Abstract
This Selected Issues paper on the United States explains the behavior of inflation and unemployment during 1997–98. The paper highlights that a simple Philips curve equation relating inflation to the unemployment gap has overpredicted inflation since 1993. The mean forecast error for 1994–97 is greater than zero by an amount equivalent to two-thirds of the standard deviation of the forecast error. The paper also examines the developments in the U.S. stock prices. Alternative approaches to social security reform are also discussed.
I. EXPLAINING THE RECENT BEHAVIOR OF INFLATION AND UNEMPLOYMENT1
1. Low rates of inflation have been recorded in recent years despite a decline in the unemployment rate to levels that previously would have been associated with rising inflation. Indeed, over the period since 1990, there has been a positive correlation between the inflation rate and the unemployment rate, indicating that more than the traditional Philips curve relationship is at work. This phenomenon could be the result of a series of fortuitous, transitory shocks or of a permanent change in the structure of the economy leading to a lower natural rate of unemployment (NAIRU).
2. In order to evaluate these possibilities, alternative estimates of NAIRU were derived and various Philips curve equations were estimated over the period 1960–93, incorporating variables to reflect price shocks (such as changes in import prices and unit labor costs). The alternative measures of the natural rate and the Philips curve equations were then tested to see how well they forecasted inflation over the period 1994–97. The results suggest that the NAIRU may have fallen slightly, but this change, on its own, is not sufficient to explain recent inflation. The main explanation for recent performance of inflation appears to be that there have been a number of favorable price shocks; in particular, the cost of imports has fallen sharply as the dollar has appreciated.
3. A simple Philips curve equation relating inflation to the unemployment gap (the difference between the actual rate of unemployment and NAIRU) has overpredicted inflation since 1993 (Table 1 and the upper panel of Chart 1).2 The mean forecast error for the period 1994–97 is greater than zero by an amount equivalent to two-thirds of the standard deviation of the forecast error. Positive errors would appear to be too pervasive to have been the result of random shocks or measurement error.3
United States: Estimates of the Philips Curve 1/
(1961 Q2–1993 Q4)
The table shows the sum of coefficients on four lags of the variables. The statistic in parentheses is the p-value from a Wald Test of the hypothesis that sum of coefficients on the variable is zero. The lower the p-value, the lower the probability that the variable has no effect on inflation. If, for example, the p-value is 0.04, the null hypothesis of zero effect cannot be rejected at the 1 percent significance level, but it can be rejected at the 5 percent significance level.
Rate of change variables are scaled to measure annualized percentage rate of change.
United States: Estimates of the Philips Curve 1/
(1961 Q2–1993 Q4)
| (1) | (2) | (3) | |
|---|---|---|---|
| Model | Basic Model | Natural Rate Model | Supply Shocks Model |
| Lagged inflation | 1.016 | 1.006 | 1.002 |
| (0.000) | (0.000) | (0.000) | |
| Unemployment gap | -0.246 | -0.361 | -0.255 |
| (0.007) | (0.004) | (0.033) | |
| Change in real unit labor cost | - | - | 0.079 |
| (0.398) | |||
| Change in relative price of imports | - | - | 0.072 |
| (0.001) | |||
| Adjusted R2 | 0.755 | 0.754 | 0.803 |
| Mean forecast error | 0.38 | 0.27 | 0.002 |
| (Standard deviation) | (0.58) | (0.52) | (0.638) |
The table shows the sum of coefficients on four lags of the variables. The statistic in parentheses is the p-value from a Wald Test of the hypothesis that sum of coefficients on the variable is zero. The lower the p-value, the lower the probability that the variable has no effect on inflation. If, for example, the p-value is 0.04, the null hypothesis of zero effect cannot be rejected at the 1 percent significance level, but it can be rejected at the 5 percent significance level.
Rate of change variables are scaled to measure annualized percentage rate of change.
