# Confucius confusion: analyst forecast dispersion and business cycles

## Abstract

### Purpose

Financial analysts have been found to be overconfident. The purpose of this paper is to study the ramifications of that overconfidence on the dispersion of earnings estimates as a predictor of the US business cycle.

### Design/methodology/approach

Whether aggregate analyst forecast dispersion contains information about turning points in business cycles, especially downturns, is examined by utilizing the analyst earnings forecast dispersion metric. The primary analysis derives from logit regression and Markov switching models. The analysis controls for sentiment (consumer confidence), output (industrial production), and financial indicators (stock returns and turnover). Analyst data come from Institutional Brokers Estimate System, while the economic data are available at the Federal Reserve Bank of St Louis Economic Data site.

### Findings

A rise in the dispersion of analyst forecasts is a significant predictor of turning points in the US business cycle. Financial analyst uncertainty of earnings estimate contains crucial information about the risks of US business cycle turning points. The results are consistent with some analysts becoming overconfident during the expansion period and misjudging the precision of their information, thus over or under weighting various sources of information. This causes the disagreement among analysts measured as dispersion.

### Originality/value

This is the first study to show that analyst forecast dispersion contributions valuable information to predictions of economic downturns. In addition, that dispersion can be attributed to analyst overconfidence.

## Keywords

#### Citation

Cox, R., Dayanandan, A., Donker, H. and Nofsinger, J. (2018), "Confucius confusion: analyst forecast dispersion and business cycles", *Review of Behavioral Finance*, Vol. 10 No. 2, pp. 130-145. https://doi.org/10.1108/RBF-04-2017-0041

### Publisher

:Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited

## 1. Introduction

In the stock market, financial analysts are information intermediaries who collect, analyze and digest complex data about the firm and its external (macroeconomic) environment and produce information about the stock value and probable earnings of the firm. They research and compile their information from quantitative valuation techniques from macroeconomic, industry, and firm-level data. They also use softer sources of information through interviewing executives, customers, bankers, and company advisers. Therefore, analyst earnings estimates are likely to provide important insight into forecasting the business cycle.

We examine analyst estimates from a behavioral framework. Specifically, we adapt the psychological bias of overconfidence. Analysts have been found to be overconfident, or equivalently, optimistic (see Butler and Lang, 1991; Chopra, 1998), and Conroy *et al.* (1997). Odean (1998) defines overconfident investors as those who overestimate the precision of their information. Misjudging the precision of information leads to over or under weighting various sources of information. Janus *et al.* (2013) develops a model in which overconfident analyst underweights statistical information. In Bosquet *et al.* (2015) model, overconfident analysts overweight their own private information. Alternatively, Odean’s model results in the overweighting of anecdotal information, such as that gathered through interviews. If all analysts have the same information and ability, and behave rationally, then their estimates will be homogeneous. As some analysts become overconfident, the estimates will become more heterogenous. We estimate the level of analyst heterogenous beliefs through analyst dispersion in earnings estimates. The greater the degree of dispersion, the greater the overconfidence exhibited by analysts.

Since analysts’ forecasts are forward-looking, it embeds not only expectations about the firm’s future profitability but also an assessment about the macroeconomic environment in which the firm operates. Disagreement among analysts about each firm’s earnings can then be attributed to under or overweighting the precision of information about the future macroeconomic environment or the firm’s performance. For example, Peng *et al.* (2016) find that accounting accruals can generate heterogeneous investor beliefs. Nofsinger (2012) illustrates how cognitive limitations and psychological biases exacerbate asset bubbles and the business cycle. For example, investors tend to attribute the profits gained in a bull market to their own skill. This leads to overconfidence and behaviors that extend economic growth and asset prices. From the context of our study, an economic expansion will increase the level of analyst overconfidence and greater earnings estimate dispersion.

We extend the literature by examining how analyst overconfidence at the aggregate level contains relevant information about the stage of the business cycle, e.g., expansion or contraction. Our study examines whether aggregate analyst forecast dispersion contains macroeconomic information about turning points in US business cycles, especially downturns. To eliminate the possibility of endogeneity between financial analyst forecasts and turning points in business cycles, we use the 12-month lagged analyst forecast dispersion. This approach is novel since existing literature focus on more traditional economic forecast variables (like industrial production, returns in stock market), liquidity (trading volume) and sentiment (consumer confidence) indicators. Our measure of dispersion comes from the Institutional Brokers Estimate System (IBES) data (*n*=889,152) over the period 1976 through 2015 for firms listed on the New York Stock Exchange (NYSE), American Stock Exchange (AMEX), and NASDAQ. This period contains multiple US business cycles. The empirical results show that one year ahead analyst forecast dispersion is a statistically significant predictor of turning points in the US business cycles. In addition, we find strong evidence that dispersion of analyst forecasts is a good predictor of impending recessions.

The remainder of the paper begins with a related literature review on analyst earnings estimates in the next section. In Section 3, we describe our data and methods. In Section 4 presents our empirical tests and we conclude the paper in the last section.

