What's up with the Phillips Curve? A study of the missing disinflation in the Eurozone during the Great Recession.

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What’s up with the Phillips

Curve?

A study of the missing disinflation in the Eurozone

during the Great Recession

Bachelor thesis

written by

Alberto Pavia Soto

11652136

under the supervision of Andr´as Lengyel, MPhill, in partial fulfillment of the requirements for the degree of

Bachelor in Economics and Business Economics

Faculty of Economics and Business Unversity of Amsterdam

The Netherlands June 2020

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This thesis constructs a simple expectations-augmented unemployment Phillips curve `a la Friedman (1968) to study the relationship of inflation and the unemployment rate in the Euro area during the Great Recession and the Sovereign Debt Crisis. This research is motivated by the phenomenon of the missing disinflation, which saw inflation levels decrease significantly less dur-ing the recession than previous estimations predict it would. To study this, I regress four different iterations of actual inflation and inflation expectations: HICP and core HICP, and SPF and backwards-looking expectations. In a linear model without an intercept and estimated with Newey-west standard errors, only a regression using a core inflation measure and SPF data cor-rectly explains the behaviour of inflation during this period. The conclusion, based on previous theory and empirical data, is that the source of this devi-ation of core values from headline measures is due to the oil price increase that occurred during that period.

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1. Introduction

For the last decade, Europe has lived its worse economic crisis since the end of World War II. This period marked an official recession in the Eurozone during 33 months: between Q2-2008 and Q2-2009, and from Q4-2011 un-til Q1-2013. The recession marked a “lost decade” (Piroli, 2015) in which 2007 levels of output per capita took until the end of the year 2014 to re-cover. Furthermore, the unemployment rate almost doubled, and the rate of poverty, measured in severe material deprivation, rose dramatically (Duiella Turrini, 2014). Arguably, despite all these indicators, the fascinating event that happened during this time is the unexpected behaviour of inflation. The Phillips curve is a theoretical equation that relates the deviations of inflation from expectations with the deviations of the level of unemployment from its natural rate. In previous years, the curve has shown that inflation falls significantly when the level of unemployment increases. However, during the Great Recession, the unemployment rate in the continent increased dramat-ically, whereas inflation did not fall as much as expected. This phenomenon is called the “missing disinflation”, and is one of the leading research pri-orities of macroeconomists. At the end of the crisis, inflation did not rise to the level that predictions believed, a twin phenomenon that is called the “missing inflation”.

Several theories attempt to explain this phenomenon. Although some theories argue the relationship established in the Phillips curve is “dead”, other researchers have looked for alternative explanations to the missing dis-inflation puzzle, which vary from a structural flattening of the relationship of unemployment and inflation to temporal variations in prices that mitigated the effect of the recession in the price level. However, before evaluating these theories, the importance of the Phillips Curve for monetary policy should be examined.

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monetary policy is a tricky endeavour: the variable that central banks tar-get, inflation, cannot directly be changed. Instead, what policymakers do is to monitor and manipulate a series of variables, called monetary indica-tors. A monetary indicator is “some readily observable economic time series which can be used to scale monetary of fiscal influences on economic activ-ity” (Keban, 1970). Through the use of these indicators, the inflation rate is affected. However, two complications arise with its use. First, the strength of an indicator depends on the strength of its correlation with the price level, so only variables that have a long-standing, stable relationship are prone to be used. Second, monetary policy generally occurs with a lag; that is, there is a delay between the implementation of policies that affect the inflation rate and the observation of their effects on it. These two complications show why the use of the Phillips curve is important in monetary policy, and why exploring a possible alteration of its behaviour is crucial. If there is indeed a constant relationship between unemployment and the price level, current unemployment can be used to predict the inflation rate in future periods, and conduct monetary policy based on those predictions rather than on current values. Furthermore, a relationship like this could allow central banks to use monetary policy not only to achieve price stability but also to guarantee full employment, which is not currently an attribution of the European Central Bank. If the Phillips curve no longer holds in its current form, as could be indicated by the missing disinflation and missing inflation events, forecasts of future inflation would be incorrect, which means that monetary policy conducted today could have a high level of bias.

Therefore, this paper will evaluate whether a simple Phillips curve can explain the missing disinflation and to a smaller extent, the missing inflation that happened in the Eurozone during the Great Recession and the Sovereign Debt Crisis.

This dissertation will investigate the source of the missing disinflation through an empirical model, and it will link it to the distortionary effect that oil prices may have had at the price level. A simple expectations-augmented Phillips curve will be constructed and evaluated against two measures of inflation: a headline indicator and a core indicator. In line with previous research and intuition, the hypothesis is that a core inflation measure can explain most of the behaviour of inflation during this period, with head-line measures of inflation painting a misleading image of the behaviour of inflation.

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Phillips curve will be explored, together with the phenomenon of the miss-ing disinflation and its proposed explanatory theories. Subsequently, the research design will start by describing how the dataset used is obtained and constructed. The model will also be displayed, together with the diagnostic tests needed to prove that the regressions provide accurate results. In the re-sults and discussion chapter, the model, as well as its possible consequences, will be debated. Finally, the conclusion will wrap up the dissertation, expos-ing the strengths and weakness of the model, its main conclusions, as well as suggestions for future research on the topic.

