Ebook Precautionary Demand for Money in a Monetary Business Cycle Model
In this paper, we study, theoretically and quantitatively, aggregate business cycle implications of precautionary demand for money. It is an outstanding challenge in the literature to account for business cycle behavior of nominal aggregates and their interaction with real aggregates. Business cycle models that have tried to incorporate money through, for example, cash-in-advance constraints, have done so while assuming that agents face only aggregate risk, which has resulted in the demand for money being largely deterministic, in the sense that the cash-in-advance constraint almost always binds. Such models have unrealistic implications for the dynamics of nominal variables, as well as for interaction between real and nominal variables, when compared to data (see, e.g., Cooley and Hansen, 1995).
Yet precautionary motive for holding liquidity seems to be strong in the data, and its nature suggests that idiosyncratic risk may play a key role for money demand, as shown in Telyukova (2009). In that paper, it is documented, for example, that the median household has about 50% more liquidity than it spends on average per month, and that controlling for observables, liquid consumption exhibits volatiity consistent with the presence of significant idiosyncratic risk. Thus, aggregate implications of idiosyncratic risk and resulting precautionary money demand are important to investigate, especially given the unresolved questions regarding monetary business cycles. The goal of this paper is to conduct such an investigation. The set of questions we want to answer is: What are the aggregate implications of precautionary demand for money? Can it help account for business cycle dynamics of velocity of money, interest rates and inflation, and their interaction with real variables?
Existing monetary business cycle models that incorporate money demand via a cash-in-advance constraint, such as cash-credit good models, calibrated to aggregate data, cannot account for aggregate facts such as variability of velocity of money, correlation of velocity with output growth or money growth, correlation of inflation with nominal interest rates, and others, as Hodrick, Kocherlakota and Lucas (1991) have shown. The reason is that in such models, the only type of uncertainty the households face in these models is aggregate uncertainty. The magnitude of this uncertainty in the data is not large enough to generate significant precautionary motive for holding money in the model, so that the cash-in-advance constraint almost always binds. Then, money demand in the model is made equivalent to cash-good consumption, tightly linking volatility of money demand to volatility of aggregate consumption. Aggregate consumption, in turn, is not volatile enough in the data to generate observed volatility of money demand (or its inverse, velocity) or other nominal aggregates.
We show that incorporating precautionary demand for money generated by unpredictable idiosyncratic variation, in combination with aggregate uncertainty, makes a crucial difference in the ability of the model to account for monetary facts mentioned above, by breaking the link between money demand and aggregate consumption. Agents generally hold more money than they spend, and money demand is no longer linked to average aggregate consumption, but rather to consumption of agents whose preference shock realizations make them constrained (i.e. they spend all of their balances) in trade. We show that velocity of money can be significantly more volatile in this heterogeneous-agent setting, thanks to the unconstrained agents, who are absent in previous models with only aggregate risk. The presence of both constrained and unconstrained households is key to the qualitative and quantitative results. In other words, idiosyncratic risk in this context does not average out in a way that can be adequately captured by a representative agent model, as Hodrick et al (1991) in fact anticipated in the discussion of their results (p. 380). In addition, the magnitude of idiosyncratic volatility is much higher than aggregate volatility: the standard deviation of aggregate consumption is 0.5%; we will measure the standard deviation of idiosyncratic consumption shocks to be around 19%.
We study this link qualitatively and quantitatively in a model that combines, in each period, two types of markets in a sequential manner, and where both aggregate and idiosyncratic uncertainty are present. The first-subperiod market is a standard Walrasian market, which we will term, somewhat loosely, the “credit market”. The second market is also competitive, but characterized by anonymity and the absence of barter possibility, which makes a medium of exchange - money - essential in trade. We term this market the “cash market”. This setup is consistent with both cash credit good models a la Lucas and Stokey (1987) and monetary search models in the style of Lagos and Wright (2005). The credit market is much like a standard real business cycle model, with the production function being subject to aggregate productivity shocks. Two features distinguish this market from the RBC framework. First, households have to decide how much money to carry out of this market for future cash consumption. Second, part of the output in the credit market is carried into the cash market by retail firms, who buy these goods on credit and subsequently transform them into cash goods. This introduces an explicit link between the real and monetary sectors of the economy, as credit-market capital becomes indirectly productive in the cash market.
