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Household Labor Market Choices and the Demand for Recreation.

I. INTRODUCTION

In the text book allocation of time, individuals divide their time between labor and leisure based on a constant wage rate. These models break down when the wage rate depends on the amount of time allocated to work or when constraints in the labor market fix the amount of work time. Recent applications of models of the demand for recreation often account for labor market distortions that influence the marginal wage (Bockstael, Strand, and Hanemann).

Recreational-demand models have dealt with the behavior of a single individual. Becker has shown that the traditional model also breaks down when household members share housework. When spouses jointly produce household goods and work for constant wages, it would not be optimal for both spouses to be in the labor market simultaneously. Consequently, even in the constant-wage model, the wage rate many not be an individual's opportunity cost of time when joint household decisions are considered. This paper derives and estimates models of the demand of recreation in the context of decisions by households with two members.

Including the household structure in models of the demand for recreation complicates the data gathering and estimation. One needs good reasons to increase the complexity of what is essentially the valuation of time. There are at least three good reasons. The first is that, based on the empirical research in this paper, the valuation of recreational opportunities appears to be systematically reduced by incorporating the joint allocation of time. The second concerns surveys and data-gathering efforts. Many studies based on large surveys, such as the National Marine Fisheries Service survey of recreational fishing, fail to distinguish between individual and household activity, making empirical results ambiguous. Economists need to think carefully about the individual versus the household in designing surveys and in measuring welfare.

The third reason for developing a more realistic model of household recreational activities concerns the significant changes in household structure that have occurred over the past five decades. Table 1 shows several variables that influence the household's allocation of time. Unless models of the demand for recreation can incorporate these real world changes, it is hard to take seriously their claims for influencing the allocation of resources in the real world.

Trends for the age distribution of the population, female labor force participation rate and the growth in single-parent families for the past five decades are given in Table 1. The significant increase in the female labor force participation rate has two implications for recreational demand. Household income increases and time for household chores becomes scarcer. A trend having a coincidental impact on household time allocation is the proportion of single-parent families. As Table 1 shows, the proportion of single-parent families has grown from about one-eighth to one-fifth of all families. This suggests greater time constraints, especially when there are fixed costs of household maintenance. Further, to the extent that single-parent households are that way because of divorce, they tend to be poorer. The best known change is the aging of the population. The proportion of people 65 or older has increased by about a half. It means a growing proportion of the population who do not make their decisions based on labor market tradeoffs, because of the high proportion of retirement among people in this age group.
TABLE 1

SELECTED ECONOMIC CHANGES AFFECTING DEMAND FOR RECREATION

                          Female         Families
         Population     Labor Force      with Only
         65 or Older    Participation    One Parent
Year        (%)          Rate (%)        Present (%)

1950       8.4            33.9              -
1960       9.2            37.7            12.8
1970       9.8            43.3            13.2
1980      11.3            51.5            17.5
1990      12.5            57.5            20.9 (1989)

Source: "Statistical Abstract of the U.S." 1990. In Economic
Report of the President. 1994.


These forces change the opportunity cost of time, the amount of time available, and the real income of households. The trends mean changes in the exogenous variables in models of the demand for recreation, and each variable has shown to play a significant role in these models. These changes reflect a growing complexity for household allocation of time. These complexities cannot be harmlessly ignored when joint household decisions are considered.

This paper derives household demand for recreation based on what the labor supply literature has called the "unitary" or "exchange" model of intra-household resource allocation (see Apps and Rees 1996; Chiappora 1992; Haddad, Hoddinott, and Alderman 1994). This is essentially the Becker model, in which the household is assumed to maximize a household preference function. The alternative, which has great appeal in development literature, is a household bargaining model, also known as the "transfer" model (Apps and Rees 1996) or the "collective" model (Haddad, Hoddinott, and Alderman). In the "transfer" model, members with separate utility functions bargain over income, consumption, or time allocation. All of these models reflect the growing importance of the household, rather than the individual, in labor supply models, and by implication, recreation demand.

Researchers who have done empirical research in non-market valuation have always confronted the issue of the individual versus the household in aggregating individual model results to the population. But in most cases, the household and its structure has been ignored at the conceptual level. Smith and Van Houtven (1998) provide a framework for understanding the conceptual issues associated with non-market valuation and the household.

