MEMORANDUM. No 33/2003. The Effects of Taxes and Socioeconomic Variables on Market Work and Home Production in Norway in the Years 1970 to 2000

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1 MEMORANDUM No 33/2003 The Effects of Taxes and Socioeconoic Variables on Market Work and Hoe Production in Norway in the Years 1970 to 2000 Christoph Schwierz ISSN: Departent of Econoics University of Oslo

2 This series is published by the University of Oslo Departent of Econoics P. O.Box 1095 Blindern N-0317 OSLO Norway Telephone: Fax: Internet: e-ail: econdep@econ.uio.no In co-operation with The Frisch Centre for Econoic Research Gaustadalleén 21 N-0371 OSLO Norway Telephone: Fax: Internet: e-ail: frisch@frisch.uio.no No 32 No 31 No 30 No 29 No 28 No 27 No 26 No 25 No 24 No 23 List of the last 10 Meoranda: John K. Dagsvik, Steinar Strø and Zhiyang Jia A Stochastic Model for the Utility of Incoe. 39 pp. Karine Nyborg, Richard B. Howarth, and Kjell Arne Brekke Green consuers and public policy: On socially contingent oral otivation. 23 pp. Halvor ehlu A Finer Point in Forensic Identification. 13 pp. Svenn-Erik Maelund Effects of the Spanish Influenza Pandeic of on Later Life Mortality of Norwegian Cohorts Born About pp. Fedor Iskhakov Quasi-dynaic forward-looking odel for joint household retireent decision under AFP schee. 59 pp. Henrik Wiig The Productivity of Social Capital. 22 pp. Tao Zhang Identifying treatent effects of active labour arket prograes for Norwegian adults. 45 pp. Tao Zhang A Monte Carlo study on non-paraetric estiation of duration odels with unobserved heterogeneity. 89 pp. Karine Nyborg and Kjetil Telle The Role of Warnings in Regulation: Keeping Control with Less Punishent. 31 pp. Maria Kalvarskaia Savings behaviour when households havean access to occupational pensions. 50 pp. A coplete list of this eo-series is available in a PDF forat at:

3 The Effects of Taxes and Socioeconoic Variables on Market Work and Hoe Production in Norway in the Years 1970 to 2000 Christoph Schwierz 1 March 2003 Abstract This paper analyses significant forces of the allocation of tie to different hoe production activities, as developed by Gronau, in a data set consisting of decennial tie-use surveys of Norwegian households. The theoretical fraework consists of joint allocation of tie odel, where household decisions to allocate tie between the arket and the household are analyzed siultaneously. The estiation takes place within a liited dependent variables fraework. As an alternative to the usually eployed Tobit odel, Cragg s double-hurdle odel is used, so as to be able to odel individual decisions in a two step fraework, discerning between the wish to participate and the aount of tie to invest in different activities. The conclusion of the paper is that taxation has a significant effect on the allocation of tie to arket and non-arket activities. There is evidence in favour of ore disaggregation of tie-use, but the overall essage of the hoe production literature that explicit consideration of the arket-versus-hoe production argin can iprove estiates of labor supply elasticities - is upheld. Keywords: hoe production, allocation of tie, double-hurdle odel, labor supply elasticities This paper is part of the project Own production, taxation and tax evasion - a theoretical and epirical study in the Frisch Centre (Research Council project nuber /510). The project leader is Jon Strand fro the Departent of Econoics in Oslo University. Acknowledgeents. I a grateful to Jon Strand and Steinar Strø for helpful suggestions on the paper and Odd Vaage fro Statistics Norway for providing the data set used in this paper. I also want to thank y colleagues fro the Frisch Centre for the productive and friendly atosphere during y work at the institute. 1. College of Europe Natolin Capus, Ul. Nowoursznowska 84, Warsaw, Poland. Eail: chschwierz@gx.de

4 Contents Page Contents 2 1 Introduction Hoeeconoics and the otivation of the study A brief outline of the Norwegian tax syste 6 2 The theoretical odel The Gronau odel Restrictions and extensions of the odel fraework Epirical specification of the odel 20 3 The data Soe rearks on tie-use data The current data set 25 4 The estiation procedure Estiation of wage and incoe variables The double-hurdle odel 34 5 The estiation results Effects of taxes, wages and incoe variables Effects of other socioeconoic variables 43 6 The conclusion 45 7 Appendix 46 8 Bibliography 55 1

5 1 Introduction 1.1 Hoe econoics and the otivation of the study The theory of hoe production plays a role in the realization that econoic considerations are as iportant in the hoe sector as in the arket 1. This reark by Reuben Gronau points out that for a long tie households and their production activities have been neglected by econoists, although econoic considerations can play an equally iportant role in the households as in the arket. As countries industrialize, a large part of household production of food, clothing, furniture and housing is transferred to business organizations and then purchased by households. Nevertheless, even in a world apparently doinated by the arket, a large aount of household production is necessary. While the arket econoy produces any goods and services not produced by households, in any cases the arket and the household are in direct copetition, producing identical or siilar goods and services. With few exceptions, econoic textbooks focus on households as consuers and fail to discuss households as producers using their own labor and capital. Households are presented to the odern student of econoics as places of consuption. Econoics theory focuses on consuer behaviour, which concerns the choice of households on the quantities of the coodities they choose to purchase, given the liitations of their oney incoes and the prices of coodities. The purpose of this study will be to analyse the significant forces of the allocation of tie to different household production activities. This will be done in a joint allocation of tie fraework, where household decisions to allocate tie between the arket and the household will be analyzed siultaneously. While the ajor interest of this study will be to discern the effects of arginal taxes on labor incoe on the allocation of tie between arket, household work and leisure, it will also provide soe insight on the effects of socioeconoic variables influencing the allocation of tie. Since the Norwegian tax syste has undergone severe changes in the last 30 years, the author hopes to find significant effects of arginal tax rate changes on labor incoe to changes in tie use of households. This study analyses a large data set fro four Norwegian tie-use surveys distributed over a period of 30 years. It therefore potentially not only allows to discern the effects of socioeconoic factors in a 1 Gronau (1997), p

