EX,PIM Endogenous

EX,PIM Endogenous

The level of exports, EX, and the price of imports, PIM, are exogenous in the US model. These two variables are endogenous in the MCA, MCB, and MCC models, and one can use these models to examine how EX and PIM change when other variables change. For a fiscal policy change, such as a change in COG, federal government purchases of goods, it is the case that EX and PIM are not affected very much in the MCA, MCB, and MCC models if RS, the short term interest rate, is kept unchanged. If, on the other hand, RS is allowed to change (say the Fed responds to a decrease in COG by allowing RS to decrease), then EX and PIM are noticeably affected. A decrease in RS, for example, leads to a depreciation of the dollar against the other currencies, which increases US exports and the price of imports. Therefore, any experiment with the US model alone that results in a change in RS will be missing an important channel, namely the effects of RS on EX and PIM.

Although this problem is completely eliminated if one works with the MCA, MCB, or MCC model, these models are more difficult to work with than is the US model. It is possible, however, to approximate the effects of RS on EX and PIM and then incorporate this approximation into the US model. This approximation is as follows. An experiment was run using the MCC model in which the equation determining RS (the Fed interest rate reaction function) was dropped from the model and RS was decreased by one percentage point from its base value in 2006:1. The values of RS from 2006:2 on were kept unchanged from the base values. No other changes were made to the MCC model, which means, for example, that all the other countries' interest rate reaction functions were retained. The MCC model was solved for the RS change for the 2006:1-2009:4 period, and the percentage deviations in EX and PIM from their base values were recorded for each quarter. Let a_i denote the percentage deviation in EX in quarter i, and let b_i denote the percentage deviation in PIM in quarter i. i is 1 for 2006:1, 2 for 2006:2, and so on.

The approximate equation for EX is then:

EX = EX^* + EX^*[a₁(RS - RS^*) + a₂(RS_-1 - RS^*_-1) + ... + a₁₆(RS_-15 - RS^*_-15)]

where EX^* is the base value of EX and RS^* is the base value of RS. The approximate equation for PIM is:

PIM = PIM^* + PIM^*[b₁(RS - RS^*) + b₂(RS_-1 - RS^*_-1) + ... + b₁₆(RS_-15 - RS^*_-15)]

where PIM^* is the base value of PIM. If these two equations are added to the US model, then any change in RS relative to its base values will change EX and PIM relative to their base values, and the changes in EX and PIM will be approximately what would be the case in the MCC model.

If you want to have these two equations included in the US model, the only thing you need to do is have your password be EXPIM. The base values that are used are always the historical values up to the beginning of the forecast period and the base forecast values for the forecast period. You cannot change these base values, and you cannot modify the two approximation equations. Also, changing EX and PIM exogenously will have no effect if you are using the EXPIM option. The approximation equations override any changes you might make to EX and PIM.

The main use of the EXPIM option is when you are working with the forecast period and are running experiments off the base forecast values. Most of the experiments in The US Model Workbook are of this kind, and so you can run the experiments both with and without the EXPIM option to see how much difference the endogeneity of EX and PIM makes.

The values of a_i from the MCC model experiment are (i=1,...,16): -.00026, -.00040, -.00048, -.00052, -.00053, -.00057, -.00056, -.00055, -.00055, -.00054, -.00053, -.00052, -.00050, -.00049, -.00048, -.00047.

The values of b_i from the MCC model experiment are (i=1, ...,16): -.00228, -.00205, -.00188, -.00177, -.00136, -.00130, -.00125, -.00121, -.00103, -.00101, -.00099, -.00097, -.00087, -.00085, -.00082, -.00080.