Suppose that you have two groups of shocks say **SHOCK1** and **SHOCK2**. You can apply the shocks in different orders
or you can apply them both at once. Does the order in which you apply the shocks affect the results?

More precisely, there are 3 possible scenarios.

**Scenario 1.** Apply SHOCK1 to the starting data to produce updated data SIM1A.UPD. Call this SIM1A. Then apply SHOCK2 starting from
the updated data SIM1A.UPD obtained by applying SHOCK1. Call this SIM1B. Suppose that the updated data at the end of SIM1B is SIM1B.UPD

**Scenario 2.** Apply SHOCK2 to the starting data to produce updated data SIM2A.UPD. Call this SIM2A. Then apply SHOCK1 starting from
the updated data SIM2A.UPD obtained by applying SHOCK2. Call this SIM2B. Suppose that the updated data at the end of SIM2B is SIM2B.UPD

**Scenario 3.** Apply both SHOCK1 and SHOCK2 to the starting data. Call this SIM3. Suppose that the updated data at the end of SIM3
is SIM3.UPD

Suppose that the same closure is used in all simulations.

Will these simulations produce different results?

The answer depends on exactly what you mean by this question.

- The results of SIM1A and SIM2B (both sims in which SHOCK1 is applied) will be similar but different. The same shocks are applied but the starting data is different. SIM1A starts from the original starting data whereas SIM2B starts from the updated data SIM1B.UPD.
- The combined results of the two sims in Scenario 1, or of the two sims in Scenario 2 should be the same. And these should be the same as the results of Scenario 3.

To illustrate and explain the above assertions, we discuss below simulations using the GTAP model.

The results reported below were obtained using version 6.1 (August 2001) of GTAP.TAB and the version 5 GTAP data. In particular the starting data and aggregation are those supplied with version CHP10 under RunGTAP version 3.10 (June 2001). These data are based on the 10-commodity, 10-region aggregation used in Chapter 10 of the GTAP book. For more details, see the Version information for this version under RunGTAP.

In this example, SHOCK1 consists of removing all import tariffs between regions JPN (Japan) and E_U (European Union) while SHOCK2 consists of removing all imports tariffs between regions JPN (Japan) and NAM (North America - ie, US and Canada). The standard closure for this version of GTAP was used in all simulations. In order to solve the model very accurately in each case, automatic accuracy was used requiring at least 99 percent accuracy to at least 6 figures. Accuracy criterion was "data". The solution method was Gragg 8,10,12 steps.

The table below shows the vgdp (percentage change in the value of GDP) for the different regions for the various simulations and Scenarios.

vgdp SIM1A SIM1B SIM2A SIM2B SIM3 SIM1(C) SIM2(C) AUS -0.428945 -1.004211 -1.15528 -0.276768 -1.42885 -1.428848 -1.428850 NAM -0.595005 -0.474254 -0.63982 -0.429357 -1.066426 -1.066437 -1.066429 E_U -0.573541 -0.818898 -0.77885 -0.61367 -1.387743 -1.387742 -1.387744 JPN 2.519856 2.476276 2.650392 2.345955 5.05852 5.058530 5.058524 NIE -0.739434 -1.801931 -1.962532 -0.576828 -2.528039 -2.528040 -2.528039 ASN -0.769920 -1.976249 -2.1851 -0.558044 -2.73095 -2.730953 -2.730950 CHN -0.526525 -1.262104 -1.377405 -0.410229 -1.781984 -1.781983 -1.781983 SAS -0.466294 -0.916548 -0.989574 -0.392882 -1.378569 -1.378568 -1.378568 LTN -0.403943 -1.278396 -1.37138 -0.310044 -1.677171 -1.677175 -1.677172 ROW -0.826465 -0.639811 -0.697167 -0.769185 -1.460988 -1.460988 -1.460989

The results in column SIM1(C) are the combined results from SIM1A and SIM1B, compounded by the formula 100*[(1+x1/100)*(1+x2/100)-1] where x1 and x2 are the results from SIM1A and SIM1B respectively. [This is the correct way to combine percentage change results from two simulations.] Similarly the results in column SIM2(C) are the combined results from SIM2A and SIM2B.

- The shocks in simulations SIM1A and SIM2B are the same, but these simulations start from different data. This explains why, for example, the JPN results (2.519 in SIM1A and 2.345 in SIM2B) are similar but slightly different.
- The combined results [in columns SIM1(C) and SIM2(C)] are almost identical and they are almost identical to the results of SIM3. This illustrates the second point above that the combined results are not affected by the order of applying the shocks.

Not all variables in the model would show such good agreement. Similar agreement should be obtained for all linear variables which come from a
natural levels variable (as does vgdp). Variables such as qgdp (GPD quantity index) and pgpd (GDP price index) do not have a natural levels
variable associated with them. The combined results for such variables will not, in general, be quite the same, but will depend slightly on the
order in which the shocks are applied. [We say that the results for such variables are somewhat **path dependent**.]

The qgdp results for Japan from the simulations above are shown below.

qgdp SIM1A SIM1B SIM2A SIM2B SIM3 SIM1(C) SIM2(C) JPN 0.140382 1.007582 0.987118 0.141348 1.146399 1.149378 1.129861

Here the combined qgdp result from SIM2A and SIM2B is slightly different from the combined result from SIM1A and SIM1B and from SIM3.

Of course most linear variables (changes or percentage changes) in most GE models do come from natural levels variables so their results are not path dependent. But price and quantity indexes of the kinds used in GTAP and ORANI are somewhat path dependent. [So are the different terms in the GTAP welfare decomposition.]

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