Stages And Causes Of The Business Cycle Economics Essay
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According to Burns and Mitchell(1946), who were the first that investigate the modern research methods of the economic fluctuations, economic fluctuations is a continuous model of recession, recovery, growth and decline of the economic activities around from a long-term trend. The continuous character of this model justifies the expressions 'cyclical fluctuations' and 'business cycle' although the movements have neither constant duration nor constant length.
The perception that the economists had about the economic fluctuations changed with time and differs according to different schools of thought(the economic science is a social science and all the social sciences have political economy flavour).
Before Keynes, the researchers of the economic fluctuations observed prosperity periods and crises periods. However, in 1930 economists understood that this discrimination didn't express the reality because during the growth period it is reasonable that there will be prosperity .However, it is also possible for the prosperity to coexist with unemployment , an indicator that is in the core of the crisis. That has an a consequence these two expressions (prosperity and crisis) to be replaced with the expressions 'peak' and 'trough'. The peak corresponds to the maximum point of GDP of the last time period of the economic growth. Similarly, the trough corresponds to the last time period where there is reduction in the economic activity.
I would like to define and explain some terms that I will use to my later analysis and are fundamental in the understanding of the business cycle and the economic fluctuations.
It is worth mentioning that the term 'business cycle' does not only refer to one variable, for example the GDP which is the main indicator of the economic activity, but also refers to other variables like investment, consumption, expenditures, prices etc.
Moreover an important point is that the variability of the economic fluctuations is not the same for all the variables. For example, the cycle of the investment has significantly greater variability than those of GDP.
Another significant point that we will focus on later, is that if we use the GDP as the general rate of the economic activity then the other economic variables is possible to either commove or lead or lag the GDP cycle.
Particularly, a variable commove with the GDP if the peak of the variable coincide with the peak of the GDP. If the peak of the variable is presented in time before the peak of the GDP then this variable leads the cycle of GDP. Otherwise, this variable lags the cycle of GDP.
Furthermore, some variables move in the opposite direction. It is observed that the increase of the GDP is accompanied from decrease in unemployment. These variables are 'countercyclical'. In the opposite case when the cyclical fluctuations are positively correlated with the cyclical fluctuations of the GDP(like consumption, investment, employment, the money supply and the money demand), we call these variables 'procyclical'. There exist also variables that are neither positively nor negatively correlated with GDP and we call them 'uncorrelated' (like real wages).
Historical evidence and Theories
The reasons of the economic fluctuations became the objective of extensive discussion from the 18th century.
Before 1819 the classical economists rejected the existence of periodicity in the economic crises supporting that they are caused by uncorrelated externals factors (like a war).Jean Charles Leonard de Sismoni and Robert Owen were the first economists who after studying the Panic of 1825,they argued that overproduction and underconsumption were responsible for this economic crisis during the peacetime.
In 1860, Clement Juglar identified the presence of medium-duration economic cycles (Juglar fixed investment cycle 7-11 years).Around a millennium later, other types of cycles were discovered. So there is a discrimination of the cycles according to their periodicity. The Kitchen inventory cycle which lasts from 3 to 5 years discovered by Joseph Kitchin (1923).The Kuznet infrastructural investment cycle (15-25 years) which was investigated by Simon Kuznets(1924).Very important was the contribution of Nikolai Kondratiev, which is known for his research about 'long waves' of duration 45-60 years. The above mentioned economists intended to establish first the statistical existence of the cycles than interpreted them economically.
Of course the answer to the question 'Why do the business cycles exist? 'is not easy and it depends on the economic and political school of thought.
The classical economists (Smith, Ricardo, Mill, Marshall, Malthous, Pigou) consider that a change in the demand curve can be compensated by a corresponding change in the supply curve and reversely, and as a result the GDP deviates from its potential value which is expressed by the long-term trend. That is done through the price mechanism in the different markets (including the labour market, which classical economists found as a secondary importance phenomenon with transitive only character). As a consequence , prices consist the equalizing-corrective factor which guarantees the equality between the real and potential GDP and the avoidance of cyclical fluctuations.
