Engle's ARCH motion prediction model with the simulation data with Python

 This is introduced in my cartoon video of Yukkuri Kaisetsu (Touhou Project fan-art):

Auto-Regressive Conditional Heteroscedasticity (ARCH)

ARCH was developed by an economist Robert F. Engle III having won the 2003 Nobel Memorial Prize in Economic Sciences for its achievement.

Dependent variable: the variance error terms of the first regression:

The explanatory variable X can be the lagged dependent variables and/or the other variables: 

Then, it find the coefficient γ of the lagged squared error terms with reference to the log-likelihood: 

 

Generalised Auto-Regressive Conditional Heteroscedasticity (GARCH)

GARCH assumes the variance of the error term symmetrically varies depending the average size of the error terms in pervious time steps. It adds the lagged variance on the explanatory variable of the second regression with reference to the log-likelihood for finding the coefficients γ and δ:

 

 Simulation Data with Python

The following exhibits display the simulation data evaluated using ARCH to illustrate how ARCH functions.

To facilitate the visual representation of this simulation, the most basic form of Engle's ARCH, as introduced in the Wikipedia entry below, has been implemented.

Ref: https://en.wikipedia.org/wiki/Autoregressive_conditional_heteroskedasticity

This simplified simulation demonstrates motion prediction for intercepting incoming flying projectiles with erratic movements, resembling the fluctuations of a stock price.

Following is my Python codes: 

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.


-------------------------------------------------------------------------------
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.


---------------------
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...!

Recession in 2024

 

The major recession is coming in 2024 for certain by means of both the international financial analysis and the astrological analysis (from the later half of 2024)! In terms of the international finance, the short-term United State (US) bond interest rate is higher than the long-term counterpart now. This infers to forecast the economic outlook of a few years ahead is worse than the one at the recent time period. In terms of the astrological analysis, the square aspect of Jupiter and Neptune has almost always triggered the world gross domestic product (GDP) decline. This is econometrically experimented in my own research.

The current interest rate hike of the US and the Western European central banks is recently notable due to the ongoing price inflation pressure. However, the long-term (3 to 5 years) rate still stays low, and this implies the low growth of both the GDP representing the combination of both the price inflation and the production output level in a few years ahead. This phenomenon has almost always taken place approximately 2 years before the world-wide recession strikes owing to the financial statistics. Therefore, it is most likely to have the recession in 2024.

The modern Western astrology denotes the aspects of Jupiter and Neptune combined representing the financial flow. Jupiter represents expansion and wealth whilst Neptune represents ambiguity and flash-flood. Therefore, the combination of what each of these two plants represents indeed explains the financial market. The soft aspects such as the triangle 120 degree and the sextile 60 degree tend to induce the reasonable financial wealth growth whereas the hard aspects such as the opposition 180 degree and the square 90 degree tend to induce hard challenges for the financial wealth creation.

When the world GBP (US$ base) is regressed on three explanatory variables based on trigonometric functions, their correlation shows that astrological representation actually holds as it explains! The first explanatory variable is based on the equation of the cube root of 1 minus two times the modulus of 0.5 subtracted by the modulus of the cosine. This variable is maximised at the 60 and 120 degrees whilst it is minimised at 0, 90, and 180 degrees. The second explanatory variable is the modulus of the sine which is maximised at the 90 degree square aspect. The third explanatory variable is simply the cosine which is maximised at the 0 degree conjunction whereas it is minimised at the 180 degree opposition. 

All these three coefficients' confidence levels are above 90 percent. The third variable's correlation was mild whereas the conjunction aspect is positively correlated while the opposition aspect is negatively correlated. The first variable's correlation is slightly below 95 percent which is still convincing. It seems to be difficult to use the 95 percent confidential interval to determine the confidence level by using such a relatively rough fluctuant indicator like the world GDP level.  Then, using the 90 percent confidence level is worth off to be used for the alternative measure. 

The most intensive and interesting result is the second explanatory variable's correlation which is above 95 percent with its negative correlation with the dependent variable, the world GDP! By means of the statistical inference, this can conclude that this is certain to happen in the future when this correlation takes place. Thus, this is certain that the world GDP declines when Jupiter and Neptune from the square aspect which is going to take place in 2024.

