CC BY
3
UDC 330.43.
Ivkin Alexey The first year master course student "International Finance" faculty Financial University under the Government of the Russian Federation
Moscow, Russia
THE INFLUENCE OF ECONOMIC GROWTH ON THE FINANCIAL SECTOR BY EXAMPLE OF PORTUGAL
Abstract
The paper assesses the influence of certain macroeconomic factors on financial sector development in Portugal. Data Envelopment Analysis (DEA) is applied to determine the extent to which these factors affect the financial sector, and to suggest which indicators play a more critical role.
The subject of this paper is to identify the key determinants of foreign exchange reserves in Portugal using annual data for 20 years' period (from 1995 - 2015).
The results confirm that the relationship between economic variables and financial ones (foreign exchange reserves) exist. The empirical part is dedicated to 2-Stage OLS regression model.
Key words: foreign exchange reserves, Portugal, 2-Stage OLS, financial variables, economic variables, import, GDP, external debt, interest rates.
Introduction
The financial system comprises all financial markets, instruments and institutions. Today I would like to address the issue of whether the design of the economic system matters for the growth of the financial sector. My view is that the answer to this question is yes. According to cross-country comparisons, individual country studies as well as industry and firm level analyses, a positive link exists between the sophistication of the economic growth and the financial sector. While some gaps remain, I would say that the financial system is vitally linked to economic performance. Nevertheless, economists still hold conflicting views regarding the underlying mechanisms that explain the positive relation between the degree of of the economic growth and financial sector development.
Some economists just reject the idea that the finance-growth relationship is vital. For instance, Robert Lucas asserted in 1988 that economists badly over-stress the role of financial factors in economic growth. Moreover, Joan Robertson declared in 1952 that "where enterprise leads, finance follows". According to this view, economic development creates demands for particular types of financial arrangements, and the financial system responds automatically to these demands.
Other economists strongly believe in the importance of the economic growth for the financial sector. They address the issue of what the optimal economic system should look like. Overall, the notion seems to develop that the optimal financial system, in combination with a well-developed legal system, should incorporate elements of both direct, market and indirect, bank-based finance. A well-developed financial system should improve the efficiency of
financing decisions and thereby favoring a better allocation of resources.
Literature review
Most quantitative literature on international reserve holdings is based on theories developed in the 1960s, when the world adhered to the Bretton Woods System and the global capital flows were relatively small. The framework of analysis on reserve adequacy and optimality could be classified by the methodologies used into two categories: ratios as tools of analysis and regression analysis. The following gives a chronological retrospect of previous study.
Ratio Analysis Reserve to import ratio The most widely used ratio method was the ratio of reserve to import first generalized by Triffin (1947, 1960). It is argued that the demand for reserves should move in line with the trend in international trade since receipts and payments were observed to be volatile. He concludes that major countries should maintain a constant reserve to import ratio ranging from 20 percent as a minimum to 40 percent maximally.
However, this method was born with almost equal number of critics and advocators. Machlup (1966) discredits the theoretical basis for the assumed rigid reserve-import ratio as it lacks of evidence and theory on why such ratio should remain constant across countries or through time. As his defense, three other ratios, including reserve to largest annual reserve losses, reserve to domestic money and quasi money, reserve to liabilities of central banks, were used to explain the behaviors of 14 industrial countries from 1949 to 1965. He stated that "on purely economic grounds, reserves are held only for the purpose of being eventually used." However, this ex parte assumption also neglects a precautionary nature of reserves, especially under fixed exchange rate regime. Similarly, Olivera (1969) theoretically argues that precautionary demand for reserves should reflect variance of changes in annual imports, implying that a constant reserve-import ratio leads to a significant overestimation of present and future demands. 6
The IMF started to measure the adequacy of reserves in the 1950s by the ratio of reserve to import. European Central Bank (2006) regards four months' import coverage as the "rule of thumb". Since the major function of foreign exchange reserves is protecting a country from the uncertainty of international trade, the ratio of reserve to import has almost been included in all analysis on this subject.
Impact of Import on Foreign External Reserves in Portugal from 1996 to 2014 is depicted on the graph № 1
Reserve to domestic money supply
Because enough stockpiles of international reserves would substantially improve the credibility of a country's currency, the ratio of reserve to domestic money indicates the potential of capital flight from domestic currency. Machlup (1966) was the first one who managed to use this ratio, although he finally obtained a contradictory conclusion that the demand for reserves is independent of any identifiable variable. The procedure of the functioning of reserve holding is nevertheless sound while ratios act unstable through time. This evidence is proved by Frenkel (1971), who performed a regression equation on 55 countries, and the coefficient of domestic money supply was statistically significant, especially for less developed countries. Furthermore, Frenkel and Johnson (1976) expatiate that international reserves will increase if the demand for money exceed supply and vice versa. In that sense, international reserves are a residual. Based on this view, Frenkel (1978) suggests combine the demand for international reserves theory and the monetary approach to the balance of payments, followed by an attempted analysis by Lau (1980). Interestingly, Edwards (1984) empirically explores the relationship between reserve flows and domestic credit creation by using 23 fixed exchange rate developing countries and concludes that domestic credit cannot be considered completely exogenous but partial evidence.
Impact of Money Supply (M1) on Foreign External Reserves in Portugal from 1996 to 2014 is depicted on the graph № 2
Reserve to debt ratio
Brown (1964) gives an analysis of the reserve to net external balance ratio on the ground that reserves function as a cushion against future balance of payments deficits. It is assumed that this ratio reflects an economy's financial ability to serve its existence.
External debts, especially in times of a sudden stop in short-term external debt flows. Greenspan and Guidotti (1990) suggest that developing countries, with limited access to international capital market, should at least cover all their debts.
Impact of External Debt on Foreign External Reserves in Portugal from 1996 to 2014 is depicted on the graph № 3
An overview of macroeconomic situation in the country
Background
Mainland Portugal is geographically located in Europe's West Coast, on the Iberian Peninsula. It is bordered by Spain to the North and East and by the Atlantic Ocean to the West and South, therefore being in a geo strategic location between Europe, America and Africa.
In addition to the mainland, Portugal's territory also includes the Autonomous Regions of the Azores and Madeira, two archipelagos located in the Atlantic Ocean.
Portuguese borders have remained unchanged since the XIII Century, making Portugal one of the oldest countries in the world, with nearly 900 years of history that clearly demonstrates its strong identity and internal cohesion.
Population
Portugal's population is estimated at 10.3 million, of which 50% are economically active. The demographic concentration is higher near the coastal areas, with Lisbon (the capital city) and Porto showing the highest population density.