The Keynesian economists believe that the business cycle is the result of the changes in the aggregate demand. When price and inflation expectations are a bit inflexible then the swifts in the aggregate demand can cause large swings in real output. Furthermore, they aspire that the price mechanism is not enough to prevent the creation of cyclical fluctuations either from the demand or the supply side. From the demand side they think that investment and GDP do not correspond sufficiently to the increase of the money supply or the interest rate. As far as the supply is concerned, it cannot corresponds properly due to the rigidity in the labour market. That means that the wages cannot decrease more than to the point where it is determined exogenous by historical, social or institutional factors.
The monetarists support that the price mechanism in the labour market is decisive for the mechanism that equalize the demand with the supply.
According to their most eminent representative, Milton Friedman, the working population has asymmetric or incomplete information regarding the conditions that prevail in the general labour markets but they have complete information only for the labour market they are working. As a result the movement from the one labour market to the other that may equalize the supply with the demand is not possible, because of the lack of information.
New classical economics are mainly associated with the work of Robert Lucas ,adopted Friedman's opinion ,regarding the lack of information in the labour market, but for this school of thought the expectations are shaped rationally , taking into consideration the current estimates for the recurrent evolution. According to Friedman's theory the expectations are shaping through the readjustment of the past errors. Provided that in Lucas theory the expectations are shaping rationally, then in the long-run the information errors approximate zero. Consequently, according to new classical economists and also Friedman the cyclical fluctuations owed to the information errors of the economic institutions regarding the 'accurate' prices that equalize the supply with the demand.
For Keynesian and monetarist economists the recessions indicate the failure of some markets to clear. There is another group of economists who claim that the recession is inside the structure of the economy, is an inextricable part of all economies. These economists introduced the real business cycles models (RBC models) which support that the existence of recession periods is the most efficient operation of the economy. The most popular economists of them are Finn Kydland and Edward Prescott (Chicago school) who were the winner of the 2004 Nobel Memorial Price in Economics for their contribution in the understanding of the business cycles(1982). This theory supports that the fluctuations are the results of real shocks in the economy like technological shocks .RBC models are based on supply shocks rather than demand shocks(like Keynesian theories) and they encourage the government to deal with long-run structural changing policies because according to them in the sort-run there is nothing that monetary and fiscal policy can do to control the fluctuations.
Differences are observed not only in the creation frame of the cyclical fluctuations but also in the methodological frame. There are important differences between the older economists (1930-1950) and the newer. The recent theoretical models are formulated in uncertain environment (stochastic environment) whereas the older models were developed under certain conditions (deterministic models).In this important jump ,the contribution of the swift growth of econometrics and the technological advances is unquestionable .
The empirical investigation of the business cycle, namely the statistical analysis of the data include the estimate of the duration, the variability and the intense of the cyclical fluctuations of particular macroeconomic variables such as GDP, consumption, investment, expenditures, prices etc. Moreover this study includes the investigation of lags ,leads, or the absence of correlation between this variables and the general rate of the economic activity which is the GDP.
What is the business cycle?
During the recession period ,the wages decrease and the unemployment level increases. On the other hand, when the recession period ends then the economy entries the growth period where the wages rise and the unemployment declines. The business cycle refers to the fluctuations to all the macroeconomic variables through time. We measure the fluctuations around a long-term trend.
Mitchell (1913,1927) represented business cycles as a sequence of expansions and contradiction, particularly focused on turning points and phases of the cycle. These cycles are known as classical business cycles.
Lucas(1977) defined the business cycle as the deviations of aggregate real output from trend. Lucas viewed the business cycle facts as the statistical properties of the comovements of deviations from the trend of the macroeconomic aggregates with those of real output. These cycles are known as growth cycles or deviation cycles.
Although the term 'business cycle' implies that the economic fluctuations are regular and predictable ,they are not.
The more common are the recessions the more erratic they are. Sometime the one recession period is near the other. Sometime they abstain a lot.
