1. Industrial Structure and Capital Flows. Where is Capital Going and Why
Industrial Structure and Capital Flows Where is Capital Going and Why? – How Traditional Macro-Theory Fails at Explaining the Reality Author Keyu Jin Presented by Jingyun Cui

2. Overview – What Is This PowerPoint All About?
A Typical Theory Building Process
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Publish!
Get the conclusion and send it to some journal editors
Wait…What?
Something is not explained by the current theory
How to fix?
Think about how to fix the problem
Do it!
Now it’s the part to actually save this world
Why?
Find out what is causing the problem
Check… a bit
Do some analysis to double check the new theory
Author did quant analysis and found some empirical material to test her theory

3. Overview – Before We Start
Some Helpful Macroeconomics Concepts
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Balance of payments measures all of a country’s transactions with its partner. Current account is one of the two components of a country’s balance of payments, the other being the capital account.
Current account consists of the balance of trade, net primary income (net earnings on foreign investments).
𝐶 𝐴 𝑡 =𝑁𝑒𝑡 𝐹𝑜𝑟𝑒𝑖𝑔𝑛 𝐴𝑠𝑠𝑒 𝑡 𝑡 −𝑁𝑒𝑡 𝐹𝑜𝑟𝑒𝑖𝑔𝑛 𝐴𝑠𝑠𝑒 𝑡 𝑡−1
Current Account and Balance of Payments
International Capital Flow
Convergence effect, also known as the catch-up effect), is the idea that developed countries face diminishing return to capital so that capital will flow from these countries to developing countries.
Neoclassical growth theory predicts an increase in the labor force/productivity will leads to a net capital inflow.

4. This paper tries to fix this problem!
Background – What Is Happening Right Now?
Mismatch Between Traditional Theory and Reality
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
This paper tries to fix this problem!
Classical Macro Theory
Reality
Increase in the labor-force or labor productivity in a country induce a net capital inflow
Capital flow from developed countries to developing countries
“Convergence” effect, which channels capital toward where the effective capital- labor ratio is lower
Trade and financial integration and rapid labor force and labor productivity growth in emerging markets lead to a net capital outflow for these markets
Capital flows from emerging markets to capital-intensive markets
“Composition” effect, which offsets the “Convergence” effect

5. Background – Why Is This Happening? (1/2)
Where Neoclassical Theory Fails
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Problematic theories we are using right now
Inaccurate Standard Open-economy Models
Untenable Underlying Assumption
Missing Influence of Macro Dynamics
Unaddressed Composition Effect
The standard models are the one-good or two-good stochastic growth models of large open economies. These models do not account for factor-proportions trade. Also, their overlapping generations structure are not essential.
Standard open-economy models predict net capital inflow into developing countries, which is the opposite of what is happening. This is caused by the fact that they assume that countries cannot engage in intra-temporal commodity trade but only in intertemporal trade. However, large scale forces can alter a country’s structure of trade.
Currently, models do not examine the impact of convergence effect and composition effect separately. Such models cannot explain the fact that capital are flowing from emerging markets to economies that become more specialized in capital-intensive sectors.
“The conventional analyses of international macroeconomic dynamics on the structure of trade as well as the aggregate feedback effects of trade pattern” while “their interaction can be crucial in determining the global allocation of capital”.

6. Background – Why Is This Happening? (2/2)
Where Neoclassical Theory Fails
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Problematic theories we are using right now
Inaccurate Standard Open-economy Models
Untenable Underlying Assumption
Missing Influence of Macro Dynamics
Unaddressed Composition Effect
The standard models are the one-good or two-good stochastic growth models of large open economies. These models do not account for factor-proportions trade. Also, their overlapping generations structure are not essential.
Standard open-economy models predict net capital inflow into developing countries, which is the opposite of what is happening. This is caused by the fact that they assume that countries cannot engage in intra-temporal commodity trade but only in intertemporal trade. However, large scale forces can alter a country’s structure of trade.
Currently, models do not examine the impact of convergence effect and composition effect separately. Such models cannot explain the fact that capital are flowing from emerging markets to economies that become more specialized in capital-intensive sectors.
“The conventional analyses of international macroeconomic dynamics on the structure of trade as well as the aggregate feedback effects of trade pattern” while “their interaction can be crucial in determining the global allocation of capital”.

