The trouble some issues encountered while modelling the economic growh together with a new exponential modelling

 

The following text is AI (ChatGPT plus) generated with reference to my current issue in mathematical modelling of the macroeconomic growth theory. 

---  

This week I had an interesting little incident at the boundary between economics and mathematics.

I was checking an exponential model for an economic growth / Total Factor Productivity (TFP) problem. After going back to the mathematical formulation and implementing it carefully in MATLAB, the objective function $Q(\phi)$ showed a clear minimum.

At first sight, that sounds encouraging: the optimisation problem has a well-defined solution.

However, when I reconstructed the corresponding TFP trajectory using the parameters associated with that minimum, the result did not reproduce the observed trajectory satisfactorily.

So I found myself in an interesting situation:

the mathematics said, “Here is the optimum,” while the economic data replied, “Not so fast.” 😅

This does not necessarily mean that the exponential approach is mathematically wrong. Rather, it raises a more interesting question: is this particular model structure appropriate for representing the empirical behaviour of TFP?

At the moment, I am therefore also comparing the result with a penalised smoothing spline, which appears to represent the trajectory more naturally.

For me, this has been a useful reminder that finding a mathematically neat optimum is not the same thing as finding a good empirical model. Optimisation, model specification, and interpretation all have to work together.

The investigation is still ongoing, so this is not a final conclusion — just one of those small research episodes where economics and mathematics refuse to cooperate quite as politely as expected.

 

Leontief Model Simulation with Python Part 2: Experimental Attempt of Eigenvalue Problem when a matrix is singular i.e. non-invertible

 

This piece of my experimental attempt is based on the paper Singularity in the Discrete Dynamic Leontief Model by István Ábel1, Imre Dobos https://pp.bme.hu/so/article/view/8432/7719 .  This paper was accidentally found while searching for "Matrix Pencil for financial analysis".  Yet, this method is different from the Matrix Pencil (MP) method used in my current researching topic.  Nonetheless, this mathematical modelling applying the eigenvalue problem for the cross sectional econometric model is interesting enough to entice me. 

Honestly speaking, I have not fully understood their method behind because it is really off-topic from my current time series modelling. At the same time, I would like to keep this topic for my near future reference as I will be able to use my Linear Algebra application gained from my current research project. At least, I have attempted solving their mathematical modelling while learning by imitation. Therefore, it is likely to contain some error which I have to spend a sufficient amount of time for investigating and learning this realm of research. 

In terms of this example, the capital coefficient matrix C_i,i is singular containing a row containing zeros i.e. non-inversible. Therefore, the method of the eigenvalue problem is applied instead of using C_i,i^(-1).  Lambda (Greek letter) denotes the eigenvalue of the following equation. The error margin is kept below 1% or 5% at most.

My Python codes are displayed below:

 

# importing necessary tools

import matplotlib.pyplot as plt

import networkx as nx

import numpy as np

import pandas as pd

import random

import math

import statistics

import networkx as nx

import scipy.linalg

from scipy.stats import qmc

RefList=[

' https://en.wikipedia.org/wiki/Input%E2%80%93output_model'

,

' https://www.youtube.com/watch?v=KmVfmISjayA&t=134s'

,

' https://www.youtube.com/watch?v=z_9HwKet8G0&t=301s'

,

' https://www.sciencedirect.com/science/article/pii/S0895717710001093'

,

' https://pp.bme.hu/so/article/view/8432 https://pp.bme.hu/so/article/view/8432/7719'

]

print('Referring to the following articles and YouTube videos: \n')

for k in range(len(RefList)):

    print(RefList[k])

print(' \n')

print('x_i,t: the vector of output levels \n')

print('d_i,t: the vector of final demands (excluding investment) \n')

print('L: the Leontief input–output matrix \n')

print('C: the capital coefficient matrix \n')

print('C: The following equation is used when these matrices are non-singular i.e. inversible. \n')

# The following follows the example shown in the paper

# Index: Industrial Sectors

Sctrs=['Sec1','Sec2','Sec3']

print(f'There are {len(Sctrs)} industrial sectors. \n')

L = np.array([[0.3,0.3,0.3],[0.4,0.1,0.5],[0.3,0.5,0.2]])

Pdf_L = pd.DataFrame(data = L,index = Sctrs,columns = Sctrs)

display('The input–output matrix: L =',Pdf_L)

