Does disagreement among oil price forecasters reflect volatility? Evidence from the ECB surveys

International Journal of Forecasting 32 (2016) 1178–1192

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International Journal of Forecasting journal homepage: www.elsevier.com/locate/ijforecast

Does disagreement among oil price forecasters reflect volatility? Evidence from the ECB surveys Tarek Atalla a , Fred Joutz a,b,∗ , Axel Pierru a a

King Abdullah Petroleum Studies and Research Center (KAPSARC), Saudi Arabia

b

Department of Economics at The George Washington University, United States

article Keywords: Disagreement Forecaster Oil price Survey Volatility

info

abstract We examine quarterly oil price forecasts from the Survey of Professional Forecasters conducted by the European Central Bank. We present three empirical findings, all of which are robust to the number of respondents considered. First, the dispersion of forecasts is correlated positively with the average forecast error for all forecast horizons. Second, at the current and next quarter horizons, the oil price volatility observed through to the end of the forecast horizon statistically explains the disagreement among oil forecasters. Third, we use the disagreement among forecasters to derive a measure of the price volatility which is correlated well with the volatility observed ex post. When the forecast horizon is one quarter ahead, the disagreement-based volatility is equal to the price volatility observed subsequently, plus a small add factor. These results support the view that the disagreement among forecasters reflects the price volatility. © 2016 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

1. Introduction When the disagreement between oil-price forecasters increases, does this mean that the future oil price has become more uncertain and the market more volatile? We address this issue empirically using crude oil price forecasts from the European Central Bank’s quarterly Survey of Professional Forecasters (SPF). The existing literature on the disagreement among forecasters relates mostly to macroeconomic forecasting. In this paper, we consider forecasts of the crude oil price. This allows us to use the price volatility as a measure of the level of uncertainty surrounding the forecasted variable. We therefore attempt to evaluate the interrelationships

∗ Corresponding author at: King Abdullah Petroleum Studies and Research Center (KAPSARC), Saudi Arabia. E-mail addresses: [email protected] (T. Atalla), [email protected], [email protected] (F. Joutz), [email protected] (A. Pierru).

between oil price volatility and the disagreement among oil-price forecasters. The disagreement between forecasters is usually measured by the dispersion of the point forecasts of the panel of respondents. By assessing the correlation between disagreement and the oil price volatility, this paper examines the view that a more volatile oil price leads to a greater disagreement among forecasters. This view does not necessarily conflict with other potential reasons why forecasters disagree. Patton and Timmermann (2010) discuss sources for disagreement among forecasters. For instance, different forecasters may have different information sets at the time when the forecast is made. This may be due to the relative importance and use of oil prices in their business and models. Forecasters may disagree about which exogenous variables are relevant or the way in which these variables translate into a specific price level. They may use different approaches: expert opinions, simple models of the market alone, or larger macroeconomic models. Disagreement can also result from strategic behaviors by certain forecasters.

http://dx.doi.org/10.1016/j.ijforecast.2015.09.009 0169-2070/© 2016 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

T. Atalla et al. / International Journal of Forecasting 32 (2016) 1178–1192

For example, they might attempt to influence the oil market or gain attention from the media. Lamont (2002) hypothesizes that forecasters who are paid according to their relative abilities might scatter, since it is hard to win when making forecasts that are similar to those of others, or if there is clustering or herding. In addition, we explore the issue under study further by suggesting an alternative approach. Since the SPF point forecasts relate to quarterly average oil prices, the distribution of the forecasts can be viewed as the distribution of the average price over the quarter considered. This raises the question, how can we infer an oil price volatility measure that is consistent with this distribution? Based on an assumption about the process generating prices that is standard in financial markets, namely that the logarithm of the oil price follows a random walk, we suggest a formula that derives a price volatility from the distribution of forecasts. This simple reduced-form model serves as a benchmark for translating disagreement into volatility. We apply this formula to the SPF and study the correlation between the resulting disagreementbased volatility and the oil-price volatility that is actually observed after each survey round. The remainder of the paper is organized into five sections, beginning with a literature review. Section 3 examines the sample from the SPF. A first look at disagreement and uncertainty is taken in Section 4. Next, we assess the oil-price volatility that is observed after each forecast is made. We then study the relationships between forecasters’ disagreement and oil-price volatility; and the final section concludes. 2. A review of the literature The macroeconomic literature provides several explanations for disagreement among forecasters.1 Special attention2 has been paid to the relationship between disagreement and the uncertainty surrounding forecasted variables. Such studies have attempted to correlate measures of the dispersion among survey forecasts with forecast errors and proxies for macroeconomic uncertainty. Regarding oil prices, the disparity among forecasters’ models and beliefs may lead to forecasts that are more divergent when the oil price volatility is higher. Thus, a more volatile oil price will lead to a greater disagreement among forecasters. Moreover, the positions that oil market participants take with futures and options contracts are based in part on their expectations about the macroeconomy and commodity market(s). Thus, feedback on the volatility can be provided by the relative disagreements or expectations regarding financial commodity market prices and returns.

1 For instance, Döpke and Fritsche (2006), Dovern, Fritsche, and Slacalek (2012), Lahiri and Liu (2005, 2006), Lahiri, Teigland, and Zaporowski (1988), and Siklos (2013) all tried to identify variables that could influence the disagreement over inflation forecasts. 2 For instance, Bowles et al. (2007) argue that disagreement among survey responses is a proxy for uncertainty, to the extent that different forecasters have different assessments of the macroeconomic and commodity market outlooks.

