Bachelor thesis...Bachelor thesis Department of Statistics Nr 2014:x Measuring Real Economic Uncertainty in Sweden Alexander Thorleifsson, Johan Malmström Bachelor Thesis, 15 hp within

Bachelor thesis

Department of Statistics

Nr 2014:x

Measuring Real Economic

Uncertainty in Sweden

Alexander Thorleifsson, Johan Malmström

Bachelor Thesis, 15 hp within Statistics III, VT2014

Supervisor: Pär Stockhammar

Abstract

The main question studied through this thesis has been what impact economic

uncertainty really has on the development of GDP. The aim has been to forecast the

future development of GDP, based on the current real uncertainty level. The

motivation for this is to underpin fiscal policy decisions. We have therefore

constructed a new index measuring real economic uncertainty and named it, real

economic uncertainty index for Sweden (REU). The REU index is constructed by

using three independent components; disagreement among official forecasts regarding

GDP and CPI from nine different institutions and the conditional variance of

households’ and firms’ expectations about the future. Based on previous measurements

for estimating economic uncertainty, our index is proposed to serve as a tool for

analysing the growth of GDP. The REU index provides strong indications that real

uncertainty is countercyclical; the index rises sharply during the financial crisis of

2008-2009 and displays low levels during the economically strong years of 2004-2007.

The REU index can be considered a good approximation of the progress, and provide

an overall picture of the real economic uncertainty. Presented analysis in Vector

Autoregressive (VAR) models provide support that increased real economic

uncertainty leads to a temporary decline in economic activity and the index precedes a

structural break in GDP growth.

Keywords: economic uncertainty, index, GDP growth, Vector Autoregressive model,

impulse-response.

Sammanfattning

Huvudfrågan att besvara med denna uppsats har varit vilken påverkan egentligen

ekonomisk osäkerhet har på utvecklingen av BNP. Syftet är att kunna prognostisera

framtida utveckling av BNP, utifrån aktuell real osäkerhetsnivå. Detta för att kunna

underbygga finanspolitiska beslut. Vi har därför konstruerat ett nytt index som mäter

realekonomisk osäkerhet och har fått namnet; realekonomiskt osäkerhetsindex för

Sverige (REO). REO är konstruerat av tre oberoende komponenter; oenighet bland

officiellt publicerade prognoser gällande BNP och KPI samt den betingade variansen

av hushållens och företagens förväntningar på framtiden. Baserat på tidigare

mätmetoder för att estimera ekonomisk osäkerhet så är vårt index tänkt att fungera

som ett verktyg för att analysera utvecklingen av BNP. REO indexet ger starka

indikationer på att real osäkerhet är kontracyklisk, indexet stiger kraftigt under

finanskrisen 2008-2009 och ligger på låga nivåer under de ekonomiskt starka åren

2004-2007. Indexet kan därför anses vara en bra approximation på utvecklingen, samt

ge en samlad bild av realekonomisk osäkerhet. Genomförda analyser i Vector

Autoregressiva (VAR) modeller styrker att ökad realekonomisk osäkerhet leder till en

temporär nedgång i den ekonomiska aktiviteten samt att vårt index föregår ett

trendbrott i BNPs utveckling.

Nyckelord: ekonomisk osäkerhet, index, utveckling av BNP, Vector Autoregressiv modell, impuls-respons.

Acknowledgements

We thank Pär Stockhammar, Greta Gram and Alex Spetz for comments and research support.

List of Abbreviations

ADF Augmented Dickey-Fuller test

AIC Akaike information criterion

ARCH Autoregressive Conditional Heteroskedasticity

CPI Consumer Price Index

CVE Conditional Variance of Expectations

Disagreement (GDP) the spread in GDP growth forecasts

Disagreement (CPI) the spread in CPI growth forecasts

EPU European Policy Uncertainty

ESI Economic Sentiment Indicator

ETS Economic Tendency Survey

FiD Ministry of Finance National

GARCH Generalized Autoregressive Conditional Heteroskedasticity

GDP Gross Domestic Product

GFCF Gross Fixed Capital Formation

HUI HUI Research

LO Swedish Trade Union Confederation

NIER National Institute of Economic Research

RB the Swedish Riksbank

REU Real Economic Uncertainty Index for Sweden

SEB Skandinaviska Enskilda Banken

SHB Svenska Handelsbanken

SIC Schwarz information criterion

SN Confederation of Swedish Enterprise

TED Acronym formed from T-Bill and ED, the ticker symbol for the Eurodollar futures contract

VAR Vector Autoregression

Table of Contents

1 Introduction .............................................................................................................. 9

1.1 Background .......................................................................................................... 9

1.2 An Uncertainty Index for the Real Economy in Sweden ................................. 11

1.2.1 Purpose ..................................................................................................... 11

1.2.2 Goals ......................................................................................................... 11

1.2.3 Working Hypotheses ............................................................................... 11

1.2.4 Delimitations ............................................................................................ 11

1.2.5 Our Real Economic Uncertainty (REU) Index ....................................... 12

1.3 Disposition ......................................................................................................... 12

2 Data ........................................................................................................................ 14

3 Methodology .......................................................................................................... 18

3.1 The Index Components ..................................................................................... 18

3.1.1 Forecasts ................................................................................................... 18

3.1.2 Expectations among Households and Businesses ................................... 20

3.2 Weights ............................................................................................................. 23

3.3 Choosing the Best Weighted Index .................................................................. 26

3.4 Methods of Analysis .......................................................................................... 27

3.4.1 Vector Autoregression (VAR) .................................................................. 27

3.4.2 Granger Causality .................................................................................... 27

3.4.3 The Impulse Response Function ............................................................. 28

3.4.4 Comparisons ............................................................................................. 28

4 Results .................................................................................................................... 29

4.1 Real Uncertainty and GDP ............................................................................... 29

4.2 Comparison to Other Indices ............................................................................ 33

5 Discussion ............................................................................................................... 34

5.1 Analysis and Practical Implementation of the Results ..................................... 34

5.2 Methodological Criticism .................................................................................. 35

6 Conclusions ............................................................................................................. 37

6.1 Suggestions for Further Studies ....................................................................... 37

References ....................................................................................................................... 38

Web ................................................................................................................................. 38

Bibliography ................................................................................................................... 38

7 Appendix ................................................................................................................. 40

7.1 GDP Components ............................................................................................. 40

7.2 Information Criteria .......................................................................................... 40

7.3 ARCH(1) ............................................................................................................ 41

7.4 PCA Output ....................................................................................................... 42

7.5 AR Root Tables (VAR Stability Tests) ............................................................. 42

7.6 Augmented Dickey-Fuller Tests ....................................................................... 43

7.7 Likelihood Ratio (LR) Test................................................................................ 45

7.8 Links to Data Sources ........................................................................................ 45

1 Introduction

In this introduction background of the thesis, previous studies and problem description is presented initially. Together they lead us to a presentation of our constructed index with purpose, goals, delimitations and a short summary of our analysis.

1.1 Background

The economic condition of a country and its growth is primarily measured by its Gross Domestic Product (GDP). A variety of variables affect GDP and it is therefore difficult to predict its future growth. At the same time it is important for the government to forecast real economy, the GDP growth as accurately as possible, since the projections work as reference for government policy and economic development. Unexpected shocks are not possible to forecast, shocks that may lead to adverse cyclical and reduced GDP growth. These disturbances often coincide with increased uncertainty about the future among households, businesses and the financial sector. According to studies on the topic such as Baker et al (2013) economic policy uncertainty has increased in recent years, both in the United States and in the EU.

