1. International Capital Mobility and Structural Transformation
국금연구회 발표
International Capital Mobility and Structural Transformation
Kyungsoo Kim, Wankeun Oh, and E. Young Song

2. Prolog Balassa Samuelson effect vs. Baumol effect (cost disease)
Production ft.: 𝑋=𝐴 𝐿 𝑋 , 𝐴>1 ;𝑌= 𝐿 𝑌 and 𝐿 = 𝐿 𝑋 + 𝐿 𝑌
Labor mobility: 𝑊= 𝑃 𝑋 𝐴= 𝑃 𝑌
𝑃 𝑌 =𝐴, 𝑃 𝑋 =1 → 𝑃 𝑌 = 𝐴 >0
2nd hypothesis of BS effect vs. Baumol effect (growth disease)
Nominal GDP: 𝑋+ 𝑃 𝑌 𝑌=𝐴 𝐿 𝑋 + 𝑃 𝑌 𝐿 𝑌 =𝐴 𝐿 𝑋 +𝐴 𝐿 𝑌 =𝐴 𝐿
Real GDP: 𝑋+ 𝑃 𝑌 𝑌=𝐴 𝐿 𝑋 + 𝐴 𝐿 𝑌 =𝐴 𝐿 − 𝐿 𝑌 (𝐴− 𝐴 ) ●
𝐿 𝑌 / 𝐿 1

3. Literature Unbalanced growth pioneered by Baumol (1967)
Ngai and Pissarides (2007), Acemoglu and Guerrieri (2008)
Herrendorf, Rogerson and Valentinyi (2013)
Neo-classical growth model and financial integration
Gourinchas and Jeanne (2006, 2013), Antunes and Cavalcanti (2013)
Performance of capital account liberalization
Eichengreen (2001), Obstfeld (2009), Kose, Prasad, Rogoff, and Wei (2009), Rodrik and Subramanian (2009)

4. This paper
presents a neo-classical growth model and shows the structural transformation (ST) implied by capital account opening
It is Ramsey model of two goods, tradables and nontradables
When 𝑟 𝑎 ≠ 𝑟 𝑓 instantaneous capital flows fill the gap and ST follows
𝑟 𝑎 > 𝑟 𝑓
Capital flows in and this small open economy generates Dutch disease and it may take long before it approaches to generalized balanced growth path (GBGP)
Capital flows out and reverse Dutch disease develops before it goes close to GBGP

5. Ramsey model in a small open economy
Short run and long run impact of capital opening
Neoclassical growth model with two goods
Autarky economy
Impact of capital opening

6. Model: warming up 𝑀𝑎𝑥 0 ∞ log 𝑐 exp[− 𝜃−𝑛 𝑡] 𝑑𝑡 𝑠.𝑡 𝑎 = 𝑟−𝑛 𝑎 +𝑊− 𝑐
𝑠.𝑡 𝑎 = 𝑟−𝑛 𝑎 +𝑊− 𝑐
lim 𝑡→∞ 𝑎 exp − 0 𝑡 𝑟 𝑠 −𝑛 𝑑𝑠 ≥0 →
𝑐 = 𝑟−𝜃 𝑐
𝑎 = 𝑟−𝑛 𝑎 +𝑊− 𝑐
lim 𝑡→∞ 𝑎 exp [− 0 𝑡 𝑟(𝑠)−𝑛 𝑑𝑠]=0
𝑄= (𝐴𝐿) 1−𝛼 𝐾 𝛼 = 𝑐 𝑇 𝐿+ 𝐾 +𝑋

