Hungarian monetary policy before and after the recession

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University of Amsterdam

Faculty of Economics and Business

Hungarian monetary policy

before and after the recession

Gábor Biró – 11400129

MSc Economics – Monetary Policy & Banking

11

th

July, 2017

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Statement of Originality

This document is written by Student Gábor Biró who declares to take full responsib-ility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Acknowledgements

I am beholden to dr. Marcelo Zouain Pedroni for his help, constructive criticism and vivid ideas. I would like to thank Balázs Horváth, Máté Kormos and Zsombor Varga, who were always there to help me when I was stuck with a problem at three o’clock – no matter whether it was in the dawn or in the afternoon.

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Abstract

In this thesis, I answer the following question: How did Hungarian monetary policy change due to the recession in 2008? My results show that decision makers at the central bank put more emphasis on the inflation gap after the recession than before. In contrast, reactions on output gap and changes in the exchange rate are less important after the recession when adjusting the rates. I find evidence for the following explanation in my findings: hysteresis makes policymakers act quickly and aggressively in response to a recession, to reduce the depth and persistence of the downturn. I also estimate the optimal simple rules in a DSGE framework and find that the central bankers deviated more from the optimum before the recession than after it.

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List of Figures

3.1 Day-to-day and 3 month interest rates . . . 7

3.2 Output gap estimates . . . 8

3.3 Core inflation, HICP and HICP forecast rates . . . 9

3.4 HUF/EUR exchange rates . . . 10

4.1 The fit of the contemporaneous rules . . . 14

5.1 The fit of the backward-looking rule using the own output gap estimate . 19 5.2 The fit of the forward-looking rules . . . 21

B.1 The fit of the contemporaneous rules using the deviation of the core infla-tion from the Maastricht target . . . III B.2 The fit of the contemporaneous rules using the deviation of the HICP from

the sovereign target . . . IV B.3 The fit of the contemporaneous rules using the three month rate as

de-pendent variable . . . V B.4 The fit of the backward-looking rules using different inflation measures . VII B.5 The fit of the forecast-based rules using the deviation of the inflation

ex-pectations from the Maastricht target . . . IX B.6 The fit of the backward-looking rules using the three month rate as

de-pendent variable . . . X B.7 The fit of the forecast-based rules using the three month rate as dependent

variable . . . XII

C.1 Day-to-day and 3 month interest rates . . . XII C.2 Core inflation, HICP and HICP forecast rates . . . XIII C.3 Output gap estimates . . . XIII C.4 HUF/EUR exchange rates . . . XIV

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List of Tables

1.1 The inflation targets of the MNB . . . 2

4.1 Contemporaneous Taylor rules . . . 12

4.2 Testing the hysteresis hypothesis . . . 15

5.1 Backward looking rules . . . 18

5.2 Forward-looking Taylor rules . . . 20

6.1 Optimal simple rule feedback coefficients . . . 23

6.2 Comparing the estimated rule to the optimal one . . . 24

A.1 Parameters used in Section 6 . . . I

B.1 Contemporaneous rules with different inflation measures . . . II B.2 Contemporaneous Taylor rules with 3 month rates as dependent variables IV B.3 Backward looking rules with different inflation measures . . . VI B.4 Forward-looking Taylor rules with the deviation from the Maastricht

cri-terion as inflation . . . VIII B.5 Backward looking rules with 3 month rates as dependent variables . . . . X B.6 Forward-looking Taylor rules with 3 month rates as dependent variables . XI

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1. Introduction

Since Taylor (1993) modeled the decisions of the Federal Reserve with a simple mon-etary reaction function, many papers have been written which try to generalize one coun-try’s monetary policy with a simple function. Even – to some extent – central banks’ monetary policy decisions are affected by this rule. In this thesis I model the Hungarian monetary reaction function, to answer the following question: How did Hungarian mon-etary policy change due to the recession in 2008? I do so by estimating multiple Taylor-type equations – broadened with changes in the exchange rates as inter alia proposed by Clarida et al. (1998) – with the Generalized Method of Moments (GMM) estimator on monthly data provided by the Central Bank of Hungary (Hungarian: Magyar Nemzeti Bank, henceforth: MNB) and Eurostat (June 2001 - February 2017).

Since Hungary is a small, open economy, including exchange rates in the Taylor rule is reasonable. In 2015, for instance the imports made up 75% of the GDP, while the exports made up 82% of it. An important cornerstone in the politics of the current government is to keep the current account positive, and the surplus as big as possible. In 2015, the cur-rent account surplus was 7.8% of the GDP, so Hungary is extremely exposed to exchange rate fluctuations. Moreover, on February 26, 2008 the MNB abandoned the flexible peg of the Forint to the Euro within a fluctuation band and adopted a free floating exchange regime vis-a-vis the Euro as reference currency.

The first month of the dataset I use is June 2001, because Hungary adopted an infla-tion targeting regime in this month, which succeeded the previous exchange rate target regime. In the first few years of the IT framework, the target was set lower and lower, until it eventually reached the target given in the Maastricht treaty. I collected the in-flation targets of the MNB in Table 1.1.

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Table 1.1: The inflation targets of the MNB

Target rates Reference period Date adopted

7% December 2001 June 2001 4.5% December 2002 June 2001 3.5% December 200 December 2001 3.5% December 2004 October 2002 4% December 2005 October 2003 3.5% December 2006 November 2004 3% Continuous August 2005

3% ±1 percentage point Continuous March 2015

Source: MNB

Although neither the question nor the estimating method is a novelty in the literature, to my knowledge no articles were written so far which compare the pre- and post-recession monetary policies in Hungary. Since GDP and thus output gap is published quarterly by the MNB and the Hungarian Central Statistics Office (Hungarian: Központi Statisztikai Hivatal, henceforth: KSH), I collect different indicators, define them as cyclical positions and compress them into an output gap estimate, which I use besides the usually used industrial production.

I find that decision makers at the central bank put more emphasis on the inflation gap after the recession than before, and the Taylor principle, which states that if inflation is growing with one percentage point the central bank should raise interest rates with more than one percentage point holds in the latter period. On the contrary, reactions on output gap and changes in the exchange rate are less important after the recession when adjusting the rates. This holds whether I use my own output gap estimation or the industrial production as output gap. The estimates also show that the natural level of the interest rate was higher, around 7-8% before and lower, around 4-5% after the crisis in 2008. The benchmark model I use shows that only inflation is the focus of central bankers when adjusting rates after the recession. That is a consequence of hysteresis, as Yellen (2016) states, hence it makes policymakers react stronger on the biggest problem - here growing inflation - which claims the significance from other variables. I estimate multiple types of Taylor rules besides the ’basic’ one: backward- and forward looking rules. I also check the sensitivity of the models to changes in inflation measures (core inflation and HICP, with sovereign and Maastricht targets) and changes in dependent variables (day-to-day and three month rates), and can say that the results are robust to

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using different measures of inflation and interest rates.

