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An 'Optimal' Phillips-Curve
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I F.\(
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AN 'OPTIMAL' PHILLIPS-CURVE J.
Elmeskov
Th" t:Clllllllllir CUI/wit. ClljJfllh"/iI'll. Df'llIIwrh
Abstract . The paper describes how an optimization p r ocedure may be utilized to uncover a relationship between wage - in f lation and unemp l oyment in a macro econometric model taking the who l e interp l ay of a ll the model ' s equ ations into consideration . The idea is to select a number of policy i nstrument s and then with the use of these instruments to mi nim i ze wage - increases whi le the unemployment r ate i s kept fixed . This is done for a number of diffe r ent unemployment rat es , and the result is an effic i ency frontier which connects points of min i mum wage increases obtainable for a certain rate of unemployment . The shape of this efficiency frontier is i nfluenced by the interp l ay of a l l equations in the model and by the limitations put on the use of the policy instruments . The shape of the efficiency f r ontie r is discussed and it is compared with the shape of the partial re l ationsh i p between unemployment and wage-inflation in the mode l' s wage - equation seen in isolat i on. Keywords . Economics; Identification ; Modelling; Optimisati on; Par ame t e r Estimation .
I NI'ROD ucr ION
the picture . Withi n certain politically de termined boundari es the government may choose the values of its ins t rument a l var iables so as to realize the combi nation of inflation and unemployment which it finds most favourable . In making this choi ce the government is confronted wi th a tr ade- off between obtainable unemployment and i nflation rates .
Seen in isolat i on a wage - relation of the tra ditional Phillips - curve type determines a well - defined trade - off between unemployment and (wage-)inflation. This trade - off can be shown graphically by keep i ng al l other var i ables in the wage - relation constant and then plotting corresponding values of inflation and unemployment rates in a diagram . But this t r ade-off is not very informative when the wage-relation is embedded in a simultaneous macro - economic model and questions are asked about the relation between unemployment and pay rises for the model as a whole . I t has no longer any meaning to regard a trade - off where the other variables in the wage - re l a tion are not free to vary. If , for instance , pay rises are increased by a lowe r ing of the unemployment rate this will increase prices , and with price increases entering the wage relation pay rises will be further increased . Obviously the wage-relation interacts with the other equations of the model , and the relationship between unemployment and inflation in some sense implicitly given in the model may look somewhat different from the trade - off in the isolated wage - relation .
The question is now how to uncover such a political l y obtainable trade - off be t ween un employment and inflation . Although it may not be possible to solve the simultaneous model analytically it is obvious that diffe rent combi nations of unemployment and inflat i on can be found by simu l ating t he model wi th different va l ues f or the policy ins tr u ments. For each combi nation of values of the i nstrument a l variab l es t h e r e wil l be a co rrespo?d i ng l evel of unemployment and inflation . However , these different combinations of unemployment and inflat i on cannot be said to cons titu t e a we l l - def in ed trade - of f be tween these two var iables . P l ot t ed in a diagram with unemployment and pay- rises along the axes t he combi nations found are likely to look l i ke the result of firing a shotgun. In Chow & Megdal (1976) it is suggested , that the use of an optimization t echn i que
If one is concerned with the combinations of unemployment and inflation which are obtainable for the government it is obvious that constraints on the economic policy must enter
1S0 far only a single period is consid ered
323
324
J. Elmeskov
migth facilitate the uncovering of an implicit trade-off between unemployment and inflation . The idea , which is being follo wed here , is to se l ect a number o f i nstrumental variables that are allowed to vary within given boundaries and then min i mize the inf l ation rate while keeping the unemployment rate fixed . By repeating this procedure for a number of fixed unemployment rates an efficiency frontier is es t ab li shed, which l inks unemployment rates a nd the corresponding mi nimum pay rises obtain abl e wi t h the chosen set of instrumental var i ab l es and the boundaries imposed on their variation. If ones interest is in the political l y obtainable trade-off the instruments shou l d be those which the government is free to vary within political boundaries . If ones interes t is more in examining the comp l ex inter-relationships of the mode l the selection of instrumental variab l es may be a little more delicate . In a macro- econometric model some instruments may have exactly identical impacts on the model solution, and it is obviously only necessary to employ one instrument out of such a group of instruments . On the other hand if the models full interplay is to be set in motion one must pick as many policy instruments with different effects as possible . If only a subset of these policy variables with different effects is employed , the shape of the efficiency frontier may change drastica l ly according to which subset is being used . Also the boundaries imposed on the variat i on of the instruments are of crucial importance. One set of boundaries on the instrumental variables may make the efficiency frontier look very different from the efficiency frontier obtained with another set of boundaries . It may also be worth noting that the boundaries at least in the more political ly ori ented analysis need not only take the form of direct limitati ons put on the variations of the chosen instrumental variables . The boundaries could also take the form of re strictions on the development in certain key variables as for instance the balance of payments. One could argue , however, that such policy - induced constraints may also belong to a more techni ca l examination of the unemployment-inflation relationship in a model. This statement could find support in the fact that government policy hard l y can be described as totally exogenous . If the wage - re l ation has been estimated over a time- period where government policy has been subject to certain limitations, then it is obvious that these limitations must be drawn into consideration when testing the reasonability of the wage - relations interplay with t he rest of the model . When more than one period of time is consi dered (what is usually necessary to bring
the full i nterplay of all equations in the model into action) the non-dominated combi nations of unemployment rates and inflatio n rates be l ong to a 2*T-dimensional space , where T is the number of time periods . To be able to give a graphic presentation of the solutions to the experiments reported below i t has been decided to minimize the average pay increases over the time horizon for given constant unemployment rates . This means that it may be possible to get lower mini mum average pay increases for the same ave rage unemployment rate s by letting the unem ployment rate be free to vary ove r the time horizon. MODEL , WAGE - RELATION AND DATA The computations which will be described below were carried through with a medium - sized (163 equations) econometric mode l of the Danish economy , SMEC3. The model which is used for projections ~nd policy analysis by the Economic Council is based on yearly data. It is a traditional demand - oriented model in the Keynesian tradition . The behavioral relations in the model include private consumption, fixed investments , inventories , exports , imports and prices. The model has a very aggregated structure with on ly one endogenous production sector (private sector minus primary production ) . On the institut ional side the description of taxes and othe r transfers to and from the public sector is rather de tailed. The model does not contain any monetary sector. Interest rates are assumed to be unaffected by the different economic developments in the experiments described below (this assumption may not be quite as unreasonable as it sounds , as the monetary p olicy in Denmark to a large extent is cond ucted to secure the financing of the balance of payments deficit , w~ich is kept cons tant through the experiments , cf . be l ow) . The wage - equation which describes the annual percentage increas e in hourly earnings in the endogenous production sector is n~t estimated by means of regr ession analysis . 2 An independent government - financed advisory body 3It is the nominal interest rate which is kept fixed throughout . Undoubtedly a fixed real rate of interest would have been more reasonable. 4Actually , this wage- relation is not normally included in SMEC3, which is usually used with an exogenous wage r ate . The wage - rela tion was constructed in connection with a research project at the University of Copen hagen (Rosted (1980)), where it was used in another model. Despite the transplantation which includes a shift in the data used, the relation fits the wage - development through the 197 0 'es rather well .
An 'Optimal' Phillips - Curve
Instead the coefficients have been 'guesstimated ' on the basis of different available investigations concerning the link between wage - increases and the other factors entering the wage - equation. The calculations reported below may be seen as a test for the reliability of the equation . The relation can be written: DW + + + + + +
.5 .8
* DPC .7 * Dm .5 * DPR .5 * ATP . 1 * l / UR . 05 * log (ARUB)
(1 )
where DW
Percentage increase in hourly earnings
DPC
Average price- increase of private consumption goods over the last two years
Dm
Percentage change in working time
DPR
Average productivity increases over the last three years
mp
Absolute change in direct tax pressure on wage income
UR
Mean rate of unemployment over the last two years
ARUB
Average unemployment benefit relative to wage over the last two years
The first term (apart from the constant) in dicates that price rises will press up the hourly earnings although the wage lags behind prices and price rises are not fully compensated by wage increases. A large part of the effect from price increases can be ascribed to the indexation of wages which was in force in Denmark when the computations were made but recently has been abandoned (at least temporarily). The equations determining prices of final demand components in SMEC3 links the development in fac tor costs and import prices together by means of input-output based weights. This means that the model contains a wage - price spiral . This interdependence is strengthened by an assumption of no change in the functional distribution of income meaning that the profit per unit of output is linked to the development in wages corrected for pro ductivity changes. The term representing the influence of the percentage change in working time is not very interesting in connection with the present subject as the working time is treated as an exogenous variable throughout this paper . In the version of the SMEC3 model used for the present purpose changes in productivity from the base-line simulation is generated