6 certain point of tie but also their changing influence on the allocation of tie through tie. To the author s knowledge this is the first analysis of a variety of household activities on the basis of Norwegian tie-use data. As has been shown by Kapteyn and Koorean (1987), such a disaggregated analysis of household work ay be better able to locate the effects of socioeconoic factors than a purely aggregated analysis of household production, since little oveent in aggregated household work ay ask considerable shifts in its coponents. The fraework of analysis will be a odel of tie allocation. Models of tie allocation ascribe econoic significance to hoe production and try to odel explicitly which socioeconoic factors affect the productive activities of the household. They date back to the 1970s and have given rise to a diverse literature, aong which household production has fored an iportant topic. In the first odels the household is seen as a production unit which cobines interediate goods with the tie of household ebers to produce basic coodities 2. The fraework of the odels is general, static, and ephasizes responses of individuals to arket prices, tie prices, incoes, and technologies influencing the production function of hoe goods. Household ebers are faced with a choice between paid arket work, unpaid doestic work and leisure. Although these early odels accept a considerable siplification and restriction of possible echanis influencing household production activities, they allow for easy predictions and testability of odel hypotheses. However, since the eergence of the first odels ore elaborate tie use odels appeared ephasizing joint production or interteporal tie use. For a review of the literature see Juster and Stafford (1991) and for ore recent developents since 1990 see Klevarken (1999). The basic idea of allocation of tie odels was introduced by Becker (1965). According to Becker, arket goods and services can only generate utility if they are cobined with the consuer s tie. For exaple: Having a ticket for the cinea does not generate utility. The consuer needs tie to go to the cinea, watch the fil and return hoe. So huan beings experience utility fro the coodities produced in the household with a cobination of interediate arket goods and household tie. Norally there are several techniques available to produce a final coodity. Since there are interediate tie inputs, which in ost cases can be substituted by arket inputs, people with differing tie values will choose different production strategies, i.e. people with a high wage rate ay choose less tie- 2 See Becker (1965) and Gronau (1977) and (1986). 3

7 intensive, but financially ore costly technologies ore often than people with a lower wage rate. Although in real world it is very difficult to obtain inforation on interediate arket goods used in hoe production, this study will use tie inputs inforation for further analysis. In chapter 1.2 a few ajor features of the Norwegian tax syste and the ajor changes of the arginal tax rates on labor incoe fro the year 1970 to the year 2000 will be presented. In chapter 2.1 the theoretical fraework of a household production odel will be discussed. It will be an extended version of the basic Gronau odel of hoe production, presented as a siultaneous equations odel with one equation for arket work and one for the different household activities. Beyond that a graphical representation will be given in order to better illustrate the functioning of the odel. Chapter 2.2 will present the ost iportant restrictions of the odel and possible extensions of the odel fraework proposed by econoic literature. In chapter 2.3 the epirical specification of the odel will be given, where assuptions about the for of the arginal rate of substitution between consuption and leisure and the arginal productivity of hoe production will be ade. In chapter 3.1 soe general rearks on the characteristics of tie use data will be discussed. Since tie use data often has the disadvantage of reporting too any zeros for a particular tie use category, this disadvantage will have to be put up with during the estiation. After the presentation of ajor characteristics of the actual data set in chapter 3.2, the estiation procedure will be discussed in chapter 4. The first part of the chapter will deal with the estiation of wage variables, since they have not been provided in detailed for by the original data sets. This will be done by the use of the two-step Heckan estiation procedure. Also, specific assuption will have to be ade to get estiates of nonlabor incoe. Beyond that the proble of endogeneity of the arginal tax rate will be discussed and estiates of tax rates will be presented. Since any of the individuals have reported zero tie-use on different activities, the estiation will have to take place within a liited dependent variables fraework. Although this proble is usually dealt with a Tobit odel, Cragg s double-hurdle odel will be estiated as an alternative to the Tobit odel in chapter 4.2. The advantage of the doublehurdle odel is that it allows distinguishing between wrong and correct zeros, while the Tobit odel takes for granted that all reported zeros can be regarded as the outcoe of individual choice. Due to the specific characteristic of tie-use to data to report too any 4