Politics
The Republic of Portugal is a Parliamentary democracy, based on the respect and the effective guarantees for fundamental rights and freedoms and the separation and interdependence of powers. Under the Portuguese Constitution, sovereign powers are vested in the President of the Republic, the Assembly of the Republic, the Government and the Courts.
The current President of the Republic is Marcelo Rebelo de Sousa, who was elected in January 2016.
Legislative power lies with the Parliament (Assembly of the Republic) represented by 230 members which are elected by popular vote to serve a four-year term.
Executive power lies with the Government, headed by the Prime Minister, the Ministers and the Secretaries of State. The current Prime-Minister is Antonio Costa, leader of the socialist party, who took office in November 2015.
Table 1. Portugal Economics Data Summary. Source: INE (National Statistics Office), Banco de Portugal
Summary
Area: 92 212 .0 sq km
Population (thousands): 10 337 (2015)
Working population (thousands): (thousands): 5 195(2015)
Population density (inhabit./sq km): 112.6 (2015)
Official designation: Republic of Portugal
Capital: Lisbon (2.1 million inhabit.- metropolitan area)
District Capitals: Aveiro, Beja, Braga, Bragada, Castelo Branco, Coimbra, Évora, Faro, Funchal (in Madeira), Guarda, Leiria, Ponta Delgada (in the Azores), Portalegre, Porto, Santarém, Setúbal, Viana do Castelo, Vila Real and Viseu.
Main religion: Roman Catholic
Language: Portuguese
Currency: EUR = 1.1212 USD (average rate in August 2016)
Picture 1. Portugal Geography. Source: INE (National Statistics Office),
Banco de Portugal
Infrastructures
As a member of EU Portugal is undoubtedly a country with a highly developed infrastructure. It is comprised of:
Road Infrastructures: Portugal has a developed road network, comprised of motorways (AE), main roads (IP)
Rail Network: The rail network comprises 2 544 km providing North-South connection down the coastline and East-West across the country.
Airports: There are 15 airports. On the mainland the three major international airports are located in the coastal cities of Lisbon, Porto and Faro.
Economy
Economic structure
Following the trend of its European partners, over the last decades one of the most important characteristics of the structure of the Portuguese economy is the increase in the services sector that contributed, in 2015, with 75.8% of GVA and employed 68.1% of the population. Agriculture, forestry and fishing generated only 2.4% of GVA and 7.5% of employment while industry, construction, energy and water represented 21.9% of GVA and 24.5% of employment.
Picture 2. GVA Breakdown - 2015. Source: INE (National Statistics
Office)
Note: GVA - Gross Value-added
Picture 3. Employment Breakdown - 2015. Source: INE (National
Statistics Office)
Current economic situation and outlook
In May 2014, the Government announced the end of the Economic and Financial Assistance Programme - PAEF (agreed with the EU and the IMF in May 2011), without resorting to additional external financial assistance thus gaining access to international debt markets.
After three years of the Programme, the Portuguese economy has made significant progresses in the correction of a number of macroeconomic imbalances, having implemented measures of a structural character in several areas.
In 2015, according to the INE (National Statistics Office), the Portuguese economy registered an increase of 1.5% in volume, year on year (after +0.9% in 2014 and -1.1% in 2013). This recovery was due to the positive performance of domestic demand (+2.5% in relation to 2014), reflected in the increase of private
consumption (+2.6%) and an increase in public consumption (+0.6% in relation to the previous year, after various years of successive falls). Also the gross fixed capital formation increased in 2015 (+4.1%).
According to the same source, the increase of real export growth in goods and services was 5.2% during the last year (with the goods sector increasing 5.9% and services 3.1%), while imports increased 7.6%. The combined current and capital account balance in 2015 was positive, achieving 1.7% of GDP.
In the 2nd quarter 2016, according to INE, GDP registered an increase of 0.9% in volume, year on year.
Table 2. Portugal Economic Indicators 2012-2016. Sources: INE -National Statistics Office, Banco de Portugal, European Commission, Eurostat Notes: (a) Forecast: Banco de Portugal (June 2016), European
Economic Indicators 2012 2013 2014 2015 2016
GDP Million EUR 168 398 170 269 173 446 179 369 184 477
Real change -4.0 -1.1 0.9 1.5 1.3
Million USD 216 358 226 135 230 423 199 010 208 459
Per capita (PPS) EU = 100 79 80 80 79 79
Private consumption Million EUR 111 610 111 144 114 360 118 184 121 151
Real change -5.5 -1.2 2.2 2.6 2.1
Public consumption Million EUR 31 177 32 501 32 165 32 534 33 332
Real change -3.3 -2.0 -0.5 0.6 1.1
Investment/GFCF Million EUR 26 672 25 122 25 772 26 974 27 583
% of GDP 15.8 14.8 14.9 15.0 15.0
Real change -16.6 -5.1 2.8 4,1 0.1
GFCF (excl. construction) % of GDP 6.9 7.0 7.4 7.5 n.a.
Real change -11.8 4.1 9.3 4.0 n.a.
Population '000 inhabitants 10 515 10 457 10 401 10 358 10 299
Employment '000 individuals 4 581 4 450 4 513 4 576 4 616
Unemployment '000 individuals 836 855 726 647 595
Rate of economic activity % of total population > 15 years old 60.2 59.3 58.8 58.6 n.a.
Unemployment rate Portugal % of active population 15.5 16.2 13.9 12.4 11.6
Overall balance - General Government % of GDP -5.7 -4.8 -7.2 -4.4 -2.7
Public Debt % of GDP 126.2 129.0 130.2 129.0 126.0
Current Account Balance Billion EUR -3.0 2.6 0.1 0.8 0.6
% of GDP -1.8 1.5 0.1 0.4 0.3
HCPI - Portugal Annual change -average 2.8 0.4 -0.2 0.5 0.7
HCPI - Euro Area Annual change - 2.5 1.3 0.4 0.0 0,2
average
International trade
According to data released by the Banco de Portugal, in the last five years exports and imports of goods and services registered annual average growth rates of 4.9% and 1.2%, respectively. The trade balance of goods and services was positive between 2012 and the 1st half 2016, inverting the negative tendency registered in the past.
Table 3. Portugal International Trade (Goods and Services) 2011-2016. Source: a) Banco de Portugal (Trade in Goods and Services); b) INE - National
Var. 2016 Var.
