13. Other Possible Experiments
13.1 Combinations of Policies
13.2 Effects of Changing State and Local Government Variables
13.3 Imposing Rational Expectations on the Model
13.4 Making Major Changes to the Model
13.5 Supply Side Experiments
13.6 Counterfactual Experiments
References

The suggested experiments in this manual by no means exhaust the possible experiments that can be performed. Indeed, the manual is really only meant to get you started on your way to your own analysis of macroeconomic questions and issues. This chapter presents a few more possible experiments for you to ponder.

13.1 Combinations of Policies
It is best when first learning about the properties of a model to change only one exogenous variable at a time. Otherwise, one can get hopelessly lost in trying to figure out what is affecting what. In practice, however, one is usually concerned with more than one exogenous variable at a time. The government may want to know the consequences of changing both taxes and government expenditures at the same time. A business forecaster may want to know the outcome of an increase in import prices and an increase in exports. You would probably want to change state and local government expenditures or taxes at the same time that you change federal grants in aid to state and local governments.

Now that you have gone through the workbook, you should not be shy about trying more complex sets of exogenous variable changes. If you know the consequences of changing one variable at a time, you should be able to explain the outcome when many variables are changed. A common type of experiment to perform is to pick a target path for some endogenous variable, say the federal government deficit, and keep changing policy variables until the target path is roughly met. You can answer questions like the following. What combinations of monetary and fiscal policy changes would lead to the target path being met, and are any of these combinations politically feasible? The variety of these types of experiments is quite large. Note also that you can phase in changes in policy variables. It is not necessary, for example, to have COG change by $20 billion from the first quarter on or to have RS change by one percentage point beginning immediately. The changes can differ by quarters and gradually work up to the final change that is desired.

Don't forget that any experiment that you choose can be performed with different versions of the model. The types of changes in the model that were made in Chapters 9-11 can be made for any experiment.

13.2 Effects of Changing State and Local Government Variables
The tax and spending variables of the state and local government sector are similar to those of the federal government sector. These variables are changed using option 3 of the main menu. The same types of experiments that were performed in Chapter 5 for the federal government can be performed for the state and local governments.
13.3 Imposing Rational Expectations on the Model
In some cases it is possible to impose rational expectations on the model. Consider the bond market and the bond rate RB. RB is determined in the model by the term structure equation 23, where RB is a function of current and lagged values of the short term interest rate RS. If there are rational expectations in the bond market, then RB should instead be a function of current and expected future values of RS, where the expected future values of RS are what the model predicts them to be.

Say we take an seven quarter horizon and we take RB to the be average of RS and the next six future values of RS:

RB = (1/7)(RS + RS+1 + RS+2 + RS+3 + RS+4 + RS+5 + RS+6)

where the future values of RS are those predicted by the model. Can this version of the model be analyzed using the program. The answer is yes, with a little extra work. The way this is done is as follows.

  1. Specify the above equation for RB and the same equation for RM. Drop equations 23 24.
  2. Pick a prediction period, say 2011:3-2013:3. Choose eight future values of RS for the eight quarter period beyond the end of the prediction period (i.e., for the period 2013:4-2015:3). These eight values will remain the same throughout the analysis; they are your guesses as to what the RS values will be in these eight quarters.
  3. Given your guessed values and the base values of RS, compute RB from the above equation for each quarter of the prediction period (2011:3-2013:3). Do the same for RM. (If the RM equation is the same as the RB equation, then RM is always equal to RB.) Enter these values of RB and RM into the program (you can do this because equations 23 and 24 are dropped and thus RB and RM are exogenous).
  4. Solve the model for the 2011:3-2013:3 period (making no other changes). The new solution values of RS will in general be different from the base values you used to compute RB and RM. Now use these new values of RS to compute new values of RB and RM and enter the new values of RB and RM into the program. Solve the model again. Use the new values of RS to compute new values of RB and RM, enter the new values of RB and RM, and solve again. Keep doing this until the new solution values of RS are close to the values from the previous solution. At this point you have converged. The values of RB and RM are consistent with the future values of RS, and expectations in the bond and mortgage market can be said to be rational. Convergence can usually be achieved to a reasonable level of accuracy in less than 10 iterations.
  5. You are not really done at this point, however, because presumably you would like to use this new version of the model to analyze policy changes. Call the last dataset you created in step 4 (the dataset for which convergence was achieved) BASER. This is your base dataset for the new version of the model. Now take BASER as your base dataset and make a policy change, such as a change in COG. Solve the model, and call the new dataset NEWA. (Remember that the use of BASER as the base dataset means that RB and RM are treated as exogenous.) NEWA is not, however, the final dataset to compare to BASER because the predicted values of RS in NEWA are not consistent with the values of RB and RM that are in the dataset. You must now change the values of RB and RM (using the above equation) to be consistent with the new values of RS. Enter these in the program and solve again. Keep doing this until you reach convergence. Call the dataset at the point of convergence NEWR.
  6. You can now compare the solution values in NEWR with those in BASER. These differences are the effects of the policy change in the new version of the model, the version in which there are rational expectations in the bond and mortgage markets.