But what does increased uncertainty lead to and what is the impact on GDP as a result of it? These questions are initially answered by referring to previous published literature on the subject and Bernanke (1983) concludes that high uncertainty give companies incentive to postpone planned investments and recruitment due to the accompanying uncertainty about future demand for the firms’ products and services. When uncertainty decreases and the future becomes clearer, companies once again starts hiring and implementing delayed investments. An increased uncertainty level also affects households and their propensity for consumption. Instead, households tend to increase their will to save during periods of high uncertainty. These two factors affect GDP negatively, since the consumption of households and the investment of businesses account for about two thirds of the total Swedish GDP, see Appendix 7.1 for details. The Government therefore desires, as early as possible, to get an indication of changes in uncertainty level in order to achieve accurate forecasts and forming policies to meet economic downturns.

The topic of economic uncertainty is relatively young; little research about economic uncertainty indices and adequately measures has been published so far. The first problem all economists face, is to define uncertainty and especially economic uncertainty. The future is always uncertain. It is not possible to predict various unexpected events, since they can occur at any time. Uncertainty can be compared to risk, where events follow a probability distribution and can be estimated. According to Knight (1964) it is not possible to estimate uncertainty. It is therefore difficult to define economic uncertainty based on Knights arguments since it is a latent variable. Among economists and analysts, there is considerable divergence in defining economic uncertainty and no consensus has been reached.

There is currently no robust index of real economic uncertainty in Sweden with direct link to GDP growth but some previous studies have approached the subject and discussed how to approximate economic uncertainty. The Swedish Riksbank conducts the most relevant and influential Swedish research on the subject, written by Sandahl

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et al (2011) where they present a stress index measuring uncertainty in the financial sector as a consequence of the unexpected financial crisis of 2008. Their index is composed of four components, three stress indicators representing the capital markets; (i) implicit volatility in the stock market, (ii) TED spreads, and (iii) bond spreads. The one indicator representing the currency market is volatility. These four indicators provide, according to the Riksbank’s first version, an adequate picture of observed financial uncertainty. In the year 2013, the Riksbank updated and further developed the index, made by the authors Johansson and Bonthron (2013), which mainly added more indicators, extended the comparative time period and used ranked indicators rather than absolute indicators.

The Ministry of Finance (FiD) is the State agency on behalf of the Swedish Government that performs the forecasts underpinning policy actions. The FiD mainly do their predictions based on various macroeconomic indicators obtained from different agencies and interest groups. In a report by Bjellerup and Shahnazarian (2013), they concluded with various tests that the inclusion of the Riksbank’s stress index along with their own macro indicators provide better forecasts of GDP growth than without the stress index components. They base their assumption and conclusion on the transformation mechanism, which describes how a disturbance and increased uncertainty in the financial sector transmits to the real economy and affect GDP growth. The FiD gets, when including the stress index, an additional component approximating the latent variable uncertainty and improves their forecast model.

In recent years some international research on the topic has been conducted and the most well-known is the studies of Baker et al (2013) that has created an economic policy uncertainty index for the United States. Later they also developed indices for the EU and some other economies. Their index is a new measure of economic policy uncertainty for the United States and dates back to 1985 with the help of three components: (i) the existence of policy-related words of economic uncertainty in the 10 largest newspapers in the United States; (ii) the number and projected revenue effects of federal tax code provisions set to expire in future years and (iii) the extent of disagreement among economic forecasters about future government purchases and future inflation. In Baker et al (2013), the authors present strong evidence that political uncertainty has increased since the financial crisis and also finds evidence that the increased uncertainty has impeded economic recovery.

Other international studies that attempted to measure uncertainty have used similar methods. These include surprise indices that summarize surprises in economic data and deviation from consensus forecasts were the consensus in this context is produced by averaging expert forecasts while the dispersion of individual forecasts around this average is made into a measure of uncertainty as in Zarnowitz and Lambros (1983) and Scotti (2012). The relationship between uncertainty and recessions is a common thread through many of the studies performed on this subject. In Bloom et al (2007), recessions are partly caused by increased uncertainty, which in turn creates a fall in productivity growth. Existing research has also focused on qualitative survey data, as in Fuss and Vermeulen (2008) who base their measure of uncertainty on business surveys in which companies report their own subjective outlook on future performance, specifically on future demand and changes in output prices.

An index measuring real economic uncertainty has to date not been developed for the Swedish economy but sources from the National Institute of Economic Research (NIER) argues for a need and interest for one. The Riksbank’s stress index can to be seen as an approximation of economic uncertainty and the transformation mechanism is an acceptable assumption; increased uncertainty in the financial sector leads to negative growth of GDP. But wouldn’t it be quite better if there existed an index that exclusively measured the real economic uncertainty of Sweden? In the following paper, focus is given to constructing an economic uncertainty index and try to solve the problem of defining real uncertainty.

1.2 An Uncertainty Index for the Real Economy in Sweden

1.2.1 Purpose

The purpose of this thesis is to develop an appropriate index of real economic uncertainty that can be seen as a complement to the Riksbank’s financial stress index. Our index can be seen as a new and creative element in the debate about the economic uncertainty and how to measure it. Furthermore, our index should facilitate comparisons between different periods of uncertainty. This will lead to a greater understanding and insight of what causes real economic uncertainty and how it affects the real economy in Sweden.

1.2.2 Goals

The main goal and the core of this thesis is to consider the observed real problem; the absence of a robust real economic uncertainty index, and translate it into a statistical problem and solve it in the best way possible. Our goal with this thesis is therefore to develop a useful statistical model and forecasting tool for estimating future GDP. It shall also be easy to update and not require advanced statistical skills to use.

1.2.3 Working Hypotheses

In order to achieve our goals with this thesis, we state two hypotheses that we try to answer by using relevant models and test procedures. These are: (i) Is it possible to develop a useful real economic uncertainty index for Sweden and if so; how should this index be designed, which suitable components measure real economic uncertainty in a proper way and what kind of model gives the best forecast? (ii) What impact has an uncertainty shock, based on the created index, on Swedish GDP and its components?

1.2.4 Delimitations

Based on limited time and budget for this thesis, the following delimitations has been made in order to design the most accurate and comprehensive thesis as possible for its specific purpose. This thesis is focused on the challenge of a statistical development and construction of a useful model for its specific purpose. In a wider perspective, one could also go into the macro-economic arguments and recommendations that our index could provide. This is outside the scope of the thesis but is possible to be developed at a later time or by others. We will only examine the economy of Sweden and the experienced real economic uncertainty. The REU index can be seen as a first

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version and it would be very time consuming to also study and develop relevant components for other countries. It is however possible that the REU index can work as a foundation and inspiration for developing similar indices for other countries. Studies and analysis is only made in relation to GDP and its components, if additional time and resources had been available, it would have been interesting to examine and evaluate the index’s effect on unemployment and inflation. Our purpose is to develop an accurate uncertainty index for the real economy so no financial uncertainty has been taken into account.

1.2.5 Our Real Economic Uncertainty (REU) Index

The way we handle the problem of defining real economic uncertainty is to utilize expectations and forecasts as an approximate measure. We have created an uncertainty index for Sweden with the help of three components: (i) the spread in GDP growth forecasts from nine official Swedish institutions (ii) the spread in Consumer Price Index (CPI) forecasts from the same nine institutions and (iii) the conditional variance in households’ and businesses’ expectation of the future, collected from the business tendency survey present by the NIER. After a comparison of differently weighted indices, our final index was composed by the following weights: 0,25% in disagreement (GDP), 0,25% in disagreement (CPI) and 0,5% in conditional variance of expectations (CVE). This index, which best represents the uncertainty in the real economy was analysed using a Vector Autoregressive (VAR) model. By using the same VAR model, an impulse response analysis was performed, describing how an increase of one standard deviation in real uncertainty affects Sweden’s GDP.

Our target audience for this thesis is primarily statistics students at the Bachelor level but also other students and people interested in statistics and econometrics can have use of this paper. Since NIER initially requested a measure of real uncertainty, they can take much interest in this paper as well.

1.3 Disposition

Part 1 – Introduction

In this introduction background of the thesis, previous studies and problem description is presented initially. Together they lead us to a presentation of our constructed index with purpose, goals, delimitations and a short summary of our analysis.

