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1 Macroeconomics LECTURE SLIDES SET 6 Professor Antonio Ciccone Macroeconomics Set 6 Slide 2 2 Ideas and Economic Growth Macroeconomics Set 6 Slide 3 3 Producing output versus ideas Ideas: non-rival, accumulable input Ideas: may be excludable (patents, secrecy) or not Ideas: producing them lowers current, but increases future output Macroeconomics Set 6 Slide 4 4 Producing output versus ideas Question: what is the growth process for a given allocation of inputs between producing output and producing ideas? Characterize the join evolution of ideas and output in the spirit of Solow Macroeconomics Set 6 Slide 5 5 1. A FRAMEWORK FOR ANALYZING GROWTH WITH RESEARCH AND DEVELOPMENT Quantity of output produced fraction of total capital stock used in production fraction of total labor force used in production taken to be exogenous; in the spirit of Solow Slide 6 6 = level of technology = stock of ideas ideas: non-rival inputs = new ideas, which are created by using capital, labor, and old ideas in the RESEARCH AND DEVELOPMENT (R&D) process Macroeconomics Set 6 Slide 7 7 Production of new ideas Research and Development (R&D) technology fraction of total capital stock used in R&D fraction of total labor force used in R&D taken to be exogenous; this is in the spirit of Solow Slide 8 8 Returns to scale to K and L in production of IDEAS could be increasing or decreasing: DECREASING: replicating inputs could lead to same discoveries being made twice INCREASING: doubling inputs could lead to more than twice the discoveries because of interactions among researchers ( the whole is more than sum of its parts ) Macroeconomics Set 6 Slide 9 9 Also, what is the link between stock of ideas and new ideas? presumably : OLD ideas are useful for developing new ideas : doubling stock, doubles discoveries holding inputs L and K constant : effect of stock of ideas on creation less than proportional : effect of stock of ideas on creation more than proportional Macroeconomics Set 6 Slide 10 10 : ideas keep growing at same rate even if resources allocated to R&D constant growth of ideas accelerates when resources allocated to R&D constant to keep growth of ideas constant, more and more resources must be allocated to R&D Macroeconomics Set 6 Slide 11 11 2. GROWTH WITH RESEARCH AND DEVELOPMENT: THE CASE WITHOUT CAPITAL Quantity of output produced Production of new ideas Population growth (exogenous): Macroeconomics Set 6 Slide 12 12 Growth of ideas ( ) Macroeconomics Set 6 Slide 13 13 CASE 1: Balanced (constant) growth path Macroeconomics Set 6 Slide 14 14 Is the BGP stable? Graph on the vertical axis against on the horizontal axis Check that is increasing when below and decreasing when above Macroeconomics Set 6 Slide 15 15 0 STABILITY OF BGP Slide 16 16 Note that implies that a faster population growth n translates into faster growth of ideas in the balanced growth path. Is there empirical support for the positive relationship between n and the long run growth rate? Hard to test as we need long time series for that; but Michael Kremer 1993, QJE used population growth data going back to 1 Million B.C. Macroeconomics Set 6 Slide 17 17 Why does an increase in not raise the long run growth rate? Reason analogous to why increase in savings rate s in the Solow model does not increase long run growth: Decreasing returns Note that yielded Increase in a l increase the short-run growth rate of ideas But when 18 IMPORTANT TO NOTE: Balanced growth path growth rate: there can only be long run growth of ideas and output if: n>0 if n=0, there is NO long run growth Macroeconomics Set 6 Slide 19 19 R&D and endognous growth Hence, there can be long run growth even without exogenous technological progress BUT the growth rate is linked to population growth, which we dont usually think of as a policy parameter Macroeconomics Set 6 Slide 20 20 CASE 2: Hence implies ever accelerating growth Macroeconomics Set 6 Slide 21 21 In this case, a small increase in ends up having a very large effect on the stock of ideas in the long run An increase in implies short term increase in growth of ideas (as before) these additional ideas further increase the growth of ideas when for any future time t, the growth rate will be higher after the increase in Macroeconomics Set 6 Slide 22 22 CASE 3: NOW, there is long run growth even if n=0!!! Macroeconomics Set 6 Slide 23 23 Population Growth and Technological Change One Million B.C. to 1990 Macroeconomics Set 6 Slide 24 24 How can we detect the long-run impact of ideas? 1)Presumably, over most of human history, new ideas where simply the by-product of human acticity. So let us imagine that the number of new ideas is proportional to the number of people alive at some point in time. 2)If we had a measure of TFP for a very very long time, we could check on the link between TFP growth an population. But we do not. 3)The only data that we have for a very very long time is population size. The question is therefore how can we use population data to find out about the link between population and the number of new ideas? Macroeconomics Set 6 Slide 25 25 How can we detect the long-run impact of ideas? 4) Malthusian hypothesis: over much of human history, TFP growth was offset by population growth. 5) As a result, we can observe TFP growth by looking at population growth. Macroeconomics Set 6 Slide 26 26 TFP Growth and Decreasing Returns to Labor Assume the following production function: where: indicates the level of technological progress is population is land At least for a pre-industrial society, it may make sense to have only labour and land as production inputs. Note that the production function has constant returns to scale: the replication argument is valid! (ie, double the amounts of input, and you double output) Macroeconomics Set 6 Slide 27 27 The Malthusian Hypothesis Now express the production function in per-capita terms: and assume that population increases when is above some subsistence level. This will reduce output per capita, so that it is reasonable to assume - if population growth reacts fast enough - that population will constantly adjust such that always holds. Macroeconomics Set 6 Slide 28 28 Malthusian Population Level We can solve for the population level that corresponds to What does it mean? In the absence of changes in, population will be constant Ceteris paribus, population will be proportional to land area If separate regions have different levels of technology, population or population density will be increasing in Macroeconomics Set 6 Slide 29 29 CONSTANT Technological Progress and Population Growth Now: enter technological progress. Assume What does this imply for population growth? implies Population will grow at a constant rate. True? Macroeconomics Set 6 Slide 30 30 NOTE: Population of 3 billions was reached around 1900. Slide 31 31 New Ideas and Population If every individual has the same probability of inventing something new, and HENCE Population growth is itself proportional to population, which appears true over much of human history. Macroeconomics Set 6 Slide 32 32 A Natural Experiment Consider a "natural experiment": the end of the last ice age around 10 000 B.C., when previously connected land masses (Eurasia+Africa, the Americas, Australia, Tasmania) were separated and technological diffusion wasn't possible any more. Assumptions: These 4 regions had shared the same basic technology up to that point. Hence, their populations must have been proportional to the land areas (larger areas more population). Macroeconomics Set 6 Slide 33 33 4 Separated Regions Macroeconomics Set 6 Slide 34 34 The natural experiment: results Macroeconomics Set 6