<p>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.</p>
<p><span class="math-container">$$
\Delta \ln y_t = \beta_0 + \beta_1*\Delta \ln y_{t-1} + \epsilon_t
$$</span></p>
<p>where <span class="math-container">$\epsilon_t$</span> is the error term.</p>
<p>From the regression output, however, <span class="math-container">$\beta_1$</span> 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.</p>
<p>So why is <span class="math-container">$\beta_1$</span> close to 1? What should I do?</p>
<p>Many thanks!</p>

CC BY-SA 4.0
2021-04-23T13:09:43.570Z
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
CC BY-SA 4.0
2021-05-01T11:48:37.883Z
@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
CC BY-SA 4.0
2021-05-02T14:46:29.770Z
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
<gdp><time-series><autoregressive>
Modelling GDP growth rates with an AR(1) process
Ben
# Modelling GDP growth rates with an AR(1) process

(Asked by: username_0 on 2021-04-23)

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!

**Tags:** gdp, time-series, autoregressive

> **Comments:**
> **username_1**: 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.  
> **username_2**: @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.  
> **username_1**: 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 !!!!!  

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## 0 answers

