Abstract
We find that the Friedman rule is not optimal with real government transfers and distortionary taxation. As transfers cannot be taxed, a positive nominal net interest rate is the indirect way to tax the additional income derived from transfers. This result holds for heterogeneous agents, standard homogeneous preferences, and constant returns to scale production functions. The presence of real transfers changes the standard optimal taxation result of uniform taxation. Higher transfers imply higher optimal inflation rates. We calibrate a model with transfers to the US economy and obtain optimal values for inflation substantially above the Friedman rule.
Similar content being viewed by others
Notes
Governments usually provide transfers as in-kind transactions or as specific services, such as scholarships or medical procedures, or periodically adjust nominal transfers to maintain their real value. The definition of transfer in the Bureau of Economic Analysis is “a transaction in which one party provides a good, service, or asset to another party without receiving anything directly in return.”
A function \(U(c_{1},c_{2},1-l)\) is additively separable in leisure if it can be written as \(U(c_{1},c_{2},1-l)=F(c_{1},c_{2})+G(1-l)\). A function F(x), \(x\in \mathbb {R}^n\), is homogeneous of degree r, where \(r \in \mathbb {Z}\), if \(F(\lambda x)=\lambda ^{r}F(x)\) for all \(\lambda >0\).
We consider here that the transfer \(z_{it}\) implies the additional income of \(p_{t}(1+\tau _{2t})z_{it}\) in (4). The interpretation is that \(z_{it}\) has a market value of \(p_{t}(1+\tau _{2t})z_{it}\). However, instead of being indexed to the price gross of taxes, another possibility is that transfers are indexed only to the price level, that is, \(p_{t}z_{it}\). We discuss the effects of valuing transfers at \(p_{t}(1+\tau _{2t})z_{it}\) or \(p_{t}z_{it}\) in Sect. 4.
A sufficient condition for that to happen is \(R>1\).
This can be done either with a tax over the initial wealth or by making the initial price level approach infinity (when \(W_{i0}>0\)).
Proposition 1 only requires \(z_{it}\ne 0\), but we focus on the case \(z_{it}>0\). As we do not allow for lump-sum taxes, transfers cannot be negative to any household.
For example, in Werning (2007), positive transfers are optimal if the weights on poor households are high enough or if there is enough inequality.
Tiago Cavalcanti suggested this functional form for the utility function.
This result is also a consequence of the fact that, in this formulation, \(z_{t}=z\) and \(g_{t}=g\) in the household budget constraint.
We interpret the case \(\theta =1\) as the logarithmic utility. The logarithmic utility function is not homogeneous, but there exists a monotonic transformation to the logarithmic utility that describes the same preferences and implies a homogeneous utility function.
It is common to assume the same tax rate for cash and credit goods. This is done, for example, in Cooley and Hansen (1992).
Erosa and Ventura (2002) find that inflation acts as a regressive consumption tax, increasing inequality, as lower-income households tend to use more cash as a percentage of their total expenditures.
Federal transfers of social benefits to persons include social security, medicare, veterans’ benefits, unemployment insurance, and other transfers. Social security and medicare are about 70% of social benefits since the mid-1960s. Veterans’ benefits decreased from 70% of social benefits in 1947 to 5% in 2016. Unemployment insurance from 2000 to 2016 is on average 4% of social benefits. Total government transfers include federal social benefits, medicaid, state and local transfers, and transfers to the rest of the world. Medicare and medicaid together comprise about 40% of total government transfers. Government expenditures include consumption expenditures and gross investment. For these computations, we use data from the Federal Reserve Bank of St. Louis FRED dataset.
To avoid confusion, we do not suppress the subscript t in \(c_{it}\) and \(l_{it}\).
In Appendix, we provide an alternative proof of this result.
