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Applicability of Newton’s law of cooling in monetary economics
Accepted Manuscript Appraisal of monetary economy by Newton’s law of cooling Jadranka Ðurovi´c Todorovi´c, Zoran Tomi´c, Nebojša Deni´c, Dalibor Petkovi´c, Nenad Koji´c, Jelena Petrovi´c, Biljana Petkovi´c
PII: DOI: Reference:
S0378-4371(17)31251-7 https://doi.org/10.1016/j.physa.2017.12.030 PHYSA 18960
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Physica A
Received date : 22 September 2017 Revised date : 12 November 2017 Please cite this article as: J.˙u. Todorovi´c, Z. Tomi´c, N. Deni´c, D. Petkovi´c, N. Koji´c, J. Petrovi´c, B. Petkovi´c, Appraisal of monetary economy by Newton’s law of cooling, Physica A (2017), https://doi.org/10.1016/j.physa.2017.12.030 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Highlights (for review)
Highlights
Inflation is a phenomenon which attracts the attention of many researchers. With the development of economy and market, inflation developed as well. We will apply Newton’s Law on Cooling in this paper to determine the long-term dynamics of inflation in Serbia and Croatia.
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Appraisal of Monetary Economy by Newton’s Law of Cooling Jadranka Đurović Todorović1, Zoran Tomić1, Nebojša Denić2, Dalibor Petković3*, Nenad Kojić4, Jelena Petrović5, Biljana Petković1 1
University of Niš, Faculty of economics, Adress: Trg Kralja Aleksandra ujedinitelja 11, 18000, Niš 2 University of Priština, Faculty of sciences and matematics, Lole Ribara 29, 38220 Kosovska Mitrovica 3 University of Nis, Pedagogical Faculty in Vranje, Partizanska 14, 17500 Vranje, Serbia 4 University of Priština, Faculty of economics, Address: Filipa Višnjiča bb, 38220 Kosovska Mitrovica 1 University of Niš, Faculty of economics, Adress: Trg Kralja Aleksandra ujedinitelja 11, 18000, Niš 5 University of Niš, Faculty of Sciences and Mathematics, Adress: Višegradska 33, 18000 Niš *Corresponding auhor: [email protected]
ABSTRACT Inflation is a phenomenon which attracts the attention of many researchers. Inflation is not a recent date phenomenon, but it has existed ever since money emerged in world’s first economies. With the development of economy and market, inflation developed as well. Today, even though there is a considerable number of research papers on inflation, there is still not enough knowledge about all factors which might cause inflation, and influence its evolution and dynamics. Regression analysis is a powerful statistical tool which might help analyse a vast amount of data on inflation, and provide an answer to the question about the factors of inflation, as well as the way those factors influence it. In this article Newton’s Law on Cooling was applied to determine the long-term dynamics of inflation in Serbia and Croatia. Key words: CPI, monetary aggregates, Serbia, Croatia, Newton’s law of cooling
1. INTRODUCTION
Inflation can be defined as a continuous increase of general price level or a continuous decrease in the value of money. Many authors have been trying to define inflation in different ways in order to explain its consequences in detail as well. The best definition of inflation has been given by prof. Hamid Filipović, who defines it in the following way: “Inflation is an economic and financial phenomenon which occurs
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due to disruptions in factors of production, and the consequences are the growth of money supply by issuing banknotes and credit money without adequate backing in metal or goods, which further influences redistribution of net national product at the expense of poorer people, and to the benefit of the wealthy”. (quotes). Inflation is not a new phenomenon. The first signs of inflation arose in ancient times when precious metals were used as money. For example, when gold was used as money, the rulers of the time used to collect golden coins, melt them and then mix with other metals such as lead and copper, only to coin the alloy again and put those coins back into circulation. The nominal value of those coins remained the same, but the real value decreased. In such a way, those in authority issued a greater amount of many than the one which could be issued based on the amount of gold in their possession, thus realizing profits by decreasing the value of newly forged coins. This led to increasing the amount of money in circulation without a change in demand, which further lead to a decrease in the value of money. All of that caused a downfall of purchasing power, which meant that people could by less goods for the same amount of money, while the price of goods was increased due to the drop in the value of money. There are numerous examples in history showing how this technique was used. The consequences of inflation are numerous and can be classified into two groups: positive and negative. Some authors identify inflation with alcoholism. In the beginning, inflation is slow and has positive effects since it leads to expansion in production and employment, as well as increase of prices and salaries. Later it becomes obvious that those effects are ostensible, i.e. that the increase in salary is only nominal and not real, and economic entities try to anticipate the inflation rate. If those defining the economic policy do not react in time with appropriate instruments and measures, it will lead to a lack of trust with economic entities which might further lead to hyperinflation, rejecting national currency and a collapse of national economy. In contemporary research, significant attention is given to studying inflation dynamics and its correlation with macroeconomic indicators, such as unemployment rate, income and money supply [1, 2, 3]. There are also papers on rational expectations of economic entities about inflation dynamics [4]. Regression analysis of inflation and macroeconomic indicators was used in study [5], such as unemployment rate, exchange rate, PPI, monetary aggregates and granted loans, and they have discovered that those indicators had influence on the level of inflation in Romania. Newton's law of cooling was applied in research [6] in order to describe long-term inflation dynamics and he managed to successfully apply this concept of physics in the field of economics. It has also been proved that dynamics of monetary aggregates can be described by applying the same model. A substantial number of contemporary researchers are interested in identifying the signs of inflation and macroeconomic indicators which could be used by those determining economic policy to choose the adequate instruments and measures. This is why the main goal of many central banks in the world is to maintain the price levels and why inflation targeting strategy is enforced. Multiple regression procedure is widely used procedure for different topics [7, 8]. There is also potential to use artificial intelligence methods [9, 10, 11, 12]. In this paper Newton's law of cooling is applied to determine whether this model can be used to describe long-term inflation dynamics and monetary aggregates by using the example of Serbia and Croatia.
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2. METHODOLOGY
Inflation is the consequence of certain instabilities in economy. It is manifested in the rise of prices or a continuous decrease in the value of money [13]. Numerous authors have been trying to define inflation in various ways in order to describe its meaning and consequence in as many details as possible. The author of this paper considers that the best definition was given by Hamid Filipović: “Inflation is an economic and financial phenomenon which occurs due to disruptions in factors of production, and the consequences are the growth of money supply by issuing banknotes and credit money without adequate backing in metal or goods, which further influences redistribution of net national product at the expense of poorer people, and to the benefit of the wealthy” [13]. Inflation is not a new phenomenon. The first signs of inflation arose in ancient times when precious metals were used as money. For example, when gold was used as money, the rulers of the time used to collect golden coins, melt them and then mix with other metals such as lead and copper, only to coin the alloy again and put those coins back into circulation. The nominal value of those coins remained the same, but the real value decreased. In such a way, those in authority issued a greater amount of many than the one which could be issued based on the amount of gold in their possession, thus realizing profits by decreasing the value of newly forged coins. This led to increasing the amount of money in circulation without a change in demand, which further lead to a decrease in the value of money. All of that caused a downfall of purchasing power, which meant that people could by less goods for the same amount of money, while the price of goods was increased due to the drop in the value of money. There are numerous examples in history showing how this technique was used. One of those was Plikrat, king of Sparta, who paid Dionysius, king of Syracuse, in counterfeit money 540 BC. There are several types of inflation, and various criteria for classification. According to its intensity inflation can be creeping, walking, and galloping hyperinflation. Creeping inflation is when inflation rate is not above the average value of 5%. Walking inflation is characterized by annual price increase rate between 5% and 15%. If the price increase is slow, the citizens have confidence in the national currency because they know that in the future they will be able to buy approximately the same amount of goods as today and for the same amount of money. Galloping inflation is when the average inflation rate is over 15%. This leads to insecurity in economy and leads to serious disruptions. Money gradually loses its value, while real interest rates turn negative. Galloping inflation, as a rule, quickly grows into hyperinflation. The most widely accepted attitude is the one provided by Philip Cagan who was the first to seriously take into consideration hyperinflation and its effects in his book Monetary Dynamics of Hyperinflation in 1956. Cagan defined hyperinflation as the one which occurs when monthly rate of inflation is at least 50%. According to its duration inflation can be latent, sporadic and chronic inflation. Latent inflation is when there is a continuous increase in price levels, such where economic entities do not lose their trust in currency and do not convert it into property or other tangible assets. Sporadic inflation is when there is a single increase in price levels, which can be caused by tax increase (consumption tax) or by an increase in goods import. Chronic inflation is when monthly inflation rate stays over 5% for longer than 5 years. According to geographic origin, inflation can be domestic and imported. Imported inflation is a consequence of interdependence between countries that take part in international trade. Domestic inflation is the one which initially occurred in domestic economy.
