1 00:00:17,679 --> 00:00:25,118 okay let's uh let's start um So the plan 2 00:00:21,320 --> 00:00:28,320 for today is to wrap up this growth uh 3 00:00:25,118 --> 00:00:31,480 Theory section of the of the course and 4 00:00:28,320 --> 00:00:34,320 um I I I want to sort of 5 00:00:31,480 --> 00:00:35,878 conclude by showing you what we can and 6 00:00:34,320 --> 00:00:38,480 cannot explain with the mods we have 7 00:00:35,878 --> 00:00:41,079 looked up to now and almost as a matter 8 00:00:38,479 --> 00:00:43,599 of accounting I will tell you what do we 9 00:00:41,079 --> 00:00:45,439 need to fill which gaps do we need to 10 00:00:43,600 --> 00:00:48,160 fill in order to explain sort of the 11 00:00:45,439 --> 00:00:51,718 great dispersion we see in income per 12 00:00:48,159 --> 00:00:55,279 capita across the world um but before I 13 00:00:51,719 --> 00:00:55,280 do that I need to finish the previous 14 00:00:57,280 --> 00:01:03,640 lecture and so let me let me do that H I 15 00:01:01,198 --> 00:01:05,879 had shown you this table remember in the 16 00:01:03,640 --> 00:01:09,640 in the complete model the model that has 17 00:01:05,879 --> 00:01:13,239 a a productivity growth unemployment and 18 00:01:09,640 --> 00:01:16,640 and and population growth um we 19 00:01:13,239 --> 00:01:19,599 concluded that imbalanced growth H the 20 00:01:16,640 --> 00:01:21,280 following happened no uh obviously if we 21 00:01:19,599 --> 00:01:24,759 pick the right normalization the right 22 00:01:21,280 --> 00:01:27,159 normalization here was ER effective 23 00:01:24,759 --> 00:01:30,478 workers so that productivity 24 00:01:27,159 --> 00:01:32,600 productivity times a population or 25 00:01:30,478 --> 00:01:35,640 workers and so if we normalize the 26 00:01:32,599 --> 00:01:37,158 variables by that H we get obviously 27 00:01:35,640 --> 00:01:39,118 zero growth that's what it means to have 28 00:01:37,159 --> 00:01:40,600 a balanced growth in which all the 29 00:01:39,118 --> 00:01:44,000 relevant variables are growing at the 30 00:01:40,599 --> 00:01:47,158 same rate H so Capital per effective 31 00:01:44,000 --> 00:01:48,920 worker will will be a state that's 32 00:01:47,159 --> 00:01:52,799 that's a diagram we plot remember the 33 00:01:48,920 --> 00:01:54,840 diagram we plot was output per effective 34 00:01:52,799 --> 00:01:56,640 worker against Capital per effective 35 00:01:54,840 --> 00:01:59,240 worker and that diagram has a steady 36 00:01:56,640 --> 00:02:01,920 state okay and that steady state at the 37 00:01:59,239 --> 00:02:04,560 steady state or the balance growth point 38 00:02:01,920 --> 00:02:07,159 then we have that H the normalized 39 00:02:04,560 --> 00:02:09,199 variables grow at the rate of zero 40 00:02:07,159 --> 00:02:12,920 Capital per worker has to grow at the 41 00:02:09,199 --> 00:02:14,759 rate G GA because Capital per effective 42 00:02:12,919 --> 00:02:17,439 worker is not growing so Capital per 43 00:02:14,759 --> 00:02:19,840 worker will be growing at the rate GA 44 00:02:17,439 --> 00:02:21,439 the same applies for output per worker 45 00:02:19,840 --> 00:02:23,239 output per effective worker is not 46 00:02:21,439 --> 00:02:25,680 growing that's balanced growth but 47 00:02:23,239 --> 00:02:27,200 therefore output per worker will be 48 00:02:25,680 --> 00:02:29,959 growing at the rate 49 00:02:27,199 --> 00:02:32,959 GA um 50 00:02:29,959 --> 00:02:36,159 these are the exogenous drivers a you 51 00:02:32,959 --> 00:02:40,080 know output per worker we assume no a 52 00:02:36,159 --> 00:02:42,759 well sorry labor is is GA is exogenous 53 00:02:40,080 --> 00:02:45,480 in this model and so is GM population 54 00:02:42,759 --> 00:02:46,878 growth is some constant we take it's not 55 00:02:45,479 --> 00:02:49,359 something we try to explain within the 56 00:02:46,878 --> 00:02:52,399 model okay but the two drivers of 57 00:02:49,360 --> 00:02:54,280 absolute growth will be GA and GN and so 58 00:02:52,400 --> 00:02:57,120 capital in the St state will be growing 59 00:02:54,280 --> 00:02:59,439 at the rate GA plus GN output will be 60 00:02:57,120 --> 00:03:02,680 growing at the rate GA plus GN so that's 61 00:02:59,439 --> 00:03:04,959 balance grow okay now let me give you an 62 00:03:02,680 --> 00:03:07,200 example so you can do see that suppose 63 00:03:04,959 --> 00:03:09,080 that our production function is is this 64 00:03:07,199 --> 00:03:10,958 we call that the a cop Douglas 65 00:03:09,080 --> 00:03:14,040 production 66 00:03:10,959 --> 00:03:15,640 function K to the 1 minus Alpha a n to 67 00:03:14,039 --> 00:03:17,079 the alpha does this function have 68 00:03:15,639 --> 00:03:20,639 constant 69 00:03:17,080 --> 00:03:25,000 returns to scale yes the sum of the 70 00:03:20,639 --> 00:03:27,439 exponents is one okay anyways but so uh 71 00:03:25,000 --> 00:03:30,039 take the log of both sides the change in 72 00:03:27,439 --> 00:03:32,158 the log is the rate of growth and so you 73 00:03:30,039 --> 00:03:33,959 get that the rate of growth of output is 74 00:03:32,158 --> 00:03:36,560 equal to 1 minus Alpha the rate of 75 00:03:33,959 --> 00:03:39,280 growth of capital plus Alpha time the 76 00:03:36,560 --> 00:03:42,319 rate of growth of effective workers okay 77 00:03:39,280 --> 00:03:44,759 so in balanced growth GK will be growing 78 00:03:42,318 --> 00:03:46,560 at the rate GA plus GN and therefore 79 00:03:44,759 --> 00:03:48,919 output will also be growing at the rate 80 00:03:46,560 --> 00:03:51,080 GA plus GN okay so that's what you have 81 00:03:48,919 --> 00:03:54,639 in the table and if you want to look at 82 00:03:51,080 --> 00:03:57,079 a variable like this Capital per worker 83 00:03:54,639 --> 00:03:59,919 then output per worker then you you need 84 00:03:57,079 --> 00:04:02,120 G gy minus GN 85 00:03:59,919 --> 00:04:03,878 H so subtract the GN and you can 86 00:04:02,120 --> 00:04:06,519 subtract both sides then it's going to 87 00:04:03,878 --> 00:04:09,959 be equal to GA okay I subtract GM from 88 00:04:06,519 --> 00:04:12,200 the right hand side H this one and that 89 00:04:09,959 --> 00:04:14,920 one cancel and I get GA on the right 90 00:04:12,199 --> 00:04:16,759 hand side that's the way you use that 91 00:04:14,919 --> 00:04:21,798 expression to fill all this all these 92 00:04:16,759 --> 00:04:24,040 blanks okay that's the that's St so I I 93 00:04:21,798 --> 00:04:27,799 think I stopped right before that this 94 00:04:24,040 --> 00:04:30,919 this slide or at this slide which is you 95 00:04:27,800 --> 00:04:33,120 know if I look at this the table GN is 96 00:04:30,918 --> 00:04:34,478 pretty easy to compute in most places 97 00:04:33,120 --> 00:04:36,918 there are places in the world where we 98 00:04:34,478 --> 00:04:39,319 sort of cannot even measure birth and 99 00:04:36,918 --> 00:04:42,079 death so it's difficult but in most 100 00:04:39,319 --> 00:04:45,680 places H you can measure GN the rate of 101 00:04:42,079 --> 00:04:47,359 FR of population H quite accurately and 102 00:04:45,680 --> 00:04:48,959 the question we have though is how do we 103 00:04:47,360 --> 00:04:51,280 measure technological progress It's also 104 00:04:48,959 --> 00:04:53,638 easy to measure the growth in the stock 105 00:04:51,279 --> 00:04:56,879 of capital it's investment minus 106 00:04:53,639 --> 00:05:00,478 depreciation uh but how do we measure H 107 00:04:56,879 --> 00:05:03,839 GA no the rate of technological progress 108 00:05:00,478 --> 00:05:07,159 and uhh the first proposal on how to do 109 00:05:03,839 --> 00:05:09,319 it was also by Bob solo H that was a 110 00:05:07,160 --> 00:05:11,400 second contribution he had in this in 111 00:05:09,319 --> 00:05:13,599 growth Theory well it was also growth 112 00:05:11,399 --> 00:05:14,959 measurement how do we measure GA it 113 00:05:13,600 --> 00:05:16,879 turns out that the only way you're going 114 00:05:14,959 --> 00:05:19,599 to have output per capita growing over 115 00:05:16,879 --> 00:05:21,879 time outut person growing over time is 116 00:05:19,600 --> 00:05:23,520 due to GA so we might as well try to 117 00:05:21,879 --> 00:05:26,279 measure that since it's such an 118 00:05:23,519 --> 00:05:31,198 important variable for sort of the 119 00:05:26,279 --> 00:05:33,239 growth of er the growth of uh happiness 120 00:05:31,199 --> 00:05:36,000 if you get one indicator of happiness is 121 00:05:33,240 --> 00:05:37,680 output per C per worker well such an 122 00:05:36,000 --> 00:05:40,560 important driver we need to be able to 123 00:05:37,680 --> 00:05:42,400 measure it and and the basic idea that 124 00:05:40,560 --> 00:05:43,879 Bob solo had is is essentially something 125 00:05:42,399 --> 00:05:49,439 you could have taken from 126 00:05:43,879 --> 00:05:51,120 1401 it's extremely simple it says ER 127 00:05:49,439 --> 00:05:53,800 there are some assumptions behind this 128 00:05:51,120 --> 00:05:57,918 but you know in in