to the retrospective-prospective entry of living costs into wage inflation. The separate processes by which these elements enter have not and probably cannot be identified. Therefore, for example, the equation for wage inflation (2) is derived from several elementary but unspecified relations designating:

1. The wage response to unanticipated inflation (i.e., unexpected real income losses) in the past.

2. The wage response to expected current inflation.
3. The mechanism by which expectations are generated.

The inflation severity factor, represented here by (PP--ß3),

2

B3 attempts to capture the changes in these substructures which occur when a severe, persistent inflation is generated.

The empirical analysis yields several significant facts about these coefficients:

1. a1+a2=a3. This reflects the equivalent price response to cost inflation induced by changes in input price and in productivity.

2. aa2=a3=1. This indicates the complete (unitary) transmission of cost changes into price changes or a stable distribution of output among factors.

3. B1. This denotes the incomplete sensitivity of money wages to moderate inflation.

4. 80. Together with B,<1, the response of money wage change to excess demand or supply in the labor market yields the unemployment-inflation tradeoffs available at high unemployment rates. The value of B1 creates the potential for explosive inflation if demand policy puts pressure on labor resources.

5. B+82-1. This precludes a stationary equilibrium value for inflation at unemployment rates below 4%. It represents the complete marginal transmission of high level price inflation into wage inflation.

6. B3, the critical value for average annual inflation, is approximately 2.5.

A two-track model.-The structure of the inflation severity factor

captures the change in wage sensitivity to prices. (P+P1- - B2)

2

is the difference between average annual inflation and the estimated critical value. Given that this difference is included only if positive, i.e., if inflation is designated "severe," equation (2) will yield a markedly different tradeoff in periods of persistent inflation than in periods of relative price stability. The wage equations are the following: (2a) if inflation is non-severe:

We first solve the model for p, in terms of u, ignoring the lags. The corresponding Phillips Curves are: (3a) non-severe inflation:

1

(a1tan) B1] [(αst as) Bot (au+as) B1 (1/u)—a,g)]
;] [(as+as)

The empirical result that (a,+a2) B1 is less than one but greater than zero assures us of the existence of a stable set of unemploymentinflation possibilities.

(36) severe inflation:

According to the statistical estimates, division by the bracketed term on the left is now impossible in that this term is insignificantly different from zero.2 (a+a2) equals one, as noted above, to reflect the full transmission of cost increases to prices. If inflation is severe, (B1+B2) = 1 and the marginal effect of living cost inflation on wage demands is unitary. The inflation term therefore drops out of the formula and the rate of unemployment is determined by the trend rate of productivity increase and the structure of the labor market:

Given the historically estimated values of the parameters and trend productivity, the minimum stationary value for u is approximately 4.2 percent.

The notion of two tracks, and only two, is undoubtedly subject to question. A better formulation, if the data had permitted, might have been a multiple track version recognizing several ranges of severity. But even as estimated, the model is not as dichotomous as these condensed versions might suggest. The lag structures in wage and price equations extend four to eight periods and lend flexibility to the transition. Furthermore, the condensed versions may give a false first impression: that if price inflation is greater than 2.5 percent, the price component of wage inflation is the full value of current and past increases in the cost of living whereas if price inflation is less than 2.5 percent, only B2 percent (approximately 50 percent in the context of this model) is represented in higher wage costs. But only the marginal effect of sustained inflation above 2.5 percent is unitary, not the average effect, and the marginal effect of the current single year inflation is only approximately 0.75.

The role of lags.-Recognizing that a2=-(1-a1), equation (1) can be easily rewritten to clarify the source of relatively flat short run

curves:

2-1

: The tradeoff becomes progressively steeper in models of this type as the product (a+a2) (B1+B2) approaches unity. This is the reason the long run Phillips Curve sketched in the previous section is not strictly vertical. The estimated sum of the unit labor cost coefficients in the output price equation (corresponding to X1+X2) is 1.000. The sum of the living cost coefficients in the wage equation corresponding to (8182) is 0.992. The price bridge equation transmits only 94% of output price inflation into consumption price inflation. Therefore the product equivalent to (ai+a:) (B1+B22) is only 0.94 rather than unity.

In an expansion, current wage inflation will exceed past wage inflation, hence (w1-1-w) will be negative and price change will be less than the long run value corresponding to the current cost change. The larger the relative weight of lagged cost increases (a2), the flatter the short run Phillips Curve will be relative to the long run curve. This effect is augmented in the labor market by the presence of lagged price elements representing the incomplete adaptation of expectations to accelerating prices.

A contraction presents the opposite problem: the delayed responses retard the cooling-off process initiated by restrictive demand policies. The best way to visualize the result is to think of a cycle beginning at high unemployment. As unemployment is reduced, a path below the steady-state curve is pursued. Assume unemployment below the critical rate has been achieved with little inflation. If policy makers fail to perceive the source of their good luck-the lagged responsesand seek to maintain the low unemployment rate, inflation will accelerate.

