Media’s impact on inﬂation expectations

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Media’s impact on inflation expectations

Anita Einarsdottir

Master of Philosophy in Economics Department of Economics

University of Oslo

May 2018

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c Anita Einarsdottir May 2018

Media’s impact on inflation expectations http://www.duo.uio.no

Print: Reprosentralen, Universitetet i Oslo

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Preface

First of all, I would like to thank my supervisor Leif Anders Thorsrud for his invaluable help and encouragement. He has shown great interest in my thesis and supported me throughout this process. I am grateful to Larsen and Thorsrud for allowing me to use their work with newspaper data in my analysis. I would also like to thank Norges Bank for providing me with the data and inspiring me to write this thesis. Finally, I would like to thank my co-supervisor Nicolai Ellingsen who has given me useful feedback and input throughout this process. Any inaccuracies or errors are my own responsibility.

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Summary

Inflation expectations are essential for understanding inflation dynamics. However, there is little knowledge regarding how these expectations are formed. Survey data observe di↵erent inflation expectations among groups, which violates the assumption of standard economic theory. In particular, all agents are assumed to be rational and therefore have the same expectations. As a response to this, Carroll (2003) suggests that media plays a vital role in explaining di↵erences in inflation expectations. I build on this idea, and evaluate how di↵erent news topics a↵ect the inflation gap of Norwegian households and financial economists. This paper includes various type of news reported in Dagens Næringsliv and find that di↵erent news topics a↵ect the inflation gap between households and financial economists. Consequently, the results suggest that media impacts the inflation gap.

The sticky information model adopted from Carroll (2003), postulates that only a fraction of the agents in the economy absorb the newest information that rational professional forecasters transmit through media every period. I test whether the assumption of rational forecasters holds empirically, and find that financial economists are rational in forecasting the inflation rate, whereas households are not.

The model assumes that professional forecasters’ view is transmitted in the news, which is absorbed slowly, so the households’ inflation expectations will consist of some previous information, i.e., the experts’ past inflation forecasts. I evaluate this hypothesis by performing a cointegration test, which indicates whether households expectations and experts forecast move together in the long run. I find evidence for a cointegrating relationship, which I interpret as support for the theoretical model.

Carroll (2003) finds that the American households inflation expectations are sticky, in the sense that they infrequently update their expectations. I consider which degree the Norwegian households expectations are sticky, and find that the updating seems to be more significant for the Norwegian households compared to the American study done by Carroll (2003). This implies that media has a more prominent e↵ect on inflation

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expectations in Norway, as households update themselves more frequently.

I analyze how media reports, given in the Norwegian business paperDagens Næringsliv (DN), a↵ects households’ and financial economists’ expectations. Do media reports move households’ closer to rational forecasts? I measure the gap between households’

expectations and financial economists forecast and identify how di↵erent news topics influence the inflation gap. I find that di↵erent news topics have a variable e↵ect on the inflation gap. The results are found using a subjective variable selection of news topics and a formal variable selection by Lasso. I suggest a possible interpretation, namely that households do not capture the e↵ect of all given news topics. It may seem like households update their inflation expectations according to the news that is readily interpretable and has a direct impact on inflation. Financial economists, on the other hand, seem to understand the mechanisms of how inflation is a↵ected through various channels and therefore update their expectations accordingly. These findings suggest that news reports are significant for explaining di↵erences between households and financial economists inflation expectations, which should be examined further.

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1 Introduction

Inflation expectations are essential for understanding inflation dynamics in the New Keynesian model (Gal´ı, 2015). As central banks’ operational target is to keep inflation low and stable, inflation expectations are of crucial interest. However, these expectations are not directly observable. One way to circulate this problem is to measure inflation expectations through survey data. Standard economic theory assumes that all agents are rational and therefore have the same expectations. However, this is not what we observe. Expectations vary substantially among di↵erent groups in the survey data. Understanding and acknowledging heterogeneity in inflation expectations may improve the accuracy of monetary policy. Surprisingly, little is known regarding how these expectations are formed and what can explain the di↵erences in the inflation expectations.

As a response to this, Mankiw & Reis (2001) developed the idea that information is sticky, which indicates that agents only update their expectations periodically. Building on this idea, Carroll (2003) developed a model where media coverage may explain the gap in inflation expectations. He assumes that people obtain inflation forecasts from reports in media. Since people update themselves infrequently, it may take some time for new information to be processed by all agents in the economy. He finds that more frequent media coverage makes people more rational, in the sense that the inflation gap between households and professional forecasters decreases. Lamla & Lein (2008) extend the model by Carroll (2003), and include a tone variable to capture which direction people should revise their expectations. Thus, if rational forecasts are transmitted in the media, the tone may improve peoples’ forecast. However, if media emphasize negative news compared to positive one, the tone may cause a media bias and deteriorate the forecasts.

In this paper, I build on the analysis done by Carroll (2003) and Lamla & Lein (2008) and analyze how various types of news reports a↵ect the inflation gap between households and financial economists. In particular, I include various types of news,

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which represents news topics reported in media, and analyze how these types of news a↵ect the inflation gap between households and financial economists. For example may a change in the oil price a↵ect the activity in the economy and accordingly a↵ect the inflation expectations. It is therefore plausible to assume that people are influenced by multiple news stories, even though inflation is not directly mentioned in the newspaper.

Such e↵ects are not captured by Carroll (2003) and Lamla & Lein (2008), who use inflation reports given in the news. My hypothesis is the following: To the extent that people use newspaper to update their inflation expectations, various news topics may be of significance to explain the the expected inflation gap between households and rational forecasters. Hence, media reports may influence peoples’ inflation expectation and thereby also the gap between households and rational forecasters. My contribution to the literature is identifying which type of news topics impact the inflation gap between households and financial economists.

As opposed to the method used in Carroll (2003) and Lamla & Lein (2008), my approach adds more value in explaining the movement in the Norwegian inflation gap.

In particular, I use a tone and intensity measure for type of news, while Carroll (2003) and Lamla & Lein (2008) use an aggregate intensity measure of inflation reports. I find that the volume and tone variables of various news topics are significant, where the same intensity variables are not. Hence, this analysis includes the tone and volume of news topics and captures what type of news can explain movement in the inflation gap. This is not addressed in Carroll (2003) and Lamla & Lein (2008).

The paper concentrates on Norway. To address my hypothesis, I use the most comprehensive survey data on inflation in Norway conducted on behalf of Norges Bank.