8 zeros for the single arket and household activities, this has already been shown to be iportant in previous studies. In chapter 5 the estiation results will be discussed. Chapter 5.1 contains detailed results on own- and cross-wage-elasticities of the supply of labor to both arket and hoe activities, as well as the corresponding nonlabor incoe elasticities. Chapter 5.2 will discuss the effects of the other socioeconoic variables used in the estiation. Finally chapter 6 will conclude the discussion of the study and ake soe proposals to iprove future research on this topic. 1.2 A brief outline of the Norwegian tax syste As stressed by Noor (2000) the Norwegian tax syste is characterized by a stronger ephasis on incoe redistribution, a wider social safety net and a broader provision of social services than ost other OECD countries. A key to the design of the Norwegian tax syste is also the overriding objective to keep reote areas populated, notwithstanding an overall very low population density. Beyond that the Norwegian econoy is characterised by the availability of huge natural resources (oil, gas, hydropower, forestry and fisheries), that have served to fund the expansion of the welfare state and have influenced the tax syste. These features of the Norwegian econoy have been conducive to calls for preferential tax treatent of specific sectors or regions, resulting in a tax syste that by the late 1980s was blurred by a plethora of special exeptions and allowances. Spurred by developents in other OECD countries, Norway ipleented a broad tax refor in Both the personal incoe taxation and the corporate taxation were refored. The ain purpose was to reduce taxinduced distortions to a iniu by lowering the tax rates and broadening the tax base. Thus incentives to work and save should be increased and incentives of tax avoidance and activities in the black arket should be decreased. The refor also involved a significant step towards a ore neutral tax syste with respect to the type of econoic activity and the organisational and financial structure of such activity. The centrepiece of the refor was the ove towards a pure dual incoe tax in 1992, which strictly separates the taxation of labour and capital incoe at the level of individual taxpayers. The dual incoe tax syste taxes all fors of capital incoe at a rate of 28 per cent while labour incoe is taxed at a higher progressive rate. 5

9 Figure 1 shows the developent of arginal tax rates (in %) of arried couples by tax assessed incoe in constant Norwegian crowns for the years 1970, 1980, 1990 and For the years depicted in the figure the ajor developents up to 2000 can be suarized in two points. First, there is a decrease of the nuber of different arginal tax rates for a given year since While seven different arginal tax rates existed in the year 1980, only 3 arginal tax rates reained in The second odification of the tax syste had the effect of gradual decreases in the arginal tax rates. With 70.2 per cent the arginal tax rates on wage incoe were at its peak at the end of the 1980s. This top arginal rate has been reduced to 49.3 per cent for a salaried eployee in FIGURE 1 MARGINAL TAX RATES ON WAGE INCOME IN 1970, 1980, 1990 AND This variation in the tax rates for given incoe levels is so large that one ight expect observable adjustent effects in labor supply as a result of these changes. In a cross section 3 The arginal tax rates have been obtained fro the following publications of Statistics Norway: Aktuelle Skattetall (1984), p. 21; Aktuelle Skattetall (1991), p.21 and Noor (2000),pp In 2000 a new bracket in the surtax, applied to personal (labour and pension) incoe of NOK and above, has been introduced. The rate is 19.5 per cent, which raises the top arginal rate for personal incoe by six percentage points. However, as ephasized by Aaberge et al. (1995, p.636) there could be a considerable difference between the effective and foral arginal tax rates. In 1979 all interest payents were deductible against a axial arginal tax rate, while later deductions were only allowed against a arginal tax rate of 28 percent. These changes in deduction rules iplie that differences between the effective rates are uch saller as copared to the differences in foral tax rates. 6

10 study for arried Swedish ales for the years 1984, 1986 and 1988 Flood (1998) finds indications that both the degree of progressivity and the tax level produce different labor supply elasticities. This stes fro the fact that a higher nuber of kinks, i.e. ore differentiation in arginal tax rates, produces a higher probability to find individuals close to a kink iplying stronger incentive effects. Another interesting result fro this study is, that not only the nuber of kinks but also their location is iportant. A long initial segent as the one in the above Figure for the year 1990 followed by a large degree of progressivity iplies very different estiated supply elasticities copared to the year 1970, which has, on average, lower levels but a higher progressivity especially for saller incoes. Another characteristic of the Norwegian tax law is, that arried couples are required to file their incoe returns jointly. Separate filing was introduced as an option in 1957, and in 1970 the syste of differentiated tax schedules, according to the nuber of dependents, was replaced by a siplified version with two tax schedules: one for single persons and for spouses filing separately, and a ore favorable one for arried couples filling jointly, as well as for single parents. Of course, the proble of joint taxation has the negative effect of high arginal taxes on the second incoe. A Norwegian study by Aaberge et al. (2000) finds an increase in the labor supply of arried woen with equalized tax schedules across arital status. The few ajor facts about the Norwegian tax syste show that very detailed inforation about working hours, wage rates and incoes ay be necessary in order to odel labor supply behaviour in a ore accurate way. These inforation are necessary in order to get a good representation of the individual budget sets, which ay approxiate the coplex iplications of different tax legislation and transfer systes of ost Western countries. However, data sets which provide detailed inforation on tax and incoe variables are seldo, and the data sets used in this study give rather rough inforation on these variables. This proble will be dealt with in chapter The theoretical odel 2.1 The Gronau odel The odel introduced by Gronau (1980) which shall be y analytical fraework and shall serve for further estiation purposes, akes a distinction between work, leisure and 7

