The Scope of Allocation Differences in Concepts and Results

Transcription

1 The Scope of Allocation Differences in Concepts and Results Abstract Public debate on the right level of wage demands is vigorous in. Employers usually argue that too high demands will cost jobs, while unions argue that higher wages are needed to stimulate demand. Thus, the scope available for wage increases that will not lead to cuts in jobs needs to be determined to evaluate whether wage demands are actually too high or not. This paper shows some possible ways of deriving that scope of allocation and at the same time tests these in a multi-country comparison. The conclusion is that small changes in the derivation lead to large changes in the outcome in terms of the multi-country comparison. It is not possible to derive a unique procedure to classify a wage policy as employment enhancing or restricting using the scope of allocation since a different but equally valid derivation might lead to an opposite conclusion. Introduction The years since 99 saw diverging developments in labour markets in European countries and the. At the same time there are significant differences between the countries in the bargaining methods. Various degrees of unionisation, coverage rates and cooperation between the wage setting parties exist. All these factors affect the development of wages and will thus presumably also have an influence on employment level. The concept of the 'scope of allocation' can be used to describe this influence. This is the scope available for increases in wages, given an inflation target and improvements in productivity. In theory, an employment-friendly wage policy does not make full use of this scope. However, there are many more factors, e.g. labour market rigidities affecting employment, which is why we cannot make inferences about employment changes from the scope of allocation. For work with the concept of scope of allocation to be possible, it has to be adapted for empirical analyses. The aim of this paper is to show how small changes in assumptions when the scope of allocation is derived lead to large differences in results in a cross-country comparison. The choice of countries was done under the following considerations. and are two highunemployment countries and also the largest European economies. and the Netherlands have relatively low unemployment. The is the largest and presumably most flexible economy in the world. In the first part this paper derives the scope of allocation. In the second part this theoretical background is used to analyse how the scope of allocation was used in,,, the Netherlands and the. The chosen time-span is 995 to. The last part of the paper highlights the differences in outcome between the different methods used. Derivation To classify a wage policy as employment enhancing, wage increases have to be put in relation to productivity gains. Under a number of simplifying assumptions firms' labour demand remains constant as long as real wage costs and productivity increase at the same rate. Firms demand more labour when marginal productivity is larger than the real marginal labour costs. If the marginal cost of extra labour is larger than its marginal productivity, the firm makes losses and dismisses employees. An implicit condition is decreasing marginal returns of labour. Other conditions affecting labour demand, such as a changing market situation, are more of a medium-term nature and will not be considered in this short-term discussion. The German Council of Economic Experts (SVR) derived the scope of allocation in its annual report. This derivation is repeated here (equations to ). The labour demand condition is derived from the profit maximisation target of a firm. Max L Π t = P t ( Y t )Y t W t ( L t )L t RK t Note that R is constant and the capital stock does not adjust to short-term labour fluctuations. The firm faces a constant elasticity demand function Y t d =bp t δ, where b is a level parameter and δ the absolute value of the price elasticity of demand. A standard production function Y t =F(A t,l t,k t ) is assumed as well. A rather strong assumption is that the firm optimises profits only with respect to labour; prices are taken as given. This Cf. Sachverständigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung: 'Staatsfinanzen konsolidieren _ Steuersystem reformieren', Jahresgutachten /, pp () 7