II. HOUSEHOLD AND LABOR MARKET STRUCTURE IN MODELS OF THE DEMAND FOR RECREATION

The travel cost model of the demand for recreation was formalized by recognizing that a decision to consume the services of a site involved the allocation of time. Although early models equated the opportunity cost of recreation with the wage rate, researchers such as Cesario and Knetsch (1970) understood the potential for overestimating the opportunity cost of time through this procedure, and the implications for consequent overestimation of welfare effects.

In an attempt to give formal structure to the insights of Cesario and Knetsch (1970), McConnell and Strand (1981) developed a model that allowed the wedge between the opportunity cost of time and the wage rate to be determined empirically. Smith, Desvousges, and McGiven (SDM) (1983) tested this model by estimating the demand for about twenty-four Corps-of-Engineers sites. They demonstrated that a model in which the opportunity cost of time is a constant proportion of the wage, as assumed by McConnell and Strand (1981), could lead to absurd results. SDM set the stage for further analysis by developing a model with two-time constraints - one for work and one for non-work time. Because time is not fungible in such a model, the wage rate does not necessarily represent the opportunity cost of time.

Bockstael, Strand, and Hanemann (BSH) (1987) constructed a model for two kinds of institutional settings: one in which the individual can substitute income for leisure, and another in which such substitution is not feasible. The BSH model has clear empirical implications. When substitution is feasible, demand is modeled with opportunity cost of time as part of the cost of a trip. With no feasible substitution between work and leisure, recreation has no parametric opportunity cost, so that the time required for a trip is included as a separate argument. This model is widely used, and approximates labor market effects for a given individual well, given the quality of data available.

Taking a different tack, Larson (1993) modeled the choice of the amount of time spent visiting natural resources, rather than the demand for trips. This model permits labor and leisure to be substituted for one another at a constant wage rate, but breaks the direct link between wages and the opportunity cost of time by allowing work to yield utility. Larson's model does not easily yield estimates of the value of access to recreational sites.

The extant literature recognizes the link between the demand for recreation and the supply of labor, but models the decisions of a single individual. The following section adapts these models to the behavior a household of two individuals.

III. A MODEL OF HOUSEHOLD LABOR SUPPLY AND RECREATION DEMAND

The basic structure is a unitary model of the household with two members (spouses) who substitute perfectly in home production, but who earn different wages in the formal labor market. This development is based on Becker (1981).

No Constraints in the Labor Markets

The two spouses face fixed wages. Each spouse (labeled 1 and 2) faces the time constraint:

[T.sub.i] = [H.sub.i] + [L.sub.i] + [F.sub.i] i = 1, 2 [1]

where [T.sub.i] is total time available, [H.sub.i] is time at work, [L.sub.i] is leisure and [F.sub.i] is time spent towards home production. The unitary utility function depends on consumption of a Hicksian bundle, x, bought at price, p, home produced goods, q, and leisure of each spouse, [L.sub.1], and [L.sub.2]:

u = u (x, q, [L.sub.1], [L.sub.2]). [2]

The constraints on utility maximization include the time constraints, the income generation equation, the budget constraint, and the household production function. Income is given by:

y = [y.sub.0] + [w.sub.1][H.sub.1] + [w.sub.2][H.sub.2], [3]

where [y.sub.0] is non-wage income, and [w.sub.i] are the wage rates. The budget constraint is

y = px,

and the household production function

q = q([F.sub.1] + [F.sub.2]), [4]

where q([F.sub.1] + [F.sub.2]) is an increasing concave function of the sum of spousal effort, implying perfect substitutability between spouses. The model assumes no disutility from household chores.

This model leads to specialization: one spouse works and the other does household production. This can be seen by posing the problem as a two stage optimization. In the first stage, the problem is to minimize the cost of producing the quantity [q.sup.0]. The cost of producing q is the foregone market wages. Hence the problem will be

minimize [w.sub.1] [F.sub.1] + [w.sub.2][F.sub.2],

subject to q([F.sub.1] + [F.sub.2]) = [q.sup.0].

This leads to a corner solution, because of the linear isoquant and linear budget constraint. Consequently, when both members have the opportunity to work unconstrained at constant wage rates, the one with the higher wage will be employed outside the home and the other will specialize in housework. Both individuals will enjoy some leisure.

