Inflation Unemployment Output

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 CPI_t 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)

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, GalÃ 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

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:

–anticipated inflation rate at time t,

U_N— 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.

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:

.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

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. Furthermore,from the figure ,it can be seen that there does not exist so-called vertical expectation-augmented ,or long-run Phillips Curve in Japan between 1980 to 2007.

As a result, the intuition that monetary policies have no effects on controlling output as well as unemployment has failed to confront the economic reality in Japan.If looking into the economic history of Japan after 1980, it is obvious that monetary policies as well as other macroscopic policies,like fiscal policies in Japan have been playing an important part in economic operations. For instance, between 1988 and 1990, Japanese government adopted expansionary monetary policies, lowering its official interest rate to 2.5%.Consequently, inflation rates kept increasing and unemployment rates had been witnessed a declining trend. At that time, the Phillips Curve in Japan presented its original form.However, it appears that macroeconomic policies have not given full scope to stimulate the rejuvenation of Japanese economy. It is the permanently-existing problems within Japan’s fiscal and financial systems, not the rational expectations of Japanese citizens, causes such phenomenon(Feng,1998).Therefore, it can be concluded that Expecation-Augmented Phillips Curve under rational expectations fails to confront the economic data in Japan and the implications are not testified.

The explanations of the coefficients and constant are : 1)in each period, the inflation rates will spontaneously rise 0.5655 each year regardless of the fluctuations of other economic variables;2) the influence of last year’s inflation inertia is 0.7789, implicating that 77.89% of the last year’s inflation will be passed onto the next year; the coefficient of the influence of output gap on inflation rate is 0.404, which means that when the actual output level exceeds the potential output level by every one percentage point, the inflation rate will increase 0.404% correspondingly and vice versa.The actual inflation As can be found out from this table, the predicted inflation rates in most years are significantly different from the actual inflation rates and also in some years the predicted trend of inflation rates movement is ,which implies that the expectational behaviour of the public is not rational. Therefore, it can be concluded that the proposition that macroeconomic policies are invalid to affect output and unemployment does not hold water with the british economic situation.

So as to make this empirical finding more convincing and vigorous, it is essential to briefly look into the economic development in the UK after 1980. During the 1980s, the new Prime Minister, Magarate Thatcher, brazenly discarded Keynesian economic policies applied by previous government soon after she came into power. Instead, she boldly put monetary policies into practice,owing to which , British economy had gradually cast off the shadow of stagnation and achieved rapid development under lower inflation rates. At the time, inflation rates and unemployment rates had gradually declined. In the 1990s, Britain experienced economic recessions from 1990 to 1992, the unemployment rate has soared from 7.04% in 1990 to 10.39% in 1993. In order to remedy such situation, the British government had employed moderate macroeconomic policie. On one side, basic interest rate had been lowered from 10% to 6%; on the other side, policy makers maintained neutral fiscal policies. Owing to the combination of monetary and fiscal policies, British economy not only had been witnessed a gradual recovery but also presented a stable, rapid growth trend after 1993. Furthermore, the unemployment rate keeping declining and the inflation rates of most years have been kept below 3%. It cannot be denied that the rejuvenation of British economy owes to the monetary and fiscal policies of the government. Thus, it can be concluded that macroscopic policies can effectively regulate and control the economy to a great extend and implications of Expectation-Augmented Phillips Curve under rational expectations fail to confront the economic reality in Britain.

Summary

The analysis of Japan and UK above tells the story that rational expectations behaviour rarely exists in real life, hence the inflation expectations of the public cannot offset the effects of macroeconomic policies on output or unemployment control. In other words, macroscopic economic policies are still effective. On account of this, it can be concluded that the theoretical Expectations-Augmented Phillips Curve under rational expectations assupmtion is barely a universally applicable principle.The restriction of

Chapter V Brief introduction of New Keyensian Phillips curve models and some evaluations