11 household production tie. In his fraework household utility depends on two coodities: consuption goods (X) and leisure tie (L) U = U(X,L), where it is assued that individual welfare (U) is strictly increasing, quasi-concave and twice differentiable. The household can obtain consuption goods in two ways. First, it can produce the at hoe (Z). The second way to obtain consuption goods is to becoe a wage-earner and use the earnings to purchase consuption goods ( X M ) on the arket. Total goods consuption stes fro goods purchased at the arket or goods produced at hoe. X = X M + Z for i = 1, n. (1) Hoe goods are produced using arket inputs ( X H ) and tie inputs (i.e., tie spent at a particular hoe production activity H ), Z = f (X,H) (2) H subject to decreasing arginal productivity f H 8 > 0,f > 0,f 0, and f HH < 0. X H X X < The axiization proble is subject to three constraints: 1. The budget constraint specifying that in this one-period odel arket consuption cannot exceed oney incoe. X M WN + V t(i) (3) where W is gross wage per hour, N is hours of arket work, V is non-labour incoe and t is the total aount of incoe taxes paid, which is a function of taxable incoe I. Taxable incoe is defined as WN+V-D, where D is total deductions. This extension of the budget constraint used in Gronau (1980) is specified in Flood (1987b), who analyzes the effects of taxes on arket and non-arket labour supply in Sweden. In the following I will largely use his extended odelling structure. However, in contrast to his study I will also present the estiation results for disaggregated hoe production activities as well as a different estiation technique. The second constraint is the tie constraint L + H + N = T (4) Specifying that tie (T) is a scarce resourse to be allocated aong its three uses leisure, work at hoe and work in the arket. The last constraint is a non-negativity constraint H, N 0. (5) The tax-function in (3) is approxiated by H H

12 9 ) I (I t t t j j + = (6) where j I is the sallest taxable incoe in the observed tax-bracket j, j t is the tax payable at that incoe and t is the arginal tax-rate. Now (3) can be substituted into (6), which results in j j M I t t ) t V(1 N W X + + (7) where ) t W(1 W = is the arginal wage rate. Thus the individual chooses inputs of tie to axiize utility subject to the technological (2), tie (4), non-negativity (5) and budget constraints (7), specifically N) H L (T ) X I t t ) t V(1 N (W,f (H),L) U(X N) H L (T ) X I t t ) t V(1 N (W L) Z,, U(X j j j j M + µ + + λ + = + µ + + λ + Λ = (8) which yields the following first order conditions: λ µ = Λ Λ µ = = Λ = λ = Λ S X L 0 L L 0 X U X (9) = = λ µ µ Λ = Λ 0 ) f H(S 0 H U H 0 f S 0 f 0 H Z Z H (10) = = λ µ µ = λ 0 ) f N(S - 0 N U N 0 W S 0 W 0 W N U (11) Thus the first order conditions are given as,

13 H(S f ) = 0 (12) N(S W ) = 0 where S is the arginal rate of substitution between consuption and leisure, also called the shadow wage of leisure and f is the arginal productivity in hoe production. Condition (12) says, that for an interior solution with respect to H (H>0) the shadow wage of leisure ust equal the shadow wage of hoe production, while no tie will be spent on hoe production if f <S. However, fro (10) follows that S f, the shadow wage of leisure ust be at least as large as the shadow wage of hoe production. Condition (13) says that for an interior solution with respect to N (N>0), the shadow wage of leisure ust equal the arginal wage rate, while if (13) W < S hours of arket work will be zero. Also fro (11) we know S W, that is, the shadow wage of leisure ust be at least as large as the arginal wage rate. In order to illustrate further the functioning of the odel in cases of a change of nonlabor incoe and a change of the arginal tax rate, a graphical representation of the odel will be given 5. First, consider Figure 2,where the curved line represents the production function. Note, that it runs fro right to left: if the consuer is at point T, then all available tie is spent on leisure. At point H, HT is spent on household production, at the expense of leisure. Between H and T the slope of the production function is larger, than the slope corresponding to the wage rate W (that is, f > ). Therefore, between H and T it is ore efficient to produce W consuption through household production, than through paid labour and purchasing the goods on the arket. But beyond H the consuer will work on the arket, as his or her productivity there is larger, than his or her productivity at hoe. Now consider the following two outcoes. A consuer with preferences as indicated by the indifference curve in Figure 2 will supply labor on the arket of the aount LH. In point E the arginal rate of substitution between leisure and consuption (S) equals the wage rate ( W ). But in Figure 3 a consuer with a relatively strong preference for leisure is depicted. Here the consuer will supply no labor on the arket since the shadow wage of leisure is higher than the wage rate. 5 Good illustrative explanations of the odel can be found in Koorean and Wunderlink (1997) and Bryant (1990). 10

14 Now consider a change in non-labour incoe V. In Figure 4 the consuer looses all its initial nonlabor incoe. Since such a change cannot be expected to change the relative prices of labor and goods in the arket, or the basic paraeters of the production function, it siply shifts the household s total budget line down in a parallel fashion. FIGURE 2 INDIVIDUAL WITH STONG PREFRENCES FOR MARKET LABOR FIGURE 3 INDIVIDUAL WITH STRONG PREFERENCES FOR LEISURE FIGURE 4 INDIVIDUAL WITH SHIFT IN NONLABOR INCOME FIGURE 5 DECREASE IN THE MARGINAL TAX RATE ON LABOR INCOME 11

