The Positively Sloped IS Curve and the Balance of Payments: An Extension of Cebula's Model

Yannacopoulos, Nicos A. Article The Positively Sloped IS Curve and the Balance of Payments: An Extension of Cebula's Model Kredit und Kapital Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Yannacopoulos, Nicos A. (1982) : The Positively Sloped IS Curve and the Balance of Payments: An Extension of Cebula's Model, Kredit und Kapital, ISSN 0023-4591, Duncker & Humblot, Berlin, Vol. 15, Iss. 2, pp. 275-279, https://doi.org/10.3790/ccm.15.2.275 This Version is available at: https://hdl.handle.net/10419/292928 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Introduction In his paper entitled "The Upward Sloping IS Curve and the Control of Income and the Balance of Payments" Barrows (1974) investigated, among others, the effects of monetary and fiscal policy on the balance of payments. He assumed (following Silber (1971)), that the positively sloped IS curve is obtained if all the propensities to spend out of income sum to more than unity. However, in another contribution, Cebula (1976) retained the standard assumption that the propensities to spend out of income sum to less than unity, but following the suggestions by Yarrow (1975) and Weber (1970) he assumed that consumption and investment are increasing functions of the rate of interest. These assumptions are also consistent with a positively sloped IS curve. The policy implications of Cebula1 s model in a closed economy have been investigated by Cebula himself (Cebula 1976), and Tavlas (1980). The purpose of this paper is to extend the analysis, within the framework of Cebula's model, to include the effects of monetary and fiscal policy on the balance of payments, under a fixed exchange rate regime. II. Cebula's Model and its Extension Following Barrows (1974) we can write a model for an open economy, the equilibrium conditions of which are: (1) Y = C0 + C (Y, i) + I0 + I (Y, i) + B (Y) + G (commodity market) (2) L0 + L (Y, i) = M0 + K (i) (money market) (3) F = B (Y) + K (i) (balance of payments) The notation is standard: Y = income, I = investment, C = consumption, i = the rate of interest, L = the demand for money, Mo = the supply of money, G = govOPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.15.2.275 | Generated on 2023-01-16 12:47:44 276 Nicos A. Yannacopoulos ernment spending, B = the net balance of trade, K = the net capital inflow, and F = the balance of payments function. Co, lo, Lo are levels of consumption, investment and demand for money, respectively, which do not depend on changes in income or the rate of interest. Differentiating equations (1), (2) and (3) give: (4) dY = dCo + CydY + C{ di + dl0 +IydY + l{ di + BydY + dG (5) dL0 + LydY + L{ di = dM0 + di (6) dF = By dY + Kt di where Cy is the marginal propensity to consume out of income ly the marginal propensity to invest out of income, Q and Ii the response of C and I to a change in the rate of interest, Li the response in the demand of money to a change in the rate of interest, Ly the response in the demand of money to a change in income, Ki the response of net capital flow from abroad to a change in the rate of interest and By the response of the balance of trade to a change in income. The following restrictions are imposed on the system: 1 > Cy > 0 , 1 > Iy > 0 , Ly> 0 , Lt< 0 , K{ > 0 , By <0 Cebula (1976), however, assumes that interest responsiveness of both consumption and investment are positive (i.e. Ci > 0, h > 0) and the propensities to spend out of income sum to less than unity (i.e. Cy + Iy<C 1) so that the slope of the IS curve: di 1 — Cy — ly — By (7) = — > 0 W dY Ci + Ii This is consistent with the condition for stability in Cebula1 s model: -U, (8) \ - Cy~ ly - B?J Ci + Ii > (Li - Ki) which says that the system is stable if the slope of the LM curve (the right hand term) is less than the slope of the IS curve (the left hand term). The equations (4), (5), and (6) can be solved for the three endogeneous variables dY, di and dF. Barrows (1974, p. 957) gives the solution for dF (which interests us here), from which he derives the following policy multipliers (Barrows, 1974 p. 958 and p. 960): OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.15.2.275 | Generated on 2023-01-16 12:47:44 Positively Sloped IS Curve and the Balance of Payments 277 (9) (10) êF = - {(1 ~ Cy - ly - By) Kj + By (Ci + Ij)} ÏÏM0 - {(1 -Cy-IyBy) (Li - Ki) + ('Ci + I{) Ly} &F ô G Ly Ki — By (Li Kù - {(1 -Cy-IyBy) (Li - Ki) + (Ci + li) Ly} It can be easily shown that, under Cebula1 s assumptions and given the condition (8), the denominator in the multipliers (9) and (10) is positive. Whether the net outcome of an increase in money supply (or the government expenditure) on the balance of payments is unfavourable / &F \ / #F &F \ Um^ < < 0 ) or favourable > 0, > 0 j will depend on the numerator of the multipliers (9) and (10). # F The condition for (11) or (12) #M0 <0is: (1 -Cy-IyBy) > By (Q + /¿) (j -Cy-Iyci + h By) > Bn, K{ This means that a deficit in the balance