In the popular imagination, economists are constantly forecasting economic performance… and getting it wrong.
I’ve decided to get in on the action too.
Statistical model as baseline
Here, I will be explaining a basic statistical model that predicts GDP performance by extrapolating from previous GDP results. This is a standard approach with time series data, but I do not believe that it is particularly reliable.
This model is provided as a benchmark against which more advanced models can be judged.
I will be predicting quarter-on-quarter, seasonally adjusted, real GDP growth. This is GDP growth over each three-month period, where the effects of seasonality and inflation have been removed.
We would ideally train the model with as much data as possible. However, it is clear that GDP growth has been more stable and less volatile from around 1990. This suggests a fundamental change (what statisticians call a structural break) in the British economy. As such, I am building my model based on data from Q1 1994, which still provides a good 24 years of data. This gives a year’s gap from two major economic events -the UK moving to a floating exchange rate after leaving the European Exchange Rate Mechanism (ERM) on Black Wednesday in September 1992, and the resulting shift to inflation targeting as the Government’s monetary policy objective in October 1992.
When dealing with time series data, we usually require that they are «stationary». This means that their properties (e.g. mean, variance, etc.) do not vary with time.
GDP is not stationary because it grows with time. However, we are using the quarterly GDP growth rate which is primarily a first differenced series. It is thus more likely to be stationary. In reality however, one can almost just discern from the above chart that GDP growth rate reduces ever so slightly over time. We are growing a little slower each year. However, this is not a large factor and the series appears largely stationary and fit for our purpose. An augmented Dickey-Fuller test confirms this.
> adf.test(window(datats, 1994), alternative="stationary") Augmented Dickey-Fuller Test data: window(datats, 1994) Dickey-Fuller = -3.9173, Lag order = 4, p-value = 0.01648 alternative hypothesis: stationary
Autoregressive model fit
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An examination of the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots suggests that the GDP growth rate has an AR(1) signature. It can be modelled as an autoregressive model of order 1. This means that the current value of GDP growth rate is affected by its previous value.
Various additional terms were tested to augment the model.
The final model specification is as follows.
Taken together, the model suggests:
- A long run average of 0.58% quarterly GDP growth rate in the absence of economic shocks.
- A correction effect where a large GDP increase/decrease is likely to be followed by a smaller GDP increase/decrease.
- The correction effect is asymmetric for increases and decreases in GDP.