## 2. Related literature

### 2.1 Analysts forecasts

Some of the literature on financial analysts has focused on the ability of analysts’ forecast dispersion to forecast future stock market returns. Banerjee and Green (2015) put this in the context of a model in which uniformed traders are uncertain about fundamentals and uncertain about the sentiment of other traders. As traders gradually learn about the motives of other traders, the equilibrium price reacts more strongly to bad news than to good news. High analyst dispersion indicates that analysts are experiencing more uncertainty in the firm fundamentals, the sentiment of other analysts, or both. The evidence shows that firms with more uncertain earnings (higher dispersion of analysts forecast) have lower risk adjusted returns (Diether *et al.*, 2002; Johnson, 2004; Sadka and Scherbina, 2007; Barron *et al.*, 2009; Li and Wu, 2014). This appears to also occur in international markets, especially those with a greater demand for the forecasts (Hwang and Li, 2018). In addition, the most successful financial analysts have a superior ability to forecast earnings. Cox and Kleiman (2000) find that these top analysts achieve their superior earnings guidance results due to their skill rather than luck. In addition, Brown and Mohammad (2010) conclude that analyst forecasting ability is valid over many firms, and is not just tied to a specific firm for which they may have access to inside information.

Another method of analyzing the impact of analysts on stock prices is to conduct an event study centered around analyst recommendations. Gleason and Lee (2003) report a faster stock price reaction for celebrity analysts and in firms covered by a higher number of analysts. Further, Chang and Chan (2008) show that better information is transmitted when analysts change to a sell recommendation, rather than a change to a buy recommendation. Conrad *et al.* (2006) report another asymmetry. When there has been a large stock price run-up, there is an equal chance the analyst will upgrade or downgrade the recommendation. But after a large stock price decline, a downgrade recommendation is more probable.

More specific to our study, a strand of research examines the relationship of forecasts to changes in the business cycle. Johnson (1999) documents a positive association between economic growth and earnings persistence as well as earnings response coefficients. Brockman *et al.* (2010) illustrate that the stock market cycle is not the same as the economic cycle. Auret and Golding (2012) show that real stock prices from the Johannesburg Stock Exchange leads real economic activity in South Africa. Lee *et al.* (2008) present data linking analysts’ five-year EPS growth predictions to the current business cycle. Lahiri and Wang (2013) evaluate economists’ business cycle forecasts and find only one-quarter ahead forecasting accuracy. Moreover, Lamont (2002) observes that older, more established professional economists issued more radical economic forecasts that were misaligned with consensus expectations, e.g. greater forecast dispersion. Kim and Na (2016) use the time series of forecast dispersion, instead of the cross-section, and find that it contains systematic risk components that are priced in stock returns.

### 2.2 Hypothesis

Regarding financial analyst forecast dispersion, Diether *et al.* (2002) find evidence of a negative relationship between analysts’ earnings forecast dispersion and future stock returns. They conclude that an increase in dispersion among analyst forecasts is due to an increase in information asymmetry. That is, the lower level of consensus about a firm’s future earnings is associated with lower returns. Johnson (2004) confirms this negative relationship between dispersion levels and future returns. Avramov *et al.* (2009, 2013) explain the puzzling negative cross-sectional relation between dispersion in analysts’ earnings and future stock returns in terms of financial distress, as proxied by credit rating downgrades. Buraschi *et al.* (2013) find that differences in earnings forecasts are the most significant variable for explaining both the time series and cross-section of credit spreads. Note that this is consistent with our story. Overconfident analysts overweight their own private information (Bosquet *et al.*, 2015). After a long expansion period, some analysts become overconfident. They underweight the importance of the quantitative information that leads to downgrades and/or overweight softer sources of information, like interviews with optimistic corporate leadership. The analysts that do not suffer from overconfidence catch the turning point of the success of the firms, while the overconfident analysts do not. The confusion among analyst forecasts results in the dispersion in aggregate analyst forecasts, which predicts a decline in the business cycle. This story is similar to that of Hribar and Yang (2016), who examine CEO forecasts and find that overconfident CEOs are more likely to miss on their forecasts. Our main hypothesis addresses this relationship between analyst forecast dispersion and the likelihood of a recession. Our formal hypothesis is presented as follows:

*H1.*

A rise in the aggregate analyst earnings forecast dispersion (AEFD) significantly increases the probability of an economic downturn.

## 3. Sample and methodology

In this study, we investigate the ability of analysts to forecast the US business cycle turning points using their earnings predictions disagreements as a crucial signal variable. Our tests include independent variables of analyst earnings dispersion with varying lags to capture the relationship. In addition, we control for traditional forecasting variables, including consumer confidence, industrial production, stock market returns, and trading volume.

Specifically, our data include monthly observations from January 1976 to December 2015. We use the index of industrial production (IPI), consumer confidence index (CCI), excess stock market returns (Rm-Rf), trading volume (TURN), and three control variables based on size and value (Fama and French, 1993) and price momentum factor (Carhart, 1997), i.e., the Carhart four-factor model with additional economic variables. Consumer confidence is gathered from the University of Michigan Index of Consumer Sentiment, whereby the index in the first quarter of 1966 is 100. Industrial production data are assembled from the Federal Reserve Bank of St Louis (FRED, Federal Reserve Economic Data) utilizing the Industrial Production Index (2007=100). Industrial Production is defined as the percentage change in the industrial production index in each month (FRED series ID=INDPRO). The percentage change in the industrial production index is a widely used indicator for estimating macroeconomic activity. Stock market returns and trading volume are compiled from the Center for Research in Security Prices (CRSP). We estimated the market return by calculating the equally weighted return of all firms listed on the NYSE, AMEX, and NASDAQ in each month. Volume is defined as the average ratio between monthly total volume and the outstanding shares of all firms listed on the NYSE, AMEX, and NASDAQ in each month, where share prices are at least $5 each using the CRSP database in order to exclude illiquid stocks. Our primary variable of interest is AEFD. These variables are detailed in Table AI.

