The Phillips curve; a useful tool after all?
Inflation expectations in the Netherlands
Master’s Thesis
“The effects of monetary policy on the economy today depend importantly not only on current policy actions, but also on the public’s expectations of how policy will evolve . ... Indeed, expectations matter so much that a central bank may be able to help make policy more effective
by working to shape those expectations.”
- Ben Bernanke (2013)
Rosa van der Drift
Student number 10740244
University of Amsterdam Master of Science in Economics
Monetary Policy and Banking Supervisor: Dr. Marcelo Zouain Pedroni
The Phillips curve; a useful tool after all?
Inflation expectations in the Netherlands
Rosa van der Drift
Student number 10740244
Abstract Inflation dynamics in advanced economies have produced three Phillips curve puzzles. This study investigates whether these three anomalies—missing disinflation, excessive disinflation and a flattening of the curve—are also puzzles for the Netherlands. First, I do not find support for a period of missing or excessive disinflation. Second, I do not find support for a structural break, suggesting that the curve is stable over time. Thus, all three puzzles are not puzzles for the Netherlands. However, after 2010 another puzzle emerges; the curve shifts up by 0.686 percentage points. I am not able to explain this upward shift; therefore, the Phillips curve is not a useful tool for the Netherlands.
Statement of originality This document is written by Student Rosa van der Drift who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Supervisor: Dr. Marcelo Zouain Pedroni July 14, 2018
Contents
1 Introduction 1
2 Literature Review 3
2.1 The Phillips curve . . . 3
2.2 Missing and excessive disinflation . . . 5
2.3 The slope of the Phillips curve . . . 6
2.3.1 The slope of the curve in the eurozone . . . 6
2.3.2 The slope of the curve in the Netherlands . . . 7
2.3.3 An explanation to the flattening . . . 7
2.4 Inflation expectations . . . 9
2.5 No curve . . . 10
3 Data 11 4 Results 12 4.1 The excessive and missing disinflation periods . . . 12
4.2 The slope of the Phillips curve . . . 13
4.2.1 The slope of the Phillips curve overtime . . . 16
4.2.2 The steepening of the curve post crisis . . . 16
4.3 An explanation to the shift of the curve . . . 18
4.3.1 Inflation expectations overtime . . . 20
4.3.2 Have inflation expectations become more or less firmly anchored . 21 4.4 Allowing for different versions of the Phillips curve . . . 22
4.4.1 Can different versions of the Phillips curve account for the shift . 24 5 Conclusion and discussion 26 References 28 A Derivation of the Phillips curves 31 A.1 The expectations-augmented Phillips curve . . . 31
B Transformation of the Consumer Survey 35
C Robustness to different measures of expectations 38
D Additional Tables and figures 40
D.1 Additional figures . . . 40
D.2 Additional tables . . . 42
List of Figures
1 The Dutch Phillips curve relation overtime . . . 82 Labour-market trends in the Netherlands . . . 8
3 CPI Inflation surprises and the unemployment gap . . . 13
4 Rolling regression of the slope of the Phillips curve . . . 17
5 Inflation expectations overtime . . . 20
6 Rolling Regressions of inflation expectations over actual inflation . . . 22
B.1 Quantification of pentachotomous survey data . . . 36
D.1 CPI inflation surprises for experts and households . . . 40
D.2 Rolling regression of the intercept of the Phillips curve . . . 41
List of Tables
1 The slope of the Phillips curve . . . 152 Sub-sample stability of the slope of the Phillips curve . . . 19
3 Comparison of several versions of the Phillips-curve . . . 23
4 Structural break test for different version of the Phillips curve . . . 25
B.1 Root mean square error for the six scaling factors . . . 37
C.1 which measure of expectations is the best proxy for firms’ expectations? . 39 D.1 Structural break test for professional inflation expectations . . . 42
1
Introduction
The global financial crisis of 2007–2008 is often compared to the Great Depression: the most severe financial crisis since the 1930s. A major difference is that the Great Depres-sion was accompanied by severe deflation, while the global financial crisis was not. This fact calls into question the supposedly inverse relationship between economic slack and inflation, i.e. the Phillips curve relationship (Hall, 2013). An inability to rely on this framework may hamper the success of monetary policy, as understanding current inflation dynamics on the basis of the Phillips curve is fundamental to the primary objective of the European Central Bank (ECB). However, not only monetary policy is affected, but the uncertainty also affects firms making investment decisions and unions negotiating wage contracts. Therefore, I seek to answer the following question: Do inflation dynamics in the Netherlands give support to the Phillips curve?
Inflation dynamics from advanced economies result in three Phillips curve anomalies, namely: periods of missing and excessive disinflation and a flattening of the slope (IMF, 2013; Friedrich, 2014 Coibion and Gorodnichenko, 2015; Yellen, 2017). In this thesis I investigate whether these anomalies are also puzzles for the Netherlands. I especially focus on the Netherlands, since little research has been conducted for the Netherlands. The existing literature mainly focusses on inflation dynamics of the eurozone (Hubert and Le Moigne, 2014). However, Fitzgerald et al. (2013) argue that an analysis using regional data leads to different results than a Phillips curve based on aggregate data. More specifically, they conclude that using state-level data, rather than national data, restores the Phillips Curve relationship for the United States.
Regarding the first two anomalies, I use an analysis similar to that provided by Coibion and Gorodnichenko (2015), in which I plot the Phillips curve and the scatters from the supposed periods of missing or excessive disinflation. In this analysis, I allow for three different measures of inflation expectation: backward-looking, household and professional expectations. In contrast to data from advanced economies, the scatters are not centred at the outer part of the graph. From which I conclude that both, excessive and missing disinflation, are not puzzles for the Netherlands.
As for the third puzzle, I first analyse the slope of the Phillips curve over the entire sample (1989–2018). In contrast with economic theory, I find for a purely
backward-looking Phillips curve an insignificant slope coefficient (Friedman, 1968). However, when I allow for professional expectations, I find that the slope is indeed negative. From which I—in line with Lucas (1973)—conclude that a Phillips curve should be based on rational inflation expectations, rather than adaptive expectations. Thereafter, I use a rolling regression to assess whether the slope is stable over time. The rolling regression suggests that the slope decreases after 2010. I perform a structural break test to test this steepening. I do not find evidence in support of a structural break; thus, the slope is over time. Therefore, all three puzzles which are puzzles for advances economies, are not puzzles for the Netherlands.
Nevertheless, from the structural break test it follows that after 2010, the Phillips curve shifted upwards. Galati et al. (2011) argue that the global financial crisis might have resulted in less anchored inflation expectations, which could explain the upward shift. I analyse the degree of anchoring by using a rolling regression of inflation expecta-tions over actual inflation. I do not find that the degree of anchoring changed; therefore, I am not able to explain the upward shift of the Phillips curve.
Finally, as the predicting power of a standard Phillips curve is fairly low, and another version of the curve might not be subjected to the shift, I allow for different versions of the curve. From which I conclude that a New Keynesian Phillips curve using professional inflation expectations and a version of the New Keynesian Phillips curve which allows for both a backward- and forward-looking component explain the data best. Unfortunately, both curves also subjected to the upward shift. From which I conclude that inflation dynamics do not give support to the Phillips curve, i.e. the curve is not a useful tool for the Netherlands.
