**Working** **Paper**

No. 145. October 2016

Do Inflation Expectations

Granger Cause Inflation?

By Pär Stockhammar and Pär Österholm

National Institute of Economic Research

Do Inflation Expectations Granger

Cause Inflation?

Pär Stockhammar and Pär Österholm

October 2016

We are grateful to seminar participants at the National Institute of Economic Research for

valuable comments on this paper.

National Institute of Economic Research, Box 3116, 103 62 Stockholm, Sweden

e-mail: par.stockhammar@konj.se Phone: +46 8 453 5910

Örebro University, School of Business, 701 82 Örebro, Sweden

e-mail: par.osterholm@oru.se Phone: +46 70 862 8986

WORKING PAPER NO 145, OCTOBER 2016

PUBLISHED BY THE NATIONAL INSTITUTE OF ECONOMIC RESEARCH (NIER)

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Abstract

In this paper, we investigate whether survey measures of inflation expectations

in Sweden Granger cause Swedish CPI-inflation. This is done by

studying the precision of out-of-sample forecasts from Bayesian VAR

models using a sample of quarterly data from 1996 to 2016. It is found

that the inclusion of inflation expectations in the models tends to improve

forecast precision. However, the improvement is typically small

enough that it could be described as economically irrelevant. One exception

can possibly be found in the expectations of businesses in the National

Institute of Economic Research’s Economic Tendency Survey; when

included in the models, these improve forecast precision in a meaningful

way at short horizons. Taken together, it seems that the inflation expectations

studied here do not provide a silver bullet for those who try to

improve VAR-based forecasts of Swedish inflation. The largest benefits

from using these survey expectations may instead perhaps be found

among analysts and policy makers; they can after all provide relevant

information concerning, for example, the credibility of the inflation target

or challenges that the central bank might face when conducting

monetary policy.

JEL classification code: C32, F43

Keywords: Bayesian VAR, Granger causality, Out-of-sample forecasts

3

Sammanfattning

I denna studie undersöks om enkätbaserade mått på inflationsförväntningar

i Sverige Grangerorsakar den svenska KPI-inflationen. Detta görs genom

att studera precisionen i ”out-of-sample”-prognoser från Bayesianska VARmodeller

på kvartalsdata 1996-2016. Införandet av inflationsförväntningarna

i modellerna tenderar att förbättra prognosprecisionen. Dock är skillnaden

så liten att den oftast kan beskrivas som ekonomiskt irrelevant. Ett

undantag utgörs möjligen av företagens inflationsförväntningar i Konjunkturbarometern;

när dessa inkluderas i modellerna förbättras prognosprecisionen

på korta horisonter i en utsträckning som är relevant. Sammantaget förefaller

det inte som om de studerade inflationförväntningarna kan utgöra en

silverkula för de som försöker ta fram förbättrade VAR-baserade prognoser

för svensk inflation. Möjligen är det istället analytiker och policymakare

som huvudsakligen kan dra fördel av inflationsförväntningarna; de kan trots

allt ge relevant information rörande till exempel trovärdigheten hos inflationsmålet

eller utmaningar som centralbanken kan stå inför vid genomförandet

av penningpolitiken.

4

Contents

1. Introduction ...................................................................................... 6

2. Inflation-expectations data ............................................................. 8

3. Methodology ..................................................................................... 9

3.1 The Bayesian VAR model .................................................... 10

3.2 Granger causality ................................................................... 11

4. Forecast comparisons .................................................................... 13

5. Sensitivity analysis .......................................................................... 16

6. Conclusions ..................................................................................... 17

References ................................................................................................ 19

Appendix A – Data ................................................................................. 21

Appendix B – Steady-state priors ......................................................... 22

Appendix C – RMSFEs and relative RMSFEs ................................... 23

5

1. Introduction

Survey measures of inflation expectations are often given a lot of attention

when they are published. There are several reasons for this. For example, in

an inflation targeting economy, inflation expectations are considered to

provide information about the credibility the central bank’s inflation target.

Poorly anchored long-run inflation expectations can be interpreted as the

inflation target having credibility problems. 1 One policy implication of this

is that if the target is not explicitly stated – or expressed clearly enough – it

should be made more transparent. In addition, inflation expectations play a

key role as a determinant of future inflation in many widely employed models

nowadays. 2 It is therefore of great importance to investigate if they provide

useful information to analysts and forecasters who aim to understand

and predict the evolution of inflation. 3,4

In this paper, we aim to improve the understanding of how survey

measures of inflation expectations relate to future inflation. More specifically,

we assess the usefulness of survey measures of inflation expectations in

Sweden from a forecast perspective. This is done by investigating whether

inflation expectations Granger cause inflation. Inflation expectations are

said to Granger cause inflation if they improve the forecast precision relative

to a model which does not include inflation expectations. We make use

of the state-of-the-art mean-adjusted Bayesian VAR (BVAR) framework of

Villani (2009) to conduct an out-of-sample forecast exercise using quarterly

data from 1996 to 2016. Two benchmark models without inflation expecta-

1 See, for example, Gürkaynak et al. (2007) and Beechey et al. (2011).

2 This includes the New-Keynesian DSGE model, which has become a workhorse within many

central banks; see, for example Adolfson et al. (2007) and Christoffel et al. (2011).

