RDP 2011-06: Does Equity Mispricing Influence Household and Firm Decisions? Appendix C: Bootstrap Methodology

90 per cent confidence intervals are constructed using the following semi-parametric bootstrap procedure:

  1. Using the procedure outlined in Section 3, I obtain estimates of the semi-structural residual vector Inline Equation conditioning on Inline Equation and the instruments Inline Equation and zt (recall zt is the relevant instrument for mispricing shocks, either forecast dispersion, option volatility or valuation confidence).
  2. Randomly draw with replacement (by column) from the matrix of estimation residuals and Inline Equation, so that in effect a form of ‘pairs’ bootstrap is used that accounts for the joint empirical distribution of the errors and the instrument used in identification. One thousand random samples of length T = 83 are drawn.
  3. Simulate data to construct the vector Inline Equation using

    for t = 1, …, T and for i = 1, …, 1,000 where i is an index identifying the relevant draw in Step 2, and where Inline Equation are the point estimates used to construct the statistics of interest discussed in the main text.[53]

  4. For each artificial sample, i, estimate Inline Equation and then construct the estimated impulse response function (moving average) matrices Inline Equation for i = 1,…, 1,000. Note that Inline Equation is treated as known and is not re-estimated with each sample.
  5. Construct Hall percentile confidence intervals following Lütkepohl (2006). Let Inline Equation be the 5 and 95 percentiles of the statistic Inline Equation where Inline Equation is the estimated impulse response function based on the observed data, j quarters after the initial shock of interest. The Hall confidence interval is given by


For brevity, I abstract from deterministic terms. In implementation I allow for an unrestricted constant in the SVECM. [53]