The structure of the thesis is as follows: Section 2 discusses the literature available on this topic. I describe the dataset in Section 3. Section 4 gives the main results, and finally Section 5 concludes and discusses my findings.
2
Literature Review
In this section, I first describe the Phillips curve. Then I discuss three anomalies of the Phillips curve framework which are present in advanced economies, and which I research later on for the Netherlands. These puzzles are: missing disinflation, excessive disinflation, and a flattening of the slope of the Phillips curve. Next, I argue that allowing for different measures of inflation expectations might solve these puzzles, a question which is also researched in this thesis. Thereafter, I end with the residual hypotheses. That is, simply no Phillips curve exists.
2.1
The Phillips curve
The Phillips curve, named after William Phillips (1958), is an empirical model which describes the inverse relationship between wage changes and unemployment. Samuel-son and Solow (1960) extend Phillips’ work by finding evidence to support a negative relationship between unemployment and inflation. Intuitively, an increase in aggregate demand increases gross domestic product (GDP) and decreases unemployment as firms employ more workers. As a response, workers demand higher wages, which causes wage inflation. Higher inflation increases the demand for goods, which allows firms to raise their prices. Therefore, unemployment falls and inflation increases.
Thus, according to Samuelson and Solow (1960), the Phillips curve describes a policy trade-off: policy-makers can decrease unemployment, but this can only be done at the expense of higher inflation. Milton Friedman (1968) criticises the Keynesian Phillips-curve. He states that if policy-makers would consistently aim policy at reducing the unemployment rate, then following the trade-off they would have to accept high inflation. However, the public eventually gets used to the high level of inflation and demands higher wages, which results in higher inflation without lower unemployment—that is, a vertical, long-run Phillips curve. This line of thought has been restated by Lucas into a more general form, the well-known Lucas critique (Lucas, 1976).
Thus, according to Friedman (1968) and Lucas (1976), the correct formulation of the inflation-unemployment trade-off is an ‘expectations-augmented’ Phillips curve of the following form: 1
πt = Etπt+1− κugapt , (1)
where πtstands for inflation at time t, and Etπt+1 reflects the expected inflation of period
t+1 as of time t. ugapt is the difference between the unemployment rate and its natural rate, that is, the unemployment gap. Finally, κ is the slope coefficient for the unemployment gap. Friedman states that inflation expectations are determined adaptively; thus, the last period’s level of inflation changes people’s expectations and so feeds into today’s inflation. This intuition modifies the curve into:
πt = πt−1− κugapt , (2)
where πt−1 is inflation of the previous period. Lucas (1973) criticises the use of adaptive
expectations, he argues that expectations should be based on a perceived policy regime and not just on recent history.
New Keynesian economists responded to the Lucas critique by introducing ratio-nal expectations and micro-foundations (Robberts, 1995). They argue that the New Keynesian Phillips curve (NKPC) is defined as follows:2
πt= βEtπt+1− κugapt , (3)
where β and κ reflect the slope coefficient for expected inflation and the unemployment gap, respectively. Thus, according to the NKPC, firms base their current price settings on expected future inflation (given their current information set).
Empirically, New Keynesian models do not fit the data well (McCallum, 1998). Inflation depends heavily on its own lagged values. Yet, the NKPC only allows for a forward-looking inflation term, which makes it unable to explain inflation persistence 2A derivation can be found in Appendix A.2. However, the NKPC as derived in Appendix A.2
relies on a strong assumptions, namely Calvo pricing (Calvo, 1983), in which firms change their prices according to a Poisson process (i.e., a ‘lottery’). Yet, there are different ways of formulating sticky prices, such as menu cost (Golosov and Lucas, 2007) and long-term labour contracts (Fischer, 1977). These more plausible assumptions have implications that are very similar to the NKPC. However, they provide inconvenient expressions, therefore I only derive the NKPC based on Calvo pricing.
(McCallum, 1998). A solution proposed by Gal´ı and Gertler (1999) is the hybrid NKPC, which introduces a source of persistence. That is, the model allows for a fraction of firms to rely on past inflation as a prediction for future price development:
πt= βfEtπt+1+ βbπt−1− κugapt (4)
The condition βf + βb = 1 is often imposed on the hybrid NKPC to satisfy the
natural-rate hypothesis in response to the Lucas critique (McCallum, 2007). This approach is considered by many to be a good compromise between the pure rational expectations micro-based approach of the NKPC and the more pragmatic expectations-augmented Phillips curves.
Alternatively, some economists use the output gap—that is, the difference between output and its natural level—rather than the unemployment gap. Output gaps reflect the state of the business cycle more than unemployment gaps do (Billmeier, 2004). Thus, using the output gap as a measure of economic slack might lead to different results. How-ever, in line with Coibion and Gorodnichenko (2015), I only consider the unemployment gap as a measure of economic activity, since the unemployment rate is both a simple and transparent metric and does not require me to take a strong stand on the nature of trends, i.g. productivity.
2.2
Missing and excessive disinflation
Data from advanced economies gives support for inflation dynamics which cannot be ex-plained within the Phillips curve framework (Coibion and Gorodnichenko, 2015; Friedrich, 2014). This apparent puzzle led some economists to conclude that the Phillips curve may have outlived its usefulness (Yellen, 2017). However, no research on this anomaly has been conducted for the Netherlands. There is research available on this topic for the eurozone as a whole, but Fitzgerald et al. (2013) argue that an analysis using regional data may lead to different results. To overcome this aggregation bias, I analyse whether this puzzle is apparent in Dutch data. However, before presenting the analysis I first describe existing literature on these puzzles.
The first puzzle, missing disinflation, was observed in advanced economies over the period 2009–2011 (Friedrich, 2014). During this time, inflation rates were consistently
higher than what would have been expected given the Phillips curve relationship. The second puzzle, excessive disinflation, started in 2012, when inflation rates in advanced countries were weakening rapidly despite the ongoing economic recovery.
Amberger and Fendel (2017) research these puzzles for the eurozone. The authors find that during the European sovereign debt crisis, inflation in the eurozone remains fairly stable despite deflationary pressures. Disinflation is significant in the periods fol-lowing the crisis. Thus, the authors conclude that the missing disinflation and excessive disinflation puzzles are present in the eurozone.
On the other hand, Hubert and Le Moigne (2016) argue that results based on a eurozone analysis suffer from an aggregation bias. Based on a regional data Hubert and Le Moigne (2016) find a significant divergence between eurozone countries. The authors conclude that Northern countries (Germany, France), demonstrate a general tendency towards excessive disinflation, while countries on the periphery (Spain, Italy, Greece), exhibit periods of missing disinflation. Thus, I research whether inflation dynamics of the Netherlands give support for excessive disinflation rather than missing disinflation.
2.3
The slope of the Phillips curve
The next puzzle relates to the slope of the Phillips curve. Data from advanced economies supports a flattening of the slope, starting from the Great Recession (IMF, 2013; Blan-chard et al., 2015). An flattening implies that the slope is not stable overtime, which is a crucial assumption when predicting inflation on the basis of the Phillips curve. More-over, the IMF finds no significant slope coefficient for a price-augmented Phillips curve. Which implies that more economic slack does not, on average, result in higher inflation. Therefore, this study investigates the slope of a Dutch Phillips curve.
