Edward Renshaw
Professor of Economics
State University of New York at Albany
In this essay we will continue to assume that the US economy is reasonably competitive (or regulated to the point of approximating that objective) and that the aggregate supply curve is equivalent to a marginal cost equation which holds technology, capital input and the nominal wage rate constant and can be derived from a Cobb-Douglas production function with constant returns to scale.
While these assumptions may not be exactly correct they have many advantages from a pedagogical point of view such as: (a) simplicity, (b) compatibility, (c) mathematical tractability, (d) linkages between variables that are probably correct from a directional point of view even if the economy is not perfectly competitive or the production function truly Cobb- Douglas, (e) ease with which the equations for these curves can be linked to other ideas in macroeconomics, and (f) the prospect of being able to push the theory of aggregate demand and supply far enough to be useful and exciting from an empirical point of view. A simplified version of the supply growth equation which was derived in Essay 8 is especially useful when it is combined with a shifting Phillips curve to estimate a natural unemployment rate where, in the absence of supply shocks, there is no tendency for the inflation rate to either accelerate or decelerate.
Nobel laureate Robert Solow has noted, in a personal communication, that the supply curve derived from the Cobb-Douglas production function with constant returns to scale implies a short run real-wage elasticity of demand for labor equal to: - 1/(1-b).
When "b" equals 2/3 this implies an elasticity of 3 which is much too large to be supported by common observation, especially during periods of recovery from an economic recession. At that point in the business cycle most companies have a surplus of capital and workers that are not fully employed and can expand their output very rapidly without hiring much additional labor.
The implication is that the demand curve for labor is not something that can be neatly derived from a production function that ignores the costs of hiring, firing and retraining new employees. This would be a serious criticism of the supply-side economics examined in this set of essays if our primary goal was to provide a detailed explanation of what happens in the labor market.
The beauty of the supply curves that can be derived from Cobb-Douglas production functions, however, is their flexibility. By altering one's assumptions in a very simple way one can easily obtain supply functions and derived demand equations for labor and capital that range all the way from being perfectly elastic to perfectly inelastic.
When wages are assumed to be variable and equal to an expected price level (Pe) one can set Pe equal to the actual price level in the short run aggregate marginal cost equation (5), that was derived in Essay 8 for a competitive world, and quickly obtain the vertical supply curve that is so dear to the hearts of some rational expectationists. When Pe is assumed to be a function of lagged prices, however, one doesn't get the nice spirally adjustments to a permanent shift in the growth rate for nominal GDP that Robert Gordon in his early editions of Macroeconomics was so fond of.
When expectations are adaptive our log linear supply curve implies that there can be "permanent output and employment effects" associated with a change in the growth rate for nominal GDP. The evidence in support of permanent effects is most apparent in connection with recessions.
Bluestone and Harrison reported in (1982) that with every one percent increase in the U.S. unemployment rate, 920 more people commit suicide, 650 commit homicide, 500 die from heart and kidney disease and cirrhosis of the liver, 4000 are admitted to state mental hospitals and 300 are sent to state prisons. There are a total of 37,000 more deaths and 20,000 more heart attacks. Unemployed workers are also more likely to experience dizziness, rapid heart beat, troubled sleep, back and neck pain and high blood pressure.
By making the capital stock a function of investment and investment dependent upon the interest rate one can show that lower interest rates, other things equal, should help to shift the aggregate supply curve to the right. By letting the autonomous shift variable be a function of energy consumption and letting the amount of energy consumed be a negative function of the price of energy one can incorporate the idea of energy supply shocks into this representation of supply-side economics.
There can also be some advantages in making supply-side economics simpler rather than more complicated. In Essay 8 we emphasized the marginal cost or supply growth equation:
%P = -%b + [(1-b)/b]%Q - [1/b]%A - [(1-b)/b]%K + %W (1)
The coefficient, b, in this equation is the share of GDP going to labor. While this share has been remarkably constant over long intervals of time, which bridge years of peak prosperity, it is rather unstable on a year-to-year basis. A number of studies have shown, however, that labor productivity and the share of GDP going to labor tend to be cyclical in character and inversely related to each other in the short run (Okun, 1981).
