OVER VIEW OF KEY MESSAGES: MACRO 2 Carl-Johan Dalgaard Department - PowerPoint PPT Presentation

OVER VIEW OF KEY MESSAGES: MACRO 2 Carl-Johan Dalgaard Department of Economics University of Copenhagen

ISSUES AND REGULARITIES 1. Time series evidence: “Kaldorian Facts” and Non-Kaldorian dynam- ics 2. Cross Country Evidence: A. International growth di ff erence B. International income di ff erences C. Global inequality. 2

TIME SERIES EVIDENCE 3

11,0 10,5 10,0 log Real GDP per capita 9,5 9,0 8,5 8,0 7,5 7,0 1870 1885 1900 1915 1930 1945 1960 1975 1990 2005 Figure 1: Log real GDP per capita in the US, 1870-2006. Data source: Johnston and Williamson (2007) In some ways mysterious: Two world wars (total collapse of trade af- ter no. 1; globalization again after end of 2nd), structural change (agriculture-industry-services), mass education, origin of the Welfare State (DNK); female labor participation etc. In spite of this: constant growth at about 2% per year. 4

THEORETICAL PERSPECTIVE The main way in which we can explain this “fact” is as a representation of the steady state growth path In the Solow model ( Ch. 3 and 5) we have, in the steady state, that: ∙ µ K ¶ ∗ ¸ α µ ¶ α ¡ ¢ t 1 − α s 1 − α A 0 (1 + g ) t ≡ y ∗ y ∗ 1 + g ∗ t = A t = y 0 Y n + δ + g Hence log ( y t ) = log ( y 0 ) + t log [(1 + g )] ≈ log ( y 0 ) + g ∗ y t ³ ´ α 1 − α A 0 , and s Hence, the “intercept” (in the fi gure) is given by n + δ + g the slope represents technological progress g ∗ y = g. In the human capital augmented model (ch. 5) the intercept also de- pends on the investment rate in human capital. 5

THEORETICAL PERSPECTIVE In the open economy model growth in income per capita will also need technological change. Hence, the predictions of this model is very much like the basic Solow model. If land enters the production function, the “Solow model” yields a slightly di ff erent result " # t µ X ¶ κ β + κ ∙ µ K ¶ ∗ ¸ α (1 + g ) β/ ( β + κ ) ¡ ¢ t β 1 − α y ∗ 1 − α t = A ≡ y 0 1 + g y 0 (1 + n ) κ/β + κ L 0 Y Hence, the “intercept” is also depends on the land-labor ratio, and the slope represents technological progress and population growth y = (1 + g ) β/ ( β + κ ) 1 + g ∗ (1 + n ) κ/β + κ 6

THEORETICAL PERSPECTIVE In endogenous growth models (ch. 8) g y is endogenously determined. In the “AK” model” ( y t = Ak t ) we have that ( k t +1 /k t ) ∗ − 1 = ( y t +1 /y t ) ∗ − 1 = sA − ( n + δ ) 1 + n and so µ ¶ t ¡ ¢ t 1 + sA − ( n + δ ) y ∗ t = y ∗ 1 + g ∗ ≡ y 0 y 0 1 + n Note, however, that if s (for instance) is increasing over some period in time, g (the slope in Figure 1) should be accelerating (become steeper). It has, in the OECD, while growth has not accelerated... critique. The learning-by-doing model might also suggest L matters to the size of g ∗ y ; scale e ff ects. 7

THEORETICAL PERSPECTIVE In the semi-endogenous growth model (ch. 8) ! α + φ Ã 1 − φ φ 1 − α ¡ ¢ t ≡ y 0 ¡ ¢ t s y ∗ 1 − φ 1 + g ∗ 1 + g ∗ t = L y y g ∗ 0 A + δ φ where 1 + g ∗ 1 − φ . Hence, this model would suggest the level y ≡ (1 + n ) of population matters to the “intercept”, whereas the growth rate of the labor force matters to the growth rate of output. However: Evidence does not seem to support a positive association between g y and n ; rather a negative one. 8

KALDOR’S LIST OF FACTS ( 1) No tendency for GDP per capita growth to decline, constant growth. (2) Constant relative shares (wL/Y, rK/Y). (3) Constant r. THEORY ³ ´ ˜ In general we have assumed y t = A t f k t . Competitive markets imply r = f 0 ³ ´ h ³ ´ − f 0 ³ ´ i ˜ ˜ ˜ ˜ k t , w t = A t f k t k t k In steady state ˜ k t = ˜ k t +1 = ˜ k ∗ . If so, r is constant. Moreover, rK/Y = f 0 ³ k ∗ ´ ³ k ∗ ´ ˜ k ∗ /f ˜ ˜ . Hence relative share are also constant in the steady state. If f is Cobb-Douglas ... 9

NON-KALDORIAN DYNAMICS Currently poor countries rarely display the same sort of “persistency” in growth performance. 7,40 7,30 7,20 7,10 7,00 log GDP per capita 6,90 6,80 6,70 6,60 6,50 6,40 6,30 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 Figure 2: Growth of GDP per capita in Zambia 1955-2000 - No so Kaldorian. Data: Penn World Tables Mark 6.1. Judged from time series evidence such as this (see also the textbook for other illustrations) it is safe to conclude that growth rates are not “relatively constant” over time, in poor places. We want to understand why Kaldor might be right in some places, and not in other places. 10