the basic competitive 129 00:05:53,800 --> 00:05:59,840 model you have that that um you can 130 00:05:57,918 --> 00:06:04,120 compute the contribution of each each 131 00:05:59,839 --> 00:06:08,719 factor of production to to Output H by 132 00:06:04,120 --> 00:06:11,439 the payment it receives okay so under 133 00:06:08,720 --> 00:06:13,440 this assumption no suppose that that 134 00:06:11,439 --> 00:06:15,759 you're spending in workers 135 00:06:13,439 --> 00:06:18,598 $30,000 a 136 00:06:15,759 --> 00:06:20,199 year so that means in a competitive 137 00:06:18,598 --> 00:06:22,598 equilibrium in the labor market and so 138 00:06:20,199 --> 00:06:24,120 on that the worker is contributing to 139 00:06:22,598 --> 00:06:26,759 production 140 00:06:24,120 --> 00:06:28,598 $30,000 okay I'm not going to deal with 141 00:06:26,759 --> 00:06:30,360 markups and things like that here but 142 00:06:28,598 --> 00:06:32,639 that's a basic idea you can adjust all 143 00:06:30,360 --> 00:06:36,120 these formulas to include markups but 144 00:06:32,639 --> 00:06:41,199 let me not do that so that also tells 145 00:06:36,120 --> 00:06:45,959 you that if you increase 146 00:06:41,199 --> 00:06:50,280 um er employment by 10% you'll also 147 00:06:45,959 --> 00:06:52,038 going to increase output by 10% times 148 00:06:50,279 --> 00:06:54,879 whatever is the contribution of Labor to 149 00:06:52,038 --> 00:06:59,079 Output okay and that's what I have here 150 00:06:54,879 --> 00:07:02,879 the contribution of H to Output of 151 00:06:59,079 --> 00:07:07,959 adding workers is going to be that times 152 00:07:02,879 --> 00:07:10,759 Delta n i can divide by H by y both 153 00:07:07,959 --> 00:07:13,399 sides and here multiply and divide by n 154 00:07:10,759 --> 00:07:16,840 and I get that the the the rate of the 155 00:07:13,399 --> 00:07:22,000 the the rate of growth in 156 00:07:16,839 --> 00:07:24,959 output due to a a a rate of growth in 157 00:07:22,000 --> 00:07:26,439 employment is equal to the labor share 158 00:07:24,959 --> 00:07:30,120 that's called the labor share is the 159 00:07:26,439 --> 00:07:36,199 wage Bill W * n divided by total total 160 00:07:30,120 --> 00:07:39,959 uh Revenue uh sales and uh uh times the 161 00:07:36,199 --> 00:07:42,759 rate of growth of H population or 162 00:07:39,959 --> 00:07:45,598 workers is the same here so I'm going to 163 00:07:42,759 --> 00:07:48,800 call this GYN it's the rate of growth of 164 00:07:45,598 --> 00:07:51,959 output due to the rate of growth in 165 00:07:48,800 --> 00:07:54,639 population is equal to this this labor 166 00:07:51,959 --> 00:07:58,719 share which I'm going to call that Alpha 167 00:07:54,639 --> 00:08:00,038 times GM okay I can do exactly the same 168 00:07:58,720 --> 00:08:01,599 with capital 169 00:08:00,038 --> 00:08:02,839 and you can do if you have more factor 170 00:08:01,598 --> 00:08:05,639 of production you can do the same for 171 00:08:02,839 --> 00:08:07,239 each factor of production so but in this 172 00:08:05,639 --> 00:08:09,598 simple example we have only two factors 173 00:08:07,240 --> 00:08:12,240 of production labor and capital so I can 174 00:08:09,598 --> 00:08:16,199 do the same for Capital and I can say 175 00:08:12,240 --> 00:08:18,720 the contribution of of Capital Growth to 176 00:08:16,199 --> 00:08:20,960 Output growth is going to be equal to 177 00:08:18,720 --> 00:08:23,319 the capital share which is the compl of 178 00:08:20,959 --> 00:08:26,038 the labor share so it's it's total 179 00:08:23,319 --> 00:08:29,639 revenue minus the wage wage payment the 180 00:08:26,038 --> 00:08:32,080 wage Bill divided by total revenue h 181 00:08:29,639 --> 00:08:35,080 times the rate of growth of capital okay 182 00:08:32,080 --> 00:08:38,440 so the contribution of H to Output 183 00:08:35,080 --> 00:08:40,599 growth of the rate of growth of capital 184 00:08:38,440 --> 00:08:44,560 is is 1 minus Alpha which is the share 185 00:08:40,599 --> 00:08:48,200 of capital times uh the rate of growth 186 00:08:44,559 --> 00:08:49,119 of capital okay so that means if I sum 187 00:08:48,200 --> 00:08:53,839 the 188 00:08:49,120 --> 00:08:56,480 contribution of Labor and capital I have 189 00:08:53,839 --> 00:08:57,920 I I'm left with the residual which is 190 00:08:56,480 --> 00:08:59,920 whatever is the rate of growth I have in 191 00:08:57,919 --> 00:09:02,078 output I know how much I'm getting from 192 00:08:59,919 --> 00:09:03,919 labor I know how much I'm getting for 193 00:09:02,078 --> 00:09:05,919 Capital if there is any difference it 194 00:09:03,919 --> 00:09:08,679 must be due to that thing I don't not 195 00:09:05,919 --> 00:09:12,159 observe which is technological progress 196 00:09:08,679 --> 00:09:12,159 okay that's the logic of all this 197 00:09:12,480 --> 00:09:16,039 stuff go back for example to this 198 00:09:14,600 --> 00:09:20,759 production function I'm saying I know 199 00:09:16,039 --> 00:09:22,679 the contribution that K has to Output 200 00:09:20,759 --> 00:09:25,720 growth I know the contribution that n 201 00:09:22,679 --> 00:09:27,799 has to Output growth well the only thing 202 00:09:25,720 --> 00:09:29,639 I'm missing is the contribution that a 203 00:09:27,799 --> 00:09:32,240 has to Output growth which say don't 204 00:09:29,639 --> 00:09:34,039 observe but I observe output growth I 205 00:09:32,240 --> 00:09:36,440 observe Capital Growth I observe 206 00:09:34,039 --> 00:09:37,120 employment growth so I can solve out 207 00:09:36,440 --> 00:09:39,519 what 208 00:09:37,120 --> 00:09:43,600 is the technological technological 209 00:09:39,519 --> 00:09:45,679 progress a growth okay and that's that's 210 00:09:43,600 --> 00:09:48,040 called it's called the solo residual by 211 00:09:45,679 --> 00:09:50,759 the way okay but that's the way the rate 212 00:09:48,039 --> 00:09:52,879 of growth of GA of a is measured the 213 00:09:50,759 --> 00:09:56,439 rate of growth of output minus the 214 00:09:52,879 --> 00:10:01,120 contribution to growth of er employment 215 00:09:56,440 --> 00:10:03,040 population and capital 216 00:10:01,120 --> 00:10:05,519 any question about 217 00:10:03,039 --> 00:10:07,480 that no makees 218 00:10:05,519 --> 00:10:11,919 sense 219 00:10:07,480 --> 00:10:13,639 somewhat okay good so anyway so there's 220 00:10:11,919 --> 00:10:17,278 a huge industry of measuring these kind 221 00:10:13,639 --> 00:10:18,360 of things of course uh let me give you 222 00:10:17,278 --> 00:10:22,278 an 223 00:10:18,360 --> 00:10:27,200 example h on how to use this accounting 224 00:10:22,278 --> 00:10:28,879 um so China 78 2017 that's an episode in 225 00:10:27,200 --> 00:10:30,040 which China was growing very very 226 00:10:28,879 --> 00:10:32,000 strongly 227 00:10:30,039 --> 00:10:36,240 ER on 228 00:10:32,000 --> 00:10:37,679 average China grew at over 7% out 229 00:10:36,240 --> 00:10:40,919 progress over 230 00:10:37,679 --> 00:10:43,559 7% now by the formula I showed you 231 00:10:40,919 --> 00:10:46,278 before if I ask you the question well 232 00:10:43,559 --> 00:10:48,119 what was behind that growth how much was 233 00:10:46,278 --> 00:10:50,480 a contribution of Labor how much was a 234 00:10:48,120 --> 00:10:53,519 contribution of capital and how much was 235 00:10:50,480 --> 00:10:55,680 a contribution of technological progress 236 00:10:53,519 --> 00:10:57,959 well there are some things we can 237 00:10:55,679 --> 00:10:59,719 measure fairly well population growth 238 00:10:57,958 --> 00:11:01,919 during this period in China was around 239 00:10:59,720 --> 00:11:05,399 1.7% per 240 00:11:01,919 --> 00:11:07,599 year there was a massive amount of 241 00:11:05,399 --> 00:11:08,720 investment the Capital stock was growing 242 00:11:07,600 --> 00:11:12,159 at a rate of 243 00:11:08,720 --> 00:11:15,720 99.2% per year and the residual you can 244 00:11:12,159 --> 00:11:17,078 compute it using the solo approach H is 245 00:11:15,720 --> 00:11:21,440 around 246 00:11:17,078 --> 00:11:24,799 4.2% okay so that 7.2% is a result of 247 00:11:21,440 --> 00:11:28,839 the weighted average of these three 248 00:11:24,799 --> 00:11:32,240 things okay so that's basic explanation 249 00:11:28,839 --> 00:11:36,480 of ER the growth in China during that 250 00:11:32,240 --> 00:11:38,639 that period now just looking at this not 251 00:11:36,480 --> 00:11:42,920 don't look at at the 252 00:11:38,639 --> 00:11:45,839 diagram what jumps immediately just if 253 00:11:42,919 --> 00:11:45,838 you just look at this 254 00:11:46,480 --> 00:11:51,800 part what jumps to you 255 00:11:49,320 --> 00:11:55,680 immediately let me ask you differently 256 00:11:51,799 --> 00:11:55,679 does it look like balanced 257 00:11:56,120 --> 00:12:02,799 growth do you think that that that's 258 00:11:59,360 --> 00:12:05,680 balanced growth that in other words do 259 00:12:02,799 --> 00:12:08,838 you think that China had a arrived to 260 00:12:05,679 --> 00:12:11,359 its state and and that growth is a 261 00:12:08,839 --> 00:12:13,800 result of what was happening in that 262 00:12:11,360 --> 00:12:13,800 stady 263 00:12:16,198 --> 00:12:20,759 state 264 00:12:18,399 --> 00:12:23,120 no but what is it that 265 00:12:20,759 --> 00:12:25,838 looks that tells you that that that's 266 00:12:23,120 --> 00:12:25,839 not the same 267 00:12:26,799 --> 00:12:30,559 state balanc growth is when everything 268 00:12:29,159 --> 00:12:34,679 everything is growing at the same rate 269 00:12:30,559 --> 00:12:37,719 no everything you have you know 270 00:12:34,679 --> 00:12:41,359 meaning all the endogenous 271 00:12:37,720 --> 00:12:44,278 variables ER unnormalized are growing at 272 00:12:41,360 --> 00:12:46,839 the same at the same rate as the 273 00:12:44,278 --> 00:12:46,838 exogenous 274 00:12:47,278 --> 00:12:54,278 variables so what is it that it would 275 00:12:49,879 --> 00:12:57,078 nearly jump to me here is say 276 00:12:54,278 --> 00:12:59,240 7.2% that's less than than the rate of 277 00:12:57,078 --> 00:13:02,638 growth of capital 278 00:12:59,240 --> 00:13:04,639 so so I know that there Capital over 279 00:13:02,639 --> 00:13:08,278 output was Rising so that's not a state 280 00:13:04,639 --> 00:13:12,240 state I know that I can see it in a 281 00:13:08,278 --> 00:13:14,799 different way I know that in a steady 282 00:13:12,240 --> 00:13:17,560 state in balanced 283 00:13:14,799 --> 00:13:19,838 growth the rate of growth of output and 284 00:13:17,559 --> 00:13:22,838 of capital should be the sum of the rate 285 00:13:19,839 --> 00:13:24,360 of growth of population plus the rate of 286 00:13:22,839 --> 00:13:27,600 technological 287 00:13:24,360 --> 00:13:31,278 progress okay that's 288 00:13:27,600 --> 00:13:34,159 5.9% but capital was growing at 289 00:13:31,278 --> 00:13:36,919 99.2% not 290 00:13:34,159 --> 00:13:40,120 5.9% so I do know that that's a period 291 00:13:36,919 --> 00:13:42,679 in which China was growing 292 00:13:40,120 --> 00:13:44,440 Beyond its steady state or balanced 293 00:13:42,679 --> 00:13:47,000 growth rate of 294 00:13:44,440 --> 00:13:48,839 growth and I know more than that I know 295 00:13:47,000 --> 00:13:50,600 that the reason that was happening is 296 00:13:48,839 --> 00:13:52,920 because there was more capital 297 00:13:50,600 --> 00:13:54,079 accumulation than you would expect in 298 00:13:52,919 --> 00:13:56,759 the stady 299 00:13:54,078 --> 00:13:59,120 state when are you likely to see a 300 00:13:56,759 --> 00:14:01,000 situation like that in which capital 301 00:13:59,120 --> 00:14:03,320 accumulation is faster than the rate of 302 00:14:01,000 --> 00:14:04,720 growth of capital in the St State and 303 00:14:03,320 --> 00:14:08,199 it's faster than the rate of growth of 304 00:14:04,720 --> 00:14:10,600 output that is that's a a period in 305 00:14:08,198 --> 00:14:14,120 which we have transitional growth been 306 00:14:10,600 --> 00:14:18,480 pulled you know growth above the state 307 00:14:14,120 --> 00:14:22,198 state growth is being pulled by capital 308 00:14:18,480 --> 00:14:22,199 accumulation when does that 309 00:14:27,559 --> 00:14:33,599 happen do to mind first is economies are 310 00:14:31,360 --> 00:14:36,039 like transitioning from command market 311 00:14:33,600 --> 00:14:39,519 economies I believe and also the second 312 00:14:36,039 --> 00:14:44,039 thing that comes to mind is potentially 313 00:14:39,519 --> 00:14:47,278 um um countries recovering from like War 314 00:14:44,039 --> 00:14:49,480 periods okay that's a deep deep deep 315 00:14:47,278 --> 00:14:51,120 answer I wanted something simpler which 316 00:14:49,480 --> 00:14:54,278 is 317 00:14:51,120 --> 00:14:57,720 what I I want to say so the economy is 318 00:14:54,278 --> 00:14:59,600 not in a state state that's clear but 319 00:14:57,720 --> 00:15:01,959 what do we also know we know that the 320 00:14:59,600 --> 00:15:04,560 Capital stock is below its stady state 321 00:15:01,958 --> 00:15:07,359 level and that could be as a result of 322 00:15:04,559 --> 00:15:09,439 of the the things you described you had 323 00:15:07,360 --> 00:15:12,680 a war so your Capital stock was wiped 324 00:15:09,440 --> 00:15:14,639 out or H you had a period in which 325 00:15:12,679 --> 00:15:17,239 saving rate was very low and now you're 326 00:15:14,639 --> 00:15:19,079 going to high saving rate episode with 327 00:15:17,240 --> 00:15:21,399 that a lot of that is what happened in 328 00:15:19,078 --> 00:15:23,679 in souis Asia in particular actually was 329 00:15:21,399 --> 00:15:26,078 a fast increase in the rate of in the 330 00:15:23,679 --> 00:15:28,559 say a sharp rise in this in the saving 331 00:15:26,078 --> 00:15:32,078 rate but the bottom what I so what I had 332 00:15:28,559 --> 00:15:33,559 in mind is for one of these reasons 333 00:15:32,078 --> 00:15:35,919 that's a situation where the initial 334 00:15:33,559 --> 00:15:37,479 Capital stock was below the stady state 335 00:15:35,919 --> 00:15:39,318 and so you have a period of transitional 336 00:15:37,480 --> 00:15:41,839 growth in which investment rate is more 337 00:15:39,318 --> 00:15:44,318 than you need to do to maintain the 338 00:15:41,839 --> 00:15:47,160 stock of capital per effective worker 339 00:15:44,318 --> 00:15:49,879 know there's a positive gap between the 340 00:15:47,159 --> 00:15:51,879 the green line and the and and the and 341 00:15:49,879 --> 00:15:54,958 the red line and that's what leads you 342 00:15:51,879 --> 00:15:58,439 transitional growth until you reach a c 343 00:15:54,958 --> 00:16:01,239 state if things do not change meaning 344 00:15:58,440 --> 00:16:05,319 population growth remain the same as in 345 00:16:01,240 --> 00:16:07,240 that period and the and the the rate of 346 00:16:05,318 --> 00:16:09,318 technological progress Remains the Same 347 00:16:07,240 --> 00:16:12,720 As in that period we know that the 348 00:16:09,318 --> 00:16:15,198 balanced growth rate of China is 349 00:16:12,720 --> 00:16:20,680 5.9% 350 00:16:15,198 --> 00:16:25,159 okay it's 5.9 because it's 07 plus 351 00:16:20,679 --> 00:16:26,879 0.42 now so so that 7.2% average there 352 00:16:25,159 --> 00:16:28,559 you're likely to see it and actually 353 00:16:26,879 --> 00:16:33,559 there's an average that has numbers like 354 00:16:28,559 --> 00:16:38,198 15 % very early on H to close to 6% or 355 00:16:33,559 --> 00:16:40,239 so on the last stage H so that's that's 356 00:16:38,198 --> 00:16:41,159 would be a stady state now that I think 357 00:16:40,240 --> 00:16:45,120 is an 358 00:16:41,159 --> 00:16:46,679 overestimate because H uh we know the 359 00:16:45,120 --> 00:16:48,240 rate of population growth is declining 360 00:16:46,679 --> 00:16:51,758 very rapidly in China it's turning 361 00:16:48,240 --> 00:16:53,600 negative okay so so so for the rate of 362 00:16:51,759 --> 00:16:54,959 growth of output China is going to is 363 00:16:53,600 --> 00:16:56,600 unless there's a big change in 364 00:16:54,958 --> 00:16:58,318 technological progress in the process of 365 00:16:56,600 --> 00:17:00,680 technological progress it's going to be 366 00:16:58,318 --> 00:17:04,599 pretty difficult for China to grow a lot 367 00:17:00,679 --> 00:17:07,240 more than 5% I think going forward and 368 00:17:04,599 --> 00:17:08,558 that creates some problems but but 369 00:17:07,240 --> 00:17:10,599 that's what it is that's what this model 370 00:17:08,558 --> 00:17:11,959 tells you you need to change something 371 00:17:10,599 --> 00:17:13,759 and the things you can change in this 372 00:17:11,959 --> 00:17:15,759 model are what well you could induce 373 00:17:13,759 --> 00:17:17,640 higher saving rate you would get more 374 00:17:15,759 --> 00:17:19,679 transitional growth out of that more 375 00:17:17,640 --> 00:17:23,400 capital accumulation that's costly that 376 00:17:19,679 --> 00:17:25,280 means less consumption and so on H or it 377 00:17:23,400 --> 00:17:27,519 could be some technological breakthrough 378 00:17:25,279 --> 00:17:30,038 but that's a probably would affect the 379 00:17:27,519 --> 00:17:32,519 whole world in any event but that's the 380 00:17:30,038 --> 00:17:36,400 kind of things you 381 00:17:32,519 --> 00:17:38,400 okay good so that's that's 382 00:17:36,400 --> 00:17:41,280 uh so 383 00:17:38,400 --> 00:17:44,480 so is is the models we have developed 384 00:17:41,279 --> 00:17:47,200 here sort of are quite good to explain 385 00:17:44,480 --> 00:17:49,519 you know uh catching up processes 386 00:17:47,200 --> 00:17:51,720 catching up growth and and and to 387 00:17:49,519 --> 00:17:54,918 understand what are the where are 388 00:17:51,720 --> 00:17:58,319 economies converging o over 389 00:17:54,919 --> 00:18:00,320 time what I want to next is I I want to 390 00:17:58,319 --> 00:18:02,639 end up trying to explain remember one of 391 00:18:00,319 --> 00:18:04,038 the