isaacmeza/power_simulations

This repository includes several examples of power simulations. The idea of any power simulation is to approximate the (expected) DGP with Monte-Carlo simulations, and then estimate statistical power given an identification method..

Power simulation

Statistical power $(1-\beta)$ refers to the likelihood/probability of detecting an effect where a non-zero effect is present, i,e. given a null $H_0 : \theta = 0$, and its alternative $H_1 : \theta \neq 0$, the power is defined as

$$1-\beta = \Pr(\text{reject } H_0 | H_1 \text{ is true})$$

To estimate the power of our main specification, we use Monte Carlo simulation by replicating the data generating process of our experiment:

$$(X,Y)\sim F$$

where F is a very general distribution and can be as complex as desired.

Given this synthetic data, together with an identification method we will estimate the parameters of interest of the model and compute its power. For instance, we might use a linear conditional mean model:

$$\mathbb{E}[Y|X]=\theta^{\mathsf{T}}X$$

In general, we will describe (approximate) power as a function of sample size and effect size, and it will be a non-decreasing function in this two arguments.

In this repository you can find several examples of power simulations of varying complexity.