I also estimate an optimal simple rule for Hungary, using a New Keynesian small open economy framework described by Galí (2008) and find that the policymakers deviate from the optimal policy. According to the estimated and optimal rules, Hungarian monetary policy was not welfare maximizing before the recession: the reaction to inflation and output gap was too soft, while exchange rate coefficients have wrong signs, where signi-ficant. It is still not welfare maximizing after the crisis, but it is clear that policymakers made improvements in minimizing welfare loss to achieve the optimal monetary policy; the deviation is higher in the period before the recession and a convergence towards wel-fare maximizing shows up in the period after the crisis, but the difference is still notable between the optimal and the empirically estimated coefficients.

The structure of the thesis is the following: a review of the literature on the topic is provided in Section 2. I then describe the dataset in Section 3 and in Section 4 I present the benchmark estimations. I estimate alternative Taylor rules in section 5, while I derive an optimal rule and compare my findings to it in Section 6. I conclude the results in Section 7, and provide robustness checks in Appendix B.

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2. Literature review

It is a vast topic when it comes to analysing Hungarian monetary policy. In the last two decades, authors wrote vast amount of papers on Taylor rules in Hungary, especially in the years after Hungary joined the European Union1_{. In this section I summarize and}

review review of this literature. For clarity, I distinguish between two groups in the liter-ature: some authors find that the policymakers do respond to exchange rate fluctuations, but some authors do not find evidence for this.

Paez-Farrel (2007) conducted a research on Central-European countries’ monetary policy rules, his estimations for Hungary were on 2002-2006 data. Instead of HICP, core inflation was used for the inflation measure in the estimated Taylor-type rules. The pa-per found that the decision-makers in Hungary tend to respond to the real exchange rate when adjusting monetary policy. Moreover, Hungary represented the more aggressive inflation-responding rules (alongside Poland) in the Central European region. In order to converge to the common currency zone, certain measures have to be met. The effective-ness of the convergence with the used instrument rules is analysed by Orlowski (2010) on 1999-2009 data. The estimation method for Taylor-type rules is OLS which is different from the usual GMM method most papers use. This model shows that the MNB responds strongly to the exchange rate gap and is insulated from the inflation gap and the output gap. Popescu (2013) estimated models on monthly data between 2001-2012, calculat-ing the output gap from the industrial production index. He concludes that Hungary is leaving space for a parallel stabilization of the exchange rate besides the fundamental goal, price stability. Moreover, he states that the Taylor principle holds, as the nominal interest rate increases to a higher extent than inflation.

Ziegler (2012) conducted a research on monetary policy of Central and Eastern European countries, including Hungary on data between 1995-2008. It also includes the last quarter of 2008, which distracts the estimation, moreover interest rates for Hungary are proxied by the average of the lending and deposit rate. Nevertheless, the paper concludes that

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exchange rates have a negative impact on the interest rate. An MNB analyst also ana-lysed monetary policy reaction functions for Hungary, Hidi (2006) estimates multiple Taylor-type rules on data between 2001-2006. He concludes that on monthly data ex-change rate has a stronger effect than on quarterly data, however the latter is closer to the time-horizon of the MNB. Also, movements in the domestc interest rates, inflation and the HUF/EUR exchange rate are similar to the advanced economies’.

In the past decade, lot of papers were written in this topic which basically – with a few exceptions – shared the same attributes: dependent variable is the 3-month interbank in-terest rate, the estimation method is GMM, changes in exchange rates are included in the models, multiple rules (backward- and forward-looking, contemporaneous) are estimated. A recent manuscript Abaligeti et al. (2017) however, estimates a time varying parameter Taylor rule for the Hungarian monetary policy, with Kalman-filter on data from 2001 to 2015 and observes that there are multiple subperiods because of the changing economic conditions. According to this article, between 2001 and 2007, monetary policy focused on stabilizing the implicit goal on the EUR/HUF rate, from 2008 until 2011 the prime target of the monetary policy was to protect the exchange rate, while after 2012 the focus was on forward looking inflation gap.

In the early 2000s, Maria-Dolores (2005) estimated Taylor-rules for Hungary and found that backward-looking rules apply better than others estimated with GMM. However, his model did not include exchange rates and the dataset he uses has observations between 1998-2003, with inflation targeting only introduced in 2001. He concludes that Hungary followed the ’classic’ Taylor-rule, driven by the desire to join the European Union and the European Monetary Union. Another study was conducted by Siklos (2006) on monthly data between 1996-2005. He estimates multiple Taylor-type rules for Hungary, including the exchange rates in the models. His conclusion is that the interest rate policy of Hungary has been lower then it would have been needed to meet the Maastricht standards, and only the forecast-based rule comes close to mimic the ECB’s interest rate policy. Vašíček (2009) examines Hungarian monetary policy rules on data between 1999-2007 which is also cross-cut by the regime change towards inflation targeting in 2001. According to the results, forward-looking rules have higher explanatory power than backward-looking ones, and inflation targeting countries’ monetary policy responds significantly to domestic inflation, however Hungary reacted weaker on expected inflation than other countries in the region (Poland, Romania).

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between 1994-2008. That period is cut in half by the change of monetary policy regime, is however justifiable because of the managed float exchange rate Hungary has been in-troduced in 2008. They use a cointegration approach and find that interest rate setting differs strongly between regimes, and a strong focus is on inflation during periods of more flexible exchange rate arrangements. Regős (2013) has estimates on monthly data between 2003-2012, including sovereign risk in the policy rules. He states that changing exchange rates for sovereign risk in the estimation results in a better fit, and also that different output gap estimations can result in a better fit – though they are less under-pinned theoretically. Also, output gap becomes significant when estimating on quarterly data instead of monthly in the model. He includes ’sensitivity checks’ - controls his model for changing inflation measures between HICP and core inflation, different output gap estimates, different risk measurements and concludes his findings are not sensitive to data manipulations.

Another perspective is investigated in the working paper of the MNB, Jakab et al. (2010) which analyses optimal monetary policy rules for Hungary in a DSGE framework. According to this paper, adding the nominal exchange rate to the policy rule does not, but including wage inflation does improve the welfare significantly. In a more open economy optimal policy should react to domestic inflation more strongly and gets more concerned with nominal, as opposed to real variables. Jakab et al. (2010) suggest that a simple inflation targeting rule with a high enough feedback coefficient on domestic inflation can approximate the welfare-maximizing monetary policy relatively well, as the empirical rule reacts to different types of shocks similar to the simple Taylor-type rules.

Comparing my findings to the existing literature the estimates for the first period belong to the group which finds exchange rate fluctuations are in focus when setting interest rates. The estimates for the second period, however, fit in the group which finds no evidence for this. The reaction on inflation links these two groups - and the models I use - together: almost all papers find that inflation is in the main focus, no matter if closing the inflation gap, fulfilling the Maastricht-criteria or just reacting on HICP. I also find that policymakers reacted strongly on inflation before the crisis - and to an even higher extent after it, satisfying the Taylor principle.

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3. Data

In this section, I briefly describe the dataset I use. All of the data I work with is provided by the MNB, Eurostat or OECD. I use the day-to-day interbank interest rates as dependent variable, because of availability issues: the time series of the three month rates has gaps in it. As robustness check I also run my estimates with the three month rates as dependent variable. To complete the void time series I use multiple imputation1_.

