1. Introduction

In several instances, Federal Reserve officials have stated that if the stance of U.S. monetary policy had not tightened in 1994, the inflationary risks associated with exceeding potential output would have been large and the process of containing these inflationary forces would have required a much more severe tightening in monetary conditions. This view may be based on a model with an asymmetric output-inflation nexus in which inflation and inflation expectations respond more to positive output gaps than they do to negative gaps. ^2/

If this view of the world is correct, then allowing the economy to produce in excess of its potential will be costly because the monetary tightening and negative output gaps that will be required later to rein in inflationary pressures will be larger than otherwise. ^3/ Indeed, policy rules that fail to guard against overheating will result in significantly larger monetary business cycles and permanent losses in output. ^4/ Moreover, policy rules that guard against the emergence of excess demand will reduce the variance of aggregate demand and raise the mean level of output.

This view of the business cycle is significantly different from that embodied in linear models of the output-inflation process. Indeed, linear models suggest that there are small costs or perhaps even some benefits from delaying interest rate hikes in the face of positive aggregate demand shocks that drive output above potential.

Despite the obvious importance of this issue for the conduct of monetary policy, econometric studies of the United States have generally not found evidence that capacity constraints create a significant nonlinearity in the output-inflation nexus. Indeed, Gordon (1994), for example, claims that there is no evidence of nonlinearity in the U.S. data, while Eisner (1994) presents evidence that inflation may respond more to negative gaps than to positive gaps. ^1/ The linear models estimated by Gordon imply that the average level of output will be independent of the parameters in the monetary policy rule, while Eisner’s model predicts that policies that increase the variance of output will actually raise the average level of output. An exception is the work by Laxton, Meredith, and Rose (1994), which shows that, if the Phillips Curve is assumed to be identical across the G-7 economies, there is fairly strong evidence of asymmetries. In a more recent paper, Turner (1995) relaxes this restriction and finds some evidence of asymmetry in the U.S. data.

This paper builds on the results reported by Turner and argues that the inability of previous empirical work to discern evidence asymmetries in the U.S. data has been the result of the use of inappropriate measures of the output gap. The remainder of this paper is organized in the following way. Section 2 presents the basic model that is used to test for the existence of asymmetry in the U.S. output-inflation process. In Section 3, empirical results are presented that confirm the existence of asymmetries in the U.S. data. Section 4 employs a small model of the U.S. economy to compare the policy implications of the asymmetric model with those of the linear model.

2. Models of the Phillips curve

The Phillips curve model of inflation assumes that inflation is driven by inflation expectations and the output gap. The simplest form of the model can be written as:

where: π is inflation, π^e is expected inflation, “gap” is the difference between actual output and a measure of potential output, and ε^π represents a disturbance term. The disturbance term represents the effects on inflation of factors other than aggregate demand. This could include cost-push factors such as an exogenous increase in wage demands or the effect of large changes in relative prices such as the change in the price of crude oil that occurred in the 1970s.

Equation 1 implies that the main source of inertia in inflation dynamics is rigidities in expectations. If combined with an assumption of model-consistent or rational expectations, the model implies that inflation can be adjusted costlessly. In other words, an announced and credible reduction in the target inflation rate can be achieved without any output costs as long as the expected inflation term in Equation 1 moves one-for-one with the announced change in the target.

The fact that it has proved difficult to reduce inflation without creating a negative output gap has led to a number of extensions to the above model of inflation. One extension considers the possibility that inflation is costly to adjust (for example, owing to the existence of contracts). This argument is often used to justify the addition of lagged values of inflation on the right-hand-side of Equation 1. In this case, even a fully credible announced change in the inflation target would not be achieved without some output costs in the short run. A second extension focuses on how expectations are formed. For example, if there is a backward-looking element to expectations formation, the addition of lagged inflation in Equation 1 also can be justified. Thus, additional lags in Equation 1 can arise either from intrinsic inflation dynamics, which are independent of expectations, or from inertia in expectations formation, or both. ^1/

The resulting model is often referred to as the “backward- and forward-looking components” model (see Buiter and Miller (1985)). In this model, inflation is determined, at least partially, by historical conditions--the backward-looking component--while the forward-looking component responds to new information about the future. The extended dynamic model can be written as:

This equation, however, is linear in that the effect on inflation of a disturbance or a change in the gap is the same (in absolute value) regardless of whether output is above or below potential. By contrast, in an asymmetric model of the Phillips curve, inflation would respond differently to changes in the output gap depending on whether the economy was above or below its long-run potential. A simple extension of the model that would test the hypothesis of asymmetries would add positive output gaps to the model and test if the estimated parameter(s) on the additional term(s) can help explain inflation. ^2/

Gordon (1994) examines this issue by augmenting his simple, backward-looking, inflation-unemployment model with positive unemployment gaps but finds no statistical evidence in favor of either asymmetry. These results contrast with those reported by Laxton, Meredith, and Rose (1994), who find strong empirical evidence in the G-7 data that positive output gaps have more powerful effects on inflation than negative output gaps. One explanation for the different results could be that the assumptions used by Gordon and others may have been biased against finding asymmetric effects in the Phillips curve. In particular, it is critical for econometricians to recognize the implications of asymmetry for the measurement of the output gaps that enter the Phillips Curve in order to identify properly the asymmetric model.

