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

Next, we compare systems (27) and (28). They differ not only in their dependent and independent variables but also in the number of equations. Consequently, they are complicatedly nonnested, as stated in the first section. Nonnested models have often been tested using the J test of Davidson and MacKinnon (1981) or the Cox test of Pesaran (1974).

The J test is usually used to compare systems that have the same number of equations and the same dependent variables. Using that test, Lopez (1984) attempted to compare separable and nonseparable models which have different numbers of equations. His method requires a complicated transformation of the models to apply the J test (see [22] of Lopez). Moreover, this transformation might not maintain properties of the original models, which might engender inappropriate comparisons of the models. (8)

In contrast the Cox test does not require this type of strict correspondence between two systems; instead, it compares their likelihoods. As Mizon and Richard (1986) indicate, it can be interpreted as an encompassing test that evaluates the extent to which the null model explains an important characteristic (likelihood, parameters, etc.) of the alternative. In our case we can use a Cox-type test of Smith (1992), which compares their GMM objective functions instead of their respective likelihoods.

We evaluate the GMM objective function for model (28) in two ways when we test the null model (27) against the alternative (28). (9) One is to evaluate it on the assumption that model (28) is correct. The other is to evaluate its probability limit, assuming that model (27) is correct. We interpret that model (27) can explain model (28) if the difference between the two values is sufficiently small. Smith (1992) shows that the difference is asymptotically normal. The definition and computation of the Cox-type statistic are complicated. For that reason they are explained in the Appendix.

Empirical Analysis

Although the use of micro data is preferable in estimating AHM, this study uses aggregate data for the following reasons. Lopez (1984) and Sonoda and Maruyama (1999) use aggregate data to estimate AHM under the HET and RES hypotheses. Furthermore, most Japanese studies have used aggregate data to estimate AHM (e.g., Kuroda and Yotopoulos (1980) and Arayama (1986)). For that reason, estimating AHM under the two hypotheses using Japanese aggregate data at least makes practical sense.

Use of aggregate data renders the discrete choices of farm households unobservable, which might cause a major problem. In our case the problem is related to whether Japanese farm households employ nonfamily workers in rice farming or not, and whether their members work at nonfarm firms or not. As inferred from the hours of hired farm labor and the number of nonfarm workers shown in table 1, only a very limited number of farm households use significant hours of nonfamily labor and supply none of their members' labor to nonfarm firms. Consequently, we are not likely to observe a serious difference between the two AHMs estimated from our aggregate (but not so highly aggregated) data and those estimated from the original micro-data.

Data

We use aggregate data for rice-farming households in Japan, which are mainly adapted from the Survey of Farm Household Economy by Types of Farm Households (FHET) (Japan, Ministry of Agriculture, Forestry and Fisheries 1982-1991). We also use data from the Statistics of Prices and Wages in Rural Areas (PWRA) (Japan, Ministry of Agriculture, Forestry and Fisheries 1982-1991) and the Annual Report on the Consumer Price Index (RCPI) (Japan, Management and Coordination Agency 1982-1991).

Annual aggregate data are available for seven paddy-scale classes in eight regions for 1982-1991. (10) The paddy-scale classes include 0.5-1.0, 1.0-1.5, 1.5-2.0, 2.0-2.5, 2.5-3.0, 3.0-5.0, and 5.0 ha and larger. The regions include Tohoku, Hokuriku, Kanto-Tosan, Tokai, Kinki, Chugoku, Shikoku, and Kyushu, which cover almost the entire area of Japan. We would have 10 (years) x 7 (scale classes) x 8 (regions) = 560 observations if data were to constitute a complete time-series cross-section. However, our incomplete data include only 283 observations, reflecting the actual situation: a small number of farm households operate large paddy areas. (11)

Table 1 shows the means and standard deviations of variables used in empirical analyses. The price of consumption commodities is obtained from the general index by region in RCPI. The Divisia price indexes of other variable inputs and capital goods are constructed using expenditures for relevant items in FHET and the price indexes for the same items in PWRA. Using FHET data, the price of rice is obtained by dividing the gross revenue derived from rice sales by the amount of rice produced.