References
Adão, B., Silva, A.C.: Government financing, inflation, and the financial sector. Nova SBE Working Paper Series 621 (2018)
Arbex, M.: A quantitative analysis of tax enforcement and optimal monetary policy. Macroecon. Dyn. 17(5), 1096–1117 (2013)
Atkinson, A.B., Stiglitz, J.E.: The structure of indirect taxation and economic efficiency. J. Publ. Econ. 1(1), 97–119 (1972). https://doi.org/10.1016/0047-2727(72)90021-7
Attanasio, O.P., Guiso, L., Jappelli, T.: The demand for money, financial innovation, and the welfare cost of inflation: an analysis with household data. J. Polit. Econ. 110(2), 317–351 (2002). https://doi.org/10.1086/338743
Avery, R.V., Elliehausen, G.E., Kennickell, A.B., Spindt, P.A.: The use of cash and transaction accounts by American families. Fed. Reserve Bull. 72(3), 179–196 (1987)
Carey, D., Rabesona, J.: Tax ratios on labour and capital income and on consumption. OECD Econ. Stud. 35(2002/2), 129–174 (2002)
Castañeda, A., Díaz-Giménez, J., Ríos-Rull, J.: Accounting for the U.S. earnings and wealth inequality. J. Polit. Econ. 111(4), 818–857 (2003). https://doi.org/10.1086/375382
Cavalcanti, T.V.V., Villamil, A.P.: Optimal inflation tax and structural reform. Macroecon. Dyn. 7(3), 333–362 (2003). https://doi.org/10.1017/S1365100502020096
Chari, V., Christiano, L.J., Kehoe, P.J.: Optimality of the Friedman rule in economies with distorting taxes. J. Monet. Econ. 37(2), 203–223 (1996). https://doi.org/10.1016/S0304-3932(96)90034-3
Chari, V., Kehoe, P.J.: Optimal fiscal and monetary policy. In: Taylor, J.B., Woodford, M. (eds.) Handbook of Macroeconomics, vol. 1C, chap. 26, pp. 1671–1745. Elsevier, Amsterdam (1999). https://doi.org/10.1016/S1574-0048(99)10039-9
Cooley, T.F., Hansen, G.D.: The welfare costs of moderate inflations. J. Money Credit Bank. 23(3), 483–503 (1991). http://www.jstor.org/stable/1992683
Cooley, T.F., Hansen, G.D.: Tax distortions in a neoclassical monetary economy. J. Econ. Theory 58(2), 290–316 (1992). https://doi.org/10.1016/0022-0531(92)90056-N
Correia, I.: Consumption taxes and redistribution. Am. Econ. Rev. 100(4), 1673–1694 (2010). https://doi.org/10.1257/aer.100.4.1673
Correia, I., Teles, P.: The optimal inflation tax. Rev. Econ. Dyn. 2(2), 325–346 (1999). https://doi.org/10.1006/redy.1998.0040
Cunha, A.B.: The optimality of the friedman rule when some distorting taxes are exogenous. Econ. Theor. 35(2), 267–291 (2008). https://doi.org/10.1007/s00199-007-0236-5
Diaz-Gimenez, J., Glover, A., Rios-Rull, J.V.: Facts on the distributions of earnings, income, and wealth in the united states: 2007 update. Fed. Reserve Bank Minneap. Q. Rev. 34(1), 2–31 (2011)
Erosa, A., Ventura, G.: On inflation as a regressive consumption tax. J. Monet. Econ. 49(4), 761–795 (2002). https://doi.org/10.1016/S0304-3932(02)00115-0
Friedman, M.: The optimum quantity of money. In: Friedman, M. (ed.) The Optimum Quantity of Money and Other Essays, pp. 1–50. Aldine, Chicago (1969)
Kennickell, A.B., Starr-McCluer, M., Sunden, A.E.: Family finances in the US: recent evidence from the survey of consumer finances. In: Federal Reserve Bulletin, vol. 83, pp. 1–24 (1997)