One important implication is that the mean value of the gap that enters the Phillips curve will be negative if the curve is convex--i.e., if excess demand shocks have a large effect on inflation. Only in the case of global linearity will it be appropriate to impose a mean value of zero. In other words, in order to test the hypothesis that positive gaps have larger effects on inflation than negative gaps, it is critical that the mean value of the output gap that enters the Phillips Curve be unconstrained.

For example, the Phillips curve should be specified as

where gap^* = y - ȳ + α and gappos^* represents the positive values of these adjusted gaps. Here we define ȳ to be the value of potential output in a linear and purely symmetric world. If positive gaps have larger effects than negative gaps--if γ > 0--and there is some variance in aggregate demand conditions, α must be less than zero for inflation to be bounded. ^1/ If short-run capacity constraints are truly a feature of the U.S. economy, imposing α to be zero will bias γ towards zero and bias standard tests for the presence of asymmetry towards false rejection. The implications of not accounting for the possibility that α < 0 are discussed in the following section.

3. Testing for asymmetries in the U.S. data

The trend level of output is measured using a simple two-sided moving average filter of actual output. In Laxton, Meredith, and Rose (1994) trend output was measured as a simple five-year, centered moving average of actual output (a two-year horizon, forwards and backwards). In this paper, the same approach is used, but the results are reported for a range of alternative horizons (the parameter k below) in the two-sided filter. ^2/

A very small value of k implies that potential output is highly correlated with actual output and, in the limit, when k = 0, potential output is set equal to actual output at all points in time. This would be consistent with an extreme real-business-cycle view of the world, where prices adjust instantaneously to changes in excess demand. A very large value of k would be consistent with a view that most of the variation in output is associated with movements in the output gap. Given the considerable uncertainty about the role of demand and supply shocks in the economy, results and hypothesis tests are reported for a large range of k values. ^1/

Table VI-1 reports econometric estimates of Equation 3 under the assumption that α = C, for values of k ranging from 5 to 16 (quarters). In order to hold the estimation period fixed to see how alternative gap measures performed in explaining the same inflation experiences, the sample period for each regression ended in 1990QIV (since the two-sided filter with k = 16, requires data on actual output for the years 1991 to 1994). In order to keep the model parsimonious and to take into account the possibility that the measure of inflation expectations used (from the Michigan Survey) has information content for explaining movements in actual inflation, a specification was chosen that includes the contemporaneous value of one-year-ahead inflation expectations as well as 4 lags, where each lag is assumed to have the same weight. In addition, a lagged inflation term was added to allow inflation to allow for intrinsic inertia in inflation dynamics. ^2/

Based on these assumptions the value of k that minimizes the standard error of the inflation equation is 8. This estimate suggests that variation in the output gap--as opposed to potential output is the dominant source of variation in output at business cycle frequencies. The preferred model has two noteworthy features. First, it would appear to reject the hypothesis that γ > 0 at the usual confidence levels and conclude that there was no compelling evidence of asymmetry in the U.S. Phillips curve. Second, with k = 8 the coefficient on the output gap is statistically significant, so there is evidence that inflation is related to the output gap--a Phillips curve exists.

Table VI-1.

United States: Biased Tests of Asymmetry

^1/T-statistics in parentheses.

Table VI-1.

