A Note on Tax Multiplier

Chang, Wen-ya; Lai, Ching-chong Article A Note on Tax Multiplier Kredit und Kapital Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Chang, Wen-ya; Lai, Ching-chong (1990) : A Note on Tax Multiplier, Kredit und Kapital, ISSN 0023-4591, Duncker & Humblot, Berlin, Vol. 23, Iss. 3, pp. 351-357, https://doi.org/10.3790/ccm.23.3.351 This Version is available at: https://hdl.handle.net/10419/293177 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. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. 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However, in an interesting paper Holmes and Smyth (1972) propose that the transactions demand for money should be a function of disposable income (national income after tax) rather than national income based on theoretical and empirical viewpoints, and challenge the conventional wisdom. As a result, they find that the tax multiplier may be positive depending on the relative shifts in the IS and LM curves. The question is, are their results robust enough to sustain changes in the specification of the macroeconomic equations? Consider the consumption and the investment function. Weber (1970) argues that consumption is positively related to the interest rate, and Yarrow (1975) claims that for the growth-maximizing firms, as opposed to the profit-maximizing firms, investment may be an increasing function of the interest rate. Cebula (1976), Tavlas (1980, 1982), and Jaeger (1981) put these two findings into an IS-LM framework and obtain some interesting results which are contrast with the conventional wisdom1. In addition, Yan- * The authors are grateful to an anonymous referee for his helpful suggestions and comments on an earlier draft of this paper. Needless to say, any remaining shortcomings and errors are our responsibility. ** Associate Professor, Department of Economics, Fu-Jen Catholic University, Taiwan. *** Research Fellow, Sun Yat-Sen Institute for Social Sciences and Philosophy, Academia Sinica, and Professor, Graduate Institute of Industrial Economics, National Central University, Taiwan. 1 To obtain the conclusions reached by Cebula, it is sufficient that an increase in the interest rate raises the sum of consumption and investment; it is not required that the increased interest rate will raise both. There are a few empirical studies which show that an increase in the interest rate may at least raise the sum of the two, that is, raise the total expenditure. For the positive impact that interest rate has on consumption, see Boskin (1978) and Carlino (1982); and for the insensitivity of investment with respect to interest rate, see White (1970) and Clark (1979). OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.23.3.351 | Generated on 2023-01-16 12:59:36 352 Wen-ya Chang and Ching-chong Lai nacopoulos (1982) and Lai and Chang (1987) apply the main characteristics of Cebula (1976) model to the open economy, and investigate the effects of monetary and fiscal policies on the balance of payments and the impact of currency devaluation on domestic output in the context of fixed exchange rates, respectively. In line with these studies, this paper attempts to reevaluate the conclusion reached by Holmes and Smyth (1972) by adopting Cebula's (1976) specification of the consumption and investment functions. We find that the tax multiplier is always negative, which runs in sharp contrast with the Holmes and Smyth (1972) assertion. The remainder of the paper is arranged as follows. Section II presents the analytical framework. The tax multiplier under alternative specifications is discussed in section III. Finally, the concluding remarks are presented in section IV. II. The Model Except for the fact that the money demand function incorporates the specific feature emphasized by Holmes and Smyth and that the expenditure function embodies the characteristics of the Cebula model, the analytical framework is basically that of standard IS-LM model. The model consists of the following two equations: (1) V = E(yvy, r) + G; (2) M = L(y — vy, r); where y = national income; E = expenditure on consumption and investment; r = a proportional tax rate; yd — {y~W) = disposable income; r = interest rate; G = government expenditure; M = supply of money; L = demand