3 That inflation expectations actually matter can be exemplified by the fact that the Riksbank –

rather unnecessarily – raised the policy interest rate in September 2008, partly motivated by high

inflation expectations. The Riksbank’s governor Stefan Ingves stated that he wanted to “see a

reduction in inflation and inflation expectations before easing monetary policy” (Sveriges

Riksbank, 2008, p. 18).

4 There is a reasonably large literature looking at the importance of survey expectations of

inflation, with varying results. See, for example, Nunes (2010) who generally found a small

empirical role for survey expectations in the United States or Adam and Padula (2010) who found

survey expectations to be an important factor of inflation in the United Kingdom. Fuhrer (2012)

concluded that short-run inflation expectations have a significant role in explaining US inflation

since the beginning of the 1980s, while long-run expectations generally did not have the same

direct influence over the same period. Canova and Gambetti (2010) found that one-year ahead

inflation expectations consistently had predictive content in the United States 1960-2005.

Wimanda et al. (2011) showed that CPI inflation in Indonesia is significantly determined by,

especially, backward-looking inflation expectations. Studying VAR estimates, Clark and Davig

(2008), found that shocks to short- and long-term inflation expectations result in some passthrough

to actual inflation in the United States.

6

tions are used for our analysis: i) a univariate autoregressive model and ii) a

trivariate BVAR model including inflation, the unemployment rate and the

three month treasury bill rate. We accordingly study the forecast performance

of four model sizes. This is done at forecast horizons from one up

to twelve quarters – a reasonable focus given that the ability to predict inflation

at short to medium term horizons is what matters to policy makers

such as central banks.

Methodologically, this study is close to other papers using out-of-sample

forecast performance to assess Granger causality of various variables for

inflation; see, for example Bachmeier et al. (2007), Gavin and Kliesen

(2008), Berger and Österholm (2011) and Scheufele (2011). It is also related

to studies which rely on VARs to investigate the relationship between survey

measures of inflation expectations and inflation, such as Clark and

Davig (2008) and Canova and Gambetti (2010). We make a number of

contributions relative to the previous literature though. First, Sweden was

one of the early adopters of inflation targeting when the policy was declared

in 1993. It is of general interest to investigate the issue of Granger causality

of survey measures of inflation expectations for inflation in this environment.

Second, we provide evidence concerning which survey expectations

actually have additional information value for Swedish inflation. Third, we

conduct the analysis in a framework – the mean-adjusted BVAR of Villani

(2009) – which has not previously been used to assess the Granger causality

of survey measures of inflation expectations for inflation.

Our results indicate that while inflation expectations might Granger cause

Swedish inflation, the quantitative improvement in forecast precision is

often small enough to be empirically irrelevant.

The rest of this paper is organised as follows. Section 2 briefly presents the

survey data on inflation expectations used for our analysis. The BVAR

model and the concept of Granger causality are discussed in Section 3. In

Section 4, we present the results from our out-of-sample forecast exercise.

We conduct a sensitivity analysis in Section 5. Finally, Section 6 concludes.

7

2. Inflation-expectations data

We assess the forecasting properties of inflation expectations from Sweden’s

two main surveys: TNS Sifo Prospera’s inflation survey – which is

conducted on behalf of the Riksbank – and the Economic Tendency Survey of

the National Institute of Economic Research.

TNS Sifo Prospera asks approximately 235 businesses and organisations

about their inflation expectations at the one-, two- and five-year horizon

four times a year. In the main text, we study the expectations that typically

receive the most attention, namely the “overall” inflation expectation for

each horizon; this is generated by taking the arithmetic mean over all respondents

(by horizon). 5

In the National Institute of Economic Research’s Economic Tendency Survey,

both households and businesses are asked about their inflation expectations.

Approximately 1 500 households and 6 500 business are interviewed. 6

Unlike the TNS Sifo Prospera survey though, the respondents are only

asked about the one-year-ahead inflation expectation.

All together, we accordingly get five series of inflation expectations. These

data are shown in Figure 1, together with CPI inflation, for the sample

1996Q1-2016Q1. CPI inflation is calculated as the year-on-year percentage

change in the CPI (

t

P ), that is, 100P

P 1 4

.

t

t

t

As can be seen from the figure, the inflation expectations all show roughly

the same pattern. 7 For example, all five series increased noticeably between

2005 and 2008 in line with the increase in actual inflation during that period.

Similarly, a fall in expectations is present in all series following the glob-

5 The results from the survey are also available for five other subcategories: money market

players, employee organisations, employer organisations, manufacturing companies and trade

companies. Money market players are interviewed every month and are generally given most

attention in the media. However, this study shows that forecast precision is almost identical when

using the inflation expectations of money market players instead of the overall measure; see

tables A2, A3, A8 and A9 in Appendix C. Data on the money market players’ inflation expectations

are displayed in Figure A2 in Appendix A.

6 The households are asked every month and the businesses once every quarter. For the

households we use the mean of all respondents after excluding extreme values; monthly values

have been converted to quarterly using the arithmetic mean.

7 The correlation between the different categories of inflation expectations varies between 0.63

and 0.98.

8

al financial crisis. It can also be noted how inflation expectations have drifted

down in the last few years, as the Riksbank has had problems with target

achievement. 8

Figure 1. Data.