plots I showed you very early on is 392 00:18:02,640 --> 00:18:07,360 that there's great 393 00:18:04,038 --> 00:18:09,640 dispersion H in income per per person 394 00:18:07,359 --> 00:18:11,879 per capita across the world and also 395 00:18:09,640 --> 00:18:15,240 some countries are sort of not catching 396 00:18:11,880 --> 00:18:17,640 up and which is especially in Africa and 397 00:18:15,240 --> 00:18:19,480 so on and I want to try to understand so 398 00:18:17,640 --> 00:18:20,520 people have put lots of effort in trying 399 00:18:19,480 --> 00:18:22,679 to 400 00:18:20,519 --> 00:18:24,839 understand why do we have these 401 00:18:22,679 --> 00:18:27,798 differences and so I'm going to expand a 402 00:18:24,839 --> 00:18:30,879 little bit the model we have H to show 403 00:18:27,798 --> 00:18:32,720 you few things people have explored and 404 00:18:30,880 --> 00:18:34,200 and then I'm going to conclude that 405 00:18:32,720 --> 00:18:37,519 those things that people have explored 406 00:18:34,200 --> 00:18:39,080 sort of can't explain it either and then 407 00:18:37,519 --> 00:18:42,639 as I'm going to go back sort of to 408 00:18:39,079 --> 00:18:46,199 growth accounting so sort of thing I did 409 00:18:42,640 --> 00:18:49,640 for China there and try to explain what 410 00:18:46,200 --> 00:18:51,279 what what seems to be ER behind all 411 00:18:49,640 --> 00:18:53,880 these big disparities we have in the 412 00:18:51,279 --> 00:18:57,038 world so the first thing I'm going to do 413 00:18:53,880 --> 00:18:59,159 is just it's useful as an exercise even 414 00:18:57,038 --> 00:19:01,599 I'm going to start with h I'm going to 415 00:18:59,159 --> 00:19:03,360 modify the the solo mod a little bit so 416 00:19:01,599 --> 00:19:05,678 this is like the production function I 417 00:19:03,359 --> 00:19:10,639 showed you before but rather than having 418 00:19:05,679 --> 00:19:14,480 n here I'm going to have H and H is just 419 00:19:10,640 --> 00:19:17,440 n our old n population labor for there 420 00:19:14,480 --> 00:19:22,440 but a scale up by this human capital 421 00:19:17,440 --> 00:19:23,840 Factor okay so what this says is that 422 00:19:22,440 --> 00:19:26,080 that human 423 00:19:23,839 --> 00:19:29,359 capital is 424 00:19:26,079 --> 00:19:31,399 really is the population 425 00:19:29,359 --> 00:19:34,399 times something that controls for the 426 00:19:31,400 --> 00:19:36,320 level of schooling of that population 427 00:19:34,400 --> 00:19:37,640 okay so a big candidate for difference 428 00:19:36,319 --> 00:19:38,918 across the world is that you know that 429 00:19:37,640 --> 00:19:42,520 certain populations are far more 430 00:19:38,919 --> 00:19:45,480 educated than others so so 431 00:19:42,519 --> 00:19:47,519 this does exactly that s is an 432 00:19:45,480 --> 00:19:49,798 increasing function of the numbers of 433 00:19:47,519 --> 00:19:52,759 years of schooling and there is a big 434 00:19:49,798 --> 00:19:54,599 micro evidence literature trying to 435 00:19:52,759 --> 00:19:56,240 estimate what is the value of thats what 436 00:19:54,599 --> 00:20:00,000 is the value of an extra unit of 437 00:19:56,240 --> 00:20:02,319 schooling for a human capital and so on 438 00:20:00,000 --> 00:20:03,720 and sort of the estimate depends on what 439 00:20:02,319 --> 00:20:05,798 kind of a schooling are we talking about 440 00:20:03,720 --> 00:20:08,960 is primary secondary thary whatever but 441 00:20:05,798 --> 00:20:11,798 on average that's a number around 0.1 442 00:20:08,960 --> 00:20:14,000 okay so one extra year of schooling 443 00:20:11,798 --> 00:20:16,079 raises sort of human capital by about 444 00:20:14,000 --> 00:20:19,038 10% so the whole population increases 445 00:20:16,079 --> 00:20:22,359 the average by one year 446 00:20:19,038 --> 00:20:25,119 year um that adds about 10% to human 447 00:20:22,359 --> 00:20:27,279 capital so is as if you had increased 448 00:20:25,119 --> 00:20:30,319 population by 10% so it makes a 449 00:20:27,279 --> 00:20:33,119 difference now is it's pretty hard to 450 00:20:30,319 --> 00:20:35,599 raise for a country one year of 451 00:20:33,119 --> 00:20:37,119 schooling for the average takes a lot of 452 00:20:35,599 --> 00:20:38,759 time but when you look in the 453 00:20:37,119 --> 00:20:40,439 crosssection there's huge difference 454 00:20:38,759 --> 00:20:42,919 across the world between numbers of 455 00:20:40,440 --> 00:20:44,720 years of schooling and that accounts for 456 00:20:42,919 --> 00:20:46,080 a big part of the difference in income 457 00:20:44,720 --> 00:20:51,079 per 458 00:20:46,079 --> 00:20:53,599 capita anyways so let me um do a balanc 459 00:20:51,079 --> 00:20:58,199 growth exercise with this this expanded 460 00:20:53,599 --> 00:20:59,319 Model H and see how far we can get so so 461 00:20:58,200 --> 00:21:00,919 the first thing I'm going to do is I'm 462 00:20:59,319 --> 00:21:05,158 going to normalize everything by 463 00:21:00,919 --> 00:21:06,600 effective work sorry by workers okay so 464 00:21:05,159 --> 00:21:08,080 I'm going to divide every all the 465 00:21:06,599 --> 00:21:09,918 variables I'm going to show you are 466 00:21:08,079 --> 00:21:12,639 going to be divided by 467 00:21:09,919 --> 00:21:16,200 n 468 00:21:12,640 --> 00:21:19,600 now notice that I'm dividing by n not by 469 00:21:16,200 --> 00:21:22,240 a * n or a * 470 00:21:19,599 --> 00:21:24,558 H 471 00:21:22,240 --> 00:21:27,679 or so so there's a difference with the 472 00:21:24,558 --> 00:21:30,038 previous analysis and I I can always 473 00:21:27,679 --> 00:21:32,240 divide and the model we had I can always 474 00:21:30,038 --> 00:21:34,839 divide by whatever I want all my 475 00:21:32,240 --> 00:21:36,558 variables I divided by effective workers 476 00:21:34,839 --> 00:21:39,278 because I wanted to have a diagram where 477 00:21:36,558 --> 00:21:42,359 the curves were not moving around but I 478 00:21:39,278 --> 00:21:43,679 can divide by whatever I want and and 479 00:21:42,359 --> 00:21:45,079 and I will divide by different things 480 00:21:43,679 --> 00:21:47,679 depending on the analysis I want to 481 00:21:45,079 --> 00:21:50,439 conduct now I know that once I divide by 482 00:21:47,679 --> 00:21:53,840 population only not by a times 483 00:21:50,440 --> 00:21:56,360 population and education perhaps H I 484 00:21:53,839 --> 00:21:59,558 cannot draw my previous diagram the the 485 00:21:56,359 --> 00:22:01,759 diagram with the saving uh output per 486 00:21:59,558 --> 00:22:03,119 per effect per worker and so on because 487 00:22:01,759 --> 00:22:05,119 those curves are going to be moving so 488 00:22:03,119 --> 00:22:07,079 it's not very friendly but I can divide 489 00:22:05,119 --> 00:22:09,719 by whatever I want and I had I'm I want 490 00:22:07,079 --> 00:22:14,000 to divide here by just population so 491 00:22:09,720 --> 00:22:17,720 little H will be simply a big H divided 492 00:22:14,000 --> 00:22:22,319 by n okay remember that big H was just e 493 00:22:17,720 --> 00:22:26,679 to U time n so that's that output per 494 00:22:22,319 --> 00:22:31,359 worker will be just the will be K 495 00:22:26,679 --> 00:22:33,840 Capital divided by n and here is Big H 496 00:22:31,359 --> 00:22:37,079 divided by n which is little H okay so 497 00:22:33,839 --> 00:22:40,038 all this now is measured as output per 498 00:22:37,079 --> 00:22:42,599 worker or per 499 00:22:40,038 --> 00:22:45,519 population per 500 00:22:42,599 --> 00:22:47,278 person now remember what I can do here 501 00:22:45,519 --> 00:22:49,960 is then I know that the rate of growth 502 00:22:47,278 --> 00:22:52,480 of output per person is going to be 503 00:22:49,960 --> 00:22:55,840 equal to 1 minus Alpha times the rate of 504 00:22:52,480 --> 00:22:58,159 growth of capital per person plus Alpha 505 00:22:55,839 --> 00:23:02,240 time the rate of growth of a Time the 506 00:22:58,159 --> 00:23:05,000 rate of growth of age in which age is is 507 00:23:02,240 --> 00:23:07,278 this H years of schooling 508 00:23:05,000 --> 00:23:10,359 transformation okay now if you think 509 00:23:07,278 --> 00:23:12,519 about the steady state H it doesn't make 510 00:23:10,359 --> 00:23:14,558 any sense that GH at some point will 511 00:23:12,519 --> 00:23:16,918 become zero I mean we can increase 512 00:23:14,558 --> 00:23:19,678 education but at some point we cannot be 513 00:23:16,919 --> 00:23:22,640 all going to you know 150 years of 514 00:23:19,679 --> 00:23:25,120 education so that is unlike capital and 515 00:23:22,640 --> 00:23:27,559 things like that you can increase for a 516 00:23:25,119 --> 00:23:28,839 while education but but at some point 517 00:23:27,558 --> 00:23:31,158 there's a limit I mean you're not going 518 00:23:28,839 --> 00:23:34,359 to do a post post post post PhD blah 519 00:23:31,159 --> 00:23:36,278 blah blah okay so in the stady state we 520 00:23:34,359 --> 00:23:40,240 know that