We develop an econometric methodology to infer the path of risk premia from large unbalanced
panel of individual stock returns. We estimate the time-varying risk premia
implied by conditional linear asset pricing models where the conditioning includes instruments
common to all assets and asset specific instruments. The estimator uses simple
weighted two-pass cross-sectional regressions, and we show its consistency and asymptotic
normality under increasing cross-sectional and time series dimensions. We address
consistent estimation of the asymptotic variance, and testing for asset pricing restrictions
induced by the no-arbitrage assumption in large economies. The empirical illustration on
returns for about ten thousands US stocks from July 1964 to December 2009 shows that
conditional risk premia are large and volatile in crisis periods. They exhibit large positive
and negative strays from standard unconditional estimates and follow the macroeconomic
cycles. The asset pricing restrictions are rejected for the usual unconditional four-factor
model capturing market, size, value and momentum effects.