CLASS #14: ECONOMIC GROWTH: SOME EMPIRICAL REGULARITIES

• The rule of 69
• Accounting for growth
• Some empirical regularities about growth

If Y_t is GDP, the growth rate of GDP is defined as:

$$G_t \equiv \frac{Y_t-Y_{t-1}}{Y_{t-1}} \simeq \ln{Y_t}-\ln{Y_{t-1}}$$

We are interested in GDP per capita (better measure of living standards):

$$y_t \equiv \frac{Y_t}{N_t}$$

therefore the growth rate in GDP per capita is

$$g_t \equiv \ln y_t-\ln y_{t-1}=\ln{Y_t}-\ln{Y_{t-1}}-(\ln{N_t}-\ln{N_{t-1}})$$

Some facts about growth rates.

• The growth rate over n years is the sum of the annual growth rates:
  
  $$\ln{y_n}-\ln{y_0}=\sum_{t=1}^n(\ln{y_t}-\ln{y_{t-1}}) =ng$$
  
  
  if the growth rate is constant.
  The Rule of 69
  or
  Small differences in growth rates in the long run matter

• If a country grows at the growth rate of g per year, how long would it take for the country to double its GDP per capita?
  
  $$n=\frac{(\ln{2y_0}-\ln{y_0})}g=\frac{\ln{2}}g =\frac{69}{100 \times g}$$
  
  

• question: If the difference in growth rates between country 1 and country 2 is g, and if the two countries start at the same GDP level, how long does it take for country 1 to have twice the level of income of country 2?

Countries	growth rate	doubling time
United States	2.3%	30
Avg industrial nations	3.6%	20
India	1.4%	49
Egypt	3.4%	20
Japan	7.1%	10
Taiwan	6.5%	11
Singapore	7.5%	9

I do not see how one can look at figures like these without seeing them as possibilities. Is there some action a government of India could take that would lead the Indian economy to grow like Indonesia or Egypt's? If so, what exactly? If not, what is it about the ``nature of India" that makes it so? The consequences for human welfare involved in questions like these are simply staggering...

Nobel Prize winner Robert E. Lucas (1989)

B

[tbp] 1985 US $, source: Maddison

Countries	1870	1913	1950	1989	1870-1989
US	2,247	4,854	8,611	18,317	1.8
UK	2,610	4,024	5,651	13,468	1.4
Germany	1,300	2,606	3,339	13,989	2.0
Japan	618	1,114	1,563	15,101	2.7

E

Growth as a recent phenomenon of world history

Growth in Europe (Maddison 1982)

Epoch	growth rate	doubling time
Agrarianism	0.0%	$\infty$
Advanced Agrarianism	0.1%	690
Merchant Capitalism	0.2%	345
Capitalism	1.6%	43

Growth Accounting

Assume Cobb-Douglas production function. If we take the logs of the production function:

$$ln(Y_t) = ln(A_t) + \alpha ln(K_t) + (1-\alpha) ln(N_t)$$

at time t and t-1 and subtract:

ln(Y_t) -ln(Y_t-1) =ln(A_t)-ln(A_t-1) +

$$+ \alpha (ln(K_t)-ln(K_{t-1}) ) + (1-\alpha) (ln(N_t)-ln(N_{t-1}))$$

Alternatively, output per capita can be written as:

$$ln(y_t) = ln(A_t) + \alpha ln(k_t)$$

So we have that:

$$ln(y_t) -ln(y_{t-1}) = ln(A_t)-ln(A_{t-1}) + \alpha (ln(k_t)-ln(k_{t-1}) )$$

Total Factor Productivity (``Solow Residual")

The part of growth in output that is not explained by growth in the two inputs, labor and capital.

ln(A_t)-ln(A_t-1) = ln(Y_t) -ln(Y_t-1)-

$$-\alpha (ln(K_t)-ln(K_{t-1}) ) - (1-\alpha) (ln(N_t)-ln(N_{t-1}))$$

The Asian Miracle? (Young 1982) TFP growth in South East Asia

Hong Kong	2.3%
Taiwan	2.6%
South Korea	1.7%
Singapore	0.2%
OECD	0.7%
Europe	1.3%

Inspiration (Hong Kong, Taiwan ...) versus Perspiration (Singapore).

Empirical regularities of economic growth (Romer 1989):

• Output per capita shows continuing growth.
• There are wide differences in growth rates across countries.
• The capital/output ratio is steady.
• The growth rate of output is not fully explained by the growth of inputs: growth accounting leaves a residual.
• Across countries, how much a country grows on average shows no correlation with how rich or poor a country is: it is not the case that poor countries grow faster than rich countries or viceversa.
• Growth in the volume of trade is positively correlated with the growth in output.
• Population growth is negatively correlated with the level of income.

Accounting for human capital

What you want to measure is not the number of bodies you put at work, but their input to production, i.e., the efficiency of each hour put into production. This depends on education - human capital.

Assume Cobb-Douglas production function, with human capital:

$$Y_t=A_tK_t^{\alpha}H_t^{\alpha}N_t^{1-2\alpha}$$

where H is human capital, or

$$y_t=A_tk_t^{\alpha}h_t^{\alpha}$$

where k and h are respectively physical and human capital per worker.

This means that per capita output growth is:

$$\ln{y_{t+1}}-\ln{y_t}=$$

$$=\alpha(\ln{k_{t+1}}-\ln{k_t})+ \alpha(\ln{h_{t+1}} -\ln{h_t})+\ln{A_{t+1}}-\ln{A_t}$$

You can make assumptions on how human capital enters the production function, try to measure it (years of schooling per capita), and see whether it explains differences in growth - and in levels.

What did we learn?

• Growth is really important!
• Small differences in growth rates matter!
• Growth depends on capital accumulation but also ...
• on productivity (the Solow residual - see Hong Kong!)
• ... and on human capital.