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### 4.16 Shock Decomposition

Command: shock_decomposition [VARIABLE_NAME]…;
Command: shock_decomposition (OPTIONS…) [VARIABLE_NAME]…;

  Description

  This command computes the historical shock decomposition for a given sample based on the Kalman smoother, i.e. it decomposes the historical deviations of the endogenous variables from their respective steady state values into the contribution coming from the various shocks. The `variable_names` provided govern for which variables the decomposition is plotted.

  Note that this command must come after either `estimation` (in case of an estimated model) or `stoch_simul` (in case of a calibrated model).

  Options

  `parameter_set = `calibration` | `prior_mode` | `prior_mean` | `posterior_mode` | `posterior_mean` | `posterior_median` | `mle_mode``

    Specify the parameter set to use for running the smoother. Note that the parameter set used in subsequent commands like `stoch_simul` will be set to the specified `parameter_set`. Default value: `posterior_mean` if Metropolis has been run, `mle_mode` if MLE has been run.

  `datafile = FILENAME`

    See datafile. Useful when computing the shock decomposition on a calibrated model.

  `first_obs = INTEGER`

    See first_obs.

  `nobs = INTEGER`

    See nobs.

  `use_shock_groups [= STRING]`

    Uses shock grouping defined by the string instead of individual shocks in the decomposition. The groups of shocks are defined in the shock_groups block.

  `colormap = STRING`

    Controls the colormap used for the shocks decomposition graphs. See `colormap` in Matlab/Octave manual for valid arguments.

  `nograph`

    See nograph. Suppresses the display and creation only within the `shock_decomposition`-command, but does not affect other commands. See plot_shock_decomposition for plotting graphs.

  `init_state = BOOLEAN`

    If equal to , the shock decomposition is computed conditional on the smoothed state variables in period , i.e. the smoothed shocks starting in period are used. If equal to , the shock decomposition is computed conditional on the smoothed state variables in period . Default:

  Output

  MATLAB/Octave variable: oo_.shock_decomposition

    The results are stored in the field `oo_.shock_decomposition`, which is a three dimensional array. The first dimension contains the `M_.endo_nbr` endogenous variables. The second dimension stores in the first `M_.exo_nbr` columns the contribution of the respective shocks. Column `M_.exo_nbr+1` stores the contribution of the initial conditions, while column `M_.exo_nbr+2` stores the smoothed value of the respective endogenous variable in deviations from their steady state, i.e. the mean and trends are subtracted. The third dimension stores the time periods. Both the variables and shocks are stored in the order of declaration, i.e. `M_.endo_names` and `M_.exo_names`, respectively.

Block: shock_groups;
Block: shock_groups(OPTIONS…);

  Shocks can be regrouped for the purpose of shock decomposition. The composition of the shock groups is written in a block delimited by `shock_groups` and `end`.

  Each line defines a group of shocks as a list of exogenous variables:

      SHOCK_GROUP_NAME   = VARIABLE_1 [[,] VARIABLE_2 [,]…];
      'SHOCK GROUP NAME' = VARIABLE_1 [[,] VARIABLE_2 [,]…];

  Options

  `name = NAME`

    Specifies a name for the following definition of shock groups. It is possible to use several `shock_groups` blocks in a model file, each grouping being identified by a different name. This name must in turn be used in the `shock_decomposition` command.

  Example

      varexo e_a, e_b, e_c, e_d;

      …

      shock_groups(name=group1);
      supply = e_a, e_b;
      'aggregate demand' = e_c, e_d;
      end;

      shock_decomposition(use_shock_groups=group1);

  This example defines a shock grouping with the name `group1`, containing a set of supply and demand shocks and conducts the shock decomposition for these two groups.