7. How is Jin Addressing this Problem
Background – How Is Jin Solving These Problems? (1/2)
Upgrading the model
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
How is Jin Addressing this Problem
Developing a stochastic two-country overlapping generations model with production and capital accumulation.
Multiple tradable sectors that differ in factor intensity are incorporated to capture factor-proportions-based trade, and financial capital is allowed to flow across borders.
Isolate the convergence effect and the composition effect.
Analytical tractability.
Closed-form solutions can be found.
Inaccurate model
The standard open-economy are the one-good or two- good stochastic growth models of large open economies that do not address factor-proportions trade.
Current models cannot address the impact of the composition effect.

8. How is Jin Addressing this Problem Missing Composition Effect
Background – How Is Jin Solving These Problems? (2/2)
Addressing the Composition Effect
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
How is Jin Addressing this Problem
Convergence effect and composition effect coexist.
In the integrated framework it’s possible to isolate the convergence effect and the composition effect to examine their disparate impact on capital flows. In the special case, in which the most labor- intensive sector uses only labor as an input to production, isolates the composition effect.
Additional assumption is needed to provide closed-form solution under two- country stochastic growth model.
Missing Composition Effect
The convergence effect and the composition effect co-exist and their combined force determine the tide of capital flow. Current theory focuses only on the standard convergence effect.

9. Framework – The Model Description Set up the imaginary world
FOREIGN
Framework – The Model Description
Set up the imaginary world
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background 4 1 2 3 5 6
Earth-500R
Intermediate goods are combined to produce a composite good that is used for consumption and investment
Each country uses identical technology to produce intermediate goods I, which are traded freely and costlessly
Labor input consists only of domestic labor, and IGP* firms are subject to country-specific productivity
Each country has an overlapping generations economy with young and old consumers. Young consumer supplies one unit of labor while the old only consume
There are two countries, Home (h) and Foreign (f)
Preferences and production technologies are assumed to have the same structure and parameter value
HOME
*IGP firms: Intermediate-goods-producing firm

10. Production Technologies
Analysis – Key Factors in the Model (1/13)
Part I – Production Technologies
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Production Technologies
Gross production of intermediate good 𝑖 in country 𝑗:
Where K represents capital, A represents labor productivity, and 𝑁 is the labor population. α can be seen as capital intensity measurement.
There is also the composite good for Con. and Inv.,
𝐼 𝑖𝑡 𝑗 = 𝑘=1 𝑚 𝛾 𝑘 1 𝜃 𝑥 𝑘𝑖,𝑡 𝑗 𝜃−1 𝜃 θ θ−1
Where x donates the amount of good 𝑘 used for investment in that sector 𝑖 of country 𝑗; also, summation of 𝛾 equals to 1, and 𝜃 is always greater than 0.
𝑌 𝑖𝑡 𝑗 = 𝐾 𝑖𝑡 𝑗 α𝑖 𝐴 𝑡 𝑗 𝑁 𝑖𝑡 𝑗 1−α𝑖
Consumers
Market Clearing
Equilibrium

11. Production Technologies
Analysis – Key Factors in the Model (2/13)
Part I – Production Technologies
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Production Technologies
Because all goods can be traded freely, the law of one price holds for all intermediate goods, and their prices can be donated as 𝑝 𝑖𝑡 . Since preferences are symmetric across countries, its associated investment price index is
𝑃 𝑡 = 𝑖=1 𝑚 𝛾 𝑖 𝑝 𝑖𝑡 1−𝜃 −𝜃
Which is normalized to 1 for simplicity.
Then, we have the capital used in producing goods 𝑖 in country 𝑗 augmented by 𝐼 𝑖𝑡 𝑗 and 𝐾 𝑖𝑡 𝑗 . The law of motion for 𝐾 is given by 𝐾 𝑖,𝑡+1 𝑗 =𝐺 𝐾 𝑖𝑡 𝑗 , 𝐼 𝑖𝑡 𝐽 , where 𝐺() is nondecreasing and linearly homogeneous in 𝐾 & 𝐼
𝐾 𝑖,𝑡+1 𝑗 =𝑎 𝐼 𝑖𝑡 𝑗 𝜙 𝐾 𝑖𝑡 𝑗 1−𝜙
Where 𝜙~ 0,1 & 𝑎 is greater than 0.
Consumers
Market Clearing
Equilibrium