325
in a rather simple relationshipS linking employment to production with a short lag. The scope for productivity developments very different from the base- line simulation is rather limited . This is of course a draw back in simulations where the development in production , investment etc. is quite different from what it was in the base- l ine simulation . As a result of this nearly exogenous growth in productivity , the productivity term in the wage - relation wi l l give approxi mately the same contributi on to wage -i ncreases no matter how the rest of the model be haves . The tax pressure is included in the wage-equation from the motivation that wage - earners will try to seek compensation for higher taxes through wage increases. The fifth term in the wage - equation is the traditional Phillips - curve term. Finally the wage - equation includes a term which describes the influence from the size of unemployment benefits relative to wage . In turn the size of the unemployment benefit is influenced by the wage increases as the model includes an equation describing the mechanism through which the size of the un employment benefit is regulated . However, the main effect from wages on unemployment bene fits appears with a lag . The inclusion of this term in the wage-equation means that besides the wage - price spiral the model also contains a wage-unemployment benefit spiral. utilizing the data base behind the forecast from the chairmanship of the Economic Council of june 1980 the model was simulated for the six years 1978-83 . This simulation for med the base-line upon which the experiments was conducted. The mean rate of unemployment and mean wage increases for the ghole period is plotted as point 0 in fig. 1. Afterwards 11 policy variables were chosen as instruments to minimize the average wage increases over the time period while keeping the unemployment rate pegged to a specific figure. The instruments chosen included dif ferent kinds of government expenditure , direct and indirect tax rates, investment taxes and depreciation rates. A set of boundaries indicating the possible field of variation was imposed on the instruments. Also a set of more technical bounds was im5
For computational reasons it was not possible to use the vintage - relationship normally included in this version of SMEC3 to explain productivity development .
6 Care must be exercised in the interpretation of this point in connection with the shown curves, as the curves are drawn for a fixed rate of unemployment through all six periods , where the unemployment rate behind point 0 is fluctuating over the time horizon.
J. Elmeskov
326
TABLE 1
Decomposition of average wage increases
Rate of unemployment
3 5 7 9
constant
.5 .5 .5 .5
% % % %
prices
5.5 4.4 4.1 4.0
Contribution from working producdirect time tivity tax
.3 .3 .3 .3
posed on the possible solutions (these can be exemplified by the upper limit of 100 % on capacity utilization). As indicated in the introduction an emphasis on the politically obtainable efficiency frontier combining points of fixed unemployment rates and minimum average wage increases could lead to the introduction of boundaries which are not put directly on the variation of the policy instruments. As an example of such a political constraint (apart from those bounding the variation of the policy instruments) it has been chosen to conduct the experiments under the condition that the balance of payments in none of the years must be worse than in the baseline run. For the Danish economy the balance of payments is probably the most prominent limitation for political actions, although one can discuss the rather arbitrary bound consisting of the b.o.p.development in the base-line simulation. However, for the present purpose it does not matter very much exactly which limitation is put on the b.o.p.development as long as a limitation is being put. RESULTS With the model, data, instruments and bounds as described above 4 optimizations were conducted. In each the rate of unemployment was pegged to a fixed rate (3, 5, 7 and 9 % respectivily) and the average yearly increases in hourly earnings were minimized over the chosen period. The resulting efficiency frontier is drawn in fig. 1 (the curve marked 'optimal' Phillips-curve). To be able to compare this with the partial trade-off between unemployment and pay increases from the wage relation seen in isolation the latter has been drawn by inserting the four fixed unemployment rates into the relation's unemployment term. To facilitate a comparison of the two curves the curve based on the isolated wage relation has been pushed up so that it intersects the 'optimal' Phillips-curve for a fixed rate of unemployment of 3 %. 7
The programmes used are developed by dr. Arne Drud, see Drud (1978), Drud (1979) and Drud & Meeraus (1980).
1.2 1.3 1.3 1.3
.1 .0 .0 .0
unemployment
3.1 1.9 1.4 1.1
unemp.benefit
-2.4 -2.3 -2.3 -2.2
Average wage increase
8.3 6.2 5.4 5.0
As can be seen from the figure the 'optimal' Phillips-curve is the steepest of the two curves. To see why this is the case the average wage increases in the four experiments has been decomposed in table 1 in order to see the contribution of each term in the wage-equation.
