Gaffney (1970-71): Tax-Induced Slow Turnover of Capital

Overview

"Tax-Induced Slow Turnover of Capital" is a five-part series Mason Gaffney published in the American Journal of Economics and Sociology running from vol. 29 (1970) through vol. 30, no. 1 (January 1971), expanding a shorter 1967 article of the same title in the Western Economic Journal 5(4): 308–23.[1] Gaffney's own footnote in his later "Toward Full Employment with Limited Land and Capital" (1976) describes the relationship directly: the AJES series is "much more fully treated than in the [1967] WEJ" version, with the land-income material specifically at AJES 29(3): 409–24.[2] This page reads and mines the full unabridged series — obtained as Gaffney's own posted copy at masongaffney.org, which runs continuously through all five installments in one PDF — rather than relying on the two second-hand routes by which the wiki previously touched it: I1's 1976 footnote, and a partial reprint of the series' Appendix II inside Gaffney's 1977 Alaska oil-leasing report.[1]

The series carries mathematical appendices credited jointly to Gaffney and several collaborators (Michèle Consigny, William Vickrey, Matthew P. Gaffney Jr., Ralph Krause, and Joseph Holzinger), reflecting seminar circulation at RFF, UCLA, UC Santa Barbara, and UC Berkeley in the late 1960s.[1] A 1971 rejoinder, "Time, Taxes, Turnover, and Intensity" (AJES, catalogued in the wiki's Gaffney corpus triage as O11), responds point-by-point to a critique by Thomson and Goldstein; it was fetched for context on this wave and confirms the triage's characterization — it is a technical priority-and-terminology dispute (a mislabelled "income tax" that is actually a land tax; credit for the Faustmann-formula rediscovery; "yield" vs. "excise" vs. "gross" tax terminology) that restates rather than extends the parent series' substantive results, so it is not separately mined here.[3]

Part I: Four Classes of Real Assets and the Bias to Longevity

Part I sets up the taxonomy the whole series works within: appreciating assets (trees, cattle — point-input, point-output, whose yield is entirely salvage value at maturity); "full salvage" or constant-value assets (the "Bessie the milk cow" model — yields a steady income and returns full initial value at the end of a fixed life, used for its analytical simplicity); depreciating assets (plant and equipment, yielding a cash flow that mixes income and capital recovery); and land (infinite life, appreciates more often than it depreciates).[1] Gaffney's central claim, worked through each class in turn, is that ordinary excise and income taxation biases investors toward longer maturities and slower capital turnover — because deferring tax liability to a later date is itself a form of return, so investments structured to defer income (rather than realize it currently) gain an implicit tax subsidy. He traces the macro stakes to Böhm-Bawerk and Wicksell's argument that faster capital turnover expands the number of jobs a fixed capital fund can finance — the same "wages-flow" mechanism the wiki's marginal-productivity page carries only via Gaffney's 2008 retrospective (K2008); here it is Gaffney's own 1970 working of the same turnover-and-employment link, six years before he builds it into the full K·T macro model on I1.[1]

Part II: The Excise-Tax Case and an Early ATCOR Precursor

Part II works the mathematics of excise (gross-receipts) taxation on the point-input, point-output case, showing algebraically that any positive excise tax rate makes the after-tax return negative for maturities below a threshold that rises with the tax rate — a formal proof of the longevity bias sketched in Part I.[1] It then examines expensing (writing off capital investment immediately, in year zero, as a current cost) as a hypothetical fix, and derives a result with a direct bearing on the wiki's ATCOR page: because land cannot legally be expensed (it is not a depreciable cost) while capital investment can be, universal expensing of capital "tends to convert the corporate income tax, which exempts wages, into a tax on land income" — since only land income remains inside the tax base once capital's return is fully sheltered.[1] Gaffney immediately qualifies the result (expensing has several practical defects — it favors old, established, cash-rich taxpayers; it discriminates against sub-annual investments; land can be gamed into the expensed category by disguising it as an old building's purchase price) and recommends the ad valorem land-value tax as the cleaner instrument for reaching the same base.[1] Priority note: this is a formal 1970 statement of the mechanism the wiki's ATCOR page currently traces only to 1994's "negative shifting" language in The Corruption of Economics — see the cross-link added to concepts/atcor.md below. It is narrower than the full ATCOR claim (Gaffney derives it specifically for capital-expensing under the corporate income tax, not as a general theorem about all taxes), so it is presented as a precursor to the mechanism, not a restatement of ATCOR itself.