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The consequences of inflation are numerous and can be classified into two groups: positive and negative. Some authors identify inflation with alcoholism. In the beginning, inflation is slow and has positive effects since it leads to expansion in production and employment, as well as increase of prices and salaries. Later it becomes obvious that those effects are ostensible, i.e. that the increase in salary is only nominal and not real, and economic entities try to anticipate the inflation rate. If those defining the economic policy do not react in time with appropriate instruments and measures, it will lead to a lack of trust with economic entities which might further lead to hyperinflation, rejecting national currency and a collapse of national economy. Consequences of inflation can be direct and indirect. Direct consequences of inflation can be positive and negative. The positive direct consequences are: encouraging economic growth and growth of production, stimulating investments and consumption. Negative direct consequences are decreasing the real value of money, decreasing currency rates, decreasing export and increasing import, increasing prices of goods and services; it also disables economic entities from conducting proper calculations and plans, there is economic instability, a complete neglect of long-term development goals, neglecting the principles of economy, there is seemingly a growth of income and ostensible positive business result, while all goods have a chance on the market, and there are also psychological factors. Indirect consequences are mostly reflected in income distribution. When inflation occurs, everyone with fixed incomes lose the value of those incomes because their real value is decreased, i.e. they will be able to purchase a lesser amount of goods for the same amount of money. This refers to retirement pays, savings, scholarships, public sector salaries and so on. Likewise, there is an effect of monetary illusion where at the beginning of inflation people expect that their salaries have really increased, while the fact is that the increase is only nominal, and not real. This effect is noticed only at a later stage of inflation. During inflation people try to get rid of money by turning it into goods and foreign currency. Because of inflation low salaries lead to redistributing profits, at the expense of poorer people in the society but for the benefit of those who are wealthy. The state can also benefit from inflation. The increase of public revenues (fees and taxes, customs) at the rate bigger than the growth of net national product means that the state takes larger part in the process of distributing net national product. In this period, the government will use the financing of budget deficit, since they will pay their creditors the same amount of money, the value of which will be far lesser from its value when the debt incurred.
2.1. THEORIES AND MEASURING INFLATION There are many causes of inflation and there is rarely only one factor which causes it. The initial impulse is usually caused by one factor, but soon new impulses arise, as a consequence of different factors. Depending on whether the first causes of inflation stem from demand or costs, there is demand-pull inflation and cost-push inflation. In addition to the already mentioned theories of inflation, there is also structural theory of inflation according to which inflation is caused due to structural maladjustments in economy. There are two main theories of demand-pull inflation: classical and Keynesian. According to classical approach, inflation is a monetary phenomenon. Since prices of goods are reflected in money, there has to be certain connection between money and price levels. Quantitative theory of money provides explanations of inflation based on classical explanations. The second part of this paper will provide further discussion on this approach. Inflation rate depends on whether the economy is in the stage of full employment and whether there are inflationary expectations.
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Chicago school of monetary economics believes that velocity of money is not a constant, as considered by quantitative theory of money, but a stable and predictable function of a certain number of variables. On the long run, velocity of money is very stable, with a slight downward trend. This is why inflation without an increase in money supply is impossible in the long run. In a shorter period of time, monetary changes will mostly effect the growth of production, while on the long run they will influence only prices. Keynesian theoryrejects the presumption about a functional interdependence between money and aggregate expenditure. Prices cannot increase unless money supply increases as well, while they can remain unchanged provided that the money supply increases more rapidly than production. In the stage of full employment, an increase in effective demand cannot lead to an increase in production and employment, but can only cause the growth of general price levels. In the stage of full employment, nominal income growth, along with unchanged savings tendency, encourages imbalance between aggregate demand and aggregate supply, and leads to price increase. Price increase will continue until the government reduces the level of disposable income. This is precisely where Keynes believed fiscal policy had a significant role. According to the theory of cost-push inflation, inflation is caused by the growth of costs in the production of goods and service provision, without a change in demand. The increase in one category of costs which is not compensated by an adequate reduction in other cost categories pushes the prices upwards. Growing costs put pressure on prices, and so the spiral of costs and prices moves upward. According to the structural theory of inflation, a fault in demand-supply coordination in sectors is the cause of inflation. Underdevelopment of a whole branch of industry leads to an increase in prices of goods and services, even though there is a surplus in aggregate demand. If an important economic sector is in question, like construction and agriculture, the increase of prices in those sectors is further distributed on all other sectors and causes inflation. If there is a surplus in aggregate demand, structural inflation can become very strong. Inflation is usually assessed on thebasis of inflation rate. Inflation rate is calculated as the percentage rate of the price levels from the previous time period subtracted from the price levels of the current period, and divided with price levels from the previous period.
Inflation can be measured by using various price indexes: producer price index, consumer price index and GDP deflator [14]. In practice, CPI is mostly used. CPI, Consumer Price Index, is a measurement of price levels of a chosen group of products used by an average consumer. It is calculated in the following way:
When calculating total consumer price index, a certain weight is attributed to each goods price on the list and it is calculated as weighted average price of goods.
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Producer Price Index (PPI) measures the average changes in prices of goods produced by domestic producers. In addition to these indexes, cost of life index, GDP deflator and core inflation are used more and more. Cost of life index measures changes in the level of average costs of life. Retail price index measures changes in the level of average retail prices. GDP deflator measures price levels of all new produced final goods and services in an economy and core inflation. It is calculated by dividing nominal GDP by real GDP, and then multiplying by 100. Core inflation is a measurement of inflation which has been used for a couple of decades. It is calculated based on the changes in retail price levels of seasonal goods and services which are formed according to market conditions. This does not include costs of electricity, municipal and other services, medicines, etc. [15]. European Central bank used Harmonised Index of Consumer Prices (HICP) for determining inflation and price stability. This index is an indicator of consumer prices, which was constructed in accordance with the methodology used in European Union countries. In the euro area HICP is a weighted average of price indices of member states who have adopted the euro. The primary aim of ECB is to maintain price stability, which is defined as maintaining the year to year increase of HICP of not more than 2% for the medium term.