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Surprisingly enough, there has been little empirical research analyzing the disagreement among oil price forecasters. Unlike macroeconomic variables, the oil price volatility, whether implied or realized, is available as a straightforward measure of the uncertainty surrounding the oil price. To the best of our knowledge, the only study relating disagreement to volatility is that by Singleton (2012), who uses monthly oil price forecasts reported by Consensus Economics. He finds that a higher dispersion of forecasts is correlated positively with increases in the futures price volatility. Two other studies have used the European Central Bank’s SPF oil price forecasts. Pierdzioch, Rulke, and Stadtmann (2010) analyze whether oil price forecasters herd or anti-herd. Reitz, Rulke, and Stadtmann (2012) investigate whether regressive and extrapolative expectations exhibit significant nonlinear dynamics. Neither of these studies was concerned with the issues discussed in this paper. Our contribution focuses only on the behavior of the survey panel. We do not look at the dependency between respondents when measuring forecast uncertainty, as did Driver, Trapani, and Urga’s (2013) cross-section panel analysis of employment data. 3. SPF oil price forecasts The European Central Bank (ECB) has been publishing quarterly assumptions/forecasts of Brent crude oil prices in its SPF since the first quarter of 2002.3 These oil price forecasts refer to the average nominal spot price of Brent over the quarter. The survey includes participants from the financial sector (mostly banks), non-financial research institutes, and employer or employee organizations. Our sample period is from 2002Q1 to 2012Q4, which includes 44 survey rounds. Note that the forecasters in the ECB professional survey only provide point estimates of the oil price, with no information on the underlying probability distribution. The replies to the SPF are typically sent4 between the 16th and 21st of January (Q1 survey), April (Q2 survey), July (Q3 survey) and October (Q4 survey). Thus, the survey participants have access to market information for the first 15 days of each quarter. Initially, the SPF surveyed forecasters for the current quarter and the next four quarters, which we will refer to as horizon 0–4 forecasts. After 2010Q1, though, the ECB stopped collecting fourquarter-ahead forecasts. In the first year, there were about 35–40 participants, with participation fluctuating between 45 and 55 thereafter. Fig. 1 illustrates the time series of available currentquarter (horizon-0) forecasts.5 3 The SPF collects point and probability estimates for Euro area annual HICP inflation, annual GDP growth, and the unemployment rate. In addition, they also ask the participants to provide the assumptions that they use for the ECB’s interest rate for refinancing operations, the crude oil price, the USD/EUR exchange rate, and the annual change in the compensation cost per employee or labor costs. 4 According to a communication with Victor Lopez Perez at the ECB-SPF on December 3rd, 2012. 5 Since the participants tended to provide forecasts at all possible horizons, the numbers are similar for all horizons, and are available upon request.

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55

50

45

40

35

Q3 20

12

4

1

11 Q 20

Q2

11 Q 20

10

09

Q3 20

Q4

Q1

08

20

20

Q2

08 20

07

Q3

20

Q4

06

05

20

20

20

05

Q1

Q2

Q3

04

Q4

03

20

20

02 20

20

02

Q1

30

Fig. 1. Number of forecasts available per quarter (horizon 0, 90 forecasters).

Fig. 2. Actual average prices and SPF mean forecasts (all horizons, 90 forecasters). Table 1 Numbers of forecasters providing certain minimum numbers of forecasts, per horizon. Source: Survey of Professional Forecasters, European Central Bank. Number of forecasts

Current, one, two and three quarters ahead

Four quarters ahead

37 or more 30 or more 20 or more 10 or more At least one

24 35 55 71 90

N/A 11 45 61 85

Since the scope for disagreement may be related to the number of respondents, it is necessary to check whether our results depend on the numbers of forecasters in each survey. The levels of participation of individual forecasters vary, as some (1) enter later than 2002Q1, (2) leave permanently at some stage, and/or (3) do not contribute on a consistent basis. All of these factors contribute to the production of an unbalanced panel. Thus, after examining the participation levels of the individual forecasters, we define five arbitrary groups of forecasters, based on the number of forecasts provided by each forecaster. Table 1 presents the numbers of

participants in each group, based on certain minimum numbers of forecasts. The smaller number of participants at the four-quarter-ahead horizon is due to the ECB’s decision to stop asking about this horizon in surveys after 2010Q1. Our analysis focuses more on the first horizon set, because the sample period is longer. 24 participants provided 37 forecasts or more, while 35 participants contributed at least 30 times. The remaining three groups included 55, 71, and 90 participants, respectively. Fig. 2 shows the mean forecasts from the group of 90 forecasters and the actual quarterly average nominal Brent

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Table 2 ADF unit root tests for the difference in natural logs of the actual quarterly Brent oil price and the forecasts by horizon. Horizon

Lag length

ADF test

Implied coefficient

AIC

Panel (a) 90 participants with at least one response 2002Q1–2012Q4 0 1 −5.409** −0.071 1 3 −4.283** −0.090 2 1 −5.803** 0.279 3 1 −5.236** 0.504 4 3 −3.672* 0.316

−4.560 −3.286 −3.239 −3.619 −3.120

Panel (b) 71 participants with 10 responses or more 2002Q1–2012Q4 0 1 −5.409** −0.071 1 3 −4.283** −0.090 2 1 −5.803** 0.279 3 1 −5.236** 0.504 4 3 −3.672* 0.316

−4.560 −3.286 −3.239 −3.619 −3.120

Panel (c) 55 participants with 20 responses or more 2002Q1–2012Q4 0 1 −5.399** −0.068 1 3 −4.280** −0.087 2 1 −5.822** 0.279 3 1 −5.225** 0.505 4 3 −3.691* 0.321

−4.568 −3.289 −3.244 −3.621 −3.146

Panel (d) 35 participants with 30 responses or more 2002Q1–2012Q4 0 1 −5.305** −0.050 1 3 −4.242** −0.076 2 1 −5.782** 0.279 3 1 −5.306** 0.504 4 3 −3.629* 0.323

−4.632 −3.301 −3.240 −3.662 −3.138

Panel (e) 24 participants with 37 responses or more 2002Q1–2012Q4 0 1 −5.377** −0.061 1 3 −4.195* −0.068 2 1 −5.834** 0.272 3 1 −5.366** 0.498 4 3 −3.569 0.335