Portugal's 2011 2012 2013 2014 2015 % %
International Trade 2015/ 2011c Jan/Ju n 2016/ 2015
Trade in goods and services (a)
Exports (fob) Million EUR 42 828 45 213 47 48 303 054 49 826 3.9 24 811 -1.4
Imports (fob) Million EUR 59 551 56 374 57 013 59 032 60 310 0.4 29 816 -1.4
Balanc e(fob) Million EUR -16 723 -11 161 -9 710 -10 978 -10485 -- -5 005 --
% of GDPe -7.9 -5.0 -4.0 -4.6 -4.3 -- -4.2 --
With regards to exports and imports of goods, in the first half 2016 there was a reduction of 1.4% in both over the same period, according to date from INE (National Statistics Office), corresponding to a coverage ratio of 83.2%. The trade balance of goods continues to show a deficit in the first half 2016, verifying, however, a reduction over the same period.
Table 4. Portugal International Trade (Goods) 2011-2016. Source: INE -
National Statistics Office
Var. 2016 Var.
Portugal's 2011 2012 2013 2014 2015 % %
International Trade 2015/ 2011c Jan/Ju n 2016/ 2015
Trade in goods(a)
Exports (fob) Million EUR 61 595 64 380 68 70 610 814 74 516 4.9 35 867 -1.3
Imports (fob) Million EUR 68 048 64 151 65 414 68 849 71 218 1.2 34 830 -2.0
Balanc e(fob) Million EUR -6 452 229 3 196 1 965 3 299 -- 1 037 --
% of GDPe -4.3 -0.5 1.0 0.4 0.8 -- 1.2 --
In the 1st half 2016, machinery and tools continue to be the most exported products (15.3% of the total), followed by vehicles and other transport material (12.1%), plastics and rubber (7.7%), base metals (7.5%) and clothing (6.2%). These five main product groups represent 48.8% of the total exported by Portugal in that period (against 47.8% in the same period of 2015).
The principal destination for exports of goods is the EU (76.9% in the 1st half 2016), followed by NAFTA (5.7%), PALOP (3.7%), MAGREB (2.9%) and MERCOSUL (1.4%). Portugal's main clients - Spain, France, Germany, United Kingdom and the USA - together represent around 63.7% of total exports in that period.
Picture 4. Goods Exports Geography. Picture 5. Main Clients.
Source: INE -National Statistics Office Source: INE - National
Statistics Office
Picture 6. Exports - Main Products. Source: INE - National Statistics
Office
In relation to the imports of goods, machinery and tools, vehicles and other transport material, chemicals and agricultural products and mineral fuels, lead the ranking in foreign purchases made during the 1st half 2016, representing 61.6% of the total (against 63.3% in the 1st half 2015) . The EU was the origin of the majority of imported products over this period with 78.1% of the total, followed by MERCOSUL (3.3%), NAFTA (2%), PALOP (1.2%) and MAGREB (1%). Spain, Germany, France, Italy and the Netherlands continue to be the main suppliers, together representing 64.9% of imports made during the 1st half 2016.
Picture 7. Goods Imports Geography. Picture 8. Main suppliers. Source: INE -National Statistics Office
Source: INE - National Statistics Office
Picture 9. Imports - Main Products. Source: INE - National Statistics
Office
International Investment
Foreign direct investment flow into Portugal (Directional principle)
According to data from the Banco de Portugal and the Directional Principle, the flow of Foreign Direct Investment into Portugal (FDI), in net terms, registered an amount close to 5.4 billion Euros in 2015 (-5.1% in relation to 2014). The highest value in the last five years was registered in 2012, when FDI reached 6.9 billion Euros and in 2014 with 5.7 billion Euros.
In the 1st half 2016 the registered value of FDI was higher than 3.9 billion Euros (-33.5% in comparison to the same period in 2015).
Portuguese Foreign Direct Investment (PFDI), in net terms, was close to 4.5 billion Euros in 2015 (+47.5% in comparison to the previous year). The highest value during the period 2011-2015 was in 2011 (nearly 9.7 billion Euros).
In the 1st half 2016 PFDI value reached around 1 billion Euros (-76.7% in comparison to the same period in 2015).
Mit Ht] MU MM MIS
N. ■ »» ■ M»
Picture 10. FDI Flows. Source: Banco de Portugal Unit: Million of Euros (net values) Note: Directional Principle: reflects the direction or influence investment, that is, Portuguese Foreign Direct Investment (PFDI) and Foreign
Direct Investment in Portugal (FDI)
Portuguese external direct investment stock (Directionalprinciple)
In terms of stock of Foreign Direct Investment (FDI) into Portugal, at the end of December 2015, 105.5 billion Euros (+7.5% in relation to the value in December 2014) were registered. At the end of the 1st half 2016 the stock in FDI in Portugal totalled 109.3 billion Euros (+2.6% in relation to June 2015).
However, in relation to stock of Portuguese Foreign Direct Investment (PFDI) this represented close to 54.7 billion Euros in December 2015 (+11.6% in relation to December 2014). In June 2016 the stock of PFDI rose to nearly 55.8 billion Euros (+0.7% in relation to June 2015).
Picture 11. Stock of FDI. Source: Banco de Portugal Unit: Position at the end of the period in Million Euros Note: Directional Principle: reflects the direction or influence investment, that is, Portuguese Foreign Direct Investment (PFDI) and Foreign Direct Investment in Portugal (FDI)
Foreign direct investment stock in Portugal by country of origin (Directional principle)
In global terms the European Union was the principle origin of FDI in Portugal, with a quota of 88% in June 2016, highlighting, on an intra-Community level, the Netherlands and Spain (with 24.3% and 23% of the total, respectively), Luxembourg (19.3%), United Kingdom and France (7.1% and 5.1% respectively). Within the non-EU countries (12% of the total), the following countries are highlighted: Brazil (2.3% of the total), the USA (1.6%), Switzerland and China (with quotas of 1.5% each).
Picture 12. FDI by Country of Origin. Source: Banco de Portugal Unit: Position at the end of June 2016 (% of the total)
Portuguese foreign direct investment stock by country of destination (Directional principle)
The European Union was also the main destination of PFDI in global terms, with a contribution of 73.9% in June 2016, highlighting, on an intra-Community level, the Netherlands and Spain with quotas of 40.4% and 17.6% of the total, respectively, followed by Luxembourg with 4.7%. Within the non-EU countries (26.1% of the total in June 2016), the following countries are highlighted: Angola, Brazil and USA, with quotas of 6.9%, 6.1% and 2.2% respectively.
Picture 13. FDI by Country of Destination. Source: Banco de Portugal Unit: Position at the end of June 2016 (% of the total)
Tourism
In 2015, the Portuguese tourism trade balance was 7.8 billion Euros, having increased by 10.8% in relation to 2014.
