Capitalize Costs, Not Claims

1. The Apparent Contradiction

Two positions I have defended appear, at first sight, to pull in opposite directions. First: corporate profits and asset bases are understated because research and development (XRD), advertising (XAD), and software development outlays are expensed as incurred rather than capitalized on the balance sheet. Second: the 2008 System of National Accounts (SNA) treatment of “intellectual property products” (IPP) as investment overstates GDP, because the recorded magnitudes are neither traceable nor auditable. Ireland’s revised 26.3% GDP growth for 2015 — Krugman’s “leprechaun economics” — is the canonical exhibit: a surge in national output with no corresponding domestic production.

If capitalizing intangibles corrects the firm’s accounts, how can capitalizing intangibles corrupt the nation’s GDP? The resolution is that “capitalization” names two distinct operations, and the two critiques attack opposite sides of that distinction.

2. Position One: Expensing Discards Auditable Information

XRD, XAD, and software development costs are actual cash outlays — payroll, vendor invoices, contractor payments — recorded in the income statement and traceable to ledger entries. Immediate expensing has two effects. It depresses current operating profit compared to economic profit whenever the expenditure stream is growing, and it omits the accumulated stock of self-created intangibles from the asset base. Both the numerator and the denominator of any profit-rate indicator are misstated, and the distortion is systematic, not random.

The remedy is mechanical: capitalize the observed outlays at historical cost and amortize them — a perpetual inventory applied to expenditure flows. No valuation judgment or discount rate controversy enters the construction. The inputs are audited transactions; the output is a cost basis. The algebra is in Appendix A.1, where I show that the flow adjustment to profits nets to zero, while the revised asset base rises, so the measured profit rate adjusts toward its economic value.

3. Position Two: SNA Intangibles Manufacture Unauditable Information

The SNA 2008 classifies IPP as gross fixed capital formation. In the textbook case, the entry would record domestic R&D production. In the empirically dominant case for small open economies, the entry records the transfer value of moved legal ownership — an intra-group valuation of an IP portfolio migrated for tax purposes. The Irish 2015 episode is the paradigm: the GDP surge reflected no domestic R&D payroll, no invoices, no production — only a self-declared valuation of migrated intangibles ownership, produced by the very transfer pricing apparatus whose outputs are unverifiable by construction.

There is no cost basis to audit. The recorded magnitude is mark-to-model, and the model belongs to the taxpayer. Where Position One complains that accounting convention discards observable information, Position Two complains that national-accounts convention manufactures unobservable information.

4. The Reconciliation

Capitalization of observed cost flows is admissible; capitalization of declared asset values is not. The two positions apply the same evidentiary criterion — traceability to observable transactions — and reach opposite conclusions because the underlying data differ in kind, not because the principle wavers.

This is the same criterion that positions the perpetual inventory method (PIM) as a reliable cost basis rather than a rival to present value. A perpetual inventory of R&D outlays is an auditable construction; the SNA’s IPP transfer entries are present-value assertions smuggled into the national accounts.

5. A Sharper Implication: The Valuation Excess

The two critiques imply a measurable object. If accumulated cost is the admissible capitalization and declared transfer value is the recorded one, their difference is the valuation excess — the part of the national-accounts entry with no expenditure counterpart. Cost-based capitalization can correct the firm-level understatement of profits and expose the national-accounts overstatement of GDP. Appendix A.2 formalizes the point and shows the valuation excess as the wedge that moved through the Irish accounts in 2015.

The prescription for both literatures is the same. Trust the ledger; distrust the appraisal.

References

Aitken, A. C. (1935). On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42-48. Canonical reference for least-squares estimation.

Goldsmith, R. (1951). A perpetual inventory of national wealth. Studies in Income and Wealth, Vol. 14. NBER. Transposition of the perpetual inventory to national-wealth estimation; the difference-equation structure predates economics.

United Nations et al. (2009). System of National Accounts 2008. New York. Classifies intellectual property products as produced fixed assets.

Central Statistics Office (2016). National Income and Expenditure 2015. Dublin. Source of the revised 26.3% Irish GDP growth figure.

