Expectations in Economics
Expectations in Economics
Expectations play a major role in determining the behaviour of the economy. How agents respond to change in policy determines the size and sometimes the direction of the economy's response to the change. The importance of expectations is an old theme in macroeconomics. Nearly all the economic decisions people and firms make - whether to buy bonds or stocks, whether or not to buy a machine depend on their expectation of future profits, or future interest rates. In real world people form expectations for every activity they do. When it comes to economic activity the agents in the economy also form expectations. These expectations can be in relation to expected rise or decrease in price of any goods or services. Therefore the policy maker's should take into account the expectations of the people.
Until 1970, macroeconomists based the formation of expectations on animal spirit and backward looking rules. These were called as regressive expectations or adaptive (error learning) expectations. In early 1970 Robert Lucas and Thomas Sargent argued that economists should assume that people have rational expectations that people look to the future and do the best job they can in predicting it.
Economists work with many scenarios for how managers, workers, and investors go about forecasting the future and forming their expectations. The main formulations about expected inflation are static expectations, regressive expectations adaptive expectations and rational expectations. This essay sticks mainly to comparing and contrasting the behaviour of the economy in which people have rational expectations and adaptive expectations.
THE ROLE OF EXPECTATIONS
The stability of the macro economy depends critically upon the expectations of decision makers concerning future macroeconomic conditions, i.e., the loci of the aggregate demand and supply curves. The economy can remain stable only as long as decision-makers' expectations match actual conditions fairly closely, i.e., when there are no surprises.
Two recently emerging economic theories shed light on the lack of predictability of public policy makers. The major hypotheses in economists for constructing the expected value of a variable are adaptive and rational expectation hypothesis.
ADAPTIVE EXPECTATIONS
Adaptive expectations are when agents learn from past experience, which they extrapolate into expectations for future events. In other words adaptive expectations prevail when people assume the future will be like the recent past. Thus under adaptive expectations the rate of inflation expected for next year might be the rate of inflation last year. So if today's inflation rate is 3 % with adaptive expectations agents think that next period's inflation rate will be 3 %. Under this, the simplest adaptive expectation assumption, we would have is
????t????
The simple adaptive expectation assumption is that, the expected inflation rate is equal to the lagged inflation rate. The aggregate supply curve is thus
????t??????????Y - Y*?
We can use this aggregate supply curve, together with aggregate demand curve to study the dynamic adjustment of the economy to changes in policy. We can use the following adaptive expectation rule ?e t-?e t-1 = ? (? t-1-?e t-1) to find out actual and expected inflation rates.
For e.g. an imaginary situation is stated below
Inflation Rate
Time
Actual
Expected
Unanticipated
0
0%
0%
0%
2%
0%
+2%
2
4%
2%
+2%
3
6%
4%
+2%
4
8%
6%
+2%
From the above table we can see that at all periods, actual inflation exceeds expected inflation. Thus the unanticipated inflation rate is positive as actual inflation rises by 2% every year. This is due to the forecasting rule that is backward looking (adaptive / error learning), there is systematic under prediction of inflation rate. In other words agents make systematic forecasting errors. On the other hand if, actual inflation fell by 2% every year there would be systematic under prediction of the inflation rate.
If the inflation rate is rising, the public systematically under predicts what the inflation rate will be next period. If the inflation rate is falling, then the public systematically over predicts the rate of inflation for next period. Thus, with adaptive expectations the public can be systematically fooled if inflation is accelerating or decelerating.
Using the long run and short run Phillips curve to determine the relationship between natural rate of unemployment and inflation under adaptive expectations.
? = Actual inflation
?e = Expected inflation
UN = Natural Rate Of Unemployment
U1 = Change in Natural Rate Of Unemployment
LRPC = Long Run Phillips Curve
SRPC = Short Run Phillips Curve
As shown in the above diagram if inflation rises to 4% people expect ? to be 2%. This is a movement along SRPC0 from point 0 to point 1. Unemployment falls to U1, which is less than UN. In the next period the economic agents look at what inflation was before period and adjust their price expectations and expect inflation equal to 4%. But the policy makers can increase inflation to 6% (through monetary expansion) and move along the SRPC1, which would keep the unemployment at U1, which is less than UN. The same process continues into period 3.
The idea is that if agents have adaptive expectations and respond to rising inflation with a lag, the policy makers could use monetary policy to permanently reduce the unemployment rate below the natural rate.
If inflation were perfectly predictable then it would be no problem if the inflation rate rose 2% a year (assuming that inflation is low). We could include this fact in all contracts that are written in the economy. There would be no damage done to those who lend. So predictability here is the key. If you are a wage negotiator who forms expectations adaptively, you'll systematically lose out.