2.3.1 The slope of the curve in the eurozone
Research on this topic is available for the eurozone. Amberger and Fendel (2017) find, on the basis of output gaps, that the slope coefficient of the Phillips curve decreases uniformly in the early 2000s for all eurozone counties. The flattening fades out in 2007/2008, and the slope coefficient remains stable at this level. These drastic changes of the Phillips curve relationship over time hampers the accuracy at which the Phillips curve predicts inflation (Fitzgerald et al., 2013). However, the dynamics on the basis of unemployment gaps differ,
as the coefficients remain surprisingly stable. These results might be more reliable, since output gaps are more likely to reflect the state of the business cycle (Billmeier, 2004).
2.3.2 The slope of the curve in the Netherlands
Figure 1 displays the Phillips curve for the Netherlands, estimated over different time intervals. The figure suggests that from 2000 until 2009, the slope has become flatter, perhaps even zero. However, starting from 2010 the slope seems to have decreased again. These dynamics are inconsistent with above described dynamics of the Phillips curve in the eurozone, on the basis of unemployment gaps (Amberger and Fendel, 2017). There-fore, I formally test whether the slope of the Dutch Phillips curve is stable over time; that is, is the slope puzzle also a puzzle for the Netherlands? But first, why did the curve flatten? I discuss a possible explanation which could have resulted in a flattening of the slope in the next subsection.
2.3.3 An explanation to the flattening
Haldane (2017) proposes an explanation for a flattening of the curve. He argues that a series of labour-market trends—such as the move to greater self-employment—have caused workers to become more ‘divisible’. This divisibility can be explained by pre-financial crisis trends such as the decline in union membership. Panel a of Figure 2 suggests that the degree of unionisation in the Netherlands declined, especially after 2011. More recent explanations include the rise in temporary work and zero-hours contracts, both of which have significantly increased in the Netherlands (see Panel b of Figure 2).
Moving to more self-employment and less unionisation results in less collective bar-gaining power. A workforce that is more easily divided allows for weaker wage growth for a given level of unemployment. According to the wage-price spiral, firms would have to raise prices to protect profit margins from the rising costs, and employees would try to push their nominal after-tax wages upward to catch up with rising prices (Knotek and Zaman, 2014). Therefore, wages chase prices and prices chase wages. Using this intuition, Haldane’s explanation also holds for the price Phillips curve.
Figure 1: The Dutch Phillips curve relation overtime
Note: The curve plots the relationship between inflation surprises (πt− EtπEXt+1) and the unemployment
gap. Inflation is measured by the consumer price index, and inflation expectations are defined as one-year ahead expert expectations. The blue scatters reflect data from 1989–1999. The blue line displays the fitted relation of the scatters in the corresponding period. While green and red reflect the periods 2000–2009 and 2010–2018, respectively.
Figure 2: Labour-market trends in the Netherlands
(a) Trade union membership
Note: the figure represents the number of union membership in the Netherlands. Source: CBS, own calculations
(b) Percentage of flexworkers
Note: the figure represents temporary labour contract as a fraction of the total amount of labour contracts Source: CBS, own calculations
2.4
Inflation expectations
However, perhaps an inappropriate measure of inflation expectations is being used and another would not find support for such a flattening. Economists have long emphasised the importance of expectations in determining macroeconomic outcomes. Expectations affect wage negotiations, as higher expected inflation leads to calls for higher nominal wages (de Haan et al., 2016). Higher wages lead to higher prices for goods and services if firms raise their prices in response to higher costs. Thus, allowing for different measures alters the Phillips curve and might solve the slope, missing disinflation and excessive disinflation puzzle. Therefore, I allow for three different measures of inflation expectations in my analysis, namely backward-looking, household and professional expectations.
A considerable amount of academic literature evaluates different inflation forecasts and forecasting methods. However, no paper has yet compared these different measures of inflation expectations for the Netherlands. For Germany, Scheufele (2011) finds that household surveys, which are conducted among relatively unsophisticated consumers, out-perform most of the competing models. Yet, he concludes that the survey of professional forecasters is superior to household inflation expectations. He states that professional forecasters process information earlier and more efficiently than households. Therefore, surveys of professional forecasters are more effective than consumer surveys when it comes to forecasting inflation.
In contrast to these findings, Coibion and Gorodnichenko (2015) demonstrate that for the United States, the professional forecast is inferior to the household survey. More-over, the authors state that the use of household expectations can account for the missing disinflation for the United States. But why would we focus on household inflation ex-pectations to approximate the inflation exex-pectations of firms? Since doing so contradicts the standard hypothesis that firms hire professional forecasters to guide their pricing decisions.
First, no quantitative measure of the inflation expectations of firms is available in the Netherlands. Such a survey does exist in New Zealand, however. On the basis of this survey, Kumar et al. (2015) conclude that managers forecast much higher levels of inflation than actually occur, as their perception of inflation is systematically higher than actual inflation. Moreover, most managers appear to rely on their personal shopping
experience to make inferences about aggregate inflation. Thus, the authors find that firms’ inflation expectations are more in line with household expectations. Intuitively, business owners are also households, which could make the household forecast a better proxy of firms’ inflation expectations.
2.5
No curve
Alternatively, some economists argue that the Phillips curve does not exist. Keynes, after the Great Depression, posited a world in which, absent government intervention, labour markets did not clear even with lags. In this world, unemployment could get stuck at high levels even though wages fell; fiscal policy is therefore required to bring unemployment down. Another explanation proposed by Roger Farmer (2013) argues that the statistical evidence for a natural rate of unemployment is unconvincing. He claims that there are multiple equilibria in the labour market.
3
Data
This section briefly describes the dataset I use. For the empirical portion of this study, data was extracted from four sources: the Organisation for Economic Co-operation and Development (OECD), the International Monetary Fund (IMF), Consensus Economics and the European Commission (EC). I have made use of all available data on the Nether-lands from 1989 to 2017, on a quarterly basis. The price measure is the consumer price index (CPI), as only data of professional expectations is available on this topic. The variable is obtained through the OECD database (base year is 2010). Commodity and oil prices (WTI) are provided by the IMF. Furthermore, the unemployment rate and the non-accelerating inflation rate of unemployment (NAIRU) is extracted from the OECD. Professional inflation expectations are provided by Consensus Economics, a London-based macroeconomics survey firm. Data on households’ inflation expectations is pro-vided by the Consumer Survey of the European Commission (EC). In contrast to the Michigan Survey, which Coibion and Gorodnichenko (2015) use, the EC Consumer Survey provides a qualitative measure of household inflation expectations. This data limitation forces me to quantify the survey.
In accordance with Batchelor and Orr (1988), Nielsen (2003), Vogel (2008) and D¨opke et al. (2008), I use the probability method to quantify this pentachotomous qual-itative survey into a quantqual-itative time series.3 The method assumes symmetric intervals
across the five potential answers to the question ’By comparison with the past 12 months, how do you expect that consumer prices will develop in the next 12 months?’. Using these intervals and assuming an aggregated probability distribution function, quantiles can be calculated. From these quantiles I am able to find an expression of expected inflation.
