# Private signals [closed]

Following the literature of information asymmetry (see in Kyle among others), we have seen that many papers introduce a private signal, that is

$$S=\tilde{v}+\tilde{e}$$ where, $$(\tilde{v},\tilde{e})$$ are uncorrelated, $$\tilde{v}\sim N(\bar{v},\sigma_{v}^2)$$ denotes the payoff of the risky security that is traded among the traders in the market and $$\tilde{e}\sim N(0,\sigma_{e}^2)$$ is an error term (white noise if i am not mistaken). My question is, does this noisy signal increase or decrease the variance that the infroemd trader learns privately?

• Did you calculate the distribution of $S$? That should give you the answer, if I am not mistaken. – user28372 Jun 13 '20 at 15:45
• $\sigma_{v}^2$ is the uninformed trader's prior variance (or, what is the same thing, the informed trader's "signal intensity"). If both traders are risk neutral, as in Kyle, $\sigma_{e}^2$ should play no role. In comparison, Grossman-Stiglitz starts with a similar set up for asset payoff but with CARA traders, and in that case $\sigma_{e}^2$ would enter into the endogenous constants determined in equilibrium. – Michael Jun 13 '20 at 16:07