Labour Economics 11 (2004) 293 – 313 www.elsevier.com/locate/econbase

The myth of worksharing Arie Kapteyn a,*, Adriaan Kalwij b, Asghar Zaidi c a

RAND, 1700 Main Street, Santa Monica, CA 90407, USA b Tilburg University, Netherlands c London School of Economics, UK

Received in revised form 5 April 2003; accepted 5 August 2003

Abstract Worksharing is considered by many as a promising public policy to reduce unemployment. This paper reviews the most pertinent theoretical and recent empirical contributions to the literature on worksharing. Next, we provide new empirical evidence on this issue by a longitudinal cross-country analysis of the long-run effects of a reduction in working hours on employment and wages, exploiting aggregate data for 16 OECD countries. The conclusions of the theoretical literature survey are indecisive: the efficacy of worksharing as an employment enhancing policy tool depends heavily on the setting in which the analysis takes place. In line with recent empirical studies, our results do not support the proposition that worksharing promotes employment. The results show a positive direct effect on employment of a reduction in working hours. However, taking into account indirect effects, in particular the upward effects on wages, we find that the long-run effect becomes small and insignificant. D 2003 Elsevier B.V. All rights reserved. JEL classification: C33; E24; J2; J3 Keywords: Employment; Hours of work; Panel data

1. Introduction In public discussions, the idea of worksharing often emerges as a potential instrument for reducing unemployment, or equivalently to increase the number of people in paid employment. The idea is usually based on the simple notion that in a given period a

* Corresponding author. Tel.: +1-310-393-0411x7973; fax: +1-310-451-7084. E-mail address: [email protected] (A. Kapteyn). 0927-5371/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.labeco.2003.08.001

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fixed amount of labour input required to produce a fixed volume of goods and services can be shared between persons who are already employed and those who are unemployed. It is argued that in this way a trade-off can be made between positively valued leisure of the employed and unwanted leisure of the unemployed. The idea appears to be particularly popular in Europe, but it also has a venerable history in the US.1 However, economists as well as employers are mostly sceptical about the success of this policy prescription. The fallacy2 of this seemingly simple idea is made clear in the literature especially by its impact on wages, wage costs, and output. In this study, we seek to provide a review of the most pertinent theoretical and empirical contributions to this literature, and in addition provide new empirical evidence on the efficacy of worksharing in increasing employment based on a comparison of economies over time and across countries. The rest of this paper is organised in three sections. Section 2 reviews the most relevant literature and discusses the most important factors determining the employment effects of a reduction in working hours. Section 3 presents new empirical evidence regarding the consequences for employment of a reduction in working hours based on a panel of 16 OECD-countries. Final conclusions are drawn in Section 4.

2. Literature review The form of worksharing examined in this study is the reduction of the standard or contractual hours worked per time period, often referred to as ‘‘shorter hours’’. Other forms of worksharing such as early retirement of the currently employed (e.g. Layard et al., 1991) or job sharing (e.g. Dreze, 1985; Roche et al., 1996) are not examined here. However, the insights in the employment effects of shorter hours will bring out many important issues that are also relevant for other forms of worksharing. This section reviews the most pertinent theoretical and recent empirical contributions to the literature on worksharing. In a previous version of this study (Kapteyn et al., 2000), we provide a more extensive literature overview and a review of some selected public policy experiments in European countries with respect to worksharing.

1

For example, during the height of the recession in 1933, Alabama’s senator Hugo Black introduced a bill prohibiting ‘‘interstate commerce in goods produced in ‘any mine, quarry, mill, cannery, workshop, factory, or manufacturing establishment’ that worked its employees more than thirty hours a week’’ (Davis, 1979, p. 97). Likewise, during the industrial revolution at the beginning of the 19th century the Luddites destroying the looms that put them out of work were acting upon the same assumption that the total lump of labour was fixed and hence any labour-saving technical progress would reduce employment. 2 The governments of France and Italy have recently introduced a cut in the legal working week to 35 h as a way to reduce unemployment. This seems to make excellent sense to a lot of people, mainly from a simple intuition that so many workers complain about being overworked, while one in nine Europeans is idle? However, it is depressing that supposedly responsible governments continue to pretend to be unaware of the old ‘lump of labour’ fallacy: the illusion that the output of an economy and hence the total amount of work available are fixed (‘‘One lump or two?’’, The Economist, October 25th 1997).

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2.1. Worksharing and actual working hours3 Calmfors and Hoel (1988) examine in a seminal article the response of a costminimizing firm to a reduction in standard hours, holding output fixed.4 They show that a firm’s response in the demand for workers and hours per worker differs corresponding to the initial situation, i.e. before the reduction of standard hours. If in the initial situation the firm required its workers to work overtime the reduction in standard hours is shown to increase actual working hours, and hence total employment falls. The reason for this seemingly counterintuitive result is the following: the reduction in standard hours increases the price of a worker since the firm has to pay more overtime hours, but has left the price of an additional hour unaffected. In response to this change in the relative price, the firm will use more of the input of which the price has not changed (hours) and will use less of the input of which the price has gone up (employees). If in the initial situation all workers worked standard hours then the employment effect depends on the new optimal situation. If the optimal situation remains that all workers work standard hours, then clearly the number of hours will fall and employment will go up. It is possible, however, that it will become advantageous to the firm to require its workers to work overtime, in which case it cannot be said a priori what the employment effects of a reduction in standard hours will be. In the case where initially actual hours were less than standard hours, conceivably the reduction in standard hours may move the optimal situation to a situation where all workers work standard hours, or even to a situation where it is optimal to work overtime. Additionally in this case, it is not possible to state a priori what the employment effects will be. The empirical evidence on the reaction of actual hours to a change of standard hours indicates that actual hours follow standard hours, though possibly not completely. Hunt’s (1999) empirical work—using data from the German Socio-Economic Panel—suggests that at least for ‘‘Arbeiter’’ (hourly workers) in manufacturing a 1-h fall in standard hours led to a fall in actual hours of between 0.85 and 1.0. De Regt (1988) finds that a 1% reduction in standard hours reduces actual hours by 0.89% for the Netherlands over the period 1954– 1982, whereas according to Hart and Sharot (1978) a 1% reduction in the standard hours for the UK over the period 1961– 1972 resulted in a 0.92% reduction in actual working hours. Kalwij and Gregory (2000), using British data over the period 1975 –1999, find that a 1-h fall in standard hours leads to a 0.1-h increase in overtime hours. Jacobson and Ohlsson (2000) find that actual working hours and legislated working hours move together in the long run and conclude that policy makers can influence actual hours by using legislated working hours as an instrument. Thus, the conclusion drawn from the empirical literature is that actual working hours appear to be moving in the same 3

Contensou and Vranceanu (2000) provide an overview of a wide range of theoretical models of the determination of working hours, with and without union bargaining. 4 To be more precise, they examine a situation in which a firm produces a fixed level of output according to a production function in which labour input is equal to the number of persons employed times the number of hours worked in efficiency units. Efficiency per hour may initially increase with hours but will eventually fall if the number of hours increases. Furthermore, capital input is fixed. The labour cost of one worker consists of a fixed cost and the salary as determined by the contractual hours of work plus any overtime hours that are paid with an overtime premium.

