WEBVTT 00:00:00.000 --> 00:00:01.461 align:middle line:90% 00:00:01.461 --> 00:00:02.435 align:middle line:90% [SQUEAKING] 00:00:02.435 --> 00:00:03.896 align:middle line:90% [RUSTLING] 00:00:03.896 --> 00:00:05.844 align:middle line:90% [CLICKING] 00:00:05.844 --> 00:00:17.540 align:middle line:90% 00:00:17.540 --> 00:00:18.530 align:middle line:90% RICARDO CABALLERO: OK. 00:00:18.530 --> 00:00:20.540 align:middle line:90% Let's start. 00:00:20.540 --> 00:00:25.520 align:middle line:84% So the plan for today is to wrap up this growth theory 00:00:25.520 --> 00:00:27.420 align:middle line:90% section of the course. 00:00:27.420 --> 00:00:33.945 align:middle line:84% And I want to conclude by showing you what we can 00:00:33.945 --> 00:00:36.320 align:middle line:84% and cannot explain with the models we have looked up till 00:00:36.320 --> 00:00:37.110 align:middle line:90% now. 00:00:37.110 --> 00:00:39.980 align:middle line:84% And almost as a matter of accounting, 00:00:39.980 --> 00:00:42.630 align:middle line:84% I will tell you, what do we need to fill-- 00:00:42.630 --> 00:00:44.450 align:middle line:84% which gaps do we need to fill in order 00:00:44.450 --> 00:00:48.500 align:middle line:84% to explain the great dispersion we see in income per capita 00:00:48.500 --> 00:00:49.790 align:middle line:90% across the world. 00:00:49.790 --> 00:00:53.695 align:middle line:84% But before I do that, I need to finish the previous lecture. 00:00:53.695 --> 00:00:58.040 align:middle line:90% 00:00:58.040 --> 00:01:00.920 align:middle line:90% And so let me do that. 00:01:00.920 --> 00:01:02.450 align:middle line:90% I had shown you this table. 00:01:02.450 --> 00:01:05.150 align:middle line:84% Remember, in the complete model-- the model 00:01:05.150 --> 00:01:10.730 align:middle line:84% that has a productivity growth, unemployment, and population 00:01:10.730 --> 00:01:16.220 align:middle line:84% growth, we concluded that in balanced growth, 00:01:16.220 --> 00:01:18.650 align:middle line:90% the following happened. 00:01:18.650 --> 00:01:20.990 align:middle line:84% Obviously, if we pick the right normalization-- 00:01:20.990 --> 00:01:25.350 align:middle line:84% the right normalization, here, was effective workers. 00:01:25.350 --> 00:01:31.320 align:middle line:84% So the productivity times population or workers. 00:01:31.320 --> 00:01:34.460 align:middle line:84% And so if we normalize the variables by that, 00:01:34.460 --> 00:01:36.250 align:middle line:90% we get, obviously, zero growth. 00:01:36.250 --> 00:01:38.750 align:middle line:84% That's what it means to have a balanced growth, in which all 00:01:38.750 --> 00:01:42.260 align:middle line:84% the relevant variables are growing at the same rate. 00:01:42.260 --> 00:01:46.830 align:middle line:84% So capital per effective worker will be a steady state. 00:01:46.830 --> 00:01:48.470 align:middle line:90% That's the diagram we plot. 00:01:48.470 --> 00:01:50.810 align:middle line:84% Remember, the diagram we plot was 00:01:50.810 --> 00:01:54.260 align:middle line:84% output per effective worker against capital 00:01:54.260 --> 00:01:55.320 align:middle line:90% per effective worker. 00:01:55.320 --> 00:01:57.500 align:middle line:84% And that diagram has a steady state. 00:01:57.500 --> 00:02:00.060 align:middle line:84% And that steady state-- at the steady state 00:02:00.060 --> 00:02:02.280 align:middle line:84% or the balanced growth point, then we 00:02:02.280 --> 00:02:06.960 align:middle line:84% have that the normalized variables grow at the rate of 0. 00:02:06.960 --> 00:02:11.160 align:middle line:84% Capital per worker has to grow at the rate gA 00:02:11.160 --> 00:02:14.110 align:middle line:84% because capital per effective worker is not growing. 00:02:14.110 --> 00:02:17.220 align:middle line:84% So capital per worker will be growing at the rate gA. 00:02:17.220 --> 00:02:19.910 align:middle line:84% The same applies for output per worker. 00:02:19.910 --> 00:02:21.932 align:middle line:84% Output per effective worker is not growing. 00:02:21.932 --> 00:02:22.890 align:middle line:90% That's balanced growth. 00:02:22.890 --> 00:02:27.000 align:middle line:84% But therefore, output per worker will be growing at a rate gA. 00:02:27.000 --> 00:02:29.810 align:middle line:90% 00:02:29.810 --> 00:02:31.850 align:middle line:84% These are the exogenous drivers-- 00:02:31.850 --> 00:02:35.840 align:middle line:90% output per worker, we assume-- 00:02:35.840 --> 00:02:37.400 align:middle line:90% well, sorry. 00:02:37.400 --> 00:02:41.040 align:middle line:84% Labor is exogenous in this model. 00:02:41.040 --> 00:02:42.110 align:middle line:90% And so is gN. 00:02:42.110 --> 00:02:45.110 align:middle line:84% Population growth is some constant we take. 00:02:45.110 --> 00:02:47.460 align:middle line:84% It's not something we try to explain within the model. 00:02:47.460 --> 00:02:51.710 align:middle line:84% But the two drivers of absolute growth will be gA and gN. 00:02:51.710 --> 00:02:53.690 align:middle line:84% And so capital in the steady state 00:02:53.690 --> 00:02:56.270 align:middle line:84% will be growing at the rate gA plus gN. 00:02:56.270 --> 00:02:59.150 align:middle line:84% Output will be growing at the rate gA plus gN. 00:02:59.150 --> 00:03:01.290 align:middle line:90% So that's balanced growth. 00:03:01.290 --> 00:03:04.580 align:middle line:84% Now, let me give you an example so you can do-- 00:03:04.580 --> 00:03:07.220 align:middle line:84% suppose that our production function is this. 00:03:07.220 --> 00:03:11.840 align:middle line:84% We call that the Cobb-Douglas production function. 00:03:11.840 --> 00:03:14.640 align:middle line:84% K to the 1 minus alpha AN to the alpha. 00:03:14.640 --> 00:03:19.400 align:middle line:84% Does this function have constant returns to scale? 00:03:19.400 --> 00:03:23.570 align:middle line:84% Yes, the sum of the exponents is 1. 00:03:23.570 --> 00:03:26.870 align:middle line:84% But-- so take the log of both sides. 00:03:26.870 --> 00:03:29.250 align:middle line:84% The change in the log is the rate of growth. 00:03:29.250 --> 00:03:32.060 align:middle line:84% And so you get that the rate of growth of output 00:03:32.060 --> 00:03:35.180 align:middle line:84% is equal to 1 minus alpha, the rate of growth of capital, 00:03:35.180 --> 00:03:39.170 align:middle line:84% plus alpha times the rate of growth of effective workers. 00:03:39.170 --> 00:03:42.080 align:middle line:84% So in balanced growth, gK will be 00:03:42.080 --> 00:03:43.970 align:middle line:90% growing at the rate gA plus gN. 00:03:43.970 --> 00:03:45.800 align:middle line:84% And therefore, output will also be 00:03:45.800 --> 00:03:47.780 align:middle line:90% growing at the rate gA plus gN. 00:03:47.780 --> 00:03:50.070 align:middle line:84% OK, so that's what you have in the table. 00:03:50.070 --> 00:03:53.510 align:middle line:84% And if you want to look at a variable like this, capital 00:03:53.510 --> 00:03:56.060 align:middle line:84% per worker, then output per worker, 00:03:56.060 --> 00:03:59.990 align:middle line:90% then you need gY minus gN. 00:03:59.990 --> 00:04:03.420 align:middle line:84% So subtract the gN, and you can subtract on both sides. 00:04:03.420 --> 00:04:05.120 align:middle line:84% Then it's going to be equal to gA. 00:04:05.120 --> 00:04:09.170 align:middle line:84% And subtract gN from the right-hand side. 00:04:09.170 --> 00:04:10.970 align:middle line:84% This one and that one cancel, and I 00:04:10.970 --> 00:04:12.780 align:middle line:90% get gA on the right-hand side. 00:04:12.780 --> 00:04:15.830 align:middle line:84% So that's the way you use that expression to fill 00:04:15.830 --> 00:04:18.390 align:middle line:90% all these blanks. 00:04:18.390 --> 00:04:20.649 align:middle line:90% That's steady state. 00:04:20.649 --> 00:04:23.440 align:middle line:84% So I think I stopped right before that-- 00:04:23.440 --> 00:04:28.450 align:middle line:84% this slide or at this slide, which is-- 00:04:28.450 --> 00:04:31.420 align:middle line:84% if I look at this, this table, gN is pretty easy 00:04:31.420 --> 00:04:33.290 align:middle line:90% to compute in most places. 00:04:33.290 --> 00:04:36.070 align:middle line:84% There are places in the world where we cannot even measure 00:04:36.070 --> 00:04:40.300 align:middle line:84% birth and death, so it's difficult. But in most places, 00:04:40.300 --> 00:04:44.020 align:middle line:84% you can measure gN, the rate of growth of population, 00:04:44.020 --> 00:04:45.435 align:middle line:90% quite accurately. 00:04:45.435 --> 00:04:46.810 align:middle line:84% And the question we have, though, 00:04:46.810 --> 00:04:48.685 align:middle line:84% is, how do we measure technological progress? 00:04:48.685 --> 00:04:51.895 align:middle line:84% It's also easy to measure the growth in the stock of capital. 00:04:51.895 --> 00:04:54.640 align:middle line:84% It's investment minus depreciation. 00:04:54.640 --> 00:05:00.140 align:middle line:84% But how do we measure gA, the rate of technological progress? 00:05:00.140 --> 00:05:06.670 align:middle line:84% And the first proposal on how to do it was also by Bob Solow. 00:05:06.670 --> 00:05:10.280 align:middle line:84% That was the second contribution he had in growth theory. 00:05:10.280 --> 00:05:11.960 align:middle line:84% Well, it was also growth measurement. 00:05:11.960 --> 00:05:13.348 align:middle line:90% How do we measure gA? 00:05:13.348 --> 00:05:14.890 align:middle line:84% It turns out that the only way you're 00:05:14.890 --> 00:05:17.950 align:middle line:84% going to have output per capita growing over time or output 00:05:17.950 --> 00:05:20.520 align:middle line:84% per person growing over time is due to gA. 00:05:20.520 --> 00:05:22.340 align:middle line:84% So we might as well try to measure 00:05:22.340 --> 00:05:25.130 align:middle line:84% that since it's such an important variable 00:05:25.130 --> 00:05:28.430 align:middle line:90% for the growth of-- 00:05:28.430 --> 00:05:31.380 align:middle line:90% the growth of happiness. 00:05:31.380 --> 00:05:35.060 align:middle line:84% If you give one indicator of happiness is output per worker, 00:05:35.060 --> 00:05:37.040 align:middle line:84% well, such an important driver-- we 00:05:37.040 --> 00:05:39.320 align:middle line:90% need to be able to measure it. 00:05:39.320 --> 00:05:41.570 align:middle line:84% And the basic idea that Bob Solow has is, 00:05:41.570 --> 00:05:45.050 align:middle line:84% is essentially something you could have taken from 1401. 