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2. Literature Review

2.1 The origins of the Phillips Curve

Since the origins of economics as a science, one of its primary goals has been the study of money. In a series of lectures at King’s College, Keynes (1932) distinguished a barter and a monetary economy. He stated that barter economies are those where money acts as an intermediary, but only to mea-sure the share of actual output rewarded to labour. In this case, the study of money cannot provide many insights, as it does not provide any information about the state of real economy variables, like unemployment or economic growth. In a monetary economy, however, money is not just a means of ex-change, but also an influential factor in the economy, like happens in modern economies. Money is then another dimension that has to be studied sepa-rately for its effects on the real economy. Keynes emphasises the importance that monetary and fiscal policy has on the real world, and he uses it to achieve his two main goals: to explain the reason why modern economies experience periodic booms and recessions and to explain the incomplete utilisation of labour in modern economies; that is, the source of unemployment (1937).

After Keynes, many economists have looked for relationships between real economy and monetary indicators. Monetary policy is now understood to be an essential part of economics. Arguably, the most critical monetary indicator is inflation. Inflation is “the rate of increase in prices over a given period of time” (Oner, 2010). The process of keeping inflation low and stable, called price stability, is the primary attribution of central banks. In the European Union, the European Central Bank is the sole institution that is in charge to keep prices “below, but close to 2% over the medium term” (ECB, 2020). Price stability improves the transparency of the price mechanism, reducing the premium that inflation causes on interest rates, reducing the distortions on the tax system, avoiding hedging against price increases, and

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contributing to price stability (ECB, 2020).

Inflation is essential not only by itself but also through its effect on other elements. One of these elements is unemployment. Although achieving full employment is not part of the ECB’s foundational statute, Frankfurt pays close attention to the level of employment for policy decisions (Hein, 2002). A relationship between unemployment and inflation could be useful for cen-tral bankers in two ways. First, providing a way of forecasting the effects of monetary policy. Because monetary policy always acts with a lag, it is hard for central bankers to carry out adequate actions (Matthews, Giuliodori & Mishkin, 2013). If there were a relationship of this tool with unemployment, its study could provide a better image of the effects of policy decisions. Sec-ond, because every society wishes to use its human capital stock as fully as possible, a relationship between both variables could lead to central banks taking measures to ensure full employment.

The most notable and fruitful analysis of the relationship between unem-ployment and inflation is the Phillips Curve. A.W. Phillips first introduced it in 1958. In his article, published in the journal Economica, Phillips describes the empirical relationship between unemployment and the rate of change of money wage rates in the United Kingdom using data from 1861 until 1967. When arguing his research, he alludes to the logical relationship between unemployment and wages, and between wages and prices. When jobs are scarce, workers are more willing to work for lower salaries, because often their main alternative is not working and not earning any income. This way, the average wage rate decreases in periods with high unemployment, like re-cessions. When workers earn a lower wage, they have less disposable income to spend on consumption, so they tend to buy fewer goods. If this happens to a significant amount of workers, which is a reasonable assumption in times of economic downturn, the aggregate demand for goods decreases, which makes prices decrease to sell excess production. As said earlier, a general decrease in the price level causes an increase in unemployment. Similarly, when the unemployment rate is low, the business has a hard time finding new workers. As a result, wages increase and, to the extent this happens to a big enough group of people, the general wage rate increases. Workers then have more disposable income for consumption, which eventually causes an increase in the general price level.

Phillips’ main contribution was empirically confirming this logical rela-tionship and stating it in a formal model. He defined it as

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y + a = b ∗ xc

or log(y + a) = log(b) + c ∗ log(x)

Where y is the rate of change of wage rates, x is the unemployment rate, b and c are constants estimated by least squares, and a is a constant estimated by trial and error.

Phillips observed a clear tendency of the change in wage rates to be higher when unemployment is low, or smaller/negative when unemployment is high (p. 290). He also observed asymmetry between the changes: when unemployment is low, wages increase at a higher rate than they decrease when unemployment is high, due to price rigidities.

Figure 2.1: Original Phillips curve. Source, Phillips (1958)

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research focused on replicating the model for different countries. Once it was proven that this relationship holds in every country, more advanced versions followed. Samuelson and Solow (1960) found that a similar neg-ative relationship existed for the United States. However, Phillips’ theory did not go unchallenged. As King and Watson (1994) recall, there was a big divide between theories about the nature and existence of the Phillips curve. On the one hand, were the neoclassical and monetary economists. For them, the Phillips Curve was a faux relationship, caused by an identifi-cation error. Indeed, Lucas (1972) and Sargent (1971) argued that changes in inflation respond only to inflation expectations, meaning that an estima-tion of the Phillips curve is not correctly identified if it does not include a proper behavioural model. The “abnormal” period of the 1970s helped this point, in which U.S. data seemed to imply that the relationship between in-flation and unemployment had become positive, rather than negative. On the other hand, there stood the (Neo)Keynesian economists. For this strand of thought, the Phillips curve is an excellent tool to estimate the effects of monetary policy in society despite short-run deviations.