According to the Banco de Portugal, tourism revenue in Portugal has seen a sustainable growth during the period 2011-2015, having reached an annual average increase of 8.9%. In 2015, revenue nearly reached 11.5 billion Euros (value that represents about 15.4% of the total Portuguese exports of goods and services), registering a significant increase of 10.2% in relation to the previous year.
In the 1st half 2016, tourism revenue registered an increase of 9.2% in relation to the same period of the previous year, reaching nearly 5 billion Euros.
The main markets generating tourism revenue to Portugal, in the 1st half 2016, were the United Kingdom (with 18.3% of the total), France (15.5%), Spain (13.2%), Germany (12%) and the Netherlands (4.9%), that together made 63.9% of the total for this period.
The empirical part
This work investigates the relationship between a number of endogenous (dependent) factors and exogenous (independent) ones.
Table 5. Variables Used
Variable Description Explanation Unit of measure
Endogenous variables
M1 t money supply for period t M1 includes currency i.e. banknotes and coins, plus overnight deposits. M1 is measured as a seasonally adjusted Source: The Organisation for Economic Cooperation and Development https://data.oecd.org/money/narrow-money-m1.htm Index based on 2010=100.
ExtRes t foreign exchange reserves for period t Total reserves minus gold. Comprise special drawing rights, reserves of IMF members held by the IMF, and holdings of foreign exchange under the control of monetary authorities. Gold holdings are excluded. Source: International Financial Statistics (IFS) http://www.imf.org/external/index.htm Millions of US Dollars
Exogenous variables
GDP t Gross Domestic Product for period t Monetary measure of the market value of all final goods and services produced in a period Source: International Financial Statistics (IFS) http://www.imf.org/external/index.htm Billions of Euros
C t Consumption expenditures for period t It consists of the expenditure incurred by resident households on individual consumption goods and services Source: International Financial Statistics (IFS) http://www.imf.org/external/index.htm Billions of Euros
Exp t Export from Portugal for period t Selling goods and services produced in the home country to other markets Source: International Financial Statistics (IFS) http://www.imf.org/external/index.htm Millions of US Dollars
Imp t Import in Portugal for period t Purchasing goods and services produced in foreign markets Source: International Financial Statistics (IFS) http://www.imf.org/external/index.htm Millions of US Dollars
STrate t Short-term interest rate for period t The rates at which short-term borrowings are effected between financial institutions Source: International Financial Statistics (IFS) http://www.imf.org/external/index.htm % per annum
LTrate Long-term interest rate for period t The rates at which long-term borrowings are effected between financial institutions Source: International Financial Statistics (IFS) http://www.imf.org/external/index.htm % per annum
ExRate t Currency exchange rate for period t Exchange rate between two currencies is the rate at which one currency will be exchanged for another http://fxtop.com/en/hi stori cal -exchange-rates.php?YA=1&C1=EUR&C2=USD&A= Euro/USD
1&YYYY1=1990&MM 1=01&DD 1=0
1&YYYY2=2017&MM2=02&DD2=05&LANG=e
n
Debt t Debt for period t Total debt a country owes to foreign creditors, complemented by internal debt owed to domestic lenders The rates at which long-term borrowings are effected between financial institutions Source: International Financial Statistics (IFS) http://www.imf.org/external/index.htm Millions of US Dollars
The benchmark data collected are presented in table 6
Table 6. Benchmark data
'year' M1' 'ExtRes 'GDP' 'C' 'Exp 'Imp 'ST rat e' 'LTra te' 'Debt' 'Ave rage EU R U SD'
Y Y X X X X X X X X
1996 21,9 0 15917, 66 93,09 60,82 25,3 6 32,0 4 7,3 7 8,56 101300,1 7 1,29
1997 25,3 0 15659, 97 100,9 8 64,94 28,0 7 36,3 2 5,7 4 6,36 123205,3 0 1,13
1998 28,8 0 15824, 62 110,1 0 69,84 30,8 2 41,0 4 4,3 1 4,88 165028,1 4 1,11
1999 33,1 0 8427,1 2 119,6 4 75,57 31,6 7 44,0 5 2,9 6 4,78 169163,4 4 1,07
2000 37,5 0 8908,6 9 128,4 7 81,26 36,2 2 50,4 0 4,3 9 5,60 197636,9 5 0,92
2001 41,5 0 9666,6 0 135,8 3 85,14 37,2 5 51,1 3 4,2 6 5,16 220904,9 3 0,90
2002 45,5 0 11179, 11 142,6 3 89,27 38,4 3 50,2 3 3,3 2 5,01 286544,8 2 0,95
2003 51,0 0 5875,8 5 146,1 6 92,24 39,1 0 49,2 4 2,3 3 4,18 388761,1 7 1,13
2004 57,0 0 5174,0 7 152,3 7 96,80 41,5 3 54,1 1 2,1 1 4,14 458108,0 0 1,24
2005 64,8 0 3478,6 9 158,6 5 102,1 1 42,4 1 56,8 6 2,1 8 3,44 444064,5 6 1,24
2006 73,2 0 2063,6 4 166,2 5 107,3 0 49,7 4 63,4 3 3,0 8 3,91 556431,0 6 1,26
2007 79,2 0 1257,7 8 175,4 7 113,7 1 54,4 1 67,8 1 4,2 8 4,42 691413,3 3 1,37
2008 83,6 0 1309,4 0 178,8 7 118,4 9 55,6 7 73,0 5 4,6 3 4,52 659482,1 1 1,47
2009 91,5 0 2454,8 9 175,4 5 113,5 1 47,5 1 59,6 6 1,2 3 4,21 751399,1 3 1,39
2010 100, 00 3651,9 1 179,9 3 118,3 3 53,7 5 67,3 5 0,8 1 5,40 716060,9 0 1,33
2011 104, 10 1974,6 0 176,1 7 115,9 6 60,4 1 67,9 5 1,3 9 10,24 639408,8 2 1,39
2012 108, 70 2196,0 2 168,4 0 111,6 1 63,5 0 64,3 6 0,5 7 10,55 690431,7 8 1,28
2013 117, 2777,5 170,2 111,1 67,2 65,5 0,2 6,29 706896,1 1,33
80 2 7 4 8 7 2 3
2014 127, 10 4869,3 5 173,0 8 114,0 6 69,3 6 69,0 3 0,2 1 3,75 648748,9 2 1,33
Correlation analysis
We have conducted the correlation analysis for the purpose of assessment the internal relationships between factors.
Correlation analysis typically gives us a number result that lies between +1 and -1. The +ve or -ve sign denotes the direction of the correlation. The positive sign denotes direct correlation whereas the negative sign denotes inverse correlation.