of payments after a monetary expansion occurs if the slope of the IS curve (the left hand term of (12)) is greater than the slope of the FF' curve (the right hand term of (12)), i.e. the curve expressing the conditions of equilibrium in the foreign sector.1 êF >0 is: And the condition for^M^ (13) (1 -Cy-IyBy) K{ < By (Q + Ij) or (14) ly ~ BJJ Ci + h < Ki Which says that the slope of the FF' curve is greater than the slope of the IS curve. These conditions are not the same with those derived by Barrows (1974) for the Silber-Barrows model. To be more precise the condition 1 The FF' curve is the locus of pairs of i and Y which produce balance of payments equilibrium. Its slope is obtained by differentiating equation (3). FF' curve is the same with Barrow's HH curve (Barrows, 1974, p. 958). 19 Kredit und Kapital 2/1982 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.15.2.275 | Generated on 2023-01-16 12:47:44 278 Nicos A. Yannacopoulos for a deficit in the balance of payments after a monetary expansion in Cebula1s model in the same with the condition for a surplus in the Silber-Barrows model; and the condition for a surplus in the balance of payments after a monetary expansion in Cebula's model is the same with the condition for a deficit in the Silber-Barrows model. The condition for - êF ê G (15) <0 is: Ly Ki < By (Lj — K-i) or (16) Li — Ki < Bu Ki i.e. a deficit in the balance of payments occurs, following an expansion in the government expenditure when the slope of the LM curve is less than the slope of the FF' curve. And it is easily verified that a surplus in the balance of payments occurs when the slope of the LM curve is greater than the slope of the FF curve. These conditions are the same with those derived by Barrows (1974). III. Conclusions It turns out that the different assumptions on which Cebula's and Silber1 s models are based affect only the conditions under which an expansionary monetary policy affects the balance of payments. The conditions for the effects of the fiscal policy remain the same in both models. References Paul Barrows (1974): "The upward sloping IS curve and the control of income and the balance of payments". The Journal of Finance. — Richard J. Cebula (1976): "A brief note on economic policy effectiveness" Southern Economic Journal. — William L. Silber (1971): "Monetary policy effectiveness: the case of a positively sloped IS curve". The Journal of Finance. — George Tavlas (1980): "Economic policy effectiveness in Hicksian analysis: an extension" Kredit und Kapital. — Warren Weber (1970): "The effects of interest rates on aggregate consumption" American Economic Review. — George Yarrow (1975): "Growth maximisation and the firm's investment function" Southern Economic Journal. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.15.2.275 | Generated on 2023-01-16 12:47:44 Positively Sloped IS Curve and the Balance of Payments 279 Zusammenfassung Positiv verlaufende IS-Kurven und die Zahlungsbilanz: eine Erweiterung des Cebulaschen Modells Dieser Beitrag befaßt sich mit den bei festen Wechselkursen im Rahmen des Cebulasehen Modells auftretenden Auswirkungen der Geldund Finanzpolitik auf die Zahlungsbilanz und vergleicht sie mit den von Barrows erhaltenen Ergebnisse für das Modell von Silber-Barrows. Es wird festgestellt, daß die unterschiedlichen Annahmen des Cebula sehen und des Silber-Barrotuschen Modells lediglich die Bedingungen beeinflussen, unter denen eine expansionistische Geldpolitik eine Wirkung auf die Zahlungsbilanz ausübt. In beiden Modellen bleiben die Bedingungen für eine Beeinflussung durch die Finanzpolitik gleich. Summary The Positively Sloped IS-Curve and the Balance of Payments: An Extension of Cebula's Model This paper deals with the effects of monetary and fiscal policy on the balance of payments within the framework of Cebula's model, under a fixed exchange rate regime, and compares them with the results obtained by Barrows for the Silber-Barrows model. It is found that the different assumptions on which Cebula's and SilberBarrows model are based affect only the conditions under which an expansionary monetary policy affects the balance of payments. The conditions for the effects of the fiscal policy remain the same in both models. Résumé Les courbes positives Investissement-Epargne et la balance des paiements: une extension du modèle de Cebula L'article s'intéresse dans un régime de taux de change fixes et dans le contexte du modèle de Cebula aux effets de la politique monétaire et financière sur la balance des paiements et les compare aux résults obtenus par Barrows sur le modèle de Silber-Barrows. L'auteur établit que les diverses hypothèses des modèles de Cebula et de Silber-Barrows n'influent que sur les conditions dans lesquelles une politique monétaire expansionniste exerce une action sur la balance des paiements. Dans les deux modèles, les conditions d'intervention de la politique financière demeurent identiques. 19* OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.15.2.275 | Generated on 2023-01-16 12:47:44