2.2. MONETARY AGGREGATES Monetary aggregate is a term which covers a group of various financial instruments, i.e. physical paper and other financial resources like cash. Monetary aggregates are monetary indicators which are used to determine the quality and function of money in an economy, but also to conduct monetary policy and industry liquidity and liquidity of other sectors [13]. If industry is compared to a living organism, money can be identified with the blood in the body. Blood plays a vital role in the functioning of the organism (e.g. it transfers oxygen to organs). It is of vital importance that all organs have adequate oxygen levels and be supplied with an adequate amount of blood. Therefore, in order for economy to function well, it is necessary that there is an adequate quantity of money circulating, which is enough to satisfy the needs of all economic entities so that they can conduct their business as required, and so that the industry can expand its production. Those in charge of monetary policy need to conduct regular monitoring of money supply which is in circulation (not only paper money, but coins and other forms as well). Likewise, it is essential that financial resources be placed on the market and into industry when issuing money. For everything mentioned to be controlled, quantitative indexes are required to provide signals for those in charge of monetary policy, so that the adequate measures and instruments of monetary politics can be applied. There are three concepts used to define money supply. They are the following [13]: 1. Theoretical concept, 2. Empirical concept and 3. Operative concept.
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Theoretical concept primarily focuses on the function of money. There are various definitions of money supply in theory. There are four wider aspects that can be differentiated: 1. Traditional concept argues that the focus should be on the function of money as a means of payment, which involves defining money supply as a sum of money in circulation and demand deposits with commercial banks. This view has been accepted by many scientists, and is therefore accepted in many countries as a definition of money supply. 2. Another concept was proposed by Milton Friedman and the representatives of reformulated quantity theory of money. They claim that unlike traditional concept, which emphasized the function of money as means of payment, the definition of money supply needs to be broader and should emphasise the function of money as means of liquidity. According to this attitude, money refers to cash money, demand deposits and fixed term deposits. 3. Next concept is suggested by Gurley and Shaw, who expanded the definition of Milton Friedman. Supporters of this third conception of money supply state that the debts with certain non-bank financial institutions, especially savings and loans associations and insurance organizations, can be viewed as near replacements for liabilities with commercial banks. In this way, money supply is defined as consisting of the money in circulation, demand deposits, fixed term deposits and liquid financial assets, which are liabilities of previously mentioned non-bank financial institutions. 4. The forth concept is the most extensive. According to this concept, in addition to the elements previously mentioned, the definition of money supply should also include line of credit. This means that money supply includes all forms of financial liquidity, i.e. in addition to liquid financial forms which can be measured it should also include those which cannot be measured. This concept stems from the attitudes of Redcliff’s reports on economic liquidity. The next concept to be considered is the empirical definition of money. According to it, money supply should be defined in such a way that the supply of money gives a clear connection between monetary aggregates and stable functionality of the real economic development. There are two main groups of pragmatic approach in defining money. The first concept is based on the belief that a definition which is to be used should be based on a specific issue. More precisely, monetary aggregates should be defined so that the definition achieves stable functional relationship between monetary aggregates and non-monetary variables. Another pragmatic approach uses statistical method of identifying key points in the field of financial forms listed according to the level of liquidity. In such a way, real money can be differentiated from near money. As a specific approach to empirical definition of money supply we could mark the first attempt to establish the level of all types of financial resources which are assessed to have certain monetary characteristics. One of the most popular suggestions for creating weighted aggregates was given by William Barnett in the early 1980s. Each of the elements of money supply gains its weighted value between 0 and 1, depending on the production costs, i.e. opportunity costs. For example, cash money has the greatest opportunity cost and gains a high weight. Operative definitions of money supply are those definitions which are identified by central banks and which have official application. In the next part of this paper, we will provide a definition of monetary aggregates which are used by National bank of Serbia and Croatian National Bank. National Bank of Serbia has defined three monetary aggregates: M1, M2 and M3. M1 (money supply) is the narrowest monetary aggregate, which consists of cash money and demand deposits. M2 (liquid resources) consists of M1 and near money (demand deposits, 1 year savings deposits, fixed-term deposits
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for a period of maximum 1 year and 1 year bonds). Aggregate M3 consists of M2, reserves of companies, letter of credit insurance, and guarantee for foreign loans [13]. Croatian National Bank has defined three aggregates: M0, M1 and M4. MO (primary money) includes monetary base of active banks which earn money from other banks, cash money in banks, bank deposits at CNB, treasury bills for CNB deposits and other domestic sectors at CNB. M1 (money supply) is comprised of cash money in currency, monetary deposits (resources of non-banking sectors on bank accounts and other accounts used for payments, deposits of other bank institutions and domestic sectors at CNB). M4 (broad money)comprises of aggregate M1, savings and fixed term deposits, foreign currency deposits, bonds and money market instruments [16].
2.3. EXCHANGE RATE AND DISCOUNT RATE Exchange rate is the price of foreign currency expressed in domestic currency. In the course of history, it existed in different systems of exchange rates: gold standard (1880 - 1914), fluctuating exchange rate (1919 - 1925), gold exchange standard (1925 - 1931), controlled flexible exchange rates (1932 - 1939), Bretton Woods fixed exchange rate (1946 - 1973) and flexible exchange rates (1973 to present) [17]. The most significant systems are systems of fixed and flexible exchange rates. Exchange rate is determined on the basis of several factors that influence its fluctuation, but also on the basis of the system of exchange rates which will be used. The following factors are the most important: [13]:
The size of the country Openness of the economy to foreign investments The level of development of domestic financial market Inflation Domestic and foreign shocks The credibility of economic policy
Discount rate is a classical instrument of monetary policy. In those countries where central bank loans are the dominant form of primary emission of money, a change of interest rate for those loans can become a determining factor in forming exchange rates in the financial system. However, the idea of directly controlled primary money is not completely acceptable for central banks of developed countries, precisely because of short-term instability of exchange rates [18]. Discount rate is a minimal interest rate charged by the central bank for giving loans to other banks [19]. Discount rate depends of the realization of the goals of monetary policy, which may often be conflicted. Discount rates of foreign countries are also a principal factor in determining discount rate. If domestic discount rate is higher than foreign discount rates, it can attract hot money. Increased cashflow of foreign currency means growth of money supply which exceeds the required scope, which consequentially causes inflation. The opposite effect is achieved if domestic discount rates are lower than foreign, which leads to outflow in foreign currency, which may further cause growing demand of foreign currency thus causing exchange rate increase.
2.4. REGRESSION ANALYSIS AND NEWTON’S LAW OF INFLATION
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Various researches are being conducted today in order to determine the importance of monetary aggregates for maintaining price level stability. Ndjokou has shown in his paper that it is important to define good monetary aggregates in order to maintain price level stability in countries of BEAC zone. Adedoyin emphasized that in case of Nigeria there is a connection between monetary aggregates and inflation levels in the country [20]. Frederic researched which strategy is the best for maintaining price level stability in industrial countries. On the cases of Germany and Switzerland, he proved that targeting monetary aggregates has satisfactory results, while in other countries inflation targeting led to best results [21].
