Calculating Correlation, Stolper-Samuelson Theorem, And Ricardian Model Using Data From Paraguay And Poland

Interpretation of correlation coefficient between Openness and GINI Index for Paraguay and Poland

Correlation between Openness and the GINI Index for each nation:

Paraguay
Indicator Name	Exports of goods and services (current US$)	Imports of goods and services (current US$) Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper	GDP per capita (current US$)	GDP (current US$)	GINI index (World Bank estimate)	openness = (X+M)/GDP
2001	3459319570	2727373823	1417.261	7.66E+09	54.6	0.807388793
2002	3402825624	2298406126	1148.23	6.33E+09	57.3	0.901358887
2003	3625989129	2623501714	1174.779	6.59E+09	54.9	0.948602359
2004	4371893087	3307792347	1408.528	8.03E+09	52.3	0.955912704
2005	5083809323	4018039423	1507.146	8.73E+09	51.4	1.042038865
2006	6252319090	5221045741	1809.711	1.06E+10	53	1.077700041
2007	7818347667	6461917817	2312.193	1.38E+10	53	1.035183617
2008	9993980610	9166237324	3059.992	1.85E+10	50.7	1.035456255
2009	8210295841	7130137358	2599.596	1.59E+10	49.1	0.962996073
2010	11036468064	10313046052	3225.592	2E+10	51	1.065848792
2011	13186264509	12621883682	3988.012	2.51E+10	52.3	1.028226124
2012	12278348692	11979621541	3855.538	2.46E+10	47.6	0.986284003
2013	14356651476	12983600420	4479.906	2.9E+10	47.9	0.943876964
2014	13954911448	13242370791	4712.823	3.09E+10	50.7	0.880707726

Poland
Year	Imports of goods and services (current US$)	Exports of goods and services (current US$)	GDP per capita (current US$)	GDP (current US$)	GINI index (World Bank estimate)	Openess= (X+M)/GDP
2001	58766945944	5.19E+10	4981.199	1.91E+11	32.8	0.580751947
2002	63908088235	5.71E+10	5196.933	1.99E+11	34.1	0.609244563
2003	78406788377	7.26E+10	5693.524	2.18E+11	34.9	0.694373057
2004	94256069554	8.74E+10	6681.179	2.55E+11	35.4	0.71213167
2005	1.09184E+11	1.06E+11	8021.252	3.06E+11	34.5	0.702749609
2006	1.3768E+11	1.31E+11	9040.77	3.45E+11	33.7	0.777913937
2007	1.80703E+11	1.66E+11	11260.32	4.29E+11	33.5	0.806620046
2008	2.28993E+11	2.02E+11	14001.45	5.34E+11	33.7	0.807544541
2009	1.67514E+11	1.64E+11	11542.02	4.4E+11	33.6	0.752259133
2010	2.01543E+11	1.92E+11	12597.86	4.79E+11	33.2	0.821083264
2011	2.35386E+11	2.25E+11	13890.7	5.29E+11	32.8	0.870827228
2012	2.24547E+11	2.22E+11	13143.52	5E+11	32.4	0.893274621
2013	2.32599E+11	2.43E+11	13780.19	5.24E+11	32.5	0.906918664
2014	2.51529E+11	2.59E+11	14339.67	5.45E+11	32.1	0.937329374

Using Excel, the correlation between the GINI Index and openness for each nation is calculated. For Paraguay the correlation coefficient is -0.25798 and for Poland it is -0.60988.

Correlation
Paraguay	-0.25798
Poland	-0.60988

Gini Index is a statistical measure for income inequality. It is used to estimate inequality in income distribution and also in wealth distribution in the economy. The GINI index ranges from 0 to 1 where the value 0 indicates perfect income equality and 1 represents perfect income inequality among the population (Staff, 2018).

The Openness Index is calculated as the ratio of total trade, i.e. (exports plus imports), to the country’s GDP (“Trade openness”, 2018).

Openness= (Exports + Imports) / (Gross Domestic Product) =(X + M) / (GDP)

The interpretation of the Openness Index is: the higher the index the larger the influence of trade The higher the trade openness, the higher will be the trade’s influence on domestic activities.

Paraguay has a negative relationship (-0.257) between trade openness and the GINI Index which means that as the inequality rises, i.e. the GINI Index rises, the trade openness will fall down. Since the negative relationship is not very strong, the damage will not be severe.

Poland also has a negative relationship (-0.6098) between trade openness and the GINI Index which means that as the inequality rises, i.e. the GINI Index rises, the trade openness will fall down. Since the negative relationship is strong (greater than 0.5) the damage will be slightly severe.

The negative impact will be more on Poland than on Paraguay.

1. Stolper – Samuelson Theorem:

According to the Stolper Samuelson Theorem, if the relative price of a labour intensive good rises in an economy, then the producers of labour intensive good will be better off than the producers of capital intensive good (“Stolper-Samuelson Theorem (SST) | Theorems | Economics”, 2018). 

The Stolper-Samuelson Theorem is valid when certain conditions are fulfilled by the market. It establishes a relationship between factor price ratio and commodity price ratio. If the price of labour intensive good will rise, then an increase in the production of that good will increase the demand for labourers which will put upward pressure on the wage rate. Due to increase in the price of labour intensive good, the production of capital intensive good will fall and this will not only reduce the demand for capital but also reduce the rental rate (Salvatore, 2016).

In the above diagram as the price of apparel rises, which is labour intensive, the real wage rate rises and the rental rate falls, hence proving the theorem. E is the initial equilibrium and E’ is the new equilibrium after the price rise in the apparel.

