Estimating a hybrid New Keynesian Phillips curve for Sweden: An instrumental variables approach

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Estimating a hybrid New Keynesian Phillips curve for Sweden: An instrumental variables approach

By Alexander Czarnota

Department of Economics Uppsala university

Master’s thesis

Supervisor: Erik Öberg

Spring term, 2020

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Abstract

Previous estimates suggest that there has been a flattening of the Swedish Phillips curve after the

global financial crisis of 2008. This apparent flattening is a global phenomenon that has led many

economists to search for an explanation. Recent studies suggest that part of the apparent flattening

can be explained by failure to overcome the endogeneity problem of the Phillips curve that arise

from measurement error and cost-push shocks. In this study I investigate this previously unexplored

potential explanation for the Swedish data by estimating a hybrid New Keynesian Phillips curve for

Sweden using the instrumental variables approach of Barnichon and Mesters (2020). The approach

uses a sequence of lagged monetary policy shocks as instruments and relies on weak instrument

robust test statistic for inference. The point estimates vary substantially with changes in the number

of lagged instruments and the weak instrument robust confidence intervals are not significant for

any number of lags. This indicates that the weak instrument problem is too severe for the Swedish

data to provide a practical solution to the puzzle of the Swedish Phillips curve. The conclusion from

this study is therefore that is not possible to estimate an unbiased hybrid New Keynesian Phillips

curve for Sweden using aggregate time series data.

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Table of contents

1. Introduction 1

2. Literature review 5

2.1 The endogeneity problem of the Phillips curve and its potential solutions 5

2.2 The Swedish Phillips curve 8

3. Theory 10

3.1 The New Keynesian framework in a small open economy 10 3.2 The New Keynesian IS equation for a small open economy 11 3.3 The New Keynesian Phillips curve for a small open economy 11

4. Data 13

4.1 Monetary policy shocks 13

4.2 Construction of quarterly shocks 18

4.2 Output gap, inflation and expected inflation 20

5. Method 22

5.1 Instrumental variables regression 23

5.2 Instrument validity 24

5.3 Weak instrument robust inference 26

5.4 Almon-restriction 28

6. Results 30

7. Robustness analysis 32

8. Discussion 36

9. Conclusion 38

References 40

Appendix 45

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1. Introduction

The Phillips curve is a structural equation relating measures of economic slack to inflation.

The basic idea of the Phillips curve is that when the economic activity is above (below) it’s natural level, there will be an upward (downward) pressure on wages, which in turn leads to an upward (downward) pressure on prices. It was originally estimated by Phillips (1958), who showed a negative relationship between unemployment and wage growth in the United

Kingdom for the period 1861-1957. Since then, the Phillips curve has been a central part of macroeconomic theory and it is also part of the basis on which modern central banks set monetary policy.

Recent estimates suggest that there has been a flattening of the Phillips curve globally, i.e., that the relationship between economic slack and inflation has become weaker (e.g., IMF, 2013; Blanchard, Cerutti and Summers, 2015). Some studies even suggest that inflation can now be approximated and forecasted by a statistical process unrelated to economic slack (e.g., Stock and Watson, 2007). Attempting to explain this phenomenon is an ongoing research question and no conclusion has yet been reached, neither on the cause nor on the size of the slope coefficient. McLeay and Tenreyro (2019) show that empirical estimates of a flatter Phillips curve can be explained by the endogeneity problem which arises from cost-push shocks and measurement error in the independent variables and that a steeper slope appears for U.S. data if these problems are controlled for.

To illustrate the endogeneity problem, consider the modern and improved specification of the Phillips curve called the “hybrid New Keynesian Phillips curve” (e.g. Galí and Gertler, 1999), which relates inflation to expected inflation, one-period lagged inflation, a measure of

economic slack such as the output gap (i.e., the difference between output and the natural

flexible-price level of output), and supply factors. Because output gap and expected inflation

are unobserved and thus have to be estimated, they are subject to measurement error. Also,

the economy is subject to (possibly) autocorrelated cost-push shocks, which affect inflation

and the output gap. For example, an unexpected increase in oil price leads to an increase in

inflation and a decrease in output gap due to increased input costs and an increase in output

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for oil producers. Unless these cost-push shocks are controlled for, estimates of the hybrid New Keynesian Phillips curve will suffer from omitted variable bias (OVB). This in turn could explain part of the apparent flattening of the Phillips curve globally if the severity of the endogeneity problem has changed over time.

Data presented by the Swedish central bank (the Riksbank) show that the relationship between economic activity and wage growth in Sweden appears to have weakened since 2011,

indicating a flattening of the Phillips curve. Inflation, however, has increased to the two percent target (Riksbank, 2018). This seemingly contradicting result – that the relationship between economic activity and wage growth have weakened but inflation has increased – indicate that there are cost-push shocks in the Swedish data.

In this study I attempt to estimate an unbiased hybrid New Keynesian Phillips curve for Sweden. This is a crucial first step in order to be able to explain the puzzle of the Swedish Phillips curve. So far, recent studies of the Swedish Phillips curve (e.g., Jonsson and

Theobald, 2019) have focused on trying to explain the apparent flattening without addressing the endogeneity problem. But without unbiased estimates of the coefficient, such studies are likely to draw the wrong conclusion. It is possible that the apparent flattening of the Swedish Phillips curve can, at least partially, be explained by the endogeneity problem.

To estimate the hybrid New Keynesian Phillips curve for Sweden I use the instrumental variables (IV) approach of Barnichon and Mesters (2020). Their approach, developed using U.S. data, uses monetary policy shocks as instruments. In the New Keynesian framework, monetary policy shocks affect output and thus also inflation. Monetary policy shocks are also assumed to be uncorrelated with supply factors and hence also uncorrelated with the cost-push shocks. This makes monetary policy shocks both relevant and exogenous instruments,

meaning that they can be used to purge the data of measurement error and cost-push shocks in an IV regression.

Because monetary policy affects macroeconomic variables several quarters ahead, Barnichon

and Mesters (2020) use a sequence of lagged monetary policy shocks as instruments to

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capture the full effect of the shocks on the endogenous variables. Monetary policy shocks are assumed to have a low correlation with the endogenous variables, especially for the more recent period during which the variation as well as the variance contribution of monetary policy shocks on output and inflation has fallen. These two facts cause two problems: many instruments and weak instruments, both of which lead to imprecise and potentially biased estimates. To solve the many instruments problem Barnichon and Mesters exploit the fact that the impulse responses of monetary policy shocks on the variables in the hybrid New

Keynesian Phillips curve are thought to be well approximated by quadratic polynomial functions, which makes it possible to reparametrize the coefficients of the instruments as quadratic polynomial functions. This in turn reduces the number of instruments to three, making the model just-identified (i.e., the number of instruments equals the number of endogenous regressors). To ward against weak instruments, they rely on the Anderson-Rubin (AR) (Anderson and Rubin, 1949) statistic for inference. The AR confidence intervals cover the true parameter values in 95 percent of the samples regardless of instrument strength. And in the just-identified setting with weak instruments, Moreria (2009) shows that the AR

statistic is the uniformly most accurate unbiased test, meaning that is has the highest power of any other test. Also, when the instruments are strong, the AR test does not sacrifice power compared to the conventional t-test (see Andrews, Stock and Sun, 2019).