−4.640 −3.297 −3.242 −3.642 −3.145

Sample period: 2002Q1–2012Q4. Column 2 reports the number of lags for the dependent variable when minimizing the Akaike Information Criterion (AIC). A maximum of three lags was considered. The ADF specification included a constant and a trend. The critical values for the ADF statistics at the 5% and 1% levels are −3.53 (*) and −4.21 (**) respectively. The sample period for the four-quarter horizon is shorter, due to that part of the survey being discontinued in 2010Q1. Thus, the critical values are −3.57 (*) and −4.31 (**), respectively.

spot prices.6 The plot shows the classic pattern of hedgehog forecasts. The black line shows the path of the average Brent spot price, and the individual brown lines give the forecasts at all horizons for each survey round. Almost without exception, the mean forecasts under-predicted the growth in oil through to 2008Q2. The participants then missed the collapse in oil prices that started in the next quarter and ran until 2009. Thereafter, they resumed under-predicting, but did include some growth in oil prices. The median forecasts show the same pattern. The quarterly average Brent spot oil price appears to be an integrated process with at least one unit root. Engle and Granger (1987) and Granger (1981) argue that the forecast of an integrated process must be integrated itself. This is the case here: the null hypothesis of a unit root for all series of mean forecasts in natural logarithms cannot be rejected, while it is rejected when considering the differenced series.7 We test whether the difference between the log levels of the average Brent spot price and the mean forecast 6 Calculated as the average of daily closing prices (source: EIA). 7 These results are not provided here to save space, but are available upon request.

has a unit root. The results are reported in Table 2 for each group of forecasters, using ADF tests specified with up to three lags of the dependent variable, and with a constant and trend. The table gives the horizon, the lag length chosen by the AIC, a t-test, the implied coefficient, and the AIC. The null hypothesis of a unit root is rejected at either the 5% or 1% significance level for all samples and horizons, except for the four-quarter horizon with the sample of 24 forecasters. In that case, the ADF t-test is right at the 5% margin. Moreover, the implied coefficient is 0.34, which numerically is quite a long way from unity. We are comfortable in concluding that this series is stationary, which is consistent with the Engle–Granger hypothesis. 4. Disagreement and uncertainty: A first view This section discusses the different concepts applied when using a survey of forecasters to derive information from the panel. We proceed by defining forecast errors, disagreement within the panel’s participants, and the issue of forecast uncertainty, then conduct a simple test of forecast errors and disagreement. The notation and empirical work are in natural logarithms. Let Fi,t be the forecast of the average price in quarter t made in quarter t − h by the ith forecaster. Note that

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all forecast-related variables should include the subscript h, indicating the time horizon of the forecast considered. However, we simplify the notation in the main body of the paper by omitting the subscript. Thus, the forecast error ei,t is given by: ei,t = At − Fi,t = λt + εi,t

= aggregate error + idiosyncratic error.

(1)

The actual average oil price during quarter t , At , minus the forecast of that price by the ith participant, Fi,t , is composed of an aggregate error faced by all forecasters, λt , plus the participant’s idiosyncratic error, εi,t . The aggregate error is a common shock faced by all forecasters, and is assumed to be uncorrelated with the idiosyncratic errors. By definition, the latter are assumed to be uncorrelated with each other. The dispersion of point forecasts across the panel of participants is typically given by the difference between the ith forecaster and the central tendency of the panel, whether mean or median. We choose the mean here, in order to construct an index as per Lahiri and Liu (2005).8 Thus, our observed disagreement among participants in the survey is the variance of their point forecasts, which can be written as: dt =

=

1

N  (Fi,t − F¯t )2

N 

 ei,t −

N − 1 i=1

N 1 

N j=1

2 ,

e j ,t

(2)

where F¯t is the average forecast and N is the number of forecasters considered. As Eq. (2) shows, the observed disagreement is also the variance of the forecasters’ errors. Thus, the expected disagreement among forecasters is the expected squared dispersion from the mean forecast of the variances of errors σε|2 i,t . Dt ≡ E [dt ] =

=

=

1

N − 1 i =1

N 

N i=1

 E



N − 1 i=1 N 1 

N 

1

σε|2 i,t .

σε|i,t + 2

uncertainty, Ut , associated with a particular horizon for a panel is measured by time-varying aggregate shocks and the mean of the panel participant’s individual variances: 2 Ut = v ar (At − Fi,t ) = σλ| t +

N − 1 i=1 1

Fig. 3. Absolute forecast error vs. square root of disagreement group of 90 forecasters.

εi ,t − N 1 

N 2 j =1

N 1 

N j =1

σε|j,t − 2

2 εj ,t 2 N

 σε|i,t 2

(3)

The last equality above is the average variance of the idiosyncratic errors; the variance of the aggregate or common error has been removed. This can proxy for the expected disagreement or dispersion of the forecasters. Bomberger (1996, 1999) and Rich and Butler (1998) discuss disagreement as a measure of uncertainty. Following Zarnowitz and Lambros (1987), the forecast error

8 Lahiri and Liu’s (2005) approach has been used in a number of other papers like Lahiri and Sheng (2010) and Lahiri et al. (1988), several of which are listed in the reference list. The medians in our sample groups do not appear to be significantly different.

N 1 

N t =1

σε|2 i,t = σλ|2 t + Dt . (4)

This definition implies that the forecast uncertainty is equal to the (time-varying) variance of the accumulated aggregate shocks over the forecast horizon plus the expected disagreement, Dt . Therefore, disagreement among the forecasters must be smaller than the forecast uncertainty. However, the proportion of the uncertainty that is contributed by the disagreement is not known, but depends on the forecast horizon, the variability of the aggregate shocks over time, and the perceptions of the forecasters over the forecast horizon. Standard assumptions about the properties of forecast errors, especially for non-stationary series, suggest that both the disagreement and the uncertainty will grow with the horizon. Giordani and Soderlind (2003) suggest that disagreement is a better proxy of inflation uncertainty than previously thought. But, forecasters appear to underestimate uncertainty. However, we cannot say with certainty that either one will grow relatively faster than the other. If the disagreement reflects forecast uncertainty, one would expect a positive correlation between the forecast dispersion and the subsequent forecast error. Döpke and Fritsche (2006) suggest that the dispersion of idiosyncratic errors will be correlated with the aggregate error. The existence of such a correlation is apparent9 for the currentquarter forecast (horizon 0) in Fig. 3, which shows a plot of the absolute value of the average forecast error e¯ t versus the square root of the observed dispersion of forecasts. We convert the expected disagreement measure to its square root in order to ensure the comparability of the forecast errors.

