An impulse response function describes how shocks to a system of equations affects those equations over time. In economics, one might be interested in understanding how a sudden and unexpected change in one variable impact another variable over time. Following the data and SVAR calculations in the previous post, this entry will graph impulse response functions and generate tables to illustrate how a one-unit change in the log difference in income and investment impacts consumption.
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GENERATING IMPULSE RESPONSE FUNCTIONS IN STATA
Like in the previous post, calculations were made in the form of a structural vector autoregressive model using the Cholesky decomposition on consumption, investment, and income on the German economy.
Impulse response function and other innovations need to be saved in a file before STATA can access that file and generate graphics. The follow steps clear an existing irf file, replace the old file with a new record, and saves it where the user specifies. The last two commands are the ones that generate the IRF. Note that the “oirf” command yield “orthogonal impulse response functions,” which in this case correspond to selecting a Cholesky decomposition for the contemporaneous effects matrix.
The blue line above represents the impulse response function, and the grey band is the 95% confidence interval for the IRF. Notice how at about t= 3 (t is in quarter units), the response dies out after having a sharp bound and becomes statistically insignificant. Like in the previous post, the contemporaneous effect of 10% in dln_inc is a little more than 4% for consumption. An unexpected increase in income would impact consumption immediately, and these would last about one year. Two quarters later, after the initial increase in consumption, you would expect to see another spike in consumption as some of the feedback effects of the initial shock reverberate throughout the economy, especially investment gains.
Why the Rebound in Consumption Two Quarters Later?
The graph above shows that the unexpected increase in income tends to provide a positive jolt to investment about two quarters later. Increased consumption may cause businesses to invest more in technology and infrastructure, while households may invest more in residential housing. The large confidence interval, which includes zero indicates that after an unexpected increase in income, this investment may or may not materialize. This result makes sense as a rational producer would infer that some of the increased sales have been brought about by this windfall income, and thus making capital investments may not be a sound course of action since sales may drop off once the extra income is gone. There is weak evidence that some investments will occur with a sudden increase in income about two quarters after the windfall.
The increase in investments increases income in the short run, but the results are not statistically significant. Much like the second IRF above, the increase in investments starts to return some income to the economy. The reaction of consumption to investment gains leads to the second quarter spike in original IRF, where consumption responds to an impulse in income.
The causal interpretations above are possible because of the restrictions placed on the SVAR, which in this case conveniently followed were Cholesky. In a future post, limits on the SVAR will change to see how these unexpected changes in the economy dynamically impact each other.
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About the Author
JJ Espinoza is Senior Full Stack Data Scientist, Macroeconomist, and Real Estate Investor. He has over ten years of experience working in the world’s most admired technology and entertainment companies. JJ is highly skilled in data science, computer programming, marketing, and leading teams of data scientists. He double-majored in math and economics at UCLA before going on to earn his master’s in economics, focusing on macro econometrics and international finance.