Expectations

Introduction

Discussion^{1 2 3}

Definition

In macroeconomics, expectations are given a central place. Expectations are the unobservable opinions about the future that the individuals would form in their minds.⁴

Types of Expectations

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Adaptive Expectations

Adaptive Expectations⁵, wherein at each new time period (e.g. 2024, 2025) the individual revises his expectations in view of his Expectational Error⁶, i.e. the discrepancy between the current price and the actual current price.

$$\text{Expectation}=\sum \text{Past Expectations}+\text{Expectational Error}$$

The expectation of the new time period is formed as the sum of past expectations with expectational error weighted by the coefficient of revision of expectation⁷

$$P^e=P_{-1}^e+\lambda \left(P_{-1}-P_{-1}^e\right)$$

where, $P^e$ is next year’s rate of inflation⁶ that is currently expected. $P_{-1}^e$ is this year’s rate of inflation that was expected last year. $P$ is this year’s actual inflation rate and $\lambda$ can be between $0$ and $1$ and is called the error adjustment term.

For example⁷,

• if $\lambda =0$, we are not correcting from our mistakes or errors
• if $\lambda =1$, we are over-correcting
• if $\lambda =0.7$, we are giving $70\%$ weightage for past mistakes.

Rational Expectations

We first discuss the limitations of Adaptive Expectations⁸

Assumptions⁹

1. Wages and prices are fully flexible
2. Economic agents are rational, i.e. they intelligently pursue their self-interest.
3. Perfectly competitive markets

Rational expectations¹⁰ , where agents never make systematic errors and therefore the long run equilibrium position is always achieved and sustained except for random (non-systematic errors). Government intervention is powerless to affect the economy even in the short run¹¹

• When forming expectations, the individuals see all the available information¹².⁹
• Muth in 1961 contributed to Rational Expectation.¹³
• PIP by Sargent and Wallace¹⁴

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Assuming rational expectations, increasing money supply would shift the aggregate demand from $A{D}_1$ to $A{D}_2$ without reaction from the supply side. Thus equilibrium is at $E_2$.

Later, when households realize that the real-wage has fallen, the Aggregate Supply curve will shift backward from $A{S}_1$ to $A{S}_2$ leading the equilibrium $E_3$, where the output $Y$ remains at the original level. Thus money is neutral.

¹¹

Footnotes

1. Households form an expectations that price of commodities in the future will rise up and so the rational decision (to maximize the value of money spent) is to buy more of that product and store it for future use (when the rates will be high) ↩

2. Producers may want to produce more in order to meet a rise in demand that they expect. ↩

3. Whenever an announcement of the policy happens, immediately the investors, producers, manufacturers etc will start making expectations

   • “it can be inflationary/deflationary”
   • “I think this sector will grow, let’s buy stocks”
   ↩

4. Expectations are subjective in nature and they are assumptions about the events that are going to happen in the future. ↩

5. In our phone there is an adaptive brightness that enables the smartphone to automatically adjust to the environment’s brightness. Adjusting to the necessity ↩

6. Take the example of Inflation, $P^{e2025}$ (in the year 2024, what will be the inflation during the next financial year, 2025). Say, we thought that inflation would be $P^e=6\%$. But in reality $P=4\%$ in 2025 (present). The difference is referred to as Expectational Error (EE)

   • Now later, we asked ourselves again in 2025 what $P^{e2026}$ is going to be.
   • This time we will be careful. This is because we have adapted to our previous mistake. Say, we predicted $4\%$ but the actual value turned out to be $5\%$.
   • We still made EE, but we improved $2\%\to 1\%$.
   • We try to correct ourselves every time, but we do not try to understand why the error is happening. If we always try to only correct our errors. (Here, we didn’t understand the reason for underestimation of the interest rates.)
   • Backward looking: we look at our previous mistakes to fix/improve our predictions (expectations)
   • There is recency bias and we don’t consider the long past.
   ↩ ↩²

7. That quantifies the Magnitude of correction. $\lambda$ is what percentage of mistakes are you giving to the past errors that you have made.

   • $\lambda =0=0\%$ you are not accounting for any correction
   • $\lambda =1=100\%$
   ↩ ↩²

8. Say the price of tomatoes have come up to $70$, farmers will expect a growth to $100$ and so all farmers start to sow tomatoes, so after 2 months we have a market which is flooded with tomatoes. Because of this the market price of tomatoes fall to $10$. So, the farmers now think that there is no profit in growing tomatoes and thus they stop growing, and the prices of the tomatoes come up to $70$ again. This happened because the farmers were not literate to understand the reason for why this price fluctuation was happening. Literacy is critical. We are entangled into the cob-web model.

   • the reason was scarcity, which the farmers didn’t realize
   ↩

9. Individuals form expectations based on available information.

   • we have a set of information ${\theta }_t$
   • most important assumption: Full and Free information (perfect competition, Classical Model assumptions).
   ↩ ↩²

10. This is closely associated to Neo-classical school of economic thought ↩

11. In a normal scenario, we will notice that $M^S\to Y\uparrow$ (output rises due to increased money supply)

    • $M^S\uparrow \to r\downarrow \to I\uparrow \to Y\uparrow$
    • or with lag effect $M^S\uparrow \to P\uparrow \to \text{Profits}\uparrow \to \text{AS}\uparrow \to Y\uparrow$.
    • or $M^S\uparrow \to r\downarrow \to \text{AD}\uparrow \to Y\uparrow$
    ↩ ↩²

12. When information is free, there is no price for information. (Like trying to sell sand in the desert). And there is no scope for error (full information) ↩

13. This was developed by Muth in the 1960s. ↩

14. In rational expectations, the policies are not effective (Classical Model). Proved by Sargant and Wallace (PIP) ↩