GDP Growth by Debt Acceleration

July 07, 2025 by Ednaldo Silva
About the Author
Ednaldo Silva
Ednaldo Silva
(Ph.D. Econ.) is a leading economist with over 25 years’ experience in transfer pricing.
He is founder and former managing director of RoyaltyStat, an online database of royalty rates extracted from license agreements. Dr. Ednaldo Silva was the first Sr. Economic Advisor at the IRS Office of Chief Counsel, a drafting member of U.S. 26 IRC section 1.482 (1992, 1993, 1994) transfer pricing regulations. He introduced the “comparable profits method” (CPM in the US and TNMM in the OECD), “best method” rule, multiyear profit analysis, and the concept of arm’s-length represented by a range of results, rather than a point estimate.
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Consider the reduced-form GDP (behavioral) equation:

(1)      Yt = At + b ΔDt - r Dt-1

where:

a)  Yt is GDP in period t from 1 to T,

b)  At is “autonomous” (Kaleckian) gross accumulation (C + I + X − M),

c)  ΔDt ≡ Dt - Dt-1 is new government debt issuance (debt financing),

d)  b is the fiscal multiplier on debt-financed spending,

e). r Dt-1 are interest payments on the existing debt stock, and

f)  r (viewed as a constant here) is the average interest rate on the government debt.

Equation (1) is basic and applies to any economy, capitalist or socialist, rich or poor.

Taking the one-period (forward) difference, ΔXt ≡ Xt - Xt-1, and noting the second difference Δ2Dt ≡ ΔDt - ΔDt-1, we get:

        ΔYt = ΔAt + b [(Dt - Dt-1) - (Dt-1 - Dt-2)] - r (Dt-1 - Dt-2)

(2)    ΔYt  = ΔAt + b Δ2Dt - r ΔDt-1

Divide both sides of equation (2) by Yt to express the per-period growth rates:

(3)     gt ≡ (ΔYt) / (Yt) = [ΔAt + b Δ2Dt - r ΔDt-1] / (Yt)

where gt = ΔY / Y is the one-period GDP growth rates.

The Domar condition of debt sustainability
In his article “Burden of Debt and National Income” (1944), Evsey Domar shows that if we define the debt-to-GDP ratio dt ≡ Dt / Yt, its law of motion (discrete-time analogue) is:

         Δdt = (ΔDt) / (Yt) - dt-1 (ΔYt) / (Yt) = (st + r Dt-1) / (Yt) - gt dt-1

 (4)    Δdt = st / Yt + (r - gt) dt-1,

where st ≡ ΔDt - r Dt-1 is called the primary deficit.

Setting Δdt = 0 for a steady debt-to-GDP ratio gives:

d* = (s / Y) / (g - r),

which is finite (and positive) only if g > r.

Conversely, if g < r then Δd > 0 and the debt/GDP ratio explodes. Hence the growth rate of GDP must exceed the interest rate for public debt to be sustainable.

Recasting equation (3) as a Domar-style inequality
From equation (3), debt sustainability (g > r) becomes:

(5)     (ΔAt + b Δ2Dt - r ΔDt-1)/(Yt) > r ==> ΔAt + b Δ2Dt > r (Yt + ΔDt-1).

To obtain a growth rate above the borrowing rate r, the net injection of autonomous demand growth (ΔA) plus the acceleration of debt-financed spending (b Δ2D) must cover the interest drain on past debt: r ΔDt-1.

In summary, Domar’s condition is about nominal GDP growth vs. nominal interest rates;

Domar (1944) shows that if:

dt = (Dt) / (Yt)

is the debt‐to‐GDP ratio, its approximate law of motion is:

(7)     Δdt ≈ (rnominal - gnominal) dt-1 + (primary deficitt) / (Yt).

In steady state (no change in d), we need to satisfy:

gnominal > rnominal

to prevent Δdt > 0 from becoming uncontrolled by monetary or fiscal policy..

References

Evsey Domar, "The 'Burden of the Debt' and the National Income," American Economic Review (December 1944): https://www.jstor.org/stable/1807397

Gross accumulation is a concept from Michał Kalecki, Theory of Economic Dynamics (2nd edition), George Allen & Unwin, 1965.

 

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