1 00:00:00,400 --> 00:00:03,050 从原因到结果的路径 2 00:00:03,050 --> 00:00:05,539 既黑暗且危险的 3 00:00:05,539 --> 00:00:08,900 但是计量经济学的武器非常强大 4 00:00:09,211 --> 00:00:13,700 当目睹平行趋势时 我们掌握了双重差分法 5 00:00:14,450 --> 00:00:16,850 ♪ [] ♪ 6 00:00:20,100 --> 00:00:21,423 计量经济学大师在寻找 7 00:00:21,423 --> 00:00:24,800 令人信服的 「其他条件不变的比较」 8 00:00:25,100 --> 00:00:29,419 理想的对比是 9 00:00:29,419 --> 00:00:30,600 看起来相似的处理组和对照组 形成对照 10 00:00:30,600 --> 00:00:34,630 但有时这种可比性是难以捉摸的 11 00:00:34,630 --> 00:00:36,805 在没有处理的情况下 12 00:00:36,805 --> 00:00:40,100 当处理组及对照组类似地演变时 13 00:00:40,100 --> 00:00:42,307 即使起点不同 14 00:00:42,307 --> 00:00:44,900 也有望进行因果推断 15 00:00:45,600 --> 00:00:48,400 针对平行演化的武器 16 00:00:48,664 --> 00:00:50,886 大师说的「平行趋势」 17 00:00:50,886 --> 00:00:53,233 叫做「双重差分法」… 18 00:00:53,233 --> 00:00:54,420 - 双重差分法... 19 00:00:54,420 --> 00:00:56,900 - ...或简称为DD - 好的 20 00:00:56,900 --> 00:00:59,987 - 现在让我们看看 DD 21 00:00:59,987 --> 00:01:02,888 如何帮助我们了解美国历史上 22 00:01:02,888 --> 00:01:04,370 最重要的经济事件之一 23 00:01:05,300 --> 00:01:08,300 - 现在我们一起回顾大萧条的情況— 24 00:01:08,800 --> 00:01:12,200 我国有史以来最严重的经济灾难 25 00:01:13,100 --> 00:01:16,200 在 1933 年失业率达到 25%— 26 00:01:16,600 --> 00:01:19,114 这是之前或之后从未见过的水平 27 00:01:19,473 --> 00:01:22,100 数百万国民失去了家园或土地 28 00:01:22,600 --> 00:01:24,737 Suicide spiked, and hungry families 29 00:01:24,737 --> 00:01:26,766 relied on soup kitchens and bread lines 30 00:01:26,766 --> 00:01:28,155 to keep from starving. 31 00:01:29,400 --> 00:01:31,589 - Economists argue fiercely 32 00:01:31,589 --> 00:01:34,000 over the causes of the Great Depression. 33 00:01:34,000 --> 00:01:36,983 Most agree, however, that a key piece of the puzzle 34 00:01:36,983 --> 00:01:39,458 is an epidemic of bank failures. 35 00:01:39,800 --> 00:01:41,900 This was before deposit insurance. 36 00:01:42,100 --> 00:01:46,513 So if your bank went bankrupt, your savings disappeared with it. 37 00:01:46,513 --> 00:01:47,672 - [Cashier] Closing your account? 38 00:01:47,672 --> 00:01:48,892 - [Customer] Yes, sir. I'm closing my account. 39 00:01:48,892 --> 00:01:50,616 I wouldn't leave a nickel in this bank. 40 00:01:52,600 --> 00:01:56,100 - Faced with a banking crisis, the Central Bank has a choice: 41 00:01:56,400 --> 00:01:58,524 lend freely to troubled banks 42 00:01:58,524 --> 00:02:01,100 or stand aside and refuse to lend. 43 00:02:01,500 --> 00:02:05,440 Lending freely to banks in trouble is called "easy money." 44 00:02:05,440 --> 00:02:08,100 Refusing to lend is called "tight money." 45 00:02:10,200 --> 00:02:12,872 - [Joshua] Monetarist masters Milton Friedman and Anna Schwartz 46 00:02:12,872 --> 00:02:14,882 famously called the Great Depression 47 00:02:14,882 --> 00:02:16,350 the "Great Contraction," 48 00:02:16,800 --> 00:02:18,262 accusing the Federal Reserve 49 00:02:18,262 --> 00:02:21,200 of inflicting a misguided policy of tight money 50 00:02:21,200 --> 00:02:24,000 on the nation's teetering financial institutions. 51 00:02:24,360 --> 00:02:25,743 They argued that easy money 52 00:02:25,743 --> 00:02:27,895 would have kept many banks in business, 53 00:02:27,895 --> 00:02:29,700 shortening the Great Depression. 54 00:02:30,400 --> 00:02:32,110 But others disagree! 