**Willem Naudé**- Institute for Economics and Statistics, University of Oxford

However, using programs such as GAMS and GAUSS to illustrate the benefits of AGE modelling often just serve to add to the difficulty of understanding an already complex subject, since these programs are far from user-friendly and are quite difficult and extremely time-consuming to operate.

A potential way to ease the teaching of AGE modelling is by using TK SOLVER PLUS. This software may be suitable for teaching AGE models since (a) it is not too expensive (£395), (b) it comes conveniently on one 3 1/5 inch diskette, (c) it is straightforward to use in the context of AGE models, with two to three keyboard strokes at most needed, and (d) it contains an efficient on-line help facility to rescue the lone student experimenting late at night.

As a suggestion on how to use TK SOLVER in teaching I provide an example based on hypothetical data.

To implement an AGE model one needs a consistent database. A Social Accounting Matrix (SAM) is an example of such a consistent database and can be defined as a numerical representation of the economic cycle. A SAM therefore embodies the "only fundamental law" of economics, namely that for every expenditure there should exist a corresponding income. The following SAM was constructed (since it serves to teach the most important concept).

**Table 1:** Extremely Simple SAM (all figures in £million)

Some of the most basic principles of SAMS can be explained with the help of Table 1. For instance, the convention that all income of institutions is received alonga row and all expenditure incurred down a column. In the atble households, as the owners of production factors such as capital and labour, receive in row 2 the amount of £15360 million. The way it is spent is shown down column 2, namely £9790 million on final consumption, £2109 million on taxes to the government and £2587 million on imported goods. The balance, £874 million, is saving.

(1) Y = C + I + G + X (2) C = a + b.YD (3) YD = (1-t).Y (4) GS = t.T - G (5) X = XBAR - .RER (6) M = MBAR + .YD + .RER (7) FS = M - X (8) I = FS + GS + (YD - C - M)In these equations standard notation has been used. Y = income, YD = disposable income, t = tax rate, RER = real excahnge rate, XBAR = autonomous exports, MBAR = autonomous imports, FS = foreign saving, GS = government saving. Apart from equations (2), (5) and (7), all the expressions are identities, a characteristic that this model has in common with other aggregated macroeconomic models, such as the IMF Polak model, which is one of the models that have been applied most frequently in the world.

For the elementary static model, as illustrated in this paper, the student need only know two keyboard strokes to use TK SOLVER: the "/" stroke, to invoke a side menu of command options for use within a window, and the "=" stroke, to jump from the variable to the rule sheet and vice versa.

The "Rule Sheet" is where equations are entered. Equations are entered as they appear on
the page, with the exception that multiplication uses the computer's asterisk. Equations are
entered one under another, by pressing

Once all the equations have been entered the screen should look as in Table 2.

**Table 2:** Screen shot of Rule Sheet in TK SOLVER

===================RULESHEET=================== S Rule------------------------------- Y = C + I + G + X C = a + b*YD YD = (1-t)*Y GS = T*Y-G X = XBAR - *RER M = MBAR + *YD + *RER FS = M-X I = FS+GS+(YD-C-M) _______________________________________________

Using the "=" command the user should now jump to the variable screen. All the unknowns in the model, including the parameters, will be listed in the order in which they were entered in the Rule Sheet. The Variable Sheet should look as in Table 3.

**Table 3:** Screen shot of the Variable Sheet in TK
SOLVER

===============VARIABLE SHEET================== St Input---Name---Output-------Unit----Comment----------------- Y C I G X C a b YD t XBAR RER M MBAR FS I ______________________________________________________________

Table 3 shows that the Variable Sheet consists of six columns. The first column from the left is the "status" column, which is used to distinguish between endogenous and predetermined/exogenous variables, as will be shown below. The second column is the "input" column. In this column the base year values - from the SAM and from calibration - must be entered. It is also these values for the predetermined variables which are manipulated for policy analysis.

The "name" column contains the name of the variable, while the "output"column is reserved for the output following a perturbation/experiment. The "unit" column can be used to describe the unit of measurement used, in this case Pounds - in most cases I would recommend that the students ignore this column since most of the time the units involved will be obvious from the SAM. Finally the "comment" column can be used to keep notes, or as I prefer, to copy the coontents of the "input" column (base year dataset) into. This facilitates comparison with the "output" column after an experiment has been performed, since TK SOLVER will erase the original input once an output is generated.

The convention in AGE models is to equate all prices in the base year to 1, so that the RER is set equal to the base year value. A real exchange rate devaluation is then defined as an increase in RER and a revaluation as a decline in RER. The other parametersneed to be calibrated. In TK SOLVER this is done by first entering the values of all the knowns from the SAM in the input column. All unknowns, to be calibrated, should be set equal to 1 as an initial starting value. After this has been done, to calibrate for instance a and b, the student should jump to the Rule Sheet and in the "S" (status) column type "C" (for cancel) next to each equation, except the one in which a and b appear, namely equation 2.

Now jump back to the Variable Sheet. Because there is now only one equation that is active - i.e. not cancelled - but two unknowns to be estimated - a unique solution cannot be found. An assumption needs to be made about either the slope or the intercept of the consumption function. In the present case, saving is assumed to be small, so that it is assumed that b = 0.9. This value is entered next to be in the input column. Now type in the "status" column, next to a, "G" (for "guess"). This will ask TK SOLVER to solve for the value of a, given C, YD and b. To initiate the solver, press the function key F9. In the output column next to a will appear the value -2135.9. To take it back as an input, go to the status column next to a and press G twice, to "pull back" a and to cancel the guess status.

