Fisher's ideal index oor Spaans

Fisher's ideal index

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índice ideal de Fisher

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Fisher-ideal index
índice ideal de Fisher
Fisher Ideal index
índice ideal de Fisher

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Fisher’s ideal index is the geometric mean of the Laspeyres and Paasche indexes.
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SOLUTION Fisher’s ideal index is 137.57.
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EXAMPLE Determine Fisher’s ideal index for the data in Table 17–3.
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In this section the findings for the Fisher ideal index are outlined.
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17.39 The approach of the previous section is followed for the Fisher ideal index.
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Thus if P satisfies T1, T11, T12 and T13, it must equal the Fisher ideal index PF.
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B.4 Fisher ideal index revisited
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Hence, as r becomes very large in magnitude, the index Pr can differ substantially from, say, P2 = PF, the Fisher ideal index.
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Hence, as r and s become very large in magnitude, the indices Pr and Ps* can differ substantially from, say, P2 = PF, the Fisher ideal index.
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Thus for r large in magnitude, Pr can differ substantially from the Törnqvist-Theil price index, the Walsh price index, and the Fisher ideal index.37
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17.53 When r = 2, Pr defined by (17.28) simplifies to PF, the Fisher ideal price index and Qr* defined by (17.30) simplifies to QF, the Fisher ideal quantity index.
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17.43 When r = 2, PR defined by equation (17.35) simplifies to PF, the Fisher ideal price index, and Qr* defined by equation (17.37) simplifies to QF, the Fisher ideal quantity index.
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17.48 When r = 2, Qr defined by equation (17.23) simplifies to QF, the Fisher ideal quantity index, and Pr* defined by equation (17.25) simplifies to PF, the Fisher ideal price index.
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The Törnqvist-Theil index seemed to be best from the stochastic viewpoint, and the Fisher ideal index was supported from the axiomatic viewpoint in that it best satisfied the quite reasonable tests presented.
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The Fisher ideal price index, PF, defined by equation (15.12);
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Taking an average of them led to the Fisher ideal price index PF defined by equation (15.12) above.
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It can be verified that when r = 2, Qr simplifies into QF, the Fisher ideal quantity index.
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Now recall the definition of the Fisher ideal price index PF defined by equations (15.12) or (17.9):
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It then can be shown that the Fisher ideal quantity index corresponds exactly to a homogeneous quadratic aggregator.
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Below, some 20 tests are listed that turn out to characterize the Fisher ideal price index.
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Taking an average of them led to the Fisher ideal price index PF defined by equation (15.12).
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17.41 Instead of starting with the a translog function for the revenue function of the Törnqvist index, the assumption of the Fisher ideal index is that the unit revenue function takes a homogeneous quadratic form given by
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The Fisher ideal price index thus emerges as perhaps the “best” evenly weighted average of the Paasche and Laspeyres price indices.
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Using the product rule, the unit revenue function can be derived to yield analogous results for the Fisher ideal price index.
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Thus, the Fisher ideal price index emerges as perhaps the best evenly weighted average of the Paasche and Laspeyres price indices.
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