The problem of economic fluctuations can be clear looking at figure 1.
The figure demonstrates the increase of the real GDP of the Greek economy for the period 1988-2008.
If the economy had a 3% growth rate, that growth rate would not be smooth. The growth rate oscillate at 3% per year(this is the trend) as the straight line shows, but there are significant fluctuations from the trend. The recession periods are periods where the production of commodities and services decrease and it is represented in the graph with the negative growth rate of GDP.
Concisely, we can say that the business cycle is the phenomenon of the recurrent fluctuations of the general economic activities that are observed in a period of time.
Discrimination of the business cycles
At one time, economists believed that the business cycle was regular with predictable duration, but nowadays we believe that the cycles is irregular with different frequency ,magnitude ,duration and different impacts on the economy.
According to their periodicity and intense, the business cycles can be separated into:
1) Long-term cycle or Kondradiev cycle.
The total duration is 50 years from which 20 years corresponds to the economic growth period ,then follows a 10 years stability period (at high levels) and in the last stage there are 20 years of recession.
2)Medium-term cycle or Juglar cycle.
This cycle consists of an average7 to 10 years and it is usually referred as 'the business cycle'.
3)Short-term cycle or Kitchin cycle.
It is known as the 'commercial cycle' and lasts 3-4 years.
Stages of the business cycle
Figure 2:The stages of the business cycle, Source: Wikipedia
Joseph Schumpeter( ) was the first economist who supports that the Juglar cycle has four stages.
Nowadays, all business cycles can be distinguished into four stages. The graph above is a diagrammatic representation of the business cycle.
The stages of the business cycle and their main characteristics are the following:
1)Growth or expansion :at the beginning of this stage there is excess demand for commodities and services. In order the economy to produce them ,the output production and the employment should increase. Then the unemployment rate decreases and at the same time the GDP and the national income increase. The rise in total demand and production cause profits and the profits motivate people and industries to invest. However, as the expansion continues it causes an increase in the general level of prices, and the the first inflationist tendencies are obvious.
2)Peak :At the maximum point of the cycle the production and employment are in a really high level .Its the highest point between the end of the growth and the beginning of the recession. The economy reaches the full employment level and overconsumption is also observed. The GDP, the most important macroeconomic indicator is at the maximum point. However the prices become higher and higher and we can also perceive high inflation levels.
3)Recession or contraction: Recession is the period where the economy is shrinking. The characteristics of recession are the opposite from growth. In this stage there is a decline in the aggregate demand and a general slowdown in economic activity which lead the production to decrease. The GDP, the employment ,the inflation , the incomes fall during this period and in that pessimistic and uncertain environment there are no investment opportunities. If this stage lasts long and the prices continues to fall then deflation can appear.(deflation occurs when the prices are actually dropping-not disinflation)
4)Though: The though poses the end of the recession. The production is in its lowest level and the unemployment level is really high. Moreover the demand for goods is insufficient as the income level is really low and the inflation is high. The general enterprising climate discourages the investments and the majority of people and companies wait for the 'event' that will end this stage.
Causes of business cycle
Many economists can agree that an ideal level for the economy is that of full employment(For James Tobin that means 0% level of unemployment, for William Beveridge that means 3% whereas for many other popular economists like John Maynard Keynes it fluctuates between 3%-10%). At this level all people who are able and are willing to work can find a job at the prevailing wage and unemployed workers can find work instantly. The inflation level is constant and all the inputs the economy can use, are producing outputs. The full employment level will rise when the population increases and when new technological developments are found. If nothing else disturbs the economy there is no reason why the economy come out from the full employment level.
However, business cycles occur because disruptions to the economy shove the economy above or below the full employment level.
The causes of the business cycles are distinguished between endogenous and exogenous.
As endogenous reasons we can consider some variables which are determined out of the economic system like wars and revolutions, elections, changes in the price of oil, immigration, scientific developments, technological advances, financial bubbles.
