The investment analysis aims at making the theoretical considerations of section 2.3.2, pp. 91 et seq., fruitful for an empirical investigation of Polish farm house- holds’ investment behaviour. In principle, it would be possible to base an em- pirical investment function on the flexible accelerator (2-56), p. 98. The optimal capital stock is a function of the arguments of M(.) including optimal E, which
in turn is determined by the household’s preferences (see also KUIPER and
THIJSSEN 1996, p. 458). A broadly similar approach has been used in the ad-
justment costs literature, although devoid of E, for example by LOPEZ (1985).
However, estimation of the capital adjustment coefficient B is not the primary goal of the present study.81 In contrast, in the empirical analysis, I want to focus on the basic implication of the financial constraints model, namely that invest- ment depends on available collateral and credit access. I will therefore attempt to extract the essence of the model by means of an estimable reduced-form invest- ment equation. This can be written as follows:
) , , , (E E Z p I I = & (3-6)
In this equation, the capital stock, the output price, and the existing volume of equity E are taken as given at the beginning of the planning period. The change in E, denoted E&, is the result of the optimal plan of the decision maker in the current period.82 In contrast to conventional neoclassical investment equations
(ELHORST 1993, p. 170), note the presence of equity formation and the equity
stock as financial variables.
Unfortunately, the empirical implementation of (3-6) faces a number of prob- lems related to E&. First, E& is difficult to measure if interpreted as a general im-
80
Since D. BENJAMIN (1992) solely focuses on the significance of demographic characteris-
tics, he uses the number of family members plus the fractions of several demographic cate- gories (sex, age) as separate regressors in a log-linear labour demand equation (pp. 301- 304). This type of specification can be derived from a scaling model in spirit of POLLAK
and WALES (1981).
81
Note that B cannot be estimated directly but is usually calculated indirectly from its deter- mining functions (LOPEZ 1985, p. 45; WITZKE 1993, p. 210). In addition, B may be non-
constant (MACCINI 1991, p. 24).
82
provement in collateral availability or even more broadly in credit-worthiness. Second, E& is not exogenous because it is ultimately determined by the consump- tion preferences of the household. Furthermore, as argued by WITZKE (1993, p.
266), dynamic or long-term adjustment decisions of the household via E& may generally be regarded as unimportant if the equilibrium of the system is dis- torted in each period by newly incoming information (for example with regard to the access to credit function) and a subsequent revision of the optimal plan. On theoretical grounds, this of course calls into question the usefulness of the entire dynamic model. On the other hand, the existence of short-run distortions corresponds to the stated perception of borrowers who still experience that the maximum loan amount is externally dictated by the bank. According to the model of section 2.3.2, borrowers know the marginal cost of borrowing depend-
ent on their E and thus the amount of credit they obtain, an assumption that
should exclude any perceived excess credit demand.
For these reasons, I replaced E& by the change in net borrowing, K& . The ob- served level of net borrowing K& might be regarded as the ultimate outcome of household preferences, its credit worthiness, plus all types of short-term distor- tions. Note that the inclusion of K& has three further advantages: first, K& is eas- ily observed. Second, K& can be assumed to be exogenous for rationed borrow- ers who said that they wanted to borrow more. Third, it opens the opportunity to directly investigate the relationship between new borrowing and investment. The latter is of particular interest for the current study due to its policy implications. Since the government actively supports credit expansion in the farm sector, the marginal effect of credit on investment is quite valuable information; the point is further explored below. If K& is included into the investment equation, E can be dropped, since its only effect on I is through K& . Two further modifications con- cern the exclusion of prices, for the same reason as in the output supply model discussed previously, and the inclusion of a vector of dummy variables
ζ
, cap- turing regional and farm specific effects.I also experimented with two further dummies indicating the year of investment, and thus capturing any effects of changed overall price relations and other year- specific effects (see similarly CALOMIRIS et al. 1986, p. 458). Year effects might
be included because, although the data-set is cross-sectional in nature, it com- prises pooled investment data for a period of three years. However, these effects turned out to be not significant in any of the estimations and were hence ne- glected.
The investment equation is again estimated only for households classified as credit-rationed according to the qualitative criterion of section 3.3.3, pp. 146 et seq. I assume that the financial constraints model of investment is applicable only for these households. Furthermore, this procedure reduces the danger of endogeneity of the credit variable K& . Since the relevant information is available from the Probit equation, I can again test for selectivity by including the IMR. The estimating investment equation is therefore:
i i i i i i I K Z I = ( & , ,ζ )+
ε
iff γzi +ui >0 (3-7) The determination of K& is hence analysed by the first-stage Probit equation,which contains variables of collateral availability and creditworthiness as well as demographic characteristics of the household, see section 3.3.3.
