انتخاب بهینه ابزار سیاست پولی در یک اقتصاد با شوک واقعی و نقدینگی

Faced with real and nominal shocks, what should a benevolent central bank do, fix the money growth rate or target the inflation rate? In this paper, we make a first attempt at studying the optimal choice of monetary policy instruments in a micro-founded model of money. Specifically, we produce an overlapping generations economy in which limited communication and stochastic relocation creates an endogenous transactions role for fiat money. We find that when the shocks are real, welfare is higher under money growth targeting; when the shocks are nominal and not large, welfare is higher under inflation targeting. While under inflation targeting, it is always optimal to pursue an expansionary policy, it is never optimal to do so under money growth targeting.

How should a monetary authority decide whether to use the money stock or the interest rate as its policy instrument of choice? Using a stochastic IS-LM model, with reduction in variability of aggregate output as the yardstick, Poole (1970) was the first to pose this ‘instrument problem’. His advice was clear and precise: when the shocks are real in nature, fix the money supply; if the shocks are monetary, fix the interest rate. This prescription continues to guide monetary authorities around the globe even today and remains to date among the most influential policy counsels in monetary economics. Surprisingly, though, Poole's instrument problem has received almost no attention in formal micro-founded models of money, a lacuna we attempt to remedy in this paper.1 To that end, we produce a two-period lived pure-exchange overlapping generations model in the tradition of Townsend (1987) where limited communication and stochastic relocation create an endogenous transactions role for fiat money.2 At the end of each period a fraction (deterministic or random) of agents is relocated (the ‘movers’) to a location different from the one they were born in and the only asset they can use to ‘communicate’ with their past is fiat money. This allows money to be held even when dominated in rate of return. The other asset is a commonly available linear storage technology with a fixed real return. The ‘stochastic relocations’ act like shocks to agents’ portfolio preferences and, in particular, trigger liquidations of some assets at potential losses. They have the same consequences as ‘liquidity preference shocks’, and motivate a role for banks that take deposits, hold cash reserves, and make other less liquid investments. Depending on agents’ risk aversion, the banks’ cash reserves are sensitive/insensitive to the real return on money. We study two variants of this model, one in which there are real shocks (the young-age endowment of the agents is stochastic), and one where the fraction of agents relocating is itself random (liquidity preference or monetary shocks). In either case, banks can promise a real return to only the non-movers. For the movers, the banks can promise an amount of money (paid out of the bank's reserve holdings) but not the real return on it. To see this, consider the case of endowment shocks. Here, the bank cares about next period's endowment because the latter will potentially influence that period's money demand and hence the price level and therefore affect the return on money between this period and the next. But next period's money demand depends on the following period's endowment, and so on. We assume that all agents know the distributions of the real or monetary shocks and form expectations about the return on money conditional on these distributions. We focus solely on long run stationary equilibria under which agents expectations are coordinated across time, i.e., expectations of one generation are validated by the behavior of the next and so on ad infinitum. Can the model tell us if inflation targeting (or interest rate targeting) is superior in an ex ante welfare sense to money growth targeting, and when? As a benchmark, we start by studying the deterministic case. Here, as originally noted by Poole, ‘it obviously makes no difference whatsoever whether the policy prescription is in terms of setting the interest rate or in terms of setting the money stock…’. The best policy, as discussed in Bhattacharya et al. (2005) is to hold the money stock fixed (zero inflation). Here the social opportunity cost of using money is the lost return from storage while the private opportunity cost of money is the nominal interest rate; these are equalized when the net inflation rate is zero. In the deterministic case, since every period is exactly the same, the government faces a static problem and hence cares only about this intratemporal margin. With shocks, however, the government's problem is generically no longer static; an intertemporal (intergenerational) margin appears. Since shocks hit different generations asymmetrically, the government has to pay attention to providing some amount of intergenerational insurance. To achieve this, the government may opt to trade off intratemporal for intertemporal efficiency and this may cause optimal monetary policy to deviate from the zero inflation policy. When shocks are introduced, we are able to make a fair bit of analytical progress under the assumption of logarithmic (henceforth ‘log’) utility. When the economy is hit with i.i.d. shocks to the endowment drawn from a general distribution, we can show that the ex ante welfare maximizing (henceforth ‘optimal’) net money growth rate is zero (fixed money supply). The corresponding optimal inflation targeting policy calls for positive inflation. We are also able to show that an optimally chosen fixed money growth rate is welfare superior to an optimally chosen fixed inflation rate. For the class of CRRA utility functions with coefficient of relative risk aversion φφ, computations reveal that the optimal net money growth rate is negative for φ<1φ<1, zero for φ=1φ=1, and negative again for φ>1φ>1. For the entire range of φφ studied, the corresponding optimal inflation targeting policy calls for positive inflation and optimal monetary targeting is welfare superior to optimal inflation targeting. For the most part, the situation is exactly reversed when the shocks are monetary in nature, that is they affect the fraction of agents relocating. For logarithmic utility, we can prove that optimal monetary targeting involves a negative net money growth rate while the corresponding optimal inflation targeting policy calls for positive inflation. For ‘small enough’ liquidity shocks, we can also prove that inflation targeting does a better job than monetary targeting; this result is however reversed for ‘large’ shocks. Numerical experiments confirm that the flavor of these results carries over to the CRRA case for a wide range of φφ. Overall, two strong themes emerge. First, our results indicate that when the shocks are real, welfare is higher under money growth targeting; when the shocks are nominal and not large, welfare is higher under inflation targeting. Secondly, while under inflation targeting it is always optimal to pursue an expansionary policy, it is never optimal to do so under money growth targeting. Almost all the work done in this area employs models with sticky or staggered prices, and very few, use welfare criteria to answer Poole's original question. Using a deterministic overlapping generations model, Smith (1994) compares the two targeting procedures in terms of their efficiency properties and goes on to isolate a ‘tension between efficiency and determinacy’ of monetary equilibria reminiscent of the nineteenth century quantity theory versus real bills doctrine controversy. This tension is not a focus of our analysis. Liquidity shocks in the random relocation environment (and their relation to banking crises) have also been studied in Champ et al. (1996), Smith (2002), and Antinolfi and Keister (2006). Our treatment of liquidity shocks is different from that in these papers (see footnote 9 on this). In a closely related paper, Gomis-Porqueras and Smith (2003) study the optimal level of interest rate smoothing under seasonal fluctuations. They consider deterministic two-period cycles of endowments, relocation, and storage returns and characterize the properties of periodic equilibria under monetary and interest rate targeting. By computing periodic interest rate policies that maximize welfare, they show that liquidity shocks require relatively higher interest rate smoothing than endowment shocks. Our paper substantially enlarges the scope of the analysis undertaken by Gomis-Porqueras and Smith (2003). Not only do we evaluate the best rule for each monetary policy instrument, we also rank monetary targeting against interest rate targeting for each type of shock, an exercise closer in spirit to Poole (1970). It is also worth reiterating that, while our results hold for the whole class of CRRA preferences, all of our results for logarithmic preferences are derived analytically, allowing us to clearly lay out the economic intuition that underlie these results. More importantly, by undertaking a dynamic rational expectations equilibrium approach, our paper makes a theoretical advance; it enables a tractable analysis of price-level uncertainty within a stationary setting and within the context of the aforementioned literature on stochastic relocation models, a feature not present in the earlier papers. The plan for the rest of the paper is as follows. In the next section, we outline the baseline model without uncertainty and compute optimal monetary policies. In Section 3, we study the role of endowment uncertainty in shaping the optimal choice of monetary instruments. In Section 4, we do the same with money demand shocks. Section 5 presents the results from the computational experiments under CRRA utility. In Section 6 we revert to logarithmic preferences for studying state-contingent rules and then contrast them with the optimal money growth and inflation rules. In that section, we also discuss the welfare implications of monetary injections that are implemented through proportional transfers. Section 7 concludes. Proofs of all major results are in the appendices.