From the above-analysed Phillips curve, it is clear that these Phillips Curve models fail to confront data obtained from the reality and experience. Studies of Phillips curve must be able to explain problems ,such as the sustainability of inflation, shocks caused by monetary policies and the effects of policies aiming to bring down inflation. In recent years, researches on Phillips curve are based on microeconomic foundations including economic behaviours of firms and households so as to deduce the relationship between price fluctuations and aggregate variable fluctuations. Such analysis usually assumes that market environment is mainly monopolistic and the possibilities of price fluctuation will be restrained, as a result, price does not possess complete flexibility. This is known as the New Keynesian Phillips Curve, which can be regarded as the outcome of the combination of the Keynesian economic theories and real economic period theory. On one hand,Keynesian economy emphasizes on the stickiness of wage and price, mainly focusing on the impact brought about by aggregate demand; while on the other hand, real economic period theory points out that price is completely flexible. Moreover, it lays particular stress on supply analysis, taking supply as the core element of the economic activities changes in reality.

The basic models of New Keyensian Phillips Curve are characterized by its micro-analysis frame. According to the model, price is set to be sticky and real economic activities,such as output gap or unemployment, are substituted by marginal cost. Recent works about the New Keyensian Phillips Curve mainly concerntrate on verifying the validity of this assumption and the core question here is to find out to which extent that forward-looking or backward-looking models can reflect the features of inflation. This theoretical analysis can be applied into many aspects, for instance, tests and estimations of New Keyensian Phillips Curve within different economic systems as well as the study of New Keynesian Phillips Curve in an open economy. This part will focus not only on theoretically analysing basic and major models of New Keynesian Phillips Curve but also on briefly evaluating these models.

The New Keynesian Phillips Curves

Conventional Phillips Curves clarify the relationship between inflation rate and output gaps or unemployment rate, nevertheless, it is undeniable that such models are inconsistent with experience and reality. Thus,economists have to establish models which are able to be in accordance with empirical evidences. Amongst the recently established papers, inflation is related to marginal cost under the assumption of sticky prices. Gali and Gertler(1999) suggested to measure marginal cost with actual unit labour cost. They held the ideas that manufacturers expected future marginal cost by forward-looking or backward-looking expectations and the stickiness of price is rooted in contract wage. Furthermore, they also found out that unit labour cost is statistically significant and quantitatively important, .

The New Keynesian Phillips Curves are first put forth by Rotemb erg(1982) and Calvo(1983) which emphasize on the significance that sticky nominal wages and prices have on backward-looking expectations of individuals and producers. In Rotemberg(1982)’s model, the core analytical formula is formulated as below:

(Rotemberg,1982)

Here c is the ratio of cost from price change and cost caused by deviation from the optimal price, is interpreted as the structrual parameter. In this model, the price- adjustment behaviour of producers is costly and the cost depend on changes of prices.In Calvo(1983)’s model, manufacturers within an monopolistic competition environment optimally set their prices with the frequency of price adjustment as restriction. Synthesizing the optimal price setting behaviour of individual manufacturers,the correlation of inflation and expected inflation can be established. In the light of this model, Phillips Curve can be described as below:

(Calvo, 1983)

Again applying the Okun’s Law, the formula above can be equivalently interpreted as:

In these formulasÂ¼Å’ represents inflation rate at time T, y_tis the output gap, u_tis the rate of unemployment ,u^*is the natural rate of unemployment, is the propotion of

manufaturers who adjust price during each period, is a parameter which is bigger than zero. From this formula, it can be concluded that current inflation rate is a function of expecation of inflation rate of next period and the deviation of unemployment rate from the natural rate of unemployment.Calvo’s model is usually considered to be the Standard New Keynesian Phillips Curve.

The standard New Keynesian Phillips Curve, presumes that market environment is monopolistic and competitive, hence prices possess the feature of stickiness. and producers have rational expectations. The major contribution of the New Keynesian Phillips Curve underlines the effect of direct nominal rigidity has on the understanding of Phillips Curve. In this standard New Keynesian Phillips Curve model, aggregate prices come from the optimal behaviour of manufacturers. Nominal rigidity with the combination of optimal behaviour can formulate forward-looking dynamic mechanism of inflation. What is important about this model is that nominal rigidity is embedded into Dynamic Stochastic General Equilibrium,which provides the phenomenon that price level adjusts slowly with economic situations with micro-foundation.