9 The scatter diagrams are similar for all groups of forecasters.

T. Atalla et al. / International Journal of Forecasting 32 (2016) 1178–1192

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Table 3 Regression of the current quarter absolute survey forecast error on the disagreement at horizon 0, all groups. Sample of forecasters 2002Q1–2012Q4 90 71 55 35 24

Variable

Estimated coefficient

p-value

Adj R2

SER

ARCH (2) p-value

Constant Slope Constant Slope Constant Slope Constant Slope Constant Slope

−0.014

0.722 0.387 0.722 0.373 0.820 0.688 0.856 0.336 0.970 0.397

0.236

0.054

0.005

0.226

0.054

0.039

0.131

0.054

0.265

0.223

0.051

0.006

0.264

0.050

0.005

1.584 −0.013 1.575 0.008 1.262 −0.005 1.522 −0.001 1.553

The models are estimated using the Newey and West (1987) heteroscedasticity and autocorrelation correction in EViews 7.0. The null hypothesis for the slope is that it equals unity.

We test this relationship10 by regressing the absolute value of the forecast error e¯ t against the disagreement or dispersion of forecasts. For each sample group and forecast horizon, we estimate the following regression:

 |¯et | = α + β Dt + ut .

(5)

By definition, standard rational expectations multi-horizon forecasts with quadratic loss functions have at best a moving average error process at one less than the horizon. We therefore use the general covariance estimator developed by Newey and West (1987), which is consistent in the presence of both heteroscedasticity and autocorrelation of an unknown form. Table 3 shows the regression results from Eq. (5) when the forecast horizon is the current quarter.11 The measure of disagreement has explanatory power at all horizons. A 1% increase in the dispersion/disagreement leads to a 1.25%–1.50% increase in the absolute value of the survey sample forecast error. However, the null hypothesis that the estimated slope coefficients are unity cannot be rejected in all cases. The constant is not significant in all regressions.12 There is evidence of conditional heteroscedasticity, but not autocorrelation. However, the sample size is too small for further investigation to be meaningful. 5. Comparing disagreement among forecasters and expost oil price volatility Forecast evaluations assume that the responses are conditional on all publicly available information. Patton and Timmermann (2011) discuss updating forecasts in real

10 Döpke and Fritsche (2006) apply a similar approach to the dispersion of growth and inflation forecasts from a panel of German professional forecasters, and do not find any statistical evidence that dispersion is a reasonable measure of the forecast uncertainty. 11 The results for horizons 1–4 are available from the authors upon request. 12 The regressions at the one-quarter horizon had a poor fit, with the slope and constant terms having imprecise estimates. The disagreement coefficient showed marginal explanatory power, but still less than 10%. The constant term had marginal explanatory power at a horizon of one quarter ahead that seemed to improve with the smaller samples of forecasters. The constant was significant for horizons 2–4, growing from about 20% for two quarters ahead to 50% for four quarters ahead.

time. In this section, we examine the relationship between forecasters’ disagreement and the oil price volatility, observed through to the end of the forecast horizon. The section is divided into four parts. The first part develops two alternative measures of the oil-price volatility observed ex post. Next, we test whether these ex-post price volatility measures are reflected in the observed disagreement. Third, we show that a disagreement measure of the volatility based on point forecasts can be derived under the assumption that oil prices follow a Brownian motion process. Fourth, we test whether this disagreement-based volatility explains the ex-post volatility. 5.1. Measures of the ex-post volatility We want to assess the extent to which the disagreement among forecasters can be explained by the price volatility observed subsequently. Our approach attempts to address a potential drawback in forecast evaluations. A comparison of the oil price volatility over the entire quarter and the disagreement for the average quarterly oil price needs to incorporate the partial information about the current quarter when the surveys are submitted. However, we do not know the dates on which the individual forecasts were actually made. The replies to the SPF are submitted between the 16th and 21st of the first month of each quarter. The survey participants will be using the latest available information that is pertinent to their business, but this may not be the same for all participants. Those who are involved mostly in the oil market are likely to concentrate on the latest available information in the commodity space, while respondents who focus on global macroeconomic models may not update their forecasts with the same frequency.13 Using the end-of-business-week closing prices for each week, we therefore calculate two alternative measures of the volatility that is observed subsequently. The first measure assumes that the survey responses reflect the volatility that is observed between the first week of the current quarter and the end of the forecast horizon. The second measure considers the price volatility that is observed after the deadline for submitting responses to the ECB, and does not include the volatility that is observed prior to the submission deadline. 13 Note that the SPF preserves the confidentiality of the forecasters.

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Fig. 4. Timeline for quarter and survey in measuring full quarter volatility vt ,h and deadline adjusted volatility wt ,h .

Fig. 4 illustrates the calculation of the two volatility measures. Let N (h) be the number of weekly prices observed from the start of quarter t until the end of the forecasted quarter at horizon h. We estimate the following two realized volatility series, both of which are computed as the standard deviation14 of price returns. The ‘‘full quarter’’ volatility vt , defined in Eq. (6), corresponds to the assumption that the forecasts are produced when the first weekly price for the quarter is observed. It measures the volatility observed ex post between the start of quarter t and the end of the forecasted quarter:

    vt = 

N (h)−1

1



N (h) − 1





ln

k=1

Pk+1

ln

 −

pk



PN (h) P1

N (h)

 2  , (6)

where Pk is the kth weekly price observed during the period considered. The ‘‘deadline adjusted’’ volatility wt , defined in Eq. (7), corresponds to the assumption that the forecasts are produced just before the deadline for returning the questionnaire to the ECB. It measures the volatility observed ex post between the deadline and the end of the forecasted quarter:

    wt = 

1 N (h) − s

N (h)−1

 k=s





ln Pk+1 Pk

ln

 −



PN ( h )

 2

Ps

N (h) − s + 1

 , (7)

where s is the number of weekly prices realized before the survey submission deadline.15 Fig. 5 shows a plot of the ‘full quarter’ and ‘deadline adjusted’ volatilities, which are close, even for the current quarter.