Part 2 – Data

In order to simplify for the reader, we present a separate section with our data sources in which we explain how and where this data was collected.

Part 3 - Methodology

With the purpose to give the reader a deeper understanding and a clear view of how our work has been done, this section is a description of which empirical methods have been used and what decisions have been made to lead us closer to our goals. The most important parts are the descriptions of our choice of components, how they have been weighted and the method of analysis.

Part 4 – Results

In the result section, we apply our methods of analysis to our index and present the outcome. Simple VAR models have been used for impulse response analysis and comparisons with other uncertainty indices are presented.

Part 5 - Discussion

In the discussion of the thesis, our analysis is presented and how the results can be implemented practically. In this section we also present our own methodological criticism.

Part 6 - Conclusions

In this final section our conclusions are presented based on the purpose of the thesis. In order to inspire and state the importance of the subject, the last part of this thesis describes our suggestions for further research on the topic.

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2 Data

In order to simplify for the reader, we present a separate section with our data sources in which we explain how and where this data was collected.

Three data sources have been used to construct our uncertainty index; CPI forecasts, GDP forecasts, and future expectations of businesses and households from the Economic Tendency Survey (ETS) published by the National Institute of Economic Research.

The forecasts are gathered from nine different institutions. These are the Ministry of Finance (FiD), National Institute of Economic Research (NIER), Confederation of Swedish Enterprise (SN), the Swedish Riksbank (RB), Swedish Trade Union Confederation (LO), HUI, and the banks Nordea, Skandinaviska Enskilda Banken (SEB), and Svenska Handelsbanken (SHB). The forecasts concern the annual percentage change in CPI and percentage GDP growth for the next year. In Appendix 7.8, links to all data sources are presented.

Figure 2.1 Nine official GDP growth forecasts for next year

-3,00

-2,00

-1,00

0,00

1,00

2,00

3,00

4,00

5,00

Per

cent

FiD HUI SN NIER LO NORDEA RB SEB SHB

Figure 2.2 Nine official CPI forecasts for next year

The ETS is targeted to businesses and households and is constructed to capture trends in various economic variables. The asked questions concern future development and expectations but also the current situation of different economic variables. Because of the focus in measuring uncertainty we extract only the data on expectations. These are based partly on the household’s expectations of the Swedish economy twelve months into the future and partly on the expectations by the total private sector of future employment numbers.

The household expectations data are based on interviews each month with 1500 Swedish households with a target population of 16 to 84 year olds. Correspondingly, the questions in the private sector survey refer mostly to the next three months but a few questions refer to the expectations for the next six months. The results of the surveys are presented in net balance numbers, which is the difference between the percentages of respondents who responded positively and negatively to a question. For example, if 40 percent of companies report that they expect the employment numbers to increase and 10 percent that it will decrease (50 percent expect unchanged numbers) then the net figure is 30 (40-10=30). The net figures can vary between -100 (all respondents are negative) and +100 (all respondents are positive). The study is qualitative and contains therefore no questions about absolute numbers. Respondents answer only with qualitative response options such as higher/unchanged/lower. The model for the survey is based on the original Economic Sentiment Indicator (ESI) by the European Commission (2014).

-1,00

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1,00

2,00

3,00

4,00

5,00

Per

cent

FiD HUI SN NIER LO NORDEA RB SEB SHB

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Figure 2.3 Net balances of businesses’ and households’ expectations of future economy. Source: National Institute of Economic Research

Although the forecast data goes back to 1994, the expectations data are only available back to 2001, which will force us to limit the time horizon of our uncertainty index to between 2001Q1 and 2013Q4. As shown in figure 2.3, our expectations data is initially extracted in a monthly format, but is later converted to quarterly data to fit the forecast data.

Figure 2.4 Swedish percentage GDP growth and subcomponents. Source: Statistics Sweden

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Businesses Households

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GDP, market price Imports, goods and services

Household Consumption Government spending

Gross fixed capital formation (GFCF) Inventory Investments

Exports, goods and services

The GDP components displayed in figure 2.4 and which we use in vector autoregressive models are imports, exports, household consumption, government spending, gross fixed capital formation (GFCF), and inventory investments. This data is extracted from Statistics Sweden, link is presented in Appendix 7.8. Unsurprisingly, the exports, imports, and GFCF responded most negatively in response to the financial crisis of 2008 while for example government spending even increased slightly during this time, which is not especially surprising in a Keynesian economic context.

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3 Methodology

With the purpose to give the reader a deeper understanding and a clear view of how our work has been done, this section is a description of which empirical methods have been used and what decisions have been made to lead us closer to our goals. The most important parts are the descriptions of our choice of components, how they have been weighted and the method of analysis.

3.1 The Index Components

There is currently no index describing real economic uncertainty but there is a lot of methods in previous studies, both international but mainly from the stress index provided by the Riksbank’s, that can be applied in our thesis. One of the most important parts of our investigation is to find and evaluate different components to create the best possible index representing real uncertainty. Based on the problems discussed in the introduction, we have chosen to construct our index with the help of three components, two representing real economic uncertainty experienced by professional forecasters and one representing the real economic uncertainty perceived by households and businesses.

In the work with this, different choices have been made. Primarily, we have chosen to focus on information that can represent real economic uncertainty, so all forms of financial data has been rejected. Referring to the User guide to the Economic Tendency Survey by NIER (2014b), we primarily focus on using only expectations and forecasts for further development of measuring uncertainty. Both expectations and forecasts are forward looking variables that theoretically should fall, be negative, in advance of anticipated recessions. While quantitative statistics of actual outcomes show changes in objective conditions, the expectation data show how agents interpret and evaluate the future. The quantitative statistics often come with substantial lag, while the data from expectation surveys and professional forecasters is available much earlier.

By measuring the disagreement among professional forecasters, an approximation of real economic uncertainty can be done. This measure of uncertainty has a long tradition; see for example Bomberger (1996) and Giordani and Söderlind (2002). High dispersion of the cross-sectional forecasts should suggest high uncertainty, whereas in times when the institution’s point forecasts are clustered, where some kind of consensus is in place, suggest low uncertainty. Correspondingly, to measure real economic uncertainty among businesses and households we use the conditional variance of their future expectations. This method is appropriate to model and forecast variance so it is often used to estimate and forecast the volatility of stocks, currencies and commodities in the financial sector, according to Wooldridge (2002, p. 401).

3.1.1 Forecasts

The first two constructed components of our uncertainty index utilizes forecasts from nine different institutions. The cross-sectional, interquartile range of these forecasts concerning the annual percentage change in CPI and percentage GDP growth is treated as approximations of uncertainty. This can be expressed as follows

𝑅𝑎𝑛𝑔𝑒𝑡 = 𝑀𝑎𝑥(𝑋𝑖𝑡) − 𝑀𝑖𝑛(𝑋𝑖𝑡) (3.1)

where X is the observed point forecast for institute i published in quarter t. All the institutions do not publish their forecasts quarterly, resulting in some loss of data for certain quarters, see figures 2.1 and 2.2 for a visual indication of this.

Figure 3.1 shows how the range of GDP forecasts steadily declined throughout the 90’s following the Swedish banking crisis from 1990-1994. Also, during and after the financial crisis of 2008 and onwards the GDP forecast disagreement rose to over 2 percentage points but has since stabilized to around 1 percentage point.

Figure 3.1 Interquartile range of GDP forecasts, percentage-point spread. Source: NIER and own calculations

The CPI forecast disagreement is displayed in figure 3.2. The time series peak at over two percentage points at two different occasions, around the second quarter of 2002 and the fourth quarter of 2008.

0

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2,5

3

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Figure 3.2 Interquartile range of CPI forecasts, percentage-point spread. Source: NIER and own calculations

As noted by Giordani and Söderlind (2002) this method of measuring the dispersion between individual forecasts has the advantage of being readily available and easy to compute but the disadvantage of becoming meaningless if the institutions have the same information and use the same model. This is not a problem in our case since the forecasts are all different from each other.