United States: Biased Tests of Asymmetry

Estimated
	equation:	$x_t=\delta {\overline{x}}_{t+1}^{*}+\left(1-\delta \right){\pi }_{\mathrm{t}-1}+\beta {\mathrm{gap}}_{\mathrm{t}}^{*}+\gamma {\mathrm{gappos}}_{\mathrm{t}}^{*}+{ϵ}_{\mathrm{t}}^{\pi }$
where:		$\begin{array}{ccc}\mathrm{gap}*& =& y-y*=y-\overline{y}+\alpha ,\mathrm{gapps}*=\mathrm{positive}\mathrm{values}\mathrm{of}\mathrm{gap}*\\ {\overline{\pi }}_{t+1}^{*}& =& -2({\mathrm{t\pi }}_{t+4}^{*}+t-1{\pi }_{t+3}^{*}+t-2{\pi }_{t+2}^{*}+t-3{\pi }_{t+1}^{*}+t-4{\pi }_t^{*})\hfill \\ \pi & =& \mathrm{Percent}\mathrm{change}\mathrm{in}\mathrm{the}\mathrm{CPI}\mathrm{at}\mathrm{annual}\mathrm{rates}\hfill \\ {\pi }_{t+1}^{*}& =& \mathrm{Michigan}\mathrm{Survey}\mathrm{measure}\mathrm{of}\mathrm{inflation}\mathrm{expectations}\hfill \\ y& =& \frac{1}{2k+1}\left[y_t+\underset{i+1}{\overset{k}{\mathrm{\Sigma }}}{y}_{t+i}+y_{t-i}\right]\hfill \end{array}$
Data: U.S. Quarterly Data, 1964QI-90QIV.
		Estimated Coefficients 1/
k		α	γ	β	δ	R2	σ
5		0.00	0.285	0.593	0.547	.7739	1.6499
		(0.96)	(3.34)	(4.73)
6		0.00	0.302	0.497	0.556	.7761	1.6296
		(1.20)	(3.32)	(4.91)
7		0.00	0.281	0.435	0.562	.7769	1.6387
		(1.27)	(3.10)	(5.02)
8		0.00	0.231	0.414	0.564	.7787	1.6321
		(1.12)	(3.13)	(5.07)
9		0.00	0.192	0.391	0.564	.7785	1.6331
		(0.99)	(3.15)	(5.14)
9		0.00	0.00	0.484	0.552	.7765	1.6328
			(4.54)	(4.61)
10		0.00	0.174	0.362	0.563	.7774	1.6371
		(0.93)	(3.12)	(5.25)
11		0.00	0.154	0.341	0.560	.7765	1.6403
		(0.86)	(3.09)	(5.31)
12		0.00	0.134	0.326	0.557	.7761	1.6421
		(0.79)	(3.14)	(5.33)
13		0.00	0.110	0.316	0.555	.7747	1.6469
		(0.67)	(3.22)	(5.28)
14		0.00	0.907	0.308	0.552	.7736	1.6510
		(0.57)	(3.29)	(5.21)
15		0.00	0.745	0.301	0.549	.7725	1.6548
		(0.48)	(3.39)	(5.13)
16		0.00	0.059	0.296	0.545	.7713	1.6594
		(0.39)	(3.48)	(5.04)

^1/T-statistics in parentheses.

View Table

Table VI-1.

United States: Biased Tests of Asymmetry

Estimated
	equation:	$x_t=\delta {\overline{x}}_{t+1}^{*}+\left(1-\delta \right){\pi }_{\mathrm{t}-1}+\beta {\mathrm{gap}}_{\mathrm{t}}^{*}+\gamma {\mathrm{gappos}}_{\mathrm{t}}^{*}+{ϵ}_{\mathrm{t}}^{\pi }$
where:		$\begin{array}{ccc}\mathrm{gap}*& =& y-y*=y-\overline{y}+\alpha ,\mathrm{gapps}*=\mathrm{positive}\mathrm{values}\mathrm{of}\mathrm{gap}*\\ {\overline{\pi }}_{t+1}^{*}& =& -2({\mathrm{t\pi }}_{t+4}^{*}+t-1{\pi }_{t+3}^{*}+t-2{\pi }_{t+2}^{*}+t-3{\pi }_{t+1}^{*}+t-4{\pi }_t^{*})\hfill \\ \pi & =& \mathrm{Percent}\mathrm{change}\mathrm{in}\mathrm{the}\mathrm{CPI}\mathrm{at}\mathrm{annual}\mathrm{rates}\hfill \\ {\pi }_{t+1}^{*}& =& \mathrm{Michigan}\mathrm{Survey}\mathrm{measure}\mathrm{of}\mathrm{inflation}\mathrm{expectations}\hfill \\ y& =& \frac{1}{2k+1}\left[y_t+\underset{i+1}{\overset{k}{\mathrm{\Sigma }}}{y}_{t+i}+y_{t-i}\right]\hfill \end{array}$
Data: U.S. Quarterly Data, 1964QI-90QIV.
		Estimated Coefficients 1/
k		α	γ	β	δ	R2	σ
5		0.00	0.285	0.593	0.547	.7739	1.6499
		(0.96)	(3.34)	(4.73)
6		0.00	0.302	0.497	0.556	.7761	1.6296
		(1.20)	(3.32)	(4.91)
7		0.00	0.281	0.435	0.562	.7769	1.6387
		(1.27)	(3.10)	(5.02)
8		0.00	0.231	0.414	0.564	.7787	1.6321
		(1.12)	(3.13)	(5.07)
9		0.00	0.192	0.391	0.564	.7785	1.6331
		(0.99)	(3.15)	(5.14)
9		0.00	0.00	0.484	0.552	.7765	1.6328
			(4.54)	(4.61)
10		0.00	0.174	0.362	0.563	.7774	1.6371
		(0.93)	(3.12)	(5.25)
11		0.00	0.154	0.341	0.560	.7765	1.6403
		(0.86)	(3.09)	(5.31)
12		0.00	0.134	0.326	0.557	.7761	1.6421
		(0.79)	(3.14)	(5.33)
13		0.00	0.110	0.316	0.555	.7747	1.6469
		(0.67)	(3.22)	(5.28)
14		0.00	0.907	0.308	0.552	.7736	1.6510
		(0.57)	(3.29)	(5.21)
15		0.00	0.745	0.301	0.549	.7725	1.6548
		(0.48)	(3.39)	(5.13)
16		0.00	0.059	0.296	0.545	.7713	1.6594
		(0.39)	(3.48)	(5.04)

^1/T-statistics in parentheses.