After the 1980s, and with the arrival of the Neoclassical Synthesis, these two opposing theories converged. Nowadays, there is little doubt about the existence of the curve or its usefulness. King and Watson (1994) show that, for the United States, there is a strikingly stable negative correlation over the business cycle between inflation and unemployment. This conclusion follows after an expectations-augmented Phillips Curve. This type of curve adds a term for the inflation expectations because research (Friedman, 1968) has shown that the behaviour of inflation depends to a great extent on the pricing decisions that agents in the economy make, which are based on their expectations about the future price level.

In the Eurozone, the Phillips curve is also said to hold, albeit with some particularities. Because the labour market is less flexible in Europe – due to stronger labour unions and worker protection laws – the fluctuations in the relative level of wages are smaller than in other developed economies. However, this does not mean that a Phillips curve cannot correctly describe the relationship that inflation deviations and unemployment gaps have, but it is instead an indication about its relative shape. However, due to the Eurozone’s short life, this data has not been as researched as in the United States or the United Kingdom.

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2.2 The missing disinflation

The outbreak of the 2008 financial crash and the subsequent recession has called into question the current effectiveness of the curve. In Europe, this era was especially challenging for the economy due to two twin recessions: the Great recession of 2007-2009 and the Sovereign Debt Crisis of 2010-2013. During this period, the gross domestic product of the Euro Area fell by dramatic levels, and the unemployment numbers rose to 12%, even reaching 26.3% in Spain or 27.47% in Greece (OECD, 2019).

(a) Inflation rate, Eurozone. (b) Unemployment rate, Eurozone.

Figure 2.2: A comparison of the evolution of inflation and unemployment between 1997 and 2020 in the Euro Area.

Throughout this time, sustained high unemployment levels accompanied higher than predicted inflation rates. According to the Phillips curve, the fall in output and wage rates caused by the recession would have caused a persistent decline of inflation. Such a drop in prices would have put Europe into a downwards spiral of deflation. The drop in the aggregate price level was therefore much smaller than predicted. Furthermore, during the post-recession phase unemployment figures increased, while inflation remained stagnant. Such an event also contradicts the predictions of the curve, which indicate that inflation would rise to significantly higher levels. The deviations from predictions observed in both periods have caused speculation about a change in the historical relationship between unemployment and inflation.

The absence of a persistent decline in inflation after the recession is named “missing disinflation” after Coibon and Gorodnichenko (2015). Furthermore, the absence of a significant pick-up in inflation levels during the subsequent

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recovery is called ”missing inflation” after Constˆancio (2015). Several theo-ries have attempted to explain this phenomenon and consist of two categotheo-ries. On the one hand, some think that the Phillips curve relationship has disap-peared, or weakened so much it has lost its utility. Hall and Sargent (2018) write that the Phillips curve has lost its effectiveness at modelling the evo-lution of inflation because it cannot precisely describe its behaviour and is not resistant to reforms in macroeconomic policy. On the other hand, some think that the puzzle of the missing disinflation is due to changes in inflation dynamics. Del Negro et al. (2020) divide this last branch of theories in four different explanations: (i) a mismeasurement of inflation or the slack of the economy; (ii) a flattening of the wage Phillips curve; (iii) a flattening of the price Phillips curve and (iv) a flattening of the aggregate demand relation-ship that is induced by an improvement in the ability of policy to stabilize inflation.

Other sets of influential theories argue that inflation has lost its long-established link with the level of slack in the economy because inflation rates are well anchored nowadays (Bernanke, 2007). An anchoring of inflation expectations means that economic agents believe in the ability of the central bank to keep inflation at target, so they have no incentive to deviate their pricing decisions from this level. As a consequence, agents always set prices to this target level, regardless of the level of inflation. Even if not all authors agree with this theory, they agree that during the Great Recession there was a tendency to mute disinflationary pressures due to a better anchoring of inflation expectations (Williams 2009, Stock and Watson 2010). However, as Coibion and Gorodnichenko (2015) conclude in their research for the US, a recent flattening of the curve could not fully account for the levels of missing disinflation observed.

Other reasonings provide a more optimistic view of the factors that made the Phillips relationship not correctly predict the mild inflation dynamics during the recession. Coibion and Gorodnichenko (2015) make an exhaustive review of different hypotheses – a change in slope, a structural change, alter-native measures of inflation expectations – and conclude that the origin of the missing disinflation is the over-sensitivity of small firm inflation expectations to the contemporary increase in oil prices. To study this, they substitute the usual inflation expectations indicators used in Phillips curve research by a survey of household expectations. According to them, household expecta-tions are a better proxy for small firm inflation expectaexpecta-tions because small firms are more sensitive to highly visible prices than to aggregate-economy

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indicators. Because the toughest part of the Great Recession coincided with a global rise in oil prices, the deflationary pressures caused by the recessions appeared to be smaller. Similarly, the subsequent decline in oil prices may be the source of the missing inflation. Because the most common measure of inflation expectations, the Survey of Professional Forecasters, does not take into account the distortion that oil generates towards the perception of the aggregate price level, Phillips curves do not correctly identify inflation expectations. Ball and Mazumder (2019) prove something similar, using a simple Phillips curve with measures of inflation that take out both the di-rect and indidi-rect effects of energy prices in the aggregate price level. They conclude that this approach explains most of the inflation behaviour during the recession.

