We show that this model provides a solid representation of the formation of household inflation expectations.

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(1)EUROPEAN INFLATION EXPECTATIONS AND INFORMATIONAL RIGIDITIES. Mirre Terpstra†. June 2014. Supervised by: Diego Ronchetti. Abstract: We investigate the Carroll model of informational rigidities for European inflation expectations. We transform European survey data into quantitative data and estimate several versions of the sticky-information model. We show that this model provides a solid representation of the formation of household inflation expectations.. JEL Classification Numbers: D84, E31 Keywords: Inflation expectations, sticky information, inflation persistence. †. University of Groningen, Faculty of Economics and Business, P.O. Box 800, 9700 AV. Groningen, The Netherlands. m.d.terpstra@rug.nl, MSc Thesis: EBM877A20. 1.

(2) 1. Introduction Inflation expectations play a central role in economic theory and policy. Not only in the processes of the formation of real economic variables such as wages or the level of consumption, but also in the transmission mechanisms of monetary policy, inflation expectations are crucial. The ECB, for example, explicitly mentions the role of expectations in maintaining a low level of inflation (European Central Bank, 2011). Regarding price dynamics and inflation expectations the standard approach in current macroeconomics is the New Keynesian Phillips curve (NKPC) as it was proposed by Calvo (1983). Since then, several authors have deviated from this approach and its crucial assumption of rational expectations. Mankiw and Reis (2002) argue that their model of sticky information leads to a better representation of actual economic observations. In this model, information is rigid, as some part of the population is slow to adjust to new information. This subtle difference severely changes the dynamic pattern of prices in response to economic shocks. Carroll (2003) elaborated on this sticky-information approach by providing a microeconomic foundation for the formation of inflation expectations. In short, it models the dissemination of information from professionals to households. Since the late nineties the European monetary policy is determined by the European Central Bank, therefore the present study analyzes different models for the creation of inflation expectations using data of the Euro Area as a whole. This paper shows that the parsimonious sticky-information model well represents also the formation of household inflation expectations in Europe. To derive the results, European data obtained from questionnaires are first transformed into quantitative data. Then, the sticky-information model is shown to offer a parsimonious and useful representation of the process of formation of household inflation expectations in Europe. Although we can find several empirical applications of the sticky-information model in the literature, to the best of our knowledge, most research has focused on US data, and no attempt has been done to check the performance of the stickyinformation model for data of the Euro Area as a whole. This limit in the current literature is due to two facts. First, data on household inflation expectations in Europe 2.

(3) have been collected over a shorter time period than in the US. Second, European data are mostly qualitative and in form of questionnaires, while US data are quantitative.. 2. Literature Review Since the 1970s most macroeconomic models have their foundation in the Rational Expectations Hypothesis. In particular, the NKPC, that is the most dominant theoretical model in macroeconomics for the past few decades 2, has rational expectations at its heart. Despite its broad diffusion, the NKPC has been shown to perform poorly in empirical studies and to fail to reproduce various stylized facts in macroeconomic data. First of all, inflation appears to be very persistent across time (Fuhrer & Moore, 1995) and ‘inflation inertia’ appears to play a large role in the inflation process when it is related to the unemployment rate (Gordon, 1997). Moreover, Mankiw (2001), who tried to model the effect of monetary policy on inflation and unemployment, has shown that inflation responds to a contractionary monetary shock with a delayed, gradual fall. Besides failing to reproduce these stylized facts, the NKPC also has certain odd predictions. As pointed out by Ball (1994), the price staggering setting of the NKPC yields the surprising result that preannounced disinflations, when credible, cause economic booms rather than recessions. Contrary to the common understanding that disinflation is, in fact, costly in actual economies. Hence, a series of papers departed from the Rational Expectations Hypothesis and developed different views on expectations such as ‘learning’. In this stream of literature it is assumed that agents do not have full information about the true economic model or the objectives of the central bank; rather they make estimates of these crucial parameters using all the available information and constantly update their forecasts as a result of economic shocks. Moreover, agents have informative asymmetries, and Sims (2003) proposes the rational inattention approach as a method to describe expectations. This approach assumes that people are constrained in their ability to acquire and process information: they have limited capacity process and update information. Following Sims (2003), Mankiw and Reis (2002) extend this 2. McCallum (1998) even calls the NKPC ‘the closest thing there is to a standard specification’. of monetary analysis.. 3.

(4) microeconomic approach to a macroeconomic model of output and inflation. Their main assumption is that information is disseminated slowly throughout the population. In every period, only a specific fraction of agents updates its information, resulting in heterogeneous expectations. Mankiw and Reis (2002) define this phenomenon as disagreement. In their model the staggered behavior of information is very similar to the role rigid prices play in the NKPC as it was developed by Calvo (1983). Firms, instead of adjusting slowly prices as in Calvo (1983), adjust slowly their information set. Therefore, Mankiw and Reis (2002) define this model as the sticky-information Phillips curve (SIPC). Although it is a subtle change to the NKPC the dynamic pattern of prices and output in response to shocks changes drastically. The response of inflation to a monetary shock becomes far more gradual. Moreover, an anticipated disinflation causes a recession, rather than a boom. These responses are consistent with how central bankers view their influence on the economy. Besides presenting a theoretic alternative to the NKPC, the autors also provide some preliminary empirical evidence on the SIPC. In a follow-up paper Mankiw et al. (2004) suggest several approaches for empirical testing. Instead of focusing on firms updating their information, the theory is extended to normal households facing certain costs of updating their information. The notion of disagreement is extended to the fact that households are probably slower in updating their set of information than professionals, although Mankiw et al. (2004) do not provide a theoretical reason for this phenomeno. Using US surveys of professional economists and consumers they test whether their sticky-information model provides statistically different results than the standard NKPC, assuming that the rate of dispersion is larger among economists than among the general public.3 They conclude that their model of sticky information is better at reproducing the stylized facts. Their findings confirm that inflation expectations are inconsistent with rational expectations and adaptive expectations. Instead they observe a pattern of disagreement in US expectations. This is consistent with their model of sticky information in which only a fraction of the population updates its information every period. Although the authors recognize the limitations of their research, they provide a good starting point for further research on the dynamics of inflation expectations. 3. Mankiw et al. (2004) recognize though that this rate of dispersion might not be constant over. time.. 4.

