1. Introduction

A number of groups monitoring the U.S. economy have revised downward their projections of potential output following the recent revisions to the national income and product accounts, which introduced new, chain-linked estimates of real GDP. Moreover, many observers also have lowered their estimates of the natural rate of unemployment, in light of the low level of inflation in the United States over a period in which the economy apparently has been operating at or near full capacity.

The purpose of this paper is to present updated estimates of potential output and the natural rate of unemployment for the United States using a variety of conventional techniques and to assess whether these variables are significant determinants of inflation. Using three standard techniques, potential output growth is estimated to be between 2.1 to 2.2 percent per annum. The natural rate of unemployment is estimated to be in the range of 5.5 to 6.1 percent. Using these estimates, the paper finds that both the cyclical position of the economy and the speed of labor market adjustment play an important role in explaining movements in inflation over the recent period. ^1/

The paper is organized as follows. Section 2 discusses various estimates of potential output. Section 3 presents a time varying estimate of the natural rate of unemployment. Section 4 tests for the significance of the natural rate in a variety of equations determining inflation. Section 5 offers some conclusions.

2. Estimates of potential output

Three common techniques used to calculate potential output are the segmented trend, univariate Hodrick-Prescott (HP) filter, and production function methods. ^2/ The segmented-trend method assumes that the rate of growth of potential output shifts at specific structural points but is constant between those points. Recursive residual tests were used to identify break points in the chain-linked real GDP series over the period from the third quarter of 1959 to the third quarter of 1995. These tests identified break points in the fourth quarter of 1973 and in the fourth quarter of 1989. The first break point corresponds to the first oil price shock and is consistent with the break usually found in analyses of the previous fixed-weight real GDP series; ^1/ the second break point corresponds to the end of the upward trend in the labor force participation rate.

Based on the segmented-trend method, the growth rate of potential output is estimated at 3.8 percent during the 1960-73 period, 2.8 percent during the 1974-89 period, and 2.1 percent since 1989. The level of potential output was calculated by applying the potential growth estimates to the full employment output level, which is estimated to have occurred in the first quarter of 1960, near the peak in the business cycle as defined by the National Bureau of Economic Research (NBER) (Chart 1). ^2/

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UNITED STATES: REAL GDP AND ALTERNATIVE MEASURES OF POTENTIAL OUTPUT

(In trillions of dollars)

Citation: IMF Staff Country Reports 1996, 093; 10.5089/9781451839487.002.A003

Sources: Bureou of Economic Analysis, U.S. Department of Commerce; and staff estimates.

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The HP filter approach to modeling potential output is less restrictive than the segmented-trend approach but suffers from extreme sensitivity to end points when using quarterly data. ^3/ Another feature of the HP approach is that the trend component of output calculated using this filter varies smoothly over time, thus generally reducing the amplitude of the implied output gap relative to other measures. In order to limit the sensitivity of the filter to end-of-sample data points, it was applied to annual data. In turn, the annual estimates that were produced were interpolated to a quarterly frequency. Using the HP filter, potential output growth was estimated at 2.2 percent per year over the 1990-95 period.

The aggregate-production function approach provides an alternative way of estimating potential output growth by decomposing output into its basic determinants—labor input, the capital stock, and total factor productivity. ^4/ The standard specification assumes a Cobb-Douglas production function with constant share parameters for labor and the capital stock based on their respective shares in national income. Total factor productivity is derived as a residual. In the calculation of potential output described below, both the labor and capital inputs were smoothed using the HP filter. The long-term estimate of total factor productivity (TFP) was obtained by regressing TFP on pre- and post-1974 dummies and on the change in the unemployment rate (in order to account for cyclical variations in productivity), and then calculating the value of TFP with the change in unemployment set to zero. ^1/ This procedure resulted in an estimate of total factor productivity growth of 1.3 percent per annum before 1974 and 0.6 percent subsequently. Combining the total factor productivity estimate with the contribution from the factor inputs yields an estimate of potential growth of 2.1 percent per annum over the 1990-95 period.

3. Estimating the natural rate of unemployment

Estimates of the natural rate of unemployment have been reexamined in light of the recent favorable inflation performance, which has coexisted with levels of unemployment traditionally thought to represent full-employment. For example, in the latest Economic Report of the President, the Council of Economic Advisers has lowered its estimate of the natural rate from 6 percent to the range of 5 ½ to 5 ¾ percent. Moreover, the view that the natural rate in the United States varies over time is gaining credence. ^2/

An often-used method of estimating a time-varying natural rate is referred to as the structural approach. In this approach, estimates of disequilibrium in the product and labor markets are combined with various structural variables to explain the unemployment rate (see Adams and Coe (1990) for a general discussion of this method). This approach was adopted below, except that the unemployment rate is expressed in relation to the employment-population ratio and the participation rate, with separate equations being estimated for these two ratios. ^3/

