A central, but largely untested, assumption in the modern literature o
n financial markets is that investors trade strategically, taking acco
unt of the effect of their trades on prices. We use a simultaneous equ
ations approach motivated by theoretical analysis to test this assumpt
ion empirically. The results point to a strong and negative cross-sect
ional relation between the average trade size and estimated fixed and
variable costs of transacting per share, consistent with strategic tra
ding. We also find that average trade size is positively related to re
turn volatility, the standard deviation of trading volume, and the pro
portion of shares held by institutional investors.