3.1.2 Expectations among Households and Businesses

With the intention to broaden the index and to obtain a more comprehensive representation of Sweden’s experienced uncertainty, we constructed a component representing variation among the Swedish households' expectations and private sectors’ view of the future. The purpose of this third and last component is that it shall act as a counterweight to the institute's vision of the future.

One possible representation of the component could have been the variation among the Economic Tendency Indicator publish by NIER (2014a), which is a compilation of both expectations and outcomes from businesses and households and dates back to January 1993. One of our criteria has been to exclude variables of outcomes in our final index so this time series was not appropriate to use. Instead we studied only time series of expectations from the Tendency Indicator since expectations provide a better measure of uncertainty than actual outcome and can earlier give an indication of changes in the economy. For more information and raw data, see section 2. Two time series was extra interesting among many; (i) household’s expectations about the their future economy and (ii) the expectations by the total private sector of future employment numbers. The weight of 0,8 was given to the private sector and 0,2 to households, which gave us the combined time series representing the final, underlying component of expectations. The proportion of weights of the component was derived by NIER (2014a) and their previously assigned and preferred weights in the published

0

0,5

1

1,5

2

2,5

ETS. Unfortunately this time series only presents observations back to January 2001 but we argue for the importance of representative data in favour of large number of observations representing actual outcomes. With no actual outcome in the index, we have seen that the risk of bias should reduce.

Since the variation in expectations has been chosen to represent real uncertainty, it was therefore appropriate to use a time series of the conditional variance from the weighted time series of expectations. This argument has been presented previously, for example by Bomberger (1996). Conditional variance describes the variance in the error

term 𝜇𝑡 and how it systematically depends on previously observed residuals. The conditional variance of the error term therefore varies over time while the

unconditional variance remains constant. Conditional variance is expressed 𝜎𝑡2 and is

denoted as

𝜎𝑡2 = 𝑣𝑎𝑟(𝜇𝑡|𝜇𝑡−1, 𝜇𝑡−2, … ) = 𝐸 [(𝜇𝑡 − 𝐸(𝜇𝑡))

2| 𝜇𝑡−1, 𝜇𝑡−2, … ] (3.2)

where ut is a white noise error term and it is usually assumed that the mean of the

error term E(𝜇𝑡 ) = 0, so

𝜎𝑡2 = 𝑣𝑎𝑟(𝜇𝑡|𝜇𝑡−1, 𝜇𝑡−2, … ) = 𝐸[𝜇𝑡

2| 𝜇𝑡−1, 𝜇𝑡−2, … ] = 𝛼0 + 𝛼1𝜇𝑡−12 (3.3)

Low conditional variance represents low uncertainty and vice versa. Accordingly to Agung (2009, p. 419), one model designed to model and forecast variance is the ARCH (Autoregressive Conditional Heteroskedasticity) of Engle (1982). For additional reading about conditional variance, see Brooks (2008, p. 386-388). By using the analysis software Eviews and SAS, various tests where done and a new, adequate time series that could be used as a component in the final index was developed. In some cases ARCH is not suitable for the purpose, instead a GARCH (Generalized Autoregressive Conditional Heteroskedasticity) of Bollerslev (1986) could be a more appropriate model. This model allows the conditional variance also to be dependent on its own lagged conditional variances and is denoted

𝜎𝑡2 = 𝛼0 + 𝛼1𝜇𝑡−1

2 + 𝛽𝜎𝑡−12 (3.4)

This equation could be compared with equation (3.3) to see the distinction. We have been working in Eviews to analyze possible models and do comparison of different ARCH and GARCH models. When comparing several different models, a variety of information criterions were available as measure of the relative quality of the models. The most well-known is the Akaike Information Criterion (AIC), which rewards goodness of fit and penalize extra variables (risk of overfitting). When constructing a model there is always a trade-off between these two aspects and the AIC presents values for each compared model in relation to the number of variables. The model with minimum AIC is preferred. AIC uses the likelihood function for the model as reference for goodness of fit. It is therefore possible to use the likelihood value for computing a likelihood ratio test or a modified version of AIC, the Schwarz information criterion (SIC) to compare models. The SIC imposes a stronger penalty for additional variables; see the formulas of AIC and SIC demonstrated in Appendix 7.2 and the likelihood ratio test in Appendix 7.3. The output is shown in table 3.1 below and displays the different

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models with AIC values and log likelihood values that best describe the time series of conditional variance.

Table 3.1: Comparison of different ARCH models

Model Akaike Information Criterion (AIC)

Log Likelihood

GARCH (2,2) 7,487 -597,668

GARCH (1,1) 7,475 -598,724

GARCH (1) 8,152 -654,274

ARCH (1) 7,463 -598,745

ARCH (2) 7,475 -598,715

Both AIC values and log-likelihood values are very similar for the four models but the ARCH(1) is still the model that gets the best AIC value (lower is better). From the output, presented in Appendix 7.3, one can se that the p-value for the independent variable is significant at the one per cent level. The model should thereby be considered acceptable based on the rule of thumb1. As an extra control and to test if a GARCH model adds necessary information for model the conditional variance (extended version of ARCH), we performed a log likelihood ratio test for ARCH(1) and GARCH(1,1). These two models were chosen for the test since they present the two lowest AIC values in table 3.1. The test is performed as follows.

Log-likelihood ratio test:

H0: Reduced model, ARCH(1) is suitable H1: Full model, GARCH(1,1) is more appropriate

−2 × (𝑙𝑛𝐿0 − 𝑙𝑛𝐿1) = −2 × (−598,745 − (−598,724)) = 0,042 (3.5)

Under the null hypothesis the likelihood statistic follows a chi-square distribution with one degree of freedom. With a significance level of 5%, the critical value is 3.841. Our

estimated value is 0,042 < 3,841. We can’t reject the null hypothesis; the ARCH(1) is a suitable model.

1

Agung (2009, p. 440) describes: “Based on the rule of thumb, if a conditional variance model has an insignificant

independent variable with a p -value >= 0.20, then the conditional variance model should be modified. Corresponding

to a p -value< 0.20, a conclusion can be made that the corresponding independent variable has a significant effect,

either positive or negative, on the dependent variable at the 0.10 significant level. In other words, if all independent

variables of any model have p -values < 0.20, then the models should be considered as acceptable or good models.”

In the analysis program SAS, a new time series representing the conditional variance was produced by the ARCH(1) model. This time series is the third and final component of our index of real economic uncertainty. The component is called Conditional Variance of Expectations, abbreviated CVE, and is illustrated in figure 3.3 below.

Figure 3.3 Conditional variance of businesses’ and households’ expectations (standardized). Source: NIER and own calculations

3.2 Weights

When constructing our uncertainty index we first standardize each component so that each observation is related to the average and standard deviation of the series reference period (2001Q1 to 2013Q4). The three time series are illustrated together in figure 3.4 below.

Figure 3.4 Index components (standardized). Source: NIER and own calculations

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24

All of the three time series follow each other more or less during the whole time period so one can think that different weights do not matter. With the intention to make a high performing index it is important to compare various weightings so we propose three different weights assigned to the components.

The first one is a simple, equal weighting of 1/3 for each component. The second index is our own subjective, and preferred, index; 1/4 on each of the Disagreement (GDP) and Disagreement (CPI) components and 1/2 on the CVE component. Because CVE captures both businesses and households, placing a bigger emphasize on this component in contrast to the equal weighting is theoretically more reasonable. Finally, we perform a Principal Component Analysis (PCA) and obtain the weights 0,558 on the Disagreement (GDP) component, 0,271 on the Disagreement (CPI) component, and 0,170 on the CVE component.