The AEFD is based on monthly earnings per share analyst forecasts of US firms listed on the NYSE, AMEX and NASDAQ during January 1976 to December 2015. We collected analysts’ earnings per share forecast data from the summary IBES database from the beginning in 1976. To be included in the database, we require firms to have at least five analyst forecasts for the fiscal year earnings in each month. A firm can disappear from the IBES database for a variety of reasons (acquisition, bankruptcy, going private) and also when no analyst makes a forecast on the firm. However, once a firm has appeared in IBES, its estimates will remain in the database forever. This assures that the IBES database is free from survivorship bias. We conduct the analysts’ earnings forecast dispersion as the standard deviation of analyst’ earnings forecast, which measures the confusion about future earnings among financial analysts. Consistent with Sheng and Thevenot (2012), we did not use the coefficient of variation for estimating forecast dispersion because dividing the standard deviation by the mean would cause biased estimates within the context of predicting economic downturns. This is because the means of earnings per share will be low during recessions and therefore cause high coefficients of variations.

We use a logit regression model to detect if analyst dispersion, along with the other factors, are indicators of economic contraction periods. We estimated the following logit regression model:

*t*). Lagged variables are identified by (

*t*−1), (

*t*−3), (

*t*−6), and (

*t*−12); CCI, Consumer Confidence (CCI) is the monthly consumer confidence index published by the University of Michigan (Index 1st Quarter 1966=100); IPI, defined as the percentage change in the industrial production index in each month (FRED series ID=INDPRO); Rm-Rf, Excess return on the market, value-weight return of all CRSP firms incorporated in the USA and listed on the NYSE, AMEX, or NASDAQ that have a CRSP share code of 10 or 11 at the beginning of month

*t*, good shares and price data at the beginning of

*t*, and good return data for

*t*minus the one-month treasury bill rate (from Ibbotson Associates); TURN, Volume (TURN) is defined as the average ratio between monthly total volume and the outstanding shares in each month, where share prices are at least $5 each using the CRSP database; SMB, Small Minus Big is the average return on the three small portfolios minus the average return on the three big portfolios for each month; HML, High Minus Low is the average return on the two value portfolios minus the average return on the two growth portfolios for each month; MOM, Mom is the average return on the two high prior return portfolios minus the average return on the two low prior return portfolios. The six portfolios used to construct Mom each month include NYSE, AMEX, and NASDAQ stocks with prior return data. To be included in a portfolio for month

*t*(formed at the end of month

*t*-1), a stock must have a price for the end of month

*t*−13 and a good return for

*t*−2. In addition, any missing returns from

*t*−12 to

*t*−3 must be -99.0, CRSP’s code for a missing price. Each included stock also must have ME for the end of month

*t*−1;

*t*– m

*t*is time and m is the number of months prior to the current period

*t*.

We also complement the logit analysis with the Markov switching method to illustrate regime shifts in the business cycles and the relevance of AEFD. In the Markov switching methodology (Hamilton, 1989), time series data are divided into those that are low regime (recession) and high regime (expansion). The basic idea is that parameters of the econometric model are not constant over time. In our case, we expect that analyst forecast dispersion (∂) will be higher during a recession than during expansion periods. The Markov switching method provides opportunities for estimating recession probabilities and dating recessions (Levanon, 2010). We used the following model:

*S*

_{2}is the state for contraction periods.

The National Bureau of Economic Research (NBER) supplies the dates of the US business cycle (expansion or contraction). During our 1976-2015 time period, there were six expansion and five contraction periods. The expansion periods were: January 1976-December 1979, July 1980-June 1981, November 1982-June 1990, March 1991-February 2001, November 2001-November 2007 and June 2009-December 2015. The contraction periods were: January-June 1980, July 1981-October 1982, July 1990-February 1991, March-October 2001 and December 2007-May 2009.

## 4. Empirical results

### 4.1 Descriptive statistics

Figure 1 shows the analyst forecast dispersion over the period 1976-2015 for the current year forecasts (*σ*_{1}) and the next year forecasts (*σ*_{2}). NBER documented recessions are indicated by the shaded periods. Although both forecasts show the same pattern over the period, the magnitude of analyst forecast dispersion for next year’s estimates, *σ*2, has a higher magnitude. The graph shows that analyst forecast dispersion widens during downturns in the business cycle. It appears that dispersion in both the current and one-period ahead forecasts have information content in predicting economic downturns.

Figure 2 shows the analyst upward and downward recommendation revisions over the period 1976-2015. Revisions are an important aspect to our overconfidence hypothesis because of conservatism bias. Conservatism bias is a mental process where people cling to their prior opinions or forecasts, disregarding new information (Hoppe and Kusterer, 2011). After a long expansion period, some analysts become overconfident and they underweight the importance of the quantitative information that leads to downgrades. Thus, conservatism bias could be the mechanism for which analyst forecast dispersion is related to economic turning points. The graph shows that the proportion of downward revisions is higher than the proportion of upward revisions during recessions. Table I reports the average forecast dispersion each month for the current year (*σ*_{1}), which averages 0.1418 over the sample. The average is 0.2507 for the next year (*σ*_{2}). The forecast dispersion almost doubled for the next period, which indicates that there is more uncertainty among financial analysts for estimating the earnings per share further out in time. Indeed, the monthly average standard deviation of dispersion for next year, *σ*_{2}, is greater than the current year, *σ*_{1}, for all 40 years.

In addition, Table I reports that the average fraction of positive revised estimates (UP) is 0.1322 vs 0.1634 for negative revised estimates (DOWN). Whereas, 0.7044 of analyst estimates was not revised from the previous period. There is a general trend over the sample for analyst to both upgrade and downgrade estimates more often. Thus, analyst appears to be more active in the last ten years of the sample than the earlier period.

