A system comparison approach to distinguish two nonseparable and nonnested agricultural household models.

--. 2000. "The Behavior of Agricultural Households under Constrained Off-Farm Employment: An Alternative Decomposition of Their Comparative Statics Analysis." Journal of Rural Economics 72:109-21.

(1) The only exception is Lopez (1984), who used a nonnested test to make a systemic comparison of separable and nonseparable models.

(2) Among workers who are mainly engaged in family farming in Japan, the share of family members over 60 years old was 66% in 2000 (Census of Agriculture, Ministry of Agriculture, Forestry and Fisheries). Nonfarm firms seldom employ older members partly because a mandatory retirement age is often set at 55 or 60.

(3) Table 1 shows that rice-farming households employed non-family workers annually for 14 hours during 1982-1991, which constitutes less than 1% of total farm work hours.

(4) The estimation and comparison methods proposed in this study are applicable to models that include three or more types of (family) labor. For their comparative statics analysis, we can extend the method proposed by Sonoda (2004).

(5) Equation (10) is obtained by combining equation (2) with the definitions of leisure hours.

(6) Equation (19) is obtained by combining equation (13) with the definition of leisure hours.

(7) Hours of farm and nonfarm work are set to reflect data shown in table 1.

(8) His test includes another difficulty: decreasing returns to scale are assumed for the separable model, but constant returns to scale are assumed for the nonseparable one.

(9) The Cox-type statistic is originally defined by "centering" the difference between the GMM objective functions for the null and alternative models, as shown in (2.4) of Smith (1992). It is asymptotically equivalent to the statistic explained here.

(10) The FHET data are available until 1994, but we use data in the same period as Sonoda and Maruyama (1999, 2000) for convenience of comparison.

(11) Our incomplete time-series cross-section data do not cause the econometric problems of missing observations stated in Griliches (1986). Therefore, it seems plausible to deal with our incomplete data by simply assuming a fixed-effect model.

(12) We choose [RD.sub.r] x TT and [SD.sub.s] x TT, allowing for results of the overidentifying restrictions test of Hansen (1982).

(13) When we test the joint exogeneity of lnRK, p(lnRK), and q(lnRK), the Hausman statistic is 0.313, implying that the exogeneity of real capital stock RK is not rejected. This result seems to reflect the facts that our period of observation is not so long and that mechanization in rice farming had already been established in the 1980s; consequently, substitution of machinery for labor was not as large as before.

(14) The respective adjusted coefficients of determination are 0.98 and 0.93 when we regress endogenous regressors lnF and In [L.sub.f] on this combined set of instruments.

(15) As the name indicates, the data in FHET are generated by classifying those in the Survey of Farm Household Economy by various types of farm households.

(16) Pensions and gifts in FHET were used as nonlabor income V, but sets of instruments including it did not yield a result that passes the OIR test.

(17) When we regress endogenous regressors [[??].sup.*], [[??].sup.HET] and [[??].sup.RES] on set IV-1, the respective adjusted coefficients of determination are 0.87, 0.95, and 0.90. Similar coefficients are, respectively, 0.87, 0.88, and 0.90 when we regress them on set IV-2.

(18) Using the set IV-l, we obtain similar results for comparison of uncorrected and corrected standard errors and for the comparative statics analysis shown below. See the supplementary appendix (Sonoda 2007) for these results as well as estimated parameters of the AIDS under the RES hypothesis.

(19) It is better to separate the case for y = [w.sup.*] from the other cases in equation (31), but we use a common expression for all of them for simplicity. We must interpret [([partial derivative] In [t.sub.i]/[partial derivative]ln [w.sup.*]).sub.const] as [partial derivative]ln [t.sub.i]/[partial derivative] ln [w.sup.*]. A similar interpretation applies to equation (32).

(20) We find one exception to this relation when we compare the elasticity of farm labor supply [L.sup.S.sub.f] with respect to the price r (0.46) and the similar elasticity of nonfarm labor supply [L.sub.m] (0.58). This result is obtained because the substitution effect in the former is large, although it is dominated by the corresponding income effect.

