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J Popul Econ (1996) 9:429-439 - -Journa l of

_population Economics © Springer-Verlag 1996

Demographic composition of farm households and its effect on time allocation

Ayal Kimhi

Department of Agricultural Economics and Management, Hebrew University, P.O. Box 12, Rehovot 76100, Israel (Fax: 972-8466267)

Received September 1, 1994 / Accepted March 19, 1996

Abstract. The decis ions o f farmers to work on or o f f the fa rm depend in pa r t on househo ld c o m p o s i t i o n and the pa r t i c ipa t ion pa t te rns o f o ther fami ly members . This is because o f the di f ferent ia l income effects resul t ing f rom the h o u s e h o l d ' s j o in t budge t cons t ra in t and the t ime and money costs imposed by different househo ld members , and because o f the subs t i tu tab i l i ty or com- p l emen ta r i t y between the fa rm labor inputs o f different househo ld members . This pape r demons t ra tes this po in t by es t imat ing a j o in t l a b o r pa r t i c ipa t i on m o d e l o f fa rm opera to rs and thei r spouses, in which pa r t i c ipa t i on decis ions are cond i t i oned on househo ld compos i t ion . The mode l is es t imated as a mul t ivar ia te p robi t m o d e l with fixed effects, by quasi m a x i m u m l ike l ihood methods . The results are consis tent with the hypotheses tha t the t ime costs imposed on the househo ld by smal l chi ldren are larger than the money costs; tha t the relat ive i m p o r t a n c e o f t ime costs is decreas ing as chi ldren grow up; and tha t the fa rm labor inputs o f o lder chi ldren are complemen t s to the couple ' s f a rm l abo r inputs bu t those o f p r ime-age adul t s are substi tutes.

J E L classification: J 22, J 43

Key words: F a r m labor, a l loca t ion o f time, mul t ivar ia te p rob i t

An earlier version of this paper was presented at the 1994 meeting of the European Society for Population Economics, Tilburg, The Netherlands. This research relies in part on my Ph.D. dissertation at the University of Chicago. I am grateful to Gary Becker, Joe Hotz, Yair Mundlak, Kevin Murphy, and Yoram Weiss for their useful suggestions and guidance. The research was completed while I was visiting at the University of Maryland. I thank the Department of Agricultural and Resource Economics and the Maryland Agricultural Experiment Station for financial support. Specific constructive comments were also made by Paul Schultz, John Er- misch, and anonymous referees. Finally, I express my gratitude to the staff of the Central Bureau of Statistics in Israel, especially Haim Regev and Meir Rothchild, for providing the data used here. Responsibility for the contents of this paper remains exclusively mine. Responsible editor: John E Ermisch

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1. Introduct ion

A. Kimhi

Most empirical analyses of farmers' time allocation deal with individual decisions (Sumner 1982; Bollman 1979; Lopez 1986) or at most husband-wife decisions (Huffman and Lange 1989; Gould and Saupe 1989; Lass and Gempesaw 1992; Kimhi 1994). However, the existence of other family members and their economic behavior may affect time allocation decisions in various ways. Think, for example, about a simple model of a household which pools resources and maximizes a joint utility function. An additional dependent in the household will reduce household members' consumption and make them work more. On the other hand, an additional household member which contributes to household income over and above his share in consumption will make other family members work less (all this is true pro- vided that leisure is a normal consumption good). The situation is even more complicated in farm households, since there could be complementarity or substitution in farm production between the labor inputs of different household members. This would create an interdependence between the time allocation decisions of various family members, in addition to that created by the household budget constraint.

Family members of various age groups affect time allocation between farm and off-farm work differently. Small children and old people, which can be classified as dependents, generally impose a cost on the household, not only in terms of consumption goods but also in terms of time spent in house work. If farm work is a better complement to house work than is off-farm work, it is expected that prime-age household members will work more on the farm and less off the farm (for a given total labor supply), in households that include more dependents. Total labor supply may decrease or increase depending on whether the time cost of dependents is higher or lower relative to their money costs, and also depending on the relative magnitudes of the price elasticity and the income elasticity of the demand for leisure.