(5) Inspired by models of the spread of disease from epidemiology literature Carroll (2003) revisits the microeconomic foundations of the sticky-information approach. He proposes a model with diffusion of information from professional forecasters to the general public. It achieves a similar equation for the evolution of mean inflation expectations as Mankiw and Reis (2002). However, Carroll (2003) somewhat relaxes the assumption that information updating is costly and assumes that a fraction of the general population simply does not receive certain or does not read the ‘most recent forecasts’ and assumes that the information collected in a previous period is still valid instead. Carroll (2003) provides a theoretical foundation for the spread of information throughout the economy and he tests his epidemiological model in the same fashion as Mankiw et al. (2004), again using US survey data. Using similar rates of information dispersion he confirms that these models with information rigidities are a sound representation of US expectation formation. Although the sticky-information approach seems to have been used extensively for US data, European data is, to this date, somewhat neglected. Khan and Zhu (2002) were among the first to extend research to the international domain but they only used data from Canada, the United Kingdom and, again, the US. So far, the only paper we could find that exclusively examines the European sample is Döpke et al. (2008) who model expectation data from four major EU economies: France, Germany, Italy and the United Kingdom. Döpke et al. (2008) closely follow the approach in Carroll (2003) and their findings support the usefulness of the stickyinformation approach for the representation of the formation of household expectations. They fail, however, to explain some assumptions they make on the structure of household expectations, although this could significantly affect their results on the speed of information adjustment. The current paper employs the approach in Carroll (2003) for data covering the entire EU. The reason that European data is ignored is two-sided. First of all, most European data is qualitative, implying that this has to be converted to quantitative data first before it can be applied to empirical research. Although the literature provides several methods for quantifying surveys of many different setups, the conversion process is not straightforward, and, more importantly, requires some additional assumptions on the structure of expectations that could undermine the empirical results. As mentioned, Döpke et al. (2008) insufficiently recognize these assumptions. 5.

(6) Another problem with European data is the timing. US surveys have been running since the early 1950s whereas systematic European surveys started to develop in the late 1980s, more than 35 years later. Nonetheless, more and more European data has become available; hence, this paper tests whether the sticky information approach is as useful for modeling European data as it is for US data.. 3. The model 3.1. Sticky-information Phillips curve It takes a few steps to go from the original model of sticky information (Mankiw & Reis, 2002) to the epidemiological model of expectation formation by Carroll (2003). Originally, Mankiw and Reis (2002) assumed that firms gather information and set optimal prices accordingly. Yet, during every period just a fraction of firms obtains new information, while the other firms set prices based on old plans. Mankiw and Reis (2002) then devise a variation of the Phillips curve where inflation depends on output, expectations of inflation and expectations of output growth: the so-called sticky-information Phillips curve. Although we leave the formal steps of the derivation of the SIPC to the Appendix, it should be noted that the SIPC has one very important implication for inflation expectations. Whereas in the standard sticky-price model current expectations of future conditions play a central role (Fischer, 1977), in the sticky-information approach relevant expectations are past expectations of current conditions. This subtle difference drastically changes the dynamic pattern of prices and output in response to shock. As we explained in the previous section the response of inflation to a monetary shock becomes far more gradual and an anticipated disinflation causes a recession, rather than a boom. Carroll (2003) adopts this sticky-information approach and tries to model which fraction of agents actually updates their information and why. His approach can be seen as a micro-economic foundation of the SIPC; it leaves the rather unrealistic notion of firms randomly updating their information aside. It provides additional testable implications which do not follow directly from the original SIPC. This paper will follow Carroll (2003) and try to model the formation of expectations in a stickyinformation environment.. 6.

(7) 3.2. The epidemiology of household inflation expectations Suppose a set of experts makes rational forecasts on inflation, collecting all relevant information and having a sound understanding of the economic model. These forecasts are published4. Households face a certain cost if they want to update their information and read the published forecasts. Hence, in every period only a fraction λ updates its inflation expectations. The remaining (1 – λ) simply continues to believe the last forecast they have read. The evolution of the mean household (HH) inflation (π) expectation (E) follows:

(8)

(9) ,

(10) , 1 , 1 , . .. 1. Where , and

(11) , respectively denote one-period ahead expectations of inflation for households and experts. This expression for inflation expectations is. identical to the one proposed by Mankiw and Reis (2002), except that in their framework it is assumed that every agent updates their expectations by computing their own forecasts under the assumptions of rational expectations and every agent has the same probability of updating. Naturally, real published forecasts do not contain expectations of every period into the infinite future. Moreover, it is unlikely that any agent will remember these patterns forever. Even if these assumptions would be true, it would still be impossible to test equation (1), since most surveys only contain data about households’ expectations one year ahead. In order to derive a testable model Carroll (2003) makes some additional assumptions about the households’ view on the inflation process. Moreover, the model is adjusted to account for the fact that all the forecasts are made one year ahead instead of one period.5 The algebraic derivation, outlined in Carroll (2003), leads to the following equation, formulated for annual inflation rates: ,

(12) , 1 , 2. 4. In Carrol (2003) his model forecasts are published in newspapers. Every inflation article. contains a complete forecast of the inflation rate for all future quarters and any person that reads such an article can recall the entire forecast.. 7.

(13) Note that equation (2) is based on the assumption that households create expectations on a quarterly scale. As we will see later on, this paper will also try to model the formation of household expectations on a monthly scale. Equation (2) then becomes: ,

(14) , 1 , 3. Unlike equation (1), equation (2) and (3) are empirically testable with the available survey data. Moreover, we are able to relax the assumption that households obtain and remember inflation forecasts for every period in the infinite future.. 4. Expectation data 4.1. Sources To test the sticky-information model on European data, we use two kinds of data: proxies for the inflation expectations for households and proxies for the inflation expectations for the professionals. For households only one source is available, namely, the Joint Harmonised EU programme of Business and Consumer surveys programme conducted by the European Commission (EC). It is a monthly survey conducted among common households in all member countries of the EU since January 1985. It contains data for the individual countries but also for the two aggregates: the European Union and the Euro Area. As mentioned this research will use the later6. Unfortunately data from the EC its Consumer survey is qualitative and requires some modification to be applicable for research. We will return to that later. To model the expectations of professionals, this paper, which aims at studying the performance of inflation expectations model for the Euro zone, uses the Survey of Professional Forecasters (SPF). The SPF, conducted by the ECB since the last quarter of 1998, immediately following the establishment of a single currency, provides forecasts for inflation in the Euro area as a whole. It asks a panel of professional forecasters affiliated with financial or non-financial institutions based within the. 6. For both the survey results and the actual inflation the composition of the Euro Area has. changed over time. From the initial 12 countries that joined the monetary union: Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal and Spain to the current 18 participants with newcomers: Cyprus, Estonia, Latvia, Malta, Slovakia and Slovenia.. 8.