However, this expression is dependent on a scaling factor. Six different scaling factors are considered in this thesis: lagged inflation, an ARMA model, recursively Hodrick-Prescott (HP) filtered inflation, and the mean of past inflation (3, 6 and 12 months). Out of the six, an ARMA(3,4)-model4 minimises the root mean square error (RMSE)
and therefore is the normalisation considered in the remainder of this thesis.
3Details are provided in Appendix B Transformation of the Consumer Survey
4The lag length of both the AR- and the MA-terms is chosen according to the Akaike and Schwarz
4
Results
In this section, I analyse whether the anomalies of the Phillips curve—the excessive disinflation, missing disinflation and flattening of the slope coefficient—are apparent in Dutch data. Thereafter, analyse the effect of the Economic and Monetary Union and global financial crisis on inflation expectations, since more or less anchored inflations expectations might have resulted in a shift of the Phillips curve. Finally, I end with an analysis of different versions of the curve.
4.1
The excessive and missing disinflation periods
In this subsection, I assess whether the periods of missing and excessive disinflation ob-served in advanced economies are also present in data from the Netherlands (Friedrich, 2014). In order to test for these puzzles, inflation surprises for backward-looking infla-tion expectainfla-tions are scattered against the unemployment gap in Figure 3. The time interval for the red dots reflects post-crisis inflation dynamics, on the basis of the time intervals defined by Friedrich (2014). That is, 2009Q4–2011Q4 and 2012Q1–2013Q3 for the missing and excessive disinflation, respectively. The blue line represents inflation surprises predicted as a function of the unemployment gap prior to the global financial crisis (1985Q1–2007Q3).
For the first puzzle, the missing disinflation, one would expect inflation surprises to be systematically larger compared to their historical pattern; yet, only the second quarter of 2010 and 2011 fall outside the band of pre-crisis scatter. This suggests that only during these quarters inflation was well above what might have been expected given the severity of the economic downturn. For the second puzzle, we would expect the reverse to be true. However, the scatters are centred on the upper part of the curve; yet, they are still within the band of pre-crisis data.
Appendix Figure D.1 displays the same graph, but it allows for different measures of inflation expectations. Panels a&b and c&d use expert and household inflation ex-pectations, respectively. Nevertheless, the conclusion remains the same; in contrast to data from most advanced economies, I do not find convincing evidence to support either puzzle (Amberger and Fendel, 2017; Coibion and Gorodnichenko, 2015; Friedrich, 2014; Hubert and Le Moigne, 2016).
Figure 3: CPI Inflation surprises and the unemployment gap
(a) The period of missing disinflation
(2009Q4-2011Q4)
(b) The period of excessive disinflation
(2012Q1-2013Q3)
Notes: Panels a and b show the scatter plots of inflation surprises (πt− EtπBACKt+1 ) and the
unemploy-ment gap. Empty blue circles show observations for the global financial crisis. Filled red circles show observations for the stated time period. The solid blue line represents inflation surprises predicted as a function of the unemployment gap prior to the global financial crisis (1985Q1–2007Q3).
4.2
The slope of the Phillips curve
As the missing and excessive disinflation puzzles are not puzzles for the Netherlands, I move to another anomaly, the insignificant slope of the Phillips curve. Using the same method as Coibion and Gorodnichenko (2015), the standard Phillips curve is defined as follows:5
πt− Etπt+1= c + κU Etgap+ vt, (5)
where πt stands for inflation at time t, which is measured by the CPI. For inflation
expectations (Etπt+1), I use three different definitions. First, I use backward-looking
inflation expectations:
Etπt+1 =
1
4(πt−1+ πt−2+ πt−3+ πt−4), (6)
where a period is defined by one quarter. Second, I use the survey of household inflation expectations (EHH
t πt+1), which is expected inflation of period t + 1 based on the
informa-tion set available at time t. And finally, I use expert inflainforma-tion expectainforma-tions (EtEXπt+1).
5In this expression, t reflects a year; i.e., a yearly Phillips curve relationship. However, it is estimated
Furthermore, U Etgap reflects the unemployment gap—that is, the measure of economic activity. c is the constant, vt is the error term and κ is the slope of the curve.
All versions of this regression are estimated by ordinary least squares (OLS), as well as instrumental variables (IV). IV is used to control for possible correlation between the output gap and the error term. The instruments used for the IV regression are in line with the ones Amberger and Fendel (2017) use.6 That is, the second and third lag of the
unemployment gap (U Et−2gap and U Et−3gap), and the second lag of the consumer price index (PCP I
t−2 ) are used as an instrument for the unemployment gap.
The IV method relies on two assumptions: instrumental relevance and exogeneity (Angrist and Imbens, 1995). The former assumes that instruments are relevant predictors of the endogenous regressors—that is, the covariance between the instrument and the explanatory variable is non-zero. The unemployment rate is likely to reflect some degree of persistence; therefore, instrumental relevance is likely to be met. Nevertheless, I perform a Cragg-Donald Wald weak instruments test for each regression. If the F-statistic of this test is larger than its corresponding critical value, then the instruments are indeed relevant.
The second assumption requires that the instruments are not correlated with the error term. Unfortunately, this unverifiable; it can never be proven, but can sometimes be disproven (Stock and Watson, 2011). An overidentification test verifies whether in-struments are correlated with the error term. If we reject the null, then inin-struments contradict and thus are invalid. However, again due to the unverifiability, failure to reject does not necessarily mean that exogeneity holds.
Statistical evidence regarding the Phillips curve is formally presented in Table 1. For backward-looking and household inflation expectations, I find an insignificant slope coefficient for the unemployment gap. This implies that a positive unemployment gap does not, on average, result in disinflationary pressures, which contradicts the intuition behind the short-run Phillips curve. Yet, when using professional expectations, the slope is indeed significant at a 95% confidence interval. Neither IV assumption—instrumental 6Coibion and Gorodnichenko (2015) only use the first lag of the unemployment gap as an instrument
for the unemployment gap. Due to this exact identification, one cannot verify whether instrument exogeneity holds. When using both the first and the second lag of the unemployment gap, I fail to reject the null hypothesis of the over-identification test, suggesting that one or both of the instruments are invalid. When using the second and third lag, the J-statistic improves, while the instruments remain relevant. This finding suggests that the first lag of the unemployment gap is an invalid instrument.
