Group Abstract

Message Boards

WOLFRAM COMMUNITY

89 Views

5 Replies

1 Total Like

View groups...

Follow this post

Share this post:

GROUPS:

Syntax error using RecurrenceTable function simulatin Stock-Flow Consistent model

Lawrence Winkler

Lawrence Winkler, UW Madison (retired)

Posted 3 days ago

See attached NB. A manipulate module using the RecurrenceTable function detects a syntax error which I have been unable to see. More eyes on what might be obvious to others might help.

POSTED BY: Lawrence Winkler

5 Replies

Sort By:

Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 2 days ago

You use `g` as a function in `RecurrenceTable` and as a number in `Manipulate`. I tried this: RecurrenceTable[{y[t] == Subscript[c, s][t] + Subscript[g, s][t], Subscript[\[CapitalDelta]h, s][t] == Subscript[h, s][t] - Subscript[h, s][t - 1], Subscript[\[CapitalDelta]h, h][t] == Subscript[h, h][t] - Subscript[h, h][t - 1], Subscript[c, s][t] == Subscript[c, d][t], Subscript[g, s][t] == Subscript[g, d][t], Subscript[c, d][t] == c1 yd[t] + c2 Subscript[h, h][t - 1], td[t] == \[Theta] y[t - 1], yd[t] == y[t] - \[Theta] y[t - 1], y[0] == 0, Subscript[c, s][0] == 0, yd[0] == 0, Subscript[h, h][0] == 0, Subscript[h, s][0] == 0, td[0] == 0} /. {Subscript[g, s] -> g, \[Theta] -> taxRate, c1 -> consumeRate, c2 -> overspend} /. {taxRate -> 1, consumeRate -> 1, overspend -> 1}, {g, td, y, yd, Subscript[c, d], Subscript[c, s], Subscript[g, d], Subscript[h, h], Subscript[h, s], Subscript[\[CapitalDelta]h, h], Subscript[\[CapitalDelta]h, s]}, {t, 1, 50}] and it gives this warning: RecurrenceTable::underdet: There are more dependent variables than equations, so the system is underdetermined.

You use g as a function in RecurrenceTable and as a number in Manipulate. I tried this:

RecurrenceTable[{y[t] == Subscript[c, s][t] + Subscript[g, s][t], 
    Subscript[\[CapitalDelta]h, s][t] == 
     Subscript[h, s][t] - Subscript[h, s][t - 1], 
    Subscript[\[CapitalDelta]h, h][t] == 
     Subscript[h, h][t] - Subscript[h, h][t - 1], 
    Subscript[c, s][t] == Subscript[c, d][t], 
    Subscript[g, s][t] == Subscript[g, d][t], 
    Subscript[c, d][t] == c1 yd[t] + c2 Subscript[h, h][t - 1], 
    td[t] == \[Theta] y[t - 1], yd[t] == y[t] - \[Theta] y[t - 1], 
    y[0] == 0, Subscript[c, s][0] == 0, yd[0] == 0, 
    Subscript[h, h][0] == 0, Subscript[h, s][0] == 0, 
    td[0] == 0} /. {Subscript[g, s] -> g, \[Theta] -> taxRate, 
    c1 -> consumeRate, c2 -> overspend} /. {taxRate -> 1, 
   consumeRate -> 1, overspend -> 1}, {g, td, y, yd, Subscript[c, d], 
  Subscript[c, s], Subscript[g, d], Subscript[h, h], Subscript[h, s], 
  Subscript[\[CapitalDelta]h, h], Subscript[\[CapitalDelta]h, s]},
 {t, 1, 50}]

and it gives this warning:

RecurrenceTable::underdet: There are more dependent variables than equations, so the system is underdetermined.

POSTED BY: Gianluca Gorni

Karl Fraser

Posted 1 hour ago

sanity check ClearAll[y, yd, td, cd, hs, cs, gs, ts, hh, dHs, dHh]; eqns = {y[t] == cs[t] + gs[t],dHs[t] == hs[t] - hs[t - 1],dHh[t] == hh[t] - hh[t - 1],cs[t] == cd[t],gs[t] == gd[t],ts[t] == td[t],cd[t] == c1 * yd[t] + c2 * hh[t - 1],td[t] == \[Theta] * y[t - 1],yd[t] == y[t] - \[Theta] * y[t - 1],y[0] == 0, cs[0] == 0,yd[0] == 0, hh[0] == 0,hs[0] == 0, td[0] == 0, gs[0] == 0,gs[1] == g };(all your recurrences) vars = {y, yd, td, cd, hs, cs, gs, ts, hh, dHs, dHh}; init = {y[0] == 0, cs[0] == 0, yd[0] == 0, hh[0] == 0, hs[0] == 0, td[0] == 0, gs[0] == 0, dHh[0] == 0, gs[1] == 20}; RecurrenceTable[Join[eqns, init], vars, {t, 1, 10}] Still gives - There are more dependent variables than equations, so the system is underdetermined. So I rewrote it, think I got it correct (, but hope it helps). ClearAll[y, taxes, yd, c, h, hg, g]; Manipulate[ Module[{sim}, sim = RecurrenceTable[{ g[t] == Piecewise[{{g1, t <= switchTime}, {g2, t > switchTime}}], taxes[t] == taxRate y[t], yd[t] == y[t] - taxes[t], c[t] == income yd[t] + wealth h[t - 1], y[t] == c[t] + g[t], h[t] == h[t - 1] + yd[t] - c[t], hg[t] == hg[t - 1] + g[t] - taxes[t], h[0] == 0, hg[0] == 0}, {y, c, yd, taxes, h, hg, g}, {t, 1, periods}]; ListLinePlot[ sim[[All, #]] & /@ {1, 2, 5, 7}, PlotLegends -> {"y", "c", "h", "g"}, PlotRange -> All, AxesLabel -> {"Time", "Value"}, ImageSize -> Large]] , {{g1, 20, "initial g"}, 1, 30, 1, Appearance -> "Labeled"}, {{g2, 30, "new g"}, 1, 50, 1, Appearance -> "Labeled"}, {{taxRate, 0.2, "tax rate \[Theta]"}, 0., 1., 0.05, Appearance -> "Labeled"}, {{income, 0.6, "income \[Alpha]1"}, 0., 0.99, 0.05, Appearance -> "Labeled"}, {{wealth, 0.4, "wealth \[Alpha]2"}, 0., 1., 0.05, Appearance -> "Labeled"}, {{switchTime, 20, "switch time"}, 1, 49, 1, Appearance -> "Labeled"}, {{periods, 50, "periods"}, 20, 100, 1, Appearance -> "Labeled"}]