The survey reports expectations of households, businesses, economists and labor organizations. The news topic time series are decomposed by Larsen & Thorsrud (2015) and represents a quantity measure from Norway’s biggest and most read business paper,Dagens Næringsliv (DN). The news topics are constructed using a topic model and measure the frequency and tone of the news. I use these news topics data to capture the e↵ect news stories may have in influencing the inflation gap.

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The theoretical framework given by Carroll (2003) which I build on, postulates some fundamental assumptions that need to be fulfilled for media to play a role.

First, theexperts in the theory are considered to be rational. The hypothesis is that households’ inflation expectations vary due to diverse absorption of information, which slowly extends in the economy. Present information is transmitted through rational professional forecaster to media and then in various degree obtained by the households.

I test the assumption of rational forecaster by analyzing the survey data from Norges Bank. I find that financial economists are the most rational group and accordingly give the most precise forecast. Contrarily, households are the least rational group, and there is insufficient coherence between survey expectations and actual inflation rate.

Second, there exists a long-run relationship between households’ and financial economists’ expectations. As the model assumes that information is absorbed slowly, the households’ inflation expectations will consist of some previous information, i.e., the experts’ past inflation forecasts. I perform a cointegration test, which indicates whether households’ expectations and experts’ forecast move together in the long run.

I find evidence for a cointegrating relationship, which I interpret as support for the theoretical model.

Third, I evaluate to which degree households’ inflation expectations are sticky. The updating seems to be more significant for the Norwegian households compared to the American households as found in Carroll (2003), which may imply that media has a more substantial e↵ect on inflation expectations in Norway.

Given these findings, I turn to my main hypothesis and analyze how di↵erent news topics impact the inflation gap between households and financial economists. The news data consists of 80 news topics, which makes the variable selection challenging.

First, I select six news topics according to economic intuition and find that positive macroeconomics news increases the gap between households and financial economists.

Surprisingly, the ”inflation category” represented by the news topicmonetary policy is not significant, which implies that other news topics are more important in explaining the movement in the inflation gap. Secondly, I preform a formal variable selection, given

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by Lasso (Tibshirani, 1996). I find that news aboutmacroeconomic events, export, and foreign-related news are essential for describing the inflation gap between households and financial economists. This may not be surprising, as Norway is a small open economy depending on trade. The positive macroeconomic news appears to increase the inflation gap, and positive foreign and export-related news seem to narrow the inflation gap. One possible explanation is that households do not seem to understand how inflation is a↵ected through foreign and export channels, and therefore do not capture the e↵ect of all given news in media. Households may only absorb the news that are directly linked to the Norwegian economy and may not understand the e↵ect that foreign and export-related news has for inflation. However, financial economists seem to capture how changes in export and foreign news impact the inflation rate, and update their inflation expectations accordingly. Hence, this interpretation that only financial economists react to such news, implies that the inflation gap narrows.

In sum, my results support the sticky information hypothesis adopted from the literature. Namely that households only absorb new information, from time to time.

Further, this paper identifies which information, given by the news topics, impacts the expected inflation gap between households and financial economists.

I perform all the analysis in the software R. The rest of the paper is structured as followed; section 2 describes the literature. Section 3 describes the theoretical framework. Section 4 describes the survey data and the newspaper data. In section 5, I test the empirical assumptions of the theoretical model. Section 6 examines which impact media has on the inflation gap. First, a subjective variable selection is performed and then a formal variable selection according to Lasso. Section 7 concludes.

2 Literature

The theory for inflation targeting is based on New Keynesian macro models, and the expectations are considered as essential for the formation of inflation dynamics (Gal´ı, 2015). Prices are regarded as ”sticky,” and agents must, therefore, take future costs

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into account. A model of staggered prices by Calvo (1983) has been used in the New Keynesian theory to explain rigidity’s in price-setting. The idea is that only a fraction of firms can update their prices in a given period, and the remaining firms are stuck with the same price as in the last period. In each period, the price adjustment follows a stochastic schedule, and each firm has the equal probability to be in the fraction of firms that can reset their prices, independent of the last time the firm was able to readjust their prices. If a firm expects inflation to rise, it is sensible to assume that they might increase prices with the same amount. Hence, inflation expectations have a direct e↵ect on actual inflation.

As prices are determined by current and future expectations about the economy, agents are considered to be forward-looking and rational. The rational expectation hypothesis developed by Muth (1961) states that all agents in the market have equal access to the same information and future expectations are formed by the ”true” structure of the economy. Agents have full information about the economic situation and take all information into account when making a decision or forecast. This is in contrast with adaptive expectation modeling, where expectations are formed based on recent events, hence the agents are considered to be backward-looking. A simple equation can explain adaptive expectations

⇡^e =⇡_t ₁ (1)

where inflation expectations are assumed to be the same as they were in the last period. However, Lucas (1972) argued that rational expectations are more satisfactory concerning information about expectation and forecasting, compared to the adaptive expectation hypothesis. Rational expectations should therefore give a more precise forecast and not make systematic errors about future developments.

Empirical studies observe the stickiness in prices, but also show that it can be con- venient not to consider all agents homogeneously, as we observe di↵erences in survey data. Druant et al. (2009) show that firms on average tend to keep prices unchanged

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around 10 months.¹ Erlandsen (2014) finds that Norwegian firms on average tend to change their prices every 8.5 months. However, when empirically testing the rational assumption Bryan et al. (2001a), Bryan et al. (2001b) and Jonung (1981) find di↵erences among groups when looking at data on household inflation expectations. Among groups with lower income and no college education, individuals report systematically higher expectations. Bryan et al. (2001a) also finds di↵erences in inflation expectation among men and women. Such findings suggest heterogeneity in expectations, and violates the assumption of rational agents in the New Keynsian model.

However, the price stickiness given by Calvo (1983) has been criticized in the literature. Critics of price stickiness have shown it to be inconsistent with the assumption of agents continuously optimizing prices. Accordingly, Phelps (1970) presented the idea that imperfect information gives the real e↵ects of monetary policy. Lucas (1973) argued that price rigidities result from lack of information regarding prices relevant for the agents’ decisions, hence agents observe the real state of the economy with a delay, which causes price stickiness. Mankiw & Reis (2001) developed the idea that information is sticky, and may therefore explain the di↵erences in prices and expectations. In every period, all people have the possibility to update their expectations, but information extends slowly in the economy. The slow dispersion may arise because of the cost of updating according to new information. The decision makers may rationally form an expectation based on incomplete information, explained by rational inattention. Sims (2010) show that the rational inattention, meaning that people have limited information processing capacity, may explain frictions and delays in macroeconomic dynamics.

