Adaptive expectations

Adaptive expectations is an economic theory describing how individuals form forecasts about future values of economic variables by adjusting their previous expectations based on the gap between what they expected and what actually occurred ^[1]. Under this framework people revise their beliefs gradually in response to forecast errors relying primarily on past observations rather than incorporating all available information about underlying economic relationships. The concept has been influential in macroeconomic analysis particularly in understanding inflation dynamics and the relationship between inflation and unemployment.

Historical development

The formal treatment of adaptive expectations emerged in the 1950s and 1960s as economists sought to model how individuals form beliefs about future economic conditions. Philip Cagan introduced an adaptive expectations approach in his 1956 analysis of hyperinflation examining how people adjusted their expectations of money growth during periods of rapid price increases ^[2]. His work demonstrated that expectations could be represented as a weighted average of past observations with recent values receiving greater weight.

Milton Friedman incorporated adaptive expectations into his permanent income hypothesis of consumption published in 1957. He argued that consumers distinguish between temporary and permanent changes in income and that expectations of permanent income are formed adaptively based on past income observations. This application showed how the expectations framework could explain consumption behavior that appeared puzzling under simpler assumptions.

Friedman and Edmund Phelps independently applied adaptive expectations to the analysis of the Phillips curve in the late 1960s ^[3]. They argued that the apparent trade-off between inflation and unemployment observed by A.W. Phillips would disappear in the long run as workers adapted their inflation expectations to actual experience. This expectations-augmented Phillips curve became central to monetarist economics and challenged prevailing Keynesian views about the permanence of the inflation-unemployment trade-off.

The influence of adaptive expectations diminished following the development of rational expectations theory by John Muth in 1961 and its application to macroeconomics by Robert Lucas and Thomas Sargent in the 1970s. Rational expectations held that economic agents should use all available information efficiently rather than relying only on past values. The stagflation of the 1970s appeared to support the rational expectations critique and led to widespread adoption of rational expectations in academic economics.

Despite the dominance of rational expectations in economic theory, adaptive expectations remains relevant for practical forecasting and for describing actual expectations formation documented in survey data. Empirical evidence suggests that many individuals form expectations in ways more consistent with adaptive than rational models.

The adaptive expectations mechanism

The basic adaptive expectations model specifies that expected values of a variable are revised based on the difference between the previous expectation and the actual realized value ^[4].

Mathematical formulation

The adaptive expectations formula for a variable such as inflation can be expressed as:

Expected inflation next period = Expected inflation this period + adjustment parameter × (Actual inflation this period - Expected inflation this period)

The adjustment parameter determines how quickly expectations respond to forecast errors. A higher value means faster adjustment toward actual values while a lower value means more persistence in expectations. When the adjustment parameter equals one, expected values equal the most recent actual value. When it equals zero, expectations never change.

This formulation can be rewritten to show that current expectations equal a weighted average of all past actual values with geometrically declining weights. The most recent observation receives the highest weight and the influence of past observations diminishes with time. This backward-looking characteristic distinguishes adaptive from rational expectations.

Error correction interpretation

Adaptive expectations embodies an error correction mechanism where individuals learn from their mistakes. If actual inflation exceeds expected inflation people revise their expectations upward. If actual inflation falls short of expectations they revise downward. Over time this process should drive expectations toward actual values.

The speed of convergence depends on the adjustment parameter and the pattern of the underlying variable. For a constant variable expectations will eventually converge exactly. For a variable following a trend expectations will perpetually lag behind never fully catching up. This limitation is an important weakness of the adaptive approach.

Applications in macroeconomics

Adaptive expectations has been applied extensively to understand inflation dynamics, labor markets and monetary policy ^[5].

The expectations-augmented Phillips curve

The original Phillips curve suggested a stable inverse relationship between inflation and unemployment that policymakers could exploit to achieve desired combinations of the two variables. Friedman and Phelps challenged this view by incorporating adaptive expectations into the analysis.

Under the expectations-augmented Phillips curve, the relationship between inflation and unemployment depends on expected inflation. Workers bargain for wages based on their expectations of future prices. If policymakers engineer higher inflation than expected workers initially accept lower real wages and unemployment falls below its natural rate. However as workers adapt their expectations to higher actual inflation they demand correspondingly higher nominal wages. The temporary reduction in unemployment reverses while higher inflation persists.

This analysis implies that there is no permanent trade-off between inflation and unemployment. In the long run, after expectations fully adjust, unemployment returns to its natural rate regardless of the inflation rate. The long-run Phillips curve is vertical at the natural rate of unemployment.

Inflation persistence

Adaptive expectations helps explain why inflation tends to persist once established ^[6]. When past inflation influences current expectations and expectations affect wage and price setting, high inflation in the past leads to high expected inflation which generates high actual inflation in the present. This inertia makes reducing inflation costly because expectations adjust only gradually.

