Swiss real GDP and the output gap
2024-06
The state of the business cycle as measured by the output gap is seen as an important driver of inflation in most economies. Whether that is so in Switzerland is less clear, given how open the economy is. Nevertheless, it is useful to consider how to compute it.
“Traditional” output gaps
To be clear, here I have in mind the “traditional” or, perhaps better, the “old-fashioned” notion of an output gap as the difference between real GDP and a smooth trend.
The simplest approach is to regress the logarithm of real GDP on a deterministic time trend. If the growth rate of real GDP is stable over time, that might work well.1
Remarkably, that is the case in Switzerland. The graph below shows the logarithm of real GDP and a fitted linear time trend. The slope of the time trend measures the growth rate of trend, or “potential”, GDP. As the graph suggests, the growth rate has been remarkably constant at 1.8% per year in the more than 40 years of data plotted.
Source: OLS regression of the log of real GDP on a time trend; data from SECO.
I think of the deviations from the trend in the graph as a measure of the output gap. Looking at the graph, three episodes stand out.
The first is the boom in the early 1990s, when real GDP rose 7% over trend. One driver of the boom was spending related to German unification, which occurred that year and which spilled out across Europe.
The second is the boom that ended in late 2008 after the collapse of Lehman Brothers in September that year. Swiss real GDP fell from being more than 4% above trend to being below trend for four quarters.
The third the collapse of economic activity in 2020Q2 as covid hit the economy and real GDP fell 8% below trend.
What does this model tell us about the likely growth of real GDP in the coming quarters? Two factors will matter for growth forecasts.
The rate of trend growth. The analysis above suggest that it is constant.
The gradual disappearance of the output gap, which will lower the forecast if the output gap is positive and raise it if the output gap is negative.
At the end of the sample in 2024Q1, output is estimated to be 0.2% below trend. The second factor is therefore going to be of negligible importance. But had the output been larger (or smaller), it would have played a role.
The dynamics of the output gap
To incorporate how the output gap affects growth forecasts, I need to model its dynamics. The easiest way to do so is to re-estimate the simple model for the output gap, but allow the residuals (the output gap) to follow a second-order autoregressive process, AR(2).
This leads to an estimated AR(1) parameter of 1.33 and an AR(2) parameter of -0.40.2 These parameter estimates imply that a sudden increase in the output gap will build up further over time before gradually disappearing. This is illustrated in the figure below, which shows how a sudden 1% increase in the output gap leads to further increases for two quarters until real GDP is about 1.4% above trend and then gradually disappears. That process is very slow; after 5 years output is still 0.1% above trend.
Source: My calculations from an OLS regression of the log of real GDP on a deterministic time trend, allowing for AR(2) errors; data from SECO.
Forecasts from the model
Applying this model, I obtain a forecast of four-quarter growth of 1.5% in 2024Q2, 1.7% in 2024Q3 and 1.9% in 2024Q4. Given that four-quarter growth was 0.8% in 2024Q1, the model yields an estimate of average annual GDP growth in 2024 of 1.5%. This strikes me as high, given developments in the external environment and the openness of the Swiss economy.
I am keen to hear comments on this approach and how others go about estimating the Swiss output gap.
The work reported here is preliminary and may be subject to errors. It should not be seen as constituting investment advice. Readers are advised to seek professional investment advice.
Sometimes it may be helpful to also enter that trend squared and cubed.
Since the massive covid shock has an outsize effect on the estimates of these parameters that determine the behavior over time of the output gap, the model is estimated on data spanning 1980Q1 – 2019Q4 and 2021Q3 – 2024Q1, that is, the covid period is dropped.
I suppose if you want to add bells and whistles you could jointly estimate output gap and neutral real rate a la Laubach and Williams (although I hasten to add, I'm not a fan of the approach myself).