(15) European Union for their short- and long term expectations of key macroeconomic variables on a quarterly basis. Previous studies such as Döpke et al. (2008) and Paloviita (2008) have used data from Consensus Economics as source of professional inflation expectations. These studies have not been focused on the situation of the entire Euro zone taken as a whole, and they have not used data for the entire EU such as the SPF.7 4.2. Issues As mentioned, two problems arise using the Consumer survey of the EC and the SPF. First of all the frequency: whereas the Consumer survey is conducted on a monthly basis, the SPF is only collected quarterly. Both Döpke et al. (2008) and Carroll (2003)8 should have faced this frequency issue, yet do not mention this issue. To solve for these different frequencies either the survey among households has to be transformed into quarterly data or the survey among experts has to be converted to monthly data. The structure of the sticky-information model provides no reason to prefer any method. However, both Carroll (2003) and Döpke et al. (2008) have converted their surveys into quarterly data. To see whether or not this has any effect on the estimations will use both frequencies and compare the results. For converting quarterly data to monthly data we have used linear interpolation. Since, the time series of professional expectations follow a random walk, we have no reason to adopt another method.9 For the transformation of monthly to quarterly data applied two methods. First, we took the average of all three monthly observations in a quarter as a representation of the entire quarter. Second, we only took the final monthly observations of the respective quarter as a representation of the entire quarter. So for example, to derive a forecast for the second quarter of 2011, we have used the. 7. One of the few papers that we could find that did use the SPF was a study by Koop and. Onorante (2012) who estimate New Keynesian and Neoclassical Phillips curves, using a technique called dynamic model averaging: a relatively new statistical method which allows the set of explanatory variables change over time. 8. The Michigan survey of Consumers is conducted monthly whereas the Survey of. Professional Forecasters conducted by the Federal Reserve Bank of Philadelphia uses quarterly data. 9. For completeness we have also interpolated the data using the cubic spline method and. constant interpolation, but this did not seem to significantly change the structure of the series.. 9.

(16) monthly forecast of June 2011. This was done to match the timing of the SPF which was usually conducted at the end of every quarter.10 4.3. Carlson-Parkin method As mentioned the results from the survey among households have to be quantified. Since we know the proportions of the responses (also see Appendix VI), we can adopt the probability method of quantification. This method was developed by Theil (1952) and later reused by several authors. It is now commonly known as the Carlson-Parkin method for their seminal renewal of the probability approach (Carlson & Parkin, 1975). Originally, the method was devised for a trichotomous survey i.e. a survey with three possible answers. The method was redesigned by Batchelor and Orr (1988) to match pentachotomous surveys, in other words, surveys with five possible answer categories. Since the ECB questionnaire that is used in this paper also has a pentachotomous setup we follow Bathelor and Orr (1988) to derive actual values for the household expected inflation. We leave the formal derivation of the CarlsonParkin method to the Appendix. In short, each respondent is supposed to answer a question about future inflation and how they perceived inflation in the past. It is assumed that the response is given on the basis of a subjective probability distribution function, conditional on the information set available to consumers. Agents will report that they expect no change in the price level if they expect inflation to be in an interval around zero. Moreover, agents expect no change in inflation if their expectation falls within an interval around the inflation they have perceived in the past. This allows us to derive expressions for expected inflation as a function of perceived inflation. However, in order to derive actual values for expected inflation we need to make some assumptions on the underlying distribution function and the perceived past inflation rate (Berk, 1999). 4.4. The distribution of expectations The expectations distribution function describes how mean inflation expectations are distributed across individual respondents to the survey. Since we do not have access to the individual responses to the surveys due to privacy reasons, it is 10. For the exact timing of the questionnaire see the web page of the ECB. In general the. deadline to reply was at the half of the second month, while the results were published in the second week of the last month http://www.ecb.europa.eu/stats/prices/indic/forecast/html/index.en.html. 10.

(17) difficult to obtain conclusive empirical evidence on the form of the distribution function. Most papers that apply the Carlson-Parkin method apply a normal distribution for its statistical convenience. Carlson and Parkin (1975) justify this approach by appealing to the Central Limit Theorem. There are downsides to assuming a normal distribution, however. There are empirical reasons to expect that the distribution of expectations reject normality. First of all, there has always been an upward trend in prices; hence we have reason to believe that the distribution of expectations is asymmetrical. Research by Carlson (1975) and Lahiri and Teigland (1987) has shown that inflation expectations are predominantly positively skewed. Moreover, the same authors have shown that the actual distribution of the inflation forecasts is more peaked than the normal distribution. To cope with this previous χ -distribtution. Berk (1999) has shown, however, that these variations of distribution. literature has also adopted a logistic, a central- and a noncentral t-distribution and the. actually provide less accurate results. Finally, Nielsen (2003) provides an excellent comparison of the possible approaches to quantifying a pentachotomous survey. She. examines five possible different distribution functions and finds they provide no better forecasts. Since testing all these different approaches is beyond the scope of this paper, we will follow Nielsen (2003) and assume a normal distribution. 4.5. The perceived past inflation rate As mentioned, the perceived past inflation rate is used for scaling. Hence, we have to choose this rate. A simple choice is the real time inflation rate available to respondents at that time. However, it seems unlikely that the rate of inflation perceived by the general public is exactly equal to the actual rate of inflation. Moreover, respondents do not actually know this rate, since usually the rate of inflation of the current period is published in the next period. We cannot use information that is unavailable to households. Fortunately, the survey also provides us information on how respondents have perceived inflation for the past 12 months. Nielsen (2003) adopts several definitions of the perceived inflation rate as the scaling parameter. First of all, she uses two direct measures of inflation: the lagged real-time inflation rate available to consumers at that time and the mean of actual inflation over the entire period of the time-series, which could be regarded as a moderate rate of inflation. Second, she considers the answers that were given by consumers to a previous survey question regarding the past inflation rate. In short, it asks how 11.