From table 1 it is readily seen that the most important factor in making the 'optimal' curve steeper is the price term. Another - although much smaller - effect in the same direction comes from the direct tax. In the opposite direction pulls both the productivity and the unemployment benefit term. The existence of the wage-price spiral in the model is of course a main factor in the explanation of the price term's contribution to the steepness of the 'optimal' Phillips-curve. When unemployment is low wage rises tend to be high and these high wage rises tend to push up price increases which in turn influence the wage rises etc. But also the balance of payments restriction is a major factor explaining the influence of the price term. The point is, that lower wage- and price-inflation improves the competitive position of Denmark relative to other countries. The improvement in the competitive position allows the government to pursue a more relaxed fiscal policy without worsening the balance of payments relative to the base-line simulation. The relaxation of the fiscal policy taking the form of an easing of indirect tax pressure tends to reduce wage increases thereby bringing about a further improvement in the competitive position etc. Of course this last mechanism interacts with the wage-price spiral to further multiply the effect. The instruments directly influencing the direct tax pressure on wage-earners show very much the same development through all the optimizations. The effect of the direct tax term which tends to make the 'optimal' Phillips-curve steeper therefore cannot be ascribed to changes in instruments. The effect is a rather more technical one, being the result of the mechanism through which the intervals in the progressive Danish tax system is regulated. In essence, some sort of fiscal drag effect can be observed,
An 'Optimal' Phillips-Curve
due to the fact that the income brackets in the Danish tax system is regulated on the basis of a general price index which is influenced by import prices. As the import prices are exogenous in the conducted experiments there is a tendency for the regulation of the interval limits in the tax system to lag further behind income when wage rises are high than when wage rises are lower. This means that with high wage increases a larger fraction of the total income is placed in the higher brackets in the tax system where the taxation is heavier. As mentioned above the productivity and unemployment benefit terms have a weak flattening effect on the 'optimal' curve. Of these the influence from the productivity is the weakest being mainly the result of different growth-profiles in the four optimizations. The influence from the unemployment benefit term can be ascribed to the fact that unemployment benefits are regulated on the basis of lagged wage increases. This means that with higher wage increases the unemployment benefit tends to lag further behind the wage. CONCLUSIONS In the experiments reported above it was seen, that it was possible to uncover some sort of implicit trade-off between pay rises and unemployment in a simultaneous macroeconometric model, and that this trade-off deviated from the corresponding trade-off in the wage relation seen in isolation. Although the experiments may be said to have a somewhat provisional character, they seem to indicate that the utilized method can be of some help for instance in comparing different wage relations. If it is possible to
327
impose boundaries on the use of instruments which is close to the ones the politicians faced during the period over which a wage relation was estimated, the technique may even give some indication of possible simultaneous equation bias. The point is, that if the wage relation in itself fits the historical development rather well, this is not necessarily true for the model as a whole, if the 'isolated' Phillips-curve deviates from the 'optimal' Phillips-curve. Whether or not the technique will be suited for such uses is not clear from the present paper. Obviously more has to be done before one is in possession of a ready-to-go tool. REFERENCES Chow, Gregory C. & Sharon Bernstein Megdal (1976). An Econometric Definition of the Inflation-Unemployment Trade-off. Econometric Research Prog. Memo 203, Princeton Un. Princeton, U.S.A. Drud, Arne (1978). An Optimization Code for Nonlinear Econometric Models Based on Sparse Matrix Techniques and Reduced Gradients. Annals of Economic and Social Measurement, 6/5, U.S.A. Drud, Arne (1979). Combining an Optimal Control Program with the Time Series Processor System. Tech. Note 15, Research Proj. 671-58, World Bank, Washington,DC, U.S.A. Drud, Arne & Alexander Meeraus (1980). CONOPT - A System for Large Scale Dynamic Nonlinear Optimization, User's Manual. Tech. Note 16, Research Proj. 671-58, World Bank, Washington, DC, U.S.A. Rosted, J~rgen (1980). Man~vremuligheder i dansk ~konomi - nogle modelberegninger, K~benhavn, Danmark.
328
J. Elmeskov
Average wage increases
I
%
x 0 10
8
' isolated ' Phi llips-curve
6
' optimal ' Phillips - curve 4
2
3
Fig.
