سیاست های پولی و مالی بهینه زمانی که پول ضروری است

We study optimal fiscal and monetary policy in an environment where explicit frictions give rise to valued money, making money essential in the sense that it expands the set of feasible trades. The two main results are that the Friedman Rule is typically not optimal, and the long-run capital income tax is not zero. Neither of these results is due to any incompleteness of the tax system, as can sometimes occur in standard Ramsey analysis. Rather, by developing a precise notion of margins of adjustment using standard concepts of MRS and MRT, we show that the tax system in our model is complete. The need to distort cash-intensive activity in some sense causes a nonzero capital tax in our model. This deep connection between monetary issues and fiscal policy is in contrast to existing models of jointly-optimal fiscal and monetary policy, in which the monetary aspects of the economic environment have little to do with capital taxation prescriptions. Taken together, these findings reframe some conventional wisdom from baseline Ramsey models.

Monetary theory has made important advances of late, ones that enable researchers interested in applied policy questions to consider explicit frictions that give rise to valued money. In this paper, we build on the work of Lagos and Wright [31] and Aruoba et al. [9] to study optimal fiscal and monetary policy, in the tradition of Lucas and Stokey [32] and Chari et al. [15]. Two main results emerge from our work: the Friedman Rule is typically not optimal, and the optimal long-run capital income tax is not zero. The first result is opposite that of standard flexible-price Ramsey monetary models. The second result, although also obtainable in standard flexible-price Ramsey models, is driven by a unique connection between monetary policy and fiscal policy present in our model that is absent in reduced-form models of money demand. Taken together, these results reframe conventional wisdom from baseline Ramsey monetary analyses. The contribution of Lagos and Wright [31] and Aruoba et al. [9] – hereafter, LW and AWW, respectively – was to integrate search-based monetary theory, in the spirit of Kiyotaki and Wright [26,27], with standard dynamic general equilibrium macroeconomics. This integration makes the study of policy questions much easier and more relevant than in earlier search-based models. However, these models have been criticized on two grounds. First, they superficially resemble standard cash-in-advance (CIA) or money-in-the-utility-function (MIU) models, making some question whether they really are any deeper than reduced-form models of money. This point has been raised by, among others, Howitt [23]. Second, until now, the policy questions addressed in these new models have been largely confined to the long-run welfare costs of inflation. When parameterized to seem as close as possible to standard CIA and MIU models, the quantitative answers they have yielded to this question are similar to those obtained with CIA and MIU models, further adding to the sense that these new models simply re-invent CIA or MIU. In this paper, we ask a different policy-relevant question, the jointly-optimal fiscal and monetary policy, and even when we parameterize the model to look very similar to standard reduced-form models of money, we reach conclusions very different from those reached by Chari et al. [15] – hereafter, CCK – and others. Our results thus show that the answers to policy questions may indeed be very different once monetary frictions are treated seriously. Our first main result is that the nominal interest rate is typically positive because it is optimal to tax activities that require cash.1 The reason behind this result is that, because all final goods should be taxed to some degree as part of an optimal tax system, taxation of cash activities is naturally part of the second-best allocation. This prescription is simply standard Ramsey theory. In the LW and AWW environments, the explicit spatial and informational frictions that make money essential (in the sense of Kocherlakota [28] that it expands the set of feasible trades) render inflation the most natural way of taxing activities that require money. As we discuss, our results can be reconciled both technically and conceptually with those of CCK. Interestingly, Kocherlakota [29] conjectured that the Friedman Rule may not be optimal in a Ramsey problem in search-based models. Our results show his conjecture is correct.Our second main result is that capital income subsidies are optimal in the long run, for two distinct reasons. First, the holdup problems in capital investment that AWW show arise in this environment (that is, the fact that some parties must make unilateral capital investment decisions but then share the fruits of the capital via production in bilateral trades) lead to inefficiently-low capital accumulation, which in turn calls for, perhaps not surprisingly, optimal capital-income subsidies. The second rationale highlights the idea that capital-tax policy can depend on the primitive reasons for money demand. In a version of our model where the capital holdup problem is eliminated, the optimal monetary policy, which entails a deviation from the Friedman Rule, in turn distorts private-sector capital accumulation. Inflation thus acts as an indirect tax on capital accumulation, which a capital-income subsidy (either partially or wholly) offsets. The first channel above can be viewed as a monetary counterpart to Acemoglu and Shimer [1], who demonstrate, in a purely real environment, that search and bargaining frictions in labor markets lead to holdup problems in capital investment.While they do not explicitly draw optimal taxation implications, it seems clear from their analysis that capital subsidies would be optimal in their bargaining environment. However, in a version of their model with no holdup problem, there would not be any need to subsidize capital, which is a novel result of our model. Thus the second channel is a nontrivial interaction between monetary and fiscal policy. In this sense, our optimal capital-taxation prescription is driven by fundamentally monetary issues, in contrast to the studies of Schmitt-Grohe and Uribe [37] and Chugh [18], in which capital-taxation prescriptions are, qualitatively, independent of the monetary policy prescription or even whether or not money demand is modeled. Neither the non-zero capital tax nor the deviation from the Friedman Rule in our analysis has anything to do with incompleteness of the tax system. Completeness or incompleteness of a tax system is a concept that can be defined in both monetary models and purely real models. In the literature on optimal capital taxation, the examples of Correia [19], Jones et al. [24], and Armenter [5] illustrate that incompleteness of the tax system typically leads to non-zero capitalincome taxation. This is because the capital tax ends up imperfectly substituting for the ability to create certain wedges. Similarly, one can easily show that in the monetary models of Chari and Kehoe [16], if the tax system were incomplete, the Friedman Rule would not be optimal because a positive nominal interest rate serves as an imperfect substitute for the ability to create a wedge in the consumption-leisure margin. In our analysis, neither the deviation from the Friedman Rule nor the non-zero capital tax arises due to any inability on the part of the government to create any wedges. The rest of our work is organized as follows. Section 2 describes the environment, characterizes the private sector equilibrium and describes efficient allocations. Section 3 presents the Ramsey problem and presents our results. Section 4 provides further perspectives on and intuition for our results and proves that the tax system is complete in the sense defined above.

