1 Four facts on the U.S. historical growth experience, aka the Kaldor facts

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1 1 Four facts on the U.S. historical growth experience, aka the Kaldor facts In 1958 Nicholas Kaldor listed 4 key facts on the long-run growth experience of the US economy in the past century, which have revealed to be still true today and true, to a large extent, in several other developed countries: 1. Thesharesofincomedevotedtocapital( ) and to labor ( ) are roughly constant at, respectively, 13 and 23 of total GDP. 2. The average growth rate per capita has been positive and relatively constant over time (approximately 18% from 1870). 3. Historically, consumption, investment, capital and output have all grown at the same (constant) rate. A consequence is that the great ratios and are constant over time, respectively to 7 and 15. In light of this property, we say that growth is balanced. 4. The real return on capital shows no upward or downward trend, it is constant around 5% The Cobb-Douglas production function is the simplest one that is consistent with fact 1, under the additional assumption of competitive input markets. Suppose Then, from firm s optimization: = (1 ) + = 1 1 = 1 = (1 ) 1 =(1 ) = 1 = µ µ ( + ) =(1 ) As one can see, both the labor share and the capital share of income are independent of time, as consistently with Kaldor fact #1. A caveat to keep in mind is that, in the last 20 years there seems to be a downward trend in the labor share. Data on sources of income (e.g., wages and salaries, dividends, interests, and profits) from the National Accounts can be used to compute and 1 = 1

2 2 Some basic notions of continuous time dynamics In growth theory, it is customary (and convenient) to study models in continuous time. What is the difference between continuous and discrete time? There are two key differences. 1. Notation: instead of we use the notation () so time becomes an argument of our aggregate variables, which are functions of time. 2. Changes of variables over time: consider the difference between and + in the discrete interval of time and take the limit as goes to zero: ( + ) () () lim = () 0 where the "dot" notation indicates the derivative with respect to time. Moreover, the growth rate of in the interval can be written as and taking the limit for 0 ( + ) () () µ ( + ) () 1 lim = 1 ( + ) () lim = 1 () 0 () 0 () () () Finally, note that time derivatives of logarithms are growth rates by simple application of the chain rule: [log ()] = 1 () = () () () 3 Growth Accounting One can use the aggregate production function, in particular the Cobb-Douglas specification, to perform a simple growth-accounting exercise, due to Solow (1957), in order to understand the sources of economic growth. Consider a slightly modified version of theaggregateproductionfunctionasabove,i.e. () = () () [ () ()] 1 2

3 where () is human capital, or quality of labor input. Let s modify slightly this equation as () = () () [ () () ()] 1 where () is the working age population and () the labor force participation rate () (). Take logs and differentiate with respect to time, using the techniques explained above: () () = () () + () () () +(1 ) +(1 ) () () +(1 ) () () () (1) Equation (1) shows that output growth is the sum of four components, from last to first: growth in the quality of labor (), growth in working-age population (), growth in the participation rate (), capital input () growth, plus the growth rate of total factor productivity () Given data on inputs and output, and the capital and income share and 1 that we can calculate from National Accounts as explained above, one can recover residually () which is, otherwise unobserved directly. 1 For this reason, () is often called the Solow residual. In per capita (or, more precisely per worker) terms, the same decomposition becomes = = + +(1 ) +(1 ) + +(1 ) +(1 ) where is income per capita and is capital per capita. In the literature, growth in capital per worker the fact that () isoftenreferredtoascapital deepening. Notethatwehaveused = = 2 = 1 Note that we need also data on (), otherwise our measure of () also includes quality of labor. Quality of labor can be measured directly through average years of education in the population, for example. 3

4 Therefore () = and similarly for We can illustrate the usefulness of the Solow growth decomposition with three examples: 1. In the US From , growth in output per hour worked has been 25%, capital per hour contributed by 08%, quality of labor input for 02% and TFP growth for 15% (from Jones, Table 2.1). The labor productivity slowdown of the 1970s-1980s is due to slow growth in TFP. 2. Countries in South-East Asia (SEA) are typical examples of growth miracles in the past 30 years (see Table 8.4 in Williamson). The growth accounting exercise, performed this time on aggregate output, shows that most of output growth is not due to TFP growth, but to factor accumulation, i.e., capital and labor. The key reason behind this phenomenon is the demographic transition, i.e. a fall in fertility rate and rise in life expectancy. This change in demographics leads to more investment in human capital (Becker s quantity-quality trade-off in children), and to more savings (capital accumulation) for life-cycle reasons. The implications arethatsucheconomicboomistemporary,itcannotlast.itwillexhaustassoon as the demographic transition is complete. 3. Countries in Sub-Saharian Africa (SSA) are typical examples of growth disasters. Growth accounting shows that this disastrous performance is due to extremely low growth. Why such low growth rates of TFP? Current research emphasizes that the key factor in impeding growth in SSA has been the combination of war, corruption and dictatorships which has led to large political and economic instability and extremely low protection of property rights. These are all factors that, in a simple growth accounting exercise, show up as different levels and growth rate of the Solow residuals. An example (in positive) is Botswana, which had growth rates of 7% since 1970 (vis-a-vis no growth for the rest of SSA). Botswana is a stable democracy which ranks in the top 50 countries in the index of economic freedom (compiled by the Heritage Foundation & the Wall Street Journal), while almost all the other countries in SSA rank in the bottom of the country distribution. 4