7. Normalization of variables
𝑐≡ 𝑐 𝐴 , 𝑎≡ 𝑎 𝐴 , 𝑤≡ 𝑊 𝐴 , 𝑘≡ 𝐾 (𝐿𝐴) , 𝑥≡ 𝑋 𝐿𝐴 , 𝑔≡ 𝐴 𝐴 →
𝑐 = 𝑟−𝜃−𝑔 𝑐
𝑎 = 𝑟−𝑛−𝑔 𝑎+𝑤−𝑐, lim 𝑡→∞ 𝑎 exp − 0 𝑡 𝑟 𝑠 −𝑛−𝑔 𝑑𝑠 =0 →
𝑐(0)= 𝜃−𝑛 ( 𝑎(0)+ 0 ∞ 𝑤 𝑡 exp − 0 𝑡 𝑟 𝑠 −𝑛−𝑔 𝑑𝑠 𝑑𝑡 )
𝑦≡ 𝑄 𝐿𝐴 = 𝑘 𝛼 =𝑐+ 𝑘 + 𝑛+𝑔 𝑘+𝑥
𝑟= 𝛼 𝑘 𝛼−1 ;𝑤=(1− 𝛼)𝑘 𝛼 →
𝑐 = 𝛼 𝑘 𝛼−1 −𝜃−𝑔 𝑐 → 𝑟 𝑎 = 𝛼 𝑘 𝛼−1 =𝜃+𝑔 in steady state
𝑘 = 𝑘 𝛼 − 𝑛+𝑔 𝑘−𝑐−𝑥

8. Ramsey model: autarky economy (𝑥=0)
E: ss with 𝜃
E’: ss with 𝜃 ′ <𝜃
𝑐 =0
𝑐 =0 F’
𝑘 = 𝑘 𝛼 − 𝑛+𝑔 𝑘−𝑐=0 E’ E F k

9. Ramsey model: small open economy with 𝑟 𝑎 > 𝑟 𝑓
𝑐 =0
𝑐 =0 F ●
E: autarky 𝑟= 𝑟 𝑎
E’: open economy 𝑟= 𝑟 𝑓
𝑘 +𝑥= 𝑘 𝛼 − 𝑛+𝑔 𝑘−𝑐=0 E’ E k

10. Capital opening: 𝑟 𝑎 > 𝑟 𝑓 >𝑛+𝑔
E → F
Immediately 𝑟= 𝑟 𝑓 , and capital flows in instantaneously up to the level 𝑟 𝑓 =𝛼 𝑘 𝛼−1 and wage should rise permanently, 𝑤=(1−𝛼) 𝑘 𝛼
𝑐 should jump up at 𝑡=0 since 𝑐 0 = 𝜃−𝑛 𝑎 0 + 𝑤 𝑟 𝑓 −𝑛−𝑔 and 𝑥= 𝑘 𝛼 − 𝑛+𝑔 𝑘−𝑐<0 when the effect of 𝑐 dominates 𝑘
𝑎 0 (=𝑘 0 +𝑏 0 ) should remain constant tied to the level of 𝑘 in autarky, but 𝑘 jumps up at the moment of opening, and therefore 𝑏(0) turns negative

11. Path to generalized balanced growth
From 𝑐 = 𝑟−𝜃−𝑔 𝑐, c falls at the rate of
𝑐 =− 𝑟 𝑎 − 𝑟 𝑓 𝑐 and converges to zero as 𝑡→∞
As 𝑐 keeps on declining, 𝑎 must too. Because 𝑘 is constant, 𝑏 declines during the entire period of transition
As 𝑐→0, −𝑏→ 𝑤 𝑟 𝑓 −𝑛−𝑔 +𝑘 and 𝑥→ 𝑘 𝛼 − 𝑛+𝑔 𝑘
Current account 𝐵 = 𝑛+𝑔 𝐵<0, 𝑏≡ 𝐵 𝐿𝐴
Trade account 𝑋 = 𝑛+𝑔 𝑋>0, 𝑥≡ 𝑋 𝐿𝐴
( 𝑐 𝐿) ={𝑛+𝑔−( 𝑟 𝑎 −𝑟 𝑓 )} 𝑐 𝐿

12. Ramsey model: small open economy, 𝑟 𝑓 > 𝑟 𝑎
𝑐 =0
𝑐 =0
E: autarky economy 𝑟= 𝑟 𝑎
E’: open economy 𝑟= 𝑟 𝑓
𝑘 +𝑥= 𝑘 𝛼 − 𝑛+𝑔 𝑘−𝑐=0 E E’ ● F k