When [w.sub.1] [greater than] [w.sub.2], the household will choose [L.sub.1], [L.sub.2], and x to

maximize u(x, q([T.sub.2] - [L.sub.2]), [L.sub.1], [L.sub.2]) - [Lambda][[y.sup.*] - xp - [w.sub.1][L.sub.1]], [5]

where full income [y.sup.*] = [y.sub.0] + [T.sub.1][w.sub.1]. The solutions to this optimization have the following form:

x = x(p, [w.sub.1], [y.sup.*], [T.sub.2])

[L.sub.j] = [L.sub.j](p, [w.sub.1], [y.sup.*], [T.sub.2]) for j = 1, 2

[H.sub.1] = [H.sub.1](p, [w.sub.1], [y.sup.*], [T.sub.2])

[F.sub.2] = [F.sub.2](p, [w.sub.1], [y.sup.*], [T.sub.2]). [6]

Because 1 is in the labor market, increases in [T.sub.1] are equivalent to increases in full income, while increases in [T.sub.2] imply more time.

This system is not quite a standard neoclassical system with fixed prices and a single income constraint, because the choice variables do not all have a linear price. The choice variables x, and [L.sub.1], have the standard interpretation, in that they provide utility and are purchased at a constant price. But [L.sub.2] is chosen by the trade-off between the marginal utility of household goods and of leisure:

[u.sub.q]q[prime]([T.sub.2] - [L.sub.2]) = [[u.sub.L].sub.2],

and has no parametric price. A parametric price is a price that is constant with respect to the individual. When prices are endogenous, not parametric, the standard neoclassical demand results do not hold.

To make the problem relevant to modeling the demand for recreation, let the household choose trips to a recreation site instead of leisure. For simplicity, I will explain household trips, rather than spousal trips. Let z be the quantity of household trips, that is, trips taken by both spouses. Each household trip represents a trip for member I and a trip for member 2. More z brings marginal utility for 1 and 2, with the lost opportunities for time for 2 and the cost of time for 1 (because only 1 is in the labor market), as well as the out-of-pocket costs for the trip. The utility function is [Mathematical Expression Omitted].(2) Let the out-of-pocket costs (travel costs, admission costs, etc.) be c and the travel time required be t. With [w.sub.1] [greater than] [w.sub.2], the time constraints become [T.sub.1] = [H.sub.1] + tz for 1 and [T.sub.2] = [F.sub.2] + tz for 2. The budget constraints becomes

[y.sup.*] = xp + ([w.sub.1]t + c)z. [7]

To model consistently the demand for sites rather than leisure, it is necessary to keep track of time appropriately. Only recreation time, not travel time, provides utility. The recreation time spent on site is embedded in the utility function. The household chooses the z, knowing the fixed time requirements. The utility function becomes 1(3)

[Mathematical Expression Omitted].

This is maximized subject to the collapsed budget constraint [7]. The first order condition for z:

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is the marginal utility for spouse 1, and [Mathematical Expression Omitted] marginal utility for spouse 2. The right-hand side measures the utility cost of time and money spent, and the left-hand side the sum of the marginal utility for each spouse.

The solution can be viewed as if the price were linear or as the complete reduced form. In the linearized price case, the first order condition is expressed as

[Mathematical Expression Omitted].

Assuming approximate linearity at this point, take [Mathematical Expression Omitted] as a constant, and solve the Marshallian demand (absorbing p into the function):

z = g(c + [w.sub.1]t + [p.sub.z]t, [y.sup.*], [T.sub.2]) [8]

The full price of z, a household trip, is c + [w.sub.1]t + [p.sub.z]. The trouble with this approach is the absence of parametric information about [Mathematical Expression Omitted]. There is no obvious way to estimate it jointly with the demand for trips.

The theoretically sound and more practical approach, based on BSH solution, specifies the demand for z as a function of out-of-pocket costs (c) and time costs. Hence the demand function is

z = [f.sup.*](c + [w.sub.1]t, t, [y.sup.*], [T.sub.2]) [9]

c + [w.sub.1]t is the full monetary cost of the trips, t is the time cost of the trip, [y.sup.*] is full income, and [T.sub.2] is the time endowment separate from full income. The equilibrium is the same both cases, but in [8] the cost is linearized.

This model differs subtly from the BSH model where corner solutions emerge from kinks in the time or budget constraints. In the family labor supply model, the jointness of decisions yields the corner solutions. The individual budget constraints are smooth. Corner solutions emerge because spouses' labor inputs into household production are perfect substitutes but their constant wage rates differ.

