Inflation,Unemployment and Output: Empirical Study and Theoretical Analysis of the Evolution of Phillips Curve
Abstract
Phillips curve has been a very controversial topic in the macroeconomic domain.This paper will mainly analyze the evolution of the Phillips Curve which was put forward by Alban William Phillips in 1958. First, some background knowledge will be discussed for further analysis of the relationship between inflation and unemployment. Second, the focus will be on the existing literature of the study of Phillips curve. Third, the empirical study and theoretical analysis of the dramastic evolution of the Phillips curve over the past decades will be carried out. This chapter consists of 4 parts: (1) theoretical analysis of the original Phillips curve and test the explanatory power of Phillips curve using the data from the US ;(2)exam mainstream propositions against the theory built on Phillips curve by introducing the Non-accelerating inflation rate of unemployment (NAIRU)and inflation expectations; (3) on the basis of part 2, derive the expectation-augmented Phillips curve and apply this new model to the practice to examine how well it fits the real world data;(4)briefly interpreting the theoretical formation of the New Keynesian Phillips curve(NKPC). Finally,after looking into the evolutionary process of Phillips curve, conclusions will be drawn.
Key words: inflation, unemployment, output, Phillips curve, inflation expectations
Chapter I Introduction
Inflation and unemployment are regarded as the core research areas in modern macroeconomics. They are not only two major macroeconomic indexes measuring the overall national or regional economic performance but also crucial basis for governments to formulate macroscopic economic policies. Hence, the study of the interrelationship between inflation and unemployment is requisite. However, the history of the theoretical and empirical analysis of this mysterious relationship between inflation and unemployment dated back to 1958. In 1958, a paper titled <<The Relationship between Unemployment and the Rate of Change of Money Wages in the United Kingdom 1861-1957 >> written by Alban William Phillips was published in the quarterly journal Economica. In his paper, Phillips showed how he observed an inverse and nonlinear correlation between money wage change rates and unemployment rates in the British economy over the period examined. This exciting empirical finding had filled the gap in contemporary macroeconomics development. Since the first coming-up of Phillips Curve, a great number of economists have been following the footprints of A.W. Phillips studying the interconnection between inflation rate and unemployment rate. In the past decades, Phillips Curve has been witnessed a significant evolution from its original simply constructed form to more sophisticated shapes. Neo-classical economics, monetarism together with rational expectations theorists have made great contributions to the perfection of Phillips Curve.Although Phillips Curve has stimulated considerable disputes among the academia, it is beyond all doubt that Phillips Curve is playing an active role in expounding economic fluctuations as well as in explaining the impacts of macroeconomic policies.This dissertation will not only take a close look at the gradual evoluting progress of Phillips Curve but also test and verify the validity of theoretical implications given by different Phillips Curves.
Chapter II Background
Since Phillips curve studies the correlation between inflation rate and unemployment rate,two elementary definitions need to be clarified here. Firstly, the widely accepted definition of inflation is the increase in the average prices of goods and services in the term of money(Romer,2006). When there exists inflation in an economy, money in circulation will be devalued as well as the purchasing power of money is decreasing The rate of inflation can be calculated with the following expressions:
Inflation rate= or inflation rate=
Here CPIt denotes the consumer price index at time t and denotes the average price level at time t. From the neo-Keynesian macroeconomic aspect, there are three major categories of inflation: demand-pull inflation, cost-push inflation and built-in inflation. Demand-pull inflation suggests that as there are rises in the aggregate demand, the aggregate demand curve right-upwards is moved right-upwards, intersecting the aggregate supply curve at a higher price level. Cost-push inflation is also called “supply shock inflation,” caused by the increasing costs of producers. As costs increase for firms, producers tend to increase the prices of goods or services, passing the extra costs on to consumers in the form of price rises.drops in aggregate supply due to increased prices of inputs, for example. Take a price increase of crude oil for instance, producers for whom crude oil is part of their raw materials would then lift their product prices to a higher level so as to maximize the profits. Built-in inflation, related to the price-wage spiral, explains inflation in the view of adaptive expectations. Because employees tend to keep their wages up (gross wages have to increase above the CPI rate to net to CPI after-tax) with prices, costs go up and the employers would rise the prices to transfer the increased costs to consumers. Built-in inflation reflects events in the past, and so might be seen as hangover inflation. Monetarists conclude that inflation should always be considered as a monetary phenomenon from the empirical study of monetary history (http://en.wikipedia.org/wiki/Inflation)
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Second, unemployment rate is another very important macroeconomic index used in economic studies and evaluation of the overall economic performance of different countries or regions. Unemployment describes the state of a person who is able and available to work, however, is out of work and presently actively seeking a job. Generally speaking, the unemployment rate is the ratio of those who are the labour force is currently unemployed. Unemployment is usually categoried as follows: Frictional unemployment,occuring at the same time that when a worker moves from one job to another.While one is in search of a job, he is considered to be experience a frictional unemployment; Structrural unemployment, aroused by the mismatches between job offers and potential workers; Cyclical unemployment also known as Keynesian unemployment, normally considered to be caused by insuffiecient labour demand; Classical unemployment, existing if real wage rates are set above the market-clearing level.