00:05:45.050 --> 00:05:46.610 align:middle line:90% It's extremely simple. 00:05:46.610 --> 00:05:51.150 align:middle line:84% It says-- there are some assumptions behind this. 00:05:51.150 --> 00:05:54.590 align:middle line:84% But in the basic competitive model, 00:05:54.590 --> 00:05:59.420 align:middle line:84% you have that you can compute the contribution 00:05:59.420 --> 00:06:05.390 align:middle line:84% of each factor of production to output by the payment 00:06:05.390 --> 00:06:06.560 align:middle line:90% it receives. 00:06:06.560 --> 00:06:12.260 align:middle line:84% So under this assumption, suppose that you're spending, 00:06:12.260 --> 00:06:16.670 align:middle line:90% in workers, $30,000 a year. 00:06:16.670 --> 00:06:20.100 align:middle line:84% So that means, in a competitive equilibrium in the labor market 00:06:20.100 --> 00:06:23.510 align:middle line:84% and so on, that the worker is contributing, to production, 00:06:23.510 --> 00:06:25.658 align:middle line:90% $30,000. 00:06:25.658 --> 00:06:27.950 align:middle line:84% I'm not going to deal with markups and things like that 00:06:27.950 --> 00:06:28.450 align:middle line:90% here. 00:06:28.450 --> 00:06:29.730 align:middle line:90% But that's the basic idea. 00:06:29.730 --> 00:06:32.420 align:middle line:84% You can adjust all these formulas to include markups. 00:06:32.420 --> 00:06:34.100 align:middle line:90% But let me not do that. 00:06:34.100 --> 00:06:45.230 align:middle line:84% So that also tells you that if you increase employment by 10%, 00:06:45.230 --> 00:06:48.140 align:middle line:84% you're also going to increase output 00:06:48.140 --> 00:06:53.030 align:middle line:84% by 10% times whatever is the contribution of labor to output. 00:06:53.030 --> 00:06:54.780 align:middle line:90% And that's what I have here. 00:06:54.780 --> 00:07:00.650 align:middle line:84% The contribution to output of adding workers 00:07:00.650 --> 00:07:04.130 align:middle line:84% is going to be that times delta N. 00:07:04.130 --> 00:07:09.410 align:middle line:84% I can divide, by Y, both sides, and here, multiply 00:07:09.410 --> 00:07:10.700 align:middle line:90% and divide by N. 00:07:10.700 --> 00:07:15.710 align:middle line:84% And I get that the rate of growth 00:07:15.710 --> 00:07:22.970 align:middle line:84% in output due to a rate of growth in employment 00:07:22.970 --> 00:07:24.800 align:middle line:90% is equal to the labor share. 00:07:24.800 --> 00:07:26.300 align:middle line:84% That's called the labor share-- it's 00:07:26.300 --> 00:07:33.200 align:middle line:84% the wage bill, W times N divided by total revenue sales 00:07:33.200 --> 00:07:40.460 align:middle line:84% and times the rate of growth of a population or workers 00:07:40.460 --> 00:07:41.550 align:middle line:90% is the same here. 00:07:41.550 --> 00:07:44.450 align:middle line:90% So I'm going to call this gYN-- 00:07:44.450 --> 00:07:48.770 align:middle line:84% is the rate of growth of output due to the rate of growth in 00:07:48.770 --> 00:07:52.760 align:middle line:84% population is equal to this labor share, which-- 00:07:52.760 --> 00:07:54.590 align:middle line:90% I'm going to call that alpha-- 00:07:54.590 --> 00:07:57.350 align:middle line:90% times Gn 00:07:57.350 --> 00:07:59.637 align:middle line:84% I can do exactly the same with capital. 00:07:59.637 --> 00:08:01.970 align:middle line:84% And you can do-- if you have more factors of production, 00:08:01.970 --> 00:08:04.340 align:middle line:84% you can do the same for each factor of production. 00:08:04.340 --> 00:08:07.280 align:middle line:84% But in this simple example, we have only two factors 00:08:07.280 --> 00:08:09.200 align:middle line:84% of production-- labor and capital. 00:08:09.200 --> 00:08:11.010 align:middle line:84% So I can do the same for capital. 00:08:11.010 --> 00:08:15.590 align:middle line:84% And I can say the contribution of capital growth 00:08:15.590 --> 00:08:19.370 align:middle line:84% to output growth is going to be equal to the capital 00:08:19.370 --> 00:08:22.050 align:middle line:84% share, which is the complement of the labor share. 00:08:22.050 --> 00:08:26.810 align:middle line:84% So it's total revenue minus the wage payment, the wage bill, 00:08:26.810 --> 00:08:31.460 align:middle line:84% divided by total revenue, times the rate of growth of capital. 00:08:31.460 --> 00:08:35.510 align:middle line:84% So the contribution to output growth 00:08:35.510 --> 00:08:39.950 align:middle line:84% of the rate of growth of capital is 1 minus alpha, 00:08:39.950 --> 00:08:44.480 align:middle line:84% which is the share of capital, times the rate of growth 00:08:44.480 --> 00:08:45.560 align:middle line:90% of capital. 00:08:45.560 --> 00:08:50.990 align:middle line:84% So that means if I sum the contribution of labor 00:08:50.990 --> 00:08:56.210 align:middle line:84% and capital, I'm left with a residual, which is-- 00:08:56.210 --> 00:08:58.660 align:middle line:84% whatever is the rate of growth I have in output-- 00:08:58.660 --> 00:09:00.630 align:middle line:84% I know how much I'm getting from labor. 00:09:00.630 --> 00:09:02.772 align:middle line:84% I know how much I'm getting from capital. 00:09:02.772 --> 00:09:04.230 align:middle line:84% If there is any difference, it must 00:09:04.230 --> 00:09:06.600 align:middle line:84% be due to that thing I do not observe, 00:09:06.600 --> 00:09:08.640 align:middle line:90% which is technological progress. 00:09:08.640 --> 00:09:10.505 align:middle line:84% That's the logic of all this stuff. 00:09:10.505 --> 00:09:13.297 align:middle line:90% 00:09:13.297 --> 00:09:15.380 align:middle line:84% Go back, for example, to this production function. 00:09:15.380 --> 00:09:16.838 align:middle line:84% I'm saying, I know the contribution 00:09:16.838 --> 00:09:21.200 align:middle line:90% that K has to output growth. 00:09:21.200 --> 00:09:24.170 align:middle line:84% I know the contribution that N has to output growth. 00:09:24.170 --> 00:09:27.280 align:middle line:84% Well, the only thing I'm missing is the contribution 00:09:27.280 --> 00:09:30.400 align:middle line:84% that A has to output growth, which I don't observe, 00:09:30.400 --> 00:09:32.240 align:middle line:90% but I observe output growth. 00:09:32.240 --> 00:09:35.000 align:middle line:84% I observe capital growth, employment growth. 00:09:35.000 --> 00:09:40.240 align:middle line:84% So I can solve out what is the technological progress-- 00:09:40.240 --> 00:09:41.240 align:middle line:90% A growth. 00:09:41.240 --> 00:09:46.250 align:middle line:84% And thus, it's called the Solow residual, by the way. 00:09:46.250 --> 00:09:50.650 align:middle line:84% But that's the way, the rate of growth of A is measured. 00:09:50.650 --> 00:09:54.010 align:middle line:84% The rate of growth of the output minus the contribution to growth 00:09:54.010 --> 00:09:58.575 align:middle line:84% of employment, population and capital. 00:09:58.575 --> 00:10:01.130 align:middle line:90% 00:10:01.130 --> 00:10:03.820 align:middle line:90% Any question about that? 00:10:03.820 --> 00:10:04.580 align:middle line:90% Nope? 00:10:04.580 --> 00:10:06.500 align:middle line:90% Makes sense? 00:10:06.500 --> 00:10:08.360 align:middle line:90% Somewhat? 00:10:08.360 --> 00:10:10.100 align:middle line:90% OK, good. 00:10:10.100 --> 00:10:12.770 align:middle line:84% So anyway-- so there's a huge industry 00:10:12.770 --> 00:10:16.890 align:middle line:84% of measuring these kind of things, of course. 00:10:16.890 --> 00:10:22.560 align:middle line:84% Let me give you an example on how to use this accounting. 00:10:22.560 --> 00:10:26.310 align:middle line:90% So China '78, 2017-- 00:10:26.310 --> 00:10:30.120 align:middle line:84% that's an episode in which China was growing very, very strongly. 00:10:30.120 --> 00:10:36.570 align:middle line:84% On average, China grew at over 7%, output-- 00:10:36.570 --> 00:10:38.440 align:middle line:90% over 7%. 00:10:38.440 --> 00:10:41.740 align:middle line:84% Now, by the formula I showed you before, 00:10:41.740 --> 00:10:43.330 align:middle line:84% if I asked you the question, well, 00:10:43.330 --> 00:10:45.710 align:middle line:90% what was behind that growth? 00:10:45.710 --> 00:10:47.600 align:middle line:84% How much was the contribution of labor? 00:10:47.600 --> 00:10:49.520 align:middle line:84% How much was the contribution of capital? 00:10:49.520 --> 00:10:51.110 align:middle line:84% And how much was the contribution 00:10:51.110 --> 00:10:52.820 align:middle line:90% of technological progress? 00:10:52.820 --> 00:10:56.970 align:middle line:84% Well, there are several things we can measure fairly well. 00:10:56.970 --> 00:11:00.710 align:middle line:84% Population growth during this period in China was around 1.7% 00:11:00.710 --> 00:11:02.890 align:middle line:90% per year. 00:11:02.890 --> 00:11:06.380 align:middle line:84% There was a massive amount of investment. 00:11:06.380 --> 00:11:10.760 align:middle line:84% The capital stock was growing at a rate of 9.2% per year. 00:11:10.760 --> 00:11:13.700 align:middle line:84% And the residual-- you can compute it using the Solow 00:11:13.700 --> 00:11:14.960 align:middle line:90% approach-- 00:11:14.960 --> 00:11:18.410 align:middle line:90% is around 4.2%. 00:11:18.410 --> 00:11:22.820 align:middle line:84% So that's-- 7.2% is a result of the weighted average of these 00:11:22.820 --> 00:11:25.680 align:middle line:90% three things. 00:11:25.680 --> 00:11:30.990 align:middle line:84% So that's basic explanation of growth 00:11:30.990 --> 00:11:33.390 align:middle line:90% in China during that period. 00:11:33.390 --> 00:11:36.520 align:middle line:90% Now, just looking at this-- 00:11:36.520 --> 00:11:39.480 align:middle line:90% don't look at the diagram. 00:11:39.480 --> 00:11:42.810 align:middle line:90% What jumps immediately? 00:11:42.810 --> 00:11:44.060 align:middle line:90% If you just look at this part. 00:11:44.060 --> 00:11:47.370 align:middle line:90% 00:11:47.370 --> 00:11:50.210 align:middle line:90% What jumps to you immediately? 