Understanding why inflation expectations di↵er may improve the accuracy of monetary policy. Norges Bank’s inflation expectation survey, show that expectations vary among di↵erent groups. Such findings imply that the population groups may have diverse information about the economy, and therefore form di↵erent expectations. Hence,

1Wage Dynamics Network (WDN) developed the survey. It was implemented by 17 national central banks in the euro area in 2007-2008. More than 17 000 firms participated.

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sticky information and rational inattention may be a possible explanation for why we observe di↵erent expectations in the survey data.

3 Theoretical framework

I build my analysis on the theoretical idea put forward by Mankiw & Reis (2001) about information stickiness, by Carroll (2003) about the role of media, and by Lamla & Lein (2008) about the tone importance of media reports.

The model introduced by Mankiw & Reis (2001) takes rational inattention into account, and assumes that information about macroeconomic events extends slowly in the market and expectations are only updated from time to time. This assumption is based on the costs of updating or acquiring new information and is therefore named sticky-information model. The purpose of the model is to explain why people have di↵erent expectations. In every period only a fraction of the firms obtains the newest information about the current state of the economy and estimates optimal prices according to the information. The remaining firms continue to set prices relative to old and outdated information. This implies that inflation expectations do not immediately respond to changes in the economy, which is also more consistent with the empirical evidence.

An extended version of Mankiw & Reis (2001) is given by Carroll (2003). The model proposes that the expectation formation develops from consumers updating their expectations by news in media. Hence, people obtain their inflation forecast from news in media, which are considered to transmit the opinions of rational professional forecasters. It is assumed that people absorb the economic content of news infrequently, and this inattention cause ”stickiness” in inflation expectations. Carroll (2003) suggests that the empirical households’ expectations are not rational in the usual way, but the dynamics where households obtain news from rational professional forecasters make households rational.

Further, the model assumes that each inflation article holds the same information

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about a complete forecast of the inflation rate, that people can remember. In each quarter, share of individuals read and absorb the newest inflation information. The remaining 1 share do not process the new information and continue to use the last information gained in the previous quarter to forecast the inflation rate. Newspaper forecast is assumed to transmit professional forecasters view of inflation in periods t made in quartert. Defining⇡_t^eas the aggregate quarterly inflation expectations at time t and denoting ⇡_s^f_|_t as the newspaper forecast for period s, made in period t, gives:

⇡_t+1|t^e = ⇡_t+1|t^f + (1 )( ⇡^f_t+1|t ₁+ (1 )( ⇡^f_t+1|t ₂+....)). (2)

The equation shows the relationship between aggregate expectations and news forecast, that represents professional forecasters view. In periodt, share of the population will read the current newspaper forecast for the next quarter,⇡_t+1|t^f . While the remaining fraction (1 ) maintain the information and views held in the previous quarter, t 1, of the period t+ 1’s inflation rate. The periodt 1 views implies that a fraction of people came across an article in t 1 and absorbed the newspaper forecast for the next period, t+ 1⁰s forecast, ⇡^f_t+1_|_t ₁, and a fraction (1 ) maintain their period t 2 beliefs about inflation forecast in period t+ 1. The recursive structure leads to the rest of the equation.

If it is assumed that people forecast inflation solely based on experience, the inflation forecast will look like equation (1) on page 5, and expectations formation would be identical to adaptive expectations. However, the model assumes that people believe the experts have some more information about future economic events. Thus, the forecast from professional forecasters, i.e., media news, is more accurate than the adaptive expectations forecast people can form themselves. The inflation process is thereby captured by experts forecast cited in the news and unforecastable inflation shocks.

People believe experts presented in the news are capable of forecasting the next periods inflation rate², and that inflation evolve according to a random walk after

2Annual inflation forecast is made to equal four times the quarterly forecast so that the twelve- months inflation expectations can be used empirically.

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that. The forecast for the next period is, therefore, the best forecast of subsequent quarters, implying ⇡^f_t_|_t ₁ =⇡_t+1^f _|_t ₁,⇡^f_t+2_|_t ₂ =⇡^f_t+4_|_t ₂. Substituting this into equation (2) gives the following:

⇡_t+4^e _|_t = ⇡^f_t+4_|_t + (1 )⇡_t+3^e _|_t ₁. (3) The final equation shows the aggregate one-year inflation expectation is a weighted average between the rational forecast based on the newest available information and previous quarter aggregate inflation expectations.

The theoretical model adapted from Carroll (2003) assumes heterogeneity in households’ inflation expectations since information is slowly distributed in the economy. The current information arises from professional forecasters, which is spread to the households through media. As households update themselves infrequently, Carroll (2003) assumes that households’ expectations accommodate some previous inflation forecasts made by experts. The empirical results show that households on average roughly update their inflation forecast once a year. Such findings suggest that people periodically absorb new inflation forecast which results in stickiness in households’ expectations.

Main baseline for the model assumes that in periods with more inflation news, the frequency of updating will be more significant. Carroll (2003) performs a statistical test which evaluate whether higher news coverage is associated with more rational households. He estimates the inflation gap between households’ and experts’ expectations and defines the inflation index as the news, which reflects the explanatory variable in the model. Carroll (2003) finds that higher news coverage is consistent with more rational inflation expectations, as the inflation gap decreases. This is merely due to more frequent media reports make it more likely for people to read and absorb the news and therefore update their beliefs according to the rational forecast. Periods with more reporting than average gives a which is almost equal 0.7, while periods with lower intensity news coverage give = 0.2. Such results suggest faster-updating speed when the news coverage increases. Akerlof et al. (1996) find that workers do not

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care about updating themselves on the inflation rate unless when ignoring becomes costly due to high inflation. Periods with high news coverage correspond to periods with higher inflation in Carroll’s estimation, which makes the model by Akerlof et al.

(1996) consistent with the findings in Carroll (2003).

The extension by Lamla & Lein (2008) examines whether media reports impact the gap between households’ expectations and rational forecasters’ expectations. They address the importance of the tone in reports, which Carroll (2003) does not take into account. Studies by Hetherington (1996) and, Doms & Morin (2004) indicate that media a↵ect opinions and possible produce a media bias. However, if no media bias occurs, the tone of the reports should narrow the gap and bring consumer inflation expectations closer to experts forecast. They find various results. In periods where inflation is high, the media reports increases as to when inflation is low. Newspaper articles limit the gap, whereas TV news causes media bias.