Kimbrough, K.P.: The optimum quantity of money rule in the theory of public finance. J. Monet. Econ. 18(3), 277–284 (1986). https://doi.org/10.1016/0304-3932(86)90040-1
Lucas Jr., R.E., Stokey, N.L.: Optimal fiscal and monetary policy in an economy without capital. J. Monet. Econ. 12(1), 55–93 (1983). https://doi.org/10.1016/0304-3932(83)90049-1
Mendoza, E.G., Razin, A., Tesar, L.L.: Effective tax rates in macroeconomics: cross-country estimates of tax rates on factor incomes and consumption. J. Monet. Econ. 34(3), 297–323 (1994). https://doi.org/10.1016/0304-3932(94)90021-3
Mulligan, C.B., Sala-i-Martin, X.: Extensive margins and the demand for money at low interest rates. J. Polit. Econ. 108(5), 961–991 (2000). https://doi.org/10.1086/317676
Nicolini, J.P.: Tax evasion and the optimal inflation tax. J. Dev. Econ. 55(1), 215–232 (1998). https://doi.org/10.1016/S0304-3878(97)00063-1
Phelps, E.S.: Inflation in the theory of public finance. Swed. J. Econ. 75(1), 67–82 (1973). http://www.jstor.org/stable/3439275
Ramsey, F.P.: A contribution to the theory of taxation. Econ. J. 37(145), 47–61 (1927). http://www.jstor.org/stable/2222721
Schmitt-Grohé, S., Uribe, M.: Optimal fiscal and monetary policy under imperfect competition. J. Macroecon. 26(2), 183–209 (2004). https://doi.org/10.1016/j.jmacro.2003.11.002
Schmitt-Grohé, S., Uribe, M.: The optimal rate of inflation. In: Friedman, B.M., Woodford, M. (eds.) Handbook of Monetary Economics, vol. 3B, chap. 13, pp. 653–722. Elsevier, Amsterdam (2010). https://doi.org/10.1016/B978-0-444-53454-5.00001-3
Silva, A.C.: Taxes and labor supply: Portugal, Europe, and the United States. Port. Econ. J. 7(2), 101–124 (2008). https://doi.org/10.1007/s10258-008-0029-1
Silva, A.C.: Rebalancing frequency and the welfare cost of inflation. Am. Econ. J. Macroecon. 4(2), 153–183 (2012). https://doi.org/10.1257/mac.4.2.153
Werning, I.: Optimal fiscal policy with redistribution. Quart. J. Econ. 122(3), 925–967 (2007). http://www.jstor.org/stable/25098865
Acknowledgements
We are grateful for the comments and suggestions of Tiago Cavalcanti and two anonymous referees. We are also grateful for the discussions and suggestions of Carlos da Costa, Juan Pablo Nicolini and Pedro Teles.
Author information
Authors and Affiliations
Corresponding author
Additional information
The views in this paper are those of the authors and do not necessarily reflect the views of the Banco de Portugal. Silva thanks the hospitality of the Banco de Portugal, where he wrote part of this paper, and acknowledges financial support from Banco de Portugal, FCT, NOVA FORUM, and Nova SBE Research Unit. We acknowledge financial support from ADEMU. This work was funded by FCT Fundação para a Ciência e Tecnologia (FCT PTDC/IIM-ECO/4825/2012, UID/ECO/00124/2013 and Social Sciences Data Lab, Project 22209), by POR Lisboa (LISBOA-01-0145-FEDER-007722 and Social Sciences Data Lab, Project 22209) and POR Norte (Social Sciences Data Lab, Project 22209).
A Appendix
A Appendix
We provide an alternative proof to Proposition 2 of Sect. 4.
Proposition 2
When transfers follow path 2, the inflation tax is a more efficient instrument than the labor income tax.