Command: realtime_shock_decomposition [VARIABLE_NAME]…;
Command: realtime_shock_decomposition (OPTIONS…) [VARIABLE_NAME]…;

  Description

  This command computes the realtime historical shock decomposition for a given sample based on the Kalman smoother. For each period , it recursively computes three objects:

  - realtime historical shock decomposition for , i.e. without observing data in . This results in a standard shock decomposition being computed for each additional datapoint becoming available after `presample`.
  - forecast shock decomposition for , i.e. the -step ahead forecast made for every is decomposed in its shock contributions.
  - realtime conditional shock decomposition of the difference between the realtime historical shock decomposition and the forecast shock decomposition. If vintage is equal to , it computes the effect of shocks realizing in period , i.e. decomposes . Put differently it conducts a -period ahead shock decomposition from to , by decomposing the update step of the Kalman filter. If `vintage>0` and smaller than `nobs`, the decomposition is conducted of the forecast revision .

  Like shock_decomposition it decomposes the historical deviations of the endogenous variables from their respective steady state values into the contribution coming from the various shocks. The `variable_names` provided govern for which variables the decomposition is plotted.

  Note that this command must come after either `estimation` (in case of an estimated model) or `stoch_simul` (in case of a calibrated model).

  Options

  `parameter_set = `calibration` | `prior_mode` | `prior_mean` | `posterior_mode` | `posterior_mean` | `posterior_median` | `mle_mode``

    See parameter_set.

  `datafile = FILENAME`

    See datafile_shock_decomp.

  `first_obs = INTEGER`

    See first_obs.

  `nobs = INTEGER`

    See nobs.

  `use_shock_groups [= STRING]`

    See use_shock_groups.

  `colormap = STRING`

    See colormap.

  `nograph`

    See nograph. Only shock decompositions are computed and stored in `oo_.realtime_shock_decomposition`, `oo_.conditional_shock_decomposition` and `oo_.realtime_forecast_shock_decomposition` but no plot is made (See plot_shock_decomposition).

  `presample = INTEGER`

    Data point above which recursive realtime shock decompositions are computed, i.e. for .

  `forecast = INTEGER`

    Compute shock decompositions up to periods, i.e. get shock contributions to k-step ahead forecasts.

  `save_realtime = INTEGER_VECTOR`

    Choose for which vintages to save the full realtime shock decomposition. Default: .

  Output

  MATLAB/Octave variable: oo_.realtime_shock_decomposition

    Structure storing the results of realtime historical decompositions. Fields are three-dimensional arrays with the first two dimension equal to the ones of oo_.shock_decomposition. The third dimension stores the time periods and is therefore of size `T+forecast`. Fields are of the form:

        oo_.realtime_shock_decomposition.OBJECT

    where OBJECT is one of the following:

    `pool`

      Stores the pooled decomposition, i.e. for every realtime shock decomposition terminal period it collects the last period’s decomposition (see also plot_shock_decomposition). The third dimension of the array will have size `nobs+forecast`.

    `time_*`

      Stores the vintages of realtime historical shock decompositions if `save_realtime` is used. For example, if `save_realtime=[5]` and `forecast=8`, the third dimension will be of size 13.

  MATLAB/Octave variable: oo_.realtime_conditional_shock_decomposition

    Structure storing the results of realtime conditional decompositions. Fields are of the form:

        oo_.realtime_conditional_shock_decomposition.OBJECT

    where OBJECT is one of the following:

    `pool`

      Stores the pooled realtime conditional shock decomposition, i.e. collects the decompositions of for the terminal periods . The third dimension is of size `nobs`.

    `time_*`

      Store the vintages of -step conditional forecast shock decompositions , for . See vintage. The third dimension is of size `1+forecast`.

  MATLAB/Octave variable: oo_.realtime_forecast_shock_decomposition

    Structure storing the results of realtime forecast decompositions. Fields are of the form:

        oo_.realtime_forecast_shock_decomposition.OBJECT

    where OBJECT is one of the following:

    `pool`

      Stores the pooled realtime forecast decomposition of the -step ahead effect of shocks on the -step ahead prediction, i.e. .