sanity check

ClearAll[y, yd, td, cd, hs, cs, gs, ts, hh, dHs, dHh];
eqns = {y[t] == cs[t] + gs[t],dHs[t] == hs[t] - hs[t - 1],dHh[t] == hh[t] - hh[t - 1],cs[t] == cd[t],gs[t] ==     gd[t],ts[t] == td[t],cd[t] == c1 * yd[t] + c2 * hh[t - 1],td[t] == \[Theta] * y[t - 1],yd[t] == y[t] - \[Theta] * y[t - 1],y[0] == 0, cs[0] == 0,yd[0] == 0, hh[0] == 0,hs[0] == 0, td[0] == 0, gs[0] == 0,gs[1] == g };(*all your recurrences*)
vars = {y, yd, td, cd, hs, cs, gs, ts, hh, dHs, dHh};
init = {y[0] == 0, cs[0] == 0, yd[0] == 0, hh[0] == 0, hs[0] == 0, td[0] == 0, gs[0] == 0, dHh[0] == 0, gs[1] == 20};
RecurrenceTable[Join[eqns, init], vars, {t, 1, 10}]

Still gives -

There are more dependent variables than equations, so the system is underdetermined.

So I rewrote it, think I got it correct (, but hope it helps).

ClearAll[y, taxes, yd, c, h, hg, g];
Manipulate[
 Module[{sim},
  sim =
   RecurrenceTable[{
     g[t] == Piecewise[{{g1, t <= switchTime}, {g2, t > switchTime}}],
     taxes[t] == taxRate y[t],
     yd[t] == y[t] - taxes[t],
     c[t] == income yd[t] + wealth h[t - 1],
     y[t] == c[t] + g[t],
     h[t] == h[t - 1] + yd[t] - c[t],
     hg[t] == hg[t - 1] + g[t] - taxes[t],
     h[0] == 0,
     hg[0] == 0},
    {y, c, yd, taxes, h, hg, g},
    {t, 1, periods}];
  ListLinePlot[
   sim[[All, #]] & /@ {1, 2, 5, 7},
   PlotLegends -> {"y", "c", "h", "g"},
   PlotRange -> All,
   AxesLabel -> {"Time", "Value"},
   ImageSize -> Large]]
 , {{g1, 20, "initial g"}, 1, 30, 1, Appearance -> "Labeled"},
      {{g2, 30, "new g"}, 1, 50, 1, Appearance -> "Labeled"},
      {{taxRate, 0.2, "tax rate \[Theta]"}, 0., 1., 0.05, 
  Appearance -> "Labeled"},
      {{income, 0.6, "income \[Alpha]1"}, 0., 0.99, 0.05, 
  Appearance -> "Labeled"},
      {{wealth, 0.4, "wealth \[Alpha]2"}, 0., 1., 0.05, 
  Appearance -> "Labeled"},
      {{switchTime, 20, "switch time"}, 1, 49, 1, 
  Appearance -> "Labeled"}, {{periods, 50, "periods"}, 20, 100, 1, 
  Appearance -> "Labeled"}]

POSTED BY: Karl Fraser

Lawrence Winkler

Lawrence Winkler, UW Madison (retired)

Posted 14 hours ago

I fixed most errors but still have issues. The key is: I want to use RecurrenceTable (and other functions) to simulate the models in Monetary Economics by Wynne Godley, et al. These models define what is called Stock-flow consistent models. The Levy economic institute, part of Bard College, which is associated with Columbia University continue to research this area. From what I've seen, there are packaged solutions in R (and some other modeling systems like EViews) simulate these models using the typical array and do loop constructions which, in my mind, hide the basic models behind these constructs, or are black-boxes. It seems like Mathematica should be able to simulate these models with relative ease using RecurrenceTable. I've cleaned up some of the coding thus far, but still mathematica is unhappy with the result. In this latest interation, Mathematica results in dumping some RecurrenceTable without generating a computation. (and giving no reason for its failure). Attachments: EconSim3.nb

POSTED BY: Lawrence Winkler

Lawrence Winkler

Lawrence Winkler, UW Madison (retired)

Posted 1 day ago

Thanks to all. I haven't been using Show Expression. This gives me some critical information I haven't used before, not only this issue but some from past modules where I fat-fingered some entry.

POSTED BY: Lawrence Winkler

Karl Fraser

Posted 2 days ago

Hello, Looking VERY closely at the ClearAll line, one can see that comma after gd is smaller than the other commas. If you use Show Expression from Cell Menu, you see the offending section as: RowBox[{ SubscriptBox["g", RowBox[{"d", ",", " "}]], Clearly there is a corruption after the gs Subscript and in the gd Subscript. The small comma is part of the Subscript, so delete it and add the comma after the Subscript.

POSTED BY: Karl Fraser

Reply to this discussion

Reply Preview

Attachments

Remove Add a file to this post

Follow this discussion

or Discard

Feedback