2.5. NEWTON’S LAW OF COOLING ON THE EXAMPLE OF INFLATION When warm bodies are left out on the open they start to cool down slowly. Isaac Newton discovered that the rate of temperature cooling is proportional to the excess of temperature heat compared to the temperature of surroundings. This is called Newton’s Law of Cooling. It remained unknown whether Newton attempted to describe this phenomenon theoretically, but this conclusion was reached by means of experiment [22]. Newton’s law of cooling can show mathematically that temperature changes happen in time and that they are proportional to the difference between body temperature and the temperature of its surrounding environment:
where T is body temperature at a certain time T, and To is temperature of surrounding environment and k is constant of proportionality which describes the dynamics of cooling/heating of the body. If the value is bigger, the body quickly heats and cools down, and vice versa. By solving differential equation, we get the following:
and when the equation is solved we get:
The resulting equation presents the final formula which describes the heating and cooling of the body. Parameter A is a constant, . If the value of the constant of proportionality (k) is smaller than zero, than this parameter describes the process of cooling of the body which is surrounded by the environment which has temperature To as long as the body temperature becomes the same as the temperature of its environment. Newton’s law of cooling applied on inflation dynamics can be presented in the following way. Let us assume that price level change in a unit of time is in direct proportion with price levels in the observed period of time, i.e.
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where P is price level, t is time, k is coefficient of proportionality which describes dynamics of price level change. By following the previous equation we get:
a final version of a model where A is initial price level for the observed time period, i.e. when t=0. For the sake of empirical check, a version with natural logarithms will be used:
This formula will be used for the analysis of monetary aggregates dynamics, with a slight change where A in this case will be the starting level of monetary aggregate for the observed period of time, k will be a coefficient of proportionality which will show monetary aggregate dynamics for the observed period.
3. Results 3.1. EMPIRICAL ANALYSIS OF THE APPLICATION OF NEWTON’S LAW OF COOLING FOR LONG-TERM CHANGES OF CPI INDEX
For this empirical analysis, we have used data for Serbia and Croatia. Data for Croatia were collected from Croatian National Bank website for the period from January 1998 until August 2015, on a monthly basis. Data for Serbia were collected from National Bank of Serbia website for the period from January 2007 until August 2015, on a monthly basis. Data analysis was conducted in OriginPro 9 program, where we have conducted analysis of long-term inflation dynamics and long-term monetary aggregates by using the previously described model. On the example of Serbia, the analysis was conducted for M3 monetary aggregate, while on the example of Croatia M4 monetary aggregate was analysed. Based on the analysis of changes of CPI index for Croatia the following charts and results were reached as it shown in Figure 1.
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26,4 26,2 26,0
ln(M3)
25,8 25,6 25,4 25,2 25,0 24,8 24,6 0
100
200
Period (Meseci) Period (Months)
Figure 1: Chart of changes of CPI index for Croatia for the period from 1998 until 2015 (Source: Croatian National Bank, data processing conducted by authors) In the Figure we can see that for the observed time period there was a growth of CPI and that there is a growing trend which becomes constant for the last time period. Based on the conducted analysis the following values of parameters were assessed: k=0.00228±0.00002 and lnA = 70.2±0.2. Coefficient of determination is 0,98281, which means that 98,28% of changes were explained by this model for the example of Croatia. The analyses that are to be conducted in future can be used to check the prognoses provided by this model.
5,3 5,2 5,1
ln(CPI)
5,0 4,9 4,8 4,7 4,6 0
20
40
60
80
100
120
Period(Months) (Meseci) Period
Figure 2: Chart of changes of M4 aggregates for Croatia for the period from 1998 until 2015(Source: Croatian National Bank, data processing conducted by authors)
In Figure 2 we can see that there is a growing trend of M4 aggregate changes, where at the beginning there was an enormous growth, and a moderate growth in the second part. Based on the conducted analysis the following parameter values were assessed: k=0.00847±0.00002 and lnA = (6.1±0.1)10. Coefficient of determination is 0,90456 which means that 90,46% of changes were explained by the given model. The result confirms the applicability of the model on the observed data on the given example of Croatia.
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By comparing the assessed values of CPI and M4 aggregate, it is clear that in both cases there are growing trends of the observed variables. It can be noticed that the growth dynamics of monetary aggregate is bigger than that of CPI. If we apply Poisson’s analysis, we get correlation coefficient of 0,98358, which means there is a high level of correlation of the observed data for the example of Croatia. On the example of Serbia, the following charts and parameters were reached after an analysis was conducted as it shown in Figure 3.
5,3 5,2 5,1
ln(CPI)
5,0 4,9 4,8 4,7 4,6 0
20
40
60
80
100
120
Period(Months) (Meseci) Period
Figure 3: Chart of changes of CPI index in Serbia for the period from 2007 until 2015(Source: National Bank of Serbia, data processing conducted by authors)
The chart in Figure 3 shows that there is a growing trend of CPI index in the example of Serbia, which was stable for the observed period. Based on the conducted analysis, the following values of parameters were assessed: k=0.0060±0.0001 and lnA = 106.5±0.7. The coefficient of determination is 0,96668 which means that 96,67% of changes were described by the given model.
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28,4 28,2 28,0
ln(M3)
27,8 27,6 27,4 27,2 27,0 0
20
40
60
80
100
120
Period(Months) (Mesec) Period
Figure 4: Chart of changes of M3 aggregates in Serbia for the period from 2007 until 2015 (Source: National Bank of Serbia, data processing conducted by authors) Figure 4 shows that M3 aggregate had a growing tendency which was stable for the last part of the observed period, while it was exceptionally big at the very beginning. On the basis of the assessed data the following value of parameters were reached k=0.0095±0.0002ilnA = (7.8±0.1)11. The coefficient of determination is 0,93638 which means that 93,64% of changes were explained by this method. The reached result confirms the applicability of the model for describing long-term changes of monetary aggregates on the example of Serbia. By comparing the values of CPI and M3 aggregate we can see that there is a growing tendency in both cases, but that growth dynamics of monetary aggregate is larger than that of CPI. By applying Poisson’s analysis, we have gained the value of correlation coefficient of 0,98437, which proves a large correlation of the observed data on the example of Serbia.
4. CONCLUSION
Inflation is a phenomenon which has been drawing attention of scientists for a long time. Despite a vast application of mathematics and statistical apparatus, we have been able to learn only one portion of information about the characteristics of inflation and what inflation really is. We still do not have detailed answers to the question how inflation comes to existence, what the causes of inflation are and what is the dynamics of inflation. By applying regression analysis and the analysis of a vast quantity of historical data, we could gain answers to these questions. Some papers have analysed numerous factors which could lead to inflation. There is a group of scientific papers which have tried to apply the existing models in physics in order to describe phenomena which exist in economy. This field of science is referred to as econophysics. One particular model which attracted the attention of researchers is Newton’s law of cooling. This model has been successfully applied and analysed on the stock markets, on the example of inflation and monetary aggregates.
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This paper analysed the application of Newton’s law of cooling in order to determine inflation dynamics and monetary aggregates on the example of Serbia and Croatia. Research has shown that the model can be used to successfully describe inflation dynamics and monetary aggregates in Serbia and Croatia, since the value of coefficient of determination in both cases was over 0,90. Similarly, it was shown that the model can be used to describe changes of monetary aggregates in those countries, since there was high coefficient of correlation between the values and dynamics of monetary aggregates and inflation. For future research, the number of countries should be expanded, as well as the extent of data on the bases of which further testing of the applicability of the model will be conducted, on the example of inflation and monetary aggregates.
