The Role of Information

Within this subsection we explore different measures of herding and its impact on forecast accuracy. As per Jame et al. (2016) and Hong et al. (2000), we first consider the boldness of a forecast as it might be relevant to explaining relative accuracy. The boldness statistic measures the extent to which the individual forecast deviates from the Consensus. The larger the boldness statistic is, the less herding there is between analysts. Boldness is computed as follows,

|F_i,tpop−Ff ull_t |

Fpop_t

whereF_i,tpopis the forecast (i) of the population (either Estimize or Consensus) made for month (t),Ff ull_t

is the average forecasts made for month (t) among all populations (i.e. Estimize and Consensus combined), andFpop_t is the average forecast for month (t) within that population (Estimize or Consensus).

We compute boldness for every forecast from the Estimize and the Consensus samples. The average monthly boldness for the Estimize sample is 0.13 and the average monthly boldness for the Consensus sample is 0.12.

To examine if boldness is associated with relative forecasting accuracy, we group the boldness for Consensus (Estimize) into bins: low, medium and high boldness. For each bin we compute the AFE, take the difference between the Consensus and Estimize AFE, and test the equality of means via a two tailed t-test.

In Table 3.7 we find that the average forecast error is in fact different for Consensus than it is for Estimize, across all boldness bins. However, the differences do not appear to vary systematically across bins for either As Reported nor Revised, suggesting little impact of boldness upon forecast accuracy.

Table 3.7: Boldness for As Reported and Revised NFP Data

The top 3 rows are results using As Reported NFP data and the bottom 3 rows are results using Revised NFP data. Boldness is computed as |F

pop i,t −F

f ull t |

Fpopt

for every individual forecast,i, from the Consensus and Estimize sample and grouped into bins: low, medium and high boldness. AF E as defined in Table 2, andN is the number of forecasters. The superscripts “C” and “E” denote Consensus and Estimize, respectively. “Diff.” is the differenceAF EC−AF EE, andpvalreports the p-value for the test of the equality of means. The *, **, *** denote statistical significance at the10%,5%, and1%levels, respectively. The sample is from May 2014 - February 2017.

As Reported

Boldness AF EC NC AF EE NE Dif f. pval

low 46.38 988 50.55 623 -4.17 0.00*** medium 46.34 1182 54.31 637 -7.97 0.00*** high 51.93 1080 59.91 658 -7.97 0.00*** Revised low 61.26 988 53.17 623 8.09 0.00*** medium 49.90 1182 58.71 637 -8.82 0.00*** high 56.69 1080 63.56 658 -6.87 0.01***

Following Barron et al. (1998) we investigate whether the information sets of Estimize and Consensus can explain their relative forecasting accuracy. We define information diversity,ρ, as follows:

ρ= C V, whereV = _N1 PN i=1ViandC= 1 N PN

i=1Ci.Barron et al. (1998) definesVias the level of uncertainty for

analyst (i) andCias the mean covariance between analyst (i)’s beliefs and the rest of the analysts’ beliefs.

V can be thought of as the overall uncertainty for all analysts, andC can be interpreted as the common uncertainty. This common uncertainty,C, is different from the overall uncertainty, V, becauseC is the common uncertainty based off of the analysts’ reliance on incorrect common information. All analysts are relying on some degree of public information, which is potentially inaccurate, to form their individual forecasts.

Within this framework, ρ is the ratio of common uncertainty to overall uncertainty. Asρ → 1, all analysts’ beliefs are converging to some common belief based off of the publicly available information used. Herding is generally defined as a high degree of agreement among predictions by analysts. Thus, a highρ

potentially indicates a high degree of herding among analysts. Asρ→0, all analysts’ beliefs are diverging from the imprecise common information available to all.

Unfortunately, the above definedρrequires data that is unobservable, and so cannot be directly calculated. To circumvent this, Barron et al. (1998) shows that the measures ofV andρcan be recovered with observable data as such: V = (1− 1 N)D+SE (3.4.1) ρ= SE− D N (1− 1 N)D+SE . (3.4.2)

In the above definition,Dis the unconditional sample variance of the forecasts andSEis the expectation of mean squared forecast. The interpretations ofV andρremain unchanged despite using the above construction.

We computeρandV for every month from the Estimize and the Consensus samples. For the Consensus sample, the average monthlyρis0.98and the average monthlyV is 3,645. For the Estimize sample, the average monthlyρis0.98and the average monthlyV is 4,394. When we compute both measures using the Revised data, the average values ofρremain unchanged while the average monthlyV for Consensus increases to 5,450 and for Estimize to 5,328.

To examine if uncertainty and diversity is associated with relative forecasting accuracy, we group the monthly calculated measures for Consensus (Estimize) into bins: low, medium and high boldness. For each bin we compute the AFE, take the difference between the Consensus and Estimize AFE, and test the equality of means via a two tailed t-test.

In Table 3.8 we find that the average forecast error is in fact different for Consensus than it is for Estimize, within the low diversity and low uncertainty bins using Revised data. We find no other statistically different average forecast errors across the bins. Within subsection 3.4.5, we formally test the impact of herding upon forecast accuracy via multivariate regressions.