Concerning the causes of unemployment, different schools of thought hold different points of view. Keynesian economists take the demand deficiency for products and service as the major cause of unemployment.Different from Keynesian economics,other schools of theory emphasize on structural problems and deficiencies in labour market. However, Classical or neo-classical theorists against these explanations focuses more on external regulationary interventions, namely minimum wages restrictions and taxes, which from their standpoints may lead to discouragement in employment. Apart from these ideas, others imputes unemployment to voluntary choices of the unemployed. (http://en.wikipedia.org/wiki/Unemployment)
Inflation and unemployment can be costly for both individuals and the society. On one hand, for instance, increasing inflation rates will lead a decline in consumers’ confidence and eventually influence the aggregate demands as well as the overall economic performance. On the other hand,since the unemployed have no income, it is difficult for them to meet their basic living demands,which may cause loss of self-esteem, mental stress and physical illness. Unemployment may result in unstable and turbulent situation in the society. And too high unemployment rate can lead to increasing crime rates and lay hindrance to economic development , which would eventually cause depression.
Chapter III Literature Review
Phillips Curve tends to bring the logical relationship between inflation and unemployment or output to the light. Since the first coming-out of Phillips Curve in 1958, its elaborated economic relation between these variables has been questioned and amended for 50 years.Alban William Phillips(1958) officially proposed the original form of Phillips Curve. This curve, derived by regressing emipirical figures of unemployment rates and change rates of money wage in Britain from 1861-1957, displayed a negative, nonlinear correlation between these two variables..First, Phillips observed the data from 1861-1913 and ran a regression to obtain a function of money wage change rate and unemployment rate. He declared that this function was also able to explain the relation between these two variables within a time span between 1913-1957. In addition to this, Phillips considered that such relationship was quite stable. Lipsey(1960) entrusted relatively powerful theoretical clarification to Phillips Curve by starting his analysis from the supply and demand theory of single labour market.There are three main points in his model:1).wage inflation rate is explained with excessive demand of labour market and money wage change rate moves in the same direction as excessive demand of labour; 2).It does not mean that there is no unemployment when no excessive demand exists in labour market, which indicated the presence of frictional unemployment;3).excessive demand for labour has a negative correlation with unemployment rate. Combining these above-listed key points, Lipsey proved the adverse,nonlinear correlation between these two variables. In the same year, Samuelson and Solow(1960) made improvement to the existing literature on Phillips Curve. They set up a price formula in the form of cost addition, which can be interpreted that price of goods is determined by money wage rates and labour productivity rates. By differentiating the function and employing the function of original Phillips Curve, the negative correlation between inflation rate and unemployment rate is established. They regard that the Phillips Curve is a combination of all points which can be equivalently interpreted as any corresponding economic policy. This famous inflation-unemployment Phillips Curve, revealing the inflation-unemployment trade-off, has soon become essential theoretical support for governments to draft their economic policies.