Constraints in the Labor Market

When hours of workers are fixed, a two-member household may be represented by two members both choosing household work and leisure and between them choosing household work and leisure. We could also consider the case where one member works fixed hours and one member chooses hours at a fixed wage.

Consider the case where both members work fixed hours. The household budget is given by

[y.sup.**] = [y.sub.1] + [y.sub.2] + [y.sub.0],

when [y.sub.i] is the ith member's earned income and [y.sub.0] is exogenous income. Each member's time constraint is given by [Mathematical Expression Omitted], where [Mathematical Expression Omitted] is the time available after work: [Mathematical Expression Omitted] where [Mathematical Expression Omitted] is the fixed work time. Let tz = [L.sub.i], where t is the amount of time required for the trip. Let c = out-of-pocket costs of a trip. Then the choice problem becomes

[Mathematical Expression Omitted]. [10]

Here [Mathematical Expression Omitted] is the utility function which results from defining preferences on z rather than L. The relevant first order condition is:

[Mathematical Expression Omitted].

The fact that both members tradeoff household production for leisure at declining marginal values (as opposed to a constant wage rate) means that they can both choose positive values for [F.sub.i]. Both do household work and both enjoy leisure. Fixities in the labor market for both spouses induce interior solutions in household production. With hours of work fixed, the constant wage no longer dictates that one spouse do household work and the other earn income. And at the margin, each spouse makes the labor-leisure tradeoff relative to the value of household work.

Solving for the Marshallian demands without linearizing yields the following function (equivalent to 9):(4)

[Mathematical Expression Omitted]. [11]

The demand function depends on own price, quantity of travel time, the sum of time available for both members, and income. Time and income work similarly; for time or income effects, it is the total time available for both household members that matters. Time has a shadow value that changes in the opposite direction of [Mathematical Expression Omitted]. For households who have high institutionally fixed hours, [Mathematical Expression Omitted] will be low and the shadow value of time high. The productivity of household work in the function q([F.sub.1] + [F.sub.2]) also affects the shadow value of time. A reduction in [Mathematical Expression Omitted], with all else constant would reduce [F.sub.1] + [F.sub.2]. This would increase the marginal product of household labor, (q[prime]), and raise the marginal value of household production, [Mathematical Expression Omitted], hence increasing the shadow value of time and the endogenous opportunity cost of recreational time.

The model we have just examined is symmetric with respect to household members. Both work and they substitute their time between household production and leisure. Suppose the institutional setting is such that one member works fixed hours (member 2), while the other member allocates time between household production and leisure (member 1). The choice problem becomes:

[Mathematical Expression Omitted],

subject to [y.sup.***] = cz + xp,

where [y.sup.***] = [y.sub.0] + [y.sub.2] and [Mathematical Expression Omitted].

The standard solution for the demand function in this case is very close to the previous case:

[Mathematical Expression Omitted]. [12]

The difference between this expression and the previous model ([11]) lies in the time and full-income effects. Income here is reduced from [y.sup.**] (= [y.sub.0] + [y.sub.1] + [y.sub.2]) in [11] to [y.sup.***] (= [y.sub.0] + [y.sub.1]) in [12] and time is increased by [Mathematical Expression Omitted] from [Mathematical Expression Omitted]. The out-of-pocket cost of the trip will not be affected. Consequently, the separate arguments for the available stock of time and income have to be strong enough to provide evidence that a change in labor market circumstances that is not reflected in wage rates, influences recreation demand. Experience suggests that while arguments about time will be significant, arguments about income frequently will not be. An alternative interpretation, exploited in the empirical application below, is to allow the marginal effect of time to differ. For households with more time, the marginal effect of time will be less. When [T.sub.1] and [T.sub.2] are not observable, this will be the approach.

This analysis has identified three models for the demand for recreation that vary according to the labor market situation of spouses. These models can be written compactly as

Z = F(P, t, Y, T) [13]

Where P = constant cost per trip, t = travel time, Y = full income, and T = the time endowment. For specification [9], one spouse works at a constant wage and as a consequence, the second spouse does not work but does household production:

P = c + [w.sub.1]t

Y = [y.sub.0] + [w.sub.1]T

T = [T.sub.2].

For [11], both household members work for fixed hours of work, and divide their residual time between recreation and household production:

P = c

Y = [y.sub.0] + [y.sub.1] + [y.sub.2]

[Mathematical Expression Omitted].