The descriptive statistics for our variables are shown in Table I. The difference between the median and mean of analysts forecast dispersion is 0.01 for *σ*_{1} and *σ*_{2}. This indicates that analyst forecast dispersion distributions are not skewed. The mean value of consumer confidence is 85.396 with a minimum of 51.7 and a maximum of 112 over the period. The descriptive statistics for industrial production, monthly returns, and turnover are also presented in the table. The correlation coefficients between these variables (not tabulated) are all below 0.3, which indicates a low degree of collinearity. We also calculated the total number of analyst estimates which is 889,152 with an average of 11.4 analysts following a firm.

### 4.2 Empirical tests

Initially, we evaluate the relationship of the analyst variables (number of analyst forecasts, fraction of positive and negative revisions, and forecast dispersion of the current year and the next year) and the US business cycle. Table II presents the variation in earnings estimates, the proportion of positive and negative forecast revisions and analyst forecast dispersion (*σ*_{1} and *σ*_{2}) separately for NBER economic expansion and economic contraction periods during 1976-2015. We tested the difference in means for each of the four metrics UP, DOWN, and AEFD (*σ*_{1}, *σ*_{2}) between expansion and contraction periods. When the economy is expanding (contracting) there is a greater (smaller) fraction of revised positive (negative) analyst estimates. The table shows that the fraction of upward revisions is 0.02 larger during expansion periods compared to contraction periods. On the other hand, the fraction of downward revisions is 0.06 higher during contraction periods. Both results are statistically significant at the 1 percent level.

When the business cycle is in an expansion (contraction) period the analysts estimated dispersion is lower (higher). The analyst dispersion for the current period (*σ*_{1}) is 0.05 larger during the recession period. Furthermore, the analyst dispersion for the next period (*σ*_{2}) is 0.13 larger during economic downturns. The *p*-values are statistically significant at the 1 percent level for both differences in mean. The results show that the dispersion of analyst forecasts, reflecting analyst disagreement, were substantially lower during economic expansion than economic contraction periods.

We next present our regression analysis. Tables III and IV show the results of logit regressions where the dependent variable is the business cycle (one during expansion period and zero otherwise). To eliminate the possibility of endogeneity between financial analyst forecasts and turning points of business cycles, we also use lagged analyst forecast dispersion as the proximate determinant of turning points in business cycle. More specifically, we use forecast dispersion of one month (*t*−1), three months *(t*−3), six months *(t*−6) and one year *(t*−12) ahead of an economic contraction period. We begin by reporting the regressions for the four lagged forecast dispersion variables using the current period earnings estimates in Panel A of Table III. In each of the four models, the coefficient for the analyst dispersion is significantly negative at the 1 percent level. In addition, the coefficients of the lagged forecast dispersion become less negative the further ahead of the contraction period. This illustrates that lagged higher dispersion is associated with economic recession. Since dispersion is lagged, from one to twelve months, it is predicting the recession. Note that this result is consistent with our hypothesis. Namely, as some analysts become overconfident toward the end of an expansion period, they underweight quantitative data and/or overweight qualitative data. The result is that the aggregate earnings forecasts become more diverse. As Nofsinger (2012) shows, higher levels of cognitive errors and psychological biases are associated with economic turning points. Lastly, the results can also be interpreted as a low level of forecast dispersion predicts economic expansion. Indeed, this finding can be considered to be a corollary to our main hypothesis in that overconfidence dissipates during the economic contraction, which leads to less forecast dispersion.

In Panel B of Table III, we add the macroeconomic variables, such as consumer confidence index (CCI), percentage change in industrial production (IPI), excess market returns (Rm-Rf), trading volume (TURN), and control variables related to size, value and momentum (SMB, HML, MOM) to the logit regressions. The results show that consumer confidence and industrial production have significantly positive coefficients in all four regression models. Volume, excess stock market returns (Rm-Rf), and the other control variables (SMB, HML, MOM) are not significantly related to predicting US business cycles. Regardless of the prediction power of these traditional economic forecasting variables, analyst dispersion continues to provide strong predictive ability. Like the results in Panel A, all four dispersion coefficients are significantly negative at the 1 percent level. The logit models have McFadden R-squared statistics ranging from 54.58 to 61.93 percent. Further, the models correctly estimate the business cycle stage at least 93.34 percent of the time and as much as 94.36 percent of the time. The coefficient of the one month lagged period dispersion (−0.373) is almost twice the magnitude of the twelve-month lagged variable (−0.195). This suggests that confusion among financial analysts about earnings estimates increases the closer to the actual economic downturn.

The results also hold for the next year analysts’ earnings forecasts (*σ*_{2}). Table IV shows that the predictive ability of analyst earnings estimates dispersion continues to predict the business cycle, even for one year ahead forecasts. Again, all four models show significantly negative coefficients for the dispersion variables. Once more, consumer confidence and industrial production, and excess stock market return (albeit the latter at a reduced significance level) are positively correlated to the business cycle stage in the next period.

The evidence in Tables III and IV show that analyst forecast dispersion has a sizeable and statistically significant impact in predicting economic downturns. The coefficients of analyst dispersion of the current period and lagged periods are negative and statistically significant. An increase in forecast dispersion, which indicates disagreement of analysts about future earnings estimates, will increase the likelihood of a contraction period.