One implication of this inverse relationship is that the gains from improved technology and changes in other resources that have been left out of the Cobb-Douglas production function will tend to be distributed to consumers and/or labor at a fairly steady growth rate. We will assume that the percentage change in the share of GDP going to labor plus its reciprocal multiplied by the percentage change in the autonomous shift variable, A, can be decomposed into a steady growth rate, q, and a more random error or supply shock component, s:
%b + [1/b]%A = q - s (2)
When the log linear production function is characterized by constant returns to scale, the percentage change in capital input and the percentage change in output in the marginal cost equation will have the same coefficient, (1-b)/b, but opposite signs. In the analysis which follows we will assume that a portion of the capital stock can be unemployed and that the flow of productive services from the employed stock will fluctuate in proportion to changes in real GDP so that:
%K = %Q (3)
While it may not be realistic to assume that the capital input, output ratio is always constant, it is reasonable to suppose that an upward trend in this ratio will increase q and that unsystematic changes will be picked up by the shock term, s. Substituting assumptions (2) and (3) into equation (1) gives us the simplified marginal cost or "supply growth" equation:
%P = %W - q + s (4)
When q and s are both equal to zero, the inflation rate will be equal to the growth rate for wages or labor compensation. In column (1) of Table 9.1 we show the December-December growth rates for the Department of Labor's employment cost index representing total compensation in private industry. Dec.-Dec. growth rates for the all item CPI less food and energy, the so-called core inflation rate, are shown in column (2) and the differences in these two growth rates are shown in column (3).
Over the 17 year period from 1979-96 the growth of compensation was about equal, on the average, to the core inflation rate in spite of some variation from one year to the next. The largest discrepancies occurred from 1980-82 when the Fed tightened credit enough to tip the US economy into back to back recessions in a successful effort to end the specter of double digit inflation.
Between 1979 and 1985 the trade weighted value of the US dollar appreciated more than 60 percent before gradually sinking to a more normal level. This in turn made US exporters less competitive and led to an explosive growth of imports which damaged the bargaining power of workers in many industries from 1984 to about 1992.
The data in the first three columns of Table 9.1, however, would strongly suggest that the most important determinant of inflation in the long run is the growth rate for labor compensation.
The good news with regard to the possibility of a wage-price spiral is that cost of living escalator clauses have gone out of fashion making wage inflation less responsive to food and energy price shocks. In 1990, for the first time since 1960, the growth of average hourly earnings slowed during a year containing a peak in business activity. High unemployment in Europe and most developing countries and the globalization of manufacturing have made many industrial unions more concerned about job security than a possible resumption of wage-price inflation.
Since the publication of an article by Edmund Phelps in (1967) on expectations of inflation and optimal unemployment over time and Nobel Laureate Milton Friedman's presidential address before the American Economic Association in (1968), the notion of a natural unemployment rate has become a central part of macroeconomics (Cross 1995). This rate is often thought of as being equal to the unemployment rate that will keep inflation from accelerating or decelerating in the absence of economic recessions and other adverse developments such as crop failures and oil price shocks.
George Perry of the Brookings Institution was one of the first to recognize in (1970) that changes in the composition of the labor force can affect the aggregate unemployment rate. There is no consensus, however, as to how one should estimate the natural unemployment rate (Renshaw 1991 and 1995) and those estimates which have been published from time to time have sometimes varied a great deal. In this essay we will use equation (4) and a shifting Phillips curve to obtain an estimate of the natural unemployment rate.
Phillips (1958) was among the first economists to show that the growth of labor compensation is significantly influenced by changes in the unemployment rate. In the 1970s, however, the Phillips curve became in the words of Arthur Okun, "an unidentified flying object." Okun (1981), on the other hand, is also noted for the observation that we all operate, more or less, with a "view of lagging and shifting short run Phillips curves."
Browne (1989) has shown that a large part of the shift in the Phillips curve can be explained on the basis of a lagged inflation rate. From 1980- 96 the Dec.-Dec. increases in the employment cost index minus the core inflation rate in the preceding year in column (4) of Table 9.1 were about equal to 2.696 percentage points minus a little less than one-half of the December unemployment rate:
%W - %P(-1) = 2.696 - .473U (5)
When this version of the shifting Phillips curve is substituted into our supply growth equation (4), when both q and s are assumed to be equal to zero, we obtain:
%P = %P(-1) + 2.696 - .473U (6)
What is probably an upper limit to the "natural" or "full" employment rate for the US economy can now be obtained by letting, %P = %P(-1), and solving the remainder of equation (6) for U = 2.696/.473 = 5.7 percent. This estimate turns out to be the same as an estimate obtained by Geoffrey Tootell, an economist at the Federal Reserve Bank of Boston, in (1994). He concluded that the natural rate was probably in the vicinity of 5.7 percent at the end of 1993. For a more recent collection of essays on the natural rate with some estimates a bit lower than 5.7 percent see the Journal of Economic Perspectives Winter 1997.