On the contrary, Friedman(1968) and Phelps(1967), regarded as the founders of monetary theory, oppose the conclusions drawn from Phillips Curve. Their theory is built on two major hypothesis: first, natural rate of unemployment hypothesis. They argued that if the labour market and production market are both in the equilibrium, then there exists a unique rate of unemployment, that is the natural rate of unemployment ; second, they suppose that individuals tend to anticipate future trends in accordance with past time knowledge and information, which is generally considered as the adaptive expectations They agreed with the inflation-unemployment trade-off in the short run; nonetheless, because of the presence of adaptive expectations of the public, the unemployment rate will be Phillips Curve must be a vertical line in the long-run. This typical monetarism viewpoint indicates that expansionary monetary or fiscal policies may effect the output level and unemployment temporarily but have no permanent impacts on the economy.
However, Lucas(1972) deemed that adaptive expectations hypothesis of monetarism is not applicable to the economic reality and concluded that the natural unemployment hypothesis was not consistent with the adaptive expectations. He then proposed the rational expectations hypothesis, on the basis of which he indicated that, as individuals tended to make rational expectations with all the information available to them. Besides,Lucas(1976) advanced the famous but controversial Lucas Critique which suggested that rational expectations could cause the policy-authority’s attempts to affect output level or unemployment by refering to the traditional output-inflation relationship to fail. Other rational expectation theorists,like Sargent and Wallace(1975) and Barro(1976) also suggested that only random aggregate demand shocks could influence output and unemployment. As a result, from rational expectations theorists, macroeconomic policies, like monetary policies aiming to reduce the number of the unemployed, have no effects in the long run or even in the short run. However, sceptics against rational expectations assumption argued that if individuals held rational expectations, the Phillips Curve built on that assumption had strong implications that appeared to be not supported by the data.(Romer,2006)
In the 1980s and 1990s, on the basis of rational expectations theory, new Keynesian economists put forward amendments to the Expectation-Augmented Phillips Curve. Calvo(1983) regarded current inflation rate could be explained by a function of the expected inflation rate of the next period and the deviation of unemployment rate relatively to the natural unemployment rate. Unfortunately, this forward-looking model had been a failure at expounding the dynamic effects that monetary policies had on inflation and unemployment. With respect to the disadvantages of Calvo’s forward-looking model, Galí and Gertler (1999) indrafted backward-looking expectations, intergrating the forward-looking, rational expectations based model, and eventually formulated the Hybrid New Keysian Phillips Curve.In fact, this model has been proved to have a stronger explanatory power (Mankiw,2001).Another influential model, called Information Stickiness Phillips Curve, was proposed by Mankiw and Reis(2002),. Within their model, they presumed that information possessed a feature of stickiness and finally reached the same conclusion as original Phillips Curve did that government can still
.
Chapter IV Empirical Studies and Theoretical Analysis
The Original Phillips Curve in 1960s
Alban William Phillips , a New Zealand-borned economist published a famous article named << The Relation between Unemployment and the Rate of Change of Money Wages in the United Kingdom, 1861-1957>> in the quarterly journal Economica. In his paper, A.W. Phillps (1958) assumed that the extend to which the demand of a good or a services was related to the supply of such good and service would determine the expected trend of price movement. From his standpoint, this hypothesis was one of the elements that influenced the rate of change of money wage rates. He broke the time span from 1861 to 1957 into three time intervals, 1861-1913, 1913-1948 and 1948-1957. First, Phillips operated a non-linear regression on unemployment rate and the rate of change of money wage rates and got the curve as shown below:
Then he applied this curve into analysis of the relationship between these two variables within other time intervals to test whether this curve was fitted in other data sets . And finally, Phillips drew an conclusion that ,from the empirical analysis of this relationship, it was obvious that there did exist a non-linear, negative correlation of these two variables.This is the most original form of Phillips Curve, while the most commonly-known Phillips Curve sketched by Samuelson and Solow(1960) using US data is shown below:
Figure 2 Modified Phillips Curve(P. Samuelson and R.Solow, 1960)
This figure clearly shows an inverse, nonlinear relationship between inflation and unemployment Although the original Phillips Curve has spurred many critiques after its birth, it cannot be denied that the original Phillips Curve is able to explain the correlation between inflation rate and unemployment rate in 1960s in many western industrialized countries, like the UK and the USA. As a great number of papers have proved this fact, in the following part, only the relationship between inflation rates and unemployment rates of the US from 1960 to 1969 will be studied.