The method developed by Barnichon and Mesters (2020) has a theoretical appeal because the inference is valid regardless of instrument strength as long as the instruments are exogenous.

Its empirical appeal, however, is partly determined by how well it performs when estimated on other data sets as well as on other structural equations with similar specifications as the hybrid New Keynesian Phillips curve.

In this study I use high-frequency identified (HFI) monetary policy surprises (e.g. Kuttner, 2001) as proxies for monetary policy shocks. This method of estimating monetary policy shocks is applicable to Swedish data from 1998:4. During this period monetary policy in Sweden has been set systematically, which has resulted in less exogenous variation in

monetary policy shocks as well as a reduced variance contribution of monetary policy shocks on output and inflation (see Ramey, 2016). The variation of monetary policy shocks in

Sweden for the period 1998:4-2019:4 is lower than the variation of monetary policy shocks in

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the United States during the period estimated by Barnichon and Mesters (2020). It is also possible that the variance contribution is lower in Sweden, which means that the effect of a monetary policy shock of the same size is lower in Sweden as compared to the U.S. This in turn worsens the weak instrument problem which increases the width of the AR confidence intervals. Because the method of Barnichon and Mesters (2020) has not been applied to any other country apart from the U.S., it is unclear whether it can be used to solve the Phillips curve puzzle in a country like Sweden which has low variation and variance contribution of monetary policy shocks.

The relevance of this study, I argue, is two-fold. First, attempting to estimate unbiased

coefficients of the Phillips curve is of interest for the Riksbank and central banks in general as the Phillips is part of the basis on which monetary policy is set, which in turn has

consequences for the entire economy. Second, evaluating the external validity of a method and/or results is an important part of research. The purpose of this study is to fill both of these gaps.

In the main specification I estimate the hybrid New Keynesian Phillips curve using the IV approach of Barnichon and Mesters (2020) with monetary policy shocks as instruments.

Because of the short relatively data sample, I do not divide the sample in order to investigate a potential flattening of the slope, I only focus on the first step of obtaining unbiased estimates.

The results show that the point estimates vary substantially with the number of lagged

monetary policy shocks used as instruments. The weak instrument robust confidence intervals are not significant for any coefficient, regardless of instrument lag length. For comparison I also estimate the hybrid New Keynesian Phillips curve using OLS and the traditional method (described in section 2.1) of using lagged macroeconomic variables as instruments. The point estimates vary between these two methods, which indicate that there is endogeneity in the Swedish aggregate time series data.

The remainder of this study is organized as follows. Section 2 provides a literature review of

the estimation problem of the Phillips curve and the possible solutions as well as a review of

recent estimates of the Swedish Phillips curve. Section 3 describes the New Keynesian

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framework, the New Keynesian IS equation, and hybrid New Keynesian Phillips curve.

Section 4 describes the estimates I use as proxies for Swedish monetary policy shocks as well as the data on inflation, output gap, and expected inflation. Section 5 presents the general instrumental variables regression method as well as the weak instrument robust method of Barnichon and Mesters (2020). The results are presented in Section 6 and a robustness

analysis is conducted in Section 7. The results are discussed in Section 8. Section 9 concludes.

2. Literature review

In this section I expand the discussion about the problems with estimating the Phillips curve and the potential solutions. I also discuss previously published estimates of the Swedish Phillips curve and how they relate to my study.

2.1 The endogeneity problem of the Phillips curve and its potential solutions

McLeay and Tenreyro (2019) summarize the problem with identifying an empirical Phillips curve as follows. “[…] the identification challenge arises from the presence of cost-push shocks to the Phillips curve and the partial accommodation of these by monetary

policymakers. The size of the simultaneity bias is magnified because monetary policy seeks to offset any demand shocks that, in practice, might otherwise help identify the curve.” (p. 22).

They present three main methods that can be used to isolate the demand-driven variation in inflation, which then can be used to recover a structural Phillips curve from the data: (i) Control for supply shocks, (ii) estimate the coefficients using regional data, and (iii) estimate the coefficients using an IV regression with instruments that are uncorrelated with the cost- push shocks.

An example of an attempt to control for supply shocks is made by Gordon (2013), who

includes control variables for food and energy price inflation, relative import price inflation,

changes in trend labor productivity, and dummies reflecting the start and end of the Nixon

price controls in the 1970s when estimating a U.S. Phillips curve. His estimates suggest a

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flattening of the Phillips curve, estimated using the unemployment gap as the forcing variable, from -0.50 to -0.31 when he extends his sample from 1962-1996 to 1962-2013. As discussed by McLeay and Tenreyro (2019), however, this estimated flattening could be due to a

decrease in the relationship between economic activity and inflation or the fact that there may be more supply shocks than successfully controlled for and that the importance of these shocks may vary over time. This is a general problem when attempting to control for

confounding variables which makes methods that rely on exogenous variation more reliable.

The second alternative suggested by McLeay and Tenreyro (2019) of estimating the Phillips curve at a regional level relies on the assumption that monetary policy does not respond to regional demand shocks. An increase in regional demand will increase regional economic activity, which will lead to an increase in regional inflation. Without being offset by monetary policy, the regional demand shocks can be used to estimate regional Phillips curves. The national Phillips curve is in turn assumed to be made up of the sum of the regional Phillips curves. Including time fixed effects to control for aggregate cost-push shocks, McLeay and Tenreyro (2019) find a steeper Phillips curve when they estimate it using aggregated regional data compared to OLS estimates on national U.S. data during the period 1990-2017.

It is unclear whether there is enough regional variation to estimate regional Phillips curves for Sweden, which has less autonomous regions than the U.S. or a monetary union such as the Euro area. There is also a problem of obtaining regional data on the variables of the hybrid New Keynesian Phillips curve. Expected inflation, for example, is to the best of my

knowledge, not available at a regional level in Sweden. Because of these two problems with estimating regional Phillips curve for Sweden, I employ the third suggested strategy of using an IV regression instead.