Appendix A. Algebra

A.1 Cost-based capitalization of expensed intangibles

Let X(t) denote the observed intangible outlay in period t (XRD, XAD, or capitalized software development), and let δ be the amortization rate, 0 < δ < 1. The perpetual inventory of costs is the forced first-order linear difference equation:

\quad K(t) = X(t) + (1-\delta)\,K(t-1)

with solution by superposition:

\quad
K(t)=(1-\delta)^tK(0)+\sum_{s=0}^{t-1}(1-\delta)^sX(t-s)

Under a stationary outlay stream X(t) = X for all t, the stock converges to the steady state:

\quad K^{*} = \frac{X}{\delta}

Reported operating profit P expenses the outlay in full. The cost-capitalized restatement adds back the expensed outlay and deducts amortization of the accumulated stock:

\quad P'(t) = P(t) + X(t) - \delta\,K(t-1)

In the steady state, δ K* = δ (X / δ) = X, so P' = P: the flow adjustment nets to zero. The correction operates entirely through the denominator. With A the reported asset base, the profit rate restates as:

\quad r = \frac{P}{A}
\;\longrightarrow\;
r' = \frac{P'}{A+K}

so that, in the steady state, r' = P / (A + K*) < r. Reported profit rates on intangible-intensive firms are overstated relative to their cost-capitalized values — equivalently, the asset base is understated — and the understatement of the balance sheet is what makes the income statement misleading. Off the steady state, with outlays growing at rate g, the flow adjustment X(t) - δ K(t-1) > 0, so reported profit itself is understated in addition to the asset base. Every entry in this construction — X(t), δ, K(t) — is either an audited transaction or a stated amortization policy. No appraisal enters.

A.2 The valuation excess in the national accounts

Consider an IP portfolio developed under the cumulative cost history {X(s)}, with cost-basis stock K(T) as in A.1. Suppose legal ownership is transferred to jurisdiction j at declared value V. Under SNA 2008, jurisdiction j records gross fixed capital formation of V, and GDP in j rises accordingly:

\quad \Delta GDP(j) = V

The admissible, transaction-traceable magnitude is the cost basis K(T). Define the valuation excess:

\quad E = V - K(T)

E is the portion of the national-accounts entry with no expenditure counterpart anywhere in the consolidated group’s ledgers. It is the output of the taxpayer’s valuation model — discount rates, projected royalty streams, assumed useful lives — none of which is auditable against transactions. When V is large compared to the recipient economy, ΔGDP(j) = V produces the leprechaun signature: recorded output growth of 26.3% (Ireland, 2015) against real domestic growth estimated at 4% to 6%.

The decomposition V = K(T) + E separates the two critiques. Recording K(T) would be cost-based capitalization — admissible under Position One, and small. Recording V records K(T) plus the unauditable appraisal E — inadmissible under Position Two, and in the tax-motivated cases, E dominates. The contradiction dissolves: both positions demand that the capital account contain only magnitudes traceable to transactions.

A.3 Detailed derivations regarding steady state and transitional path dynamics for the stock of capitalized costs, cost capitalized restatement of operating profits and adjusted cost capitalized profit rates (by Florian Semani)

Define the asset accumulation equation up to period t, with initial stock at time 0 of K0 and outlays of Xt at any time t:

\quad
K_t=X_t+(1-\delta)K_{t-1}

Expanding over k periods: 

\quad
K_t
=
X_t+\cdots+(1-\delta)^kX_{t-k}
+
(1-\delta)^{k+1}K_{t-k-1}

Letting k = t - 1:

\quad
K_t
=
X_t+\cdots+(1-\delta)^{t-1}X_1
+
(1-\delta)^tK_0

Therefore: 

\quad
K_t
=
W_t
+
(1-\delta)^tK_0

where: 

\quad
W_t
=
\sum_{j=0}^{t-1}
X_{j+1}(1-\delta)^{\,t-j-1}

Consider now the case where Xt = X in every period. In this case we define:

\quad
W_t^{*}
=
\sum_{j=0}^{t-1}
X(1-\delta)^{\,t-j-1}

Multiplying by (1 - 𝛿):

\quad
(1-\delta)W_t^{*}
=
\sum_{j=0}^{t-1}
X(1-\delta)^{\,t-j}

We then have: 

\quad
W_t^{*}
-
(1-\delta)W_t^{*}
=
\delta W_t^{*}

On the other hand: 

\quad
W_t^{*}
-
(1-\delta)W_t^{*}
=
X-(1-\delta)^tX

and therefore: 