The extended model by Lamla & Lein (2008) is estimated by measuring the gap in absolute value between the consumers’ survey (C_t) and the professional forecaster (P_t) 12-months expectations,AbsGapExp_t =ABS(C_t P_t). The explanatory variables are given by the number of inflation reports in a given month, divided by the maximum number of reports, which is in line with Carroll (2003). The tone is captured as positive, negative or neutral, regarding whether reports indicate that inflation rate is rising, falling or unchanged.

In section 5, I test the theoretical assumption imposed by Carroll (2003) empirically using the Norwegian survey data. The hypotheses I test are; First, are professional forecasters rational? Second, are the survey data of households and financial economists cointegrated? Third, to which degree are the Norwegian households’ expectations sticky?

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4 Data

In this section, the survey data conducted by Norges Bank and the newspaper data is presented. The data is quarterly, and covers the period 2002-2017. The survey measures inflation expectations for various groups in terms of expected twelve-month change in the consumer price index (CPI) at di↵erent horizons. As Carroll (2003) uses the one-year horizon, I center my analysis for this horizon.

The newspaper corpus consists of a sample from the most read business newspaper, Dagens Næringsliv (DN). The data set is generously provided to me by Larsen &

Thorsrud (2015).³ They compose textual data into time series by breaking down the data into news topics with a Latent Dirichlet Allocation (LDA) model. Thorsrud (2016) transforms news topics made in Larsen & Thorsrud (2015) into tone adjusted time series, by using dictionary-based techniques which identifies the tone.

4.1 Survey data

Inflation expectations in Norway are measured through surveys, which reflect agents’

perception of future inflation. There are several surveys available, as Consensus Fore- casts⁴ and Norges Banks regional network of businesses also report inflation expectations indirectly⁵. However, this analysis is based on the most comprehensive expectations survey. The survey was established in 2002 Q1, and is conducted by Epinion on behalf of Norges Bank.⁶ A sample of households, business leaders, economists in the financial sector and the academia, and the parties in the workforce - employer and employee organizations are asked about their future forecasts. All the groups are asked explicitly about their inflation expectations in one year, and the reported expectations

3I emphasize that Larsen and Thorsrud (2015) constructed the data set, and I am grateful to them for allowing me to use their work in my analysis.

4Consensus Forecast is monthly published by Consesus Economic Inc. which reports inflation expectations for di↵erent institutions in a large number of countries.

5The 300 businesses respond to their expectations regarding future views for employment, produc- tion and their own prices.

6I want to thank Norges Bank for providing me with the data. Epinion has conducted the expectation survey since 2015 Q1. Opinion and TNS Gallup previously did the survey.

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are shown Figure 1. Households expectations are significantly higher than the other groups.

Figure 1: Average expected inflation in one year’s time. Twelve-month change. Percent

Note: Figure 1 shows the average expected inflation rate in one year’s time for the various groups measured by twelve-month change. Data from 2002 Q1 - 2017 Q4, where the households inflation expectation for one year start in 2002 Q3. Sources: Epinion, Opinion and TNS Gallup.

The survey is usually performed at the beginning of the second month in the quarter.

The groups are asked in some di↵erent time period, where the periods overlap each other. Consequently, there might be some di↵erent knowledge within the groups, due

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to various response time.

Households are asked about the change in prices on goods and services measured by twelve-month change in the CPI. CPI measures the price of accumulated goods, and is the most common inflation measure. Households are interviewed by phone, and the telephone interview is conducted with a random selection of 1000 individuals from Norwegian households. The household average inflation expectations are calculated without extreme values, where average projection values above and below 11 percent are excluded (Erlandsen & Ulvedal, 2017). The time series for households was revised in 2018 Q1, for 2015-2017 which might also have caused structural breaks. I build my analysis of the original data.

The remaining groups are asked about the general price of goods and services in one year’s time, measured by twelve-month growth in CPI. Online surveys are given to the remaining groups. There are about 500 business leaders that participate in the survey, and the average inflation expectations are calculated similar to households’ expectations, excluding extreme values of +/- 11 percent (Erlandsen & Ulvedal, 2017).

For the remaining skilled groups; economists and parties in the workforce, the par- ticipation rate is lower. There are about 30 economists in academia that participate, and about 20 participants in the groups; economists in the financial sector, employer and employee organizations. Their average inflation expectations are calculated by excluding outliers of +/- 8 percent (Erlandsen & Ulvedal, 2017).

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Table 1: Descriptive statistics. Inflation expectations on average and standard deviations. 2002 Q1 - 2017 Q4. Percent

1 year Economist in academia 2,16

(0,4)

Economist in finance 2,00 (0,31)

Employer organizations 2,14 (0,36)

Employee organizations 2,19 (0,48)

Business leaders 2,45 (0,39)

Households 2,95

(0,42)

Note: The table shows average inflation expectations, measured as expected 12-months change in CPI in one year’s time. Data from 2002 Q1 - 2017 Q4, where the households inflation expectation for one year start in 2002 Q3. The parenthesis give the standard deviation. Sources: Epinion, Opinion and TNS Gallup.

Table 1 shows that inflation expectations for households and business leaders have on average been higher than for the remaining groups. The four remaining groups report lower inflation expectations and the variation is smaller for the financial economists, see standard deviations. All groups, except households, report lower inflation expecta-

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tions than the central bank target of 2,5 percent. However, the twelve-month change in the CPI has on average been 1,98 percent from January 2002 - December 2017. Figure 2 shows the actual inflation rate measured by the twelve-month change CPI.

Figure 2: Actual inflation rate measured by CPI. Twelve-month change. Percent

Note: Figure 2 shows the twelve-month change in CPI. Data from 2002-2017. Sources:

Norges Bank and Statistics Norway

As shown in Table 1 inflation expectation vary among the groups. From the following, it is critical to address how the groups form their expectations, and whether the assumption of the theoretical model holds. This is done in section 5. However, in the next section I describe the news data.

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4.2 News data

The DN news corpus, i.e., the entire assortment of words and articles, attains all news articles published in 2002-2017, gathered from Retriever’s “Atekst” database. Larsen &

Thorsrud (2015) start by filtering out common words and names, which is not expected to obtain any information about the subject of an article. Such words can for example beis, thereandare. Furthermore, they use an algorithm which cut down words to their relevant word stems. A word stem has an individual stem, where a part of the word is typical to all of its inflected variants. For example, the stem ofwaitingis wait. Finally, Larsen & Thorsrud (2015) estimate a corpus measure called term frequency-inverse document frequency (tf-idf), which weigh the importance of the words in explaining a given article. Higher frequency of a word in an article gives higher tf-idf score of that word. However, if the word is frequent in all articles, the words tf-idf score will decrease. The result gives a final corpus which includes around 250 000 stems with the highest tf-idf score.