12. Production Technologies
Analysis – Key Factors in the Model (3/13)
Part I – Production Technologies
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Production Technologies
Comparing to the standard capital accumulation equation with adjustment costs,
𝐾 𝑖,𝑡+1 𝑗 = 1−𝛿 𝐾 𝑖𝑡 𝑗 + 𝐼 𝑖𝑡 𝑗 − 𝑏 𝐼 𝑖𝑡 𝑗 𝐾 𝑖𝑡 𝑗 − 𝛿 2 𝐾 𝑖𝑡 𝑗
Where 𝛿 is depreciation rate. Our log-linear model and standard model are equivalent up to the second order.
Now, let 𝑞 𝑖𝑡 𝑗 be the price of capital. It is the price, in term of the composite good, of acquiring one unit of capital at the end of the current period to be carried into the next period; it is also the additional 𝐼 𝑖𝑡 𝑗 needed to augment 𝐾 𝑖,𝑡+1 𝑗 by one unit. Thus,
𝑞 𝑖𝑡 𝑗 = 1 𝑎𝜙 𝐼 𝑖𝑡 𝑗 𝐾 𝑖𝑡 𝑗 1−𝜙 & 𝑞 𝑖𝑡 𝑗 𝐾 𝑖,𝑡+1 𝑗 = 𝐼 𝑖𝑡 𝑗 𝜙
Consumers
Market Clearing
Equilibrium

13. Production Technologies
Analysis – Key Factors in the Model (4/13)
Part I – Production Technologies
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Production Technologies
Wage rate per unit of labor is given by,
𝑤 𝑖𝑡 𝑗 = 1 − ∝ 𝑖 𝑝 𝑖𝑡 𝑌 𝑖𝑡 𝑗 𝑁 𝑖𝑡 𝑗
And 𝑤 𝑖𝑡 𝑗 = 𝑤 𝑡 𝑗 because labor is mobile between sectors within each country.
Ultimately, we also want to know the rate of return to capital. By breaking down return into rental earned, which is ∝ 𝑖 𝑝 𝑖𝑡 𝑌 𝑖𝑡 𝑗 / 𝐾 𝑖𝑡 𝑗 , and rental earned in the capital adjustment process, which is the marginal contribution of capital in augmenting capital stock for use in the next period times relative price of capital, ⅆ 𝐾 𝑡+1 𝑗 ⅆ 𝐾 𝑖 𝑗 𝑞 𝑖𝑡 . Dividing return by price,
𝑅 𝑖𝑡 𝑗 = ∝ 𝑖 𝑝 𝑖𝑡 𝑌 𝑖𝑡 𝑗 𝐾 𝑖𝑡 𝑗 + (1−𝜙) 𝐼 𝑖𝑡 𝑗 𝜙 𝐾 𝑖𝑡 𝑗 𝑞 𝑖,𝑡−1
Consumers
Market Clearing
Equilibrium

