Inter Macro Review weeks 5-7 PDF

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Inter Macro Weeks 5-7:

Phillips Curve 

Using the production function we can write output in terms of unemployment (u) and the natural rate of unemployment (un)

Dynamic Model Inputs: 1. Output equation: output depends negatively on real interest rate



Therefore Y bar minus Yt indicates the output gap

2. Fisher equation: real interest rate is nominal interest rate less expected inflation



This model uses an inflationary expectation -- inaccuracies may occur

3. Expectations-augmented Phillips curve: inflation depends on expected inflation and output gap

o Φ represents sensitivity of inflation towards the output gap 4. Adaptive expectations: expected future inflation equal to current actual inflation  Expected future inflation equal to current actual inflation

5. Monetary policy rule: nominal interest rate set in response to inflation and output gap  Nominal interest rate it set by central bank according to rule

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Input the Fisher relation, allows us to create:

Notation:

Long Run Equilibrium 

LRE: inflation rates are stable (inflation is constant over periods) and any external shocks are at 0

Dynamic AS Curve (Short Run) 

We can model this using adaptive expectations and the Phillips curve

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o High levels of economic activity lead to higher levels of inflation and vice-versa Changes in these variables shift the DAS curve

Dynamic AD Curve (Short Run)

 

A downward sloping relation between real output Yt and inflation πt Changes in the variables shift the DAD curve

Solving Equilibrium:  Start in long-run equilibrium  Change one of the exogenous variables, y, v t, εt, or π*  Hold the other exogenous variables constant  Use DAS and DAD curves to determine both o (i) impact effects o (ii) impulse responses (dynamic effects)  We can then substitute output gap into the DAS curve to calculate the equilibrium levels of output and inflation Long-Run Growth:  Sustained increases in real output over time

Aggregate Production Function: 

Relationship between aggregate output and inputs, capital and labour

Productivity: 

We can write both output and capital on a per worker basis

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Therefore:

Solow Model:

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Change in capital stock per worker given by investment per worker sf(k t) less depreciation per worker δkt o investment > depreciation, capital stock rises, k t+1 > kt o investment < depreciation, capital stock falls, kt+1 < kt

Steady State:



Where capital per worker does not change between periods

Consumption:

Production function:  Index A captures all contributions to output not due to K and N, hence A often referred to as total factor productivity or TFP

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Reflected in new per worker rates effective rates

Growth Rates:  Growth rate variable (Xt)

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Thus, reflect the growth rate of output per effective worker

o

Where gY is output growth, ga is technological growth and g n is employment growth

Capital Accumulation:  CA formula as:

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Using effective labour we can yield

Convergence  

In the long run --> poorer countries should "catch up" to wealthier ones Either o Absolute convergence: countries with the same g N, gA and the same s,a,δ should have the same output per worker in the long run

o

Conditional convergence: countries with the same gN, gA and different s,a,δ should grow at the same rate, but have different levels in the long run of output per worker...