55 00:02:32,110 --> 00:02:33,769 If banks are insolvent 56 00:02:33,769 --> 00:02:35,954 because of unwise lending decisions, 57 00:02:35,954 --> 00:02:38,900 then bailouts just encourage more foolishness. 58 00:02:39,600 --> 00:02:42,965 Economists called this problem "moral hazard." 59 00:02:42,965 --> 00:02:46,100 The debate over bailouts and moral hazard continues today. 60 00:02:46,500 --> 00:02:48,599 Should financial behemoth Lehman Brothers 61 00:02:48,599 --> 00:02:51,500 had been allowed to fail on the eve of the Great Recession, 62 00:02:52,000 --> 00:02:54,703 in an ideal world, we'd answer this question 63 00:02:54,703 --> 00:02:58,400 by applying different Fed policies to randomly selected regions. 64 00:02:59,000 --> 00:03:00,250 But we can still learn a lot 65 00:03:00,250 --> 00:03:02,119 by using differences-in-differences 66 00:03:02,119 --> 00:03:06,300 to compare trends across areas with different monetary policies. 67 00:03:10,810 --> 00:03:12,522 - [Camilla] How's that even possible? 68 00:03:12,522 --> 00:03:15,623 Don't the same Fed policies apply to all banks in the U.S.? 69 00:03:15,623 --> 00:03:17,400 - [Man] Yeah. - Good question. 70 00:03:17,700 --> 00:03:21,484 The Federal Reserve System is divided into 12 districts, 71 00:03:21,484 --> 00:03:23,860 each headed by a regional bank. 72 00:03:24,301 --> 00:03:27,467 Today, Fed policy is set at the national level. 73 00:03:27,467 --> 00:03:31,973 But in the 1930s, regional Feds could do pretty much as they liked. 74 00:03:31,973 --> 00:03:33,276 - [Man] Ah, interesting. 75 00:03:33,276 --> 00:03:35,500 - And here's what's so awesome about that. 76 00:03:35,500 --> 00:03:39,302 In 1930, the Atlanta Fed, running the 6th district, 77 00:03:39,302 --> 00:03:41,473 followed an easy money policy, 78 00:03:41,473 --> 00:03:45,400 sending wheelbarrows of cash to rescue insolvent institutions. 79 00:03:45,900 --> 00:03:48,816 The St. Louis Fed, running the 8th district, 80 00:03:48,816 --> 00:03:50,668 followed a tight money policy. 81 00:03:51,100 --> 00:03:53,900 "Let fail the foolish!" they said in St. Louis. 82 00:03:54,300 --> 00:03:58,225 And so a natural experiment in monetary policy was born. 83 00:03:58,701 --> 00:04:02,000 Even better, this is a within-state experiment. 84 00:04:02,000 --> 00:04:04,347 The border between the 6th and the 8th districts 85 00:04:04,347 --> 00:04:06,762 ran smack through the middle of Mississippi. 86 00:04:07,300 --> 00:04:09,321 So northern Mississippi had tight money, 87 00:04:09,321 --> 00:04:11,870 while southern Mississippi had easy money, 88 00:04:11,870 --> 00:04:15,200 but under the same state laws and banking regulations in both. 89 00:04:15,520 --> 00:04:16,853 - [Teacher] The treatment group 90 00:04:16,853 --> 00:04:19,985 is the district 6 part of Mississippi, 91 00:04:19,985 --> 00:04:23,100 which had access to easy money during the crisis. 92 00:04:23,800 --> 00:04:25,091 The control group 93 00:04:25,091 --> 00:04:27,800 is the district 8 part of Mississippi, 94 00:04:27,800 --> 00:04:30,225 which had tight money during the crisis. 95 00:04:31,300 --> 00:04:34,040 The key year in our natural experiment 96 00:04:34,040 --> 00:04:35,400 was 1930. 