14. Production Technologies Production Technologies
Analysis – Key Factors in the Model (5/13)
Part II – Consumers
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Production Technologies
Production Technologies
Consumers N t j evolves according to,
𝑙𝑛 𝑁 𝑡 𝑗 =𝑙𝑛 𝑁 𝑡−1 𝑗 + 𝜖 𝑁,𝑡 𝑗
Where 𝜖 is simply an independent random variable.
For young consumer who earns wage 𝑤 𝑡 ℎ , and uses his wage both on consumption 𝑐 𝑡 𝑦,ℎ , and on purchasing capital,
𝑐 𝑡 𝑦,ℎ = 𝑤 𝑡 ℎ − 𝑗=ℎ,𝑓 𝑖=1 𝑚 𝑞 𝑖𝑡 𝑗 𝑘 𝑖,𝑡+1 ℎ,𝑗
Assume consumers consume all resources when old. At 𝑡+1, their consumption, which is financed entirely by capital, is
𝑐 𝑡+1 0,ℎ = 𝑗=ℎ,𝑓 𝑖=1 𝑚 𝑅 𝑖,𝑡+1 𝑗 𝑞 𝑖𝑡 𝑗 𝑘 𝑖, 𝑡 1 ℎ,𝑗
Consumers
Market Clearing
Equilibrium

15. Production Technologies Production Technologies
Analysis – Key Factors in the Model (6/13)
Part II – Consumers
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Production Technologies
Production Technologies
The lifetime utility of consumption that a Home consumer born in the beginning of 𝑡 maximizes is,
𝑈 𝑡 = 𝑐 𝑡 𝑦,ℎ 1−𝜌 1−𝜌 +𝛽 𝐸 𝑡 𝑐 𝑡+1 𝑜,ℎ 1−𝜌 1−𝜌
Where 𝛽 denotes discount factor. 𝐶 𝑡 𝑦,𝑗 & 𝐶 𝑡+1 𝑜,𝑗 denote consumption of the young and the old consumer at each time period.
The aggregate consumption index in 𝑗 at 𝑡 is,
𝐶 𝑡 𝑗 = 𝑖=1 𝑚 𝛾 𝑖 1 𝜃 𝑐 𝑖𝑡 𝑗 𝜃−1 𝜃 𝜃 𝜃−1
Where 𝑐 𝑖𝑡 𝑗 represents consumption demand. Consumption price index is as same as the investment price index 𝑃 𝑡 .
Consumers
Market Clearing
Equilibrium

16. Production Technologies
Analysis – Key Factors in the Model (7/13)
Part III – Market Clearing
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Production Technologies
Consumers
Equilibrium
Production Technologies
The intermediate goods market clear when global demand equals supply. Let 𝑌 𝑖𝑡 𝑔 denotes output, clearing requires
𝑌 𝑖𝑡 𝑔 = 𝑗=ℎ,𝑓 𝑐 𝑖𝑡 𝑗 + 𝑗=ℎ,𝑓 𝑘=1 𝑚 𝑥 𝑘𝑖,𝑡 𝑗
Where 𝑐 𝑖𝑡 𝑗 = 𝛾 𝑖 𝑝 𝑖𝑡 −𝜃 𝐶 𝑡 𝑗 & 𝑥 𝑘𝑖,𝑡 𝑗 = 𝛾 𝑖 𝑝 𝑖𝑡 −𝜃 𝐼 𝑖𝑡 𝑗
Let 𝐼 𝑡 𝑗 = 𝑖=1 𝑚 𝐼 𝑖𝑡 𝑗 denotes aggregate investment, replacing 𝑐 𝑖𝑡 𝑗 & 𝑥 𝑘𝑖,𝑡 𝑗 into output equation, we have,
𝑝 𝑖𝑡 𝑝 𝑘𝑡 = 𝛾 𝑖 𝛾 𝑘 𝑌 𝑘𝑡 𝑔 𝑌 𝑖𝑡 𝑔 𝜃
Which shows the relative price of any two goods falls with respect to an increase in the relative output of the two goods with an elasticity 1 𝜃 . When 𝜃=1, output changes are offset by price changes so that nominal value of output remain unchanged
Consumers
Market Clearing

