Why a Useful Forecast Can Still Be Wrong
The application-to-employer gap is not explained by a simple choice between accurate information and irrational optimism. Expectations in the application data predict which businesses are more likely to enter and how much employment they may reach, yet they also overshoot outcomes systematically and do not move one-for-one with them. The useful question is what kind of information a forecast contains, how selection changes the observed averages, and what the evidence can—and cannot—say about the beliefs behind the number.
Predictive power is not calibration
A forecast can be useful in two different senses. It can help rank cases: applicants who expect more employment may, on average, realize more employment than applicants who expect less. Or it can be calibrated in level: an expectation of four employees should correspond, on average, to an outcome of four employees, with no systematic tendency to overshoot or undershoot. The first property is predictive association. The second is calibration. The Census evidence supports the first while rejecting the stronger second claim.
The study tests the relationship with a standard forecast regression. In plain language, it asks how realized employment changes as expected employment changes. If expectations were both unbiased and efficient in the strongest conventional sense, the fitted relationship would pass through zero when no employment was expected and would rise one-for-one with the forecast. The joint benchmark is an intercept of zero and a slope of one.
The estimated slopes are far below that benchmark: 0.288 for all applications and 0.261 among applications with positive expected employment. Both specifications also have positive intercepts. In the equivalent regression of forecast error on expected employment, the slopes are 0.712 and 0.739. These are two ways of displaying the same underlying pattern. As expectations become larger, realized employment does rise, but the gap between the expected and realized values tends to widen rather than remain constant.
The slope is easier to interpret with a hypothetical example. If the relationship were literally one-for-one, raising a plan from two employees to six would raise the average realized outcome by four. A slope below one says that the realized increase is smaller than the forecast increase. It does not say that every business expecting six will hire fewer than every business expecting two, or that no high-expectation application can outperform its plan. It describes the average relationship across a selected population. Some businesses can be pleasantly surprised, some can fail, and the fitted line can still rise less steeply than the line of perfect calibration.
The positive intercept adds another qualification. At low expected values, realized employment need not be lower than the expectation; the line’s intercept can place average outcomes above a small forecast. That is consistent with unexpected entry and with entrants whose scale exceeds a zero or modest plan. At higher forecast levels, the slope below one makes overprediction more prominent at the margin. A single overall average therefore cannot describe the whole distribution.
The authors also estimate models that separate the entry decision from employment conditional on entry. Expected maximum employment is a strong predictor of both whether positive employment appears and how large realized employment is among those that enter. Conditional employment still rises less than proportionally with expectations. The model choice changes the treatment of the many zero outcomes and of selection into positive employment, but the substantive result survives: expectations contain signal and error at the same time.
This is why rejecting the benchmark should not be translated immediately into “applicants are irrational.” The benchmark assumes that the analyst observes the same information set as the person making the forecast and that the forecast fully summarizes the part of that information that matters for realized employment.