In order to estimate the Phillips curve using an IV regression it is necessary to find

instruments that are correlated with the dependent variables and uncorrelated with cost-push

shocks, i.e. instrument that are relevant and exogenous in IV terms. Traditionally, lagged

macroeconomic variables have been used as instruments to estimate the Phillips curve (e.g.,

Galí and Gertler, 1999). Lagged variables are thought to be correlated with the endogenous

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variables but uncorrelated with current period cost-push shocks and measurement error. As shown by Mavroeidis, Plagborg-Møller and Stock (2014), however, estimates using this approach have displayed both high sampling uncertainty as well as high specification

uncertainty, as minor changes to the data or model specification yield very different estimates.

They show that in a sample of 16 well-cited studies on U.S. data, the point estimates for expected inflation vary between 0.33 and 0.94 and the point estimates for the forcing variable vary between 0.004 and 0.08. They also run simulations for a large number of specifications and estimation strategies, which show even larger variations in the point estimates.

There are three main problems with using lagged macroeconomic variables as instruments, all of which lead to biased and imprecise estimates. These problems can in turn explain the uncertainty of the estimates shown by Mavroeidis, Plagborg-Møller and Stock (2014). First, lagged variables are often weak instruments, meaning that conventional inference is

unreliable. Second, using several variables and several lags causes the number of instruments to be large relative to the sample size. This also causes the model to be over-identified, meaning that there is no weak instrument robust method for conducting inference that has correct size and power (see Andrews, Stock and Sun, 2019). Third, as shown by Zhang and Clovis (2010), the error term in the hybrid New Keynesian Phillips curve for the U.S. is autocorrelated of order four. This means that the cost-push shocks are autocorrelated and the exogeneity condition is violated.

One way to circumvent the last problem, as discussed in Barnichon and Mesters (2020), would be to use lagged variables with longer lag length than the autocorrelation of the cost- push shocks. They point out, however, that increasing the lag length faces a tradeoff between being uncorrelated with the cost-push shocks and instrument relevance. The increased lag length needed in order for the instruments to be uncorrelated in with the cost-push shock will worsen the weak instrument problem.

The method developed by Barnichon and Mesters (2020) of using a sequence of past

monetary policy shocks as instruments solves all three problems listed above. (i) The

exogeneity condition is satisfied regardless of the order of autocorrelation in the cost-push

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shocks, (ii) the model is just-identified, and (iii) the inference is robust to weak instruments.

Using this method, they estimate a hybrid New Keynesian Phillips curve with output gap as the forcing variable for the period 1969-2007 using the narrative monetary policy shocks of Tenreyro and Thwaits (2016) (which is an extension of the shocks estimated by Romer and Romer, 2004) as instruments. When comparing their method to the traditional method, they find that using lagged macro variables as instruments (i) under-estimates the coefficient on output gap and (ii) over-estimates the coefficient on expected inflation. They also compare the estimates of the period 1969-2007 to the period 1990-2017. The coefficients for the second period are estimated using HFI monetary policy shocks. This comparison shows that the coefficient on output gap has decreased from 0.28 to 0.12 for the period 1990-2017 and the coefficient on expected inflation has increased from 0.42 to 0.71, suggesting a flattening of the Phillips curve and an increased importance of expected inflation. They point out, however, that the different estimates may be caused by differences in imperfections of the monetary policy shocks used in the two samples and not by genuine changes in the underlying Phillips curve.

In summary, out of the three methods suggested by Mcleay and Tenreyro (2019) to solve the endogeneity problem of the hybrid New Keynesian Phillips curve, the IV approach is the most reasonable for Swedish data. Because the method of Barnichon and Mesters (2020) solves the problems that causes high sampling and specification uncertainty from using lagged

macroeconomic variables as instruments, their method is theoretically superior. This motivates why I apply it to the Swedish data in this study.

2.2 The Swedish Phillips curve

Data presented by the Riksbank (2018) shows that the relationship between unemployment and wage growth has weakened in Sweden for the period 2011-2018 compared to 2000-2010.

The relationship between unemployment and inflation, however, has increased for the latter

period. The reason for this contradicting result, they argue, is that other factors than economic

activity have affected wage growth and inflation. For example, they list changes in labor

supply and lower wage growth in the Euro area as reasons for the lower wage growth and

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higher oil prices, weaker domestic currency, and higher expected inflation as reasons for the higher inflation. The Riksbank (2018) study suggest that there are cost-push shocks in the Swedish data and thus also the necessity to get rid of the influence of these shocks in order to estimate and unbiased Swedish Phillips curve.

Jonsson and Theobald (2019) estimate that the slope coefficient of unemployment on wage growth in Sweden has flattened from the interval -0.52 to -04 during 2000-2007 to the interval 0.14 to 0.06 during the period 2010-2018. They show formally how changes in the Swedish labor market can explain this apparent flattening of the Phillips curve. Specifically, they use a model of the labor market and show that reduced matching efficiency, lower unemployment benefits, and weaker bargaining power among employees are all possible explanations for a flatter wage Phillips curve. The study does not, however, address the endogeneity problem of the Phillips curve and whether changes in the severity of that problem can, at least partially, explain the apparent flattening.

Karlsson and Österholm (2019) compare models with time-varying parameters to models with constant parameters when estimating a Swedish Phillips curve for the period 1995-2018. They find mixed evidence in favor of a stable dynamic relationship between the unemployment rate and inflation. Their results do not, however, suggest a flattening of the Phillips curve in the later years of the sample, which they argue is evidence against the flattening as an explanation for the low inflation in the years following the financial crisis.

Frohm (2019) studies survey data from Swedish firms and finds a positive relationship between firms’ resource utilization and inflation expectations on the one hand and firms’

selling prices on the other, indicating a positive sloping Phillips curve. Data on firm level is

not subject to the same cost-push shocks and partial accommodation by monetary policy as

aggregate data, which suggest that it can be used to estimate and unbiased Phillips curve. The

survey data used does not, however, provide quantitative measures of resource utilization, so

it cannot be used to obtain point estimates of the relationship at an aggregate level.

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In summary, these studies show mixed evidence regarding the flattening of the Swedish Phillips curve. There are strong indications that there are cost-push shocks in the data which blurs the relationship between economic activity and inflation. The fact that these shocks have not been adequately controlled for in these studies along with the argument made in section 2.1 that the IV approach of Barnichon and Mesters (2020) is the most appropriate for the Swedish data supports the relevance of my study.

3. Theory

This section provides a theoretical description of how monetary policy and thus also monetary policy shocks affect economic outcome as well as a motivation for the specification of the New Keynesian Phillips curve I attempt to estimate.

