I am using the Local Projection for Mediation Analyses and wondering how to plot the impulse response function for the final or total indirect effect: the model is defined below
M_{t+h} = \alpha^{h}_{0} + \alpha^{h}_{1}D_{t} + \alpha^{h}_{2}X_{t} + u_{t}
Y_{t+h} = \beta^{h}_{0} + \beta^{h}_{1}D_{t} + \beta^{h}_{2}\hat{M_{t+h}} + \beta^{h}_{3}X_{t} + \epsilon_{t}.
I have estimated the impulse response for \alpha^{h}_{1} and \beta^{h}_{2} individually and do have the confidence interval.
However, my main question and struggle is how can I construct the confidence interval for the parameter of interest: \alpha^{h}_{1} \times \beta^{h}_{2}.
M_{t+h} = \alpha^{h}_{0} + \alpha^{h}_{1}D_{t} + \alpha^{h}_{2}X_{t} + u_{t}
Y_{t+h} = \beta^{h}_{0} + \beta^{h}_{1}D_{t} + \beta^{h}_{2}\hat{M_{t+h}} + \beta^{h}_{3}X_{t} + \epsilon_{t}.
I have estimated the impulse response for \alpha^{h}_{1} and \beta^{h}_{2} individually and do have the confidence interval.
However, my main question and struggle is how can I construct the confidence interval for the parameter of interest: \alpha^{h}_{1} \times \beta^{h}_{2}.
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