1 . The ' optimal '
5
7
Phil l ips - curve
9
Constant rate of unemployment ,
©
I F.\(
t hl l ;lIl1 i(
-' foddling ;11](1 ( :olllro\ of I>C. l 'S.\ I ~IK\
hOlllllllil· ... . \\·; I ... hing'llItI
AN 'OPTIMAL' PHILLIPS-CURVE J.
Elmeskov
Th" t:Clllllllllir CUI/wit. ClljJfllh"/iI'll. Df'llIIwrh
Abstract . The paper describes how an optimization p r ocedure may be utilized to uncover a relationship between wage - in f lation and unemp l oyment in a macro econometric model taking the who l e interp l ay of a ll the model ' s equ ations into consideration . The idea is to select a number of policy i nstrument s and then with the use of these instruments to mi nim i ze wage - increases whi le the unemployment r ate i s kept fixed . This is done for a number of diffe r ent unemployment rat es , and the result is an effic i ency frontier which connects points of min i mum wage increases obtainable for a certain rate of unemployment . The shape of this efficiency frontier is i nfluenced by the interp l ay of a l l equations in the model and by the limitations put on the use of the policy instruments . The shape of the efficiency f r ontie r is discussed and it is compared with the shape of the partial re l ationsh i p between unemployment and wage-inflation in the mode l' s wage - equation seen in isolat i on. Keywords . Economics; Identification ; Modelling; Optimisati on; Par ame t e r Estimation .
I NI'ROD ucr ION
the picture . Withi n certain politically de termined boundari es the government may choose the values of its ins t rument a l var iables so as to realize the combi nation of inflation and unemployment which it finds most favourable . In making this choi ce the government is confronted wi th a tr ade- off between obtainable unemployment and i nflation rates .
Seen in isolat i on a wage - relation of the tra ditional Phillips - curve type determines a well - defined trade - off between unemployment and (wage-)inflation. This trade - off can be shown graphically by keep i ng al l other var i ables in the wage - relation constant and then plotting corresponding values of inflation and unemployment rates in a diagram . But this t r ade-off is not very informative when the wage-relation is embedded in a simultaneous macro - economic model and questions are asked about the relation between unemployment and pay rises for the model as a whole . I t has no longer any meaning to regard a trade - off where the other variables in the wage - re l a tion are not free to vary. If , for instance , pay rises are increased by a lowe r ing of the unemployment rate this will increase prices , and with price increases entering the wage relation pay rises will be further increased . Obviously the wage-relation interacts with the other equations of the model , and the relationship between unemployment and inflation in some sense implicitly given in the model may look somewhat different from the trade - off in the isolated wage - relation .
The question is now how to uncover such a political l y obtainable trade - off be t ween un employment and inflation . Although it may not be possible to solve the simultaneous model analytically it is obvious that diffe rent combi nations of unemployment and inflat i on can be found by simu l ating t he model wi th different va l ues f or the policy ins tr u ments. For each combi nation of values of the i nstrument a l variab l es t h e r e wil l be a co rrespo?d i ng l evel of unemployment and inflation . However , these different combinations of unemployment and inflat i on cannot be said to cons titu t e a we l l - def in ed trade - of f be tween these two var iables . P l ot t ed in a diagram with unemployment and pay- rises along the axes t he combi nations found are likely to look l i ke the result of firing a shotgun. In Chow & Megdal (1976) it is suggested , that the use of an optimization t echn i que
If one is concerned with the combinations of unemployment and inflation which are obtainable for the government it is obvious that constraints on the economic policy must enter
1S0 far only a single period is consid ered
323
324
J. Elmeskov
migth facilitate the uncovering of an implicit trade-off between unemployment and inflation . The idea , which is being follo wed here , is to se l ect a number o f i nstrumental variables that are allowed to vary within given boundaries and then min i mize the inf l ation rate while keeping the unemployment rate fixed . By repeating this procedure for a number of fixed unemployment rates an efficiency frontier is es t ab li shed, which l inks unemployment rates a nd the corresponding mi nimum pay rises obtain abl e wi t h the chosen set of instrumental var i ab l es and the boundaries imposed on their variation. If ones interest is in the political l y obtainable trade-off the instruments shou l d be those which the government is free to vary within political boundaries . If ones interes t is more in examining the comp l ex inter-relationships of the mode l the selection of instrumental variab l es may be a little more delicate . In a macro- econometric model some instruments may have exactly identical impacts on the model solution, and it is obviously only necessary to employ one instrument out of such a group of instruments . On the other hand if the models full interplay is to be set in motion one must pick as many policy instruments with different effects as possible . If only a subset of these policy variables with different effects is employed , the shape of the efficiency frontier may change drastica l ly according to which subset is being