2 problem solves to: where: Y t = L t η t W t ( + η t ) P t ( δ t ) W t L t = L t W t Using a Cobb-Douglas production function, α tkt α t Y t = A t L t () () should be wage restraint. Therefore employment effects can be deducted again to obtain a figure for labouradjusted productivity increase. ln Y t ---- L t i L ln Y t = ( α L t ) lnl t t According to eq. the change in marginal productivity is: ln Y t L t = lnα + ln Y ---- t t L t (9) () the marginal productivity of labour can be derived: while according to eq. it is: Y t α t α t = α L t A t K t L t = t Y t α t ---- L t () ln Y t L = ln Wt + lnκ t P t () Combining and gives: where: Y t α t ---- L t W t = κ P t t + η t κ t = δ t (5) If we assume lnκ = and combine 9, and, the condition for a wage development that retains constant employment can be derived. ln W t P t = lnα + ln Y ---- t + ( α t L t t ) lnl t From eq. 5 it follows that: α t W t L t = P t κ α α t t A t K t If employment is to be constant, i.e. lnl =, the following wage policy should be used: ln W t α t = lnα (7) P t t A t K t if κ remains constant. Real wages should grow in line with changes in total factor productivity, the capital stock or the elasticity of substitution of labour. From the production function the change in average productivity can be derived: employment effect ln Y t ---- = α L t lnl t + ( α t ) lnl t t α t lnk t + ( α t ) lnk t + lna t When the number of workers decreases, average productivity increases. This increase in productivity might suggest the possibility of larger wage increase, which runs counter to the intuitive knowledge that there (6) (8) lnw t lnp t lnα t ln Y t = ( α t ) lnl t () Nominal wages thus can rise by as much as the sum of inflation, the change in the marginal rate of substitution and the labour-adjusted change in average productivity. The problem is how to measure the marginal rate of substitution. From 5 the labour share in inputs can be derived. W t L t α t = ---- P t Y t κ t () Under the assumption of κ = the marginal rate of substitution is equal to the labour share. On the basis of this model various methods can be used to calculate the scope of allocation. Several approaches will be applied below. The first two make use of the share of labour to represent α. Method uses data based on hours worked, method, per-head data. In all cases the labour variable is based on change in total hours worked in per-hour methods and change in employment in per-head methods. This interpretation of α was proposed by the SVR. Of course, the assumption of κ = is very tricky. Horn and Logeay () alter- Cf. Gustav A. Horn and Camille Logeay: 'Kritik am lohnpolitischen Konzept des Sachverständigenrats', Wirtschaftsdienst, pp. 6-6, Hamburgisches Welt-Wirtschafts-Archiv. L t 7

3 nated the derivation. It is usually assumed that technology and therefore the elasticity of substitution is constant in the short term. Consequently, an alternative measure is to drop the term lnα t since it is assumed to be constant, and to take the average labour share as α. Productivity is still adjusted for employment changes. Methods and make use of this, using data based on hours worked and on persons employed, respectively. These methods have the drawback of using the share of labour to approximate the elasticity of substitution. Furthermore, wage restraint will not solve the problem when a lack of demand causes a cut in jobs and thus a rise in average productivity. Instead, demand would fall even further. Therefore, labour-adjusted productivity will not be used in the following method, which was also proposed by Horn and Logeay. On the assumption that the elasticity of substitution is constant over shorter time horizons, growth in average productivity correlates with growth in marginal productivity (see equation ). Trending this value also excludes cyclical influences. Therefore methods 5 and 6 calculate the scope of allocation by using trended average productivity and inflation. Method 5 uses data based on hours worked, method 6, data based on the number of employees. lnw t = lnp t + ln Y L -- () The standard calculations use actual inflation to establish how employment friendly the wage-setting policy is. However, actual inflation and inflation target are often different. Since inflation targets in the presence of a credible central bank are relevant for wage setting negotiations, it is interesting to see how the picture would look if the central bank had succeeded in meeting its inflation target. This analysis, using the inflation target, is done as well as the normal analysis. GDP divided by the total number of hours worked in a year or by the number of employees. The number of hours worked differs between different sources, e.g. OECD and Eurostat, as often these are estimates. Since only growth rates matter bias should be small or nonexistent. Nominal labour costs are calculated using total compensation of employees in the economy divided by the corresponding figure of employees or hours. The labour share is wage compensation over GDP. The trended average productivity is the average productivity increase over the relevant period. All data are taken as growth rates. The inclusion of an inflation target is slightly problematic as a central bank usually takes the CPI as the relevant measure, and on average this is larger than the GDP deflator. For the the cumulated CPI values over the period are 5.6 percentage points higher than the cumulated GDP deflator values, which amounts to close to three quarter percentage points per year. Therefore the inflation target is assumed at.5% per year. For the European countries in the EMS the inflation target of the German Bundesbank and of the ECB is the relevant target. The Bundesbank did not officially have an inflation target. Nevertheless, Clarida et. al. 6 estimated this at % except for 997 and 998, when it was.75%. The ECB's official target is a maximum of %. Since all countries have different inflation every year no general rule on how much the CPI overstates the GDP deflator can be given. Therefore the actual inflation target values are used. Results First a general overview of the results is given, followed by a presentation of results for each method, and finally the different results are compared in a summary. The data base The analysed period is the time from 995 to. The data for, and are from the OECD, the data for the Netherlands from the OECD and Eurostat, and those for from Statistisches Bundesamt (Federal Statistical Office). 5 Since the GDP deflator is the more relevant inflation figure for employers, it is used here instead of the CPI. Average productivity is General results For every period the difference between inflation plus (adjusted) productivity increase and nominal labour costs has been calculated. If the result is positive the scope of allocation has not been fully used, while a negative result means that the scope of allocation has been overdrawn. The calculated values fluctuate widely. To deliver a clearer picture the values are cumulated over Cf. OECD Statistics: 'Main Economic Indicators', Paris. Cf. Eurostat: 'Economic Indicators', Luxembourg. 5 Cf. Statistisches Bundesamt: 'Volkswirtschaftliche Gesamtrechnung', Wiesbaden. 6 Cf. R. Clarida and M. Gertler: 'How the Bundesbank Conducts Monetary Policy', Working Papers 96, C.V Starr Center for Applied Economic Research, New York University