17. Production Technologies
Analysis – Key Factors in the Model (8/13)
Part III – Market Clearing
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Production Technologies
Consumers
Equilibrium
Production Technologies
Next, domestic labor markets clear when,
𝑖=1 𝑚 𝑁 𝑖𝑡 𝑗 = 𝑁 𝑡 𝑗
Because of world resource constraint, we have the total amount of final goods in the world,
𝑌 𝑡 𝑔 = 𝐶 𝑡 𝑔 + 𝐼 𝑡 𝑔
Where 𝐶 𝑡 𝑔 = 𝑗 𝑁 𝑡 𝑗 𝑐 𝑡 𝑦,𝑗 + 𝑁 𝑡−1 𝑗 𝑐 𝑡 𝑜,𝑗 & 𝐼 𝑡 𝑔 = 𝑗 𝐼 𝑡 𝑗 .
Lastly, GDP can be defined as total consumption and market value of capital stock,
𝐺𝑃 𝐷 𝑡 𝑗 = 𝑖=1 𝑚 𝑝 𝑖𝑡 𝑌 𝑖𝑡 𝑗 + 1−𝜙 𝜙 𝐼 𝑡 𝑗
Consumers
Market Clearing

18. Analysis – Key Factors in the Model (9/13)
Key assumption needed for a semi-closed form solution
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
All assumptions are important for analytical convenience, and will be relaxed later during the quantitative analysis section.
Assumption 1
Unitary elasticity of substitution of intermediate goods (Θ = 1).
Assumption 2
Consumers have logarithmic preferences (ρ = 1).
Assumption 3
The capital-adjustment technology is log-linear, as in equation K i,t+1 j .
Let’s get back!

19. Production Technologies
Analysis – Key Factors in the Model (10/13)
Part IV – Equilibrium
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Market Clearing
Consumers
Production Technologies
Production Technologies
Production Technologies
Consumers
Assuming logarithmic utility, the optimal consumption of a young consumer in 𝑡 is a constant fraction of present value of lifetime resources, which is simply the wage earned by the young. The optimal consumption is therefore,
𝑐 𝑡 𝑦.𝑗 = 1 1+𝛽 𝑤 𝑡 𝑗
Let 𝐶 𝑡 𝑦,𝑗 = 𝑁 𝑡 𝑗 𝑐 𝑡 𝑦,𝑗 be the aggregate consumption of the young cohort. Global consumption 𝐶 𝑡 𝑦,𝑔 is a constant fraction of world labor income 𝑊 𝑡 𝑔 . With a unitary elasticity of substitution, 𝑊 𝑡 𝑔 is a constant share 𝑠 𝑙 = 𝑖 𝛾 𝑖 (1− 𝛼 𝑖 ) of world output. Then, the global investment-output ratio is a constant,
𝐼 𝑡 𝑔 𝑌 𝑡 𝑔 =𝜓 𝑠 𝑙
Where 𝜓= 𝜙𝛽 1+𝛽
Consumers
Equilibrium

20. Production Technologies
Analysis – Key Factors in the Model (11/13)
Part IV – Equilibrium
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Market Clearing
Consumers
Production Technologies
Production Technologies
Production Technologies
Consumers
Then, we represent investment in each sector of each country by,
𝐼 𝑖𝑡 𝑗 = 𝜇 𝑖𝑡 𝜂 𝑖𝑡 𝑗 𝐼 𝑡 𝑔
Where 𝜇 & 𝜂 represent industry-level and country-level investment share of the global investment.
LEMMA 1: The share of global investment allocated to industry is a constant where,
𝜇 𝑖 =( 𝛾 𝑖 𝛼 𝑖 )/( 𝑘=1 𝑚 𝛾 𝑘 𝛼 𝑘 ) ∀𝑡
The greater 𝛾 𝑖 & 𝛼 𝑖 , the greater investment in industry level.
The country-share of global investment in any industry is very important in determining the evolution of a country’s aggregate capital stock and aggregate investment,
𝜂 𝑖𝑡 𝑗 =(1 −𝜆) 𝑘=1 ∞ 𝜆 𝑘 𝐸 𝑡 ( 𝑌 𝑖,𝑡+𝑘+1 𝑗 𝑌 𝑖,𝑡+𝑘+1 𝑔 )
Consumers
Equilibrium