### 4.3 Robustness tests

We also conduct several different types of robustness tests of these results. First, there are several options the literature uses to proxy for the macroeconomics variables. To examine whether our results depend on the choice of these variables, we replaced the consumer confidence index (CCI) with the consumer price index (FRED=CPILFESL) and replaced the percentage change in industrial production index (IPI) with the civilian unemployment rate (FRED=UNRATE) obtained from the US Bureau of Labor Statistics. In addition, we substituted the S&P500 Index returns for market returns (RET). For robustness testing purposes, we replaced these macroeconomic variables separately and in combination. The estimates of the coefficients of analyst dispersion (not tabulated) remain qualitatively unaffected and robust. We also checked for industry-effects by calculating the AEFD for each industry separately. We found no empirical evidence of a specific industry effect.

Furthermore, we conduct a battery of model fit and out-of-sample tests. To begin, we used the Hosmer-Lemeshov goodness-of-fit statistic for assessing calibration. We found a *χ*^{2}-value of 5.9709 (*p*-value=0.6505) which indicates that our model fits reasonably well. We also computed an out-of-sample forecasting test, whereby we estimate our model over the period 1976 to 1995 and used these model estimates to predict the recession periods over the period 1996 to 2015. The Theil inequality coefficient is equal to 0.1192. This outcome shows that the forecasting power of the model is relatively good, as the Theil inequality coefﬁcients is less than 0.3 (Theil, 1966).

In addition, we also estimate the Markov switching model, Equation (2), using current AEFD as the indicator variable. Specifically, the analyst forecast dispersion is *μ*_{1} in normal times and *μ*_{1}+ *μ*_{2} during contraction periods. The results are presented in Table V. We find that the monthly analyst forecast dispersion is 0.118 during normal times in the expansion period and 0.303 (*μ*_{1}+ *μ*_{2}) during contraction periods. Both parameters (*μ*_{1}, *μ*_{2}) are statistically significant at the 1 percent level. We also tested whether parameter *μ*_{2} is significantly different from *μ*_{1} by performing the Wald coefficient test. The statistical results show that the parameter *μ*_{2} for contraction periods is significantly higher than the parameter *μ*_{1} for expansion periods. There is considerable state dependence in the transition probabilities (*π*) with a relatively higher probability of remaining in the origin regime (0.985 for expansion periods, 0.032 for contraction periods). The transition probabilities are statistically significant at the 1 percent level.

From the Markov switching model, using AEFD as the indicator variable, we can also compute the time series probability of a recession. Figure 3 shows that the filtered transition probabilities are high for the dotcom recession (2001-2002) and financial crisis (2008-2009), as well as for the oil crisis in the early1980s. Figure 4 shows that the financial analyst dispersion stayed high during this period. It also shows the high volatility of the residuals during recession periods. The two regimes show different volatilities. During expansion times, the standard deviation of the residual is 0.019, which is statistically significant at the 1 percent level. While the standard deviation appears larger in recession periods with *σ*_{2} being 0.025 (significant at the 1 percent level). These results indicate that there is more disagreement among financial analysts during contraction periods. The probabilities stayed high during the mid-1980s and early 1990s.

## 5. Conclusions

We examine analyst estimates from the perspective of the psychological bias of overconfidence. Analysts have been found to be overconfident in that they overestimate the precision of their information. Misjudging the precision of information leads to over or under weighting various sources of information. An overconfident analyst will underweight statistical information or overweight anecdotal information. As some analysts become overconfident during an economic expansion, the estimates will become more heterogenous. Analyst dispersion in earnings estimates is our measure of the degree of analyst overconfidence. The greater the degree of dispersion, the greater the overconfidence exhibited by analysts.

From the context of our study, an economic expansion will increase the level of analyst overconfidence and greater earnings estimate dispersion. We examine whether aggregate analyst forecast dispersion contains information about turning points in business cycles, especially downturns. Utilizing the AEFD metric, we provide evidence of its predicting the turning points of business cycles in the USA. Along with other variables, like sentiment (consumer confidence), output (industrial production), and financial indicators (stock returns and turnover), AEFD has substantial power in predicting turning points of business cycles.

