Are aggregate corporate earnings forecasts unbiased and efficient?

Abstract

In this article, we analyze the properties of professional aggregate corporate earnings forecasts with regards to accuracy, unbiasedness, and efficiency. Using a large panel of forecasts for the years 1992–2011, we find that forecast errors are in general large, and the magnitude of forecast errors varies substantially across forecasters. Forecasts are however directionally accurate, especially during periods of slowdown. We find evidence of an underprediction bias, as forecasters failed to predict the strong growth of corporate earnings that took place over the past two decades. Forecasts biases and forecast errors are particularly large during periods of economic instability such as recession years, suggesting that biases originate in forecasters’ slow adjustment to structural shocks. Finally, we reject forecast efficiency, and find evidence of overreaction to new information, as evidenced by the negative autocorrelation of forecast revisions. Forecasters overreact equally strongly to good and bad aggregate earnings news, resulting in excessive forecast volatility.

Appendix

1.1 Unbiasedness test

The estimates of the forecasters’ biases, $\phi _{i}$ can obtained by the following simple mean of forecasting errors:

$$\begin{aligned} \hat{\phi }_{i}=\frac{1}{TH}\sum _{t=1}^{T}\sum _{h=1}^{H}(A_{t}-f_{i,t,h}) \equiv \frac{1}{TH}\sum _{t=1}^{T}\sum _{h=1}^{H}e_{i,t,h} \end{aligned}$$

(5)

For statistical inference, we use the forecasting error decomposition model of Davies and Lahiri (1995) introduced in (2). To estimate the macro shocks and the idiosyncratic components, we first compute the centered forecast error: $\hat{v}_{i,t,h}=A_{t}-F_{i,t,h}-\hat{\phi _{i}}.$ The common macro shocks, $\hat{\lambda }_{t,h}$, can be obtained by averaging the centered forecasting errors over each separate target year and forecast horizon:

$$\begin{aligned} \hat{\lambda }_{t,h}=\frac{1}{N}\sum _{i=1}^{N}\hat{v}_{i,t,h} \end{aligned}$$

(6)

While the estimated idiosyncratic shocks are the difference of each centered forecasting error minus the common macro shocks, $\hat{\lambda }_{t,h}$, that is:

$$\begin{aligned} \hat{\varepsilon }_{i,t,h}=\hat{v}_{i,t,h}-\hat{\lambda }_{t,h} \end{aligned}$$

(7)

We test the significance of the biases using the GMM covariance matrix $Var( \hat{\phi })=(X^{\prime }X)^{-1}X^{\prime }\Sigma X(X^{\prime }X)^{-1},$ where $X$ is a vector of ones. To estimate $\Sigma$ we need to compute the non-zero covariances between the composite error terms $v$’s, that are:

$$\begin{aligned} {\text {Cov}}(v_{i,t_{1},h_{1}},v_{i,t_{2},h_{2}})&= \min \{h_{1},h_{2}\} (\sigma _{u}^{2}+\sigma _{i}^{2})\,\hbox {if}\,t_{1}=t_{2}\\ {\text {Cov}}(v_{i,t_{1},h_{1}},v_{i,t_{2},h_{2}})&= \min \{h_{1},h_{2}-12\}(\sigma _{u}^{2}+\sigma _{i}^{2})\,\hbox { if }\,t_{1}=t_{2}-1\,\hbox { and }\,h_{2}\ge 12\\ {\text {Cov}}(v_{i,t_{1},h_{1}},v_{j,t_{2},h_{2}})&= \min \{h_{1},h_{2}\}\sigma _{u}^{2}\hbox { for }i\ne j,\hbox { if }t_{1}=t_{2}\\ {\text {Cov}}(v_{i,t_{1},h_{1}},v_{j,t_{2},h_{2}})&= \min \{h_{1},h_{2}-12\}\sigma _{u}^{2}\hbox { for }i\ne j,\hbox { if }t_{1}=t_{2}-1\hbox { and }h_{2}\ge 12 \end{aligned}$$

For the estimation of $\sigma _{u}^{2}$ and $\sigma _{i}^{2},$ see Davies and Lahiri (1995).

1.2 Efficiency test

For the individual efficiency test, we first obtain the OLS estimates of the coefficient in Eq. (4), $\hat{\beta }_{i}$, for each forecaster. To test the hypothesis that $\beta _{i}=0$, we use the GMM estimator of the variance of $\hat{\beta }$ for which we need to know the covariance matrix of the error terms $Var(\hat{\beta })=(r^{\prime },r)^{-1}r^{\prime }\Xi r(r^{\prime },r)^{-1}.$ Where $r$ is the vector of lagged forecasting revisions, and $\Xi$ is the error covariance matrix. To estimate $\Xi$ we compute the non-zero covariances between the composite error terms $\xi$’s, that are:

$$\begin{aligned} {\text {Cov}}(\xi _{i,t_{1},h_{1}},\xi _{i,t_{2},h_{2}})&= \sigma _{u}^{2}+\sigma _{i}^{2} \hbox { if }t_{1}=t_{2}\hbox { and }h_{1}=h_{2},\hbox { or }t_{1}=t_{2}-1\hbox { and } h_{1}=h_{2}-12\\ {\text {Cov}}(\xi _{i,t_{1},h_{1}},\xi _{j,t_{2},h_{2}})&= \sigma _{u}^{2}\hbox { for }i\ne j \hbox { if }t_{1}=t_{2}\hbox { and }h_{1}=h_{2},\hbox { or }i\ne j\hbox { if }t_{1}=t_{2}-1\hbox { and } h_{1}=h_{2}-12 \end{aligned}$$