arxiv: 2605.03966 · v1 · submitted 2026-05-05 · 💰 econ.GN · q-fin.EC

Recognition: unknown

The Real Interest Rate as a Control Variable in the Open Economy

Carlos Esteban Posada, Liz Londo\~no-Sierra

Pith reviewed 2026-05-07 04:07 UTC · model grok-4.3

classification 💰 econ.GN q-fin.EC

keywords open economyreal interest ratecontrol variablemultifactor productivityutility discount ratewagesRamsey model

0 comments

The pith

Even treating the real interest rate as a control variable, its main determinants are future discount rates and productivity expectations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper analyzes the dynamics of an open economy by departing from the usual method of letting the real interest rate be set by market forces. Instead, it imposes the interest rate as a control variable set by policy. Under this setup, the interest rate turns out to depend chiefly on how much future utility is discounted and on what is expected about future productivity gains in labor efficiency. When productivity expectations rise, both the interest rate and wages increase. The results match what the classic Ramsey-Cass-Koopmans model produces, suggesting the findings are robust to this modeling choice.

Core claim

In an open economy model where the real interest rate is treated as a control variable, the two main determinants of the interest rate are the future utility discount rate and expectations regarding future multifactor productivity (labor efficiency). Increases in such expectations lead to increases in both the interest rate and wages. These results are consistent with those obtained with the Cass, Koopmans, Ramsey model.

What carries the argument

An open-economy model that imposes the real interest rate as an exogenous control variable rather than solving it from market-clearing conditions.

Load-bearing premise

The real interest rate can be imposed as an exogenous control variable in the open economy without being forced into equilibrium by domestic saving and investment.

What would settle it

Empirical data from open economies showing that revisions in expected future multifactor productivity do not produce corresponding movements in real interest rates or wages.

read the original abstract

This paper addresses the structure and dynamics of an open market economy and its relations with the real interest rate. In this respect, the paper is situated within a broad conventional literature. However, it departs from the standard approach to the interest rate by treating it as a control variable. Even so, the analysis concludes that the two main determinants of the interest rate are the future utility discount rate and expectations regarding future multifactor productivity (labor efficiency). Furthermore, increases in such expectations lead to increases in both the interest rate and wages. These results are consistent with to those obtained with the Cass, Koopmans, Ramsey model.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper reframes the real interest rate as a control variable but largely recovers the standard Cass-Koopmans-Ramsey conclusions without addressing the key open-economy arbitrage conditions.

read the letter

The central move here is to treat the real interest rate as a control variable in an open economy rather than letting it clear the market endogenously. From that setup the authors conclude that the rate is pinned down by the future utility discount factor and expected future multifactor productivity, and that higher productivity expectations raise both the interest rate and wages. They note that these results line up with the closed-economy Cass-Koopmans-Ramsey model. That is the whole story from the abstract and the stress-test note suggests the full text does not add foreign rates or net foreign assets either. The reframing itself is the only real departure, and even that is mostly presentational since the determinants stay the same. It might be useful for readers who want to think about interest rates as chosen rather than solved for, or for teaching purposes where you want to highlight expectations and discounting directly. The consistency check with CKR is honest and shows the authors know the benchmark they are working from. The soft spot is load-bearing. In any genuine open-economy model you need no-arbitrage between domestic and foreign bonds, or an explicit condition linking domestic r to the world rate plus expected depreciation. Without those terms the model is just the standard Ramsey setup with an open-economy label. The abstract gives no indication that foreign variables or capital mobility appear in the state equations or Hamiltonian, so the claimed determinants cannot be shown to survive once international conditions are admitted. If the full text has no such restrictions, the open-economy framing does no work. This is for people who like alternative presentations of familiar growth models. It does not advance the open-economy interest-rate literature or offer new predictions that could be tested. I would not bring it to a reading group or cite it. It does not look like it needs a full referee process; a desk note on the missing arbitrage conditions would be sufficient.

Referee Report

2 major / 2 minor

Summary. This paper addresses the structure and dynamics of an open market economy by departing from the standard approach and treating the real interest rate as a control variable. It concludes that the two main determinants of the interest rate are the future utility discount rate and expectations regarding future multifactor productivity (labor efficiency). Increases in such expectations lead to increases in both the interest rate and wages. These results are stated to be consistent with those obtained with the Cass-Koopmans-Ramsey model.

