indirect inference

Given a dataset of real observations and a generative model with parameters $\backslash theta$ for which no likelihood function can easily be provided.

Then we can ask the question of which choice of parameters $\backslash theta$ could have generated the observations.

Since a maximum likelihood estimation cannot be performed, indirect inference proposes to fit a (possibly misspecified) auxiliary model$\backslash hat\{y\}\_\{\backslash text\{aux\},\; \backslash phi\}$ to the observations, which will result in a set of auxiliary model parameters $\backslash phi\_\backslash text\{obs\}$ after fitting. This is done repeatedly for the output of the generative model for different $\backslash theta$. We then seek a fitted model with parameters $\backslash phi\_\backslash text\{gen\}(\backslash theta^*)\; \backslash approx\; \backslash phi\_\backslash text\{obs\}$ so that the generative process with parameters $\backslash theta^*$ could have generated the observations.

By using the auxiliary model as an intermediary, indirect inference allows for the estimation of the generative model's parameters even when the likelihood function is not easily accessible. This method can be particularly useful in situations where traditional estimation techniques are not feasible or computationally prohibitive.

• Method of simulated moments

• Drovandi, Christopher C. "ABC and indirect inference." Handbook of Approximate Bayesian Computation (2018): 179-209. https://arxiv.org/abs/1803.01999

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Category:Estimation methods

Category:Macroeconomics