97 00:04:35,800 --> 00:04:37,439 Caldwell & Company, 98 00:04:37,439 --> 00:04:40,377 a massive financial empire in the South, 99 00:04:40,377 --> 00:04:41,987 came crashing down. 100 00:04:42,700 --> 00:04:46,000 Banking is a business built on confidence and trust. 101 00:04:46,500 --> 00:04:49,151 The Caldwell meltdown caused a panic 102 00:04:49,151 --> 00:04:53,049 that led to a widespread bank run all at once. 103 00:04:53,049 --> 00:04:55,114 Depositors wanted their money back, 104 00:04:55,114 --> 00:04:58,200 causing banks to go bankrupt and shut their doors. 105 00:05:01,000 --> 00:05:03,321 We'll use differences-in-differences 106 00:05:03,321 --> 00:05:06,614 to measure the effect of contrasting monetary policies 107 00:05:06,614 --> 00:05:09,164 in response to the Caldwell crisis. 108 00:05:12,500 --> 00:05:16,279 This figure plots the number of banks in Mississippi by year, 109 00:05:16,279 --> 00:05:18,762 for the 8th and 6th districts. 110 00:05:19,273 --> 00:05:21,413 Let's start in 1929, 111 00:05:21,413 --> 00:05:24,200 a year before the Caldwell crash. 112 00:05:24,200 --> 00:05:27,565 There are 169 banks open in the 8th, 113 00:05:27,565 --> 00:05:31,242 and 141 banks open in the 6th. 114 00:05:31,242 --> 00:05:32,574 Over the next year, 115 00:05:32,574 --> 00:05:37,000 we see a similar handful of banks fail, in both districts. 116 00:05:37,400 --> 00:05:40,135 The change in the number of banks in operation 117 00:05:40,135 --> 00:05:42,168 is remarkably similar -- 118 00:05:42,168 --> 00:05:44,600 that's what parallel trends look like. 119 00:05:45,500 --> 00:05:48,783 In November 1930, Caldwell crashes, 120 00:05:48,783 --> 00:05:50,400 and the panic begins. 121 00:05:51,200 --> 00:05:53,917 Banks failed frequently in the 8th district, 122 00:05:53,917 --> 00:05:55,300 which had tight money. 123 00:05:55,800 --> 00:05:58,712 But the decline is slower in the 6th district, 124 00:05:58,712 --> 00:06:00,247 which had easy money. 125 00:06:00,800 --> 00:06:03,000 Diverging trends in this period 126 00:06:03,000 --> 00:06:06,602 might be attributable to easy versus tight money. 127 00:06:06,602 --> 00:06:12,020 In July of 1931, the 8th district abandons tight money, 128 00:06:12,020 --> 00:06:14,420 so now both districts are easy. 129 00:06:14,700 --> 00:06:16,900 Parallel trends are restored. 130 00:06:17,300 --> 00:06:19,229 In a counterfactual world, 131 00:06:19,229 --> 00:06:22,420 where the 6th district follows a tight money policy, 132 00:06:22,420 --> 00:06:23,800 what might have happened? 133 00:06:24,201 --> 00:06:28,547 If we extrapolate the trend of the 8th district to the 6th, 134 00:06:28,547 --> 00:06:29,900 it would look like this. 135 00:06:30,290 --> 00:06:33,095 So the treatment-effective easy money 136 00:06:33,095 --> 00:06:36,462 is how much the 6th district deviated from the path 137 00:06:36,462 --> 00:06:38,900 implied by the 8th district trend. 138 00:06:41,244 --> 00:06:44,475 How many banks did the easy money treatment save? 139 00:06:44,475 --> 00:06:49,021 This table reports data for the treatment group, district 6, 140 00:06:49,021 --> 00:06:50,162 in the first row, 141 00:06:50,162 --> 00:06:54,237 and data for the control group, district 8, in the second row. 142 00:06:54,237 --> 00:06:57,494 The first column shows the number of banks in business 143 00:06:57,494 --> 00:07:00,613 before the crisis began in 1930. 