As endogenous reasons we mean the variables that are determined inside the economic system and they cause by themselves the business cycles. Some of them are:
Monetary policies that attribute the fluctuations in the extension or the shrinkage of the money supply (Milton Friedman)
The investment theories that are based on the interaction between the increase of the production and the investment.(Paul Samuelson)
The theories regarding the labour market which attribute the economic fluctuations in the price stiffness(wages) (Robert Lucas)
Shifts in the aggregate demand curve
Shifts in the aggregate supply curve
Monetary policy and economic fluctuations
Taking into account the fact that investment is an important ingredient of GDP and the fact that investment is determined among other variables also by the monetary variables like the interest rate, we deduce that the monetary policy is a significant element of the economic fluctuations. Generally speaking, monetary policy is any policy related to the money supply.
Monetary policy can cause recessions and booms. The interest rate is an important factor for the growth of the money stock. A company can cancel or postpone a financial or extension (investment the build of a new factory) because the cost of borrowing is high. Similarly, a consumer can cancel or postpone a new loan or the buy of the new house because the high interest rate can make this movement unaffordable.
So the institution or the government that decide the interest rate for a country of for a group of countries (like Europe) can generate booms or recessions.
There are two schools of thinking regarding the relation between the monetary policy and the economy. The Keynesian economists consider the private sector inefficient and unstable and support that the stabilization of the output can be done only by the intervention of the public sector. According to Keynes, the government needs to stress the fiscal policy actions and the central bank the monetary policy actions. The Keynesian economists support the government intervention especially during recession periods and the focus on boosting the government expenditures and decreasing the taxes in order to bolster up the aggregate demand. Nowadays, the current financial crisis is considered to be the worst since the Great Depression of 1930. All markets are suffering, many institutions ruins, many banks collapsed and the policy makers accept Keynes analysis after moving away the neoclassical models and governments and banks move to an unprecedented monetary and more fiscal expansion. The financial crises of 2008 has been characterised as the period of the resurgence to Keynesian economics. In growth period they suggest measures to decrease the aggregate demand such as increase of the interest rate. For Keynesian economists there is an indirect link between the GDP and the monetary policies.
The other school of thought consists of the classical, new classical and monetarist economists who support the minimization of the government intervention in the economic activities. They think that government's role is to control the money supply and make the future expected expansions known to the public in order to reduce the inflation and has nothing to do with the demand. In addition this theory impose policies in favour of free markets.
For both schools of thought the 'equilibrium' is fundamental whereas their interpretation is different. For Keynesian economists the equilibrium expresses a situation where there is no tendency for change ,while for the liberals the equilibrium is a situation where the supply equals the demand.
The question now is how does the monetary policies affect the real GDP according to these schools of thought?
The Keynesian economists think that the monetary expansions rise the supply of loanable funds and that cause the decrease of the interest rate. The lower rates cause increase in the expenditures on investment and as a result the real GDP grows. They do not believe that the economy is always near the natural level of real GDP.
On the other side, the monetarists argue that the money demand is stable and not easily affected to changes in the interest rates. In the short-run they support that the monetary expansions may increase the real GDP by increasing the aggregate demand. For them, the economy is not at or near the full level of real GDP except in the long-term where economy is operating at the full employment level of the GDP. In this case, monetary expansions can lead to persistent inflation (deflation: when the growth rate of GDP has a negative sign) and not to changes in the real GDP.
Stabilization of economy imposing macroeconomic policies
The appropriate macroeconomic policy can dampen the business cycle but do not eliminate it. It is observed that the macroeconomic policies that the government impose, have important influence to the short-term fluctuation of the output and the employment and as a result to the alleviation of the cycle :
1)Mainly directly through the government expenditures
2)Indirectly through the adjustment of the equilibrium between the consumption and the savings level (imposing taxes and monetary policies)
In order to avoid the intense fluctuations of the output and the employment the government can impose fiscal policies and 'automatic stabilizers' such as taxes and unemployment benefits. If the economy entries the recession period, the output and the unemployment increase. The unemployment benefits secure an income for the unemployed workers which bolster the aggregate demand from a sharp decrease of the income.