Table 1: The slope of the Phillips curve
Backward-Looking Household expectations Expert expectations
OLS IV OLS IV OLS IV
(1) (2) (3) (4) (5) (6) U EtGAP -0.130 -0.125 -0.075 -0.169* -0.222** -0.373*** (0.115) (0.119) (0.094) (0.101) (0.098) (0.102) Observations 113 113 113 113 113 113 R-squared 0.006 0.006 0.002 -0.001 0.020 0.011 J-statistic 1,603 4,555 4,163 (0.449) (0.103) (0.125) F-statistic 83.722 83.722 83.722
Note: The estimated specification is πt− Etπt+1 = c + κU Etgap+ vt, where πt reflects inflation, which
is measures by the consumer price index. Etπt+1 stands for expected inflation, U EtGAP reflects the
unemployment gap, vt is the error term and c is a constant. The results of backward-looking and the
one year ahead survey of household and expert inflation expectations are displayed in column 1&2, 2&3 and 4&5, respectively. Column 1, 3 & 5 are estimated by OLS and 2, 4 &6 by IV. For IV regressions the second and the third lag of the unemployment gap is used as an instrument. J-statistic corresponds to the Hansen J-test of overidentifying restrictions, the p-value is reported in parentheses. Results of the Cragg-Donald Wald weak instrument test are reported as F-statistic. A 5% critical value of 13.91 applies to all IV regressions. Newey-West standard errors are reported in parentheses. ***,**,* indicate significance at 1%, 5%, 10% respectively.
relevance or exogeneity—is violated, which allows us to look at an IV estimation of the regression. When using IV, the slope of the expert-augmented Phillips curve further decreases to -0.373, and it is now statistically significant at a 99% confidence interval. Furthermore, for a household-augmented Phillips curve, the slope of the curve is now statistically significantly different from zero, but only at the 10% level. Therefore, the evidence on the slope of this curve is ambiguous. All in all, a Phillips curve based on professional expectations is more in line with economic intuition than a purely backward-looking curve.
However, one should note that the R2 of all six regressions is fairly low. For the regression with the highest R2, only 2% of the variance of the dependent variable can
be explained by the model. Especially when predicting inflation—which is where policy-makers use the curve for—a low R2is problematic. I investigate whether different versions
of the Phillips curve improve the fit of the regression in Section 4.4. However, before doing so when predicting inflation on the basis of the Phillips curve one assumes slope to be stable (or ‘structural’) over time (Fitzgerald et al., 2013). Therefore, in the next two subsections I analysis whether the Phillips curve is a structurally invariant relationship
4.2.1 The slope of the Phillips curve overtime
In this section, I use a rolling regression to display the slope of the Phillips curve over time. The IMF (2013) finds support for a flattening of the slope starting from the Great Depression. However, due to data limitations I am not able to analyse the Dutch Phillips curve over this time period. Nonetheless, from Figure 4 it follows that until roughly 1997, a small flattening of the curve occurs.
Thereafter, for backward-looking and household inflation expectations, the slope co-efficient remains relatively stable at zero, while the slope of an expert-augmented Phillips curve is steeper. During the global financial crisis, the slope for all expectation measures seemingly increases. This trend reverts in 2010 when the slope decreases. For all three expectations measures the 2010 decrease is the sharpest slope change.7 In the next
sec-tion I formally test whether the steepening after the global financial crisis is a significant structural break. For now, I only perform this test on largest deviation, becausep if I do not find evidence to support a structural break, then smaller deviation will also not support this hypothesis.
4.2.2 The steepening of the curve post crisis
To test whether the increased flattening where Panel a, b and c of Figure 4 point at is significant, I regress the following:
πt− Etπt+1= c + κU EtGAP + λU E GAP
t I≥10,t+ θI≥10,t+ vt, (7)
where I≥10,t is a dummy variable which is equal to one from 2010Q1 to 2018Q1. λ and
θ are both slope variables. Again, this equation is estimated using both OLS and IV, as the dummy variable could be correlated with the error term. I use the same instruments as in the previous section, but I add the interaction of the dummy with the lags as an instrument for the interaction term.
7One could argue that the expert-augmented Phillips curve flattens starting from 2005. Therefore,
in Appendix Table D.1 I allow for a structural break from 2005 till 2012 and from 2012 till 2018. I do not find evidence in support of a structural break
Figure 4: Rolling regression of the slope of the Phillips curve
(a) Backward-looking inflation
expecta-tions (b) Expert inflation expectations
(c) Household inflation expectations
Notes: Panel a, b and c display the rolling regression of the slope coefficient for backward-looking, professional and household expectations, respectively. The Phillips curve is defined as πt− Etπt+1 =
c + κU Etgap+ vt, πt reflects inflation, which is measures by the consumer price index. Etπt+1 stands
for expected inflation, U EtGAP reflects the unemployment gap, vt is the error term and c is a constant.
For a steepening, the following hypotheses apply: H0 : λ = 0, and
H1 : λ < 0.
Table 2 display the result of the structural break. I do not find support for a structural break for all six regressions. Thus, no steepening of the curve has occurred, i.e. the slope of the curve ought to be stable over time. Noteworthy is that the dummy variable in columns 1 and 6 is significantly positive, which implies that after 2010, the Phillips curve shifted upwards. 8 Since, I concluded that a Phillips curve based on expert inflation
expectations is more plausible and both IV assumptions are not violated, a shift of the curve by 0.686 percentage points at 5% significance is problematic for the stability of the Phillips curve. Due to the global financial crisis, it is likely that inflation expectations have become less firmly anchored, which could have resulted in an upward shift of the curve (Galati et al., 2011). Therefore, I analyse the dynamics of inflation expectations in the following section.
4.3
An explanation to the shift of the curve
In this section, I analyse how inflation expectations evolve over time. Recent outstanding literature discusses that more anchored inflation expectations could have shifted the Phillips curve downward (Brainard, 2017).9 However, the results from Section 4.2.2 suggest that the reverse is true. The upward shift of the Phillips curve after 2010 might be explained by less firmly anchored inflation expectations due to the global financial crisis (Galati et al., 2011). As inflation expectations play a crucial role in the Phillips curve relationship, I analyse them thoroughly in this section. Finally, I use a rolling regression to examine how the anchoring of expectations has evolved over time.
8A rolling regression of the intercept is presented in Appendix Figure D.2
9An upward (downward) shift does not affect the coefficient of the relationship between inflation and
the unemployment gap, but at any given level of the unemployment gap it will generate a higher (lower) rate of growth in prices.
Table 2: Sub-sample stability of the slope of the Phillips curve
Backward-Looking Household expectations Expert expectations
OLS IV OLS IV OLS IV
(1) (2) (3) (4) (5) (6) U EGAP t -0.080 -0.110 -0.020 -0.173 -0.224* -0.436*** (0.138) (0.138) (0.114) (0.132) (0.117) (0.143) U EGAP t I≥10,t -0.433 -0.345 -0.266 -0.165 -0.206 -0.262 (0.264) (0.333) (0.256) (0.316) (0.255) (0.305) I≥10,t 0.526* 0.494 0.179 0.280 0.397 0.686** (0.286) (0.315) (0.294) (0.331) (0.274) (0.327) Observations 113 113 113 113 113 113 R-squared 0.021 0.020 0.006 0.001 0.027 0.010 κ + λ -0.513** -0.455 -0.286 -0.338 -0.430* -0.698*** (0.223) (0.289) (0.226) (0.275) (0.225) (0.258) J-statistic 2.673 4.679 4.245 (0.263) (0.097) (0.120) F-statistic 39.231 39.231 39.231
Note: The estimated specification is πt− Etπt+1 = c + κU EGAPt + λU EtGAPI≥10,t+ θI≥10,t+ vt. πt
reflects inflation, which is measures by the consumer price index. Etπt+1 stands for expected inflation.