CPI-inflation

TNS Sifo Prospera, 1 year

5

3.5

4

3.0

3

2.5

2

2.0

1

1.5

0

1.0

-1

0.5

-2

96 98 00 02 04 06 08 10 12 14

0.0

96 98 00 02 04 06 08 10 12 14

TNS Sifo Prospera, 2 years

TNS Sifo Prospera, 5 years

3.0

3.2

2.5

2.8

2.0

2.4

1.5

2.0

1.0

96 98 00 02 04 06 08 10 12 14

1.6

96 98 00 02 04 06 08 10 12 14

NIER, businesses, 1 year

NIER, households, 1 year

3.0

4

2.5

2.0

3

1.5

2

1.0

0.5

1

0.0

96 98 00 02 04 06 08 10 12 14

0

96 98 00 02 04 06 08 10 12 14

Note: All variables are measured in per cent. The inflation expectation series of households in the

NIER survey have been converted from monthly to quarterly data using the arithmetic mean.

3. Methodology

There are different ways to assess whether inflation expectations have predictive

power for inflation. In this paper, we primarily rely on an out-ofsample

forecast exercise using a BVAR model. 9 In this section, we first

8 For a discussion about the problems associated with the anchoring of inflation expectations; see,

for example, Beechey et al. (2011).

9 In the sensitivity analysis presented in Section 5, we also use VAR models estimated with

classical methods.

9

present the model and then discuss the issue of establishing Granger causality

in an out-of-sample framework.

3.1 The Bayesian VAR model

We use the Bayesian VAR model given by

G

Lx

μ η ,

t

(1)

t

as the main tool for our analysis. As can be seen from equation (1), the

model is expressed in deviations from its steady state. This feature was

introduced by Villani (2009) and has the benefit that an informative prior

distribution for the steady-state values of the variables in the system – the nx1

vector μ – can be specified. Obviously, this can be particularly useful when

forecasting Swedish inflation seeing that the Riksbank has an explicitly stated

inflation target. 10

G L I G1 L

G mL is

The rest of the model is defined as follows:

m

a lag polynomial of order m ; the lag length of the model is in all cases set to

m 4 . x

t

is an nx1 vector of stationary variables and

iid error terms fulfilling E η

0 and η

η Σ

t

t

t

E .

η

t

is an nx1 vector of

The priors of the model largely follow convention in the literature. For Σ

the prior is given by

G G

p

n1 2

Σ Σ and the prior on vec G

1

G

m

, is given by G

vec ~ N 2 θ ,

mn

G

Ω G

, where

. It can be

noted that the priors on the dynamics have been modified somewhat relative to

the traditional Minnesota prior; this is standard when using Villani’s specification.

11 The prior on μ is given by μ ~ θ ,

N and is specified in detail in

n

μ

Ω μ

Table A1 in Appendix B. The hyperparameters of the model are also in line

10 Villani’s specification of the BVAR can improve forcast accuracy when it comes to inflation. This

has been shown by, for example, Beechey and Österholm (2010).

11 The prior mean on the first own lag for each variable is here set equal to 0.9 and all other

coefficients in G have a prior mean of zero.

10

with mainstream choices in the literature: We set the overall tightness to 0.2, the

cross-variable tightness to 0.5 and the lag decay parameter to 1.

3.2 Granger causality

In this paper, we are interested in whether inflation expectations have predictive

power for CPI inflation. If inflation expectations contain information

which is useful when forecasting CPI inflation that is not found in

other variables, we conclude that inflation expectations Granger cause CPI

inflation.

Granger causality can be analysed both within sample and out-of-sample.

We choose to assess Granger causality out-of-sample rather than within

sample. 12 There are several reasons for choosing this approach. First, it is

closer to Granger’s original idea and it can be noted that evaluating out-ofsample

forecast performance was called the “sound and natural approach” to

establish Granger-causality by Ashley et al. (1980, p. 1149). Second, out-ofsample

forecasts are also convenient to use since within-sample tests are

difficult to implement in a multivariate framework. 13 Finally, out-of-sample

forecast performance presents a higher hurdle than within-sample tests,

given the well-known tendency for overfitting models when relying on

within-sample analysis.

In this setting, Granger causality requires that the out-of-sample forecast

performance of a BVAR model including inflation expectations is better

than that of an otherwise identical model excluding inflation expectations.

We will make two comparisons here. The first is between a univariate model

of CPI inflation and a bivariate model with CPI inflation and inflation

expectations. In this case, we define the vector x

t

in equation (1) as

12 Within-sample Granger causality tests have been employed by, for example, Stock and Watson

(1989), Friedman and Kuttner (1993) and Us (2004).

13 It is easy to test for Granger causality within-sample in a bivariate framwork. For example, if

lags of inflation expectations were found to be non-zero in a regression of CPI inflation on its own

lags and lags of inflation expectations, we would conclude that inflation expectations Granger

cause CPI inflation. However, when the number of variables is larger than two and the forecasting

horizon is larger than one period, it becomes more complicated; see, for example, Lütkepohl

(2005) for a discussion.

11

t

t

x

(2)

in the univariate case and

x (3)

t

e

t

t

e

in the bivariate case, where

t

is CPI inflation as defined above and

t

is an

inflation expectation series. If the root mean square forecast error (RMSFE) of

the bivariate model is lower than that of the univariate model at a given horizon,

we conclude that inflation expectations Granger cause CPI inflation at this

horizon. Non-causality is present if the forecasting performance of the

bivariate model is worse than that of the univariate model.