## Figures

Descriptive statistics

Variable | Mean | Median | SD | Min. | Max. |
---|---|---|---|---|---|

AEFD (σ_{1}) |
0.1418 | 0.1326 | 0.0384 | 0.0618 | 0.2706 |

AEFD (σ_{2}) |
0.2507 | 0.2430 | 0.0781 | 0.0581 | 0.5056 |

Recommend (UP) | 0.1322 | 0.1019 | 0.0860 | 0.0398 | 0.5267 |

Recommend (DOWN) | 0.1634 | 0.1441 | 0.0752 | 0.0552 | 0.5524 |

CCI | 85.396 | 88.400 | 12.546 | 51.700 | 112.000 |

IPI | 0.1762 | 0.2350 | 0.6778 | −4.1253 | 2.1471 |

TURN | 2.1183 | 1.4018 | 4.3975 | 0.4052 | 88.7296 |

Rm-Rf | 0.6265 | 1.0300 | 4.4490 | −23.2400 | 12.4700 |

SMB | 0.2553 | 0.1200 | 2.9353 | −15.2800 | 18.7300 |

HML | 0.3068 | 0.1700 | 2.8909 | −11.2500 | 12.9100 |

MOM | 0.6951 | 0.7700 | 4.4160 | −34.5800 | 18.3800 |

**Notes:** This table presents summary statistics of the variables in the multivariate analysis. Analyst earnings forecast dispersion is the average standard deviation (from mean estimates for each firm from different analyst forecasts) over the current period (*σ*_{1}) and next year (*σ*_{2}). Data on analyst earnings forecast dispersion are from the summary IBES file. Analyst recommendations (UP) is the proportion of upward revisions of total estimates in each month. Analyst recommendations (DOWN) is the proportion of downward revisions of total estimates in each month. Consumer confidence (CCI) is the monthly consumer confidence index published by the University of Michigan (Index 1st Quarter 1966=100). The variable industrial production (IPI) is defined as the percentage change in the industrial production index in each month (FRED series ID=INDPRO). The monthly industrial production data were collected from the Federal Reserve Bank of St Louis (FRED, Federal Reserve Economic Data). TURN is defined as the average ratio between monthly total volume and the outstanding shares in each month, where share prices are at least $5 each using the CRSP database. Excess return (Rm-Rf) is the monthly value-weight return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX, or NASDAQ minus the one-month Treasury bill rate. Small Minus Big (SMB) is the average return on the three small portfolios minus the average return on the three big portfolios for each month (Fama and French, 1993). High Minus Low (HML) is the average return on the two value portfolios minus the average return on the two growth portfolios for each month (Fama and French, 1993). Mom (MOM) is the average return on the two high prior return portfolios minus the average return on the two low prior return portfolios for each month. The six portfolios used to construct Mom each month include NYSE, AMEX, and NASDAQ stocks with prior return data (see website of French)

Business cycles and financial analyst forecasts

Business cycles 1976-2015 | No. OBS | UP | DOWN | AEFD (σ_{1}) |
AEFD (σ_{2}) |
---|---|---|---|---|---|

A. Expansion periods |
|||||

January 1976-December 1979 | 28,654 | 0.1202 | 0.0919 | 0.1207 | 0.1722 |

July 1980-June 1981 | 11,943 | 0.1060 | 0.1306 | 0.1739 | 0.2599 |

November 1982-June 1990 | 129,734 | 0.0877 | 0.1540 | 0.1856 | 0.3123 |

Mar 1991-February 2001 | 241,726 | 0.1186 | 0.1421 | 0.1224 | 0.2124 |

November 2001-November 2007 | 147,352 | 0.1844 | 0.1772 | 0.1148 | 0.2883 |

June 2009-December 2015 | 240,477 | 0.1915 | 0.2081 | 0.1194 | 0.2150 |

Total | 799,886 | 0.1354 | 0.1573 | 0.1363 | 0.2400 |

B. Contraction periods |
|||||

January 1980-June 1980 | 5,419 | 0.1131 | 0.1214 | 0.1688 | 0.2348 |

July 1981-October 1982 | 17,748 | 0.0765 | 0.1823 | 0.2106 | 0.3304 |

July 1990-February 1991 | 11,807 | 0.0803 | 0.1910 | 0.1494 | 0.2156 |

Mar 2001-October 2001 | 15,677 | 0.0995 | 0.2154 | 0.1662 | 0.3200 |

December 2007-May 2009 | 38,615 | 0.1494 | 0.2663 | 0.1892 | 0.4320 |

Total | 89,266 | 0.1148 | 0.2219 | 0.1829 | 0.3675 |

C. Differences in means |
|||||

Contraction-Expansion periods | −0.0206*** | 0.0646*** | 0.0466*** | 0.1275*** | |

p-values |
(0.000) | (0.000) | (0.000) | (0.000) |

**Notes:** This table presents analyst forecasts variables during business cycles. The statistics are cross-sectional means over each period. The sample contains NYSE, AMEX, and NASDAQ firms with at least five analyst forecasts of fiscal year earnings in a given month. The sample period is from January 1976 to December 2015. Data on analyst earnings per share (EPS) forecasts are from the Summary IBES file. UP is the average number of upward revisions as a fraction of the total number of estimates over each period. DOWN is the average number of downward revisions as a fraction of the total number of estimates over each period. DISP(*σ*) is the average standard deviation of analyst forecasts over each period. DISP(*σ*_{1}) is the average standard deviation of analyst forecasts over the current year (*σ*_{1}). DISP(*σ*_{2}) is the average standard deviation of analyst forecasts over the next year (*σ*_{2}). ***Significant at the 1 percent level

Logit Regressions on business cycles and financial analyst current period forecasts (*σ*_{1})

Variable | Predicted Sign | (1) | (2) | (3) | (4) |
---|---|---|---|---|---|

Panel A: Forecast Dispersion |
|||||

Intercept | +/− | 6.684*** (0.729) |
5.477*** (0.648) |
4.646*** (0.606) |
3.575*** (0.576) |

AEFD (t−1) |
(−) | −0.295*** (0.041) |
– | – | – |

AEFD (t−3) | (−) | – | −0.224*** (0.038) |
– | – |

AEFD (t−6) |
(−) | – | – | −0.173*** (0.036) |
– |

AEFD (t−12) |
(−) | – | – | – | −0.106*** (0.035) |

McFadden R^{2} |
17.83% | 11.01% | 6.81% | 2.60% | |

LR-statistic | 61.63*** | 37.99*** | 23.45*** | 8.91*** | |

Percent correct | 89.14% | 87.84% | 87.97% | 88.03% | |

No. of observations | 479 | 477 | 474 | 468 | |

Panel B: Includes traditional business cycles prediction variables |
|||||

Intercept | +/− | −1.242 (1.824) |
−2.280 (1.813) |
−4.349*** (1.775) |
−4.440*** (1.734) |