Zero signifies no correlation. And the closer the number moves towards 1, the stronger the correlation is. Usually for the correlation to be considered significant, the correlation must be 0.5 or above in either direction.
The most significant correlation of ExtRes can be observed with the GDP factor, stated for -0,943. Simultaneously, The most significant correlation of Ml can be traced with Exp factor, for 0,978.
Table 7. Correlation analysis
M1' Ext Res' GD P' C' Exp Imp STrat e LTrate Debt Avera geEU R US D'
M1' 1,00 0
ExtRes' 0,80 1 1,00 0
GDP' 0,88 5 0,94 3 1,00 0
C' 0,90 7 0,93 8 0,99 7 1,00 0
Exp' 0,97 8 0,80 5 0,87 8 0,89 8 1,00 0
Imp' 0,89 1 0,91 2 0,96 9 0,97 5 0,91 8 1,00 0
STrate' 0,80 8 0,67 4 0,73 0 0,72 1 0,74 9 0,65 7 1,000
LTrate' 0,14 1 0,08 1 0,10 0 0,05 2 0,15 0 0,05 0 0,007 1,000
Debt' 0,93 0 0,89 0,95 6 0,96 9 0,90 1 0,92 2 -0,719 0,018 1,000
9
AverageE UR USD' 0,67 9 0,60 9 0,61 6 0,66 2 0,62 7 0,60 9 -0,324 0,144 0,764 1,000
System of equations
For the analysis, a system of interrelated linear equations was made
ln(M1) = a1+b11*ln(GDP)+b12*ln(C)+b13*ln(Exp)+b14*STrate + el equation 1
In(ExtRes)=a2+b21*ln (M1) +b22*ln(Imp)+b23*ln(ExRate) +b24*ln (Debt) +b25*LTrate+e2 - equation 2
where, Equation 1
ln(M1) = a1+b11*ln(GDP) +b12*ln(C)+b13*ln(Exp)+b14*STrate + e1
The assumption of the suggested equations system is that the analyzed economic factors can be approximated by a log-normal distribution. Further on, the testing of the hypothesis is provided.
Taking the logarithm of a factor when constructing a linear regression model minimizes the relative (not absolute) deviation from the regression line.
The given system of equations belongs within the recursive type, since the endogenous factor Ml from the first equations at the same time serves as the explaining factor for the second equation.
Thus occurs the following mechanism of assesing the model parameters: The first step provides estimates of the parameters of equation l, and as a result of the estimated model we obtain Ml theoretical values estimation (the values are unbiased).
Further on, the above mentioned values are used to assess the parameters of equation 2 during the second stage of the recursive equations system identification.
Step 1 of 2 OLS
Estimation of the parameters of the given form of model in relation to the endogenous ln(M1)
ln(M1) = a1+b11*ln(GDP)+b12*ln(C)+b13*ln(Exp) +b14*STrate + e1 Linear regression model (scheme) from MATLAB: lnM1~1+lnGDP+lnC+lnExp+STrate Table 8. F-statistics
Number o f observations 19
Error degrees of freedom 14
Root Mean Squared Error 0.0407
R-squared 0.996
Adjusted R-Squared 0.995
F-statistic vs. constant model 820
p-value 1.99e-16
The regression relation significance is shown by p-value of dispersion analysis (F-statistics). The null hypothesis that R2=0 has been rejected, therefore, the model is significant. The value of R2 is high (R-squared = 0.996).
Using the coefficients of the regression model the following statistical results are obtained:
Table 9. t-statistics
Estimate SE tStat pValue
(Intercept) -1.6369 0.55337 -2.9581 0.010379
STrate -0.054972 0.0082429 -6.6691 1.0626e-05
lnGDP -3.2546 0.72353 -4.4982 0.00050089
lnExp 0.70304 0.11617 6.0517 2.9787e-05
lnC 4.2762 0.76433 5.5947 6.6078e-05
According t-test (student statistics), all factor's coefficients are relevant (p-value<0.05), hence we should not exclude any of it from the regression equation. As a result of analysis the repression equation is as follows: ln(M1) = - 1.6369 - 32546*ln(GDP)+ 42762*ln(C)+ 0.70304*ln(Exp) -0.054972 *STrate
In order the F and t criterial were valid, it is obligatory that the values of our variables were distributed normally.
As calculated values are the logariphms to the factors, it means that our factors are distrubuted log-normally.
First and foremost, let us conduct the non-parametric test of Colmagorov-Smirnov. The findings are below.
Table 10. Kolmogorov-Smirnov test
Type of output Values Clarification of the output values
Ksstat (Kolmogorov-Smirnov statistics) 0.1122 Test statistic nonnegative scalar value Test statistic of the hypothesis test, returned as a nonnegative scalar value. The one-sample Kolmogorov-Smirnov test is a nonparametric test of the null hypothesis that the population cdf of the data is equal to the hypothesized cdf. The two-sided test for "unequal" cdf functions tests the null hypothesis against the alternative that the population cdf of the data is not equal to the hypothesized cdf. The test statistic is the maximum absolute difference between the empirical cdf calculated from x and the hypothesized cdf: where ~F(x) is the empirical cdf and G(x) is the cdf of the hypothesized distribution.
Cv (critical 0.3014 Critical value is a nonnegative scalar value
value) Critical value, returned as a nonnegative scalar value.
p-value 0.9489 P-value scalar value in the range [0,1] p-value of the test, returned as a scalar value in the range [0,1]. p is the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. Small values of p cast doubt on the validity of the null hypothesis.
h 0 h — Hypothesis test result 1 1 0 Hypothesis test result, returned as a logical value. If h = 1, this indicates the rejection of the null hypothesis at the 0,05-significance level. If h = 0, this indicates a failure to reject the null hypothesis at the 0,05-significance level.
The findings show that the hypothesis of normalcy of distribution can be accepted (h = 0).
Hence, we can claim that the M (money supply) meets long-normal distribution.
Hence, we can conclude that the previous tests results (F-test, t-test) were relevant.
Normal probability plot of residuals is depicted on graph № 4 Graph 4. Normal probability plot of residuals
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Table 11. Durbin-Watson test
Type of output Values Clarification of the output values
DW 2.1665 Durbin-Watson test statistic The test statistic for the Durbin-Watson test is where T is the number of observations, and et is the residual at time t.
P 0.4307 The p-value for the Durbin-Watson test of the null hypothesis that the residuals from a linear regression are uncorrelated. The alternative hypothesis is that there is autocorrelation among the residuals. The p-value of the Durbin-Watson test is the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. A significantly small p-value casts doubt on the validity of the null hypothesis and indicates correlation among residuals.
In order to verify residuals for the presence of auto regression, the Durbin-Watson test was conducted.