Older children may provide farm labor or help in house work, besides imposing money and time costs on the household. Hence, their net effect on the time allocation of adult household members cannot be determined in ad- vance. Other adults provide farm labor and/or contribute off-farm income. If they work only off the farm, they affect decisions of other household members only through the household budget constraint. If they work on the farm, other complementarity or substitution effects prevail as in the previous examples, and the overall effects of their existence and economic behavior on the time allocation of other household members are ambiguous.

This study demonstrates the effects of the existence of family members of various age groups on the time allocation decisions of farm operators and their spouses, by modelling the couple's joint farm and off-farm labor participation decisions. Specifically, two participation equations of the probit type are estimated for each person (one for farm participation and one for off-farm participation), using data from the 1981 Census of Agriculture in Israel. The resulting four-equation probit model is estimated by quasi maximum likelihood (QML) methods, allowing for village-specific fixed effects.

Comparative static results of the traditional single utility household model are relatively easy to derive. In more sophisticated models of household behavior such as collective or bargaining models (Chiappori 1988; Horney

D e m o g r a p h i c c o m p o s i t i o n o f f a r m h o u s e h o l d s 431

and McElroy 1988; Bourguignon and Chiappori 1992; Lundberg and Pollak 1994), more results are likely to be ambiguous. I will not refer to any specific behavioral model in this paper, but rather treat the predictions of the single utility model as first-order approximations, and analyze the results accor- dingly.

The theory of time allocation decisions of farm couples is discussed in Sect. 2. Section 3 deals with comparative statics of the theoretical model. The empirical model and estimation strategy are presented in Sect. 4. In Sect. 5, I describe the data and report the results of the estimation. Section 6 con- cludes with a discussion of the findings and their implications.

2. The theoretical model

Assume a household utility function of the form U(C-co, Th--to;Zu), where C is total household consumption, T h is the vector of household members' home time, and Zu is a vector of utility shifters. Home time is a residual including, among other things, time devoted to household work and leisure. The parameters Co and to are subsistence levels of consumption goods and home time, respectively. These are assumed to be independent of the household time-allocation decisions. Total time endowment of each household member (T) can be used for farm work (Tf), off-farm work (Tm), and/or home time. Therefore, the time constraint is, in vector notation, T f + T m +T h = T. This is a strict equality since Th is a residual by defini- tion. Farm work and off-farm work are subject to nonnegativity constraints. A similar constraint is not necessary for home time if we maintain the usual regularity assumption that marginal utility goes to infinity as the relevant argument (in this case, home time) approaches zero.

Consumption is constrained by total household income. Income is composed of: (i) farm income (Yf), which is a function of the vector including each household member's farm labor supply, Tf; (ii) off-farm labor income, which is the sum of the off-farm earnings of each household member (Y / ,

i . which is a function of the time allocated to off-farm work Tm), and (iii) o t h e r income . (Y o). The resulting budget constraint is C = Yf(Tf;Zf)+

l l . l ~iYm(Zm,Zm)+Yo, where Zj are exogenous shifters of function j. The strict equality is guaranteed by a non-satiation assumption.

The household optimization problem is to maximize utility subject to the time, budget, and nonnegativity constraints. The labor participation conditions, for participation in farm and off-farm work, respectively, are a subset of the Kuhn-Tucker conditions (Kimhi 1994). In vector notation:

o r / o T~_< (0 U/OTh)/(O U/O C) ; (9

O Y m / O T m <_ (O U/O T h )/(O U/O C ) . (2)

The right-hand-side is the marginal rate of substitution (MRS) between home time and other consumption goods. Hence, participation (an internal solution) occurs when the equality is strict.

