Sep 16

Adaptive expectations

Adaptive expectation models are ways of predicting an agent’s behaviour based on their past experiences and past expectations for that same event. They are first used by Irving Fisher in his book “The Purchasing Power of Money”, 1911, and further developed in the 1940s and 1950s, especially by Phillip Cagan in his article “The Monetary Dynamics of Hyper-Inflation”, 1956 and, most famously, by Milton Friedman in 1957, in his book “A Theory of the Consumption Function”.

Models are usually based around the following formula:

E_tx_t+1 is our expectation (E) in year t for a variable x in the year t+1. It is based on our expectation from the year before (t-1) for variable x in our current year, and a weighted proportion of our past expectations. Remember that our expectations from last year were, in turn, based on those of the year before, so all our expectations from the first time we ever dared assume anything are contained within the equation.

λ will depend on how much we were off last year versus this year: if our predictions are proving to be volatile, we will be more likely to adjust them. It will also depend on how much groundbreaking new information we have received, rendering previous expectations useless. Basically, it depends on how much we feel we might have been off last year when we predicted things for next year.

The easiest way to know how adaptive expectations work, is to understand the expectations-augmented Phillips curve. Using also this same curve, it is also easy to understand how rational expectations work.

Sep 11

Lope Gallego

Phillips curve: NCM’s view

New Classical Macroeconomics takes expectations one step further than monetarists did when using adaptive expectations. Rather than supposing that agents will learn to adjust their behaviour based on past experiences, they apply rational expectations, and directly assume that:

All agents have sufficient working knowledge of the economy and its basic structural relationships to anticipate cause and effect;
All agents assume that markets naturally reach an equilibrium;
Information is perfect: market force drivers are ‘common knowledge’.

This all signals a return to the cornerstones of neoclassical economics, and although in practical terms it may be a slight stretch, it means taking the expectations-augmented Phillips curve one step further:

As New Classical Macroeconomics views it, agents are able to anticipate future events without needing to have experienced them previously. This time around, agents will anticipate expansionist monetary policies, and therefore skip point B. Agents have sufficient working knowledge of the economy and monetary policy is transparent enough for agents to directly associate a fall in interest rates with a rise in inflation. Therefore, they waste no time in asking for salary raises (the change on inflation expectations shift the curve directly to point C), and inflation rises before a drop in unemployment is ever reached. Expansionist monetary policy is not even effective in the short term. In the very short term, a small effect might exist, but only as a result of the time needed for expectations to lead to action.

The only way for monetary policy to work under these scenarios is for it to be enough of a surprise and of enough magnitude to pose an economic shock. If agents are not expecting dramatic policy, they have no time to put themselves in order. In this way, economic policy must go beyond expectations, otherwise even an inkling that the government is likely to act will lead to agents immediately counteracting policy, probably before policy is even enacted.

Sep 10

Lope Gallego

William Sharpe

William F. Sharpe
William Forsyth Sharpe, born in 1934, is an American economist and Professor of Finance at Stanford University. In 1990 he won the Nobel Prize in Economic Sciences along with Harry Markowitz and Merton Miller. He was awarded this prize for his contribution to the theory of price formation for financial assets

Sharpe used Makowitz´s previous work on the portfolio theory as a basis and developed in 1952 the capital asset pricing modelknown as CAPM, which is used for pricing financial assets. An investor can determine its portfolio risk exposure, by choosing a combination of fixed income securities and equity securities. He also developed the so-called Sharpe ratio which measures the return of an asset according to the level of risk taken. His innovating discoveries and theories were included in his “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk”, 1964.

Sep 9

Lope Gallego

Franco Modigliani

Franco Modigliani, 1918-2003, was an American, Italian born economist, and Professor at the Massachusetts Institute of Technology. He has mainly worked in the fields of savings and financial markets, and his pioneering analyses in these subjects granted him the Nobel Prize in Economic Sciences in 1985.

The life-cycle hypothesis raised by Modigliani in his “The Life Cycle Hypothesis of Savings, the Demand for Wealth and the Supply of Capital”, 1966, tries to explain and rationalize the level of savings in the economy. As Modigliani explained, consumers seek for stable consumption levels throughout their lives; this is why they save during their working years since later, during their retirement, they will only have their savings. This proposition complements Friedman´s permanent income hypothesis, whereby consumers adjust their consumptions patterns when their income varies.