C = np.array([[0.3,0.4,0.45],[0,0,0],[0.6,0.8,0.9]])

Pdf_C = pd.DataFrame(data = C,index = Sctrs,columns = Sctrs)

display('The capital coefficient matrix: C =',Pdf_C)

# Identity Matrix

I=np.identity(len(C))

Pdf_I = pd.DataFrame(data = I,index = Sctrs,columns = Sctrs)

display(f'I: {len(C)} by {len(C[0])} identity matrix',Pdf_I)

print(' \n')

print('Leontief formula: x_i,t = L x_i,t + C _i,i (x_i,t+1 - x_i,t) \n')

print('Then, it is converted to:  x_i,t+1 = C_i,i^-1 {(I_i - L_i,i + C_i,i) x_i,t}    \n')

print('On the other hand, the capital coefficient matrix C_i,i is singular containing a row containing zeros i.e. non-inversible. \n ')

print('Therefore, the method of the eigenvalue problem is applied instead of using C_i,i^(-1) as follows. \n ')

print(f"Lambda (Greek letter) denotes the eigenvalue of the following equation (Ref. {RefList[4]} : ")

print('1. x_i,t+1 C_i,i = (I_i - L_i,i + C_i,i) x_i,t } \n')

print('2. Lambda x_i,t C_i,i = (I_i - L_i,i + C_i,i) x_i,t } \n')

print('3. Lambda C_i,i = (I_i - L_i,i + C_i,i) } \n')

# Eigenvalue finding

E= scipy.linalg.eig(C, (I - L + C))

for k in range(len(E[0])):

    print(round(E[0][k].real,18))

# Using the positive real number eigenvalue

EigVal=E[0].real

Where=(np.where(EigVal==max(EigVal)))[0][0]

Lambda=EigVal[Where]

print(f"The maximum eigenvalue used is Lambda= {Lambda} .")

# Corresponding Engenvector denoted as Rho (Greek letter)

ind=np.where(E[0] == Lambda)

ind[0][0]

Rho=E[1][:,ind[0][0]]

print(' \n')

# Let's denote the initial values of production of 3 sectors

x_0=np.array([392999.32,422999.27,446999.23])

Pdf_x_0 = pd.DataFrame(data = x_0,index = Sctrs)

display("Let's denote the initial values of production of 3 sectors: x_i,0 =",Pdf_x_0)

x_1=x_0/Lambda

Pdf_x_1 = pd.DataFrame(data = x_1,index = Sctrs)

display("Then, x_i,1 = x_i,0 / Lambda  =",Pdf_x_1)

Right=np.dot(L,x_0)+np.dot(C,x_1-x_0)

print(f"Then, the right hand side (I_i - L_i,i + C_i,i) x_i,t is {Right} , \n")

Left=x_0

print(f"and the left hand side (I_i - L_i,i + C_i,i) x_i,t is {Left}. \n")

print(f"The percentage difference between the left-hand side and the right-hand side is {(Left-Right)/Right}. \n")

 

The mysterious Japanese macroeconomic factor: The national debt per GDP is 251.93%!

 

... well, Japanese national debt percentage of GDP is over 200%! This is one of the mysterious Japanese macroeconomic factors.

One of the reason is that approximately 90% or more of Japanese national bond holders are Japanese nationals. This is why the government can keep these bond holders even with a substantially low interest rate. The hidden cost of this policy is incurred upon Japanese economy because the government is hardly able to raise the interest rate even during the inflationary period.

 

Furthermore, the value of Japanese national bond is so stable that the capital loss risk is low. Because there is still a regular coupon payment (the income gain) with the low capital loss risk at the moment, the majority private banks in Japan keep holding the national bond as the secure asset. The majority Japanese citizens are so risk-averse that they hardly split their saving to private investment: Then, the private bank simply shift their saving account money to the national bond purchase. Although the coupon payment is not so high, the risk premium is still lower than any private bond for the moment. Their risk-averse personality is one of the strong drive of stabilising the national bond price. 

Nevertheless, it is sceptical to assume this mechanism can keep going on. Japanese economy has been stagnated for multiple decades since the last economic bubble burst in 1990s. Nowadays, Japanese economic indices show that Japanese economic strength is even weaker than before. In addition, the entire macroeconomic strength will keep going down due to the ongoing ageing population combined with the constant substantial population decline.

