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The reason for this is that gross domestic product is such a hugely complicated thing to measure that there are sure to be mistakes made when calculating it.
When you calculate GDP using the income method, you tend to get a different result than you get using the expenditure method. This is, again, just because of how complicated it is to measure all this data.
The statistical discrepancy is just half of the difference between the two measures. So, in other words, if one measure said GDP is $10.1 Trillion and the other said it is $10.3 Trillion, we halve the difference and say that it is really $10.2 Trillion.
We do not add any statistical discrepancy to GDP while computing GDP by either expenditure or income approach. However, as the GDP calculated by these two methods differ slightly due to statistical errors. We can call this difference as the statistical discrepancy. To minimize the errors in GDP computation due to statistical errors, we can use an average of the GDP calculated by the two methods rather than the GDP arrived at by using any one of the two method.
Please note that this kind of average does not guarantee more accurate estimate of GDP every year. It only results in decrease in average errors over the years.
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