The correlation betweeen currency value based on JPY vs the great circle distance from Kiev, Ukraine

 

 

I have been surprised at how much depreciated Japanese Yen (JPY) against the other currencies has been already.  However, I have realised that the appreciation of each currency by means of JPY is different.  I have guessed that the appreciation rate is lower as the region using this currency is closer to Ukraine where the conflict with Russia is ongoing.  Therefore, I have regressed these FX rate based on JPY with the natural log of their great circle distance from Kiev minus 6.6, and the coefficient is as predicted as shown this graph.

Data from Mizuho Bank: https://uranaisearchastrology.files.wordpress.com/2022/04/2021-2204_fx_mizuho_dist.xlsx

Econometrics meets Astrology: Regressing the world GDP on the aspects of Jupiter and Neptune

In the European astrology, the aspects of Jupiter and Neptune denote the economic/financial prosperity.  Since I started the European astrology, I have become keen to test if the astrological chart can actually be interpreted by econometrical analysis because these aspects are based on the numerical values of these aspects' angles.  

The combination of Jupiter (expansion and growth) and Neptune (ambiguity and liquidity) represents the financial fortune of individuals, companies, and each different time transit.  It is believed that it is a bubble aspect when these two planets form the soft aspects such as the conjunction 0 degree (while it simultaneously induces the hard), the triangle 120 degree, and the sextile 60 degree. On the other hand, it is a broke/crisis aspect when these two planets form the hard aspects such as the opposition 180 degree and the square 90 degree (and also the conjunction simultaneously).  

Then, the following 3 explanatory variables generated by the trigonometric function are created: 

1. The most complex indicator showing a higher value when the aspect angle is close to the soft aspect while a lower value when the aspect angle is close to the hard aspect.  

This could not catch up the positive effect of the zero degree. But, instead of making the valuable excessively complex, the 3rd explanatory variable represents the positive effect of the zero degree angle (Conjunction). 

2. Just a modulus of the sine of the radians representing the effect of the square 90 degree aspect.  The negative effect of another hard aspect angle 180 degree angle (Opposition) is shown by the following 3rd explanatory variable.

3.  The most simple cosine of the radians indicating the highest value at the zero degree angle (Conjunction) and the lowest value at the 180 degree angle (Opposition).

Therefore, the equation for the ordinary least squares (OLS) becomes as the displayed one. 

The coefficient of B1 is expected to be positive, B2 is negative, and B3 is mildly positive.

The result is amazing!  The coefficients of these explanatory variables have turned up to be what expected to be! 

These significances cannot expected to be so strong and the model in general looks rough because this statistical analysis based on a rough and extraordinarily big picture such as a transit aspect of the world GDP in a single chart. 

In order to expect to create a stronger model with stronger significance levels, it requires more precise pictures of the target objects such as the more complex aspects, each individual regional aspects', etc.  

Nevertheless, this can be said to be a big achievement for an econometrician and an astrologist because this analysis actually indicates such a rough estimator as the astrological aspect is able to estimate the world economic outlook to the certain extend! 

Data references:

• The aspect angle of Jupiter and Neptune: 葉月綾乃の占星術ブログ
• The world total GDP: worldometre

* You may download the excel file basing this analysis by clicking here.*

Strange Daily JPY Negative Correlation with TOPIX

It is said that Japanese Yen (JPY) moves awkwardly in the market because JPY tends to be appreciated while Japanese economy indicates the sign of downturn at least in the short run. This trend is often perpetuated even in the middle run. This surprises majority investors observing JPY trends.

In the long run, this awkward trend of JPY is usually corrected to follow the major indices of Japanese economy, such as major Japanese corporate stocks, with their positive correlation as same as the other major currencies of OECD countries such as US dollar (USD). Nevertheless, the market almost always demonstrates the notable negative correlation between JPY and a major Japanese stock index such as Tokyo Stock Price Index (TOPIX) while the observers and the participants monitoring it.

Majority of these individuals monitor JPY with the USD, the most traded pair of JPY, so USD/JPY (USD value based on JPY) is frequently used for the main reference to scale the change in JPY value. The following regression analysis based on the Ordinary Least Squares (OLS) for the time series analysis assesses this phenomenon by regressing the log difference of daily USD/JPY on the log difference of daily TOPIX in the time series.

*** Please note that the positve correlation of USD/JPY means the negative correlation of JPY/USD, and vice versa ! ***

 

The sign is positive , and its t-value is 13.3 which is way higher than the Dickey-Fuller critical value t = 2.89.

Then, in order to determine whether this time series correlation is valid or just a coincidence with no statistical validity, the residuals (the error terms) of the aforementioned OLS are tested by the autocorrelation analysis as follows. The first difference of the residuals are regressed on the lagged residuals. The test is to detect whether or the error term is corrected itsself, so the eroor correction model is recognised.

