I expect that some of you are completely lost in the debate over the relationship between interest rates and inflation that has been going on lately. I'm hoping this will provide some general background on monetary models that will help to sort things out, at least at a very general level.
But the main reason for doing this is to emphasize something that has not been talked about much, how the empirical evidence led economists to move away from flexible price models and consider models featuring wage and price rigidities (and for those of you ready to jump on me about the empirical evidence regarding wage and price rigidities, how the evidence changes with disaggregation and the like, those objections have been presented here, e.g. see this post for one example, or even better, see here, or better yet, scroll down here).
This is an important, too little discussed point. In models with flexible prices, matching the short-run dynamics contained in actual U.S. data with a defensible theoretical model is a challenge, one that can only be overcome with assumptions that are highly unpalatable. We do much better when we add wage inflexibility, but that alone is not enough to get both the size and the sign of all the correlations in the data correct, and it also fails to match the magnitude and duration of the responses to shocks. When price rigidities are tacked onto the model so that both price and wage inflexibilities are present, we get much closer in matching signs of correlations, durations, and magnitudes contained within U.S. data.
Even then, problems remain. One has to do with whether the actual degree of price rigidity in the data is enough to generate the persistence and magnitudes that are needed -- that's the point of the papers linked above. Another is the need to assume unrealistic values for labor supply elasticities in order to get the right degree of labor responsiveness in the model. The values needed do not match the estimated values. In addition, the Calvo pricing assumption is often attacked as ad hoc instead of being derived from first principles, an unrealistic approximation of the true process (e.g. it's not state dependent), and so forth. And this list is by no means exhaustive.
But these models -- New Keynesian models -- are the best we have presently in terms of matching the data empirically. Some proponents of alternatives, e.g. flexible price models, will protest that they can, in fact, do as well or better at matching the data, but they will rely upon assumptions, decompositions, shock characteristics and the like that the larger profession has deemed unsupportable. When the proponents of alternatives to the New Keynesian model produce a model of their own that does a better job of explaining the data without resorting to these assumptions, then it will be time to pay more attention. But for now, for policy analysis in particular, the New Keynesian models are the best we have. I understand that, particularly recently, best does not necessarily imply good -- the models need to be fixed and some people, like Stiglitz don't think they can be fixed at all. But, again, for now they are the best we have, particularly in terms of matching the empirical evidence and for policy analysis.
This is from Carl Walsh's book "Monetary Theory and Policy" (I need to get my hands on his 3rd edition). The sections below provide some background on the evolution of monetary models, as well as more on the point about needing wage and price rigidities to match the empirical evidence:
2 Money-in-the-Utility Function
The neoclassical growth model, due to Ramsey (1928) and Solow (1956), provides the basic framework for much of modern macroeconomics. Solow's growth model has just three key ingredients: a production function allowing for smooth substitutability between labor and capital in the production of output, a capital accumulation process in which a fixed fraction of output is devoted to investment each period, and a labor supply process in which the quantity of labor input grows at an exogenously given rate. Solow showed that such an economy would converge to a steady-state growth path along which output, the capital stock, and the effective supply of labor all grew at the same rate.
When the assumption of a fixed savings rate is replaced by a model of forward-looking households choosing savings and labor supply to maximize lifetime utility, the Solow model becomes the foundation for dynamic stochastic models of the business cycle. Productivity shocks or other real disturbances affect output and savings behavior, with the resultant effect on capital accumulation propagating the effects of the original shock over time in ways that can mimic some features of actual business cycles (see Cooley 1995).
The neoclassical growth model is a model of a nonmonetary economy, and while goods are exchanged and transactions must be taking place, there is no medium of exchange -- that is, no "money" -- that is used to facilitate these transactions. Nor is there an asset, like money, that has a zero nominal rate of return and is therefore dominated in rate of return by other interest-bearing assets. To employ the neoclassical framework to analyze monetary issues, a role for money must be specified so that the agents will wish to hold positive quantities of money. A positive demand for money is necessary if, in equilibrium, money is to have positive value.