00:11:50.210 --> 00:11:51.720 align:middle line:90% Let me ask you differently. 00:11:51.720 --> 00:11:53.980 align:middle line:84% Does it look like balanced growth? 00:11:53.980 --> 00:11:57.060 align:middle line:90% 00:11:57.060 --> 00:12:01.730 align:middle line:84% Do you think that that's balanced growth? 00:12:01.730 --> 00:12:03.680 align:middle line:84% In other words, do you think that China 00:12:03.680 --> 00:12:08.570 align:middle line:84% had arrived to its steady state, and that growth 00:12:08.570 --> 00:12:12.025 align:middle line:84% is a result of what was happening in that steady state? 00:12:12.025 --> 00:12:17.090 align:middle line:90% 00:12:17.090 --> 00:12:17.690 align:middle line:90% No. 00:12:17.690 --> 00:12:21.600 align:middle line:84% [LAUGHS] But what is it that looks-- 00:12:21.600 --> 00:12:24.095 align:middle line:84% that tells you that that's not the steady state? 00:12:24.095 --> 00:12:27.700 align:middle line:90% 00:12:27.700 --> 00:12:29.320 align:middle line:84% Balanced growth is when everything 00:12:29.320 --> 00:12:30.620 align:middle line:90% is growing at the same rate. 00:12:30.620 --> 00:12:34.020 align:middle line:90% 00:12:34.020 --> 00:12:40.630 align:middle line:84% Meaning all the endogenous variables are normalized, 00:12:40.630 --> 00:12:45.620 align:middle line:84% are growing at the same rate as the exogenous variables. 00:12:45.620 --> 00:12:48.180 align:middle line:90% 00:12:48.180 --> 00:12:53.000 align:middle line:84% So what is it that it would merely jump to me here is that-- 00:12:53.000 --> 00:12:55.110 align:middle line:90% uh-oh, 7.2%-- 00:12:55.110 --> 00:12:59.180 align:middle line:84% that's less than the rate of growth of capital. 00:12:59.180 --> 00:13:03.780 align:middle line:84% So I know that there, capital over output was rising. 00:13:03.780 --> 00:13:05.570 align:middle line:90% So that's not a steady state. 00:13:05.570 --> 00:13:07.480 align:middle line:90% I know that. 00:13:07.480 --> 00:13:09.580 align:middle line:90% I can see it in a different way. 00:13:09.580 --> 00:13:15.680 align:middle line:84% I know that in a steady state, in balanced growth, 00:13:15.680 --> 00:13:18.560 align:middle line:84% the rate of growth of output and of capital 00:13:18.560 --> 00:13:21.050 align:middle line:84% should be the sum of the rate of growth of population 00:13:21.050 --> 00:13:25.990 align:middle line:84% plus the rate of technological progress. 00:13:25.990 --> 00:13:28.420 align:middle line:90% That's 5.9%. 00:13:28.420 --> 00:13:34.970 align:middle line:84% But capital was growing at 9.2%, not 5.9%. 00:13:34.970 --> 00:13:38.560 align:middle line:84% So I do know that that's a period in which. 00:13:38.560 --> 00:13:43.360 align:middle line:84% China was growing beyond its steady state or balanced growth 00:13:43.360 --> 00:13:45.250 align:middle line:90% rate of growth. 00:13:45.250 --> 00:13:46.820 align:middle line:90% And I know more than that. 00:13:46.820 --> 00:13:48.550 align:middle line:84% I know that the reason that was happening 00:13:48.550 --> 00:13:49.990 align:middle line:84% is because there was more capital 00:13:49.990 --> 00:13:54.730 align:middle line:84% accumulation than you would expect in the steady state. 00:13:54.730 --> 00:13:57.970 align:middle line:84% When are you likely to see a situation like that 00:13:57.970 --> 00:14:01.300 align:middle line:84% in which capital accumulation is faster than the rate of growth 00:14:01.300 --> 00:14:03.850 align:middle line:84% of capital in the steady state and is faster 00:14:03.850 --> 00:14:05.450 align:middle line:84% than the rate of growth of output? 00:14:05.450 --> 00:14:08.620 align:middle line:84% That is, that's a period in which we 00:14:08.620 --> 00:14:12.940 align:middle line:84% have transitional growth being pulled-- 00:14:12.940 --> 00:14:15.340 align:middle line:84% growth above the steady state growth 00:14:15.340 --> 00:14:19.350 align:middle line:84% is being pulled by capital accumulation. 00:14:19.350 --> 00:14:20.495 align:middle line:90% When does that happen? 00:14:20.495 --> 00:14:28.265 align:middle line:90% 00:14:28.265 --> 00:14:29.640 align:middle line:84% STUDENT: Two things come to mind. 00:14:29.640 --> 00:14:33.230 align:middle line:84% First is economies that are transitioning from command 00:14:33.230 --> 00:14:34.985 align:middle line:90% market economies, I believe? 00:14:34.985 --> 00:14:36.860 align:middle line:84% And also, the second thing that comes to mind 00:14:36.860 --> 00:14:44.930 align:middle line:84% is, potentially, countries recovering from war periods. 00:14:44.930 --> 00:14:47.660 align:middle line:84% RICARDO CABALLERO: OK, that's deep answer. 00:14:47.660 --> 00:14:52.010 align:middle line:84% I wanted something simpler, which is-- 00:14:52.010 --> 00:14:53.330 align:middle line:90% I wanted to say-- 00:14:53.330 --> 00:14:55.630 align:middle line:84% so the economy is not in a steady state. 00:14:55.630 --> 00:14:56.790 align:middle line:90% That's clear. 00:14:56.790 --> 00:14:58.980 align:middle line:90% But what do we also know? 00:14:58.980 --> 00:15:02.420 align:middle line:84% We know that the capital stock is below its steady state level. 00:15:02.420 --> 00:15:07.110 align:middle line:84% And that could be as a result of the things you described. 00:15:07.110 --> 00:15:09.950 align:middle line:84% You had a war, so capital stock was wiped out. 00:15:09.950 --> 00:15:14.150 align:middle line:84% Or you had a period in which saving rate was very low. 00:15:14.150 --> 00:15:16.970 align:middle line:84% And now you're going to a high saving rate. 00:15:16.970 --> 00:15:19.940 align:middle line:84% [INAUDIBLE] A lot of that is what happened in Southeast Asia, 00:15:19.940 --> 00:15:20.870 align:middle line:90% in particular. 00:15:20.870 --> 00:15:24.200 align:middle line:84% Actually, it was a fast increase in the rate-- 00:15:24.200 --> 00:15:26.730 align:middle line:90% a sharp rise in the saving rate. 00:15:26.730 --> 00:15:29.010 align:middle line:84% But the bottom-- so what I had in mind 00:15:29.010 --> 00:15:32.430 align:middle line:84% is for one of these reasons, that's 00:15:32.430 --> 00:15:34.560 align:middle line:84% a situation where the initial capital stock was 00:15:34.560 --> 00:15:35.902 align:middle line:90% below the steady state. 00:15:35.902 --> 00:15:37.860 align:middle line:84% And so you have a period of transitional growth 00:15:37.860 --> 00:15:39.420 align:middle line:84% in which the investment rate is more 00:15:39.420 --> 00:15:42.990 align:middle line:84% than you need to do to maintain the stock of capital 00:15:42.990 --> 00:15:44.610 align:middle line:90% per effective worker. 00:15:44.610 --> 00:15:50.920 align:middle line:84% It's a positive gap between the green line and the red line. 00:15:50.920 --> 00:15:53.280 align:middle line:84% And that's what leads to transitional growth 00:15:53.280 --> 00:15:55.770 align:middle line:90% until you reach a steady state. 00:15:55.770 --> 00:15:59.550 align:middle line:84% If things do not change, meaning population growth 00:15:59.550 --> 00:16:02.280 align:middle line:84% remain the same as in that period, 00:16:02.280 --> 00:16:06.630 align:middle line:84% and the rate of technological progress 00:16:06.630 --> 00:16:08.620 align:middle line:84% remains the same as in that period-- 00:16:08.620 --> 00:16:12.115 align:middle line:84% we know that the balanced growth rate of China is 5.9%. 00:16:12.115 --> 00:16:15.955 align:middle line:90% 00:16:15.955 --> 00:16:22.860 align:middle line:84% It's 5.9%, because it's 0.017 plus 0.42. 00:16:22.860 --> 00:16:26.348 align:middle line:84% So that's 7.2% average that you are likely to see. 00:16:26.348 --> 00:16:27.890 align:middle line:84% And actually, this is an average that 00:16:27.890 --> 00:16:34.160 align:middle line:84% has numbers like 15% very early on to close to 6% or so 00:16:34.160 --> 00:16:36.470 align:middle line:90% on the last stage. 00:16:36.470 --> 00:16:39.230 align:middle line:90% So that would be a steady state. 00:16:39.230 --> 00:16:41.720 align:middle line:84% Now, that, I think, is an overestimate 00:16:41.720 --> 00:16:46.100 align:middle line:84% because we know that the rate of population growth 00:16:46.100 --> 00:16:50.630 align:middle line:84% is declining very rapidly in China-- is turning negative. 00:16:50.630 --> 00:16:53.570 align:middle line:84% So for the rate of growth of output, China-- 00:16:53.570 --> 00:16:56.030 align:middle line:84% unless there's a big change in technological progress-- 00:16:56.030 --> 00:16:57.738 align:middle line:84% in the process of technological progress, 00:16:57.738 --> 00:16:59.870 align:middle line:84% it's going to be pretty difficult for China 00:16:59.870 --> 00:17:04.490 align:middle line:84% to grow a lot more than 5%, I think, going forward. 00:17:04.490 --> 00:17:06.180 align:middle line:90% And that creates some problems. 00:17:06.180 --> 00:17:07.685 align:middle line:90% But that's what it is. 00:17:07.685 --> 00:17:09.060 align:middle line:84% That's what this model tells you. 00:17:09.060 --> 00:17:10.310 align:middle line:90% You need to change something. 00:17:10.310 --> 00:17:12.990 align:middle line:84% And the things you can change in this model are what? 00:17:12.990 --> 00:17:15.030 align:middle line:84% Well, you could induce higher saving rate. 00:17:15.030 --> 00:17:17.060 align:middle line:84% You could get more transitional growth out 00:17:17.060 --> 00:17:18.839 align:middle line:84% of that, more capital accumulation. 00:17:18.839 --> 00:17:19.710 align:middle line:90% That's costly. 00:17:19.710 --> 00:17:22.280 align:middle line:84% That means less consumption and so on. 00:17:22.280 --> 00:17:25.190 align:middle line:84% Or it could be some technological breakthrough, 00:17:25.190 --> 00:17:28.950 align:middle line:84% but that probably would affect the whole world, in any event. 00:17:28.950 --> 00:17:33.375 align:middle line:84% But that's the kind of things you expect. 