15 Consequently, the consuer s deand for goods and for leisure will decrease as long as both are considered as noral goods. The decrease in leisure eans, of course, that the aount of tie spent working will increase. As the decrease in V has no effect on the household production function, for individuals, who already supply labor to the arket all the increase in work tie will be in arket work tie. This change is represented by L L in Figure 4. However, for individuals as in Figure 3, who did not supply labour to the arket before the drop in V, the change in work tie will result in an increase of household labour supply. For large enough decreases in V they ay even enter the labour arket. An interesting prediction is, that if a sufficient nuber of coodities are inferior and tie intensive, arket tie ay decrease due to a decrease in non-labor incoe. To y knowledge this has not been tested yet, surely because of the unavailability of data about the interediate goods entering the household production function. This latter result runs counter to the predictions of conventional labor supply odels, where a drop in nonlabor incoe has an unabiguous effect on labor supply in the arket. But what does epirical work say about the effects of a change in nonlabor incoe? Several studies confir, that both ales and feales, arried and single, devote less tie to arket work as nonlabor incoe rises. In a suary of feale labor supply Heckan and Killingworth (1986) point to estiates of nonlabor incoe elasticities of around As to the effects to household work Gronau (1977, Table 3) finds that an increase in nonlabor incoe of $1000 per year leads to a decline of 44 hours in the annual tie spent in household work by white uneployed, arried woen. However, Kapteyn & Koorean (1987, pp ) find that household work tie of eployed individuals is unresponsive to changes in nonlabor incoe. In general however, it sees that there exists a wide consensus, that for both en and woen leisure is a noral, incoeinelastic good. Now let us consider the effect of a decrease in the arginal tax rate on tie use. In Figure 5 the initial equilibriu point is E with HT hours spent on housework, LH hours spent on arket work and the rest on leisure tie. Since the wage rate is also the shadow price of leisure, a decrease in the arginal tax rate which increases the arginal wage rate results in an increase in the price of leisure. Therefore the individual will substitute arket work for leisure. This is called the consuption substitution effect, since it increases the individual s total consuption. On the other hand, since an increase in the wage rate increases arket productivity relative to household productivity, the individual will substitute arket work for household work. This is called the production substitution effect and aounts in Figure 5 to 12

16 HH. The total substitution effect of the own-wage-rate increase on arket work, then, is the su of the production substitution and the consuption substitution effects. However, so far I have not considered the fact that a rise in the individual s wage rate increases the household s real incoe. With the increase in real incoe increases the household s deands for goods and leisure, so long as both are noral goods. This is the incoe effect of the rise in the wage rate. The total own-wage-rate effect is thus the su of the production and consuption substitution effects and the incoe effect, which can be either negative or positive depending on the ability of the incoe effect to offset the two substitution effects. Thus, the supply curve to the labor arket can be positive or backward bending and negative. The total own-wage-rate effect on household work is ade up solely by the production substitution effect. As the wage rate rises the tie spent in household work declines due to a shift of household to arket production. Thus, a decline in the arginal tax rate on labor incoe should decrease the aount of household work done. The total own-wage-rate effect on leisure is ade of the consuption substitution effect and the incoe effect. As the price of leisure rises relative to goods, the household substitutes goods for leisure. As the rise in the wage rate increases real incoe, ore leisure is deanded. Thus the effect of a decrease in the arginal tax rate on labor incoe on leisure is abiguous, depending on which effect is stronger. What evidence on these hypotheses was found by earlier studies? The suaries given by Pencavel (1986) for en and by Killingsworth and Heckan (1986) for woen suggest that the total own-wage-rate effects on labor supply run in opposite directions for en and woen. While ales labor supply is ostly negative and inelastic in the neighborhood of 0.12, the evidence given by Killingsworth and Heckan (1986) reports positive elasticities for woen. Thus feales see to increase the tie spent in the arket with an increased real wage rate, while en see to have a backward bending labor supply curve. However, Flood (1987b) finds positive own-wage-rate elasticities for Swedish en, so the evidence is not clear-cut. For Norway Aaberge et al. (2000) find own-wage elasticities of 0.17 and 0.37 and cross-elasticities of 0.03 and 0.12 for ales and feales respectively. As to the effects of wage rate changes on the household work of individuals, Gronau (1977) found that household work declines with increasing own-wage rates. This result is confired by Kapteyn and Koorean (1987) and Flood (1987b) for feales, while no effect can be found on the aount of household work done for ales. Therefore, ales household work sees to be unresponsive to changes in the arginal tax rate on labor incoe. 13