When one member works fixed hours and the second does home production, we have equation [12]:

P = c

Y = [y.sub.0] + [y.sub.1]

[Mathematical Expression Omitted].

For empirical analysis, amounts of time, [T.sub.1] and [T.sub.2], are not observable. Hence neither time nor full income is available. To test the implications of this model, the standard specification will be altered in two ways. First, the cost per trip will be calculated for both spouses depending on the degree of flexibility in the labor market. If both spouses are flexible, both of their opportunity costs will be included. For the influence of time, the amount of time will be made to depend on the household's labor market flexibility and its influence will be felt through the marginal trip time.

IV. SOME EMPIRICAL ANALYSIS

The implications of the structure of the household can be explored with the appropriate dataset. Because this model explores a new dimension in recreational behavior, correct data are not readily available. The following examples illustrating the models derived are based on a dataset gathered in 1986.(5) The survey gathered information on New Bedford, Massachusetts, households and their visits to local beaches. This dataset is unusual in having considerable information about spousal employment and other family issues. It also has several fairly severe handicaps. The surveyed households live quite close to beaches (which are the sites analyzed), so that the commitment of travel time is not as substantial as it would be for a broader survey. Further, the survey does not indicate the number of household members per trip. Absent that information, I assume that both spouses take the trip, and that the travel cost, c, covers both spouses.

The empirical analysis tries to demonstrate the differential impact of time constraints and the opportunity cost of time. A means of comparison will be provided in the form of a simple model that ignores family structure, given in equation [15] below.

For the first model incorporating household structure, I base the specification solely on the extent of labor market participation, rather than on the feasibility of substituting non-work hours for work. The questionnaire ascertains three levels of employment: full time, part time, and not working. With two spouses, this creates nine combinations of labor market participation for households. Table 2 shows the distribution of these employment patterns for the households with two spouses.

The full sample totals 535 households who were interviewed by phone concerning their beach use. I estimate demand functions for two beaches in the study. For specification of the first set of models, I devise three degrees of flexibility, depending on labor market penetration of the two spouses.

a. No flexibility

Both spouses work full time.

b. Some flexibility

One spouse full time, one part time

One spouse employed part time, one not employed

One spouse full time, one not employed

c. Full flexibility

Both spouses not employed

Both spouses employed part time

These pairs are symmetric; for example, a household could be categorized as having some flexibility (category b), if spouse 1 is part time, and spouse 2 is not working, or spouse 2 is part time and spouse I is not working.

Household Employment Structure Limited to Labor Market Participation

The intent is to use the basic equation [13], based on labor-market participation, for estimation that accounts for household-employment structure. However, these models cannot be estimated directly because the appropriate measures of time are not observed. To incorporate the core economic forces, I concentrate on the implied role of the endogenous value of time. And although [13] cannot be directly estimated, it helps understand the effect of time constraints. For categories a and c, the opportunity cost of time is not a parameter, either because both spouses are employed full time or because neither spouse works. Hence we cannot use the wage rate as a parameter in measuring their marginal value of time. The time constraint demonstrates its influence on behavior through travel time. The tighter the time constraint, the greater the negative influence of travel time. Hence for categories a and c, the time constraints are quite different in that households with two full-time workers have a higher marginal value of time, other things equal. Those with some flexibility are assumed to make their recreation choices at the opportunity cost of the wage rate. And because the spouses appear to be more flexible, their time is valued as a parameter, the wage rate. This leads to the following specification:

[Mathematical Expression Omitted] [14]
TABLE 2
NUMBER OF, AND PERCENTAGE OF HOUSEHOLDS IN SAMPLE, BY
EMPLOYMENT PATTERN

Spouse 2

                 Full Time        Part Time       Not Employed
Spouse 1       Number    %      Number      %    Number      %

Full Time       133     24.9%    20      3.7%     127     23.7%
Part Time        31      5.8%     2       .4%      37      6.9%
Not Employed     54     10.1%    10      1.9%     121     22.6%


where [D.sub.i] = 1 if the family is in the ith category of labor market flexibility. The variable [P.sub.sub] is a price of substitute variable, calculated for the nearest beach in the same way as the own price. This equation was estimated as a tobit.(6) The other variables are:

t = round trip travel time

[w.sub.i] = after tax wage rate, based on the occupational group

c = round trip travel cost at 8.2 cents per mile.