RATIONAL EXPECTATIONS
Muth's (1961) concept of rational expectations was that agents make use of all available relevant information by deriving their expectations of the future values of variables from the underlying true economic model that generates the variable to be forecast. In simple words people use all the information they have to predict the future. Expectations are based on all available information, not just past information but also predictions about current and future policy. Therefore people are in a position to adapt to any changes in the price level with immediate effect. Under rational expectations agents ...
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RATIONAL EXPECTATIONS
Muth's (1961) concept of rational expectations was that agents make use of all available relevant information by deriving their expectations of the future values of variables from the underlying true economic model that generates the variable to be forecast. In simple words people use all the information they have to predict the future. Expectations are based on all available information, not just past information but also predictions about current and future policy. Therefore people are in a position to adapt to any changes in the price level with immediate effect. Under rational expectations agents adapt their expectations of future inflation rate to changes in actual inflation rate almost immediately, as they are believed to have perfect or all information in the economy.
An important point to be noted is that under Rational expectations people may make mistakes in predictions but will adjust expectations to policy changes i.e. people will not make systematic mistakes. The rational expectation view cannot be captured in a simple mechanical form such as ??????t ??????t argues that there can be no formula for expected inflation that is independent of the actual behaviour of inflation.
The Main Properties of Rational Expectations
Consider a model of a random-walk process
X t + 1= x t + e t + 1
Where e ~ N (0, ? 2) and E [e t + I e t + j ] = 0, i.e., no serial correlation. Under the rational-expectations hypothesis, all agents are supposed to know this underlying model.
E t x t + 1 = E [x t + 1 | I t ]
= E[x t | I t] + E [e t + 1| I t]
= E t x t
= x t
The forecasting error can be given as xt+1 - Etxt+1. The expected error is
E [x t + 1 - E t x t + 1] = E [x t + e t+1 - x t]
= Eet+1
= 0
That is, the rational expectation, E t x t + 1, is an unbiased predictor of xt+1. The rational expectation is an efficient predictor of x t + 1, if the variance of the prediction error is smaller than that of any other possible predictor. The error variance is
E [x t + 1 - E t x t + 1]2 = E[x t + e t + 1 - x t]2
= E(et+1)2
= ? 2
Now consider a new estimator, û t+1 = x t + bz t. Then, the variance of the error is
E [x t + 1 - û t + 1 ] 2 = E[ x t + e t + 1 - x t - bz t]2
= ? 2 + b 2 E z t 2
which is bigger than ? 2
Rational expectations imply that forecast errors are serially uncorrelated, but only in the case of one-period ahead forecasts. In general, forecast errors will be correlated to the length of the forecast horizon. But the forecast errors won't be correlated with any information known at the time the forecast is made. The minimum variance of the prediction error implies full (efficient) utilisation of available information. Thus, the property of no serial correlation relates directly to the concept of efficiency.
Using the long run and short run Phillips curve to determine the relationship between natural rate of unemployment and inflation under rational expectations.
As shown in the above diagram if inflation If the policy makers increase inflation by 1% (from 1%to 2%), then people adjust expectations if the policy maker's policy is systematic and could be predicted. Therefore although the SRPC0 shifts to SRPC1 unemployment remains unchanged at UN. As the policy maker in period 2 changes the inflation rate from 4% to 6%, people anticipate these changes in prices. Thus, their price expectation change, which shifts SRPC1 to SRPC2 leaving unemployment unchanged at UN. Any systematic policy by the authorities will not be able to change unemployment if people have rational expectations. In the example above people did not make systematic mistakes. On the other hand if the policy maker's policy were not systematic (i.e. random) the people will guess wrong and unemployment will not remain the same.
According to rational expectations, decision-makers reason, analyse, as well as extrapolate. The decision maker takes into account what government policy makers might do in regard to any emerging situation, and thus to modify their behaviour in response both to the situation and what the policy makers might do in response to it.
For e.g., instead of surprising the economy with a demand stimulus, the government makes public announcement that it is implementing an expansionary monetary policy with the intention of increasing the output of the economy above the normal operating capacity. Rational decision makers will be sure of an inflationary process, but they will be sceptical that the policy can sustain output above the normal operating capacity for long. Thus, when they make their employment and output decisions for the future months, they adjust their list prices and issue wage increases in anticipation of the ensuing inflation, without ever-increasing real output.