Chart VI-1 illustrates the linear Phillips curve relationship when γ is constrained to equal zero and the model is chosen to maximize the fit of the inflation equation. In this case the optimal k, when both γ and α were imposed to be equal to zero was 11. This equation produced an estimate of δ of 0.548 and for β of 0.524. The top panel in Chart VI-1 plots potential output, under the assumption that α and 7 are equal to zero. The middle panel presents the percent change in the CPI measured at annual rates along with the Michigan Survey of one-year-ahead CPI inflation expectations. The bottom panel presents the difference between inflation and its backward- and forward-looking components, e.g.,

and the contribution of the output gap, as measured by the coefficient times the output gap, e.g., β gap_t. As can be seen in the chart, there is a tendency for the linear model to underpredict inflation during the two inflationary episodes in the 1970s when there was large and persistent excess demand.

Table VI-2 reports the results of estimating the same model, except this time α is estimated simultaneously along with the other parameters of the model. In this case, the optimal k parameter is 12. Based on this preferred model, there is clear evidence that positive gaps have larger effects on inflation than negative gaps. This is a very similar finding to what was reported in Laxton, Meredith, and Rose (1995). Indeed, the estimated coefficient on the positive gaps (β + γ) is 1.1 or about five times greater than the coefficient on the negative gaps. The estimated value of α is -1.3, suggesting that the mean value of the output gap that enters the Phillips curve is, on average, 1.3 percentage points below measures that are based on trend measures of output. Chart VI-2 illustrates the results for the asymmetric model. In this case, potential output in the top panel is raised by 0.013 to be consistent with the logical implications of this form of asymmetry.

These results illustrate that the output-inflation experience of the United States is consistent with an asymmetric Phillips curve. In particular, the data suggests that the effect on inflation of changes in the output gap is much larger if the economy is above potential. Moreover, the results suggest that the existence of this asymmetry is likely to be falsely rejected unless consideration is given to the downward effect of asymmetries on the average level of the output gap.

Table VI-2.

United States: Asymmetric Modal of the U.S. Output-Inflation Tradeoff

^1/T-statistics in parentheses.

Table VI-2.

United States: Asymmetric Modal of the U.S. Output-Inflation Tradeoff

Estimated
	equation:	${\mathrm{\pi }}_t=\delta {\overline{\mathrm{\pi }}}_{t+4}^{*}+(1-\delta ){\mathrm{\pi }}_{\mathrm{t}-1}+\mathrm{\beta }{\mathrm{gap}}_{\mathrm{t}}^{*}+\gamma {\mathrm{gappos}}_{\mathrm{t}}^{*}+{ϵ}_{\mathrm{t}}^{\pi }$
where:		$\begin{array}{ccc}{\mathrm{gap}}^{*}& =& y-y^{*}=y-\overline{y}+\alpha ,{\mathrm{gappos}}^{*}=\mathrm{positive}\mathrm{values}\mathrm{of}{\mathrm{gap}}^{*}\hfill \\ {\overline{\begin{array}{c}\mathrm{\pi }\end{array}}}_{\mathrm{t}\mathrm{+}\mathrm{4}}^{\mathrm{*}}& =& .2({}_t{\pi }_{t+4}^{*}+{}_{t-1}{\pi }_{t+3}^{*}+{}_{t-2}{\pi }_{t+2}^{*}+{}_{t-3}{\pi }_{t+1}^{*}+{}_{t-4}{\pi }_t^{*})\hfill \\ \mathrm{\pi }& =& \mathrm{Percent}\mathrm{change}\mathrm{in}\mathrm{the}\mathrm{CPI}\mathrm{at}\mathrm{annual}\mathrm{rates}\hfill \\ {\mathrm{\pi }}_{\mathrm{t}\mathrm{+}\mathrm{4}}^{\mathrm{*}}& =& \mathrm{Michigan}\mathrm{Survey}\mathrm{measure}\mathrm{of}\mathrm{inflation}\mathrm{expectations}\hfill \\ y& =& \frac{1}{2k+1}[y_t+\underset{i+1}{\overset{k}{\mathrm{\Sigma }}}{y}_{t+1}+y_{t-1}]\hfill \end{array}$
Data: U.S. Quarterly Data, 1964QI-90QIV.
		Estimated Coefficients 1/						Wald Test: SL(α, γ = 0)
k		α	γ	β	δ	R2	σ
5		-0.354	0.878	0.458	0.566	.7776	1.6445	0.087
		(0.99)	(1.83)	(2.59)	(4.65)
6		-0.441	0.873	0.384	0.576	.7816	1.6296	0.032
		(1.23)	(2.19)	(2.64)	(4.91)
7		-0.547	0.813	0.337	0.582	.7821	1.6275	0.022
		(1.44)	(2.36)	(2.55)	(5.01)
8		-0.670	0.780	0.308	0.585	.7844	1.6192	0.015
		(1.73)	(2.64)	(2.61)	(5.20)
9		-0.770	0.758	0.282	0.586	.7850	1.6168	0.004
		(2.09)	(3.21)	(2.60)	(5.48)
10		-0.893	0.772	0.254	0.587	.7851	1.6164	0.010
		(2.72)	(3.00)	(2.52)	(5.87)
11		-1.149	0.918	0.218	0.591	.7873	1.6081	0.004
		(3.27)	(2.99)	(2.47)	(6.07)
12		-1.256	0.925	0.202	0.593	.7892	1.6010	0.001
		(3.66)	(3.16)	(2.43)	(6.13)
13		-1.369	0.916	0.189	0.600	.7890	1.6017	0.001
		(3.67)	(3.13)	(2.47)	(5.99)
14		-1.478	0.896	0.177	0.595	.7879	1.6058	0.007
		(3.13)	(2.72)	(2.43)	(5.88)
15		-1.661	0.919	0.166	0.593	.7862	1.6123	0.002
		(3.38)	(2.69)	(2.47)	(5.79)
16		-1.712	0.866	0.161	0.587	.7834	1.6229	0.010
		(3.02)	(2.56)	(2.49)	(5.58)