Moreover, when the aggregate income decreases the total taxes income of the government also decreases and the disposable income remains constant.
It is worth mentioning that the stabilizing policies which have not an automatic character are related to the 'lag' problem, according to which the time of the delay in the detection of the problem or in the decision for intervention and activation of the policy, can contribute in the deterioration of the problem.
The case of Greece
Especially in this period, when Greece is facing several serious socioeconomic problems which have been enlarged due to the global crisis the implementation of a study concerning the investigation of the impact of the IMF, EC and ECB programmes for bailout will be of high contribution for policy makers, not only in Greece but in European Union in general. Greece, as one of the euro zone Member States faces economic problems which make borrowing by the markets not viable. The borrowing from the IMF, EC and ECB seemed to be the last resort borrowers for Greece. On the other hand the conditions under which the loans will be given to Greece will have a serious effect on the future for the entire Greek economy. All of the measures are oriented to the decrease of public deficits but concentrate only to the cuts of wages and salaries for the public servants, the pensioners and the employees of the private sector. This policy is expected to lead to the decrease of the demand site at present which will result in a further depression of the internal economy while in terms of current account for trade is possible to show better performance after the cut of the labour cost. Such expected results make the prognosis for the cost outcome for the entire economy at the completion of the program more interesting.
Before continuing I would like to mention some serious economical-political events from the 1950 up to now which will help us to realize why Greece has so serious problems after the financial crises of 2008.Which was the economic conditions which lead the Greek deficit to be the highest in the Euro Area zone? How is it possible for a small country like Greece to have a public deficit of 300 billion Euros? From where they came from?
However, Greece is not the only country whose budget deficit exceed 3% of the GDP which is a rule among the euro zone nations. But a look at the root of the deficit and the debt is important.
I separate the time periods into four categories.
1)The Greek miracle 1950-1974
After the second World-War and the civil war (1946-1949) the Greek economy was destroyed and (recession period). There were no infrastructure, capitals, investment opportunities. The depreciation of drachma and the hyper-inflation deteriorate the economic situation of the Greek economy. The Marscall plan(1948-1951) and the Truman Doctrine(1947) helped the Greek economy as a large amount of capitals reinforced the Greek economy and in 1950 many macroeconomic variables(like output, investment level) become at the same level as before the second World War. However ,the inflation r eached the 10% and the Greek deficit the 25% of the GDP.
From 1950 and afterwards the Greek economy began to recover rapidly. Afterwards the big depreciation of 1953 which took place for developmental reasons, the Greek Prime Minister undertook liberal economic policies releasing somehow the international trade while, because of the economic stability ,the Greeks began to entrust the drachma and to save up in drachmas instead of gold that was up to then the general rule. That increased the saving levels and at the same time contributed to the reduction of inflation. The Greek economy was in an unprecedented growth period and that lead to the Greek miracle.
The destroyed Greece of 1948 began the decade of 1950 and 1960 to be developed with a growth rate that nowadays we can see only in China, that is to say growth rate around 10% each year. Greece had the most rapid growth rate (with Japan) in the all world. Greece signed customs union with the European Community of November 1962. Greece in 1960 knew a scary growth, new buildings, new streets, new factories, cheap workforce, big increase of productivity, big domestic investments from the savings that had begun from 1953. The paradise of each businessman and enterprises.
At the period of dictatorship (1967-1974) the inflation was increased, the public debt was tripled, the growth was stopped abruptly and the corruptness of the government put barrier in European ambitions of Greece.
2)The postwar period 1974-1990
The change of regime found the Greek economy in stagnation and the international economy to be deplored. The liberal government followed tight economic policy without benefits, decreased little the inflation and Greece entries the growth period with the national product to be increased by 3%-4% per year. Moreover, the decade 1970 was the first petrol crisis and the Keynesian model starts to rock internationally. Greece had still enough margins of growth but this international conditions did not allow. Nevertheless Greece became member of the European Economic Community and the Greek economy late but regularly faces the international difficulties. That period the public debt was in the levels of the 28% of GDP. The next roughly 10 years the country will be sunk in a economic swamp and will come in front of enormous economic dead ends.
