Documentation | MacroSim

Model Specification

Hyperion is built upon a standard New Keynesian Dynamic Stochastic General Equilibrium (DSGE) model. This framework is widely used by central banks and academic economists to analyze business cycle fluctuations and policy transmission. It consists of three key components: an IS curve describing demand, a Phillips curve describing supply and inflation dynamics, and a monetary policy rule.

1. The Dynamic IS Curve

The Investment-Savings (IS) curve represents the demand side of the economy. It is derived from the household's Euler equation, linking consumption today to expected future consumption and the real interest rate.

$$ y_t = E_t y_{t+1} - \frac{1}{\sigma} (i_t - E_t \pi_{t+1} - r^n_t) $$

$ y_t $: Output gap (deviation from potential)
$ E_t y_{t+1} $: Expected future output gap
$ i_t $: Nominal interest rate (set by Central Bank)
$ E_t \pi_{t+1} $: Expected future inflation
$ \sigma $: Intertemporal elasticity of substitution (Risk aversion)
$ r^n_t $: Natural rate of interest (Technology/Preference shocks)

2. New Keynesian Phillips Curve

The Phillips curve represents the supply side. It is derived from the profit-maximization problem of monopolistically competitive firms facing sticky prices (Calvo pricing). It relates inflation to expected future inflation and marginal costs (output gap).

$$ \pi_t = \beta E_t \pi_{t+1} + \kappa y_t + u_t $$

$ \pi_t $: Current Inflation rate
$ \beta $: Discount factor (approx 0.99)
$ \kappa $: Slope of the Phillips curve (price stickiness)
$ u_t $: Cost-push shock (e.g., oil price shock)

3. Monetary Policy Rule (Taylor Rule)

The Central Bank closes the model by setting the nominal interest rate. It reacts to deviations of inflation from target and output from potential. We also include interest rate smoothing.

$$ i_t = \rho i_{t-1} + (1-\rho)(\phi_\pi \pi_t + \phi_y y_t) + v_t $$

$ \phi_\pi $: Weight on inflation (usually > 1, Taylor Principle)
$ \phi_y $: Weight on output gap
$ \rho $: Interest rate smoothing parameter
$ v_t $: Exogenous monetary policy shock

Agent Interactions

Households

Maximize lifetime utility. They supply labor to firms, consume goods, and save by holding bonds or equity. They face a trade-off between consuming today vs. saving for tomorrow (Euler Equation).

Firms

Rent capital and hire labor to produce goods. They operate in monopolistic competition and face costs when adjusting prices (sticky prices), leading to the New Keynesian Phillips Curve.

Central Bank

The monetary authority. It sets the nominal interest rate to stabilize inflation around a target (usually 2%) and output around its potential level.

Fiscal Authority (Government)

Collects lump-sum taxes from households and consumes a portion of output. Fiscal shocks ($g_t$) act as demand shifters in the IS curve.