used . Also the boundaries imposed on the variat i on of the instruments are of crucial importance. One set of boundaries on the instrumental variables may make the efficiency frontier look very different from the efficiency frontier obtained with another set of boundaries . It may also be worth noting that the boundaries at least in the more political ly ori ented analysis need not only take the form of direct limitati ons put on the variations of the chosen instrumental variables . The boundaries could also take the form of re strictions on the development in certain key variables as for instance the balance of payments. One could argue , however, that such policy - induced constraints may also belong to a more techni ca l examination of the unemployment-inflation relationship in a model. This statement could find support in the fact that government policy hard l y can be described as totally exogenous . If the wage - re l ation has been estimated over a time- period where government policy has been subject to certain limitations, then it is obvious that these limitations must be drawn into consideration when testing the reasonability of the wage - relations interplay with t he rest of the model . When more than one period of time is consi dered (what is usually necessary to bring
the full i nterplay of all equations in the model into action) the non-dominated combi nations of unemployment rates and inflatio n rates be l ong to a 2*T-dimensional space , where T is the number of time periods . To be able to give a graphic presentation of the solutions to the experiments reported below i t has been decided to minimize the average pay increases over the time horizon for given constant unemployment rates . This means that it may be possible to get lower mini mum average pay increases for the same ave rage unemployment rate s by letting the unem ployment rate be free to vary ove r the time horizon. MODEL , WAGE - RELATION AND DATA The computations which will be described below were carried through with a medium - sized (163 equations) econometric mode l of the Danish economy , SMEC3. The model which is used for projections ~nd policy analysis by the Economic Council is based on yearly data. It is a traditional demand - oriented model in the Keynesian tradition . The behavioral relations in the model include private consumption, fixed investments , inventories , exports , imports and prices. The model has a very aggregated structure with on ly one endogenous production sector (private sector minus primary production ) . On the institut ional side the description of taxes and othe r transfers to and from the public sector is rather de tailed. The model does not contain any monetary sector. Interest rates are assumed to be unaffected by the different economic developments in the experiments described below (this assumption may not be quite as unreasonable as it sounds , as the monetary p olicy in Denmark to a large extent is cond ucted to secure the financing of the balance of payments deficit , w~ich is kept cons tant through the experiments , cf . be l ow) . The wage - equation which describes the annual percentage increas e in hourly earnings in the endogenous production sector is n~t estimated by means of regr ession analysis . 2 An independent government - financed advisory body 3It is the nominal interest rate which is kept fixed throughout . Undoubtedly a fixed real rate of interest would have been more reasonable. 4Actually , this wage- relation is not normally included in SMEC3, which is usually used with an exogenous wage r ate . The wage - rela tion was constructed in connection with a research project at the University of Copen hagen (Rosted (1980)), where it was used in another model. Despite the transplantation which includes a shift in the data used, the relation fits the wage - development through the 197 0 'es rather well .
An 'Optimal' Phillips - Curve
Instead the coefficients have been 'guesstimated ' on the basis of different available investigations concerning the link between wage - increases and the other factors entering the wage - equation. The calculations reported below may be seen as a test for the reliability of the equation . The relation can be written: DW + + + + + +
.5 .8
* DPC .7 * Dm .5 * DPR .5 * ATP . 1 * l / UR . 05 * log (ARUB)
(1 )
where DW
Percentage increase in hourly earnings
DPC
Average price- increase of private consumption goods over the last two years
Dm
Percentage change in working time
DPR
Average productivity increases over the last three years
mp
Absolute change in direct tax pressure on wage income
UR
Mean rate of unemployment over the last two years
ARUB
Average unemployment benefit relative to wage over the last two years
The first term (apart from the constant) in dicates that price rises will press up the hourly earnings although the wage lags behind prices and price rises are not fully compensated by wage increases. A large part of the effect from price increases can be ascribed to the indexation of wages which was in force in Denmark when the computations were made but recently has been abandoned (at least temporarily). The equations determining prices of final demand components in SMEC3 links the development in fac tor costs and import prices together by means of input-output based weights. This means that the model contains a wage - price spiral . This interdependence is strengthened by an assumption of no change in the functional distribution of income meaning that the profit per unit of output is linked to the development in wages corrected for pro ductivity changes. The term representing the influence of the percentage change in working time is not very interesting in connection with the present subject as the working time is treated as an exogenous variable throughout this paper . In the version of the SMEC3 model used for the present purpose changes in productivity from the base-line simulation is generated