Principal Component Analysis (PCA) is a multivariate statistical method, which is useful for identifying patterns in the data. The method is often used when analyzing large data sets since the PCA compress the data and reduce the number of variables, without losing much information. Another great advantage of PCA, which is our main purpose of using it, is that the PCA converts possibly correlated variables into new, uncorrelated variables by using an orthogonal transformation. These new components are called principal components, and are in decreasing level representing most variance possible from the data set. PCA can be made using either a covariance matrix or a correlation matrix of the original data. When using a correlation matrix the original data will be standardized by the PCA and since we already have standardized data we will use a covariance matrix. The output is illustrated below in tables 3.2 and 3.3, from where we base our analysis.

Table 3.2: Eigenvalues of the Covariance Matrix

Eigenvalue Difference Proportion Cumulative

1 1.825 0.938 0.558 0.558

2 0.887 0.331 0.271 0.830

3 0.557 0.170 1.000

Table 3.3: Eigenvectors

Principal Component

1 2 3

Disagreement (GDP)

0.646 -0.433 -0.629

Disagreement (CPI)

0.502 0.862 -0.078

CVE 0.576 -0.265 0.774

The first step of the analysis is to evaluate how many principal components shall represent the original data. This can, according to Sharma (1996, p. 76-79) be made by

referring to different rules, depending on the purpose of the analysis. The ‘eigenvalue-greater-than-one-rule’ argues for only using principal components with an eigenvalue exceeding one. The elbow method is another that argues for using the same number of principal components as where the ‘elbow’ occurs, in our case two (see Appendix 7.4). The third and last of the most common rules refers to the degree of explanation; the number of principal components shall cumulatively explain at least 80 percent of the variance in the original data set. For more information about PCA, see Sharma (1996, chapter 4)

We chose to use all computed principal components in our suggested index and do not lose any information. One can argue that only the first principal component should be used, based on the ‘eigenvalue-greater-than-one-rule’, but the purpose for us is not to reduce the number of variables when we originally just have three variables. We argue for a use of all three principal components, the first representing the variance in disagreement (GDP), the second representing the variance in disagreement (CPI) and the third and last principal component representing CVE. The argument for this is found in table 3.3 where disagreement (GDP) has the highest portion of variance (0.646) of the three original components in column 1. Further, we can see that disagreement (CPI) has the highest value (0,862) in column 2 and CVE the highest value (0,774) in column 3. Finally we weight the new suggested index by the proportions given in table 3.2.

A comparison of the indices can now be done and figure 3.5 illustrate our three different weighted indices together.

Figure 3.5 Index weight alternatives (standardized). Source: own calculations

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It is clear, after studying Figure 3.5, that all three indices follow each other closely during the whole time period. By constructing a correlation matrix it can be shown that our subjective index correlates highly with both of the alternatives (0,980 with the equally weighted index and 0,938 with the PCA index). The correlation between the PCA alternative and the equally weighted index is 0,957, see the correlation matrix in table 3.4.

Table 3.4: Correlation matrix of weight alternatives

Index PCA Equal Subjective

PCA 1,000

Equal 0,957 1,000

Subjective 0,938 0,980 1,000

3.3 Choosing the Best Weighted Index

Three different suggested indices were composed but we still did not know which one of them that best explained GDP. We estimated therefore bivariate vector autoregressive (VAR) models2 with our differently weighted indices together with GDP as endogenous variables. We compared the overall AIC values where a lower value is better. The output is displayed in table 3.5 and suggests that the subjective weighted index is the most appropriate compared to the other ones with an AIC value of 5.7. This suggests that the subjective index has the highest degree of explanation of GDP. In the Root column we have included the root values that all were less than one, which prove that the models fulfill the VAR stability criteria. This verifies that the variables are appropriate for this VAR model. For detailed output see Appendix 7.5. Table 3.5 displays the results with one lag in accordance to the Schwarz information criterion (SIC), which we use because we did not want to consume too many degrees of freedom due to our relatively small data set. Recall that the SIC imposes a stronger penalty for additional variables.

Table 3.5: Comparison of weight alternatives in bivariate VARs, with GDP as accompanying variable

Index Root Lag (SIC) Lag (AIC) Overall SIC Overall AIC

PCA <1 1 9 6.268 6.041

Equal <1 1 10 6.040 5.812

Subjective <1 1 5 5.934 5.707

AIC: Akaike information criterion

SIC: Schwarz information criterion

2 See chapter 3.4.1 for more information on VAR models.

3.4 Methods of Analysis

To achieve meaningful results for our analysis we have mainly used bivariate vector autoregressive (VAR) models. To place our constructed index in a wider context we also compared it too other indices measuring uncertainty.

3.4.1 Vector Autoregression (VAR)

While autoregressive models only model one series yt in terms of its own past, vector autoregressive (VAR) models consider several series. An example of a simple bivariate VAR(1) with series yt and zt and only one lag consist of equations

𝑦𝑡 = 𝛿0 + 𝑎1𝑦𝑡−1 + 𝛾1𝑧𝑡−1 + 𝑢1𝑡 (3.6)

𝑧𝑡 = 𝜂0 + 𝛽1𝑦𝑡−1 + 𝑝1𝑧𝑡−1 + 𝑢2𝑡 (3.7)

where ut is a white noise error term with zero expected value given past information on y and z and each variable depends only upon the previous values of yt and zt but can be extended to depend on different combinations of the previous k values of both variables. This is a generalization of the univariate autoregressive model. The VAR model was initially popularized by Sims (1980) who argued that a set of variables should not be predetermined as exogenous or endogenous if there is true simultaneity among them, they should instead be treated on an equal footing. This means that the variables do not need to specify, they are all treated as endogenous.

First of all, and before estimating equations 3.6 and 3.7, we needed to decide the appropriate lag length, k. By using the advantage of information criterions like the Akaike or Schwarz, we choose the lag length that minimized the value of these criteria. The choice of lag length is associated with problems; including too few could lead to specification error, while including too many could consume too many degrees of freedom and also risk multicollinearity. For more details on VAR, see Wooldridge (2002, p. 598-599). The variables included in the VAR also needed to be checked for stationarity. For our analysis to be reliable, our time-series needed to be stationary. This implies that the mean, the variance, and the autocovariance are not a function of time. To test this, all the variables have been subjected to the so-called augmented Dickey-Fuller (ADF) test. We do not go into details about the specifics of this test, for more info see for example Brooks (2008, p. 327-329).

3.4.2 Granger Causality

VAR models like the one in equation 3.6 and 3.7 have allowed us to test if, for example, past observations of z help to forecast yt after controlling for past observations of y. If it is possible to observe that

𝐸(𝑦𝑡|𝐼𝑡−1) ≠ 𝐸(𝑦𝑡|𝐽𝑡−1) (3.8)

where It-1 holds information of past y and z, while Jt-1 holds only information of past y, it can be said that z “Granger-causes” y. Tests of this form were developed by Granger (1969) and although it is named a “causality test” in reality it only imply a correlation

28

between the current value of y and past values of z. It could be that movements in z directly cause movements in y but it does by no means prove it. The Granger Causality test was an integral part of this thesis for testing whether movements in our uncertainty index “causes” changes in GDP, and therefore whether our index is a good tool for forecasting GDP. For more details on Granger Causality see Brooks (2008, p. 311-312)

3.4.3 The Impulse Response Function

Although the Granger causality test is a good way to examine the relationship between variables in a VAR model, it does not provide any answers to whether there is a positive or negative relationship between them or how long the effect is for one of the variables. For this purpose the impulse response function of the VAR’s do a much better job, and gives the response of the dependent variable in the VAR model to shocks in the error terms, such as u1 or u2 in equations 3.6 and 3.7. To exemplify this, suppose that it occurs an increase of one standard deviation to u1. This will naturally have an effect on yt but since yt also appears in the zt equation, this variable will also be affected. Correspondingly, a shock in the zt error term, u2, will have an effect on yt. The impulse response function traces out the impact of such shocks for several periods in the future. For more details on impulse responses see Brooks (2008, p. 298-304) or Gujarati (2009, p. 853-854).