Nevertheless, some economists point out its drawbacks. Andersen(1998) argued that it was crucial to take price-stickiness rather than wage-stickiness into account for the impacts on dynamic price and output fluctuation. Besides, these models implicate that the rate of inflation does not possess the feature of persistence.Furhrer and Moore(1995) argue that inflation steers the movement of output gap, in another word, current rise of inflation rate will indicate the following raise of output gap, and verse vice. However, empirical evidences suggest exactly the opposite, showing that current output gap is negatively related to lagged inflation rate. Furhrer and Moore(1995) also imply that the model itself can hardly explicate the fact that inflation is persistent. Apart from that, Mankiw(2001) finds out that the model has weak explanatory power about the effects of monetary policy shocks have on inflation. What is worse, the New Keynesian Phillips Curve cannot explain the fact that inflation fluctuation is positively related to the economic activity level.

The Hybrid New Keynesian Phillips Curve

As can be seen in the analysis above, standard New Keynesian Phillips Curve is a model constructed on forward-looking theories. In the view of the fact that New Keynesian Phillips Curve is not consistent with reality, many researches have improved their methods and the most significant is to reintroduce backward-looking expectations which has been neglected for a long time into the formulation of expectation. As the rising of rational expectation models, backward-looking model has been gradually ingored. However,in order to overcome difficulties in empirical studies, the recurrence of backward-looking model is inevitable.Masson et al.(1992) advanced the earlier form of hybrid New Keynesian Phillips Curve model. While, GalÃ and Gertler (1999) made significant changes to the forward-looking assumption.They suppose that the number of manufacturers equals to a unity. Among them, the proportion of k adopt forward-looking expectation methods and the left proportion of (1-k) employ backward-looking expectations. As a result, price formula at time T can be formulated as follows:

Â¼Å’

Here, p^f_t is the price of forward-looking manufacturers, while p^b_t is the price of backward-looking manufacturers. The price-setting expression for (1-k) manufacturers who are forward-looking is :

.The meanings of the symbols in the above formula are: –subjective discounted factor; — the percentage of manufacturers who choose to maintain their original price; mcⁿ_t -the log of marginal cost. And the price-setting behaviour of backward-looking manufacturers is determined by the equality:

Synthesizing the above-mentioned formulas, the representation of the Hybrid New Keynesian Phillips Curve can be obtained and written as:

, –potential measurement error

(; ;

)( GalÃ and Gertler ,1999)

This new interpretation of New Keynesian Phillips Curve is the mixture of forward-looking and backward-looking expectations.In’s paper, they also drew some important conclusions after employing this model into empirical tests and analysis:the majority of manufacturers take forward-looking behaviour.This Hybrid New Keynesian Phillips Curve can effectively simulate as well as test the real inflation fluctuations.

THE STICKY INFORMATION MODEL

Mankiw and Reis(2002), put forward their Sticky Information Model built on the past achievements of Calvo’s model. Within the background setting of this model, every manufacturer will work out its own price during each period. Nonetheless, manufacturers gather information and recalculate the optimal prices in a relatively slow way. During every time period, there are always a part of the manufacturers able to capture new information about economic conditions so as to set the new path along which the optimal price can be obtained, but other manufacturers decide their prices by sticking to their previous plans together with former information. In the Sticky Information model, manufacturers,who carry out their price adjustment before time j, set their prices at time t equal the expected prices of time t at time (t-j) . From this model, the price adjusting equation can be obtained:

This equation sufficiently displays the feature of short-run Phillips Curve: output fluctuates with price level in the same direction, in another word, price level rises when output increases and price level drops when there is output decrease. As output and unemployment rate are adversely correlated, in short run inflation rate in the representation of price level will move in an opposite direction against unemployment rate. By introducing the one-period lagged price function, the formula revealing the relationship of inflation and output is shown as below:

() is named the Sticky Information Phillips Curve by Mankiw and Reis.is a structural parameter which indicates the sticky level of informtion at a particular time, in other words, is the probability that manufacturers update their information, the bigger is , the more manufacturers apply the updated information and vice versa. represents the extent to which optimal relative price is sensitive to output gap. is the rate of output gap increase.From this expression, it is obviously shown that inflation is dependent on output, anticipated inflation and expected output gap increase. This Phillips Curve infers the same economic explanation of the connection between inflation and unemployment as the Hybrid New Keynesian Phillips Curve and the Original Phillips Curve doÂ¼Å’that is inflation rate is negatively bound up with the unemployment rate. This conclusion is in agreement with consistent traditional Phillips Curve,again giving the policy makers theoretical foundation of inflation and unemployment,output control. Therefore, governments still can find their policy equilibrium among inflation,output and employment. (Mankiw and Reis,2002)