    `time_*`

      Stores the vintages of -step out-of-sample forecast shock decompositions, i.e. , for . See vintage.

Command: plot_shock_decomposition [VARIABLE_NAME]…;
Command: plot_shock_decomposition (OPTIONS…) [VARIABLE_NAME]…;

  Description

  This command plots the historical shock decomposition already computed by `shock_decomposition` or `realtime_shock_decomposition`. For that reason, it must come after one of these commands. The `variable_names` provided govern which variables the decomposition is plotted for.

  Further note that, unlike the majority of Dynare commands, the options specified below are overwritten with their defaults before every call to `plot_shock_decomposition`. Hence, if you want to reuse an option in a subsequent call to `plot_shock_decomposition`, you must pass it to the command again.

  Options

  `use_shock_groups [= STRING]`

    See use_shock_groups.

  `colormap = STRING`

    See colormap.

  `nodisplay`

    See nodisplay.

  `graph_format = FORMAT`
  `graph_format = ( FORMAT, FORMAT… )`

    See graph_format.

  `detail_plot`

    Plots shock contributions using subplots, one per shock (or group of shocks). Default: not activated

  `interactive`

    Under MATLAB, add uimenus for detailed group plots. Default: not activated

  `screen_shocks`

    For large models (i.e. for models with more than shocks), plots only the shocks that have the largest historical contribution for chosen selected `variable_names`. Historical contribution is ranked by the mean absolute value of all historical contributions.

  `steadystate`

    If passed, the the -axis value of the zero line in the shock decomposition plot is translated to the steady state level. Default: not activated

  `type = `qoq` | `yoy` | `aoa``

    For quarterly data, valid arguments are: `qoq` for quarter-on-quarter plots, `yoy` for year-on-year plots of growth rates, `aoa` for annualized variables, i.e. the value in the last quarter for each year is plotted. Default value: `empty`, i.e. standard period-on-period plots (`qoq` for quarterly data).

  `fig_name = STRING`

    Specifies a user-defined keyword to be appended to the default figure name set by `plot_shock_decomposition`. This can avoid to overwrite plots in case of sequential calls to `plot_shock_decomposition`.

  `write_xls`

    Saves shock decompositions to Excel-file in the main directory, named `FILENAME_shock_decomposition_TYPE_FIG_NAME.xls`. This option requires your system to be configured to be able to write Excel files.7

  `realtime = INTEGER`

    Which kind of shock decomposition to plot. INTEGER can take following values:

    - `0`: standard historical shock decomposition. See shock_decomposition.
    - `1`: realtime historical shock decomposition. See realtime_shock_decomposition.
    - `2`: conditional realtime shock decomposition. See realtime_shock_decomposition.
    - `3`: realtime forecast shock decomposition. See realtime_shock_decomposition.

    If no vintage is requested, i.e. `vintage=0` then the pooled objects from realtime_shock_decomposition will be plotted and the respective vintage otherwise. Default:

  `vintage = INTEGER`

    Selects a particular data vintage in for which to plot the results from realtime_shock_decomposition selected via the realtime option. If the standard historical shock decomposition is selected (`realtime=0`), `vintage` will have no effect. If `vintage=0` the pooled objects from realtime_shock_decomposition will be plotted. If `vintage>0`, it plots the shock decompositions for vintage under the following scenarios:

    - `realtime=1`: the full vintage shock decomposition for
    - `realtime=2`: the conditional forecast shock decomposition from , i.e. plots and the shock contributions needed to get to the data conditional on `vintage`, with .
    - `realtime=3`: plots unconditional forecast shock decomposition from , i.e. , where and .

    Default:

#### Footnotes

### (7)

In case of Excel not being installed, https://mathworks.com/matlabcentral/fileexchange/38591-xlwrite--generate-xls-x--files-without-excel-on-mac-linux-win may be helpful.

Next: Calibrated Smoother, Previous: Model Comparison, Up: The Model file [Contents][Index]