The government changed in 1981 (-1989) and the socialistic government is in the wheel of the Greek economy. The big economic crises finished in 1982 but at the same time the inflation reached the 20% of the GDP, the public debt jumped in 1989-1990 to the 100% of the GDP while the government expenditures do not have any developmental vision and the deficits reached also the 20% of the GDP.
The debt of 680 billion of drachmas in 1980 became 11 trillion of drachmas in 1990.In order to transfer this number in euros we could say that the 11 trillion that we owed in 1990 is the same like we say today 32 billions of Euros. That is to say the debt from 1990 up to today is 10 times higher in absolute numbers. Therefore from 1980 until today the debt has increased at 200 times reaching today the roughly 300-320 billion of Euros.
The decade of 1980 Greece entered again a recession period where the productivity of work collapsed, the enterprises faced completely unstable economic environment while they had moreover to face strong trade unions, counterproductive labour culture, big increases of wage and restrictions in the increases of prices of their products. In addition the unemployment level from 2,4% in 1980 became 6,4% in 1990.
3)The neoliberal period 1990-2002
The liberal government (1990-1993) undertook tight economic policies but the economy could not come back in competitive orbit. The public debt had already a unverifiable ascendant orbit while the GDP remained stable because of the restrictive policies. That period began the first privatizations of public organisms.
In 1994 the government became socialistic and after 3-4 years the deficits decreased, the inflation came back in one-digit number after roughly 20 years and the Minister of Finance attempted more privatizations than any other Minister of Finance in the world.
That period, the effort in order to put Greece in the Economic and Monetary Union was intense. Thus, in March 1998 the drachma was depreciated and the European equivalent became 353,109 drachmas per Euro.
While in 2001 Greece became a member of the IMF, the first revaluation of drachma took place and from 353,109 equivalence was shaped into 340,75. The growth jumped after a lot of years in 4%, the investment levels increased, the productivity of work increased, the unemployment decreased, the inflation approached zero and the debts declined. The public deficit continued to increase but no additional problems were caused as the GDP increased with positive rates.
4)The destructive period for Greece 2002-2010
As we saw in the theoretical study of the business cycle the growth period is followed by the recession period. The main element of this period, element that Greece could not manage, they are the low interest-rates. With the entry of Greece in the IMF the interest-rates that the citizens and the state were borrowed, fall dramatically. From 1997 many people and companies has begun to borrow from the banks. From 2001 and afterwards the government borrowed extremely high amounts from other banks in Europe. The public deficit increased more because of the Olympic Games of 2004 as a huge amount of capitals came from abroad.
After the Olympic games and after 2-3 years expansive and "social" economic policy (2001-2004), the first structural problems appeared. The competitiveness of work began to fall, the growth rate began to decrease, the deficit and also the public debt increased. And as long as this vicious circle continued, the government continued to borrow in order to enfranchise "social" benefits in order to substitute the purchasing force that was lost because of the lack of competitiveness.
Furthermore, the international conditions changed after 2001. The recession of the world- economies stopped Greece's growth opportunities initially. After 2003 the growth came back internationally, but Greece's weaknesses began to burden her backs.
Consequently, late and regularly the lack of competitiveness, the increased public debt, the decreased productivity concerning the international competition, the big deficits ,the new economic crisis that began to appear from 2007 brought the Greek economy in a new precipice.
The chart below represents the root of the Greek deficit as % of the GDP.
Description of the methods for the estimation of the business cycles
In this chapter the interest is focused on the basic characteristics of the main macroeconomic variables of the Greek business cycles. The study of an economic variable can be done with the separation of its root into economic growth phenomena and business cycles phenomena. So there are two components: the component of growth(trend component) and the business cycle component (cyclical component).