This paper revisits the classic issue of the optimal choice of monetary instruments faced by central bankers around the world. To that end, we produce a two-period lived pure-exchange overlapping generations model in the tradition of Townsend (1987) and Champ et al. (1996) where limited communication and stochastic relocation create an endogenous transactions role for fiat money. We study two kinds of shocks, real shocks (to the endowment) and liquidity shocks (to the fraction of agents relocating). First, our results indicate that when the shocks are real, welfare is higher under money growth targeting; when the shocks are nominal and not large, welfare is higher under inflation targeting. Secondly, while under inflation targeting it is always optimal to pursue an expansionary policy, it is never optimal to do so under money growth targeting. We also examined alternative mechanisms for conduct of monetary policy. We find that there is no role for targeting rules when monetary injections are implemented through proportional money transfers. The equilibrium under proportional transfers can be obtained by a fixed money supply; the transfers are irrelevant. Similarly, conduct of open market operations would also have no welfare effects. The models used in this paper do not include productive capital. It is safe to conjecture that adding capital would have strong implications for many of the results primarily because a propagation mechanism for shocks would then appear. Similarly, one could explore the likely impact on our results of assuming serially correlated shocks. There again, one can hazard a guess that for low levels of shock persistence, the results in the current paper would most likely continue to hold. In any case, these appear to be interesting avenues for future work.