17 The study by Kapteyn and Koorean (1987) also suggests that the effect of a change in the own-wage-rate on leisure in abiguous. For both ales and feales an increase in the wagerate increased tie spent in entertainent and social activities, while it reduced tie spent on sports or reading and watching TV. The differences in the effects of wage-rate changes on ales and feales production activities and leisure are usually explained by the specialization of function and division of labor hypotheses 6. Given that husband and wife are substitutes in household work, it siply states that each spouse should specialize in arket or household work according to their coparative advantage. If the arginal productivity of tie in household work is the sae for both spouses and the wage rate the husband coands in the arket is higher than the wife s wage rate, then the household will be able to consue ore goods and services, if the wife specializes in household work and the husband in arket work 7. Such specialization iplies that the household work of those specialized in arket work will be less responsive to wage rate changes than the household work of those specialized in household work. Thus, the before entioned evidence sees to be consistent with the specialization hypotheses. Another interesting effect refers to cross-wage-rates. Consider an increase in the wage rate of the husband. First, the trade-off between her household production and her arket work reains unchanged, so that her household production tie use will not change. However, the aount of tie she spends in arket work will change depending on whether the spouses leisure ties are copleents of substitutes for each other. If they are copleents then her leisure tie will fall as his falls due to the substitution effect of a wage increase. If they are substitutes then she will substitute her leisure for his leisure as the substitution effect reduces his leisure tie. Furtherore, the incoe effect of the rise in his wage rate will increase the deand for her leisure. The total effect on her leisure and arket work will therefore depend on whether her leisure is a substitute for or copleent of her husband s leisure and on the strength of the incoe effect. For uneployed wives the increase in his wage rate effects only the division of her tie between household work and leisure. The substitution effect will increase her leisure tie and decrease her household work tie, if her leisure is a substitute for her husband s, and 6 See e.g. Bryant (1990), pp Since this is a static odel, the long-run consequences of this optial choice stay out of sight. By working in a household, one learns and becoes ore and ore experienced in household production. By working in the labor arket, the productivity of paid labour increases, which will norally lead to an increase in wages, thus leading to a self-reinforcing specialization function. This ay be one reason why, once uneployed, it can becoe increasingly difficult for woen to enter the labor arket. 14

18 inversely, if it is a copleent. The incoe effect will increase the deand for her leisure and lower the tie she spends on household work. As to the epirical evidence of cross-wage-rate effects Gronau (1977) found that the eployed arried feale s arket work tie falls, her leisure tie rises, and her household work tie reains unchanged, when her husband s wage rate increases. Kapteyn and Koorean (1987) found the sae results for woen, indicating that their leisure is a gross substitute for their husbands. However, they found also, that the husbands tie use was uch less responsive to changes in wives wage rates than wives tie use to changes in husbands, which can be seen once again as a confiration of the specialization of function hypotheses. Concluding the discussion of the effects of the Gronau odel fraework it can be said, that it akes the analysis of any testable econoic hypotheses possible, which already have experienced confiration in different studies. 2.2 Restrictions and extensions of the odel fraework In the next step the restrictions of the odel fraework shall be discussed. The present odel relies particularly on the assuption of the exclusion of joint production in the household production technology. Joint production occurs, if an activity serves a ixture of goals, or when two activities are done at the sae tie. For exaple, playing with children can be considered as a production activity, but for any parents it will be a leisure activity as well. Gronau s odel in fact excludes joint production. The exclusion of joint-production is quite counter-intuitive. Graha & Green (1984) estiated a version of the Gronau odel in which they allowed for a type of joint production. In their odel a household utility is deterined by the level of consuption, and the level of effective leisure of the spouses. If the consuer enjoys direct utility fro a household production activity, part of the tie spent on hoe production can in fact be considered as leisure tie. These hours plus pure leisure tie, together for what is called effective leisure. The other part of the tie spent on hoe production is called effective hoe production tie input. Therefore, hoe production allows for a for of joint production. To consider the difference in possible predictions when allowing for joint-production consider the following exaple. A parent whose hourly wage exceeds the arket price of one hour of child care has to choose between buying professional child care on the arket and taking care of the child by hiself. In the Gronau odel the parent has two options to provide for child care. The first option is to take care of the child 15

19 hiself at hoe. The second option is to earn oney with his job and purchase child care on the arket. In the odel without jointness, the parent chooses the latter option. In the odel with jointness, however, he will choose to take care of the child herself if a sufficiently large share of the tie spent on this activity is valued as leisure. While the jointness extension is an attractive one, it also raises the question of identifiability. Graha s and Green s (1984) odel was not identified, so that they had to consider several special cases. One of these cases is for exaple non-jointness, which served as a sufficient restriction for the identification proble. Kapteyn and Koorean (1987) argued this result would be due to the way in which joint production is introduced by Graha and Green into their odel being fundaentally indistinguishable fro a odel without joint production. Furtherore earlier estiates of this type of odels were not very successful 8. Newer results, however, see to be ore proising, but are restricted to special cases 9. It is because of this ajor proble of identifiability that strong assuptions have to be ade to distinguish between differences in production technology and individual preferences, as has already been shown very early by Pollak et al. (1975). The consequence for the Gronau odel is, that welfare is not affected by the coposition of X, that is U X M = U. As noted by Flood Z (1987a) the iplication of this assuption is that the decision to buy goods on the arket or to produce the at hoe will be based on productivity in hoe production and arket wages and not on differences in preferences between arket- and hoe produced goods. Therefore arket goods and hoe-ade goods are here considered as perfect substitutes, what ight be a quite unrealistic assuption. Evidently such substitutability exists. Consider table 1, which shows averages of tie spent on arket and household work and leisure for arried eployed and uneployed ales and feales fro the current data set. The fact that individuals working in the arket sector spend uch less tie working at hoe leads to the opinion that there is, in fact, substantial substitutability between arket and non-arket activities. In particular, individuals not working in the arket sector do enjoy ore leisure, on average, but the difference in uch saller than the difference in tie spent in arket work See e.g. Kerkhofs (1991). 9 See e.g. Kerkhofs and Koorean (2002). 10 In two studies Benhabib et al. (1990 and 1991) show that a siultaneous treatent of the arket and hoe sector considerably iproves the perforance of their real business cycles odels and helps to solve questions relating to productivity cycles.their explanation relies heavily on the high elasticity of substitution between hoe and arket goods. 16