3.4.4 Comparisons

Finally, we have compared our REU index with the European Policy Uncertainty (EPU) index of Baker et al. (2013) as well as the stress index of the Riksbank. This cannot be seen as an explicit proof of check or an evaluation of its quality since the three indices are both geographically different and have different structures. However, as an interesting examination, correlations have been calculated and the time series plotted against each other for visual comparison.

4 Results

In the result section, we apply our methods of analysis to our index and present the outcome. Simple VAR models have been used for impulse response analysis and comparisons with other uncertainty indices are presented.

4.1 Real Uncertainty and GDP

We have found that, in bivariate VARs, shocks in our uncertainty index leads to large and prolonged negative effects on economic activity. VAR models with corresponding impulse responses were used in this context to be an approximate indicator of potential effects that our uncertainty index may have. The studied variables in relation to our index are Swedish quarterly GDP and its individual components measured in percentage growth rate compared to the same quarter the previous year extracted from Statistics Sweden. For visual comparison with the REU index, see figure 4.1. Both series have been standardized with a mean of zero and a standard deviation of one.

Figure 4.1 The REU index and GDP growth (standardized). The shaded recession period is defined as quarters with negative GDP growth (2008Q4-2009Q4). Source: NIER, Statistics Sweden, and own calculations.

The REU index and the GDP components were all tested with the augmented Dickey-Fuller test and were all stationary at the 5% significance level except for the overall GDP variable that was stationary at the 8% significance level. This was important to take into account in the VAR models, especially when performing and interpreting the Granger Causality tests. For detailed output from these tests, see Appendix 7.6.

By looking at figure 4.2 we can see that a positive innovation of one standard deviation or 0,6 percentage points in uncertainty is followed by a fall in GDP with a peak negative response of about -0,8 percentage points after 3 quarters. Similar, but more extreme, is the response of exports and imports following the impulse of an uncertainty shock. Figure 4.3 displays these results were a one standard deviation

30

increase in our uncertainty index is followed by a sharp decline of about -2 percentage points in exports and about -3 percentage points in imports after 3 quarters. However, a strong recovery is notable in import growth following an uncertainty shock. After 6-7 quarters imports have completely recovered and started to show positive numbers. This clear tendency of reversion is not as evident in the exports response, even at a very long time horizon as 12 quarters. As is evident from this analysis we have chosen to analyze the REU index in relation to both imports and exports, not in terms of net exports. This method is more instructive since the net exports are weakly correlated with the overall state of the economy and therefore also with the real economic uncertainty.

Figure 4.2: Response of GDP growth to one standard deviation (0,6 percentage points) innovation in REU index

As initially expected and after looking at the graph of GDP components in figure 2.4, the response of the three components household consumption, government consumption, and inventory investments was weak. We can conclude that shocks in our uncertainty index are significantly followed by a decline in GDP and more specifically in imports, exports, and Gross Fixed Capital Formation (GFCF). These results, although based on a slightly different empirical approach, is similar to the results and estimated effects of uncertainty shocks studied in Baker et al. (2013) and Bachmann et al. (2010).

Figure 4.3: Response of GDP components to one standard deviation innovation in REU index

By performing a Granger causality test we wanted to answer the question if changes in our index caused changes in GDP. If this is the case, that changes in our index causes changes in GDP, and not vice-versa, it could be concluded that the REU index “Granger-causes” GDP or that there exists “unidirectional causality” from our index to GDP, see Brooks (2008, p. 311-315).

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The resulting Table 4.1 shows strong evidence of unidirectional Granger-causality between our uncertainty index and overall GDP, with a p-value of 0,04. The lag lengths are chosen with the help of the Schwarz information criterion, choosing the number of lags that minimize this value. Even stronger Granger-causality was found in relation to variables GFCF and exports. Interestingly, our only incidence of bidirectional causality was found in relation to the imports variable. This means that changes in our uncertainty index seem to cause changes in imports and vice versa.

One should, again, be aware that the word “causality” does not necessarily imply that GDP changes as a direct consequence of changes in uncertainty but rather that there exist a clear chronological ordering of movements in the two series where our index foreshadows GDP, especially GFCF, imports, and exports.

Table 4.1: VAR Granger Causality

Dependent variable

Independent variable Chi-sq Lags (SIC) Prob.

REU Index GDP 0.006 1 0.938

GDP REU Index 4.427 1 0.035

REU Index Exports 0.045 1 0.832

Exports REU Index 7.758 1 0.005

REU Index Consumption 0.246 1 0.619

Consumption REU Index 1.248 1 0.264

REU Index Imports 12.230 3 0.007

Imports REU Index 12.000 3 0.007

REU Index GFCF 0.101 1 0.750

GFCF REU Index 10.358 1 0.001

REU Index Inventory 0.128 1 0.720

Inventory REU Index 2.326 1 0.127

REU Index Gov Spending 0.005 1 0.942

Gov Spending REU Index 1.263 1 0.261

4.2 Comparison to Other Indices

Other uncertainty related indices that have been relevant for comparison to ours include the European Economic Policy Uncertainty (EPU) index developed by Baker et al. (2013) and the financial stress index constructed by the Swedish Riksbank, see Sandahl (2011). The financial stress index is constructed to function as a tool when analyzing the development of financial markets and is comprised of four “stress indicators”, three of which are related to capital markets and one related to the foreign exchange market. The European EPU index differs in that policy rather than financial uncertainty is measured. It is 50% comprised of a news-based index counting articles containing terms like “uncertainty” and other relevant terms and 50% weight on forecaster disagreement related to CPI inflation and government budget balance.

Figure 4.4 shows our uncertainty index plotted alongside the financial stress index and the European EPU index. Our index is unsurprisingly more correlated (correlation=0,627) with the stress index than the EPU (correlation=0,412), owing to the fact that the first two are Swedish-centered while the EPU is focused on other European countries including France, Germany, Italy, United Kingdom, and Spain. Sweden has notably been spared from the prolonged high levels of uncertainty that has plagued the rest of Europe in the aftermath of the financial crisis, seeing a relatively stable decline ever since.

Figure 4.4: Our Real Economic Uncertainty (REU) Index for Sweden plotted alongside the European Policy Uncertainty (EPU) index developed by Baker et al. (2013) and the Stress Index developed by the Swedish Riksbank. For comparison, GDP growth is also included (all series standardized).

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5 Discussion

In the discussion of the thesis, our analysis is presented and how the results can be implemented practically. In this section we also present our own methodological criticism.

5.1 Analysis and Practical Implementation of the Results

Impulse response functions in simple bivariate VARs showed statistically significant negative responses in four out of six GDP growth components including GDP growth itself. It is hardly surprising that the government spending variable did not render significant declines in response to increases in uncertainty since the government has an incentive to increase investments in times of uncertainty when private investments come to a halt, in accordance with contracyclical fiscal policy.

The Granger Causality tests showed that our index is a distinct forward looking variable in relation to GDP. But because our index showed highest significance in relation to the components Exports, Imports, and GFCF but also because the GDP variable showed relatively low significance (p-value=0,08) in the ADF test we can conclude that our uncertainty index can best be used to forecast those three subcomponents of GDP and less so GDP itself. In other words, our index is a good tool for explaining movements in GDP after government spending and household consumption has been subtracted.

Although these results are interesting and useful, studies like Bachmann (2010) have shown that the causality between uncertainty and recessions are not always as clear cut as these results might suggest. Uncertainty breeds slowdowns and slowdowns breed uncertainty. But as long as uncertainty levels can predict GDP levels, as a pure forecasting tool, it does not really matter if it is real causation or not as long as it is a forward looking variable helping us to foresee changes in the real economy. In that respect, we can say that we have succeeded with our objective.