Since the economic recession of 1990-91 the employment cost index has been increasing about .2 percent faster that the CPI without food and energy. When q in equation (4) is assumed to equal .2 and equation (5) is substituted into (4) our estimate of the natural unemployment rate is reduced to only 5.3 percent.
The important point, however, is not this conclusion but the fact that by subtracting the preceding year's inflation rate from the current year's growth of compensation one can quickly verify Browne's finding that there is an inverse relationship between these differences and the unemployment rate and that by substituting the resulting relationship into a simplified supply growth equation such as equation (4) obtain an estimate of the natural unemployment rate. If it is presumed that some of the benefits from improvements in productivity will accrue to labor in the future, "q" in equation (4) will be positive and estimates of the natural unemployment rate will be less than when q is assumed to be equal to zero.
Theory based estimates of the natural unemployment rate, however, should always be supported by a more pragmatic look at the data. In Table 9.2 the first differences associated with the all item CPI inflation rate are rank ordered in terms of the average values of the civilian unemployment rate. The data in this table suggest that economic recessions have been the only "sure cure" for inflation. Since 1948 we have never had an increase in the CPI inflation rate in any year containing a recessionary trough in economic activity as defined by the National Bureau of Economic Research.
When the civilian unemployment rate has been in excess of 6.2 percent, the inflation rate for the CPI has almost always declined or remained very stable. The only notable exception is 1977 when the US economy was still recovering from the prolonged recession of 1973-75 and a slump in the growth of labor productivity caused the index of labor cost per unit of output in manufacturing to accelerate from a depressed 2.9 percent in 1976 to 6.5 percent.
Changes in unit labor cost have the distinction of being one of the best inflation indicators--in the absence of major wars, crop failures and oil price shocks in the midst of prosperity. In column 3 of Table 9.2 we identify those years when the CPI inflation rate may have been adversely affected by increases in labor costs amounting to 3.3 percent or more. Large increases in food and energy prices are also identified. When changes in the inflation rates are examined from this perspective one is left with the impression that the unemployment rate might have been reduced to five percent or less in the 1980s--without triggering a big increase in the inflation rate--if it weren't for the oil price shocks of 1987, 1989 and 1990 when the average price of crude oil increased 23.1, 26.1 and 26.3 percent respectively.
The case for optimism with regard to an eventual return to a lower unemployment rate (in the absence of food and energy price shocks) is bolstered somewhat by the slow recovery from the recession of 1990-91 and the fact that the year-to-year growth rates for payroll employment are a better inflation indicator than the unemployment rate, by itself. See Table 9.3.
During the 14 years when payroll employment increased by 3.3 percent or more there was only one year (1959) when the inflation rate declined and that decline only amounted to a dip of one-tenth of a percentage point.
It should also be noted the US has seldom experienced an increase in the all item CPI inflation rate when the year-to-year growth in payroll employment was less than 2.5 percent unless there was an increase in domestic crude oil prices amounting to 20 percent or more (as was the case in 1974, 1990 and 1996). The only other exception from 1949-95 is 1963, when the all item inflation rate for the CPI temporarily accelerated by .3 percentage points in response to higher prices for services and some commodities. Higher grain and oil prices, though, could make 1996 another exception.
Since 1989 payroll employment has been increasing at an average rate of about 1.5 percent per year. Though anemic by past standards this rate is about fifty percent higher than the one percent growth rate for the adult population 16 and over from which our official labor force is recruited.
The economic recession of 1990-91 and the slow recovery of employment opportunities help to explain the downward drift in the inflation rate for the all item CPI from 6.1 percent in 1990 to only 2.5 percent in 1995.
Layoffs at many business enterprises and a comparatively slow improvement in overall employment opportunities have harmed some workers and their families. This has encouraged some economists and business leaders to criticize central banks in the more industrialized countries for keeping interest rates high and depressing job markets (Wilke 1996).
There is an encouraging possibility, however, that a "slower and more steady employment growth rate" might make it possible to eventually bring the unemployment rate in the US down to about the 5.0 percent level without triggering a big increase in the inflation rate--in the absence of rapidly rising food and energy prices. History would suggest, in any event, that production bottlenecks and inflationary increases in labor cost per unit of output are less likely to occur when employment opportunities are increasing at a moderate pace than when the economy is growing at an unsustainable rate.