We view our work and results as a first step in taking more seriously the new class of microfounded models of money as a laboratory for studying policy questions. Our central findings are that the Friedman Rule is typically not the optimal policy and that the long-run optimal capital-income tax is not zero. Our analysis of optimal monetary policy connects broadly with those being conducted by others in micro-founded models of money demand – for example, Berentsen and Monnet [11]. In light of recent results regarding asset taxation in the new dynamic public finance literature – for example, Golosov et al. [21] and Albanesi and Sleet [3] – and the attempt of Albanesi and Armenter [2] at reconciling them with standard Ramsey results, it may be interesting to know how or whether the capital-taxation implications of a micro-founded model of monetary exchange square with this growing body of knowledge. Besides this, there are of course a number of ways one might want to modify our framework. Monopoly power in goods and labor markets are thought by many to be important realistic features. It would be straightforward to introduce monopoly power in the CM. The results of Schmitt-Grohe and Uribe [36] and Chugh [17] suggest that inflation in such an environment would be partly a direct tax on the money rent we identify and partly an indirect tax on producers’ and labor suppliers’ rents. It may be interesting to know quantitatively how these direct and indirect uses of the inflation tax interact. Once one has monopoly power in the CM, one could go further in adding elements monetary policy makers often think are important, such as nominal rigidities in prices and wages. For example, Aruoba and Schorfheide [8] show that when one replaces the typical “cashless” assumption of a Calvo-type model with micro-founded frictions for the use of cash, welfare implications are altered significantly. Investigating both long-run and short-run optimal policy – be it monetary alone or monetary and fiscal jointly – in the presence of both temporary nominal rigidities and deep-rooted frictions underlying monetary trade also seems likely to yield new insights. Pushing our first step in different directions, another interesting issue to study may be the nature of and solution to the time-inconsistency problem of the Ramsey policy in this sort of environment. It is not clear how the time-consistency results of, say Alvarez et al. [4] or Persson et al. [34], would extend to our environment. Neither is it clear how the emerging results in the aforementioned new dynamic public finance literature, which places at center stage distributional concerns, might extend to a version of our environment in which money holdings were allowed to differ across households. This paper is also part of a larger effort underway in the literature studying the policy implications of deep-rooted, non-Walrasian frictions in goods markets, money markets, and labor markets. A central focus of this larger project has been to think about what sorts of departures from typicalWalrasian frameworks impinge importantly on conventional policy prescriptions derived from standard models. Much progress has recently been made using micro-founded models of labor market transactions – for example, Walsh [40], Trigari [39], Krause and Lubik [30], Arseneau and Chugh [6], Faia [20], to name just a few. We think much progress is in the offing using micro-founded models of money as well.