1. Two Ratios, One Regime Change
Plot two ratios from FRED over 1950-2025. The first is private nonresidential equipment investment as a share of GDP: it has oscillated within a narrow band, roughly 5 to 7 percent, for four decades, dipping in recessions (2001, 2008-2009, 2020) and recovering, but exhibiting no trend growth. The second is federal debt held by the public as a share of GDP: it has risen from about 25 percent in the 1970s to 98 percent in fiscal year 2025, with gross federal debt at approximately 121 percent of GDP — levels last seen at the close of the Second World War.
The investment in equipment share of GDP has stagnated while the debt ratio has grown several-fold, and that this divergence marks a substitution in the source of measured GDP growth: from private capital accumulation, the engine Harrod and Domar placed at the center of growth theory, toward debt-financed demand. The divergence is a gap in growth rates of two ratios, not a crossing of levels, and it is masked in the headline investment data by a component — intellectual property products — that no auditor can verify.
2. The Harrod-Domar Structure
Harrod (1939) and Domar (1946) formalized the warranted growth rate as:
(1)\quad g(t) = \frac{s(t)}{v(t)} - d where s(t) = I(t)/Y(t) is the gross investment share of output, v(t) = dK(t)/dY(t) is the incremental capital-output ratio, and d is the depreciation rate. The economics is transparent: output growth is internally generated by the accumulation of “productive capital.” Investment plays a dual role — it is a component of current demand and the increment to future capacity. The warranted rate is the growth path along which the capacity created by investment is absorbed by the demand investment generates.
Harrod-Domar assigns no growth role to public debt. Debt finance can bridge a demand shortfall — the Keynesian function — but it creates no capacity. In the accounting of Equation 1, a debt-financed transfer raises Y(t) on the demand side without raising K(t), and therefore raises measured growth today at the price of no warranted growth tomorrow.
3. Why Equipment Only: The Decomposition
Measured gross private nonresidential fixed investment decomposes into three components:
(2) \quad I(t) = I_E(t) + I_S(t) + I_{IP}(t)Equation 2. E = equipment; S = structures; IP = intellectual property products.
The Harrod-Domar savings term is total investment, and restricting attention to equipment is a deliberate identification choice that must be defended, not assumed. The defense rests on the evidentiary status of the three components.
Equipment and structures are transaction-verified. They consist of arm’s-length purchases of priced goods and construction services, observable in Census shipments data, import records, and construction spending surveys, and — decisively — they generate depreciation schedules that appear as structured line items on IRS Form 4562, filed under penalty of perjury. The magnitudes admit reconciliation against legally attested corporate accounts.
Intellectual property products do not. IPP is now the largest of the three components, approximately USD 1.5 trillion annually, exceeding both equipment and structures. Its evidentiary basis is as follows. R&D expenditures are estimated from the NSF/Census BERD survey; software from the Economic Census and Service Annual Survey; entertainment originals from industry sources. These are voluntary or survey-based instruments carrying no audit trail, no penalty of perjury, and no reconciliation requirement against tax filings. Nor could they be reconciled: IRS Form 1120 collects no separate line item for R&D or software expense. When these costs are disclosed at all, they are dispersed across unstructured attachments to Form 1125-A, negative entries in Other Income, or the unstructured Other Deductions statement. Own-account software — software firms build for internal use — appears nowhere identifiable in any tax filing and is valued by the BEA at imputed cost: programmer wages marked up by assumption. R&D is deflated with input-cost indices because no output price for R&D exists or can exist. And the entire category was reclassified from intermediate expense to final investment by accounting fiat in the 2013 comprehensive NIPA revision, adding roughly 3 percent to the level of GDP overnight without any change in underlying economic activity.
The critique targets the standard, not the agency. The 2013 reclassification implements SNA 2008, and every OECD statistical office does the same. But international consensus on a convention does not supply the convention with an evidentiary basis. The standing test applied on this blog to any claim asserted as probative evidence is that it must be both algebraically expressible and empirically testable. IPP investment satisfies the first condition and fails the second: it is the only major GDP component whose magnitude cannot be checked against any legally binding record, whose prices are imputed rather than observed, and whose classification as investment is definitional rather than transactional.