^1/T-statistics in parentheses.

View Table

Table VI-2.

United States: Asymmetric Modal of the U.S. Output-Inflation Tradeoff

Estimated
	equation:	${\mathrm{\pi }}_t=\delta {\overline{\mathrm{\pi }}}_{t+4}^{*}+(1-\delta ){\mathrm{\pi }}_{\mathrm{t}-1}+\mathrm{\beta }{\mathrm{gap}}_{\mathrm{t}}^{*}+\gamma {\mathrm{gappos}}_{\mathrm{t}}^{*}+{ϵ}_{\mathrm{t}}^{\pi }$
where:		$\begin{array}{ccc}{\mathrm{gap}}^{*}& =& y-y^{*}=y-\overline{y}+\alpha ,{\mathrm{gappos}}^{*}=\mathrm{positive}\mathrm{values}\mathrm{of}{\mathrm{gap}}^{*}\hfill \\ {\overline{\begin{array}{c}\mathrm{\pi }\end{array}}}_{\mathrm{t}\mathrm{+}\mathrm{4}}^{\mathrm{*}}& =& .2({}_t{\pi }_{t+4}^{*}+{}_{t-1}{\pi }_{t+3}^{*}+{}_{t-2}{\pi }_{t+2}^{*}+{}_{t-3}{\pi }_{t+1}^{*}+{}_{t-4}{\pi }_t^{*})\hfill \\ \mathrm{\pi }& =& \mathrm{Percent}\mathrm{change}\mathrm{in}\mathrm{the}\mathrm{CPI}\mathrm{at}\mathrm{annual}\mathrm{rates}\hfill \\ {\mathrm{\pi }}_{\mathrm{t}\mathrm{+}\mathrm{4}}^{\mathrm{*}}& =& \mathrm{Michigan}\mathrm{Survey}\mathrm{measure}\mathrm{of}\mathrm{inflation}\mathrm{expectations}\hfill \\ y& =& \frac{1}{2k+1}[y_t+\underset{i+1}{\overset{k}{\mathrm{\Sigma }}}{y}_{t+1}+y_{t-1}]\hfill \end{array}$
Data: U.S. Quarterly Data, 1964QI-90QIV.
		Estimated Coefficients 1/						Wald Test: SL(α, γ = 0)
k		α	γ	β	δ	R2	σ
5		-0.354	0.878	0.458	0.566	.7776	1.6445	0.087
		(0.99)	(1.83)	(2.59)	(4.65)
6		-0.441	0.873	0.384	0.576	.7816	1.6296	0.032
		(1.23)	(2.19)	(2.64)	(4.91)
7		-0.547	0.813	0.337	0.582	.7821	1.6275	0.022
		(1.44)	(2.36)	(2.55)	(5.01)
8		-0.670	0.780	0.308	0.585	.7844	1.6192	0.015
		(1.73)	(2.64)	(2.61)	(5.20)
9		-0.770	0.758	0.282	0.586	.7850	1.6168	0.004
		(2.09)	(3.21)	(2.60)	(5.48)
10		-0.893	0.772	0.254	0.587	.7851	1.6164	0.010
		(2.72)	(3.00)	(2.52)	(5.87)
11		-1.149	0.918	0.218	0.591	.7873	1.6081	0.004
		(3.27)	(2.99)	(2.47)	(6.07)
12		-1.256	0.925	0.202	0.593	.7892	1.6010	0.001
		(3.66)	(3.16)	(2.43)	(6.13)
13		-1.369	0.916	0.189	0.600	.7890	1.6017	0.001
		(3.67)	(3.13)	(2.47)	(5.99)
14		-1.478	0.896	0.177	0.595	.7879	1.6058	0.007
		(3.13)	(2.72)	(2.43)	(5.88)
15		-1.661	0.919	0.166	0.593	.7862	1.6123	0.002
		(3.38)	(2.69)	(2.47)	(5.79)
16		-1.712	0.866	0.161	0.587	.7834	1.6229	0.010
		(3.02)	(2.56)	(2.49)	(5.58)