Inflation=30.9574(RUNR)-4.1372
Suppose the policy makers face the unemployment rate 5% at the beginning of time t and they set up a goal to achieve 2% unemployment rate at time t+3 by reducing 1% unemployment rate during each time period. Table 2 below vividly shows how the whole inflation-unemployment trade-off process works. According to the unemployment rates and inflation rates from the table, two key points can be revealed: 1)The higher unemployment rate is, the lower the inflation rate is. It shows that there does exist an inverse relationship between inflation rates and unemployment rates, which is consistent with Phillips Curve’s implication.2) The increasing trade of inflation rate to achieving same percentage point of unemployment rate explicitly illustrates the nonlinear property of the original Phillips Curve.
empirical studies were tentative and further research needed to be carried out to uncover the mysterious relationship between unemployment,wage rates and prices(1958).If looking deeply into the theoretical formulation of Phillips Curve, it is not difficult to find out that the existence of Phillips Curve greatly relies on economic conditions and environment of the United Kingdom from 1861 to 1957. At that time, economic fluctuations were relatively slow and mild compared to recent decades and also labour market was highly competitive. These economic features determined the validity of Phillips Curve as well as the applicability of the macroeconomic policies indicated by Phillips Curve during that time.
Nonetheless, even though Phillips Curve does exist under certain economic systems within certain time span, it is merely an empirial equation which fails to be testified rather than a universally acknowledged principle.¼ˆa graph needed here¼‰ Phillips Curve has inevitable limitations as its existence requires strict or even harsh pre-conditions. First, the original Philllips Curve is established on the theoretical assumption that money wage change rate or inflation rate and unemployment rate display a considerably stable correlation. Every individual point representing the inflation rate and unemployment rate of each year can be linked only because of the assumption that they are not correlated with time t. In other words, it is supposed that inflation rate is a function of unemployment rate, which is presumed to be stable across different time and not related to time t. In fact, such assumption has little theoretical foundation and disobeys the reality. With time changing, the structure, environment together with other elements of an economy will transform, hence, such function revealing the interaction between inflation and unemployment may modify accordingly. For example, at time t, inflation-unemployment function is Gt, while at time t+n, the function form changes into Gt+n which is different from the function at time t. Consequently, it is not plausible to apply a single, stable function to the empirical analysis.Second, the original Phillips Curve has over-idealized the assumption that inflation rate can actively and directly react upon any fluctuation of unemployment rate. Wage is not only impacted by the supply-demand relation of labour market but also influenced by wage rigidity, anticipated inflation rates and other factors which sometime can be more influential. The reaction of inflation rate upon change of unemployment rate is rather insensetive and indirect.Third, in Samuelson and Solow(1960)’s modified Phillips Curve model,the price formula does not suffiently reveal the real interrelationship between inflation rate and money wage change rate. According to them, the increase of employees’ wage causes inflation, which is also known as wage-push inflation. However, other factors, such as the increase of prices of raw and processed materials, the pulling effect of aggregate demand, are much more influential than wage-push effect itself.(Zhu,2000)
Expectations-Augmented Phillips Curve
Adaptive expectations and Natural Rate of Unemployment
Despite many economists advocated the theory built on Original Phillips Curve, Milton Friedman(1966) first criticized the conclusion drawn from the Original Phillips Curve and put forward his argument that the long-run, stable inflation-unemployment trade-off was merely an illusion which from his viewpoint did not exist at all. Friedman (1968) and Phelps(1967) introduced adaptive expectations which had been neglected by Phillips,Lipsey,Samuelson and Solow as well as the natural unemployment rate into their investigations. Adaptive expectational behaviour is that people anticipate what will happen in the future based on the past time information. The natural rate of unemployment can be interpreted as the only unemployment rate in the state that both production market and labour market achieve equilibrium given population, technology and labour participation ratio. With these two key concepts, eventually formed the Expectations-Augmented Phillip Curve was derivedwhich can be written in the following forms:
1
–anticipated inflation rate at time t,
UN— natural unemployment rate(Chen,2007).
