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Note: CM = Child mortality, the number of deaths of children under age 5 in a year per 1000 live births. FLFP = Female literacy rate, percent. PGNP = per capita GNP in 1980. TFR = total fertility rate, 1980-1985, the average number of children born to a woman, using age-specific fertility rates for a given year. Source: Chandan Mukherjee, Howard White, and Marc Whyte, Econometrics and Data Analysis for Developing Countries, Routledge, London, 1998, p. 456.

for the period 1861-1957, Phillips obtained a curve whose general shape resembles Figure 6.6b (Figure 6.8).19

As Figure 6.8 shows, there is an asymmetry in the response of wage changes to the level of the unemployment rate: Wages rise faster for a unit change in unemployment if the unemployment rate is below Un, which is

19A. W. Phillips, "The Relationship between Unemployment and the Rate of Change of Money Wages in the United Kingdom, 1861-1957," Economica, November 1958, vol. 15, pp. 283-299. Note that the original curve did not cross the unemployment rate axis, but Fig. 6.8 represents a later version of the curve.

186 PART ONE: SINGLE-EQUATION REGRESSION MODELS

FIGURE 6.8 The Phillips curve.

called the natural rate of unemployment by economists [defined as the rate of unemployment required to keep (wage) inflation constant], and then they fall for an equivalent change when the unemployment rate is above the natural rate, ft, indicating the asymptotic floor for wage change. This particular feature of the Phillips curve may be due to institutional factors, such as union bargaining power, minimum wages, unemployment compensation, etc.

Since the publication of Phillips' article, there has been very extensive research on the Phillips curve at the theoretical as well as empirical levels. Space does not permit us to go into the details of the controversy surrounding the Phillips curve. The Phillips curve itself has gone through several incarnations. A comparatively recent formulation is provided by Olivier Blanchard.20 If we let nt denote the inflation rate at time t, which is defined as the percentage change in the price level as measured by a representative price index, such as the Consumer Price Index (CPI), and UNt denote the unemployment rate at time t, then a modern version of the Phillips curve can be expressed in the following format:

where nt = actual inflation rate at time t nf = expected inflation rate at time t, the expectation being formed in year (t — 1)

20See Olivier Blanchard, Macroeconomics, Prentice Hall, Englewood Cliffs, N.J., 1997, Chap. 17.

UNt = actual unemployment rate prevailing at time t Un = natural rate of unemployment at time t ut = stochastic error term21

Since n is not directly observable, as a starting point one can make the simplifying assumption that = nt—1; that is, the inflation expected this year is the inflation rate that prevailed in the last year; of course, more complicated assumptions about expectations formation can be made, and we will discuss this topic in Chapter 17, on distributed lag models.

Substituting this assumption into (6.7.3) and writing the regression model in the standard form, we obtain the following estimating equation:

where fy = —fi2Un. Equation (6.7.4) states that the change in the inflation rate between two time periods is linearly related to the current unemployment rate. A priori, fy2 is expected to be negative (why?) and fy is expected to be positive (this figures, since fy2 is negative and Un is positive).

Incidentally, the Phillips relationship given in (6.7.3) is known in the literature as the modified Phillips curve, or the expectations-augmented Phillips curve (to indicate that nt—1 stands for expected inflation), or the ac-celeratonist Phillips curve (to suggest that a low unemployment rate leads to an increase in the inflation rate and hence an acceleration of the price level).

As an illustration of the modified Phillips curve, we present in Table 6.5 data on inflation as measured by year-to-year percentage in the Consumer Price Index (CPIflation) and the unemployment rate for the period 1960-1998. The unemployment rate represents the civilian unemployment rate. From these data we obtained the change in the inflation rate (nt — nt—1) and plotted it against the civilian unemployment rate; we are using the CPI as a measure of inflation. The resulting graph appears in Figure 6.9.

As expected, the relation between the change in inflation rate and the unemployment rate is negative—a low unemployment rate leads to an increase in the inflation rate and therefore an acceleration of the price level, hence the name accelerationist Phillips curve.

Looking at Figure 6.9, it is not obvious whether a linear (straight line) regression model or a reciprocal model fits the data; there may be a curvilinear relationship between the two variables. We present below regressions based on both the models. However, keep in mind that for the reciprocal model the intercept term is expected to be negative and the slope positive, as noted in footnote 18.

Linear model: (n - nt-1) = 4.1781 - 0.6895 UNt t = (3.9521) (-4.0692) r2 = 0.3150

21Economists believe this error term represents some kind of supply shock, such as the OPEC oil embargoes of 1973 and 1979.

188 PART ONE: SINGLE-EQUATION REGRESSION MODELS

TABLE 6.5 INFLATION RATE AND UNEMPLOYMENT RATE, UNITED STATES, 1960-1998

Observation

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