Structural determinants of the employment-population ratio are assumed to include the relative minimum wage and the unionization rate. ^1/ The relative minimum wage is defined as the ratio of the minimum wage to average earnings in the nonfarm business sector multiplied by the share of youth aged 16-24 in the labor-force. The minimum wage variable is weighted by the share of youth because more than 50 percent of minimum wage recipients are under 25 years of age. This captures changes in the availability of the minimum wage by incorporating changes in the youth composition of the labor force. A high minimum wage relative to the average wage rate is assumed to generate an excess supply of low-skilled workers and cause the employment-population ratio to fall. The unionization rate is defined as the ratio of union members to the total labor force. An increase in the unionization rate is expected to affect the bargaining process between firms and workers, causing wages to rise and employment to fall, other things equal.

The participation rate is specified as a function of the child-dependency ratio and a nonlinear trend. Since 1989, the participation rate has remained stable at about 66 percent. The most recent Economic Report of the President argues that this development is related to the recent stability in the child-dependency ratio. Between the late 1960s and the early 1980s, the ratio of children per woman aged 20 to 54 fell considerably, which allowed an increasing fraction of women to enter the labor force. However, since the mid-1980s, the child-dependency ratio has been relatively stable. The inclusion of the nonlinear trend picks up the influence of improvements in the educational attainment of females, which also has facilitated their entry into the labor force.

Both the employment-population ratio and the participation rate are assumed to depend on the output and wage gaps so that cyclical movements in both variables can be isolated. The output gap is defined as the log difference between real GDP and potential output, where potential output is derived using the segmented-trend method discussed above. The wage gap is measured by the change in real compensation per hour relative to output per hour in the nonfarm business sector. In the long run, both the output and wage gaps are zero and have no effect on the labor market; however, over the short run both variables have significant effects on the labor market. Positive output gaps raise both the employment-population ratio and the participation rate, whereas positive wage gaps would be expected to increase the participation rate but to lower the employment-population ratio. Over the recent period, the economy has been primarily subject to labor demand shocks so that the real wage and employment have moved in the same direction. ^1/

The preferred specifications for the employment-population ratio and the participation rate were estimated using annual data because of the unavailability of the unionization rate at a higher frequency. The Johansen-Juselius technique was used to determine whether a cointegrating vector exists in the employment equation because most of the variables are nonstationary over the sample period. ^2/ The trace statistic indicated the presence of two cointegrating vectors, and tests of exclusion restrictions on both the unionization rate and the relative minimum wage indicated that both variables were necessary in the cointegrating vector. ^3/

Having determined the existence of cointegrating vectors between the explanatory variables, the coefficients were estimated using ordinary least squares (OLS). ^4/ The results in Table 2 indicate that, as expected, the employment-population ratio is negatively related to the unionization rate and the relative minimum wage. The effect of the output gap on the employment-population ratio is positive. The effect of the wage gap is also positive, suggesting that shocks to the economy are mostly labor demand shocks so that the real wage and employment move together. Both the output and wage gaps are also positively related to the participation rate, although the magnitudes of the coefficients are smaller than for the employment-population ratio, which implies that the unemployment rate is inversely related to the cycle.

Table 1.

UNITED STATES: Unit Root Tests on Annual Data ^1/

^1/See text for data definitions. The Weighted Symmetric τ test involves a weighted double-length regression in which the dependent variable is regressed on leads and lags of its own changes; see Pantula (1994) for more details. The Dickey-Fuller (DF) τ test involves regressing the dependent variable on its own lags and its own lag level; asymptotic probability values for the DF τ test were obtained from Mackinnon (1994). An asterisk denotes significance at the 10 percent level.

Table 1.

UNITED STATES: Unit Root Tests on Annual Data ^1/

Variable	Weighted Symmetric τ Test		Dickey-Fuller τ Test
emp-pop	-2.7		-5.4
Δemp-pop	-3.8*		-3.4*
partr	-1.2		0.5
Δpartr	-3.4*		-2.5
union	1.6		-1.2
Δunion	-3.0*		-0.9
relmw	1.0		0.1
Δrelmw	-2.6		-3.4*
chdep	3.3		0.3
Δchdep	-1.0		2.4
ogap	-3.4*		-8.0*
wgap	-2.9		-2.2

^1/See text for data definitions. The Weighted Symmetric τ test involves a weighted double-length regression in which the dependent variable is regressed on leads and lags of its own changes; see Pantula (1994) for more details. The Dickey-Fuller (DF) τ test involves regressing the dependent variable on its own lags and its own lag level; asymptotic probability values for the DF τ test were obtained from Mackinnon (1994). An asterisk denotes significance at the 10 percent level.

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Table 1.