13. Ramsey model in a small open economy
Short run and long run impact of capital opening
Neoclassical growth model with two goods
Autarky economy
Impact of capital opening

14. Back to paper: two good autarky model
𝑀𝑎𝑥 0 ∞ log 𝑐 exp[− 𝜃−𝑛 𝑡] 𝑑𝑡
𝑠.𝑡 𝑎 = 𝑟−𝑛 𝑎 +𝑊− 𝑒
lim 𝑡→∞ 𝑎 exp[− 0 𝑡 𝑟(𝑠)−𝑛 𝑑𝑠]≥0
𝑐 = 𝑐 𝑇 1−𝜎 𝑐 𝑁 𝜎 .
𝑒 =𝑝 𝑇 𝑐 𝑇 + 𝑝 𝑁 𝑐 𝑁 →
𝑒 = 𝑟−𝜃 𝑒
𝑎 = 𝑟−𝑛 𝑎 +𝑊− 𝑒
lim 𝑡→∞ 𝑎 exp[− 0 𝑡 𝑟(𝑠)−𝑛 𝑑𝑠]=0

15. 𝑄 𝑇 = 𝐴 𝑇 𝐿 𝑇 1−𝛼 𝐾 𝑇 𝛼 = 𝑐 𝑇 𝐿+ 𝐾 +𝑋 (T market equilibrium condition)
𝑄 𝑁 = 𝐴 𝑁 𝐿 𝑁 1−𝛼 𝐾 𝑁 𝛼 = 𝑐 𝑁 𝐿 (N market equilibrium condition)
𝐾 𝑇 + 𝐾 𝑁 =𝐾, 𝐿 𝑇 + 𝐿 𝑁 =𝐿, 𝐿 𝐿 =𝑛
𝑔 𝑇 (= 𝐴 𝑇 𝐴 𝑇 ) = 𝑔 𝑁 (= 𝐴 𝑁 𝐴 𝑁 ) =𝑔 (balanced growth assumption)
When both goods are produced
𝑝 𝑇 =1= 𝜙 𝐴 𝑇 − 1−𝛼 𝑊 1−𝛼 𝑟 𝛼 , 𝜙= 𝛼 −𝛼 1−𝛼 − 1−𝛼
𝑝 𝑁 =𝜙 𝐴 𝑁 − 1−𝛼 𝑊 1−𝛼 𝑟 𝛼
𝐾 𝐿 = 𝐾 𝑇 𝐿 𝑇 = 𝐾 𝑁 𝐿 𝑁 = 𝛼 1−𝛼 𝑊 𝑟

16. Normalization of variables
𝑒≡ 𝑒 𝐴 𝑇 , 𝑐 𝑇 ≡ 𝑐 𝑇 / 𝐴 𝑇 , 𝑐 𝑁 ≡ 𝑐 𝑁 / 𝐴 𝑇 , 𝑐≡ 𝑐 𝐴 𝑇 , 𝑎≡ 𝑎 𝐴 𝑇 , 𝑤≡ 𝑊 𝐴 𝑇 , 𝑘≡ 𝐾 (𝐿 𝐴 𝑇 ) , 𝑘 𝑇 ≡ 𝐾 𝑇 ( 𝐿 𝑇 𝐴 𝑇 ) , 𝑘 𝑁 ≡ 𝐾 𝑁 ( 𝐿 𝑁 𝐴 𝑇 ) , 𝑥≡ 𝑋 (𝐿 𝐴 𝑇 )
𝑒 = 𝑟−𝜃−𝑔 𝑒
𝑎 = 𝑟−𝑛−𝑔 𝑎+𝑤−𝑒
lim 𝑡→∞ 𝑎 exp[− 0 𝑡 𝑟 𝑠 −𝑛−𝑔 𝑑𝑠]=0 →
𝑒(0)= 𝜃−𝑛 ( 𝑎(0)+ 0 ∞ 𝑤 𝑡 exp − 0 𝑡 𝑟 𝑠 −𝑛−𝑔 𝑑𝑠 𝑑𝑡 )