20 Table 1 Tie Use and Eployent for all four surveys Activity Married Male Married Feale (hrs/wk) Eployed Not Eployed Eployed Not Eployed MARKET WORK Household Work Leisure Sleep and other Additional evidence on substitutability, although not so clear cut, can be provided by the following table 2. There I have calculated hours of hoe and arket work for a subsaple of individuals in five wage groups. It can be clearly noted, that woen substitute between tie in the arket and in hoe production as the wage varies. For en, however, the substitutability sees less evident 11. TABLE 2 TIME USE AND WAGES Woen Men Averages (Work=hrs/wk) Wage Group Wage Group Gross Wage Rate MARKET WORK Household Work Total Work Consequently, the assuption of perfect substitutability of hoe for arket goods sees not only to arise fro the necessity to assure identification and thus create issues of estiation and interpretation, but sees also to be backed by epirical data, especially in the case of feales. Another restriction of the odel is, that it originally describes only a single person household, while later odels ephasized the role of household production with two or ore individuals. 11 The wage groups in 1999 NOK were: 1=[0, 110], 2=[110, 130], 3=[130, 150], 4=[150, 170], 5=[170,300] 17

21 In general there are two different types of these odels. In the first type it is assued that the household is a single utility axiizing agent with the utility function i U = U(X,L ) i =,f, where and f stand for the ale and the feale partner respectively 12. In these odels each household partner has also his own household production function Z i i i i = f (X,H ) i =,f H While one advantage of this odel is its ephasis of the interaction between the partners choices, thus being able to ake predictions about intrahousehold allocation of tie and input resources, it has been criticized for its lack of icroeconoic soundness. The reason for this is, that a ultiperson household cannot be odelled as a single individual because it contradicts the neoclassical point of departure by which every individual should be characterized by his/her own preferences, as ephasized by Fortin and Lacroix (1997) and Kawaguchi (1994). One result of this so called unitary odel is that the allocation of consuption and tie are independent of the eber of the household actually receiving the incoe. In this odel, all incoes are pooled into the faily s coon budget. The underlying eaning of incoe pooling is, that there exists an altruistic faily head that will neutralize any reallocation of intrahousehold incoe. In any epirical applications of the odel by Fortin and Lacroix (1997) and Kawaguchi (1994) this prediction has been falsified, while a recent study by Aronsson et al. (2001) did not so 13. The theoretical and epirical criticis of the unitary approach gave rise to collective household production odels where each individual is characterized by his or her own utility function, specifically U i i i i = U (X,l ) i =,f. so that each spouse axiizes his/her own utility. This is the so called collective odel approach used e.g. by Aronsson et al. (2001) 14. Although the unitary and collective odels give a better description of actual household behaviour by including the allocative and consuptive decisions of both spouses, their application is liited due to data availability reasons. They require accurate data on tie-use 12 See e.g Blundell and Walker (1986). 13 In this study it is found that Swedish couples ight choose to pool their sources of incoe into a faily budget, since woen s earnings relative to their husband s are rather equal as copared to en and woen in other countries. It ight thus ake sense to pool incoe and share financial decisions. 14 Another way of getting around the unitary fraework is the use of a cooperative bargaining odel within a gae theoretical fraework, see e.g. Daunfeldt (2001). 18

22 of both spouses not available in the data set analyzed in this study, since only one person per each household has been asked to keep a tie-use diary. Therefore and because of the probles of identification entioned within the application of the Graha and Green odel I will ake use of the priordial Gronau odelling structure. 2.3 Epirical specification of the odel Now, let us get back to the epirical specification of the odel. As pointed out by Gronau (1980, p. 409) the estiation of the hoe production function is difficult, since not only the aount of interediate goods used for hoe production is unknown, but also it is ipossible to separate which share of total household consuption stes fro arket and hoe produced goods. Hence he chooses an indirect approach by estiating the arginal productivity of tie in hoe production. This approach is also applicated by Flood (1987b, p. 5). It is assued that: S = β C + γ s f = β f h H + γ C + δh + u f n N + u where C is a vector of individual variables and s u s and u f (14) (15) are error ters. If the indifference curves between leisure and consuption are assued to be convex as in the graphical illustrations above, then γ h and γ n should be greater than zero. On the other hand it follows fro the assuption of decreasing arginal returns, that δ in equation (15) should be negative. Now I substitute (14) and (15) into (12): H(S f ) = H( β C + γ βf H = γ h s h H + γ h n N + u s h - β βs γ n u f -u s C - N + δ γ δ γ δ Substitution of (14) into (13) gives, f C δh u ) = 0 f (16) (17) N(S W ) = N( β C + γ H + γ N + u W ) 0 (18) N s h n s = β γ 1 1 s h = C H + u s + W (19) γ n γ n γ n γ n Thus the following syste of equations eerges: H if RHS>0, otherwise H=0 (20) = γ h N + βhc + u h 19