14 See for instance Matar, Al-Fattah, Atallah, and Pierru (2013) and Sadorsky (2006); we do not adjust returns for the convenience yield here. When the price is assumed to follow a geometric Brownian motion, as in Section 5.3, its volatility has to be estimated as the standard deviation of price returns. 15 This is typically between the 17th and 24th of the first month; for each quarter, s is the last weekly price prior to the deadline indicated by the ECB at: http://www.ecb.int/stats/prices/indic/forecast/shared/files/SPF_ rounds_dates.pdf?06a8d73c8231cca300071f251923c9b9.

5.2. Does the ex-ante disagreement reflect the ex-post volatility? In this section, we compare the two measures of the volatility observed ex post with a normalized measure16 of the ex-ante disagreement, δt , defined as the ratio of the standard deviation of survey forecasts to the mean forecast for the panel:

√ δt =

Dt F¯t

.

(8)

The larger the dispersion of the survey participants’ individual responses relative to the mean forecast, the greater the disagreement among the forecasters. Fig. 6 contains plots of the disagreement measure δt and the deadline-adjusted volatility wt for each horizon, using the full sample of 90 participants. The ‘‘link’’ between the oil price volatility and the survey disagreement measures weakens as the horizon increases. The disagreement is more than twice the deadline-adjusted volatility after the current quarter. However, the movements in disagreement do appear to be correlated for the current quarter and first quarter horizons; though the deadline-adjusted volatility appears to be smoother than the disagreement among forecasters thereafter, with the forecasters seeming to over-respond to events and information. The fact that the dispersion of the survey participants’ forecasts grows with the horizon may be due to misspecifications of their models. This phenomenon is a property of (individual) forecasts of processes with a unit root. Fig. 7 illustrates the same information in scatter plots, with the associated regression lines, for all horizons. We use the five samples to test for the existence of relationships between forecasters’ disagreement and the two volatility measures. Based on Fig. 7, we estimate bivariate regressions for the current-quarter and onequarter-ahead horizons only:

δt = α + βvt + ut δt = α + βwt + ut .

(9) (10)

Table 4 provides the results of the regressions in Eqs. (9) and (10). Once again, we use the general covariance

16 For alternative measures of forecast disagreement, see for instance Siklos (2013).

T. Atalla et al. / International Journal of Forecasting 32 (2016) 1178–1192

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Fig. 5. Ex-post volatility measures current quarter – full quarter (blue) and deadline adjusted (red).

estimator developed by Newey and West (1987), which is consistent in the presence of both heteroscedasticity and autocorrelation of an unknown form. The null hypothesis for the slope coefficient is unity. In the current quarter, the results depend on the measure used for the ex-post volatility, but this is less true at the one-quarter horizon. In the table, the intercepts range from 1% to 3% when the full-quarter volatility is considered, and from 2% to 4% when the deadline-adjusted volatility is considered. Almost all of the intercepts are significant at the 1% level. The sample consisting of the 24 participants who replied in more than 37 quarters has the smallest numerical value for both measures. This estimate is not significant when using the ex-post full quarter volatility in the current quarter. The null hypothesis that the slope coefficient is unity is never rejected when considering the full current quarter volatility, but is rejected for all samples except for the 24 participants for the deadline-adjusted volatility. The slope estimates range from 0.6 to 0.75. When considering the deadline-adjusted volatility, the null hypothesis is not rejected when the forecast horizon is one quarter ahead. Numerically, the slopes on the full-quarter volatility measures are close to unity; on the other hand, those on deadline-adjusted volatility measures tend to be lower numerically, but indistinguishable from one statistically. When the forecast horizon is the current quarter, the adjusted R2 value ranges from 0.44 to 0.57 in the regressions using the full-quarter volatility and from 0.26 to 0.38 for the deadline-adjusted volatility, respectively. In the one-quarter-ahead regressions, the adjusted R2 value falls between 0.2 and 0.4. We find evidence of conditional heteroscedasticity in the current quarter regressions. This is a common property when modeling nominal prices, and has been studied in various previous studies of forecast surveys. Again, our sample is small and at the aggregate level; meaning that further analysis is probably of limited

value. This issue could be examined further in a follow up study looking at the individual forecasts.17 When considering the group of 90 forecasters, the disagreement and volatility move in opposite directions in 13 of the 44 quarters. As was emphasized by Bowles et al. (2007) and Zarnowitz and Lambros (1987), it would be quite possible for the overall level of uncertainty to increase at the same time as forecasters increasingly agree with each other about the most likely direction. This may have occurred in the turmoil following 2008Q2. The disagreement index decreased (with the forecasters predicting a continuation of the sharp increase observed over the previous quarters), whereas the realized volatility increased (with a fall in the oil price). On the other hand, the disagreement index increased after 2012Q2, with an increasing divergence among forecasters’ assessments of the economic outlook or geopolitical issues, while the market became less volatile. In short, unless there is an unanticipated turning point shock within a quarter, the disagreement or uncertainty among forecasters is approximately equal to the recent volatility plus a small add factor. 5.3. Calibration of the volatility based on disagreement The ECB SPF panel contains point forecasts for quarterly average prices. Since each forecast is a price averaged over a quarter, the observed disagreement cannot be compared to the actual oil price volatility directly. So how can we infer an oil price volatility measure that is consistent with the observed disagreement? Under the standard assumption that the oil price follows a geometric Brownian motion (i.e., the natural logarithm of the price follows a random walk), we suggest

17 The results of White’s (1980) tests and the ARCH tests of Engle, Hendry, and Trumble (1985) are available upon request.