The second comparison we take into account other, potentially important, variables.

This is done using a trivariate model with CPI-inflation, the unemployment

rate and the three month treasury bill rate

x u

i

(4)

t

t

t

t

and a model with four variables defined as

x , (5)

t

e

u i

t

t

t

t

where

u

t

is the unemployment rate in the age group 15-74 years (seasonally

adjusted using Tramo/Seats), i t

is the three month treasury bill rate and

e

and

t

are defined as above. The trivariate specification seems like a reasonable

benchmark for a “larger” model. Trivariate VARs with these variables are

commonly used in the macroeconomic literature; see, for example, Cogley and

Sargent (2001), Primiceri (2005) and Ribba (2006).

t

We focus on the RMSFE of the models and do not conduct any hypothesis

tests regarding the forecast precision. We argue that this is a reasonable ap-

12

proach when evaluating the addition of a variable to a model. 14 When the purpose

of the model purely is forecasting, the forecaster would – in the choice

between two models that are considered equally likely a priori – generally choose

the model with the smallest RMSFE. 15

4. Forecast comparisons

In this section we analyse the out-of-sample forecast performance using quarterly

data from 1996Q1 to 2016Q1. 16 Data on CPI inflation and inflation

expectations are given in Figure 1. The unemployment rate and three

month treasury bill rate are shown in Figure A1 in Appendix A. 17

We compare the forecasting performance of the bivariate specification in equation

(3) with the univariate specification in equation (2). In addition, we compare

the forecasting performance of the fourvariate specification in equation (5) with

the trivariate specification in equation (4). 18 More specifically, the out-of-sample

forecast exercise is conducted the following way: All models are first estimated

for a training period of eight years, using data from 1996Q1 to 2003Q4. 19 Forecasts

one to twelve quarters ahead (2004Q1-2006Q4) are then generated and

forecast errors are recorded. The sample is then extended one quarter, the models

are re-estimated and new forecasts twelve quarters ahead are generated. This

procedure stops at the end of the sample; the last forecasts are generated based

on an estimation using data from 1996Q1 to 2015Q4. The forecast comparisons

in this study are thus based on between 38 and 49 forecasts depending on the

forecast horizon.

14 To our knowledge, no valid test exists to test the null hypothesis of equal forecasting

performance in our setting. The problem is that we compare forecasts from nested models

estimated with Bayesian methods at forecast horizons exceeding one.

15 However, if one wants to do scenario analysis – where the effect of one variable on another is

of interest – it is not unreasonable to choose the model with a higher RMSFE. As an extreme

example, consider the case where a univariate model has the smallest out-of-sample RMSFE. Of

course, such a model can not tell us anything about what happens when other related variables

vary.

16 The inflation target policy was declared in 1993 but it was not until 1996 that interest rates

began to come down to more normal levels.

17 Note that the inflation expectations and the three month treasury bill rate are not revised.

Hence, the latest vintage is equal to real-time data. Inflation and the unemployment rate are

subject to minor revisions. The fact that we do not use real-time data for these variables should

hence have only minor effects on our results. For a discussion concerning real-time data, see

Croushore and Stark (2001).

18 The forecast precision of the individual categories of inflation expectations when they are not

used in models (but simply used as predictors of future inflation as they are) are shown in Table

A7 in Appendix C.

19 The numerical evaluation of the posterior distribution is conducted using the Gibbs sampler and

the number of draws is set to 10 000.

13

The differences in RMSFE for CPI-inflation between the univariate model and

the bivariate ones are shown in Figure 2. 20 A positive RMSFE difference signals

that the particular inflation expectation series contributes to better out-ofsample

forecasts.

Looking at the inflation expectations from the NIER’s survey first, it can

be noted that the two bivariate models with these included have lower

RMSFEs than the univariate model at forecast horizons up to seven and

eight quarters when household and business expectations are used respectively.

The improvement in RMSFE peaks at the two to three-quarter horizons.

The reduction in the RMSFE relative to the univariate model is larger

when business expectations are used. However, improvements are typically

small relative to the level of the RMSFE. Only at the three shortest horizons

when using the business expectations can a reduction of the RMSFE

of more than thirteen per cent be found; see Table A5 in Appendix C.

Figure 2. Reduction in RMSFE by adding inflation expectations to the univariate

model of CPI-inflation

.16

.12

.08

.04

.00

-.04

1 2 3 4 5 6 7 8 9 10 11 12

Prospera, 1 year

Prospera, 2 years

Prospera, 5 years

NIER, businesses

NIER, households

Note: Reduction in RMSFE is given in percentage points on the vertical axis. A positive number

indicates that the model with inflation expectations has a lower RMSFE than the model without

inflation expectations. Forecast horizon in quarters on the horizontal axis.

20 The RMSFEs of the different models are given in Tables A2 and A3 in Appendix C. Table A4 in

Appendix C gives the RMSFEs of two commonly used benchmarks, namely a naïve forecast and a

recent mean forecast.