The results of backward-looking and one-year ahead household and expert inflation expectations are displayed in column 1&2, 2&3 and 4&5, respectively. U EGAP
t reflects the unemployment gap. I≥10,t
is a dummy variable which is equal to one from 2010Q1 to 2018Q1. λ and κ are both slope variables, vt is the error term and c is a constant. Column 1, 3 & 5 are estimated by OLS and 2, 4 &6 by IV.
For IV regressions the second and the third lag of the unemployment gap is used as an instrument. The J-statistic corresponds to the Hansen J-test of overidentifying restrictions, the p-value is reported in parentheses. Results of the Cragg-Donald Wald weak instrument test are reported as F-statistic. A 5% critical value of 11.04 applies to all IV regressions. Newey-West standard errors are reported in parentheses. ***,**,* indicate significance at 1%, 5%, 10% respectively.
4.3.1 Inflation expectations overtime
To determine whether household inflation expectations differ from those of their profes-sional counterpart, Figure 5 displays these expectations and actual inflation over time. Due to the quantification process, household inflation expectations follow inflation more closely, such that they are more volatile than professional expectations. Furthermore, the figure points to periods in which both expectation measures are well above ECB’s ‘close but below 2%’ target, thus suggesting that inflation expectations are not fully anchored.
Figure 5: Inflation expectations overtime
Note: the black dashed line displays CPI inflation. The green and the red line reflect one-year ahead household and professional inflation expectations, respectively.
A major change for inflation expectations in the Netherlands was the introduction of the euro (de Haan et al. 2016). The launch of the Economic and Monetary Union in 1992 was accompanied by a gradual decrease of professional inflation expectations (see Figure 5). The decrease in household inflation expectations is less visible, as such expectations tend to follow inflation. Note that from 1994, professional inflation expectations are persistently higher than actual inflation, decreasing only after the introduction of the euro in 1999. However, these dynamics are again not visible for households—a limitation caused by the quantification process.
4.3.2 Have inflation expectations become more or less firmly anchored Unfortunately, only data is available on one pre-euro event, as Consensus Economics only began collecting data from 1989 onward. Due to this data limitation, I am not able to thoroughly compare in a more qualitative way whether inflation expectations have become more anchored. A method proposed by the IMF (2013) to overcome this problem is to regress the following:
Etπt+1− π∗ = α + β(πt− π∗) + t, (8)
Again, Etπt+1 reflects inflation expectations which is measured by household and
profes-sional expectation. πt is actual inflation measured by the consumer price index and t
is the error term. Furthermore, π∗ is the central bank’s target level of inflation. Given that the ECB defines price stability as ‘an increase in inflation below, but close to, 2 percent’, a target of 1.9 applies (IMF, 2013). If both α and β are close to zero, then inflation expectations are strongly anchored to the inflation target. More specifically, a zero β coefficient implies that expectations are not influenced by the contemporaneous level of inflation, and a zero α means that the inflation expectations are centred at the target level.
The estimates of the coefficients of the rolling regression are plotted in Panel a and b of Figure 6 for professional and household inflation expectations, respectively. The estimates for β for both expectation measures are close to zero for the entire period. Yet, for household inflation they are a bit more volatile, suggesting that household inflation expectations are more persistent than professional ones.
Clearly, the α coefficient deviates from zero more than β. For both expectation mea-sures we see that before 2002, α is systemically greater than zero. As β is roughly around zero, this implies that inflation expectations were higher than ECB’s target. Thereafter, the reverse holds; that is, α is below zero, suggesting that inflation expectations were be-low 1.9%. Noteworthy is that α seems to have converted to zero, which again contradicts the belief formulated by Galati et al. (2011). All in all, for now, due to the variability it is safe to say that inflation expectations have not become significantly more anchored.
Thus, I do not find evidence to support the idea that inflation exceptions might have shifted the Phillips curve. Not being able to find an explanation for the shift results
Figure 6: Rolling Regressions of inflation expectations over actual inflation (Net of inflation target)
-2 -1 0 1 2 C o e ffici e n ts 1990 1995 2000 2005 2010 2015 α β
(a) Professional inflation expectations (b) Household inflation expectations
Note: the blue line reflects the constant (α) of the rolling regression: Etπt+1− π∗= α + β(πt− π∗) + t. β
represents the slope coefficient on the difference between actual inflation and target. And π∗is the ECB’s target inflation, which is set at 1.9%. Panel a and b display the rolling regression for professional and household expectations (Etπt+1), respectively. πt is actual inflation which is measured by the consumer
price index. Finally, t reflects the error term. A window of twenty quarters applies (Amberger and
Fendel, 2017).
in the conclusion that inflation dynamics in the Netherlands do not lend support for a structural Phillips curve relationship. However, perhaps I am using an inappropriate version of the Phillips curve. In the next section, I first assess which versions explain the data best. Thereafter, I test whether the two superior versions also find support for a shift of the curve.
4.4
Allowing for different versions of the Phillips curve
Finally, I compare different variations of the Phillips curve in order to determine which version of the curve fits the data best. First, I regress the traditional Phillips curve:10
πt− Etπt+1= c + κU Etgap+ vt, (9)
When the curves allow for a forward-looking inflation component, I regress it twice, using the survey of household inflation expectations and the professional forecast. Thereafter, I extend Coibion and Gorodnichenko’s (2015) study by allowing for a NKPC curve and
10Where again, π
tstands for inflation at time t, which is measured by CPI. (Etπt+1) reflects inflation
a hybrid NKPC:
πt = βEtπt+1+ c + κU Etgap+ vt (10)
πt= βEtπt+1+ (1 − β)πt−1+ c + κU Etgap+ vt (11)
In these equations a slope coefficient (β) is introduced on inflation expectations. Fur-thermore, the hybrid NKPC allows for a backward looking component πt−1. The results
of all Phillips curve are presented in Table 3 below.
Table 3: Comparison of several versions of the Phillips-curve
BL-PC FL-HH FL-EX NKPC-HH NKPC-EX HNKPC-HH HNKPC-EX 0.597** EHH t πt+1 0.411** (0.268) (0.174) EEX t πt+1 0.885*** 0.928*** (0.184) (0.204) πt−1 0.403 0.072 (0.268) (0.204) U Etgap -0.130 -0.075 -0.222** -0.302** -0.249** -0.097 -0.216** (0.115) (0.094) (0.098) (0.128) (0.110) (0.104) (0.103) Observations 113 113 113 113 113 113 113 Adjusted R-squared 0.003 0.001 0.011 0.084 0.103 0.028 0.101 Notes: The first column reflects the traditional, purely backward-looking Phillips curve. The second and the third display the results for a forward-looking Phillips curve, only using household and expert expectations, respectively. Columns three and four regress a New Keynesian Phillips curve, which does not restrict the expectation coefficient to unity, again for both households and experts. The last two columns regress Equation 3: the hybrid NKPC. Newey-West standard errors are in parentheses. ***,**,* indicate significance at 1%, 5%, 10% respectively.
Using economic intuition, we expect a negative relationship between inflation (sur-prises) and the unemployment gap. Therefore, a traditional Phillips curve, a NKPC and hybrid NKPC all using expert inflation expectations, or an NKPC which uses household inflation expectations make more sense. However, from an econometrics point of view, this method is not correct; one must rely on the model which fits the data best.