The interest rates over time are seen in Figure 3.1.

2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. 0 2 4 6 8 10 12 14 % DTD rates 3 month rates

Figure 3.1: Day-to-day and 3 month interest rates

As for the output gap, it is not calculated monthly, only quarterly with the GDP. It

1_{The concept of MI is to use the distribution of the observed data - alongside with random components}

to imitate uncertainty - to estimate a set of values for the missing data. Multiple datasets are created and analysed individually but identically during the process to obtain a set of parameter estimates which are combined into the parameter estimates, variances and CIs. (White et al., 2011, pp. 378)

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is common in the existing literature to calculate output gap from industrial production (e.g.:Clarida et al. (1998), Maria-Dolores (2005), Frömmel et al. (2011)). Besides, I try to estimate it with business cycle indicators. My method is based on Balatoni (2014): I collected data for unemployment rates, industrial production, inflation, base interest rates, and the M1 supply, and defined them as different cyclical positions, weighted them according to their correlation with the GDP and got an indicator. I seasonally adjusted the data with TRAMO-SEATS method (specification RSA4) also used by the KSH, then applied a Hodrick-Prescott filter to estimate the gap (smoothing parameter 129600 (Ravn & Uhlig, 2002)). The two approaches I use to capture the output gap can be seen in Figure 3.2. When it comes to forward-looking estimates, I use the Economic Sentiment Indicator provided by the Eurostat.

2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. −4 −3 −2 −1 0 1 2 3 % Own estimation Industrial production

Figure 3.2: Output gap estimates

I use two approaches to measure inflation: the Harmonised Index of Consumer Prices (HICP) is the common way to describe price inflation. However, the goal of the MNB is to react on the core inflation, rather than reacting on seasonal fluctuations originated from food or energy prices (Regős, 2013). Both inflation measures appear in the relevant literature, in the benchmark models I use the core inflation, but as robustness test I substitute the measure to the HICP. I calculate the forward-looking inflation gap from the yearly forecasts provided by the OECD, by linearly interpolating it to monthly data. The inflation rates can be seen in Figure 3.3.

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2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. −2 0 2 4 6 8 10 % Core inflation HICP HICP forecast

Figure 3.3: Core inflation, HICP and HICP forecast rates

The HUF/EUR exchange rates can be seen in Figure 3.4, along with the flexible peg to the Euro and the floor and ceiling of the exchange rate band. As Regős (2013), I also use the 6 month change in exchange rates, meaning I subtract the t − 6th data from the one in time period t and compare the change to the t − 6th value. There is a structural break in the time series, as the flexible peg within a fluctuation band was abandoned by the MNB. It was in effect from 1 October 2001, and is succeeded by a free-floating exchange rate regime from 26 February 2008. Frömmel et al. (2011) includes a variable which models the fluctuation band, but it is neither significant, nor affecting the values of other parameters, hence I exclude it from the estimations. They - and Regős (2013) - conclude that it is a consequence of the broad enough band which was implemented not to confront with monetary policy. This statement is weakened by the fact that the MNB had to intervene at the floor in 2003 because the Hungarian Forint was exposed to a speculative attack. Before the analysis to avoid spurious regression, I tested the stationarity of the time series I use with both Augmented Dickey-Fuller and Philips-Perron tests and find that they are either stationary or first order integrated, the Johansen cointegration test shows there is cointegrating relation between the variables in all of the models, so I reject the hypothesis of spurious regressions.

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2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. 240 260 280 300 320 HUF/EUR rates Band margins Central parity

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4. The benchmark model

In this section specify the models I estimate, with an outlook to their strengths and limitations. First of all, I define my time intervals: ’before the recession’ is June 2001 - February 2008, and ’after the recession’ is June 2009 - February 2017, which means respectively 80 and 92 months.

4.1 Estimations

The contribution Taylor (1993) made with giving an exact shape for monetary policy decisions was a huge step towards making central banks’ decisions more transparent. His simple reaction function (equation 4.1) linked the nominal interest rate to the inflation gap and the output gap. The original rule can be written as:

it = α + πt∗+ βπ ·πbt−1+ βy·ybt−1 (4.1) where itis the nominal interest rate in time period t, πt∗ denotes the inflation target,πbt−1 and y_bt−1 denote respectively the inflation gap (the deviation of the actual inflation from

the target) and the output gap. This rule, specified with _bπ = 1.5 and _by = 0.5 described the postwar US monetary policy relatively well. However, Hungary, in opposition to the United States of America is a small, open economy. Multiple papers, including Clarida et al. (1998) and Hidi (2006) state that includnig exchange rates in the monetary policy rule in this case can improve the fit of the rule to the actual policy followed by the central banks. Taylor (2001) however argues this statement, stating that it does not necessarily contribute to the rule. Empirical evidence shows that including changes in exchange rates instead of exchange rates on level does indeed improve the fit of the model (Regős, 2013). As Clarida et al. (1997) and Clarida et al. (1998) state, central banks tend to avoid steep changes in interest rates, so they set interest rates in a way described by equation 4.2:

it= ρ · it−1+ (1 − ρ) · i∗t (4.2)

where the parameter ρ represents the weight of the previous period value of the nominal interest rate (interest rate smoothing), it−1 is the nominal interest rate in the previous

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period and i∗_t is the estimated value of the nominal interest rate in the current period, while et denotes the percentage change of the EUR/HUF exchange rate over the last six

months, compared to the previous value, as in Regős (2013). The benchmark models I use are in a contemporaneous setting, described in equations 4.3 and 4.4.

it= α + π∗t + βπ· ˆπt+ βy · ˆyt+ δ · et (4.3)

it= ρ · it−1+ (1 − ρ) · [α + πt∗+ βπ ·πbt+ βy·ybt+ δ · et] (4.4) I estimate the ’basic’ or contemporaneous rules with the day-to-day rate as dependent variable, my own output gap estimate, and the deviation of the core inflation from the sovereign target as inflation gap. To estimate the model I use the Generalized Method of Moments, using second and third lags of the endogenous variables as instruments. Instead of the usual 5% level, I investigate the significance of the variables on 1% (or higher) levels. I show the results in Table 4.1.

Table 4.1: Contemporaneous Taylor rules

Without smoothing With smoothing

Before After Before After

Constant 7.983∗∗∗ 3.750∗∗∗ 7.467∗∗∗ 3.691∗∗∗ (0.067) (0.235) (1.108) (0.239) Output gap -0.929∗∗∗ -0.029 -0.659∗∗∗ 0.187 (0.032) (0.109) (0.194) (0.112) Inflation 0.651∗∗∗ 1.301∗∗∗ 1.066∗∗ 1.253∗∗∗ (0.048) (0.079) (0.410) (0.055) Exchange rate 0.067∗∗∗ 0.018 0.507∗∗∗ 0.054∗∗ (0.009) (0.013) (0.120) (0.019) Smoothing 0.876∗∗∗ 0.750∗∗∗ (0.019) (0.058) R2 _0.75 _0.82 _0.94 _0.98

Standard errors in parentheses

∗ _{p < 0.05,}∗∗ _{p < 0.01,}∗∗∗ _{p < 0.001}

Most of the variables are significant on the observed levels, but output gap seems to lose significance in the ’after the recession’ period both in the smoothed and non-smoothed

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model. A possible explanation is given by Smets (1998) who states that output gap un-certainty can reduce the response to the current estimated output gap relative to current inflation in a restricted instrument rule. According to Regős (2013), the coefficient of the constant can be interpreted as a natural level of interest rate which would be met, if the output would be on its natural level and inflation were on the target. The models show that there was a higher level of interest rates before the recession, around 7.5-8%, while after the recession it decreased to around 3.7%. The central bankers tend to react harder on inflation after the recession according these models, furthermore both models show that the Taylor principle1 _{holds in the latter period. The smoothing parameter declined,}

which means that the central bank focuses to a lesser extent on avoiding steep changes in the interest rates.