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direction as standard hours. This implies a positive employment effect of worksharing if there are no offsetting effects through changes in other determinants of employment such as total output. Calmfors and Hoel (1988) examine the effect of worksharing on output by assuming that firms aim at profit maximization. Then an increase in labour cost entailed in a standard working time reduction leads to a ‘‘scale effect’’ which reduces total output and total labour use. Hence, any positive employment effects may be mitigated, and even reversed, if output is affected. 2.2. Worksharing and wages Allowing for an interaction of hours and wages is seen to be of prime importance for the evaluation of the employment effects of worksharing. Calmfors (1985) examines a situation in which there is one union with monopoly power in setting wages, although the goals of achieving higher wages are constrained by the risk of unemployment. Given the wage set by the union, firms then decide on employment and working hours. The union is assumed to maximize the average utility of its members, which includes employed as well as unemployed. Given the production technology and the union’s objective function, one can derive the reaction of employment to normal hours. It turns out that the sign of the reaction depends on the parameters of the production function and utility function parameters. Different authors have therefore reached different conclusions. Houpis (1993) considers a number of different wage determination models and estimates of crucial parameters from the literature. His evidence points towards a positive effect of a reduction in working hours on employment. Booth and Schiantarelli (1987) use the same model as Calmfors (1985), but make specific assumptions about the production function (Cobb –Douglas) and the utility function of workers (Stone –Geary) and use empirical evidence from the literature to establish reasonable parameter values. On the basis of this calibration of their model they conclude that ‘‘the employment effect of a cut in hours is more likely to be negative’’. They also look at several variants of the model, including dynamic ones, and efficient bargaining models, where unions decide on both wages and employment. Their overall conclusions remain the same: shorter hours are likely to induce higher unemployment. A somewhat different variant is due to Booth and Ravallion (1993) who employ a framework very similar to that of Calmfors and Hoel (1988), but they abstract from overtime. They apply their model to aggregated data for the UK and Australia and find that in the UK a cut in hours may have a positive effect on employment. For Australia, the results are ambiguous. The disaggregated results for Australia show that in 7 out of 12 industries the employment will increase as a result of a cut in working hours (when wages and hours have been bargained efficiently). A number of other authors have investigated the direct effect of shorter hours on wages. Hunt (1999) uses the micro-dataset of the German Socio-Economic Panel (GSOEP) to analyse the effect of the reduction in standard working hours that were achieved by trade unions in (West) Germany starting from 1985. The author finds that although the reduction in standard working hours led to a fall in actual working hours (see Section 2.1), the fall in earnings is almost fully compensated for by a rise in the hourly wage rate. These results are inconsistent with the hypothesis that reductions in standard working hours are

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accompanied by wage restraints, as argued by Houpis (1993). Franz and Smolny (1994) reach slightly different conclusions. On the basis of a quarterly macro-time series model for German manufacturing from 1970 – 1989, they find that in certain industries hourly wages rose as a result of a reduction in standard hours but by and large workers are only partly compensated for the shorter working week. Nymoen (1989) uses quarterly Norwegian manufacturing data and finds a strong short-term effect of standard hours on wages (the possibility of a full compensation in earnings for the fall in hours lies within the 95% confidence interval of the estimated parameter), but in the long run the effect disappears. Holmlund and Pencavel (1988) find a positive effect of a reduction in hours on wages, using Swedish data for the manufacturing and mining sector. In line with this latter result, Jacobson and Ohlsson (2000) find a negative long-run relationship between wages and working hours in the private sector in Sweden over the period 1970– 1990. Estimates by Dur (1997) for the Netherlands show significant effects of a reduction in the number of contractual hours on wages. He finds that a 1% reduction in working time will increase the hourly wage by about 0.45%. Friesen (2002), for Canada, also reports substantially higher wages in jurisdictions with lower standard hours. Obviously, the results of Dur (1997), Hunt (1999) and Friesen (2002) contrast with the results presented in Houpis (1993) who believes that (hourly) wages are not likely to rise as a result of a reduction in working hours. In addition, Freeman (1998) discounts the possibility that wage demands from trade unions are the principal reason for the minimal effect of worksharing policies. This is because most trade unions recognize that a demand for full compensation of the reduction in working hours makes worksharing costly and potentially counter-productive. He refers to the fact that at least in some countries where the worksharing policy is pursued (for instance Belgium and the Netherlands) wage restraint is generally viewed as a necessary component of worksharing agreements. Altogether, the theoretical evidence (and opinions) on the wage effects of shorter hours appears to be mixed but the empirical evidence appears to point in the direction of shorter hours increasing wages. The extent to which this (possible) increase in wages offsets any positive effects of worksharing on employment is investigated in Section 3. 2.3. Heterogeneity, labour supply and inflation Freeman (1998) suggests that one of the principal reasons for a limited success of a worksharing policy lies in the difference between the skills of unemployed and employed persons. The studies referred to above have implicitly assumed that all workers are homogeneous, i.e. their skills are identical or differ only in level, not in type. To the extent that the unemployed are different from the employed, what matters is whether their skills are complements or substitutes. Suppose for instance that most of the unemployed are unskilled and that skilled and unskilled labour are complements. It is then conceivable that a reduction in work time of skilled labour actually decreases the demand for unskilled labour and therefore for the unemployed (Freeman, 1998; Bauer and Zimmermann, 1999). Freeman (1998) also mentions the labour supply response as one of the principal reasons behind a limited success of worksharing policies. In the situation where a reduction of standard hours is accompanied by a fall in income, and the household has a preference for income over leisure, the reduction in the official working time of one

