Economics 208. Lecture 6. Cross-Country Convergence

Transcription

1 Economics 208 Lecture 6 Cross-Country Convergence February 15, 2007

2 Convergence Facts: Great divergence Then club convergence

3 4.5 Log Income per Capita Western Europe Western Offshoots Japan Latin America Eastern Europe & Former USSR Asia (excluding Japan) Africa

4 Log Per Capita Income, 15 richest countries in ,000 10,000 US Switz NZ Austral Can Den UK Swed NL Nor Belg Fr Fin Germ Austria 1,

5 10,000 1,000 US(normalized) Mauritania Mali Cape Verde China Mongolia Burma Burkina Faso Tanzania Botswana Burundi Malawi Lesotho Guinea GuineaBissau Ethiopio+Eritrea

6 Solow model can t account for great divergence or for countries outside the convergence club (all countries should have the same long run growth rate) AK model can t account for the convergence club (all countries should have an independent growth rate) Will derive a Schumpeterian model of club convergence Relies on technology transfer and Gerschenkron s advantage of backwardness.

7 Basic elements Y t L Ait x it di, it p it 1 x it A it, where 1 / 1 1 Technology transfer Innovations make use of global knowledge A it A t A i,t 1 with probability it with probability 1 it where A t is the world technology frontier In equilibrium it for all i, t where g is given A t 1 g A t 1.

8 The advantage of backwardness Average productivity A t A it dt Productivity growth A t A t 1 A t 1 A t A t 1 A t A t 1 g t A t A t 1 A t 1 A t A t 1 A t 1 prod y growth frequency size of innovation prod y growth absorptive capacity gap 1. far from frontier big gap large innovations g t g distance shrinks 2. close to frontier small innovations g t g distance grows 3. Some intermediate distance is a stable steady state: g t g distance constant

9 More formally A t A t 1 A t 1 So in terms of proximity a t A t /A t a t 1 1 g a t 1 which converges in the long run to a 1 g g a t 45 degree μ 1 μ a 1+ g + t 1 μ a 0 a * a 1 a t-1

10 Steady state a 1 g g Main implications 1. All countries with 0 converge in growth rate, since a 0 2. Countries with no innovation are not part of the convergence club 3. For club members, determines relative income in the long run, not growth 4. So the theory explains a. the world growth rate b. each (member) country s relative productivity

11 Research arbitrage Innovation technology N t c A t 2 /2 A t, 0 where N t is R&D expenditure Assume (so 1) The equilibrium maximizes A t c A t 2 /2 A t Case 1: If then the first-order condition c implies / 0 Case 2: If then the maximization problem has no positive solution, so 0

12 Finance as a source of divergence So far we have supposed that the frequency of innovations is independent of distance to frontier. But with finance constraints it might vary with distance and create a disadvantage to backwardness As frontier advances you need bigger investments to keep innovating at the same frequency (with the same probability) But far from the frontier you may be limited by local incomes Therefore the frequency of innovations decreases when far from frontier Whether or not a country converges depends on whether the advantage of backwardness (increased size) outweighs the disadvantage (frequency).

13 Suppose the credit multiplier: with c t 1 A t 1 w t c t t t 2 /2, Since w t A t c t 1 a t where 1 g 1. When binding, increasing in proximity a t a t a t 2. More likely to be binding far from frontier (a small) or with low financial development ( small) at / Three possible cases, depending on degree of financial development

14 a t g a t a t+1 ( ) a t F 1 ( ) a t F 2 45 o 0 a 0 a() c * a a t Case 1: A high degree of financial development. Country is not credit constrained at the steady state

15 a t g a t a t+1 45 o ( ) a t F 2 ( ) a t F 1 0 a a() c 0 â * a a t Case 2: An intermediate degree of financial development. Country is credit constrained at the steady state but still converges to a positive distance a.

16 a t g a t a t+1 45 o ( ) a t F 1 ( ) a t F 2 0 a 0 * a a t Case 3: A low degree of financial development. Country is so severely constrained that the only steady state is at a 0. The country s growth rate falls to something less than that of the world frontier.

17 Evidence Aghion, Howitt and Mayer-Foulkes (2005): g i 0 f F i y y i fy F i y i x X i i g i is average per-capita GDP growth, F i financial development (private credit) y i initial (1960) log of per-capita GDP X i other regressors all expressed as differential from US where g i i y i y i y i 0 f F i x X i i y fy F i (steady state) i y fy F i (convergence speed if 0) So if y 0 and fy 0 then financial underdevelopment can cause divergence.

18 Table 4: Growth, Financial Intermediation, and Initial Gap in GDP per capita Private Credit IV using Legal Origins IV using Initial Values OLS Liquid Liabilities Bank Assets Commer - Central Private Credit Liquid Liabilities Bank Assets Commer - Central Private Credit Liquid Liabilities Bank Assets Commer - Central Constant 2.065* * 1.97* 1.74* ** 2.07** 3.06 (2.06) (1.84) (1.79) (0.04) (2.36) (2.16) (2.29) (0.71) (3.43) (3.26) (2.89) (0.94) F (-0.93) (-1.04) (-1.07) 0.00 (-0.23) (0.11) (-0.11) (-0.22) (-1.29) (-1.07) (-0.96) (-0.29) y gap 1.51** 2.65** 1.89** * 0.97* 0.81* ** 1.62** 1.35** (3.14) (3.12) (3.57) (1.04) (2.29) (2.02) (2.11) (0.25) (4.05) (3.81) (3.74) (1.68) Fy gap -0.06** -0.08** -0.08** ** -0.02* -0.3** ** -0.04** -0.05** (-5.35) (-3.68) (-5.07) (-1.29) (-3.71) (-2.48) (-3.14) (-7.02) (-4.74) (-5.94) (-1.81) first-stage p-value: F first-stage p-value:fy p-value of Sargan test R # obs Notes: Dependent variable: average growth rate of per-capita real GDP, F is average Financial Intermediation , y gap is the difference between log per-capita GDP 1960 in each country and the USA. (t-statistics in parentheses) ** significant at 1% level * significant at 5% level + significant at 10% level

19 Summary 1. Solow model a. Conditional convergence in levels occurs through capital accumulation. b. Absolute convergence in growth rate because technological progress is the same for all 2. AK model can t explain convergence 3. Schumpeterian approach a. Conditional convergence in levels for club members, occurs through technology transfer b. Absolute convergence in growth rates for club members c. Club membership defined by profitability of innovation, especially financial conditions d. Non members diverge in levels and growth rate.