The coefficients of the output gap before the recession are negative and significant, their significance loss after the recession could mean a focus change towards inflation, which would be underpinned by the diminishing significance of the exchange rate in both models. While in the smoothed model the coefficient is still significant - but as in the backward-looking model, smaller than before - on a 1% level, in the model without in-terest rate smoothing it completely loses significance. The positive coefficient translates to, if the exchange rate depreciates, the central bank raises the rates. Possible explan-ations are avoiding the excess volatility of the exchange rate, protecting the importers from extreme price growth and protecting those who have foreign currency loans (Regős, 2013). As those which were denominated in CHF and EUR, are denominated in HUF after 2014, a smaller coefficient after the recession is understandable. Moreover, Hungary has vast amount of exports to the EU (especially Germany), for which the payments are in euros. Hence, an unofficial target can be holding the HUF/EUR exchange rates at a constant, high level in order to improve the current account of the country and to avoid twin deficits.

Figure 4.1 shows the fit of the contemporaneous rules to the actual interest rate. The estimated rule with smoothing has a high correlation coefficient with the actual rates, which is understandable, since the lag of the dependent variable is included in these equations. Nevertheless, the estimates without smoothing show a good fit too, and the models describe the latter period better than the previous.

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2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. 0 2 4 6 8 10 12 % Actual Estimated Smoothed

Figure 4.1: The fit of the contemporaneous rules

4.2 Testing the hysteresis hypothesis

As I mentioned earlier, the significance loss of the coefficients can be explained with multiple reasons, most likely with keeping the current account positive, to avoid twin deficits. Also, another explanation for the significance loss of the coefficients can be what Yellen (2016) states: hysteresis makes policymakers act quickly and aggressively in response to a recession, to reduce the depth and persistence of the downturn. Hence, the coefficient of one variable (here the inflation) claims the significance with its size and importance from the other variables. I am testing this hypothesis, by estimating the monetary policy rules for 2.5 years following the recession. My ’after’ period in this case is June 2009-December 2011, which means 30 months. Although the observed time interval is short, clear evidence for legitimating the hysteresis hypothesis comes from my estimations, which I show in Table 4.2. The previously significant output gap and ex-change rate coefficients are smaller than before the recession, and even lose significance on 1% level. In contrary, coefficients of the inflation become bigger and stay significant on all levels. According to the model with interest rate smoothing, the Taylor principle holds for this shorter period too.

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Table 4.2: Testing the hysteresis hypothesis

Before 2.5 years after Before 2.5 years after

Constant 7.983∗∗∗ 5.459∗∗∗ 7.467∗∗∗ 6.213∗∗∗ (0.067) (0.049) (1.108) (0.447) Output gap -0.929∗∗∗ -0.201∗ -0.659∗∗∗ 0.391 (0.032) (0.080) (0.194) (0.238) Inflation 0.651∗∗∗ 0.714∗∗∗ 1.066∗∗ 1.153∗∗∗ (0.048) (0.076) (0.410) (0.291) Exchange rate 0.067∗∗∗ -0.029∗ 0.507∗∗∗ -0.110 (0.009) (0.014) (0.120) (0.057) Smoothing 0.876∗∗∗ 1.350∗∗∗ (0.019) (0.212)

∗ _{p < 0.05,}∗∗ _{p < 0.01,}∗∗∗ _{p < 0.001}

4.3 Strengths and limitations

Gross Domestic Product is published quarterly by the KSH, hence the MNB calcu-lates output gap on a quarterly basis. But since there are monthly board meetings and monthly interest rate movements are not unusual, most likely if the central bankers follow some kind of Taylor-type simple monetary policy rule, they use monthly data. In the existing literature described in section 2 authors tend to use both approaches. While monthly data provide more observed time periods and more detailed movements in vari-ables, quarterly data uses the exact measurement of GDP. Both approaches have their positive and negative consequences, I choose to estimate the models on monthly data, because as Smets (1998) states, output gap is hard to measure without errors, and this uncertainty can reduce the response to the current estimated output gap relative to cur-rent inflation in a restricted instrument rule.

The benchmark models I use include the core inflation instead of the HICP - since the goal of the MNB is to react on the core inflation, rather than reacting on seasonal fluctuations originated from food or energy prices (Regős, 2013). Using this inflation

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measurement is also not a novelty in the literature, but to avoid identifying false relations between the variables I also use the HICP as inflation measure in the models I present in Section B. A serious limitation could be that inflation forecast is provided by OECD on a yearly basis and to get monthly data I linearly interpolated the forecasts. In reality it is highly unlikely that in a year, inflation forecasts were following a linear pattern.

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5. Other estimated rules

Beside the basic Taylor rule, there are more variants of monetary policy rules. I am also estimating backward-looking rules, which link interest rates to variables from the precious period, and forward-looking rules, which are based on forecasts. Equations 5.1 and 5.2 show the backward- and forward-looking rules, respectively, and equation 5.3 shows the forward-looking rule with interest rate smoothing.

it= α + πt−1∗ + βπ·πbt−1+ βy ·byt−1+ δ · et−1 (5.1) it= α + πt+12∗ + βπ ·πbt+12+ βy · ˆyt+12+ δ · et (5.2) it= ρ · it−1+ (1 − ρ) · [α + πt+12∗ + βπ·πbt+12+ βy· ˆyt+12+ δ · et] (5.3) Concerning the forward-looking rules, I choose to use a 12 month forecast. Although the transmission mechanism of central banks tend to be longer, 1.5-2 years (Regős, 2013), using a rule with one year forecasts is common in the existing literature (e.g.: Clarida et al. (1998), Regős (2013), Abaligeti et al. (2017)). Since it is uncommon in the exist-ing literature to use forecasted exchange rates, I include exchange rate changes in the forward-looking rules from the period the interest rate is set.