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3. Research design

3.1 Data Description

The data for this research is from several sources. To measure inflation, the model uses two indicators. The first one is the harmonized index of consumer prices provided by the Eurostat (2020), and which is compiled by the Federal Reserve Bank of Saint Louis. This measure of inflation is relevant because it is the one communicated to the public by the European Central Bank and therefore, the one that most agents use to form inflation expectations. The second one will be the core consumer price index, defined as all items non-food, non-energy, created by the Organisation for Economic Co-Operation and Development (OECD, 2020) and also compiled by the FRED.

Inflation expectations come from the Survey of Professional Forecasters conducted by the European Central Bank and obtained through the ECB Statistical Data Warehouse (2020). Based on previous literature like Ball and Mazumder (2019), these expectations follow 5-year forecasts. Furthermore, the model also uses as a check of robustness a measure of backwards-looking expectations constructed through an equation that uses the same inflation measure as is used in its regression. The measure for the level of employment used is the harmonized unemployment rate, which originates in the OECD (2020). The measure for base unemployment is the non-accelerating wage rate of unemployment or NAWRU obtained from the OECD.

All of these indicators are for the Eurozone-19 countries: Austria, Bel-gium, Cyprus, Estonia, Finland, France, Germany, Greece, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Portugal, Slovakia, Slovenia, and Spain; with standard weights set by the European Central Bank.

The data for the analysis of oil prices and their contributions to headline inflation measures comes from the OECD (2020) Main Economic Indicators

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data. This dataset contains the consumer price index for energy (fuel, elec-tricity gasoline) in quarterly growth rates from the same period last year. This series, unlike the rest, corresponds to all the European Union-28 mem-bers, rather than to the Eurozone-19 members. Despite this, the assumption is that no significant changes occur within both groups.

The model uses quarterly data. Therefore, the measures of core inflation, HICP, and unemployment rate are quarterly ones. NAWRU has a yearly structure but, on the assumption that the underlying factors that determine the natural level of unemployment in an economy change slowly, the data is made quarterly by assigning the rate of one year to the quarters in that year. The fact that, even on an inter-annual basis, the NAWRU data in the sample is very compact, with a total amplitude of just 1.1 percentage points and a maximum yearly shift of 0.3%, justifies this assumption. The SPF data is also provided yearly and is quartered identically as the NAWRU following the same reasoning. All the values have different periods for which they are available, with the harmonized unemployment rate being available from the third period of 1990 until the first period for 2020, and the shortest one is the SPF, which is only available starting from 2003.

Another important thing for the model is the timeline of the series. Usu-ally, series like inflation are revised, meaning that they are adjusted at a later date to fit the actual behaviour of the indicator better. However, this research assumes that agents look at currently available data when forming inflation expectations. Therefore, all the series used will not contain any revised ex post data.

3.2 Model design

As was explained in the literature review above, since the original estimation made by Phillips, several models have been proposed. In this dissertation, the model for the Phillips Curve originates on a simple version of a textbook Phillips curve used by Ball and Mazumder (2019). This model is specified `

a la Friedman (1968), where he assumed that core inflation depends on ex-pected inflation and the level of slack in the economy. As this research is concerned with the effect of employment on inflation, the measure of slack in the economy used will be the gap between the harmonized unemployment rate and the non-accelerating wage rate of unemployment.

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πt− πte= α(u − u∗)t−1+ t

Where πtis the inflation rate in period t, πteis the expected inflation rate

for period t, (u − u∗₎

t−1 is the difference between the unemployment rate

u and the natural unemployment rate u∗, averaged from period t − 4 until period t − 1, α is the variable of interest that is estimated in the model, and t is the error.

This basic model assumes that the deviations of inflation from inflation expectations depend on the deviation of unemployment from its natural or base rate. Ball and Mazumder justify the use of this unemployment gap in previous literature like Stock and Watson (2009) and their previous research of the Phillips curve in the US (2019). Because the quarterly unemployment data enters the regression as a four-period average, seasonal variations in employment smoothen out. Furthermore, taking the difference between per-centage measures of actual and natural unemployment allows for an interpre-tation of the gap as the percentage change of the deviation of unemployment from the non-wage-accelerating rate. Furthermore, this model does not in-clude a constant in the regression under the assumption that, if the model holds actual inflation is the same (or close) as expected inflation when the level of employment does not deviate from its natural level.

To test the hypothesis that a core inflation measure can explain the phe-nomenon of the missing disinflation observed in the Euro area, this simple model runs with two different measures for inflation: “headline” inflation – defined as the harmonized index of consumer prices – and “core/base” inflation – defined as the price index of all items non-food, non-energy –.

Furthermore, two different measures of inflation expectations will be used: the annual Survey of Professional Forecasters with 5-year ahead estimations, and a measure of expected inflation assuming backwards-looking expecta-tions. The rationale for this choice is that previous research on the topic, most notably Coibon and Gorodnichenko (2015), has indicated that profes-sional forecasters expectations may be a poor proxy for the inflation expec-tations of (small) firms. Therefore, an alternative measure is constructed based on the assumption that agents construct their inflation expectations with previously available data by averaging the actual inflation rates for the previous four quarters:

Etπt+1=

1

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The Survey of Professional Forecasters asks professional agents what they think the inflation rate will be in five years. The value of the SPF for 2020 is, therefore, the average of the 5-year ahead expectations formulated in 2015. This choice arises from previous literature.