eventually in the long run 521 00:23:36,278 --> 00:23:43,919 this GH is equal to zero so this this 522 00:23:40,240 --> 00:23:46,200 economy we expanded to include years of 523 00:23:43,919 --> 00:23:47,880 schooling has the same sort of balanced 524 00:23:46,200 --> 00:23:50,679 growth characteristics of the economy I 525 00:23:47,880 --> 00:23:54,278 just showed you before okay so that that 526 00:23:50,679 --> 00:23:57,000 in that economy Capital per person will 527 00:23:54,278 --> 00:23:59,798 grow at the rate GA and output per 528 00:23:57,000 --> 00:24:01,839 person will grow at the rate GA output 529 00:23:59,798 --> 00:24:04,079 will grow at the rate GA plus GN so 530 00:24:01,839 --> 00:24:06,959 exactly the same as we had before not 531 00:24:04,079 --> 00:24:09,879 not not so up to now adding human 532 00:24:06,960 --> 00:24:12,480 capital doesn't change our conclusions 533 00:24:09,880 --> 00:24:14,080 about balanced growth it will change 534 00:24:12,480 --> 00:24:15,640 some conclusions that are important 535 00:24:14,079 --> 00:24:18,278 that's the reason I'm introducing this 536 00:24:15,640 --> 00:24:20,320 variable but doesn't change this this 537 00:24:18,278 --> 00:24:21,798 conclusion so this model which is a 538 00:24:20,319 --> 00:24:23,918 little expansion of the previous model 539 00:24:21,798 --> 00:24:27,079 we had has the same balanced growth 540 00:24:23,919 --> 00:24:28,880 characteristics as the model I show you 541 00:24:27,079 --> 00:24:31,000 before 542 00:24:28,880 --> 00:24:33,760 so let me do a little bit of algebra 543 00:24:31,000 --> 00:24:38,000 with it h so from the capital 544 00:24:33,759 --> 00:24:41,079 accumulation equation I know that so let 545 00:24:38,000 --> 00:24:43,240 me remember the capital accumulation now 546 00:24:41,079 --> 00:24:49,839 written in in 547 00:24:43,240 --> 00:24:54,640 per in per per person will be H you 548 00:24:49,839 --> 00:24:56,519 know KT + one this is remember little K 549 00:24:54,640 --> 00:25:00,320 minus 550 00:24:56,519 --> 00:25:00,319 KT equal to 551 00:25:00,798 --> 00:25:06,079 s * y 552 00:25:04,519 --> 00:25:09,639 d 553 00:25:06,079 --> 00:25:11,639 minus Delta plus 554 00:25:09,640 --> 00:25:14,159 n 555 00:25:11,640 --> 00:25:17,759 k 556 00:25:14,159 --> 00:25:20,799 t wait why do I have a Delta plus n 557 00:25:17,759 --> 00:25:23,558 minus plus GA there remember that in the 558 00:25:20,798 --> 00:25:26,079 previous mod I have a Delta plus n plus 559 00:25:23,558 --> 00:25:26,079 GA 560 00:25:26,359 --> 00:25:30,319 there did I make a mistake 561 00:25:33,000 --> 00:25:36,679 actually this is a useful exercise for 562 00:25:37,480 --> 00:25:43,558 you you remember they had a Delta plus n 563 00:25:40,398 --> 00:25:46,119 plus plus G there 564 00:25:43,558 --> 00:25:48,879 no what's 565 00:25:46,119 --> 00:25:50,278 wrong I just told you that this economy 566 00:25:48,880 --> 00:25:51,520 at least in balanced growth is exactly 567 00:25:50,278 --> 00:25:57,079 the 568 00:25:51,519 --> 00:25:57,079 same so you make a mistake 569 00:26:01,798 --> 00:26:07,759 no the reason I had the ga there is 570 00:26:04,720 --> 00:26:10,399 because I was looking at the change in 571 00:26:07,759 --> 00:26:12,319 capital per effective worker I'm looking 572 00:26:10,398 --> 00:26:13,879 now at the change in capital per worker 573 00:26:12,319 --> 00:26:16,278 not per effective worker so I don't have 574 00:26:13,880 --> 00:26:17,840 that a in the denominator so I don't 575 00:26:16,278 --> 00:26:21,278 need to account for the rate of growth 576 00:26:17,839 --> 00:26:24,519 of the denominator due to an increase in 577 00:26:21,278 --> 00:26:27,079 technology I don't need that so but I 578 00:26:24,519 --> 00:26:32,359 that also means well and and so what I 579 00:26:27,079 --> 00:26:32,359 can do is you know divide both sides by 580 00:26:32,599 --> 00:26:35,879 KT that's 581 00:26:37,480 --> 00:26:40,960 KT and this 582 00:26:43,200 --> 00:26:50,038 is the rate of growth of K no is the 583 00:26:47,278 --> 00:26:50,038 rate of growth of 584 00:26:51,319 --> 00:26:56,678 K but in a steady state the rate of 585 00:26:54,398 --> 00:26:59,918 growth of K Capital per worker is equal 586 00:26:56,679 --> 00:26:59,919 to what 587 00:27:01,558 --> 00:27:09,879 GA is the rate of growth of Technology 588 00:27:04,000 --> 00:27:12,640 that's the so this in a state state this 589 00:27:09,880 --> 00:27:14,399 is equal to 590 00:27:12,640 --> 00:27:17,159 G 591 00:27:14,398 --> 00:27:18,879 okay and so what I wrote there is I 592 00:27:17,159 --> 00:27:24,159 think should be exactly 593 00:27:18,880 --> 00:27:27,440 that is it yes good okay that's what I 594 00:27:24,159 --> 00:27:31,240 did and what did I do why did I do this 595 00:27:27,440 --> 00:27:34,000 for well because now I can you know you 596 00:27:31,240 --> 00:27:36,640 know that I can know I can measure Delta 597 00:27:34,000 --> 00:27:39,558 Del Delta is a yeah I can measure Delta 598 00:27:36,640 --> 00:27:43,679 I can measure n 599 00:27:39,558 --> 00:27:49,759 h um and I can measure 600 00:27:43,679 --> 00:27:52,080 GA so this implies that I can solve out 601 00:27:49,759 --> 00:27:57,480 in a steady state for what is the level 602 00:27:52,079 --> 00:28:00,079 of capital per ER effective worker okay 603 00:27:57,480 --> 00:28:02,480 that I can solve from this equation and 604 00:28:00,079 --> 00:28:05,158 it's equal to this expression here 605 00:28:02,480 --> 00:28:07,558 notice a few interesting things here is 606 00:28:05,159 --> 00:28:09,960 capital per effective worker each of 607 00:28:07,558 --> 00:28:14,240 them is divided by n so I can also look 608 00:28:09,960 --> 00:28:16,360 at Big K over a times big h no h is 609 00:28:14,240 --> 00:28:18,759 increasing in the saving 610 00:28:16,359 --> 00:28:20,199 rate that you already had in the model 611 00:28:18,759 --> 00:28:21,839 we discussed before if the saving rate 612 00:28:20,200 --> 00:28:25,360 is higher then the you're going to end 613 00:28:21,839 --> 00:28:28,119 up with a higher Capital ER perir 614 00:28:25,359 --> 00:28:31,079 effective worker ratio in yesterday's St 615 00:28:28,119 --> 00:28:33,798 is decreasing in population growth you 616 00:28:31,079 --> 00:28:38,079 all these things you already saw before 617 00:28:33,798 --> 00:28:40,639 okay so now that I have this expression 618 00:28:38,079 --> 00:28:42,319 for K Over H I can go back to my 619 00:28:40,640 --> 00:28:46,240 production 620 00:28:42,319 --> 00:28:49,558 function to this and sticking 621 00:28:46,240 --> 00:28:52,079 there this this value and I get that 622 00:28:49,558 --> 00:28:56,440 output at time T once you're in the 623 00:28:52,079 --> 00:28:58,158 balance growth path is equal to a t time 624 00:28:56,440 --> 00:29:01,159 h 625 00:28:58,159 --> 00:29:03,760 time K over a h to 1us Alpha just just 626 00:29:01,159 --> 00:29:06,640 solve for that and the point being is 627 00:29:03,759 --> 00:29:10,919 that now I can write this as YT is equal 628 00:29:06,640 --> 00:29:13,159 to a times e to so human capital times 629 00:29:10,919 --> 00:29:15,120 this expression here so human the point 630 00:29:13,159 --> 00:29:17,600 is human capital doesn't affect the 631 00:29:15,119 --> 00:29:21,678 stady state growth but it does affect 632 00:29:17,599 --> 00:29:23,599 the income per capita that you have have 633 00:29:21,679 --> 00:29:26,440 and it makes a big difference I'll show 634 00:29:23,599 --> 00:29:26,439 you 635 00:29:26,720 --> 00:29:31,480 okay so when people try to explain 636 00:29:29,240 --> 00:29:33,839 difference across the world they notice 637 00:29:31,480 --> 00:29:36,360 that they were missing a big component 638 00:29:33,839 --> 00:29:39,839 and and that big component is 639 00:29:36,359 --> 00:29:42,398 education so let's compare what I want 640 00:29:39,839 --> 00:29:45,798 to do next is you know I can do this for 641 00:29:42,398 --> 00:29:48,199 every country in the world okay and I 642 00:29:45,798 --> 00:29:51,158 can compare it with the 643 00:29:48,200 --> 00:29:53,080 US okay I can do this for every every 644 00:29:51,159 --> 00:29:54,519 country in the world and let's compare 645 00:29:53,079 --> 00:29:56,319 it with and I can compare it with any 646 00:29:54,519 --> 00:29:58,200 other country in the world but just you 647 00:29:56,319 --> 00:30:00,038 know let's compare it with the largest 648 00:29:58,200 --> 00:30:03,038 country in the world in terms of output 649 00:30:00,038 --> 00:30:06,679 that's a us so let's let's see what we 650 00:30:03,038 --> 00:30:10,119 get so so I'm going to take output per 651 00:30:06,679 --> 00:30:12,519 capita in everywhere and divided by the 652 00:30:10,119 --> 00:30:15,719 same expression for the 653 00:30:12,519 --> 00:30:20,079 US and I'm going to Define that variable 654 00:30:15,720 --> 00:30:23,759 as y i hat so for Country I say 655 00:30:20,079 --> 00:30:26,558 