Evaluations OF New Keynesian Phillips Curves

On the basis of the analysis above, it can be concluded that The New Keynesian Phillips Curves are established on the foundation of monopolitic competition, clearly describing the core concept of Keynes Economic theory, thereby deduce the interrelationship between inflation rate and output or unemployment rate. Traditional Phillips Curves are either static,namely that inflation is not influenced by its lagged value and expected value, or backward-looking, which means that inflation can be impacted by its lagged value.The New Keynesian Phillips Curves retain the features of traditional Phillips Curves, meanwhile they emphasize to a higher degree that inflation rates are determined by the changes of manufacturers’ marginal costs and the expectations of future economic environment.Hence, the New Keynesian Phillips Curves can expound the economic flutuations in reality more thoroughly and explicitly. However,the New Keynesian Phillips Curves are not that perfect and flawless. Rudd and Whelan (2005) argues that the New Keynesian Phillips Curves cannot describe the dynamic fluctuations of inflation accurately. At the same time, they also critisized the applications of unit labour cost and rational expectations within New Keynesian Phillips Curve models. As a result, further research needs to be conducted.

Chapter VI Conclusions

With the development and gradual progress of economies, the studies of Phillips curve has experienced an impressive process of continuingly expanding and deepening. Original forms of Phillips curve fully explain the underlying economic phenomeons in western industrialized countries in 1960s. Furthermore, original Phillips curve revealing the relationship between inflation rate and unemployment rate provides governments in western countries with sufficient theoretical evidences to utilize fiscal as well as monetary policies in order to stablize their economies and to stimulate employment at the same time. However, stagnation experienced by many countries during last decades questioning the conclusions drawn from the traditional Phillips Curve spurs modern monetarism and rational expectations theorists to criticize and make amendments to the imperfect Phillips Curve. Monetarists advance natural unemployment hypothesis and apply adaptive expectation into their analysis, while school of rational expectation theory hold the viewpoint that macroscopic policies, whether monetary or fiscal, have no effects on stablizing output level and unemployment fluctuations. Nevertheless, evidences suggest that their micro-analysis of market clearing plus the invalidity of policies are entirely divorced from economic actuality. Fortunately, New Keynesian economists ingeniously employ wage-price stickiness,non market clearing and rational expectations hypothesis to reformate Phillips Curve. On account of the truth that forward-looking models are contrary to the reality, the Hybrid New Keynesian Phillips Curve introducing the backward-looking assumption and Sticky Information Phillips Curve are proposed. This breakthrough of New Keynesianism re-establishes the substitution relationship between inflation and unemployment and once again builds theoretical foundation for governments to intervene economic development so as to achieve higher level of economic performance.

It cannot be denied that Phillips Curve has initiated the researches on the relationship of inflation, unemployment and output, despite of its incompleteness and imperfection.According to the evidences of more countries and a wider range of time, the nonlinear, negatively related relationship between the rate of inflation and unemployment rate cannot be widely verified. The inflation rate and unemployment rate is obviously not directly related but there exists a more indirect correlation between these two variables. For this indirect interrelationship, within different time spans and economic enviroment, Phillips Curve displays various shapes,positively related and uncorrelated connections between them.Besides, it is proved that no inevitable causality is between inflation rate and unemployment rate, however, there does exist some uncertain stochastic relationship. The interrelationship between inflation, unemployment and output varies depending on different economic preconditions as well as different economic structures.For most economic researchers and theorists,what is the most crucial is not to simply negate existing Phillips Curves but to comprehend their limitations and drawbacks, so that it is possible to depict the connection between inflation rate and unemployment rate in a more complete, continously improving way. Hence, policies makers are likely to be provided with more pratical and effective economic regulating and controlling approaches so as to pursue economic prosperity and stablity as well as continously improving social welfare.

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Pang Mingchuan

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