^1/T-statistics in parentheses.

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United States Interpreting U.S. Inflation with a Linear Model

Citation: IMF Staff Country Reports 1995, 094; 10.5089/9781451839470.002.A006

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United States Interpreting U.S. Inflation with an Asymmetric Model

Citation: IMF Staff Country Reports 1995, 094; 10.5089/9781451839470.002.A006

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4. Policy implications of asymmetries

This section provides a brief discussion of policy implications of linear and asymmetric models of inflation dynamics described above. In particular, the trade-offs faced by a monetary authority are compared by simulating the effect of aggregate demand in a small model of the macro-economy. The effects of a monetary policy rule in which the authorities delay the adjustment in interest rates in response to an increase in demand pressures is compared to a policy rule in which the authorities react in advance of the actual emergence of inflation pressures and the policy control process. The model, which is essentially the same as the one used in Clark, Laxton, and Rose (1995), is sketched below.

If the economy features the asymmetric form of inflation dynamics, then a delay in responding to an inflationary demand shock will engender higher inflation expectations and necessitate a relatively more severe tightening of monetary conditions in the future. In contrast to the linear case, where policy errors are more easily corrected, asymmetric inflation dynamics mean that delaying interest rate hikes in the face of excess demand results in a larger cumulative output loss; the monetary authority is required to impose a much more severe monetary reaction than otherwise in order to reign in higher inflationary pressures. Indeed, an important prediction of the asymmetric model is that the seeds of large recessions are planted when an economy is allowed to exceed its potential.

The model’s equations are listed in Table VI-3. In addition to the two versions of the Phillips curve, the model defines the real interest rates as the nominal short-term interest rate less expected inflation. An aggregate demand equation (in terms of the gap) is defined, in which aggregate demand is assumed to be negatively related to the real interest rate lagged two quarters. The lagged effect of interest rates (and monetary policy) on aggregate demand is noteworthy, since it has important implications for the effectiveness of monetary policy. The aggregate demand equation also is a function of lagged values of the gap, which implies that the effects of demand shocks take time to dissipate. ^1/ The effect of these assumptions is that 5-6 quarters of a persistent real interest rate hike of 100 basis points would reduce the output gap by 0.4 percentage points.

These properties of output dynamics and the monetary policy transmission mechanism have an important implication for the design of monetary policy rules, namely, that monetary policy cannot offset completely the effects of shocks. There will be cycles in economic activity and there will be temporary deviations of inflation from its target level. Thus, the model implies that it will be important for the monetary authorities to be forward-looking in its actions.

Table VI-3.

United States: A Small Simulation Modal of the U.S. Output-Inflation Process

Table VI-3.

