Business Cycle Measurement and Macroeconomic Variables: Chapter 3 Study Notes

Business Cycle Measurement

Introduction to Business Cycles

The business cycle refers to the fluctuations in economic activity, particularly in real Gross Domestic Product (GDP), around its long-term growth trend. Understanding these cycles is essential for analyzing macroeconomic stability and policy responses.

• Business cycles are defined as fluctuations about trend in real GDP.

• Turning points in the deviations of real GDP from trend are called peaks (local maxima) and troughs (local minima).

• Persistent positive deviations from trend are known as booms, while persistent negative deviations are called recessions.

• Amplitude measures the size of the deviation from trend.

• Frequency refers to the number of cycles (peaks and troughs) within a given period.

Example: The Canadian economy has experienced several recessions, such as those in 1974-1975 (oil prices), 1981-1982 (tight monetary policy), 1990-1992 (oil prices and monetary policy), 2008-2009 (financial crisis), and 2020-2021 (COVID-19).

Detrending Macroeconomic Data

Methods of Detrending

Detrending is the process of removing the long-term growth component from economic time series to isolate cyclical fluctuations. This is crucial for analyzing business cycles.

• The first step is often to take the logarithm of the series, e.g., $\ln(Y)$, to stabilize variance and interpret growth rates.

• Some variables, such as the trade balance, are expressed as a percentage of output (e.g., $\frac{TB}{Y}$) because they can be negative.

• The second step involves applying a detrending method, such as the Hodrick-Prescott (HP) Filter, which separates the growth component (trend) from the cyclical component.

• The cyclical component is the difference between the raw data and the growth component.

Example: For Canadian real GDP per capita, the HP filter is used to extract the trend and cyclical components from the log-transformed data.

Stylized Facts of Business Cycles

Irregularities in GDP Fluctuations

Business cycle fluctuations in GDP are characterized by irregular amplitude and frequency. There is no fixed pattern in the size or duration of cycles.

• Some fluctuations are large, most are small.

• Some cycles last longer than others; there is no regularity in their frequency.

Correlation and Co-movement of Macroeconomic Variables

Macroeconomic variables often move together with real GDP, either positively or negatively. The degree and direction of co-movement are measured by correlation coefficients.

• Procyclical variables: Deviations from trend are positively correlated with real GDP (e.g., imports, consumption, investment).

• Countercyclical variables: Deviations from trend are negatively correlated with real GDP.

• Acyclical variables: No significant correlation with real GDP (correlation coefficient close to zero).

Example: In Canada, government consumption expenditure is considered acyclical.

Leading, Lagging, and Coincident Variables

Macroeconomic variables can be classified based on the timing of their peaks and troughs relative to real GDP.

• Leading variables: Peaks and troughs precede those of real GDP. The correlation coefficient between $y_t$ and $x_{t-j}$ for $j > 0$ is larger than for $j = 0$.

• Lagging variables: Peaks and troughs follow those of real GDP. The correlation coefficient between $y_t$ and $x_{t+j}$ for $j > 0$ is larger than for $j = 0$.

• Coincident variables: Peaks and troughs coincide with those of real GDP. The correlation coefficient between $y_t$ and $x_t$ is largest.

Example: The stock index (TSE Composite Index) tends to lead real GDP in Canada.

Behavior of Key Macroeconomic Variables

Components of GDP

The main components of GDP include consumption (C), investment (I), government spending (G), and net exports (NX). Their cyclical behavior provides insights into economic dynamics.

• Consumption (C): Procyclical and less variable than GDP.

• Investment (I): Procyclical, coincident, and more variable than GDP.

• Government spending (G): Often acyclical.

• Net exports (NX): Can be procyclical or countercyclical depending on the economy.

Price Level and Inflation

The price level and inflation rate are important indicators of macroeconomic stability.

• Price level (P): Shows essentially zero correlation with real GDP.

• Inflation rate (i): Positively correlated with real GDP, consistent with the Phillips curve relationship.

Labor Market Variables

Labor market indicators such as employment, real wage, and average labor productivity are crucial for understanding the business cycle.

• Employment (N): Procyclical, lagging, and less variable than GDP.

• Average labor productivity (Y/N): Procyclical, coincident, and less variable than GDP.

Summary Table: Correlation and Variability of Key Variables

The following table summarizes the correlation coefficients and variability of percentage deviations from trend for major macroeconomic variables (Canadian data, pre-COVID-19):

Variable	Correlation with GDP	Standard Deviation (% of GDP SD)
Consumption	0.84	83%
Investment	0.66	295%
Employment	0.87	94%
Labour Productivity	0.47	53%

Business Cycle Anomalies During the Global Pandemic

The COVID-19 pandemic led to several anomalies in macroeconomic behavior:

• The negative percentage deviation from trend in employment was larger than for real GDP.

• Average labor productivity rose above trend.

• Investment rose above trend when real GDP was still below trend.

• The negative percentage deviation in consumption from trend was larger than for real GDP.

Additional info: These anomalies highlight the unique impact of the pandemic on different sectors and variables, deviating from typical business cycle patterns.

Key Formulas and Equations

• Log transformation: $\ln(Y)$

• Trade balance as percentage of output: $\frac{TB}{Y}$

• Correlation coefficient: $\rho_{xy} = \frac{\text{Cov}(x, y)}{\sigma_x \sigma_y}$

• Hodrick-Prescott Filter: Used to separate trend and cyclical components in time series data.