# Modelling GDP growth rates with an AR(1) process

I am trying to model the growth rates of real output per worker. I read that GDP growth rates are often assumed to be stationary and are modelled using an AR(1) process, so I took logs and then took first difference. Then I estimated the following AR(1) model using OLS with robust standard errors. I use Stata.

$$\Delta \ln y_t = \beta_0 + \beta_1*\Delta \ln y_{t-1} + \epsilon_t$$

where $$\epsilon_t$$ is the error term.

From the regression output, however, $$\beta_1$$ is approximately 0.9, and the 95% confidence interval contains 1? Does this mean the process is non-stationary? I conducted some quick unit root tests (DF-GLS and KPSS), and the log of GDP per worker is non-stationary in levels, but stationary in first difference, as expected.

So why is $$\beta_1$$ close to 1? What should I do?

Many thanks!

• Hi: Estimating an AR(1) with OLS results in biased estimates so, if STATA has an MLE algorithm for the AR(1), I would try that instead. Also, your results are saying that growth rates are ( close to ) a random walk with non zero mean but this does not contradict your first finding. – mark leeds Apr 23 at 13:09
• @markleeds, I am afraid MLE of AR model parameters is biased, too. But bias is not the only thing to care about; variance is equally important. Getting rid of the bias may make the estimator further removed from the target on average, and that is what really matters. – Richard Hardy May 1 at 11:48
• Hi Richard: good point. I'm not clear on methodologies for getting rid of bias but I always had the impression ( maybe I read it somewhere ) that using the MLE was a better approach than using OLS. That could just be a figment of my imagination though !!!!! – mark leeds May 2 at 14:46