3.1 The New Keynesian framework in a small open economy

The New Keynesian framework is used for studying the transmission mechanism of monetary policy and other macroeconomic shocks. More specifically, the framework attempts to

describe the relationship between monetary policy, inflation, and the business cycle. This framework constitutes the base of the larger forecasting models used by modern central banks, including the Riksbank. The key assumption of the New Keynesian framework is that there exists some short-run nominal rigidity in the economy. This allows for changes in the short-term nominal interest rate (i.e. the monetary policy instrument used by central banks) to have an effect on the real interest rate, which in turns affects real macroeconomics variables (Galí, 2015).

In the extension to a small open economy, as presented in Galí (2015), the economy is

assumed to be infinitesimally small relative to the world economy, which means that its

actions and performance does not have an impact on the rest of the world. This assumption is

valid for Sweden but not necessarily for larger economies such as the United States or the

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Euro area. The assumption that monetary policy affects real variables in the short run remains in the small open economy extension.

3.2 The New Keynesian IS equation for a small open economy

The effect of monetary policy on output is described by a dynamic IS equation, which in the simplest form relates output to expected output in the next period and the real interest rate.

The IS equation can be written in terms of the log output gap and the real interest rate gap as:

𝑦̃

𝑡

= 𝐸

𝑡

[𝑦̃

𝑡+1

] +

1

𝜎𝜐

(𝑖

𝑡

− 𝐸

𝑡

[𝜋

𝐷,𝑡+1

] − 𝑟

𝑡𝑛

) (1) where ỹ

𝑡

is the log output gap in period t, i.e. the difference between output and the natural flexible-price level of output (𝑦̃

𝑡

≡ 𝑦

𝑡

− 𝑦

𝑡𝑛

), 𝐸

𝑡

[𝑦̃

𝑡+1

] is the expected value of the log output gap in period t+1,

1

𝜎𝜐

measures the sensitivity of the log output gap in period t to interest rate changes, 𝑖

𝑡

is the nominal interest rate, 𝐸

𝑡

[𝜋

𝐷,𝑡+1

] is the expected domestic inflation, and 𝑟

𝑡𝑛

is the natural interest rate.

Equation (1) relies on the presence of short-run nominal rigidity in the sense that without it, the real interest rate, defined as the difference between the nominal interest rate and the expected future domestic inflation (𝑟

𝑡

= 𝑖

𝑡

− 𝐸

𝑡

[𝜋

𝐷,𝑡+1

]), becomes equal to the natural interest rate. This in turn implies that the output gap follows a random walk, i.e. 𝑦̃

𝑡

= 𝐸

𝑡

[𝑦̃

𝑡+1

], and is independent of monetary policy.

3.3 The New Keynesian Phillips curve for a small open economy

For a small open economy, the New Keynesian Phillips curve relates domestic inflation to expected future domestic inflation and the log output gap as follows:

𝜋

𝐷,𝑡

= 𝛽𝐸

𝑡

[𝜋

𝐷,𝑡+1

] + 𝜅

𝜐

𝑦̃

𝑡

, (2)

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where 𝛽 is the small open economy’s discount factor, and 𝜅

𝜐

is a parameter for which the value depends on the degree of openness, the substitutability between domestic and foreign goods, the degree to which firms can adjust their prices, and other structural parameters related to firms’ markups (see Galí, 2015 chapter 3 and chapter 8 for a detailed description as well as the derivation).

In this study, following e.g., Barnichon and Mesters (2020) and Mavroeidis (2005), I estimate a so called “hybrid New Keynesian Phillips curve”, as proposed by Galí and Gertler (1999), which includes a term for one-period lagged inflation:

𝜋

𝐷,𝑡

= 𝛽𝐸

𝑡

[𝜋

𝐷,𝑡+1

] + 𝜅

𝜐

𝑦̃

𝑡

+ 𝛾𝜋

𝐷,𝑡−1

, (3) where 𝜋

𝐷,𝑡−1

is the domestic inflation in the previous period. This term is added based on the assumption that a fraction of firms updates their prices based on a backward-looking rule of thumb (Mavroeidis, Plagborg-Møller and Stock, 2014).

Finally, as in Mavroeidis, Plagborg-Møller and Stock (2014), adding an unrestricted unobserved disturbance term, 𝑢

𝑡

, yields the following specification of the hybrid New Keynesian Phillips curve:

𝜋

𝐷,𝑡

= 𝛽𝐸

𝑡

[𝜋

𝐷,𝑡+1

] + 𝜅

𝜐

𝑦̃

𝑡

+ 𝛾𝜋

𝐷,𝑡−1

+ 𝑢

𝑡

(4) The authors state that: “𝑢

𝑡

can be interpreted as measurement error or any other combination of unobserved cost-push shocks, such as shocks to the markup or to input (e.g., oil) prices.”

(p. 129). As discussed above, 𝑢

𝑡

is assumed to be autocorrelated as well as correlated with the

endogenous variables. Equation (4) is the specification of the hybrid New Keynesian Phillips

curve that I attempt to estimate.

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4. Data

In this section I present the data I use to estimate the hybrid New Keynesian Phillips curve.

The data consists of estimated proxies for monetary policy shocks, output gap, inflation, and expected inflation.

4.1 Monetary policy shocks

In this study I use high-frequency identified monetary policy shocks for the period 1998:4- 2019:4 as instruments to estimate the New Keynesian Phillips curve for Sweden. The shocks are estimated using the method of Kuttner (2001) and are defined as the unexpected change in the Riksbank’s policy rate (the repo rate) at the time of a monetary policy announcement. The unexpected change in the repo rate is in turn defined as the change in the price of an interest rate derivative which has the repo rate (or a close proxy) as the underlying interest rate over a short period around the monetary policy announcement. This method relies on the weak form of the efficient market hypothesis, which states that all available public information should be reflected in asset prices and new information should be reflected in the prices “instantly”

(Fama, 1970). This means that the price of an interest rate derivative which has the repo rate as the underlying interest rate just before a monetary policy announcement should reflect the market’s expectation of the Riksbank’s action. The change of the price “just after” and “just before” - typically defined as a 30-minute window up to a full day - can therefore be

interpreted as the unexpected change of the monetary policy announcement, and this unexpected change can in turn be interpreted as an exogenous shocks.

Barakchian and Crowe (2013) list four conditions that need to be fulfilled in order for the

estimated shocks to be exogenous. First, there exist a market interest rate that is a close proxy

for the policy rate. Second, there is no systematic variation in the risk premia of the market

interest rate used as a proxy for the policy rate at the monetary policy announcements. Third,

there is no other information released during the time window for which the unexpected

reaction to the monetary policy announcement is estimated other than the announcement itself

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Figure 1: The repo rate and 3-month STIBOR

that affect the estimates. Fourth, the monetary policy announcement should not reflect the central bank’s private information about the economic outlook. These conditions are discussed in turn below.

