Estimating Kyle's lambda

Over 250 days, daily signed order flow $y_d$ (buyer- minus seller-initiated volume) in a stock has standard deviation 2 lakh shares, and the sample covariance between the daily close-to-close price change and $y_d$ is $3\times10^6$ ₹·shares. (a) Estimate $\lambda$ by OLS and compute the implied impact of a 1 lakh-share imbalance. (b) In Kyle's model, why is the regression of $v$ (not $p$) on $y$ the right check of $\lambda$, and what does each regression recover in the simulation of Exercise m05_kyle? (c) Give two reasons why the OLS slope from real daily data may be biased as an estimate of causal impact.