When comparing the REU index with the EPU and the Stress Index, a couple of observations are notable; the REU index peaks much higher in 2008Q4 than that of the EU. Also, Swedish real economic uncertainty has steadily declined ever since, while the EPU has stayed at a high level. One should probably be cautious while trying to find explanations to individual differences in observations between these indices since they are methodologically different, the much higher peak of the REU in 2008 could therefore be hard to explain reasonably. From the long term trends however, like the REU and the EPU since 2008, we can probably infer that real economic uncertainty in Sweden is much lower than in the rest of the EU (countries studied include Spain, Italy, UK, France, and Germany). This can also be an explanation to the stark contrast between the overall health of public finances between these regions.

Because our REU index shows to be a good predictor of GDP, institutes like NIER and the Ministry of Finance can possibly benefit from it as a forecasting tool. Also, by combining our index with the stress index of the Riksbank, a powerful model for measuring broad-based uncertainty can be created. Other possible beneficiaries include investors in Sweden, especially large foreign companies, wishing to estimate the risk involved in an investment and the general health of the Swedish economy.

5.2 Methodological Criticism

Several caveats related to vector autoregression and forecast disagreement as a proxy for uncertainty was examined and evaluated. During the work with this thesis we have faced different problems and a variety of choices. This section will therefore present critique and discussion of what could have been done differently.

One could reflect over the number of components our index was founded on and think that it should include more components than three. We are aware of this and it is often better with more components than fewer in an index, provided that the components are relevant. Many previous studies have had problems, including having different views, both in defining and measuring economic uncertainty. This has led to no clear references and theoretical foundation have been available to us, which has further resulted in a difficulty in finding data representing real economic uncertainty. Priority has therefore been given to the selection of components rather than on the number of components. We have investigated several other possible components but these have all had weaknesses in representing real economic uncertainty and were therefore not included in this thesis.

The period of time covered by our index can be considered short and contain insufficient number of observations for reliable estimates or forecasts. This is something we were aware of and we would have liked to avoid it in order to convince possible critics. Unfortunately, the published data on the expectations of households and firms from NIER were only available back to 2001. Priorities had to be made and we focused exclusively on expectations and were therefore forced to use these time series. There are possibly different methods of recreating and approximating data further back but we did not have enough time for that in this thesis.

A relevant and important question is related to how often and easily the index can be updated. During the work with our index, this issue have all along worked like a guide and formed the basis for many of the choices we made. The index can definitely be updated at the end of each quarter, after the previously presented agencies have released their forecasts for GDP and CPI. The Expectations of households and firms from NIER, representing the underlying time series of the third component, are released each month so if there is a possibility to convert the agencies’ forecasts to monthly data, this would reduce the time between updates significantly. The REU index is easy to update and we have constructed a user friendly excel file where it is simple to insert all the published data and create an updated version of the time series graph.

In the data section, where the raw data of the agencies’ forecasts are displayed, an observant viewer can detect that not all time series are complete. There are missing forecasts a number of times from some of the agencies that only publish three forecasts per year. It may be argued that when reduced data is used, the components are losing ability to represent real economic uncertainty. This is true but our impression is that the reduced information is negligible and that the data set contains enough observations for each quarter in which the discrepancy between the agencies are calculated.

Runkle (1987) argues that calculating impulse responses without confidence bands make it impossible to draw any meaningful conclusions about the effects. Confidence

36

intervals should therefore always accompany the impulse response function and because they typically are very wide, meaningful inference is still often hard to make. To this end, we made sure to include these and examined them with a critical eye.

Even though the method of measuring disagreement among forecasters as a proxy for uncertainty has been celebrated, other studies have found problems with this approach. Diether et al. (2002) show that a high dispersion in analysts’ forecasts could simply indicate differences in opinion rather than in uncertainty. Furthermore, in a critical look on Bomberger (1996), Rich and Butler (1998) show in an empirical study no support for this approach. They question the conclusions drawn from studies that have used forecast disagreements to measure macroeconomic uncertainty. Jurado et al. (2013) turn against the fact that the forecasters that are typically sampled are “practioner forecasters and analysts that are known to display systematic biases and omit relevant forecasting information”. This clearly indicate an importance of having a versatile group of forecasters. The group of nine forecasters that we have gathered data from, including both independent research institutions, banks, trade unions, and interest organisations should fulfil this criterion. One might argue that The Confederation of Swedish Enterprise and Swedish Trade Union Confederation are both inherently biased but this should not pose an overall problem thanks to our otherwise dependable group of forecasters.

6 Conclusions

In this final section our conclusions are presented based on the purpose of the thesis. In order to inspire and state the importance of the subject, the last part of this thesis describes our suggestions for further research on the topic.

With our initial goal of developing a real economic uncertainty index and a model for estimating future GDP we have completed several steps. We found that disagreement among forecasters and expectations of households and businesses were appropriate sources to build upon and are components that have been rigorously tested as measures of uncertainty in other countries. Assigning different weights to these components helped in the process of finding the best possible model. What we found was that, on average, an uncertainty level increase of one standard deviation is followed by a fall in GDP with a peak negative response of about -0,8 percentage points after 3 quarters. By testing individual GDP components, foreign trade and gross fixed capital formation were found to be most sensitive to uncertainty with some signs of causality while government spending was the least sensitive.

6.1 Suggestions for Further Studies

This paper can be seen as a first version of a real economic uncertainty index for Sweden. There is therefore great potential for improvement and some have been noticed by the authors during the work but have not been implemented, mainly because of time constraints. Further research that could lead to potential improvement of the index is to implement an attempt to extend the time period of the underlying time series. This would create a more robust index based on more historical variations in real economic uncertainty leading to better forecasts of GDP. Further studies with intention to increase the number of relevant components could also improve the model, or constructing a new index for the purpose by finding better explanatory variables.

In the best of worlds, the index would be updated weekly but reasonable would be if an update were done in the end of every month. Further studies regarding the subject could help, either by replacing the components disagreement (GDP) and (CPI) or in any way manipulate our raw datasets across agencies forecasts for GDP and CPI to be measured monthly. It would also be valuable to, with empirical methods, construct indices for specific industries to evaluate how different sectors of the economy are affected by a shock in uncertainty.

Finally, with our index as a foundation, similar real economic uncertainty indices can be constructed for other countries and economies. This would create greater understanding, both among political leaders and the public around the world, for what increasing economic uncertainty leads to.

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References

Web European Commission (2014). Economic Sentiment Indicator (Electronic) Available: http://ec.europa.eu/economy_finance/db_indicators/surveys/index_en.htm (2014-04-03)

National Institute of Economic Research (2014a). Economic Tendency Survey (Electronic) Available: http://www.konj.se/1040.html (2014-04-03)

National Institute of Economic Research (2014b). User Guide Economic Tendency Survey (Electronic) http://www.konj.se/download/18.2cabf50a141002857ee147b/User-Guide-Economic-Tendency-Survey.pdf (2014-04-03)

Bibliography

Agung, I. G. N. (2009) Time Series Data Analysis Using Eviews, John Wiley & Sons (Asia) Pte Ltd

Bachmann R., Elstner S., and Sims E. R. (2010) Uncertainty and Economic Activity: Evidence from Business Survey Data, National Bureau Of Economic Research

Baker, S.R., Bloom, N., and Davis S.J. (2013): “Measuring Economic Policy Uncertainty,” Stanford mimeo.

Bernanke, B. (1980): “Irreversibility, Uncertainty and Cyclical Investment,” National Bureau Of Economic Research

Bjellerup, M., Shahnazarian, H. (2013): “Hur påverkar det finansiella systemet den reala ekonomin?”. Ekonomiska avdelningen på Finansdepartementet

Bloom, N. (2009): “The Impact of Uncertainty Shocks,” Econometrica, 77, pp. 623- 685.

Bloom N., Floetotto M., Jaimovich N., Saporta I., and Terry S., (2011): “Really Uncertain Business Cycles,” Stanford mimeo.

Bollerslev T., (1986) Generalised autoregressive conditional Heteroskedasticity, Journal of Econometrics, 33 (1986), pp. 307–327

Bomberger, William A. "Disagreement as a Meastire of Uncertainty." Joumal of Money, Credit, and Banking 28 (1996), 381-92.