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household member may increase the labour supply of other household members. Alternatively, the household member whose hours are cut may start looking for a second job. If there are demand constraints on extending the working time of persons already employed, additional members of the household may start looking for work, and thus there will be an ‘‘added worker effect’’. Riechel (1986) reports on high growth in the participation rate of women and in the preparedness to work overtime in the Netherlands during the period in which income losses were observed. In the author’s view, this trend suggests a substantial added worker effect. Kooreman and Kapteyn (1985) have investigated the interaction of labour supply of spouses in the context of a household labour supply model. In line with Riechel’s observation, they estimate that the hours worked by the female partner will increase just enough to maintain the level of household income of before the mandatory reduction of hours worked by the male partner. Moreover, as female wage rates are generally lower than male wage rates, the additional number of hours worked by the female in the household will on average be more than the reduction in hours by the male. Similarly, Friesen (2002) reports substantially more moonlighting in Canadian jurisdictions with lower standard working hours. In contrast with these findings, Hunt (1998) reports that a by-product of the reduction in standard hours of full-time male workers in Germany was a small reduction in the hours of their wives, possibly due to complementarity of leisure between spouses. Layard et al. (1991) argue that the reduction in working hours creates an inflationary pressure by (initially) reducing unemployment, hence an increase in wages. Since the changes in working hours do not affect the mix of unemployment and inflation that the government prefers, it is very likely that the government allows unemployment to rise again in order to control inflation. The authors conclude that ‘‘the net result of shorter working hours is then no reduction in unemployment, but a reduction in output’’.

3. Empirical analysis The principal aim of the empirical analysis is to study whether or not employment is affected by a reduction in working hours in the long run. As has become clear in the previous section, various studies have been undertaken to assess the employment effects of worksharing. Generally, these studies are of a partial nature, as they either look at particular sectors or firms in establishing whether jobs have been created or saved or they consider specific aspects only, e.g. whether wages have risen as a result of worksharing. The sectoror firm-level studies are incomplete in the sense that there are several mechanisms involved that cannot be taken into account. For instance, in a firm-level study one has to abstract from the effects of worksharing in a single firm on employment in other firms. Some studies exploit the phenomenon of ‘‘natural experiments’’, as in Cre´pon and Kramarz (2002) who analyse features of the work time reduction in France around 1982 to conclude that the mandatory reduction of the working week in France reduced employment. Since potentially the effects of worksharing are complicated and wide-ranging, the natural way to study these effects is by looking at whole economies over time. For this reason, the empirical analysis carried out in this study is based on a comparison of economies over time and across countries. This emphasis on studying the overall impact

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of working time reduction can be seen as our main empirical contribution to the existing empirical literature. By looking at an aggregate level, one can accommodate several of the feedbacks and secondary effects that cannot be dealt with by analyses at the firm or sector level. The consideration of particular aspects, and in particular the wage effects, is useful to gain insight in the importance of certain mechanisms, but clearly they will also not tell the whole story. As discussed in the previous section, worksharing may affect production and inflation. The empirical analysis does treat production and inflation as potentially endogenous explanatory variables but data limitations prevent us from estimating the long run effects of a reduction in working hours on production. In this respect, we present a partial analysis. Keeping this caveat in mind, the analysis does provide new insights in the long-run effects of a reduction in working hours on wages and employment and the central role of wages in the relationship between employment and working hours. The approach adopted here takes full account of the simultaneity between employment, wages and hours. It is of importance to note that, as discussed in the previous section, the form of worksharing considered in this study is that of shorter hours and throughout this section we make inferences about the effectiveness of worksharing based on the long-run effects of a reduction in hours on employment. The implicit assumption made here is that a mandatory reduction of the working week (i.e. worksharing) results in a similar reduction in actual working hours. Strong empirical support for making this assumption has been presented in Section 2.1. The outline of this section is as follows. Section 3.1 describes the data. Section 3.2 formulates the empirical model and Section 3.3 presents and discusses the estimation results. 3.1. Data Annual data have been gathered on the employment rate, working hours, wage rates, Gross Domestic Products (GDP), Consumer Price Indices (CPI), and the shares of the population between 15 and 65 for 16 OECD countries. The data cover the time period 1960 –2001. Statistics on before tax average wages and CPI are taken from the International Financial Statistics of the International Monetary Fund (1980, 1997, 2002). The CPI is a Laspeyres price index of the cost of living and we take 1990 as reference year (1990 = 100). Statistics on employment and the share of the population between 15 and 65 years of age are taken from the Labour Force Statistics of the Organization for Economic Co-operation and Development (1988, 2002). Employment is defined as the number of persons in paid work or self-employment. International comparable statistics on GDP, annual hours of work and population size have been provided by the Groningen Growth and Development Centre (GGDC)5. Real GDP is in 1990 US dollars and corrected for differences across countries in purchasing power. Hours of work are the average actual working hours per year of the employed population. GGDC does not provide yearly information on hours of work before 1979. Hours of work information over the years 5 We use data from the ‘‘Total Economy Database’’ and a detailed description of these data can be found on: http://www.eco.rug.nl/ggdc. The GGDC collects data from the official international statistics.

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Table 1 Observation period per country Country

Period

Number of observations

Australia Canada France West Germany Greece Ireland Italy Japan Netherlands New Zealand Norway Portugal Spain Sweden United Kingdom United States All

1971 – 2001 1963 – 2001 1970 – 2001 1963 – 1990 1979 – 1998 1979 – 2001 1966 – 2001 1971 – 2000 1971 – 2001 1971 – 2001 1963 – 1996 1974 – 1993 1977 – 2001 1963 – 2001 1970 – 2001 1960 – 2001

31 39 32 28 20 23 36 30 31 31 34 20 25 39 32 42 493

1960– 1978 have been taken—if available—from the Labour Force Statistics6 (OECD) whenever the hours information over the later years of the OECD matched those of the GGDC, since only then we can be certain that the source of information is the same. Given these statistics, we define the employment rate as employment over the population between 15 and 65 years of age, the wage rate as the average real hourly wage rate (index, 1990 = 100) and working hours as the average number of actual hours worked per week. In the empirical analysis, a logarithmic specification together with the countryspecific effects will control for differences in purchasing power and the fact we used wage rate indices rather than real wage rates. The raw data contains information on 22 OECD countries. Insufficient information is available for Austria, Belgium, Denmark, Finland, Luxembourg and Switzerland and we therefore exclude these from the analysis. For the remaining 16 countries (see Table 1), not all the necessary information is available in every year. Of the potential 672 observations, i.e. 42 yearly observations for each of the 16 countries, 168 observations have been excluded because of missing values. Most of the missing values are on the working hours or the wage rate in the earlier years of the observation period. The statistics for Germany are influenced by the reunification of East and West Germany and for this reason only observations of West Germany up to 1990 are included (11 exclusions). Altogether, these years and countries form 493 observations. Table 1 reports the observation periods for the 16 countries used in the empirical analysis. Table 2 reports averages for the employment rate, weekly hours of work and the share of the population between 15 and 65 years of age for three sub-periods: the years up to and

6

We used the OECD website: http://www1.oecd.org/scripts/cde/viewbase.asp?DBNAME = lfs_data.