Adaptive Expectations when applied To Aggregate Demand and Aggregate Supply Framework
For example, the monetary authorities decides to try to increase the real output of its economy above the normal operating capacity by increasing the money supply, but it implements the expansionary monetary policy as a surprise, i.e. without making any public announcement. This action stimulates liquidity-sensitive purchases and shifts the aggregate demand curve to the right from AD1 to AD2 as illustrated in the above Figure. The demand stimulus does indeed induce an increase of output above the normal operating capacity as the economy adjusts from E1 to E2, but it also sets in motion a process of demand-pull inflation. In a short time, consumers realise that prices are higher today than they were yesterday, and they were higher yesterday than the day before. It therefore appears reasonable to expect prices to be higher tomorrow than today, and even higher the day after tomorrow. Thus, it would be wise to go ahead and make anticipated purchases today rather than wait for the higher future prices, even if the items are not needed until a future date. The current purchases add to today's demand for those items and virtually insure rising prices tomorrow. But as noted earlier, when decision makers are surprised by the realisation that prices are higher than they had counted on when they made their employment and output decisions, they will tend to adjust their employment and output plans to lower levels so that the aggregate supply curve shifts from AS1 toward AS2. This results in further inflation, but of the cost-push variety, until the economy adjusts to its normal operating capacity E3 in the long run.
Rational Expectations When Applied To Aggregate Demand And Aggregate Supply Framework
Like wise under rational expectations when the policy makers, following a systematic model, announce that it will increase (decrease) the money supply agents anticipate the change in the price level. Therefore this result in is a simultaneous shift in AD and AS which offset one another, leaving output unchanged and yielding a higher (lower) price level.
ADAPTIVE EXPECTATIONS Vs RATIONAL EXPECTATIONS
If people have adaptive expectations, then a drop in the money supply would result in a recession. Output would fall below the potential level of output and the price level would not rise by as much as it would have risen otherwise. Under adaptive expectations agents follow a partial-adjustment or error-correction mechanism, and as such they do not satisfy the law of iterated expectations. The change in expectations from t to t-1 is not random and does not have zero mean. It depends on Pt-1. This means that expected forecasts are not identically equal to current forecasts, and forecast errors are auto correlated. With adaptive expectations, agents update their price expectations with a lag. Given adaptive expectations agents can be systematically fooled into underestimating the price level, which means that output can be permanently maintained beyond the potential level of output. But we cannot count on systematic errors by people for policy purposes. People will eventually catch on.
Under rational expectations agent's forecasts on economic variables are based on reasoned and intelligent analysis of past and available data. The main advantage of rational expectations is that the agents do not make systematic errors unlike in adaptive expectations where forecast errors have a systematic pattern. The agents will be able to understand the monetary authority's pattern of behaviour. Under rational expectations in order to make rational microeconomic decisions, the agents in the economy must be able to predict not only what is likely to happen in the macro economy, but also what government officials are likely to try to do about any macroeconomic problem, which emerges. The two main problems of rational expectations may be the problem of correct prediction of future events. The second is the dimensions of uncertainty. The second one might not be so serious, except that the actions of neither monetary nor fiscal authorities turn out to be very predictable. And there are good reasons for their lack of predictability, i.e. their propensity to implement policy surprises.
(a) Policy Implication for Establishing A New And Lower Rate of Inflation.
Using the IS-LM curve we can easily see what will happen when the monetary authorities try to adjust inflation rate
Fig 1 Adaptive Expectations Fig 2 Rational Expectations
Inflation and Interest Rate Equilibrium
Under Adaptive expectations
When money supply increases (decreases) inflation increases (decreases). This will lead to a decrease (increase) in unemployment from the natural rate of unemployment. When applied to aggregate demand and aggregate supply curve an increase (decrease) in money supply will increase (decrease) output as price increases (decreases). Therefore monetary authorities will be able to maintain output permanently beyond (below) the potential level of output. A word of caution is that in the long run people will eventually catch on. When the monetary authorities decide to set a low level of inflation, then the monetary authorities have to just keep the inflation rate at a lower rate for every period. As people have adaptive expectations they will expect the inflation rate what it was during the previous period. Therefore their expectations will be also a low level of inflation rate. For example faced with high inflation due to past excessive money supply growth, a government that suddenly cut money supply growth back to a much lower rate would precipitate first a huge recession, followed eventually by a large boom. This sequence would lead to the rejection of the policy. If however money supply growth is slowly cut, each step would induce a small recession but after a few steps this would come on top of revival from the first steps; while the economy would be making steady long-run progress back to low inflation, the side-effects in lost output and unemployment would be more tolerable politically. This argument is obviously a strong one if this model is correct.
However it is not clear that even gradual steps would be easy to undertake politically because the length of time an economy would be suffering from (mild) recession would be very long.