4 Table Total hours worked Year-on-year change (%) Table Total Employment Year-on-year change (%) Cumulated 995 to Source: Federal Statistical Office; DIW Berlin calculations Cumulated 995 to Source: Federal Statistical Office; DIW Berlin calculations. the whole period to show the overall tendency and effect for a longer time-span. The difference between the cumulated actual inflation and inflation target numbers is nearly the same for all methods and corresponds to the cumulated deviations of actual inflation from targeted inflation. In, cumulated inflation was 6. percentage points (pp) lower; in the it was.5 pp lower and in the Netherlands 5.8 pp higher than the targets. In inflation was 7. pp lower than targeted, and in it was the same as targeted inflation. In order to show the fluctuations in the scope of allocation the standard deviation has been calculated as well. It is multiplied by to allow an easy visual comparison with the percentage point numbers. Finally, the actual year on year changes in total employment (cf. Figure Method ; actual inflation Figure Method ; inflation target

5 table ) and in total hours worked (cf. table ) are relevant as well since the use of the scope of allocation should influence these. The cumulated change in hours is smaller than the cumulated change in employment, a fact that is caused by part-time work and working time reductions. Method This method uses data based on hours worked and a changing labour share to represent a changing elasticity of substitution of labour. Furthermore, productivity increases are employment adjusted. The description of the results for method first covers the individual years (cf. figures and ) and then the cumulated values (cf. table ). The most obvious phenomenon is the fact that from 996 to all countries exercised wage restraint, except for in and in 996. An imagined average line through all values would look like an inverted parabola with the peak in 997. The Netherlands has an exceptionally high value in, and has a large negative value in. The cumulated values reveal that actually has a negative value, meaning the scope of allocation has been overdrawn by.8 pp. The Netherlands had a very strong wage restraint of nearly 7 pp in the seven years, which gives an average of % per year. When inflation target is taken as a yardstick, the inverted parabola shape through the average values becomes even more pronounced. and have large positive values, while that for the Netherlands is much smaller. Method Method (cf. figures and ) is like method, the only difference being the use of data per person employed instead of hours worked. The use of per-head data has a large impact on the values in the second part of the time period from 998 onwards. Most of them are larger now, and in there is only one slightly negative value. Table Cumulated Percentage Points of, 995 to + wage restraint, excessive wage demands Changing labour share, employment adjusted per hour Method Actual inflation.7%.5% 6.89%.7%.78% Standard deviation (.) (.5) (.) (.8) (.5) Inflation target 6.9% 7.%.%.7% 5.75% Standard deviation (.7) (.8) (.87) (.6) (.) per employee Method Actual inflation.8%.% 9.7%.99%.% Standard deviation (.87) (.) (.7) (.5) (.5) Inflation target 9.96% 6.5%.9% 5.% 8.9% Standard deviation (.6) (.5) (.68) (.7) () Constant labour share, employment adjusted per hour Method Actual inflation.95%.5% 6.%.%.77% Standard deviation (.) (.7) (.68) (.) (.69) Inflation target 5.% 7.9%.%.8% 8.9% Standard deviation (.68) (.67) (.5) (.8) (.8) per employee Method Actual inflation.%.8% 9.%.96%.95% Standard deviation (.8) (.) (.) (.5) (.7) Inflation target 8.5% 6.97%.5%.99% 9.7% Standard deviation (.) (.7) (.) (.6) (.8) Average productivity, no adjustment per hour Method 5 Actual inflation.%.%.56%.5%.6% Standard deviation (.6) (.5) (.85) (.8) (.) Inflation target.7%.% 9.%.% 9.% Standard deviation (.8) (.7) (.7) (.) (.99) per employee Method 6 Actual inflation.89%.9%.%.%.78% Standard deviation (.8) (.7) (.69) (.8) (.79) Inflation target.6%.9% 5.89%.8%.% Standard deviation (.) (.) (.) (.) (.79) Source: OECD; Eurostat; Federal Statistical Office; DIW Berlin calculations. 77