If you work through and understand this example, you can probably think of other ways of adding rational expectations to the model. (See Section 11.7 in Fair (1984) for the case in which there are rational expectations in the stock market.) Iteration in the above manner is fairly straightforward and not too much extra work once you get practiced.

13.4 Making Major Changes to the Model
The program is limited in how much you can change the model. You can drop equations, change coefficients, and add or subtract right hand side variables. You cannot, however, add new equations (except ones that have been dropped previously), change the left hand side variable in existing equations, or reestimate the equations. Fortunately, there is software that allows these types of changes to be made. If you use the US model in EViews or Fair-Parke, respecify the existing equations, add new equations, reestimate, and then solve the new version. In fact, if you don't like anything in the US model except the identities (which no one can complain about since they are always true), you can start from scratch and specify your own stochastic equations. Once you get your version of the model specified and estimated, you can use EViews or Fair-Parke to change policy variables and examine the model's properties. The range of possibilities here is essentially endless.
13.5 Supply Side Experiments
Some "supply side" experiments are not sensible to perform within the model. The main example concerens the variable LAM in equation 94. If, say, you increase LAM, this makes labor more productive. If labor is suddenly more productive, there is more excess labor on hand, which has a negative effect on employment demand and hours paid for (JF and HF). These are not likely to be the effects one has in mind when considering exogenous productivity increases. There is simply no direct way in which productivity increases stimulate demand in the model, and if this is what one has in mind, the model is of really no use for this purpose. Supply experiments like price shocks are fine to run, but you should probably stay away from changing LAM.

Regarding supply side experiments, note that changing variables like tax rates that affect the labor force have supply side components. If personal tax rates are lowered, more people enter the labor force looking for work (the quantity of labor supplied increases). This in and of itself, however, does not create new jobs, only more people looking for jobs. Unless something is done to create new jobs, the main thing that happens when the labor force increases is that the unemployment rate increases. (A tax cut, of course, also stimulates demand, and so in this example new jobs will be created.)

13.6 Counterfactual Experiments
It is easy with the model to ask questions like "what would the economy have been like had something that was done not been done or had something that was not done been done?" These "counterfactual" questions are popular with economic historians, among others. Experiment 7.2 is a counterfactual one, where we are asking what the economy would have been like had the price of imports not risen in the 1970s.

This workbook has not stressed counterfactual experiments because it is easier to learn about the properties of the model (and hopefully about the economy) by running simpler experiments. If you have worked through the experiments in this workbook, you are now ready to launch into counterfactual experiments if you wish. You should now have no trouble understanding the results from such experiments. How would the economy have been different had President A done x, y, and z instead of what he actually did? What if c, d, and e had not happened? What if f, g, and h had happened? There is room for many term papers here, so you can now get to work.

References
Fair (1984): Specification, Estimation, and Analysis of Macroeconometric Models, Harvard University Press, 1984.
Fair (1994): Testing Macroeconometric Models, Harvard University Press, 1994.
Fair (2004): Estimating How the Macroeconomy Works, Harvard University Press, 2004.