Proof
Consider the simple economy of Sect. 4 with the path of transfers following path 2, \(e_{i}=1,\)\(g=0\), and \(\tau _{c}=0.\) Define \(\varGamma _{t} \equiv \frac{1}{1-\tau _{t}}\) and \(c_{t}\equiv f \left( \varGamma _{t} R_{t} \right) \) as the value of consumption that solves Eqs. (43) and (47). Define the instantaneous indirect utility as \(V \left( \varGamma _{t}R_{t} \right) \equiv U(f\left( \varGamma _{t}R_{t}\right) , 1-f\left( \varGamma _{t}R_{t}\right) )\), using the fact that \(c_{t}=l_{t}.\) Since U is strictly concave, the optimal allocation is stationary, which implies that \(\varGamma _{t}\) and \(R_{t}\) should be stationary too. It is trivial to see that V is decreasing in \(\varGamma R\). Therefore, the optimal tax policy solves the problem \(\min \nolimits _{\varGamma ,R}\varGamma R\) subject to the government budget constraint
Suppose that \(0<\tau <1\), \(\varGamma \equiv \frac{1}{1-\tau }>1\) and that \( \varGamma \) and R satisfy (A.1). We can show that it is always possible to decrease \(\varGamma \ge 1\) and increase R so that \(\varGamma R\) decreases and the constraint (A.1) is still satisfied. As a result, the solution of the problem cannot involve \(\varGamma >1\). First, a change in \( \varGamma \) together with a change in R so that \(\frac{\mathrm{d}\varGamma }{\mathrm{d}R} = -\frac{\varGamma }{R}\) maintains the value of \(\varGamma R\) constant. Consider an increase in R, \(\mathrm{d}R>0\). If \(\varGamma \) changes by \(\mathrm{d}\varGamma = -\frac{\varGamma }{R} \mathrm{d}R -\varepsilon \), for \(\varepsilon >0\), then, as \(\mathrm{d}\left( \varGamma R\right) = \varGamma \mathrm{d}R+R\mathrm{d}\varGamma \), this change in \(\varGamma \) and R implies a change in \( \varGamma R\) equal to \(-R\varepsilon <0\). On the other hand, \(\mathrm{d}\varGamma \) and \(\mathrm{d}R\) change government revenues by \((\frac{1}{\varGamma ^{2}}f\left( \varGamma R\right) + \frac{\varGamma R-1}{\varGamma }f^{\prime }\left( \varGamma R\right) R)\mathrm{d}\varGamma +(f\left( \varGamma R\right) +\left( \varGamma R-1\right) f^{\prime }\left( \varGamma R\right) )\mathrm{d}R\). With \(\mathrm{d}\varGamma =-\frac{\varGamma }{R}\mathrm{d}R-\varepsilon \), this change in government revenues is equal to
As \(\varGamma R>1\) and \(f\left( \varGamma R\right) >0\), the coefficient on dR is strictly positive. Therefore, for any \(\mathrm{d}R>0\), there is a sufficiently small \( \varepsilon >0 \) such that the expression in (A.2) is positive. This means that \(\varGamma R\) decreases, but government revenues increase. We then have that a pair \(\left( \varGamma ,R\right) \), with \(\varGamma >1\), cannot be the solution to the Ramsey problem as there is a decrease in the labor tax rate and an increase in the nominal interest rate such that the distortion \( \varGamma R \) decreases and government revenues do not decrease. It follows that the solution to the Ramsey problem requires \(\varGamma ^{*}=1\). Moreover, setting \(\varGamma ^{*}=1\) in (A.1) implies that \(R^{*} \) is equal to the smallest value that satisfies \(\left( R-1\right) f(R) = z\). As \(\varGamma = \frac{1}{1-\tau }\) and \(z>0\), \(\tau =0\) and \(R>1\).\(\square \)
Rights and permissions
About this article
Cite this article
Adão, B., Silva, A.C. Real transfers and the Friedman rule. Econ Theory 67, 155–177 (2019). https://doi.org/10.1007/s00199-018-1105-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00199-018-1105-0