UNITED STATES: Unit Root Tests on Annual Data ^1/

Variable	Weighted Symmetric τ Test		Dickey-Fuller τ Test
emp-pop	-2.7		-5.4
Δemp-pop	-3.8*		-3.4*
partr	-1.2		0.5
Δpartr	-3.4*		-2.5
union	1.6		-1.2
Δunion	-3.0*		-0.9
relmw	1.0		0.1
Δrelmw	-2.6		-3.4*
chdep	3.3		0.3
Δchdep	-1.0		2.4
ogap	-3.4*		-8.0*
wgap	-2.9		-2.2

^1/See text for data definitions. The Weighted Symmetric τ test involves a weighted double-length regression in which the dependent variable is regressed on leads and lags of its own changes; see Pantula (1994) for more details. The Dickey-Fuller (DF) τ test involves regressing the dependent variable on its own lags and its own lag level; asymptotic probability values for the DF τ test were obtained from Mackinnon (1994). An asterisk denotes significance at the 10 percent level.

Table 2.

UNITED STATES: Determinants of the Components of the Unemployment Rate ^1/

^1/Regressions were estimated using annual observations over the 1971-95 period. An asterisk denotes significance at the 10 percent level. Standard errors in parenthesis.

Table 2.

UNITED STATES: Determinants of the Components of the Unemployment Rate ^1/

	Dependent Variable
	Employment-Population Ratio		Participation Rate
Explanatory variable
Trend			0.449
Trend squared			-0.006
Child-dependency ratio			-0.021
Output gap	0.33		0.072
Wage gap	0.14		0.058
Union rate	-0.48
Minimum wage	-0.23
Descriptive statistics
R-squared	0.99		0.99
ADF statistic	-3.63	*	-4.45	*
Estimate of the Natural Rate in 1995
Ulr	0.058	*
	(0.0016)

^1/Regressions were estimated using annual observations over the 1971-95 period. An asterisk denotes significance at the 10 percent level. Standard errors in parenthesis.

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Table 2.

UNITED STATES: Determinants of the Components of the Unemployment Rate ^1/

	Dependent Variable
	Employment-Population Ratio		Participation Rate
Explanatory variable
Trend			0.449
Trend squared			-0.006
Child-dependency ratio			-0.021
Output gap	0.33		0.072
Wage gap	0.14		0.058
Union rate	-0.48
Minimum wage	-0.23
Descriptive statistics
R-squared	0.99		0.99
ADF statistic	-3.63	*	-4.45	*
Estimate of the Natural Rate in 1995
Ulr	0.058	*
	(0.0016)

^1/Regressions were estimated using annual observations over the 1971-95 period. An asterisk denotes significance at the 10 percent level. Standard errors in parenthesis.

Chart 2 indicates that the long-run employment-population ratio rises linearly until the late 1980s when the profile flattens out. ^1/ Subsequently, the decline in the relative minimum wage was more moderate, and, therefore, there was little upward pressure on employment from this variable. The long-run participation rate rises until 1989, when it stabilizes at about 66 percent reflecting a levelling off of the child dependency ratio.

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UNITED STATES: COMPONENTS OF THE UNEMPLOYMENT RATE

(In percent)

Citation: IMF Staff Country Reports 1996, 093; 10.5089/9781451839487.002.A003

Sources: Bureou of Labor Statistics, U.S. Department of Labor; and staff estimates.

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The estimates of long-run employment-population ratio and participation rate were combined to generate a time-varying natural rate as follows:

where U* is the natural rate of unemployment, (E/P)* is the long-run estimate of the employment-population ratio, and (L/P)* is the long-run estimate of the participation rate.

The lower panel of Chart 2 indicates that the natural rate follows an inverted U-shaped pattern, comparable to the profile of the natural rate estimated by Adams and Coe. In the 1970s, the natural rate rose rapidly owing to a less rapid rise in the equilibrium employment-population ratio than in the participation rate because of the relative constancy of the relative minimum wage and the unionization rate. This pattern was reversed in the early 1990s when the equilibrium participation rate stabilized and the employment-population ratio rose as a result of a continuing decline in the relative minimum wage and the unionization rate.

The point estimate for the natural rate of unemployment in 1995 is 5.8 percent, slightly above the average unemployment rate of 5.6 percent for that year. A confidence interval for this estimate can be calculated using the Delta-method approximation to the non-linear function defined in equation (1). ^2/ This method yielded a standard error of 0.16 so that a 95 percent confidence interval for the natural rate lies in the range of 5.5 percent to 6.1 percent.

An increase in the minimum wage of 90 cents from $4.25 to $5.15 per hour has been proposed, half occurring in July 1996 and the remainder in July 1997. Estimates of the effect of this increase on employment suggest job losses of 100,000 to 300,000. ^1/ The effects of the proposed increase in the minimum wage were simulated using the specification for the natural rate of unemployment discussed above. Raising the minimum wage by 90 cents causes the natural rate of unemployment to rise by 0.3 percentage point, holding all other factors constant. This estimate is comparable to the upper end of the range of estimated job losses mentioned above, because a decline in employment of 300,000 would yield a 0.3 percent rise in the unemployment rate (assuming that the unemployed remained in the labor force).

