Reproducing some of the Old QMM results

(A recap)

Andrew Pua

2025-10-28

Day 2

  1. Recap

    • Take the old QMM workfile as a given, save a new file to play around with.
    • Get acquainted with the components.
    • Try reproducing some of the RMSE/RMSPE figures.
    • Conduct a dynamic simulation and reproduce the historical simulation.
    • Conduct a simulation experiment involving a change in bgirx.

Day 2

  1. New QMM vs Old QMM

    • What the new QMM looks like
    • Small version of new QMM
    • Enlarge the small version
    • Workflow

What “solve the model” means

Deterministic solution

\[\begin{eqnarray*} Y_t&=& C_t+I_t \\ C_t &=&\widehat{\beta}_0+\widehat{\beta}_1 Y_t \\ I_t &=&\widehat{\gamma}_0+\widehat{\gamma}_1 I_{t-1} \end{eqnarray*} \] Solve for \(Y_t\) and \(C_t\) at every point in time for period under consideration.

What “solve the model” means

\[\begin{eqnarray*} Y_t &=& \frac{\widehat{\beta}_0+\widehat{\gamma}_0}{1-\widehat{\beta}_1}+\frac{\widehat{\gamma}_1}{1-\widehat{\beta}_1}I_{t-1} \\ C_t &=& \widehat{\beta}_0+\widehat{\beta}_1\left(\frac{\widehat{\beta}_0+\widehat{\gamma}_0}{1-\widehat{\beta}_1}+\frac{\widehat{\gamma}_1}{1-\widehat{\beta}_1}I_{t-1}\right) \end{eqnarray*}\]

Static vs dynamic solution

Basics

  1. Open an untouched workfile.
  2. Save a new workfile to play around with.
  3. Workfile contains series, equations, model objects. Pay attention to the icons.

Historical simulation

  1. Refer to Section 4 of the old QMM final report.
  2. Simulation period is from 1989q1 to 2002q4.

How to reproduce results

  1. Think of the workflow.

  2. Checklist

    • Copy of untouched workfile - what does it look like?
    • Equations
    • Model object
    • Solve model over 1989q1 to 2002q4: What changed?

How to reproduce results

  1. Compute RMSE/RMSPE.

    • series sq_diff_mm = (mm-mm_0)^2
    • series sq_per_diff_mm = ((mm-mm_0)/mm)^2
    • scalar rmse_mm = @sqrt(@mean(sq_diff_mm))
    • scalar rmspe_mm = @sqrt(@mean(sq_per_diff_mm))*100

  2. Try reproducing one of the rows of the table.

How to reproduce Figure 2

  1. Simulation period is 1981q1 to 2002q4
  2. You want to compare the actual path of a list of tracked endogenous variables against their baseline paths produced by the QMM.
  3. Relatively straightforward with Proc > Make Graph.

Context of Figure 3

  1. Simulation period is 1981q1 to 2002q4
  2. Experiment: A 10 percent increase each quarter in BSP’s gross international reserves (bgirx) on which outcomes ?

How to reproduce Figure 3

  1. Think of the workflow. Are you planning to change an exogenous or an endogenous variable?

  2. Checklist if changing an exogenous variable:

    • Baseline _0
    • Define new scenario
    • Create a new path for the exogenous variables _1
    • Solve under new scenario

How to reproduce Figure 3

  1. Checklist if changing an endogenous variable:

    • Baseline _0
    • Define new scenario
    • Create a new path for the endogenous variable _A – this is the “add factor”, choose an endogenous variable shift
    • Solve under new scenario