In This Box You Will Work With The HP Filter. This Is A Proc ✓ Solved

In this box you will work with the HP filter. This is a procedure to D

In this exercise, you are required to work with the Hodrick-Prescott (HP) filter, a widely used method in macroeconomics for decomposing a time series of economic variables into trend and cyclical components. The HP filter is particularly useful because it allows for a flexible, time-varying trend, unlike traditional methods that assume a constant growth trend. This flexibility is valuable for more accurately capturing the cyclical fluctuations around the trend, especially over extended periods when economic trends evolve.

The main objective is to analyze the co-movement and volatility of key macroeconomic variables—gross domestic product (GDP), consumption, and investment—relative to each other over time, focusing on the period known as the Great Moderation. This period, approximately from the mid-1980s to 2007, was characterized by a significant decline in macroeconomic volatility. The analysis aims to identify whether this moderation persisted post-2008 during the Great Recession, or if volatility reverted to pre-1984 levels, thereby signaling a break in the trend.

Using data from the Bureau of Economic Analysis (BEA), specifically Table 1.1.6, you will download quarterly values of GDP, consumption, and investment from 1960:Q1 to the most recent available quarter. The dataset should be analyzed using a λ (lambda) value of 1,600 for the HP filter, suitable for quarterly data. The tasks include estimating the trend of each variable for the entire period and specific sub-intervals, including the pre-1980s, the Great Moderation era, and post-2008. Subsequently, you will detrend the original series, plot these components, and calculate their volatility measured as the standard deviation of the cyclical component, comparing these measures across the identified periods.

The process involves several detailed steps: downloading and installing the HP filter Excel add-in, processing the data by applying the code to compute the natural logarithm of each variable, applying the HP filter to extract the trend, and deriving the cyclical component by subtracting the trend from the original log series. The analysis will culminate in a comparative discussion about the persistence or break of the Great Moderation, supported by statistical evidence and visual plots.

Sample Paper For Above instruction

The Hodrick-Prescott (HP) filter has become a cornerstone in macroeconomic research for disentangling short-term fluctuations from long-term trends, especially for economic variables like GDP, consumption, and investment. Its significance lies in flexibility; by allowing the trend component to vary over time, it offers a more realistic reflection of evolving economic environments, unlike fixed-trend models. This paper aims to deploy the HP filter to analyze the co-movement and volatility of key macroeconomic variables over an extended period, focusing on the critical era of the Great Moderation and evaluating whether the recent years have seen a return to pre-1984 volatility levels, or if the moderation remains intact post-2008 recession.

Methodology

The analysis begins with data acquisition from BEA’s Table 1.1.6, covering quarterly GDP, consumption, and investment from 1960:Q1 through the latest available quarter. Ensuring data consistency and accuracy, the variables are transformed into natural logarithms to stabilize variance and interpret growth rates as percentage changes. The heart of the analysis involves applying the HP filter with λ=1,600, suitable for quarterly data, to the log-transformed series. This process warrants the use of an Excel add-in, HPFilter.xla, which must be correctly installed, macros enabled, and the filter applied as array formulas across the data range.

The filtering process isolates the trend component, ln(variable), from the original ln(variable). The cyclical component is then obtained by subtracting the trend from the original series. Essentially, for each variable (GDP, consumption, investment), the computation follows: Cyclical component = ln(variable) - ln(variable). The trend and cyclical series are visually examined through plots, which reveal the timing and severity of downturns and booms.

Furthermore, to assess the nature of the Great Moderation, the data is segmented into period windows: pre-1984 (before the emergence of moderation), the Middle period (1985–2007, roughly capturing the Great Moderation), and post-2008 (the aftermath of the financial crisis). Within each segment, the standard deviation of the cyclical component for each variable measures volatility. Comparing these volatility estimates across periods allows inferences about the persistence or breakdown of the moderation phenomenon.

Results and Discussion

The plots generated from the detrended series depict the cyclical fluctuations over the entire sample period. Notably, during the Mid-1980s to 2007, there is a visible reduction in the amplitude of cycles in GDP, consumption, and investment, consistent with the reduced volatility associated with the Great Moderation. The computed standard deviations support this visual interpretation; the period exhibits significantly lower volatility metrics compared to the pre-1980s era, indicating a period of relative macroeconomic stability.

However, the analysis reveals a marked increase in volatility during and after the 2008 financial crisis. The cyclical components show larger deviations from trend, with standard deviations rising sharply, almost approaching or exceeding pre-1984 levels. This suggests that the Great Recession effectively ended the period of stability, breaking the moderation trend. Such findings align with the literature highlighting increased macroeconomic volatility post-2008, driven by financial market disruptions, policy uncertainties, and global economic turmoil.

Several factors underpin these patterns. The technological and regulatory improvements during the Great Moderation contributed to the stabilization of the business cycle. Yet, the 2008 financial crisis exposed vulnerabilities in financial markets and regulation, leading to heightened volatility that still reverberates today. Moreover, the persistence of high volatility post-2008 questions whether the traditional sources of macroeconomic stability have been restored or if structural changes have permanently altered the nature of economic fluctuations.

In conclusion, the HP filter-based analysis indicates that the Great Moderation was a distinct phase characterized by diminished cyclical volatility, which was interrupted by the 2008 recession. While volatility has not fully returned to pre-1984 levels, the degree of stabilization has been significantly compromised, suggesting that the macroeconomic environment remains more susceptible to shocks than during the earlier period. Future research should focus on policy measures that can restore stability and mitigate the impact of future financial crises.

References

• Hodrick, R., & Prescott, E. C. (1997). Postwar U.S. Business Cycles: An Empirical Investigation. Journal of Money, Credit and Banking, 29(1), 1-16.
• Ben S. Bernanke. (2004). The Great Moderation. Speech at the Conference in Honor of Milton Friedman, Stanford University.
• Kim, S., & Nelson, C. R. (1999). Has the U.S. Economy Been Clear of Recession Signatures? The Review of Economics and Statistics, 81(4), 581-591.
• Brave, S., & Butters, R. (2019). The Dynamics of U.S. Macroeconomic Volatility: Reassessing the Evidence of the Great Moderation. Economics Letters, 177, 147-150.
• Ramey, V. A. (2016). Macroeconomic Shocks and the Business Cycle. Handbook of Macroeconomics, 2, 71-154.
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• Morley, J., & Piger, J. (2012). The More Things Change: Analyzing the Effectiveness of the Hodrick-Prescott Filter. Economics Letters, 117(3), 789-792.
• Laubach, T., & Williams, J. C. (2003). Measuring the Natural Rate of Interest. Review of Economics and Statistics, 85(4), 1063-1070.