As a proxy for the market’s expectation of the future repo rate I use daily data on forward rate agreements (FRAs) with the 3-month STIBOR as the underlying interest rate. STIBOR stands for Stockholm interbank offered rate, which is the rate at which a number of banks are willing to lend to each other without security for certain durations, in this case three months. The 3- month STIBOR rate has been on average 26 basis points above the repo rate during the sample period, making it a close proxy to the repo rate, as shown in Figure 1.

The FRA contracts are available for 1 to 12 3-month periods ahead and are constructed as contracts for difference (CFD). This means that a buyer of a FRA contract either pays or receives a cash amount corresponding to the interest rate difference between the agreed

-1,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00

1998-10-01 1999-05-03 1999-11-25 2000-06-28 2001-01-22 2001-08-21 2002-03-19 2002-10-16 2003-05-20 2003-12-12 2004-07-19 2005-02-10 2005-09-08 2006-04-03 2006-10-31 2007-05-31 2007-12-27 2008-07-28 2009-02-24 2009-09-22 2010-04-22 2010-11-15 2011-06-15 2012-01-09 2012-08-07 2013-03-05 2013-10-02 2014-05-06 2014-11-28 2015-07-06 2016-02-01 2016-08-29 2017-03-22 2017-10-19 2018-05-22 2018-12-13 2019-07-19 Repo rate STIBOR 3M

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interest rate of the contract and the actual 3-month STIBOR for the period to which the contract applies. This makes the contracts good proxies for the expected future 3-month STIBOR, which in turn makes them good proxies for the expected future repo rate. The contracts expire two bank days prior to the third Wednesday of the last month in each quarter, i.e. approximately two weeks before the beginning of a new calendar quarter. In order for the contracts to better match the calendar quarters, following Åhl (2017), I combine data on the first and second 3-month ahead contract into one contract using the weights

5

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on the first contract and

1

6

on the second.

1

The monetary policy shocks are estimated by the following equation:

𝑠ℎ𝑜𝑐𝑘

𝑠

= 𝐹𝑅𝐴

𝑠

− 𝐹𝑅𝐴

𝑠−1

(5)

where 𝐹𝑅𝐴

𝑠

is the closing price of the adjusted FRA contracts the day of the monetary policy announcement at time s and 𝐹𝑅𝐴

𝑠−1

is the closing price of the adjusted FRA contracts the day before the announcement.

Regarding the second condition, Figure 1 also show that there has been some volatility in the risk premia, measured as the difference between the two series, during the period of interest.

The most notable increases in the risk premia occurred during the period leading up to

outbreak of the financial crisis in September 2008 and during 2011. Based on the figure alone it does not appear that there has been a systematic variation in the risk premia at the monetary policy announcements, indicating that the second exogeneity condition is fulfilled. Estimating the volatility of the risk premia at the days of monetary policy announcements, however, is beyond the scope of this paper. Nakamura and Steinsson (2018) show for U.S. data that monetary policy shocks effect real interest rates, and that the effect is driven by changes in expected future short-term interest rates as opposed to changes in risk premia of market interest rates. Assuming this is true for the Swedish data as well, the potential bias of the estimated monetary policy shocks from changes in the risk premia at the monetary policy announcements is likely to be small.

1 The main results remain even without this adjustment.

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Ideally intraday data should be used to estimate monetary policy shocks instead of daily data.

This reduces the risk of the estimates being affected by other news released during the same day (exogeneity condition three). As I do not have access to intraday data for the FRA

contracts, I use daily data instead. One potential source of bias from other news is the fact that on 41 out of the 156 monetary policy announcements Norges Bank, the Bank of England, the European Central Bank, and/or the Federal Reserve made monetary policy announcements on the same day.

2

In Appendix A, I estimate the effect of these central banks’ monetary policy announcement on the adjusted 3-month STIBOR FRA contracts. The results show no significant effect of monetary policy announcements made by Norges Bank, the Bank of England, or the Federal Reserve. Only announcements made by the European central bank show a significant effect. The estimated effect is uncertain, however, due to very low

variation in the HFI monetary policy shocks for the Euro area. Nonetheless, it is possible that there might be a small bias in the shocks from other news for some of the conflicting dates.

As a robustness test against potential effects from other news affecting the estimates, I use the monetary policy shocks estimated by Sandström (2018), who uses intraday data for STINA- swaps for the period 2003:1-2015:2. These shocks are estimated during the time-window 09.15 am to 12.15 pm, which means that they only coincide with monetary policy

announcements made by Norges bank and the Bank of England. The drawback of these shocks is that they cover a shorter period than the FRA shocks. Using these shocks as instruments instead of the FRA shocks does not change the main conclusion of the results, which indicate that news from the European central bank does not pose a problem in practice.

Finally, if the monetary policy announcements contain systematic release of information about the economic outlook that moves the market’s expectations - so called “information shocks” - the estimated monetary policy shocks can be biased. This can happen if the central bank has access to private information about the economic outlook and/or if the central bank can consistently produce better forecasts based on public information than the market. Romer

2 Monetary policy announcements by the FED are usually made in the afternoon. Because of the time difference these announcements are made after close of business in Sweden. However, some of the announcements by the FED were made earlier during the day. To err on the side of caution I count both the announcements made the day before and the same day as the announcements by the Riksbank.

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and Romer (2000) show that the Federal Reserve appears to possess information about the future state of the economy that is not known to market participants and that the Fed can forecast inflation and output better than the market. Jarociński and Karadi (2020) disentangles the monetary policy shocks from the information shocks for the U.S and the Euro area using a structural vector autoregression and find that regular HFI estimates are biased by information shocks and that they underestimate the effectiveness of monetary policy.

I am unaware of any private information available to the Riksbank that is communicated at their monetary policy announcements that could potentially affect the market’s forecast about the future state of the economy. Riksbank (2020) evaluates its forecasting performance compared to other government and market forecasters for the period 2010-2019. The study finds that the Riksbank had the highest accuracy of forecasting GDP and unemployment, was in line with the average for inflation, and the least accurate in forecasting the repo rate. Based on this study it is possible that there is an information effect from the Riksbank’s monetary policy announcements if the announcements cause the market to update its forecast on GDP and unemployment. Disentangling potential information shocks of the Riksbank’s monetary policy announcements is beyond the scope of this study, however. And I am unaware of any previous estimates of information shocks for Swedish data. I can therefore not exclude the possibility that my estimated monetary policy shocks are biased due to information shocks.

The size and sign of that potential bias is unknown.

In summary, the estimated monetary policy shocks might not be completely exogenous due to variation in the risk premia, monetary policy announcements made by the European central bank release at the same day, and information about the future economic state of Sweden.

However, the sign and size of the shocks are in line with other estimates of Swedish as well as

international monetary policy shocks, which suggest that they are good proxies for the true

shocks and thus can be used as instruments to estimate the hybrid New Keynesian Phillips

curve for Sweden.