The final corpus is decomposed into news topics that reflect articles content. Larsen

& Thorsrud (2015) use a Latent Dirichlet Allocation (LDA) model to do so. Blei et al.

(2003) introduced the LDA model which is an unsupervised learning algorithm. The model observes words appearing in an article and a topic is assigned to each word that is making the article. Hence, an article is a probability distribution over topics, and a topic is a probability distribution over words.

In the model, one has to specify how many topics to include. Larsen & Thorsrud (2015) estimate that 80 topics classify a satisfying statistical decomposition of the DN corpus. The LDA model then reads the text as words with a probability to belong to a topic. An article will thereby consist of di↵erent topics, with unlike weighting.

The topics are not named by the LDA process, but labeled subjectively from the most important words in the topic. All the estimated topics and labeling are shown in Table 11 in Appendix A. It is important to emphasize that all words appear in all topics, but weighted di↵erently. Larsen & Thorsrud (2015) find that all 80 topics share at least

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one word with another topic when including the first 17 words. This indicates that di↵erent topics relate to each other, both in terms of meaning and theme.

Next, Larsen & Thorsrud (2015) convert the decomposition of the DN corpus into time series. They calculate the frequency of each topic expressed in the newspaper each day. This number sums to one for all topics given every day. For the whole sample, each topic will on average have approximately the same probability to be presented in the newspaper. However, for shorter time periods as quarters, this may vary. The time series given in Larsen & Thorsrud (2015) illustrates an intensity measure of how much DN writes about a specific topic in a given time. For richer discussion of the decomposition, see Larsen & Thorsrud (2015).

Figure 3: Tone adjusted time series for individual news topics

Note: The tone adjusted time series show six out of 80 news topics. Data from 2002-2017.

Sources: Larsen & Thorsrud (2015) and Thorsrud (2016)

From the following, Thorsrud (2016) composes a tone adjusted time series, where

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Figure 3 illustrates six news topics that are tone adjusted. I suggest that the figures reflect important events in the economy, by giving two examples. The figure that illustrates ”wage payments” shows that the negative reporting increased in 2009-2010 and in the period of 2014-2016. Norges Bank (2018) reports that the annual wage growth decreased in these periods, which seems to be captured in the figure. The

”macroeconomics” figure, reports negative news in 2014-2016. This may be associated with the lower economic activity that Norway experienced in this period, due to the fall in oil price. Hence, the tone adjusted news topics figures seem to capture some important events in the economy. Table 6 on page 27 reports the most important words associated with the news topics that are illustrated.

To tone adjust the time series, Thorsrud (2016) finds which article is best explained by a given topic each day, and then identifies the tone in that specific article.

The tone, positive or negative, is determined by counting positive words and negative words in the text, such that each article reflects the fraction of positive and negative words. Thorsrud (2016) addresses Harvard IV-4 Psychological Dictionary to classify positive/negative words, and translate the words into Norwegian. The translated words contain 40 positive and 39 negative words, and for each article the count process gives two statistics which contains the number of positive and negative words. These data are normalized, so that every article observed reveals the fraction of positive and negative words in the given day, and used to tone the topic frequencies. For technical details, see Thorsrud (2016).

5 Testing the theoretical assumptions empirically

Before addressing my main research contribution, I test if the assumptions imposed by Carroll (2003) holds for the Norwegian data. To summarize, I test whether experts’

forecasts are rational, whether there exists a long-run relationship between households’

and experts’ expectations and whether the Norwegian households’ inflation expectations are sticky.

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If the forecasters are rational, the average forecast error should equal zero (Mincer

& Zarnowitz, 1969). This is given by E(u) = 0, where u_t = (⇡_t - ⇡_t^e_|_t ₄). Forecasters may systematically overestimate (underestimate) the actual inflation rate if the sign is negative (positive). This simple test is given in Table 2. The results show that all groups systematically overestimate actual inflation, given by the negative sign of E(u). However, the economists and the parties in the workforce perform substantially well. The financial economists’ forecasts are nearly exact and therefore considered to be most rational. Households are far worse o↵ in forecasting the inflation rate, and overestimate the inflation rate significantly.

Table 2: Average forecast errors for the CPI one-year expectations Households Business

leaders

Financial economist

Economist in academia

Employee org.

Employer org.

E(u) -1.033 -0.468 -0.030 -0.171 -0.201 -0.166

Note: The test calculates the average forecast error (Mincer & Zarnowitz (1969)), where E(u) = E(⇡) - E(⇡^e). Positive (negative) E(u) indicates that forecaster underestimates (overestimates) actual inflation rate. Data from 2002-2017.

A more formal test is given by the least squares regression (Mincer & Zarnowitz, 1969)

⇡_t =↵+ ⇡_t^e_|_t ₄+v_t. (4)

where the expectation survey is a rational and unbiased inflation forecast, if the constant term equals zero and the coefficient equals one (Roberts, 1997). Di↵erences between expectation and actual inflation, should be random and not able to predict.

This is captured by the error termv_t, which is assumed to be normal and white noise.

I test this assumption by computing a F-statistic, which is a statistic used to test the joint hypothesis for more than one of the regression coefficient. The joint hypothesis restrict the values:

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H₀ :↵= 0 and = 1 vs. H₁ :↵6= 0 and/or 6= 1 (5) where the null hypothesis indicates rational and unbiased forecasts. If any restric- tions under the null hypothesis are false, the joint hypothesis is rejected (Stock &

Watson, 2012).

I estimate equation (4) by ordinary least squares (OLS). The results are given in Table 3. The point estimates for the individual regression are given by the estimated coefficients and ↵. The joint hypothesis that the constant and the coefficient is, respectively, zero and one are shown in the F-test. Significance levels indicate the confidence of rejection of the null hypothesis. The F-test is rejected for all groups at a 10 percent level, except for the economists. This implies that the test for rational and unbiased forecasts can not be rejected for the economists. The point estimates seem to correlate little with actual inflation for all groups expect the financial economists, where the -coefficient is significantly di↵erent from zero at a 10 percent level. For the remaining groups, the point estimates are rather far o↵.

Table 3: CPI rational and unbiased test for one-year inflation expectations Households Business

leaders

Financial economist

Economist in

academia Employee org. Employer org.

-0.526 (0.328)

0.383 (0.364)

0.802*

(0.452)

0.469 (0.361)

0.103 (0.351)

0.216 (0.392)

↵ 3.480***

(0.979)

1.041 (0.902)

0.367 (0.918)

0.970 (0.789)

1.752**

(0.780)

1.515*

(0.853)

F-test 30.461*** 5.909*** 0.137 2.355 6.357** 2.778*

Note: One years inflation expectations values are estimated by OLS based on equation (4).