14

When the inflation expectations of TNS Sifo Prospera are employed, we

find that the results are similar regardless of whether the one-, two- or fiveyear

inflation expectations are studied (see Figure 2). It can be noted

though that the profile of the difference in RMSFEs is different to when

the NIER’s survey data were used. Forecast precision is actually reduced at

short horizons. At horizons of four quarters or larger, the RMSFE is reduced

when the inflation expectations are included in the model but the

reduction in the RMSFE is very small; in no case is the RMSFE reduced by

more than 0.04 percentage points.

The differences in RMSFEs between the trivariate model and fourvariate ones

are shown in Figure 3. In general, we find that inflation expectations tend to

Granger cause inflation; the RMSFEs of the fourvariate models are generally

lower than that of the trivariate model. Similar to the comparison between

the univariate and bivariate models above, we again find that the profile of

the improvement in forecast precision differs depending on which survey

has been used. The two series from the NIER’s survey both reduce the

RMSFE the most at the three-quarter horizon whereas the three series

from the TNS Sifo Prospera survey appear to be most useful at longer horizons.

Comparing Figures 2 and 3, it can be seen that the three series from the

TNS Sifo Prospera survey reduce the RMSFE approximately as much when

moving from a trivariate to a fourvariate model as when moving from a

univariate to a bivariate model. The largest improvement in forecast precision

– when comparing the fourvariate models and the trivariate model

over all horizons and inflation expectation series – is found at the threequarter

horizon when the NIER’s business expectations are used; the fourvariate

model then has an RMSFE which is 0.12 percentage points lower

than the trivariate model. This is a non-negligible improvement – corresponding

to a nine per cent reduction in the RMSFE; see Table A6 in Appendix

C. However, the results shown in Figure 3 do not point to quantitatively

meaningful reductions in RMSFEs in general.

15

Figure 3. Reduction in RMSFE by adding inflation expectations to the trivariate

model of CPI-inflation

.12

.08

.04

.00

-.04

-.08

1 2 3 4 5 6 7 8 9 10 11 12

Prospera, 1 year

Prospera, 2 years

Prospera, 5 years

NIER, businesses

NIER, households

Note: Reduction in RMSFE is given in percentage points on the vertical axis. A positive number

indicates that the model with inflation expectations has a lower RMSFE than the model without

inflation expectations. Forecast horizon in quarters on the horizontal axis.

Summing up, we have found that adding inflation expectations to a model

generally tends to reduce the RMSFE and, hence, that inflation expectations

Granger cause inflation. However, the magnitude of the improvement

is typically small and often not quantitatively meaningful. Our results are

accordingly not very encouraging concerning the usefulness of the inflation

expectations when it comes to improving the precision of VAR-based inflation

forecasts in practice.

5. Sensitivity analysis

Bayesian estimation makes use of priors which can affect the conclusions.

An easy and transparent way to assess the importance of the priors (and

hyperparameters) is to simply abandon the Bayesian framework completely

and conduct the exercises using a classical framework.

In this section we accordingly perform the same out-of-sample forecast

exercise as that described in Section 4 but with the traditional VAR model

G

L x c η ,

t

(6)

t

16

where c is an nx1 vector vector of intercepts;

G L, x

t

and

η

t

are all defined

as above. The model is here estimated using classical methods, that is, the

estimated parameters of (6) maximizes the likelihood function.

Results are shown in tables A10 to A13 in Appendix C and are generally in

line with the results discussed in Section 4. The only meaningful improvement

in RMSFE found is at short horizons when the expectations of businesses

in the National Institute of Economic Research’s Economic Tendency

Survey are used. It can be noted that the RMSFEs of the bivariate classical

VAR models are generally smaller than those of the bivariate BVAR models,

a finding that perhaps is somewhat surprising given that the BVARs

often are considered better forecasting tools than VARs estimated with

classical methods. In addition, the reductions compared to the benchmark

univariate model are typically bigger using classical VARs. However, the

problems associated with overparameterisation do show up also in this

study. For the larger VARs, forecast precision often deteriorates when inflation

expectations are included in the model; see Tables A11 and A13 in

Appendix C and compare them with the corresponding BVAR results in

Tables A3 and A6.

6. Conclusions

In this paper, we have taken the forecaster’s perspective on survey

measures of inflation expectations and investigated whether inflation expectations

in Sweden Granger cause Swedish CPI-inflation. This was done by

studying the accuracy of out-of-sample forecasts from Bayesian VAR models.

It was found that the inclusion of inflation expectations in the models

tends to improve forecast precision. The improvement is typically very

small though and does in general not seem economically relevant. One

exception can possibly be found in the expectations of businesses in the

National Institute of Economic Research’s Economic Tendency Survey; when

included in the models, these improve forecast precision at short horizons

in a meaningful way. It accordingly appears that the survey measures of

inflation expectations studied in this paper are of limited usefulness to

those who try to improve VAR-based forecasts of Swedish CPI inflation.

17

In order to achieve a quantitatively meaningful improvement, he or she

should most likely look elsewhere.

That the inflation expectations do not seem particularly useful to VAR

modellers does not mean that they are collected in vain though. From a

policy perspective, survey expectations can still provide relevant information

concerning, for example, the credibility of the inflation target or

other challenges that a central bank might face when conducting monetary

policy.

18

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20

Appendix A – Data

Figure A1. Unemployment rate and interest rate.

