their error variance in making predictions, and overweigh their own forecasts
relative to those of others.^5
The second aspect of our theory is biased self-attribution: the confidence
of the investor in our model grows when public information is in agreement
with his information, but it does not fall commensurately when public in-
formation contradicts his private information. The psychological evidence
indicates that people tend to credit themselves for past success, and blame
external factors for failure (Fischoff 1982, Langer and Roth 1975, Miller
and Ross 1975, Taylor and Brown 1988). As Langer and Roth (1975) put it,
“Heads I win, tails it’s chance”; see also the discussion of DeLong, Shleifer,
Summers, and Waldmann (1991).
2 .The Basic Model: Constant ConfidenceThis section develops the model with static confidence. Section 3 considers
time-varying confidence. Each member of a continuous mass of agents is
overconfident in the sense that if he receives a signal, he overestimates its
precision. We refer to those who receive the signal as the informed, I; and
those who do not as the uninformed, U. For tractability, we assume that the
informed are risk neutral, whereas the uninformed are risk averse.
Each individual is endowed with a basket containing security shares, and
a risk-free numeraire that is a claim to one unit of terminal-period wealth.
There are 4 dates. At date 0, individuals begin with their endowments and
identical prior beliefs, and trade solely for optimal risk-transfer purposes.
At date 1, Is receive a common noisy private signal about underlying secu-
rity value and trade with Us.^6 At date 2, a noisy public signal arrives, and
further trade occurs. At date 3, conclusive public information arrives, the
security pays a liquidating dividend, and consumption occurs. All random
variables are independent and normally distributed.
The risky security generates a terminal value of θ, which is assumed to be
normally distributed with mean θ
- and variance σθ^2. For most of the work
we set θ
=0 without loss of generality. The private information signal re-
ceived by Is at date 1 is
s 1 =θ+, (1)466 DANIEL, HIRSHLEIFER, SUBRAHMANYAM
(^5) See Alpert and Raiffa (1982), Fischhoff, Slovic, and Lichtenstein (1977), Batchelor and
Dua (1992), and the discussions of Lichtenstein, Fischoff, and Phillips (1982), and Yates (1990).
(^6) Some previous models with common private signals include Grossman and Stiglitz (1980),
Admati and Pfleiderer (1988), and Hirshleifer, Subrahmanyam, and Titman (1994). If some
analysts and investors use the same information sources to assess security values, and interpret
them in similar ways, the error terms in their signals will be correlated. For simplicity, we as-
sume this correlation is unity; however, similar results would obtain under imperfect (but
nonzero) correlation in signal noise terms.