for money. Using subscripts with the relevant variables to indicate partial derivatives, we will impose the following restrictions on the behavior function: 1 > EVd > 0, Er ^ 0, LVd > 0, Lr < 0. It is worth mentioning that the assumption Er> 0 is conformable with the findings of Weber (1970) and Yarrow (1975). Equations (1) and (2) are the equilibrium conditions for the commodity market and money market, respectively. The demand for money is specified to be a function of disposable income, which is the main argument of Holmes and Smyth (1972). OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.23.3.351 | Generated on 2023-01-16 12:59:36 A Note on Tax Multiplier III. The Impact of Tax Policy 353 We first examine the effects of a change in tax policy. Totally differentiating the system with respect to r, we have (3) Eyd (1 " T) " Lyd (1 " T) L 1Er] 1 = \yE»d J LdrJ LyLydd (4) By Cramer's rule, it implies that dy y [LrEyd - ErLyd] d r where A = Lr[EVd( 1 - r) - 1] - ErLyd( 1 — r) > 0 according to Routh-Hurwitz stability condition. It is worth pointing out that the stability condition imposes a restriction related to the relative steepness between the IS curve and the LM curve.2 We will mention it in due time. We now use the result stated in equation (4) to discuss the performance of a tax policy under alternative specifications of the expenditure function. 1. The Holmes-Smyth Specification Following conventional analysis, Holmes-Smyth specifies Er< 0; then the stability condition A > 0 is always met. So from equation (4), we obtain (5) dy . — as (LrEydErLyd)> 0 a r Moreover, from equation (3) we have (6) (7) dr yEVd dr IS Er dr VLyd dr LM Lr < 0 < 0 From equation (3) the slopes of the IS and LM curves are given by 9r dr ~dy is LM [Eyd (l-T)-l] Er ^ 0 Lr > 0 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.23.3.351 | Generated on 2023-01-16 12:59:36 354 Wen-ya Chang and Ching-chong Lai yEyd VLv< Er > Lr which imply that a tax cut will make IS curve and LM curve shift upwards, respectively. According to equations (6) and (7), we can express (5) in the following manner dy . (8) Equation (8) is exactly the conclusion of the Holmes and Smyth analysis. It indicates that the larger the shift in LM curve is relative to the shift in IS curve due to a change in tax rate, the more likely the perverse tax multiplier will prevail. 2. The Cebula Specification Alternatively, if we adopt Cebula's specification, Er > 0, the stability condition (A > 0) requires that the slope of the IS curve be greater than that of the LM curve. Then from (4) we have dy (9) —<0 d r Equation (9) reveals that, in the presence of the Holmes and Smyth consideration, the national income will always be expansionary as government undertakes a tax cut policy. This result contrasts with the Holmes and Smyth assertion. These contrast results can be illustrated clearly by using the IS-LM apparatus. As is evident, the IS schedule is negatively sloped under the Holmes-Smyth specification, while a positively sloped IS schedule prevails under the Cebula specification. In figure 1, the initial equilibrium is at E0; initial output is y0. Under the Holmes-Smyth situation, in response to a tax cut from r0 to Ti, both lSHs{ ^o) and LM(t0) shift upward to ISHs(*i) and LM(Ti), respectively. As indicated in figure 1, the domestic output will depress from y0 to yHs provided that LM shifts upwards by a greater distance than IS does. Next, we turn to examine Cebula's circumstance. Following a tax cut from t0 to Ti, ISc(t0) shifts downward to ISC(ti), while LM(R0) again shifts upward to LM(ti). Obviously, the domestic output will increase from y0 to yc in figure l.3 3 Equations (6) and (7) tell us that the shifts of the IS and LM curves depend on y. Therefore, in figure 1, the shifts upward and downward from IS hs(t0), ISC(t0) and LM(t0) should not be parallel. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.23.3.351 | Generated on 2023-01-16 12:59:36 A Note on Tax Multiplier 355 IV. Concluding Remarks Based upon a standard IS-LM macromodel, this paper reexamines the effects of tax policy on domestic output. It is shown that the specification of the expenditure function plays an important role in determining the performance of tax policy. Under the Holmes-Smyth specification, a tax cut policy will depress domestic output provided that LM shifts upwards by a greater distance than IS does. However, if we adopt Cebula's specification, a tax cut will definitely stimulate domestic output, rather than depress it, even if the Holmes-Smyth claim that the money demand is a function of disposable income rather than national income, is taken into consideration. Figure 1 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.23.3.351 | Generated on 2023-01-16 12:59:36 356 Wen-ya Chang and Ching-chong Lai References Boskin, M. J.: "Taxation, Saving, and the Rate of Interest," Journal of Political Economy, Vol. 86 (April 1978), pp. 25 - 53. - Carlino, G. A.: "Interest Rate Effects and Intertemporal Consumption," Journal of Monetary Economics, Vol. 9 (March 1982), pp. 223 - 234. - Cebula, Richard J.: "A Brief Note on Economic Policy Effectiveness," Southern Economic Journal, Vol. 43 (October 1976), pp. 1174 - 1176. - Clark, P. K.: "Investment in the 1970s: Theory, Performance, and Prediction," Brooking Papers on Economic Activity, (1979), pp. 73 - 113. - Holmes, James M. and Smyth, David J.: "The Specification of the Demand for Money and the Tax Multiplier," Journal of Political Economy, Vol. 80 (1972), pp. 179 - 185. - Jaeger, Klaus: "Economic Policy Effectiveness in Hicksian Analysis: A Note," Kredit und Kapital, 14. Jahrg. (1981), pp.177 - 179. - Lai, Ching-chong, and Chang, Wen-ya: "Currency Devaluation with Flexible Wages: An Application of the Cebula Model," Journal of Macroeconomics, Vol. 9 (Fall 1987), pp. 625 - 635. - Tavlas, George S.: "Economic Policy Effectiveness in Hicksian Analysis: An Extension," Kredit und Kapital, 13. Jahrg. (1980), pp. 252 - 262. - Tavlas, George S.: "Economic Policy Effectiveness in Hicksian Analysis: A Reply," Kredit und Kapital, 15. Jahrg. (1982), pp. 429 - 433. - Weber, Warren: "The Effect of Interest Rate on Aggregate Consumption," American Economic Review, Vol. 60 (September 1970), pp. 591 - 600. - White, W. H.: "Interest Inelasticity of Investment Demand - The Case from Business Attitude Surveys Re-examined," in Readings in Macroeconomics, edited by Mueller, M. G., pp. 95 - 113. New York: Holt Reinhart and Winston, 1970. - Yannacopoulos, Nicos A.: "The Positively Sloped IS Curve and the Balance of Payments: An Extension of Cebula's Model," Kredit und Kapital, 15. Jahrg. (1982), pp. 275 - 279. - Yarrow, George: "Growth Maximization and the Firm's Investment Function," Southern Economic Journal, Vol. 41 (April 1975), pp. 580 - 592. Zusammenfassung Bemerkungen zum Steuermultiplikator Die Schlußfolgerung von Holmes und Smyth (1972), die in der Literatur starke Beachtung fand, zeigt, daß eine Politik der Steuersenkung die Inlandsproduktion senken kann, sofern die Geldnachfragefunktion mehr durch das verfügbare Einkommen als durch das Volkseinkommen determiniert wird. Dieser Aufsatz übernimmt die Spezifikation von Cebula (1976) für die Konsumund Investitionsfunktionen und kommt zu dem Ergebnis, daß die Holmes-Smyth-Behauptung in diesem verbesserten Modell keine Gültigkeit hat. Summary A Note on Tax Multiplier* The conclusion of Holmes and Smyth (1972), which has received wide attention in the literature, indicates that a tax cut policy may depress domestic output if the money demand function is determined by disposable income rather than national OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.23.3.351 | Generated on 2023-01-16 12:59:36 A Note on Tax Multiplier 357 income. This paper adopts the Cebula (1976) specification of the consumption and investment functions, and finds that the Holmes-Smyth assertion is not valid under this amended framework. Résumé Une remarque sur le multiplicateur fiscal La conclusion de Holmes et Smyth (1972) qui a fortement attiré l'attention dans la littérature, indique qu'une politique de réduction fiscale peut faire diminuer l'output national si la fonction de demande monétaire est déterminée par le revenu disponible plutôt que par le revenu national. Ce travail adopte la description de Cebula (1976) des fonctions de consommation et d'investissement et montre que l'assertion d'HolmesSmyth n'est pas valide dans ce contexte modifié. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.23.3.351 | Generated on 2023-01-16 12:59:36