If an interior solution occurs for all choices (all household members work both on and off the farm), the endogenous variables {C, Th, Tf, Tin} can be

432 A. Kimhi

specified as functions of all the exogenous variables Z,, ZT, Zm, Yo, and T. This is the reduced-form solution. Using the reduced-form solution in (1) and (2), one can determine which of the labor participation conditions is satisfied in the following manner. The participation condition of T), for example, is derived by putting in (1) the reduced-form solutions of all the endogenous variables other than T), and imposing T ) = 0. Stated differently, the structural participation condition for T) is derived by evaluating (1) at T~ = 0. The reduced-form participation condition is derived by further plugging the reduced-form solutions for the other endogenous variables. The 2 n reduced- form participation equations (where n is the number of household members) have the general form:

fJ(Zu, Zf, Zm, Yo, T)<-gJ(Zu, Zf, Zm, Yo, T ) , j = 1 . . . n ; (1')

hJ(zJ)<-gJ(Zu, Zf, Zm, Yo, T) , j = 1 . . . n ; (2')

where farm nonparticipation occurs if gJ-fJ> 0 and off-farm nonparticipation occurs if g J -h J> O. AS these functional forms reveal, the model does not generate any exclusion restriction, unless there exists a person-specific variable in Zm that does not appear in Z , or in Zf.

3. Comparative static analysis

Due to data limitations, only probabilities of participation as predicted by the model will be estimated. Hence, I will present a comparative static analysis of the probabilities of participation rather than the actual choices. Assume that the participation equations include random disturbance terms, perhaps due to optimization errors. Subject to certain regularity conditions on the distributions of these random disturbances, there is a one-to-one corre- spondence between the probability of participation and the size of gJ-fJ or g J -h j. Specifically, the probability of farm participation is decreasing with gJ-fJ and the probability of off-farm participation is decreasing with gJ -- h j.

Assume, for simplicity, that the household is composed of two adult members only, a male and a female, and that the existence of small children is reflected in larger subsistence levels of consumption goods and female's home time only. Hence, the effect of small children on the participation probabilities comes only through the MRS's gJ. Denote the male and female variables by superscripts m and f, respectively. Then, around the optimal choices:

0 gm/O tfo = 1(0 2 U/O CO T~)" (0 U/O Try)

- (O 2 V/O r 7 O T{)" (O U/O C)]" (O V/O C ) - 2 ;

Ogm/O c o = [(0 2 U / O C 2 ) • (0 U/O Try) - (0 2 U/O T'~O C)

• (o u / o c ) ] . (o u / o c ) - z ;

(3)

(4)

Demographic composition of farm households 433

Ogf/O tfo = {(0 2 U/O CO Tf) . (O U/O T f ) - [0 2 U/O (Tfh)2] • (0 U/O C)}

• ( O U / O C ) - 2 ;

0 gf/O c o = [(0 2 U/O C2) • (0 U/O Tfh) - (0 2 U/O T f 0 C)" (0 U/O C)]

• ( O U / O C ) - 2 .

(5)

(6)

If, for example, all cross-derivatives of the utility function are positive, then (4) and (6) are negative and (5) is positive, while the sign of (3) is ambiguous. Therefore, without further assumptions, no conclusions about the effect of small children on participation patterns can be reached. However, the results do indicate that farm participation and off-farm participation of the same individual will be affected similarly. If the time cost of small children is dominant over their money cost, it is more likely that female's participation will be negatively affected by the presence of small children. The opposite is true when the money cost of small children is dominant. For the male household member, similar conclusions are achieved only if (3) turns out to be positive. This is possible, for example, when the complementarity in consumption between female's home time and other goods is much stronger than the complementarity between male's home time and female's home time.

The presence of older children is expected to affect the MRS in a similar fashion (perhaps with smaller magnitudes). However, they also affect the marginal return to farm labor if they supply labor to the farm. Suppose that older children's farm labor input is the first element of Zf. Then, in order to find their effect on the farm participation probabilities, one has to evaluate 0 2 Yf/O TTOZlu in addition to (3) and (4) for males, or 0 2 Yf/O T~OZlu in addition to (5) and (6) for females. Hence, the results also depend on whether the older children's farm labor input is a substitute or a complement to the labor input of each adult household member.