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Table 2 Average employment rate, weekly hours of work and the share of the population between 15 and 65 years of age Employment rate (%)

Weekly hours of work (actually worked)

Share of the population between 15 and 65 (%)

Period

< 1980

1981 – 1990

>1990

< 1980

1981 – 1990

>1990

< 1980

1981 – 1990

>1990

Australia Canada France West Germany Greece Ireland Italy Japan Netherlands New Zealand Norway Portugal Spain Sweden United Kingdom United States

66.1 61.4 63.6 66.7

65.2 66.9 59.0 62.3

67.7 67.7 58.9 –

36.7 36.9 36.0 36.1

35.9 34.5 32.5 32.0

35.7 34.2 31.0 –

64.0 62.8 62.8 64.6

66.2 68.1 65.5 69.4

66.7 67.9 65.3 –

54.4 57.6 53.6 69.9 53.4 64.1

55.0 52.8 52.9 70.9 54.6 65.7

53.9 57.7 52.3 74.5 66.8 68.9

38.6 39.3 34.8 41.4 30.9 34.7

37.2 37.1 32.3 40.2 28.3 34.4

37.2 34.4 31.4 36.3 26.7 34.0

63.9 58.8 66.3 67.8 64.2 61.4

65.8 60.1 68.7 68.5 68.2 65.0

67.5 64.7 68.4 69.2 68.3 65.4

65.6 64.3 52.4 74.5 69.6

74.3 64.4 46.6 79.7 66.6

72.0 67.5 49.9 72.4 69.3

33.5 37.5 38.5 32.2 35.9

28.2 36.1 36.0 29.4 33.7

27.4 34.6 35.0 30.8 33.3

62.8 63.0 62.9 65.1 63.0

64.2 65.0 64.9 64.5 65.3

64.6 67.5 68.0 64.0 65.1

62.6

68.3

72.0

37.0

35.2

35.3

62.1

66.3

65.7

including 1980, the years 1981 –1990 and the years from 1991 onwards.7 For the same sub-periods, Table 3 reports percentage changes for all variables. Tables 2 and 3 show that the levels and trends over time of the employment rate differ considerably across countries. The English-speaking countries have relatively high employment rates and have remarkable similar employment rates at the end of the 1990s. Japan experienced high employment rates over the entire observation period. Up to the end of the 1980s, Norway and Sweden experienced the highest employment rates among the 16 countries and their employment rates decreased thereafter to the level of English-speaking countries. The employment rate in the Netherlands increased rapidly during the 1980s and 1990s up to the level of English-speaking countries. In the 1990s, France, Greece, Italy and Spain have notably low employment rates. Table 3 shows that most countries, with the exceptions of New Zealand and Portugal, experienced high real wage growth during the 1970s and a slowdown thereafter. Table 2 shows that the levels of working hours differ considerably across countries and that all countries experienced a downward trend in working hours. However, the downward trend has come to a halt at the end of the 1970s for the Englishspeaking countries—with the exception of Ireland—while almost all European countries continue to decrease working hours up to the end of the 1990s. The exception is Sweden, which has experienced an increase in the average working hours during the 1980s and 1990s. Table 3 shows that the real GDP per capita is generally increasing with time. Especially Ireland—the Celtic tiger—has experienced incredible growth since the 1980s. 7

For the remaining three variables, we only observe indices.

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Table 3 Average percentage changes per year for all variables Employment rate

Weekly hours of work (actual worked)

< 1980 1981 – 1990 >1990

< 1980 1981 – 1990 >1990

Period

< 1980

1981 – 1990

Australia Canada France West Germany Greece Ireland Italy Japan Netherlands New Zealand Norway Portugal Spain Sweden United Kingdom United States

 0.25 0.72  0.28  0.37

0.38 0.48  0.55  0.04

0.26 0.01 0.44 –

2.32 2.46 4.84 4.85

0.02 0.21 1.47 2.03

1.65 0.35 1.26 –

 0.65  0.75  0.88  0.96

 0.07  0.08  0.80  0.83

 0.14  0.04  0.72 –

0.08  2.01  0.04 0.01  0.51  0.01

0.03  0.66 0.05 0.30 1.31 0.33

0.19 1.87 0.01 0.33 1.61 0.69

1.75 1.65 5.02 3.78 2.04 0.66

1.12 1.33 1.04 1.85 0.26  1.84

0.18 3.00 0.05 1.87 0.34  0.21

 0.37  1.98  0.71  0.63  0.75  0.25

 0.49  0.53  0.25  0.44  1.05  0.19

0.05  1.27  0.38  1.10  0.26  0.02

1.02  1.15  3.40 0.55  0.07

 0.03 1.02 0.00 0.24 0.27

0.39  2.52 1.30  0.93  0.02

2.96  4.00 4.48 1.71 2.50

0.97 0.62 1.17 0.84 2.55

1.34 1.37 0.88 1.59 1.95

 1.49  1.40  1.56  1.25  0.93

 0.55  0.24  0.95 0.28  0.02

 0.29  1.74  0.04 0.31  0.30

0.25

0.89

 0.10

1.14

 0.72

0.19  0.45

0.08

 0.09

Period Australia Canada France West Germany Greece Ireland Italy Japan Netherlands New Zealand Norway Portugal Spain Sweden United Kingdom United States