Disinflation under adaptive expectations requires maintaining actual inflation below expected inflation long enough for expectations to adjust downward. During this adjustment period the economy operates below potential with higher unemployment than would prevail under stable inflation. The sacrifice ratio measures the cumulative output loss required to permanently reduce inflation.

Monetary policy implications

Under adaptive expectations monetary policy can affect real economic variables in the short run by creating inflation surprises ^[7]. If policymakers expand money supply faster than expected, inflation exceeds expectations and real wages fall temporarily boosting employment. However these effects are transitory and attempting to exploit them repeatedly results only in higher inflation without lasting employment gains.

This analysis supported the monetarist prescription for stable, predictable monetary policy. Rather than attempting to fine-tune the economy through activist policy, central banks should provide a stable nominal anchor that allows expectations to settle at low inflation.

Comparison with rational expectations

Rational expectations theory emerged as an alternative that addressed perceived limitations of adaptive expectations ^[8].

Key differences

Rational expectations assumes that individuals use all available information efficiently to form expectations rather than relying only on past values of the variable being forecast. Expected values under rational expectations equal the true mathematical expectations conditional on available information. Forecast errors are random and unpredictable with no systematic patterns.

Under adaptive expectations individuals ignore potentially useful information about the structure of the economy and the likely effects of policy changes. They make systematic errors that could in principle be corrected through better use of information. Critics argued this violated basic principles of economic rationality.

Policy implications

The policy implications differ significantly between the two approaches. Under adaptive expectations policy can have real effects by surprising individuals whose expectations adjust only gradually. Under rational expectations policy effects are limited because individuals anticipate policy actions and their consequences. Only truly unexpected policy changes affect real variables, and systematic policy rules have no real effects once understood.

The distinction is particularly important for evaluating the costs of disinflation. Under adaptive expectations reducing inflation requires a period of elevated unemployment while expectations adjust. Under some versions of rational expectations a credible commitment to lower inflation could reduce expectations immediately without transitional costs.

Empirical evidence

Survey evidence on actual expectations suggests that neither pure model perfectly describes how people form beliefs ^[9]. Expectations exhibit some backward-looking characteristics consistent with adaptive formation but also respond to announced policy changes and publicly available information. Professional forecasters appear more sophisticated than households, and different groups may use different expectations formation processes.

Many modern models incorporate elements of both approaches, using adaptive learning as a boundedly rational alternative to full rational expectations. These hybrid approaches acknowledge cognitive limitations while allowing for some forward-looking behavior.

Advantages of adaptive expectations

The adaptive expectations framework offers several practical benefits ^[10]:

• Provides simple implementable forecasting rules requiring only past data
• Captures observed persistence in expectations documented in surveys
• Explains gradual adjustment patterns in inflation and other variables
• Offers tractable framework for analyzing policy effects
• Acknowledges cognitive limitations and information processing costs
• Consistent with behavior observed in experimental settings

Limitations of adaptive expectations

The approach has significant conceptual and empirical weaknesses ^[11]:

• Ignores potentially valuable information about economic relationships
• Implies systematic forecast errors that rational agents should eliminate
• Cannot explain rapid adjustments to clearly communicated policy changes
• Performs poorly when variables follow trends or structural breaks occur
• Provides no mechanism for expectations to lead rather than lag actual values
• Vulnerable to Lucas critique that relationships change when policy changes

Adaptive expectations — recommended articles

Decision making — Planning — Risk management — Strategy — Management — Financial management — Organization — Change management — Efficiency

References

• Friedman M. (1968), The Role of Monetary Policy, American Economic Review, Vol. 58, No. 1.
• Phelps E.S. (1967), Phillips Curves, Expectations of Inflation and Optimal Unemployment over Time, Economica, Vol. 34, No. 135.
• Cagan P. (1956), The Monetary Dynamics of Hyperinflation, in Studies in the Quantity Theory of Money, University of Chicago Press.
• Muth J.F. (1961), Rational Expectations and the Theory of Price Movements, Econometrica, Vol. 29, No. 3.
• Lucas R.E. (1972), Expectations and the Neutrality of Money, Journal of Economic Theory, Vol. 4.

Footnotes

1. Friedman M. (1968), pp. 1-8
2. Cagan P. (1956), pp. 25-35
3. Phelps E.S. (1967), pp. 254-265
4. Friedman M. (1968), pp. 8-12
5. Phelps E.S. (1967), pp. 265-275
6. Friedman M. (1968), pp. 12-15
7. Friedman M. (1968), pp. 15-17
8. Muth J.F. (1961), pp. 315-335
9. Lucas R.E. (1972), pp. 103-124
10. Cagan P. (1956), pp. 35-40
11. Muth J.F. (1961), pp. 335-340

Author: Sławomir Wawak