# Economic growth in a DSGE model, despite mean-zero shocks

The DSGEs I've seen have steady-states, and mean-zero shocks.

Can these predict growth in GDP / capital etc?

Is this possible despite them being equilibrium models, or do you have to completely change your approach and switch to a Solow-Swan-type model to predict GDP growth?

Yes, there are DSGE models that can be used for forecasting.

These models typically have a particular kind of steady-state, which is, more precisely, called balanced growth path (BGP). On the BGP (in the absence of shocks), key indicators growth at the same constant rate. For example, GDP, household consumption, investment all grow at 2% a year. This is consistent with constant steady-state ratios of the indicators over GDP, for example $$\frac{K}{Y}$$ and $$\frac{C}{Y}$$ would be constant, while indicators grow at the same rate.

The rate itself is often built in as an assumption, based on economic priors and analysis done outside of the DSGE model (for example estimates of labor-productivity growth). Because of this fact, forecast of equilibrium growths are not just boring, but not really forecasts. However, an economy is hardly ever on its balanced growth path, so the strength of these models is in describing the dynamics back towards equilibrium, for example after a shock to global oil prices. Immediately after the shock hits, investment will typically fall at a faster rate than GDP, and then grow faster after the impact has bottomed out.

Note that these models need to be related to actual data via estimation, often using the Kalman Filter to identify unobservable variables, such as the output gap, and shocks (such as a technology shock).

To see how data can be related to model variables, consider the measurement equation (assuming the use of a Kalman filter). $$Y$$ is actual GDP in quarterly frequency, $$\hat{y_t}$$ is the deviation of output from its trend level at time $$t$$, and 2% is the assumed annual growth rate. Then this can be fed into the model as $$\log Y_t - \log Y_{t-1} - 0.005 = \hat{y}_t - \hat{y}_{t-1}$$ This means in particular that the model solution can be translated back into numbers that are consistent with actual data and hence can be used for forecasting.

References: For an overall good and detailed example, see the ECB's New Area Wide Model. It includes a section on model dynamics (4), and one on how assumptions are built into the model (3.2 & 3.3). The references in that paper are also worth checking out. For an even more modern version, see their new model, which includes many more financial market dynamics.

• Awesome, thanks for the detail and links! Aug 21, 2021 at 16:23
• @Mich55 in addition to the references in the +1 answer above I would also recommend you to have a look at Wickens Macroeconomic Theory a dynamic stochastic equilibrium approach - it’s quite comprehensive text and if I remember correctly it has an online companion with some example code
– 1muflon1
Aug 21, 2021 at 17:18