17. Path to balanced growth
𝑄 𝑇 𝐿 𝐴 𝑇 = 1−𝜆 𝑘 𝑇 𝛼 = 1−𝜎 𝑒+ 𝑘 + 𝑛+𝑔 𝑘+𝑥, 𝜆= 𝐿 𝑁 𝐿
𝑝 𝑁 𝑄 𝑁 𝐿 𝐴 𝑇 =𝜆 𝑝 𝑁 𝐴 𝑇 𝐴 𝑁 −(1−𝛼) 𝑘 𝑁 𝛼 =𝜎 𝑒
1=𝜙 𝑤 1−𝛼 𝑟 𝛼
𝑝 𝑁 = 𝐴 𝑇 𝐴 𝑁 1−𝛼 𝜙 𝑤 1−𝛼 𝑟 𝛼 →
𝑝 𝑁 = 𝐴 𝑇 𝐴 𝑁 1−𝛼 , when both goods are produced and
𝑝 𝑁 𝑄 𝑁 𝐿 𝐴 𝑇 =𝜆 𝑘 𝑁 𝛼 =𝜎 𝑒
𝑘=𝑘 𝑇 = 𝑘 𝑁 = 𝛼 1−𝛼 𝑤 𝑟

18. 𝑦≡ 𝑄 𝑇 + 𝑝 𝑁 𝑄 𝑁 𝐿 𝐴 𝑇 = 𝑘 𝛼 =𝑒+ 𝑘 + 𝑛+𝑔 𝑘+𝑥→
𝜆= 𝑝 𝑁 𝑄 𝑁 𝑄 𝑇 + 𝑝 𝑁 𝑄 𝑁
𝛼 𝑘 𝛼−1 =𝑟
𝑒 = 𝑟−𝜃−𝑔 𝑒
𝑎 = 𝑟−𝑛−𝑔 𝑎+𝑤−𝑒
𝑒 = 𝛼 𝑘 𝛼−1 −𝜃−𝑔 𝑒
𝑘 = 𝑘 𝛼 − 𝑛+𝑔 𝑘−𝑒

19. Proposition 1
The economy converges to a unique balanced growth path in autarky. On the path, 𝑟=𝜃+𝑔, and 𝑄 𝑇 , 𝑄 𝑁 , 𝐾, 𝐾 𝑇 , 𝐾 𝑁 all grow at the rate of 𝑛+𝑔. Aggregate consumption expenditure ( 𝑒 𝐿), and the aggregate consumption of the tradable good, the nontradable good, and the composite consumption good also grow at the rate of 𝑛+𝑔. 𝐿 𝑇 and 𝐿 𝑁 grow at the same rate of 𝑛. The output and employment share of the nontradable sector remains constant, and is given by 𝜆= 𝜎 𝜃+𝑔−𝛼 𝑛+𝑔 𝜃+𝑔 ∈(0, 1).

20. Ramsey model in a small open economy
Short run and long run impact of capital opening
Neoclassical growth model with two goods
Autarky economy
Impact of capital opening

21. Moment of capital opening 𝑟 𝑎 > 𝑟 𝑓 ,
𝑘 should jump up permanently ( 𝛼𝑘 𝛼−1 = 𝑟 𝑓 )
consumption expenditure instantly jumps up from
𝑒(0)= 𝜃−𝑛 {𝑎(0)+ 𝑤 0 𝑟 𝑓 −𝑛−𝑔 },
𝜆 ( =𝐿 𝑁 𝐿 ) may jump up or down, but likely jumps up considering the size of 𝛼
𝜆 𝑘 𝑁 𝛼 =𝜎𝑒
when the effect of consumption expenditures dominates x jumps down
𝑥= 𝑘 𝛼 − 𝑛+𝑔 𝑘−𝑒