Expected 12-months change in the CPI for one year’s time is contained by Epinion’s survey.

Quarterly data from 2002 Q1 to 2017 Q4, where the households inflation expectation for one year start in 2002 Q3. Standard deviations in parentheses. F-values from testing the joint hypothesis↵=0 and = 1. Heteroscedasticity-corrected standard errors are used for the test. The stars indicate: ^⇤p<0.1;^⇤⇤p<0.05;^⇤⇤⇤p<0.01

The tests indicate that financial economists are most rational in forecasting the

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inflation rate. I can not reject the hypothesis that ↵ = 0 and = 1 which implies a rational and unbiased forecast. Subsequently, I consider this group to be the experts according to theory. On the contrary, households are the least rational in forecasting and quite far o↵ in point estimates. ↵ is significantly di↵erent from zero, and a slightly high coefficient indicates that households systematically overestimate inflation rate, which is consistent with the simple test reported in Table 2. Hence, I continue the analysis using the most rational group, financial economists, and the least rational group, households. Accordingly, financial economists serve as the experts and households represent the aggregate inflation expectations in the theory.

As shown in section 3, the theory adapted from Carroll (2003) suggest a cointegration relationship between households’ and financial economists’ expectations. I test whether the variables in equation (3) are cointegrated, which indicates if expectations of experts and households move together in the long run. Engle & Granger (1987) developed a test for cointegration, where two time series are said to be cointegrated if they share a common trend component. The Engle-Granger approach assumes that the two variables are integrated of order one, I(1), so I start o↵ by performing a Dickey-Fuller test.

Table 4: Augmented Dickey-Fuller test

⇡^e t-statistics 1 % critical value 5 % Critical value

Households -0.739 -2.576 -1.960

Experts -0.398 -2.576 -1.960

Note: The Augmented Dickey-Fuller test is of the form yt =µyt 1+"t, where the null hypothesis of having a unit root isµ= 0. If the null hypothesis is not rejected, it implies that yt is integrated of order one. The test statistics have a distribution which is non-Gaussion leading to di↵erent critical values.

Dickey & Fuller (1979) test for a unit root against the alternative of stationarity. As shown in Table 4, the Augmented Dickey-Fuller test does not reject the null-hypothesis of a unit root for variables of households’ and financial economists’ expectations. These results imply that the variables are integrated of order one, I(1).

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I then proceed to test for cointegration between households’ expectations and experts’ forecast. First step is to estimate equation (3) by OLS. The Augmented Dickey- Fuller test implied that both variables are I(1), and the next step is to check whether the estimated residuals contain a unit root or not. If the residuals are stationary, the variables in the regression, namely households’ and experts’ inflation expectations, are cointegrated. I test whether the estimated residuals are stationary by conducting an Augmented Dickey-Fuller test on the residuals. The results from implementing this test to households’ expectations and experts’ inflation forecast are shown in Table 5. I reject the null hypothesis of no cointegration, as the test statistics are larger in absolute value than the critical values. The results suggest evidence for cointegration between the survey measures. I find that households’ expectations move towards the professional forecasters’ expectations and interpret such findings as support for the sticky information model by Carroll (2003).

Table 5: Engle-Granger test for cointegration

eˆ_t t-statistics 1 % critical value 5 % Critical value

I(1) residuals -5.800 2.567 1.941

Note: The test reported are from Engle-Granger and test whether the estimated residuals are stationary or not. The null hypothesis is no-cointegration and rejection of the null hypothesis, implies evidence for cointegration. Critical values are reported in MacKinnon (2010).

The estimated relationship imposed in the theory, is given for the Norwegian households’ in the following equation:

Households_t = 0.527^⇤⇤⇤⇥Experts_t + 0.636^⇤⇤⇤⇥Households_t ₁. (6) Equation (6) describes Carroll’s model of sticky information. The model excludes a constant term and explains a basic description of how inflation expectations are formed. If actual inflation rate and the rational forecast made by experts were fixed,

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households expectations would gradually converge to the constant rate. On the other hand, the model assumes that households have significantly higher inflation expectations than experts, which is consistent with the summary statistics in Table 1. I find that Norwegian households inflation expectations are less sticky, as the coefficients for experts forecast is greater in magnitude compared to the results from the American data.

Hence, the Norwegian households seem to update themselves more frequently than the American households, I suggest that there is a bigger role for media in a↵ecting the inflation expectations. In the next section, I investigate how the Norwegian newspaper DN a↵ects the inflation gap between households and financial economists.

6 Medias impact on the inflation gap

In this section, the models imposed by Carroll (2003) and Lamla & Lein (2008) are extended. I estimate a model which includes explanatory variables that account for both the volume and tone reported in DN. I analyze how the inflation gap is a↵ected by various news topics, and estimate the following equation by OLS:⁷

AbsGapExp_t =↵+ ₁N ews^y_t + ₂AbsGapExp_t ₁+"_t (7) where equation (7) combines the models given by Carroll (2003) and Lamla & Lein (2008). The news variable, N ews^y, captures the e↵ect of the tone and volume of the given news topic reported in DN. y represents the di↵rent news topics. Equation (7) accounts for whether the expected inflation gap increases or decreases concerning positive or negative media reports. Positive ₁ suggests that more positive (negative) information increases (decreases) inflation expectation gap. Whereas, a negative ₁ implies that positive (negative) information narrows (expands) the inflation gap. The last periods’ gap is included in the regression, in case of correlation with the current

7I use heteroscedasticity and autocorrelation consistent estimators.

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news topics, and which also captures the e↵ect of previous media reports. Hence, the lagged gap is included to correct for persistence in the gap. "_t captures the noise.

Figure 4: The average expected inflation gap between households and financial economists. Percent

Note: The expected inflation gap is given by households - financial economists survey data for one year’s time expectations. Data from 2002 Q3 - 2017 Q4. Sources: Epinion, Opinion and TNS Gallup.