At the start of the second-subperiod cash market, agents are subject to uninsurable idiosyncratic preference shocks which determine how much of the cash good they want to consume, but the realization of the shock is not known at the time that agents make their portfolio decisions. This generates precautionary motive for holding liquidity. In our model, we are able to show analytically how the idiosyncratic shocks, and the resulting heterogeneity of households with respect to being constrained in the cash market, result in amplified dynamics of velocity of money. We also show that absent idiosyncratic shocks, the model produces counter factual price and other nominal dynamics for values of the coefficient of relative risk aversion in the standard range in RBC literature.
Another contribution of our work is the calibration of the model. To our knowledge, all the existing models of the types mentioned above that have looked at aggregate behavior of nominal variables have been calibrated to aggregate data. Instead, we also use micro survey data on liquid consumption from the Consumption Expenditure Survey, like in Telyukova (2009), to calibrate idiosyncratic preference risk in our cash market. Using these data, we are able to discipline our calibration further than is commonly the case. In general, preference risk of the type that creates precautionary liquidity demand has not been measured in calibration of other aggregate models, and in the few contexts where precautionary liquidity demand has appeared, it has been treated as a free parameter (e.g. Faig and Jerez, 2007). Our use of micro data allows us to be very disciplined in our approach.
Once calibrated, we solve the model computationally to investigate the effects of real productivity shocks and monetary policy shocks. We find that precautionary demand for money makes a dramatic difference for the model in terms of helping it account for a variety of dynamic moments related to nominal aggregates in the data. We test these results by also computing a version of the model where we shut down the idiosyncratic risk, and find that without it, the model is incapable of reproducing any of the key nominal moments in the data, much as previous literature has suggested.
Our results lead us to conclude that in many monetary contexts, especially those aimed at accounting for aggregate data facts, it is important not to omit idiosyncratic uncertainty that gives rise to precautionary demand for money. As one example, omitting this empirically relevant mechanism may cause the standard practice of calibrating monetary models to the aggregate money demand equation, as has been done in many cash-in-advance models and monetary search models, to produce misleading results for parameters and incorrect quantitative implications. We demonstrate this by calibrating a version of the model without idiosyncratic shocks to target some data properties of aggregate money demand. With this targeting, we find that, first, the model requires some parameter values well outside the standard range in macroeconomics (e.g. a very low risk aversion parameter), and second, even when the model targets money demand, its quantitative performance is still far inferior to the model with precautionary demand, along both nominal and, importantly, real dimensions.
This paper is related to several strands of literature. On the topic of precautionary demand for liquidity, the key mechanism in our model is close to Faig and Jerez (2007), Telyukova and Wright (2008) and Telyukova (2009). In Telyukova and Wright (2008) and Telyukova (2009), the idiosyncratic uncertainty about liquidity need is shown, respectively theoretically and quantitatively, to be relevant for household portfolio decisions to hold liquid assets and credit card debt simultaneously. Faig and Jerez (2007) look at the behavior of velocity and nominal interest rates over the long run. They find that with precautionary liquidity demand, the simulated time series of velocity over the last century, interpreted as a series of steady states, fits the empirical series well. Lagos and Rocheteau (2005) study steady state properties of a monetary economy with idiosyncratic preference shocks. On the broad subject of accounting for aggregate behavior of nominal variables, a recent paper is Wang and Shi (2006). In their model, however, search intensity is the key mechanism behind velocity fluctuations over the business cycle.
The paper is organized as follows. Section 2 describes the model and characterizes the equilibrium. Section 3 demonstrates analytically the impact of precautionary demand for money on the dynamic behavior of money, velocity and interest rates. Section 4 describes our calibration strategy, and section 5 details the solution algorithm. Section 6 presents our results and discusses the quantitative role of precautionary liquidity demand. We then discuss how omission of precautionary demand may lead model calibration and implications astray (section 7) and show how precautionary demand affects welfare costs of inflation (section 8). Section 9 concludes.
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