On one hand, Friedman and Phelps admitted the validity of original Phillips Curve as well as the temporary trade-off between inflation and unemployment in short run, however, they also pointed out that such short-run Phillips Curve was not stable for the presence of people’s adaptive expectations. It tended to keep moving right-upwards and , as a result, would eventually become a vertical line in long run which had the only equilibrium unemployment rate, the natural rate of unemployment.
Figure5 shows the evolving process of short- run Phillips Curve into long-run vertical form and it can be described as follows(Friedman, 1966,1968):
Suppose the initial starting point A with the natural unemployment rate U and the corresponding inflation rate I. Now the government applies expansionary monetary policy in pursuit of lower unemployment rate, so the inflation rate is lifted to a higher level I1. Employers take this price rise as a sign of more aggregate demand so that they increase their employees’ money wages according to the extend which price level rises to stimulate an increase in their outputs. Since employees have monetary illusions from the beginning in short run, they naively think that their real wages have been lifted and thereby put more effort into their work, as a result inflation and unemployment rates end up at point B. In fact, they have confused real wage rates with nominal wage rates. Meanwhile, the rise of price level is always greater than that of money wage rates, hence real wage rates are declining. Consequently, employers manage to increase their demands for labour causing the unemployment rate moving from original level U to a lower level U1. However, employees soon realize that the increases of their money wages do not make them better off because of the rise of average price level. Thus, they tend to negotiate with employees to ask for more increases in their money wages. Therefore, to offset extra costs of production, employers have to fire certain number of their employees, making the unemployment rate trace back from U1 to its original point U. What needs to be pointed out here is that at this time the inflation rate is no longer I but I1 instead,which refers to point C in the graph. Similarly, again executing expansionary monetary policies will lead the inflation rate going up to a even higher level I2 still with the starting point unemployment rate U. As a result ,in the long run, Phillips Curve modifies itself into a vertical line. This theory had been criticized throughout the beginning of 1970s by many Keynesian theorists, but the gradual appearance of stagnation in many western countries,like US, in late 1970s tallies with this theory.
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The policy implication from this monetarism viewpoint is that expansionary monetary policies and other macroeconomic policies aiming to trade high inflation with lower unemployment are effective in the short run but will be invalid within the long run. On one hand, monetarists admit the effectiveness of monetary policies within the period when unemployment rate gradually adjust to the natural level. On the other hand, they assert artificial expansionary economic policies can only deviate unemployment rate from the natural unemployment rate temporarily, but they fail to affect unemployment rate or output level permanently. Friedman (1968) and Phelps(1967)alert policy makers, if they attempt to adopt policy menu drawn from the Original Phillips Curve to trade higher inflation with lower unemployment level, they cannot cause any substantial influence on the economy permanently. What is worse, in the long run, high-inflation monetary policies will not only result the spiral rises of inflation but also exacerbate economic fluctuations.
Rational Expectations Theory
Different from the adaptive expectations hypothesis, Muth first put forth rational expectations hypothesis and it was Robert Lucas who carried forward the rational expectations theory. Muth (1961) interpreted rational expectational behaviour as individuals made attempts to utilize any available information to anticipate future fluctuations of economic variables such that they could avoid lost and seek for maximal benefits. when anticipating the future value of an economic variable, individuals will not only refer to the past values of this variable but also employ all the available information about the economic structure to form his expectation. The formation mechanism of rational expectations is determined by other variables within the model, in other words, is endogenous. Rational expectations theorists consider that the principles guiding the government to form its policies are also common knowledge to the public and private agents are able to make rational expectations by suffiently utilizing these principles and all other information.