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[16] Franić I., (2011), Statistička analiza monetarnih agregata i kreditnih agregata od 2000.-2009., Diplomski rad, Ekonomski fakultet, Sveučilište u Splitu [17]
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[20] Adedoyin I.S., (2006), Monetary Aggregate Targeting and Inflation in Nigeria, Agrosearch, Vol.8, No.1, pp. 81-92 [21] Frederic S. Mishkin, (2000), From Monetary Targeting to Inflation Targeting: Lessons from the Industrialized Countries, Bank of Mexico Conference, "Stabilization and Monetary Policy: The International Experience," Mexico City, November 14-15, 2000 [22]
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PII: DOI: Reference:
S0378-4371(17)31251-7 https://doi.org/10.1016/j.physa.2017.12.030 PHYSA 18960
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Physica A
Received date : 22 September 2017 Revised date : 12 November 2017 Please cite this article as: J.˙u. Todorovi´c, Z. Tomi´c, N. Deni´c, D. Petkovi´c, N. Koji´c, J. Petrovi´c, B. Petkovi´c, Appraisal of monetary economy by Newton’s law of cooling, Physica A (2017), https://doi.org/10.1016/j.physa.2017.12.030 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Highlights (for review)
Highlights
Inflation is a phenomenon which attracts the attention of many researchers. With the development of economy and market, inflation developed as well. We will apply Newton’s Law on Cooling in this paper to determine the long-term dynamics of inflation in Serbia and Croatia.
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Appraisal of Monetary Economy by Newton’s Law of Cooling Jadranka Đurović Todorović1, Zoran Tomić1, Nebojša Denić2, Dalibor Petković3*, Nenad Kojić4, Jelena Petrović5, Biljana Petković1 1
University of Niš, Faculty of economics, Adress: Trg Kralja Aleksandra ujedinitelja 11, 18000, Niš 2 University of Priština, Faculty of sciences and matematics, Lole Ribara 29, 38220 Kosovska Mitrovica 3 University of Nis, Pedagogical Faculty in Vranje, Partizanska 14, 17500 Vranje, Serbia 4 University of Priština, Faculty of economics, Address: Filipa Višnjiča bb, 38220 Kosovska Mitrovica 1 University of Niš, Faculty of economics, Adress: Trg Kralja Aleksandra ujedinitelja 11, 18000, Niš 5 University of Niš, Faculty of Sciences and Mathematics, Adress: Višegradska 33, 18000 Niš *Corresponding auhor: [email protected]
ABSTRACT Inflation is a phenomenon which attracts the attention of many researchers. Inflation is not a recent date phenomenon, but it has existed ever since money emerged in world’s first economies. With the development of economy and market, inflation developed as well. Today, even though there is a considerable number of research papers on inflation, there is still not enough knowledge about all factors which might cause inflation, and influence its evolution and dynamics. Regression analysis is a powerful statistical tool which might help analyse a vast amount of data on inflation, and provide an answer to the question about the factors of inflation, as well as the way those factors influence it. In this article Newton’s Law on Cooling was applied to determine the long-term dynamics of inflation in Serbia and Croatia. Key words: CPI, monetary aggregates, Serbia, Croatia, Newton’s law of cooling
1. INTRODUCTION
Inflation can be defined as a continuous increase of general price level or a continuous decrease in the value of money. Many authors have been trying to define inflation in different ways in order to explain its consequences in detail as well. The best definition of inflation has been given by prof. Hamid Filipović, who defines it in the following way: “Inflation is an economic and financial phenomenon which occurs
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due to disruptions in factors of production, and the consequences are the growth of money supply by issuing banknotes and credit money without adequate backing in metal or goods, which further influences redistribution of net national product at the expense of poorer people, and to the benefit of the wealthy”. (quotes). Inflation is not a new phenomenon. The first signs of inflation arose in ancient times when precious metals were used as money. For example, when gold was used as money, the rulers of the time used to collect golden coins, melt them and then mix with other metals such as lead and copper, only to coin the alloy again and put those coins back into circulation. The nominal value of those coins remained the same, but the real value decreased. In such a way, those in authority issued a greater amount of many than the one which could be issued based on the amount of gold in their possession, thus realizing profits by decreasing the value of newly forged coins. This led to increasing the amount of money in circulation without a change in demand, which further lead to a decrease in the value of money. All of that caused a downfall of purchasing power, which meant that people could by less goods for the same amount of money, while the price of goods was increased due to the drop in the value of money. There are numerous examples in history showing how this technique was used. The consequences of inflation are numerous and can be classified into two groups: positive and negative. Some authors identify inflation with alcoholism. In the beginning, inflation is slow and has positive effects since it leads to expansion in production and employment, as well as increase of prices and salaries. Later it becomes obvious that those effects are ostensible, i.e. that the increase in salary is only nominal and not real, and economic entities try to anticipate the inflation rate. If those defining the economic policy do not react in time with appropriate instruments and measures, it will lead to a lack of trust with economic entities which might further lead to hyperinflation, rejecting national currency and a collapse of national economy. In contemporary research, significant attention is given to studying inflation dynamics and its correlation with macroeconomic indicators, such as unemployment rate, income and money supply [1, 2, 3]. There are also papers on rational expectations of economic entities about inflation dynamics [4]. Regression analysis of inflation and macroeconomic indicators was used in study [5], such as unemployment rate, exchange rate, PPI, monetary aggregates and granted loans, and they have discovered that those indicators had influence on the level of inflation in Romania. Newton's law of cooling was applied in research [6] in order to describe long-term inflation dynamics and he managed to successfully apply this concept of physics in the field of economics. It has also been proved that dynamics of monetary aggregates can be described by applying the same model. A substantial number of contemporary researchers are interested in identifying the signs of inflation and macroeconomic indicators which could be used by those determining economic policy to choose the adequate instruments and measures. This is why the main goal of many central banks in the world is to maintain the price levels and why inflation targeting strategy is enforced. Multiple regression procedure is widely used procedure for different topics [7, 8]. There is also potential to use artificial intelligence methods [9, 10, 11, 12]. In this paper Newton's law of cooling is applied to determine whether this model can be used to describe long-term inflation dynamics and monetary aggregates by using the example of Serbia and Croatia.