The sign is negative, and its t-value is -26.43 so the absolute value is way higher than the Dickey-Fuller critical value 2.89, and then the error correlation model holds.

The equation of this estimates of the autocorrelation is expanded as follows.

Then it can be expressed as shown in the graph below:

This pattern of JPY mechanism is caused by the obsolete transaction system of the entire banking and monetary function. The obsoleteness is characterised by both the inefficient physical mechanical equipment of the currency transaction of money and assets among banks and investors and the rigid traditional bureaucracy of government, central bank, and private banks in Japan.

Whenever, the market participants switch their holding assets with the others, the system requires them to convert their assets to the national currency JPY before purchasing the alternative asset. Furthermore, due to the slow transaction in this inefficiency, there is a significant lag of exchanging different assets. Therefore, it consequently induces them to hold JPY cash in their transaction process.

In addition, majority Japanese citizens have a strong faith in holding cash and the middle to high income Japanese citizens have a remarkably high propensity of saving (This is why the majority share of the government bonds is owned by these middle to high income earners. They have a strong tendency to hold cash all the more when the value of stock, bonds, and other equities started being depreciated. This accelerates the appreciation of JPY during the downturn on the top of the obsolete system inefficiency.

By contrast, during the upward market, the short run JPY depreciation may seem to be depreciated when TOPIX rises. Instead of TOPIX affecting JPY, this case scenario is that the depreciation of JPY causes to stimulate TOPIX because of the two reasons. Japanese economy is a heavily export driving economy so JPY depreciation increases the export demand and the revenue of the exporters trading by means of foreign currencies. Another reason is simply because of the transactional motive of the traders attempting to mitigate the fincial loss of their revenue from the depreciated JPY by replacing JPY with the other foreign currencies or any available, safe, and stable assets.

Happiness related to Monarchy, One Party, and Democracy

Published on 12/07/2012 12:57 British Summer Time



Jeremy Bentham created an algebraic formula demonstrating the sum of utility derived from how national political system is structured. The algebraic formula is as follows:

Increasing the weight on one branch of these three decreases the weight on the other two branches. Bentham argued that the current (Contemporary) British system balances the weights among these three branches at the feasible level to maximise the utility.

Nonetheless, Bentham also insisted on abolition of sovereign = monarchy or dictator when his/her existence starts reducing the sum of utility rather than increasing it, and then the revolution shall be emerged. The coefficients of these variable, their sign (+/-), and their significance vary across different time, place (culture and civilisation), and occasion (GDP growth, etc).



At the contemporary time period when Bentham was alive, there was little objective ways to measure the sum of individuals' happiness in each nation in the world. By contrast, due to the development of the information technology, we have become able to collect some peer assessed numerical indices of various social scientific data sets. This happiness index is also collected by objective view points and survey methods under an academic peer assessment. Thus, it is interesting to assess Benthamite calculus owing to this world happiness index.

The data showing how the political system is structured in each nation in the world is quoted from "The Independent Map of the world in 2005". The binary variables are used as the indices to show how one nation's politics is structured e.g. Absolute Monarchy, One Party system, or Indirect/Direct Democracy. There is only one change from the original Benthamite algebra, which is that Aristocracy implies the executive member of a national legislature. As Bentham mentioned Aristocrats were those who have wisdom to govern, so it is equivalent to the government and bureaucratic elites. (He mentioned the House of Lord whose member is not elected from citizens. So, as the members of the legislature is directly appointed by an authoritarian legislation not by individual citizens) Then, many countries governed by one party technocratic policy is seen to be a pure aristocratic system. Absolute monarchy is assumed not to have any influential technocratic institution i.e. aristocracy. (Saudi Arabia and Morocco) whereas the constitutional monarchist nations have an influential parliament (E.g. Arab Emirates). All indirect democratic countries hold both Aristocracy = Technocratic Legislature and Democracy. They are still democratic but not the pure direct democracy. Only the nation seen to be a pure direct democratic is Switzerland in this analysis. Thus, the binary variable representing Monarchy is zero, the binary variable representing Aristocracy is 1, and the binary variable representing Democracy is 1.


**************** An important note ****************

The binary variables are usually 0 or 1, but there are some exceptions.