The nonfarm wage rate is obtained by dividing the salaries and wages in nonagricultural gross income by the total hours of nonfarm work. Empirical studies employing micro-data commonly replace the wage rate, when thus constructed, with the predicted one in estimating their labor supply function to allow for measurement errors in work hours (e.g., Sahn and Alderman 1988). Instead, we choose a standard solution to the measurement error problem in estimating AIDS models: we use a set of instrumental variables that includes exogenous factors affecting the nonfarm wage. One reason for our choice is that variations in a predicted wage are smaller than those in the original wage, particularly when we use aggregate data, which often makes estimated parameters less precise. Also, the FHET surveys work hours of farm households by asking them to record their daily work hours throughout the year, from which we infer that those work hours do not include overly large errors.

The amount of rice produced, hours of family farm labor and total area planted are obtained from FHET. Quantities of other variable inputs, capital stock and purchased commodities are obtained by dividing their expenditures or value in FHET by their respective price indexes. The endowed time of farm, nonfarm and total workers is estimated as [T.sub.i] = 16 x 365 x [N.sub.i] (i = f, m, t), where [N.sub.f] and [N.sub.m], respectively, represent the numbers of farm and nonfarm workers; also, [N.sub.t] [equivalent to] [N.sub.f] + [N.sub.m]. Other production costs OC aside from the cost qF of other variable inputs and the number NF of household members are available from FHET for subsequent analysis.

Finally, a set-aside program in Japan was introduced to assuage the mounting surplus of rice in the late 1960s. Since that time, the government has set annual targets for fallow paddy areas, and rice-farming households have complied with that program to receive compensatory payments and avoid a sharp decline in the price of rice. The intensity rate SAP of the set-aside program is defined by the farm household's fallow paddy area as a fraction of its total paddy area. Its data are obtained from FHET.

Estimation of Production Side and Variations in the Internal and Non farm Wages

To deal with our incomplete time-series cross-section data, we simply assume fixed effects and express the coefficients [b.sub.x] and [b.sub.F] in (25) and (26) as:

(29) [b.sub.z] = [b.sub.z,0] + [summation over (r)] [[pi].sub.z,r][RD.sub.r] + [summation over (s)][[rho].sub.z,s][SD.sub.s] (z = X, F;r = 1, ..., 7;s = 1, ..., 6)

where [RD.sub.r] and [SD.sub.s], respectively, denote regional and paddy-scale dummies. After substituting (29) into (25) and (26), we estimate them using GMM.

In (25), (26) and (29), exogenous variables suitable for instrumental variables are a constant term, lnRK, lnA, lnSAP, TT, p, q, [RD.sub.r], and [SD.sub.s]. Substitution of (29) into (25) produces cross terms between dummies and endogenous regressor lnF. Therefore, we construct a basic set of instruments by adding [RD.sub.r] x TT and [SD.sub.s] x TT to the exogenous variables described above. (12) Furthermore, to allow for cross and quadratic terms between endogenous regressors lnF and ln[L.sub.f] in (25), we construct cross and quadratic terms among lnRK, lnA, lnSAP, TT, p, and q and combine them with the basic set in various ways. We eventually choose plnRK, plnA, plnSAP, [(In A).sup.2], [p.sup.2], qlnRK, and qlnA to combine them with the basic set. (13) The combined set yields the estimation results shown in table 2, (14) which: satisfies monotonicity (in all inputs) and concavity (in variable inputs) of the production function; passes the overidentifying restrictions (OIR) test of Hansen (1982) at the 5% level; and yields the most stable t-values of the parameters.

We can estimate the internal wage from this result, table 1 shows the mean of the internal wage (687 yen/hour) at about one-half that of the nonfarm wage (1302 yen/hour). The remainder of this subsection describes these wages as exhibiting different and sufficient variations for our purpose of identifying the two demand systems. Detailed variations in the internal wage are examined systematically in the final subsection.

The sources of variation in the nonfarm wage w are attributed to education, age, sex, region, and macroeconomic factors, whereas those in internal wage [[??].sup.*] are attributed to all factors affecting the farm household's behavior. Consequently, the latter is expected to vary in a more complicated manner. Actually, the coefficients of variation of w and [[??].sup.*] are 0.22 and 0.26, respectively, and their correlation coefficient is 0.21.