United States: A Small Simulation Modal of the U.S. Output-Inflation Process

Asymmetric Phillips curve:
	${\mathrm{\pi }}_t=.593{\overline{\begin{array}{c}\mathrm{\pi }\end{array}}}_{t+4}^{*}+(1-.593){\mathrm{\pi }}_{t-1}+.202{\mathit{gap}}_t^{*}+.925{\mathit{gappos}}_t^{*}+g_t^{\mathrm{\pi }}$
	${\overline{\begin{array}{c}\mathrm{\pi }\end{array}}}_{t+4}^{*}=.2\left({}_t{\mathrm{\pi }}_{t+4}^{*}+{}_{t-1}{\mathrm{\pi }}_{t+3}^{*}+{}_{t-2}{\mathrm{\pi }}_{t+2}^{*}+{}_{t-3}{\mathrm{\pi }}_{t+1}^{*}+{}_{t-4}{\mathrm{\pi }}_t^{*}\right)$
Linear Phillips curve:
	${\mathrm{\pi }}_t=.548{\overline{\mathrm{\pi }}}_{t+4}^{*}+\left(1-.548\right){\mathrm{\pi }}_{t-1}+.524{\mathit{gap}}_t+g_t^{\mathrm{\pi }}$
Real interest rates:
	${\mathit{rr}}_t={\mathit{rs}}_t-{\mathrm{\pi }}_{t+4}^{*}$
Inflation and inflation expectations:
	${\mathrm{\pi }}_t=[{(P_t/P_{t-1})}^4-1]=100,{\mathrm{\pi }}_{t+4}^{*}=(P_{t+4}/P_t-1)=100$
Aggregate demand equation:
	${\mathit{gap}}_t=1.074{\mathit{gap}}_{t-1}-.290{\mathit{gap}}_{t-2}-.158{\mathit{rr}}_{t-2}+t_t^{\mathit{gap}}$
Policy reaction function:
	${\mathit{rs}}_t-{\mathrm{\pi }}_{t+4}^{*}=2\left({\mathrm{\pi }}_{t+3}-{\mathrm{\pi }}^{*}\right)+{\mathit{gap}}_t$
$\begin{array}{ccc}\mathrm{\pi }& =& \mathrm{CPI}\mathrm{inflation}\mathrm{at}\mathrm{annual}\mathrm{rates}\hfill \\ \mathrm{gap}& =& \mathrm{output}\mathrm{gap}\left(\mathrm{y}-\overline{\mathrm{y}}\right)\hfill \\ {\mathrm{gap}}^{*}& =& \left(\mathrm{y}-\overline{\mathrm{y}}+\alpha \right)=\left(\mathrm{y}-\overline{\mathrm{y}}\right)\hfill \\ \mathrm{rr}& =& \mathrm{real}\mathrm{interest}\mathrm{rate}\hfill \\ \mathrm{rs}& =& \mathrm{short}-\mathrm{term}\mathrm{interest}\mathrm{rate}\hfill \\ {\mathrm{\pi }}_{t+4}^{*}& =& \mathrm{one}-\mathrm{year}-\mathrm{ahead}\mathrm{inflation}\mathrm{expectations}\hfill \\ {\mathrm{\Pi }}^{*}& =& \mathrm{inflation}\mathrm{target}\hfill \\ {\mathrm{P}}_t& =& \mathrm{price}\mathrm{level}\hfill \end{array}$

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Table VI-3.

United States: A Small Simulation Modal of the U.S. Output-Inflation Process

Asymmetric Phillips curve:
	${\mathrm{\pi }}_t=.593{\overline{\begin{array}{c}\mathrm{\pi }\end{array}}}_{t+4}^{*}+(1-.593){\mathrm{\pi }}_{t-1}+.202{\mathit{gap}}_t^{*}+.925{\mathit{gappos}}_t^{*}+g_t^{\mathrm{\pi }}$
	${\overline{\begin{array}{c}\mathrm{\pi }\end{array}}}_{t+4}^{*}=.2\left({}_t{\mathrm{\pi }}_{t+4}^{*}+{}_{t-1}{\mathrm{\pi }}_{t+3}^{*}+{}_{t-2}{\mathrm{\pi }}_{t+2}^{*}+{}_{t-3}{\mathrm{\pi }}_{t+1}^{*}+{}_{t-4}{\mathrm{\pi }}_t^{*}\right)$
Linear Phillips curve:
	${\mathrm{\pi }}_t=.548{\overline{\mathrm{\pi }}}_{t+4}^{*}+\left(1-.548\right){\mathrm{\pi }}_{t-1}+.524{\mathit{gap}}_t+g_t^{\mathrm{\pi }}$
Real interest rates:
	${\mathit{rr}}_t={\mathit{rs}}_t-{\mathrm{\pi }}_{t+4}^{*}$
Inflation and inflation expectations:
	${\mathrm{\pi }}_t=[{(P_t/P_{t-1})}^4-1]=100,{\mathrm{\pi }}_{t+4}^{*}=(P_{t+4}/P_t-1)=100$
Aggregate demand equation:
	${\mathit{gap}}_t=1.074{\mathit{gap}}_{t-1}-.290{\mathit{gap}}_{t-2}-.158{\mathit{rr}}_{t-2}+t_t^{\mathit{gap}}$
Policy reaction function:
	${\mathit{rs}}_t-{\mathrm{\pi }}_{t+4}^{*}=2\left({\mathrm{\pi }}_{t+3}-{\mathrm{\pi }}^{*}\right)+{\mathit{gap}}_t$
$\begin{array}{ccc}\mathrm{\pi }& =& \mathrm{CPI}\mathrm{inflation}\mathrm{at}\mathrm{annual}\mathrm{rates}\hfill \\ \mathrm{gap}& =& \mathrm{output}\mathrm{gap}\left(\mathrm{y}-\overline{\mathrm{y}}\right)\hfill \\ {\mathrm{gap}}^{*}& =& \left(\mathrm{y}-\overline{\mathrm{y}}+\alpha \right)=\left(\mathrm{y}-\overline{\mathrm{y}}\right)\hfill \\ \mathrm{rr}& =& \mathrm{real}\mathrm{interest}\mathrm{rate}\hfill \\ \mathrm{rs}& =& \mathrm{short}-\mathrm{term}\mathrm{interest}\mathrm{rate}\hfill \\ {\mathrm{\pi }}_{t+4}^{*}& =& \mathrm{one}-\mathrm{year}-\mathrm{ahead}\mathrm{inflation}\mathrm{expectations}\hfill \\ {\mathrm{\Pi }}^{*}& =& \mathrm{inflation}\mathrm{target}\hfill \\ {\mathrm{P}}_t& =& \mathrm{price}\mathrm{level}\hfill \end{array}$