00:17:33.375 --> 00:17:33.875 align:middle line:90% Good. 00:17:33.875 --> 00:17:37.710 align:middle line:90% 00:17:37.710 --> 00:17:43.070 align:middle line:84% So the models we have developed here 00:17:43.070 --> 00:17:47.180 align:middle line:84% are quite good to explain catching up processes, 00:17:47.180 --> 00:17:51.090 align:middle line:84% catching up growth, and to understand 00:17:51.090 --> 00:17:55.670 align:middle line:84% where are the economists converging over time. 00:17:55.670 --> 00:17:57.440 align:middle line:90% What I want to do next is-- 00:17:57.440 --> 00:17:59.760 align:middle line:84% I want to end up trying to explain-- 00:17:59.760 --> 00:18:02.270 align:middle line:84% remember, one of the plots I showed you very early on 00:18:02.270 --> 00:18:07.940 align:middle line:84% is that there's great dispersion in income per person, per capita 00:18:07.940 --> 00:18:09.060 align:middle line:90% across the world. 00:18:09.060 --> 00:18:13.850 align:middle line:84% And also, some countries are not catching up, especially 00:18:13.850 --> 00:18:15.990 align:middle line:90% in Africa and so on. 00:18:15.990 --> 00:18:17.550 align:middle line:84% And I want to try to understand-- 00:18:17.550 --> 00:18:19.130 align:middle line:84% so people have put lots of effort 00:18:19.130 --> 00:18:23.450 align:middle line:84% in trying to understand why do we have these differences. 00:18:23.450 --> 00:18:25.190 align:middle line:84% And so I'm going to expand, a little bit, 00:18:25.190 --> 00:18:30.230 align:middle line:84% the model we have to show you a few things people have explored. 00:18:30.230 --> 00:18:33.530 align:middle line:84% And then I'm going to conclude that those things that people 00:18:33.530 --> 00:18:36.870 align:middle line:84% have explored sort of can't explain it either. 00:18:36.870 --> 00:18:39.440 align:middle line:84% And then I'm going to go back sort of to growth 00:18:39.440 --> 00:18:43.880 align:middle line:84% accounting. so the sort of thing I did for China there, and try 00:18:43.880 --> 00:18:50.720 align:middle line:84% to explain what seems to be behind these big disparities 00:18:50.720 --> 00:18:51.980 align:middle line:90% we have in the world. 00:18:51.980 --> 00:18:54.860 align:middle line:84% So the first thing I'm going to do is just-- 00:18:54.860 --> 00:18:58.890 align:middle line:84% it's useful as an exercise, even. 00:18:58.890 --> 00:19:01.510 align:middle line:84% I'm going to modify the Solow model a little bit. 00:19:01.510 --> 00:19:04.780 align:middle line:84% So this is like the production function I showed you before. 00:19:04.780 --> 00:19:06.480 align:middle line:84% But rather than having N here, I'm 00:19:06.480 --> 00:19:11.430 align:middle line:84% going to have H. And H is just N-- 00:19:11.430 --> 00:19:14.370 align:middle line:84% our old N-- population, labor force over there, 00:19:14.370 --> 00:19:18.280 align:middle line:84% but it's scale up by this human capital factor. 00:19:18.280 --> 00:19:26.940 align:middle line:84% So what this says is that human capital is really-- 00:19:26.940 --> 00:19:30.550 align:middle line:84% is the population times something 00:19:30.550 --> 00:19:34.370 align:middle line:84% that controls for the level of schooling of that population. 00:19:34.370 --> 00:19:36.880 align:middle line:84% So a big candidate for difference across the world 00:19:36.880 --> 00:19:40.360 align:middle line:84% is certain populations are far more educated than others. 00:19:40.360 --> 00:19:44.680 align:middle line:90% So this does exactly that. 00:19:44.680 --> 00:19:47.410 align:middle line:84% Size is an increasing function of the numbers 00:19:47.410 --> 00:19:48.800 align:middle line:90% of years of schooling. 00:19:48.800 --> 00:19:52.060 align:middle line:84% And there is a big micro evidence-- literature 00:19:52.060 --> 00:19:54.430 align:middle line:84% trying to estimate what is the value of that side. 00:19:54.430 --> 00:19:57.010 align:middle line:84% What is the value of an extra unit of schooling 00:19:57.010 --> 00:19:59.780 align:middle line:90% for human capital and so on. 00:19:59.780 --> 00:20:03.070 align:middle line:84% And the estimate depends on what kind of schooling 00:20:03.070 --> 00:20:05.250 align:middle line:84% are we talking about-- primary, secondary, tertiary, 00:20:05.250 --> 00:20:05.750 align:middle line:90% or whatever. 00:20:05.750 --> 00:20:08.900 align:middle line:84% But on average, that's a number around 0.1. 00:20:08.900 --> 00:20:13.420 align:middle line:84% So one extra year of schooling raises human capital 00:20:13.420 --> 00:20:15.682 align:middle line:84% by about 10% So the whole population 00:20:15.682 --> 00:20:17.140 align:middle line:84% increases, the average by one year. 00:20:17.140 --> 00:20:20.290 align:middle line:90% 00:20:20.290 --> 00:20:22.850 align:middle line:84% That adds about 10% to human capital. 00:20:22.850 --> 00:20:26.420 align:middle line:84% So it's as if you had increased population by 10%. 00:20:26.420 --> 00:20:28.160 align:middle line:90% So it makes a difference. 00:20:28.160 --> 00:20:32.420 align:middle line:84% Now, it's pretty hard to raise, for a country, 00:20:32.420 --> 00:20:34.950 align:middle line:84% one year of schooling for the average. 00:20:34.950 --> 00:20:36.225 align:middle line:90% It takes a lot of time. 00:20:36.225 --> 00:20:37.850 align:middle line:84% But when you look in the cross-section, 00:20:37.850 --> 00:20:40.400 align:middle line:84% there is huge difference across the world between numbers 00:20:40.400 --> 00:20:41.790 align:middle line:90% of years of schooling. 00:20:41.790 --> 00:20:44.480 align:middle line:84% And that accounts for a big part of the difference 00:20:44.480 --> 00:20:46.970 align:middle line:90% in income per capita. 00:20:46.970 --> 00:20:51.440 align:middle line:84% Anyways-- so let me do a balance growth 00:20:51.440 --> 00:20:54.410 align:middle line:84% exercise with this expanded model 00:20:54.410 --> 00:20:57.703 align:middle line:90% and see how far we can get. 00:20:57.703 --> 00:20:59.120 align:middle line:84% So the first thing I'm going to do 00:20:59.120 --> 00:21:02.180 align:middle line:84% is I'm going to normalize everything by effective work-- 00:21:02.180 --> 00:21:03.960 align:middle line:90% sorry, by workers. 00:21:03.960 --> 00:21:06.105 align:middle line:90% So I'm going to divide-- 00:21:06.105 --> 00:21:07.730 align:middle line:84% all the variables I'm going to show you 00:21:07.730 --> 00:21:10.740 align:middle line:90% are going to be divided by N. 00:21:10.740 --> 00:21:15.960 align:middle line:84% Now, notice that I'm dividing by N, not 00:21:15.960 --> 00:21:24.300 align:middle line:84% by A times N or A times H. So there is a difference 00:21:24.300 --> 00:21:26.550 align:middle line:90% with the previous analysis. 00:21:26.550 --> 00:21:28.410 align:middle line:90% And I can always divide. 00:21:28.410 --> 00:21:29.590 align:middle line:90% The model we had-- 00:21:29.590 --> 00:21:33.090 align:middle line:84% I can always divide by whatever I want, all my variables. 00:21:33.090 --> 00:21:35.190 align:middle line:84% I divide it by effective workers because I 00:21:35.190 --> 00:21:37.560 align:middle line:84% wanted to have a diagram where the curves were not 00:21:37.560 --> 00:21:38.790 align:middle line:90% moving around. 00:21:38.790 --> 00:21:41.960 align:middle line:84% But I can divide by whatever I want. 00:21:41.960 --> 00:21:43.680 align:middle line:84% And I will divide by different things 00:21:43.680 --> 00:21:46.030 align:middle line:84% depending on the analysis I want to conduct. 00:21:46.030 --> 00:21:48.780 align:middle line:84% Now, I know that once I divide by population only, 00:21:48.780 --> 00:21:53.610 align:middle line:84% not by A times a population and education, perhaps, 00:21:53.610 --> 00:21:55.650 align:middle line:84% I cannot draw my previous diagram-- 00:21:55.650 --> 00:22:00.808 align:middle line:84% the diagram with the saving, with output per worker, 00:22:00.808 --> 00:22:03.100 align:middle line:84% and so on, because those curves are going to be moving, 00:22:03.100 --> 00:22:04.230 align:middle line:90% so it's not very friendly. 00:22:04.230 --> 00:22:05.980 align:middle line:84% But I can divide by whatever I want. 00:22:05.980 --> 00:22:09.670 align:middle line:84% But I want to divide, here, by just population. 00:22:09.670 --> 00:22:15.630 align:middle line:84% So little h will be simply big H divided by N. 00:22:15.630 --> 00:22:19.470 align:middle line:84% Remember that big H was just e to epsi psi u times N. 00:22:19.470 --> 00:22:21.180 align:middle line:90% So that's that. 00:22:21.180 --> 00:22:24.970 align:middle line:90% Output per worker will be just-- 00:22:24.970 --> 00:22:31.120 align:middle line:84% will be K capital divided by N. And here is big 00:22:31.120 --> 00:22:33.670 align:middle line:84% H divided by N, which is little h. 00:22:33.670 --> 00:22:37.720 align:middle line:84% So all this, now, is measured as output per worker 00:22:37.720 --> 00:22:41.120 align:middle line:90% or per population-- 00:22:41.120 --> 00:22:43.430 align:middle line:90% per person. 00:22:43.430 --> 00:22:46.250 align:middle line:84% Now, remember, what I can do here is-- then I 00:22:46.250 --> 00:22:49.130 align:middle line:84% know that the rate of growth of output per person 00:22:49.130 --> 00:22:51.230 align:middle line:84% is going to be equal to 1 minus alpha 00:22:51.230 --> 00:22:54.710 align:middle line:84% times the rate of growth of capital per person 00:22:54.710 --> 00:22:58.100 align:middle line:84% plus alpha times the rate of growth of A times 00:22:58.100 --> 00:23:00.560 align:middle line:84% the rate of growth of h, in which 00:23:00.560 --> 00:23:05.870 align:middle line:84% h is this years of schooling transformation. 00:23:05.870 --> 00:23:09.530 align:middle line:84% Now, if you think about the steady state, 00:23:09.530 --> 00:23:11.465 align:middle line:90% it doesn't make any sense that-- 00:23:11.465 --> 00:23:13.320 align:middle line:84% gH, at some point, will become 0. 00:23:13.320 --> 00:23:15.050 align:middle line:84% I mean, we can increase education. 00:23:15.050 --> 00:23:19.550 align:middle line:84% But at some point, we cannot be all going to 150 years 00:23:19.550 --> 00:23:21.080 align:middle line:90% of education. 00:23:21.080 --> 00:23:23.550 align:middle line:84% Unlike capital and things like that-- 00:23:23.550 --> 00:23:26.600 align:middle line:84% you can increase, for a while, education. 00:23:26.600 --> 00:23:28.320 align:middle line:84% But at some point, there is a limit. 