The relationship between the unemployment gap and the output gap—termed the Okun relationship—was estimated using the estimates of the natural rate and potential output described above. The unemployment gap was regressed on the output gap and two lags of both variables to ensure that the residual was free of autocorrelation (Table 3). The estimates suggested that in the short run, the unemployment gap was roughly one fifth of the output gap, but that in the long run this ratio was roughly equivalent to one-half.

Table 3.

UNITED STATES: The Okun Relationship ^1/

^1/The equation was estimated using quarterly observations over the 1971-95 period. An asterisk denotes significance at the 10 percent level.

Table 3.

UNITED STATES: The Okun Relationship ^1/

	Dependent Variable: UGAP
Explanatory variable
UGAP(-1)	1.27	*
UGAP(-2)	-0.36	*
OGAP	0.23	*
OGAP(-1)	-0.18	*
OGAP(-1)	0.003
Descriptive statistics
R-squared	0.97
Box-Pierce autocorrelation test	29.1

^1/The equation was estimated using quarterly observations over the 1971-95 period. An asterisk denotes significance at the 10 percent level.

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Table 3.

UNITED STATES: The Okun Relationship ^1/

	Dependent Variable: UGAP
Explanatory variable
UGAP(-1)	1.27	*
UGAP(-2)	-0.36	*
OGAP	0.23	*
OGAP(-1)	-0.18	*
OGAP(-1)	0.003
Descriptive statistics
R-squared	0.97
Box-Pierce autocorrelation test	29.1

^1/The equation was estimated using quarterly observations over the 1971-95 period. An asterisk denotes significance at the 10 percent level.

4. Determinants of inflation

Recent work on the linkages between the cyclical position of the economy and inflationary pressures has emphasized the fragility of estimates of the NAIRU. In particular, Staiger et al. (1996) using a variety of Phillips curve specifications find that their typical estimate of the NAIRU has a 95 percent confidence interval ranging from 5.1 to 7.7 percent. They conclude that this level of uncertainty makes questionable the usefulness of the natural rate for explaining inflation. This section builds on the work of Staiger et al. by considering the extent to which the unemployment gap estimated in the previous section provides additional explanatory power in an inflation equation that also includes various measures of cost pressures.

The U.S. inflation rate reached a post-war peak of 13 percent in 1980 following the second oil price shock (Chart 3). ^2/ Since then, inflation has fallen and has averaged 3 percent over the period 1993-1995. The slowdown in inflation in the United States over the past decade has been associated with a similar trend in the rate of change of unit labor costs (Chart 4). The growth of unit labor costs averaged 6 ¾ percent between 1972 and 1983, but fell to 3 percent over the 1984-1995 period. The relatively low rate of inflation in recent years has surprised some analysts given the low rate of unemployment, particularly since external price pressures, captured by the rate of change in petroleum and foreign export prices before mid-1995, also seem to have intensified.

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UNITED STATES: CPI AND FOREIGN COSTS

(Percent change from year ago)

Citation: IMF Staff Country Reports 1996, 093; 10.5089/9781451839487.002.A003

Sources: Bureau of Labor Statistics, U.S. Department of Labor; and WEO.

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UNITED STATES: CPI AND DOMESTIC COSTS

(Percent change from year ago)

Citation: IMF Staff Country Reports 1996, 093; 10.5089/9781451839487.002.A003

Sources: Bureau of Labor Statistics, U.S. Department of Labor; and staff estimates.1/ The unemployment gap is defined as actual unemployment minus the natural rate, expressed in percentage points.

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a. Phillips curve specification ^1/

The approach taken in this paper is to estimate a Phillips curve relationship using the unemployment gap derived in Section 3 and to supplement the Phillips curve with variables measuring supply shocks. The basic Phillips curve relationship assumes that labor demand and supply interact so that the unemployment rate can fall below its natural rate only if workers are compensated by an increase in their expected real wage.

$\begin{array}{cc}\mathrm{\Delta }{W}_t=E\left(\mathrm{\Delta }{P}_t\right)+f\left({\mathrm{u}}_t-{\overline{\mathrm{u}}}_t\right)& \left(2\right)\end{array}$

where W is wages (Δ refers to the change in the natural logarithm of the variable), P is the aggregate price index, E(ΔP_t) represents inflation expectations at time t, u is the unemployment rate, and u is the natural rate of unemployment.