The findings showed that DW= 2.1665. P-value = 0.4307> 5%, which means that test is negative - the autocorrelation doesn't exist.
Graph 5. Plot of residuals vs. lagged residuals depicted on graph
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Adequacy verification
When verifying the model adequacy, the unselected data are being checked.
In the capacity of such data, the indicators of 2015 have been used to analyze the deviation of theoretically predicted response from the actual one. In other words, the analysis verifies, whether the practical value of the response coincides with 95% of the confidence interval constructed around the theoretically predicted value. In case the value lies inside this interval, one can say that the model is adequate.
The indicators values for 2015 are given in table 12.
Table 12. Adequacy verification
Y X X X X X
'year' 'M1' 'GDP' 'C' 'Exp' 'STrate' 'InGDP' 'lnC' 'InExp'
2015 144,5 179,54 117,82 72,81 -0,02 5,190398 4,78 4,287853
'year' Fact lnM1 Calculated value Conf.int 95% min Conf.int 95% max
2015 4.973279507552487 4.9264 4.8749 4.9780
The adequacy verification goes as follows:
Using the fitted model of the equation (1), we can find ln(M1) predicted2015. ln(M1) predicted 2015 = 4.9264. Confidence intervals of predictive values are as follow: 4.8749 = ln(M1) pred2015-tcrit*S(lnM12015) < ln(M1)2015 < ln(M1) pred 2015+tcrit*S(ln(M1)2015) = 4.9780. So, ln(M1) predicted 2015 appears to be inside the interval. Thus, the model can be called adequate.
Table 13. Goldfeld-Quandt test
Type of output Fstat df1 df2 ci p h
STrate 12.3743 7 6 2.1727 -63.3389 0.0069 1
InGDP 12.3743 7 6 2.1727 -63.3389 0.0069 1
InExp 1.6902 7 6 0.2968 - 8.6516 0.5393 0
lnC 0.3547 7 6 0.0623 - 1.8156 0.2012 0
Type of output Clarification
Fstat Value of the test statistic: two-sample F-test.
df1 Numerator degrees of freedom of the test.
df2 Denominator degrees of freedom of the test.
Ci Confidence interval for the true ratio of the population variances, returned as a two-element vector containing the lower and upper boundaries of the 100 x 95% confidence interval.
P p-value of the test, returned as a scalar value in the range [0,1]. p is the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. Small values of p cast doubt on the validity of the null hypothesis.
H h — Hypothesis test result1 | 0 Hypothesis test result, returned as a logical value.
If h = 1, this indicates the rejection of the null hypothesis at the 0,05 significance level.
If h = 0, this indicates a failure to reject the null hypothesis at the 0,05-significance level._
The results of the analysis expose heteroscedasticity for 2 of the 4 factors -for STrate u lnGDP.
Basing on the equation, let's calculate the pure ln(M1) value (unbiased), to use the given values for estimating parameters and the forthcoming assessment of equation 2.
The assessment results are provided in table14.
_Table 14. The comparison of predicted Ml and the origin
'year' Origin 'lnM1' Valuation 'vlnM1'
1996 3,086 3,042
1997 3,231 3,219
1998 3,36 3,393
1999 3,5 3,553
2000 3,624 3,647
2001 3,726 3,692
2002 3,818 3,81
2003 3,932 3,937
2004 4,043 4,062
2005 4,171 4,17
2006 4,293 4,292
2007 4,372 4,362
2008 4,426 4,472
2009 4,516 4,427
2010 4,605 4,632
2011 4,645 4,665
2012 4,689 4,728
2013 4,769 4,734
2014 4,845 4,814
Step 2 of 2OLS
Estimation of the parameters of the given form of model in relation to the endogenous ln(M1)
ln(ExtRes) =a2+b21*ln (M1)+ b22*ln(Imp)+b23*ln(ExRate)+b24*ln(Debt) +b25*LTrate+e2
Linear regression model (scheme) from MATLAB: lnExtRes~1+vlnM1+lnImp+lnExRate+lnDebt+LTrate Table 15. F-statistics
Number o f observations 19
Error degrees of freedom 13
Root Mean Squared Error 0.184
R-squared 0.965
Adjusted R-Squared 0.952
F-statistic vs. constant model 72.4
p-value 5.02e-09
The regression dependent significance is shown by p-value of dispersion analysis (F-statistics). Гипотеза, о том, что R2=0, отвергается, следовательно, модель значима. The value of R2 is high (R-squared = 0.996).
The statistical results calculated with reference to the regression model coefficients are as follow:
Table 16. t-statistics
Estimate SE tStat pValue
(Intercept) 59.607 5.6565 10.538 9.7651e-08
LTrate -0.083878 0.025633 -3.2722 0.0060634
lnImp -4.1751 0.63227 -6.6033 1.7068e-05
lnExRate 2.6295 0.69106 3.805 0.0021867
lnDebt -1.112 0.31715 -3.5063 0.0038673
vlnMl 2.1457 0.40998 5.2336 0.00016138
According t-test (student statistics), all factor's coefficients are relevant (p-value<0.05), hence we should not exclude any of it from the regression equation. As a result, the regression equation is rewritten as follows: ln(ExtRes)= 59.607 + 2.1457*ln(M1) - 4.1751 *ln(Imp) + 2.6295*ln(ExRate) - 1.112*ln(Debt) - 0.083878*LTrate
In order the F and t criterial were valid, it is obligatory that the values of our variables were distributed normally.
As calculated values are the logariphms to the factors, it means that our factors are distrubuted log-normally.
First and foremost, let us conduct the non-parametric test of Colmagorov-Smirnov. The findings are below
Table 17. Kolmogorov-Smirnov test
Type of output Values
Ksstat (Kolmogorov-Smirnov statistics) 0.1130
Cv (critical value) 0.3014
p-value 0.9461
H 0
The findings show that the hypothesis of normalcy of distribution can be accepted (h = 0).
Hence, we can claim that the ExtRes (external reserves) meets long-normal distribution.
Hence, we can conclude that the previous tests results (F-test, t-test) were relevant.
Normal probability plot of residuals is depicted on graph № 6
Graph 6. Normal probability of plot residuals
Normal protoaMKy p4ot of m4unit
In order to verify residuals for the presence of auto regression, the Durbin-Watson test was conducted.
Table 18. Durbin-Watson test
Type of output Values
DW 2.1466
P 0.3265
The findings showed that DW= 2.1466. P-value = 0.3265 > 5%, which means that test is negative - the autocorrelation doesn't exist.