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Fig. 6. Disagreement between forecasters and the ex post deadline adjusted volatility (in natural logarithms, group of 90 forecasters, all horizons).

T. Atalla et al. / International Journal of Forecasting 32 (2016) 1178–1192

1187

Fig. 7. Scatter diagram of the disagreement between forecasters vs. the ex post deadline-adjusted volatility (in natural logarithms, group of 90 forecasters, all horizons).

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T. Atalla et al. / International Journal of Forecasting 32 (2016) 1178–1192

Table 4 Forecaster disagreement regressed on the volatility information set. Variable

Coefficient

p-value

Adj R2

SER

Durbin–Watson

Constant Slope Constant Slope Constant Slope Constant Slope Constant Slope

0.019*** 1.004 0.022*** 0.947 0.026*** 0.820 0.021*** 0.862 0.014 0.905

0.010 0.983 0.007 0.775 0.000 0.180 0.004 0.380 0.190 0.666

0.574

0.013

1.674

0.531

0.013

1.608

0.453

0.013

1.580

0.446

0.014

1.650

0.439

0.015

2.017

Ex post deadline adjusted volatility 90 Constant Slope 71 Constant Slope 55 Constant Slope 35 Constant Slope 24 Constant Slope

0.032*** 0.752* 0.035*** 0.684** 0.037*** 0.601*** 0.030*** 0.671*** 0.019** 0.800

0.000 0.052 0.000 0.025 0.000 0.000 0.000 0.002 0.020 0.276

0.352

0.016

1.488

0.301

0.016

1.450

0.263

0.015

1.523

0.296

0.016

1.438

0.381

0.016

1.736

Constant Slope Constant Slope Constant Slope Constant Slope Constant Slope

0.032*** 1.073 0.034*** 1.044 0.038*** 0.949 0.033*** 0.987 0.026*** 1.060

0.000 0.724 0.000 0.826 0.000 0.809 0.001 0.957 0.003 0.769

0.382

0.019

1.345

0.357

0.019

1.302

0.299

0.020

1.236

0.293

0.021

1.480

0.346

0.020

1.597

Ex post deadline adjusted volatility 90 Constant Slope 71 Constant Slope 55 Constant Slope 35 Constant Slope 24 Constant Slope

0.043*** 0.853 0.044*** 0.824 0.048*** 0.759 0.041*** 0.812 0.035*** 0.880

0.000 0.399 0.000 0.283 0.000 0.199 0.000 0.376 0.000 0.518

0.251

0.021

1.354

0.230

0.021

1.293

0.198

0.021

1.242

0.206

0.022

1.431

0.249

0.022

1.523

Sample of forecasters Panel (a) Current quarter Full quarter ex post volatility 90 71 55 35 24

Panel (b) One quarter ahead Full quarter ex post volatility 90 71 55 35 24

The null hypothesis is that the slope coefficient is unity. *** Represent significance at the 1% level. ** Represent significance at the 5% level. * Represent significance at the 10% level.

a formula that allows us to derive the price volatility from the distribution of forecasts. We use this simple reduced-form model as a benchmark to translate the observed disagreement into a proxy for the volatility. When our method is applied to the ECB surveys, it results in a disagreement-based volatility that appears to be correlated with the volatility observed ex post at short horizons, but not as much at longer horizons. This is consistent with theory. We make the assumption that the forecasts provided at a given date and the forecasted average prices are independently and identically distributed random variables. This

allows us to infer the distribution of the average price from the distribution of the forecasts. Note that this simplifying assumption implies that: E (ei,t ) = E (At − Fi,t ) = E (At ) − E (Fi,t ) = 0

(11)

V (ei,t ) = V (At − Fi,t ) = 2V (Fi,t ) = 2Dt .

(12)

Since from Eq. (4): 2 V (At − Fi,t ) = σλ| t + Dt ,

we have:

σλ|2 t = Dt .

(13)

T. Atalla et al. / International Journal of Forecasting 32 (2016) 1178–1192

Thus, this assumption implies the further assumptions that the forecast error of each forecaster has a zero expected value, and that the expected disagreement is equal to the variance of aggregate error. Under these assumptions, the expected value and variance of At can be estimated by the mean forecast and the dispersion around the mean forecast, respectively. Let us now examine the relationship between the standard deviation of the average price and the volatility of the underlying price. We can infer the price volatility implied by this distribution based on the standard assumption that the oil price follows a geometric Brownian motion. Let us assume that the oil price follows a geometric Brownian motion, with drift µ and volatility σ (expressed on a weekly basis). For a given forecast horizon, let n be the number of prices observed during the forecasted quarter (typically around 12 for weekly data), s be the last price observed, and j be the number of prices observed between the start of the current quarter and the end of the quarter preceding the forecasted horizon. We have: F¯t =

Ps e(n+j+1−s)µ − e(j+1−s)µ

∆t =

(14)

eµ − 1

n

 2

Ps

n2

e2µ(j+n−s) (e(j+n−s)σ − 1) + 2

 × e

σ 2 (j−s)

2 2 e(σ +µ)n − eσ +µ

−

2 eσ +µ − 1 µ e + 1 2µ(j−s)