 

Python: Combination of Singular Spectrum Analysis (SSA) and Fast Fourier Transform (FFT)

 

 

This is my non-linear time series analysis combining Singular Spectrum Analysis (SSA) and Fast Fourier Transform (FFT). 

The dataset is the foreign exchange (FX) rate of Euro (EUR) based on US-Dollar (USD) obtained from Frankfurter App provided by the European Central Bank (ECB).

Implementing FFT for each reconstruction component (RC) of SSA gives us much more precise insights of the periodicity of the time series fluctuation. 

# Execute this cell to have access to the API of Frankfurter App

import requests

import json

# importing necessary tools

import networkx as nx

import numpy as np

import pandas as pd

import random

import statistics

import scipy.linalg

from numpy import linalg as LA

from scipy.stats import qmc

from scipy import stats

import statsmodels.formula.api as sm

import math

import cmath

from scipy.linalg import hankel

import scipy.odr

from scipy import odr

# For using Frankfurter app

import ast

# For graphing

import matplotlib.pyplot as plt

import matplotlib.gridspec as gridspec

import seaborn as sns

# Fast Fourier Transform (FFT) https://docs.scipy.org/doc/scipy/tutorial/fft.html

from scipy.fft import fft, ifft, fftfreq

# Showing the plots bigger

plt.rcParams["figure.figsize"] = (20,10)

# defining imaginary number

i=complex(0,1)

i

## Downloading the time series data from Frankfurter App

# Connecting to the API https://www.frankfurter.app/docs/ to get the EUR/USD rates

url = "http://api.frankfurter.app/1999-01-01.."

resp = requests.get(url,{'to':'USD'})

#print(resp.url)

#print(resp.status_code)

#print("Type:", type(resp.content))

#print(resp.content)

print("Type:", type(resp))

# Preparing for the right encoding

import ast

byte_str = resp.content

dict_str = byte_str.decode("UTF-8")

mydata = ast.literal_eval(dict_str)

print("Type:", type(mydata))

#mydata #show the accessed data

EURUSD=(mydata["rates"])

#EURUSD

#mydata #show the accessed data

EURUSD=(mydata["rates"])

#EURUSD

# Sorting the data into the Python dictionary form

Dates_EURUSD=[]

Rates_EURUSD=[]

for key, value in EURUSD.items():

    Dates_EURUSD.append(key)

    for ky,vl in value.items():

        Rates_EURUSD.append(vl)

EURUSD=dict(zip(Dates_EURUSD,Rates_EURUSD))

print('First week:',list(EURUSD.keys())[0],',  Last week:',list(EURUSD.keys())[-1])

#Rates_EURUSD

### Graph output (1) ###

NW=6 # Number of windows to slice this time series dataset

LI=math.floor(len(EURUSD)/NW) # The length of interval

fig, axs = plt.subplots(NW)

for k in range(NW):

    axs[k].plot(Dates_EURUSD[k*LI:(k+1)*LI], Rates_EURUSD[k*LI:(k+1)*LI])

print("Length of data:",len(Rates_EURUSD))

## Singular Spectrum Analysis (SSA)

print("The following refers to https://stats.stackexchange.com/questions/544105/singular-spectrum-analysis-and-their-eigentriplets")

print('This SSA method is almost identical to the one based on MATLAB "Singular Spectrum Analysis - Beginners guide" (MathWorks)')

print(' https://uk.mathworks.com/matlabcentral/fileexchange/58967-singular-spectrum-analysis-beginners-guide which I attempted to duplicate with Python. ')

# Re-defining the time series and its length

s=Rates_EURUSD;

N=len(Rates_EURUSD)

# Getting window length L and lagged length K

#L = 500-1

L = 100

K = N - L + 1

# Constructing the time lagged Hankel matrix

X=np.zeros((K,L))

for m in range (0, L):

    X[:,m] = s[m:K+m]

   

# Trajectory matrix

Cemb = np.dot(X.T,X)/K

# Eigen decomposition

eigenValues, eigenVectors = np.linalg.eig(Cemb)

idx = eigenValues.argsort()[::-1]  

eigenValues = eigenValues[idx]

eigenVectors = eigenVectors[:,idx]

# Vectors of Principal Components

PC = np.dot(X,eigenVectors)

# Pre-allocating Reconstructed Component Matrix

RC = np.zeros((N, L))