Bluestone, Barry and Bennett Harrison (1982). The Deindustrialization of America(New York: Basic Books), Chapter 3.
Browne, Lynn (1989). "The Labor Force, Unemployment Rates, and Wage Pressures," New England Economic Review, January, 21-29.
Cross, Rod (1995). The Natural Rate of Unemployment: Reflections on 25 Years of the Hypothesis(New York: Cambridge University Press).
Friedman, Milton (1968). "The Role of Monetary Policy," American Economic Review, March, 1-17.
Gordon, Robert (1990). Macroeconomics(Boston: Little Brown), Chapter 11.
Okun, A. (1981). Prices and Quantities: A Macroeconomic Analysis(Washington, D. C.: The Brookings Institution), 2.
Perry, George (1970). "Changing Labor Markets and Inflation," Brookings Papers on Economic Activity, 3, 411-41.
Phelps, Edmund (1967). "Phillips Curves, Expectations of Inflation, and Optimal Unemployment Over Time," Economica, August, 254-81.
Phillips, A. W. H. (1958). "The Relation Between Unemployment and the Rate of Change in Money Wage Rates in the United Kingdom, 1861-1957," Economica, November, 283-99.
Renshaw, Edward. (1991). "Estimating the Natural Unemployment Rate," New York Economic Review, Fall, 3-13.
----- (1995). "The Natural Rate of Unemployment: Can It Be Estimated with Any Confidence?" Journal of Policy Modeling.
Tootell, Geoffrey (1994). "Restructuring the NAIRU, and the Phillips Curve," CITE>New England Economic Review, Sept./Oct., 31-44.
Wilke, John (1996). "Global Austerity: War on Inflation Curbs World-Wide Growth Too Much Some Say," The Wall Street Journal, April 10, A1 & A12.
Dec.-Dec. % Changes
Year ------------------- Col. (1) Col. (1) December
Employ. CPI Less Minus Minus Unemployment
Cost Food and Col. (2) Col. (2) Rate
Index Energy Lagged
(1) (2) (3) (4) (5)n
1980 9.6 12.2 -2.6 -1.7 7.2
1981 9.9 9.5 .4 -2.3 8.5
1982 6.5 4.5 2.0 -3.0 10.8
1983 5.7 4.8 .9 1.2 8.3
1984 4.9 4.7 .2 .1 7.3
1985 3.9 4.3 - .4 - .8 7.0
1986 3.2 3.8 - .6 -1.1 6.6
1987 3.3 4.2 - .9 - .5 5.7
1988 4.8 4.7 .1 .6 5.3
1989 4.8 4.4 .4 .1 5.4
1990 4.6 5.2 - .6 .2 6.2
1991 4.4 4.4 .0 - .8 7.2
1992 3.5 3.3 .2 - .9 7.3
1993 3.6 3.2 .4 .3 6.5
1994 3.1 2.6 .5 - .1 5.4
1995 2.6 3.0 - .4 .0 5.6
1996 2.9e 2.6 .3 - .1 5.3
(5)n. When the December unemployment rate and a constant term are regressed on the differences in column (4) for the 1980-96 period we obtain:
%W - %P(-1) = 2.696 - .473U
(2.669) (-3.249)
Source of basic data: Economic Report of the President.
Year Civilian CPI First Differences CPI Inflation Rate
Unemployment Inflation Current Following
Rate Rate Year Year
1982 9.7 3.8 -5.1T .0
1983 9.6 3.8 .0 .1
1975 8.5 6.9 -5.4T -2.0
1976 7.7 4.9 -2.0 1.8
1981 7.6 8.9 -3.6 -5.1
1984 7.5 3.9 .1Lc - .1
1992 7.5 2.9 - .2 - .2
1985 7.2 3.8 - .1 -2.7
1977 7.1 6.7 1.8Lc 2.3
1980 7.1 12.5 - .8T -3.6
1986 7.0 1.1 -2.7 3.3
1993 6.9 2.7 - .2 .0
1958 6.8 1.8 -1.1T - .1
1991 6.8 3.1 -3.0T - .2
1961 6.7 .7 - .7T .6
1987 6.2 4.4 3.3Oil .0
1978 6.1 9.0 2.3Food 4.3
1994 6.1 2.7 .0 - .2
1949 5.9 -2.1 -5.1T 8.0
1971 5.9 3.3 -2.3 .1
1979 5.8 13.3 4.3Food,Lc,Oil - .8
1963 5.7 1.6 .3 - .6
1974 5.6 12.3 3.6Lc,Oil -5.4
1972 5.6 3.4 .1Food 5.3
1990 5.6 6.1 1.5Oil -3.0
1995 5.6 2.5 - .2 .8
1954 5.5 - .7 -1.4T 1.1
1959 5.5 1.7 - .1 - .3
1960 5.5 1.4 - .3 - .7
1962 5.5 1.3 .6Lc .3
1988 5.5 4.4 .0 .2
1996-------- 5.4--------- 3.3----------- .8Oil---------- ?
