Introduction to Neoclassical Business Cycle Theory

Aggregate Production Function: Real GDP ( $Y$ ) is defined as a function of capital, labour input, and the state of technology. It is expressed by the formula: $Y = F(K, L)$
- $Y$ represents real GDP.
- $K$ represents the aggregate capital stock.
- $L$ represents labour input (the lecturer emphasizes this is not the same as the labour force).
- The production function $F$ reflects the "state of technology."
Characteristics of Classical Theory:
- Classical theory takes the aggregate capital stock ( $K$ ), the labour input ( $L$ ), the state of technology, and aggregate production ( $Y$ ) as given variables.
- The theory is best suited for analyzing a time horizon of at least several years (the long run).
- It often (implicitly) assumes that the economy is in a long-run equilibrium or a steady state.
- Steady State Definition: An equilibrium state where key variables, such as the unemployment rate ( $u$ ), remain constant.

Natural Level of Aggregate Production ( $Y_n$ ): Defined as the level of aggregate production achieved when the economy is in a long-run equilibrium or steady state.
Drivers of $Y_n$ Growth: The growth rate of the natural level of production depends on three primary factors:
1. The growth rate of the capital stock ( $K$ ).
2. The growth rate of the population.
3. The growth rate of the state of technology.
Historical Average: In developed countries since World War II, the growth rate of $Y_n$ has been approximately $3\%$ per year. The formula is expressed as: $\frac{\Delta Y_{n,t+1}}{Y_{n,t}} = \frac{Y_{n,t+1} - Y_{n,t}}{Y_{n,t}} \approx 3\%$

Short-Run Characteristics: In the short run, the economy experiences strong fluctuations around long-run averages:
- Fluctuations of aggregate production ( $Y$ ) around the natural level ( $Y_n$ ).
- Fluctuations of the unemployment rate ( $u$ ) around the natural rate of unemployment ( $u_n$ ).
- Comovements: There are strong simultaneous movements between aggregate production ( $Y$ ), consumption, investment, and the unemployment rate ( $u$ ).
- These fluctuations consist of expansions and recessions, collectively known as the business cycle.
Okun's Law (United States Context): Describes the inverse relationship between the growth rate of real GDP and changes in the unemployment rate.
- General formula: $\frac{\Delta Y_{t+1}}{Y_t} \approx \frac{\Delta Y_{n,t+1}}{Y_{n,t}} - 2 \times \Delta u_{t+1}$
- Substituting the standard growth rate for the U.S.: $\frac{\Delta Y_{t+1}}{Y_t} \approx 3\% - 2 \times \Delta u_{t+1}$
- Empirical Data (1971–2021): Based on OECD data, the specific regression line for Okun's Law in the U.S. is plotted as: $g = 2.7\% - 1.4 \times \Delta u$ where $g$ is the growth rate of real GDP and $\Delta u$ is the change in the unemployment rate. The coefficient of determination is $R^2 = 0.68$ .
- Specific Historical Data Points Mentioned: 1974, 1975, 1980, 1981, 1982, 1983, 1984, 1991, 1998, 1999, 2000, 2001, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2020, 2021.

Origin: Theory based on John Maynard Keynes' The General Theory of Employment, Interest and Money (1936).
Short-Run Determination of Production: Unlike classical theory, where production is supply-side determined, neoclassical theory posits that aggregate production in the short run is determined by both the supply side and the demand side.
Demand-Side Drivers: Planned aggregate expenditures drive production and are influenced by:
- Animal Spirits: The level of consumer and business confidence.
- Real Interest Rate ( $r$ ).
Price Stickiness Assumption: In the short run, nominal prices are assumed to be sticky, meaning there is no inflation ( $\pi = 0$ ).
Interest Rate Relationship: Because nominal prices are sticky ( $\pi = 0$ ), any change in the nominal interest rate ( $i$ ) results in an identical change in the real interest rate ( $r$ ).
Core Logic: In the short run, planned aggregate expenditures—and consequently aggregate production ( $Y$ )—depend on animal spirits and the nominal interest rate ( $i$ ).

Keynesian Building Blocks:
1. Keynesian Cross Model: Describes the determination of $Y$ in the goods market. It takes the nominal interest rate ( $i$ ) as given and assumes inflation ( $\pi$ ) is zero.
2. Liquidity Preference Model: Describes the determination of the nominal interest rate ( $i$ ) in the money market. It takes aggregate production ( $Y$ ) as given and assumes inflation ( $\pi$ ) is zero.
The IS-LM Model:
- Integrates the Keynesian Cross and Liquidity Preference models.
- Explains how aggregate production ( $Y$ ) and the nominal interest rate ( $i$ ) adjust simultaneously to equilibrate both the goods market and the money market.
- Explicitly assumes a closed economy and zero inflation ( $\pi = 0$ ).
The Mundell-Fleming Model:
- Operates on similar principles to the IS-LM model but is adapted for a small open economy.
The AD-AS Model (Aggregate Demand - Aggregate Supply):
- An extension of the IS-LM model used to analyze scenarios where the price level ( $P$ ) changes.
- Serves as the link between short-run neoclassical business cycle theory (where $\pi = 0$ ) and long-run classical theory (where the classical dichotomy holds).
- Establishes the relation between the unemployment rate ( $u$ ) and inflation ( $\pi$ ), known as the Phillips curve.
- Caveat: The lecturer notes that this model is considered "shaky" due to the Lucas critique (1976).