Based on the idea that greater labor market involvement increases the marginal value of time, it would be expected that [absolute value of [[Beta].sub.3]] [greater than] [absolute value of [[Beta].sub.4]] as well as 0 [greater than] [[Beta].sub.3], [[Beta].sub.4].

For comparison, it is necessary to have a model that ignores household structure. So an approximate comparison, the model

[z.sub.j] = [[Alpha].sub.0j] + [[Alpha].sub.1j](c + t([w.sub.1] + [w.sub.2])) + [[Alpha].sub.2j][P.sub.sub] + [[Epsilon].sub.j] for j = 1, 2 [15]

is estimated. This treats all households as if their labor-leisure trade-off is made at the constants [w.sub.i] for the ith spouse. The models are not nested within equation [14], but for a given wage and a given value of t, they are equivalent if [[Beta].sub.4] = [[Beta].sub.3] and [D.sub.2] is one for all observations. This model is also used for comparison against a more general structured model below.

Parameter estimates for these models are given in Table 3. The observations are selected for estimation only if the household went to any beach. Among those observations, only some went to the two beaches. The price coefficient is significantly less than zero. They meet prior expectations concerning the marginal value of time. Households with tighter time constraints act as if the marginal value of time is higher, and consequently the impact of travel time is greater, as demonstrated by the estimates of [[Beta].sub.3] and [[Beta].sub.4]. For both beaches, the differences are significantly different from each zero at the 5% level for a one-tailed test.(7) The coefficients [TABULAR DATA FOR TABLE 3 OMITTED] [[Beta].sub.3] and [[Beta].sub.4] in the Tobit case are conditional covariate effects, where for time the expression is:

[Mathematical Expression Omitted]

where cf is a correction for truncation factor, which is less than one.(8) For the means for beach 1, cf = .3 approximately. Hence the numbers (-58.9, -22.9)*.3 = (-17.6, -6.87) represent for beach 1 the impact of an increase of one hour of travel time on the demand for trips for households who are fully employed and households who are not employed at all. One hour is greater than the extent of the market for these sites. The responses would be more credible if increments of, say, 15 minutes were used.

The intent of the comparison is to specify a model that has a collapsible budget constraint, so that time always has a parametric opportunity cost. Further, the comparison model does not account for the differences in household labor force participation. In the estimated comparison models, own price coefficients, ([[Beta].sub.1]), are significantly smaller in absolute value than the own price coefficients in the full models. Computationally the smaller own-price coefficient for the comparison model implies that a higher consumer surplus for the model where the budget can be collapsed and there are no time constraints. Incorporating the more realistic time constraints tends to lower estimates of consumer surplus.

Household Employment Structure Incorporating Flexibility of Occupation

Models more in the spirit of the paper would pay more attention to the opportunities for individual spouses, based on their labor-market participation and the flexibility of their employment. One model can be specified in the following way, though as before, imperfectly because of the dataset. The occupations in which individuals are employed can be classified into two groups: one occupational group has flexibility with regard to hours of work, while the other group does not. In this case, I chose the following occupational categories as flexible:

self-employed

professional (doctors, lawyers, etc.)

tradesmen (carpenter, machinist, etc.)

hourly workers (typist, laborer, etc.)

These categories are admittedly arbitrary. Within each category, it is likely that some individuals have flexibility in terms of the employment structure, while others do not. Spouses who are able to trade off time for money will have their opportunity cost of time valued at the after tax wage rate. For spouses who are not able to trade time for money according to their occupation (educators, policemen, others), time influences demand directly. With households where the time constraint is very tight, the marginal value of time will be high and the impact of travel time will be different from households where the time constraints are not so tight. To facilitate this approach to the valuation of time, I specify the following model:

[Mathematical Expression Omitted], [16]

where

j = 1, 2 for the two beaches;

[E.sub.j] = 1 if the jth spouse works in an occupation with flexible hours, 0 otherwise;

c = travel cost;

[w.sub.j] = after tax wage for the jth spouse;

[D.sub.1] = 1 if both spouses work full time, 0 otherwise;

[D.sub.3] = 1 if both spouses are not in the labor market, 0 otherwise;

[D.sub.2] = 1 - [D.sub.1] - [D.sub.3].

[P.sub.sub] = price of the closest substitute site, where the price is calculated in the same way as the own price.