For later reference, I briefly restate the expected signs of the parameters to be estimated in (3-7). By (2-55), p. 97, the relation between change in net borrow- ing and investment is unambiguously positive. The effect of Z on I depends on the size of the desired capital stock or farm size. A negative sign implies that farm sizes converge over time, whereas a positive sign implies diverging farm
sizes.
ζ
includes a dummy indicating whether the farm has permanent book-keeping, which might be taken as a measure of management skills of the farmer. It is likely that more skilled farmers invest more. A second dummy has the value of one if the farm is located in the northern region. The effect on investment is also likely to be positive.
The dependent variable in equation (3-7) poses three further specification prob- lems, to be discussed subsequently: (a) discontinuity of the investment variable, (b) censoring of the investment variable, and (c) the choice of functional form. First, investment may be discontinuous or lumpy (MUNDLAK 2001, p. 57). This
problem is ignored, justified by the fact that the volume of investment is the sum of all investment expenses over a relatively long period of three years (1997- 1999). Discontinuities therefore even out to a certain extent.83
Second, more seriously, approximately 20 percent of observations report a zero investment volume. This implies that the dependent variable is censored to some extent, which should be reflected in a possibly non-linear formulation of the model. In addition, non-linearity is also addressed more explicitly as a result of
83
An innovative approach to account for lumpy investment is to use an ordered Probit model for the investment variable, see OUDE LANSINK and PIETOLA (2002).
the third problem, which is related to the choice of the functional form. Before explaining this, it seems useful to briefly highlight the policy implications of the credit variable.
As noted earlier, the potential effect of new borrowing on investment is of key interest due to its policy relevance. A marginal effect of credit on investment equal to or larger than one implies that additional funds are completely used for productive investment. This describes a situation where subsidised credit is fully used for investment and even triggers the additional mobilisation of other finan- cial sources, which is clearly desirable from the point of view of the govern- ment. On the other hand, a marginal effect smaller than one implies that the marginal unit of credit is only partly used for the supposed investment purpose. However, the marginal effect is unlikely to be constant over the entire range of observations, as would be imposed by a linear model. It is of interest whether there are any size effects of credit use, or whether more credit implies a higher marginal investment effect. Due to the complex interactions between credit- worthiness and investment via the access to credit function, substantial non- linearities can be expected to be present. The change in the marginal credit ef- fect can be investigated by evaluating the second derivative of the investment function with regard to credit. Therefore, the latter effect should not unduly be constrained by the choice of functional form.
To address the censoring problem, I considered a Tobit model (AMEMIYA 1984;
GREENE 2000, pp. 905-926) in the estimation of the investment equation. Con-
ventional marginal effects in the Tobit model vary with different values for the regressors. They give the total effect of a change in explanatories on the ob- served, censored investment volume. In an imaginary way, the latter effect can be decomposed into an effect on the conditional mean (and thus the size) of in-
vestment plus an effect on the probability that the farm invests at all
(MCDONALD and MOFFIT 1980). The implicit assumption of the Tobit model is
that the given regressors explain both effects. In the present study, the uncen- sored part of the model is the relationship of interest, whereas the qualitative choice whether to invest or not is not analysed more deeply. Regarding the zeros as implying unobserved disinvestment might provide a rationale for this ap- proach. In this case, the marginal effects are given by the coefficients of the To- bit model (JOHNSTON and DINARDO 1997, pp. 436-439).
In the standard Tobit formulation, the level of investment is still explained by a model that is linear in parameters. However, by including higher-order polyno- mials into the equation, the model can be made more flexible. The aim of intro-
ducing more flexibility is to trace more closely the true functional relationship between credit and investment. I hence augmented the Tobit equation by a quad- ratic and a cubic term for the credit variable. This is assumed to contribute little to improve the explanatory power of the model with regard to the decision to invest at all (i.e. the qualitative choice part of the Tobit model). The virtue of this procedure is that a cubic function for the uncensored part of the investment equation obtains, which can be used for the further analysis of the credit- investment relationship.
Investment volume in thousand zł is the aggregate of all productive investment, including land, all types of agricultural machinery, farm buildings, livestock, permanent crops, to name the most important components (see the detailed de- scription in section 4.3.1, pp. 184 et seq.). Only gross investment is considered here, to avoid the difficult choice of a depreciation rate. Credit access was meas- ured as the total volume of credit with a repayment term of more than 12 months taken by the farmer in the period 1997-1999. There were 81 single loan con- tracts reported for the group of farmers under investigation. 78 percent of bor- rowers obtained at least one loan under the government program. The capital stock Z at the outset of the investment period was difficult to measure, since de- tailed statements on farm assets were only available for 1999. I used the nominal value of land owned by the farm in the beginning of the investment period, as in the Probit model. The advantage of using land as compared to other assets is that the problem of depreciation can reasonably be ignored.