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2. METHODOLOGY
Inflation is the consequence of certain instabilities in economy. It is manifested in the rise of prices or a continuous decrease in the value of money [13]. Numerous authors have been trying to define inflation in various ways in order to describe its meaning and consequence in as many details as possible. The author of this paper considers that the best definition was given by Hamid Filipović: “Inflation is an economic and financial phenomenon which occurs due to disruptions in factors of production, and the consequences are the growth of money supply by issuing banknotes and credit money without adequate backing in metal or goods, which further influences redistribution of net national product at the expense of poorer people, and to the benefit of the wealthy” [13]. Inflation is not a new phenomenon. The first signs of inflation arose in ancient times when precious metals were used as money. For example, when gold was used as money, the rulers of the time used to collect golden coins, melt them and then mix with other metals such as lead and copper, only to coin the alloy again and put those coins back into circulation. The nominal value of those coins remained the same, but the real value decreased. In such a way, those in authority issued a greater amount of many than the one which could be issued based on the amount of gold in their possession, thus realizing profits by decreasing the value of newly forged coins. This led to increasing the amount of money in circulation without a change in demand, which further lead to a decrease in the value of money. All of that caused a downfall of purchasing power, which meant that people could by less goods for the same amount of money, while the price of goods was increased due to the drop in the value of money. There are numerous examples in history showing how this technique was used. One of those was Plikrat, king of Sparta, who paid Dionysius, king of Syracuse, in counterfeit money 540 BC. There are several types of inflation, and various criteria for classification. According to its intensity inflation can be creeping, walking, and galloping hyperinflation. Creeping inflation is when inflation rate is not above the average value of 5%. Walking inflation is characterized by annual price increase rate between 5% and 15%. If the price increase is slow, the citizens have confidence in the national currency because they know that in the future they will be able to buy approximately the same amount of goods as today and for the same amount of money. Galloping inflation is when the average inflation rate is over 15%. This leads to insecurity in economy and leads to serious disruptions. Money gradually loses its value, while real interest rates turn negative. Galloping inflation, as a rule, quickly grows into hyperinflation. The most widely accepted attitude is the one provided by Philip Cagan who was the first to seriously take into consideration hyperinflation and its effects in his book Monetary Dynamics of Hyperinflation in 1956. Cagan defined hyperinflation as the one which occurs when monthly rate of inflation is at least 50%. According to its duration inflation can be latent, sporadic and chronic inflation. Latent inflation is when there is a continuous increase in price levels, such where economic entities do not lose their trust in currency and do not convert it into property or other tangible assets. Sporadic inflation is when there is a single increase in price levels, which can be caused by tax increase (consumption tax) or by an increase in goods import. Chronic inflation is when monthly inflation rate stays over 5% for longer than 5 years. According to geographic origin, inflation can be domestic and imported. Imported inflation is a consequence of interdependence between countries that take part in international trade. Domestic inflation is the one which initially occurred in domestic economy.
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The consequences of inflation are numerous and can be classified into two groups: positive and negative. Some authors identify inflation with alcoholism. In the beginning, inflation is slow and has positive effects since it leads to expansion in production and employment, as well as increase of prices and salaries. Later it becomes obvious that those effects are ostensible, i.e. that the increase in salary is only nominal and not real, and economic entities try to anticipate the inflation rate. If those defining the economic policy do not react in time with appropriate instruments and measures, it will lead to a lack of trust with economic entities which might further lead to hyperinflation, rejecting national currency and a collapse of national economy. Consequences of inflation can be direct and indirect. Direct consequences of inflation can be positive and negative. The positive direct consequences are: encouraging economic growth and growth of production, stimulating investments and consumption. Negative direct consequences are decreasing the real value of money, decreasing currency rates, decreasing export and increasing import, increasing prices of goods and services; it also disables economic entities from conducting proper calculations and plans, there is economic instability, a complete neglect of long-term development goals, neglecting the principles of economy, there is seemingly a growth of income and ostensible positive business result, while all goods have a chance on the market, and there are also psychological factors. Indirect consequences are mostly reflected in income distribution. When inflation occurs, everyone with fixed incomes lose the value of those incomes because their real value is decreased, i.e. they will be able to purchase a lesser amount of goods for the same amount of money. This refers to retirement pays, savings, scholarships, public sector salaries and so on. Likewise, there is an effect of monetary illusion where at the beginning of inflation people expect that their salaries have really increased, while the fact is that the increase is only nominal, and not real. This effect is noticed only at a later stage of inflation. During inflation people try to get rid of money by turning it into goods and foreign currency. Because of inflation low salaries lead to redistributing profits, at the expense of poorer people in the society but for the benefit of those who are wealthy. The state can also benefit from inflation. The increase of public revenues (fees and taxes, customs) at the rate bigger than the growth of net national product means that the state takes larger part in the process of distributing net national product. In this period, the government will use the financing of budget deficit, since they will pay their creditors the same amount of money, the value of which will be far lesser from its value when the debt incurred.
2.1. THEORIES AND MEASURING INFLATION There are many causes of inflation and there is rarely only one factor which causes it. The initial impulse is usually caused by one factor, but soon new impulses arise, as a consequence of different factors. Depending on whether the first causes of inflation stem from demand or costs, there is demand-pull inflation and cost-push inflation. In addition to the already mentioned theories of inflation, there is also structural theory of inflation according to which inflation is caused due to structural maladjustments in economy. There are two main theories of demand-pull inflation: classical and Keynesian. According to classical approach, inflation is a monetary phenomenon. Since prices of goods are reflected in money, there has to be certain connection between money and price levels. Quantitative theory of money provides explanations of inflation based on classical explanations. The second part of this paper will provide further discussion on this approach. Inflation rate depends on whether the economy is in the stage of full employment and whether there are inflationary expectations.
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Chicago school of monetary economics believes that velocity of money is not a constant, as considered by quantitative theory of money, but a stable and predictable function of a certain number of variables. On the long run, velocity of money is very stable, with a slight downward trend. This is why inflation without an increase in money supply is impossible in the long run. In a shorter period of time, monetary changes will mostly effect the growth of production, while on the long run they will influence only prices. Keynesian theoryrejects the presumption about a functional interdependence between money and aggregate expenditure. Prices cannot increase unless money supply increases as well, while they can remain unchanged provided that the money supply increases more rapidly than production. In the stage of full employment, an increase in effective demand cannot lead to an increase in production and employment, but can only cause the growth of general price levels. In the stage of full employment, nominal income growth, along with unchanged savings tendency, encourages imbalance between aggregate demand and aggregate supply, and leads to price increase. Price increase will continue until the government reduces the level of disposable income. This is precisely where Keynes believed fiscal policy had a significant role. According to the theory of cost-push inflation, inflation is caused by the growth of costs in the production of goods and service provision, without a change in demand. The increase in one category of costs which is not compensated by an adequate reduction in other cost categories pushes the prices upwards. Growing costs put pressure on prices, and so the spiral of costs and prices moves upward. According to the structural theory of inflation, a fault in demand-supply coordination in sectors is the cause of inflation. Underdevelopment of a whole branch of industry leads to an increase in prices of goods and services, even though there is a surplus in aggregate demand. If an important economic sector is in question, like construction and agriculture, the increase of prices in those sectors is further distributed on all other sectors and causes inflation. If there is a surplus in aggregate demand, structural inflation can become very strong. Inflation is usually assessed on thebasis of inflation rate. Inflation rate is calculated as the percentage rate of the price levels from the previous time period subtracted from the price levels of the current period, and divided with price levels from the previous period.
Inflation can be measured by using various price indexes: producer price index, consumer price index and GDP deflator [14]. In practice, CPI is mostly used. CPI, Consumer Price Index, is a measurement of price levels of a chosen group of products used by an average consumer. It is calculated in the following way:
When calculating total consumer price index, a certain weight is attributed to each goods price on the list and it is calculated as weighted average price of goods.
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Producer Price Index (PPI) measures the average changes in prices of goods produced by domestic producers. In addition to these indexes, cost of life index, GDP deflator and core inflation are used more and more. Cost of life index measures changes in the level of average costs of life. Retail price index measures changes in the level of average retail prices. GDP deflator measures price levels of all new produced final goods and services in an economy and core inflation. It is calculated by dividing nominal GDP by real GDP, and then multiplying by 100. Core inflation is a measurement of inflation which has been used for a couple of decades. It is calculated based on the changes in retail price levels of seasonal goods and services which are formed according to market conditions. This does not include costs of electricity, municipal and other services, medicines, etc. [15]. European Central bank used Harmonised Index of Consumer Prices (HICP) for determining inflation and price stability. This index is an indicator of consumer prices, which was constructed in accordance with the methodology used in European Union countries. In the euro area HICP is a weighted average of price indices of member states who have adopted the euro. The primary aim of ECB is to maintain price stability, which is defined as maintaining the year to year increase of HICP of not more than 2% for the medium term.