In the case of the unemployment gap, it is necessary to find a proper instrument for the natural rate of unemployment. The unemployment rate has the following form:

ut= tt+ ct

Where ut is the unemployment rate which is decomposed into a trend

tt and a cycle ct component. When referring to the level of “slack” in the

economy, authors refer to the cyclical component, which shows the temporal deviation of unemployment from its natural rate, tt. Therefore, the

nat-ural rate of unemployment is the rate at which the economy would settle in the absence of shocks (Orlandi, 2012). Institutional factors determine this level, and it cannot be empirically measured. Therefore, several mod-els exist as a proxy. In this research, the non-accelerating wage rate of unemployment, or NAWRU, will be used. This indicator, constructed by the Directorate-General for Economic and Financial Affairs of the European Commission, determines the natural rate by assuming that cyclical unem-ployment – which in this research is called unemunem-ployment deviation – affects wage inflation, whereas structural unemployment does not. Therefore, im-plicit in the formulation of the NAWRU is the fact that deviations from its level cause wage inflation, and thus, it is an ideal instrument to use in the study of the Phillips curve.

The measure for unemployment gap is constructed the following way: first, calculating the previous four-quarter average of the unemployment rate and the non-accelerating wage rate of unemployment. Then, calculating the difference (u − u∗₎

t−1 by subtracting the mean unemployment rate to the

mean NAWRU.

For the regression, the model uses least squares. However, due to the structure of the data, several challenges arise. The data used has a time series structure (Stock Watson, 2015). During its manipulation, it is not unusual to find autocorrelation inside a variable, meaning that the value of that variable in that period correlates with its values in previous periods. Such an event can affect the standard errors of the distribution, as it contradicts normal models, in which the regression errors are assumed to be independent and

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identically distributed – or i.i.d. – which means that cov(vt, vs) = 0 and that

var( ˆα1) =

σ_v2 T (σ2

x)2

Statistical software like Stata uses this formula to calculate the standard errors of the regressors in an OLS regression. However, in time-series data frequently cov(vt, vs) 6= 0, which means that the formula above stated is not

valid anymore. The new formula that applies is var( ˆα1) = [ 1 T ∗ σ2 v (σ2 x)2 ] ∗ fT in which ft= 1 + 2 ∗ T −1 X j=1 (T − j T )ρj

Because the only element that changes in these two expressions for the variance of the regressor is fT, the regular OLS standard errors are erroneous

by a factor of fT.

A new formula to calculate the standard error can fix this bias. This regression uses Heteroskedasticity- and Autocorrelation- Consistent (HAC) standard errors (Stock & Watson, 2015), which is consistent with previous research for simple Phillips Curves, like Ball and Mazumder (2019). HAC are robust both to heteroskedasticity – thus controlling for error variance that does not depend on the independent variable – and to autocorrelation. It has its distribution equal to the equation stated above.

Because fT is not known, it needs to be estimated. In this research the

estimator used will be the Newey-West HAC standard error estimator: ˆ fT = 1 + 2 m−1 X j=1 (m − j m ) ˜ρj

Where m is the truncation parameter estimated by the rule of thumb m = 0.75 ∗ T13

3.3 Diagnostic tests

Several diagnostic tests are conducted to check the correctness of the model above estimated. It is essential to check if the use of a Newey-West HAC

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stan-dard error is necessary. For that, two tests are conducted: a Breusch–Godfrey LM test for autocorrelation of the residuals and a Breusch-Pagan test for het-eroskedasticity. Both tests run on the four regressions estimated.

To conduct a Breusch-Godfrey LM test, the estat bgodfrey Stata com-mand is used. This test serves to detect serial correlation in the error term of the regression and to determine the appropriateness of using the Newey-West regression. In this test, the null hypothesis is that there is no serial correlation, while the alternative hypothesis being there is. After running the test for the four regressions, the coefficient is always rejected with probabil-ity > 0.99999, which means there is strong evidence that autocorrelation is present in the estimation, and therefore using HAC standard errors is needed. To conduct a Breusch-pagan test, the estat hettest Stata command is used. This test also gives information about the errors in the regression, but in this case, it tests for heteroskedasticity. The null hypothesis is that the error term is homoskedastic – has constant variance – and the alternative hypothesis is that it is heteroskedastic. Rejecting the null hypothesis would mean that the recession needs to use robust errors, something the Newey-West regression does. This test runs on all regressions, and again the null hypothesis is rejected, meaning there is heteroskedasticity in the error terms and that a Newey-West specification is appropriate.

Because of the rule of thumb stated in the previous section about the value of the m the truncation parameter, the number of lags included in the Newey–West standard errors for the coefficient estimated by OLS regression is ≈ 3 for all the regressions, where the number of observations oscillates from 69 to 78 depending on the measure for inflation expectations/actual inflation used. This choice is consistent with previous literature on the topic.