144 00:07:00,613 --> 00:07:03,673 The second column shows 1931. 145 00:07:03,903 --> 00:07:05,607 This is the key period 146 00:07:05,607 --> 00:07:08,663 when each district had differing monetary policies 147 00:07:08,663 --> 00:07:10,237 during the crisis. 148 00:07:10,237 --> 00:07:14,347 The rightmost column reports changes within the district. 149 00:07:14,347 --> 00:07:20,456 District 6 lost 14 banks, while district 8 lost 33. 150 00:07:20,456 --> 00:07:23,973 The mathematical formula for the treatment effect is simple. 151 00:07:24,400 --> 00:07:28,430 We subtract the change in banks in operation in the 8th district 152 00:07:28,810 --> 00:07:32,200 from the change in banks in operation in the 6th. 153 00:07:32,800 --> 00:07:35,700 Hence, the name "differences-in-differences." 154 00:07:37,000 --> 00:07:41,736 -14 minus -33 equals 19.\] 155 00:07:42,500 --> 00:07:46,800 We estimate that 19 banks were saved by easy money. 156 00:07:47,300 --> 00:07:50,730 In practice, tables and figures like those shown here 157 00:07:50,730 --> 00:07:52,912 are the beginning rather than the end 158 00:07:52,912 --> 00:07:54,453 of a DD analysis. 159 00:07:55,400 --> 00:07:57,100 The problem of how to gauge 160 00:07:57,100 --> 00:08:00,047 the statistical significance of DD estimates 161 00:08:00,047 --> 00:08:02,264 turns out to be exceedingly tricky, 162 00:08:02,264 --> 00:08:05,600 and a regression is typically part of the solution. 163 00:08:09,200 --> 00:08:12,336 The key assumption behind a valid DD analysis 164 00:08:12,336 --> 00:08:14,894 is that of parallel trends. 165 00:08:15,369 --> 00:08:17,842 Recall the principle of ceteris paribus. 166 00:08:17,842 --> 00:08:20,922 Our ideal comparison would have the two districts 167 00:08:20,922 --> 00:08:24,023 experience an identical business environment, 168 00:08:24,023 --> 00:08:25,997 except for one factor: 169 00:08:25,997 --> 00:08:27,916 easy or tight money. 170 00:08:29,200 --> 00:08:32,348 Both districts would have identical types of customers 171 00:08:32,348 --> 00:08:35,300 who would go bankrupt at exactly the same rate. 172 00:08:35,700 --> 00:08:38,600 The skill of their employees would be equal, and so on. 173 00:08:39,200 --> 00:08:43,498 Perfect ceteris paribus comparisons would allow us to clearly see 174 00:08:43,498 --> 00:08:46,594 the causal effect of different Fed policies. 175 00:08:46,594 --> 00:08:49,019 In this case, that's not possible. 176 00:08:49,019 --> 00:08:53,600 But the idea of parallel trends is based on a similar concept. 177 00:08:53,600 --> 00:08:57,364 If we see that the two regions experience similar trends 178 00:08:57,364 --> 00:08:59,654 in the number of banks over time, 179 00:08:59,654 --> 00:09:01,294 in the absence of treatment, 180 00:09:01,294 --> 00:09:04,407 we can assume they are good comparisons. 181 00:09:04,407 --> 00:09:07,434 We see that the two districts move in parallel, 182 00:09:07,434 --> 00:09:09,800 both before the crisis and after, 183 00:09:10,100 --> 00:09:12,400 when they have the same Fed policy. 