5 4 Empirics of Economic Growth Before presenting some of the most recent models in growth theory, it is useful to organize our thoughts around a set of key facts that theory should explain. Growth theory is concerned with questions such as: Whyisn tthewholeworlddeveloped?,whythereare countries that grow faster than others for long periods of time? Is there convergence over time among countries? Growth theory provides useful models to rationalize the existence of persistent income disparitiesacrosscountriesandtostudythenatureandthedeterminantsofthegrowth process. We use income per capita (or often, per worker) as a measure of development, where income is measured as Gross Domestic Product, GDP. There are other important measures of development, such as life-expectancy, infant mortality, education, or better measures of quality of life, like consumption and leisure. There are two key reasons why income per capita is preferred: 1) more consistent data (across countries and over time) are available; 2) the theories have predictions mainly in terms of. The comparison across countries is done with Purchase-Power-Parity (PPP) adjusted exchange rates, i.e. a similar bundle of goods (including non-tradeable goods) is compared in various countries. We can distinguish three main data sources for research on economic growth: 1. Historical annual data for 16 countries for the period from Maddison (1994) 2. Annual data on about 30 variables for about 167 countries over some or all the years assembled by Summers-Heston (1991). These are called Penn World Tables and are available at 3. There are many websites dedicated to economic growth. See for example the economic growth page of the World Bank, at A nice introductory reading on the empirics of economic growth is the book by Robert Barro, Determinants of Economic Growth, MIT Press. Below, we present some empirical regularities on growth obtained from the datasets mentioned above. 5

6 4.1 Facts on Cross-Country Income Disparity 1. There is a great disparity across countries in terms of income per capita. In 1985 the top 5% among world s countries was 20 times richer than the bottom 5%. (Table 1.1, Jones). GDP per capita in the US is 40 times bigger than in Ethiopia: workers in Ethiopia need to work 30 years, on average, to earn what a US worker earns in one year. 2. The world distribution of income per capita across countries is almost uniform. But the distribution of the world population by income per capita is very skewed, essentially because of the presence of two huge countries, China and India, in the bottom 10%. 3. World income disparity has not increased or decreased in the post-war period. 4. The world distribution of income per capita has shifted up: the richer got richer, but the poorer got richer too. 5. World growth has been faster in the 1950 s and 1960 s than in the pre-war period. Since the 1970 s growth has slowed down again, but it has picked up since the 1990s. 6. There is little persistence in growth rates: correlation in Figure 3 is only There are growth miracles and growth disasters: many examples of disasters are in Africa and Latin America. Argentina is the latest disaster. 8. Note that small differences in annual growth rate compound to huge differences in income per capita in the long-run. Consider two countries initially equal, but growing at 2% and 3% respectively for 82 years: (102) 82 =5and (103) 82 =11 The math shows that the second country will be twice as rich as the first one at the end of the period. 6

7 9. Growth rates are not correlated to initial levels of income per capita. In other words, there is no absolute convergence. The formal definition of absolute convergence is +1 = ( ),where 0 0 i.e. the growth rate is a decreasing function of the initial level of income. 10. Income per capita is strongly correlated with capital-output ratio (or investmentoutput ratio) (+), population growth rate (-), school enrollment rates (+), government size (-), political rights (+), financial development (+), trade openness (+), relative price of investment (-) Controlling for the characteristics above, growth rates are negatively correlated with initial levels of income per capita... there is some conditional convergence, i.e. convergence conditional on a number of observable characteristics of the countries. Why? The models we will study imply that these characteristics determine the steady-state income per capita of each country and that growth is proportional to the distance from the steady-state. The formal definition of conditional convergence is +1 = ( ),where 0 0 i.e., the growth rate is positively associated to the distance between current income and steady-state income per capita. Simple regression analyses can make this point clear. 2 Political rights is an index that takes into account democratic rights such as freedom of speech, fredom of press, etc. Financial development is measured by the ratio of liquid assets (currency held outside the banking system+interest-bearing assets held by bank and nonbank financial intermediaries) to GDP. 7

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