(18) households have perceived the price development in the past 12 months. Respondents can give five possible answers: ‘fallen’, ‘stayed about the same’, ‘risen slightly’, ‘risen moderately’ and ‘risen a lot’. These responses could be interpreted in two ways: either transforming it in a trichotomous question with a scaling factor representing a response threshold11, or maintaining the original question its pentachotomous setup and again using the actual inflation rate as a scaling factor. Nielsen (2003) finds that the latter, with the mean of the actual inflation over the entire period of the timeseries, provides the best forecast and is preferable, by comparing the root mean square error (RMSE) of every type of forecast with the actual level inflation in the predicted period. To do so she shifts the forecasts one-year ahead to be able to accurately compare them to the realized level inflation. Since this paper uses data from a different period, we will follow the recommendation in Nielsen (2003) to use the mean of actual inflation in the past as a scaling, but repeat her procedure and see if the choice of the scaling variable makes any difference. We then consider the model for both monthly and quarterly data, snd for different choices of the scaling variable. We then obtain three variations of the expected inflation of households, all scaled to different measurements of perceived past inflation. 4.6. How well do the forecasts forecast? We compare the different scaling parameters by means of RMSE. Moreover, we use the RMSE to see whether or not experts provide better forecasts than regular households. In general, the RMSE is calculated by (Greene, 2003): 1. $. !" "# 4 %. Where is the number of observations, " the actual time series, in this case actual. inflation and "# the forecasted series, i.e. the differently scaled expected rates of. inflation. The results of the calculation of the RMSE are summarized in Table 1. For the rate of actual inflation we have used the Consumer Price Index for the Euro Area as provided by the OECD. To actually compare the forecasts to actual inflation we 11. The answer categories ‘rise slightly’, ‘rise moderately’ and ‘rise a lot’ are comprised within. one category ‘up’, which leaves three possible responses. Derivation of these response proportions leads to mean expected inflation as a function of the response threshold. Also see Batchelor and Orr (1985).. 12.

(19) have to shift the forecasts one year ahead. The results of these shifts are illustrated in Appendix III and Appendix IV. For both quarterly and monthly data, the forecasts of professionals have the lowest RMSE and are the most accurate. As for the different variations of household expectations we can conclude that, despite methodology, expected inflation yields the best forecasts when it is scaled to the actual level of inflation. However, unlike Nielsen (2003) suggests, we believe it would be incorrect to interpret the best forecast as the best representation the actual forecast. Therefore we continue estimating our model with every different variation of household expectations. Table 1. Root mean square error of expected inflation Frequency of data Quarterly data. Variations of scaling Actual inflation Perceived inflation scaled to lagged inflation Perceived inflation scaled to mean inflation of past observations Professional expectations. Monthly data. Average. 0.716. 1.281. Last observation. 0.719. -. Average. 0.761. 1.493. Last observation. 0.760. -. Average. 0.925. 1.311. Last observation. 0.919. -. 0.382. 1.160. 57. 170. Number of observations. Due to shifting the sample period becomes 2000Q1:2014Q1 and 2000:M03:2014M04. Source: OECD, Main economic indicators (accessed 4th of June, 2014) and the Joint Harmonised EU programme of Business and Consumer surveys (accessed 27th of May, 2014). 5. Results 5.1. Granger causality Before we estimate equation (2) and (3), we will examine some properties of the time series of the expectations. The structure of the model implies that expectations of professionals are spread to households. This suggests that the expectations of experts should Granger-cause the forecasts of households. Although this does not test our model, it is a preliminary check to see whether professional forecasts are good predictors of the expectations of households. It should be important to note that Granger causality is not true causality, hence we should be careful not to draw any rigorous conclusions from the results about the true causality. Strangely 13.

(20) enough, the results in Table 2 suggest that the lags of expert expectations are no significant predictors of household expectations but instead the causality runs from households to professionals. This is contrary to what we would expect in our model of informational rigidities. A possible explanation for this result could be that experts take household expectations and perceptions into account when making their projections12. Since household expectations are in general more persistent and slower to adjust than professional expectations, it may appear that household expectations actually Granger cause professional expectations. 5.2. Informational rigidities We estimate equation (3) using ordinary least squares (OLS). 13. and see. whether or not the sticky information approach represents European survey data. Following Carroll (2003) we test several variations of our baseline model which follows from equation (3): ,'

(21) ,' ,' 4. Where j is either 4 or 12 depending on the timing of the sample: quarterly or monthly.. 1 or 1 , which follows from the original model. This in turn. In the first version of our model we do not impose the summing-up restriction. allows us to check the validity of this restriction using Wald-tests on coefficient restrictions.. 12. In a special questionnaire sent to participants of the SPF, respondents were asked to answer. questions regarding their method of forecasting. It appears that for short-term forecasts, the larger share of respondents used reduced-form models such as vector autoregressive models and vector error correction models. Although no specifics were given on the variables it is likely that previous inflation, expected inflation and the interest rate were dominant. As for long-term forecasts, the use of dynamic stochastic general equilibrium models gained popularity for the last decade (source: Results of the second Special Questionnaire for Participants in the ECB Survey of Professional Forecasters, 2013, 13. All time series have been checked for stationarity. Contrary to Döpke et al. (2008)we find. hardly any evidence for a unit root in our time series. Except for our series where perceived inflation was scaled to the mean of observations, no series show significant signs of non-stationarity. Hence, we will continue using OLS for our estimation. Results of the augmented Dickey-Fuller tests are in Appendix V. 14.

(22) Table 2. Tests for Granger non-causality. ( ,' )* !. ,. +%.