AEFD (t−1) |
(−) | −0.373*** (0.074) |
– | – | – |

AEFD (t−3) |
(−) | – | −0.283*** (0.065) |
– | – |

AEFD (t−6) |
(−) | – | – | −0.175*** (0.057) |
– |

AEFD (t−12) |
(−) | – | – | – | −0.195*** (0.063) |

Consumer Confidence (CCI) | + | 0.120*** (0.022) |
0.115*** (0.020) |
0.118*** (0.020) |
0.124*** (0.021) |

Industrial Production (IPI) | + | 2.351*** (0.451) |
2.597*** (0.453) |
2.397*** (0.437) |
2.496*** (0.434) |

Volume (TURN) | +/− | −0.045 (0.086) |
−0.043 (0.088) |
−0.007 (0.118) |
−0.023 (0.114) |

Rm-Rf | + | 0.095** (0.052) |
0.071* (0.047) |
0.074* (0.046) | 0.079** (0.045) |

SMB | +/− | 0.011 (0.095) |
−0.019 (0.091) |
−0.015 (0.088) |
−0.001 (0.089) |

HML | +/− | −0.049 (0.088) |
−0.072 (0.080) |
−0.064 (0.081) |
−0.081 (0.079) |

MOM | +/− | −0.036 (0.054) |
−0.001 (0.042) |
0.002 (0.042) |
−0.002 (0.045) |

McFadden R^{2} |
61.93% | 58.49% | 54.69% | 54.58% | |

LR-statistic | 214.02*** | 201. 48*** | 188.32*** | 187.09*** | |

Percent correct | 94.36 | 94.34 | 93.67 | 94.02 | |

No. of observations | 479 | 477 | 474 | 468 |

**Notes:** This table presents the results of logit regressions where the dependent variable is the business cycle (NBER). The business cycle equals one during an expansion period and is zero otherwise. Analyst earnings forecast dispersion (AEFD) is the average standard deviation of analyst forecasts over the current period (*σ*_{1}). Lagged variables are identified by (*t*−1), (*t*−3), (*t*−6), and (*t*−12). Consumer confidence (CCI) is the monthly consumer confidence index published by the University of Michigan (Index 1st Quarter 1966=100). The variable Industrial Production (IPI) is defined as the percentage change in the industrial production index in each month (FRED series ID=INDPRO). The monthly industrial production data were collected from the Federal Reserve Bank of St Louis (FRED, Federal Reserve Economic Data). TURN is defined as the average ratio between monthly total volume and the outstanding shares in each month, where share prices are at least $5 each using the CRSP database. Excess return (Rm-Rf) is the monthly value-weight return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX, or NASDAQ minus the one-month Treasury bill rate. Small Minus Big (SMB) is the average return on the three small portfolios minus the average return on the three big portfolios for each month (Fama and French, 1993). High Minus Low (HML) is the average return on the two value portfolios minus the average return on the two growth portfolios for each month (Fama and French, 1993). Mom (MOM) is the average return on the two high prior return portfolios minus the average return on the two low prior return portfolios for each month. The six portfolios used to construct Mom each month include NYSE, AMEX, and NASDAQ stocks with prior return data (see website of French). Standard errors are in parentheses and italics. *,**,***Significant at the 10, 5, and 1 percent level, respectively

Logit Regressions on business cycles and financial analyst next period forecasts (*σ*_{2})

Variable | Predicted sign | (1) | (2) | (3) | (4) |
---|---|---|---|---|---|

Panel A: Forecast dispersion |
|||||

Intercept | +/− | 6.302*** (0.689) |
5.731*** (0.643) |
4.729*** (0.574) |
3.897*** (0.533) |

AEFD (t−1) |
(−) | −0.151*** (0.022) |
– | – | – |

AEFD (t−3) |
(−) | – | −0.132*** (0.020) |
– | – |

AEFD (t−6) |
(−) | – | – | −0.099*** (0.019) |
– |

AEFD (t−12) |
(−) | – | – | – | −0.071*** (0.018) |

McFadden R^{2} |
17.98% | 14.55% | 8.75% | 4.61% | |

LR-statistic | 62.13*** | 50.22*** | 30.12*** | 15.81*** | |

Percent correct | 90.81% | 89.73% | 87.76% | 88.03% | |

No. of observations | 479 | 477 | 474 | 468 | |

Panel B: Includes traditional business cycles prediction variables |
|||||

Intercept | +/− | −5.009*** (1.750) |
−5.677*** (1.781) |
−5.315*** (1.709) |
−5.481*** (1.692) |

AEFD (t−1) |
(−) | −0.248*** (0.048) |
– | – | – |

AEFD (t−3) |
(−) | – | −0.212*** (0.042) |
– | – |

AEFD (t−6) |
(−) | – | – | −0.115*** (0.032) |
– |

AEFD (t−12) |
(−) | – | – | – | −0.133*** (0.034) |

Consumer confidence (CCI) | + | 0.168*** (0.026) |
0.162*** (0.026) |
0.130*** (0.021) |
0.139*** (0.023) |

Industrial production (IPI) | + | 2.285*** (0.460) |
2.228*** (0.451) |
2.435*** (0.442) |
2.655*** (0.461) |

Volume (TURN) | +/− | 0.575 (0.221) |
0.584*** (0.211) |
0.255 (0.161) |
0.322* (0.165) |