-> All the British Commonwealth nations have the binary variable denoting "Monarchy" that is 0.3 instead of either 0 or 1. These nations technically have a monarchy but s/he is not their own monarchy living in their countries, and his/her influence is not that strong as much as those nations having their own monarchy like Britain and Japan.

-> The "transient" democratic nations have the binary variable denoting "Democracy" that is 0.5 instead of either 0 or 1. It is still democratic but not a stable democracy. So, the effect of the variable "Democracy" is considered to be marginal.

**************** ***************** ****************

In addition, the Happy Planet Index (HPI) used as the dependent variable in this regression analysis is highly affected by the "natural climate" in these nations. Some nations in a certain latitude mark a significantly higher HPI than the others. Therefore, the absolute value of nation's latitude and its squared value, as the exogenous explanatory variables, are regressed on the HPI as same as the previously mentioned binary variables. The reason why the binomial function of Latitude, instead of a single variable (The linear function), is to demonstrate the parabolic function. The linear model (Regressing only on |Latitude|) only express either the right middle of equator or the North pole and the South pole are the happiest place to live. But, the HPI certainly shows that the optimum latitude to maximise the happiness is somewhere not far away from equator but not the zero latitude point.

All in all, the formula for the regression analysis is as follows:

*** The dependent variable is the natural log of the Happiness Planet Index (HPI) ***

The binomial function showing the climate effect (Latitude) is "the absolute value of Latitude + The squared value of Latitude".

In addition, there are the three binary variables. There are three binary variables showing the pure effect. The first one describes the pure effect of Monarchy. The second one describes the pure effect of Aristocracy. Then, the third one describes the pure effect of democracy.

The rest of variables are the binary variable denoting the interactive effect by two or three variables together. The interaction effect by "Monarchy" and "Democracy" is not assessed because there is no country having both monarchy and democracy without an aristocracy=technocratic executive branch.



The coefficients and their significance is as follows:

The coefficients of the variables showing the climate effect are 0.02256 for the coefficient of the absolute value of Latitude and -0.0004 for the squared variable of the latitude. Then, the formula shapes an upward parabola shown in the picture below.

Therefore, the place where the latitude is either +31 or -31 maximises the happiness of people living.



All the three binary variables denoting the single effect have a significant and positive coefficient. Both the interaction of Monarchy and Aristocracy and the interaction of Aristocracy and Democracy have a significant and negative coefficient. The coefficient of the interaction of all three variables is non-significant, so that the half of the coefficient value is used. The HPI derived from each different political structure is as follows:

This is a bar graph showing the policy effect on the H.P.I.:

These trends can be roughly visualised in a picture graph like this:

A nation with the direct democracy (Monarchy = 0, Aristocracy = 0, Democracy = 1 ) produces the highest HIP. But, Switzerland is the only nation with such a system in the world. So, it is not sure if it is still significant number of the sample to prove its superiority.

The absolute monarchist nations, (Monarchy = 1, Aristocracy = 0, Democracy = 0 ) is the second best. But, there are only Saudi Arabia and Morocco as the examples. Furthermore, all the other monarchist nations without any democratic structure (Monarchy = 1, Aristocracy = 1, Democracy = 0 ) showed the lowest HPI. Thus, it can be seen that, in general, monarchism without any degree of democracy is more likely to cause unhappiness rather than happiness.

The nations with one party system mark the second lowest HPI. Even though these nations are more efficient to be stablised than those lowest developed nations, the transient democratic nations, and any non-democratic monarchist nations. Nonetheless, they seem to sacrifice happiness for their stability.


Some of the constitutional monarchist nations with democracy seem to be happier than democratic republic nations. But, majority of the constitutional monarchist nations are less happier than democratic republic nations.

The democratic republic nations, though their democracy is indirect, such as the United States of America and France are the happiest nations next to Switzerland, the direct democratic nation.



All in all, Democratic Republican nations at the latitude of 31 or -31 seem to be the happiest ones. It also looks like that we can try to establish another Direct Democratic country because it looks like maxminising the happiness of individuals in a nation. Nonetheless, only the sample is Switzerland and it is never known if the similar model is applicable to increase the happiness in another country in reality. The democratic republic nations perform well among all. The performance of the constitutional monarchist nations with an indirect democracy varies.

Hence, this econometric analysis seems to be able to assist Jeremy Bentham having argued that, if monarchy start causing disutility rather than utility, then it is time for revolution! Perhaps, we have never known that there will be a revolution for the cause of Direct Democracy, the unknown ideal, in the near future? The Direct Democracy seems to maximise individuals' happiness at the optimum level (Though there is not enough number of the sample to prove in reality) by means of this statistic inference.



