Estimate VAR in differences / stationary variables instead of levels

[matdehaven]

VAR is currently estimated in levels, following BCA paper.

For estimating the mean-vol relationship, this creates complications.

Once solution is to instead estimate the VAR in differences for the non-stationary variables. Only inflation, interest, and the unemployment rate (and perhaps labor share?) are stationary on their own. bcadata repo.

• [x] Is labor share stationary?
• [x] Estimate VAR in differences
• [x] Add easy option in fit_var function

[matdehaven]

The labor share is relatively stationary empirically (though it has shifted down since 2000). Theoretically, there is no reason for there to be a long term trend, like we see in output, etc.

Takeaway: do not take differences of the labor share.

[matdehaven]

Created reports showing the VAR estimated in differences and then the:

• external vfci max share method
• internal vfci mean-vol relationships
• internal vfci compared to max share

There's a lot of differences to take in.

The mean-vol relationships look better for the trend variables, but output, consumption, etc still are not very strong. Interest rate is the strongest, and unemployment is also strong.

The IRFs have changed a bit when the VAR is estimated in differences, a big change is that inflation now moves as theory would predict.

The correlation between the external vfci max share shock and the BCA shock is lower than the VAR estimated in levels (0.57 vs 0.75).

The correlation between the internal vfci shock and the BCA shock is lower than the VAR estimated in levels (0.46 vs. 0.75). In fact, now the internal vfci with the largest correlation is the one constructed targeting consumption (correlation 0.62). However, the Wald-test for that heteroskedastic regression is not significant, with a p-value of 0.2099).

[matdehaven]

We should try:

• [x] Estimate the VAR in differences with only 1 lag
• [ ] Plot the IRFs as cumulative instead of changes