325
in a rather simple relationshipS linking employment to production with a short lag. The scope for productivity developments very different from the base- line simulation is rather limited . This is of course a draw back in simulations where the development in production , investment etc. is quite different from what it was in the base- l ine simulation . As a result of this nearly exogenous growth in productivity , the productivity term in the wage - relation wi l l give approxi mately the same contributi on to wage -i ncreases no matter how the rest of the model be haves . The tax pressure is included in the wage-equation from the motivation that wage - earners will try to seek compensation for higher taxes through wage increases. The fifth term in the wage - equation is the traditional Phillips - curve term. Finally the wage - equation includes a term which describes the influence from the size of unemployment benefits relative to wage . In turn the size of the unemployment benefit is influenced by the wage increases as the model includes an equation describing the mechanism through which the size of the un employment benefit is regulated . However, the main effect from wages on unemployment bene fits appears with a lag . The inclusion of this term in the wage-equation means that besides the wage - price spiral the model also contains a wage-unemployment benefit spiral. utilizing the data base behind the forecast from the chairmanship of the Economic Council of june 1980 the model was simulated for the six years 1978-83 . This simulation for med the base-line upon which the experiments was conducted. The mean rate of unemployment and mean wage increases for the ghole period is plotted as point 0 in fig. 1. Afterwards 11 policy variables were chosen as instruments to minimize the average wage increases over the time period while keeping the unemployment rate pegged to a specific figure. The instruments chosen included dif ferent kinds of government expenditure , direct and indirect tax rates, investment taxes and depreciation rates. A set of boundaries indicating the possible field of variation was imposed on the instruments. Also a set of more technical bounds was im5
For computational reasons it was not possible to use the vintage - relationship normally included in this version of SMEC3 to explain productivity development .
6 Care must be exercised in the interpretation of this point in connection with the shown curves, as the curves are drawn for a fixed rate of unemployment through all six periods , where the unemployment rate behind point 0 is fluctuating over the time horizon.
J. Elmeskov
326
TABLE 1
Decomposition of average wage increases
Rate of unemployment
3 5 7 9
constant
.5 .5 .5 .5
% % % %
prices
5.5 4.4 4.1 4.0
Contribution from working producdirect time tivity tax
.3 .3 .3 .3
posed on the possible solutions (these can be exemplified by the upper limit of 100 % on capacity utilization). As indicated in the introduction an emphasis on the politically obtainable efficiency frontier combining points of fixed unemployment rates and minimum average wage increases could lead to the introduction of boundaries which are not put directly on the variation of the policy instruments. As an example of such a political constraint (apart from those bounding the variation of the policy instruments) it has been chosen to conduct the experiments under the condition that the balance of payments in none of the years must be worse than in the baseline run. For the Danish economy the balance of payments is probably the most prominent limitation for political actions, although one can discuss the rather arbitrary bound consisting of the b.o.p.development in the base-line simulation. However, for the present purpose it does not matter very much exactly which limitation is put on the b.o.p.development as long as a limitation is being put. RESULTS With the model, data, instruments and bounds as described above 4 optimizations were conducted. In each the rate of unemployment was pegged to a fixed rate (3, 5, 7 and 9 % respectivily) and the average yearly increases in hourly earnings were minimized over the chosen period. The resulting efficiency frontier is drawn in fig. 1 (the curve marked 'optimal' Phillips-curve). To be able to compare this with the partial trade-off between unemployment and pay increases from the wage relation seen in isolation the latter has been drawn by inserting the four fixed unemployment rates into the relation's unemployment term. To facilitate a comparison of the two curves the curve based on the isolated wage relation has been pushed up so that it intersects the 'optimal' Phillips-curve for a fixed rate of unemployment of 3 %. 7
The programmes used are developed by dr. Arne Drud, see Drud (1978), Drud (1979) and Drud & Meeraus (1980).
1.2 1.3 1.3 1.3
.1 .0 .0 .0
unemployment
3.1 1.9 1.4 1.1
unemp.benefit
-2.4 -2.3 -2.3 -2.2
Average wage increase
8.3 6.2 5.4 5.0
As can be seen from the figure the 'optimal' Phillips-curve is the steepest of the two curves. To see why this is the case the average wage increases in the four experiments has been decomposed in table 1 in order to see the contribution of each term in the wage-equation.