23 N if RHS>0, otherwise N=0 (21) = γ nh + βnc + γ w W + u n with β h βf βs γ n u f -u s βs γ h 1 1 = ; γ h = - ; u h = ; βn = ; γ n = ;u n = ; γ w = W γ δ γ δ γ δ γ γ γ γ h h h In order to estiate the current odel two kinds of restriction ust be placed. First, the syste of equations has to be identified. Using the rank condition of identification I will siply delete one non significant C in (21), so that the rank condition is satisfied 15. The second restriction deals with the right hand side endogenous variables and in this odel it iplies that γ γ As pointed out by Flood (1987, p.7) this constraint can be 1 h n > interpreted in econoic ters for this odel. Since it was assued that the consuptionleisure indifference curves were convex, so that γ γ 0, and since the arginal n h, n > productivity in hoe production was assued to be decreasing with respect to H, so that δ < 0, it follows that γ γ 1. and thus the constraint is satisfied. h n < n n n 3 The Data 3.1 Soe rearks on tie-use data The data used for the estiation coes fro four Norwegian tie-use surveys fro the years 1970, 1980, 1990 and These include rich inforation on individual and household characteristics of the person interviewed and a detailed tie-use section on various arket and non-arket activities. The tie-use data has been obtained by the use of tie-use diaries the respondents had to fill out on two days of the week 17. The respondents have been asked to write down their activities of the day in intervals of 15 in for the first three surveys and in intervals of 10 in in the last survey. In order to give an idea of the richness of inforation it should just be entioned that these surveys distinguish between five ain categories, such as arket work, hoe work, personal care, education and leisure which are further iteized into 91 activities. Only a saple of these activities will be of interest for the present study. Table 3 gives an overview over the tie use categories and the single coponents they consist of. The highlighted, cursive activities will be subject to further analysis. The selection of household activities has been ade on the believe that the selected activities constitute a possible alternative for arket work. The classification provided in table 3 is not 15 For an explanation of the rank condition see e.g. Greene (1993), pp See e.g. Aeiya (1974). 17 In the 1970 survey a inor part of the respondents filled out the diarys on three different days during a week. 20

24 unprobleatic, because no objective distinction between household work and leisure can be done. The distinction criterion applied by the tie budget surveys is, that an activity that can be perfored by soeone else should be considered as household work. You can hire soeone to do the cleaning and washing for you, but you cannot hire soeone to do the entertainent or sport for you. This is the third-person criterion originally defined by Reid (1934). However, the distinction becoes less clear where productivity and personal enjoyent play both a possibly large role, i.e. in the case of joint production. Soe people enjoy cooking, gardening or taking care of their children. They thus contain both eleents of pleasure and work, aking a classification ore arbitrary. TABLE 3 CLASSIFICATION OF ACTIVITIES Classification 1 Classification 2 Classification 3 Market work Household Work And faily care Leisure Incoe producing work 18 Tie in connection to work Journey to work Housework Maintenance Gardening Work with children Leisure Ordinary work in ain occupation Overtie in ain occupation Work in secondary occupation Meals at the work place Tie spent at place of work either before or after work hours Other pauses Journey to work Food preparation, setting of table, serving, Dish washing House cleaning Washing and ironing Construction. Larger reodelling Painting, saller reodelling Maintenance and repair of dwelling and household equipent Maintenance and repair of other equipent Care of garden, lot, and anials Childcare and help to children Help with school work Other work with children Sport and outdoor recreation Entertainent Socializing Radio and television Reading Other leisure Travel in connection to leisure tie activities Before going into a ore detailed description of the individual characteristic variables used in the analysis, it is iportant to note soe particular characteristics of tie-use data in general. 18 For the years this subcategory included also the activity: Agriculture, forestry and fishing on own property/boat. This has been taken out of the analysis since it was not included in the year 2000 tie-use data and since it aounted to only a few inutes of tie-use per week in the foregoing surveys. 21

25 Juster and Stafford (1991) report a nuber of validity tests carried out in on an early tie use study for the U.S. Those tests suggest that the tie diary ethod is uch ore accurate, than survey questions asking for typical tie use. Further they are a little ore accurate than using an electronic paging device, which randoly activates the recording of a tie-use activity when receiving a signal. An exaple of this accuracy can be given by a coparison of differences between data based on questions about current hours per week including overtie and secondary jobs ( survey data ) and tie-use data fro the sae saples of people. As can be seen in figures 6 and 7 the tie-use data distributions are uch soother and have a larger variance. One explanation for this is that any respondents ay report their contracted nuber of hours disregarding or forgetting any nonwork episodes at work and any irregular overtie work. Even if asked explicitly about secondary work it ight also be difficult for the to report hours retrospectively, in particular if the respondent only works interittently in this job. Another reason is the noisiness of the data due to the fact that only a few days are observed for each respondent 19. Further inspection of the two figures reveals that the proportion of zeros reported in the tie-use data is uch higher, than that in the survey. This stes fro the fact that tie-use data are usually only collected for two different days during the week. Since arket labor supply is not equally distributed during the week this results in the observation of wrong zeros and ight lead to the wrong conclusion of the zero s outcoe being a response of the individual s deliberate choice. FIGURE 6 TIME-USE DATA FOR MEN AND WOMEN IN See Klevarken (1999), pp