United States: Estimates of the Philips Curve 1/
(1961 Q2–1993 Q4)
| (1) | (2) | (3) | |
|---|---|---|---|
| Model | Basic Model | Natural Rate Model | Supply Shocks Model |
| Lagged inflation | 1.016 | 1.006 | 1.002 |
| (0.000) | (0.000) | (0.000) | |
| Unemployment gap | -0.246 | -0.361 | -0.255 |
| (0.007) | (0.004) | (0.033) | |
| Change in real unit labor cost | - | - | 0.079 |
| (0.398) | |||
| Change in relative price of imports | - | - | 0.072 |
| (0.001) | |||
| Adjusted R2 | 0.755 | 0.754 | 0.803 |
| Mean forecast error | 0.38 | 0.27 | 0.002 |
| (Standard deviation) | (0.58) | (0.52) | (0.638) |
The table shows the sum of coefficients on four lags of the variables. The statistic in parentheses is the p-value from a Wald Test of the hypothesis that sum of coefficients on the variable is zero. The lower the p-value, the lower the probability that the variable has no effect on inflation. If, for example, the p-value is 0.04, the null hypothesis of zero effect cannot be rejected at the 1 percent significance level, but it can be rejected at the 5 percent significance level.
Rate of change variables are scaled to measure annualized percentage rate of change.
UNITED STATES ACTUAL AND PREDICTED CORE CPI INFLATION
(In percent)
Citation: IMF Staff Country Reports 1998, 105; 10.5089/9781451839500.002.A001
UNITED STATES ACTUAL AND PREDICTED CORE CPI INFLATION
(In percent)
Citation: IMF Staff Country Reports 1998, 105; 10.5089/9781451839500.002.A001
UNITED STATES ACTUAL AND PREDICTED CORE CPI INFLATION
(In percent)
Citation: IMF Staff Country Reports 1998, 105; 10.5089/9781451839500.002.A001
4. In order to evaluate the extent to which the poor forecast performance of this Philips curve equation can be attributed to changes in the natural rate of unemployment, a simple semistructural model of the NAIRU was estimated.4 The actual rate of unemployment was regressed on a quadratic time trend, several structural, and several cyclical variables. The structural variables included the dependency ratio,5 an index of minimum wages, and an index of unionization. The cyclical variables included a dummy variable reflecting recessions (as defined by the National Bureau of Economic Research), an index of co-incident indicators of the business cycle, and a variable representing the deviation of capacity utilization from its trend (Table 2).6 An estimate of the NAIRU was then calculated from the estimated equation by setting the cyclical variables equal to zero.
United States: NAIRU Equation
(1961 Q2–1997 Q3)
United States: NAIRU Equation
(1961 Q2–1997 Q3)
| Variable | Coefficient | T-Statistic |
|---|---|---|
| Constant | 2.6 | 0.27 |
| Trend | 0.13 | 1.10 |
| Trend2/1000 | -.69 | -1.49 |
| Dependency ratio | 10.42 | 0.99 |
| Minimum wage | -0.09 | -0.56 |
| Unionization | -25.66 | -2.28 |
| Change in co-incident indicators | 5.42 | 1.84 |
| Capacity utilization | -0.23 | -14.86 |
| Recession | -0.03 | -0.88 |
| Autoregressive error term | 0.95 | 35.59 |
| Adjusted R2 | 0.98 |
United States: NAIRU Equation
(1961 Q2–1997 Q3)
| Variable | Coefficient | T-Statistic |
|---|---|---|
| Constant | 2.6 | 0.27 |
| Trend | 0.13 | 1.10 |
| Trend2/1000 | -.69 | -1.49 |
| Dependency ratio | 10.42 | 0.99 |
| Minimum wage | -0.09 | -0.56 |
| Unionization | -25.66 | -2.28 |
| Change in co-incident indicators | 5.42 | 1.84 |
| Capacity utilization | -0.23 | -14.86 |
| Recession | -0.03 | -0.88 |
| Autoregressive error term | 0.95 | 35.59 |
| Adjusted R2 | 0.98 |
United States: Definitions of Variables 1/
All rates of change are expressed as annual percentage rate of change.