\quad
W_t^{*}
=
\frac{X}{\delta}
\left(
1-(1-\delta)^t
\right)

It follows that if for each period an outlay of X occurs then: 

\quad
K_t^{*}
=
W_t^{*}
+
(1-\delta)^tK_0

Or:

\quad
K_t^{*}
=
\frac{X}{\delta}
+
(1-\delta)^t
\left(
K_0-\frac{X}{\delta}
\right)

Taking limits as t moves to infinity we have: 

\quad
K^{*}
=
\lim_{t\to\infty}
\left\{
\frac{X}{\delta}
+
(1-\delta)^t
\left(
K_0-\frac{X}{\delta}
\right)
\right\}

\quad
K^{*}
=
\frac{X}{\delta}
+
\lim_{t\to\infty}
(1-\delta)^t
\left(
K_0-\frac{X}{\delta}
\right)

\quad
K^{*}
=
\frac{X}{\delta}

We have three cases in this scenario when 0 < 𝛿 < 1:

The cost capitalized restatement of the original operating profit P_t at time t, is given by: 

\quad
P'_t
=
P_t+X_t-\delta K_{t-1}

Assuming X_t= X as always, we have from above: 

\quad
P'_t
=
P_t
+
X
-
\delta
\left\{
\frac{X}{\delta}
+
(1-\delta)^{t-1}
\left(
K_0-\frac{X}{\delta}
\right)
\right\}

\quad
P'_t
=
P_t
-
\delta(1-\delta)^{t-1}
\left(
K_0-\frac{X}{\delta}
\right)

We have again three cases in this scenario: 

Note that the original profitability ratio is given by: 

\quad
r_t=\frac{P_t}{A}

where P_t is profit without the cost capitalized restatement at time t and A is the asset base prior to balance sheet restatement. 

The adjusted cost capitalized profitability ratio, is given by: 

\quad
r'_t
=
\frac{P'_t}{A+K_t}

In cases Ⅰ and Ⅲ, the adjusted profitability ratio falls relative to the original profitability ratio:

\quad
r_t
=
\frac{P_t}{A}

as denominator increases but numerator stays the same or falls. Regarding case Ⅱ we have:

\quad
r'_t
=
\frac{
P_t
-
\delta(1-\delta)^{t-1}
\left(
K_0-\frac{X}{\delta}
\right)
}{
A
+
\frac{X}{\delta}
+
(1-\delta)^t
\left(
K_0-\frac{X}{\delta}
\right)
}

while: 

\quad
Ar_t=P_t

Substituting we get: 

\quad
r'_t
=
\frac{
Ar_t
-
\delta(1-\delta)^{t-1}
\left(
K_0-\frac{X}{\delta}
\right)
}{
A
+
\frac{X}{\delta}
+
(1-\delta)^t
\left(
K_0-\frac{X}{\delta}
\right)
}

In this case we get: 

\quad
r'_t<r_t

if and only if: 

\quad
-\delta(1-\delta)^{t-1}
\left(
K_0-\frac{X}{\delta}
\right)
<
r_t
\left(
\frac{X}{\delta}
+
(1-\delta)^t
\left(
K_0-\frac{X}{\delta}
\right)
\right)

which reduces to: 

\quad
(1-\delta)^{t-1}
<
\frac{
r_tX
}{
\delta\left(\delta+r_t(1-\delta)\right)
\left(\frac{X}{\delta}-K_0\right)
}

In conclusion, it is important to differentiate between the steady state and transitional path implications for the stock of capitalized costs, the cost capitalized restatement of operating profits and adjusted cost capitalized profit rates. If the economy starts at the steady state, that is K = X / 𝛿, then stock remains same throughout the time path of the economy and restated profit is the same as original profit, while adjusted profit rate falls due to the additional balance sheet implications of the restatement.

If the economy starts at a point when K0 < X / 𝛿, it will keep adding stock over time until the limit X / 𝛿, while restated profits along the path will be higher than original profits. Regarding the adjusted profit rate, it is possible for a certain time segment starting at period 1 that the adjusted profit rate is higher than the original profit rate.

If the economy starts at a point when K0 > X / 𝛿, it will keep stock shedding over time until the limit X / 𝛿, while restated profits along the path will be lower than original profits. Regarding the adjusted profit rate, it is lower than the original profit rate along the transitional path.