Unemployment

3 months treasury bill

12

8

11

10

6

9

4

8

2

7

6

0

5

96 98 00 02 04 06 08 10 12 14

-2

96 98 00 02 04 06 08 10 12 14

Note: Both variables are measured in per cent.

Figure A2. Inflation expectations, TNS Sifo Prospera, Money market players

3.0

TNS Sifo Prospera, Money market players, 1 year

2.8

TNS Sifo Prospera, Money market players, 2 years

2.5

2.4

2.0

2.0

1.5

1.6

1.0

1.2

0.5

96 98 00 02 04 06 08 10 12 14

0.8

96 98 00 02 04 06 08 10 12 14

3.2

TNS Sifo Prospera, Money market players, 5 years

2.8

2.4

2.0

1.6

96 98 00 02 04 06 08 10 12 14

21

Appendix B – Steady-state priors

Table A1. Steady-state priors.

Variable

Prior interval

u

t

(5.0; 8.0)

t

(1.0; 3.0)

i

t

(3.0; 5.0)

e

(1.0; 3.0)

t

Note: Ninety-five per cent prior probability intervals for parameters determining the unconditional

means. Prior distributions are all assumed to be normal. Variables are defined in equations (3)

and (5).

22

Appendix C – RMSFEs and relative

RMSFEs

Table A2. RMSFEs of univariate and bivariate models.

Horizon Univariate Prospera,

1 year

Prospera,

2 years

Bivariate models

Prospera,

5 years

NIER,

businesses

NIER,

households

1Q 0.59 0.61 0.61 0.61 0.53 0.56

2Q 0.99 1.00 0.99 1.00 0.86 0.94

3Q 1.28 1.28 1.27 1.28 1.14 1.21

4Q 1.48 1.47 1.46 1.48 1.37 1.42

5Q 1.57 1.55 1.54 1.56 1.49 1.52

6Q 1.59 1.56 1.56 1.56 1.54 1.55

7Q 1.58 1.56 1.55 1.55 1.55 1.56

8Q 1.56 1.53 1.53 1.52 1.56 1.56

9Q 1.52 1.51 1.50 1.49 1.55 1.54

10Q 1.50 1.48 1.48 1.47 1.54 1.52

11Q 1.48 1.46 1.46 1.44 1.51 1.49

12Q 1.47 1.46 1.46 1.45 1.50 1.49

Table A3. RMSFEs of trivariate and fourvariate models.

Horizon Trivariate Prospera,

1 year

Prospera,

2 years

Fourvariate models

Prospera,

5 years

NIER,

businesses

NIER,

households

1Q 0.62 0.63 0.62 0.61 0.55 0.56

2Q 1.02 1.02 1.01 1.01 0.92 0.93

3Q 1.33 1.31 1.30 1.31 1.21 1.22

4Q 1.55 1.50 1.50 1.51 1.43 1.45

5Q 1.66 1.61 1.60 1.61 1.56 1.58

6Q 1.71 1.66 1.65 1.66 1.63 1.65

7Q 1.73 1.68 1.68 1.68 1.67 1.69

8Q 1.73 1.67 1.68 1.68 1.70 1.70

9Q 1.71 1.66 1.66 1.66 1.70 1.69

10Q 1.69 1.63 1.64 1.63 1.69 1.67

11Q 1.64 1.60 1.61 1.59 1.68 1.63

12Q 1.60 1.57 1.57 1.55 1.65 1.59

Table A4. RMSFEs of alternative forecasts.

Horizon

Naïve

forecast

Recent

mean

forecast

1Q 0.65 1.43

2Q 1.10 1.50

3Q 1.47 1.55

4Q 1.77 1.57

5Q 1.96 1.58

6Q 2.07 1.56

7Q 2.15 1.53

8Q 2.16 1.48

9Q 2.12 1.44

10Q 2.06 1.40

11Q 1.98 1.39

12Q 1.91 1.40

Note: The recent mean forecasts are based on the mean of the last twelve observations preceding

the forecast date.

23

Table A5. RMSFEs of the univariate model and relative RMSFEs of the

bivariate models.

Horizon Univariate

RMSFEs

Prospera,

1 year

Bivariate models (relative RMSFEs)

Prospera,

2 years

Prospera,

5 years

NIER,

businesses

NIER,

households

1Q 0.59 1.03 1.03 1.03 0.90 0.95

2Q 0.99 1.01 1.00 1.01 0.87 0.95

3Q 1.28 1.00 0.99 1.00 0.89 0.95

4Q 1.48 0.99 0.98 1.00 0.92 0.96

5Q 1.57 0.98 0.98 0.99 0.95 0.97

6Q 1.59 0.98 0.98 0.98 0.97 0.97

7Q 1.58 0.99 0.98 0.98 0.98 0.99

8Q 1.56 0.98 0.98 0.98 1.00 1.00

9Q 1.52 0.99 0.99 0.98 1.02 1.01

10Q 1.50 0.99 0.99 0.98 1.03 1.02

11Q 1.48 0.99 0.99 0.97 1.02 1.01

12Q 1.47 0.99 0.99 0.99 1.02 1.01

Note: The relative RMSFE is defined as the RMSFE of the bivariate model divided by the RMSFE of

the univariate model. A value smaller than one accordingly implies that the RMSFE of the

bivariate model is smaller than that of the univariate model.