A comparison of the coefficients of determination suggests that the NKPC which allows for expert inflation expectations is the superior model; that is, it explains most of the variance of the dependent variable, and its slope is statistically different from zero.11 This is surprising, as regressing inflation on its own lags usually yields a much
higher R2 due to the inability of these models to explain the persistence behaviour of inflation (Rudd and Whelan, 2003). The second-best model, with only a 0.2 percentage point smaller adjusted-R2, is the hybrid professional New Keynesian Phillips curve. The model also has a negative slope, but takes the Lucas critique fully into account. As a robustness check Appendix Table D.2 displays the results for an IV regression, from which the conclusion remains the same. The NKPC using expert inflation expectations fits the data best, followed by the hybrid NKPC, and the slope remains significantly different from zero.12
4.4.1 Can different versions of the Phillips curve account for the shift In this section, I perform a structural break test to assess whether the two superior models from the previous subsection also give support for a shift of the curve. This regression is similar to the one performed in Section 4.2.2.; therefore, details can be found bellow in the note of Table 4. From column 2 of Table 4 I conclude that for the NKPC the curve shifts up by 0.625 percentage points after 2010. For the hybrid NKPC the curve increases by 0.534 percentage points (see column 4). Both estimates are at a 5% level; thus, in both cases I reject the null. Since neither IV assumptions is violated, I conclude that the shift is also apparent for a (hybrid) NKPC.
of terms in a regression.
12Since superior Phillips curves tend to be those based on professional inflation expectations, which
contradicts Coibion and Gorodnichenko’s (2015) findings, Appendix B provides a robustness check in order to answer the question, what best represents firms’ inflation forecasts? Here I compare household and expert inflation and indeed conclude that firms’ inflation expectations track those of experts.
Table 4: Structural break test for different version of the Phillips curve New Keynesian Phillips curve Hybrid New Keynesian Phillips curve
OLS IV OLS IV (1) (2) (3) (4) EtEXπt+1 0.991*** 0.860*** 0.902*** 0.989*** (0.226) (0.264) (0.205) (0.212) πt−1 0.098 0.011 (0.205) (0.212) U EGAP t -0.226* -0.447*** -0.210* -0.533*** (0.121) (0.149) (0.114) (0.163) U EtGAPI≥10,t -0.204 -0.284 -0.228 0.102 (0.260) (0.303) (0.243) (0.279) I≥10,t 0.391 0.625** 0.409 0.534** (0.325) (0.311) (0.262) (0.276) Observations 113 113 113 113 R-squared 0.141 0.126 0.114 0.092 J-statistic 4.776 4.019 (0.102) (0.134) F-statistic 38.505 47.194 11.04 13.91
Note: The estimated specification is πt = Etπt+1+ c + κU EtGAP + λU EtGAPI≥10,t + θI≥10,t+ vt for
columns 1 and 2. And πt = βEtπt+1+ (1 − β)πt−1+ c + κU E gap
t + +λU EtGAPI≥10,t+ θI≥10,t+ vt ,
where U EGAP
t reflects the unemployment gap. I≥10,t is a dummy variable which is equal to one from
2010Q1 to 2018Q1. Column 1&3 are estimated by OLS and 2&4 by IV. For IV regressions the second and the third lag of the unemployment gap is used as an instrument. The J-statistic corresponds to the Hansen J-test of overidentifying restrictions, the p-value is reported in parentheses. Results of the Cragg-Donald Wald weak instrument test are reported as F-statistic. Newey-West standard errors are reported in parentheses. ***,**,* indicate significance at 1%, 5%, 10% respectively.
5
Conclusion and discussion
All in all, I do not find support for the three puzzles advanced economies are subjected to—that is, missing disinflation, excessive disinflation and a flattening of the slope of the curve. Nevertheless, another puzzle emerges: after 2010, the curve shifted upwards. More anchored inflation expectations cannot explain this upward shift, from which I conclude that the Phillips curve is not a good predictor of inflation. Thus, Dutch inflation dynamics do not give support to the Phillips curve.
It is striking that the Dutch Phillips curve did not flatten, while data from the Netherlands gives support to an explanation for a flattening. That is, the labour force has become more divisible (Haldane, 2017). Moreover, union membership in the Netherlands especially declined after 2010, when the Dutch curve seemingly steepens. Thus, Dutch inflation dynamics call Haldane’s explanation into question.
Regarding the version of the Phillips curve, an expert-augmented Phillips curve fits the data better than one based on household or backward-looking inflation expectations. However, its power to predict inflation is fairly low. Both, a NKPC and a hybrid NKPC solve this problem. The predicting power of the former is slightly better however, new classical economists would argue that a hybrid makes better economic sense. That is, it can explain the negative relationship but is vertical in the long-run. Nonetheless, both are subjected to the shift in curve, which implies that policy makers can not rely on the curves to accurately predict inflation.
Keep in mind that only the Phillips curve on the basis of unemployment gaps is considered in this thesis. Dynamics of the Phillips curve on the basis of output gaps could give different results. Therefore, an analysis of different versions of the Phillips curve is recommended, as it is possible that other versions of the curve give support for a stable Phillips curve relationship.
Another limitation regards the survey of households. Compared to the Michigan Survey of Consumers, the European Commission survey does not ask households quanti-tatively how prices will develop next year. This data limitation forces me to quantify the survey. However, it is possible that the modification does not measure what households
actually think inflation is going to be next year—that is, the generated value could differ from what households would say if they were asked quantitatively. Therefore, an analysis of the Phillips curve using a quantitative measure for household inflation expectations might lead to different results.
On the other hand, households may simply not know what average inflation dynam-ics are. For instance, van der Cruijsen and Demertzis (2015) studied the general public’s knowledge about the ECB in the Netherlands. The authors examined the inflation ex-pectations of the respondents. The mean of inflation exex-pectations was around 2.7% at the time of the survey, while the actual rate of inflation turned out to be 1.1%. Likewise, Binder (2015) finds that Americans are generally unable to identify recent inflation dy-namics with any degree of precision; barely half of consumers expect long-run inflation to be near the Federal Reserve’s 2% target.
At the end of the day, inflation expectations are important, as they are believed to influence an agent’s decision-making process, but the failure of households to under-stand inflation may lead to an incorrect interpretation of the data. Thus, an incorrect interpretation of a quantity’s measure could be as problematic as a quantified qualita-tive version. Therefore, I would advise the EC to add a quantitaqualita-tive measure to their qualitative survey and the Michigan Survey of Consumers to add a qualitative measure.
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A
Derivation of the Phillips curves
In this section, I derive the two Phillips equations I use throughout the thesis.