Modigliani also developed important theorems in the corporate finance area. The Modigliani-Miller theorem, formulated along with Merton Miller, demonstrates that under certain conditions, a firm´s value will remain unchanged, independently of weather equity or debt financing is used. Modigliani addresses this topic in his article “The Cost of Capital, Corporation Finance and the Theory of Investment”, 1958.

Sep 8

Lope Gallego

Natural rate of unemployment

The term natural rate of unemployment was introduced by Milton Friedman in 1968, in his article “The Role of Monetary Policy”, following his presidential address delivered at the annual meeting of the American Economic Association, in 1967. It is based in Knut Wicksell’ concept of “natural” rate, which defines how there will be no permanent changes in the considered variable below or above its natural level.

The natural rate of unemployment defines the level at which unemployment will remain, no matter how great the effects of monetary policy. The only way to permanently keep unemployment under its natural rate is to resort to higher and higher inflation rates, which in turn would be highly hazardous for the economy. This can be easily understood using an expectations-augmented Phillips curve.

Even though the natural rate of unemployment is usually merged in the economic literature with the term NAIRU, there are a few differences between both terms. These differences are summarized in the following grid:

	Natural rate of unemployment (NRU)	NAIRU
Theoretical starting point	perfect competition	imperfect competition
Origins of deviation	solely in labour market rigidities	in labour market rigidities; supply-side inflation
Inflationist mechanism	monetary policies	monetary policies; supply-side inflation
Type of unemployment	voluntary (therefore NRU can be assimilated to level of full employment)	voluntary; involuntary
Uniqueness of equilibrium	unique	multiple equilibria when considering open economies

Sep 8

Lope Gallego

NAIRU

The term NAIRU (non-accelerating inflation rate of unemployment) is a term first used by James Tobin in 1980, in his article “Stabilization Policy Ten Years After”. It refers to the level of unemployment at which the economy settles if monetary policy is held stable. In these terms, it can be associated to Friedman’s natural rate of unemployment.

The NAIRU is based on empirical evidence regarding inflation and unemployment. Indeed, in most countries, inflation rises when unemployment is low because of the higher demand this implies; correspondingly, inflation falls when unemployment is high. This relation explains how unemployment may be above or below the NAIRU level not only because of the effects of monetary policy, but also because other factors such as production costs or trade unions negotiation processes. The Layard-Nickell NAIRU model explains it quite simply.

Even though the term NAIRU is usually merged in the economic literature with the term natural rate of unemployment, there are a few differences between the two. These differences are summarized in the following grid:

	Natural rate of unemployment (NRU)	NAIRU
Theoretical starting point	perfect competition	imperfect competition
Origins of deviation	solely in labour market rigidities	in labour market rigidities; supply-side inflation
Inflationist mechanism	monetary policies	monetary policies; supply-side inflation
Type of unemployment	voluntary (therefore NRU can be assimilated to level of full employment)	voluntary; involuntary
Uniqueness of equilibrium	unique	multiple equilibria when considering open economies

Sep 8

Lope Gallego

Expectations-augmented Phillips curve

The expectations-augmented Phillips curve introduces adaptive expectations into the Phillips curve. These adaptive expectations, which date from Irving Fisher’s book “The Purchasing Power of Money”, 1911, were introduced into the Phillips curve by monetarists, specially Milton Friedman. Therefore, we could say that the expectations-augmented Phillips curve was first used to explain the monetarists’ view of the Phillips curve.

Adaptive expectations models led to an important shift in the perception of a government’s ability to act. Under Keynes’ money illusion, changes in nominal variables (prices, wages, etc…) were accepted by agents as real despite overall purchasing power remaining stable.