Assuming that the aggregate price is a fixed mark-up over unit labor costs and that labor productivity is constant yields

$\begin{array}{cc}{P}_t=\left(1+z\right)W_t/a& \left(3\right)\end{array}$

where z is the mark-up and a is labor productivity. Taking log differences yields

$\begin{array}{cc}\mathrm{\Delta }{P}_t=\mathrm{\Delta }{W}_t& \left(4\right)\end{array}$

Substituting this expression in Equation (2), assuming that expected inflation is proxied by past values of inflation, yields ^1/

$\begin{array}{cc}\mathrm{\Delta }{P}_t=\underset{i=1}{\overset{K}{\mathrm{\Sigma }}}\mathrm{\Delta }{P}_{t-i}+f\left({\mathrm{u}}_t-{\overline{\mathrm{u}}}_t\right)& \left(5\right)\end{array}$

Two lags of inflation (measured by the change in the core consumer price index (CPI)) were used to proxy expected inflation, and the first lag of the unemployment gap was used to measure economic slack. ^2/ Over the sample period from the first quarter of 1971 to the third quarter of 1995, the coefficient on the unemployment gap is significant. Out-of-sample forecasts conducted over the period from the first quarter of 1994 to the third quarter of 1995 indicate that the inflation rate is over-predicted by 1 ½ percent by the end of the sample period (Chart 5). ^3/ There are two possible explanations for this result. First, the relationship between the unemployment gap and inflation may have weakened over time, and therefore, the inflationary forces present in early 1994 did not result in higher inflation over the 1994-95 period. Second, the assumption underlying the standard Phillips curve that prices are determined by unit labor costs and that labor productivity is constant is incorrect, since other cost pressures may also be relevant in explaining inflation. These alternatives are considered in turn.

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UNITED STATES: ALTERNATIVE PHILLIPS CURVE SPECIFICATIONS FOR INFLATION RATE

(Percent change from year ago)

Citation: IMF Staff Country Reports 1996, 093; 10.5089/9781451839487.002.A003

Sources: Bureau of Labor Statistics, U.S. Department of Labor; and staff estimates.

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Recent work by Blomberg and Harris (1995) for the United States and by Hostland (1995) for Canada indicates that the inflationary process may have changed significantly in the mid-1980s in both countries. Blomberg and Harris consider the period since 1987 as a stable inflationary period, whereas Hostland suggests a slightly longer stable period between 1984 and 1993. The stability of the reduced-form coefficients over the whole sample period are tested using a CUSUM-squared test. The test statistic and confidence bands shown in Chart 6 indicate that the stability of the relationship begins to break down in the early 1980s, at the time of the second oil price shock. However, a stable relationship is found when the equation is re-estimated using quarterly data over the sub-period 1984-1995. Moreover, out-of-sample forecasts over the period from the first quarter of 1994 show an improvement over the earlier forecast (see Chart 5) although the coefficient on the lagged unemployment gap is now insignificant (Table 4).

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UNITED STATES: CUSUM-SQUARED STATISTIC

Citation: IMF Staff Country Reports 1996, 093; 10.5089/9781451839487.002.A003

Source: Staff estimates.

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Table 4.

UNITED STATES: Traditional Phillips Curve Specifications of the Inflation Process ^1/

^1/An asterisk denotes significance at the 10 percent level.

Table 4.

UNITED STATES: Traditional Phillips Curve Specifications of the Inflation Process ^1/

	Sample Period
	1971-1995		1984-1995
Explanatory variable
ΔCPI(-1)	1.25	*	1.33	*
ΔCPI(-2)	-0.31	*	-0.47	*
UGAP(-1)	-0.24	*	-0.08	*
Descriptive statistics
R squared	0.95		0.87
Box-Pierce autocorrelation test	38.2	*	20.6	*

^1/An asterisk denotes significance at the 10 percent level.

View Table

Table 4.

UNITED STATES: Traditional Phillips Curve Specifications of the Inflation Process ^1/

	Sample Period
	1971-1995		1984-1995
Explanatory variable
ΔCPI(-1)	1.25	*	1.33	*
ΔCPI(-2)	-0.31	*	-0.47	*
UGAP(-1)	-0.24	*	-0.08	*
Descriptive statistics
R squared	0.95		0.87
Box-Pierce autocorrelation test	38.2	*	20.6	*

^1/An asterisk denotes significance at the 10 percent level.

b. Phillips curve adjusted for supply factors

An alternative explanation for the weak effect of the unemployment gap over the recent period is that the price equation may be misspecified. In an alternative specification, input prices other than labor play a role in determining the core CPI and labor productivity is allowed to vary over the cycle. In this specification, the aggregate price is a fixed mark-up over a weighted average of unit labor costs, nonpetroleum foreign export prices (FXP), petroleum prices (PP), and farm product prices (FPP). ^1/