A.1
The expectations-augmented Phillips curve
First, Lucas (1973) assumes that economic output is a function of its natural level and price ‘surprises’. Thus, the following supply function applies:
Yt= Yn+ a(Pt− EtPt+1) (12)
where Y is log value of the actual output, Yn is log value of the natural level of output,
a is a positive constant, P is log value of the actual price level, and Etπt+1 is log value of
the expected price level. We can rewrite this equation to find an expression for prices:
Pt= Etπt+1+
Yt− Yn
a (13)
Okun’s law can be used to rewrite the output gap to an unemployment gap (Abel and Bernanke, 2005). Okun’s law is defined as:
Yt− Yn
a = −b(Ut− Un) (14)
where b is a positive constant, U is unemployment, and Un is the natural rate of
unem-ployment. Thus, substituting this in we end up with:
Pt= EtPt+1− b(Ut− Un) (15)
Subtracting last year’s price levels, acknowledging that inflation is defined as πt ≈ Pt−
Pt−1 and expected inflation as Etπt+1 ≈ Pt− EtPt+1, we arrive at the famous short-run
Phillips curve expression:
A.2
The New Keynesian Phillips Curve
For this model, price rigidity is introduced by Calvo pricing (Calvo, 1983). This assump-tion implies that in each period, only a fracassump-tion (1 − θ) of firms are allowed to change their price. Thus, when firms are allowed to change their prices, they need to take the future into account (Roberts, 1995), since prices may be fixed for many periods afterward. Assuming that, firms’ loss function is defined as:
L(zt) = ∞ X k=0 (θβ)kEt(zt− p∗t+k) 2 (17)
where β is the discount factor (0 < β < 1). zt is the log of the price firms choose
when they are allowed to change their prices, i.e. the reset price. p∗t+k is the log of the optimal price that firms would set in period t + k if there were no price rigidity. Through the summation, firms will minimise their expected losses from setting the wrong price (Et(zt−p∗t+k)2) each period. These future losses are discounted by (θβ)kinstead of simply
β, as there is a possibility that firms do get to adjust their prices. Thus, each firm will, when allowed to do so, change the price zt to a value which minimises the loss function.
This means: L0(zt) = 2 ∞ X k=0 (θβ)kEt(zt− p∗t+k) = 0 (18)
Which we can rewrite into:
∞ X k=0 (θβ)kzt = ∞ X k=0 (θβ)kEtp∗t+k (19)
As zt does not depend on k, we can use the geometric sum formula to simplify
zt 1 − θβ = ∞ X k=0 (θβ)kEtp∗t+k (20)
Thus, the solution for zt boils down to:
zt = (1 − θβ) ∞
X
k=0
This equation implies that when firms are allowed to change their prices, they will set their prices equal to the weighted average of prices they would set if they were able to change prices freely. But what prices would firms set if they were able to do so freely? We will assume that firms set prices as a fixed mark-up (µ) over marginal cost(mct)
p∗t = µ + mct (22)
Using this we can rewrite Equation 21 into:
zt = (1 − θβ) ∞
X
k=0
(θβ)kEt(µ + mct+k) (23)
By integrating forward, we can get rid of the summation in a similar manner as before and rewrite this expression as:
zt = θβEtzt+1+ (1 − θβ)(µ + mct) (24)
Using this insight gained into firms’ price setting behaviour, we can derive the behaviour of the aggregate price level. This is simply the weighted average of the prices of firms who are and who are not allowed to change their price:
pt= θpt−1+ (1 − θ)zt (25)
Which we can rearrange to find an expression for the reset price:
zt=
1
1 − θ(pt− θpt−1) (26)
Thus, we equate this expression to equation 24 and find that: 1
1 − θ(pt− θpt−1) = θβ
1 − θ(Etpt+1− θpt) + (1 − θβ)(µ + mct) (27) After some rearranging and defining inflation as πt≈t −pt−1, we find that:
πt = βEtπt+1+
(1 − θ)(1 − θβ)
A well-known simplified version of this expression is:
πt= βEtπt+1+ β(mcrt) (29)
where κ is the slope coefficient and mcr
t reflects real marginal cost (mcrt = µ + mct− pt).
However, as we do not observe firms’ real marginal cost in the data, the output gap (ygapt ) has often been used as proxy for this variable. Intuitively, when the output gap is high, there is more competition for resources. Yet, its productivity remains the same thus, the real costs of production increase by more than the increase in output gap. Thus, the assumed relationship is:
mcrt = λytgap (30)
Which implies a Phillips curve of the form:
πt= βEtπt+1+ γygapt (31)
However, by using Okun’s law (Equation 14) we can also replace the output gap with the unemployment gap:
B
Transformation of the Consumer Survey
In the survey of the EC, interviewees were asked the following question: “By comparison with the past 12 months, how do you expect that consumer prices will develop in the next 12 months? They will . . .
I. increase more rapidly (++) tEt+1
II. increase at the same rate (+) tDt+1
III. increase at a slower rate (=) tCt+1
IV. stay about the same (+/–) tBt+1
V. fall (–) tAt+1
VI. don’t know”
Following a method in line with Batchelor and Orr (1988), with Nielsen (2003), with Vogel (2008) and with D¨opke et al. (2008), I first divided the proportions of “don’t know” answers proportionally among the five answers to make sure that the following equation holds:
tAt+1+ tBt+1+ tCt+1+ tDt+1+ tEt+1= 1, (33)
where tAt+1represents the choice “fall” at period t for the upcoming period t + 1.
Assum-ing an interval (δl
t, δtu) to be around 0 ensures that respondents will answer the question
by stating that B “stay about the same (-)” if their expected price change lies within the interval. Another interval ( ˜µt− Lt, ˜µt+ Lt) exists around the subjective mean inflation
rate, for which respondents answer that prices “increase at the same rate” if the price change expected by them lies within this interval.
On the basis of above-formulated intervals and the central limit theory, the quantiles can be formulated as follows:
δtL− tµt+1 tσt+1 = F−1(tAt+1) = tat+1 (34) δU t − tµt+1 tσt+1 = F−1(tAt+1+ tBt+1) = tbt+1 (35)
Figure B.1: Quantification of pentachotomous survey data
Source: tAt+1−tEt+1reflect the answers ”increase more rapidly”, ”increase at the same rate”, ”increase
at a slower rate”, ”stay about the same” and ”fall”, respectively. δl
t, δut, ˜µt−Lt and ˜µt+ Lt are symmetric
intervals around the answer “stay about the same (-)” and ”fall”, respectively. Furthermore, Xt+1reflect
expected price changed. Source: Nielsen (2003)
˜ µt− Lt − tµt+1 tσt+1 = F−1(tAt+1+ tBt+1+ tCt+1) = tct+1 (36) ˜ µt− Lt − tµt+1 tσt+1 = F−1(tAt+1+ tBt+1+ tCt+1+ tDt+1) = tdt+1. (37)
In Equation 34-37, F−1 represents the inverse of the standard normal distribution. Nielsen (2003) finds that alternative probability-distribution functions do not signifi-cantly improve the forecasting ability. Therefore, no other distribution functions are considered in this thesis. Furthermore, tat+1reflects the value of expected inflation below
which interviewees answer that prices “fall”.
Assuming that the above-formulated intervals are symmetric (δL
t = δtU = δt and
L
t = Ut = t) allows us to express inflation expectations as follows:
Et(πt+1) = tµt+1 =
˜
µt(tat+1+ tbt+1)
tat+1+ tbt+1− tct+1− tdt+1
. (38)
The only unknown variable is the scaling factor, ˜µt, which is the measure of inflation on
which respondents base their inflation forecast. D¨opke et al. (2008) test five different normalizations for ˜µt. They conclude that the two best-performing normalizations are