In a similar way the values of MBAR and XBAR must be calculated. Here it is suggested that MBAR be set equal to 1200 to reflect perhaps the country's dependency on imported consumption items, and that the marginal propensity to import be set at the high level of 0.8 to reflect the import dependency of production processes. A value of -9213.8 will be obtained if the procedure similar to the case of a is followed. Likewise XBAR is set low, equal to 200, to reflect the fact that the exports of the country under scrutiny may not be a necessary good for the rest of the world. The resulting value is found to be -952.

In a way the closure will depend on the view of the modeller as to the binding constraints in the economy. For example, in some countries the exchange rate is kept fixed. Alternatively, with a flexible exchange rate, the balance of payments (FS) effectively becomes fixed.

The internal closure will dtermine the causality between investment and saving. For instance, it is often assumed that government expenditure is fixed or rigid over the short-run due to "ratchet" effects. Thus, government saving (GS) - i.e. the governmnet deficit - would have to adjust in the face of changes in governmnet income. This again will, through equation (8), determine the level of domestic investment.

With the closure rules specified as RER and G fixed I would suggest that the students re- arrange the order of the "Names" in the Variable Sheet, with the endogenous variables at the top, and the closure rules followed by the exogenous variables at the bottom - this is just to keep track of what is going on. The "Names" can be moved by using the "/" command and choosing "move" from the menu. The Variable Sheet should now look as follows.

**Table 4:** Final variable Sheet

=================VARIABLE SHEET================ St Input---Name---Output-------------Unit------Comment G 15360 Y 15360 G 9790 C 9790 G 1421 I 1421 G -888 GS -888 G 1435 FS 1435 G 1152 X 1152 G 2587 M 2587 G 13251 YD 13251 1 RER 2997 G -2135 a 0.9 b .137 t 200 XBAR -952 1200 MBAR 0.8 -9213 ______________________________________________________________Note that in Table 4 "G"s have been inserted in the status column next to each endogenous variable. The student should remember to "uncancel" all the equations in her rule sheet, by entering "C" again over the current "C"s. Now she should go back to the variable screen and press F9. If the calibration and closure have been correctly specified, the base year solution as found in the SAM. should be replaced in the output column. This means that the model is ready for experiments to be performed.

As an example of performing experiments on TK SOLVER and justifying the results from within the model, consider the implementation of a "social wage" policy by government, aimed at providing social safety nets. The budgetary implication of this policy is assumed to be that government expenditure (G) increase by 10 percent, from 2997 million to 3296.7 million.

In TK SOLVER this new value for G is entered in the input column next to G. To solve the model with this new value, press F9. The new values for the endogenous variables appear in the output column (see Table 5).

In Table 5 only the endogenous variables and the closure rules are shown, since the exogenous variables (apart from G) are unchanged.

By comparing the values in the output column with those in the comment column, the macroeconomic impact of the increased government expenditure cn be deduced. It is noticeable that GDP has increased slightl, by 0.006 percent to 15509. Consequently it is so be expected that consumption also increase slightly. The more substantial effects are on the government budget deficit (GS) which increases to 1167.22. Because of higher income, imports increase slightly, and this widens the balance of payments deficit. This amounts to an increase in foreign saving, but is not enough to offset the negative effects of increased consumption and government expenditure on GDP.

**Table 5:** Screen shot after experiment 1 - a 10
percent increase in G

=================VARIABLE SHEET================= St Input---Name---Output--------Unit-------Comment----------- Y 15509.112 15360 C 9905.77 9790 I 1154.64 1421 GS -1167.226 -888 FS 1537 1435 X 1152 1152 M 2689.91 2587 YD 13379.638 13251 1 RER 1 3296.7G 2997 ______________________________________________________________

It is important that students learn that the particular effects obtained from each experiment depend on the closure under wich it was performed. From Table 5 it can be seen that the above experiment was performed under the assumption of a fixed exchange rate. How would the results change if the closure was altered, i.e. under a flexible exchange rate? This can be done by fixing the balance of payments (FS) at its base year level of 1435 and making RER endogenous (inserting a "G" in RER's St column). After pressing F9 the screen should look as shown in Table 6.

The results in the output column of Table 6 reveal that an expansionary fiscal policy has more beneficial effects if the exchange rate is flexible. Compared to the results in Table 5 it is clear that GDP increases by some œ80 million more. There is also an improvement in consumption. The larger increase in output leads to larger goverment tax revenue, mitigating the impact of the social expenditure on the budget deficit. Consequently investment is not crowded out as much as when exchange rates were fixed. The reason for these benficial effects is that the greater import demand causes the exchange rate to depreciate (by 1.5 percent) and exports to increase, so that the overall balance of payments is unaffected. Thus, the beneficial effects of the flexible exchange rate are caused by mitigating the adverse impact on investment and by increasing exports.

**Table 6:** Screen shot after experiment 2 -
illustrating the effects of closure

=================VARIABLE SHEET================= St Input---Name---Output--------Unit-------Comment----------- Y 15581.12 15360 C 9961.68 9790 I 1156.44 1421 GS -1157.33 -888 RER 1.01501 1 X 1166.29 1152 M 2601.29 2587 YD 13441.763 13251 1435 FS 3296.7G

Especially in circumstances where students do not have the background to be able to learn AGE modelling on GAMS or GAUSS I am convinced that TK SOLVER can at least help the instructor to create some basic understanding of AGE modelling.

Willem Naudé

Institute for Economics and Statistics

University of Oxford

Wagner, J. (1994) Open-Economy Microeconomics on a PC using
SHAZAM. *Computers in Higher Education Economics Review*, No 21,
February, pp8-16.