## Development of Supply and Demand Functions of Pakistan’s Wheat Crop

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# 4. Conversion to an Easy-to-Use Model

# Conversion Procedure

The econometrically estimated model of Pakistan’s wheat supply and demand functions, detailed in Table-2 and explained in the preceding paragraphs, appears to be a good model in spite of certain weaknesses. It performed best among several specifications tried, both in terms of the usual diagnostic statistics and economic theory. However, this estimated model still needs to go through at least three major modifications. First, its first wheat acreage equation is an autoregressive function, which yields short-run results; it needs to be converted into a long-run version. Second, its second equation contains the predicted value of area (Â), which is estimated in the first equation; hence, Â in the second equation will have to be replaced with its estimated value. Third, the model contains an import supply (I_{s}) function but lacks an import demand (I_{d}) function to be computed as per the identity equation I_{d }= D_{d }- S_{d}.

To convert the first equation from its short run to a long run version, we first need to compute the coefficient of adjustment ( ), and then adjust the short-run equation to its long-run version. In the short-run equation, the value of the estimated coefficient on the lagged dependent variable A_{t-1 }is 0.48947, which is equal to 1 - . Hence, solving for :

=

1- 0.48947

=

0.51053

(2a)

(2b)

To convert the short-run wheat acreage equation into its long-run version, we need to divide all coefficients attached to explanatory variables and constant by the value of ( ) and omit the lagged variable from the equation. By doing so, we get the long-run version of the wheat acreage equation:

# A = 7176.9189 + 48.93934TR

(3)

Since the estimated domestic wheat supply equation includes the predicted value of variable ‘A’, which we have now estimated in equation (3), we substitute equation (3) into the former equation, allowing the domestic wheat supply equation to take the following form:

# S_{d }= -8458.219 + 2.4879 (7176.919 + 48.9393 TR) + 0.41528P_{d }+ 2.4625

# FNTW = 9397.238 + 0.41528P_{d }+ 2.4625FNTWT+ 121.7562TR

(4a)