2.2. MONETARY AGGREGATES Monetary aggregate is a term which covers a group of various financial instruments, i.e. physical paper and other financial resources like cash. Monetary aggregates are monetary indicators which are used to determine the quality and function of money in an economy, but also to conduct monetary policy and industry liquidity and liquidity of other sectors [13]. If industry is compared to a living organism, money can be identified with the blood in the body. Blood plays a vital role in the functioning of the organism (e.g. it transfers oxygen to organs). It is of vital importance that all organs have adequate oxygen levels and be supplied with an adequate amount of blood. Therefore, in order for economy to function well, it is necessary that there is an adequate quantity of money circulating, which is enough to satisfy the needs of all economic entities so that they can conduct their business as required, and so that the industry can expand its production. Those in charge of monetary policy need to conduct regular monitoring of money supply which is in circulation (not only paper money, but coins and other forms as well). Likewise, it is essential that financial resources be placed on the market and into industry when issuing money. For everything mentioned to be controlled, quantitative indexes are required to provide signals for those in charge of monetary policy, so that the adequate measures and instruments of monetary politics can be applied. There are three concepts used to define money supply. They are the following [13]: 1. Theoretical concept, 2. Empirical concept and 3. Operative concept.
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Theoretical concept primarily focuses on the function of money. There are various definitions of money supply in theory. There are four wider aspects that can be differentiated: 1. Traditional concept argues that the focus should be on the function of money as a means of payment, which involves defining money supply as a sum of money in circulation and demand deposits with commercial banks. This view has been accepted by many scientists, and is therefore accepted in many countries as a definition of money supply. 2. Another concept was proposed by Milton Friedman and the representatives of reformulated quantity theory of money. They claim that unlike traditional concept, which emphasized the function of money as means of payment, the definition of money supply needs to be broader and should emphasise the function of money as means of liquidity. According to this attitude, money refers to cash money, demand deposits and fixed term deposits. 3. Next concept is suggested by Gurley and Shaw, who expanded the definition of Milton Friedman. Supporters of this third conception of money supply state that the debts with certain non-bank financial institutions, especially savings and loans associations and insurance organizations, can be viewed as near replacements for liabilities with commercial banks. In this way, money supply is defined as consisting of the money in circulation, demand deposits, fixed term deposits and liquid financial assets, which are liabilities of previously mentioned non-bank financial institutions. 4. The forth concept is the most extensive. According to this concept, in addition to the elements previously mentioned, the definition of money supply should also include line of credit. This means that money supply includes all forms of financial liquidity, i.e. in addition to liquid financial forms which can be measured it should also include those which cannot be measured. This concept stems from the attitudes of Redcliff’s reports on economic liquidity. The next concept to be considered is the empirical definition of money. According to it, money supply should be defined in such a way that the supply of money gives a clear connection between monetary aggregates and stable functionality of the real economic development. There are two main groups of pragmatic approach in defining money. The first concept is based on the belief that a definition which is to be used should be based on a specific issue. More precisely, monetary aggregates should be defined so that the definition achieves stable functional relationship between monetary aggregates and non-monetary variables. Another pragmatic approach uses statistical method of identifying key points in the field of financial forms listed according to the level of liquidity. In such a way, real money can be differentiated from near money. As a specific approach to empirical definition of money supply we could mark the first attempt to establish the level of all types of financial resources which are assessed to have certain monetary characteristics. One of the most popular suggestions for creating weighted aggregates was given by William Barnett in the early 1980s. Each of the elements of money supply gains its weighted value between 0 and 1, depending on the production costs, i.e. opportunity costs. For example, cash money has the greatest opportunity cost and gains a high weight. Operative definitions of money supply are those definitions which are identified by central banks and which have official application. In the next part of this paper, we will provide a definition of monetary aggregates which are used by National bank of Serbia and Croatian National Bank. National Bank of Serbia has defined three monetary aggregates: M1, M2 and M3. M1 (money supply) is the narrowest monetary aggregate, which consists of cash money and demand deposits. M2 (liquid resources) consists of M1 and near money (demand deposits, 1 year savings deposits, fixed-term deposits
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for a period of maximum 1 year and 1 year bonds). Aggregate M3 consists of M2, reserves of companies, letter of credit insurance, and guarantee for foreign loans [13]. Croatian National Bank has defined three aggregates: M0, M1 and M4. MO (primary money) includes monetary base of active banks which earn money from other banks, cash money in banks, bank deposits at CNB, treasury bills for CNB deposits and other domestic sectors at CNB. M1 (money supply) is comprised of cash money in currency, monetary deposits (resources of non-banking sectors on bank accounts and other accounts used for payments, deposits of other bank institutions and domestic sectors at CNB). M4 (broad money)comprises of aggregate M1, savings and fixed term deposits, foreign currency deposits, bonds and money market instruments [16].
2.3. EXCHANGE RATE AND DISCOUNT RATE Exchange rate is the price of foreign currency expressed in domestic currency. In the course of history, it existed in different systems of exchange rates: gold standard (1880 - 1914), fluctuating exchange rate (1919 - 1925), gold exchange standard (1925 - 1931), controlled flexible exchange rates (1932 - 1939), Bretton Woods fixed exchange rate (1946 - 1973) and flexible exchange rates (1973 to present) [17]. The most significant systems are systems of fixed and flexible exchange rates. Exchange rate is determined on the basis of several factors that influence its fluctuation, but also on the basis of the system of exchange rates which will be used. The following factors are the most important: [13]:
The size of the country Openness of the economy to foreign investments The level of development of domestic financial market Inflation Domestic and foreign shocks The credibility of economic policy
Discount rate is a classical instrument of monetary policy. In those countries where central bank loans are the dominant form of primary emission of money, a change of interest rate for those loans can become a determining factor in forming exchange rates in the financial system. However, the idea of directly controlled primary money is not completely acceptable for central banks of developed countries, precisely because of short-term instability of exchange rates [18]. Discount rate is a minimal interest rate charged by the central bank for giving loans to other banks [19]. Discount rate depends of the realization of the goals of monetary policy, which may often be conflicted. Discount rates of foreign countries are also a principal factor in determining discount rate. If domestic discount rate is higher than foreign discount rates, it can attract hot money. Increased cashflow of foreign currency means growth of money supply which exceeds the required scope, which consequentially causes inflation. The opposite effect is achieved if domestic discount rates are lower than foreign, which leads to outflow in foreign currency, which may further cause growing demand of foreign currency thus causing exchange rate increase.
2.4. REGRESSION ANALYSIS AND NEWTON’S LAW OF INFLATION
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Various researches are being conducted today in order to determine the importance of monetary aggregates for maintaining price level stability. Ndjokou has shown in his paper that it is important to define good monetary aggregates in order to maintain price level stability in countries of BEAC zone. Adedoyin emphasized that in case of Nigeria there is a connection between monetary aggregates and inflation levels in the country [20]. Frederic researched which strategy is the best for maintaining price level stability in industrial countries. On the cases of Germany and Switzerland, he proved that targeting monetary aggregates has satisfactory results, while in other countries inflation targeting led to best results [21].