>1990

Real hourly wage rate

Real gross domestic product

Consumer price index

Share of the population between 15 and 65

< 1980

< 1980 1981 – 1990 >1990

< 1980 1981 – 1990 >1990

1981 – 1990

>1990

1.80 2.91 2.54 2.96

1.69 1.53 1.78 1.88

2.24 1.45 1.37 –

9.76 5.70 8.78 3.80

7.50 5.57 5.86 2.54

0.74 2.03 3.53 3.14 1.95 0.72

1.05 3.16 2.13 3.30 1.58 1.03

1.43 5.84 1.38 1.14 2.07 1.40

19.89 15.51 9.48 8.35 6.78 11.21

3.69 1.47 0.19 2.36 1.79

1.96 2.90 2.47 1.67 2.34

3.32 1.12 2.30 1.34 1.89

2.42

2.18

1.68

2.34 1.99 1.72 –

0.38 0.85 0.22 0.00

0.27 0.07 0.32 0.54

0.00 0.08  0.10 –

15.91 7.00 8.70 2.00 2.36 9.56

9.75 0.31 2.66 0.17 3.50  0.03 0.82  0.26 2.57 0.60 1.80 0.59

0.46 0.42 0.32 0.35 0.40 0.40

0.13 0.86  0.17  0.28  0.15  0.04

6.46 17.67 14.59 6.59 11.95

7.06 14.48 8.46 7.05 6.12

2.15  0.03 8.27 0.37 3.70 0.37 2.25  0.22 2.85 0.19

0.25 0.48 0.49 0.03 0.18

 0.03 0.79 0.26 0.06 0.06

4.94

4.48

 0.05

0.07

2.72

0.64

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Table 3 shows the increase in the Consumer Price Index for the three sub-periods. Inflation has clearly gone down in all countries since the 1970s. Table 2 shows that the share of the population between 15 and 65 has gone up for most countries over the observation period but the patterns clearly differ across countries (see also Table 3). 3.2. Econometric model As discussed in Section 2.2, the wage rate plays a central role in the relationship between working hours and the employment rate. A reduction in working hours may cause an increase in the wage rate and, consequently, reduce or even neutralize the presumably positive direct effect of a reduction in working hours on the employment rate. Furthermore, it may be the case that the causality runs in the opposite direction as a low level of employment may trigger a policy of reducing working hours. Given these considerations, we take fully into account the interrelationship between the employment rate, the wage rate and working hours. To be able to identify the long-run effects we include in our analysis, the Consumer Price Index (CPI), the share of the population between 15 and 65 years of age (Share 15 – 65), and real Gross Domestic Product (GDP) per capita as explanatory variables. As discussed in the introduction of Section 3, simultaneity between all these variables is taken into account by using an Instrumental Variable estimator. As instruments, we use the lagged values of all explanatory variables. In the empirical analysis, a logarithmic transformation is applied to all six variables. Let us assume that a long-run relationship exists between the vector of dependent variables Yit and explanatory variables Zit and is given by: ðI  Ui ÞYit ¼ H0;i þ Hi Zit þ Uit

i ¼ 1; . . . ; N ;

t ¼ ti0 ; . . . ; tiT :

ð1Þ

Yit is a vector containing (log-) employment rate, (log-) wage rate and (log) working hours in period t of country i, and Zit is a vector containing (log-) GDP, (log-) CPI and (log-) Share 15– 65 in period t of country i. N is the number of countries and T is the number of time periods. Uit is a vector of error terms, which are assumed to be distributed independently across time and countries. The parameters of interest are the elements of Ui and Hi and are interpreted as percentage changes in the dependent variable in the longrun as a result of a 1% change in the explanatory variable since we use a logarithmic transformation of all variables in the system. Ui is a (3  3)-matrix with zeros on the diagonal, H0,i is a (3  1)-vector of intercepts, and Hi is a (3  3)-matrix. Several elements of Hi are set equal to zero to satisfy the rank and order conditions for identification (see, e.g., Davidson and MacKinnon, 1993). We return to the issue of identification below. At this stage, it is convenient to write down the long-run relationship between a single endogenous variable (denoted by yit) and the remaining (endogenous) variables (denoted by Xit) as follows: yit ¼ h0;1 þ XitVhi þ uit

i ¼ 1; ::; N ;

t ¼ ti0 ; ::; tiT :

ð2Þ

There is, of course, a one-to-one correspondence between the parameters in Eq. (2) and the parameters in Eq. (1). The variables included in Eq. (2) may be non-stationary

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A. Kapteyn et al. / Labour Economics 11 (2004) 293–313

but are assumed cointegrated.8 This means the error term uit is assumed to be stationary. The data generating process is taken to be an AutoRegressive Distributed Lag model (ARDL( p,q)): yit ¼ li þ ci t þ

p X

kij yitj þ

j¼1

q X

dijVXitj þ ei;t

i ¼ 1; ::; N ;

t ¼ ti0 ; ::; tiT :

ð3Þ

j¼0

The error term is assumed distributed independently across time and countries. The distributed lag orders on yit and Xit, i.e. the values of p and q, are chosen in such a way that the error terms are independent across time, i.e. the errors terms are serially uncorrelated. Eq. (3) can be written in an error-correction equation from which we can identify both the long- and short-run effects: dyit ¼ li þ ci t þ /i ðyit1  hiVXit Þ þ

p1 X

k*ij dyitj þ

j¼1

q1 X

d*ij dXitj þ ei;t ;

ð4Þ

j¼0

with: /i ¼ ð1 

p X

kij Þ;

hi ¼

j¼1

i ¼ 1; ::; N ;

q X j¼0

dij =/i ;

k*ij ¼ 

p X m¼jþ1

kim ;

d*ij ¼ 

q X

dim ;

m¼jþ1

t ¼ ti0 ; ::; tiT :

The intercept term h0,i of Eq. (2) is absorbed in the country specific intercept in Eq. (4). Ideally, we would like to estimate Eq. (4) for each country separately and subsequently estimate the average long-run elasticities. This approach is better known as a Mean Group Estimator (MGE, Swamy, 1970). However, as shown by Hsiao et al. (1999), the MGE performs badly in small samples (both T and N are considered to be small in our case). An alternative is to a priori restrict all parameters in Eq. (4) to be the same across countries. This pooling of the data essentially imposes the restriction of slope homogeneity. Pesaran and Smith (1995) show that conventional estimators may yield inconsistent parameter estimates when in fact slope homogeneity does not hold. In our empirical application, slope heterogeneity may arise from the fact that institutional settings are different across the countries. This causes labour markets in different countries to react differently to changes in, for instance, working hours or inflation in the short run. Pesaran et al. (1999) suggest an alternative estimator. Basically, they assume the longrun effects to be constant across countries while the short-run effects are allowed to differ across countries. This they call the Pooled Mean Group (PMG) estimator. They discuss the asymptotic properties of PMG and show that PMG does a better job in relatively small samples compared to a MGE or a dynamic fixed effect model. For this reason, we choose 8 Hsiao (1997) provides an excellent discussion on the issues of identification of long-run effects and cointegration.

