The Lucas Island Model is an economic model formulated by Robert Lucas, Jr. Before Keynes' The General Theory of Employment, Interest and Money was written, many economists were active in the research of business cycles. [1]. In the early 1930's Friedrich Hayek introduced the idea that business cycles stems from individuals misperceptions about relative prices[2]. This idea was taken up by Lucas almost forty years later.[3]
The hypothesis that aggregate supply depends on relative prices is central to the new classical explanation of business cycles. [4] The purpose of the model is to establish the link between money supply and price and output changes in a simplified economy using Rational expectations. Lucas sought to explain the short term procyclicality of output and inflation (the “Phillips curve”) while maintaining the neutrality of money assumption.
This particular model appeared in a series of papers in the early 1970s.[5] These papers especially those by Lucas (1972), (1973) and (1975) were enormously influential in illustrating (and popularising) the power of Rational Expectations as a modelling technique. These papers show us how to use simple general equilibrium models to arrive at structural models of economic fluctuations.
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In his model, Robert Lucas eliminated the often implicit assumption in most macroeconomic models that people (agents) are easily fooled by government policy-makers. His model does not rely on any asymmetry of information between workers and firms. [6] In microeconmic theory, agents are assumed to be rational i.e their main aim is Profit maximization. Robert Lucas extended this theory to macroeconomics assuming that people would come to know the model of the economy that policymakers use. This assumption is more commonly known as rational expectations. Rational expectations is the principle that agents in an economic model use the correct conditional expectations, given their information. It should be noted, however, that rational expectations does not mean that the agents can foresee the future exactly. If expectations were systematically wrong or biased, agents would learn from their mistakes and change the way they formed expectations. Thus, based on available information, the agents make the most efficient and accurate form of expectations.
The basic idea of the model is that supply (and production) is determined by expected relative prices; when producers expect a high relative price of the good produced on their island, they produce more of it.[7]. However, supply decisions are made based on incomplete/imperfect information.
The model contains a group of N islands, with one individual on each. Each individual produces some quantity Y, which can be bought for some amount of money M. Individuals use money a given number of times to buy a certain quantity of goods which cost a certain price. In the quantity theory of money, this is expressed as MV = PY, where money supply times velocity equals price times output.
Lucas then introduced variation in the price level. This can occur through changes in the local price level of individual islands due to increased or decreased demand (i.e. asymmetric preferences, z) or through stochastic processes (randomness) that cannot be predicted (e). However, the island dweller only observes the OLG model price change, not the component price changes. Essentially, all prices can be rising, in which case the islander wants to produce the same, as his real income is the same, which is shown by (e). Or the price of his product is rising and others are not, which is z, in which case he wants to increase supply due to a higher price. The islander wishes to respond to z but not to e, but since he can only see the total price change p, (p = z + e) he makes errors. Due to this, if the money supply is expanded, causing general inflation, he will increase production even though he is not receiving as high of a price as he thinks (he confuses some of the price as an increase in z). This exhibits a Phillips curve relationship, as inflation is positively related with output (i.e. inflation is negatively related with unemployment).
The twist is that due to the rational expectations included in the model, the islander isn't tricked by long-run inflation, as he incorporates this into his predictions and correctly identifies this as pi(long-run trend inflation) and not z. This is essentially the Policy Ineffectiveness Proposition. This means in the long-run, inflation cannot induce increases in output, which means the Phillips curve is vertical.
An important consequence of the Lucas island model is that it requires that we distinguish between anticipated and unanticipated changes in monetary policy. If changes in monetary policy and the resulting changes in inflation are anticipated, then the islanders are not mislead by any price changes that they observe. This implies that the islanders learn from their past experience and form their expectations accordingly. Consequently, they will not adjust production and the neutrality of money occurs even in the short-run. With unanticipated changes in inflation, the islanders face the imperfect information problem and will adjust production. Therefore, monetary policy can stabilize output only if policymakers have more information than agents.
Lucas Model (1972) is also a type of an Overlapping generations model (OLG model) where trading is assumed to take place with rational expectations. The OLG model assumption facilitates an endogenous demand for money. The old who can neither store the goods that they produced when they were young nor produce goods when old, are found to pay the young ones for goods. Equilibrium in the market is reached when the old exchange the goods for money with the young. Every period will have its unique equilibrium level. If the money supply is constant and evenly distributed among the old, the price level is assumed to be constant i.e. when everyone is perfectly informed, the price level and the money supply will be proportional. When there is perfect information, a once and for all increase in the money supply will lead to a proportional increase in the price level and employment and production are untouched. [8]
When imperfections are introduced while revealing the money stock to both the agents(the old and the young), price rigidity can occur. Price rigidity is the the proposition that some prices adjust slowly in response to market shortages or surpluses.[9] Limiting information is possible when trading occurs in separate markets. The suppliers are not aware owing to the lack of information whether the increase in prices in any one market is caused by the general increase in price level (i.e. inflation) or that there are fewer suppliers in the market which has driven price upwards. Thereby they are faced with a signal extraction problem, the solution to which is to increase the supply when price rises but by an amount that is less than an increase in money supply.[10].
Although, the more long-lasting impact of this paper has been methodological the Lucas island model fails to prove with empirical evidence the right amount of volatility in output fluctuations caused by a combination of monetary shocks and information limitation as is implied. [11]. Also, the assumption of information limitation in the Lucas model is sometimes not evident in real life scenarios.On a more empirical level, there is too little research on imperfect information as a source of price rigidity in models with perfectly flexible prices. [12]