6 Figure Method ; actual inflation Figure Method ; inflation target This also shows in the cumulated values, where the is the only country with a similar value to before. One explanation is a stronger decrease in working time in the other countries, which makes increases in compensation per hour larger than increases in compensation per head. The Netherlands now has a very high cumulated value for wage restraint of nearly pp. Method This method (cf. figures 5 and 6) uses a trended average labour share to estimate the elasticity of substitution of labour, simulating the usual assumption of constant technology over short time-spans. Productivity increases are still adjusted by employment changes. Comparison with method does not show any big surprises. The general pattern of the use of the scope of allocation is roughly the same. However, the values tend to be more extreme, as exemplified by the Dutch value in and the French in. The wider spread in the values can be seen in the standard deviations, which are larger for all countries than with method. The cumulative values show a similar value for the Netherlands. In contrast to method, and show signs of excessive wage demands, while now has a slightly positive value. The value is smaller with.5 pp. Method Method (cf. figures 7 and 8) uses data per employee to do the same calculation as for method. Using method the inverted parabola that has characterised methods and is no longer visible at all. All values move in a narrow space between + pp and _ pp. The fact that the values seem to be closer together is underlined by the standard deviations, which are also smaller than with method. The cumulative values are all positive and do not show any surprises. For the Netherlands they are very high, as with method. The German value is higher than with the previous methods. Method 5 Method 5 (cf. figures 9 and ) circumvents the use of the labour share as an approximation for the elasticity of substitution of labour by assuming it to be constant. Furthermore, changes in employment are not accounted for in the productivity increase calculation. Productivity increases are trended over the whole period. The measurement is per-hour worked. Method 5 shows large fluctuations in the use of the scope of allocation. The Netherlands overdrew this scope by more than pp in several years, but then had strong wage restraint again in 996 and. had a large negative value of more than pp in. 78

7 Figure 5 Method ; actual inflation Figure 6 Method ; inflation target Figure 7 Method ; actual inflation Figure 8 Method ; inflation target

8 Figure 9 Method 5; actual inflation Figure Method 5; inflation target These large fluctuations also show in the standard deviations, which are relatively high for and the Netherlands. For it is small, as all values are close to. has the highest cumulative value, meaning that wage restraint, although small in absolute terms, has been largest there. Method 6 Method 6 (cf. figures and ) is the same as method 5 except for the use of data per head instead of per hours worked. Figure looks a lot more compact than figure 9. All values are closer to zero, the exception being the 998 value for the, which is the same as in method 5. The standard deviations tell the same story, the having the largest values and all other countries values smaller than one. The cumulated values for the period 995 to are quite different from those with method 5. had strong wage restraint with. pp; the Netherlands and show a roughly neutral wage development; and and the present negative values of _.9 pp and _.5 pp, respectively. Summary The analysis so far shows markedly different results in how the scope of allocation is used when different methods are applied. Therefore, a systematic analysis of what happens when switching from one method to another is needed to allow a sensible choice of method. The first choice is between the use of data based on hours worked or per-head data (cf. first part of table ). The difference is obvious; while using hours worked allows inclusion of the effects of changing working times, per-head data are more easily available. Since there have been massive changes in working times in terms of part-time work or working time reductions, perhour data should allow more exact results. In fact, for nearly all cases except for method 5 and 6 for the, the method using number of employees shows a larger cumulative value for the use of the scope of allocation than the per-hour worked method. The reason is the average reduction in working time per employee; if in the new period fewer hours are worked than in the period before, then the labour costs per hour increase more than the labour costs per employee. The difference between the two methods when employment adjustment and a changing labour share are used (methods and ) amounts to about pp in cumulation for all countries except for the, where the difference is only.6 pp. For reasons mentioned above the data based on hours worked have been used here. The second choice to be made is whether to adjust for technology change, α, which is the step from method to method. Because of data limitations the 8