1. Assume that both Paraguay and Poland are unskilled-labour abundant countries:

Using the correlation coefficient of both the country to explain the relevance of Stolepr-Samuelson Theorem:

Paraguay has a negative correlation coefficient of -0.25798 and Poland has a negative correlation coefficient of -0.60988. It represents a weak relationship between economic growth and trade for both the countries. Stolper-Samuelson theory is a fundamental theorem of the Hecksher-Ohlin model to establish the returns on capital and labour. If both the countries are labour abundant, then the relative prices of the labour will rise as compared to capital. My data is not very consistent with the Stolper-Samuelson theorem because in case of Paraguay a very strong relationship cannot be established and in case of Poland the relationship is comparatively stronger.

1. Considering the Ricardian model:

Explanation of Stolper-Samuelson Theorem with substitutable inputs case

Each home country worker can produce 2 units of Corn or 3 units of Radios per unit of time, while each foreign worker can produce 2 units of Corn or 4 units of Radios per unit of time. There are 30 workers in Home and 60 workers in Foreign.

1. Derive the relative demand curve relating the relative demand for Radios to the relative price of Radios

Price of Radios (P_R) * Quantity of Radios (Q_R) = 2/3M

Price of Corn (P_C) * Quantity of Corn (Q_s) = 1/3M

Where M = Income

Q_R / Q_C = 2 P_C / P_R

1. Derive the world relative supply curve of Radios

Calculating the opportunity cost of producing radio per unit of Cloth at Home

Labour = 30

For producing corn, unit labour required is a_LC = ½

For producing radio, unit labour required is a_LR = 1/3

a_{LR /} a_LC  = 2/3 labour is required for producing radio with respect to cloth.

Calculating the opportunity cost of producing radio per unit of Cloth at Foreign

Labour* = 60

For producing corn, unit labour required is a*_LC = ½

For producing radio, unit labour required is a*_LR = 1/4

a*_{LR /} a*_LC  = 1/2  labour is required for producing radio with respect to cloth.

Relative Quantity: (Q_R + Q_R*) / (Q_C + Q_C*) = (30/(1/3)) / (60/ (1/2)) = ¾ 

1. Determine the equilibrium relative price of Radios and the equilibrium relative quantity of Radios under free trade.

The equilibrium is established at the point where Quantity Demanded is equal to Quantity Supplied (“International Trade: Theory and Policy v1.0 | FlatWorld”, 2018).

When Q_R / Q_C = ¾,

Then P_R / P_C = 2/ (3/4) = 8/3

We can see that 8 / 3 > (a_{LR /} a_LC  = 2/3)’

In the diagram, the relative demand curve passes through the right part of the relative supply curve.

At equilibrium:

P_R / P_C = a_{LR /} a_LC  = 2/3

Q_R / Q_C = 2 P_C / P_R = 2 (3/2) = 3 

Relative Demand and Supply Curve

1. Under free trade, which country produces which good(s)? How many units?

Under free trade

a*_LR = 1/4

a*_LC  = ½

L* = 60

Foreign will produce Corn: 60 / (1/2) = 120 units.

a_LC = ½

a_LR = 1/3

L= 30

Home will produce both corn and radio since Q_R / Q_C = 3 = (Q_R + Q_R*) / (Q_C + Q_C*)

3 = Q_R / (Q_C + 120)

3 Q_C + 360 = Q_R

Home can produce any combination of corn and radio that satisfies the above equation (“Terms of Trade”, 2018)..

1. Who gains from trade? Who loses from trade? State labours’ stance towards

free trade in each country.

Both the countries gain from trade (“17.1 The Gains from Trade | Principles of Economics”, 2018). According to comparative advantage, the countries produce the commodity in which they have a lower opportunity cost. Home and Foreign countries produce according to their opportunity cost and hence both gain from trade.

Foreign is producing radios, and radio is a capital intensive good, so the labourers working in the radio production will be better off, than the workers engaged in corn production. Labourers involved in producing corn will not support free trade as much as radio producers.

In Home, both the goods are produced so the labourers will be neutral about free trade. Since labourers involved in both the industries are gaining from trade (Krugman, Obstfeld, Melitz, Yamagata & Morioka, n.d.).

References

17.1 The Gains from Trade | Principles of Economics. (2018). Retrieved from https://open.lib.umn.edu/principleseconomics/chapter/17-1-the-gains-from-trade/

International Trade: Theory and Policy v1.0 | FlatWorld. (2018). Retrieved from https://catalog.flatworldknowledge.com/bookhub/28?e=fwk-61960-ch07_s02

Krugman, P., Obstfeld, M., Melitz, M., Yamagata, H., & Morioka, S. Kuruguman kokusai keizaigaku. Maruzenshuppan.

Salvatore, D. (2016). International economics. Hoboken, NJ: John Wiley & Sons, Inc.

Staff, I. (2018). Gini Index. Retrieved from https://www.investopedia.com/terms/g/gini-index.asp

Stolper-Samuelson Theorem (SST) | Theorems | Economics. (2018). Retrieved from https://www.economicsdiscussion.net/theorems/stolper-samuelson-theorem-sst-theorems-economics/26931 

Terms of Trade. (2018). Retrieved from https://www.investopedia.com/exam-guide/cfa-level-1/global-economic-analysis/terms-trade.asp

Trade openness. (2018). Retrieved from https://www.economicsonline.co.uk/Global_economics/Trade_openness