A. Kapteyn et al. / Labour Economics 11 (2004) 293–313

305

to employ the PMG estimator. Effectively, it means we impose the following restriction on the model: hi ¼ h;

i ¼ 1; ::; N :

ð5Þ

Estimates of the elements of h are the average long-run effects. Imposing restriction (5) on Eq. (4) yields the following equation: dyi;t ¼ li þ ci t þ /i ðyi;t1  h VXi;t Þ þ

p1 X j¼1

k*ij dyi;tj þ

q1 X

d*ij dXi;tj þ ei;t :

ð6Þ

j¼0

To estimate Eq. (6), an iterative estimation procedure as proposed by Pesaran et al. (1999) has been implemented. The parameters of interest for this paper are the long-run effects. Given the long-run effects, we are able to quantify the total effect of a change in working hours on the employment rate. Moreover, we can analyse the central role of the wage rate in this. We estimate Eq. (6) using an Instrumental Variables estimator. We instrument all six variables in our model. In order to prevent any biases due to correlated measurement errors (Holtz-Eakin et al., 1988), the instruments are the lagged values of each variable of the periods this variable is not included as an explanatory variable in the system. Test statistics for the presence of a unit root in each of the six variables are reported in Table 2. The results in Table 4 show that for all series except the wage rate the null hypothesis of a unit root is accepted. We therefore assume that these series are non-stationary and integrated of order 1. The standard errors are calculated taking into account the possibility that the regressors are I(1) and the error terms are heteroscedastic. 3.3. Empirical results Eq. (6) is estimated for each of the three endogenous variables: employment rate, wage rate and working hours. GDP, CPI and Share 15 –65 are considered to be endogenous explanatory variables. As noted in Section 3.2, we need to impose several restrictions in order to satisfy the rank and order conditions for identification. The following restrictions are imposed on the model: CPI is excluded from the employment rate and working hours equations, the Share 15 –65 is excluded from the wage rate and working hours equations. For the employment rate, an ARDL(1,1), for the wage rate an ARDL(2,1) and for working Table 4 Panel unit root tests, Im et al. (2003)

Ln(Employment Rate) Ln(Wage Rate) Ln(Working Hours) Ln(Gross Domestic Product) Ln(Share Population 15 – 64) Ln(Consumer Price Index) H0: series has a unit root.

t-bar statistic

Critical value

Conclusion

 2.29  2.44  2.03  2.18  2.27  1.83

 2.41  2.28  2.41  2.28  2.28  2.41

I(1) – I(1) I(1) I(1) I(1)

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A. Kapteyn et al. / Labour Economics 11 (2004) 293–313

Table 5 Long-run relationshipsa Partial elasticities Ln(Employment Rate) Ln(Wage Rate) Ln(Working Hours) Ln(Gross Domestic Product) Ln(Share Population 15 – 64) Ln(Consumer Price Index) R-Squaredb Over-Identification Test (d.f.)b Cointegration Testc Test on Cross-Country Restrictions (d.f.)b

Ln(Working Hours)

Ln(Employment Rate) 0.22 (0.12)

 0.43 (0.07)  0.34 (0.18) 1.39 (0.11)  0.85 (0.18) 0.62 6.44 (5)  2.65 2.46 (4)

Ln(Wage Rate)  0.01 (0.04)  0.11 (0.01)

 0.40 (0.13) 0.47 (0.12)  0.05 (0.04) 0.63 6.41 (4)  3.00 3.26 (4)

0.54 9.73 (8)  2.62 3.33 (2)

a

Standard errors are in parentheses. The goodness-of-fit statistic R2, the over-identification test for testing the validity of the instruments and the test on cross-country restrictions pertain to Eq. (6). Degrees of freedom (d.f.) in parentheses and critical values 2 2 2 2 are: v0.95 (2) = 5.99, v0.95 (4) = 9.49, v0.95 (5) = 11.1 and v0.95 (8) = 15.5. c The Cointegration Test pertains to Eq. (2). Critical value:  2.28, H0: no cointegration. b

hours an ARDL(2,1) are chosen, based on the model specification tests (see Appendix A). The system is over-identified. However, adding a fourth equation to the system would yield a violation of the rank condition.9 As discussed above, we use as instruments the third and fourth period lagged values of the employment rate, wage rate, working hours and Share 15 – 65, and the second, third and fourth lagged values of GDP and CPI. In total, we have 14 instruments, excluding the constant and trend. The estimates of the long-run coefficients, as given by the h’s in Eq. (6), are reported in Table 5. For completeness, estimates of the country-specific effects (li + h0,i), trend (ci), the short-run parameters (k*ij and d*ij) and the adjustment coefficient (/i) are reported in Appendix A. Furthermore, Appendix A reports the R2 and a serial correlation test for each equation and country. Before turning to the estimation results of the long-run relationships, we discuss briefly several model specification tests reported at the bottom of Table 5. To validate the instruments used, Table 5 presents at the bottom an over-identification test for each equation. The null-hypothesis is that the instruments are orthogonal to the error terms, which is a necessary condition for consistency. This null-hypothesis is accepted for each equation. As mentioned above in the model outline, the two crucial assumptions we make are that a long-run relationship exists and Eq. (2) is a cointegrating relationship. A test of the existence of a long-run relationship for each country is equivalent to testing the null-hypothesis /i = 0 for each country. The test results reported in Appendix A show that for most countries we reject the null-hypothesis for each equation, which is in favour of the existence of a long-run relationship. Furthermore, the panel unit root tests on the error term in Eq. (2) (bottom of Table 5) are in favour of a cointegrating relationship for each of the equations. Finally, the restrictions imposed on the system of constant long-run effects across countries (Eq. (5)) are tested in the last row of Table 5. These restrictions are not rejected. 9 For example, adding an equation explaining the long-run effect of working hours on GDP would result in a violation of the rank condition for the employment rate equation.

A. Kapteyn et al. / Labour Economics 11 (2004) 293–313

307

Table 6 The long-run effects of an exogenous changea Cells: %

Employment rate

Wage rate

Working hours

A 1% change in: Employment Rate Wage Rate Working Hours

0.92 (0.04)  0.38 (0.06)  0.16 (0.19)

0.22 (0.10) 0.96 (0.05)  0.46 (0.14)

 0.03 (0.04)  0.10 (0.02) 1.05 (0.02)

a

Standard errors are in parentheses.