I present the estimates of the backward-looking rule, written in equation 5.1, with day-to-day rates as dependent variable, my own output gap estimate and the industrial production as output gap, and the deviation of the core inflation from the sovereign tar-get as inflation gap in Table 5.1. To estimate the model I used the Generalized Method of Moments, using second and third lags of the endogenous variables as instruments. Although I investigate the significance of the variables on 1% (or higher) levels, all of the estimated coefficients are significant. Compared to the benchmark model,

The models show that there was a higher level of interest rates before the recession, around 7.5-8%, while after the recession it decreased to around 3.6%. The decision makers react on the output gap in a way that if the gap is high the interest rate is cut. According to the model, it was more emphasised before the recession than after, and even lost a bit

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of significance. That holds with both output gap estimates, although the coefficients are not the same, the processes can be observed on both variables, hence in the next models I use only my own estimate for the output gap. Inflation gap - here the deviation of core inflation from the target - works in the opposite direction: the bigger the gap is, the more the central bank raises the interest rate. After the recession the Taylor principle is also met - that means, interest rates grow to a higher extent than inflation does. The changes in the exchange rate have also a positive, however small coefficient. This is in line with the estimates of the contemporaneous model, only in case of interest rate smoothing differs the coefficient significantly before the recession.

Table 5.1: Backward looking rules

Before the recession After the recession Own gap Ind. prod. Own gap Ind. prod.

Constant 7.805∗∗∗ 7.663∗∗∗ 3.686∗∗∗ 3.626∗∗∗ (0.062) (0.109) (0.180) (0.222) Output gap -1.024∗∗∗ -0.803∗∗∗ -0.195∗∗ -0.372∗∗ (0.060) (0.102) (0.072) (0.125) Inflation 0.873∗∗∗ 0.949∗∗∗ 1.251∗∗∗ 1.195∗∗∗ (0.061) (0.044) (0.054) (0.064) Exchange rate 0.196∗∗∗ 0.103∗∗∗ 0.053∗∗∗ 0.060∗∗∗ (0.018) (0.013) (0.009) (0.010) R2 0.76 0.66 0.77 0.79

∗_{p < 0.05,} ∗∗ _{p < 0.01,}∗∗∗ _{p < 0.001}

I show the fit of the backward-looking rule with my output gap estimation on Figure 5.1. The Pearson R2 coefficient shows a 76% correlation between the actual and the estimated rule both before and after the recession. Although the models perform reason-ably in both periods, backward-looking rules can not capture sudden interest rate cuts, and there is room for improvement in the fit during the recovery process between June 2009 - June 2012.

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2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. 0 2 4 6 8 10 12 % Actual Estimated

Figure 5.1: The fit of the backward-looking rule using the own output gap estimate

At last, I show the estimates of the forward-looking models in Table 5.2. I estimate these models using the Economic Sentiment Indicator as forward-looking output gap and using the interpolated HICP expectations as inflation forecast. Since exchange rates are usually not forecasted, I use the current period values of the exchange rate change in the model. Equations 5.2 and 5.3 describe the estimated models, I use the GMM with the second and third lags of the endogenous variables as instruments.

The significance of the coefficients is varying, probably because of the different vari-ables I use. Again, coefficients of the constant show, that a shift in the natural level of the interest rates occurred after the crisis, but these models lay the levels slightly higher, to approximately 8-8.5% and 4-5% respectively before and after the recession. The out-put gap is significant in the model without smoothing only, shows the dynamics as in the previous models, though. Inflation measured by the interpolated HICP forecast is significant in both models after the recession, but the Taylor principle only holds in the model with interest rate smoothing.

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Table 5.2: Forward-looking Taylor rules

Constant 8.617∗∗∗ 4.365∗∗∗ 7.919∗∗∗ 5.008∗∗∗ (0.219) (0.050) (0.872) (0.485) Output gap -0.445∗∗∗ -0.256∗∗∗ 0.103 0.315 (0.104) (0.040) (0.478) (0.254) Inflation -0.088 0.872∗∗∗ 0.078 1.386∗∗∗ (0.100) (0.028) (0.198) (0.213) Exchange rate -0.123∗∗∗ -0.050∗∗∗ -0.540 0.172∗∗ (0.019) (0.010) (0.413) (0.065) Smoothing 0.779∗∗∗ 0.936∗∗∗ (0.199) (0.017) R2 0.40 0.88 0.86 0.99

∗ _{p < 0.05,}∗∗ _{p < 0.01,}∗∗∗ _{p < 0.001}

The smoothing parameter increases between the periods, and is at a high level after the recession, which can be explained with the repeated interest rate cuts after 2011, which ought to stimulate the economy. Before the recession if the model includes interest rate smoothing, it claims the significance from other variables, meaning that according to this model the decision makers were adjusting interest rates based on previous values rather than movements in the classic Taylor rule variables. The exchange rate coefficients are inconsistent: in the model without smoothing negative, but with smoothing positive. A possible explanation for that lies in the linearly interpolated inflation forecast I use, because the transmission channel through which the exchange rate reaches the interest rates is affecting domestic and import prices, hence in connection with inflation. Thus, if inflation is not measured perfectly, it can affect the exchange rates’ effect on the interest rate.

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2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. 0 2 4 6 8 10 12 % Actual Estimated Smoothed

Figure 5.2: The fit of the forward-looking rules

I show the fit of the forecast-based models on Figure 5.2. The smoothed equation fits the actual interest rates nearly perfect in both periods. However, the rule without smoothing performs poorly compared to the other estimated equations in the period before the recession - describes the movements in the interest rates after the crisis sur-prisingly good, better than any other estimated model.

Although all of the estimated models show the same main characteristics of the pre-and post-recession Hungarian monetary policy, I would like to test how sensitive they are to using other approaches for the variables. I find that the models are robust to changes in the inflation measures and to changes in the dependent variable. As robustness check, I use the HICP inflation and its deviation from both the sovereign target and the target put down in the Maastricht treaty. I also use the 3 month rate as dependent variable instead of the day-to-day rate. I estimate the benchmark models, the backward- and forward-looking models ad compare them to their respective baseline models, to find that all the models are robust to the above mentioned changes. I provide a more detailed description of the robustness tests in Appendix B.

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6. Comparison to the optimal rule

This section builds on the model discussed in Galí (2008), Chapter 7: Monetary Policy in a Small Open Economy. I estimate optimal simple monetary policy rules for Hungary -both for the period before and after the recession - and compare my estimations to them.1

6.1 Optimal simple rules

Hungary is a small open economy. According to data by the KSH, the trade openness (sum of exports and imports in percentage of the GDP) is between 106% and 158% in the examined period. That means, monetary policy is influenced by the trade partner countries’ characteristics. I do not describe the whole model in detail, instead I present the changes I make to it, to better match the model to the case of Hungary. In the DSGE framework I only change the monetary policy rule in the following way:

it= rnt + φπ· πH,t+ φy· ˜yt (6.1)

it= ρ · it−1+ (1 − ρ) · (rtn+ φπ· πH,t+ φy· ˜yt+ φe· et) (6.2)

where equation 6.1 is the one described by Galí (2008), and equation 6.2 is the interest rate rule I use, with φe as the feedback coefficient on the exchange rate changes, and et

as the percentage change of the EUR/HUF exchange rate over the last six months, as described in section 4.1.

In the derivation of the optimal rule, I use the wealth loss function described in details in Galí & Monacelli (2005). Neither the variation in the exchange rates nor the smoothing parameter of the central bank appears in the consumers’ wealth loss function, which I show in equation 6.3.