# Reconstruct the elementary matrices without storing them

for k in range(L):

    myBuf = np.outer(PC[:,k], eigenVectors[:,k].T)

    myBuf = myBuf[::-1]

    RC[:,k] = [myBuf.diagonal(j).mean()\

               for j in range(-myBuf.shape[0]+1, myBuf.shape[1])]

       

### Graph output (2) ###

# First 6 RC

fig, ax = plt.subplots(3,2)

ax = ax.flatten()

for k in range (0, 6):

    ax[k].plot(RC[:,k])

    ax[k].set_title(str(i))

plt.tight_layout()

### Graph output (3) ###

# Plotting a graph comparison

RawSSA=RC[:,0]

for k in range(L-1):

    RawSSA=np.add(RawSSA,RC[:,k+1])

SCs=10 # Smoothed cycle components

SmoothedSSA=RC[:,0]

for k in range(SCs-1):

    SmoothedSSA=np.add(SmoothedSSA,RC[:,k+1])

plt.subplot(2,1,1)

plt.title("Original vs. Reconstructed time series")

plt.plot(s[:])

plt.plot(RawSSA)

plt.subplot(2,1,2)

plt.title("Reconstructed raw vs. smoothed time series")

plt.plot(RawSSA)

plt.plot(SmoothedSSA)

# sample spacing

Days=N*7 # Number of days

Months=N*7//30 # Number of months

Years=N*7//360 # Number of years

T=1/Months # Defining the sample spacing step-size

yf = fft(s)

xf = fftfreq(N, T) #[:N//2]

# FFT for each RC

RC_fft=[]

RC_fft_power=[]

for l in range(L):

    RC_fft.append(fft(RC[:,l])) #[0:N//2])

    RC_fft_power.append(np.abs(RC_fft[l]))

# Denoise FFT of RC

dn_RC_fft=RC_fft.copy()

dn_RC_fft_power=RC_fft_power.copy()

for j in range(len(RC_fft)):

    for k in range(len(RC_fft[0])):

        DenoisingThreshhold=(sum(RC_fft_power[j])/len(RC_fft_power[j]))

        #DenoisingThreshhold=(max(RC_fft_power[j]))*0.90

        if RC_fft_power[j][k]<DenoisingThreshhold:

            dn_RC_fft_power[j][k]=0

            dn_RC_fft[j][k]=0

        else:

            continue

# Defining the cycle length

CycLen=(xf[0:N//2]) # Cycle length

#CycLen=CycLen[::-1]

CycLen

### Graph output (4) ###

# Showing some examples of the cycle lengths of the frequencies

fig, axs = plt.subplots(7)

for k in range(1,8):

    axs[k-1].stem(CycLen,dn_RC_fft_power[-k*10][N//2-1:-1]) #[0:N//2])

# Summing all the frequencies of RCs for the inverse FFT

tp_dn_RC_fft=list(map(list, zip(*dn_RC_fft)))

tp_dn_RC_fft_power=list(map(list, zip(*dn_RC_fft_power)))

sum_dn_RC_fft=[]

sum_dn_RC_fft_power=[]

for k in range(len(tp_dn_RC_fft)):

    sum_dn_RC_fft.append(sum(tp_dn_RC_fft[k]))

    sum_dn_RC_fft_power.append(sum(tp_dn_RC_fft_power[k]))

# ### Graph output (5) ### Uncomment the following to display

#plt.stem of the denoised power stemplot

plt.stem(CycLen, sum_dn_RC_fft_power[N//2-1:-1])

plt.grid()

plt.show()

### Graph output (6) ### Uncomment the following to display

# Inverse FFT to reconstruct the time series

plt.plot(s)

plt.plot(ifft(sum_dn_RC_fft).real)