THEORY: NON-KALDORIAN DYNAMICS In general our models are consistent with Kaldor’s stylized facts, in the steady state. Outside the steady state we do not have (in general) constant relative shares; the real rate of return and the growth rate (in per capita GDP) are not constant either. Outside the steady state (in the Solow model), we have (approxi- mately) ³ ´ k ∗ / ˜ ˜ g k ≈ g + λ log k 0 , where λ is the rate of convergence. Hence, as ˜ k adjusts, the growth rate declines (in absolute value), and r t as well as r t k t /y t changes (in general). 11

CROSS-COUNTRY EVIDENCE 12

A. GROWTH DIFFERENCES .06 CHN GNQ KOR HKG .04 THA MYS ROM JPN SGP IRL LKA LUX PRT ESP LSO growth60_2000 GHA AUT PAK GRC IND EGY ITA IDN CPV BEL MUS FRA TUR ISR MAR FIN NOR PAN SYR .02 DOM GBR ISL USA MWI NPL BRA DNK ETH NLD GAB AUS PRY CHL SWE CIV IRN TTO CAN TZA GNB PHL BEN BRB CHE BFA ECU COL MEX URY ZWE CMR ZAF MLI GTM GMB MOZ COG CRI ARG UGA DZA NZL HND SLV BOL PER BDI TGO ZMB KEN NGA JAM RWA COM 0 SEN GIN VEN JOR TCD NER MDG NIC -.02 7 8 9 10 11 logy60 Figure 3: Growth in GDP per worker 1960-2000 vs. log GDP per worker 1960, 97 countries. Data source: Penn World Tables 6.2 Note : Some countries have been shrinking, on average, for 40 years! Large growth di ff erences: Up to 7 percent per year! Note also: Initially poor are not “outgrowing” initially rich; similar to “Gibrat’s Law of Proportionate E ff ect” ( fi rm’s). 13

A. GROWTH DIFFERENCES If we focus attention ot countries that are “similar”, another picture emerges IRL .035 LUX PRT ESP .03 AUT growth60_2000 GRC ITA BEL .025 FRA NOR .02 GBR ISL USA DNK NLD .015 SWE CAN 9 9.5 10 10.5 logy60 Figure 4: Growth in GDP per worker 1960-2000, 17 original OECD member countries. Data source: Penn World Tables 6.2 . 14

A. GROWTH DIFFERENCES Also true if we look at the poorest countries ... .03 GHA .02 MWI ETH growth60_2000 CIV TZA BEN BFA .01 ZWE CMR MLI MOZ COG UGA BDI NGA TGO ZMB KEN RWA 0 SEN GIN TCD NER -.01 MDG 6.5 7 7.5 8 8.5 logy60 Figure 5: Growth in GDP per worker, 1960-2000: 24 tropical sub-saharan African countries. Data sourve: Penn World Tables 6.2 Our theories better explain why . 15

THEORY: SYSTEMATIC V ARIATIONS Consider the law of motion (approximation) for the Solow model ³ ´ k ∗ / ˜ ˜ g k ≈ g + λ log k 0 This can be viewed as a linear equation (i index for country) ³ ´ ∗ ³ ´ ˜ ˜ g ki = g + λ log k i − λ log k i 0 ³ ´ ∗ ³ ´ ∗ ˜ ˜ If we are considering similar countries we have log k i ≈ log k for all i. Then ³ ´ ³ ´ ∗ ˜ ˜ g ki = a − b log k i 0 , a ≡ g + λ log k , b = λ < 0 and we would expect a clear negative link between g ki and (log) initial capital ˜ k i 0 (or GDP per capita). 16

³ ´ ∗ ³ ´ ∗ ˜ ˜ In samples where countries are very di ff erent, log k i 6 = log k for all i , the same negative association should not (necessarily) arise, unless ³ ´ ∗ ˜ we take the di ff erences in log k i into account (i.e., s, n and so on). ³ ´ ∗ ˜ To fully control for log k i the basic Solow model suggests s K and n . The augmented Solow model would suggest we also need s H . The Solow model with land would suggest X/L 0 should enter as well, and semi-endogenous growth theory would suggest L 0 should enter. The AK endogenous growth model is NOT consistent with this evidence. However an “asymptotic version" can be. 17

THEORY: GROWTH DIFFERENCES Neoclassical growth theory (Ch. 3,4,5,6, (7..see below) ) o ff ers transitional dynamics. Basically we have y ∗ / ˜ g y ≈ g + λ log (˜ y 0 ) growth di ff erences in g are not attractive; hence the “story” is that countries di ff er in terms of their distance to steady state y ∗ / ˜ log (˜ y 0 ) This is a meaningful story, as the model suggests λ is fairly low, implying lengthy transitions. Takes at least 17 years (under plausible parameter values to reach steady state) 18

THEORY: GROWTH DIFFERENCES The drawback of this “story” is that every country with less than g percent growth (say, 2%) per year, are converging from above Given the growth record, this turns out to be systematically the poorest countries Figure 6: Source: Cho and Graham, 1996. Note; The bold faced line is a 45 degree line. 19