The growth component is related to the regularizing trend of the economic variable we are dealing with. It is observed that this component is defined as the long-run trend of a time series which is characterized by small frequencies and is non stationary. Actually its really rare to find stationary time series.
The business cycle component is correlated with the cyclical component which is characterized by large frequencies and is a stationary stochastic process.
However, there is the view that the growth and the business cycle component are different phenomena and they behave according to the dynamic equilibrium theory. Many approaches have been developed for how to split a time series.
The traditional approach in the business cycle analysis of a time series is based on Burns and Mitchell (1946) who used the "subjective criteria". Specifically, the determination of a business cycle can take place with the chronological recording of the contraction and the expansion periods of the variable. Nowadays, this approach is not used but its contribution to the determination of macroeconomic variables behaviour is important.
An alternative approach is to estimate the growth component according to the theoretical growth model (Lucas 1977). According to the neoclassical growth model (steady state growth analysis) which assumes constant growth rate because of the exogenous labour-augmented technological change, the trend component is a simple linear trend and the cyclical component is the deviation of the series from the trend. The main disadvantage of this method is that actually the growth rate is not constant. However, there can be used functions of higher order (polynomials) but in this case the trends would be deterministic, which is not true.
According to theoretical and empirical studies the established opinion is that the trend in the macroeconomic time series is a non-stationary stochastic process. The most frequently approach is to use time series techniques to extract the trend from the data. The most popular and effective approaches include Hodrick-Prescott filter, the band-pass filter or the Beveridge-Nelson decomposition. In this paper the Hodrick Prescott filter will be used.
The trend component can be estimated by many ways. There are two main categories trend-models. The first category include the deterministic models whish are the linear and the polynomial models. The second category consists of the stochastic models(like the Hodrick-Prescott filter).
Some crucial points of these categories are the following:
Its trend-abstraction method is easily applied. This method assumes that the trend component is independent of the rest part of the series and can be estimated by a linear function:
Y t = Î±0 + Î±1*t + ut
where Y t: the time series, t : the trend, ut: the stochastic error term, Î±0 :the constant, Î±1: the slope term
It comes if we add the square of the trend component:
Y t = Î±0 + Î±1*t +Î±2*t+ ut
The trend-polynomial has the following form:
Y t = A + Î£Î±j*tj + ut= A(t)+ ut
It is obvious that the Î±) and Î²) come from the third form.
In these models the the trend component can be estimated by the regression of Y to A(t).The OLS estimations of the systematic part of the A(t) consists the estimation of the trend component while the estimation of the errors consists the cyclical component and other random components.
This method is not reliable, as it requires strict assumptions in the growth rates such as linearity in the growth rates in case Î±) and stability in the acceleration of the growth rate in case Î²). However, these estimation methods assume that the growth rate is important whereas actually it is observed that it is effective to assume that the growth rate is a non-stationary stochastic processes(Hamilton 1989).
2) Stochastic models
Î±)Î¤he first differences
For the abstraction of the trend we calculate the first differences of the time series we are examining. This method requires that the trend component is a time process which contains randomness and is uncorrelated with the cyclical component.
Set Y t the time series that can be written as:
Y t = Y t-1 + et
Where Y t-1 is the trend component and et is the error term of the series
If the real curve of the trend is not linear then the first differences are not enough for the trend abstraction. In addition, if the series is exponential we can apply the logarithms in order to transform it to linear.
Î²) Hodrick-Prescott filter
This method developed by Hodrick and Prescott (1980) and its scope is to extract the stochastic trend from GDP data.
The Hodrick-Prescott filter(HP filter) is used to demonstrate a nonlinear representation of a time series and it is more volatile to long-run fluctuations than short-run. The adjustment of the trend-sensitivity in short-run fluctuations is achieved with the modification of the multiplier Î».This method has some common points with the MA method but is estimated differently.Particularly, it produces a new time series which is as close as possible to the initial and the new series is as smoothest as it can be. This new time series is an estimation of the 'trend'.
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