* It was difficult to find if the model creates heteroscedasticity: Some tests said no, but the other said yes. But, this analysis was mainly composed of the binary variables, and the dependent variable used in this analysis is not a precisely scientifically accurate variable. So, the aim of test should not be strict as much as the other econometric analyses.

Econometric Analysis of Employment Rate based on New Economic Geography theory

* This was originally posted on 13th May, 2010:



Abstract:

This project attempted to create the model to indicate the significant factors influencing the employment rate in countries. As the author was sceptical about the traditional macroeconomic concepts the new economic geography theory approach is used. European countries are assessed in this project as Europe has a flexible labour mobility and is more convenient to assess the impact of language speaking ability in labour market than the USA where majority of people speak English. The Employment Rate Index (ERI), the index of employment, was based on the exponential of the employment rate subtracting the minimum employment rate in the data and then multiplied with 10 in order to make a symmetric variable (The raw data for the employment rate was very asymmetric). There are two explanatory variables are used; one indicates the employment opportunity in the other countries, and the other indicates the advantage to speak English in trade in both with other countries and within a country. Generalised Least Squares (GLS) estimates showed these two variables are significant enough to explain about the employment rate in a country.



1. Introduction:

This research was carried out to investigate to explain how the employment rate changes in terms of the New Economic Geography theory approach.



2. The reason why the data sets in European countries are used:

Europe has a flexible labour mobility as same as the USA unlike Asia and South America where people rarely change their job in their life. Europe is more convenient to assess the impact of language speaking ability in labour market than the USA where majority of people speak English. The global research encounters with lack of data set for the employment rate figure.



3. The Simultaneous Equation Problem in the traditional Macroeconomic theories:

The traditional macroeconomic theories claim that the employment rate is negatively correlated with the real wage. However, this assumption encounters with the simultaneous equation problem. The real wage rate is highly affected by the employment rate itself. For example, when the employment rate decreases, the real wage starts being depreciated in order to encourage employers to employ labour more. A part of Keynesian wage theory claims that when the employment rate decreases, the nominal wage should increase in order to encourage employees to work more.



4. The significance of using Geographic data:

The best variable explaining the unemployment rate is considered as the Gross Domestic Product (GDP). There is a high demand for productions when the GDP rises so that the demand for labour rises whilst there is a low demand for productions when the GDP falls so that the demand for labour falls. Nonetheless, John Maynard Keynes (1936) claimed that the productivity and the demand of labour is not always positively correlated. When the productivity rises, the production method can alter the labour incentive to the capital incentive. In addition, whenever the employment rate (or any variable representing it) is regressed on the GDP, it causes the endogeneity problem. Therefore, the GDP hardly becomes the best explanatory variable.

Alternatively, geographical aspects are recommended to be used as explanatory variables. Any variables used in economics tend to be measured by a common measure such as money. All variables introduced in IS-LM model are correlated each other. For example, the investment rate, the consumption rate, and the money supply are highly correlated with the productivity, and the productivity is highly correlated with these variables as well. On the other hand, the variables representing geographical aspects are not affected by any economic data generally speaking although these geographic data may affect the economic data. For instance, the geographic distance between cities and latitude (not used in this project but commonly used in the NEG theory) are not modified by any social scientific data sets.


Instead of analysing by the real wage effect inside the countries, the real wage effect in outside the countries is used to analyse the employment rate. Focusing on the graph below, rise in the real wage implies either decrease in the labour supply or increase in the labour demand. When the labour supply decreases in a country, there is a lack of labour supply or labourers in this countries are reluctant to work anymore. Therefore, there is more employment potential for immigrant labourers from outside this country. When the labour demand increases in a country, there is also more employment potential for immigrant labourers from outside this country. By contrast, fall in the real wage implies the opposite effect to the rise in the real wage by referring to the graph below.





This project used the matrix algebra (Explained in Chapter 6) to explain the employment potential in the other countries. The variable representing this is called the Wage Potential Index (WPI) in this project. In order to show this potential, the minimum distance between capital cities is used. As the countries are closer each other the effect of the real wage on employment in a country is stronger whilst as the countries are farer each other the effect of the real wage on employment in a country is weaker. The matrix algebra enables to asses this effect of all the countries surrounding the country assessed by this analysis simultaneously.