G. FURTHER EXPLORATION OF THE SEVERITY FACTOR

The sensitivity of the severity index format actually adopted to the choice of the critical value of inflation and to the exponent to which the positive excess of inflation over this value is raised was indicated earlier in the table presenting the sums of squared residuals (ch. III, table 5). Figure 13 below indicates that the implicit steady-state Phillips Curves are not significantly shifted or altered by such changes. The left hand panel presents the options for critical values of 3 percent, 5 percent, and 7 percent (corresponding to average annual inflation rates of 1.5 percent, 2.5 percent, and 3.5 percent) combined with a unit exponent, while the right hand panel indicates similar curves when an exponent of 2 is used. The left hand integer within the parentheses indicates the exponent and the right hand number designates the critical value. It can be seen that the range of results is disappointingly narrow. Any of the equations which had comparably good statistical qualities historically show the critical rate of unemployment to fall between 3.8 percent and 4.2 percent.

While these results indicate a robustness to the estimates of the critical unemployment rate, the results should not be over-interpreted, of course. The historical period on which the model is based runs only from 1955 to 1971. The inflation severity factor took on small values in the later years of the inflation of the mid-1950's, but showed large values only in the three year episode at the end of the 1960's. Thus, in some crude sense, it can be considered to be only one observation of the critical process of forming inflationary expectations. We have now begun studies to test the same ideas in earlier historical episodes.

H. THE LONG-RUN PHILLIPS CURVE IN A FLUCTUATING ECONOMY

The long run Phillips Curve estimated above assumes that the economy has a constant unemployment rate; in other words, that the level of real demand grows at the same rate as the rate of potential output. The actual economy contains lots of fluctuations. At least three characteristics of the model produce a somewhat worse long run Phillips Curve if the unemployment rate fluctuates:

INFLATION RATE

First, the effect of the demand variable in the price equation, the ratio of the real volume of orders to capacity, is asymmetrical. When orders build up there is an extra increase in prices; when orders decline there is no offsetting reduction. In a fluctuating economy there will be periods when orders do build up and add to prices.

Second, the unemployment variable appears in the nonlinear inverse form used in most studies, a form which is superior statistically. If unemployment varies around an average value, the impact on wages will be greater than if it remained at the average. The nonlinearity introduces an asymmetry, such that the positive wage deviation when the unemployment rate is below average is greater than the negative deviation caused by an equal variation in the unemployment rate above its mean. Third, in a fluctuating economy, with an average unemployment rate not too far removed from the critical rate, there will be periods when the actual unemployment falls below the critical value bringing the severity factor into play.

If the labor market pressure is sustained long enough to generate a persistent inflation, the larger wage response will shift the short run Phillips Curve to an inferior position. The wage increases which push behavior into the critical area will be followed by further wage and price increases. However, when unemployment is above average, there is no offsetting intensified effect.

We have not attempted at this stage to develop long run Phillips Curves reflecting these cyclical characteristics. We will pursue this work at a later stage.

Chapter VI. THE CHOICES BEFORE US

The preceding analysis raises difficult questions for policy without offering answers. The basic conclusion, that the Phillips Curve becomes nearly vertical at an unemployment rate near 4 percent is highly pessimistic and would imply no improvement of our potential national goals from the interim goals set eleven years ago.

A. THE LIMITS OF DEMAND POLICIES

Demand management in the United States through fiscal and monetary policies has mainly been a short-term endeavor. Each fall the Administration analyzes the economic outlook for the succeeding year and devises a fiscal program designed to achieve an attainable combination of employment and price goals over a 12 to 18 month period. After a long period of slack, when the price-wage system is in relative stability and the short run Phillips Curve favorable, the government can aim at a low unemployment rate with little fear of a quick inflation. But after the wage-price system is in rapid motion, the short run choices open to demand policy become atrocious. While Administrations may live from day to day, the nation does not. Therefore, demand policy should be based on longer term considerations as identified by the long term Phillips Curve, not the short-term trade-off.

With the existing structure of the economy, the maximum sustainable employment goal appears to be an unemployment rate of approximately 4 percent. This is not an adequate long term employment goal. The structure of unemployment by race, sex and age has improved little in the last ten years, except for an improvement for Negro women. A national goal of 4 percent implies teenager rates of 13 percent for whites and twice that for Negroes. The social costs of unemployment are high. Other countries do better than the United States.

B. THE IMPORTANCE OF STABLE, BALANCED GROWTH

While the long run Phillips Curve is inadequate under conditions of stable growth, it becomes even worse when growth comes in spurts. The asymmetric effect of backlogs of unfilled orders in product markets on price behavior adds to the wage-price spiral in strong periods without corresponding subtraction in weak periods. Sharp changes in the final demand mix, such as capital goods booms or surges of military spending, create sudden changes in the mix of the desired work force which accentuate the rate of wage increase for any given national unemployment rate. Such variations can deteriorate the long run attainable minimum rate of unemployment by several tenths of a point, resulting in a further worsening of the unemployment targets to about 4.5 percent.