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4.2 Construction of quarterly shocks

The macroeconomic variables that make up the hybrid New Keynesian Phillips curve in equation (4) are all measured per quarter and often the Riksbank makes more than one

monetary policy announcement per quarter. These two facts make it necessary to combine the estimated monetary policy shocks into quarterly shocks. This could be done by simply adding all shocks occurring in each quarter, as done by Romer and Romer (2004). However, the effect of a shock on the economy is likely to vary depending on when it occurs (shocks occurring early in the quarter are likely to have a larger effect on the economy the following quarter than shocks occurring late in the quarter). To account for this, I use the three steps used by Gertler and Karadi (2015) to create a quarterly shock series. First, I create a

cumulative daily shock series by cumulating all daily shocks over the full sample where the cumulated shock at day d is:

𝑐_𝑠ℎ𝑜𝑐𝑘

𝑑

= ∑ 𝑠ℎ𝑜𝑐𝑘

𝑠

𝑑

𝑠=1

(6)

Second, I take the quarterly average of the cumulative daily shock series where the observation at quarter t is:

𝑞𝑎

𝑡

=

𝑑𝑑=𝑑𝑡𝑇

𝑐_𝑠ℎ𝑜𝑐𝑘

𝑑

𝑡1

𝑑

𝑡𝑇

− 𝑑

𝑡1

(7) where 𝑑

𝑡1

is the first trading day and 𝑑

𝑡𝑇

is the last trading day in quarter t. And third, the quarterly measure of the monetary policy shocks is obtained by taking the first difference of the quarterly averages:

𝑠ℎ𝑜𝑐𝑘

𝑡

= 𝑞𝑎

𝑡

− 𝑞𝑎

𝑡−1

(8)

Equation (8) is the measure of monetary policy shocks I use as instruments to estimate the hybrid New Keynesian Phillips. These measures along with the quarterly sum of the repo rate changes are shown in Figure 2 for the period 1998:4 to 2019:4.

3

3 To give a clear visual representation of the size of the monetary policy shocks, I have set the

minimum value of the y-axis to -1.1. The sum of the quarterly change in 2008:4 exceeds this limit as it amounts to -2.75 percentage points.

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Figure 2: Quarterly changes in the repo rate and quarterly monetary policy shocks:

1998:4-2019:4

Figure 2 shows that the size of the shocks is rather small throughout the period. Two

exceptions are the shocks in the two quarters directly following the outbreak of the financial crisis in 2008:3, i.e., the shocks in 2008:4 and 2009:1. Out of the 86 total shocks, only 13 have an absolute value above 0.1 percentage points. And out of these 13, only one occurred after 2010 (the shock in 2014:3).

The variation of my estimated shocks is lower compared to the variation of the shocks used by Barnichon and Mesters (2020). In their main estimates they use the quarterly monetary policy shocks estimated by Tenreyro and Thwaits (2016) for the period 1969-2007. These shocks are shown in Figure 1 in Tenreyro and Thwaits (2016). Several of the shocks occurring up until the early 1980s have an absolute value of 1 percentage point and above.

The variation of the shocks falls for the post 1980 period, but almost all the shocks appear to have an absolute value above 0.1 percentage points.

-1,1 -0,9 -0,7 -0,5 -0,3 -0,1 0,1 0,3 0,5 0,7

1998:4 1999:3 2000:2 2001:1 2001:4 2002:3 2003:2 2004:1 2004:4 2005:3 2006:2 2007:1 2007:4 2008:3 2009:2 2010:1 2010:4 2011:3 2012:2 2013:1 2013:4 2014:3 2015:2 2016:1 2016:4 2017:3 2018:2 2019:1 2019:4

Repo rate change Monetary policy shock

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Figure 3: Monthly monetary policy shocks for the U.S. estimated by Gertler and Karadi (2015): 1990:m1-2012:m6.

In the second sample period of 1990-2017, Barnichon and Mesters (2020) use HFI shocks.

Figure 3 show the HFI shocks estimated by Gertler and Karadi (2015).

4

Similar to the shocks estimated by Barnichon and Mesters these shocks are estimated using the 3 month ahead fed funds future. The shocks are combined into monthly shocks so a direct comparison with my estimates is not possible. However, four main facts are discernible from the figure. First, there are more negative shocks than positive. Second, the largest shocks (in absolute value)

occurred in the early 1990s, the year 2000, and during the period leading up to the financial crisis in 2008. Third, the variation is low from 2010 and onward. And fourth, the variation appears to be lower compared to the shocks estimated by Tenreyro and Thwaits (2016).

4.3 Output gap, inflation and expected inflation

The output gap is defined as the difference between output and the natural flexible-price level of output (𝑦̃

𝑡

≡ 𝑦

𝑡

− 𝑦

𝑡𝑛

). I use quarterly log seasonal and calendar adjusted real GDP

provided by Statistics Sweden for output (𝑦

𝑡

). The natural flexible-price level of output (𝑦

𝑡𝑛

), however, is unobserved and has to be estimated. I estimate 𝑦

𝑡𝑛

using the Hodrick-Prescott

4 Figure 3 is created using the replication data for Gertler and Karadi (2015) provided by Peter Karadi.

-0,35 -0,3 -0,25 -0,2 -0,15 -0,1 -0,05 0 0,05 0,1 0,15

1990:m1 1990:m11 1991:m9 1992:m7 1993:m5 1994:m3 1995:m1 1995:m11 1996:m9 1997:m7 1998:m5 1999:m3 2000:m1 2000:m11 2001:m9 2002:m7 2003:m5 2004:m3 2005:m1 2005:m11 2006:m9 2007:m7 2008:m5 2009:m3 2010:m1 2010:m11 2011:m9

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(HP) filter presented in Hodrick and Prescott (1997). The idea behind the HP filter is to separate a time series (in this case log quarterly GDP) into a trend and a cyclical component:

𝑦

𝑡

= 𝑦

𝑡𝑠

+ 𝑦

𝑡𝑐

for t = 1, 2, 3, …, T, (9) where 𝑦

𝑡𝑠

is the trend component and 𝑦

𝑡𝑐

is the cyclical component. The separation is done by minimizing the following equation:

min

{𝑦𝑡𝑠,𝑦𝑡𝑐 }𝑡=1𝑇

{∑(𝑦

𝑡𝑐

)

2

𝑇

𝑡=1

+ 𝜆 ∑[(𝑦

𝑡+1𝑠

− 𝑦

𝑡𝑠

) − (𝑦

𝑡𝑠

− 𝑦

𝑡−1𝑠

)]

2

𝑇−1

𝑡=2

} (10)

subject to (9).