Lucas(1973) stated that adaptive expectations indicated in monetary theory give rise to systematic expectation deviations and he applied the rational expectations into his analysis of aggregate output and supply. In Romer’s book, another equivalent form of Expectations-Augmented Phillips Curve can be written as below:
(Romer,2006) 2
Here denotes inflation rate at time t, represents the expected inflation rate, is the aggregate output and means the potential aggregate at time t, stands for the unobserved aggregate supply shocks(Romer,2006).If employing Okun’s law here, another expression can be derived:
3
.Under rational expectations hypothesis, Lucas (1976),Sargent and Wallace (1975) and Barro(1976) came to a conclusion that no policy but only the unobservered random variable, for instance, random supply and demand shocks and unobserved intentional policy changes, could affect aggregate output and unemployment, which is usually regarded as the policy ineffectiveness proposition. Refering to the expressions 2&3, if this proposition is correct then it gives us a clue that
4
Previous theoretical findings before rational expectations theory suggest that macroeconomic policies are effective at least in the short run. However, rational expectations theorists assert that ,even if in the short run, government could influence neither aggregate output level nor employment. From their angle, output and unemployment drift from their natural level on account of unexpected random shocks only. As the presence of rational expectational behaviour of the main body within an economy, the effects brought about by macroscopic policies are neutralized eventually. Barro(1977) found out that the unexpected portion of policies did have impact on output and unemployment, but the anticipated part of policies were invalid. This empirical findings had provided convincing proof to support the policy ineffectiveness argument However, as Romer(2006) argued the rational expectations hypothesis
Empirical Analysis of the Expectation-Augmented Phillips Curve based on rational expectations
Methodology and Data
Empirical studies will be carried out to testify the validity of the policy ineffectiveness The methodology applied in this part is described as below. The first step is to construct the inflation expectation function.As the mechanism of inflation formation is complicated, for analytical simplicity, three simple formulas of inflation expectations formation will be applied here(Li, 2006)
Private agents tend to determine their expected future inflation rates by regressing the above-shown formulas and predicting with the most fitted model.Second, it is of great importance to test the stationarity of the time series data analyzed here with Dickey-Fuller or Augmented Dickey-Fuller tests for unit root,because the OLS regressions will be biased in the presence of nonstationarity. Third, if the all the time series are tested to be stationary, then various OLS regressions of different inflation expectation functions will be operated. By comparing the STATA outputs of three OLS regressions, a fitted model will be selected to estimate the expected inflation rates. Finally, by comparing the estimated anticipated inflation rates with the actual inflation rates, it can be concluded that whether the data obtained is consistent with equality 4, thus conclusions can be drawn.
Data analyzed here include annual inflation rates,annual unemployment rates and annual GDP gap from 1980 to 2007, obtained from the World Economic Outlook Database April 2008, International Monetary Fund. The annual inflation rates are measured in average consumer prices index and GDP gap denotes the ratio of actual output
Test of Stationarity
Following the methodology presented above, the first step is to test the stationarity of these four annual inflation rates and gdpgap time series . According to the four different types of DF tests, the STATA outputs come to a consistent conclusion that the annual inflation rates is a stationary time series. But with regards to gdpgap data, the DF tests fail to examine whether this time series is stationary, as the DF tests with no constant and with trend show stationarity of gdpgap data,but other two tests with drift and with both drift and trend give the clue that gdpgap data is nonstationary. Therefore, the ADF tests with lag=1 is operated and the results show that gdpgap data is stationary. In order to assure the accuracy of the following analysis, it is necessary to check the gdpgap figures. Fortunately, it give a clue that the gdpgap of both Japan and UK tend to
According to table 4, it is obvious that there are significant gaps between the inflation rates expected by private agents and the actual inflation rates,despite that individuals may be able to make relatively rational expectations in certain years,like in 1981 and 2002. In 1984 and 1992, the inflation expectations drift from the actual level more than one percentage point. Apart from this, for example, between 2000 and 2001, 1984 and 1985, the actual inflation rate had experienced an increase,however,the predicted inflation rates showed a declining trend. Thus it can be concluded that individual’s anticipating behaviour is not rational and the rational expectations hypothesis has violated the reality in Japan. Fu
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