Under Rational expectation
When money supply increases (decreases) inflation increases (decreases). This will not lead to a decrease (increase) in unemployment from the natural rate of unemployment (i.e. unemployment level = natural rate of unemployment). When applied to aggregate demand and aggregate supply curve an increase (decrease) in money supply will not increase (decrease) output as price increases (decreases). Therefore monetary authorities will not be able to change output permanently beyond (below) the potential level of output. When the monetary authorities decide to set a low level of inflation, then the monetary authorities have to just say that the inflation rate will be at a lower rate and should not change it. As people have rational expectations they will expect the inflation rate to be what the monetary authorities had said. Therefore the expected inflation rate will also be low and will be equal to actual rate of inflation. If the monetary authorities tell that the inflation rate will be low and actually set a high inflation rate then people with rational expectations will not believe what the authorities tell in the next period. Then in the next period the agents will expect a higher inflation rate than what the authorities tell. When expected inflation is high actual inflation will also be high. Thus under rational expectations we can tell that to set a low rate of inflation the monetary authorities have to do what they say.
If people have rational expectations, then a well announced, credible drop in the money supply would lead to a lower price level but no recession. Under rational expectations people learn from experience, and anticipate inflation and, in fact, they may even move ahead of it. This would render expansionary fiscal (and monetary) policies totally ineffective as far as unemployment is concerned. Continued expansionary policies will only bring about an inflationary spiral, i.e. law of iterated expectations. It is because they are based on all available information and incorporate all "news" as it becomes available, such as past prediction errors, so that forecast errors are not auto correlated. Under rational expectations monetarists argued that the money supply should be kept to a steady growth rate as far as possible (rules) rather than being varied in response to the perceived state of the economy (discretion). The argument was based on the difficulty of knowing the parameters, or even the economy's actual state
(b) Policy Implication in Stabilising the Economy In The Face Of Shocks.
"Stabilisation policies are those policies intended to influence the behaviour of real output or sometimes prices in an economy".
To see the implication of the stabilisation policy a simple macroeconomic model is used.
Assumptions of the model
. Monetary policy will be the only policy variable affecting demand for output.
2. The income velocity of money (u) is also held constant.
3. Fiscal policy will be held constant.
The Model Specifications:
. The Aggregate Demand Equation:
m t + u = p t +y t .........................................................(1)
The money supply (m t) is the amount of money in the economy. There are lots of definitions as to what exactly constitutes money, but for the time being, let us assume that it includes only notes and coins. The velocity of circulation (u) refers to how quickly this money 'circulates around the economy. It has to be true that m t u = p t y t. Money spent = what the money is spent on. Therefore we take it as an identity not an equation. Whatever is on the left (m t u) always equals whatever is on the right (p t y t).
2.The second equation represents the monetary authority's money supply rule.
m s t = ? y t -1 + ? t ......................................................(2)
Equation (2) is a money supply function in which government aims for a monetary target with an error. It states that the money supply is proportional to the level of economic activity 'y t -1' with the addition of a random error term allowing for unexpected monetary shocks to the system: In this money supply rule the stabilisation parameter (feedback coefficient) is ?. Only one random disturbance is included in the model for simplicity. Here e t is normally distributed with a mean of 0 and variance of ? 2. As the error shocks the economy, aggregate demand shifts up and down around D*D*, its steady state position set by m.
3.The third equation is the Aggregate Supply equation.
y t = y* + ? (p t - E t -1 p t) .............................................(3)
This equation is derived from individual supply equations for different economic agents based on actual prices and expected prices. Expectations about the agent's own price, is derived by that agent based on observations about the general price level. If the agent's actual price 'P t' exceeds the expected price value E [P t] then this situation is characterised by the agent as an increase in the relative price for the agent's product or services. Thus this agent will devote more resources to production such that Y t > Y*t where Y* represents some normal level of output by that agent. Aggregating over all agents in the economy, we have the aggregate supply function which states that actual output will exceed the normal level of output when the actual price level exceeds the expected price level perhaps due to some unanticipated shock to the economy or monetary system.