Singapore okay we take output per capita 656 00:30:23,759 --> 00:30:28,480 and we divide it by output per capita 657 00:30:26,558 --> 00:30:34,038 per person in in the 658 00:30:28,480 --> 00:30:35,960 us assume big if you see is a huge if 659 00:30:34,038 --> 00:30:37,879 that but you can do that for you know 660 00:30:35,960 --> 00:30:41,919 the US versus Singapore probably is not 661 00:30:37,880 --> 00:30:44,200 a crazy assumption to make H assume that 662 00:30:41,919 --> 00:30:46,640 they have the same rate of technological 663 00:30:44,200 --> 00:30:48,558 progress and the same technology and so 664 00:30:46,640 --> 00:30:50,159 on well the same rate of technological 665 00:30:48,558 --> 00:30:54,879 progress I'm going to assume that for 666 00:30:50,159 --> 00:30:58,200 now so then this why I had a you can 667 00:30:54,880 --> 00:31:00,919 write this it's just a this for 668 00:30:58,200 --> 00:31:04,120 Singapore divided by this for the 669 00:31:00,919 --> 00:31:06,519 US it shows it turns out to be this 670 00:31:04,119 --> 00:31:08,278 expression here 671 00:31:06,519 --> 00:31:12,880 okay 672 00:31:08,278 --> 00:31:16,119 so solo did something like this and said 673 00:31:12,880 --> 00:31:19,399 okay H assume that technology is the 674 00:31:16,119 --> 00:31:22,719 same across the world because you know 675 00:31:19,398 --> 00:31:26,158 at least for major Economist technology 676 00:31:22,720 --> 00:31:28,639 sort of can be imported and and and can 677 00:31:26,159 --> 00:31:30,840 we can have the same the same uh 678 00:31:28,638 --> 00:31:33,079 um more or less the same technology 679 00:31:30,839 --> 00:31:35,638 across the world so assume that this guy 680 00:31:33,079 --> 00:31:38,119 is equal to one and that both Singapore 681 00:31:35,638 --> 00:31:43,638 and and the US have the same rate of 682 00:31:38,119 --> 00:31:46,638 growth okay and so that means 683 00:31:43,638 --> 00:31:49,439 er um that you know countries that have 684 00:31:46,638 --> 00:31:51,119 higher saving rate will tend to have we 685 00:31:49,440 --> 00:31:54,240 know that in Bal go will tend to have 686 00:31:51,119 --> 00:31:56,558 higher output per capita so if Singapore 687 00:31:54,240 --> 00:31:59,000 has a higher saving rate than the US 688 00:31:56,558 --> 00:32:04,200 that will tend to give Singapore a 689 00:31:59,000 --> 00:32:07,679 higher income per capita okay if country 690 00:32:04,200 --> 00:32:10,679 has a a higher population growth then it 691 00:32:07,679 --> 00:32:13,880 will tend to have a lower income per 692 00:32:10,679 --> 00:32:15,240 capita and and so on so forth and so the 693 00:32:13,880 --> 00:32:18,120 question is well suppose you make this 694 00:32:15,240 --> 00:32:20,359 Assumption of equal technology and take 695 00:32:18,119 --> 00:32:21,798 this take the the we can measure the 696 00:32:20,359 --> 00:32:23,439 saving rate in different parts of the 697 00:32:21,798 --> 00:32:24,679 world the population rates in different 698 00:32:23,440 --> 00:32:26,120 part of the world and we're assuming 699 00:32:24,679 --> 00:32:28,440 that the same rate of technological 700 00:32:26,119 --> 00:32:31,479 progress everywhere how much of the 701 00:32:28,440 --> 00:32:34,000 difference we observe in income per 702 00:32:31,480 --> 00:32:36,880 capita across the world can be accounted 703 00:32:34,000 --> 00:32:39,638 by that okay so that's that was the 704 00:32:36,880 --> 00:32:42,559 first question is well suppose that that 705 00:32:39,638 --> 00:32:44,158 the technology is the same but we 706 00:32:42,558 --> 00:32:47,240 measured all these other things saving 707 00:32:44,159 --> 00:32:49,440 rate population growth H common rate of 708 00:32:47,240 --> 00:32:51,880 technological progress common 709 00:32:49,440 --> 00:32:54,120 depreciation across the world and so on 710 00:32:51,880 --> 00:32:56,880 how much can we explain of the income 711 00:32:54,119 --> 00:32:58,959 disparity and the conclusion is the 712 00:32:56,880 --> 00:33:03,039 following the conclusion of that 713 00:32:58,960 --> 00:33:05,319 experiment is that if that if if the 714 00:33:03,038 --> 00:33:08,200 only difference 715 00:33:05,319 --> 00:33:11,319 behind PE incomes per capita were sort 716 00:33:08,200 --> 00:33:13,038 of years of schooling sorry a key thing 717 00:33:11,319 --> 00:33:15,720 that I me that I forgot to measure is 718 00:33:13,038 --> 00:33:17,278 years of schooling so know if a country 719 00:33:15,720 --> 00:33:18,759 has more years of schooling will tend to 720 00:33:17,278 --> 00:33:21,079 have a higher income per capita and so 721 00:33:18,759 --> 00:33:22,759 on so if you try to explain the 722 00:33:21,079 --> 00:33:25,558 differences in income per capita across 723 00:33:22,759 --> 00:33:28,278 the world using variables like years of 724 00:33:25,558 --> 00:33:30,240 schooling H difference in Saving rate 725 00:33:28,278 --> 00:33:32,798 difference in population growth and so 726 00:33:30,240 --> 00:33:34,599 on the world would be a lot more 727 00:33:32,798 --> 00:33:38,158 egalitarian than it actually is it would 728 00:33:34,599 --> 00:33:40,638 look a lot more flatter okay so this is 729 00:33:38,159 --> 00:33:43,639 how much you can account here you put a 730 00:33:40,638 --> 00:33:47,079 bunch of lots of countries you know 731 00:33:43,638 --> 00:33:49,158 Africa and so on here and if you just 732 00:33:47,079 --> 00:33:51,480 stick in the in the equation their 733 00:33:49,159 --> 00:33:53,919 corresponding saving rate education 734 00:33:51,480 --> 00:33:56,000 levels and so on the world would be a 735 00:33:53,919 --> 00:33:58,080 lot more similar there wouldn't be the 736 00:33:56,000 --> 00:34:00,919 kind of disparities we see between some 737 00:33:58,079 --> 00:34:03,519 African countries and and and Singapore 738 00:34:00,919 --> 00:34:05,200 say we're talking about Singapore okay 739 00:34:03,519 --> 00:34:07,759 but the world doesn't look like that 740 00:34:05,200 --> 00:34:09,280 that's the point so so if you take all 741 00:34:07,759 --> 00:34:12,000 these things that make a lot of sense 742 00:34:09,280 --> 00:34:15,000 education saving rate blah you're going 743 00:34:12,000 --> 00:34:16,800 to explain a small share of the of the 744 00:34:15,000 --> 00:34:19,838 differences in income per capita across 745 00:34:16,800 --> 00:34:21,599 the world ah sorry in this this plot 746 00:34:19,838 --> 00:34:26,799 here L is our 747 00:34:21,599 --> 00:34:29,440 n l labor is our n so this y Over N our 748 00:34:26,800 --> 00:34:32,599 little Y in this 749 00:34:29,440 --> 00:34:34,679 so so not so we can't get so far we need 750 00:34:32,599 --> 00:34:39,039 something else so what else do we need 751 00:34:34,679 --> 00:34:41,519 to uh to add to really explain the 752 00:34:39,039 --> 00:34:44,519 amount of disparity we 753 00:34:41,519 --> 00:34:47,440 have 754 00:34:44,519 --> 00:34:49,079 well this the answer is again the solo 755 00:34:47,440 --> 00:34:51,358 residual it turns out that the 756 00:34:49,079 --> 00:34:54,320 assumption that A's are the same across 757 00:34:51,358 --> 00:34:56,279 the world that the level and the rate of 758 00:34:54,320 --> 00:34:58,320 grows are the same around around the 759 00:34:56,280 --> 00:35:01,560 world is just 760 00:34:58,320 --> 00:35:04,000 a very bad assumption okay the level of 761 00:35:01,559 --> 00:35:07,078 Technologies are very different across 762 00:35:04,000 --> 00:35:09,800 different parts of the world so the next 763 00:35:07,079 --> 00:35:12,800 step was say okay let's measure the 764 00:35:09,800 --> 00:35:15,079 difference in Technologies across the 765 00:35:12,800 --> 00:35:16,880 world and it turns out that if you try 766 00:35:15,079 --> 00:35:18,480 to explain so if you go out there and 767 00:35:16,880 --> 00:35:23,358 you measure the level of Technology 768 00:35:18,480 --> 00:35:24,920 across the world different places no uh 769 00:35:23,358 --> 00:35:29,639 Zimbabwe 770 00:35:24,920 --> 00:35:32,960 Singapore South Korea and so on so forth 771 00:35:29,639 --> 00:35:35,480 well and then you plot that the level of 772 00:35:32,960 --> 00:35:38,679 Technology the countries have visis 773 00:35:35,480 --> 00:35:41,639 their output per capita per worker you 774 00:35:38,679 --> 00:35:44,239 expain a big share of it okay so here is 775 00:35:41,639 --> 00:35:46,000 what you have is the relative a so 776 00:35:44,239 --> 00:35:49,279 everything is related to the US here 777 00:35:46,000 --> 00:35:51,119 okay so the the a that we measure the 778 00:35:49,280 --> 00:35:53,200 level of a that we measure I don't 779 00:35:51,119 --> 00:35:58,318 remember which year was this 780 00:35:53,199 --> 00:35:58,318 19 I don't remember when it was that 781 00:35:58,358 --> 00:36:03,559 doesn't matter H so if you measure the 782 00:36:01,159 --> 00:36:05,358 the relative level of technology in 783 00:36:03,559 --> 00:36:07,679 