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© 2026 Mark Jayson Nation

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RBC Simplified
Model

A stripped-down real business cycle model that isolates technology shocks, capital accumulation, and labor choice in a minimal dynamic framework.

Impulse response function panel

IRFs are the standard way to read a DSGE model. They trace how each endogenous variable responds to a one-time shock over time, making the propagation mechanism -- capital accumulation, intertemporal substitution, labor response -- directly visible.

Layout

Impact multiplier

1.00%

Y^0/εa,0\hat{Y}_0 / \varepsilon_{a,0}Y^0​/εa,0​

Output jump at impact per unit technology innovation. Measures the combined on-impact effect of productivity and labor response.

Output half-life

7.00

t∗:∣Y^t∗∣<0.5∣Y^0∣t^* : |\hat{Y}_{t^*}| < 0.5 |\hat{Y}_0|t∗:∣Y^t∗​∣<0.5∣Y^0​∣

Quarters until output deviation falls to half its impact value. Captures persistence from both the AR(1) shock and capital accumulation.

Investment peak

3.00%

max⁡tI^t\max_t \hat{I}_tmaxt​I^t​

Maximum percent deviation of investment from steady state. Investment typically overshoots output because the household front-loads capital formation.

Consumption-output impact ratio

9.28

C^0/Y^0\hat{C}_0 / \hat{Y}_0C^0​/Y^0​

Share of the output increase consumed at impact. Consumption smoothing means this is less than one -- the rest goes to investment.

ρa\rho_aρa​

How persistent the technology shock is. Higher values mean the productivity boost lasts longer, driving more capital accumulation.

0.50.990.9

Higher persistence stretches all IRFs rightward, amplifies the peak investment response, and delays the consumption peak.

φ\varphiφ

Controls labor supply responsiveness. Low values mean elastic hours; high values make hours nearly fixed.

0.2551

High varphi flattens the hours and output IRFs while boosting the wage response. Low varphi amplifies the labor channel.

α\alphaα

Output elasticity of capital. Higher values increase the importance of the capital accumulation propagation channel.

0.20.50.33

Higher alpha amplifies investment and capital responses and increases the persistence of output beyond what rho_a alone provides.

Kernel: irf | Viz: Impulse response function panel