1 A Recursive Dynamic Computable General Equilibrium Model For ...

the crops for which data on ‘gross’ potential land and yields is available on the cited web
page is presented in Table 1.
To proceed with the estimation of the land supply, first the yields data are sorted in
descending order (with the corresponding potentially suitable areas), and second, the
ascending area is accumulated. Then, following Tabeau et al., (2006) the variable ‘land
price’ is defined as the inverse of the potential yield (1/yield). Furthermore, for each
observation, a relative yield is calculated, dividing each potential yield by the maximum
attainable by the region. In this way, the potential relative yield lies between 0 and 1, while
the corresponding relative rental rate or land price, will have a minimum of 1. This scaling
process helps to infer the relative suitability of each country for each crop, while from an
econometrical point of view, scaling contributes to accelerate the convergence to a
solution.
Thus, the relationship between the observations on accumulated land area and
relative price follows an upward sloping curve (land supply). To improve the fit of the
estimated supply parameters (b, C and ) to the observed data points, 15 a Maximum
Likelihood non linear regression method is employed. A key advantage of Maximum
Likelihood is that it can be applied to a wide variety of models (e.g. models with binomial,
multinomial, or censored dependent variable). Irrespective of the numerical algorithm used
to find a solution to a non-linear model, the maximum likelihood estimator has good
asymptotic (for large samples) properties: it is consistent (when the sample size tends to
infinity, the expected value of the estimator approaches its true value and its variance tends
to zero); asymptotically efficient (the variance of the asymptotic distribution of the ML
estimator is smaller than the asymptotic variance of any other consistent estimator); and
estimates of the (asymptotic) variances of the estimators as a by-product of the estimation
process (Pindyck and Rubinfeld, 1998). For regression models (with a continuous
dependent variable), if we make the assumption that the error terms are normally
distributed, the maximum likelihood estimators coincide with the various least squares
estimators. Therefore, non-linear least squares could also be used. In practice, however,
results from both models could differ, but mainly because of the numerical algorithms
implemented for each method and by each econometrical package.
The econometric model to estimate then becomes:
15 The smaller is the value b, the more inelastic is the land supply curve. The smaller is C, the more elastic is
the land supply curve. The smaller is ρ, the more inelastic is the land supply curve.
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