1

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W = −(1 − α) 2 · ∞ X t=0 βt·hε λ · π 2 H,t+ (1 + φ) · ˜y 2 t i (6.3)

As for the calibration of the model, I rely again on Galí & Monacelli (2005), and introduce an employment subsidy which offsets the combined effects of market power and the terms of trade distortions. That means I set σ = η = γ = 1. I show the exact parametrization with the description of the parameters in Appendix A. For the other parameters, I col-lected data from Hungary for both periods. I find that the price-setting of the firms, the Frisch elasticity and the elasticity of substitution does not change significantly between the two periods. The firms tend to set prices yearly, the labour supply elasticity is 31-33% in the two periods, which implies φ = 3. The degree of openness is measured by the import to GDP ratio, as in Galí & Monacelli (2005). I assume a time discount factor parameter βbef ore = 0.96 and βaf ter = 0.99, so the steady-state real interest rate translates

to ρbef ore = 4% and ρaf ter = 1%. In case of variables considering the world, I collected

data for the EU, since it is the biggest trade partner of Hungary as an entity. I estimate the autocorrelation coefficients on log of Hungarian labour productivity and EU GDP, using yearly, Hodrick-Prescott filtered data. For initial values, I consider parameters of the original Taylor rule: φπ = 1.5, φy = 0.5. The exchange rate fluctuation enters the

interest rate rule I use, but does not enter the original rule, so I set the initial value of the feedback coefficient to zero (φe = 0). I show the feedback coefficients of the optimal

simple rule in Table 6.1.

Table 6.1: Optimal simple rule feedback coefficients

Before After

Output gap -0.480 -0.329

Inflation 1.417 1.515

Exchange rate -0.061 -0.084

According to the small open economy New Keynesian model, calibrated with para-meters for Hungary in the corresponding periods, monetary policy in an optimal case should react stronger on every variable after the crisis. That can be explained with the growth in country openness (αbef ore= 0.62 and αaf ter = 0.72).

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6.2 Estimated rules and optimal rules

The optimal rule I described is in a contemporaneous setting, hence when I am com-paring it to the estimated rules, I use the contemporaneous estimations, with the day-to-day rates as dependent variable, my own output gap estimation and the core inflation as inflation measure. I compare the estimated and the optimal rule (with interest rate smoothing) in Table 6.2. The dynamics of reacting on all coefficients in my estimations match the dynamics in the optimal rule. However, since the output gap coefficient is not significant in the latter period, I can not say, that policymakers followed the dynamics by the optimal rule.

Table 6.2: Comparing the estimated rule to the optimal one

Before After

Optimal Estimated Optimal Estimated

Output gap -0.480 -0.659∗∗∗ -0.329 0.187

Inflation 1.417 1.066∗∗ 1.515 1.253∗∗∗

Exchange rate -0.061 0.507∗∗∗ -0.084 0.054∗∗

Looking at the coefficients, there are deviations from the optimal feedback coefficients by all the variables. In case of the inflation, I conclude that the estimated coefficients are somewhat smaller than the optimal coefficients, meaning that central bankers should have been more strict on inflation. On the other hand, the estimated models show that policymakers reacted stricter on the output gap than they should have before the re-cession. The coefficient of the output gap becomes insignificant in the period after the recession, and has a wrong sign, too. The coefficients of the exchange rate also have the wrong sign: in the optimal rule, they are negative, in the estimated one they are positive. The deviation in the first period is quite big: 0.507 compared to −0.061, which shrinks in time, since the optimal rule suggests a somewhat stronger, negative reaction on the variation in the exchange rates, while the estimation shows that the coefficient tends to be smaller than before, but still not negative.

All in all, according to the estimated and optimal rule, Hungarian monetary policy was not welfare maximizing before the recession: the reaction on inflation is too soft, while it is too strong on the output gap, and exchange rate coefficients have wrong signs.

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It is still not welfare maximizing after the crisis, but it is clear that policymakers made improvements in minimizing welfare loss towards achieving the optimal monetary policy.

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7. Conclusion

In this thesis I model the Hungarian monetary reaction function, to answering the following question: How did Hungarian monetary policy change due to the recession in 2008? I do so by estimating multiple Taylor-type equations broadened with changes in the exchange rates with the Generalized Method of Moments (GMM) estimator on data provided by the MNB and Eurostat between June 2001 - February 2017. I split the dataset into two parts, and define two time intervals: ’before the recession’ is June 2001 - February 2008, and ’after the recession’ is June 2009 - February 2017, which means respectively 80 and 92 months. I intentionally left out the months of the recession, since it would distort the estimations.

The results show that decision makers at the central bank put more emphasis on the inflation gap after the recession than before, and the Taylor principle, which states that if inflation is growing with one percentage point the central bank should raise interest rates with more than one percentage point holds in the latter period. In contrary, reactions on output gap and changes in the exchange rate are less important after the recession when adjusting the rates. While according to the models the central bank cuts rates when the economy performs better (output is higher than its natural level), exchange rate changes have contradictory coefficients. A possible explanation for this phenomenon lies in the complexity of monetary policy transition mechanisms. Exchange rates are in connection with domestic and foreign price levels, so inflation can claim the significance of them, and even influence the coefficients. The estimates also show that the natural level of the interest rate was higher, around 7-8% before and lower, around 4-5% after the crisis in 2008. In the benchmark model only the inflation is in the focus of central bankers when adjusting rates after the recession. That is a consequence of hysteresis, as Yellen (2016) states, hence it makes policymakers react stronger on the biggest problem - here growing inflation - which claims the significance from other variables.I also check the sensitivity of the models to changes in inflation measures (core inflation and HICP, with sovereign and Maastricht targets) and changes in dependent variables (day-to-day and three month rates), and can say that my results are robust to using different measures of inflation and

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interest rates.

The conclusion Jakab et al. (2010) draws, namely that a simple inflation targeting rule with a high enough feedback coefficient on domestic inflation can approximate the welfare-maximizing monetary policy relatively well is met according to the models after the crisis, since the coefficients are above 1, the Taylor principle holds. Thus, I can say, Hungarian monetary policy is welfare-maximizing in the recent years. However, I estimated an optimal simple rule for Hungary, using a New Keynesian small open economy framework described by Galí (2008) and found that the policymakers deviate from the optimal policy. The deviation is higher in the period before the recession and a convergence towards welfare maximizing shows up in the period after the crisis, but the difference is still notable between the optimal and the empirically estimated coefficients.

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A. Parameters for section 6

Table A.1: Parameters used in Section 6

Parameter Explanation Value before Value after α Degree of openness 0.62 0.72 β Discount factor 0.96 0.99 γ

Substitutability between goods

1 1

produced in different foreign countries ε

Elasticity of substitution between goods

6 6

produced within a country

η

Substitutability between

1 1

domestic and foreign goods

from the viewpoint of the domestic consumer

θ Calvo parameter 0.75 0.75 ρa Autocorrelation of labour productivity 0.87 0.51

ρi Autocorrelation of interest rates 0.99 0.99

ρy Autocorrelation of foreign output 0.87 0.75

σ Risk aversion 1 1

σa Labour productivity innovation 0.018 0.037

σy∗ Foreign output innovation 0.02 0.012 φ Inverse Frisch elasticity 3 3 φe Initial feedback coefficient on exchange rate 0 0

φπ Initial feedback coefficient on inflation 0.5 0.5

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B. Other robustness tests

Beside the specification discussed in Section 4, I also test whether the models are robust to using different variable measurements. In this section I show the reaction of the models to the change the inflation measurements and the dependent variable.

