Notes On The Instrumental Variable Regression

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Instrumental Variable Regression We acknowledge that endogeneity of trading frequency might be a problem since the price informativeness could have a systematic influence on the trading activity. A strategy to address the endogeneity problem is to employ an instrumental variable approach. We choose the official adjustment of stamp tax on security trading as one instrumental variable. On the one hand, stamp tax, as an exogenous policy instrument, is not related to the price informativeness. On the other hand, the change of stamp tax impacts the trading activity endogenously through the channel of trading cost, e.g. a rise of stamp tax is likely to motivate less frequent trading due to the rise of trading cost. There are four adjustments…show more content…
The two stage regressions are reported in Table 8. Column 1 in Panel A shows that institutional trading frequency is decreasing in the stamp tax, which is consistent with the fact that raised stamp tax produces higher trading cost. Kleibergen-Paap rk Wald F statistic is a standard test for the weak instrument problem, which is ruled out since the p-value is 0.000. Columns 1 and 2 in Panel B suggest that the results from baseline regressions hold in IV regressions, where more frequent trading generates lower price informativeness. Difference-in-Sargan statistics show that the 2SLS and OLS estimates are the same. (p-value ranges from 0.35 to 0.55) Table 8 Instrumental Variables Regression Panel A First Stage Regression Independent Variables Dependent Variables 〖Freq_inst〗_t 〖Tax〗_t -2.039*** (-15.06) 〖Freq_inst〗_(t-1) 3.430*** (10.34) Adjusted R square 0.598 Kleibergen-Paap rk Wald F statistic (p-value) 0.000 Panel B Second Stage Regression Independent Variables Dependent Variables Info1 Info2 Freq_inst -0.0268*** -0.0303*** (-4.41) (-4.58) Freq_retail -0.0154*** -0.0174*** (-25.85) (-26.49) Turnover 5.577*** 6.146*** (22.02) (22.66) Lev 0.00791 0.0187 (0.60) (1.06) Inst 0.100*** 0.105*** (5.65) (5.44) Free -0.0607*** -0.104*** (-3.79) (-6.04) Herfindahl -0.0276 -0.0351* (-1.49) (-1.71) Mktcap -0.0214*** -0.0156** (-4.19) (-2.84) Adjusted R square 0.2964 0.313 Difference-in-Sargan statistics (p-value) 0.3773 0.514 Number of Observations 8,107 8,107 Notes:
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