Table A6. RMSFEs of the trivariate model and relative RMSFEs of the

fourvariate models.

Horizon Trivariate

RMSFEs

Prospera,

1 year

Fourvariate models (relative RMSFEs)

Prospera,

2 years

Prospera,

5 years

NIER,

businesses

NIER,

households

1Q 0.62 1.02 1.01 0.99 0.89 0.91

2Q 1.02 1.00 0.99 0.99 0.90 0.91

3Q 1.33 0.99 0.98 0.99 0.91 0.92

4Q 1.55 0.97 0.97 0.98 0.93 0.94

5Q 1.66 0.97 0.97 0.97 0.94 0.95

6Q 1.71 0.97 0.97 0.97 0.96 0.97

7Q 1.73 0.97 0.97 0.97 0.97 0.98

8Q 1.73 0.97 0.97 0.97 0.98 0.98

9Q 1.71 0.97 0.97 0.97 0.99 0.99

10Q 1.69 0.97 0.97 0.97 1.00 0.99

11Q 1.64 0.98 0.98 0.97 1.02 0.99

12Q 1.60 0.98 0.98 0.97 1.03 0.99

Note: The relative RMSFE is defined as the RMSFE of the fourvariate model divided by the RMSFE

of the trivariate model. A value smaller than one accordingly implies that the RMSFE of the

fourvariate model is smaller than that of the trivariate model.

Table A7. RMSFEs of inflation expectations

Horizon

Prospera,

1

year

Prospera,

2

years

Prospera,

5

years

Prospera

MMP,

1 year

Prospera

MMP, 2

years

Prospera

MMP, 5

years

NIER,

businesses

NIER,

house

holds

1Q 1.01 1.29 1.61 0.95 1.36 1.61 0.92 1.26

2Q 1.18 1.37 1.64 1.08 1.39 1.62 0.90 1.35

3Q 1.38 1.48 1.68 1.26 1.44 1.64 1.00 1.46

4Q 1.54 1.58 1.72 1.41 1.50 1.65 1.17 1.61

5Q 1.62 1.64 1.73 1.50 1.54 1.65 1.33 1.71

6Q 1.69 1.68 1.74 1.57 1.57 1.65 1.44 1.78

7Q 1.74 1.73 1.76 1.63 1.61 1.66 1.53 1.84

8Q 1.74 1.75 1.76 1.65 1.64 1.67 1.63 1.91

9Q 1.72 1.75 1.78 1.65 1.66 1.68 1.68 1.93

10Q 1.69 1.75 1.80 1.63 1.67 1.71 1.70 1.94

11Q 1.65 1.74 1.81 1.61 1.68 1.73 1.67 1.95

12Q 1.62 1.74 1.83 1.59 1.70 1.76 1.62 1.95

Note: The RMSFEs have been calculated by comparing the expectation with the actual value at

each horizon (regardless of the intended horizon of the inflation expectations). MMP=money

market players.

24

Figure A3. Reduction in RMSFE by adding inflation expectations to the univariate

model of CPI-inflation – Money market players

.04

.03

.02

.01

.00

-.01

-.02

1 2 3 4 5 6 7 8 9 10 11 12

Prospera, Money market players, 1 year

Prospera, Money market players, 2 years

Prospera, Money market players, 5 years

Note: Reduction in RMSFE given in percentage points on the vertical axis. A positive number

indicates that the model with inflation expectations has a lower RMSFE than the model without

inflation expectations. Forecast horizon in quarters on the horizontal axis.

Figure A4. Reduction in RMSFE by adding inflation expectations to the trivariate

model of CPI-inflation – Money market players

.07

.06

.05

.04

.03

.02

.01

.00

-.01

1 2 3 4 5 6 7 8 9 10 11 12

Prospera, Money market players, 1 year

Prospera, Money market players, 2 years

Prospera, Money market players, 5 years

Note: Reduction in RMSFE given in percentage points on the vertical axis. A positive number

indicates that the model with inflation expectations has a lower RMSFE than the model without

inflation expectations. Forecast horizon in quarters on the horizontal axis.

25

Table A8. RMSFEs of univariate and bivariate models – Money market

players.

Horizon Univariate Prospera,

1 year

Bivariate models

Prospera,

2 years

Prospera,

5 years

1Q 0.59 0.61 0.61 0.60

2Q 0.99 0.99 0.99 1.00

3Q 1.28 1.27 1.26 1.28

4Q 1.48 1.46 1.46 1.48

5Q 1.57 1.54 1.54 1.56

6Q 1.59 1.56 1.56 1.57

7Q 1.58 1.56 1.56 1.55

8Q 1.56 1.54 1.54 1.52

9Q 1.52 1.52 1.51 1.50

10Q 1.50 1.49 1.49 1.47

11Q 1.48 1.47 1.47 1.46

12Q 1.47 1.47 1.46 1.46

Table A9. RMSFEs of trivariate and fourvariate models – Money market

players.