B.1 Robustness to different inflation measures

First, I test the effect of a change of inflation measures in the ’basic’ rules. Estimates in Table B.1 are the results of the GMM estimation.

Table B.1: Contemporaneous rules with different inflation measures

Core infl. HICP Core infl. HICP

Maastricht target Sovereign target Maastricht target Sovereign target

Before After Before After Before After Before After

Constant 7.614∗∗∗ 3.750∗∗∗ 8.040∗∗∗ 3.985∗∗∗ 8.174∗∗∗ 3.393∗∗∗ 6.792∗∗∗ 3.387∗∗∗ (0.061) (0.235) (0.208) (0.082) (0.329) (0.255) (0.392) (0.491) Output gap -0.729∗∗∗ -0.029 -1.120∗∗∗ -0.051 -2.076∗∗∗ 0.161 -1.056∗∗∗ -0.161 (0.046) (0.109) (0.072) (0.032) (0.319) (0.111) (0.089) (0.157) Inflation 0.568∗∗∗ 1.301∗∗∗ 0.329∗∗∗ 0.833∗∗∗ 0.725∗∗∗ 1.199∗∗∗ 0.795∗∗∗ 0.883∗∗∗ (0.030) (0.079) (0.075) (0.027) (0.154) (0.063) (0.222) (0.044) Ex. rate 0.059∗∗∗ 0.018 0.023 0.012 0.237∗ 0.075∗∗ 0.444∗∗∗ 0.363 (0.007) (0.013) (0.016) (0.007) (0.110) (0.026) (0.119) (0.233) Smoothing 1.126∗∗∗ 0.793∗∗∗ 0.860∗∗∗ 0.816∗∗∗ (0.031) (0.057) (0.022) (0.089) R2 _0.76 _0.82 _0.63 _0.88 _0.92 _0.99 _0.94 _0.99

∗ _{p < 0.05,}∗∗ _{p < 0.01,}∗∗∗ _{p < 0.001}

The coefficients of the constant are significant in all models and further strengthen my findings of the new, lower natural level of interest rates after the recession. If I

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compare the results to the ones presented in Table 4.1, it is safe to say that the models are robust to changes in inflation measures. Similarly to the backward-looking rules, reaction on inflation is stronger after the recession, but the Taylor principle holds only if inflation is measured by the core inflation. The MNB seems to be less concerned with changes in the exchange rate according to these models, which can be explained with the transmission mechanisms through which the exchange rates affect the interest rates. While the core inflation is somewhat filtered from the exchange rates, the HICP is affected by changes in them, especially in a small open economy, where imported goods appear in the average consumer basket. Thus, if HICP is included in the models, exchange rates are less important when setting the rates. I show the fit of these rules on Figures B.1 and B.2. 2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. 0 5 10 % Actual Estimated Smoothed

Figure B.1: The fit of the contemporaneous rules using the deviation of the core inflation from the Maastricht target

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2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. 0 5 10 % Actual Estimated Smoothed

Figure B.2: The fit of the contemporaneous rules using the deviation of the HICP from the sovereign target

I also investigate the sensitivity to changing the dependent variable of the contem-poraneous rule in Table B.2.

Table B.2: Contemporaneous Taylor rules with 3 month rates as dependent variables

Constant 8.121∗∗∗ 4.619∗∗∗ 6.925∗∗∗ 4.253∗∗∗ (0.078) (0.270) (0.303) (0.463) Output gap -0.827∗∗∗ 0.156 -0.076 -0.007 (0.044) (0.109) (0.315) (0.199) Inflation 0.696∗∗∗ 1.604∗∗∗ 1.450∗∗∗ 1.660∗∗∗ (0.065) (0.094) (0.307) (0.093) Exchange rate 0.091∗∗∗ 0.031∗ 0.685∗∗∗ 0.227∗∗ (0.011) (0.016) (0.194) (0.083) Smoothing 0.892∗∗∗ 0.560 (0.031) (0.369) R2 _0.74 _0.81 _0.95 _0.98

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I compare the results of the contemporaneous rule to the results in Table 4.1. It is not excessively sensitive to the change in the dependent variable, but there are few things that I would like to elaborate on. Whilst in the forecast-based model on the day-to-day rates, output gap has significant coefficients in both the smoothed and the non-smoothed model before the recession, using the three month rate as dependent variable they become insignificant in the smoothed model, though I use my own estimates as output gap in both cases. Inflation shows the same patterns, and the Taylor principle holds after the recession in both models. The fit of this rule is seen on Figure B.3.

Figure B.3: The fit of the contemporaneous rules using the three month rate as dependent variable

Contrariwise to the output gap, exchange rate changes become significant when set-ting the rates in the model with three month rates. The tendency is, however, the same: after the recession it became less important to react on changes in the exchange rate. The smoothing parameter is also not significant after the recession, while it has a decreasing, but significant coefficient in the model with day-to-day rates. By looking at the time series in Figure 3.1, it can be explained either with the fact that three month rates are more volatile than day-to-day rates, or I can say that the imputation method I use is not perfect and causes steeper changes in the rates than the movement of the actual rates.

Next, in Table B.3 I test whether the backward-looking model is sensitive to the change of inflation measures. I use the deviation of the core inflation from the target defined in the Maastricht treaty, the deviation of the HICP from the Hungarian target, and last the deviation of the HICP from the Maastricht target. Using the Maastricht criterion as inflation target is not a novelty in the literature, Frömmel et al. (2011) for example states

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that the sovereign targets are just transitional and the ’real’ target is the convergence criterion to the EMU, specified in the Maastricht treaty. Using the Maastricht criterion as target only means change in the latter period, because since August 2005 the MNB has a 3% inflation target, which is equal to the convergence criterion.

Table B.3: Backward looking rules with different inflation measures

Core inflation HICP

Sovereign target Maastricht target Sovereign target Maastricht target

Before After Before After Before After Before After

Constant 7.805∗∗∗ 3.686∗∗∗ 7.452∗∗∗ 3.686∗∗∗ 7.778∗∗∗ 3.932∗∗∗ 6.523∗∗∗ 3.932∗∗∗ (0.062) (0.180) (0.071) (0.180) (0.173) (0.063) (0.169) (0.063) Output gap -1.024∗∗∗ -0.195∗∗ -0.786∗∗∗ -0.195∗∗ -1.366∗∗∗ -0.194∗∗∗ -1.294∗∗∗ -0.194∗∗∗ (0.060) (0.072) (0.058) (0.072) (0.087) (0.032) (0.078) (0.032) Inflation 0.873∗∗∗ 1.251∗∗∗ 0.653∗∗∗ 1.251∗∗∗ 0.472∗∗∗ 0.830∗∗∗ 0.823∗∗∗ 0.830∗∗∗ (0.061) (0.054) (0.035) (0.054) (0.096) (0.023) (0.107) (0.023) Ex. rate 0.196∗∗∗ 0.053∗∗∗ 0.167∗∗∗ 0.053∗∗∗ 0.130∗∗∗ 0.053∗∗∗ 0.263∗∗∗ 0.053∗∗∗ (0.018) (0.009) (0.018) (0.009) (0.035) (0.008) (0.039) (0.008) R2 0.76 0.77 0.75 0.79 0.62 0.89 0.73 0.89

∗ _{p < 0.05,}∗∗ _{p < 0.01,}∗∗∗ _{p < 0.001}

Again, I use GMM, with second and third lags of endogenous variables as instruments. The results in Table B.3 show that the backward-looking model is robust to changing the inflation measures. Clearly, the natural level of the interest rate changed in the aftermath of the recession, central bankers became less focused on output gap and exchange rates, while putting more emphasis on the inflation gap, regardless which measure is used.