Parts III-IV: The True-Depreciation Neutrality Theorem

Part III completes the "Bessie" constant-value case (own criteria: (a) tax income when it accrues, whether as cash or appreciated value; (b) write off assets only when and as they actually depreciate) and states the resulting synthesis tersely: "tax cash receipts, deduct cash outlays; tax appreciation, deduct depreciation."[1] It then opens the general depreciating-asset case, laying out a four-step program — (1) modify the after-tax-return equation to include a depreciation write-off term, (2) define "true" yearly depreciation as the actual drop in an asset's present value, (3) substitute true depreciation into the equation, (4) show the after-tax return equals i(1-t) for every asset life once true depreciation is allowed — which Part IV/V carries to completion in the body text.[1] This body-text derivation is the general theorem that the series' Appendix II (credited to Vickrey and Consigny, and already noted on the Alaska report page as reprinted there) proves formally with continuous-time calculus: an income tax using true economic depreciation is intertemporally neutral. The wiki's prior touch on this result via the Alaska report captured only the formal proof; this page is the first to carry the verbal derivation and worked numerical example (Table 2, showing after-tax return turning negative for maturities under 19 years at a 50% excise rate and 8% pre-tax return) that motivate it.[1]

Part IV turns to land specifically. Beyond the theoretical case (land income taxed at accrual is neutral, per the same logic as the excise-tax analysis), Gaffney catalogues institutional mechanisms by which land in practice escapes even that: taxpayers routinely allocate purchase price for land-under-an-old-building disproportionately to the (depreciable) building, writing off land's cost — "not just once, but several times" as buildings are replaced — despite the letter of the law forbidding land depreciation; percentage depletion allowances let mineral-rights value (a pure rent) go untaxed even before extraction; and "implicit expensing" (an owner foregoing current land income to capture a larger, later, tax-deferred gain) is available to landowners more than to holders of other assets because land's life is infinite.[1] The section closes on a Faustmann-formula application — reprising the same maturity condition worked in Gaffney's 1957 Financial Maturity of Timber monograph — to show that when a tax on land income is shifted (reducing site value S), the lower S delays a timber stand's optimal harvest date, because the tree's required carrying-cost return (interest on accumulated stumpage value plus interest on the now-lower S) is easier to clear.[1] This is the same "financial maturity" machinery that becomes the formal dR/dn = i(R+S) result in Appendix 3 of the 1976 Full Employment with Limited Land and Capital chapter — read together, the three works (1957 pure Faustmann economics → 1970 Faustmann-plus-taxation → 1976 full K·T macro model) form a single 19-year line of development on one mechanism, not three independent treatments.

Part V: Summary, a Constitutional Aside, and the Two Mathematical Appendices

Part V's own summary states the series' upshot plainly: the only part of the income tax that can be made "perfectly neutral" is the part that falls on land income, because land rent is a residual that cannot be shifted away by the owner the way capital and labor returns can.[1] Gaffney adds a legal aside — since his true-depreciation definition of taxable income makes an income tax "much like the property tax," he suggests the 16th Amendment's authorization of taxes on "incomes from whatever source derived" might let Congress tax property directly, free of the apportionment-among-states rule, if the Eisner v. Macomber (1920) realization doctrine were revisited — a speculative legal argument (a D-claim, Gaffney's own, not independently checked here) rather than an economic result.[1]

The series closes with two distinct mathematical proofs, both already partly on the wiki's radar via the Alaska report, now placed in their original context:

• Appendix I, credited to William Vickrey, Matthew Gaffney Jr., and Joseph Holzinger, proves that the effective after-tax rate of return on a point-input, point-output investment rises with the investment's life, for any tax rate on the maturity gain strictly between 0 and 1 — the formal version of the longevity- bias claim worked more roughly with Table 2 in Part III.[1] This proof is not the one reprinted in the Alaska report; it has no prior wiki citation.
• Appendix II, credited to Michèle Consigny (original formulation) and William Vickrey (the shortened, generalized form Gaffney published), proves the general intertemporal-neutrality theorem stated in Part III: using continuous-time present- value calculus, it shows that taxing net income after true depreciation leaves the private and public discount functions related by an identity that makes the after-tax present value of any asset's cash-flow stream equal its pre-tax cost — i.e., the tax collects revenue without distorting the timing decision at all.[1] This is the proof already reprinted, word for word modulo scan noise, as Appendix J of Gaffney's 1977 Alaska oil-leasing report, where it backs the report's claim that an ad valorem charge on oil-in-place does not bias extraction timing the way a royalty does; see that page's Part II discussion for the applied argument.[4]