22. Path to GBG generates a symptom similar to Dutch disease
A consumption boom moves labor from the tradables sector to the nontradables sector
De-industrialization in the early period of capital opening is followed by complete industrialization in the long run
𝑒 =− 𝑟 𝑎 − 𝑟 𝑓 𝑒
𝑝 𝑁 𝑄 𝑁 𝐿 𝐴 𝑇 =𝜆 𝑘 𝑁 𝛼 =𝜎𝑒 → 𝜆 /𝜆 = 𝑒 /𝑒, 𝐿 𝑁 𝐿 𝑁 =𝑛+ 𝑟 𝑓 − 𝑟 𝑎 , 𝑄 𝑁 𝑄 𝑁 =𝑛+𝑔+ 𝑟 𝑓 − 𝑟 𝑎
A consumption boom causes 𝑥 <0 (trade deficit), but then 𝑥 increases and, in a finite time, becomes positive, and keeps growing
𝑥= 𝑘 𝛼 − 𝑛+𝑔 𝑘−𝑒

23. Proposition 2
When the world interest rate is given by 𝑟 𝑓 ∈ 𝑛+ 𝑔 𝑇, 𝑟 𝑎 , the small open economy goes to a unique approximate general balanced growth path on which the economy produces both goods. On the path, the following holds:
𝑟= 𝑟 𝑓 ,
𝜆 ∗ =0,
𝑔 𝐿 𝑇 ∗ =𝑛, 𝑔 𝐿 𝑁 =𝑛− 𝑟 𝑎 − 𝑟 𝑓 ,
𝑔 𝑄 𝑇 ∗ =𝑛+𝑔, 𝑔 𝑝 𝑁 𝑄 𝑁 = 𝑛+𝑔− 𝑟 𝑎 − 𝑟 𝑓 ,
𝑔 𝐾 = 𝑔 𝐾 𝑇 ∗ =𝑛+𝑔, 𝑔 𝐾 𝑁 =𝑛+𝑔− 𝑟 𝑎 − 𝑟 𝑓 ,
𝑔 𝑒 𝐿 = 𝑔 𝑐 𝐿 = 𝑔 𝑐 𝑇 𝐿 = 𝑔 𝑐 𝑁 𝐿 =𝑛+𝑔−( 𝑟 𝑎 − 𝑟 𝑓 ).

24. Share of nontradables and total exports when 𝑟 𝑓 < 𝑟 𝑎
𝜃=0.04; 𝑛=0.01; 𝜎=0.6; 𝛼=0.3; 𝑔=0.03; 𝑟 𝑓 = 0.055

25. Capital opening 𝑟 𝑎 < 𝑟 𝑓
Behaviors of key variables are just opposite to that of 𝑟 𝑎 > 𝑟 𝑓 except that in the long run the economy will produce nontradables only
After 𝜆 hits the value of 1 at time T the economy will stop producing tradables and should be governed by different dynamics
𝑝 𝑁 𝑄 𝑁 𝐿 𝐴 𝑇 =𝜆 𝑝 𝑁 𝐴 𝑇 𝐴 𝑁 −(1−𝛼) 𝑘 𝑁 𝛼 =𝜎 𝑒, 𝑝 𝑁 = 𝐴 𝑇 𝐴 𝑁 1−𝛼 𝜙 𝑤 1−𝛼 𝑟 𝛼 and 𝜆=1
→ 𝜙 𝑤 1−𝛼 𝑟 𝛼 𝑘 𝑁 𝛼 =𝜎 𝑒 and 𝑘=𝑘 𝑇 = 𝑘 𝑁 = 𝛼 1−𝛼 𝑤 𝑟
𝑤 𝑤 = 𝑘 𝑘 = 𝑒 𝑒 = 𝑟 𝑓 − 𝑟 𝑎 and 𝑃 𝑁 𝑃 𝑁 =(1−𝛼) 𝑒 𝑒 =(1−𝛼)( 𝑟 𝑓 − 𝑟 𝑎 )
𝑄 𝑇 𝐿 𝐴 𝑇 = 1−𝜎 𝑒+ 𝑘 + 𝑛+𝑔 𝑘+𝑥 = 0 → −𝑥= 1−𝜎 𝑒+ 𝑛+𝑔+ 𝑟 𝑓 − 𝑟 𝑎 𝑛+𝑔+ 𝑟 𝑓 − 𝑟 𝑎 𝑘