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2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. 0 5 10 % Actual

Core infl. Maastricht target HICP sovereign target HICP Maastricht target

Figure B.4: The fit of the backward-looking rules using different inflation measures

The change in focusing on inflation is more pronounced when the sovereign target is used in the model, and if HICP is the measure of the current inflation instead of the core inflation, the Taylor principle does not hold after the recession, since the coefficients are below 1. I show the fit of the models in Figure B.4.

Finally, I also test whether the forward-looking model is robust to changing the sov-ereign inflation target for the one defined in the Maastricht treaty. The results are in Table B.4, and I compare them to the ones in Table 5.2.

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Table B.4: Forward-looking Taylor rules with the deviation from the Maastricht criterion as inflation

Constant 7.898∗∗∗ 4.365∗∗∗ 7.449∗∗∗ 5.008∗∗∗ (0.303) (0.050) (0.733) (0.485) Output gap -0.524∗∗∗ -0.256∗∗∗ -0.179 0.315 (0.073) (0.040) (0.259) (0.254) Inflation 0.257 0.872∗∗∗ 0.283 1.386∗∗∗ (0.149) (0.028) (0.264) (0.213) Exchange rate -0.113∗∗∗ -0.050∗∗∗ -0.279∗∗ 0.172∗∗ (0.018) (0.015) (0.108) (0.065) Smoothing 0.679∗∗∗ 0.936∗∗∗ (0.161) (0.017) R2 _0.45 _0.86 _0.89 _0.99

∗ _{p < 0.05,}∗∗ _{p < 0.01,}∗∗∗ _{p < 0.001}

As before, both the smoothed and the non-smoothed models are insensitive to the change in inflation targets. Since the sovereign target is equal to the Maastricht target after August 2005, changes can only occur in the period before the recession. In the smoothed model, the smoothing parameter is smaller than in the original model, and changes in the exchange rate become significant and negative, whilst post-recession it has a significant positive coefficient. I show the fit of the models in Figure B.5.

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Figure B.5: The fit of the forecast-based rules using the deviation of the inflation expect-ations from the Maastricht target

B.2 Robustness to different dependent variables

Another sensitivity test I make is to change the dependent variable in all of the mod-els. While I choose day-to-day money market rates in the first place because of the missing values in the three month money market rates, after the imputation the time series has zero missing values. Hence I estimate all the models with the three month rates as dependent variable. The results of the backward-looking rules with both my output gap estimate and the gap calculated from the industrial production are in Table B.5. Comparing the results to the ones in Table 5.1, I can say my results are rather robust. The shift in the natural level of the interest rates is obvious, but according to these models, the change in the three month rates was not as steep as in the day-to-day rates, since the after-recession level is around 5%, instead of the 3.5-4% in the previous model. The output gap is less in the focus of the central bankers when setting the rates, it even loses significance after the recession. The exchange rate, which shows roughly the same patterns as in the main backward-looking models, is becoming less important in the monetary policy. Reaction on inflation is on a high level even before the recession, but after it, the Taylor principle holds - exactly as in all the other backward-looking models. I show the fit of the models in Figure B.6.

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2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. 0 5 10 % Actual Own gap estimates Industrial production

Figure B.6: The fit of the backward-looking rules using the three month rate as dependent variable

Table B.5: Backward looking rules with 3 month rates as dependent variables

Before the recession After the recession Own gap Ind. prod. Own gap Ind. prod.

Constant 7.976∗∗∗ 7.854∗∗∗ 4.486∗∗∗ 4.492∗∗∗ (0.052) (0.089) (0.320) (0.306) Output gap -0.934∗∗∗ -0.729∗∗∗ -0.063 -0.194 (0.068) (0.080) (0.085) (0.162) Inflation 0.909∗∗∗ 0.968∗∗∗ 1.556∗∗∗ 1.501∗∗∗ (0.053) (0.051) (0.090) (0.083) Exchange rate 0.215∗∗∗ 0.131∗∗∗ 0.081∗∗∗ 0.086∗∗∗ (0.020) (0.015) (0.010) (0.012) R2 0.74 0.73 0.78 0.78

∗_{p < 0.05,} ∗∗ _{p < 0.01,}∗∗∗ _{p < 0.001}

Finally, I test whether the forward-looking rules are robust to changing the depend-ent variable. Comparing Tables 5.2 and B.6, I can safely say that the forecast-based estimated rules are insensitive to the changes in dependent variables. I would like to mention two notable differences: first, this model further strengthens my findings that

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the natural level of the three month rate is higher after the recession than the natural level of the day-to-day rates. Second, the Taylor principle holds in both the smoothed and non-smoothed model after the recession when using the three month rates, whilst it does not hold in the non-smoothed model which has the day-to-day rate as dependent variable. I show the fit of these models in Figure B.7.

Table B.6: Forward-looking Taylor rules with 3 month rates as dependent variables

Constant 8.696∗∗∗ 5.339∗∗∗ 8.038∗∗∗ 1.735 (0.185) (0.109) (0.660) (2.080) Output gap -0.299∗∗ -0.202∗∗ 0.274 0.703 (0.101) (0.078) (0.385) (0.474) Inflation -0.028 1.090∗∗∗ 0.100 1.383∗∗∗ (0.112) (0.042) (0.209) (0.206) Exchange rate -0.104∗∗∗ -0.039∗ -0.452 1.359 (0.017) (0.016) (0.336) (0.991) Smoothing 0.765∗∗∗ 0.964∗∗∗ (0.163) (0.018) R2 0.32 0.87 0.88 0.98

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Figure B.7: The fit of the forecast-based rules using the three month rate as dependent variable

C. Figures

2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. 0 2 4 6 8 10 12 14 % DTD rates 3 month rates

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2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. −2 0 2 4 6 8 10 % Core inflation HICP HICP forecast

Figure C.2: Core inflation, HICP and HICP forecast rates

2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. −4 −2 0 2 % Own estimation Industrial production

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2001.06. 2003.09. 2005.12. 2008.03. 2010.06. 2012.09. 2014.12. 2017.02. 240 260 280 300 320 HUF/EUR rates Band margins Central parity

Hungarian monetary policy before and after the recession

University of Amsterdam

Faculty of Economics and Business