AbsGapExp_t represents the absolute value gap between households’ and financial economist’ one year expectations, see Figure 4. It is important to point out that the gap given by (households - financial economist) is exclusively positive; however, I follow Lamla & Lein (2008) notation. The lowest measured di↵erence of 0.3 percent is given

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in 2007 Q2, 2009 Q2, and 2016 Q3. The first two periods may be associated with right before and after the financial crisis, and the last period may be related to the fall in oil price. Actual inflation is high for these given periods, except for 2007 Q2. Thus, the high inflation rate is not consistent with lower inflation gap. However, the expected inflation gap is highest in 2011 Q4 and 2013 Q1, and this is a period where actual inflation rate declines, see Figure 2. Figure 1 shows that households’ expectations increase after the financial crises, relatively to financial economists. The gap widens in this period and then narrows during 2013 2017, which is shown in Figure 4. However, the financial economists seem to increase their inflation expectations during the period of 2014-2016, where the oil price fell. There may be many reasons why the expectations vary, but this analysis addresses the e↵ect media has for explaining the di↵erences in expectations.

As I have 80 possible explanatory variables, the variable selection is challenging.

First, I subjectively select six topics according to economic intuition. Secondly, I perform a variable selection according to Lasso (Tibshirani, 1996), which is given in section 5.2.

6.1 Subjective variable selection

Rather than assuming that households only obtain information through inflation reports, I impose, perhaps, a more realistic assumption where households update their inflation expectations when various news are reported in DN. It is plausible to assume that people might update their expectations even though inflation is not directly mentioned or written about in the newspaper. Other economic events as wage increase or changes in the key policy rate might a↵ect inflation expectations. Before addressing which news topics I consider to be relevant for the inflation gap, I want to illustrate how inflation may be a↵ected through various channels.

Assume the official interest rate is changed, which may a↵ect the price level through di↵erent channels. Change in the official interest rate may cause asset prices and

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exchange rate to adjust. Inflation may be directly a↵ected by changes in the exchange rate, through imported goods which are used in consumption. Such changes may a↵ect saving and investment decisions. Household and firms may, for example, increase their saving and decrease their investment with a higher interest rate. This, in turn, can lead to changes in aggregate demand and domestic services, which may translate into changes in labor and product markets. Consequently, prices and wage-setting might be a↵ected.

Similarly, one may not be surprised that increased news about oil price a↵ects the economic view, as Norway is a small open economy depending on the oil sector (Bjørnland & Thorsrud, 2015b). The oil price fell drastically in the period 2014-2016 and Norway had to adapt to lower demand from the oil sector. A lower oil price impacts the Norwegian economy through various channels, hence the domestic market has to readjust. The krone exchange rate weakened as a consequence of the fall in the oil price and had a direct e↵ect on inflation through imported goods (Norges Bank, 2016).

The key policy rate was lowered⁸ to stabilize the economy. Norges Bank (2016) showed that lower activity in the Norwegian economy contributed to lower investments and employment fell markedly in the oil sector. A combination of lower employment, lower real wages, and uncertainty lead to lower consumption and increased savings. This e↵ect could impact other Norwegian sectors and thereby adjust the price developments.

As indicated, price developments and inflation expectations can work through many di↵erent channels, and this study therefore concentrates on various news topics. Media reports may not mention inflation directly, however other news topics may matter for inflation expectations. From economic intuition and the illustrations above, I expect the news topics monetary policy, wage payments, macroeconomics, stock market, oil price andemployment condition to be essential for the inflation gap. These news topics reflect the six out of 80 topic labels from the DN corpus which I subjectively consider to be relevant for inflation expectations. Table 6 reports the label of the topic and the most important words associated with each topic.

8Norges Bank lowered the key policy rate from 1,5 percent to 0,5 percent in the period 2014-2016.

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Table 6: Estimated topics and labeling

Label First words

Monetary policy interest rate, central bank, euro, german, inflation, point

Wage payments income, circa, cost, earn, yearly, cover, payed, salary

Macroeconomics economy, budget, low, unemployment, high, increase

Stock market stock exchange, fell, increased, quote, stock market

Oil price dollar, oil price, barrel, oil, demand, level, opec, high

Employment conditions cut, workplace, measures, salary, labor, working, employ

Note: Topics are labeled based on the meaning of the words. The Norwegian words are translated to English using Google Translate. Source: Thorsrud (2016).

I estimate a univariate regression according to equation (7), where the results of the OLS estimation are reported in Table 7 on the next page. The macroeconomics topic is the only significant news topic. Positive reporting will widen the gap, and higher negative reporting will narrow the gap. I find it interesting that the news topic monetary policy is not significant for explaining the gap, as the word inflation is one of the essential words in the topic, see Table 6. Both Carroll (2003) and Lamla &

Lein (2008) use an index where they calculate the number of inflation reports given in a specific month and divide by the maximum number of inflation stories in any year, as their volume variable. From their analysis, I would expect the topic monetary policy to have a similar e↵ect for the Norwegian data set. Thorsrud (2016) points out that Loughran & McDonald (2011) find that word lists developed for other contexts

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Table 7: Univariate regression of equation 7 Dependent variable: AbsGapExp_t

(1) (2) (3) (4) (5) (6)

Monetary Policy_t 0.042 (0.062)

W age_t 0.017

(0.056)

M acroeconomics_t 0.131^⇤⇤⇤

(0.045)

Stock_t 0.016

(0.044)

Oil_t 0.037

(0.034)

Employmentt 0.021

(0.046) AbsGapExp_t ₁ 0.551^⇤⇤⇤ 0.551^⇤⇤⇤ 0.482^⇤⇤⇤ 0.544^⇤⇤⇤ 0.544^⇤⇤⇤ 0.541^⇤⇤⇤

(0.096) (0.108) (0.110) (0.101) (0.117) (0.118) Constant 0.424^⇤⇤⇤ 0.422^⇤⇤⇤ 0.474^⇤⇤⇤ 0.429^⇤⇤⇤ 0.426^⇤⇤⇤ 0.430^⇤⇤⇤

(0.094) (0.105) (0.112) (0.100) (0.117) (0.120)

Observations 61 61 61 61 61 61

Adjusted R² 0.284 0.277 0.351 0.277 0.287 0.277

Note: ^⇤p<0.1; ^⇤⇤p<0.05; ^⇤⇤⇤p<0.01

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may be misspecified for finance. This may cause a misleading sign in macroeconomics also, due to the positive and negative words accounted for. Subsequently, this is a possible reason for why the news topic monetary policy is not significant in explaining the inflation gap. However, the volume variable of monetary policy, which is described below, is not significant either, see Table 12 in Appendix B. This implies that the

”inflation category” may not significantly explain the movement in the inflation gap between households and financial economists. The subjectively chosen news topics do not seem to have much explanatory power for the gap, except for macroeconomics.

This is also reflected by the adjusted R² which increases in the univariate regression with the news topic macroeconomics.