26. Before and after T, 𝑒 increases at the rate 𝑟 𝑓 − 𝑟 𝑎
𝑤 and 𝑘 𝑁 (=𝑘=𝑘 𝑇 ) are constant from 1=𝜙 𝑤 1−𝛼 𝑟 𝐹 𝛼 and 𝑘= 𝛼 1−𝛼 𝑊 𝑟
𝑃 𝑁 is constant
For 𝑡≥𝑇
𝑤 and 𝑘 𝑁 are increasing at the rate 𝑟 𝑓 − 𝑟 𝑎
𝑃 𝑁 is increasing at the rate (1−𝛼)( 𝑟 𝑓 − 𝑟 𝑎 )
𝑎 𝑡 is increasing at the rate 𝑟 𝑓 − 𝑟 𝑎 from
𝑒 𝑡 = 𝜃−𝑛 𝑎 𝑡 + 𝑤 exp 𝑟 𝑓 − 𝑟 𝑎 𝑡−𝑇
𝑏 𝑡 (=𝑎 𝑡 −𝑘 𝑡 ) is also increasing at the rate 𝑟 𝑓 − 𝑟 𝑎

27. Proposition 3
When the world interest rate is given by 𝑟 𝑓 > 𝑟 𝑎 , the small open economy goes to a unique generalized balanced growth path. On the path, the economy produces only the nontradable good, and the following equations hold.
𝑟= 𝑟 𝑓 ,
𝑔 𝑝 𝑁 = 1− 𝛼 𝑟 𝑓 − 𝑟 𝑎 ,
𝑔 𝑝 𝑁 𝑄 𝑁 = 𝑔 𝐾 𝑁 =𝑛+𝑔+ 𝑟 𝑓 − 𝑟 𝑎 ,
𝑔 𝑒 𝐿 = 𝑔 𝑐 𝑇 𝐿 =𝑛+𝑔+ 𝑟 𝑓 − 𝑟 𝑎 ,
𝑔 𝑄 𝑁 = 𝑔 𝑐 𝑁 𝐿 =𝑛+𝑔+𝛼 𝑟 𝑓 − 𝑟 𝑎 ,
𝑔 𝐵 = 𝑔 −𝑋 =𝑛+𝑔+ 𝑟 𝑓 − 𝑟 𝑎

28. Share of nontradables and total exports when 𝑟 𝑓 > 𝑟 𝑎
𝜃=0.04; 𝑛=0.01; 𝜎=0.6; 𝛼=0.3; 𝑔=0.003; 𝑟 𝑓 = 0.055

29. Remarks
The short run responses of the economy can be significantly altered with lower intertemporal rate of substitution
1 1−𝛾 𝑐 1−𝛾 , 1 𝛾 <1
More general case: Kim, Oh and Song (2016)
CRRA intertemporal utility function, CES atemporal utility function
𝑔 𝑇 > 𝑔 𝑁 and 𝛼>𝛽 →
Baumol’s growth disease depends on the pattern of capital flows

30. Epilog
..we argue that the effect of foreign finance is often to aggravate this investment constraint by appreciating the real exchange rate and reducing profitability and investment opportunities in the traded goods sector, which have adverse long-run growth consequences. It is time for a new paradigm on financial globalization, and one that recognizes that more is not necessarily better.
D. Rodrik and A. Subramanian Why Did Financial Globalization Disappoint? IMF Staff Papers 2009

31. FT quotes
BIS Quarterly Review