Estimating individual‐specific slopes with year fixed effects and AR(1) errors in Stata

[Gilda Firrigno]

Hi all,

I’m trying to replicate a series of regressions in which, for each forecaster i and forecast horizon h (t+1, t+2, t+5), I estimate an expectations‐augmented Phillips curve of the form
E_{t,i}\bigl[\Delta\pi_{t+h}\bigr] = \alpha_i + \beta_i\,E_{t,i}\bigl[\Delta u_{t+h}\bigr] + \frac{1}{K}\sum_{k=1}^{K}\theta_k\,\mathrm{year}_k + \varepsilon_t, \varepsilon_t = \varphi\,\varepsilon_{t-1},

• Et,i_t,i: survey‐round expectations
• Δπ, Δu: expected inflation and unemployment changes
• year_k: dummy =1 if the forecast target year = k (K=19 dummies)
• AR(1) serial correlation in ε_t

I need to run the model separately for each forecaster (i.e. get an individual slope β_i and its p‐value per person) and include year fixed effects (one dummy per target‐year, omitting a reference year) and correct the residuals for AR(1). Finally, I want to tabulate across all forecasters how many have β_i < 0 (consistent with theory) and how many are significant, etc.

My questions:

1. What is the best way in Stata to loop over each forecaster and horizon, estimate a separate regression with:
   • individual intercept α_i
   • individual slope β_i on Δu
   • time‐fixed effects
   • AR(1) errors ?
2. Which command(s) should I use? I’ve seen prais, xtreg, reghdfe, etc. – which is most appropriate to get correct SEs under AR(1) and include year dummies?
3. How do I extract and store each estimated β_i and its p‐value automatically (e.g. with postfile or statsby) so I can build the summary table?

A minimal reproducible example of my data setup:
* data: one obs per survey round * vars: forecaster_id target_period delta_pi delta_u
Any code snippets or examples of a loop using foreach forecaster + the right estimation command would be greatly appreciated!

Thanks in advance.