Compare internal VFCI estimates with different VARs

[matdehaven]

There are a few differences between the external VFCI estimates and the internal VAR VFCI estimates.

1. Estimated in differences vs. levels with lags
2. External VFCI controls for returns in the mean equation, internal VAR VFCI does not
3. Internal VAR VFCI controls for a host of other macro variables (investment, inflation, productivity, etc.)

Estimate a series of VARs to better understand the differences:

• VAR in differences, one lag, with only consumption and asset prices
• VAR in levels, two lags, with only consumption and asset prices
• VAR in levels, two lags, only consumption
• VAR in levels, two lags, consumption + other macro controls
• VAR in levels, two lags, consumption + other macro controls + asset prices

[matdehaven]

Had trouble getting even the most basic VAR (consumption in differences, one lag, with asset prices) to be the same as our VFCI estimates.

It turns out there is a large difference depending on whether the most recent data is included or not (i.e. through 2017 or through 2022). If the data samples are the same, we can get a very close match.