Substituting equations (2) and (3) in (1) yields the reduced form:
? y t -1 + ?t + u = p t + y* + ? (p t - E t -1 p t) ...................(4)
(a) If expectations are backward looking i.e. p e t - p e t-1 = ? (p t-1 - p e t-1), where 0 ? ? ??1. Then the level of output and price using the basic method can be found using the basic method.
p e t = ? (p t-1 - p e t-1) + p e t-1
p e t = ? p t-1 + (1- ?)[ ? p t-2 - ? p e t-2 + p e t-2]
p e t = ? p t-1 + ? (1- ?)p t-2 - ? (1- ?) p e t-2 + (1- ?) p e t-2]
p e t = ? p t-1 + ? (1- ?)p t-2 -+ (1- ?)2 p e t-2
By continuous forward substitution for p e t-2, p e t-3, ......
p e t = E t -1 p t = ? ? (1- ?) i p t-1+i ......................................(5)
Substituting (5) in (4) yields:
? y t -1 + ?t + u = p t + y* + ? (p t - ? ? (1- ?) i p t-1+ i )
Solving for p t we get
p t = (1/1 + ? )[? y t -1 + u - y* + ? ? ? ((1- ?) i p t-1+ i) + ? t ]
Substituting in p t and E t -1 p t in equation (3) yields solution for output:
y t = y* + ? ((1/1 + ? )[? y t -1 + u - y* + ? ? ? ((1- ?) i p t-1+ i ) + ? t - ? ? (1- ?) i p t-1+ i ])
After collecting terms in ? ? (1- ?) i p t-1+i and solving the above equation using algebra we get
y t = y* + ( ? /1 + ? )[? y t -1 + u - y* + ? t - ? ? (1- ?) i p t-1+ i ]
Now as we have got the solution for both output and price under adaptive expectations we can tell whether the monetary authorities will be able to stabilise the economy.
Under the present circumstances as the feedback parameter has enters the solution for output we can tell that monetary authorities can stabilise output in this model when expectations are adaptive. Also we can see that the shocks in the economy also affect the output.
We can see that expected prices depend not on planned money supply but on past events (past prices), which were known to the government last period. Consequently the government can plan a money supply for this period confidant that it will not be 'frustrated' by a response from expectations.
In models with backward-looking expectations stabilisation policy by government can reduce fluctuations in output provided the government chooses the appropriate monetary target.
(b) If in an economy the expectations are rational then the level of output and price can be found using the basic method.
Solution using the basic method:
While using this method for solving E t -1 p t we have to treat expectations as exogenous. Also we take the expected value of this solution at the date of the expectations and solve for the expectations.
Substitute the expectation solutions into the solution in 1, to obtain the complete solution.
E t-1 m t + u = E t-1 pt + E t-1 y t ................................( 6 )
E t-1 y t = y* + ? (E t-1 p t - E t-1 p t ) ????y* ..................( 7 )
E t-1 m t = ?y t-1 + Et-1 ? t ???? y t-1 ............................( 8 )
?E t-1 p t = ? y t-1+ u - y*
Substituting the solution for E t-1 p t in equation (4) yields solution for the price level
? y t-1+?t + u = p t + y*+ ? (p t - ? y t-1 - u + y*)
? y t-1 (1 + ? ) + ? t + u - y* + ? u - ? y* = (1 + ? ) p t
?p t = ? y t-1 - y* + u + ( 1/ 1 + ? ) ? t
Substituting the solutions for pt and Et-1pt in (3 ) yields
Y t = y* + ? ? ? y t-1 - y* + u + ( 1/1+? ) ? t - ( ? y t-1 + u - y*)?
y t = y* + ( 1 / 1 + ? ) ? t
The solution for y t (output) consists of an expected part (y*) and an unexpected part (functions of ? t) also called as the monetary surprise. Rational expectations have incorporated anything known at t-1 with implications for y at time t into the expected part, so that the unexpected part is purely unpredictable. The monetary authorities cannot influence output, as the feedback coefficient used in the money supply rule of the monetary authorities does not appear in the output solution. The shock affects output. But the authorities also cannot control this.
Conclusion
Under adaptive expectation the stabilisation policy should be stable. In face of any shocks the monetary authorities have to show a gradual change in its policy. Under rational expectations the monetary authorities should follow a policy of randomness. This is because people are found to form expectations rationally. The agents will have a model that they think the authorities will follow. They will know what the monetary authorities are going to do. Therefore when the monetary authorities follow randomness, they throw the people from their expectations, which are based on a systematic model. This will cause an effect, which may be desirable at the stage, which the economy is going through. It is a common feature of all these models that, there is an important difference between the effects of an anticipated and of an unanticipated change in any exogenous variable. By contrast, in models where expectations are formed adaptively (or as any fixed function of past data) it makes no difference. This is probably the most fundamental result of rational expectations.
Stabilisation policy will be effective under rational expectations when agents have current information even with Sargent Wallace supply curve. When the authorities follow a model like over-lapping wage control or Lucas supply curve or have automatic fiscal stabilisers then they will be able to stabilise output in the economy.
