ARIMA(1,1,1) in BLS Non-public NFP vs. ADP Primarily based ECM

I estimated three fashions, 2021-2025M08, leading to adjusted R² of between 0.54 (primarily based on ADP information) to 0.71 (primarily based on ADP information). Right here’s what I obtained for forecasts of September and October personal NFP as reported by BLS:

For the ARIMA(1,1,1) within the preliminary benchmark BLS sequence.

For an ECM within the ADP ratio of complete personal NFP to employment in corporations 20-49:

For an ECM of personal NFP to corporations 1-499:

A comparability:

Clearly, with out a lot distinction between adjusted R²‘s, there’s not a whole lot of foundation to decide on one over the opposite, though the adjusted R² for an ECT involving employment in corporations 1-499 staff vs. complete personal has the very best (at 0.71).  Utilizing the very best R² specification, change in employment is -36K and -199K in September and October (though will increase are solely doable given the big prediction intervals).

One attention-grabbing level is that I can reject the null speculation that the ratio of agency employment 1-499 to complete personal Granger causes the log distinction in BLS personal NFP (at 10% msl), however not the reverse.