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An impulse response function describes who 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 is going to graph impulse response functions and generate tables to illustrate how a one unit change in the log difference in income and investment impacts consumption.
GENERATING IMPULSE RESPONSE FUNCTIONS IN STATA
Like in the previous post, calculations were made in the form of a structural vector autoregresssive model using the Cholesky decomposition on consumption, investment, and income on the German macroeconomy.
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 an old file with a new file 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 affects 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. Just like in the previous post the contemporaneous affect of a 10% in dln_inc is a little more than 4% for consumption. The affect of an unexpected increase in income would impact consumption immediately and these affects would last about one year. After the initial increase in consumption, two quarters later you would expect to see another spike in consumption as some of the feedback affects of 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 2 quarters later. Increased consumption may cause businesses to invest more on 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 increase in investment may or may not materialize. This 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. In any event there is weak evidence that some investments will occur with a sudden increase in income about 2 quarters after the windfall.
The increase in investments is shown to increase income in the short run, but the results are not statistically significant. Much like the second IRF above the increase in investments begin to start returning some income to the economy. The reaction of investment to consumption leads to the spike in the second quarter 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 the restrictions on the SVAR will be changed to see how these unexpected changes in the economy dynamically impact each other much like we saw in the description above.