00:23:28.320 --> 00:23:31.110 align:middle line:84% I mean, you're not going to do a post post, post post, PHD, blah, 00:23:31.110 --> 00:23:31.910 align:middle line:90% blah, blah, blah. 00:23:31.910 --> 00:23:35.120 align:middle line:84% So in a steady state, we know that eventually, 00:23:35.120 --> 00:23:38.990 align:middle line:84% in the long run, this gH is equal to 0. 00:23:38.990 --> 00:23:44.850 align:middle line:84% So this economy-- expanded to include years of schooling-- 00:23:44.850 --> 00:23:47.310 align:middle line:84% has the same sort of balanced growth characteristics 00:23:47.310 --> 00:23:49.410 align:middle line:84% of the economy I just showed you before. 00:23:49.410 --> 00:23:55.770 align:middle line:84% So in that economy, capital per person will grow at a rate gA, 00:23:55.770 --> 00:23:59.340 align:middle line:84% and output per person will grow at the rate gA. 00:23:59.340 --> 00:24:01.710 align:middle line:84% Output will grow at the rate gA plus gN. 00:24:01.710 --> 00:24:05.040 align:middle line:84% So exactly the same as we had before. 00:24:05.040 --> 00:24:09.960 align:middle line:84% Up to now, adding human capital doesn't change our conclusions 00:24:09.960 --> 00:24:11.850 align:middle line:90% about balanced growth. 00:24:11.850 --> 00:24:14.170 align:middle line:84% It will change some conclusions that are important. 00:24:14.170 --> 00:24:16.390 align:middle line:84% So that's the reason I'm introducing this variable. 00:24:16.390 --> 00:24:18.940 align:middle line:84% But it doesn't change this conclusion. 00:24:18.940 --> 00:24:21.940 align:middle line:84% So this model, which is a little expansion of the previous model, 00:24:21.940 --> 00:24:24.870 align:middle line:84% we had, has the same balanced growth characteristics 00:24:24.870 --> 00:24:28.720 align:middle line:84% as the model I showed you before. 00:24:28.720 --> 00:24:32.530 align:middle line:84% So let me do a little bit of algebra with it. 00:24:32.530 --> 00:24:36.550 align:middle line:84% So from the capital accumulation equation, I know that-- 00:24:36.550 --> 00:24:40.720 align:middle line:84% so let me-- remember, the capital accumulation-- 00:24:40.720 --> 00:24:46.420 align:middle line:90% now written in per person-- 00:24:46.420 --> 00:24:52.170 align:middle line:90% will be kt plus 1-- 00:24:52.170 --> 00:24:54.110 align:middle line:90% this is little k-- 00:24:54.110 --> 00:25:11.046 align:middle line:84% minus kt equal to s times yt minus delta plus m kt. 00:25:11.046 --> 00:25:14.980 align:middle line:90% 00:25:14.980 --> 00:25:19.790 align:middle line:84% Wait, why don't I have a delta plus n minus plus gA there? 00:25:19.790 --> 00:25:23.320 align:middle line:84% Remember that in the previous model I have a delta plus m 00:25:23.320 --> 00:25:24.225 align:middle line:90% plus gA there. 00:25:24.225 --> 00:25:27.410 align:middle line:90% 00:25:27.410 --> 00:25:28.285 align:middle line:90% Did I make a mistake? 00:25:28.285 --> 00:25:33.010 align:middle line:90% 00:25:33.010 --> 00:25:35.120 align:middle line:84% Actually, this is a useful exercise for you. 00:25:35.120 --> 00:25:38.330 align:middle line:90% 00:25:38.330 --> 00:25:44.530 align:middle line:84% You remember that I had a delta plus m plus gA there, no? 00:25:44.530 --> 00:25:47.070 align:middle line:90% What's wrong? 00:25:47.070 --> 00:25:48.900 align:middle line:84% I just told you that this economy, 00:25:48.900 --> 00:25:52.410 align:middle line:84% at least in balanced growth, is exactly the same. 00:25:52.410 --> 00:25:54.380 align:middle line:90% So did I make a mistake? 00:25:54.380 --> 00:26:00.710 align:middle line:90% 00:26:00.710 --> 00:26:02.610 align:middle line:90% No. 00:26:02.610 --> 00:26:05.070 align:middle line:84% The reason I had the gA there is because I 00:26:05.070 --> 00:26:09.880 align:middle line:84% was looking at the change in capital per effective worker. 00:26:09.880 --> 00:26:12.330 align:middle line:84% I'm looking, now, at the change in capital per worker, 00:26:12.330 --> 00:26:13.420 align:middle line:90% not per effective worker. 00:26:13.420 --> 00:26:15.778 align:middle line:84% So I don't have that A in the denominator. 00:26:15.778 --> 00:26:17.820 align:middle line:84% So I don't need to account for the rate of growth 00:26:17.820 --> 00:26:22.260 align:middle line:84% of the denominator due to an increase in technology. 00:26:22.260 --> 00:26:23.020 align:middle line:90% I don't need that. 00:26:23.020 --> 00:26:25.930 align:middle line:90% 00:26:25.930 --> 00:26:30.605 align:middle line:84% And so what I can do is divide both sides by kt-- 00:26:30.605 --> 00:26:33.330 align:middle line:90% 00:26:33.330 --> 00:26:34.190 align:middle line:90% that's kt. 00:26:34.190 --> 00:26:38.250 align:middle line:90% 00:26:38.250 --> 00:26:46.930 align:middle line:84% And this is the rate of growth of k, no? 00:26:46.930 --> 00:26:48.350 align:middle line:90% It's the rate of growth of k. 00:26:48.350 --> 00:26:52.070 align:middle line:90% 00:26:52.070 --> 00:26:55.220 align:middle line:84% But in a steady state, the rate of growth of k, 00:26:55.220 --> 00:26:57.085 align:middle line:84% capital per worker, is equal to what? 00:26:57.085 --> 00:27:01.540 align:middle line:90% 00:27:01.540 --> 00:27:04.720 align:middle line:84% gA is the rate of growth of technology. 00:27:04.720 --> 00:27:13.450 align:middle line:84% So this-- in a steady state, this is equal to gA. 00:27:13.450 --> 00:27:16.960 align:middle line:90% And so what I wrote there is-- 00:27:16.960 --> 00:27:19.800 align:middle line:84% I think it should be exactly that. 00:27:19.800 --> 00:27:20.300 align:middle line:90% Is it? 00:27:20.300 --> 00:27:22.930 align:middle line:90% Yes, good. 00:27:22.930 --> 00:27:25.100 align:middle line:90% That's what I did. 00:27:25.100 --> 00:27:28.050 align:middle line:90% And why did I do this for? 00:27:28.050 --> 00:27:35.780 align:middle line:84% Well, because now I can-- you know that I can measure delta-- 00:27:35.780 --> 00:27:36.780 align:middle line:90% I can measure delta. 00:27:36.780 --> 00:27:37.675 align:middle line:90% I can measure n. 00:27:37.675 --> 00:27:40.230 align:middle line:90% 00:27:40.230 --> 00:27:44.320 align:middle line:90% And I can measure gA. 00:27:44.320 --> 00:27:49.660 align:middle line:84% So this implies that I can solve out, 00:27:49.660 --> 00:27:53.350 align:middle line:84% in a steady state, for what is the level of capital 00:27:53.350 --> 00:27:58.120 align:middle line:90% per effective worker. 00:27:58.120 --> 00:28:00.280 align:middle line:84% I can solve from this equation, and it's 00:28:00.280 --> 00:28:02.200 align:middle line:90% equal to this expression here. 00:28:02.200 --> 00:28:04.870 align:middle line:84% Notice a few interesting things here. 00:28:04.870 --> 00:28:07.030 align:middle line:90% Capital per worker-- 00:28:07.030 --> 00:28:10.750 align:middle line:84% Each of them is divided by n, so I can also look at big K 00:28:10.750 --> 00:28:17.050 align:middle line:84% over A times big H. It's increasing the savings rate. 00:28:17.050 --> 00:28:19.550 align:middle line:84% That you already had in the model we discussed before. 00:28:19.550 --> 00:28:21.400 align:middle line:84% If the saving rate is higher, then you're 00:28:21.400 --> 00:28:26.350 align:middle line:84% going to end up with a higher capital per effective worker 00:28:26.350 --> 00:28:27.940 align:middle line:90% ratio in the steady state. 00:28:27.940 --> 00:28:31.030 align:middle line:84% It's decreasing in population growth. 00:28:31.030 --> 00:28:34.210 align:middle line:84% All these things you already saw before. 00:28:34.210 --> 00:28:39.550 align:middle line:84% So now that I have this expression for K over H, 00:28:39.550 --> 00:28:44.690 align:middle line:84% I can go back to my production function, to this. 00:28:44.690 --> 00:28:47.600 align:middle line:90% And it's sticking there-- 00:28:47.600 --> 00:28:48.590 align:middle line:90% this value. 00:28:48.590 --> 00:28:51.260 align:middle line:84% And I get that output at time, t. 00:28:51.260 --> 00:28:53.390 align:middle line:84% Once you are in the balanced growth path, 00:28:53.390 --> 00:28:59.800 align:middle line:84% it's equal to A (t) times h times k over Ah 00:28:59.800 --> 00:29:00.670 align:middle line:90% to 1 minus alpha. 00:29:00.670 --> 00:29:02.290 align:middle line:90% Just solve for that. 00:29:02.290 --> 00:29:06.420 align:middle line:84% And the point being is that now I can write this as y(t) is 00:29:06.420 --> 00:29:09.280 align:middle line:90% equal to a t times-- 00:29:09.280 --> 00:29:12.140 align:middle line:84% so human capital times this expression here. 00:29:12.140 --> 00:29:15.760 align:middle line:84% So the point is, human capital doesn't affect the steady state 00:29:15.760 --> 00:29:21.800 align:middle line:84% growth, but it does affect the income per capita that you have. 00:29:21.800 --> 00:29:23.260 align:middle line:90% And it makes a big difference. 00:29:23.260 --> 00:29:24.050 align:middle line:90% I'll show you. 00:29:24.050 --> 00:29:27.850 align:middle line:90% 00:29:27.850 --> 00:29:30.750 align:middle line:84% So when people try to explain differences across the world, 00:29:30.750 --> 00:29:33.580 align:middle line:84% they notice that they were missing a big component. 00:29:33.580 --> 00:29:37.120 align:middle line:84% And that big component is education. 00:29:37.120 --> 00:29:39.250 align:middle line:90% So let's compare. 00:29:39.250 --> 00:29:41.290 align:middle line:90% What I want to do next is-- 00:29:41.290 --> 00:29:44.450 align:middle line:84% I can do this for every country in the world. 00:29:44.450 --> 00:29:49.080 align:middle line:84% And I can compare it with the US. 00:29:49.080 --> 00:29:53.255 align:middle line:84% OK, I can do this for every country in the world. 00:29:53.255 --> 00:29:55.630 align:middle line:84% And I can compare it with any other country in the world. 00:29:55.630 --> 00:29:58.830 align:middle line:84% But just-- let's compare it with the largest country in the world 00:29:58.830 --> 00:30:00.010 align:middle line:90% in terms of output. 