The European Monetary Union is inevitable, but has to be fundamentally revised

Published on 23/07/2011 09:18 British Summer Time

1. Introduction

This Eurozone crisis has been predicted by many economists. These economists put emphasis on the impact of the money supply volume on the stability of economic environments such as the price inflation rate, the unemployment rate, the gross domestic product (GDP), and the speculative trend on financial market. They argued that, when the monetary policy is unified, the common fiscal policy is also required to be established, all the member countries of this monetary union are supposed to have the financial regulation for all these countries, and the labour mobility needs to be flexible for workers in these member countries to move across these countries in order to stabilise the economic environments. In addition, the econometric analysis of the Eurozone average inflation rate indicated that the European Monetary Union (EMU) is beneficial to majority of the member countries owning to the harmonised inflation rate, but it still requires something to control the different inflation rate of each individual member country. The reason of German refusal of issuing Eurobond is assumed to be because of uncooperative attitudes of Greece. Mr. Trichet, the governor of the European Central Bank (ECB) also suggests that the EMU has to fundamentally change its overall structure before allowing any countries to keep incurring their debt. Overall, the solution of the currently ongoing Eurozone crisis is the fundamental improvement on the EMU fiscal, financial, and labour market structure, and getting rid of the common currency will never be a solution.


2. The problem caused by the monetary policy transformation

The disadvantage of abandoning the national monetary policy (to join the common monetary union) is that this country becomes no longer able to set her own interest rate and the volume of her own money supply. Greece used to be heavily relying on her own unique monetary policy, based on the money supply which was remarkably higher than the average of European countries, in order to finance her government expenditure which could not be sufficiently financed by her unsophisticated fiscal policy. However, after Greece joined the EMU, she could no longer use her high money supply. Greece may rely on the tax revenue burdened on her export revenue such as her tourist industry and the growth of her private sectors stimulated by the economic growth of the entire Eurozone economy. Nonetheless, unless she tightens her fiscal policy, when the entire Eurozone economy falls into recession and/or the demand of Greek tourist industry declines, Greece starts struggling to obtain her public finance resource. This problem has been seen in many Southern European Nations such as Italy, Spain, and Portugal. But, Greece seems to be more problematic than these Southern nations. Spanish government shows a strong commitment on tightening Spanish fiscal policy under the European central government’s induction. Italy still has her strong initiative in European economy thanks to her famous industries such as finance, manufacturing, and tourism. Portugal seems to be similar to Greece, but the quantitative data analysis shown in the next chapter indicates Portuguese suffers much less than Greece.




3. The econometric analysis of the Eurozone average inflation rate

This graph (Qualitative method) above shows the different inflation of the Eurozone countries (IMF, 2011). Majority of the Eurozone countries have a synchronised inflation rate trend from 2002 to 2010. The econometric analysis of the Eurozone average inflation rate, whose results are shown by the following figures, indicated that the price inflation of the individual countries joining the European Monetary Union (EMU) is influenced by the price inflation of the other different EMU countries.




This equation is the inflation rate of all individual Eurozone countries (〖Inflation〗_(i,t)) regressed on the inflation rate in the last year 〖Inflation〗_(i,t-1). As the coefficient of 〖Inflation〗_(i,t-1) is less than 1, this variable is stable enough to converge into a particular point in the long run as follows:




So, this proves that the Eurozone inflation rate is converging into 2% which is what the ECB targets to make! The following regression analysis proves that the GDP grows furthermore when the inflation rate becomes closer to 2%:




This result shows the natural log of the GDP in the Eurozone economy, ln⁡(〖GDP〗_(i,t) ) (Footnote 1.) , is significantly negatively correlated with the inflation rate deviating from 2% which is shown as the absolute number of the inflation rate minus 2, |〖Inf〗_(i,t)-2|. The following auxiliary regression shows both the GDP and the inflation are co-integrated each other:



〖 u〗_(i,t) is the residuals from the previous regression. As the lagged residuals 〖 u〗_(i,t-1) is negatively correlated with change in the residuals 〖∆u〗_(i,t), the variables used in the previous regression, ln⁡(〖GDP〗_(i,t) ) and |〖Inf〗_(i,t)-2|, are stable and co-integrated with the EU inflation rate, which means the movement of these variable affects on the other’s. However, the stability test for Greece and Ireland showed a relatively pessimistic result as follows:

Greek inflation on the inflation of the entire Eurozone countries



This analysis suggests that, , not only the percentage of the entire Eurozone inflation's contingency on Greek inflation rate is 47% in average, which is high,(Amended part) but also change Greek inflation is highly contingent to the entire Eurozone (Footnote 2.). Therefore, it is not only Greece suffers more than the other Eurozone countries and but also Greek economy is highly responsible on the entire Eurozone economy. This aspect may suggest both Greece and the entire Eurozone need to cooperate each other very seriously because Greece should not leave the EMU because her business cycle is already tied up with the EMU.