(23) )+ + +,'+ !. ,. .%. -. . .,'. /'. Where 0 is either 1or 22 and 3 is either 4 or 12 depending on the sample.. Variations of scaling Actual inflation Perceived inflation scaled to lagged inflation Perceived inflation scaled to mean inflation of past observations. Quarterly data Professional expectations does … does not Granger cause not Granger cause … professional expectations -. 0, ∀6 )+ 0, ∀7 F-Statistic p value F-statistic p value 2.971 0.060 40.736 0.000. Actual inflation Perceived inflation scaled to lagged inflation Perceived inflation scaled to mean inflation of past observations. 0.570. 0.569. 42.110. 0.000. 0.989. 18.805. 0.000. 2.096. 0.379 Monthly data 0.126. 62.783. 0.000. 0.364. 0.670. 64.002. 0.000. 2.300. 0.103. 28.218. 0.000. observations with 8 2 lags of independent variables. We have tested for both methods of frequency. Sample periods are respectively, 1999Q1:2014Q1 (59 observations) and 1999M03:2014M03 (170. conversion: the average observation and the last observation of every quarter and found no. significantly different results except for slightly different point estimates. The results displayed are from the second method. Source: OECD, Main economic indicators (accessed 4th of June, 2014) and the Joint Harmonised EU programme of Business and Consumer surveys (accessed 27th of May, 2014). with better point estimates of the crucial coefficient which represents the fraction. In model (2) the summing-up restriction is imposed. This should provide us. of households that update their information or the speed at which information spreads. from professionals to households. For quarterly data, we test whether or not = 0.25; the rate of dispersion assumed by Mankiw and Reis (2002) in their seminal paper. They reach this explicit value because they argue that over the course of a year everyone has updated their information, hence, only 25 percent of the population, on average, should have updated their information after one quarter. Following this line of reasoning we should test if 9 0.083 for monthly data. We have reasons to . believe that the rate of dispersion is higher in our sample than the speed of adjustment in Mankiw and Reis (2002), Carroll (2003) and Döpke et al (2008) their papers. Our sample range contains a more turbulent economic period. Carroll (2003) has shown 15.

(24) that updating is faster when inflation is ‘in the news’. Moreover, unstable inflation and increasing uncertainty increases the households their incentive to update their information. This finding is in line with Roberts (1998) who examines some relaxations of rational expectations and finds that the speed of adjustment was much larger post 1976, a period with unstable inflation, than in the pre-1976 era, a period of relatively stable inflation. In our third modification of the original model, we allow for a constant. If our model would be a perfect representation of the true process in which expectations are formed, the presence of a constant would make no sense. If, for example, expert expectations and actual inflation would reach a certain fixed level for eternity, the presence of constant would suggest that household expectations would never reach that level and be forever biased. It seems very unlikely that households would not adjust their expectations at a certain point. If our model does not perfectly represent the formation of expectations, which is very plausible, the presence of a constant might suggest some other phenomenon that has not been captured by our model. Döpke et al. (2008), for example, find a significant negative value for the constant in their sample. As an explanation they suggest that inflation rates were falling over their sample. Households may have extrapolated this downward trend into the future, resulting in the negative constant. ,' *

(25) ,' ,' 5. Our final three variations: model (4), (5) and (6) include a lagged term of actual inflation. It allows for the fact that households are to some extent backwardlooking. Some people might update their forecasts to the most recent past inflation rate that is available to them. As Carrol (2003) argues, most news covers inflation statistics of the previous period, hence we choose to model actual inflation with one lag. This is somewhat similar to models using adaptive expectations. ,' *

(26) ,' ,' ', 6. The results from all estimations are summarized following the format of Carrol (2003). For every different variation of scaled expectations we have estimated 16.

(27) all six models. In the sixth column the results from the Wald coefficiency tests are displayed. The final column presents our measure of fit: the R-squared. This procedure has been repeated for both monthly and quarterly data and one thing becomes clear immediately: Carroll (2003) his model of informational rigidities is in no way representative for monthly expectation data. This probably explains why both Döpke et al (2008) and Carroll (2003) have ignored this approach. The fact that the expected of inflation of households is so persistent on a monthly scale is, however, interesting. As we can see in Table 3, for all variations of expected household inflation, the lagged value of expected inflation explains most of the variation. Adding lagged actual inflation to the equation shows that about half of the variation of expected inflation is explained by inflation in the previous period. Most likely this is explained by the fact that expected inflation is scaled to perceived inflation, which, in turn, is either equal to actual inflation or scaled to actual inflation. To conclude, it appears that the sticky-information approach is not suitable for modeling monthly expectation data. It appears that adaptive expectation or some other form of expectations with a high degree of persistence is more suitable. The results from our estimations in using quarterly data Table 4 look more promising14. For all variations of expected inflation the first two versions of our model show significant results for expected inflation of households in the previous period and the forecasts of professionals. Moreover, the summing-up restriction is. satisfied. As for our crucial variable: the point estimate of in our second version. of the model, we see that the speed of adjustment is slightly higher than the rate. suggested by Mankiw and Reis (2002), although we cannot reject the null that it is equal to 0.25 for two variations of expected inflation of households. This certainly stresses that the definition of perceived inflation can affect results and the selection procedure should be treated with care. When examining different structures of our model a few things come to notice. First of all there seems to be no significant presence of a constant, except for our third variation of household expectations when perceived inflation is scaled to the mean of previous observations of inflation. For this variation we can say with 90 percent 14. We have tested for both methods of frequency conversion: the average observation and the. last observation of every quarter and found no significantly different results except for slightly different point estimates. The results displayed in Table 4 are from the second method.. 17.

(28) certainty that the constant is positive, unlike Döpke et al. (2008) who finds negative constant throughout their sample. The difference may be explained by the fact that contrary to the period Döpke et al. (2008) examine, uncertainty has risen. It is more likely however, that the presence of a constant is due to methodological issues. As we saw in our stationarity tests, this specific variation of expected inflation showed some signs of a unit root due to the fact that the mean of past actual inflation was slightly non-stationary. Finally, adding lagged actual inflation to our equation does not significantly change our results. It appears that households, on a quarterly scale, are hardly backwards looking, just like their US counterparts (Carroll, 2003). Households definitely seem to learn from professional forecasts rather than simply extrapolate past inflation rates. To sum up, our findings suggest that Carrol (2003) his model of informational rigidities can definitely be applied to European expectation data. Apparently, the epidemiological model is a solid representation of the formation of household inflation expectations. A few remarks should be made, however. First of all, the choice of frequency of the sample is important. Apparently, it is impossible to find traces of information dissemination in monthly data. Previous literature has failed to make any mention of this. Moreover, the selection of the scaling parameter when constructing a series for expected inflation affects the point estimates of the coefficients. This is especially important when one wants to compare the crucial parameter, the rate of information dissemination to other samples.. 6. Conclusion Inflation expectations are an important factor in price dynamics. We tried to model the dissemination of information from professionals to normal households. To sum up, our findings suggest that Carroll (2003) his model of informational rigidities can definitely be applied to the European expectation data. Apparently, the epidemiological model is a solid representation of the formation of household inflation expectations. So far the literature has been inconclusive in its approach to European expectation data. Our results suggest that the choice of frequency and the scaling parameter of expectations have a significant effect on the outcome of the sticky-information approach. Further research on informational rigidities should take 18.

