## Wednesday, March 9, 2016

### SIM3: 1) Matches G&L's SIM @ Ts=1; 2) Invariant to Ts; 3) Always satisfies ΔH = G - T

1. Matches G&L's SIM with the sample period Ts = 1 (year)

2. Sample period (Ts) invariant

3. Satisfies ΔH = ΔG - ΔT over all intervals 

To do: calculate Y, YD and C and check that they also satisfy G&L's equations over any pair of sample times.

Limitations: Gdot := dG/dt restricted to scaled step function with step at t=0. Note that this is not a fundamental limitation of the approach, it just represents more work to add generality, and this was just a quick and easy check to make sure I could do numbers 1, 2 and 3 above.

UPDATE 1: March 12, 2016, 4:54 PM
I generalized the approach below in a new post called SIM4 to handle a much broader class of government spending functions. I just did the math at this point. If you find an error, let me know (see the note under the document of equations).
END UPDATE 1

Notes:
 My ΔG here is called G in G&L, and my ΔT is called T in G&L. I reserve G for the integrated total of all government spending since t=-inf, and T as the integrated total taxes collected since t=-inf.