By construction, there are three versions of time constraints embodied in equation [16]: one for households in which both spouses are in the labor market full time, one for households in which at least one of the spouses works part time, or does not work while the other spouse works, and one for households in which neither spouse works. We would expect the marginal value of time to be highest for the first group and lowest for the third group.
TABLE 4

ESTIMATED COEFFICIENTS FOR A COMPLETE MODEL OF INDIVIDUAL SPOUSES

                                   Beach 1         Beach 2
                                   Full Model      Full Model

[[Beta].sub.0j]                      14.17           3.24
                                     (2.11)         (2.17)
[[Beta].sub.1j]                     -10.01          -1.76
                                     (2.96)         (2.16)
[[Beta].sub.2j]                       1.32           -.70
                                     (0.38)          (.71)
[[Beta].sub.3j]                     -84.19         -11.41
                                     (3.39)         (2.60)
[[Beta].sub.4j]                     -29.26          -7.77
                                     (2.05)         (2.34)
[[Beta].sub.5j]                     -43.82          -7.06
                                     (3.24)         (2.58)
[[Sigma].sup.a]                      46.71           9.54
                                    (16.79)         (14.7)

Note: Based on 370 observations. Ratio of estimated coefficients to
standard error in parentheses. The comparison model (equation [15])
is the same for each of the two more structured models and is given
in Table 3.

a [Sigma] is the square root of the variance for the error in the
Tobit.


Table 4 gives the estimated models for the two beaches(9). These models are not as well behaved as the previous set. The t-statistics are not as convincingly high as in Table 3, partly because of the induced collinearity from an additional variable. More important, the marginal value of time doesn't meet expectations. When households have very scarce time, both spouses employed, time would be scarcest. When the spouses have a combination of part time and not being in the labor force, time would be less scarce. When both spouses are not in the labor force, time would be less scarce. Hence we would expect that [absolute value of [[Beta].sub.3]] [greater than] [absolute value of [[Beta].sub.4]] [greater than] [absolute value of [[Beta].sub.5]] and further that all coefficients would be less than zero. These patterns hold up but the first pattern: [absolute value of [[Beta].sub.3]] [greater than] [absolute value of [[Beta].sub.4]] and [absolute value of [[Beta].sub.3]] [greater than] [absolute value of [[Beta].sub.5]] does hold statistically. That is, the data show that behavior is consistent with the hypothesis that for households where both spouses work, the impact of the time constraint is greater than for the cases where both spouses do not work.

The hypothesis that there is no difference in the impact of time, depending on labor market circumstances, can be tested under the hypothesis that [[Beta].sub.3] = [[Beta].sub.4] = [[Beta].sub.5]. This hypothesis cannot be rejected.

It is tempting to speculate about the causes of indifferent performance in this model. For example, unemployed spouses might not regard their excess time in the same light that retired spouses would. This could be countered by allowing age to influence the demand. Despite the inconsistent ordering the parameters, there are hints that labor market effects have some influence in the estimated models. Survey work based on the recognition of the importance of joint decisions would be necessary to confirm these hints.

The ultimate value of estimating recreational demand functions lies in calculating consumer surplus. Methodological innovations that make little difference in consumer surplus will disappear through the process of natural selection. To show that the family labor market circumstances matter, I have calculated the ratio of consumer surplus for the family labor supply model to consumer surplus for the comparison model. These ratios are: .74, .1.08 for beach 1 for models 1 and 2; and .6, .73 beach 2, models 1 and 2. Hence the family labor supply model produces lower consumer surplus for access in three out of the four cases. This may not generalize to other recreational settings. Incorporating the value of household time when spouses make joint decisions can have the effect of lowering the opportunity cost of time for labor market participants and raising it for non-participants. When there is household work to be done, the opportunity cost of time may be equated.

V. CONCLUSION

Researchers estimating the demand for recreation have recognized that institutional constraints in the labor market distort the equality between the wage rate and the marginal value of time. These models portray the behavior of a single individual. In this paper, I develop a model of the demand for recreation based on two household members sharing income and household production. In this simple model, the perfect substitutability between spouses' efforts in household production is sufficient to break the equality of wage rate and marginal value of time. Models that incorporate joint behavior of spouses are developed. Empirical versions of these models seem to imply that consumer surplus from access to recreational sites declines in comparison with a naive model in which the value of time is always equal to the wage rate.