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4. Results and discussion

Before running the regression, it is crucial to study the characteristics of the data-set constructed. The summary statistics of the data are plot in table 4.1 and give information about the evolution of the data over time. The first observation is that the HICP has a mean very close to zero. It seems, however, that there is no presence of deflationary levels in most data-points measured, but rather that there are considerable negative values that distort the positive values. The presence of these negative values shows in the high standard deviation of 0.961 and the minimum value of −4.27% that corresponds to the third quarter of 2009. This minimum value is double the size of the maximum value, 2.077%. Therefore, this shows that the HICP data has a considerable amplitude. The core inflation data, however, is much higher on average and with a much smaller amplitude. It shows a mean of 1.373%, with a standard deviation of 0.421%. The most outstanding element is that the minimum is 0.656, meaning that even in the worst quarters of the Great Recession, there was no deflation in the core indicator. The difference between both measures shows that the inflation indicator chosen has critical effects on the estimation of the Phillips curve.

Table 4.1: Summary statistics

Variable Mean Std. Dev. Min. Max. N HICP -0.113 0.961 -4.27 2.077 113 Core HICP 1.373 0.421 0.656 2.479 93 Harmonized unemployment rate 9.519 1.313 7.3 12.1 119 SPF 1.891 0.063 1.77 1.98 69 NAWRU 9.079 0.37 8.1 9.5 81 The unemployment data is not very remarkable, showing a mean of 9.519% and a standard deviation of 1.313%. It should be pointed out that

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when this paper refers to variation, it does so for the evolution over time of the aggregate Eurozone-wide value, and not about the differences between the individual unemployment (or, to that matter, inflation) rates of Euro countries. The SPF data has a mean of 1.891% and a remarkably low stan-dard deviation of 0.063. This value is compelling because it shows that, at least for professional forecasters, inflation expectations are well anchored in the European Union. The mean value, which coincides with the “below, but close to 2% over the medium term” ECB goal (2020) shows that inflation expectations are stable at the ECB goal value, and the very low standard deviation shows the trust that it will stay this way. This observation rein-forces one of the explanations for the missing disinflation provided during the literature review, which is that inflation expectations are well anchored, and that has debilitated (or eliminated) the relationship between inflation deviations and the unemployment gap.

About the non-accelerating wage rate of unemployment, or NAWRU, not much can be said. The base unemployment measure shows a mean of 9.079% and a relatively small standard deviation of 0.37. The data is stable with a minimum of 8.1% in the year 2019 and a maximum of 9.5% in the year 2013. A conclusion about the model that will be estimated follows this anal-ysis: because both SPF and the NAWRU rates are remarkably constant, this means that, in practice, the model behaves such that inflation en-tirely depends on the unemployment rate, which was anticipated by Ball and Mazumder (2019).

After running regressions for the four combinations of HICP and core in-flation and SPF and adaptive inin-flation expectations, the regression results are plot in table 4.2. Here, DifE HICP EZ is the regression using headline infla-tion and backwards-looking expectainfla-tions, DifE CHICP EZ is the regression using core inflation and backwards-looking expectations, DifSPF HICP EZ is the one that uses headline inflation and SPF inflation expectations, and DifSPF CHICP EZ is the one that uses core inflation and SPF inflation expectations.

The result of the four regressions is remarkable. Out of all of them, only DifSPF CHICP EZ is highly significant – with confidence rate big-ger than 0.999 – when regressed against the gap between core inflation and SPF inflation expectations. For the rest, DifE HICP EZ is not significant, DifE CHICP EZ only is with a p-value of 0.070 and DifSPF HICP EZ is with a p-value of 0.084, which can indicate two things: first, that the model is not correctly specified because there is some relevant indicator omitted or,

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Table 4.2: Regression table

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DifE HICP EZ DifE CHICP EZ DifSPF HICP EZ DifSPF CHICP EZ UnempDif 0.154 -0.0629 -0.603 -0.355∗∗∗

(0.163) (0.034) (0.344) (0.075)

N 77 77 69 69

Newey-West standard errors in parentheses ∗ _{p < 0.05,}∗∗ _{p < 0.01,}∗∗∗ _{p < 0.001}

second, that the model indeed shows that only a combination of core infla-tion and professional forecasters’ inflainfla-tion expectainfla-tions can correctly predict the Phillips curve. Assuming that the model is indeed correctly specified, as is suggested by previous research and by the diagnostic tests conducted, the conclusion is that, as was predicted, a core measure of inflation describes better the dynamics between inflation and the level of slack in the economy. Because the model assumes that inflation depends entirely on unemploy-ment, and because the unemployment rate is stable over time, a more stable measure of inflation like core HICP will better fit the jobless data.

This regression also shows that backwards-looking inflation expectations are not a good proxy for inflation expectations, consistent with the fact that, when conducting pricing decisions, economic agents do not look at how the economy behaved previously but rather at the information about how it will behave later on. Furthermore, this helps the hypothesis that inflation expectations are well anchored. It is important to note that both measures of inflation expectations, SPF and backwards-looking, cannot be directly compared because they have a different time horizon: SPF data is extracted from 5-year forecasts, whereas adaptive inflation expectations only look four quarters back.