5. Shared Language provides more employment opportunities

The NEG theory also uses a variable (variables) representing the human capital index (indices). This project focused on the effect of shared language in both an domestic and international trade. For both non-skilled and skilled workers, language skill is necessary to find a job opportunity. This project focused on English as it is the most commonly used shared language as a shared language in international academic and business activities. As many people speak English in a country, people there find more employment opportunities in the other countries trading with this country. As both a country and the other country trading with have more people speaking English it is more convenient to trade each other.



6. Formulae used:


* The Annual Inflation Rates are the average of the five years.


7. Regression Analysis:

The time periods used are 1995, 2000, and 2005. The countries used are United Kingdom, Ireland, Netherlands, Belgium, Luxembourg, France, Switzerland, Spain, Portugal, Germany, Austria, Czech Republic, Slovak Republic, Italy, Malta, Slovenia, Greece, Cyprus, Finland, Sweden, Norway, Denmark, and Iceland. The reason why the number of time periods and countries is restricted is due to the lack of data sets in some other countries not introduced in this project. But, the author's previously carried out research on the real GDP per capita in a global data showed it did not make a difference between using all countries in a globe and using some representative of the economic regions in a globe. Therefore, the author was confident enough to use the data set able to use as much as possible to analyse the employment in this project.


The Generalised Least Squares (GLS) was used because one of the explanatory variable, the LPI, does not vary across the time (The author could not find a data for this varying across the time), the fixed-effect estimator based the Ordinary Least Squares (OLS) could not be used due to the multicollinearity between the dummy variables used in the OLS and the variable not varying across the time. The pooled OLS should not be used as the unit specific effect in the countries is significant. There is a certain level of the employment rate fixed over the time period. Therefore, the unit specific effect is included in the dummy variable "inside the error term". The regression result is as follows:



Both the WPI and the LPI are significant and positively correlated. The Breusch-Pagan test indicates that the random effect estimate based on the GLS should be used, and the Pooled OLS is not appropriate to use. The Hausman test indicates that the hypothesis claiming there is not an endogeneity problem cannot be rejected. According to what this table shows, the GLS estimates are essential to do this regression, and there is not an endogeneity problem so that this regression analysis is consistent.



8. Conclution:

Having analysed the employment rate, the real wage in the other countries, which represents the potential for labourers in one country to be employed, the geographical figures (the geographical distance represented in this project), and learning English are significant factors influencing the employment rate. This project proved that the NEG theory is able to explain the employment rate in labour market.



Data Sources:
Gleditsch and Ward (2001) Minimum Distance Data // Kristian Skrede Gleditsch
http://pwt.econ.upenn.edu/php_site/pwt_index.php
http://www.imf.org/external/pubs/ft/weo/2010/01/weodata/weoselgr.aspx
http://en.wikipedia.org/wiki/List_of_countries_by_English-speaking_population

Empirical evidence prooving Liquidity-trap: Lower interest rate does not stimulate economy

This was posted on 4th Septermber, 2011:

Why is the economic recovery not stimulated even though the central banks offer the sizably low interest rate which is close to zero? Many people imagine that if the interest rate is low, the economy should be stimulated. The reason is that the cost for companies paying the interest rate of their debt and for entrepreneurs planning to borrow money to start their new business is low.

However, this is only the microeconomic factor, which is a static analysis focusing on the individual economic agent's performance, and does not take account of the time effect and the environment interacting with this agent's performance. This means it ignores the macroeconomic factor which is the dynamic analysis taking account of the future expectation and the wide scale economic environment.

The problem is that, even though the interest rate, the cost of borrowing, is low, if the expected return from investing to economy is low, banks and the other forms of financial institutions are reluctant to lend their money. In addition, the entrepreneurs are discouraged from borrowing money to invest to their business if the future expectation is not good for their business due to the current economic environment.

This phenomenon is called the "liquidity-trap" which was originally mentioned by Professor John Maynard Keynes. During the world economic depression in 1929, many economists thought the economy would be eventually recovered if the central bank tried to increase the liquidity of money supplied by lowering the cost of borrowing money. However, this expectation did not happen. Keynes analysed this problem by explaining the liquidity of money was stuck in their flow due to the lack of confidence in investment. Keynes also put emphasis on need of the price inflation to increase the investment volume. If the price inflation is taking place, the real value of the money borrowed at a certain past time period goes down, and the nominal value of the revenue gained at each time period keeps increasing (the real value of the revenue is kept almost constant). By contrast, if the price deflation (i.e. the "minus" inflation) occurs, the financial economic situation is the opposite effect of the inflationary period.


