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Theory-Based Models

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Macro by Mark

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Theory-Based Models

Advancedphase path

RBC Simplified

A stripped-down real business cycle setup linking productivity, capital accumulation, and intertemporal return conditions.

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Overview

A simplified RBC route that foregrounds productivity, Euler-style return conditions, and capital adjustment without full DSGE machinery.

Core question

How does a productivity-driven real economy adjust through capital and consumption?

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Variables

kkk

Capital

Productive capital stock.

yyy

Output

Output produced from capital and technology.

ccc

Consumption

Output net of replacement investment.

Assumptions

The simplified RBC route ignores nominal rigidities.

Everything runs through real productivity and capital adjustment.

A representative-agent intertemporal condition anchors the steady-state return.

The route keeps the Euler logic but not a full DSGE solution stack.

Parameters

AAA

Trend productivity

Technology

Technology scale in production.

ααα

Capital share

Technology

Curvature of production.

βββ

Discount factor

Preferences

Intertemporal patience.

δδδ

Depreciation

Technology

Capital wear between periods.

ρzρ_zρz​

Shock persistence

Shocks

Persistence of the productivity shock component.

k0k_0k0​

Current capital

State

Starting capital stock for the transition path.

z0z_0z0​

Current productivity shock

State

Current deviation from trend productivity.

Shock presets

Positive technology shock

Raises current productivity above trend.

Higher patience

Raises the discount factor and supports more capital.

Advanced

RBC

How does a productivity-driven real economy adjust through capital and consumption?

business cyclegrowthpolicy
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