2eµ(n+1+2(j−s)) eµ − 1 eµn − eµ



eµ − 1

+e eµ − 1  2µn  2 (σ 2 +2µ)n e − e2µ − eσ +2µ σ 2 (j−s) e × − e (15) 2 e2 µ − 1 eσ +2µ − 1 see Appendix. We can therefore infer the value of σ . This equation has only one solution, since the right-hand side of Eq. (15) is an increasing function of σ 2 . If we assume that the last price observed by the forecasters is the first of current quarter, i.e., s = 1 then a full-quarter disagreement-based volatility can be inferred from Eqs. (14) and (15). Alternatively, if we assume that the last price observed by the forecasters is the last price realized on the day before the deadline for sending back the filled questionnaires, s = d, then a deadline-adjusted disagreement-based volatility can be inferred from Eqs. (14) and (15). Let us now turn to the case where the forecasted quarter is the current quarter. The total number of periods is n, but the price is known until s. We therefore have: F¯0 =

s−1  Pk

n

k= 1

∆0 =

+

 2

Ps

n2

+

Ps 1 − e(n+1−s)µ

2

2eµ(n+1−s)



eµ − 1 e +1 eµ − 1



2 e(σ +µ)(n−s) − 1

σ 2 +µ

e

2µ(n−s)

e

−1

e2µ − 1

−1

−

eµ(n−s) − 1

e

We use the results from the previous section to estimate the following regressions:

vt = α + βσtf + ut

(18)

wt = α + βσ + ut ,

(19)

d t

f

where σt and σtd are the full-quarter and deadlineadjusted disagreement-based volatilities, respectively. Table 5 contains the results from the regressions in Eqs. (18) and (19) for the current quarter and one quarter ahead. The presence of heteroscedasticity and autocorrelation of unknown form are controlled for by using the general covariance estimator developed by Newey and West (1987). The estimated constants (addfactors to the volatility measures) are positive at the 1% significance level for all regressions. The constant ranges from about 1.2% to 2% (2.2% to 2.7%) when the forecast horizon is the current quarter (one quarter ahead). The slope coefficients cannot be distinguished from unity when the forecast horizon is one quarter ahead. This implies that the volatility observed ex post is approximately equal to the disagreement-based volatility plus a fixed add-factor. On the other hand, when the forecast horizon is the current quarter, the difference between the two volatility measures increases when the price is more volatile, since the slope is significantly greater than unity in most of the regressions (as panel (a) of Table 5 shows). However, we observe that the response is not as strong when the information set is based on the deadlineadjusted volatility; only the sample with 24 forecasters is significantly different from unity at the 1% level. Three of the remaining four sample slope estimates are significantly different only at the 10% level. According to the adjusted R2 measure, the best-fitting equations are the current-quarter disagreement regressions, while the worst are the one-quarter-ahead deadlineadjusted disagreement based volatility measures. The one-quarter-ahead equations show evidence of first order serial correlation. This is consistent with the expected moving average error process in forecasting theory. At the two-quarter-ahead horizon and beyond, there is a progression of results.18 Both regressions for more quarters ahead have slope coefficients that continue to decline from unity, while the constants become larger. This is consistent with the graphs that show the declining correlation between the volatility measures. The threequarter-ahead results continue with the numerical decline in the slope coefficient, and see the constant increase to nearly 3%. 6. Conclusion



eµ − 1

(σ 2 +2µ)(n−s)

−

5.4. Disagreement-based volatility from ECB surveys

This paper examines a survey of quarterly oil price forecasts from the European Central Bank. The period is from 2002 to 2012. Each survey round had about 50

e2µ(n−s) (e(n−s)σ − 1)

µ

+

(16)

1 − eµ

n

1189

−1

2 eσ +2µ − 1



. (17)

18 These tables are not provided to save space, but are available from the authors upon request.

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T. Atalla et al. / International Journal of Forecasting 32 (2016) 1178–1192

Table 5 Ex post volatility regressed on the disagreement-based volatility, all groups of forecasters. Estimate

p-value

Adj R2

SER

Durbin–Watson

Panel (a) Current quarter horizon Full quarter volatility 90 Constant Slope 71 Constant Slope 55 Constant Slope 35 Constant Slope 24 Constant Slope

0.012*** 2.017*** 0.012*** 2.046*** 0.012*** 2.087*** 0.015*** 1.987*** 0.019*** 1.943***

0.000 0.001 0.000 0.002 0.000 0.000 0.000 0.000 0.001 0.000

0.561

0.010

1.720

0.539

0.010

1.720

0.483

0.011

1.735

0.482

0.011

1.755

0.487

0.011

1.709

Ex-ante deadline-adjusted volatility 90 Constant Slope 71 Constant Slope 55 Constant Slope 35 Constant Slope 24 Constant Slope

0.017*** 1.644* 0.018*** 1.610 0.018*** 1.681* 0.019*** 1.696* 0.019*** 1.856***

0.002 0.074 0.005 0.133 0.006 0.092 0.002 0.080 0.000 0.009

0.323

0.013

1.761

0.287

0.013

1.731

0.270

0.013

1.805

0.305

0.013

1.701

0.392

0.012

1.600

Panel (b) One-quarter-ahead horizon Full quarter volatility 90 Constant Slope 71 Constant Slope 55 Constant Slope 35 Constant Slope 24 Constant Slope

0.022*** 1.197 0.022*** 1.187 0.023*** 1.119 0.026*** 1.038 0.025*** 1.143

0.000 0.305 0.000 0.351 0.000 0.532 0.000 0.848 0.000 0.526

0.333

0.012

1.149

0.321

0.012

1.178

0.279

0.012

1.123

0.268

0.012

1.229

0.313

0.012

1.300

Ex-ante deadline-adjusted volatility 90 Constant Slope 71 Constant Slope 55 Constant Slope 35 Constant Slope 24 Constant Slope

0.024*** 1.034 0.025*** 1.018 0.025*** 0.979 0.027*** 0.931 0.026*** 1.030

0.000 0.890 0.000 0.946 0.000 0.936 0.000 0.790 0.000 0.905

0.224

0.013

1.472

0.212

0.013

1.471

0.192

0.013

1.431

0.195

0.013

1.499

0.231

0.013

1.562

Group of forecasters

Coefficient

Implied volatility regressed on disagreement of forecasters, all groups of forecasters. *** Represent significance at the 1% level. ** Represent significance at the 5% level. * Represent significance at the 10% level.