(29) Table 3. Estimation results for variations of household expectations with , *

(30) , , , . monthly data. Model. *. 1 2 3. 0.125** (0.052). 4 5 6. 1 2 3 4 5 6. 1 2 3 4 5 6. 0.014 (0.040). Wald-Test on coefficient restrictions | p value. . . Expectation scaled to actual inflation 0.008 0.983***. 1 (0.040) (0.048) 0.433 -0.011 1.011. 1/12 (0.032) (0.032) 0.003 -0.082 1.021***. * 0 (0.137) (0.000) 0.019 -0.194*** 0.590*** 0.490***. 1 (0.033) (0.046) (0.038) 0.000 -0.203*** 0.597*** 0.487***. 0 (0.041) (0.050) (0.039) 0.000 0.491*** 0.387***. 1 (0.044) (0.034) 0.000 Expectation scaled to perceived inflation scaled to lagged inflation. R-squared. 0.971***. 1 (0.040) 0,272 0.998. 1/12 (0.030) 0.008 0.183** 1.033***. * 0 (0.070) (0.046) 0.010 0.758*** 0.475***. 1 (0.036) (0.043) 0.000 -0.011 0.754*** 0.478***. 0 (0.058) (0.045) (0.046) 0.000 0.770*** 0.171***. 1 (0.037) (0.028) 0.000 Expectation scaled to perceived inflation scaled to mean inflation of past observations 0.0124 0.979***. 1 (0.021) (0.032) 0.501 0.000 1.000. 1/12 (0.010) (0.010) 0.000 0.058** -0.000 0.958***. * 0 (0.026) (0.021) (0.034) 0.030 -0.051* 0.946*** 0.079***. 1 (0.025) (0.032) (0.020) 0.044 0.074*** -0.074*** 0.914*** 0.087***. 0 (0.025) (0.026) (0.033) (0.020) 0.000 0.914*** 0.050***. 1 (0.025) (0.014) 0.001 0.017 (0.033) 0.002 (0.030) -0.120* (0.062) -0.320*** (0.040) -0.314*** (0.052). Estimations are made with 181 observations from 1999M03 to 2014M04. Standard errors are denoted in brackets. *,**,*** denotes rejection of the null at the 10%, 5% and 1% significance level, respectively. Source: OECD, Main economic indicators (accessed 4th of June, 2014) and the Joint Harmonised EU programme of Business and Consumer surveys (accessed 27th of May, 2014). 19. 0.906 0.905 0.909 0.952 0.952 0.945. 0.911 0.911 0.915 0.947 0.947 0.933. 0.930 0.930 0.931 0.935 0.938 0.945.

(31) Table 4. Estimation results for variations of household expectations with quarterly data. Model 1 2 3 4 5 6. 1 2 3 4 5 6. 1 2 3 4 5 6. *. , *

(32) , , =, . . Wald-Test on coefficient restrictions| p value. . Expectation scaled to actual inflation 0.513*** 0.357***. 1 (0.129) (0.155) (0.001) 0.334*** 0.666***. 1/12 (0.080) (0.080) 0.300 -0.062 0.558*** 0.338**. * 0 (0.169) (0.178) (0.165) 0.715 0.647*** 0.569** -0.286. 1 (0.159) (0.215) (0.202) (0.223) -0.008 0.651*** 0.565** -0.284. 0 (0.172) (0.190) (0.234) (0.209) (0.180) 0.670*** 0.202. 1 (0.229) (0.174) (0.111) Expectation scaled to perceived inflation scaled to lagged inflation 0.409*** 0.476***. 1 (0.116) (0.139) (0.008) 0.274** 0.726**. 1/12 (0.111) (0.111) (0.829) -0.270 0.618*** 0.375**. * 0 (0.246) (0.223) (0.167) (0.277) 0.566*** 0.559*** -0.210. 1 (0.204) (0.165) (0.224) (0.121) -0.217 0.685*** 0.452** -0.144. 0 (0.263) (0.250) (0.211) (0.238) (0.549) 0.639*** 0.239**. 1 (0.155) (0.117) (0.019) Expectation scaled to perceived inflation scaled to mean inflation of past observations 0.202*** 0.682***. 1 (0.067) (0.104) (0.006) 0.412*** 0.588***. 1/12 (0.036) (0.036) (0.000) 0.159* 0.166** 0.621***. * 0, * > 0 (0.088) (0.069) (0.108) (0.076), (0.948) 0.295*** 0.734*** -0.118. 1 (0.093) (0.110) (0.082) (0.052) 0.140 0.243** 0.669*** -0.093. 0 (0.090) (0.098) (0.116) (0.083) (0.266) 0.639*** 0.213***. 1 (0.067) (0.040) (0.000). R-squared 0.686 0.759 0.687 0.647 0.697 0.621. 0.655 0.611 0.662 0.661 0.665 0.643. 0.728 -0.270. Estimations made with 68 observations from 1999Q1 to 2014Q1. Standard errors are denoted in brackets. *,**,*** denotes rejection of the null at the 10%, 5% and 1% significance level, respectively. Source: OECD, Main economic indicators (accessed 4th of June, 2014) and the Joint Harmonised EU programme of Business and Consumer surveys (accessed 27th of May, 2014). 20. 0.743 0.737 0.748 0.817.

(33) this finding into account; especially if the aim of research is to compare the speed of information dissemination between samples. The research on sticky information can be extended in several ways. First of all, a conclusive methodology should make it possible to reliably compare the speed of information adjustment between different time-periods but also between different regions. It would be interesting, for example, to compare the institutional differences between the US and Europe and see whether or not they have any effect on the speed of information adjustment. Furthermore, it would be possible to build on the work of Kiley (2007) and Coibion (2010). Both authors compare the results of the SIPC with a hybrid form of the NKPC which relates inflation not only to currently expected inflation and the output gap, but also to past inflation, to explain for the inertia of observed inflation. They conclude that the hybrid NKPC outperforms the SIPC for US data. It should be interesting to repeat their research for the European sample.. 21.