00:30:00.010 --> 00:30:01.120 align:middle line:90% That's the US. 00:30:01.120 --> 00:30:03.610 align:middle line:90% So let's see what we get. 00:30:03.610 --> 00:30:08.640 align:middle line:84% So I'm going to take output per capita everywhere 00:30:08.640 --> 00:30:13.520 align:middle line:84% and divide it by the same expression for the US 00:30:13.520 --> 00:30:17.470 align:middle line:84% and then define that variable as yi hat. 00:30:17.470 --> 00:30:19.370 align:middle line:90% So for country i-- 00:30:19.370 --> 00:30:23.690 align:middle line:84% say, Singapore-- we take output per capita 00:30:23.690 --> 00:30:29.410 align:middle line:84% and we divide it by output per capita per person in the US. 00:30:29.410 --> 00:30:31.990 align:middle line:90% Assume-- big, if. 00:30:31.990 --> 00:30:34.480 align:middle line:90% This is a huge, if. 00:30:34.480 --> 00:30:37.300 align:middle line:84% But you can do that for the US versus Singapore. 00:30:37.300 --> 00:30:40.720 align:middle line:84% Probably is not a crazy assumption to make. 00:30:40.720 --> 00:30:43.450 align:middle line:84% Assume that they have the same rate 00:30:43.450 --> 00:30:46.940 align:middle line:84% of technological progress and the same technology and so on. 00:30:46.940 --> 00:30:49.010 align:middle line:84% Well, the same rate of technological progress-- 00:30:49.010 --> 00:30:50.830 align:middle line:84% I'm going to assume that for now. 00:30:50.830 --> 00:30:53.260 align:middle line:90% So then this yi hat-- 00:30:53.260 --> 00:30:55.730 align:middle line:90% you can write this-- 00:30:55.730 --> 00:31:02.860 align:middle line:84% it's just this for Singapore divided by this for the US. 00:31:02.860 --> 00:31:04.865 align:middle line:84% It turns out to be this expression here. 00:31:04.865 --> 00:31:09.190 align:middle line:90% 00:31:09.190 --> 00:31:12.160 align:middle line:84% Solow did something like this and said, 00:31:12.160 --> 00:31:17.500 align:middle line:84% OK, assume that technology is the same across the world 00:31:17.500 --> 00:31:21.970 align:middle line:84% because, at least for major economies, 00:31:21.970 --> 00:31:25.360 align:middle line:90% technology can be imported. 00:31:25.360 --> 00:31:29.470 align:middle line:90% And we can have the same-- 00:31:29.470 --> 00:31:31.640 align:middle line:84% more or less, the same technology across the world. 00:31:31.640 --> 00:31:34.060 align:middle line:84% So assume that this guy is equal to 1 00:31:34.060 --> 00:31:39.632 align:middle line:84% and that both Singapore and the US have the same rate of growth. 00:31:39.632 --> 00:31:47.620 align:middle line:84% And so that means that countries that have higher savings rate 00:31:47.620 --> 00:31:49.065 align:middle line:90% will tend to have-- 00:31:49.065 --> 00:31:50.440 align:middle line:84% we know that as [INAUDIBLE] goes, 00:31:50.440 --> 00:31:53.320 align:middle line:84% we'll tend to have higher output per capita. 00:31:53.320 --> 00:31:56.600 align:middle line:84% So Singapore has a higher savings rate than the US. 00:31:56.600 --> 00:32:03.370 align:middle line:84% That will tend to give Singapore a higher income per capita. 00:32:03.370 --> 00:32:07.240 align:middle line:84% If a country has a higher population growth, 00:32:07.240 --> 00:32:11.440 align:middle line:84% then it will tend to have a lower income per capita 00:32:11.440 --> 00:32:13.120 align:middle line:90% and so on and so forth. 00:32:13.120 --> 00:32:14.800 align:middle line:84% And so the question is, well, suppose 00:32:14.800 --> 00:32:19.420 align:middle line:84% you make this assumption of equal technology and take the-- 00:32:19.420 --> 00:32:21.462 align:middle line:84% we can measure the saving rate in different parts 00:32:21.462 --> 00:32:23.670 align:middle line:84% of the world, the population rates in different parts 00:32:23.670 --> 00:32:24.260 align:middle line:90% of the world. 00:32:24.260 --> 00:32:25.480 align:middle line:84% And we're assuming that there's the same rate 00:32:25.480 --> 00:32:27.410 align:middle line:84% of technological progress everywhere. 00:32:27.410 --> 00:32:31.750 align:middle line:84% How much of of the difference we observe in income per capita 00:32:31.750 --> 00:32:35.080 align:middle line:84% across the world can be accounted by that? 00:32:35.080 --> 00:32:38.080 align:middle line:84% So that was the first question, is-- 00:32:38.080 --> 00:32:41.500 align:middle line:84% well, suppose that technology is the same, 00:32:41.500 --> 00:32:45.110 align:middle line:84% but we measure all these other things-- saving rate, population 00:32:45.110 --> 00:32:48.980 align:middle line:84% growth, common rate of technological progress, 00:32:48.980 --> 00:32:51.710 align:middle line:84% common depreciation across the world, and so on. 00:32:51.710 --> 00:32:54.990 align:middle line:84% How much can we explain of the income disparity? 00:32:54.990 --> 00:32:57.750 align:middle line:84% And the conclusion is the following. 00:32:57.750 --> 00:33:02.600 align:middle line:84% The conclusion of that experiment is that-- 00:33:02.600 --> 00:33:07.970 align:middle line:84% if the only difference behind income per capita 00:33:07.970 --> 00:33:11.390 align:middle line:84% were years of schooling-- sorry, a key thing 00:33:11.390 --> 00:33:14.070 align:middle line:84% that I forgot to measure is years of schooling. 00:33:14.070 --> 00:33:16.830 align:middle line:84% So if a country has more years of schooling, 00:33:16.830 --> 00:33:19.350 align:middle line:84% it will tend to have a higher income per capita and so on. 00:33:19.350 --> 00:33:22.580 align:middle line:84% So if you try to explain the differences in income per capita 00:33:22.580 --> 00:33:24.500 align:middle line:84% across the world, using variables 00:33:24.500 --> 00:33:27.410 align:middle line:84% like years of schooling, difference 00:33:27.410 --> 00:33:30.890 align:middle line:84% in saving rate, difference in population growth, and so on, 00:33:30.890 --> 00:33:34.560 align:middle line:84% the world would be a lot more egalitarian than it actually is. 00:33:34.560 --> 00:33:37.370 align:middle line:90% It would look a lot flatter. 00:33:37.370 --> 00:33:40.160 align:middle line:84% So this is how much you can account. 00:33:40.160 --> 00:33:43.640 align:middle line:84% Here, you put a bunch of lots of countries-- 00:33:43.640 --> 00:33:45.950 align:middle line:90% Africa and so on here. 00:33:45.950 --> 00:33:48.850 align:middle line:84% And if you just stick, in this equation, 00:33:48.850 --> 00:33:52.900 align:middle line:84% the corresponding saving rate, education levels, and so on, 00:33:52.900 --> 00:33:54.860 align:middle line:84% the world would be a lot more similar. 00:33:54.860 --> 00:33:56.860 align:middle line:84% There wouldn't be the kind of disparities 00:33:56.860 --> 00:34:01.120 align:middle line:84% we see between some African countries and Singapore, say. 00:34:01.120 --> 00:34:02.390 align:middle line:90% We're talking about Singapore. 00:34:02.390 --> 00:34:05.150 align:middle line:84% But the world doesn't look like that. 00:34:05.150 --> 00:34:06.050 align:middle line:90% That's the point. 00:34:06.050 --> 00:34:08.380 align:middle line:84% So if you take all these things that 00:34:08.380 --> 00:34:11.335 align:middle line:84% make a lot of sense-- education, saving rate, and all 00:34:11.335 --> 00:34:15.639 align:middle line:84% that-- you're going to explain a small share of the differences 00:34:15.639 --> 00:34:18.190 align:middle line:84% in income per capita across the world. 00:34:18.190 --> 00:34:18.690 align:middle line:90% Sorry. 00:34:18.690 --> 00:34:25.380 align:middle line:84% In this plot here, L is our N. L, labor, is our N. 00:34:25.380 --> 00:34:28.159 align:middle line:84% So this is y over N. Our little y in this thing. 00:34:28.159 --> 00:34:31.090 align:middle line:90% 00:34:31.090 --> 00:34:32.360 align:middle line:90% So we can get so far. 00:34:32.360 --> 00:34:33.530 align:middle line:90% We need something else. 00:34:33.530 --> 00:34:38.980 align:middle line:84% So what else do we need to add to really explain 00:34:38.980 --> 00:34:42.320 align:middle line:90% the amount of disparity we have? 00:34:42.320 --> 00:34:47.989 align:middle line:84% Well, the answer is, again, the Solow residual. 00:34:47.989 --> 00:34:50.550 align:middle line:84% It turns out that the assumption that As 00:34:50.550 --> 00:34:52.440 align:middle line:90% are the same across the world-- 00:34:52.440 --> 00:34:54.659 align:middle line:84% that the level and the rate of growth 00:34:54.659 --> 00:35:00.350 align:middle line:84% are the same around the world-- is just a very bad assumption. 00:35:00.350 --> 00:35:04.620 align:middle line:84% The level of technology is very different across different parts 00:35:04.620 --> 00:35:05.450 align:middle line:90% of the world. 00:35:05.450 --> 00:35:08.280 align:middle line:84% So the next step was to say, OK, let's 00:35:08.280 --> 00:35:13.780 align:middle line:84% measure the difference in technologies across the world. 00:35:13.780 --> 00:35:15.800 align:middle line:84% And it turns out that if you try to explain-- 00:35:15.800 --> 00:35:18.430 align:middle line:84% so if you go out there and you measure the level of technology 00:35:18.430 --> 00:35:19.450 align:middle line:90% across the world-- 00:35:19.450 --> 00:35:27.490 align:middle line:84% different places-- Zimbabwe, Singapore, South Korea, 00:35:27.490 --> 00:35:29.230 align:middle line:90% and so on and so forth-- 00:35:29.230 --> 00:35:33.640 align:middle line:84% well-- and then you plot that, the level of technology that 00:35:33.640 --> 00:35:38.540 align:middle line:84% countries have, vis-a-vis their output per capita, per worker-- 00:35:38.540 --> 00:35:40.650 align:middle line:90% you explain a big share of it. 00:35:40.650 --> 00:35:43.660 align:middle line:84% So here is what you have-- is the relative A. 00:35:43.660 --> 00:35:45.890 align:middle line:84% So everything is relative to the US here. 00:35:45.890 --> 00:35:49.150 align:middle line:90% So the A that we measure-- 00:35:49.150 --> 00:35:50.960 align:middle line:90% the level of A that we measure-- 00:35:50.960 --> 00:35:54.102 align:middle line:84% I don't remember which year was this. 00:35:54.102 --> 00:35:55.310 align:middle line:90% I don't remember when it was. 00:35:55.310 --> 00:35:58.350 align:middle line:90% 00:35:58.350 --> 00:36:00.150 align:middle line:90% Doesn't matter. 