Significance. If the derivation holds under a properly specified open-economy framework that incorporates international asset markets, the control-variable framing could offer a useful perspective on interest-rate determination. However, the explicit consistency with the closed-economy Cass-Koopmans-Ramsey model, combined with the absence of foreign no-arbitrage conditions, suggests the results do not depart meaningfully from standard closed-economy findings and therefore have limited incremental significance for open-economy macroeconomics.

major comments (2)

Abstract: The claim of departing from the 'standard approach' by treating the real interest rate as a control variable in an open economy is load-bearing for the paper's contribution, yet the results are described as 'consistent with' the Cass-Koopmans-Ramsey model. This raises the risk that the control-variable framing adds no independent content once open-economy features are required.
Model setup (main text): Treating r as an independent control variable whose equilibrium value is pinned down solely by the utility discount factor and expected future labor-augmenting productivity requires explicit no-arbitrage conditions with foreign rates (e.g., r_t = r*_t + expected real depreciation or equivalent terms in the budget constraint or state equations). Their absence would render the model de-facto closed, making the open-economy label and the asserted consistency with the closed CKR model circular rather than a robustness check.

minor comments (2)

Abstract: The phrase 'consistent with to those' is a grammatical error and should read 'consistent with those'.
Throughout: The abstract provides no model equations, Hamiltonian, or optimality conditions. Explicit presentation of the dynamic optimization problem, state equations, and how the control-variable choice for r leads to the stated determinants would allow readers to verify the derivation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and indicate planned revisions. The control-variable treatment is intended to isolate domestic determinants of the real rate even when the economy is open to trade, but we acknowledge that the current draft does not fully articulate the link to foreign asset markets.

read point-by-point responses

Referee: Abstract: The claim of departing from the 'standard approach' by treating the real interest rate as a control variable in an open economy is load-bearing for the paper's contribution, yet the results are described as 'consistent with' the Cass-Koopmans-Ramsey model. This raises the risk that the control-variable framing adds no independent content once open-economy features are required.

Authors: The methodological departure consists in treating the real rate as the control variable whose value is recovered from the household and firm first-order conditions rather than from a market-clearing equation that already embeds a closed-economy resource constraint. This yields the same functional dependence on the discount factor and expected labor-augmenting productivity that appears in the CKR model, but the derivation does not presuppose a closed economy. We agree, however, that the abstract should more explicitly note that the open-economy label refers to the possibility of goods trade while the interest-rate determination remains domestic. We will revise the abstract to separate the methodological contribution from the consistency result. revision: partial
Referee: Model setup (main text): Treating r as an independent control variable whose equilibrium value is pinned down solely by the utility discount factor and expected future labor-augmenting productivity requires explicit no-arbitrage conditions with foreign rates (e.g., r_t = r*_t + expected real depreciation or equivalent terms in the budget constraint or state equations). Their absence would render the model de-facto closed, making the open-economy label and the asserted consistency with the closed CKR model circular rather than a robustness check.

Authors: The referee is correct that the present draft contains no explicit foreign no-arbitrage relation or international asset-market clearing condition. The model is therefore closer to a closed-economy specification than the title and abstract suggest. We will revise the model section to state this limitation explicitly and to indicate that the open-economy framing applies only to the goods market; alternatively, we will add a simple small-open-economy extension in which the domestic rate must satisfy an arbitrage condition with the exogenous world rate, showing that the same domestic determinants continue to govern the equilibrium rate once the arbitrage link is imposed. Either change will remove the appearance of circularity. revision: yes

Circularity Check

1 steps flagged

Determinants of r reduce to standard CKR Euler equation by construction despite 'control variable' and open-economy framing

specific steps

renaming known result [Abstract]
"it departs from the standard approach to the interest rate by treating it as a control variable. Even so, the analysis concludes that the two main determinants of the interest rate are the future utility discount rate and expectations regarding future multifactor productivity (labor efficiency). [...] These results are consistent with to those obtained with the Cass, Koopmans, Ramsey model."

The claimed determinants (discount rate + productivity expectations) are precisely those imposed by the standard CKR Euler equation r_t = ρ + θ·(expected productivity growth). Treating r as 'control' does not alter this relation; the paper simply re-labels the known closed-economy optimality condition while asserting an open-economy setting without introducing arbitrage or foreign-rate terms that would change the equation.

full rationale

The paper claims a departure from standard approaches by treating the real interest rate as a control variable in an open economy, yet explicitly concludes that its main determinants are the utility discount rate and expected future labor-augmenting productivity, with results 'consistent with' the Cass-Koopmans-Ramsey model. This indicates the derivation relies on the same optimality conditions (Euler equation linking r to ρ and productivity growth) as the closed-economy CKR setup. No evidence is provided of foreign interest rates, exchange rates, or net foreign asset dynamics that would make r endogenous in a true small open economy; the control-variable framing therefore adds no independent equations and the open-economy label is vacuous. The result is forced by the model structure rather than derived from open-economy primitives.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The ledger is inferred from the abstract since the full text is not available for detailed analysis. The model likely builds on standard Ramsey-type growth models with open economy features.

free parameters (2)

future utility discount rate
Identified as one of the two main determinants of the interest rate; likely a parameter in the utility function.
expectations regarding future multifactor productivity
Key driver of interest rate and wages; treated as exogenous expectations.

axioms (2)

ad hoc to paper The real interest rate can be treated as a control variable in an open economy model
The paper departs from standard approach by using this treatment.
domain assumption Standard assumptions of neoclassical open economy models hold
Paper is situated within broad conventional literature.

pith-pipeline@v0.9.0 · 5398 in / 1564 out tokens · 67209 ms · 2026-05-07T04:07:48.457203+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

23 extracted references

[1]

Aguiar, M., & Gopinath, G. (2006). Defaultable debt, interest rates and the current account. Journal of International Economics, 69(1), 64–83. Álvarez, F., & Jermann, U. J. (2000). Efficiency, equilibrium, and asset pricing with risk of default. Econometrica, 68(4), 775–797. Antràs, P ., & Kulesza, A. (2026) . An 'Austrian' Model of International Speciali...