(34) References Ball, L. (1994). Credible disinflation with staggered price-setting. American Economic Review, 84(1), 282-289. Batchelor, R. A., & Orr, A. B. (1988). Inflation expectations revisited. Economica, 55(219), 317-331. Berk, J. M. (1999). Measuring inflation expectations: A survey data approach. Applied Economics, 31(11), 1467-1480. Calvo, G. A. (1983). Staggered prices in a utility-maximizing framework. Journal of Monetary Economics, 12(3), 383-398. Carlson, J. A. (1975). Are Price Expectations Normally Distributed?. Journal of the American Statistical Association, 70 (352), 749-754. Carlson, J. A., & Parkin, J. M. (1975). Inflation expectations. Economica, 42(166), 123-138. Carroll, C. D. (2003). Macroeconomic expectations of households and professional forecasters. The Quarterly Journal of Economics, 118(1), 269-298. Coibion, O. (2010). Testing the sticky information phillips curve. The Review of Economics and Statistics, 92(1), 87-101. Döpke, J., Dovern, J., Fritsche, U., & Slacalek, J. (2008). The dynamics of european inflation expectations. The B.E.Journal of Macroeconomics, 8(1), 1-23. European Central Bank. (2011). The monetary policy of the ECB (3rd ed.). Frankfurt: ECB. Fischer, S. (1977). Long-term contracts, rational expectations, and the optimal money supply rule. Journal of Political Economy, 85(1), pp. 191-205. Fuhrer, J., & Moore, G. (1995). Inflation persistence. The Quarterly Journal of Economics, 110(1), 127-159. Gordon, R. J. (1997). The time-varying NAIRU and its implications for economic policy. Journal of Economic Perspectives, 11(1), 11-32. Greene, W. H. (2003). Econometric analysis. Prentice Hall. Khan, H., & Zhu, Z. (2002). Estimates of the sticky-information Phillips curve for the United States, Canada, and the United Kingdom. Bank of Canada.. 22.

(35) Kiley, M. T. (2007). A quantitative comparison of sticky-price and stickyinformation models of price setting. Journal of Money, Credit and Banking, 39(s1), 101-125. Koop, G., & Onorante, L. (2012). Estimating Phillips curves in turbulent times using the ECB's survey of professional forecasters. European Central Bank. Lahiri, K., & Teigland, C. (1987). On the normality of probability distributions of inflation and GNP forecasts. International Journal of Forecasting, 3(2), 269-279. Mankiw, N. G. (2001). The inexorable and mysterious tradeoff between inflation and unemployment. Economic Journal, 111(471), 45-61. Mankiw, N. G., & Reis, R. (2002). Sticky information versus sticky prices: A proposal to replace the new keynesian phillips curve. The Quarterly Journal of Economics, 117(4), 1295-1328. Mankiw, N. G., Reis, R., & Wolfers, J. (2004). Disagreement about inflation expectations. NBER Macroeconomics Annual 2003, vol. 18 (pp. 209-270) National Bureau of Economic Research, Inc. McCallum, B. T. (1998). Stickiness: A comment. Carnegie-Rochester Conference Series on Public Policy, 49(1), 357-363. Nielsen, H. (2003). Inflation expectations in the EU: Results from survey data. Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes. Paloviita, M. (2008). Comparing alternative phillips curve specifications: European results with survey-based expectations. Applied Economics, 40(17), 22592270. Roberts, J. M. (1998). Inflation expectations and the transmission of monetary policy. Board of Governors of the Federal Reserve System (U.S.). Sims, C. A. (2003). Implications of rational inattention. Journal of Monetary Economics, 50(3), 665-690. Theil, H. (1952). On the time shape of economic microvariables and the Munich business test. Revue De l'Institut International De Statistique / Review of the International Statistical Institute, 20(2), pp. 105-120.. 23.

(36) Appendix I. Sticky information Phillips curve dynamics. Suppose a firm sets its price every period, but only a fraction of firms. Mankiw and Reis (2002) propose the following alternative model of price. updates their information and computes a new path of optimal prices. Other firms set prices according to old information. As in the New Keynesian model a firm its 8∗ 8 @ " 7. optimal price is given by:. Where the firm its desired price8∗ depends on the overall price level 8. ". A firm that last updated its information 3 periods ago sets the price: B ' 8∗ 8. and output. '. The aggregate price level is the average of all prices firms set: 8 !. D. 1 ' B 9. '%*. '. Putting these three equations together yields the following equation for the aggregate price level:. 8 !. D. 1 ' ' F8 @ " G 10. '%*. Taking out the first term and rewriting the summation index: 8 F8 @ " G !. D. 1 ' ' F8 @ " G 11. '%*. And defining the previous period its price level, analogous to equation (10): 8 !. D. 1 ' ' F8 @ " G 12. '%*. inflation rate 8 8 :. Subtracting equation (12) from equation (11) leads to the following equation for the F8 @ " G ! !. D. D. 1 ' ' F @ ∆" G. '%*. 1 ' ' F8 @ " G 13. '%*. Where ∆" " " is the growth rate of output. Equation (11) can be. rearranged to show:. 24.

(37) 8 I. D @. J " ! 1 ' ' F8 @ " G 14 1. '%*. Substituting equation (14) in the last term of equation (13) leads to, after some rearranging:. I. D @. J " ! 1 ' ' F @ ∆" G 15 1. '%*. This expression of inflation as a function of output, expectations of inflation and expectation of output growth is the sticky-information Phillips curve. As Mankiw and Reis (2002) note the timing of expectations is what separates it from a standard New Keynesian Phillips curve. Past expectations of current conditions play a central, in contrast to current expectations of future conditions.. 25.

