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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?

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  • $\begingroup$ Did you calculate the distribution of $S$? That should give you the answer, if I am not mistaken. $\endgroup$ – user28372 Jun 13 '20 at 15:45
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    $\begingroup$ $\sigma_{v}^2$ 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. $\endgroup$ – Michael Jun 13 '20 at 16:07