Hi,

I am a beginner in stata, trying to estimate Okun's law using data from Economic Report of the President for years between 1959-2019. My variables are pcrgdp (percentage change in real GDP), unem (civilian unemployment rate), cunem (unem – unem[n-1]). I am referring to the paper “Okun’s Law: Fit at Fifty?” (Ball et al., 2013). Link to the paper-https://www.imf.org/en/Publications/...it-at-50-40236. In this paper, they use the following equations-
  1. Ut – Ut* = β (Yt – Yt*) + εt, β < 0,
Where, Yt is the log of output, Ut is the unemployment rate, and *indicates a long-run level and β = γδ and εt = μt + δ ηt . Equation 1 is derived from-

Et – Et* = γ (Yt – Yt*) + ηt, γ > 0;
Ut – Ut* = δ (Et – Et*) + μt, δ < 0;
  1. ΔUt = α + β ΔYt + ωt,
Where Δ is the change from the previous period. In this case, differencing the levels equation (1) yields equation (2) with α= –β ΔY*, where ΔY* is the constant growth rate of potential and ωt = Δ εt

I wanted to confirm if the following stata command is equivalent to equation 1?

regress cunem lnpcrgdp

I also tried using an HP filter as used in the paper with smoothing parameters of λ= 100 and λ = 1,000, however, the command for pcrgdp did not provide any results.

tsfilter hp pcrgdp_hp = pcrgdp

Can someone confirm if the stata commands for equation 1 are correct? Furthermore, how should I estimate equation 2? Thanks for considering this!