$\begin{array}{cc}{P}_t=\left(1+z\right)\left[{\left(W_t/a_t\right)}^{\alpha }{\left(\theta {\mathit{FXP}}_t\right)}^{\gamma }{\left({\mathit{\tau PP}}_t\right)}^{\lambda }{\left({\mathit{\mu FPP}}_t\right)}^{1-\alpha -\gamma -\lambda }\right]& \left(6\right)\end{array}$

where θ, τ and μ are requirements per unit of output for nonoil imports, petroleum imports, and farm products, respectively. All requirements are assumed to be fixed over time. ^2/ Taking log differences and substituting Equation (2) yields

$\begin{array}{cc}\mathrm{\Delta }{P}_t=\alpha \underset{i=1}{\overset{K}{\mathrm{\Sigma }}}\mathrm{\Delta }{P}_{t-i}-{\mathrm{\alpha \Delta a}}_t+\mathrm{\gamma \Delta }{\mathit{FXP}}_t+\mathrm{\lambda \Delta }{\mathit{PP}}_t+\left(1-\alpha -\gamma -\lambda \right)\mathrm{\Delta }{\mathit{FPP}}_t+\mathit{\alpha }\mathit{f}\left({\mathrm{u}}_t-{\overline{\mathrm{u}}}_t\right)& \left(7\right)\end{array}$

The specification of Equation (7) indicates that only the contemporaneous cost and unemployment gap variables are relevant for explaining inflation. However, price and cost variables are simultaneously determined, and therefore to limit the simultaneity bias, lags of the explanatory variables were used. The Schwarz and Akaike criteria were used to select the lag length. ^1/ Up to eight lags were considered; the Schwarz criterion suggests estimating Equation (7) with the minimum number of lags, whereas the Akaike criterion suggests using the maximum number of lags. The equation was estimated using two lags in order to achieve a parsimonious specification that allowed for a reasonably rich dynamic lag structure. ^2/

Table 6 presents coefficient estimates and various diagnostic and exclusion restriction statistics for the equation estimated over the 1984-95 period. The table indicates that the estimated equation is able to explain a considerable fraction of the movements in the inflation rate. Lagged values of inflation provide a significant portion of this explanatory power. Moreover, labor market conditions, captured by the unemployment gap, also are significant. However, the opposite signs on the two coefficients suggest that the change in the unemployment gap or the “speed” of labor market adjustment is an important factor in the determination of inflation. Other domestic and external determinants of prices—captured by productivity growth, non-oil foreign export prices, farm and petroleum prices—are all insignificant.

Table 5.

UNITED STATES: Unit Root Tests on Quarterly Data

^1/See text for data definitions. The Weighted Symmetric τ test involves a weighted double-length regression in which the dependent variable is regressed on leads and lags of its own changes. See Pantula (1994) for more details. The Dickey-Fuller (DF) τ test involves regressing the dependent variable on its own lags and its own lag level; asymptotic probability values for the DF τ test were obtained from Mackinnon (1994). An asterisk denot’s significance at the 10 percent level.

Table 5.

UNITED STATES: Unit Root Tests on Quarterly Data

Variable	Weighted Symmetric τ Test		Dickey-Fuller τ Test
CPI	2.3		-1.2
ΔCPI	-2.6		-3.4	*
PROD	-2.8		-3.1	*
ΔPROD	-3.5	*	-3.5	*
FXP	0.1		-3.9	*
ΔFXP	-2.9		-3.2	*
PP	-0.6		-1.9
ΔPP	-3.3	*	-3.3	*
FP	-0.2		-2.4
AFP	-3.3	*	-3.6	*
(u-a)	-3.3	*	-3.1	*

^1/See text for data definitions. The Weighted Symmetric τ test involves a weighted double-length regression in which the dependent variable is regressed on leads and lags of its own changes. See Pantula (1994) for more details. The Dickey-Fuller (DF) τ test involves regressing the dependent variable on its own lags and its own lag level; asymptotic probability values for the DF τ test were obtained from Mackinnon (1994). An asterisk denot’s significance at the 10 percent level.

View Table

Table 5.

UNITED STATES: Unit Root Tests on Quarterly Data

Variable	Weighted Symmetric τ Test		Dickey-Fuller τ Test
CPI	2.3		-1.2
ΔCPI	-2.6		-3.4	*
PROD	-2.8		-3.1	*
ΔPROD	-3.5	*	-3.5	*
FXP	0.1		-3.9	*
ΔFXP	-2.9		-3.2	*
PP	-0.6		-1.9
ΔPP	-3.3	*	-3.3	*
FP	-0.2		-2.4
AFP	-3.3	*	-3.6	*
(u-a)	-3.3	*	-3.1	*

^1/See text for data definitions. The Weighted Symmetric τ test involves a weighted double-length regression in which the dependent variable is regressed on leads and lags of its own changes. See Pantula (1994) for more details. The Dickey-Fuller (DF) τ test involves regressing the dependent variable on its own lags and its own lag level; asymptotic probability values for the DF τ test were obtained from Mackinnon (1994). An asterisk denot’s significance at the 10 percent level.