Tadashi Sonoda is associate professor, Graduate School of Economics, Nagoya University (sonoda@soec.nagoya-u.ac.jp).

The author wishes to thank Yuko Arayama, Ayal Kimhi, Colin McKenzie, the editor (Paul Preckel), and three anonymous reviewers for their valuable comments. This work was partially funded by a Grant-in-Aid for Young Scientists (B), No. 14760149, from Japan's Ministry of Education, Culture, Sports, Science and Technology. Table 1. Mean and Standard Deviation of Variables, 1982-1991 Description of Variable Notation Output of rice [kg] X Hours of family farm labor [L.sub.f] Hours of hired farm labor -- Quantity of other variable inputs F

than labor Real stock of capital RK Total area planted [a] A Time trend TT Rate of set-aside program SAP Other production costs [thousand yen] OC Purchased consumption commodities C Hours of nonfarm labor [L.sub.m] Number of all household members NF Number of farm workers [N.sub.f] Number of nonfarm workers [N.sub.m] Share of farm workers among all FSHARE

workers Share of white-collar among nonfarm --

workers Share of blue-collar among nonfarm --

workers Price of rice [yen/kg] p Price of other variable inputs than q

labor Price of purchased consumption r

commodities Nonfarm work wage [yen/hour] w Internal wage [yen/hour] [[??].sup.*] (= [[??].sup.**] Description of Variable Mean (Standard Deviation) Output of rice [kg] 9320.5 (6594.9) Hours of family farm labor 1484.3 (672.6) Hours of hired farm labor 13.71 (16.991) Quantity of other variable inputs 4396.2 (2762.8)

than labor Real stock of capital 30340.2 (14066.6) Total area planted [a] 214.2 (138.7) Time trend 4.484 (2.903) Rate of set-aside program 0.1612 (0.0490) Other production costs [thousand yen] 1386.9 (781.2) Purchased consumption commodities 52971.2 (7764.2) Hours of nonfarm labor 3384.1 (734.9) Number of all household members 4.864 (0.7077) Number of farm workers 0.8700 (0.5055) Number of nonfarm workers 1.8218 (0.3880) Share of farm workers among all 0.3134 (0.1485)

workers Share of white-collar among nonfarm 0.3369 (0.1237)

workers Share of blue-collar among nonfarm 0.4446 (0.1149)

workers Price of rice [yen/kg] 324.0 (16.00) Price of other variable inputs than 105.8 (5.507)

labor Price of purchased consumption 97.77 (4.468)

commodities Nonfarm work wage [yen/hour] 1301.8 (284.4) Internal wage [yen/hour] 686.9 (175.3) Table 2. Estimated Parameters of the Production Function, 1982-1991

Coefficient

Estimate t-value [b.sub.X] -8.0095 (-2.135) [b.sub.F] -0.0194 (-0.140) [b.sub.Lf] 1.9339 (3.490) [b.sub.RK] 1.5279 (2.884) [b.sub.A] 0.0057 (0.011) [b.sub.SAP] 0.4603 (3.655) [b.sub.ETT] 0.0414 (4.062) [b.sub.F,F] 0.0780 (7.491) [b.sub.F,Lf] -0.0972 (-3.661) [b.sub.F,RK] 0.0052 (0.764) [b.sub.F,A] 0.0448 (1.776) [b.sub.F,SAP] 0.0101 (1.724) [b.sub.F,ETT] -0.0054 (-6.903) [b.sub.Lf,Lf] -0.1043 (-1.499) [b.sub.RK,RK] -0.1495 (-2.976) [b.sub.A,A] -0.0586 (-0.810) [b.sub.SAP,SAP] 0.3424 (6.204) [b.sub.ETT,ETT] 0.0049 (8.238) Note: The minimized value of the GMM objective function is estimated to be 42.46 with its corresponding p-value 0.213. The coefficients of determination for equations (25) and (26) are 0.9829 and 0.6626, respectively. Estimates of [b.sub.X] and [b.sub.F] are obtained by evaluating dummy variables at their sample means in equation (29). Table 3. Estimated Parameters of the AIDS under the HET Hypothesis for Instrument Set IV-2, 1982-1991

Coefficient Uncorrected Corrected