Irish inflation on the inflation of the entire Eurozone countries



On the other hand, Irish inflation rate is neither stable nor co-integrated with the entire Eurozone one. Therefore, Greece seems to suffer from the volatility of the inflation far more than the other Eurozone members so that she needs either the intervention by the European central government or the fiscal restructuration, or both, to calm down her inflation rate. Unlike Greece, Ireland may be benefitted when she leaves the EMU. Irish business cycle is not correlated with the Eurozone economy. But, if Ireland still wants to keep the membership, the Eurozone eventually needs to have a strong fiscal stimulus enough to enable Irish business cycle to harmonise with the entire Eurozone business cycle.

4. German refusal of participating into the Eurobond programme

The concern of Germany on Greece is that Greek catastrophic crisis will be permanent unless Greece tries to reform her fiscal policy fundamentally and cooperates with the EU central governmental policy rather than her own selfish and irrational nationalism. When a person purchases equity, s/he expects its value to be either stable in the long term or predicted to grow significantly. The value of Greek national debt seems to be neither stable in the long term nor predicted to increase its value in the short term. Even if German government is altruistic enough to sustain Greek public finance by purchasing Greek debt in order to rescue the entire Eurozone, there is a risk for Germany to be drawn into the recession or even to be bankrupt.
The Eurobond programme suggests the Eurozone countries to share both the risk and the benefit of issuing the government debts among the entire Eurozone countries rather than burdening the responsibility on each individual country for incurring the government debt. For example, as shown in the graph below, when Germany experiences the economic growth relatively higher than any other nations whilst France falls into the recession, it needs to tune the aggregate demand of both nations.


As there is no national monetary policy available for both France and Germany, one of the optimum solutions would be increasing the tax revenue of Germany to transfer it to subsidise France. The econometric analysis shown in the previous chapter indicates that French and German economies are highly contingent to each other so that French downturn has to be diverted by German contribution to save Germany herself. This is the idea of sharing the risk and benefit of the national debt and its usage under the collective responsibility among the countries.
Nonetheless, this mechanism may work efficiently and effectively because French fiscal policy does not have a problem like Greek. France and Germany have much more similar labour market situation than Greece. In addition, France and Germany are geographically closer each other than Greece. So, the labour mobility is much more flexible between France and Germany than between Greece and them. Furthermore, France and Germany balance their budget without relying on the excess money supply unlike Greece. If this case scenario were Greek instead of France, German tax revenue transfer to subsidise Greece is ineffective and inefficient.
The intervention from the European central government into Greek fiscal policy under the strict guideline of the central government is also emerged. Greece is still resisting against this intervention due to the sentimental irrational populist nationalism. The European central government regards that, in order to make this money transfer to Greece more effective and efficient, Greek fiscal reform lead by the further privatisation of the entire Greek economy are inevitably required. Greek labour market is rigid because of Greek economy’s reliance on the huge public sector, which disrupts the flexibility of the labour mobility. On the top of the inflexible labour mobility, Greek public sectors are not rational enough to balance their budget. They are not used to the market competition and the thread of bankruptcy because they are always protected by the nation unlike the private sectors. By contrast, the private sectors are much more used to balancing their budget under the market competition. As long as Greek public sectors struggle to rationalise their budget to be balanced by their own effort, the enforced privatisation seems to be only the antidote of the fiscal imbalance.
All in all, the responsibility of Greek fiscal policy should be burdened more on European central government to discourage Greek irrational populist nationalism which is notoriously uncooperative to solve this currently ongoing problem for both Greece herself and the entire Eurozone economy. In order to discourage this pathetic nationalism, the privatisation to minimise Greek national government authority can be a key solution before substituting the power of Greek nationalism with the European economic cooperation.