Brooks, C. (2008) Introductory Econometrics for Finance, Second Edition, Cambridge.

Diether, K. B., Malloy C. J., and Scherbina A. (2002): “Differences of Opinion and the Cross Section of Stock Returns”, The Journal of Finance, 57(5), 2113-2141.

Engle R.F. (1982) Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation, Econometrica, 50 (1982), pp. 987–1008

Giordani, P. and Söderlind, P. (2003): Inflation forecast uncertainty, European Economic Review

Gujarati, D. (2004) Basic Econometrics, Fourth Edition. The McGraw−Hill Companies

Johansson, T., Bonthron, F. (2013): “Vidareutveckling av indexet för finansiell stress för Sverige”. Sveriges Riksbank

Jurado, K., S. C. Ludvigson, and S. Ng (2013): “Measuring Uncertainty”, Columbia University.

Knight, F. H. (1964): “Risk, uncertainty and profit”. Reprints of economic classics, Augustus M. Kelley, Bookseller, New York 1964

Rich, R.W., Butler, J.S., (1998): “Disagreement as a measure of uncertainty: A comment on Bomberger”. Journal of Money, Credit, and Banking

Runkle, D. E. (1987): “Vector Autoregressions and Reality”, Journal of Business and Economic Statistics 5(4), 437-42

Sandahl Forss, J., Holmfeldt, M., Rydén, A., Strömqvist, M. (2011): “Ett index för finansiell stress för Sverige”. Sveriges Riksbank

Sharma, S. (1996) Applied Multivariate Techniques, John Wiley & Sons, Inc.

Wooldridge, J. M. (2002) Introductory Econometrics – A modern approach, Second Edition. South Western College.

Zarnowitz V., Lambros L.A., (1983). “Consensus and uncertainty in economic prediction”. National Bureau Of Economic Research

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7 Appendix

7.1 GDP Components

GDP MILLIONS (KR)

IMPORTS 1 455

GOODS 1 035

SERVICES 420

EXPORTS 1 659

GOODS 1 116

SERVICES 543

CONSUMPTION 2 762

HOUSEHOLD 1 764

GOVERNMENT 998

INVESTMENTS 669

GFCF 667

INVENTORY 2

TOTAL 3 634

SOURCE: SCB

7.2 Information Criteria

Information criterions according to Gujarati (2004)

Akaike Information Criterion (AIC) is defined as:

𝐴𝐼𝐶 = 𝑒2𝑘/𝑛∑ �̂�𝑖

2

𝑛= 𝑒2𝑘/𝑛

𝑅𝑆𝑆

𝑛 (7.1)

where k is the number of regressors (including the intercept) and n is the number of observations. For mathematical convenience, (X.X) is written as

ln 𝐴𝐼𝐶 = (2𝑘

𝑛) + 𝑙𝑛 (

𝑅𝑆𝑆

𝑛) (7.2)

where ln AIC = natural log of AIC and 2k/n = penalty factor

Schwarz Information Criterion (SIC)

Similar in spirit to the AIC, the SIC criterion is defined as:

𝑆𝐼𝐶 = 𝑛𝑘/𝑛∑ �̂�2

𝑛= 𝑛𝑘/𝑛

𝑅𝑆𝑆

𝑛 (7.3)

or in log-form:

ln 𝑆𝐼𝐶 = (𝑘

𝑛) ln 𝑛 + 𝑙𝑛 (

𝑅𝑆𝑆

𝑛) (7.4)

where [(𝑘/𝑛) ln 𝑛] is the penalty factor. SIC impose a harsher penalty than AIC.

7.3 ARCH(1)

Dependent Variable: Expectations

Method: ML - ARCH (Marquardt) - Normal distribution

Date: 05/15/14 Time: 14:32

Sample: 1 161

Included observations: 161

Convergence achieved after 21 iterations

Presample variance: backcast (parameter = 0.7)

GARCH = C(1) + C(2)*RESID(-1)^2 Variable Coefficient Std. Error z-Statistic Prob. Variance Equation C 10.03006 4.533564 2.212400 0.0269

RESID(-1)^2 1.020442 0.334719 3.048652 0.0023 R-squared -0.080488 Mean dependent var -3.855392

Adjusted R-squared -0.073776 S.D. dependent var 13.63192

S.E. of regression 14.12583 Akaike info criterion 7.462664

Sum squared resid 32125.79 Schwarz criterion 7.500942

Log likelihood -598.7445 Hannan-Quinn criter. 7.478207

Durbin-Watson stat 0.074110

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7.4 PCA Output

7.5 AR Root Tables (VAR Stability Tests)

Roots of Characteristic Polynomial

Endogenous variables: PCA_Index GDP

Exogenous variables: C

Lag specification: 1 1

Date: 04/27/14 Time: 11:31 Root Modulus 0.805108 0.805108

0.403970 0.403970 No root lies outside the unit circle.

VAR satisfies the stability condition.


Endogenous variables: Equal_Index GDP







Endogenous variables: Subjective_Index GDP






7.6 Augmented Dickey-Fuller Tests

These tables contain detailed outputs of unit root tests of our GDP growth data and its subcomponents.

Null Hypothesis: REU_Index has a unit root

Exogenous: Constant

Lag Length: 0 (Automatic - based on SIC, maxlag=10) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -3.201794 0.0256

Test critical values: 1% level -3.565430

5% level -2.919952

10% level -2.597905

*MacKinnon (1996) one-sided p-values.

Null Hypothesis: GDP has a unit root

Exogenous: Constant



5% level -2.925169

10% level -2.600658 *MacKinnon (1996) one-sided p-values.

Null Hypothesis: EXPORTS has a unit root

Exogenous: Constant



44

5% level -2.926622


Null Hypothesis: GFCF has a unit root

Exogenous: Constant



5% level -2.923780


Null Hypothesis: Household_Consumption has a unit root

Exogenous: Constant



5% level -2.923780


Null Hypothesis: Imports has a unit root

Exogenous: Constant



5% level -2.922449


Null Hypothesis: Inventory Investments has a unit root

Exogenous: Constant



5% level -2.923780

10% level -2.599925

*MacKinnon (1996) one-sided p-values.

Null Hypothesis: Government_Spending has a unit root

Exogenous: Constant



5% level -2.921175


7.7 Likelihood Ratio (LR) Test

H0: 𝐿𝑟 = 𝐿𝑢 the restricted model is suitable

H1: 𝐿𝑟 ≠ 𝐿𝑢 the unrestricted model is more appropriate

Likelihood ratio test is general defined according to Brooks (2008):

𝐿𝑅 = −2(𝐿𝑟 − 𝐿𝑢) ~ 𝜒2(𝑚) (7.5)

where Lr is the log-likelihood value of the restricted model, Lu is the log-likelihood value of the unrestricted model and m = number of restrictions.

7.8 Links to Data Sources

Ministry of Finance (FiD): http://www.government.se/sb/d/9513

National Institute of Economic Research (NIER): http://www.konj.se/698.html

Confederation of Swedish Enterprise (SN):

http://www.svensktnaringsliv.se/english/publications/

the Swedish Riksbank (RB): http://www.riksbank.se/en/Statistics/

Swedish Trade Union Confederation (LO): http://www.lo.se/start/lo_fakta

HUI: http://www.hui.se/en/research

Nordea: http://www.nordea.se/Markets/1585382.html

Skandinaviska Enskilda Banken (SEB):

46

http://www.seb.se/pow/wcp/index.asp?website=TAB4&lang=se

Svenska Handelsbanken (SHB): http://www.handelsbanken.se/analys

Statistics Sweden: http://www.scb.se/en_/Finding-statistics/

Documents

Bachelor thesis...Bachelor thesis Department of Statistics Nr 2014:x Measuring Real Economic Uncertainty in Sweden Alexander Thorleifsson, Johan Malmström Bachelor Thesis, 15 hp within