The dataset used to demonstrate the model has many shortcomings. A more satisfactory test can come from a dataset that keeps track of whether one or two spouses make recreational trips. In such a dataset, when the out-of-pocket costs depend on the number of travelers as well as the distance traveled, one would have more confidence in distinguishing among different models.

In this paper, I have concentrated only on households with two adults. Perhaps even more important is devising models that account for the demand and benefits from children. Many recreational activities have substantial involvement of children. It is both a substantial conceptual challenge and a practical problem to insure that these benefits are accounted for.

1 An obvious way of generalizing the model relates to the disutility of household chores. Juster and Stafford (1985) report on time diary studies which rank the "process benefits" of individual's time. The "process benefit" may best be described as the utility of the time spent, rather than the utility of the outcome. In a ranking of 30 activities, there are substantial and significant differences among the activities, from talking with children at the top, to cleaning the house at the bottom. (Juster and Stafford, Table 13.1, 336). The fact that different activities provide different "process benefits" suggests that the general activity, household production, would produce negative utility.

2 The two z's in this utility function indicate that each spouse will get the same number of trips.

3 With the time onsite per trip equal to s, the utility function would be [Mathematical Expression Omitted]. If s is constant and all households experience the same level of s, then it can be embedded in the utility function. See McConnell (1992) for details about the time budget.

4 It would also be possible to linearize the marginal cost of production and the marginal value of production and obtain a solution analogous to equation 8.

5 This study is described in McConnell (1986).

6 A negative binomial was also estimated, showing similar results.

7 The test statistic for ([[Beta].sub.3] - [[Beta].sub.4])/se([[Beta].sub.3] - [[Beta].sub.4]) is -2.12 for beach 1 and -2.06 for beach 2.

8 cf = [1 - AI(A) - [I.sup.2](A)] where A = inner product of the regressors and parameters and I is the inverse Mills ratio. See for example, Maddala 1983, 160.

9 The comparison model is equation [15], the same as found in Table 3. It simply values time at the wage rate.

References

Apps P. F., and R. Rees. 1996. "Labour Supply, Household Production and Intra-family Welfare Distribution" Journal of Public Economics 60 (May): 199-219.

Becker, G. S. 1981. A Treatise on the Family. Cambridge: Harvard University Press.

Bockstael, N. E., I. E. Strand, and W. M. Hanemann. 1987. "Time and the Recreation Demand Model," American Journal of Agricultural Economics 69 (May): 293-302.

Cesario, Frank J., and Jack L. Knetsch. 1970. "Time Bias in Recreation Benefit Studies" Water Resources Research 6 (June): 700-704.

Chiappora, P. A. 1992. "Collective Labor Supply" Journal of Political Economy. 100 (June): 347-467.

Haddad, Lawrence, John Hoddinott, and Harold Alderman. 1994. "Intrahousehold Resource Allocation: An Overview." World Bank Policy Research Working Paper 1255. February.

Juster, F. Thomas, and Frank P. Stafford, eds. 1985. Time, Goods, and Well-Being. Ann Arbor, Mich.: Survey Research Center, Institute for Social Research, University of Michigan.

Larson, Douglas M. 1993. "Joint Recreation Choices and Values of Time." Land Economics 69 (Aug.): 270-86.

Maddala, G. S. 1983. Limited-dependent and Qualitative Variables in Econometrics. New York: Cambridge University Press.

McConnell, K. E. 1986. "The Damages to Recreational Activities from PCB's in the New Bedford Harbor." Prepared for NOAA and the Department of Justice, December.

-----. 1992 "Onsite Time in the Demand for Recreation." American Journal of Agricultural Economics 74 (Nov.): 918-25.

McConnell, K. E., and I. E. Strand. 1981. "Measuring the Cost of Time in the Demand for Recreation." American Journal of Agricultural Economics 63 (Feb.): 153-56.

Smith, V. Kerry, William H. Desvousges, and Matthew P. McGivney. 1983. "The Opportunity Cost of Travel Time in Recreation Demand Models." Land Economics 59 (Aug.): 259-77.

Smith, V. Kerry, and George Van Houtven. 1998. "Non Market Valuation and the Household" Working paper. Economics Department, Duke University.

K. E. McConnell is a professor in the Department of Agricultural and Resource Economics at the University of Maryland. Thanks to the editor and an anonymous reviewer for generous comments.
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Date:Aug 1, 1999
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