5. The ECB’s point of view and warning from Mr. Trichet

Focusing on the ECB’s point of view on the current Eurozone financial havoc, the ECB executives are suffering from the dilemma between putting priority on saving the Eurozone economy and focusing on calming the inflation by suggesting the fiscal policy of all Eurozone countries to be tightened. In particular, Mr. Trichet, the governor of the ECB, always rejects the optimism on the Eurobond programme without fundamentally reconstructing the fiscal structure in the entire Eurozone. Mr. Trichet has been always suspicious about the stability of the Eurozone economy since the ECB was established. His suspicion is related to the fiscal problem mentioned in the previous chapter.
The ECB has been purchasing a large volume of the national debt of the Eurozone countries by its quantitative easing. In order to keep the value of these bonds to invest to rescue these governments, the ECB has. The ECB cannot survive without an economic activity of these nations so that the ECB needs to save the national governments of the Eurozone. Otherwise, the value of Euro becomes zero so that the ECB itself disappears. However, the expected result still cannot be seen, and the aggregate government bonds incurred has never stopped expanding. This mechanism still enables the Euro exist, but it depreciates the value of Euro further. This phenomenon causes the inflation to hike up, and then the nominal interest rate eventually needs to rise. Overall, rescuing the Eurozone countries damages the private sectors and individual citizens by a high interest rate, and it creates further government deficit which requires the further ECB’s quantitative easing, which again induces a further inflation. Mr. Trichet has already warned this spiral would occur and urged to divert from it since the beginning of the Eurozone crisis (Footnote 3.). Thus, he rejects all the optimism of perpetuating this situation.
The ECB also struggles with negotiating with the private sectors. Although the previous chapter stated the positive aspect of the private sectors in terms of the fiscal policy, the private sectors cause problem in the monetary policy set by the ECB (Footnote 4.). The private sectors are willing to raise their profit and the wage for their executives, and detest the high interest rate. These characteristics of the private sectors perpetuate the inflation which discourages an economic growth of both countries and private sectors themselves in the long term. Generally speaking, the private sectors are uncooperative to the European economic stabilisation. Although the stabilised European economy which the ECB expects to establish benefits to the private sectors in the long term, these private sectors are less interested in it than the ECB.
This aspect infers a danger for European economy which is now also fund by the private sectors. This could be the reason why Mr. Trichet is modest about the private sector contribution to rescuing the Eurozone national economies .

6. Conclusion
In conclusion, there is no optimistic prospect on this current Eurozone economic situation. In order to solve these structural instabilities, the Eurozone may need a fundamental radical revolutionary act on altering both economic and political entire structure. But, they cannot stop the European economic integration because the almost all Eurozone economies are highly correlated with each other as proven by the econometric analysis. It seriously needs an IMF of Europe, which the ECB is trying to act like. The ECB should have a much stronger authority to instruct the fiscal policy of national governments in the Eurozone as same as the IMF does to the national governments in the globe. In addition, if the priority is saving the European economy, the heavy reliance on the private sectors contribution is very risky. Hence, the ECB policy based on Trichetian Monetarism, which is tough against the irrational egos of both the national government fiscal policy and the private sectors’ short-termism, seems to be only the reliable tool, and the economic agents had better listen to it.


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Footnotes:

1. When a variable is positively skewed, it needs to be logged or transformed into the root (E.g. square root and cube root) in order to offer a reliable, unbiased, and consistent statistical analysis.

2.


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My Additional Comment added on 4th of August 2011:

Well, as I mentioned in my essay, it depends on the hamonisation of the business cycles in these candidate nations (I referred to the price inflation rate as an indicator of the business cycle). When the business cycle is harmonised (Synchronised), the monetary union becomes necessary or inevitable, such as the Greek and the other Eurozone countries' case. Otherwise, such as Irish case, it should not join the monetary union or it has to have a great intervention to artificially harmonise the cycles.

Some African nations might be benefited because they trade each other often, and their economy is not self-sustainable i.e. needs to be corroborated each other. But, they indeed need to have a common fiscal policy to modernise and tighten the fiscal policy of all these nations.

South American nations should not have the monetary union yet. These individual South American countries are too big by means of the land mass relative to their population density (I.e. The cost of the inter-country trade inside South America is higher than the benefit from it). Furthermore, these countries do not trade each other often compared to the other blocks of countries in this world such as Europe, North America, Africa, and Asia (According to the statistics shown in Economics of Monetary Union (Paul De Grauwe)).

The trade frequency of among Asian nations is the highest of all the international trade made in this world. So, as Lee Kuan Yew, the first Singaporean prime minister, said forming Asian trade community could benefit Asian nations. However, other than economic factors, the political factors exist as the obstacles which disrupt forming this trade community.

Only the person concerning the EMU whom I can truely respect and trust is Mr. Trichet and his ECB. I claim that not only the EMU national fiscal policies but also all the private enterprises in the Eurozone economy should be instructed by the ECB based on Trichetian Monetarism...!