United States: Definitions of Variables 1/
| Variable | Definition |
|---|---|
| Capacity utilization | Capacity utilization of all industry. |
| Coincident indicators | A composite index of coincident indicators. |
| Dependency Ratio | Population less than 15 years of age, plus the population greater than 65 years of age, all divided by the labor force. |
| Import prices | Implicit import price deflator from the national accounts, divided by the GDP deflator. |
| Inflation | Rate of change of CPI for urban consumers excluding the cost of food and energy. |
| Minimum wage | Minimum wage (dollars per hour) deflated by the CPI for urban consumers. |
| Unemployment | Civilian unemployment rate. |
| Unionization | Union membership as a percentage of the civilian labor force. |
| Recession | Indicator of recession as defined by the National Bureau of Economic Research (NBER) |
| Real unit labor costs | The unit labor cost of the nonfarm business sector divided by the GDP deflator. |
All rates of change are expressed as annual percentage rate of change.
United States: Definitions of Variables 1/
| Variable | Definition |
|---|---|
| Capacity utilization | Capacity utilization of all industry. |
| Coincident indicators | A composite index of coincident indicators. |
| Dependency Ratio | Population less than 15 years of age, plus the population greater than 65 years of age, all divided by the labor force. |
| Import prices | Implicit import price deflator from the national accounts, divided by the GDP deflator. |
| Inflation | Rate of change of CPI for urban consumers excluding the cost of food and energy. |
| Minimum wage | Minimum wage (dollars per hour) deflated by the CPI for urban consumers. |
| Unemployment | Civilian unemployment rate. |
| Unionization | Union membership as a percentage of the civilian labor force. |
| Recession | Indicator of recession as defined by the National Bureau of Economic Research (NBER) |
| Real unit labor costs | The unit labor cost of the nonfarm business sector divided by the GDP deflator. |
All rates of change are expressed as annual percentage rate of change.
5. This estimate of the NAIRU is shown in Chart 2, together with the actual level of unemployment and a Holdrick-Prescott filtered unemployment series.7 As can be seen from the chart, the point estimate of the NAIRU has fallen in recent years to below 6 percent, but the two-standard error band around the point estimate is approximately 1.3 percent. This implies that a 95 percent confidence interval would place the NAIRU in 1997 anywhere between just over 4 percent and just under 7 percent.8
UNITED STATES ACTUAL UNEMPLOYMENT RATE AND THE NAIRU
(In percent)
Citation: IMF Staff Country Reports 1998, 105; 10.5089/9781451839500.002.A001
UNITED STATES ACTUAL UNEMPLOYMENT RATE AND THE NAIRU
(In percent)
Citation: IMF Staff Country Reports 1998, 105; 10.5089/9781451839500.002.A001
UNITED STATES ACTUAL UNEMPLOYMENT RATE AND THE NAIRU
(In percent)
Citation: IMF Staff Country Reports 1998, 105; 10.5089/9781451839500.002.A001
6. The estimate of the NAIRU is used to recalculate the unemployment gap and then reestimate the Philips curve. The resulting Philips curve is shown in the second column of Table 1 and in the second panel of Chart 1. If the unemployment rate were to be maintained 1 percentage point above the NAIRU for a year, the inflation rate would fall by one quarter of a percentage point. The second panel of Chart 1 shows the actual and out-of-sample predicted inflation rate for the period 1994–97. It is clear that the reestimated Philips curve still consistently overpredicts the level of inflation.9 This result is not altogether surprising, given the moderate decline in the estimated NAIRU and the size of the coefficient on the unemployment gap variable in the reestimated Philips curve. These estimates imply that the NAIRU would have had to decline to below 3 percent in order to explain recent inflation.
7. Since 1993, the United States has experienced a number of favorable supply shocks (including an appreciation of the U.S. dollar), which have restrained inflation while unemployment has declined. The third column of Table 1 shows the results from a Philips curve equation including supply-shock variables. These shock variables measure changes in the dollar price of imported goods and changes in the real unit cost of labor. The point estimates have the expected signs, and the import price variable is highly significant, but the unit labor cost variable is insignificant at normal significance levels.10 The equation performs substantially better than those without supply shocks in forecasting inflation over the period 1994–97. The average error of the forecast during this period is close to zero, indicating that this equation does not systematically overpredict inflation. This can also be seen from the third panel of Chart 1, which shows actual inflation and the inflation rate predicted by the equation. Comparing this panel with the first two panels of Chart 1 suggests that the recent favorable U.S. inflation performance has been largely due to falling import prices and not to fundamental structural changes in the economy.