respondents. However, overall, 90 forecasters participated at least once, while 24 responded to more than 80% of the survey rounds. We investigate the relationship between the dispersion or disagreement among forecasters, the forecast errors, and the perceptions of oil price volatility. The empirical findings are robust to the numbers of respondents considered. First, we find that the log of the absolute value of the average forecast error is positively correlated with the log of the dispersion of forecasts around the mean forecast at all forecast horizons. In other words, the dispersion of idiosyncratic errors is correlated with the aggregate error. This supports the view that an increased disagreement

among forecasters can reflect a greater uncertainty. In addition, the average forecast error variance captures the impact of (cumulative) aggregate oil price shocks. Second, at the current and one-quarter-ahead horizons, we find statistical evidence that the oil-price volatility observed subsequently explains the level of forecasters’ disagreement. Third, we derive a measure of the price volatility from forecasters’ disagreement, and find it to be correlated well with the volatility observed ex post. When the forecast horizon is one quarter ahead, the disagreement-based volatility is roughly equal to the realized price volatility plus an add factor. The constant is

T. Atalla et al. / International Journal of Forecasting 32 (2016) 1178–1192

significant at all horizons, reflecting the aggregate shocks to oil prices. This paper has focused on the respondents as a whole. Future work could examine the behaviors of individuals, and their deviation from the central tendency of the survey respondents, with the aim of determining whether there are patterns in the oil price predictions of individual forecasters. Appendix. Proofs for Eqs. (14)–(17) Letting P¯ h be the average oil price for horizon h, we have: j +n  Pk

P¯ h =

n

k=j+1

.

(A.1)

The forecasters are assumed to know the oil price until date d. By denoting the price realized at date d as Pd , for k ≥ i we have: (j+k−d)µ

E (Pj+k ) = Pd e

(A.2)

cov(Pi+j , Pk+j ) =

Pd2 eµ(k+i+2(j−d))

(e

σ 2 (i+j−d)

(A.3)

− 1),

(A.4)

where E (·), V (·) and cov(·, ·) denote the expected value, the variance and the covariance respectively. We first consider that h ∈ {1, 2, 3, 4}. We have: N Pd  (k+j−d)µ e E (P¯ h ) = n k=1

E (P¯ h ) =

(n+j+1−d)µ

Pd e

j+n  Pk,h

n

k=j+1

−e

(j+1−d)µ

,

V (P¯ h ) =



n2

 ,

(A.7)

N 

 V (Pj+k ) + 2

k=1



cov(Pj+i , Pj+k ) , (A.8)

k̸=i

with: N 

V (Pj+k ) =

N 

k=1

k=1



cov(Pj+i , Pj+k )

2 Pd2 e2µ(k+j−d) (eσ (j+k−d) − 1)

(A.9)

k̸=i

=

n −1  n  i=1 k=i+1

E (P¯ 0 ) =

d  Pk k=1

E (P¯ 0 ) =

2 Pd2 eµ(k+i+2(j−d)) (eσ (j+i−d) − 1).

n

d−1  Pk

n

+

+

n Pd 

n k=d+1

e(k−d)µ

(A.12)

Pd 1 − e(n+1−d)µ n

1 − eµ

.

(A.13)

The variance of P¯ 0 is obtained by replacing j and n in Eq. (A.11) by d and n − d respectively, which gives:

 Pd2 2µ(n−d) (n−d)σ 2 ¯ (e − 1) V (P0 ) = 2 e n

+

2eµ(n+1−d) eµ − 1 eµ + 1 eµ − 1





2 e(σ +µ)(n−d) − 1 2 eσ +µ − 1

e2µ(n−d) − 1 e2µ − 1

−

−

eµ(n−d) − 1



eµ − 1

 2 e(σ +2µ)(n−d) − 1 2 eσ +2µ − 1

. (A.14)

(A.6)

which gives: 1

σ can be determined from Eq. (A.11) by using the disagreement index for horizon h as an estimate of V (P¯ h ). This equation yields a unique value for σ 2 , since the righthand side of the equation is an increasing function of σ 2 . Let us now turn to the case h = 0:

+

where µ can be determined from Eq. (A.6) by using the mean forecast for horizon h as an estimate of E (P¯ h ). We have:



 Pd2 2µ(j+n−d) (j+n−d)σ 2 2eµ(n+1+2(j−d)) ¯ (e − 1) + V (Ph ) = 2 e n eµ − 1  (σ 2 +µ)n σ 2 +µ µn µ e −e e −e 2 × eσ (j−d) − µ 2 +µ σ e −1 e −1 µ 2µ(j−d) e + 1 +e eµ − 1  2µn  2 (σ 2 +2µ)n − eσ +2µ e − e2µ σ 2 (j−d) e −e × (A.11) 2 e2µ − 1 eσ +2µ − 1

(A.5)

eµ − 1

n

V (P¯ h ) = V

With simple manipulations, Eq. (A.8) gives:

k=1

2 V (Pj+k ) = Pd2 e2µ(j+k−d) (eσ (j+k−d) − 1)

1191

(A.10)

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Tarek Atalla is a Research Associate part of KAPSARC’s energy systems and modeling team. His work includes modeling commodity investments, energy consumption and forecasting. He has published several articles in the fields of energy economics, oil pricing and volatility and energy financing. Tarek has Bachelor and Masters degrees in Engineering and is currently a Ph.D. candidate in energy economics at Paris IX. Frederick Joutz is a Professor in the Department of Economics at the George Washington University, where he is Co-director of the Research Program on Forecasting. He worked as a Senior Research Fellow at KAPSARC while working on this paper and energy macroeconometric modeling issues. He contributes quarterly macroeconomic forecasts to the Federal Reserve Bank of Philadelphia and the Survey of Professional Forecasters and the Economic Survey International ESI by the CES/Ifo Institute for Economic Research. Axel Pierru is a Senior Research Fellow and Program Director. He joined KAPSARC in 2011, after spending fifteen years at IFP Energies nouvelles (France). Axel received his Ph.D. in economics from Pantheon-Sorbonne University (Paris). His research is in the fields of energy economics, modeling and policy, corporate finance, and oil pricing.