The effect of the existence of other prime-age household members can be analyzed in a similar fashion. Because no definite conclusions can be reached without strong assumptions, it will not be discussed here. Older adults may have effects similar to those of small children, if they do not work on the farm, or to those of older children, if they do work on the farm.

4. Empirical model and estimation strategy

Using a first-order approximation of (1') and (2'), and denoting the sum of the random disturbances and the approximation errors by e, a generic participation equation is specified as:

aj+flujZu+~fj.Zf+flmjZm+~ojYo+fltjT+,~j<.O ; j = 1 . . . 2 n , (7)

where the fl's are appropriately dimensioned row vectors of unknown parameters, and aj is a village-specific intercept. The village subscript is omitted for simplicity. Village-specific effects are justified by varying levels of institutional constraints and transaction costs imposed by the different villages (Kimhi 1993). Strict inequality indicates nonparticipation. To the extent that

434 A. Kimhi

some explanatory variables appear in more than one of Zu, Zf, and Zm, only sums of the corresponding coefficients are identified. This is particularly true for some of the household composition variables that will be introduced in the next section. Any variables that affect the subsistence parameters c o and to are included in Z u. If cj-N(0,1) , each of these equations can be estimated by probit. Since the error terms are assumed to be correlated with each other (Kimhi 1994), a joint estimation procedure is called for in order to exploit all available information and increase the efficiency of the estimator.

Maximum likelihood estimation of multivariate probit models with more than two equations is infeasible, unless one uses simulation techniques (McFadden 1989). In the present problem, I resort to a QML method introduced by Avery et al. (1983). In their procedure, restrictions are imposed on the parameters in order to simplify the likelihood function. In the multivariate probit case, restricting any of the correlation coefficients to be zero does not affect the consistency of the other coefficients. A simple example is estimating each equation separately by univariate probit. Alternatively, every two probit equations can be estimated by bivariate probit, assuming the two residuals are uncorrelated with those of the other equations. The resulting estimators are consistent but inefficient. In order to maximize efficiency subject to the constraint that no more than two levels of numerical integration are used, I chose to maximize Lf= ~112 "q- ~13 -t- ~14 q- ~23 d- ~ 4 -'1- ~34, where ~/j is the bivariate probit log-likelihood function of equations i and j. Specifically:

~j = ~ ln B(difliXi, djfljXj, dijPij) , (8)

where summation is over individuals; B is the bivariate normal probability function; X 9 is a vector including all the explanatory variables in (7) including the village dummies and flj is its associated vector of coefficients; Pij is the correlation between e i and ej; lk equals one if participation occurs, zero otherwise; and d k - - 2 I k - 1 and dij = didj. Treating the village-specific intercepts as fixed effects, as reflected in the construction of Xj and flj, is equivalent to the first stage of the empirical model of Kimhi (1996). Consis- tent estimates of all the flj's and pij's are derived in this fashion, all in one step. In simpler versions of this QML method, any correlation coefficient that was assumed to be zero can be consistently estimated in a second stage (Avery et al. 1983). The variance-covariance matrix of the estimated coefficients is calculated by the expression H - 1 P H -1, as suggested by White (1982), where H is the matrix of second derivatives of quasi-likelihood function (8) and P is the matrix of outer products of the gradient vector of (8).

5. Data and results

The data used in this analysis are individual statistics on a subset of family farms drawn from the 1981 Census of Agriculture in Israel. They include per- sonal characteristics of the farm operators and their families, information on the farming activities, and the allocation of time of each family member in qualitative terms. I chose only observations for which the village was explicit-


ly identified, so that I will be able to use village attributes or village-specific fixed effects. After disposing of incomplete observations (in most of those the age or education variables were missing), landless families, farms which were explicitly defined as "non-farming units", and partnerships, 4626 observations from 90 villages were left and used in the empirical analysis. Table 1 includes descriptive statistics of the data set.