Plot of residuals vs. lagged residuals depicted on graph № 7 Graph 7. Plot of residuals vs. lagged residuals
0.4 0.3 0.2 0.1
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-0.1
-0.2
-0.3
-0.4
Plot of residuals vs. lagged residuals
X
X
X X
X
X
X
-0.4 -0.3 -0.2 -0.1 0 0.1
Residual(t-1 )
0.2
0.3
0.4
Adequacy verification
When verifying the model adequacy, the unselected data are being checked. In the capacity of such data, the indicators of 2015 have been used to analyze the deviation of theoretically predicted response from the actual one. In other words, the analysis verifies, whether the practical value of the response coincides with 95% of the confidence interval constructed around the theoretically predicted value. In case the value lies inside this interval, one can say that the model is adequate.
The indicators values for 2015 are given in table 19.
Table 19. Adequacy verification
Y X X X X X X X
'yea r' 'ExtR es' 'M1 'Im P' ExRat e' 'Debt 'LTra te' 'lnM1' 'InImp ' InExRat e' 'InDeb t'
201 5 6366,7 43 144 ,5 71, 5 1,1095 13 5739 84 2,42 4,973279 508 11,10779 639 0,10392 118 13,260 36
'year' Fact ln ExtRes Calculated value Conf.int 95% min Conf.int 95% max
2015 8,7588433484357 9.0816 8.5841 9.5791
The adequacy is being verified in the following way:
Using the fitted model of the equation (2), we can find ln(ExtRes) predicted 2015. ln(ExtRes) predicted 2015 = 9.0816. Confidence intervals of predictive values are as follows: 8.5841 = ln(ExtRes) pred2015-tcrit*S (ln ExtRes 2015) < ln(ExtRes)2015 < ln(ExtRes) pred2015+tcrit*S(ln(ExtRes)2015) = 9.5791. So, ln(ExtRes) predicted 2015 appears to be inside the interval. Thus, the model can be called adequate.
Table 20. Goldfeld-Quandt test
Type of output Fstat dfl df2 ci P h
LTrate 144.5314 7 6 25.3765 -739.7978 5.8517e-06 1
InImp 144.5314 7 6 25.3765 -739.7978 5.8517e-06 1
InExRate 159.1154 7 6 27.9372 -814.4476 4.3972e-06 1
InDebt 144.5314 7 6 25.3765 -739.7978 5.8517e-06 1
vlnMl 2.4571 7 6 0.4314 - 12.5768 0.2935 0
The analysis exposes heteroscedacity for a set of factors, whereas vlnM1 is characterized by homoscedacity.
Thus, it is likely that the obtained simple model can be enhanced by applying unlinear models.
Ultimate model
ln(Ml) = - 1.6369 - 3.2546*ln(GDP)+ 4.2762*ln(C)+ 0.70304*ln(Exp) -
0.054972.*STrate
ln(ExtRes) = 59.607 + 2.1457*ln(M1) - 4.1751 *ln(Imp) + 2.6295*ln(ExRate) - 1.112*ln(Debt) - 0.083878*LTrate
The final model observation and conclusions
From the perspective of the analysis of factors that influence monetary reserves formation in a country (Portugal taken as an example). We determined the difference between the effect of these factors in developed and developing countries.
Our paper is consistent with other authors when providing empirical evidence. We show that imports and money aggregate M1 have the most significant impact on monetary reserves formation. It was also exposed that foreign exchange reserves of a country debt.
The following trends have been revealed:
Money supply increase results in foreign exchange reserves accumulation. Imports decrease and foreign exchange reserves relation is negative. When national currency strengthening (accordingly, foreign currency weakening), a positive trend for Portugal foreign exchange reserves is observed.
The external bound debt growth is related to the national reserves decrease. Since in the country in question the general currency payable is euro, one can assume that the independence and national currency strengthening policy is being conducted. In other words, the external bound debt is being repaid in terms of national currency.
List of References:
1. Tregub I.V. Econometrics. Model of real system - монография, М.: 2016. 166 р.
2. Трегуб И.В. Математические модели динамики экономических систем -монография, М.: 2009.
3. Трегуб И.В. Прогнозирование экономических показателей -монография, М.: 2009.
4. Suslov M.Yu.E., Tregub I.V. Ordinary least squares and currency exchange rate // International Scientific Review. 2015. № 2 (3). С. 33-36.
5. Elias Papaioannou, Richard Portes, Gregorios Siourounis, 2006, "Optimal Currency Shares in International Reserves: The Impact of the Euro and the Prospects for the Dollar", European Central Bank Working Paper No. 694
6. Julio H. G. Olivera, 1969, "A Note on the Optimal Rate of Growth of International Reserves", The Journal of Political Economy, Vol. 77, No. 2, pp. 245-248
7. Peter B. Clark, 1970, "Demand for International Reserves: A Cross-Country Analysis", The Canadian Journal of Economics, Vol. 3, No. 4, pp. 577-594
8. Emil-Maria Claassen, 1975, "Demand for International Reserves and the Optimum Mix and Speed of Adjustment Policies", The American Economic Review, Vol. 65, No. 3, pp. 446-453
9. Dani Rodrik, 2006, "The Social Cost of Foreign Exchange Reserves", NBER Working Paper Series No. 11952
10. John Nugée, "Foreign Exchange Management", Bank of England CCBS Series, Handbooks in Central Banking, No.19
11. John R. Dodsworth, 1978, "International Reserve Economies in Less Developed Countries", Oxford Economic Papers, Vol. 30, No. 2, pp. 277-291
12. Jacob A. Frenkel, Boyan Jovanovic, 1981, "Optimal International Reserves: A Stochastic Framework", The Economic Journal, Vol. 91, No. 362, pp. 507-514
13. Peter Barton Clark, 1970, "Optimum International Reserves and the Speed of Adjustment", The Journal of Political Economy, Vol. 78, No. 2, pp. 356-376
14. Herbert G. Grubel, 1971, "The Demand for International Reserves: A Critical Review of the Literature", Journal of Economic Literature, Vol. 9, No. 4, pp. 1148-1166
15. Sebastian Edwards, 1983, "The Demand for International Reserves and Exchange Rate Adjustments: The Case of LDCs, 1946-1972", Economica, Vol. 50, No. 199, pp. 269-280