country ey relative to the 784 00:36:05,358 --> 00:36:09,400 US and then you measure the relative 785 00:36:07,679 --> 00:36:11,559 output per capita in that country 786 00:36:09,400 --> 00:36:13,440 related to the US and forget about 787 00:36:11,559 --> 00:36:15,719 everything else educational so on so 788 00:36:13,440 --> 00:36:18,480 forth you can get a pretty good 789 00:36:15,719 --> 00:36:21,598 relationship between the two okay so 790 00:36:18,480 --> 00:36:23,318 between one one half and two third of 791 00:36:21,599 --> 00:36:26,000 the difference in output per worker 792 00:36:23,318 --> 00:36:28,119 across different countries in the world 793 00:36:26,000 --> 00:36:30,480 can be attributed to the difference in 794 00:36:28,119 --> 00:36:32,760 technology level okay so that's the 795 00:36:30,480 --> 00:36:36,760 conclusion that we 796 00:36:32,760 --> 00:36:37,800 have now let me revisit the the this 797 00:36:36,760 --> 00:36:41,599 issue of 798 00:36:37,800 --> 00:36:43,119 convergence ER and and so if you if you 799 00:36:41,599 --> 00:36:44,838 what you do is you take countries that 800 00:36:43,119 --> 00:36:47,720 have more or less the same 801 00:36:44,838 --> 00:36:49,199 a and that have more or less the same 802 00:36:47,719 --> 00:36:51,759 levels of 803 00:36:49,199 --> 00:36:53,960 education then and you look at sort of 804 00:36:51,760 --> 00:36:56,079 their their the path of their output per 805 00:36:53,960 --> 00:36:59,358 capita you get that the models we have 806 00:36:56,079 --> 00:37:01,480 been discussing here work St well okay 807 00:36:59,358 --> 00:37:03,039 so here you see that you know they're 808 00:37:01,480 --> 00:37:05,639 more or less growing together there are 809 00:37:03,039 --> 00:37:07,519 Wars and stuff like that here so so 810 00:37:05,639 --> 00:37:09,679 there are great recessions and things 811 00:37:07,519 --> 00:37:13,318 like that but on average you see sort of 812 00:37:09,679 --> 00:37:16,838 the countries that that were behind sort 813 00:37:13,318 --> 00:37:20,079 of cut up and so on okay big dispers 814 00:37:16,838 --> 00:37:22,358 here they were all growing together and 815 00:37:20,079 --> 00:37:24,280 as more time passes the closer they get 816 00:37:22,358 --> 00:37:27,559 to each other because you know they're 817 00:37:24,280 --> 00:37:29,000 converging these guys the US and the UK 818 00:37:27,559 --> 00:37:33,279 were already sort of very close to the 819 00:37:29,000 --> 00:37:35,679 stady state very in 1870s while Japan 820 00:37:33,280 --> 00:37:37,560 was way behind but it was sort of in the 821 00:37:35,679 --> 00:37:40,960 same class of countries in terms of 822 00:37:37,559 --> 00:37:42,599 technology and in terms of H education 823 00:37:40,960 --> 00:37:47,480 levels and so 824 00:37:42,599 --> 00:37:49,318 on so it works pretty well H this is H 825 00:37:47,480 --> 00:37:52,318 for for more 826 00:37:49,318 --> 00:37:55,079 countries and you you plot per capita 827 00:37:52,318 --> 00:37:58,239 income in 1870 again for countries that 828 00:37:55,079 --> 00:38:01,280 have similar A's and K's uh 829 00:37:58,239 --> 00:38:02,519 A A and H and you look at the rate of 830 00:38:01,280 --> 00:38:04,560 growth and you get exactly what you 831 00:38:02,519 --> 00:38:07,559 would expect countries that were further 832 00:38:04,559 --> 00:38:09,318 behind CAU up that's Japan very fast 833 00:38:07,559 --> 00:38:11,519 rate of growth and you get this very 834 00:38:09,318 --> 00:38:13,800 negative relationship okay so this is 835 00:38:11,519 --> 00:38:16,880 the convergence model it works extremely 836 00:38:13,800 --> 00:38:18,440 well conditional on having the same a 837 00:38:16,880 --> 00:38:20,358 and AG so that's the contribution of 838 00:38:18,440 --> 00:38:22,079 this lecture it tells you I already told 839 00:38:20,358 --> 00:38:24,880 you that this convergence model Works 840 00:38:22,079 --> 00:38:28,400 quite well the point is now that it 841 00:38:24,880 --> 00:38:29,880 works very well and I had told you early 842 00:38:28,400 --> 00:38:32,440 on I think in the first lecture on 843 00:38:29,880 --> 00:38:33,838 growth that this work very well for 844 00:38:32,440 --> 00:38:35,200 certain kind of countries but then when 845 00:38:33,838 --> 00:38:37,039 we put all of them together there were 846 00:38:35,199 --> 00:38:38,838 some countries that were clearly off and 847 00:38:37,039 --> 00:38:41,639 they were mostly in Africa but you had 848 00:38:38,838 --> 00:38:44,078 countries that had low per capita income 849 00:38:41,639 --> 00:38:47,000 and they grew very little during that 850 00:38:44,079 --> 00:38:49,039 the sample I show you so here I'm 851 00:38:47,000 --> 00:38:50,280 refining that I'm saying okay now I'm 852 00:38:49,039 --> 00:38:53,318 going to tell you a little bit more what 853 00:38:50,280 --> 00:38:54,560 I mean by countries being similar and 854 00:38:53,318 --> 00:38:57,800 what I mean here is that they have 855 00:38:54,559 --> 00:39:00,358 similar A and H okay so when I look at 856 00:38:57,800 --> 00:39:02,920 countries that have similar A and H they 857 00:39:00,358 --> 00:39:04,000 work the models we have discussed work 858 00:39:02,920 --> 00:39:06,480 extremely 859 00:39:04,000 --> 00:39:08,079 well this is over a shorter period of 860 00:39:06,480 --> 00:39:11,000 time so you have more fluctuations and 861 00:39:08,079 --> 00:39:12,519 more countries but still and you know 862 00:39:11,000 --> 00:39:14,119 you can argue that Mexico and Chile 863 00:39:12,519 --> 00:39:16,239 probably do not belong with many of 864 00:39:14,119 --> 00:39:19,200 these other countries but you still get 865 00:39:16,239 --> 00:39:22,118 this negative relationship is quite 866 00:39:19,199 --> 00:39:24,480 clear now if you don't control by A and 867 00:39:22,119 --> 00:39:26,519 H you put everything together then the 868 00:39:24,480 --> 00:39:30,838 plot looks like the plot I showed you 869 00:39:26,519 --> 00:39:34,239 earlier okay so if I control by A A and 870 00:39:30,838 --> 00:39:37,358 H the moles work very well if I don't 871 00:39:34,239 --> 00:39:40,000 control for a andh then the M do not 872 00:39:37,358 --> 00:39:42,759 look that nice 873 00:39:40,000 --> 00:39:45,280 okay so this led to a literature which 874 00:39:42,760 --> 00:39:48,560 is called the conditional convergence 875 00:39:45,280 --> 00:39:51,040 literature and the idea it's almost 876 00:39:48,559 --> 00:39:53,519 accounting but the idea is the following 877 00:39:51,039 --> 00:39:55,838 so so the question that that that was 878 00:39:53,519 --> 00:39:58,800 behind this literature is well why is it 879 00:39:55,838 --> 00:40:03,119 that we have some countries 880 00:39:58,800 --> 00:40:05,720 say here no that have a very low income 881 00:40:03,119 --> 00:40:08,838 per capita and grow very slowly that's a 882 00:40:05,719 --> 00:40:13,439 puzzle how can it happen that we have 883 00:40:08,838 --> 00:40:15,000 that and the the the the story but again 884 00:40:13,440 --> 00:40:17,639 it's more accounting than an explanation 885 00:40:15,000 --> 00:40:20,679 in my view is is what is called 886 00:40:17,639 --> 00:40:23,358 conditional convergence says for some 887 00:40:20,679 --> 00:40:26,440 reason probably has to be explained in 888 00:40:23,358 --> 00:40:30,199 terms of you know institutions political 889 00:40:26,440 --> 00:40:32,440 instability or whatever for some reason 890 00:40:30,199 --> 00:40:34,439 some countries have just lower steady 891 00:40:32,440 --> 00:40:36,240 state levels of Technology lower steady 892 00:40:34,440 --> 00:40:37,599 States because they they have lower 893 00:40:36,239 --> 00:40:42,838 Technologies and they're stuck with 894 00:40:37,599 --> 00:40:45,720 lower Technologies and so on okay uh 895 00:40:42,838 --> 00:40:49,799 so so what this literature does is says 896 00:40:45,719 --> 00:40:51,838 okay let's compute the St state so let's 897 00:40:49,800 --> 00:40:53,800 accept that some countries will have 898 00:40:51,838 --> 00:40:55,960 lower level of Technology that's what it 899 00:40:53,800 --> 00:40:57,560 is maybe at some point they'll flip from 900 00:40:55,960 --> 00:41:01,199 there but you know they have been for a 901 00:40:57,559 --> 00:41:03,000 long time in in in a stock that let's 902 00:41:01,199 --> 00:41:05,639 assume that they have have a different 903 00:41:03,000 --> 00:41:08,679 level of technology so that means let's 904 00:41:05,639 --> 00:41:12,400 compute for each country its steady 905 00:41:08,679 --> 00:41:14,118 state its own steady state using its own 906 00:41:12,400 --> 00:41:15,800 technology and its own level of 907 00:41:14,119 --> 00:41:17,400 Education 908 00:41:15,800 --> 00:41:20,640 okay 909 00:41:17,400 --> 00:41:23,760 so so in particular this in this plot 910 00:41:20,639 --> 00:41:28,078 I'm going to show you er er take the 911 00:41:23,760 --> 