00:36:00.150 --> 00:36:03.900 align:middle line:84% So if you measured the relative level of technology in country 00:36:03.900 --> 00:36:07.050 align:middle line:84% I, relative to the US, and then you measure 00:36:07.050 --> 00:36:09.420 align:middle line:84% the relative output per capita in that country 00:36:09.420 --> 00:36:10.650 align:middle line:90% relative to the US-- 00:36:10.650 --> 00:36:12.240 align:middle line:84% and forget about everything else-- 00:36:12.240 --> 00:36:14.020 align:middle line:84% education and so on and so forth-- 00:36:14.020 --> 00:36:18.090 align:middle line:84% you can get a pretty good relationship between the two. 00:36:18.090 --> 00:36:22.770 align:middle line:84% So between one half and 2/3 of the difference in output per 00:36:22.770 --> 00:36:26.400 align:middle line:84% worker across different countries in the world can be 00:36:26.400 --> 00:36:29.700 align:middle line:84% attributed to the difference in technology level. 00:36:29.700 --> 00:36:33.530 align:middle line:84% So that's a conclusion that we have. 00:36:33.530 --> 00:36:39.440 align:middle line:84% Now, let me revisit this issue of convergence. 00:36:39.440 --> 00:36:43.310 align:middle line:84% And so what you do is you take countries that have, 00:36:43.310 --> 00:36:46.430 align:middle line:84% more or less, the same A and that 00:36:46.430 --> 00:36:50.810 align:middle line:84% have more or less the same levels of education. 00:36:50.810 --> 00:36:54.710 align:middle line:84% And you look at the path of their output per capita. 00:36:54.710 --> 00:36:56.900 align:middle line:84% You get that the models we have been discussing here 00:36:56.900 --> 00:36:58.780 align:middle line:90% work extremely well. 00:36:58.780 --> 00:37:02.910 align:middle line:84% So here, you see that they are, more or less, growing together. 00:37:02.910 --> 00:37:04.830 align:middle line:84% There are wars and stuff like that here. 00:37:04.830 --> 00:37:07.920 align:middle line:84% So there are great recessions and things like that. 00:37:07.920 --> 00:37:13.520 align:middle line:84% But on average, you see the countries that were behind 00:37:13.520 --> 00:37:15.890 align:middle line:90% caught up and so on. 00:37:15.890 --> 00:37:17.460 align:middle line:90% Big dispersion here. 00:37:17.460 --> 00:37:19.260 align:middle line:90% They were all growing together. 00:37:19.260 --> 00:37:23.210 align:middle line:84% And as more time passes, the closer they get to each other 00:37:23.210 --> 00:37:24.960 align:middle line:90% because they are converging. 00:37:24.960 --> 00:37:28.790 align:middle line:84% These guys-- the US and the UK were already very close 00:37:28.790 --> 00:37:34.470 align:middle line:84% to a steady state, in the 1870s, while Japan was way behind. 00:37:34.470 --> 00:37:36.920 align:middle line:84% But it was sort of in the same class of countries 00:37:36.920 --> 00:37:41.490 align:middle line:84% in terms of technology and in terms of education levels 00:37:41.490 --> 00:37:43.530 align:middle line:90% and so on. 00:37:43.530 --> 00:37:45.960 align:middle line:90% So it works pretty well. 00:37:45.960 --> 00:37:49.830 align:middle line:90% This is for more countries. 00:37:49.830 --> 00:37:54.190 align:middle line:84% And you plot per-capita income in 1870-- 00:37:54.190 --> 00:37:58.560 align:middle line:84% again, for countries that have similar As and Ks-- 00:37:58.560 --> 00:38:00.072 align:middle line:90% A's and h. 00:38:00.072 --> 00:38:01.530 align:middle line:84% And you look at the rate of growth, 00:38:01.530 --> 00:38:03.280 align:middle line:84% and you get exactly what you would expect. 00:38:03.280 --> 00:38:06.450 align:middle line:84% Countries that were further behind caught up. 00:38:06.450 --> 00:38:07.210 align:middle line:90% That's Japan. 00:38:07.210 --> 00:38:08.490 align:middle line:90% Very fast rate of growth. 00:38:08.490 --> 00:38:10.920 align:middle line:84% And you get this very negative relationship. 00:38:10.920 --> 00:38:12.690 align:middle line:84% So this is the convergence model. 00:38:12.690 --> 00:38:16.890 align:middle line:84% It works extremely well, conditional on having the same A 00:38:16.890 --> 00:38:17.490 align:middle line:90% and h. 00:38:17.490 --> 00:38:19.710 align:middle line:84% So that's the contribution of this lecture. 00:38:19.710 --> 00:38:21.720 align:middle line:84% I already told you that this convergence model 00:38:21.720 --> 00:38:23.720 align:middle line:90% works quite well. 00:38:23.720 --> 00:38:26.930 align:middle line:84% The point is now that it works very well. 00:38:26.930 --> 00:38:28.670 align:middle line:90% And I had told you early on-- 00:38:28.670 --> 00:38:30.530 align:middle line:84% I think in the first lecture on growth-- 00:38:30.530 --> 00:38:33.160 align:middle line:84% that this worked very well for certain kinds of countries. 00:38:33.160 --> 00:38:34.910 align:middle line:84% But then when we put all of them together, 00:38:34.910 --> 00:38:36.910 align:middle line:84% there were some countries that were clearly off. 00:38:36.910 --> 00:38:38.540 align:middle line:84% And they were mostly in Africa, but you 00:38:38.540 --> 00:38:41.570 align:middle line:84% had countries that had low per capita income 00:38:41.570 --> 00:38:45.620 align:middle line:84% and they grew very little during that-- the sample I showed you. 00:38:45.620 --> 00:38:47.603 align:middle line:90% So here, I'm refining that. 00:38:47.603 --> 00:38:50.270 align:middle line:84% I'm saying, OK, now I'm going to tell you a little bit more what 00:38:50.270 --> 00:38:53.010 align:middle line:84% I mean by countries being similar. 00:38:53.010 --> 00:38:57.060 align:middle line:84% And what I mean here is that they have similar A and h. 00:38:57.060 --> 00:39:01.130 align:middle line:84% So when I look at countries that have similar A and h, 00:39:01.130 --> 00:39:04.830 align:middle line:84% the models we have discussed work extremely well. 00:39:04.830 --> 00:39:06.790 align:middle line:84% This is over a short period of time, 00:39:06.790 --> 00:39:09.040 align:middle line:84% so you have more fluctuations and more countries. 00:39:09.040 --> 00:39:13.110 align:middle line:84% But still-- you can argue that Mexico and Chile probably do not 00:39:13.110 --> 00:39:15.240 align:middle line:84% belong with many of these other countries, 00:39:15.240 --> 00:39:17.520 align:middle line:84% but you still get this negative relationship. 00:39:17.520 --> 00:39:19.960 align:middle line:90% It's quite clear. 00:39:19.960 --> 00:39:22.465 align:middle line:84% Now, if you don't control by A and h 00:39:22.465 --> 00:39:24.310 align:middle line:84% and you put everything together, then 00:39:24.310 --> 00:39:27.910 align:middle line:84% the plot looks like the plot I showed you earlier. 00:39:27.910 --> 00:39:33.450 align:middle line:84% So if I control by A and h, the models work very well. 00:39:33.450 --> 00:39:36.970 align:middle line:84% If I don't control for A and h, then the models 00:39:36.970 --> 00:39:40.832 align:middle line:90% do not look that nice. 00:39:40.832 --> 00:39:42.780 align:middle line:84% So this led to a literature, which 00:39:42.780 --> 00:39:46.020 align:middle line:84% is called the conditional convergence literature. 00:39:46.020 --> 00:39:49.080 align:middle line:84% And the idea-- it's almost accounting, 00:39:49.080 --> 00:39:50.730 align:middle line:90% but the idea is the following. 00:39:50.730 --> 00:39:53.310 align:middle line:90% So the question that-- 00:39:53.310 --> 00:39:55.830 align:middle line:84% what's behind this literature is, well, why is it 00:39:55.830 --> 00:39:58.660 align:middle line:90% that we have some countries-- 00:39:58.660 --> 00:40:04.060 align:middle line:84% say, here-- that have a very low income per capita 00:40:04.060 --> 00:40:05.480 align:middle line:90% and grow very slowly? 00:40:05.480 --> 00:40:06.430 align:middle line:90% That's the puzzle. 00:40:06.430 --> 00:40:09.730 align:middle line:84% How can it happen that we have that? 00:40:09.730 --> 00:40:14.380 align:middle line:84% And the story-- but again, it's more accounting than 00:40:14.380 --> 00:40:16.060 align:middle line:90% an explanation, in my view-- 00:40:16.060 --> 00:40:19.140 align:middle line:84% is what is called conditional convergence. 00:40:19.140 --> 00:40:21.490 align:middle line:90% It says for some reason-- 00:40:21.490 --> 00:40:23.650 align:middle line:84% probably it has to be explained in terms 00:40:23.650 --> 00:40:28.330 align:middle line:84% of institutions, political instability, or whatever. 00:40:28.330 --> 00:40:32.740 align:middle line:84% For some reason, some countries have just lower steady state 00:40:32.740 --> 00:40:35.680 align:middle line:84% levels of technology, lower steady states because they 00:40:35.680 --> 00:40:37.180 align:middle line:84% have lower technologies, and they're 00:40:37.180 --> 00:40:39.350 align:middle line:84% stuck with lower technologies and so on. 00:40:39.350 --> 00:40:43.750 align:middle line:90% 00:40:43.750 --> 00:40:45.520 align:middle line:84% So what this literature does-- it says, 00:40:45.520 --> 00:40:48.610 align:middle line:84% OK, let's compute the steady state. 00:40:48.610 --> 00:40:51.130 align:middle line:84% So let's accept that some countries will 00:40:51.130 --> 00:40:53.300 align:middle line:90% have lower level of technology. 00:40:53.300 --> 00:40:54.335 align:middle line:90% That's what it is. 00:40:54.335 --> 00:40:56.210 align:middle line:84% Maybe at some point, they'll flip from there. 00:40:56.210 --> 00:40:59.163 align:middle line:84% But they have been, for a long time, 00:40:59.163 --> 00:41:03.250 align:middle line:84% in the stack that let's assume that they have a different level 00:41:03.250 --> 00:41:04.240 align:middle line:90% of technology. 00:41:04.240 --> 00:41:07.570 align:middle line:84% So that means-- let's compute, for each country, 00:41:07.570 --> 00:41:10.990 align:middle line:84% its steady state, its own steady state, 00:41:10.990 --> 00:41:14.570 align:middle line:84% using its own technology and its own level of education. 00:41:14.570 --> 00:41:18.190 align:middle line:90% 00:41:18.190 --> 00:41:23.110 align:middle line:84% So in particular, in this plot, I'm going to show you- 00:41:23.110 --> 00:41:24.340 align:middle line:90% take the values-- 00:41:24.340 --> 00:41:28.080 align:middle line:90% the value of A for 1970. 