21. Production Technologies
Analysis – Key Factors in the Model (12/13)
Part IV – Equilibrium
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Country’s share of global investment can be written as 𝐼 𝑡 𝑗 = 𝜂 𝑡 𝑗 𝐼 𝑡 𝑔 , where,
𝜂 𝑡 𝑗 = 𝑖=1 𝑚 𝜇 𝑖 𝜂 𝑖𝑡 𝑗 = 𝑖=1 𝑚 𝛾 𝑖 𝛼 𝑖 𝑠 𝑘 𝜂 𝑖𝑡 𝑗
Where 𝑠 𝑘 is the weighted-average capital share. Investment is not only associated with the size of its expected relative production, captured by 𝜂 𝑖𝑡 𝑗 , but also with its composition of production. The higher 𝛼 𝑖 is put on the expected share of future capital-intensive-goods production, the less weight is put on its expected share of labor-intensive-goods production.
By contrast, in the one-sector model, 𝜂 𝑡 𝑗 is country’s expected present-discounted value of its share of the only good produced globally. A positive, permanent, technology or lobar shock in Foreign, which effectively increases Foreign’s share of global production, would cause a large drop in Home’s share of investment.
Market Clearing
Consumers
Production Technologies
Production Technologies
Production Technologies
Consumers
Consumers
Equilibrium

22. Production Technologies
Analysis – Key Factors in the Model (13/13)
Part IV – Equilibrium
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Market Clearing
Consumers
Production Technologies
Production Technologies
The total net foreign assets of Home, donates as 𝑁𝐹 𝐴 𝑡 is the value of Home’s claims on foreigner less the value of foreigner’s claim on Home,
= 𝑖=1 𝑚 𝑞 𝑖𝑡 𝑓 𝑘 𝑖,𝑡+1 ℎ,𝑓 𝑁 𝑡 ℎ − 𝑖=1 𝑚 𝑞 𝑖𝑡 ℎ 𝑘 𝑖,𝑡+1 𝑓,ℎ 𝑁 𝑡 𝑓 = 𝑆 𝑡 𝑦,ℎ − 𝑞 𝑡 ℎ 𝐾 𝑡+1 ℎ
Where S is aggregate saving of the young 𝑆 𝑡 𝑦,𝑗 = 𝛽 1+𝛽 𝑊 𝑡 𝑗 .
The current account of Home in period t, denoted as 𝐶 𝐴 𝑡 ℎ , is
𝐶 𝐴 𝑡 ℎ =𝑁𝐹 𝐴 𝑡 ℎ −𝑁𝐹 𝐴 𝑡−1 ℎ
Finally, these equation will yield for solution.
𝐼 𝑖𝑡 𝑗 = 𝜇 𝑖𝑡 𝜂 𝑖𝑡 𝑗 𝐼 𝑡 𝑔
𝜇 𝑖 =( 𝛾 𝑖 𝛼 𝑖 )/( 𝑘=1 𝑚 𝛾 𝑘 𝛼 𝑘 ) ∀𝑡
𝜂 𝑖𝑡 𝑗 = 1 −𝜆 𝑘=1 ∞ 𝜆 𝑘 𝐸 𝑡 𝑌 𝑖,𝑡+𝑘+1 𝑗 𝑌 𝑖,𝑡+𝑘+1 𝑔
K i,t+1 j =a I it j 𝜙 K it j 1−𝜙
Production Technologies
Consumers
Consumers
Equilibrium

23. Analysis – The Composition Effect (1/3)
Additional Assumption needed
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Assumption 1
Unitary elasticity of substitution of intermediate goods (Θ = 1).
Assumption 2
Consumers have logarithmic preferences (ρ = 1).
Assumption 3
The capital-adjustment technology is log-linear, as in equation K i,t+1 j .
Assumption 4
The most labor-intensive sector uses only labor as an input and no capital in the production technology, i.e., α1 = 0.
All assumptions are important for analytical convenience, and will be relaxed later during the quantitative analysis section.
Let’s get back!

