Two methods of inferring output:
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Output = Average Yield * Acreage Sown
O = Y * S
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Output = Consumption + Net Exports
O = C + NX
C = Population * Consumption per Head
= P * CPH
Assumptions:
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Normality. Since these are all aggregates it is not unreasonable to treat these variables as Normal.
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Independent random variables. Independence is more of a contentious issue. But since we are considering not values themselves but errors it is more reasonable (e.g. while yield goes down with acreage sown due to use of less productive land, error in estimation not necessarily correlated).
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Output is corn output. We either ignore other items in the diet or assume they are converted into grain equivalent. No corrections for quality are made (e.g. wheat vs. barley)
Data
See excel workbook
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Utilisation of English and Welsh Land 1700-1850 (millions of acres). Source Figures are 5 year averages centred on year stated. See excel. Table also included below.
| Year |
Net Export of wheat and wheaten flour (000 of quarters) |
| 1700 |
48.6 |
| 1725 |
158.2 |
| 1750 |
643.8 |
| 1775 |
-149.4 |
| 1800 |
-780.0 |
| 1825 |
-587.8 |
| 1850 |
-2639.0 |