The estimated Phillips curve, using core inflation and SPF inflation ex-pectations, looks like this:

πt− πet = −0.355(u − u∗)t−1+ t

Which can be interpreted this way: when unemployment deviates from its non-wage-accelerating level by 1%, then the core inflation rate is equal to the SPF inflation expectations minus 0.355%. This model has a goodness-of-fit of 0.3618, which is not very high, but is much higher than the R2 values of

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DifE HICP EZ (0.0236), DifE CHICP EZ (0.0696), and DifSPF HICP EZ (0.1105).

When the primary regression is estimated with a constant, this constant is very significant, with a value of −0.4442719 and a Newey-West standard error of 0.0769418. This evidences that there may be a specification error with the model because, by assumption, a constant is not included (see model design). However, the R2 _{coefficient is only 0.3845, smaller than before, meaning that}

even though the coefficient may be significant, it does not help with the fit of the regression. Because of this, this research will still regard the non-constant model as correctly estimated.

The next step is to plot the respective Phillips curves. First, the curves for backwards-looking expectations using headline and core inflation are plotted in figure 4.1.

(a) Curve using headline inflation. (b) Curve using core inflation.

Figure 4.1: A comparison between Phillips curves built with HICP and core HICP using backward-looking inflation expectations for the Euro Area.

In both figures, the curve does not provide a good fit to describe the behaviour of inflation in the Eurozone. In the case of headline inflation, the curve is very flat due to two main clusters of outliers: first, on the bottom-left corner and which represents quarters between 2008 and 2009, and second on the top-middle with observations from 2010. An explanation for these values arises from the estimation of inflation expectations. The first cluster represents a period of sharp deflation that occurred after high inflation seasons, which causes backwards-looking expectations in this cluster to have very high negative values. With the second cluster, a similar explanation

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arises, but now for a period of compensatory rising inflation that was not correctly predicted by previous observations of little inflation. In the case of the curve using core inflation, the curve does not present significant clusters of outliers but still does not provide a good fit for the evolution of inflation.

Figure 4.2: Phillips curve built with core HICP and SPF inflation expecta-tions for the Euro Area.

Then, the curve for SPF inflation expectations and HICP is plotted in fig-ure 4.2. This estimation, which uses the inflation indicator most commonly available, shows the existence of the missing disinflation: a cluster of observa-tions, all of them in the bottom-left corner and which correspond to quarters between 2007 and 2009. It is evident, therefore, that a Phillips curve based on headline inflation measures cannot correctly explain this phenomenon.

Next, the curve for SPF inflation expectations and core HICP is plotted in figure 4.3. Visually, it is evident that this Phillips curve is a much better description of the evolution of the unemployment gap. Even though not all data lies in the curve, there is a noticeable downwards trend for all the data. More importantly, the problem tackled in this dissertation seems solved with this estimation: the missing disinflation present in curves that measure head-line inflation is gone. Furthermore, there seems to be little missing inflation during the subsequent recovery, which is further proof of the strength of the model. The hypothesis stated at the beginning of this dissertation is

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there-Figure 4.3: Phillips curve built with HICP and SPF inflation expectations for the Euro Area.

fore confirmed, as a simple expectations-augmented Phillips curve using core inflation indicators can correctly explain the puzzle of the missing disinflation in the Euro Area.

As an additional visual indicator, the evolution predicted by the estimated curves can be plot against actual inflation values. As backwards-inflation expectations have shown not to give a good fit, only plots using SPF inflation expectations appear here. The first one is figure 4.5 that uses HICP. Here, predictions do not offer a good fit for actual inflation data, as the curve does not seem to match actual values at any point, while also not following its overall trends.

Then, figure 4.5 with a core HICP measure is plotted. Here, the conclu-sions that arose from figure 4.3 seem weaker. This curve does seem to be a better fit of the data, matching actual core inflation more closely than the previous curve, due to their considerable difference in the goodness of fit – 0.1105 vs 0.4013 –. The plot accounts for most of the missing disinflation phenomenon, except for a bigger-than-expected dip in the first two quarters of 2010. It also shows a characteristic of the recession in Europe: the first drop in inflation that seemed to recover in the year 2011 which was then followed by a further decline due to the Sovereign Debt Crisis. However,

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Figure 4.4: Evolution of HICP and the inflation predicted by a Phillips curve that uses headline inflation and SPF inflation expectations.

Figure 4.5: Evolution of HICP and the inflation predicted by a Phillips curve that uses headline inflation and SPF inflation expectations.

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this plot shows some of the missing inflation that occurred from 2015 still unaccounted for: while the curve expects inflation to rise to its 2% target slowly, the reality shows that core inflation stabilises around the 1% level.

Figure 4.6: Evolution of HICP and core inflation over time for the Euro Area. The cause of this difference between measures of inflation stands out when plotting HICP against core HICP in figure 4.6. This plot shows that, even though the HICP does fall significantly during both the Great Recession and the European Sovereign Debt Crisis, the measure of core inflation is remarkably stable. This stableness suggests that the cause of the variation in headline inflation is not due to a change throughout all prices, but rather a fluctuation in one of the price categories that HICP measures but core HICP does not: energy or food. Based on previous literature, there were no natural events or indications that suggest that food prices varied in such a dramatic way. However, literature (Jorgensen & Lansing, 2019) shows that, during the recession, there was a worldwide increase in the price of oil, which can be seen in a plot of the price index of energy (fuel, electricity & gasoline) against both headline and core inflation in figure 4.7.