This project assessed whether positive or negative the correlation between the interest rate and the investment share of GDP. London Interbank Offered Rate has been newly introduced by the IMF, WEO Database, Country Data recently so this newly introduced variable was used as the variable representing the interest rate. Although, there are only the US and Japanese one for London Interbank Offered Rate, the USA and Japan are the best candidate countries to assess the effect of the liquidity trap because they are experiencing now! In addition this variable is a very useful indicator of the interest rate effect on economy because this interest rate index takes account of the various money transactions between various banks and the other forms of financial institutions.

* "London Interbank Offered Rate" is denoted as "the interest rate" and "the nominal interest rate" in this project.

* There are two indicators of the investment share of GDP. One is "the percentage investment share of GDP times the (natural) log of GDP", and another is "the (natural) log of the GDP times the percentage investment share of GDP"

* All the logalisms used in this project is the natural log.

* These OLS regression analyses are based on the fixed effect model which involves the dummy variables (the binary variable) for the different units (countries).

* The variable called "Time" denotes the time trend whose valometer increases as the time passes.

First of all, the simple Ordinary Least Squares (OLS) regression analysis was run. The investment share of GDP is regressed on the logged interest rate. The result offered is shown in the figure below:


This OLS regression is the percentage investment share of GDP times the (natural) log of GDP:




This OLS regression is the (natural) log of the GDP times the percentage investment share of GDP:



These results show that the positive correlation between The investment share of GDP and the interest rate. It is really disappointing for those who trust the monetary policy of both the current US Federal Reserve Bank and Bank of Japan. It is also surprising for many microeconomic financial analysts because it indicates that the business grows when the cost of borrowing and the interest payment on company-debt is high. This contradicts the basic static ( = nominal) cost and benefit analysis. Thus, these results affirm that we certainly need a complex dynamic ( = real ) cost and benefit analysis.

Is it logical to say that "We should rather increase the interest rate to recover our economy?" No, this is not logical. It is not logical to say "Higher the cost for companies and entrepreneurs is, higher the confidence of consumption and investment is".

This aspect suspects that the interest rate is not exogenous (the condition to be a good explanatory variable not being controlled by any other factors (variables)) so that it can be endogenous (controlled by some other factors. This situation leads the analysis inconsistent if this endogenous variable is used as an explanatory variable).

There is an international financial economic theory stating that the interest rate is given by the exogenous factor we are hardly able to control rather than we give the interest rate to control the economic situation. This theory suggests that the interest rate is set according the price inflation rate to make the real interest rate (the nominal interest rate minus the price inflation rate) to as zero as possible. Therefore, this theory rejects the classical and the monetarist theory of the interest rate which states that the low interest rate lowers the cost for the entrepreneurs i.e. stimulating the economy. This theory claims that the interest rate is an indicator of the price inflation. It means that, when the interest rate is high, the expected rate of the price inflation, which increases the business opportunities, is high.

* This is the theory in the developed economies where the hyper-inflation risk caused by the mal-fiscal functioning tends to be low.

All in all, there is a room to assume that the inflation rate stimulates the investment share of the GDP. Therefore, it tested if the logged investment share of GDP is positively correlated with both the interest rate and the logged price inflation rate (In the later texts, the price inflation rate is written as the inflation) as follows:


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This proves that the inflation is positively correlated with the investment share of GDP. However, there is a concern that the interest rate and the inflation are correlated each other. If the explanatory variables in one OLS regression are correlated each other, it tends to disturb the OLS analysis result.

So, it suggests to assess the endogeneity of the explanatory variable. By following Keynes' theory and the theory claiming the interest rate is given, the interest rate is assumed to be positively correlated to the inflation. This inference also claims that the Two Stage Least Square (TSLS) regression analysis, instead of the OLS, to regress the investment share of GDP. The first stage regression, which is called the "auxiliary regression", to regress the interest rate, the candidate explanatory variable of the investment share of GDP, on the inflation, the instrument variable of the interest rate, the explanatory variable.

The other reason why the inflation is wanted to be used as an instrument variable and the interest rate is wanted to be used as an instrumented explanatory variable is that this project attempted to explain the whole mechanism explained by the theory and assess if this theory actually proves the real world economic situation. Because it assumes that the interest rate is highly controlled by the inflation. Therefore, the inflation had to be used as an instrument variables so that it cannot be used as one of the explanatory variables.