8. Further evidence for this hypothesis can be found by looking at how the price of imports has changed over the last eight years. Chart 3 shows both the level and the rate of change of the relative price of imports (defined as the implicit import price deflator divided by the GDP deflator). This ratio fell more or less consistently until the first quarter of 1994, before remaining relatively constant until the second quarter of 1995. Subsequently, the ratio has fallen sharply, with this fall coinciding with the period during which the traditional Philips curve equations significantly overpredict inflation (Chart 1). Therefore, it is not surprising, that including import price changes in the Philips curve regression improves the predictive power of the equation.
UNITED STATES THE RELATIVE PRICE OF IMPORTS
(In percent)
Citation: IMF Staff Country Reports 1998, 105; 10.5089/9781451839500.002.A001
1/ Import price deflator divided by GDP deflator.2/ Annualized percent change.UNITED STATES THE RELATIVE PRICE OF IMPORTS
(In percent)
Citation: IMF Staff Country Reports 1998, 105; 10.5089/9781451839500.002.A001
1/ Import price deflator divided by GDP deflator.2/ Annualized percent change.UNITED STATES THE RELATIVE PRICE OF IMPORTS
(In percent)
Citation: IMF Staff Country Reports 1998, 105; 10.5089/9781451839500.002.A001
1/ Import price deflator divided by GDP deflator.2/ Annualized percent change.9. It is also worth noting the relative unimportance of the real unit labor cost variable. Some authors11 have expressed the view that the reason inflation was falling faster than appeared consistent with the historical relationship between unemployment and inflation was that the structure of labor costs had changed. These authors have noted that productivity was rising faster than normal and that nonwage labor costs (such as benefits) were being cut back. The results presented here suggest that these factors have not been critical in explaining recent inflation.
List of References
Gordon, Robert, 1997, “The Time-Varying NAIRU and its Implication for Economic Policy,” Journal of Economic Perspectives, Vol. 11, No. 1, pp. 11–32.
Lown, Cara and Rich, Robert, 1997, “Is There an Inflation Puzzle?,” Federal Reserve Bank of New York Policy Review, December.
Staiger, Douglas, James Stock, and Mark Watson, 1997, “The NAIRU, Unemployment and Monetary Policy,” Journal of Economic Perspectives, Vol. 11, No. 1, pp. 33–49.
Prepared by Vincent Hogan.
The inflation variable is the annualized percentage change in the CPI for urban consumers excluding food and energy costs (often referred to as “core” inflation). The NAIRU is assumed constant over the period at 6 percent.
A formal Chow test rejects the hypothesis that the average forecast error is different from zero. However, if the observed forecast errors are truly random draws from a symmetric distribution, the probability that 10 of them are positive is less than 1 out of 1,000.
The model is semi-structural because observed unemployment is regressed on variables that are expected to affect it, but without attempting to identify the underlying behavioral relationships (i.e., it is a reduced-form equation).
The dependency ratio is calculated as ratio of the dependent population (all those aged 15 and under plus all those aged 65 and over) to the labor force.
Of the structural variables, only the index of unionization was statistically significant.
The Holdrick-Prescott filter is equivalent to regressing actual unemployment on a series of time trends and then taking the fitted values. The idea is that short-run changes are “filtered” out, and what is left is the long-run trend rate of unemployment. This can be thought of as an alternative measure of the NAIRU.
These point and interval estimates are similar to those found in Staiger, Stock, and Watson (1997) and also to those in Gordon (1997).
The Philips curve equation would also systematically overpredict inflation if the Holdrick-Prescott measure of the NAIRU were used instead.
The changes in the price of imports variable picks up the effect of a change in the value of the U.S. dollar, as well as changes in the foreign currency prices of U.S. imports. The real unit labor cost variable includes changes in wages, benefits, and productivity. These results are similar to those reported by Gordon (1997). He found that import prices had a significant effect on core inflation, but that the deviation of productivity from its trend (which is reflected here in the real unit labor cost variable) did not.
See, for example, Lown and Rich (1997).
