This paper, authored by Robert J. Hodrick and Edward C. Prescott, investigates the post-war U.S. business cycles using quarterly data. The study focuses on the rapid fluctuations in real output and other macroeconomic time series, examining their comovements and serial correlation properties. Key findings include: 1. **Output Fluctuations**: Fluctuations in output are positively associated with changes in hours worked, with similar magnitude. Demographic changes are slow, while the rapid variation in hours is driven by changes in employment per person rather than population size. 2. **Capital and Productivity**: High-frequency variations in capital and productivity are weakly associated with high-frequency variations in output, contrasting with the strong associations observed in slowly varying components. Growth in output per capita is linked to increases in capital stocks and productivity, with minimal changes in hours worked. 3. **Investment and Consumption**: Cyclical investment varies more (in percentage terms) than cyclical consumption, while smoothed components show comparable percentage magnitudes in the shares of output allocated to consumption and investment. 4. **Decomposition Procedure**: The observed time series are decomposed into a cyclical and growth component. The growth component is assumed to vary smoothly over time, and the method used to estimate this component is based on minimizing the sum of squared deviations from a smooth trend. 5. **Smoothness Parameter**: The smoothing parameter λ is chosen to balance the trade-off between smoothness and accuracy. A value of λ = 1600 is selected, which results in a growth component with an annual rate of change between 2.3 and 4.9 percent over the sample period. 6. **Serial Correlation Properties**: The serial correlation properties of the rapidly varying components of the data series are analyzed, showing significant persistence in these components. 7. **Aggregated Demand Components**: Consumption of services, non-durables, and government purchases are the most stable variables, while investment components are more variable. Covariability of consumption and investment with output is stronger than that of government expenditures. 8. **Factors of Production**: Hours and output have a strong and stable positive relationship, while productivity is weakly and unstably associated with output. Capital stocks are less variable than output and negatively correlated with output, while inventory stocks are positively correlated. 9. **Monetary Variables**: Correlations between nominal money, velocity, and real money with GNP are positive, but these relationships show considerable instability over time. The study provides insights into the systematic deviations from neoclassical growth theory and highlights the importance of using multiple perspectives in understanding economic fluctuations.This paper, authored by Robert J. Hodrick and Edward C. Prescott, investigates the post-war U.S. business cycles using quarterly data. The study focuses on the rapid fluctuations in real output and other macroeconomic time series, examining their comovements and serial correlation properties. Key findings include: 1. **Output Fluctuations**: Fluctuations in output are positively associated with changes in hours worked, with similar magnitude. Demographic changes are slow, while the rapid variation in hours is driven by changes in employment per person rather than population size. 2. **Capital and Productivity**: High-frequency variations in capital and productivity are weakly associated with high-frequency variations in output, contrasting with the strong associations observed in slowly varying components. Growth in output per capita is linked to increases in capital stocks and productivity, with minimal changes in hours worked. 3. **Investment and Consumption**: Cyclical investment varies more (in percentage terms) than cyclical consumption, while smoothed components show comparable percentage magnitudes in the shares of output allocated to consumption and investment. 4. **Decomposition Procedure**: The observed time series are decomposed into a cyclical and growth component. The growth component is assumed to vary smoothly over time, and the method used to estimate this component is based on minimizing the sum of squared deviations from a smooth trend. 5. **Smoothness Parameter**: The smoothing parameter λ is chosen to balance the trade-off between smoothness and accuracy. A value of λ = 1600 is selected, which results in a growth component with an annual rate of change between 2.3 and 4.9 percent over the sample period. 6. **Serial Correlation Properties**: The serial correlation properties of the rapidly varying components of the data series are analyzed, showing significant persistence in these components. 7. **Aggregated Demand Components**: Consumption of services, non-durables, and government purchases are the most stable variables, while investment components are more variable. Covariability of consumption and investment with output is stronger than that of government expenditures. 8. **Factors of Production**: Hours and output have a strong and stable positive relationship, while productivity is weakly and unstably associated with output. Capital stocks are less variable than output and negatively correlated with output, while inventory stocks are positively correlated. 9. **Monetary Variables**: Correlations between nominal money, velocity, and real money with GNP are positive, but these relationships show considerable instability over time. The study provides insights into the systematic deviations from neoclassical growth theory and highlights the importance of using multiple perspectives in understanding economic fluctuations.