16. Sebastian Edwards, 1984, "The Demand for International Reserves and Monetary Equilibrium: Some Evidence from Developing Countries", The Review of Economics and Statistics, Vol. 66, No. 3, pp. 495-500
17. Jacob A. Frenkel, 1974, "The Demand for International Reserves by Developed and Less-Develop Countries", Economica, Vol. 41, No. 161, pp. 14-24
18. Robert P. Flood, Nancy Peregrim Marion, "The Transmission of Disturbances under Alternative Exchange-Rate Regimes with Optimal Indexing", The Quarterly Journal of Economics, Vol. 97, No. 1, pp. 43-66
19. Harry G. Johnson, 1977, "The Monetary Approach to Balance of Payments Theory and Policy: Explanation and Policy Implications", Economica, New Series, Vol. 44, No. 175, pp. 217-229
20. R. A. Mundell, 1963, "Capital Mobility and Stabilization Policy under Fixed and Flexible Exchange Rates", The Canadian Journal of Economics and Political Science, Vol. 29, No. 4, pp. 475-485
21. Matthew Higgins, Thomas Klitgaard, 2004, "Reserve Accumulation: Implications for Global Capital Flows and Financial Markets", Current Issues in Economics and Finance, Volume 10, No. 10, Federal Reserve Bank of New York
22. International Relations Committee Task Force, 2006, "The Accumulation of Foreign Reserves", European Central Bank, Occasional Paper Series, No.43
23. Joshua Aizenman, 2007, "International Reserve Management and the Current Account", NBER Working Paper No. 12734
24. IMF, 2001, "Guidelines for Foreign Exchange Reserve Management"
Appendix 1
%Model 2 clear all clc
load dsj
x=dsj(end,:);
dsj(end,:)=[];
e2=LinearModel. fit(dsj ,'lnM1~1 +lnGDP+lnC+lnExp+STrate') dsj .vlnM1=e2.Fitted;
e=LinearModel.fit(dsj,'lnExtRes~1+vlnM1+lnImp+lnExRate+lnDebt+LTrat
e')
[P DW]=dwtest(e2) % Durbi -Watson
[h,p,ksstat,cv]=kstest(e2.Residuals.Standardized) % KKolmogorov -Smirnov
GQ= GoldfeldQuandt([dsj.lnGDP dsj.lnC dsj.lnExp dsj.STrate], dsj.lnM1) [P DW]=dwtest(e) % Durbi -Watson
[h,p,ksstat,cv]=kstest(e.Residuals.Standardized) % KKolmogorov -Smirnov
GQ= GoldfeldQuandt([dsj.vlnM1 dsj.lnImp dsj.lnExRate dsj.lnDebt dsj.LTrate], dsj.lnExtRes) x.lnC=4.78
[y 1pred,yci 1] =predict(e,x) [y2pred,yci2]=predict(e2,x) y1=x.lnExtRes y2=x.lnM1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure;
hl2=line(dsj .year,dsj .ExtRes,'Color','r'); ax1 = gca;
set(ax1,'XColor','r','YColor','r')
ylabel('Foreign External Reserves, billion euros') % y-axis label legend('External Reserves','location','best') ax2 = axes('Position',get(ax1,'Position'),... 'YAxisLocation','right',... 'Color','none',... 'XColor','k','YColor','k'); line(dsj .year,dsj .M1,'Color','b','Parent',ax2)
title('Graph № 2: Impact of Ml on Foreign External Reserves in Potugal 1996 - 2014')
xlabel('year') % x-axis label
ylabel('Money Supply,(100 in 2005)') % y-axis label
legend('Money Supply','location','best')
figure;
hl2=line(dsj .year,dsj .ExtRes,'Color,,,r'); ax1 = gca;
set(ax1,'XColor,,,r,,,YColor,,,r')
ylabel('Foreign External Reserves, billion euros') % y-axis label legend('External Reserves','location','best') ax2 = axes('Position',get(ax1,'Position'),... 'YAxisLocation','right',... 'Color','none',... 'XColor','k','YColor','k'); line(dsj .year,dsj .Imp,'Color','b','Parent',ax2)
title('Graph № 1: Impact of Import on Foreign External Reserves in Potugal 1996 - 2014')
xlabel('year') % x-axis label
ylabel('Import, billions euros') % y-axis label
legend('Import','location','best')
figure;
hl2=line(dsj .year,dsj .ExtRes,'Color','r'); ax1 = gca;
set(ax1,'XColor','r','YColor','r')
ylabel('Foreign External Reserves, billion euros') % y-axis label legend('External Reserves','location','best') ax2 = axes('Position',get(ax1,'Position'),... 'YAxisLocation','right',... 'Color','none',... 'XColor','k','YColor','k'); line(dsj .year,dsj .Debt,'Color','b','Parent',ax2)
title('Graph № 3: Impact of Debt on Foreign External Reserves in Potugal 1996 - 2014')
xlabel('year') % x-axis label
ylabel('Level of Debt, billions euros') % y-axis label
legend('Level of Debt','location','best')
figure;
plotResiduals(e,'probability')%e Kolmogorov-Smirnov figure;
plotResiduals(e,'lagged')%e Darbin-Watson figure;
plotResiduals(e2,'probability')%e2 Kolmogorov-Smirnov figure;
plotResiduals(e2,'lagged')%e2 Darbin-Watson
Appendix 2
function goldfeldquandt = GoldfeldQuandt(A,y) % GoldfeldQuandt realise GoldfeldQuandt test on heteroscedosticity
% Arguments :
% A[l,m] - table of information % y[l,1] - vector of results on this informsttion % goldfeldquandt - 0 if heteroscedosticity wasn't found % 1 if heteroscedosticity was found
%sorting by feature number n B = [A y]; [m,l] = size(A); goldfeldquandt=zeros(l, 1); for i=1:l
B = sortrows(B,i); % order by i-predictor
%separating two smaller arrays at the edges
B1 = B(1:round(3*m/8),:);
B2 = B(round(5 *m/8): end,:);
y1 = B1(:,end);
y2 = B2(:,end);
B1(:,end) = [];
B2(:,end) = [];
%solving the problem of linear regression for
%these two smaller arrays
x1 = LinearModel.fit(B 1,y1);
x2 = LinearModel.fit(B2,y2);
%separate calculating of residuals
res1 = x1.Residuals.Raw;
res2 = x2.Residuals.Raw;
%using F-test for comparison of two vectors of residual
%on equlity of their dispersin
[h,p,ci,stats]= vartest2(res2,res1)
goldfeldquandt(i) = h;
end
Y^K:338.45:63
Kalimbetov Khaliknazar Karakalpak State University named after Berdakh
Senior researcher Address: T.Izimbetov street 19 Nukus, 230100 Karakalpakstan, Uzbekistan THE DIRECTIONS OF SUPPORT FOR DEVELOPMENT OF MULTI-BRANCH FARMING ENTERPRISES IN UZBEKISTAN
Abstract
The article discussed the establishment of multi-branch farming enterprises in Uzbekistan and the directions of state support for the development of multi-