00:41:30,000 values the value of a for 1970 912 00:41:28,079 --> 00:41:33,000 that's the plot I'm going to show you 913 00:41:30,000 --> 00:41:35,679 the Valu that each country had in 1970 914 00:41:33,000 --> 00:41:37,679 compute the state state level of output 915 00:41:35,679 --> 00:41:39,239 corresponding to that 916 00:41:37,679 --> 00:41:42,159 a 917 00:41:39,239 --> 00:41:45,719 okay a and over time it will be growing 918 00:41:42,159 --> 00:41:49,078 at GA whatever but but take the a of 919 00:41:45,719 --> 00:41:52,519 1970 compute the state value of 920 00:41:49,079 --> 00:41:54,720 that compare it with the current output 921 00:41:52,519 --> 00:41:56,400 over that if the current output is below 922 00:41:54,719 --> 00:41:58,239 that that means that the this country 923 00:41:56,400 --> 00:42:00,240 still needs to catch up have not with 924 00:41:58,239 --> 00:42:02,118 respect to some Universal stady state 925 00:42:00,239 --> 00:42:04,639 but with respect to its own stady state 926 00:42:02,119 --> 00:42:06,280 with its lower technology and whatever 927 00:42:04,639 --> 00:42:08,879 okay and 928 00:42:06,280 --> 00:42:11,119 then look at whether we see convergence 929 00:42:08,880 --> 00:42:14,880 or not and the answer is that you start 930 00:42:11,119 --> 00:42:16,720 recovering a this downward sloping curve 931 00:42:14,880 --> 00:42:19,720 so what does this say what is the the 932 00:42:16,719 --> 00:42:22,558 big story is telling us it's saying look 933 00:42:19,719 --> 00:42:25,959 some countries for reasons that are 934 00:42:22,559 --> 00:42:28,720 Beyond this mold just simply have much 935 00:42:25,960 --> 00:42:30,559 Lower State States 936 00:42:28,719 --> 00:42:32,519 yeah they have lower Technologies they 937 00:42:30,559 --> 00:42:35,440 don't know how to use more complicated 938 00:42:32,519 --> 00:42:38,119 technology I don't know well but that's 939 00:42:35,440 --> 00:42:40,480 what it is they have lower Technologies 940 00:42:38,119 --> 00:42:42,559 and so they have their own stady states 941 00:42:40,480 --> 00:42:44,079 which can be stady states with very low 942 00:42:42,559 --> 00:42:47,480 levels of income per 943 00:42:44,079 --> 00:42:49,480 capita now for those countries it still 944 00:42:47,480 --> 00:42:53,000 applies and that's what this picture 945 00:42:49,480 --> 00:42:56,639 shows that if they are not at their 946 00:42:53,000 --> 00:42:58,599 state state still have lower Capital per 947 00:42:56,639 --> 00:43:00,759 war effect worker than they need to have 948 00:42:58,599 --> 00:43:03,920 in their stady state that they will have 949 00:43:00,760 --> 00:43:07,359 transitional growth so they will grow 950 00:43:03,920 --> 00:43:09,519 faster than their growth in the in in in 951 00:43:07,358 --> 00:43:11,679 in their own steady 952 00:43:09,519 --> 00:43:14,239 state and that's what this picture shows 953 00:43:11,679 --> 00:43:16,039 you you know these are countries that 954 00:43:14,239 --> 00:43:20,039 that grew very little look at we have 955 00:43:16,039 --> 00:43:23,558 Japan here together with bwan I think 956 00:43:20,039 --> 00:43:26,358 ER and maybe Taiwan in the same in the 957 00:43:23,559 --> 00:43:27,839 same place okay so these are countries 958 00:43:26,358 --> 00:43:30,598 that still have lots of grows to do 959 00:43:27,838 --> 00:43:32,519 relative to their own stady State and 960 00:43:30,599 --> 00:43:34,920 they did grow a lot we know how do I 961 00:43:32,519 --> 00:43:37,119 know that well because the output I 962 00:43:34,920 --> 00:43:38,800 compute the output I compute relative to 963 00:43:37,119 --> 00:43:41,599 a steady state at the beginning of my 964 00:43:38,800 --> 00:43:43,599 sample was much lower than one that 965 00:43:41,599 --> 00:43:44,640 means that that you're not at your St 966 00:43:43,599 --> 00:43:48,559 State 967 00:43:44,639 --> 00:43:51,400 no so this variable here is the output 968 00:43:48,559 --> 00:43:53,920 you have at the beginning of the sample 969 00:43:51,400 --> 00:43:56,480 relative to what the steady state your 970 00:43:53,920 --> 00:43:58,760 steady state is how do you compute the 971 00:43:56,480 --> 00:44:00,679 stady state well you input the level of 972 00:43:58,760 --> 00:44:02,359 Technology you input the saving rate you 973 00:44:00,679 --> 00:44:04,039 input the population growth and all 974 00:44:02,358 --> 00:44:05,759 these kind of things so you have a 975 00:44:04,039 --> 00:44:08,400 number lower than one means you still 976 00:44:05,760 --> 00:44:11,040 have catching up growth to do not with 977 00:44:08,400 --> 00:44:13,119 respect to the global Universal aady 978 00:44:11,039 --> 00:44:15,679 state but with respect to your own aady 979 00:44:13,119 --> 00:44:17,400 State and when you do that you see that 980 00:44:15,679 --> 00:44:19,318 some countries that in the s in the 981 00:44:17,400 --> 00:44:21,079 total sample look like they're not 982 00:44:19,318 --> 00:44:22,599 growing and so on so forth they are 983 00:44:21,079 --> 00:44:24,680 growing they're just 984 00:44:22,599 --> 00:44:26,480 growing you know relative to their own 985 00:44:24,679 --> 00:44:28,919 stady state which has little growth and 986 00:44:26,480 --> 00:44:32,920 it has low levels of technology and so 987 00:44:28,920 --> 00:44:35,880 on and so that's a conclusion of this 988 00:44:32,920 --> 00:44:38,480 conditional convergence literature now 989 00:44:35,880 --> 00:44:41,240 it turns out that that that the world 990 00:44:38,480 --> 00:44:44,760 has become very unequal also on this 991 00:44:41,239 --> 00:44:47,558 Dimension over time this this shows you 992 00:44:44,760 --> 00:44:49,280 the ratio of GDP per worker of the 90th 993 00:44:47,559 --> 00:44:51,760 percentile to the 10th percentile 994 00:44:49,280 --> 00:44:53,280 country and so you have not only big 995 00:44:51,760 --> 00:44:55,599 difference in technology across the 996 00:44:53,280 --> 00:44:57,720 world but also you have very different 997 00:44:55,599 --> 00:44:59,519 rates of growth in techn technology 998 00:44:57,719 --> 00:45:01,639 across different countries on the world 999 00:44:59,519 --> 00:45:04,519 so this difference is sort of increasing 1000 00:45:01,639 --> 00:45:07,039 quite dramatically 1001 00:45:04,519 --> 00:45:10,559 okay I don't know what happened 1002 00:45:07,039 --> 00:45:10,558 here but 1003 00:45:10,679 --> 00:45:15,879 uh I mean I'm saying so the world 1004 00:45:14,119 --> 00:45:18,240 started with with count this is telling 1005 00:45:15,880 --> 00:45:20,280 you it started with countries that you 1006 00:45:18,239 --> 00:45:24,118 know were richer than others and that 1007 00:45:20,280 --> 00:45:26,319 distance has been rising over 1008 00:45:24,119 --> 00:45:28,960 time but sort of towards the end we 1009 00:45:26,318 --> 00:45:28,960 began to change 1010 00:45:29,119 --> 00:45:34,079 here I think that has a lot to do with 1011 00:45:31,679 --> 00:45:36,440 China that was a poor economy that grew 1012 00:45:34,079 --> 00:45:37,839 very fast During the period and it 1013 00:45:36,440 --> 00:45:39,119 wasn't very large here so it didn't 1014 00:45:37,838 --> 00:45:42,119 matter as much but then it began to 1015 00:45:39,119 --> 00:45:44,760 count a lot I think I'm not completely 1016 00:45:42,119 --> 00:45:47,318 sure that's it anyways but that's the 1017 00:45:44,760 --> 00:45:50,119 state of knowledge in this I mean 1018 00:45:47,318 --> 00:45:53,079 obviously there's a big literature 1019 00:45:50,119 --> 00:45:57,519 around follow of this and and very 1020 00:45:53,079 --> 00:46:01,160 complex even literature but but there's 1021 00:45:57,519 --> 00:46:04,559 we understand we know that that that we 1022 00:46:01,159 --> 00:46:07,358 have a you know good ways of explaining 1023 00:46:04,559 --> 00:46:11,599 how a country converges to its own EST 1024 00:46:07,358 --> 00:46:14,119 State ER that we have very poor models 1025 00:46:11,599 --> 00:46:18,160 certainly within economics if go 1026 00:46:14,119 --> 00:46:20,960 to um within growth Theory per 1027 00:46:18,159 --> 00:46:22,879 se there there a l institutions and 1028 00:46:20,960 --> 00:46:26,000 stuff like that explain some of that but 1029 00:46:22,880 --> 00:46:27,440 we have very poor models in general H to 1030 00:46:26,000 --> 00:46:29,440 understand sort of what 1031 00:46:27,440 --> 00:46:31,960 gives rise to this big 1032 00:46:29,440 --> 00:46:33,960 disparity in in the in technology 1033 00:46:31,960 --> 00:46:37,639 adoption and so 1034 00:46:33,960 --> 00:46:40,800 on so that's all that I want to say 1035 00:46:37,639 --> 00:46:42,400 about growth the next topic is we're 1036 00:46:40,800 --> 00:46:44,640 going to open the economy we're going to 1037 00:46:42,400 --> 00:46:46,400 go back to the type of models we had 1038 00:46:44,639 --> 00:46:49,838 very early on but now in the context of 1039 00:46:46,400 --> 00:46:49,838 an open economy