ECON 206 MACROECONOMIC ANALYSIS Roumen Vesselinov Class # 10

Transcription

1 ECON 206 MACROECONOMIC ANALYSIS Roumen Vesselinov Classs # 10

2 Growth an nd Ideas III Chapter 6 (3 of 3)

3 Our objectives today Wrap up Chapter 6 on Growth and Ideas and wrap up growth We interpret and discuss the Romer Model s solution We will talk about how the Solow and Romer models can be merged together to offer a more complete view of growth... We will discuss growth accounting and wrap up

4 Review of last time: The Romer Model features two sectors goods production (Y) and idea production (A) Under these circumstan ces, the growth rate of ideas (A) is a constant,, so we know that At is: And income per capita, yt, is This is exponential growth in income per capita! It is unique in what we have done so far, and it derives from the nonrivalry of ideas

5 What affects growth in the Romer Model? In this model, there 1. the size of the 2. the share of the population in science or ideas 3. the productivity of scientists 4. the starting leve el of ideas are 4 parameters: population What happens when we change these parameters? In the Romer Model, there are no transition dyn namics, only a balanced growth path

6 When increases, wha at happens to growth in yt? Ratio scale: yt At, growth is constant at Slope = Slope = Is this realistic?! If, growth increases to Over the last century or so, not really! But over long historical periods, with steady population and no growth, yes! Time, t

7 When increases, the share of scientists increases. What hap pens to yt?? Ratio scale: At, growth is constant at Slope = Slope = If, growth increases to but... The reallocation of labor toward ideas removes labor from goods production: yt must initially fall and then grow faster! Time, t

8 What can we say about our two chief models: Solow and Romer? We have seen how the So olow Model explains some things pretty well. Key among them: Why some countries grow at different rates for decades at a time based on how far they are from their steady states For example, postwar Japa an and Germany; recently Korea, which has much higher saving/investment than other SE Asian countries Now, we have seen how the Romer Model can explain that critical element left unexplained by the Solow Model: the source of long-run grow wth We can combine these two models to get a more complete view of growth, and the combination will include all of the same insights from each

9 What would the com mbined Solow-Romer model look like, if we studied it? Ideas production and goods production, just like the Romer model, combined with a cap pital stock, Kt, like in the Solow model Unfortunately, like the Rom mer model, we can t really use graphs to solve, like we did with the Solow model Instead, we d havetousem math But the key take-aways are the insights, not the math, and this combined model provid des an important combination of insights we don t have Let s just cut to the chase and examine the model s output for its insights

10 The setup Like always, production is Cobb-Douglas From the Solow Model, the capital accumulation equation From the Romer Model, the idea accumulation equation Labor is divided up between idea and goods production A constant share of the population p are scientists producing ideas

11 The combined Solow-Romer model has balanced growth paths and not steady states Just like in the Romer mo odel, in the combined model there is exponential growth in ideas, which fuels exponential growth in income per capita So there is no steady state level of income per capita, since it is always growingg according to a familiar- looking formula: But there is an equation for income per capita, yt, along a balanced growth path:

12 This shows us that as i n the Romer model: Income per capita, yt, depends on the stock of knowledge, At A new idea adds to At and since it is nonrival, it increases the income of every yperson in the economy! (In other words, yt is a function of At, and not Yt) We also see that as in the Solow model: Income per capita, yt, depends on the saving rate, s It turns out that t there are transition dynamics since capital is in the model. Why?

13 Why are there tra nsition dynamics? Capital machines, tools, buildings is in the model and must be accumulated. There are diminishing returns to capital, so each additional unit produces less and less So the growth rate diminishes as the economy accumulates capital and approaches its balanced growth path (just like approaching the steady state t in the Solow model) We now have an amended Principle of Transition Dynamics since there is no steady state, only a balanced growth path: The further below its balance ed growth path an economy is, the faster the economy will grow. Similarly, the further above its balanced growth path, the slower it will grow

14 How can we see transition dynamics in this model? Suppose an economy is on its balanced growth path, but then the saving rate s rises. What happens? Its long-run rate of growth is unaffected by s But income per capita along its new balanced growth path will be hig gher eventually:

15 What do these transition dynamics look like in a graph of income per capita over time? Ratio scale: yt Initially, growth is balanced at Slope= When the saving rate s rises, we are below our new balanced growth path at a higher y* but at the same growth rate (which is the slope) Slope = So we must transition up from our old balanced growth path, with very rapid growth at first But ultimately we reach our new balanced growth path, at the same old rate of growth but higher y* Time, t

16 Transitions involve level effects and can also include growth effects Ratio scale: yt Slope = Changes in any of the parameters will produce a level effect like this (or a reduction in the level) Changes in a select few of the parameters will also change the growth rate: Time, t

17 What is the take-away message you should re member? Not the math! Rather, the message is this: We have a theory of long- run growth: economic growth is driven by the discovery of ideas throughout the world because ideas are nonrival and yield increasing returns We also have a theory why there are differences in growth rates across countries: Transition dynamics affect growth on the way toward the balanced growth path Although all countries sho uld ultimately grow at the same rate in the very long run, we may observe their growing at different rates for long periods of time if their policies and choices for example the eir saving rates are different

18 One last topic: Growth accounting We have seen (in Chapters 4 5) how differences in total factor productivity (TFP) a residual that represents ideas, human capital, institutions, etc. account for most (67% 90%) of the differences in income per capita across countries, or over space The Romer and Solow/Rome er models tell us that t growth in ideas, and thus TFP, are key for long-term growth in incomes over time Now let us combine these tw wo perspectives: let us think about the components of growth over time in countries, and assign importance to growth in TFP, growth in capital, etc. This is called growth accounting The math, again, is not important the insights are but to proceed, take growth rates of both sides of the production function:

19 Take growth rates of fboth sides Now subtract glt Growth in Growth in Growth in income per = Total Factor + capital per person Productivity person + Growth in hours worked per person With this equation, we can decompose growth over time in income per person into growth in its com mponents to better understand the sourcess of growth

20 Growth in these components of GDP per person has changed over time in the U.S. how they have changed tells us about the sources of growth U.S. growth in: Income per person Capital per person Hours worked per person Total Factor Productivity

21 Growth accounting has produced some lively debates, for example ab bout the sustainability stainabilit of growth in Singapore and other Asian Tigers Singaporean growth in: Income per person Capital per person Hours worked per person Total Factor Productivity

22 A hint of where we re going next: In the U.S., what do we see when we graph h(labor) productivity? it 1. Interesting changes in trend 2. Fluctuations around trend!

23 What have we learned about growth? Growth in ideas and growth in TFP, not in physical inputs, is key to long-run growth that is what the Romer Model tells us The Solow Model tells us about short-run transition dynamics The Solow concept of convergence toward steady state is correct, but in reality we re really converging toward a balanced growth path: where income per person is growing at a steady rate Physical economy fundamentals like the saving/investment rate do matter for the level of inco ome per person and the transition, if not for the rate of growth (All countries should eventually transition to a single world rate of growth based on the growth in ideas) Still, the Solow/Romer framework is not complete: we also know that other things are very important for growth, namely institutions,, like the rule of law and property p rights; and education

24 Moving toward Part 2 of Econ 206: Fluctuations, booms & recessions There are wiggles as well as trends in all of our graphs of income per person, productivity, it etc. These wiggles are called business cycles, and we study them next We will begin with dis scussing unemployment, then inflation, with both long-run and short-run aspects, and then on to a model of short-run fluctuations Then we discuss government, and finally, trade and finance in the internat tional economy