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These results proved that the inflation is positively correlated with the interest rate as the theories suggest.

The fitted value of the interest rate instrumented by the inflation rate (and Time if necessary) was saved to use for the second stage regression, which is the primary regression of the TSLS analysis.

There are two analyses because "the percentage investment share of GDP times the (natural) log of GDP" and "the (natural) log of the GDP times the percentage investment share of GDP" are assessed a little bit differently. The former one was regressed on the interest rate instrumented by both the inflation rate and the Time meanwhile the latter one was regressed on the interest rate instrumented by the inflation rate only.

Both kinds of regression analyses are based on the non-linear model because there is assumed to be the optimum interest rate affected by the optimum inflation rate which maximise the investment share of GDP. The positive but reasonable rate of the inflation is a indication of the circulation of economic activities running well and the economy is expanding not too fast. However, the positive and high inflation rate decreases the real value of individual economic agents' income, and discourages saving, the source of financial economy, and supply of the investment available (The net present value of the amount of money invested declines over time). In addition, as the (nominal) interest rate is determined by the inflation rate (in order to set the real interest rate (the interest rate minus the inflation)). Therefore, in order to find the optimum inflation rate and then the optimum interest rate (= The intercept + Coeff. x "The inflation" + error) are required to find out!


The regressions below are "the percentage investment share of GDP times the (natural) log of GDP" on the interest rate instrumented by the inflation and the time trend:


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According to the three criteria (denoting the smaller number shown by each criterion implies the better model), the regression above without including the time trend as one of the explanatory variables is a better model than the other with the time trend as one of the explanatory variables. This reason would be because the time trend is already included in the instrument variable of the interest rate.

The other sorts of models with various kinds of formulae, such as the liner model ( I = a + b x R + error) and the cubic formula ( I a + b_1 x R + b_2 R^2 + b_3^3 + error ), are regressed. Nonetheless, the square formula (The second degree formula) came up as the best model to demonstrate the correlation between the investment rate times the GDP. By observing the both models above, both formulae has the global maximum value. Therefore, this result indicates that the optimum interest rate instrumented by the inflation rate exists.

The figure below contains the matrix graph (the top one) showing what the interest rate given by the inflation and the year is, and the other (the bottom one) showing what "the percentage investment share of GDP times the (natural) log of GDP" given by the interest rate instrumented by the inflation and the time trend is:



These graphs indicate the following phenomena:

# The real interest rate (the gab between the interest rate and the inflation rate) tends to be minimised as the year (Time) passes.
(This could be considered because of the global financial liberalisation which has increased the degree of competitiveness of the global financial market. )

# The optimum interest to stimulate the economic activity is between 1.77 and 2.14.

# In 1980 (and possibly before), the high inflation is discouraged the economic activity level more than the low inflation.

# In 1990 and after, the lower inflation discourages the economic activity level far more than the high inflation.


The regression below assessed "the (natural) log of the GDP times the percentage investment share of GDP" with the same method as "the percentage investment share of GDP times the (natural) log of GDP" assessed in the previous regressions.



For "the (natural) log of the GDP times the percentage investment share of GDP", the interest rate is only instrumented by the inflation because this model needed to include the time trend as one of the explanatory variables. This reason is because the dependent variable "the (natural) log of the GDP times the percentage investment share of GDP" is increasing over time so that the regression model had to involve the explanatory variable explaining this factor. It also had to exclude the time trend from the instrument variable of the interest rate in order to avoid including one same variable for two different indicators.

The figure below contains the matrix graph (the top one) showing what the interest rate given by the inflation and the year is, and the other (the bottom one) showing what "the (natural) log of the GDP times the percentage investment share of GDP" given by the time trend (Exogenous) and the interest rate instrumented by the inflation is:



These graphs indicate the following phenomena:

# The optimum inflation rate stimulating the economic activity is 2.48, and the optimum interest rate is 1.5 then.

# Lower the interest rate is implies lower the economic activity level is.



Having observed these results given by the regression analysis (based on the fixed effect model), the sizably low interest rate is less likely to increase the liquidity of the money supply flowing into economy. As Prof. Keynes suggested, the USA and Japan may need to expect the exogenous shock in their economy, such as technological growth and finding a new natural resource and/or a brand new invention, and/or the strong positive planning policy intervention other than the monetary policy.

All in all, the policy makers cannot merely control the interest rate to expect the economic recovery. Hence, the current US and Japanese monetary policy seems to be very unreliable to stimulate the economic recovery.