This figure confirms previous literature and shows that changes in oil prices are the source for the differences between core and headline inflation in this period. The HICP shows an identical, albeit at different amplitudes, movement with the prices of energy. The only two periods where overall

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(a) Energy prices vs headline inflation. (b) Energy prices vs core inflation.

Figure 4.7: A plot of the consumer price index of energy (fuel, electricity & gasoline) prices against both a headline and a core measure of inflation for the Euro Area.

and energy prices do not move together are between 2007-2009 and between 2012-2016. In the first interval – except for the sharp dip in 2009 – energy prices have very high inflation levels – around 10% yearly – whereas the HICP measure does not show such an increase. It is obvious to see how these high values in energy prices could interfere with the drop in inflation caused by the dramatic increase in unemployment, which can explain why there exists missing disinflation in this period. In the second interval, oil prices take a big dip, which is as high as 5% in the year 2015. Following the same reasoning, higher levels in inflation caused by the economic expansion of these years could be pushed down by oil prices in the event of the missing inflation. However, the subsequent rise in oil prices that is not accompanied by a notable rise in the HICP confirms the hypothesis of Ball and Mazumder (2019) that not all of the missing inflation can be accounted by a simple Phillips curve model like this.

The conclusion is that the significant variations in the level of HICP as compared to its core counterpart can be explained by the also considerable variations in oil prices during that time. The cause of the missing disinfla-tion is, therefore, not a change of the fundamental underlying reladisinfla-tionships that define the Phillips curve, but rather by the distortionary effect that a substantial shift in the price of oil had on the measure of headline inflation at the same time a global recession was happening.

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5. Conclusion

This dissertation explains the behaviour of the relationship between devia-tions from inflation expectadevia-tions and the deviation of unemployment from its natural, non-wage-accelerating level. More specifically, an explanation is given for the higher than predicted inflation levels during the bulk of the Great Recession in the Eurozone. This phenomenon, called the missing disinflation, saw inflation rates that were significantly different from those predicted by a Phillips curve.

A simple expectations-augmented Phillips curve was constructed for the Euro area. The results indicated that, even though a measure of the curve that uses the harmonized index of consumer prices cannot explain the phe-nomenon of the missing disinflation, a simple model with a core measure of the HICP has a better fit and correctly predicts the output of those obser-vations. The reason is that core measures of inflation are much more stable through different quarters, a behaviour that is similar to that of unemploy-ment. The source for the higher volatility in headline measures of inflation is the rise in global oil prices that occurred in a contemporary manner to the global recession. The missing inflation that happened during the subsequent recovery can also be partially accounted by a contemporary decrease in oil prices, although this simple expectations-augmented Phillips curve does not fully account for it.

This research opens the door for additional questions. Here, the causal relationship between the rise in oil prices and the differences between the headline and core inflation measures is studied. Additional research should be conducted to analyze the specific relationship between both variables. An important question to answer is if the behaviour of oil prices could thoroughly explain the abnormal behaviour of inflation, or if it is just a part in a long-term alteration of the Phillips curve relationship. As was revealed in this paper, other factors like the better anchoring of inflation expectations by the

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European Central Bank do not fully explain the missing disinflation but can provide an adequate image of the conditions that helped it take place, for which further study is critical. As was argued during the literature review, central banks highly depend on the Phillips relationship to conduct monetary policy. If the missing disinflation is fully accounted for by the behaviour of oil prices, it would mean that were a similar crisis to hit Europe then the actions taken by the ECB could not have prevented a deflationary cycle absent the pressures on oil prices.

Another important focus for future research is the study of different mea-sures of inflation, their stability, and their appropriateness of use in a Phillips curve. As was seen, the use of headline and core measures of inflation can profoundly affect the estimation of Phillip’s relationship. This paper estab-lishes that core inflation is an adequate measure to explain the behaviour of inflation and isolate it from oil price fluctuations. However, as Ball and Mazumder (2019) argue in their research, a core measure may not be enough to isolate oil price effects because, even though direct prices do not appear in the index, it is still a significant element that alters the price level in other industries, albeit with a lag.

Furthermore, it would also be interesting to study the role of unemploy-ment in the Euro Area, and the long-term trends that it shows concerning its effect on inflation. Trends like globalization, the digital revolution, or the changes in European society, may have further proven to debilitate the Phillips relationship, as Europe cannot be studied anymore as a closed sub-ject, but rather through its relationship with other economies. The men-tioned trends could cause a shit of tendency from increasing the wage prices towards relocating these jobs to other world regions during low unemploy-ment periods in Europe.

Even with its shortcomings, the simple model constructed in this thesis has proven to be an accurate and not complicated tool to study inflation. One conclusion of this research, therefore, could be that the concerns about the death of the Phillips curve have been overstated. It can be easy, indeed, to declare a model “dead”, rather than analyzing what the circumstances that lead to its apparent death are. One need not worry though, for the Phillips relationship is here to stay: that is what’s up with the Phillips curve.

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What's up with the Phillips Curve? A study of the missing disinflation in the Eurozone during the Great Recession.