The consequence for growth accounting is direct. The apparent stability of the headline investment share s(t) over recent decades has been purchased by composition: I_IP/Y rising while I_E/Y stagnated. The Harrod-Domar accumulation term looks intact in the aggregate only
because an unverifiable component has been substituted for a verifiable one. Restricting the accumulation base to equipment strips away the imputation layer and exposes the auditable core:
(3)\quad s_E(t) = \frac{I_E(t)}{Y(t)}4. The Gap Function and the Hypothesis
Define the debt ratio d(t) = D(t)/Y(t), where D(t) is federal debt held by the public, and the gap function:
(4)\quad G(t) = d(t) - s_E(t)
The hypothesis is that G(t) is widening: the wedge between the debt burden carried by output and the verifiable private accumulation base financed out of output has grown, and continues to grow. In 1975, d(t) was roughly 25 percent against an equipment share near 6 percent, a gap of about 19 points. In 2025, d(t) is 98 percent against an equipment share still near 6 percent: a gap of roughly 92 points. The accumulation engine has not grown with the economy; the debt has.
5. The Test
A widening gap is descriptive. The testable proposition concerns the sources of measured growth. Specify the growth-accounting regression:
(5)\quad \frac{dY(t)}{Y(t-1)} = a + b_1 s_E(t) + b_2 \Delta d(t) + e(t) Equation 5. dd(t) = d(t) – d(t-1), the change in the debt ratio.
Harrod-Domar predicts b1 > 0, with magnitude approximately 1/v[,katex], and [katex]b2 approximately zero: debt issuance is a demand-side bridge, not a source of growth, and in a well-functioning accumulation regime the change in the debt ratio should carry no systematic explanatory weight once the investment share is controlled.
The hypothesis under test is regime migration: estimated across rolling sub-periods -- pre/post-2008 and pre/post-2020 as natural break candidates, with formal Chow tests at each -- b1 decays toward insignificance while b2 rises. Estimation follows the standing conventions of this blog: annual data 1950-2025; Newey-West HAC standard errors (Bartlett kernel); coefficients reported as b +/- SE(b), the 68 percent confidence interval; no p-values. The relevant FRED series are Y033RX (real equipment investment), GDPA (nominal GDP, with the share taken from BEA Table 1.1.10), and FYGFDPUN (federal debt held by the public).
Two econometric cautions. First, s_E(t) is procyclical and dY(t)/Y(t-1) drives it contemporaneously through the accelerator, so the full development requires instrumenting or lagging the investment share; the sub-period contrast in b2 survives either treatment. Second, dd(t) is itself countercyclical by construction -- deficits widen in recessions -- so a positive b2 in later sub-periods cannot be read as automatic stabilization alone: the stabilizer mechanism operated equally in the earlier sub-periods where b2 is predicted to be null.
6. Conclusion
The U.S. growth process retains the Harrod-Domar form -- Equation 1 still holds as an identity of accumulation -- but its substance has migrated. The marginal source of measured GDP growth is shifting from equipment-driven capital deepening to debt-financed demand. The shift is masked in headline data by an intellectual property component whose magnitude no auditor can trace to a transaction, whose prices are imputed, and whose status as investment is a definitional convention adopted in 2013. When the accumulation base is restricted to its verifiable core, the picture is unambiguous: the equipment share has been flat for forty years while the debt ratio has quadrupled. The economy is not growing on its accumulation engine. It is growing on borrowed time.
References
Domar, E. (1946), Capital Expansion, Rate of Growth, and Employment, Econometrica 14(2), 137-147. The dual role of investment as demand and capacity.
Harrod, R. (1939), An Essay in Dynamic Theory, Economic Journal 49(193), 14-33. The warranted rate of growth.
Bureau of Economic Analysis (2013), Preview of the 2013 Comprehensive Revision of the National Income and Product Accounts, Survey of Current Business, March 2013. The capitalization of R&D and entertainment originals.
United Nations et al. (2009), System of National Accounts 2008. The international standard mandating IPP capitalization.
Internal Revenue Service, Form 1120, Form 1125-A, Form 4562. The structured and unstructured disclosure of capital expenditures in corporate tax filings.
Federal Reserve Bank of St. Louis, FRED series Y033RX, GDPA, FYGFDPUN, FYPUGDA188S. Data sources for estimation.