00:41:28.080 --> 00:41:30.000 align:middle line:84% That's the plot I'm going to show you. 00:41:30.000 --> 00:41:32.770 align:middle line:84% The value that each country has in 1970. 00:41:32.770 --> 00:41:36.360 align:middle line:84% Compute the steady state level of output corresponding 00:41:36.360 --> 00:41:43.170 align:middle line:84% to that A. A-- and over time, it will be growing at gA, whatever. 00:41:43.170 --> 00:41:46.430 align:middle line:90% But take the A of 1970. 00:41:46.430 --> 00:41:49.960 align:middle line:84% Compute the steady state value of that. 00:41:49.960 --> 00:41:53.270 align:middle line:84% Compare it with the current output over that. 00:41:53.270 --> 00:41:54.910 align:middle line:84% If the current output is below that, 00:41:54.910 --> 00:41:56.650 align:middle line:84% that means that this country still 00:41:56.650 --> 00:41:58.570 align:middle line:84% needs to catch up-- not with respect 00:41:58.570 --> 00:42:00.820 align:middle line:84% to some universal steady state, but with respect 00:42:00.820 --> 00:42:03.250 align:middle line:84% to its own steady state, with its lower technology 00:42:03.250 --> 00:42:04.480 align:middle line:90% and whatever. 00:42:04.480 --> 00:42:09.380 align:middle line:84% And then look at whether we see convergence or not. 00:42:09.380 --> 00:42:14.200 align:middle line:84% And the answer is that you start recovering this downward sloping 00:42:14.200 --> 00:42:14.860 align:middle line:90% curve. 00:42:14.860 --> 00:42:16.150 align:middle line:90% So what does this say? 00:42:16.150 --> 00:42:18.140 align:middle line:84% What is the big story telling us? 00:42:18.140 --> 00:42:20.500 align:middle line:84% It's saying, look, some countries, 00:42:20.500 --> 00:42:24.340 align:middle line:84% for reasons that are beyond this model, 00:42:24.340 --> 00:42:28.690 align:middle line:84% just simply have much lower steady state. 00:42:28.690 --> 00:42:29.320 align:middle line:90% Yep. 00:42:29.320 --> 00:42:30.560 align:middle line:90% They have lower technologies. 00:42:30.560 --> 00:42:33.400 align:middle line:84% They don't know how to use more complicated technology. 00:42:33.400 --> 00:42:35.020 align:middle line:90% I don't know. 00:42:35.020 --> 00:42:36.260 align:middle line:90% But that's what it is. 00:42:36.260 --> 00:42:37.900 align:middle line:90% They have lower technologies. 00:42:37.900 --> 00:42:40.180 align:middle line:84% And so they have their own steady states, 00:42:40.180 --> 00:42:43.330 align:middle line:84% which can be steady states with very low levels of income 00:42:43.330 --> 00:42:44.910 align:middle line:90% per capita. 00:42:44.910 --> 00:42:48.340 align:middle line:84% Now, for those countries, it still applies-- 00:42:48.340 --> 00:42:50.070 align:middle line:84% and that's what this picture shows-- 00:42:50.070 --> 00:42:53.730 align:middle line:84% that if they are not at their steady state, 00:42:53.730 --> 00:42:57.750 align:middle line:84% they still have lower capital per effective worker 00:42:57.750 --> 00:42:59.880 align:middle line:84% than they need to have in their steady state-- 00:42:59.880 --> 00:43:02.730 align:middle line:84% that they will have transitional growth. 00:43:02.730 --> 00:43:06.260 align:middle line:84% So they will grow faster than their growth 00:43:06.260 --> 00:43:10.500 align:middle line:90% in their own steady state. 00:43:10.500 --> 00:43:12.630 align:middle line:84% And that's what this picture shows. 00:43:12.630 --> 00:43:15.360 align:middle line:84% These are countries that grew very little. 00:43:15.360 --> 00:43:17.685 align:middle line:84% Look, we have Japan here together with Botswana. 00:43:17.685 --> 00:43:21.100 align:middle line:90% 00:43:21.100 --> 00:43:25.040 align:middle line:84% And maybe they won in the same place. 00:43:25.040 --> 00:43:27.820 align:middle line:84% So these are countries that still had lots of growth to do, 00:43:27.820 --> 00:43:30.190 align:middle line:84% relative to their own steady state. 00:43:30.190 --> 00:43:32.228 align:middle line:90% And they did grow a lot. 00:43:32.228 --> 00:43:33.020 align:middle line:90% How do I know that? 00:43:33.020 --> 00:43:35.620 align:middle line:84% Well, because the output I compute-- 00:43:35.620 --> 00:43:37.870 align:middle line:84% the output I compute, relative to the steady state 00:43:37.870 --> 00:43:41.330 align:middle line:84% at the beginning of my sample, was much lower than 1. 00:43:41.330 --> 00:43:45.450 align:middle line:84% That means that you're not at your steady state. 00:43:45.450 --> 00:43:48.570 align:middle line:84% So this variable here is the output 00:43:48.570 --> 00:43:52.260 align:middle line:84% you have at the beginning of the sample, relative to what 00:43:52.260 --> 00:43:53.520 align:middle line:90% the steady state-- 00:43:53.520 --> 00:43:55.560 align:middle line:90% your steady state is. 00:43:55.560 --> 00:43:57.060 align:middle line:84% How do you compute the steady state? 00:43:57.060 --> 00:43:59.310 align:middle line:84% Well, you input the level of technology. 00:43:59.310 --> 00:44:00.510 align:middle line:90% You input the saving rate. 00:44:00.510 --> 00:44:03.400 align:middle line:84% You input the population growth and all those kind of things. 00:44:03.400 --> 00:44:05.120 align:middle line:84% So you have a number lower than 1. 00:44:05.120 --> 00:44:06.870 align:middle line:84% It means you still have catching up growth 00:44:06.870 --> 00:44:11.250 align:middle line:84% to do, not with respect to the global universal steady state, 00:44:11.250 --> 00:44:13.480 align:middle line:84% but with respect to your own steady state. 00:44:13.480 --> 00:44:16.620 align:middle line:84% And when you do that, you see that some countries that 00:44:16.620 --> 00:44:20.010 align:middle line:84% are in the total sample looked like they are not growing and so 00:44:20.010 --> 00:44:20.680 align:middle line:90% on and so forth. 00:44:20.680 --> 00:44:21.550 align:middle line:90% They are growing. 00:44:21.550 --> 00:44:25.590 align:middle line:84% They are just growing relative to their own steady state, which 00:44:25.590 --> 00:44:28.170 align:middle line:84% has little growth, and it has low levels of technology 00:44:28.170 --> 00:44:29.640 align:middle line:90% and so on. 00:44:29.640 --> 00:44:34.290 align:middle line:84% And so that's the conclusion of this conditional convergence 00:44:34.290 --> 00:44:35.430 align:middle line:90% literature. 00:44:35.430 --> 00:44:40.560 align:middle line:84% Now, it turns out that the world has become very unequal, also, 00:44:40.560 --> 00:44:42.910 align:middle line:90% along this dimension over time. 00:44:42.910 --> 00:44:47.650 align:middle line:84% This shows you the ratio of GDP per worker of the 90th 00:44:47.650 --> 00:44:50.060 align:middle line:84% percentile to the 10th percentile country. 00:44:50.060 --> 00:44:52.240 align:middle line:84% And so you have not only big differences 00:44:52.240 --> 00:44:53.800 align:middle line:90% in technology across the world. 00:44:53.800 --> 00:44:56.020 align:middle line:84% But also, you have very different rates 00:44:56.020 --> 00:44:58.750 align:middle line:84% of growth in technology across different countries 00:44:58.750 --> 00:44:59.540 align:middle line:90% in the world. 00:44:59.540 --> 00:45:05.216 align:middle line:84% So this difference is sort of increasing quite dramatically. 00:45:05.216 --> 00:45:06.615 align:middle line:90% I don't know what happened here. 00:45:06.615 --> 00:45:13.040 align:middle line:90% [LAUGHS] These are the same. 00:45:13.040 --> 00:45:16.480 align:middle line:84% So the world started with countries-- this is telling you 00:45:16.480 --> 00:45:19.720 align:middle line:84% it started with countries that were richer than others, 00:45:19.720 --> 00:45:25.610 align:middle line:84% and that distance has been rising over time that 00:45:25.610 --> 00:45:27.380 align:middle line:84% towards the end, we began to change here. 00:45:27.380 --> 00:45:30.040 align:middle line:90% 00:45:30.040 --> 00:45:32.655 align:middle line:84% I think that has a lot to do with China. 00:45:32.655 --> 00:45:34.030 align:middle line:84% That was a poor economy that grew 00:45:34.030 --> 00:45:36.112 align:middle line:90% very fast during that period. 00:45:36.112 --> 00:45:38.570 align:middle line:84% And it wasn't very large here, so it didn't matter as much. 00:45:38.570 --> 00:45:40.450 align:middle line:84% But then it began to count a lot. 00:45:40.450 --> 00:45:41.410 align:middle line:90% I think. 00:45:41.410 --> 00:45:42.430 align:middle line:90% I'm not completely sure. 00:45:42.430 --> 00:45:43.390 align:middle line:90% That's it. 00:45:43.390 --> 00:45:47.260 align:middle line:84% Anyways-- but that's the state of knowledge in this-- 00:45:47.260 --> 00:45:51.970 align:middle line:84% obviously, there's a big literature around all of this, 00:45:51.970 --> 00:45:54.680 align:middle line:84% and very complex, even, literature. 00:45:54.680 --> 00:45:58.360 align:middle line:84% But there is-- we understand-- we 00:45:58.360 --> 00:46:04.420 align:middle line:84% know that we have good ways of explaining 00:46:04.420 --> 00:46:08.800 align:middle line:84% how a country converges to its own steady state, 00:46:08.800 --> 00:46:12.850 align:middle line:84% that we have very poor models, certainly, within economics. 00:46:12.850 --> 00:46:15.970 align:middle line:90% 00:46:15.970 --> 00:46:19.430 align:middle line:84% Or within growth theory, per se, there 00:46:19.430 --> 00:46:22.730 align:middle line:84% is little institutions and stuff like that explain some of that. 00:46:22.730 --> 00:46:25.420 align:middle line:84% But we have very poor models, in general, 00:46:25.420 --> 00:46:31.930 align:middle line:84% to understand what gives rise to this big disparity in technology 00:46:31.930 --> 00:46:34.810 align:middle line:90% adoption and so on. 00:46:34.810 --> 00:46:39.360 align:middle line:84% So that's all that I want to say about growth. 00:46:39.360 --> 00:46:41.847 align:middle line:84% The next topic is we're going to open the economy. 00:46:41.847 --> 00:46:43.680 align:middle line:84% We're going to go back to the type of models 00:46:43.680 --> 00:46:48.620 align:middle line:84% we had very early on, but now in the context of an open economy. 00:46:48.620 --> 00:47:01.000 align:middle line:90%