5

Intuitively, the HP filter is a tradeoff between minimizing the variance of the cyclical component and keeping the growth rate of the trend constant. This tradeoff is

governed by the parameter 𝜆, which is a positive number that penalizes changes in the growth rate of the trend. In the limit as 𝜆 goes to infinity, the trend component associated with the HP filter coincides with the linear trend. At the other extreme, as 𝜆 goes to zero, all of the

variation in the time series is attributed to the trend and the cyclical component is zero (Schmitt-Grohé and Uribe, 2017). I use the standard value for quarterly data of 𝜆 = 1600, as suggested by Hodrick and Prescott (1997), to estimate 𝑦

𝑡𝑛

.

As a measure of inflation, I use the 12-month percentage change in consumer price index (CPI) provided by Statistics Sweden. The data is calculated per month, so I recalculate it to quarterly data by taking the average change of the three months in each quarter.

Like the output gap, expected inflation is unobserved. In this study I use a survey measure of expected inflation as a proxy for the unobserved, true expected inflation.

6

Specifically, I use the Prospera survey of expected one year ahead quarterly mean CPI. The survey is

commissioned by the Riksbank and is based on the response of labor market parties,

purchasing managers, and money market players. Figure 4 shows expected inflation, inflation

5 See e.g. Schmitt-Grohé and Uribe (2017) appendix 1.9.2 for the first-order conditions and solution to the minimization problem.

6 See Mavroeidis, Plagborg-Møller and Stock (2014) section 3.1 for a discussion of the different approaches used in the literature to estimate expected inflation.

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22

Figure 4: Expected quarterly mean inflation one year ahead, quarterly mean inflation, and quarterly (100×log) real output gap: 1998:4-2019:4

and output gap for the full sample.

7

Two facts are evident from the figure: (i) Actual inflation is more volatile than expected inflation and (ii) the output gap and inflation correlate well, except for the periods 2000:3-2004:2 and 2015:4-2019:4.

5. Method

In this section I describe the method I use to estimate the hybrid New Keynesian Phillips curve. Section 5.1 presents the general IV regression. Section 5.2 discusses the instrument validity of monetary policy shocks. Section 5.3 discusses the problem of weak instruments and how the problem can be solved by using the Anderson-Rubin test statistic. Section 5.4 presents the Almon-restriction and how it can be used to reduce the number of instruments in order to make the IV regression just-identified.

7 There is a missing value of expected inflation for 2001:3. To the best of my knowledge, no survey was conducted in this quarter. I have filled in the missing value by interpolating the value for 2001:2 and 2001:4, which gives a value of 2.33 for 2001:3.

-6,00 -5,00 -4,00 -3,00 -2,00 -1,00 0,00 1,00 2,00 3,00 4,00 5,00

1998:4 1999:3 2000:2 2001:1 2001:4 2002:3 2003:2 2004:1 2004:4 2005:3 2006:2 2007:1 2007:4 2008:3 2009:2 2010:1 2010:4 2011:3 2012:2 2013:1 2013:4 2014:3 2015:2 2016:1 2016:4 2017:3 2018:2 2019:1 2019:4

Expected inflation Inflation Output gap

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5.1 Instrumental variables regression

The hybrid New Keynesian Phillips curve in equation (4), restated here for convenience:

𝜋

𝐷,𝑡

= 𝛽𝐸

𝑡

[𝜋

𝐷,𝑡+1

] + 𝜅

𝜐

𝑦̃

𝑡

+ 𝛾𝜋

𝐷,𝑡−1

+ 𝑢

𝑡

,

suffers from potential endogeneity problems that lead to omitted variable bias. These

problems are: (i) Expected inflation, 𝐸

𝑡

[𝜋

𝐷,𝑡+1

], is unobserved and survey measures therefore consists of both the true expected inflation as well as a measurement error. (ii) The output gap, 𝑦̃

𝑡

, is also unobserved so proxies for 𝑦̃

𝑡

also contain measurement error. (iii) The unobserved disturbance term, 𝑢

𝑡

, which captures the autocorrelated cost-push shocks, is correlated with the output gap and domestic inflation in period t and t-1. Because of the endogeneity problems, simple OLS estimates of equation (4) will be biased and inconsistent, meaning that they will not converge to the true value even in large samples. In order to overcome these problems and to obtain unbiased and consistent estimates, I use the instrumental variables approach of Barnichon and Mesters (2020) instead.

The instrumental variables regression using the two stage least square (TSLS) estimation can be written as a system of two equations called the first stage and the second stage. Rewriting equation (4) in a compact form for ease of exposition, the second stage is represented by:

𝜋

𝐷,𝑡

= 𝑤

𝑡

𝛿 + 𝑢

𝑡

, (11)

where 𝛿 = (𝛽, 𝜅

𝜐

, 𝛾)′ and 𝑤

𝑡

= (𝐸

𝑡

[𝜋

𝐷,𝑡+1

], 𝑦̃

𝑡

, 𝜋

𝐷,𝑡−1

)′. And the first stage is:

𝑤

𝑡

= 𝜌

𝑜

+ 𝜌

1

𝑧

𝑡

+ 𝑣

𝑡

, (12)

where 𝑧

𝑡

is a 𝑘 × 1 vector of instruments. Intuitively, the first stage decomposes the

endogenous variables in two parts. The first part, 𝜌

𝑜

+ 𝜌

1

𝑧

𝑡

, is the part of the endogenous

regressors that can be predicted by the instruments. The second part, 𝑣

𝑡

, is the part of the

endogenous regressors that is correlated with the error term in equation (11), 𝑢

𝑡

. In this case,

measurement error and the effect of the autocorrelated cost-push shocks. Given that the

instruments are valid, meaning that they are correlated with the endogenous regressors and

uncorrelated with the error term (i.e., relevant and exogenous), the unknown coefficients in

the first stage can be estimated using OLS. The predicted value from the first stage, 𝑤 ̂, will

𝑡

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24

then be purged of 𝑣

𝑡

and contain only the exogenous variation of 𝑤

𝑡

. The second stage can then be estimated by OLS using 𝑤 ̂ instead of 𝑤

𝑡 𝑡

. Given that the instruments are valid, the estimated coefficients in the second stage will be unbiased and consistent (Stock and Watson, 2015).

5.2 Instrument validity

The IV approach of Barnichon and Mesters (2020) uses monetary policy shocks as instruments. From a theoretical standpoint, the dynamic New Keynesian IS equation in equation (1) shows that interest rate changes, and thus also monetary policy shocks, affect the output gap, which in turn affects inflation. Thus, the existence of the dynamic New Keynesian IS equation ensures that monetary policy shocks are relevant instruments in theory.