The estimation results reported in Table 5 show that most coefficients are in line with the theoretical predictions as discussed in Section 2. A 1% increase in the wage rate results in a 0.43% decrease in the employment rate and a 0.11% decrease in working hours. A 1% increase in the employment rate, inducing a tighter labour market, results in a 0.22% increase in the wage rate and has virtually no effect on working hours. A 1% reduction in working hours results in a 0.34% increase in the employment rate. This effect is positive and (marginally) significant. Furthermore, a 1% reduction in working hours results in a 0.40% increase in the real wage rate. Table 5 reports the partial effects. To analyse the total effects of a reduction in working hours on the employment rate, i.e. taking for instance wage effects into account, we have to solve for the reduced form for employment, wages and working hours. Table 6 presents the reduced form effects. Since the equations are in logs, the reduced form coefficients in Table 6 can be interpreted as elasticities. The second column in Table 6 shows that a 1% reduction in working hours results, in the long run, in a 0.46% increase in the real hourly wage rate. This implies that weekly earnings of workers are partly compensated for the loss in working hours. This compensation diminishes the partial effect of a decrease in working hours on the employment rate. The partial effect according to Table 5 was 0.34%. But the total effect of a 1% reduction in working hours according to Table 6 is only an insignificant 0.16% increase in the employment rate. Thus, the picture emerges that an exogenous reduction in working hours causes an increase in the real wage rate and, consequently, eliminates most of the positive direct effect of a reduction in working hours on the employment rate (Table 5) and turns it into an (insignificant) effect (Table 6). The empirical results stress the importance of taking the simultaneity between employment rate, wage rate and working hours into account when addressing the effects of a reduction in working hours on the employment rate.

4. Concluding remarks This paper considers both the theoretical and the empirical cases to evaluate worksharing as a policy tool for promoting employment (or reducing unemployment). The insights obtained from the literature review are inconclusive as to the efficacy of worksharing as a means to promote employment. Our empirical analysis does not provide support for the proposition that worksharing would reduce unemployment. The results show a positive direct effect on employment of a reduction in working hours but this

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A. Kapteyn et al. / Labour Economics 11 (2004) 293–313

reduces to a small insignificant long-run effect on employment due to an increase in wages. These results are in line with recent empirical results from recent country-specific studies, in particular for France (Cre´pon and Kramarz, 2002), for Germany (Hunt, 1999) and for Sweden (Jacobson and Ohlsson, 2000). Obviously, all these considerations do not preclude one to prefer shorter hours as a means of attaining additional leisure by sacrificing income. To facilitate such possibilities at an individual level may be welfare enhancing, just as it may be welfare enhancing to create possibilities for people to work longer hours and earn more, if they wish to do so. Additionally, other arguments have been advanced in favour of worksharing, for instance that it may generate greater emancipation of women. These other arguments in favour of worksharing need to be judged on their own merit and may form a compelling reason to work shorter hours. But if one wants to increase employment, other measures are probably much more effective than worksharing.

Acknowledgements This paper grew out of the research project Working Time and Employment (Arbeidsduur en Werkgelegenheid), commissioned by the Netherlands Scientific Council for Government Policy (Wetenschappelijke Raad voor het Regeringsbeleid). The authors are grateful to Krijn van Beek of the Council, for fruitful discussions on different versions of this report. Comments on earlier versions by Rob Alessie and Klaas de Vos, and comments by Jan van Ours and two anonymous referees are also gratefully acknowledged. All correspondence to the first author: RAND, P.O. Box 2138, Santa Monica CA90407.

Appendix A . Estimates of the country specific effects (li+h0,i), trends (ci), the shortrun parameters (k*ij and d*) ij and the adjustment coefficient /i, Eq. (6) Notation: E = ln(employment rate), W = ln(wage rate), H = ln(working hours), G = ln(GDP), S=(Share of the population between 15 and 65). The abbreviations of the countries correspond row-wise to the list of countries in Table 1. Furthermore, p.e. denotes the parameter estimate and s.e. the corresponding standard error. Independence across time of the error term in Eq. (6) is a necessary condition for obtaining consistent parameter estimates. This condition can be satisfied by choosing the distributed lag in such a way that the model passes a test on serial correlation. The serial correlation test is based on the estimated residuals of Eq. (6) and the fact we employ an Instrumental Variables estimator is taken into account (Davidson and MacKinnon, 1993, Chapter 10). Results not reported here clearly showed that a ARDL(1,1) representation for the wage rate and working hours is not sufficient in order to pass the serial correlation tests for most countries. Choosing an ARDL(2,1) for the wage rate and working hours solved the most serious serial correlation problems. The results in Tables A1 –3 show that for most countries the three equations pass the test of no serial correlation.

Table A1 Employment rate equation

AU CN FR DE GR IR IT JP NL NZ NW PT ES SD UK US

DW

Trend

DH

DG

DS

Adjustment coefficient

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

0.35 1.00 0.00  1.42 0.03 0.64  0.62  1.26  0.01  3.46  0.37 0.51 0.46 0.89 0.00  0.16

0.25 1.49 0.00 0.67 0.07 0.18 0.13 0.60 0.00 0.69 0.16 0.55 0.19 0.68 0.00 0.43

 0.01  1.84 0.00 0.86 0.39 0.04 0.00  0.10 0.00 0.56 1.46  2.77 0.00 0.43 0.03  0.68

0.00 0.68 0.10 0.53 0.22 1.23 0.00 0.61 0.32 0.59 0.22 1.24 0.00 0.69 0.12 0.33

 0.22  0.42  0.24  2.24  0.01  4.37  0.18 0.36 0.18  0.31 0.00  1.87 0.16  0.25 0.59  1.24

0.19 0.50 0.28 1.71 0.00 1.16 0.21 0.66 0.23 1.26 0.00 0.81 0.07 0.16 0.09 0.67

0.00  0.19 0.07 0.00  0.09  1.57  0.01  2.37 0.03 0.00 0.01  6.09 0.00 0.48 0.35 0.31

0.00 0.52 0.05 0.20 0.14 0.32 0.00 0.70 0.09 0.20 0.20 2.20 0.00 0.67 0.34 0.51

0.53 1.87 0.00  0.14 0.11 0.32 0.10  0.19 0.00  1.07  0.15  0.09 0.19  1.01 0.00  0.60

0.16 1.76 0.01 0.53 0.10 0.56 0.19 0.86 0.00 0.77 0.08 0.20 0.11 0.35 0.00 0.26

0.31  0.42  0.53  6.70  0.01  3.64 0.90 0.88  0.25  1.46  0.01  3.67 0.21  1.12 0.09 0.71

