In his original presentation of the natural-rate hypothesis, Friedman discussed another, more reaUstic, example of how the behavior of core inflation may depend on the environment: how rapidly core inflation adjusts to changes in inflation is likely to depend on how long-lasting actual movements in inflation typically are. If this is right, then in a situation like the one that Phillips studied, where there are many transitory movements in inflation, core inflation will vary little; the data will therefore suggest a stable relationship between output and inflation. But in a setting like the modem United States, where there are sustained periods of high and of low inflation, core inflation will vary more, and thus there will be no consistent link between output and the level of inflation.

Carrying these criticisms of (5.36)-(5.37) to their logical extreme would suggest that we replace core inflation in (5.36) with expected inflation:

TTt = Trf + A(ln Yt - InTf) + ff, (5.38)

where Trf is expected inflation. This formulation captures the ideas in the previous examples. For example, (5.38) implies that unless expectations are grossly irrational, no policy can permanently raise output above its natural rate, since that requires that workers and firms forecasts of inflation are always too low. Similarly, since expectations of future inflation respond less to current inflation when movements in inflation tend to be shorter-lived, (5.38) is consistent with Friedmans example of how the output-inflatton relationship is likely to vary with the behavior of actual inflation.

Nonetheless, modern Keynesian analyses generally do not use the model of aggregate supply in (5.38). The central reason is that, as we will see in Part A of Chapter 6, if one assumes that price- and wage-setters are rational in forming their expectations, then (5.38) has strong implications-implications that, at least in the view of Keynesian economists, are not supported by the data. Alternatively, if one assumes that workers and firms do not form their expectations rationally, one is resting the theory on irrationality.

A natural compromise between the models of core inflation in (5.37) and in (5.38) is to assume that core inflation is a weighted average of past inflation and expected inflation. With this assumption, the short-run aggregate supply curve is given by

TTt = +{1- ) 1 + A(ln Yt - In Yt) + f f, 0 < < 1. (5.39)

Modern Keynesian theories typically allow for the possibility that is positive-that is, they let core inflation not just be a mechanical function of past inflation. But they typically also assume that is strictly less than 1. Thus the theories assume that there is some inertia in wage and price inflation. That is, they assume that there is some link between past and future inflation beyond effects operating through expectations.

The theories usually stop short, however, of specifying models of aggregate supply that are intended to hold generally. Instead, the models

largely fall Into two groups. The ftrst group consists of models where some type of aggregate supply curve or nominal stickiness is built up from specific assumptions about the microeconomic environment. These models (such as those of Section 5.4) typically have strong forms of nominal rigidity; they are mtended to illustrate particular issues but not to provide good approximations to actual behavior. We will encounter many of these models in the next chapter. The second group of models consists of specific formulations, such as the one in (5.36)-(5.37), that are intended to be useful summaries of aggregate supply behavior in specific situations but that are not intended to be universal.

The failure of modern Keynesian theory to develop a general model of aggregate supply makes the theory harder to apply in novel situations. It also, by making the models less precise, makes them harder to confront with the data-a point we will return to at the end of the next chapter.

5.6 Empirical Application: Money and Output

Perhaps the most important difference between real and Keynesian theories of fluctuations involves their predictions concerning the effects of monetary changes. In real-business-cycle models, purely monetary disturbances have no real effects. In Keynesian models, they have important effects on employment and output.

This observation suggests a natural test of real versus Keynesian theories: why not just regress output on money? Such regressions have a long history. One of the earliest and most straightforward money-output regressions was carried out by Leonall Andersen and Jerry Jordan of the Federal Reserve Bank of SL Louis (Andersen and Jordan, 1968). For that reason, the regression of output on money is known as the St. Louis equation.

Here we consider an example of the St. Louis equation. The left-hand-side variable is the change in the log of real GNP. The main right-hand-side variable is the change in the log of the money stock, as measured by Ml; since any effect of money on output may occur with a lag, the contemporaneous and four lagged values are included. The other right-hand-side variables are a constant, a time trend (to account for trends in output and money growth), and seasonal dummies (to control for regular seasonal movements in the variables). The data are quarterly, and the sample period is 1948-1989.

The results are

1 = 0.0070 + 0.18 AlnrHf-H 0.19 Ahimt-i (0.0022) (0.10) (0.10)

+ 0.29 Alnmf-2- 0.00 Ainmti + 0.01 Alnm, 4 (5.40) (0.10) (0.10) (0.10)

Similarly, suppose that monetary and fiscal policy are coordinated, so that the two usually move in the same direction. Then if fiscal policy affects real output, there will be a relationship between monetary policy and output movements even if monetary changes do not have real effects.

The classic reference is Goldfeld (1976).

- O.OOOlOt + 0.0043 Dlf + 0.0022 D2t + 0.0029 D3t, (0.00003) (0.0023) (0.0023) (0.0023)

= 0.113, D.W. = 1.28, s.e.e. = 0.010,

where the numbers in parentheses are standard errors. The sum of the coefficients on the current and four lagged values of the money-growth variable is 0.66, with a standard error of 0.28. Thus the estimates suggest that a 1% increase in the money stock is associated with an increase of % in output over the next year, and the null hypothesis of no association is rejected at high levels of significance.

Does this regression, then, provide powerful evidence in support of monetary over real theories of fluctuations? The answer is no. There are several basic problems with a regression like this one. First, causation may run from output to money rather than from money to output. A simple story, formalized by King and Plosser (1984), is that when firms plan to increase production, they may increase their money holdings because they will need to purchase more intermediate inputs. Similarly, households may increase their money holdings when they plan to increase their purchases. Aggregate measures of the money stock, such as Ml, are not set directly by the Federal Reserve but are determined by the interaction of the supply of high-powered money with the behavior of the banking system and the public. Thus shifts in money demand stemming from changes in firms and households production plans can lead to changes in the money stock. As a result, we may see changes in the money stock in advance of output movements even if the changes in money are not causing the output movements.

The second major problem with the St. Louis equation involves the determinants of monetary policy. Suppose the Federal Reserve adjusts the money stock to try to offset other factors that influence aggregate output. Then if monetary changes have real effects and the Federal Reserves efforts to stabilize the economy are successful, we will observe fluctuations in money without movements in output (Kareken and Solow, 1963). Thus, just as we cannot conclude from the positive correlation between money and output that money causes output, if we fail to observe such a correlatton we cannot conclude that money does not cause output.

The third difficulty with the St. Louis equation is that there have been a series of large shifts in the demand for money over the past two decades. At least some of the shifts are probably due to financial innovation and deregulation, but their causes are not entirely understood. If the Federal Reserve