Table 6.

UNITED STATES: Augmented Phillips Curve Specifications ^1/

^1/An asterisk denotes significance at the 10 percent level.

Table 6.

UNITED STATES: Augmented Phillips Curve Specifications ^1/

	Dependent Variable
	ΔCPI		ΔCPI
Explanatory variables
ΔCPI(-1)	1.00	*	1.00	*
ΔCPI(-2)	-0.03		-0.03
UGAP(-1)	-0.44	*
UGAP(-2)	0.31	*
ΔPROD(-1)	0.003		0.003
ΔPR0D(-2)	0.06		0.06
ΔFXP(-1)	0.02		0.02
ΔFXP(-2)	-0.02		-0.02
ΔFP(-1)	0.01		0.01
ΔFP(-2)	-0.01		-0.01
ΔPP(-1)	0.001		0.001
ΔPP(-2)	0.0003		0.0003
UGAP(-l)			-0.13	*
ΔUGAP(-1)			-0.31	*
Descriptive statistics
R2	0.93		0.93
Box-Pierce autocorrelation test	14.5		14.5
Exclusion restriction statistics
ΔCPI	2,395	*
ΔPROD	2.20
ΔFXP	0.67
ΔFP	0.22
ΔPP	0.91
ΔUGAP	4.20	*
Test statistics
Equality of Unemployment Gap Coefficients			5.75	*
Significance of Natural Rate of Unemployment			4.03	*

^1/An asterisk denotes significance at the 10 percent level.

View Table

Table 6.

UNITED STATES: Augmented Phillips Curve Specifications ^1/

	Dependent Variable
	ΔCPI		ΔCPI
Explanatory variables
ΔCPI(-1)	1.00	*	1.00	*
ΔCPI(-2)	-0.03		-0.03
UGAP(-1)	-0.44	*
UGAP(-2)	0.31	*
ΔPROD(-1)	0.003		0.003
ΔPR0D(-2)	0.06		0.06
ΔFXP(-1)	0.02		0.02
ΔFXP(-2)	-0.02		-0.02
ΔFP(-1)	0.01		0.01
ΔFP(-2)	-0.01		-0.01
ΔPP(-1)	0.001		0.001
ΔPP(-2)	0.0003		0.0003
UGAP(-l)			-0.13	*
ΔUGAP(-1)			-0.31	*
Descriptive statistics
R2	0.93		0.93
Box-Pierce autocorrelation test	14.5		14.5
Exclusion restriction statistics
ΔCPI	2,395	*
ΔPROD	2.20
ΔFXP	0.67
ΔFP	0.22
ΔPP	0.91
ΔUGAP	4.20	*
Test statistics
Equality of Unemployment Gap Coefficients			5.75	*
Significance of Natural Rate of Unemployment			4.03	*

^1/An asterisk denotes significance at the 10 percent level.

Out-of-sample forecasts using this specification follow the actual path of the inflation rate more closely than the standard Phillips curve specifications discussed above (see Chart 5). In particular, the increase in the inflation rate since late 1994 is captured by this specification, whereas the forecasts of the other specifications lie considerably above the actual outcome. However, this specification fails to capture the slight decline in inflation in the third quarter of 1995.

c. Tests of the importance of the natural rate and speed limit effects

The significance of the time-varying natural rate and the importance of the change in the unemployment gap compared to the level of unemployment for determining inflation are examined further below. In particular, the inflation equation is re-specified as follows:

$\begin{array}{cc}\mathrm{\Delta }{P}_t=\underset{i=1}{\overset{2}{\mathrm{\Sigma }}}\left[\mathrm{\Delta }{P}_{t-i}+{\beta }_i\left(u_{t-i}-\alpha {\overline{\mathrm{u}}}_{t-i}\right)+{\mu }_i\mathrm{\Delta }{a}_{t-i}+{\tau }_i\mathrm{\Delta }{\mathit{FXP}}_{t-i}+{\theta }_i\mathrm{\Delta }{\mathit{PP}}_{t-i}+{\lambda }_i\mathrm{\Delta }{\mathit{FPP}}_{t-i}\right]+{ϵ}_t& \left(8\right)\end{array}$

and the following hypothesis test was conducted

H₀: α = 0; H₁: α = 1.

Under the null hypothesis, the natural rate of unemployment drops out of the specification and only the unemployment rate matters, whereas under the alternative hypothesis the natural rate of unemployment has significant explanatory power. Table 6 provides the likelihood-ratio statistic for this test and indicates that the null hypothesis was rejected so that the time-varying natural rate has significant explanatory power for inflation.