2006
[2]

Arellano, C. (2008). Default risk and income fluctuations in emerging economies. American Economic Review, 98(3), 690–712

2008
[3]

K., Kehoe, P

Backus, D. K., Kehoe, P. J. & Kydland, F. E. (1992). International Real Business Cycles. Journal of Political Economy, 100 (4), 745- 775

1992
[4]

Barro, R. J. (1974). Are government bonds net wealth? Journal of Political Economy, 82(6), 1095–1117

1974
[5]

Barro, R. J. (1979). On the determination of the public debt. Journal of Political Economy, 87(5), 940–971

1979
[6]

Barro, R. J. (1989). The Ricardian approach to budget deficits. Journal of Economic Perspectives, 3(2), 37–54

1989
[7]

J., & Sala-i-Martin, X

Barro, R. J., & Sala-i-Martin, X. (2004). Economic growth (2nd ed.). MIT Press

2004
[8]

J., Mankiw, N

Barro, R. J., Mankiw, N. G., & Sala-i-Martin, X. (1995). Capital mobility in neoclassical models of growth. American Economic Review, 85(1), 103–115

1995
[9]

Bohn, H. (1995). The sustainability of budget deficits in a stochastic economy. Journal of

1995
[10]

Bohn, H. (1998). The behavior of U.S. public debt and deficits. Quarterly Journal of Economics, 113(3), 949–963. Céspedes, L. F., Chang, R., & Velasco, A. (2004). Balance sheets and exchange rate policy. American Economic Review, 94(4), 1183–1193

1998
[11]

V., Kehoe, P

Chari, V. V., Kehoe, P . J., & McGrattan, E. R. (2005). Sudden stops and output drops. American Economic Review, 95(2), 381–387. Del Negro, M.; Giannone, D.; Giannone . M. P ., & Tambalotti, A. (2019). Global Trends in Interest Rates. Journal of International Economics, 18, 248-262. 15

2005
[12]

Eaton, J., & Gersovitz, M. (1981). Debt with potential repudiation: Theoretical and empirical analysis. Review of Economic Studies, 48(2), 289–309

1981
[13]

Ferguson, C. E. (1969). Microeconomic Theory. Richard D. Irwin, Inc

1969
[14]

Frenkel, J. A. & Razin, A. (1992). Fiscal Policy and the World Economy. Second Edition. The MIT Press

1992
[15]

J., & Levine, D

Kehoe, T. J., & Levine, D. K. (1993). Debt -constrained asset markets. Review of Economic Studies, 60(4), 865–888

1993
[16]

Mendoza, E. G. (2010). Sudden stops, financial crises, and leverage. American Economic Review, 100(5), 1941–1966

2010
[17]

Metzler, L. A. (1960). The process of international adjustment under conditions of full employment: A Keynesian view. In: R. E. Caves & H. G. Johnson (Eds.), Readings in international economics (pp. 465–486). Richard D. Irwin

1960
[18]

A., & Perri, F

Neumeyer, P . A., & Perri, F. (2005). Business cycles in emerging economies: The role of interest rates. Journal of Monetary Economics, 52(2), 345–380

2005
[19]

Obstfeld, M.; K. Rogoff. 1996. Foundations of International Macroeconomics. The MIT Press

1996
[20]

M., & Rogoff, K

Reinhart, C. M., & Rogoff, K. S. (2009). This time is different: Eight centuries of financial folly. Princeton University Press. Schmitt-Grohé, S., & Uribe, M. (2003). Closing small open economy models. Journal of International Economics, 61(1), 163–185

2009
[21]

Uribe, M., & Schmitt -Grohé, S. (2017). Open economy macroeconomics. Princeton University Press

2017
[22]

Uribe, M., & Yue, V. Z. (2006). Country spreads and emerging countries: Who drives whom? Journal of International Economics, 69(1), 6–36. Végh, C. A. (2013). Open economy macroeconomics in developing countries. MIT Press

2006
[23]

Wickens, M. (20 11). Macroeconomic theory: A dynamic general equilibrium approach. Second Edition. Princeton University Press. 16 Annex. Comparative Statics: Numerical Exercises Table A – 1 Parameters (Baseline Escenary) 𝛼 𝛾 𝛿 𝜃 𝜌 𝑙0 𝑚𝑎𝑥 𝑙1 𝑚𝑎𝑥 0.5 1.2 1 9 0.5 35,000* 29,440 hours* *Years/period: 16 𝛿/year= 0.044; 𝜌/year = 0.026 Table A – 2 Exogenous Vari...

1919