However, monetarism embraced the adaptive expectations theory to mean that people would stumble once or twice on the same stone, but not a third. In this way, if the government decided on an expansionist monetary policy, inflation would rise and unemployment would fall, based on the Phillips curve. However, a second or third time around, agents would be quick to associate higher inflation with rising salaries in a vicious circle, and adjust their behaviour accordingly based on past experiences. They would anticipate that inflation would drain their purchasing power accordingly, and monetary policy would have little effect. If we see this graphically:

Initially, unemployment and inflation are at point A. The government decides to embark on an expansionist monetary policy, which floods the markets with inexpensive credit, incentivising consumption. Expectations shift to point B along the Phillips curve: unemployment is reduced through economic stimulus with a trade off in the form of inflation. However, after a short period, agents will begin to associate expansionist policies with inflation, which means a drain on their resources, and they will push for higher wages. This will stop the consumption stimulus and also deincentivise hiring. Eventually, agents will shift their expectations curves to point C. A second time around, D will be achieved, leading more or less rapidly to point E. This is why, in the long term, inflation has little effect on unemployment and vice versa. Expansionist monetary policy will lead directly to inflation, with no permanent effect on unemployment.

In summary, monetarists sustained that the Phillips curve will hold up in the short term, but not in the long term. In the long term, the Phillips curve is completely vertical and determines the natural rate of unemployment, as Friedman puts it in his article “The role of Monetary Policy”, 1968.

Sep 3

Lope Gallego

Returns to scale

The law of returns to scale explains how output behaves in response to a proportional and simultaneous variation of inputs. Increasing all inputs by equal proportions and at the same time, will increase the scale of production. Returns to scale differ from one case to another because of the technology used or the goods being produce. Therefore, it is closely related to economies of scale happening within the business’ production process.

The relation by which output increases compared to the increase in inputs is the return to scale. We can measure the elasticity of these returns to scale in the following way:

That is, the sum of the partial derivatives of production with regards to each factors multiplied by the proportion each input makes up of the whole.

Depending in the proportion by which output increases compared to inputs, there are three different kinds of returns to scale:

-Increasing returns to scale (µ>1): when total output increases more than proportionately (green);

-Constant returns to scale (µ=1): when total output increases proportionately (blue);

-Decreasing returns to scale (µ<1): when total output increases less than proportionately (red).

When dealing with Cobb-Douglas functions, we can also determine which returns of scale are present, since α+β=µ.

Aug 29

Lope Gallego

Layard-Nickell NAIRU model

The Layard-Nickell NAIRU model emerged as a reply from New Keynesian Economics to the natural rate of unemployment, devised by Milton Friedman as a criticism of the Neoclassical Synthesis’ Phillips curve. This NAIRU model comes from an article entitled “Unemployment in Britain”, 1986, by Richard Layard and Stephen Nickell.

Indeed, the Layard-Nickell NAIRU model was able to explain the paradigm shift by moving away from assumptions of a perfectly competitive labour market into a model based on wage determination by means of trade union bargaining. In a perfectly competitive market, salaries and the prices of goods are traditionally determined by considering that the price of a product is fixed via its marginal cost (and, in the case of imperfect competition, a mark-up).

Trade unions will bargain with employers in order to get higher real wages for the workers. In the adjacent figure, it can be seen how the more people is employed and represented by trade unions, the higher real wages will be, thus marking the upward sloping BRW curve (Bargained Real Wages). The explanation is quite simple: from the workers point of view, higher employment rates mean lower opportunity costs derived from job seeking; on the other hand, employers are more likely to pay higher real wages when the economy is in expansion, since they don’t want to lower production (which would happen if workers went on strike.

Once trade unions have bargained an adequate real wages, the employer will fix prices (P) considering both costs of production and mark-ups (μ). If we assume real wages (W) as the only production cost (which is a reasonable assumption, since wages usually make up for a large portion of production costs), and we take into consideration also marginal productivity (MP_L), we can find out what would be the price chosen by the employer:

and assuming the following:

we come up with the real wage:

This real wage (called Price-determined Real Wage, PRW) can be represented graphically as shown in the adjacent figure. Note that it’s a horizontal line, since for any given BRW, and at any employment level, the mark-up would be the same as well as the marginal productivity.

The reciprocal relation between wages and inflation is determined. The distance from the level of employment at equilibrium (L*) and the total labour force (L^T), is the NAIRU. When, for example, the level of employment increases, trade unions will be able to negotiate higher real wages (A). Since the employer won’t be willing to accept a decrease in its profits, the mark-up will be maintained, which will raise prices. Therefore, an increase on employment, which will take the employment level higher than the NAIRU, will end-up increasing aggregate price-levels.

