Growth transmission. Econ 307. Assume. How much borrowing should be done? Implications for growth A B A B

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1 Growt transmission Econ 307 Lecture 5 GDP levels differ dramatically across countries Wy does tis not open up uge gains from trade? According to te most simple model, very low GDP countries sould ave very ig returns to capital, and very low wages Assume Tecnologies te same Human capital quality is te same Ten opening capital markets would lead to large flows from ig income to low income countries Ric world I Current account surpluses S I Poor world Current account deficits S Autarky interest rates World interest rate A country s investment is divorced from its savings Implications for growt Te `catc-up rate sould be very very ig In standard model, you d move capital until f A '( k A ) r W f B '( k B ) A B A B k k y y How muc borrowing sould be done? Say tat a very poor economy starts wit no effective capital. It as to borrow all its capital (and can t borrow for consumption). Ten its capital stock would be equal to its debt It sould borrow until te return on capital equals te world rate of return

2 Implies a uge debt-gdp ratio r K Sare of capital.33, world rate of return equal to 0.06, ten debt is 5.5 times GDP Empirical observations sow: Generally a relatively small volume of capital flows from ric to poor (sometimes te oter way) Catc up is very slow, or even non-existent Debt GDP rarely goes over 00 percent Now we want to look more closely at te problem of te diffusion of growt across countries Were can explanation come from? Assume tat tecnologies are te same across countries (A s te same), but quality of uman capital different (we ve discussed tis somewat before) Lucas paper Assume tat tecnologies and uman capital are te same across countries, but tere are capital market imperfections, wic prevent poor countries from borrowing enoug Explanations contd.. Assume tat tecnologies differ because poor countries cannot implement or utilize tecnologies up to te `world tecnology frontier Jones capter 6 Human capital explanation y A k r A k If tecnologies te same, ten: ( ) ( ) A A a A r y B B B r y Wit equal uman capital, and capital sare equal to.33, ten tis is /00 for differences in GDP of magnitude 0 Use Jones estimate of 2.2 becomes /25 still very large

3 Lucas suggestion: external effects of uman capital γ y A k Higer average uman capital makes everyone more productive On average, we ave Re-do estimates: ( ) + γ ( ) A A a A r y B B B r y Plugging in numbers brings te ratio down to /0. Still a uge gap How to explain possibilities are structure differences in TFP, - property rigts, political stability, etc. Note tat savings rates cannot be part of differences ere we ve assume perfect capital mobility But evidence is tat savings and investment quite tigtly linked I S u Is te savings `retention coefficient Tis is estimated to be quite ig above.6 for recent data However, tere is lot of debate about tis `Migt suggest capital market imperfections One approac to capital market imperfections Extend te Mankiw Romer and Weil formulation model of bot uman and pysical capital, but countries can only borrow against pysical capital Production Function Depends on capital, uman capital, and unskilled labour BK H L β β Economy s Budget Constraint Accumulation of uman capital plus pysical capital less foreign debt equals income less consumption less debt payments less depreciation H + K D rd C δ H

4 Assume constant savings rate Also, assume country can borrow only against pysical capital, and it wises to borrow to te maximum, so tat DK (somewat unrealistic) Also, te marginal product of capital will equal te world interest rate, as before r K K Gives solution for K β β BH L r Solution like te Solow model Results ( ) H sφ BH β L β δ H Φ β < Is a constant Sows tat convergence for an open economy may be similar to a closed economy Speed of convergence depends upon β Intuition ere Want to accumulate bot uman and pysical capital Can only borrow against pysical capital Optimal borrowing is based on stock of uman capital As uman capital accumulates, borrow more so convergence is not instantaneous, as in naïve model Human and pysical capital complements in development process Convergence speed Slower tan a closed economy wit capital sare β Faster tan a closed economy wit capital sare β+

5 Criticisms of tis model Implies too ig speed of adjustment still Implies very ig level of debt to GDP More general criticism We ave taken tecnology as given in all countries But one of problems of development is countries using different tecnologies In te abstract, we migt expect tat tecnologies, wic are just knowledge, could be applied equally anywere Wy is tis not te case? Jones Capter 6 Take a small (periperal) country Wy can t it produce at te world tecnology frontier? Argument is new tecnologies are complementary wit skills need to improve skills so as to adapt tecnologies Leads to situation were skill levels restrict tecnology aquisition Production function Labour and capital, as in Romer L x() i di 0 Restriction on span of tecnology is not A, but (assumption is <A) As before, x s are capital goods, so xk Leads to production function Similar to basic Solow model ( L) K Key question is, ow does accumulate? Assume ave to devote time to build up uman capital Accumulation equation: µ ψ e u γ γ A Function of time in education u, te world tecnology frontier A, and existing stock of uman capital

6 Aspects of tis World frontier grows at rate g Growt in uman capital slower, closer to frontier (arder to learn) γ ψ A µ e u Assume constant savings rate Capital accumulation equation K K s dk L L k sk dk nk k Steady State output per worker y * s * d + g+ n s µ γ ψ u A e d + g+ n g Explanation Steady state GDP reflects basic savings determination of GDP, for given tecnology In addition, reflects efforts devoted to skill acquisition in order to build up tecnologies How does te economy adjust? Say tat beginning in a low skill economy, we ave very low relative to A, te world frontier We can describe te catc-up in two relationsips First ˆ ˆ ˆ ( ) ˆ, ˆ K, ˆ k sk d+ g+ n k k AL A Dynamics of ratio of capital to effective labour at te world frontier k ˆ* s ( d + g+ n) Steady state

7 ĥ Gives dynamic relationsip between k and k 0 Second g ˆ ψ ˆ e u γ µ ˆ Dynamics of skills to world tecnology frontier ˆ * ( ) ψ µ e u γ Steady State Left of locus, k increasing. Rigt of locus, k decreasing ˆk ĥ Gives dynamic relationsip in ĥ Put togeter k 0 0 * ĥ 0 Economy will converge to steady state from any initial point Below locus, increasing. Above locus, decreasing ˆk ˆk * ˆk Now use to sow tat Increase in resources in education will increase steady state k and. Leads to bot a rise in skills-frontier ratio and capitalfrontier ratio Increase in savings rates will increase capital to frontier ratio alone