Horizon Trivariate Prospera,

1 year

Fourvariate models

Prospera,

2 years

Prospera,

5 years

1Q 0.62 0.62 0.60 0.61

2Q 1.02 1.00 0.99 1.01

3Q 1.33 1.29 1.27 1.30

4Q 1.55 1.50 1.48 1.51

5Q 1.66 1.60 1.60 1.62

6Q 1.71 1.66 1.66 1.69

7Q 1.73 1.68 1.69 1.72

8Q 1.73 1.69 1.70 1.72

9Q 1.71 1.68 1.69 1.70

10Q 1.69 1.65 1.67 1.65

11Q 1.64 1.62 1.63 1.60

12Q 1.60 1.59 1.60 1.55

26

Table A10. RMSFEs of univariate and bivariate models – OLS

estimation.

Horizon Univariate Prospera,

1 year

Prospera,

2 years

Bivariate models

Prospera,

5 years

NIER,

businesses

NIER,

households

1Q 0.56 0.62 0.57 0.50 0.50 0.54

2Q 0.97 0.95 0.90 0.90 0.76 0.97

3Q 1.24 1.27 1.21 1.24 1.01 1.24

4Q 1.44 1.52 1.43 1.47 1.27 1.43

5Q 1.50 1.59 1.50 1.54 1.44 1.57

6Q 1.48 1.58 1.50 1.53 1.49 1.65

7Q 1.44 1.54 1.47 1.48 1.47 1.66

8Q 1.41 1.51 1.45 1.44 1.46 1.59

9Q 1.39 1.46 1.43 1.41 1.45 1.50

10Q 1.40 1.40 1.41 1.40 1.43 1.47

11Q 1.41 1.40 1.40 1.40 1.43 1.49

12Q 1.42 1.38 1.40 1.41 1.44 1.50

Table A11. RMSFEs of trivariate and fourvariate models – OLS

estimation.

Horizon Trivariate Prospera,

1 year

Prospera,

2 years

Fourvariate models

Prospera,

5 years

NIER,

businesses

NIER,

households

1Q 0.61 0.76 0.68 0.59 0.58 0.63

2Q 1.10 1.26 1.15 1.09 0.98 1.12

3Q 1.49 1.59 1.52 1.46 1.29 1.46

4Q 1.80 1.90 1.86 1.74 1.58 1.77

5Q 1.86 1.88 1.89 1.78 1.78 1.89

6Q 1.78 1.74 1.71 1.74 1.82 1.87

7Q 1.73 1.72 1.66 1.78 1.85 1.84

8Q 1.72 1.77 1.68 1.83 2.01 1.84

9Q 1.75 1.84 1.76 1.86 2.17 1.78

10Q 1.84 2.03 1.92 1.88 2.30 1.75

11Q 1.87 2.09 2.01 1.92 2.39 1.74

12Q 1.83 2.07 2.02 1.90 2.41 1.74

27

Table A12. RMSFEs of the univariate model and relative RMSFEs of the

bivariate models – OLS estimation.

Horizon Univariate

RMSFEs

Prospera,

1 year

Bivariate models (relative RMSFEs)

Prospera,

2 years

Prospera,

5 years

NIER,

businesses

NIER,

households

1Q 0.56 1.11 1.02 0.89 0.89 0.96

2Q 0.97 0.98 0.93 0.93 0.79 1.01

3Q 1.24 1.03 0.98 1.00 0.82 1.00

4Q 1.44 1.06 1.00 1.02 0.89 1.00

5Q 1.50 1.06 1.00 1.03 0.96 1.05

6Q 1.48 1.07 1.01 1.04 1.01 1.12

7Q 1.44 1.07 1.02 1.03 1.02 1.15

8Q 1.41 1.07 1.03 1.02 1.04 1.13

9Q 1.39 1.05 1.03 1.01 1.04 1.08

10Q 1.40 1.00 1.01 1.00 1.03 1.05

11Q 1.41 0.99 0.99 0.99 1.02 1.06

12Q 1.42 0.97 0.98 0.99 1.01 1.05

Note: The relative RMSFE is defined as the RMSFE of the bivariate model divided by the RMSFE of

the univariate model. A value smaller than one accordingly implies that the RMSFE of the

bivariate model is smaller than that of the univariate model.

Table A13. RMSFEs of the trivariate model and relative RMSFEs of the

fourvariate models – OLS estimation.

Horizon Trivariate

RMSFEs

Prospera,

1 year

Fourvariate models (relative RMSFEs)

Prospera,

2 years

Prospera,

5 years

NIER,

businesses

NIER,

households

1Q 0.61 1.25 1.12 0.97 0.95 1.04

2Q 1.10 1.15 1.05 0.99 0.89 1.02

3Q 1.49 1.07 1.02 0.98 0.86 0.98

4Q 1.80 1.06 1.03 0.97 0.88 0.98

5Q 1.86 1.01 1.02 0.96 0.96 1.02

6Q 1.78 0.98 0.96 0.98 1.02 1.05

7Q 1.73 0.99 0.96 1.03 1.07 1.06

8Q 1.72 1.03 0.97 1.06 1.17 1.07

9Q 1.75 1.05 1.01 1.06 1.24 1.02

10Q 1.84 1.10 1.04 1.02 1.25 0.95

11Q 1.87 1.12 1.07 1.02 1.28 0.93

12Q 1.83 1.13 1.10 1.04 1.32 0.95

Note: The relative RMSFE is defined as the RMSFE of the fourvariate model divided by the RMSFE

of the trivariate model. A value smaller than one accordingly implies that the RMSFE of the

fourvariate model is smaller than that of the trivariate model.

28

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