The results of the participation model are presented in Table 2. The estimated village-specific fixed effects are not reported in the table, but they were jointly statistically significant. Only the effects of household composition

Table 1. Descriptive statistics

Variable Mean Std. dev. Range Units

Age operator 48.9 13.2 1 6 - 80 years Age spouse 45.0 12.6 14 - 80 years Schooling operator 9.2 4.4 0 - 20 years Schooling spouse 9.0 4.7 0 - 20 years Wage operator a 118.3 43.0 42 - 254 index Wage spouse b 62.7 19.7 3 6 - 147 index Family members 0 - 3 c 0.17 0.4 0 - 3 heads Family members 4 - 6 0.29 0.5 0 - 4 heads Family members 7 - 12 0.67 0.9 0 - 5 heads Family members 13 - 18 0.77 1.1 0 - 6 heads Family members 1 9 - 21 0.39 0.7 0 - 4 heads Family members 22 - 31 0.90 1.1 0 - 7 heads Family members 32-41 0.53 0.8 0 - 4 heads Family members 42 - 51 0.55 0.8 0 - 4 heads Family members 52 - 61 0.47 0.7 0 - 4 heads Family members 62 - 71 0.26 0.6 0 - 3 heads Family members 71 + 0.16 0.5 0 - 3 heads Ethnic origin d 0.52 0.5 0 - 1 dummy Farm tenure e 19.4 10.8 0 - 59 years Years in Israel f 34.2 9.6 1 - 77 years Dairy farm 0.1 0.3 0 - 1 dummy Milk cows 2.7 9.7 0 - 118 heads Land g 32.1 28.9 1 - 800 dunams h Livestock i 6.9 20.4 0 - 394 $1000 (1981) Old capital j 23.4 44.9 0 - 7 0 7 $1000 (1981) New capital k 44.4 66.3 0 -- 2004 $1000 (1981)

a Imputed by mean wages in cells defined by sex, age, origin and schooling, taken from the 1983 Census of Population. b Imputed by mean wages in cells defined by sex, age and schooling only. c Number of family members in the relevant age groups, excluding the operator and his spouse (applies to all age groups). d Equals one if the operator is of European-American origin or native Israeli. e Number of years that the current operator is operating the farm. f For farm operator. Equals age if born in Israel. g Original land allotment (I suspect that some farmers reported actual land use, including or excluding rented lots). h I dunam = 0.23 acre. i Normative value of livestock. J Normative value of capital stock 10 years old and older. k Normative value of capital stock less than 10 years old.

436 A. Kimhi

will be discussed here in detail. The rest of the results are not much different than what others have found (Hallberg et al. 1991). Children under 3 years of age decrease the tendency of spouses to participate in both sectors, decrease operators' farm participation but increase their off-farm participation (almost all farm operators are males in this sample).

According to the comparative static analysis in Sect. 3, the result with respect to the spouse's participation indicates that young children are not as costly in terms of consumption goods as in terms of the spouse's home time. The result with respect to the operator 's participation contradicts the corn-