The coefficient estimates in Table 6 suggest that the change in the unemployment gap plays a major role in explaining inflation movements. To test whether there is any additional role for the level of the gap, the coefficients from Equation (6) are used to conduct the following test:

H₀: β₁ = -β₂.

Under the null hypothesis, there is no role for the cyclical position. The likelihood-ratio test statistic indicates that the null hypothesis is rejected, so that both the cyclical position of the economy and the speed of labor market adjustment matter for inflation. Moreover, the coefficient on the change in the gap is roughly three times the magnitude of the coefficient on the level of the gap.

From the significance of both the level of the unemployment gap and the change in the unemployment gap, a “speed-limit” effect can be defined. ^1/ This effect is defined as the change in the unemployment gap such that the inflationary effects of the change in the gap are fully offset by the deflationary effects from the level of the gap. In terms of Equation (7), the linear relationship is defined as

$\begin{array}{cc}\mathrm{\Delta }\left(\mathrm{u}-\overline{\mathrm{u}}\right)=-{\beta }_1/{\beta }_2\left(\mathrm{u}-\overline{\mathrm{u}}\right)& \left(9\right)\end{array}$

This relationship is presented in Chart 7 together with a scatter plot of both variables over the past five years. The chart indicates that, since early 1994, the economy has operated in the inflationary quadrant and therefore, holding all other variables constant, inflation should have risen over the 1994-95 period. The equation suggests that the reason for the slight decline in inflation in early 1994 is that petroleum prices fell considerably (see Chart 3).

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UNITED STATES: SPEED LIMIT EFFECT ^1/

Citation: IMF Staff Country Reports 1996, 093; 10.5089/9781451839487.002.A003

Source: Staff estimates.^1/ The speed limit effect is evident to the right of the inflation focus in the upper left panel and to the left of the inflation locus in the lower right panel. In the upper left panel, data points to the right of the inflation locus generate a rise in inflation even though there is an excess supply gap in the economy. Similarly, in the lower right panel, data points to the left of the inflation locus generate o deline in inflation even though there is on excess demand gap.

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A number of commentators have argued that the recent difficulty in observing any inflationary pressure is related to the weak growth in employee benefits in recent years. To test the robustness of the finding that the change in the unemployment gap is an important determinant of inflation, the wage component of the employment compensation index is related to two lags of itself and of inflation and to the level and change in the unemployment gap. Table 7 indicates that both unemployment gap variables are significant and that the coefficient on the change in the gap is four times the magnitude of that on the level of the gap. This result confirms the important role played by the speed of labor market adjustment in determining inflation.

Table 7.

UNITED STATES: Wage Compensation Equation ^1/

^1/An asterisk denotes significance at the 10 percent level.

Table 7.

UNITED STATES: Wage Compensation Equation ^1/

	Dependent Variable
	ΔWAGE		ΔWAGE
Explanatory variables
ΔWAGE(-1)	0.81	*	0.81	*
ΔWAGE(-2)	0.04		0.04
ΔCPI(-1)	0.09		0.09
ΔCPI(-2)	0.04		0.04
UGAP(-1)	-0.47	*
UGAP(-2)	0.38	*
UGAP(-1)			-0.09	*
ΔUGAP(-1)			-0.38	*
Descriptive statistics
R-squared	0.92		0.92
Box-Pierce autocorrelation test	13.5		13.5
Test statistic for equality of unemployment gap coefficients
LR stat	9.09	*

^1/An asterisk denotes significance at the 10 percent level.

View Table

Table 7.

UNITED STATES: Wage Compensation Equation ^1/

	Dependent Variable
	ΔWAGE		ΔWAGE
Explanatory variables
ΔWAGE(-1)	0.81	*	0.81	*
ΔWAGE(-2)	0.04		0.04
ΔCPI(-1)	0.09		0.09
ΔCPI(-2)	0.04		0.04
UGAP(-1)	-0.47	*
UGAP(-2)	0.38	*
UGAP(-1)			-0.09	*
ΔUGAP(-1)			-0.38	*
Descriptive statistics
R-squared	0.92		0.92
Box-Pierce autocorrelation test	13.5		13.5
Test statistic for equality of unemployment gap coefficients
LR stat	9.09	*

^1/An asterisk denotes significance at the 10 percent level.

5. Conclusions

This paper has presented updated estimates of potential output growth and the natural rate of unemployment and has considered the explanatory power of these variables in determining inflation. The paper estimates that potential output growth is in the range of 2.1 to 2.2 percent per annum and that the natural rate of unemployment is in the range of 5.5 to 6.1 percent.

The paper finds that the standard Phillips curve overpredicts inflation over the 1994-95 period but that recent inflation movements are well captured when supply influences and the speed of labor market adjustment are considered. This is consistent with recent work by Staiger et al., who conclude that the value of unemployment corresponding to a stable rate of inflation is imprecisely measured but that an increase in unemployment will on average be associated with a decline in future rates of inflation.