Bears On

• Concept: ATCOR — priority-note cross-link added: Part II's expensing-converts-the-income-tax-to-a-land-tax derivation is a 1970 formal precursor to the shifting-onto-rent mechanism, predating the 1994 "negative shifting" language in The Corruption of Economics by 24 years. Narrower in scope (capital-expensing specifically, not a general theorem about all taxes), so framed as a precursor mechanism, not an earlier coining of ATCOR itself.
• Research: Gaffney (1976), Toward Full Employment with Limited Land and Capital — this series is the derivational link between Gaffney's 1957 Faustmann-formula monograph and the 1976 chapter's K·T=F macro model; see Part IV above.
• Research: Gaffney (1957), Concepts of Financial Maturity of Timber — the pure Faustmann-maturity machinery this series applies, for the first time in Gaffney's corpus, to the question of how taxation (not just interest rates) shifts harvest timing.
• Research: Gaffney: Oil and Gas Leasing Policy for Alaska (1977) — reprints this series' Appendix II verbatim as Appendix J; that page's note now points back here for the appendix's original context and for the previously uncited Appendix I.
• Concept: marginal-productivity — the Wicksell wages-flow/turnover material that page carries only via Gaffney's 2008 retrospective (K2008) is a theme Gaffney was already developing in his own voice in Part I of this 1970 series; cited in prose only, not added to that page's citation apparatus, since the 2008 paper remains the fuller treatment of Wicksell specifically.
• Research: Gaffney (2016), Europe's Fatal Affair with VAT — added 2026-07-18: Gaffney's 2011 "Sales-Tax Bias against Turnover and Jobs" essay (the fuller, earlier statement of that page's "Mill Effect" argument) cites this series' Vickrey mathematical appendix directly, applying the same sales/capital-ratio turnover identity to VAT and retail sales taxes rather than the income-tax context this page covers.

Standing and Limits

This is Type-C theoretical material — formal derivations from stated assumptions, not empirical findings — and is kept out of every supported_by array on problems/benefits pages, consistent with the wiki's convention for Gaffney's other capital-theory derivations (see the Full Employment page's Bears On section for the same discipline applied to its Appendix 3 result). None of the series' claims are tested against data anywhere in the five parts; the numerical tables (e.g. Table 2) use assumed interest and tax rates to illustrate the algebra, not estimated parameters. The series is still under U.S. copyright (1970-71, well inside the wiki's public-domain cutoff), so this page paraphrases with only short quotations rather than reproducing text; the full unabridged series was OCR'd from Gaffney's own posted PDF and is not currently mirrored to the wiki as a texts/ page. O11, the 1971 rejoinder to Thomson and Goldstein, was fetched and read for context only (confirming the triage's "technical rejoinder" characterization) and is not separately mined; if it later proves to contain content beyond restating the parent series, that is future-wave work, not resolved here.

Sources

1. Mason Gaffney (1970-71), "Tax-Induced Slow Turnover of Capital" (5 parts, unabridged, including mathematical Appendices I and II), American Journal of Economics and Sociology 29-30 — used for every claim and quotation on this page except the ATCOR/marginal-productivity cross-references and the Alaska-report note; read in full (all five parts) this session via Gaffney's own posted unabridged text (free, no paywall). Free PDF (masongaffney.org); extracted text at sources/gaffney/text/I11-TaxInducedSlowTurnoverofCapital.CV.txt.
2. Mason Gaffney (1976), "Toward Full Employment with Limited Land and Capital," in Arthur D. Lynn Jr. (ed.), Property Taxes, Land Use and Public Policy (Madison: University of Wisconsin Press), footnote 40 — used for the WEJ-to-AJES expansion detail and the AJES 29(3): 409-24 land-income citation. See wiki summary.
3. Mason Gaffney (1971), "Time, Taxes, Turnover, and Intensity" (rejoinder to Thomson and Goldstein), American Journal of Economics and Sociology — fetched and read for context this session, not separately mined. Free PDF (masongaffney.org); extracted text at sources/gaffney/text/O11Time_Taxes_Turnover.CV.txt.
4. Mason Gaffney (1977), "Oil and Gas Leasing Policy: Alternatives for Alaska in 1977" — Appendix J reprints this series' Appendix II. See wiki summary.

See Also

• Gaffney (1976), Toward Full Employment with Limited Land and Capital
• Gaffney (1957), Concepts of Financial Maturity of Timber
• Gaffney: Oil and Gas Leasing Policy for Alaska (1977)
• ATCOR
• Marginal Productivity
• Mason Gaffney — author page