184 00:09:13,100 --> 00:09:16,028 The only time the districts behave differently 185 00:09:16,028 --> 00:09:18,300 is when the Fed policy is different. 186 00:09:19,400 --> 00:09:20,599 In view of this, 187 00:09:20,599 --> 00:09:24,268 Fed policy is a likely cause of diverging trends 188 00:09:24,268 --> 00:09:26,700 from 1930 to 1931. 189 00:09:27,800 --> 00:09:30,106 But we should also check for other changes 190 00:09:30,106 --> 00:09:31,703 unique to northern Mississippi. 191 00:09:31,703 --> 00:09:33,200 - [Man] Huh? - What do you mean? 192 00:09:33,500 --> 00:09:35,396 - [Teacher] Imagine that bad tornadoes 193 00:09:35,396 --> 00:09:39,100 hit northern but not southern Mississippi in 1930. 194 00:09:39,600 --> 00:09:41,950 These tornadoes devastate farms, 195 00:09:41,950 --> 00:09:44,300 causing farmers to default on loans, 196 00:09:44,551 --> 00:09:46,800 which drives their banks out of business. 197 00:09:47,400 --> 00:09:49,438 Then the 6th and 8th districts 198 00:09:49,438 --> 00:09:52,272 would differ in not one but two ways: 199 00:09:52,700 --> 00:09:55,047 Fed policy and weather. 200 00:09:55,047 --> 00:09:58,219 And we'd have trouble identifying Fed policy 201 00:09:58,219 --> 00:10:01,590 as the causal factor behind increased bank failures 202 00:10:01,590 --> 00:10:02,600 in the 8th. 203 00:10:02,600 --> 00:10:04,248 - [Man] Ceteris is not paribus. 204 00:10:07,200 --> 00:10:09,014 - DD credibility lives or dies 205 00:10:09,014 --> 00:10:10,980 with the claim that the only reason 206 00:10:10,980 --> 00:10:13,794 northern Mississippi was special in 1930 207 00:10:13,794 --> 00:10:16,161 is differing regional Fed policy. 208 00:10:16,600 --> 00:10:20,530 We're in DD heaven with strong, visual evidence of parallel trend. 209 00:10:21,277 --> 00:10:25,549 - In general, the first step in evaluating whether to use DD 210 00:10:25,549 --> 00:10:30,200 is usually this type of visual confirmation of parallel trends 211 00:10:30,200 --> 00:10:31,700 outside of the period, 212 00:10:31,700 --> 00:10:34,784 when we expect to see a treatment effect. 213 00:10:35,094 --> 00:10:36,985 The treatment in our example 214 00:10:36,985 --> 00:10:39,835 is easy money in the face of bank failures. 215 00:10:40,500 --> 00:10:45,000 Metrics masters use DD to explore effects of many policies, 216 00:10:45,800 --> 00:10:47,900 like the minimum legal drinking age, 217 00:10:48,500 --> 00:10:52,200 and environmental changes, like access to clean water. 218 00:10:52,867 --> 00:10:54,200 In our next video, 219 00:10:54,500 --> 00:10:57,035 we'll see an example of how regression is used 220 00:10:57,035 --> 00:10:59,200 to implement a DD approach. 221 00:11:00,800 --> 00:11:02,183 - [Narrator] Are you a teacher? 222 00:11:02,183 --> 00:11:05,788 Click to explore ways to use these videos in class. 223 00:11:05,788 --> 00:11:08,847 If you're a learner, make sure this video sticks 224 00:11:08,847 --> 00:11:11,200 by taking a few quick practice questions. 225 00:11:11,600 --> 00:11:14,200 Or if you're ready, click for the next video. 226 00:11:14,600 --> 00:11:17,093 You can also check out MRU's website 227 00:11:17,093 --> 00:11:20,193 for more courses, teacher resources, and more. 228 00:11:20,193 --> 00:11:21,692 ♪ [music] ♪