The particular forward-looking policy reaction function used is a variant of the rule considered by Bryant, Hooper, and Mann (1993). In setting the short-term Interest rate, the monetary authority is assumed to raise the real rate that enters the output equation when there is excess demand in the economy or inflation is expected to be above the target level three quarters ahead. The particular calibration adopted is designed to assure that inflation returns to the target level within a reasonably short period (two years, say) following a shock. The effectiveness of this policy rule is contrasted with an identical rule except that the monetary authorities are assumed to begin reacting to the demand shock with a one quarter delay.

The simulation assumes an impulse shock of 1 percent to aggregate demand--i.e., a 1 percentage point output gap opens on impact, with no further shocks. ^1/ Charts VI-3 and VI-4 illustrate the effect of the demand shock on the assumption that the Phillips curve is linear. In this case, the effect of a delayed monetary policy response is relatively innocuous. Assuming no delay, the policy rule implies an immediate 270 basis point increase in the short-term interest rate in the first quarter (see Chart VI-3). Inflation rises about 1 percentage point above its baseline level before returning to baseline by the end of 6 quarters. Output rises 1 percent above its baseline value initially, but falls below baseline in the second year, before returning to baseline. The cumulative gain in output is about 2 percent.

If the monetary response is delayed by one quarter, there is a larger hike in short-term interest rates, and inflation edges slightly higher, peaking at about 1.3 percentage points above control, but the cumulative gain in output is even larger, amounting to about 2.5 percent. This illustrates that if the inflation-output tradeoff is linear, the case for aggressive monetary resistance to inflationary demand shocks is less strong. While the monetary authority may be concerned to see inflation rise above the target by more and for a longer period of time, there is no particular cost to delaying interest rate hikes when output exceeds potential output.

This result, however, does not hold in the case of the asymmetric Phillips curve (Charts VI-5 and VI-6). Assuming that the policy response is not delayed, short-term interest rates increase by over 400 basis points in the first quarter, inflation peaks at about 2 percentage points above control. The effect on output is roughly similar to the case of a linear Phillips curve during the first few quarters. However, the larger effect on inflation in this model requires a much deeper secondary contraction. As a result, the cumulative effect on output is slightly negative.

The consequences of delaying the monetary response to the shock also are much more severe in the presence of asymmetries. Short-term interest rates must be raised substantially higher to combat the cumulating inflationary pressures, as expectations respond to the cumulating excess demand and rising inflation. Inflation now peaks at 3 percentage points above its baseline value. Moreover, in order to bring inflation back under control a much more severe contraction is required. The cumulative change in output is now substantially negative because a large contraction is needed to counteract the inflationary effects caused by the initial temporary boom.

5. Conclusions

Evidence was presented above that suggests that the short-run inflation-output tradeoff is nonlinear in the United States. This in turn implies that excess demand gaps have a larger effect on inflation than excess supply gaps. The policy implications of macroeconomic models that feature explicit short-run capacity constraints can be considerably different than those of models based on simple linear versions of the Phillips Curve. The former suggest that there may be large risks from allowing the economy to overheat, while the latter suggest that the risks may be small. In the face of the empirical evidence presented above, and the potential for significant cumulative losses in output and more extreme variation in economic conditions, the results suggest the merits of a monetary policy that acts well in advance of the emergence of actual inflation pressure.

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United States Linear Model Responses to a Temporary 1% Positive Demand Shock

Citation: IMF Staff Country Reports 1995, 094; 10.5089/9781451839470.002.A006

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United States Linear Model Responses to a Temporary 1% Positive Demand Shock: Delayed Monetary Policy Response

Citation: IMF Staff Country Reports 1995, 094; 10.5089/9781451839470.002.A006

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United States Asymmetric Model Responses to a Temporary 1% Positive Demand Shock

Citation: IMF Staff Country Reports 1995, 094; 10.5089/9781451839470.002.A006

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United States Asymmetric Model Responses to a Temporary 1% Positive Demand Shock: Delayed Monetary Policy Response

Citation: IMF Staff Country Reports 1995, 094; 10.5089/9781451839470.002.A006

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