Taxes in the benchmark data

Example of benchmark data:

   Markets  |    X       Y        W   |       CONS
   ------------------------------------------------------
       PX   |  100  -100|
       PY   |    100 -100|
       PW   |                      200|       -200
       PL   |  -20      -60               |        80
       PK   |  -60      -40               |        100
 tax  |  -20      |  20
    ------------------------------------------------------

- Taxes are negative entries in a column indicating payments by a sector. SAM does not indicate what type of tax is in place: a tax on output, on all the inputs, or on just one input.

- Corresponding positive entry should indicate government revenue, but since no government in a simplified model (the present case) the tax is redistributed as lump-sum to the consumer.

- A zero row sum for the tax indicates that all tax receipts must be paid to someone.

Calibration of benchmark tax on input

$PROD:X s:1

O:PX Q:100

I:PL Q: 20 P:2 A:CONS T:TLX

I:PK Q: 60

if supplier price of L (price received by the consumer) is 1, then buyer price (price paid by the producer) is specified as (1 + t). If the amount paid by the X sector to L (20) is equal to the tax revenue (20) Þ tax rate is 100% (TLX=t= 1=-20/-20):

· if we set supplier price PL=1 (CONS is the supplier), then the price of labor for buyers (sector X is the buyer) must be 1+t=2

· if the buyer price is unity, then the supplier price is PL=1/(1+t)=0.5

The relative price of input (PL/P) fix marginal rate of substitution on inputs MRS=const.

Note: when the benchmark price is not equal to unity, it is necessary to redefine a reference price in MPSGE, because, by default, the reference prices are equal to unity in MPSGE. Benchmark reference prices and reference quantities are needed in order to correctly fit (calibrate) the technology (production function) to the benchmark data.

Calibration of benchmark tax on output

$PROD:X s:1

O:PX Q:100 A:CONS T:TX

I:PL Q: 20

I:PK Q: 60

if buyer price (price paid by consumers) is PX=1, then supplier price of X (price received by producer) is specified as (1 - t). The tax amount paid by the X sector is equal to the tax revenue (20) Þ tax rate is 20% (TX=t = 0.2=20/100). Supplier price equals to marginal cost of production in the long run: MC = PX(1-TX). No reference price redefinition is necessary in the case of outputs, i.e. default unit normalization is applied for PX.

Note: the output tax rate (TX) will be different from the corresponding tax rate on all inputs (TI), because the tax base is different:

· marginal cost is the tax base for TI, because MC(1+TI) = PX

· PX is the tax base for TX, because MC = PX(1-TX)