Rm-Rf | + | 0.055 (0.054) |
0.068* (0.049) |
0.050 (0.047) |
0.057* (0.045) |

SMB | +/− | −0.025 (0.106) |
−0.008 (0.097) |
0.019 (0.088) |
−0.009 (0.095) |

HML | +/− | −0.091 (0.094) |
−0.072 (0.089) |
−0.078 (0.079) |
−0.107 (0.078) |

MOM | +/− | −0.011 (0.052) |
−0.012(0.051) |
−0.004 (0.045) |
−0.013 (0.045) |

McFadden R^{2} |
65.00% | 62.51% | 56.11% | 56.71% | |

LR-statistic | 224.65*** | 215. 72*** | 193.21*** | 194.41*** | |

Percent correct | 95.41% | 95.18% | 94.51% | 94.44% | |

No. of observations | 479 | 477 | 474 | 468 |

**Notes:** This table presents the results of logit regressions where the dependent variable is the business cycle (NBER). The business cycle equals one during an expansion period and is zero otherwise. Analyst Dispersion is the average standard deviation of analyst forecasts over the next period (*σ*_{2}). Lagged variables are identified by *(t−1)*, *(t−3), (t−6)*, and *(t−12)*. Consumer confidence (CCI) is the monthly consumer confidence index published by the University of Michigan (Index 1st Quarter 1966=100). The variable Industrial Production (IPI) is defined as the percentage change in the industrial production index in each month (FRED series ID=INDPRO). The monthly industrial production data were collected from the Federal Reserve Bank of St Louis (FRED, Federal Reserve Economic Data). TURN is defined as the average ratio between monthly total volume and the outstanding shares in each month, where share prices are at least $5 each using the CRSP database. Excess return (Rm-Rf) is the monthly value-weight return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX, or NASDAQ minus the one-month Treasury bill rate. Small Minus Big (SMB) is the average return on the three small portfolios minus the average return on the three big portfolios for each month (Fama and French, 1993). High Minus Low (HML) is the average return on the two value portfolios minus the average return on the two growth portfolios for each month (Fama and French, 1993). Mom (MOM) is the average return on the two high prior return portfolios minus the average return on the two low prior return portfolios for each month. The six portfolios used to construct Mom each month include NYSE, AMEX, and NASDAQ stocks with prior return data (see website of French). Standard errors in parentheses and italics. *,***Significant at the 10 and 1 percent levels, respectively

Estimation of analyst forecast dispersion with a two-regime Markov switching model

Parameters | Estimates | SE |
---|---|---|

μ_{1} |
0.118*** | 0.001 |

μ_{2} |
0.185*** | 0.002 |

σ_{1} |
0.019*** | 0.001 |

σ_{2} |
0.025*** | 0.002 |

π_{11} |
0.985*** | 0.008 |

π_{21} |
0.032*** | 0.014 |

**Notes:** This table presents results of the Markov switching method, which provides opportunities for estimating recession probabilities and dating recessions using Equation (2). ***Significant at the 1 percent level

List of Variables used in the Study

Variable | Description | Source |
---|---|---|

AEFD | Analyst earnings forecast dispersion (AEFD) is the average standard deviation of analyst earnings forecasts in each month | IBES database, Summary Statistics |

UP | UP is the average number of upward revisions as a fraction of the total number of estimates in each month | IBES database, Summary Statistics |

DOWN | DOWN is the average number of downward revisions as a fraction of the total number of estimates in each month | IBES database, Summary Statistics |

EXP | Business cycle dummy which equals one during expansion period and is zero otherwise | NBER (National Bureau of Economic Research), US Business Cycle Expansions and Contractions |

CCI | Consumer confidence (CCI) is the monthly consumer confidence index published by the University of Michigan (Index 1st Quarter 1966=100) | Federal Reserve Bank of St: Louis (FRED); University of Michigan |

IPI | The variable Industrial Production (IPI) is defined as the percentage change in the industrial production index in each month (FRED series ID=INDPRO) | Federal Reserve Bank of St: Louis (FRED) |

Rm-Rf | Excess return on the market, value-weight return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX, or NASDAQ that have a CRSP share code of 10 or 11 at the beginning of month t, good shares and price data at the beginning of t, and good return data for t minus the one-month Treasury bill rate (from Ibbotson Associates) |
Kenneth R. French website, CRSP, Ibbotson Associates |

TURN | Average ratio between monthly total volume and outstanding shares in each month (share prices are at least $5) | CRSP |

SMB | Small Minus Big is the average return on the three small portfolios minus the average return on the three big portfolios for each month | Kenneth R. French website, CRSP, Ibbotson Associates |

HML | High Minus Low is the average return on the two value portfolios minus the average return on the two growth portfolios for each month | Kenneth R. French website, CRSP, Ibbotson Associates |

MOM | Mom is the average return on the two high prior return portfolios minus the average return on the two low prior return portfolios. The six portfolios used to construct Mom each month include NYSE, AMEX, and NASDAQ stocks with prior return data. To be included in a portfolio for month t (formed at the end of month t−1), a stock must have a price for the end of month t−13 and a good return for t−2. In addition, any missing returns from t−12−t−3 must be −99.0, CRSP’s code for a missing price. Each included stock also must have ME for the end of month t−1 |
Kenneth R. French website, CRSP, Ibbotson Associates |

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Groysberg, B., Healy, P., Nohria, N. and Serafeim, G. (2011), “What factors drive analyst forecasts?”, Financial Analyst Journal, Vol. 67 No. 4, pp. 18-29.

Jorgensen, B., Li, J. and Sadka, G. (2012), “Earnings dispersion and aggregate stock returns”, Journal of Accounting and Economics, Vol. 53 Nos 1-2, pp. 1-20.

Tamura, H. (2002), “Individual-analyst characteristics and forecast error”, Financial Analyst Journal, Vol. 58 No. 4, pp. 28-35.

#### Supplementary materials