hello Guys, I need your help!!!It's about NKPC equation with GMM.

[SW JUN]

hello guys, I hope all of you are well.
Now I'm writing my MSc dissertation about NKPC inflation dynamics. My benchmark thesis is GG(1999). I mostly followed their approaches such as variables. The period is from 1989Q1 to 2019Q4 and the main variables are the inflation rate and the labor share of income. GDP deflator percentage change is a proxy of the inflation rate. Labor share income is a proxy of the marginal cost the same as GG. For instrument variables is HP filter log real GDP, Five-year Treasury constant-maturity interest rate minus 90-day Treasury bill, wage inflation and PPI commodity price inflation. When I tested the standard NKPC, I got a negative coefficient on marginal cost, X. I regressed infl c infl(-1) x and for the hybrid model, infl c infl(-1) infl(1) x.

Is it possible to get the negative coefficient on marginal cost? Because my supervisor said if I followed their approaches, the results should be similar, but they didn't have the negative coefficient on marginal cost. Is there any wrong with my approaches?

Please give me some advice.
Thank you!