9 Figure Method 6; actual inflation Figure Method 6; inflation target change in the labour share is used to approximate this technology change. Therefore, the difference in the cumulated values from method to method is the same as the change in the labour share in the respective country over the whole period (cf. second part of table ). The effect of this change on the cumulated values is mixed: in, the cumulative value is.5 pp higher, in the Netherlands.6 pp smaller and in smaller by pp. This means that the effect has a range of 6 pp between and, indicating that the change to a constant labour share has no homogeneous effect. Furthermore, was not then the only country where wage demands were excessive. On the contrary, now wage demands there were now restrictive, while and were countries with excessive wage demands. The third choice to be made is about employment adjustment, deciding between method and method 5. There is another change, the use of average productivity increases instead of the actual yearly values. However, in the cumulation this does not play a part, as the average is simply the sum of all values divided by the number of periods. The employment adjustment, on the other hand, has a very large impact on the calculated scope of allocation. In equation the term ( _ α t ) lnl t is added to the scope of allocation. In cumulation, this means that a.5 pp increase in hours worked such as happened in the Netherlands (cf. table ) makes the scope of allocation look larger. This argument can be seen in two ways: employment increased so much because the scope of allocation was not used, or the use of the scope of allocation looks so favourable because employment increased so much. The problem of method 5 is that the employment effect is left out altogether although it is certainly relevant in cases where employment increases very markedly. In such a case relatively more low-skilled workers start working again, which has an effect on average productivity. The actual results moving from method to method 5 are shown in the third part of table. A drop in the employment effect increases the German scope of allocation by a cumulated.8 pp and leaves the Danish one unchanged. The cumulated value for and that for the US are each reduced by.5 pp, while the Dutch scope of allocation looks pp smaller in cumulation. This is a very strong effect, showing that the inclusion of the employment effect has profound consequences for some countries. The final choice to be made is whether to use actual inflation or inflation target figures. The Danish value is hardly changed, but for the other countries there are significant differences. The Dutch value is reduced by 5.8 pp in cumulation, the US value increases by.9 pp, the French by 6.5 pp and the German by as much as 7.5 pp. This means that the switch from actual inflation to inflation target has the largest effect of all possible 8

10 Table Cumulated Results Per head Method.8%.% 9.7%.99%.% Per hour Method.7%.5% 6.89%.7%.78% Difference Method.%.6%.8%.%.% Changing labour share Method.7%.5% 6.89%.7%.78% Constant labour share Method.95%.5% 6.%.%.77% Difference Method.67%.97%.68%.%.55% Employment adjusted Method.95%.5% 6.%.%.77% No adjustment Method 5.%.%.56%.5%.6% Difference Method 5.9%.% 9.78%.6%.8% Actual inflation Method 5.%.%.56%.5%.6% Inflation target Method 5.7%.% 9.%.% 9.% Difference Target actual 6.5%.89% 5.77%.% 7.5% Changes in cumulative percentage points 995 to when the derivation of the scope of allocation is changed. First part is the comparison between per head (method ) and per hour (method ). Second is the comparison between changing labour share (method ) and constant labour share (method ). Third is the comparison between employment adjustment (method ) and no adjustment (method 5). Last is the comparison between actual inflation and inflation target using method 5. Sources: OECD; Eurostat; Federal Statistical Office; DIW Berlin calculations. changes, as the spread between the German and the Dutch change is pp (cf. last part of table ). Conclusion This paper showed several derivations for the scope of allocation and the effect these have on the empirical analysis. The starting point for the derivation is the profit-maximisation problem of a firm, which leads to an optimal employment decision. The scope of allocation is fully used when the optimal employment remains unchanged by a wage change. Using this idea, the scope of allocation has been derived for five countries. The result links productivity growth and inflation to wage increases. Ideally productivity growth should be adjusted to changes in technology or changes in employment. This brings about problems concerning data availability, as the labour share needs to represent the marginal rate of substitution of labour, which actually only holds under very specific conditions. Therefore, alternative methods circumventing these problems were shown. When applied to actual data for the five countries, large differences can be seen between the methods. Without commitment to one specific method it is not possible to say which country used the scope of allocation most or least, or whether there was wage restraint or excessive wage demands. The most striking example is the rank order of and the Netherlands. While using actual inflation, a changing labour share and employment adjustment (method ) the Netherlands used the scope of allocation least of all and overdrew it, using inflation target, average productivity and no employment adjustment (method 5) reverses the order, with the Netherlands having the most excessive wage demands and the most restrictive. The difficulty of explaining employment changes because of the large number of factors influencing it has already been described. The results of this analysis show that the scope of allocation alone is certainly not sufficient. Although methods to suggest a relationship, it is only superficial, as the employment change is used to calculate the scope and is therefore part of it. Looking at methods 5 and 6 there is no obvious relationship between the cumulated values of the scope of allocation and the employment change. In conclusion, calculation of the scope of allocation is not a straightforward computation exercise. The choice of method used deserves special attention and should be based on a careful evaluation of the pros and cons of each method and the special characteristics of the dataset at hand. Gustav A. Horn, DIW Berlin, and Stefan Kühn, University of Maastricht 8