Chapters 7 and 8 (Part II)

Chapters 7 and 8 (Part II) • Objective of this lecture • Learn about how to explain the differences in growth performance of different countries using the Solow model • Learn about TFP growth and the Solow residuals

(n+g+)k ska Graphical view k=s ka  (n +g+)k Investment, break-even investment k<0 k>0 Capital per effective labor, k k*

Rate of inflow, rate of outflow gk>0 n+g+d gk<0 ska-1 Capital per effective labor, k k* Graphical view(not in textbook) gk = k /k=s ka-1  (n +g+)

Variable Symbol Steady-state growth rate Steady-State Growth Rates in the Solow Model (to be derived in class) Capital per effective labor k =K/(LE ) 0 Output per effective labor y =Y/(LE ) 0 Output per capita (Y/L) =yE g Total output Y =yE L n + g

Explaining the variety of growth experiences • If all the countries were in their respective steady states, we could explain their differences in growth rate of real GDP per capita only in terms of differences in technological growth rates g. • But surely, a lot of developing countries are still below their steady states. In this case, we could explain their differences in growth performance by looking at other differences.

Variable Symbol Growth rate below or beyond the steady state Growth Rates below or beyond the steady state (to be derived in class) Capital per effective labor k =K/(LE ) gk Output per effective labor y =Y/(LE ) agk Output per capita (Y/L) =yE g + agk Total output Y =yE L n + g + agk

Explaining the variety of growth experiences • In what follows, we make use of the graphical analysis of the dynamic equation gk = k /k=s ka-1  (n +g +) to explain the variety of growth experiences • We focus on the differences in the distance from the steady state, the savings rate s, population growth rate n and the technological growth rate g as explanatory variables.

Savings rates and growth performance (not in textbook) gk = k /k=s ka-1  (n +g+) Rate of inflow, rate of outflow gk 2 gk 1 n+g+d s2 ka-1 s1 ka-1 Capital per effective labor, k k1=k2 k1* k2*

Savings rates and growth performances • Growth rate of real GDP per capita is given by • gY/L = g + a gk • From the above analysis, other things equal (so g and a are treated as the same), the higher the savings rate, the higher gk is. Hence, the higher the current growth rate of real GDP per capita gY/L.

Population growth and economic growth performance (not in textbook) gk = k /k=s ka-1  (n +g+) Rate of inflow, rate of outflow gk 1 n1+g+d gk 2 n2+g+d s ka-1 Capital per effective labor, k k1=k2 k1* k2*

Population growth and economic growth performances • Growth rate of real GDP per capita is given by • gY/L = g + a gk • From the above analysis, other things equal (so g and a are treated as the same) the higher the population growth rate, the lower gk is. Hence, the lower the current growth rate of real GDP per capita gY/L.

gk = k /k=s ka-1  (n +g+) Rate of inflow, rate of outflow gk poor gk rich n+g+d ska-1 Capital per effective labor, k kpoor krich k* Convergence(not in textbook)

Convergence • Growth rate of real GDP per capita (Y/L) is given by • gY/L = g +a gk • From the above analysis, other things equal, the farther a country is from the steady state, the higher the growth rate of real GDP per capita. • Therefore, Solow model predicts that, other things equal, “poor” countries (with lower Y/L and K/L ) should grow faster than “rich” ones.

Absolute Convergence • If absolute (or unconditional) convergence truly happens, then the income gap between rich & poor countries would shrink over time, and living standards “converge.” • In real world, many poor countries do NOT grow faster than rich ones. That is, absolute (or unconditional) convergence is not generally observed. Does this mean the Solow model fails?

Conditional Convergence • No, because “other things” aren’t equal. • In samples of countries with similar savings & pop. growth rates, income gaps shrink about 2%/year. • In larger samples, if one controls for differences in saving, population growth, and human capital, incomes converge by about 2%/year. • What the Solow model really predicts is conditional convergence - countries converge to their own steady states, which are determined by saving, population growth, and education. And this prediction comes true in the real world.

Long-run and transitional growth • From the above analyses, the savings rate, the population growth rate and the convergence effect only affect the term gk in Real GDP per capita growth rate = g + a gk • Eventually, as economies reach their respective steady states, gk=0. Real GDP per capita growth rate in the long run is only affected by g. Higher savings rate, lower population growth rate and lower initial real GDP per capita only lead to higher real GDP per capita growth rate in the meantime but not in the eventual steady states.

Technological growth rates and growth performances • Though savings rate and population growth rate only affect real GDP per capita growth rate in the transition, technological growth rate affects real GDP per capita growth rate both in the transition and in the long run. • Obviously, in the long run the growth rate of real GDP per capita is given by g. So higher g means higher real GDP per capita growth rate. How does different g affect transitional growth?

Technological growth and economic growth performance (not in textbook) gk = k /k=s ka-1  (n +g+) Rate of inflow, rate of outflow gk 1 n+g1+d gk 2 Dgk=gk2-gk1 =g1-g2 n+g2+d s ka-1 Capital per effective labor, k k1=k2 k1* k2*

Technological growth and economic growth performance (not in textbook) • Although country with a higher technological growth g1 has a lower gk, it turns out that such a country commands a higher gY/L. From the graph, gk2-gk1 =g1-g2 • Now, gY/L=g+agk. So, gY/L1-gY/L2 =(g1+agk1)– (g2+agk2) =(g1–g2)+a(gk1-gk2) =(g1–g2)-a (g1–g2) =(1-a)(g1–g2)>0

Case Study: the East Asian Miracles • East Asian miraculous performance: is it purely catch-up effect or can such miraculous growth of 6% be sustained? • Surely, East Asia might have done everything right: high savings, attraction of foreign investment through secure property rights, promotion of education, outward-oriented trade policy, control of population growth.

The East Asian Miracles • Such good policies will lead to growth increase for a while, but eventually diminishing returns will set in. For sustained growth performance, one needs technological improvement. • In practice, technological improvement is measured by something called total factor productivity (TFP) growth rate.

TFP • Think about the Cobb-Douglas production function Y=Ka(EL)1-a. We could rewrite it as Y=A KaL1-a where A=E1-a. We call A the total factor productivity (TFP).

The Solow Residual From Y=A KaL1-a We use the rules 1-3 in mathematical digression to obtain gY =gA+agK + (1-a)gL To obtain the TFP growth rate (gA), we rearrange the above equation to get gA= gY - agK - (1-a)gL The TFP growth rate obtained this way is called the Solow residual

TFP growth rates across countries

Implications of TFP growth findings • The results from Young (1995) and later on popularized by Krugman imply that the East Asian “miraculous” growth is nothing “mysterious”. TFP growth of these E. Asian countries is similar to TFP growth of the more advanced countries. • The prediction is that DMR will eventually set in and growth of these countries will diminish as time passes. (Many see the E. Asian debacle in 1998 as a sign of DMR setting in.)

Chapters 7 and 8 (Part II)