Empirically, I estimate the impulse response of monetary policy shocks on expected inflation, output gap, inflation, and one-period lagged inflation using local projection as proposed by Jordà (2005). The method consists of estimating a separate equation of the impulse response for each horizon. Taking inflation as an example, the method consists of estimating the following equation:

𝜋

𝐷,𝑡

= 𝑠ℎ𝑜𝑐𝑘

𝑡−ℎ

+ 𝜉

𝑡

for h = 1, …, H, (13) where H is the number of lagged quarters. In practice, this means estimating “H” different equations of the effect of monetary policy on inflation, expected inflation, one-period lagged inflation, and output gap respectively.

Barnichon and Mesters (2020) suggest using 12 to 20 lagged monetary policy shocks as instruments to ensure that the full effect of monetary policy shocks on the endogenous

variables of the hybrid New Keynesian Phillips curve is capture. In their estimates they use 20 lagged shocks. They base this number on the assumption that it takes 8-12 quarters for a monetary policy shock to reach its full effect on inflation. To ensure I capture the full effect of the impulse responses, I therefore estimate the local projection method for 20 lagged quarters.

The results, presented in Figure 5, show that monetary policy has a significant effect on the

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variables of interest, indicating that monetary policy shocks are relevant instruments to estimate the hybrid New Keynesian Phillips curve.

Figure 5 also show that it takes around 10 quarters for the impulse responses to reach zero.

This would suggest I use 10 lagged quarterly monetary policy shocks as instruments to estimate the hybrid New Keynesian Phillips curve. However, in the web-appendix to Barnichon and Mesters (2020), they vary the number of lagged shocks used as instruments and find that the estimates for the sample period 1969-2007 are only significant when the number of lags is larger than 10. They argue that this is because a substantial part of the impulse response of inflation that is non-zero is excluded when the number of lags is 10 or lower. To test whether this is true for the Swedish data as well, I use 10 to 20 lagged monetary policy shocks as instruments.

Figure 5: Impulse response of a one percentage point monetary policy shock on expected

inflation, output gap, inflation, and one-period lagged inflation. 1998:4-2019:4

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Regarding the exogeneity condition, monetary policy shocks are exogenous if they are

uncorrelated with the autocorrelated cost-push shocks as well as the measurement error in the estimated output gap and expected inflation. The systematic response of monetary policy to inflation makes monetary policy correlated to cost-push shocks. Monetary policy shocks, however, are innovations to the systematic conduct of monetary policy and should therefore be uncorrelated with cost-push shocks. Monetary policy shocks are uncorrelated to

measurement error in the output gap given that the assumption that money is neutral under flexible prices hold. And finally, monetary policy shocks are uncorrelated with measurement error of expected inflation given that they are uncorrelated with the inflation expectation survey measurement error term, which they are assumed to be.

5.3 Weak instrument robust inference

Even though monetary policy shocks are relevant instruments to estimate the coefficients of the New Keynesian Phillips curve, they are likely to be weak instruments, meaning that the correlation between monetary policy shocks and the endogenous regressors is low (Barnichon and Mesters, 2020). When instruments are weak, conventional approximations to the

distribution of the TSLS (and other IV) estimators are generally unreliable. That is, the IV estimators can be biased, t-tests of the estimated coefficients may fail to control size, and conventional confidence intervals may cover the true value of the coefficients less than intended, i.e. be too narrow (Andrews, Stock and Sun, 2019).

According to Andrews, Stock and Sun (2019), there is no established method for detecting

weak instruments in settings with multiple endogenous regressors and non-homoscedastic

standard errors (i.e., heteroscedastic, auto-correlated, or clustered standard errors), which is

the case for the hybrid New Keynesian Phillips curve. As in Barnichon and Mesters (2020), I

therefore assume that the instruments are weak for the Swedish data as well and I use their

proposed method of weak instrument robust inference. I base this assumption on the

arguments made by Boivin and Giannoni (2006) and Ramey (2016). Boivin and Giannoni

(2006) show that the effect of monetary policy shocks on output and inflation has fallen since

the 1980s in the U.S, i.e. that the variance contributions of the shocks has fallen. The main

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reason for this, they argue, is that monetary policy has been conducted more efficiently since then. Ramey (2016) argues that monetary policy has been set more systematically since the 1990s, which has resulted in less exogenous variation in monetary policy shocks.

Monetary policy being set more efficiently and systematically since the mid-1990s is certainly true for Sweden and the Riksbank which introduced an inflation target in 1995, announces its interest rate decisions systematically every 6-8 weeks since 1999, and publishes forecasts of the future repo rate 12 quarters ahead since 2007 (Sellin, 2018). And as shown in Figure 2, the size of the estimated monetary policy shocks for Sweden has been small during the period 1998:4-2019:4. It is therefore reasonable to believe that monetary policy shocks are weak instruments in the Swedish data as well. The relatively short sample period in this study and the relatively low variation of my estimated shocks compared to the ones used by Barnichon and Mesters (2020) suggest that monetary policy shocks are even weaker instruments for the Swedish data than for the U.S. data.

Because I assume the instruments are weak, I conduct the inference for the TSLS coefficients using a test statistic that is robust against weak instruments. Specifically, as Barnichon and Mesters (2020), I use the test statistic of Anderson and Rubin (1949). The Anderson-Rubin (AR) test of 𝐻

0

: 𝛿 = 𝛿

0

is constructed from the following distributed lag model:

𝜋

𝐷,𝑡

− 𝑤

𝑡

𝛿

0

= 𝜃

𝑠ℎ𝑜𝑐𝑘

𝑡:𝑡−𝐻

+ 𝜂

𝑡

(14) where 𝑠ℎ𝑜𝑐𝑘

𝑡:𝑡−𝐻

≡ (𝑠ℎ𝑜𝑐𝑘

𝑡

, . . . , 𝑠ℎ𝑜𝑐𝑘

𝑡−𝐻

)′. The instrument exogeneity condition implies that 𝜃 is zero under 𝐻

0

. A test of 𝐻

0

: 𝛿 = 𝛿

0

can therefore be implemented by testing 𝜃 = 0.

The AR statistic is the F-statistic testing the hypothesis that the coefficients on the instruments

are all zero. Under the null hypothesis that 𝛿 = 𝛿

0

, if the instruments satisfy the exogeneity

condition, they will be uncorrelated with 𝜂

𝑡

, and 𝐻

0

will be rejected in 5 percent of the

samples. The set of values of 𝛿 that are not rejected by a 5 percent AR test constitutes a 95

percent confidence set for 𝛿. This set will have a coverage probability of 95 percent in large

samples, regardless of instrument strength (Stock and Watson, 2015). Only the width of the

confidence set increases as instrument strength falls (Andrews, Stock and Sun, 2019).

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