0.35 0.45 0.33 2.40 0.00 1.23 0.31 1.15 0.39 2.78 0.00 1.17 0.12 0.43 0.18 1.50

 0.69  0.28  0.02  0.36 0.07  0.02  0.16  0.10  0.54  0.57  0.30  0.01 0.08  0.22  0.54  0.02

0.12 0.11 0.08 0.08 0.11 0.11 0.11 0.04 0.15 0.12 0.09 0.11 0.11 0.09 0.07 0.06

R2

Serial correlation t-test

0.77 0.47 0.83 0.85 0.41 0.76 0.32 0.58 0.52 0.54 0.56 0.41 0.89 0.59 0.90 0.49

0.39  0.18 0.54  0.18  0.21  0.08 11.6 0.71 0.10 1.47 0.50 0.26  0.59 1.73 0.10 1.15

A. Kapteyn et al. / Labour Economics 11 (2004) 293–313

Constant

309

310

Constant

AU CN FR DE GR IR IT JP NL NZ NW PT ES SD UK US

Trend

DW lagged

DE

DH

DG

DC

Adjustment coefficient

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

0.00 0.46 0.02 0.08 0.25  1.44  0.96 0.00 0.85 0.56  0.70  0.78 0.22  0.30 0.00  0.13

0.00 0.21 0.23 0.30 0.62 0.53 0.27 0.00 0.49 0.16 0.34 0.59 0.27 0.15 0.00 0.14

 0.03  0.10 0.00 1.52  0.51  0.40 0.38 0.24  0.63 0.00 0.40  0.26 2.18 1.31  1.89  1.36

0.61 0.42 0.01 0.79 0.20 0.18 0.37 0.27 0.19 0.00 0.20 0.25 0.85 0.94 0.89 0.36

0.13  0.34  1.70 0.44  0.35 0.00 0.56 0.32  1.34 0.34 0.82 0.44 0.00 0.30 0.30  0.79

0.28 0.36 0.90 0.47 0.22 0.00 0.32 0.25 0.63 0.59 0.47 0.16 0.00 0.20 0.23 1.20

 0.31 0.59 0.07 0.00 0.20 0.45 0.63  0.24 0.02 0.22 0.00 0.14 0.44  0.27  0.44 0.66

0.59 0.75 0.24 0.00 0.18 0.16 0.55 0.70 0.37 0.33 0.00 0.13 0.15 0.47 0.47 0.38

 0.21 0.00 1.53 0.37  0.01  0.55  0.35  0.52 0.00 0.89  0.31 0.01 1.13  0.31 0.07 0.00

0.32 0.01 0.73 0.08 0.13 0.19 0.09 0.16 0.00 0.41 0.22 0.44 1.10 0.31 0.14 0.00

0.45 0.34  1.38  0.39 0.32 0.14 0.00 0.47 0.36  0.24 0.48  0.54  0.60  0.01 1.50 0.64

0.20 0.17 0.50 0.53 0.24 0.16 0.00 0.39 0.12 0.14 0.24 0.16 0.21 0.00 0.69 0.18

0.36  1.72 0.17  0.47 0.00 0.46 0.59  0.05  1.35 0.23 0.09 0.00 0.32 0.21 0.02  1.77

0.20 0.75 0.26 0.20 0.00 0.31 0.23 0.32 0.82 0.31 0.16 0.00 0.25 0.20 0.66 1.24

 0.28  0.20  0.15  0.12  0.71  0.37  0.21  0.30  0.69  0.14  0.24  0.69  0.11  0.15  0.48 0.08

0.11 0.06 0.08 0.09 0.19 0.09 0.06 0.15 0.10 0.11 0.09 0.21 0.08 0.10 0.14 0.06

R2

Serial correlation t-test

0.56 0.67 0.70 0.63 0.74 0.90 0.71 0.60 0.82 0.49 0.55 0.62 0.63 0.47 0.45 0.58

1.36 0.96  0.31 0.52 0.12  1.56 0.88 0.92 0.41 0.43 1.21  0.73 0.89 0.77  0.14 0.52

A. Kapteyn et al. / Labour Economics 11 (2004) 293–313

Table A2 Wage rate equation

Table A3 Working hours equation

AU CN FR DE GR IR IT JP NL NZ NW PT ES SD UK US

DH lagged

Trend

DE

DW

Adjustment coefficient

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

p.e.

s.e.

0.72 0.43  0.16 0.13 0.00 0.41  0.10 0.49  0.14 0.00 1.17 0.07 0.27 0.08 0.00 0.63

0.32 0.20 0.07 0.06 0.00 0.14 0.17 0.12 0.09 0.00 0.30 0.24 0.12 0.08 0.00 0.28

0.00 2.28 0.53  0.01  0.14 0.00 0.11  0.06 0.29 0.05 0.00 3.23 0.17 0.02 0.20 0.00

0.00 0.59 0.20 0.10 0.08 0.00 0.22 0.13 0.06 0.03 0.00 0.62 0.10 0.05 0.12 0.00

0.12 0.16 0.08 0.00 3.14  0.03 0.27 0.15 0.00 1.10 0.99  0.09 0.17 0.00 2.35 0.47

0.21 0.10 0.10 0.00 0.75 0.37 0.14 0.11 0.00 0.39 0.34 0.18 0.14 0.00 0.74 0.21

0.10 0.05  0.01 4.29  0.10 0.06  0.03 0.00 1.77 0.22  0.03  0.46 0.00 1.28 0.44  0.01

0.12 0.07 0.00 0.88 0.25 0.23 0.08 0.00 0.76 0.15 0.10 0.10 0.00 0.41 0.19 0.09

0.04 0.00 2.00 0.54  0.16  0.05 0.00 0.73 0.38  0.21 0.39 0.00 0.78 0.33 0.02  0.08

0.05 0.00 0.49 0.22 0.29 0.15 0.00 0.33 0.25 0.13 0.20 0.00 0.51 0.19 0.04 0.05

 0.77  0.27  0.56  1.04  0.43  0.30  0.50  0.17  0.20  0.55  0.03  0.76  0.18  0.11  0.29  0.15

0.18 0.09 0.18 0.21 0.18 0.10 0.12 0.08 0.12 0.14 0.05 0.15 0.08 0.04 0.07 0.07

R2

Serial correlation t-test

0.56 0.39 0.41 0.56 0.33 0.76 0.56 0.46 0.23 0.50 0.56 0.82 0.68 0.68 0.62 0.43

0.65 0.28 0.26 0.38  0.29  0.96  1.24  0.05  0.17 0.87  0.38  0.08  1.56  0.36 1.41 2.93

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Constant

311

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