1950 5.3 5.9 8.0Lc,War .1
1989 5.3 4.6 .2Oil 1.5
1964 5.2 1.0 - .6 .9
1970 4.9 5.6 - .6T -2.3
1973 4.9 8.7 5.3Food,Lc,Oil 3.6
1965 4.5 1.9 .9 1.6
1955 4.4 .4 1.1 2.6
1957 4.3 2.9 - .1 -1.1
1956 4.1 3.0 2.6Lc - .1
1966 3.8 3.5 1.6Lc,War - .5
1967 3.8 3.0 - .5 1.7
1968 3.6 4.7 1.7Lc 1.5
1969 3.5 6.2 1.5 - .6
1951 3.3 6.0 .1Food,Lc -5.2
1952 3.0 .8 -5.2 - .1
1953 2.9 .7 - .1Lc -1.4
Footnotes for Table 9.2
Food: identifies years when the prices received by farmers for all products increased by ten percent or more.
Lc: identifies years when the percentage change in labor cost per unit of output in manufacturing increased by 3.3 percentage points or more.
Oil: identifies years with a 14 percent or more increase in domestic crude oil prices during years when the average unemployment rate was less than 6.5 percent.
T: identifies years containing a recessionary trough in economic activity as defined by the National Bureau of Economic Research.
War: identifies years when the inflation rate may have been adversely affected by a major military build-up.
Source: This table was first published in Edward Renshaw, "Unemployment and Consumer Price Inflation," Challenge, March-April 1994, pp. 59-61. The basic data are from the Economic Report of the President.
Year Payroll CPI First Differences CPI Inflation Rate
Employment Inflation Current Following
Growth Rate Year Year
1951 5.8 6.0 .1 -5.2
1966 5.2 3.5 1.6 - .5
1978 5.1 9.0 2.3 4.3
1984 4.7 3.9 .1 - .1
1965 4.3 1.9 .9 1.6
1973 4.2 8.7 5.3 3.6
1977 3.9 6.7 1.8 2.3
1959 3.8 1.7 - .1 - .3
1969 3.7 6.2 1.5 - .6
1979 3.6 13.3 4.3 - .8
1972 3.5 3.4 .1 5.3
1955 3.4 .4 1.1 2.6
1956 3.4 3.0 2.6 - .1
1950 3.3 5.9 8.0 .1
1968 3.2 4.7 1.7 1.5
1976 3.2 4.9 -2.0 1.8
1985 3.2 3.8 - .1 -2.7
1988 3.2 4.4 .0 .2
1994 3.1 2.7 .0 - .2
1967 3.0 3.0 - .5 1.7
1953 2.9 .7 - .1 -1.4
1962 2.9 1.3 .6 .3
1964 2.9 1.0 - .6 .9
1995 2.7 2.5 - .2 .8
1987 2.6 4.4 3.3Oil .0
1989 2.6 4.6 .2 1.5
1952 2.0 .8 -5.2 - .1
1963 2.0 1.6 .3 - .6
1986 2.0 1.1 -2.7 3.3
1993 2.0 2.7 - .2 .0
1996------- 2.0-------- 3.3--------- .8Oil------ ?
1974 1.9 12.3 3.6Oil -5.4
1960 1.7 1.4 - .3 - .7
1990 1.4 6.1 1.5Oil -3.0
1957 .9 2.9 - .1 -1.1
1981 .8 8.9 -3.6 -5.1
1970 .7 5.6 - .6 -2.3
1983 .7 3.8 .0 .1
1980 .6 12.5 - .8 -3.6
1971 .5 3.3 -2.3 .1
1992 .2 2.9 - .2 - .2
1961 - .4 .7 - .7 .6
1991 -1.1 3.1 -3.0 - .2
1975 -1.7 6.9 -5.4 -2.0
1982 -1.8 3.8 -5.1 .0
1954 -2.4 - .7 -1.4 1.1
1949 -2.5 -2.1 -5.1 8.0
1958 -2.9 1.8 -1.1 - .1
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