2.5. NEWTON’S LAW OF COOLING ON THE EXAMPLE OF INFLATION When warm bodies are left out on the open they start to cool down slowly. Isaac Newton discovered that the rate of temperature cooling is proportional to the excess of temperature heat compared to the temperature of surroundings. This is called Newton’s Law of Cooling. It remained unknown whether Newton attempted to describe this phenomenon theoretically, but this conclusion was reached by means of experiment [22]. Newton’s law of cooling can show mathematically that temperature changes happen in time and that they are proportional to the difference between body temperature and the temperature of its surrounding environment:
where T is body temperature at a certain time T, and To is temperature of surrounding environment and k is constant of proportionality which describes the dynamics of cooling/heating of the body. If the value is bigger, the body quickly heats and cools down, and vice versa. By solving differential equation, we get the following:
and when the equation is solved we get:
The resulting equation presents the final formula which describes the heating and cooling of the body. Parameter A is a constant, . If the value of the constant of proportionality (k) is smaller than zero, than this parameter describes the process of cooling of the body which is surrounded by the environment which has temperature To as long as the body temperature becomes the same as the temperature of its environment. Newton’s law of cooling applied on inflation dynamics can be presented in the following way. Let us assume that price level change in a unit of time is in direct proportion with price levels in the observed period of time, i.e.
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where P is price level, t is time, k is coefficient of proportionality which describes dynamics of price level change. By following the previous equation we get:
a final version of a model where A is initial price level for the observed time period, i.e. when t=0. For the sake of empirical check, a version with natural logarithms will be used:
This formula will be used for the analysis of monetary aggregates dynamics, with a slight change where A in this case will be the starting level of monetary aggregate for the observed period of time, k will be a coefficient of proportionality which will show monetary aggregate dynamics for the observed period.
3. Results 3.1. EMPIRICAL ANALYSIS OF THE APPLICATION OF NEWTON’S LAW OF COOLING FOR LONG-TERM CHANGES OF CPI INDEX
For this empirical analysis, we have used data for Serbia and Croatia. Data for Croatia were collected from Croatian National Bank website for the period from January 1998 until August 2015, on a monthly basis. Data for Serbia were collected from National Bank of Serbia website for the period from January 2007 until August 2015, on a monthly basis. Data analysis was conducted in OriginPro 9 program, where we have conducted analysis of long-term inflation dynamics and long-term monetary aggregates by using the previously described model. On the example of Serbia, the analysis was conducted for M3 monetary aggregate, while on the example of Croatia M4 monetary aggregate was analysed. Based on the analysis of changes of CPI index for Croatia the following charts and results were reached as it shown in Figure 1.
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26,4 26,2 26,0
ln(M3)
25,8 25,6 25,4 25,2 25,0 24,8 24,6 0
100
200
Period (Meseci) Period (Months)
Figure 1: Chart of changes of CPI index for Croatia for the period from 1998 until 2015 (Source: Croatian National Bank, data processing conducted by authors) In the Figure we can see that for the observed time period there was a growth of CPI and that there is a growing trend which becomes constant for the last time period. Based on the conducted analysis the following values of parameters were assessed: k=0.00228±0.00002 and lnA = 70.2±0.2. Coefficient of determination is 0,98281, which means that 98,28% of changes were explained by this model for the example of Croatia. The analyses that are to be conducted in future can be used to check the prognoses provided by this model.
5,3 5,2 5,1
ln(CPI)
5,0 4,9 4,8 4,7 4,6 0
20
40
60
80
100
120
Period(Months) (Meseci) Period
Figure 2: Chart of changes of M4 aggregates for Croatia for the period from 1998 until 2015(Source: Croatian National Bank, data processing conducted by authors)
In Figure 2 we can see that there is a growing trend of M4 aggregate changes, where at the beginning there was an enormous growth, and a moderate growth in the second part. Based on the conducted analysis the following parameter values were assessed: k=0.00847±0.00002 and lnA = (6.1±0.1)10. Coefficient of determination is 0,90456 which means that 90,46% of changes were explained by the given model. The result confirms the applicability of the model on the observed data on the given example of Croatia.
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By comparing the assessed values of CPI and M4 aggregate, it is clear that in both cases there are growing trends of the observed variables. It can be noticed that the growth dynamics of monetary aggregate is bigger than that of CPI. If we apply Poisson’s analysis, we get correlation coefficient of 0,98358, which means there is a high level of correlation of the observed data for the example of Croatia. On the example of Serbia, the following charts and parameters were reached after an analysis was conducted as it shown in Figure 3.
5,3 5,2 5,1
ln(CPI)
5,0 4,9 4,8 4,7 4,6 0
20
40
60
80
100
120
Period(Months) (Meseci) Period
Figure 3: Chart of changes of CPI index in Serbia for the period from 2007 until 2015(Source: National Bank of Serbia, data processing conducted by authors)
The chart in Figure 3 shows that there is a growing trend of CPI index in the example of Serbia, which was stable for the observed period. Based on the conducted analysis, the following values of parameters were assessed: k=0.0060±0.0001 and lnA = 106.5±0.7. The coefficient of determination is 0,96668 which means that 96,67% of changes were described by the given model.
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28,4 28,2 28,0
ln(M3)
27,8 27,6 27,4 27,2 27,0 0
20
40
60
80
100
120
Period(Months) (Mesec) Period
Figure 4: Chart of changes of M3 aggregates in Serbia for the period from 2007 until 2015 (Source: National Bank of Serbia, data processing conducted by authors) Figure 4 shows that M3 aggregate had a growing tendency which was stable for the last part of the observed period, while it was exceptionally big at the very beginning. On the basis of the assessed data the following value of parameters were reached k=0.0095±0.0002ilnA = (7.8±0.1)11. The coefficient of determination is 0,93638 which means that 93,64% of changes were explained by this method. The reached result confirms the applicability of the model for describing long-term changes of monetary aggregates on the example of Serbia. By comparing the values of CPI and M3 aggregate we can see that there is a growing tendency in both cases, but that growth dynamics of monetary aggregate is larger than that of CPI. By applying Poisson’s analysis, we have gained the value of correlation coefficient of 0,98437, which proves a large correlation of the observed data on the example of Serbia.
4. CONCLUSION
Inflation is a phenomenon which has been drawing attention of scientists for a long time. Despite a vast application of mathematics and statistical apparatus, we have been able to learn only one portion of information about the characteristics of inflation and what inflation really is. We still do not have detailed answers to the question how inflation comes to existence, what the causes of inflation are and what is the dynamics of inflation. By applying regression analysis and the analysis of a vast quantity of historical data, we could gain answers to these questions. Some papers have analysed numerous factors which could lead to inflation. There is a group of scientific papers which have tried to apply the existing models in physics in order to describe phenomena which exist in economy. This field of science is referred to as econophysics. One particular model which attracted the attention of researchers is Newton’s law of cooling. This model has been successfully applied and analysed on the stock markets, on the example of inflation and monetary aggregates.
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This paper analysed the application of Newton’s law of cooling in order to determine inflation dynamics and monetary aggregates on the example of Serbia and Croatia. Research has shown that the model can be used to successfully describe inflation dynamics and monetary aggregates in Serbia and Croatia, since the value of coefficient of determination in both cases was over 0,90. Similarly, it was shown that the model can be used to describe changes of monetary aggregates in those countries, since there was high coefficient of correlation between the values and dynamics of monetary aggregates and inflation. For future research, the number of countries should be expanded, as well as the extent of data on the bases of which further testing of the applicability of the model will be conducted, on the example of inflation and monetary aggregates.
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