9.4 DSGE MODELS

9.4 DSGE MODELS

DSGE—dynamic stochastic general equilibrium—models provide a way to generate internally consistent forecasts in a way that links the current state of the economy with agents’ forward-looking expectations of outcomes that may depend on economic policy decisions. Due to their ability to condition forecasts on future policy actions, DSGE models are well suited for conditional forecasting exercises such as scenario analysis. They can also be used to decompose forecasts in a way that improves economic interpretation—e.g., an optimistic output growth forecast may be predicated on planned future fiscal stimulus.

DSGE models start from intertemporally optimizing agents’ decisions given a set of assumptions about household preferences and firms’ production function. These are augmented with monetary and fiscal policy decision rules as well as assumptions about drivers such as shocks to technology, monetary, and fiscal policy. The models make use of macroeconomic equilibrium specifications which usually can be grouped into either neoclassical growth models or New Keynesian models that incorporate nominal and real frictions and adjustment costs.

The chief determinant of the size of a DSGE model is the extent to which the model accounts for dynamic capital accumulation effects, wage stickiness, households’ habit formation, and financial frictions.

For an exhaustive coverage of DSGE models, we refer to Del Negro and Schorfheide (2013) who describe large-, medium-, and small-scale DSGE models. As an illustration, we briefly describe their “small” DSGE model which is a special case of a model by Smets and Wouters (2003) and ignores capital accumulation, wage stickiness, habit formation, and financial frictions.

This model includes an Euler equation that links current consumption, $c_t,$ to expected future consumption, $c_{t+1}$ , and total output, $z_{t+1}$ , as well as the expected real interest rate which is given by the current nominal interest rate, $R_t$ , minus the expected rate of inflation, $E_t[{\pi }_{t+1}]$ :

$$c_t=E_t[c_{t+1}+z_{t+1}]-\frac{1}{A_c}(R_t-E_t[{\pi }_{t+1}]).\text{\hspace{1em}(9.37)}$$

Here $A_c$ measures households’ risk aversion. Households supply labor to the point where their marginal rate of substitution between consumption and leisure equals their wage which, in turn, is linked to companies’ marginal cost, $m{c}_t$ . In this simple model without capital the detrended output, ${\gamma }_t$ , is equal to the labor input, $L_t,$ and so, in equilibrium,

$$m{c}_t=c_t+\nu L_t,\text{\hspace{1em}(9.38)}$$

where v is a parameter that measures the curvature of households’ disutility of supplying labor.

Del Negro and Schorfheide (2013) show that an expectation-augmented Phillips curve can be derived to capture the trade-off between inflation and employment costs,

$${\pi }_t=b_1(\lambda )m{c}_t+b_2(\lambda )E_t[{\pi }_{t+1}]+b_3(\lambda ){\pi }_{t-1},\text{\hspace{1em}(9.39)}$$

where $\lambda$ is a set of parameters capturing price rigidity, households’ intertemporal discount rate, and the economy’s degree of price indexation.

Three types of “shocks” drive this model, namely, monetary policy shocks (or interest rate shocks), ${\epsilon }_{Rt};$ shocks to government policy (fiscal policy shocks), ${\epsilon }_{gt};$ and shocks to the trend process for output (technology shocks), ${\epsilon }_{zt}$ . These shocks are embedded in three equations that show how interest rates, government spending, and economic growth evolve.

Specifically, the central bank sets its monetary policy such that the nominal interest rate, $R_t:$ , is higher the higher are past interest rates, current inflation, and output growth in relation to the trend:

$$R_t={\rho }_R{R}_{t-1}+(1-{\rho }_R)[{\psi }_1{\pi }_t+{\psi }_2(y_t-y_{t-1}+z_t)]+{\sigma }_R{\epsilon }_{Rt},\text{\hspace{1em}(9.40)}$$

where ${\rho }_R,{\psi }_1$ , and ${\psi }_2$ are parameters of the monetary policy rule. Government spending, $g_t,$ is assumed to follow an AR(1) process,

$$g_t={\rho }_g{g}_{t-1}+{\sigma }_g{\epsilon }_{gt}.\text{\hspace{1em}(9.41)}$$

Finally, the growth rate in the economy’s trend process, $z_t,$ is given by

$$z_t=({\rho }_z-1)(1-\phi ){\tilde{z}}_{t-1}-\phi ({\tilde{z}}_{t-1}-{\tilde{z}}_{t-2})+{\sigma }_z{ϵ}_{zt},\text{\hspace{1em}(9.42)}$$

$${\tilde{z}}_t={\rho }_z(1-\phi ){\tilde{z}}_{t-1}+\phi {\tilde{z}}_{t-2}+{\sigma }_z{ϵ}_{zt},$$

where the AR(2) process ${\tilde{z}}_t$ affects the total factor process and so captures changes to technology. Naturally, this model can be amended in several ways, e.g., by changing the dynamics in (9.40), (9.41), or (9.42), or by introducing capital buildup or financial market frictions. See Del Negro and Schorfheide (2013) for further discussion and details.