Impulse Responses

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A shock to the i-th variable not only directly affects the i-th variable but is also transmitted to all of the other endogenous variables through the dynamic (lag) structure of the VAR. An impulse response function traces the effect of a one-time shock to one of the innovations on current and future values of the endogenous variables

If the innovations
are contemporaneously uncorrelated, interpretation of the impulse response is straightforward.

The i-th innovation
is simply a shock to the i-th endogenous variable
. Innovations, however, are usually correlated, and may be viewed as having a common component which cannot be associated with a specific variable. In order to interpret the impulses, it is common to apply a transformation
to the innovations so that they become uncorrelated:

To obtain the impulse response functions, first estimate a VAR. Then select View/Impulse Response... from the VAR toolbar. You will see a dialog box with two tabs: Display and Impulse Definition.

The Display tab provides the following options:•Display Format: displays results as a table or graph. Keep in mind that if you choose the Combined Graphs option, the Response Standard Errors option will be ignored and the standard errors will not be displayed. Note also that the output table format is ordered by response variables, not by impulse variables.

Display Information: you should enter the variables for which you wish to generate innovations (Impulses) and the variables for which you wish to observe the responses (Responses). You may either enter the name of the endogenous variables or the numbers corresponding to the ordering of the variables. For example, if you specified the VAR as GDP, M1, CPI, then you may either type,GDP CPI M1or,1 3 2The order in which you enter these variables only affects the display of results.You should also specify a positive integer for the number of periods to trace the response function. To display the accumulated responses, check the Accumulate Response box. For stationary VARs, the impulse responses should die out to zero and the accumulated responses should asymptote to some (non-zero) constant.

Response Standard Errors: provides options for computing the response standard errors. Note that analytic and/or Monte Carlo standard errors are currently not available for certain Impulse options and for vector error correction (VEC) models. If you choose Monte Carlo standard errors, you should also specify the number of repetitions to use in the appropriate edit box.

If you choose the table format, the estimated standard errors will be reported in parentheses below the responses. If you choose to display the results in multiple graphs, the graph will contain the plus/minus two standard error bands about the impulse responses. The standard error bands are not displayed in combined graphs.