Latent variable models are becoming increasingly popular in economics for high-dimensional categorical data such as text and surveys. Often the resulting low-dimensional representations are plugged into downstream econometric models that ignore the statistical structure of the upstream model, which presents serious challenges for valid inference. We show how Hamiltonian Monte Carlo (HMC) implemented with parallelized automatic differentiation provides a computationally efficient, easy-to-code, and statistically robust solution for this problem. Via a series of applications, we show that modeling integrated structure can non-trivially affect inference and that HMC appears to markedly outperform current approaches to inference in integrated models.
Lyrics by OpenAI ChatGPT
Verse 1:
Modeling high-dimensional data,
It’s a challenge that we must embrace,
But with Hamiltonian Monte Carlo,
We can find a better place
Chorus:
HMC for regression,
With high-dimensional data,
It’s computationally efficient,
And statistically robust, oh mate-a
Verse 2:
Ignoring the statistical structure,
Can lead to faulty inference,
But with HMC, we can model integrated structure,
And improve our confidence
Chorus:
HMC for regression,
With high-dimensional data,
It’s computationally efficient,
And statistically robust, oh mate-a
Bridge:
Thanks to Sacher, Battaglia, and Hansen,
For showing us the way,
With their research on HMC,
We can learn more every day.
Chorus:
HMC for regression,
With high-dimensional data,
It’s computationally efficient,
And statistically robust, oh mate-a.