A fundamental question in monetary economics is the following: How should we model the demand for money? How do real economies differ from Arrow-Debreu economies in ways that give rise to a positive value for money? Three general approaches to incorporating money into general equilibrium models have been followed: (1) assume that money yields direct utility by incorporating money balances directly into the utility functions of the agents of the model (Sidrauski 1967); (2) impose transactions costs of some form that give rise to a demand for money, either by making asset exchanges costly (Baumol 1952; Tobin 1956), requiring that money be used for certain types of transactions (Clower 1967), assuming that time and money can be combined to produce transaction services that are necessary for obtaining consumption goods, or assuming that direct barter of commodities is costly (Kiyotaki and Wright 1989); or (3) treat money like any other asset used to transfer resources intertemporally (Samuelson 1958). All involve shortcuts in one form or another... An important consideration in evaluating different approaches will be to determine whether conclusions generalize beyond the specific model or are dependent on the exact manner in which a role for money has been introduced. We will see examples of results that are robust, such as the connection between money growth and inflation, and others that are sensitive to the specification of money's role, such as the impact of inflation on the steady-state capital stock. ...
The ... assumption that prices and wages are perfectly flexible will be maintained... Thus, the focus is on flexible price models that emphasize the transactions role of money. The approaches adopted in these models can also be used to incorporate money into models in which prices and/or wages are sticky. The implications of introducing nominal rigidities into general equilibrium models of monetary economies are discussed in [later] chapters...
The models we have examined in this and the previous chapter are variants of Walrasian economies in which prices are perfectly flexible and adjust to ensure that market equilibrium is continuously maintained. The ... approaches discussed all represent means of introducing valued money into the Walrasian equilibrium. Each approach captures some aspects of the role that money plays in facilitating transactions. ...
However, the dynamics implied by these flexible-price models fail to capture the short-run behavior that appears to characterize modem economies.
That is perhaps not surprising; most economists believe that sluggish wage and price adjustment, absent from the models of this chapter, play critical roles in determining the short-run real effects of monetary disturbances and monetary policy. Although systematic monetary policy can have real effects with flexible prices, simulations suggest that these effects are small, at least at moderate inflation rates. To understand how the observed short-run behavior of money, interest rates, the price level, and output might be generated in a monetary economy, we need to introduce nominal rigidities, a topic discussed in chapter 5. ...
5 Money, Output, and Inflation in the Short Run
Chapter 1 provided evidence that monetary policy actions have effects on real output that persist for appreciable periods of time. The empirical evidence from the United States is consistent with the notion that positive monetary shocks lead to a hump-shaped positive response of output, and Sims (1992) finds similar patterns for other OECD economies. We have not yet discussed why such a response is produced.
Certainly the models of chapters 2-4 did not seem capable of producing such an effect. So why does money matter? Is it only through the tax effects that arise from inflation? Or are there other channels through which monetary actions have real effects? This question is critical for any normative analysis of monetary policy, since designing good policy requires understanding how monetary policy affects the real economy and how changes in the way policy is conducted might affect economic behavior.
In the models examined in earlier chapters, monetary disturbances did cause output movements, but these movements arose from substitution effects induced by expected inflation. The simulation exercises suggested that these effects were too small to account for the empirical evidence on the output responses to monetary shocks. In addition, the evidence in many countries is that inflation responds only slowly to monetary shocks. If actual inflation responds gradually, so should expectations. Thus, the evidence does not appear supportive of theories that require monetary shocks to affect labor-supply decisions and output by causing shifts in expected inflation.
In this chapter,... we move from the general equilibrium models built on the joint foundations of individual optimization and flexible prices to the class of general equilibrium models built on optimizing behavior and nominal rigidities that are employed in most discussions of monetary policy issues. ...
It is easy to see why nominal price stickiness is important. As we have seen in the previous chapters, the nominal quantity of money affects equilibrium in two ways.
First, its rate of change affects the rate of inflation. Changes in expected inflation affect the opportunity cost of holding money, leading to real effects on labor-leisure choices and the choice between cash and credit goods. However, these substitution effects seem small empirically. Second, money appears in ... the form of real money balances. If prices are perfectly flexible, changes in the nominal quantity of money via monetary policy actions will not necessarily affect the real supply of money. When prices are sticky, however, changing the nominal stock of money does initially alter the real stock of money. These changes then affect the economy's real equilibrium. Short-run price and wage stickiness implies a much more important role for monetary disturbances and monetary policy. ...