The inflation gap widens when positive macroeconomic news increases. However, it is hard to distinguish whether such news increase households’ inflation expectations or lower the financial economists’ expectations, as the gap increases. One possible interpretation of such results may be that financial economist do not react much to news published in DN, as they work within the field. Financial economists may, however, adjust their inflation expectations given by the economic situation, which DN reflects. Yet, households may react to news in DN as households do not have the same knowledge about economic conditions as financial economists. Accordingly, households may update themselves about new economic events, and this may a↵ect their future expectations. A plausible assumption would be that households increase their inflation expectations as positive macroeconomic news are reported. Higher inflation is correlated with higher economic growth and is generally associated with positive macroeconomic news.

This analysis di↵ers from Carroll (2003) and Lamla & Lein (2008), and I want to examine whether my approach improves to explain movement in the inflation gap.

In particular, I use a tone and intensity measure, while Carroll (2003) and Lamla &

Lein (2008) use an aggregated intensity measure. Carroll (2003) suggests that the intensity of the inflation index reporting matters for inflation expectations. Hence, I calculate the absolute value ofAbsN ews^y, to only capture the volume of news, which is

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consistent with Carroll (2003). I find that the absolute value of the subjectively chosen news are not significant in explaining the inflation gap, see Table 12 in Appendix B.

However, as this analysis addresses how di↵erent types of news a↵ect the inflation gap, I do not have an exact comparison with Carroll’s (2003) work. I use tone and volume variables, N ews^y, or just volume variables, AbsN ews^y, concerning news topics, while Carroll (2003) uses the aggregated volume of inflation reports. However, I find that the volume and tone variables add more value in explaining the inflation gap relative to the volume variable.

Table 8: Control for absolute values and previous news reports Dependent variable:

AbsGapExp_t AbsM acroecomics_t 0.076

(0.103) AbsM acroecomics_t ₁ 0.024

(0.101) M acroeconomics_t 0.139^⇤⇤

(0.062) M acroeconomics_t ₁ 0.002

(0.067)

AbsGapExp_t ₁ 0.467^⇤⇤⇤

(0.118)

Constant 0.417^⇤⇤⇤

(0.139)

Observations 61

Adjusted R² 0.323

Note: ^⇤p<0.1; ^⇤⇤p<0.05; ^⇤⇤⇤p<0.01

Further, I control for last period values, the volume of news, and the tone and

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volume given in the news. The results are reported in Table 8 on page 30, and suggest that the tone and volume variable for the given period, has more explanatory power than the volume variable. I therefore conclude that my approach, which includes the tone of the reports, is more valuable in explaining the inflation gap between households and financial economists. In addition, I also control for lagged values of all the subjectively chosen explanatory variables from the last period. News in the previous quarter does not seem to a↵ect the inflation gap, see Appendix B, Table 13. However, this seems reasonable as the lagged gap is included and captures the e↵ect of previous news reports. From the following, I choose to omit news variables from the last quarter in my further analysis.

I now estimate the multivariate regression of equation (7) where all the news topics subjectively chosen are included in one regression. As an article consists of all topics with various weight, there may be some correlation between the selected variables. The multiple regression looks at the relationship of all six variables to the inflation gap, controlling for each other. The results are given in Table 9 on page 32, and suggest that positive news about macroeconomics and oil seem to increase the inflation gap.

The oil price topic is only significant when the topic is influenced by other independent variables, and may be associated with macroeconomic news. Norway has around 50 percent of exports revenues are related to oil and gas (Bjørnland & Thorsrud, 2015b).

Hence, positive news about the oil price may increase the activity in the Norwegian economy. Households may absorb such news and increase their inflation expectation as higher economic growth is associated with higher inflation. The gap widens when positive news about macroeconomic events, including the oil price, are reported in DN.

From this simple analysis, I conclude that the tone adjusted time series have more explanatory power than the absolute value of news topics. I omit last periods news report as the lagged inflation gap is included and may capture the e↵ect of previous news reports. Hence, I extend the analysis according to equation (7). However, the news topics are subjectively chosen, and there might be other topics that capture the variation in inflation gap better. The next section discusses methods for formal variable

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Table 9: Multivaraiate regression of equation 7 Dependent variable: AbsGapExp_t

Monetary Policy_t 0.026

(0.077)

Wage_t 0.083

(0.062) Macroeconomics_t 0.198^⇤⇤⇤

(0.061)

Stock_t 0.030

(0.039)

Oil_t 0.068^⇤⇤

(0.033)

Employment_t 0.022

(0.051)

AbsGapExp_t ₁ 0.480^⇤⇤⇤

(0.104)

Constant 0.462^⇤⇤⇤

(0.095)

Observations 61

Adjusted R² 0.361

Note: ^⇤p<0.1;^⇤⇤p<0.05; ^⇤⇤⇤p<0.01 selection with high dimensional data.

6.2 Formal variable selection

This analysis has 80 possible explanatory variables, which makes OLS challenging.

When the number of variables exceed the number of observations, the degrees of free-

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dom becomes too large and the least squares method is not feasible. In this section I use the Lasso⁹ method for a formal variable selection. As the Lasso shrinks the coefficients towards zero, the estimation gives biased coefficients. I therefore preform a post-Lasso, to obtain unbiased coefficients. The post-Lasso regression will increase it’s variance when more variables are added, so I restrict the number of explanatory variables.

Consider the linear regression

AbsGapExp_t =↵+

X80 j=1

jN ews^j_t +"_t (8) which is used to describe the e↵ects of the news variablesN ews^j_t for the response variable AbsGapExp_t. In this multiple regression, there might be some variables that are not a↵ecting the response variable. Removing variables that do not have explanatory power, gives a more interpretable model. In Appendix D, I discuss forward stepwise regression which is an alternative method to Lasso for variable selection. Table 14 in Appendix D, shows the results of the OLS regression, obtained from the forward stepwise selection. The selected variables are similar to the selected variables from Lasso, in particular six out of nine variables are equal.

Lasso was introduced by Tibshirani (1996) and performs both variable selection and regularization to improve prediction accuracy and interpretability of the model.

Consider the previous model that explains variation in inflation expectations with p= 80 predictors. The least squares model fits estimates, ₀, ₁,...., _p that minimizes the residual sum of squares (RSS):

RSS =

Xn t=1

(AbsGapExp_t ↵

Xp j=1

jx_tj)² (9)

Lasso is similar to the least squares regression, but the coefficients are estimated by minimizing a di↵erent restriction. The coefficients, ˆ^L estimated from Lasso are

9Least Absolute Selection and Shrinkage Operator