Consider the nonlinear treatment outcome model (mathrm{E}[y mid mathbf{x}, d]=exp left(mathbf{x}^{prime} boldsymbol{beta}+alpha d ight)), where (d) is

Consider the nonlinear treatment outcome model \(\mathrm{E}[y \mid \mathbf{x}, d]=\exp \left(\mathbf{x}^{\prime} \boldsymbol{\beta}+\alpha d\right)\), where \(d\) is a binary treatment indicator. Suppose that we have available consistent estimates of \((\boldsymbol{\beta}, \alpha)\) and an estimated covariance matrix \(\widehat{\mathrm{V}}[\widehat{\boldsymbol{\beta}}, \widehat{\alpha}]\). Assume that the estimator is asymptotically normal. Outline a bootstrap or a Monte Carlo algorithm for estimating the ATE parameter and its asymptotic variance given \(\left(\mathbf{x}_{i}, d_{i}\right), i=1, \ldots, N\).