwards. Moreover, the ECB credibility24 has been declining from 2009 onwards. The
ECB credibility, as calculated from the break-even inflation rate, is estimated to be aver-aging at the level of 95% of the population (during the sample period). Moreover, market inflation expectations seem to be disconnected from any explanatory variable – leaving the Demertzis et al. (2008; 2010) credibility hypothesis to be rejected in the future. These results, however, are not to be treated lightly. The ECB credibility, as estimated from the market, has fallen from 100% in 2008 to around 90% in 2016 - reflecting the volatility of the actual inflation and struggle to stabilize the price change. The results obtained through estimation are in line with findings of Galati et al. (2016) – inflation expectations in the Eurozone are becoming less anchored. The estimated total premium is relatively volatile, averaging at the level of 0,27%.
The declining credibility can be explained within the existing framework. Considering volatility of the inflation, agents find that adaptive expectations can provide with better payoff in the future. As more and more agents act upon such expectations - it becomes
more optimal to accommodate one’s expectations above or below the target, and the harder it is to stabilize the inflation. Thus completing the vicious cycle.
I believe that the literature could benefit from more investigation on the model. Espe-cially, the used heuristics function can be falsified in Popperian sense – by conducting an experiment on the laboratory level. Statistical analysis of the premiums generated within the model should be expanded – the differences between estimators generated from both affine term model and the expectations model should be analysed. The time-varying esti-mation could be performed with stochastic volatility. Such an experiment would increase the variability of the parameters estimated. Moreover the model should be tested on other countries data.
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