From table 1 it is readily seen that the most important factor in making the 'optimal' curve steeper is the price term. Another - although much smaller - effect in the same direction comes from the direct tax. In the opposite direction pulls both the productivity and the unemployment benefit term. The existence of the wage-price spiral in the model is of course a main factor in the explanation of the price term's contribution to the steepness of the 'optimal' Phillips-curve. When unemployment is low wage rises tend to be high and these high wage rises tend to push up price increases which in turn influence the wage rises etc. But also the balance of payments restriction is a major factor explaining the influence of the price term. The point is, that lower wage- and price-inflation improves the competitive position of Denmark relative to other countries. The improvement in the competitive position allows the government to pursue a more relaxed fiscal policy without worsening the balance of payments relative to the base-line simulation. The relaxation of the fiscal policy taking the form of an easing of indirect tax pressure tends to reduce wage increases thereby bringing about a further improvement in the competitive position etc. Of course this last mechanism interacts with the wage-price spiral to further multiply the effect. The instruments directly influencing the direct tax pressure on wage-earners show very much the same development through all the optimizations. The effect of the direct tax term which tends to make the 'optimal' Phillips-curve steeper therefore cannot be ascribed to changes in instruments. The effect is a rather more technical one, being the result of the mechanism through which the intervals in the progressive Danish tax system is regulated. In essence, some sort of fiscal drag effect can be observed,
An 'Optimal' Phillips-Curve
due to the fact that the income brackets in the Danish tax system is regulated on the basis of a general price index which is influenced by import prices. As the import prices are exogenous in the conducted experiments there is a tendency for the regulation of the interval limits in the tax system to lag further behind income when wage rises are high than when wage rises are lower. This means that with high wage increases a larger fraction of the total income is placed in the higher brackets in the tax system where the taxation is heavier. As mentioned above the productivity and unemployment benefit terms have a weak flattening effect on the 'optimal' curve. Of these the influence from the productivity is the weakest being mainly the result of different growth-profiles in the four optimizations. The influence from the unemployment benefit term can be ascribed to the fact that unemployment benefits are regulated on the basis of lagged wage increases. This means that with higher wage increases the unemployment benefit tends to lag further behind the wage. CONCLUSIONS In the experiments reported above it was seen, that it was possible to uncover some sort of implicit trade-off between pay rises and unemployment in a simultaneous macroeconometric model, and that this trade-off deviated from the corresponding trade-off in the wage relation seen in isolation. Although the experiments may be said to have a somewhat provisional character, they seem to indicate that the utilized method can be of some help for instance in comparing different wage relations. If it is possible to
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impose boundaries on the use of instruments which is close to the ones the politicians faced during the period over which a wage relation was estimated, the technique may even give some indication of possible simultaneous equation bias. The point is, that if the wage relation in itself fits the historical development rather well, this is not necessarily true for the model as a whole, if the 'isolated' Phillips-curve deviates from the 'optimal' Phillips-curve. Whether or not the technique will be suited for such uses is not clear from the present paper. Obviously more has to be done before one is in possession of a ready-to-go tool. REFERENCES Chow, Gregory C. & Sharon Bernstein Megdal (1976). An Econometric Definition of the Inflation-Unemployment Trade-off. Econometric Research Prog. Memo 203, Princeton Un. Princeton, U.S.A. Drud, Arne (1978). An Optimization Code for Nonlinear Econometric Models Based on Sparse Matrix Techniques and Reduced Gradients. Annals of Economic and Social Measurement, 6/5, U.S.A. Drud, Arne (1979). Combining an Optimal Control Program with the Time Series Processor System. Tech. Note 15, Research Proj. 671-58, World Bank, Washington,DC, U.S.A. Drud, Arne & Alexander Meeraus (1980). CONOPT - A System for Large Scale Dynamic Nonlinear Optimization, User's Manual. Tech. Note 16, Research Proj. 671-58, World Bank, Washington, DC, U.S.A. Rosted, J~rgen (1980). Man~vremuligheder i dansk ~konomi - nogle modelberegninger, K~benhavn, Danmark.
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J. Elmeskov
Average wage increases
I
%
x 0 10
8
' isolated ' Phi llips-curve
6
' optimal ' Phillips - curve 4
2
3
Fig.
1 . The ' optimal '
5
7
Phil l ips - curve
9
Constant rate of unemployment ,