The Mathematical Model, Specifications, and Est imat ions
2.2. Structural Change and Supply of Resources
2.2.1. Number of farms
The agricultural sector is divided into two sectors representing "full-time" (more than 20 hectares of arable land) and "part-timen farms (less than 20 hectares).
The core of the structural change process, that is, the enlargement of the average farm size, is the behavior of small farms. By contraction, small farms supply resources (mainly land) for the expansion of large farms. The rate of change in the number of small farms depends on the profitability in farming compared to profitability in activities outside agriculture. Since small farmers are milk pro- ducers to a large extent, relative profitability is represented by the relative price of milk. The rate of change in number of small farms is thus explained as fol- lows:
-3.07
A S F F l - - e ~ a . g
SFFl (2.1)
(t-value)
where
A indicates time differential SFFl is the number of small farms P l o is the milk price
P19 is the price in the nonagricultural sector e is natural logarithm
R 2 is 0.71 DW is1.36
Given the number of small farms, their arable land resources are calculated by using the relation between the average farm size and the number of farms in that group. Remaining land is distributed among the large farms.
2.2.2. Supply of arable land change in the data base due t o a new registration procedure. Acreage of pasture (Ap) is estimated as a function of the number of cows and the rate of "technical changen represented by time (t). Subscript -1 indicates a one-period time lag.
Fallow land (A,) is a single function of the development of the total land stock.
Pasture land released by a declining number of dairy cattle might be abandoned or transformed t o cropland ( A , ) , depending on the quality of the land. As a land quality indicator, the share of pasture land out of total land stock is used. The transformation is described by a Spillman function (2.4). For equations (2.2) and (2.3), R2 = 0.99 and D W = 1.5; for equation (2.4), D W = 1.20.
The land model focuses on technical relationships rather than on pure economic factors. When alternative approaches, based on the relative profitability of plant production, have been used, these show a very weak or insignificant impact of prices. This is perhaps due t o lack of sufficient variability in prices. Equations (2.2-2.4) have been estimated on time series data for the period 195@1978, since the main changes in the total supply of arable land occurred during the late 1950s and the early 1960s.
2.2.3. Farm family labor supply
The supply of family labor (i.e., the number of hours per farm and year, FL) is explained by the income earned per hour ( W) and a time trend (as a proxy for technical development). From the theoretical point of view, nothing can be said about the slope of the labor supply function since positive as well as negative slopes are consistent with theory. Our estimated functions exhibit negative slopes, indicating that farmers compensate for decreasing income per hour by working more and by working less if income is improving.
F L l = 0.003 x t-0.17 x ~ 1 - O . l ~
(-17.74) (-14.8) (-1.21)
(2.5) (t-value)
(2.6)
(-0.95) (t-value) For equations (2.5) and (2.6), respectively, R2 = 0.97 and 0.82;
D W
= 1.31 and 1.0. The total supply of farm labor is then calculated asTFL 1 = FL1 x SFFl (2e7)
2.2.4 Hired labor
The total input of hired labor (HL) is estimated for each farm sector as a func- tion of the price ratio of capital and hired labor (PHLIPK) and a time trend.
HL1 = e2.67 x (PK/PHL)~.'* x t-0.09 (2.9)
(27.52) (15.36) (-1.78) (t-value)
HL2 = e3.95 x ( P K I P H L ) ' . ~ ~ x t-0.05 (2.10)
(37.30) (6.80) (-0.84) (t-value)
For equations (2.9) and (2.10), respectively, R2 = 0.99 and 0.98;
D W
= 2.8 and 0.6. Total agricultural labor supply is finally determined by adding hired labor to equations (2.7) and (2.8).2.2.5. Agricultural investment
Two types of investment goods in farming are distinguished: machinery and buildings.
Machinery
Investments in machinery are explained as a process of substitution of mechani- cal equipment for labor. Optimal levels of labor inputs and capital stocks are calculated for seven different crops in the two farm sectors, based on Cobb-Douglas production functions with constant returns to scale and on prices of labor and capital. Actual application rates are then determined by an accelerator-type of model.
K and L are existing levels of capital and labor, respectively. O K and O L are the optimal levels of capital and labor for the seven crops in the two farming sec- tors.
Equalizing marginal products of labor and capital with the price ratio between capital and labor P k / P I results in the following optimal levels of labor ( O L ) and capital ( O K ) :
Aij is the existing level of acreage of each crop in each farm sector; a and b are coefficients in the production functions:
Estimation and testing
The production functions (2.14) have been estimated for the seven crops and the two farm sectors. Crop-specific data on capital and labor inputs are not directly available. Time series, however, have been generated, combining public income statistics, bookkeeping results from annual surveys, and special productivity studies, to separate aggregate input volumes of labor and capital for different crops and sectors over time.
In Table 10 coefficients in the production functions are shown. All the parameters are significant at the 5% level and t-values are high. The large sec- tor has a higher capital elasticity for all commodities.
In the next step, the accelerator functions (1.11) are estimated, and the total levels of hired labor and capital in plant production can be calculated as:
Table 10. Parameters of the plant production function.
Total net investment in machinery is finally given by:
and can (corrected for depreciation) be compared with data on gross investments in machinery. As an alternative, K and L can be compared to data on machinery stocks and labor inputs, indicating a good correspondence with model results, particularly for labor. As far as machinery investments are concerned, one should note that many other factors, such as inflation expectations, tax sys- tem changes, etc., which cannot be included here, also affect investment
The two farm sectors' shares of the total building capital (SBK) depend on the number of farms in each sector and are estimated as
SBKl = (0.09
+
0.004 x t) x SFFl (2.16)and normalized as
NSBKl = SBKl
SBKl
+
SBK2NSBK2 = 1 - NSBKl
Consequently, the building capital in each sector is calculated as B K 1 = N S B K l x B K
B K 2 = NSBK2 x B K
2.2.6. Fertilizers
In the plant allocation models, net revenues t o land, labor, capital, and fertilizers are maximized. The reason for including fertilizers among the fixed factors in the allocation procedure is t o stabilize the plant model solution. As production functions for most plant commodities are logarithmic, fertilizer inputs will become very sensitive to price changes a t the upper end of the yield response function. Furthermore, the procedure can be justified by the facts that the rela- tive distribution will be the same without the restriction and that the use of fer- tilizer represents a "level of technologyn. The total level of fertilizers is deter- mined as:
where PV is a plant commodity producer price index, and PF is the price of fer- tilizers.