(38) Appendix II. Carlson-Parkin method ECB questionnaire Nielsen (2003) provides an excellent explanation of Batchelor and Orr (1998) their derivation, and since the ECB questionnaire that is used in this paper also has a pentachotomous setup we follow her adaption of the Carlson-Parkin method. The ECB Consumer survey asks two questions relating to the consumer price index. The questions and the respective possible answers are in Table 5. The terms ‘A’, ‘B’ etc. refer to the percentage of the respondents in each response category.. Table 5. ECB questionnaire Q5. How do you think that consumer. Q6. By comparison with the past 12. prices have developed over the last 12. months, how do you expect that. months? They have…. consumer prices will develop in the next 12 months? They will…. A’ fallen (--). A fall (--). B’ stayed about the same (-). B stay about the same (-). C’ risen slightly (=). C increase at a slower rate (=). D’ risen moderately (+). D increase at the same rate (+). E’ risen a lot (++). E increase more rapidly (++). F’ don’t know [N]. F don’t know [N]. Source: The Joint Harmonised EU Programme of Business and Consumer Surveys User Guide (updated 4th of July 2007). We know the proportions of responses A, B, C, D and E (and F)15. Assume for any kind of survey that the respondent i to a survey taken at time t forms a subjective probability distribution function defined over the percentage change in prices expected for the next period. The individual subjective probability distribution functions can be aggregated to a joint probability distribution function KF,LΩ G,. where , is the future rate of inflation at time t for the period N 1 and Ω is the 15. The response category ‘don’t know’ will be divided up proportionally and added to the. other categories (Batchelor & Orr, 1988).. 26.

(39) information set available to households at time t. Moreover, F,LΩ G O, where O, is the mean expected value of at time t for period N 1. The. individual responses can be regarded as independent drawings from the population. and allow us to derive expressions for the standard deviation, but most importantly for the average expected inflation rate.. Table 6. Response tresholds of the ECB questionnaire Q6. By comparison with the past 12 months, how do you expect that consumer prices will develop in the next 12 months? They will… fall if. , P Q. Q R , R Q. stay about the same if. Q R , P Ô /. increase at a slower rate if. Ô / R , R Ô /. increase at the same rate if. Ô / P ,. increase more rapidly if. Figure 1. Arbritrary distribution function of mean inflation expectations. 27.

(40) Next, assume for this specific pentachotomous survey that respondents are expected rate of future inflation falls within an interval around zero, or Q R. supposed to report that prices will stay about the same (inflation will be zero) if the O, R Q . Also, respondents will answer that no change in the rate of inflation is that they have perceived in the past Ô or Ô / R Ô R Ô / . Note that expected when their expectation falls within the interval centered on the price change. we assume that both indifference intervals are symmetric. Hence, the response categories can be organized as in Table 6. The boundaries of these intervals, denoted as response thresholds, are to be determined by data. Figure 1 illustrates this classification for an arbitrary distribution function; A, B, C, D and E represent the proportions of responses. Since these proportions change over time, we write T, ,. U, , V, etc.. In terms of the aggregated probability distribution function the. proportions of response can be written as: T, W, P Q LΩ Y. [\. K, LΩ Z , ]FQ G. D. U, WQ R , R Q LΩ Y. [\. [\. ]FQ G ]FQ G. V, WQ R , P Ô / LΩ Y. K, LΩ Z ,. _ \ `\ ^. [\. ]F Ô / G ]FQ G. a, W Ô / R , R Ô / LΩ Y ]F Ô / G ]F Ô / G. , W, b Ô / LΩ Y. D. _ \ `\ ^. 1 ]F Ô / G. K, LΩ Z ,. _ \ `\ ^. _ \ `\ ^. K, LΩ Z ,. K, LΩ Z ,. Where ] ∙ is the cumulative distribution function of KF, LΩ G. Using a standardized variable and specifying a distribution function yields. 28.

(41) d, ] FT, G . Q O, e,. f, ] FT, U, G . Q O,. g, ] FT, U, V, G . e,. Ô / O,. Z, ] FT, U, V, a, G . e,. Ô / O, e,. Since T, U, V, a, , 1 there is no need to specify the. inverse cumulative distribution function of ,, as it becomes redundant. unknowns in our system in relation to the perceived inflation rate Ô .. Rearrangement of the previous equations leads to a general solution for the four O, Ô .. e, Ô . Q. Ô . /. Ô .. . . . d, f, . d, f, g, Z, 2. d, f, g, Z, d, f, . d, f, g, Z, g, Z, . d, f, g, Z,. Since we know the proportions as T, , U, , V, and a, we can. calculate d,, f,, g, and Z, assuming a certain distribution function.. Moreover, we need to find a measurement for the mean perceived inflation rate Ô . As mentioned in the paper, we will follow Nielsen (2003) and assume a normal distribution. Our inverse cumulative distribution functions are then given by: d, Φ FT, G. f, Φ FT, U, G. g, Φ FT, U, V, G. Z, Φ FT, U, V, a, G. Where Φ ∙ is the cumulative standard normal distribution function. 29.

(42) Appendix III. Variations of monthly shifted expected and actual inflation rate of inflation. Due to shifting the sample period becomes 2000M03:2014M04. Source: OECD, Main economic indicators (accessed 4th of June, 2014) and the Joint Harmonised EU programme of Business and Consumer surveys (accessed 27th of May, 2014). 30.

(43) Appendix IV. Variations of quarterly shifted expected and actual inflation rate of inflation. Due to shifting the sample period becomes 2000Q1:2014Q1. Source: OECD, Main economic indicators (accessed 4th of June, 2014) and the Joint Harmonised EU programme of Business and Consumer surveys (accessed 27th of May, 2014). 31.

(44) Appendix V. Augmented Dickey-Fuller Test of dependent variable ∆" )* " ) ∆" ) ∆" ⋯ ), ∆", j. Dependent variable Household expectations Scaled to actual inflation Perceived inflation scaled to lagged inflation Perceived inflation scaled to mean inflation of past observations Professional expectations Actual inflation. Quarterly t-Statistic -4.745. Monthly t-Statistic -2.670. Prob. 0.000. -3.323. 0.071. -2.981. 0.038. -2.902 -3.800 -2.765. 0.169 0.023 0.069. -2.280 -2.920 -2.962. 0.180 0.045 0.040. Prob. 0.081. Where 8 is the number of lags and j is a stationary random disturbance term. If k 1 is a. root of the characteristic equation: k k ,. ,. )* k. ,. ) ⋯ ), 0, then the stochastic. process has a unit root. Sample periods are respectively, 1999Q3:2014Q1 (59 observations) and 1999M03:2014M03 (170 observations). 32.

(45) Appendix VI. Proportions of responses to survey questions How do you think consumers prices have developed over the last 12 monhts? They have... By comparison with the past 12 months, how do you expect that consumers prices will develop in the next 12 monhts? They will…. 33.

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No results found