Anything that affects wage formation or unemployment rates is likely to affect inflation. Thus, fixing salaries above what they would be in a competitive labour market leads to higher prices, which increases inflation and reduces real wages. In a similar fashion, an increase in unemployment benefits drives salaries above what would naturally be determined, with similar effects. In this “battle of the mark-ups” between employers and employees, the NAIRU rises. This aims to explain the structural factors between some countries having a higher or lower “natural” unemployment rate than others. Empirically, it is interesting for example to note that only 15% of salaries in the US are fixed by trade unions, whereas in some countries of Europe, such as France, Italy or Spain, famed for having a naturally high NAIRU, almost 75% of employees are covered by a collective agreement.

Aug 29

Lope Gallego

Business cycles

Business cycle, as Joseph Schumpeter saw it, is the economic activity fluctuation that occurs over time, and that comes from the succession of expansionary and contracting seasons. It is analysed comparing real GDP to potential GDP (Y*). There are a few common characteristics, which help differentiate cycles, such as its phases, the way it oscillates, the periodicity and a few stylized facts:

1. Phases:

Four phases can be distinguished, following Richard Lipsey’s classification:

-Trough or depression (A), characterized by a high rate of unemployment and low consumption levels in relation to its real capacity;

-Expansion or recovery (B) of previous employment, income and consumption levels, that usually comes together with a rising in prices;

-Peak (C), distinguished by factors full use, high investment and shortage of labour, particularly for high-skilled jobs;

-Recession (D), demands fall causing unemployment and decreasing production levels.

2. Oscillations:

-Oscillant cycles:

·regular oscillations (cyan);

·irregular, convergent oscillations (red);

·irregular, divergent oscillations (green).

-Non-oscillant cycles:

·convergent (red);

·divergent (green).

3. Periodicity:

Economic cycles have been classified depending in their periodicity. The most common are:

-Very short cycles, with duration of 30-40 months; also known as Kitchin cycles, whose studies saw in stock rotation the origin of these cycles;

-Short cycles, with duration of 7-11 years; also known as Juglar cycles, which origin is based on subsequent inventions;

-Long cycles with duration of 15-25 years; commonly known as Kuznets cycles, whose analysis placed the origin of cycles in demographic factors such as birth rates or migrations;

-Very long or Kondratiev cycle with duration of 50-60 years. This cycles originate with breakthroughs in capital goods, such as the steam engine or the Internet.

4. Stylized facts:

Both over time and between countries (a few of numerous reviewed by Robert Lucas in his article “Understanding Business Cycles”, 1977):

-There is positive correlation between variables, which helps smooth fluctuations;

-Co-movement between some variables:

·output fluctuates in the same direction in different sectors (although different amplitudes may apply);

·investment and consumption are clearly pro-cyclical: investment leads and is more volatile, consumption lags and is rather stable;

·income: real wages and profits are pro-cyclical;

·employment and labour force are also pro-cyclical.

-Expansions are usually longer than recessions.

Many papers and works have been written on business cycles and different points of view have taken form. Keynesian economics tries to deal with the economic fluctuation to minimize their impact. Business cycles are seen as a proof of market failure, and justify government intervention in order to assure the correct level of economic activity. Until the optimum level of employment has not been reached, the economy will not be readjusted. Depending on the cycle phase, expansionary or contractionary economic policies may be used.

New Classical Macroeconomics supporters have also dealt with economic cycles, and as a result the Real business cycle theory arises as an alternative view to Keynesian´s. Kydland and Prescott, and in general the Chicago School, are mostly related with the development of this theory. For them, cycles are explained by technological shocks. The fluctuations in the economy are seen to be produced by shifts in the supply curve, as a result of changes in productivity levels. These shocks can be caused by different factors: technology innovation, unusual weather conditions, changes in raw material prices, new policies and regulatory measures, etc. What is basic for these shocks to occur is an alteration in the effectiveness of either capital or labour factors, and therefore changing productivity. As a result in changes in the production quantity, the supply curve shifts, implying a new equilibrium point in the supply and demand model. Thus they believe that economy will reach its new equilibrium point, through the forces of demand and supply in itself, without the need for a government intervention. In fact from their view, government intervention will only worsen the situation.