Thanks to all for the help. My code is now working nicely. I plan to make some changes to the equations by converting them to equating the left sides == 0, and see if RecurrenceTable can handle it.

There is one inconvenience which I would like to eliminate. When I change the parameters of the simulation, the plot reverts back to choosing the first 5 variables as selected rather than remembering the last variables selected for display. I'm not clear on how that can be accomplished. I'm not even sure how to prompt AI to give me some hints.

Attachments:

EconSim3.nb

Progress in simulating Stock-Flow economic model.

Now however, RecurrenceTable aborts when the number of iterations is 30, but succeeds with 25 iterations. There isn't an indication of what limit has been exceeded.

The process is fairly slow, and given the more complex models promise to need 100 or more equations, handling and estimating the time limits will be necessary.

Attachments:

EconSim3.nb

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"}]

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.

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.