Table 2. Participation model results a

Variable Farm Off-farm

Operator Spouse Operator Spouse

Age 7.69 (9.44) 4.49 (6.07) 9.16 (11.3) 4.87 (5.63) (Age)2/100 -6 .43 (11.0) -3 .95 (6.75) -9 .03 (14.8) -6 .32 (8.64) Schooling 0.148 (1.72) 0.057 (0.61) 0.172 (2.00) 1.37 (12.6) Imputed wage -0.431 (3.90) -0 .657 (5.68) 1.49 (13.6) 2.32 (17.5) Other's age -4 .80 (5.95) 1.28 (1.74) - 1.96 (2.67) -6 .14 (7.84) Other's (age)2/100 4.17 (6.73) - 1.21 (2.24) 1.27 (2.15) 4.83 (8.16) Other's schooling 0.698 (7.39) 0.956 (11.0) -0 .222 (2.45) -1 .03 (10.5) Other's wage -0.800 (6.09) -0.135 (1.31) 0.121 (1.04) 0.959 (8.58) Origin 0.107 (3.25) 0.122 (4.36) -0.203 (7.51) -0.081 (2.76) Tenure 0.156 (1.75) 0.012 (0.15) -0.103 (1.29) -0.159(1.79) Years in Israel -0 .090 (0.88) 0.421 (5.04) 0.625 (6.70) 0.207 (2.I1) Dairy farm 0.069 (0.50) 0.386 (3.55) 0.693 (5.34) 0.530 (3.98) In (cows) -0 .432 (1.99). -0 .724 (4.65) -1 .66 (8.17) -0 .779 (3.99) In (land) 3.65 (26.6) 1.09 (8.27) - 1.94 (16.6) - 0.673 (5.26) In (livestock) 0.991 (17.3) 0.624 (13.9) -0 .212 (4.73) -0 .306 (5.85) In (old capital) 0.911 (25.1) 0.587 (19.0) -0.648 (21.2) -0.161 (4.64) In (new capital) 1.32 (29.7) 0.952 (23.1) -1 .17 (28.3) -0 .196 (4.31) C h i l d 0 - 3 -0.038 (1.61) -0 .099 (4.69) 0.055 (2.62) -0.133 (5.96) C h i l d 4 - 6 0.140 (7.57) 0.008 (0.49) -0.097 (6.10) -0.154(8.98) Child 7 - 1 2 0.030 (2.67) 0.071 (7.13) -0 .039 (3.90) -0 .114 (9.85) Child 13 -18 0.037 (3.69) -0 .004 (0.39) -0.025 (2.95) -0.021 (1.90) Adult 19-21 0.003 (0.21) -0 .058 (3.95) 0.062 (4.63) 0.071 (4.21) A d u l t 2 2 - 3 1 -0.097 (10.1) -0 .094 (9.58) 0.018 (2.03) 0.024(1.93) A d u l t 3 2 - 4 1 -0.278 (10.1) -0.095 (3.84) -0 .046 (1.53) 0.201 (5.96) A d u l t 4 2 - 5 1 -0.243 (4.79) -0 .149 (3.29) 0.227 (3.85) 0.221 (3.20) Adult 52 -61 0.137 (1.34) -0.081 (1.20) -0 .209 (2.88) -0 .266 (3.71) Adult 62 -71 0.046 (0.81) -0 .092 (2.34) 0.163 (3.69) 0.266 (6.55) A d u l t 7 2 - 8 1 -0.052 (1.69) -0 .058 (2.12) -0 .010 (0.31) 0.123 (4.08)

Correlation matrix

Farm Operator 1 Spouse 0.2687 (7.13) 1

Off-farm Operator -0.5219 (18.0) -0.0835 (2.44) 1 Spouse -0.0590 (1.42) -0.4312 (14.0) 0.1283 (3.49)

a Asymptotic t-ratios in parentheses. See Table 1 for description of variables.


parative static analysis, since it was predicted that farm participation and off- farm participation will react in the same direction to the existence of small children. Actually the negative coefficient of small children in the operator 's farm participation equation is not significant at the 5 % level. Another possible reason is that home time of both the operator and the spouse is linked to the existence of small children in ways other than through the subsistence levels.

Older children (up to 18 years of age) increase farm participation and decrease off-farm participation of both adult family members. This is sup- ported by the comparative static analysis only if the farm labor inputs of older children have a sufficiently high degree of complementarity with the couple's farm labor inputs. The positive correlation (0.27) between the residuals of the two farm participation equations indicates that such a complementarity is likely to exist. Another explanation is that farm work is a better complement to house work, so as children are growing and their money cost is increasing relative to their time cost, household members' tendency to work on the farm rises before their tendency to work off the farm rises.

