Inflation Expectations and Phillips curve

[hardmann]

Hi Tom,
I decided to use monthly r, inflation, GDP to jointly estimate r* with LM model.But when I deal with LW model with monthly data,I found in https://www.newyorkfed.org/research/policy/rstar R code, LW model set inflation with 8 lags in phillips curve while calculate Inflation expectations as follows,

Code: Select all

y.pi <- (inflation + Lag(inflation,k=1) + Lag(inflation,k=2) + Lag(inflation,k=3))/4
x.pi <- cbind(Lag(inflation,k=4),
              Lag(inflation,k=5),
              Lag(inflation,k=6))
data.pi    <-  cbind(y.pi, x.pi, union = TRUE)
end.period <- length(y.pi)
PI.EXP <- rep(NA,1,end.period+6)
for (t in seq(4,(end.period-39),1)){
    Y <- data.pi[seq(t,t+39,1),1]
    X <- cbind(as.matrix(data.pi[seq(t,t+39,1),c(2,3,4)]),
               rep(1,length(Y)))
    beta <- solve(t(X)%*%X)%*%t(X)%*%Y
    PI.EXP[t+48] <- c(as.matrix(data.pi[t+43,c(2,3,4)]),1)%*%beta
}

I know it's a bit inappropriate to post the R code here, but I think this is the best way to describe how it calculates expectations, so please forgive my rudeness.I just want to know why it Why is it calculate Inflation expectations this way?when I use monthly inflation data,can I just calculate average of the sum of inflation and its 11 lags as Inflation expectations?I know it's a basic question, but I searched it and didn't find an answer to my doubt.

with much appreciation,
H

[TomDoan]

I'm not sure what your question is. The LW model is for quarterly data; and that is code for quarterly data. We have the RATS code for generating the estimates of the inflation expectations in our LW code so you don't have to hack through R code. Are you asking why they used rolling sample one-year-ahead forecasts of inflation to measure inflationary expectations? I assume the year ahead matched with what their model needed, but the use of the 10 year rolling window is likely just completely arbitrary---given that they have to give up 10 years worth of observations to do that, I assume they found that a shorter window was just too volatile, and a longer window costs too many usable data points.