24. Analysis – The Composition Effect (2/3)
Interaction between output and investment
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Proposition 1: With Assumption 1-4, the share of Home’s investment in any industry 𝑖, 𝜂 𝑖𝑡 , is a constant and is equal to its initial share of world capital stock in that sector.
𝜂 𝑖𝑡 = 𝐾 𝑖0 ℎ 𝐾 𝑖0 𝑔 ∀𝑡
Combining with 𝐼 𝑡 𝑔 𝑌 𝑡 𝑔 =𝜓 𝑠 𝑙 & 𝜂 𝑖𝑡 𝑗 = 1 −𝜆 𝑘=1 ∞ 𝜆 𝑘 𝐸 𝑡 𝑌 𝑖,𝑡+𝑘+1 𝑗 𝑌 𝑖,𝑡+𝑘+1 𝑔 , we have,
𝐼 𝑡 𝑗 = 𝑖=1 𝑚 𝜇 𝑖 𝜂 𝑖0 𝑗 𝜓 𝑠 𝑡 𝑌 𝑡 𝑔
This means increase in 𝑌 caused by a positive labor force/productivity shock will also leads to an increase in 𝐼, in such a way that more investment is allocated to the country that has a higher initial, weighted-average capital share.

25. Analysis – The Composition Effect (3/3)
Other solutions
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Another way to understand allocation of saving across countries is by analyzing a country’s supply of saving relative to tis demand for investment. Author shows that because the young who work and earn labor income are the savers in the economy, a country’s supply of savings derives from its capacity to generate labor income. That said, country’s saving to GDP ration at anytime depends on its relative capital-labor ratio. Since,
𝑊 𝑡 𝑗 𝐺𝑃 𝐷 𝑡 𝑗 = 1 𝑘 𝑡 𝑗 𝑠 𝑘 𝑠 𝑙 + 𝛽 1−𝜙 1+𝛽 +1
Then,
𝑆 𝑡 𝑦,𝑗 𝐺𝑃 𝐷 𝑡 𝑗 = 𝛽/(1+𝛽) 𝑘 𝑡 𝑗 𝑠 𝑘 𝑠 𝑙 + 𝛽 1−𝜙 1+𝛽 +1
And,
𝐼 𝑡 𝑗 /𝜙 𝐺𝑃 𝐷 𝑡 𝑗 = 𝑘 𝑡 𝑗 𝛽/(1+𝛽) 𝑘 𝑡 𝑗 𝑠 𝑘 𝑠 𝑙 + 𝛽 1−𝜙 1+𝛽 +1

26. Analysis - Quantitative Analysis
Extending into Multi-period OLG setting
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Two-period OLG Framework
Multi-period OLG Framework
Apply to two global events
Here author extends the analytical two-period OLG framework to a multi-period OLG setting, allowing for an additional nontradable sector. And then use that framework to examine two important global events in the past. She examines what the almost-simultaneous advent of emerging economies implies for international capital flows. Also, increasing labor force in emerging market will have its impact on the current account with the help of factor-proportions trade.

27. Summary and Conclusion
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
There is a mismatch between what neo-classical macroeconomic theory predicts and what is really happening
Author developed a general-equilibrium framework that integrates a factor-proportions paradigm of trade and financial capital flows, allowing for their interplay
This paper take into account the composition effect, which coexist with the standard, classical convergence effect.
Real-world Events
New Framework
Composition Effect

28. Summary and Conclusion
Other Materials
Overview
Background
What is happening
Why is this happening
How Is Jin Solving These Problems
Framework
Analysis
Key Factors in the Model
The Composition Effect
Quantitative Analysis
Summary
Introduction
Background
Productivity Growth and Capital Flows: The Dynamics of Reforms
By Francisco J. Buera and Yongseok Shin (2011)
“Standard economic theory predicts that capital should flow into countries experiencing a sustained increase in total factor productivity (TFP). The evidence from developing countries over the last three decades contradicts this prediction.”
Patterns of International Capital Flows and Productivity Growth: New Evidence
By Margaux MacDonald (2015)
“Recent evidence from developing and emerging economies shows a negative correlation between growth and net capital inflows, a contradiction to neoclassical growth theory.”