The number of other adults between the ages 19 and 51 increases off-farm participation and decreases farm participation of both spouses. It seems that additional adults are substitutes for the couple in farm work, given current farm characteristics, and therefore the operator 's and spouse's tendency to work off-farm is increasing with the number of prime-age household members. This is in line with the common view that Israeli family farms are too small to provide work to more than two full-time adults, due to land regulations and capital market restrictions that prevent expansion (Kimhi 1993).

The results with respect to older adults (between the ages 52 and 81) are not so clear. It looks like for the spouse the effect is similar to that of prime- age adults, i.e. higher off-farm participation and lower farm participation. As for the operator 's participation tendencies, the effect of the presence of old household members has no particular pattern, though a higher tendency to farm and a lower tendency to work off-farm seems to dominate. Probably the effects of older adults are subject to large noises due to variability in time and money costs and in their ability to work on the family farm.

When a measure of other adults' farm work was included as an explanatory variable in the participation equations, the results did not change qualitatively, though the coefficients tended to be larger in absolute value. The measure was constructed in the following manner: farm labor supply of each individual is reported as an index, where "1" stands for working up to 1/3 of the time on the farm, "2" - up to 2/3, and "3" - full time. These indexes were simply added across adults, other than the farm operator and spouse, in each household. This variable had a strong positive effect on farm participation probability and a strong negative effect on off-farm participation probability. However, there is no reason to think that other adults' time allocation decisions are pre-determined, so including this variable is likely to result in inconsistent estimation due to the correlation between an explanatory variable and the disturbances.

Finally, I estimated the joint participation model separately for households with and without other adults. Even after restricting the village- specific intercepts to be the same in the two subsamples, the hypothesis that

438 A. Kimhi

the other parameter estimates are the same was statistically rejected in low significance levels. This implies that time allocation decisions of farm operators and their spouses depend strongly on the existence of other adult household members.

6. Conclusions

The time allocation of farm operators and their spouses is affected by the existence of other household members. The effects on their farm and off-farm participation decisions can be summarized as follows. When the family includes children up to 3 years of age, the spouse tends to specialize in house work, while the operator tends more to work off the farm and less on the farm. The most likely reason is that yound children impose a cost in terms of home time mainly on the spouse. This makes the spouse more likely to specialize in home production, and hence the operator becomes more likely to engage in income-generating activities. When the family includes older children, their cost in terms of home time is decreasing relative to their money cost, so spouses are more likely to work outside the house. Their tendency to work on the farm increases and their tendency to work off the farm decreases, in the presence of older children, perhaps because older children's farm labor input is a complement to the couple's farm work.

Other adults are, on average, substitutes for the couple in farm work. The couple's tendency to work on the farm decreases while their tendency to work off the farm increases, when other adults are members of the households. Also, when looking separately at households with and without other adults, it is found that their participation patterns depend differently on the explanatory variables. Overall, the results suggest that household composition is an important factor in the decision process of the household regarding time allocation of its members. Not controlling for household composition in empirical work could lead to incorrect conclusions.

Several qualifications are worth mentioning here, regarding the possible endogeneity of household composition to the time allocation decisions. First, the linkages between fertility and female labor supply are well documented in the economic and demographic literature (e.g. Hotz and Miller 1988; Kahn and Whittington 1994). It is possible, hence, that a large number of children is a result, rather than a cause, of female's lack of off-farm labor oppor- tunities. Since this paper deals with a one-period decision rather than a com- plete life-cycle model, the results can be viewed as conditioned on the number of children just as they are conditioned on farm attributes. Second, the existence of other adults may be related to considerations of intergenerational succession (Kimhi 1995). Here the implications are not clear. For example, the existence of an adult succeeding child may be more likely when the parents are working off-farm so that he takes care of the farm operation, or when the parents are not working off the farm since the farm is very profitable, so that the child is there waiting to succeed his parents.

In light of these qualifications, a possible extension of the current ap- plication could be to add equations for other household members to the model. The cost in terms of numerical optimization would not be too large when using the QML method. Another extension is to have the number of children as another endogenous variable.


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