The first Difference-in-Differences analysis. 1 British physician John Snow was one of the fathers of modern...

Transcribed Image Text:

The first Difference-in-Differences analysis. 1 British physician John Snow was one of the fathers of modern epidemiology, the study of how illness moves through a population. Studying an outbreak of cholera in London in 1849, Snow challenged the conventional wisdom that the disease is caused by bad air. He thought cholera might be caused by bad water instead, an idea he first laid out in his 1849 essay "On the Mode of Communication of Cholera." A further cholera outbreak in 1853 and 1854 claimed many lives in the London neighborhood of Soho. Snow attributed the Soho epidemic to water from a pump on Broad Street. Not afraid to give a natural experiment a helping hand, he convinced the local parish council to remove the handle of the Broad Street pump. Cholera deaths in Soho subsided soon after, though Snow noted that death rates in his Broad Street treatment zone were already declining... In an 1855 revision of his essay, Snow reported death rates by district and water source for various parts of London. He noted that many of the high-death-rate districts in South London were supplied by one of two companies, the Southwark and Vauxhall Company or the Lambeth Company. In 1849, both companies drew water from the contaminated Thames in central London. Starting in 1852, however, the Lambeth Company drew from the river at Thames Ditton, an uncontaminated water source upstream. Snow showed that between 1849 and 1854 deaths from cholera fell in the area supplied by the Lambeth Company but rose in that supplied by the Southwark and Vauxhall Company. Use the description above and Table XII from Snow below to answer this question. a) (1) In Gertler et al (2016)'s notation, what are Y and P in this question? b) (1) What are the two groups in the difference-in-differences analysis? c) (1) Interpret John Snow's concern from the first paragraph in the language of Gertler et al. (2016) d) Draw the typical difference-in-differences graph, labeling points using data from Table XII. There is more than one right way to do this. You should: i. (1) Show the treated group trend. ii. (1) Show the comparison group trend. iii. (1) Show the counterfactual trend for the treated group. e) (1) What is your difference-in-differences estimate of the effect of P on Y from part a)? There is more than one correct answer. f) (1) What assumption do you have to make for your estimate in e) to be causal? Do you believe the assumption? TABLE XII. Deaths Deaths from Sub-Districts. Cholera in 1849. from Cholera in 1854. Water Supply. St. Saviour, Southwark. 283 371 St. Olave 157 161 St. John, Horsleydown 192 148 St. James, Bermondsey. 249 362 St. Mary Magdalen 259 244 Leather Market 226 237 Rotherhithe* 352 282 Wandsworth. Battersea 97 59 Southwark & Vaux- hall Company only. 111 171 8 9 235 240 92 174 Putney. Camberwell Peckham Christchurch, Southwark 256 113 Kent Road 267 174 Borough Road 312 270 London Road 257 93 Trinity, Newington 318 210 St. Peter, Walworth 446 388 St. Mary, Newington 143 92 Waterloo Road (1st) 193 58 Waterloo Road (2nd) 243 117 Lambeth Church (1st) 215 49 Lambeth Church (2nd). 544 193 Kennington (1st) . 187 303 Kennington (2nd) 153 142 Brixton 81 48 . Clapham 114 165 St. George, Camberwell 176 132 Norwood Streatham Lambeth Company, and Southwark and Vauxhall Compy. 2 10 154 15 Lambeth Company Dulwich 1 Sydenham 5 12 only. 12 First 12 sub-districts 2261 2458 Southwk.& Vauxhall. Next 16 sub-districts . 3905 2547 Both Companies. Last 4 sub-districts 162 37 Lambeth Company. A small part of Rotherhithe is now supplied by the Kent Water Company. The first Difference-in-Differences analysis. 1 British physician John Snow was one of the fathers of modern epidemiology, the study of how illness moves through a population. Studying an outbreak of cholera in London in 1849, Snow challenged the conventional wisdom that the disease is caused by bad air. He thought cholera might be caused by bad water instead, an idea he first laid out in his 1849 essay "On the Mode of Communication of Cholera." A further cholera outbreak in 1853 and 1854 claimed many lives in the London neighborhood of Soho. Snow attributed the Soho epidemic to water from a pump on Broad Street. Not afraid to give a natural experiment a helping hand, he convinced the local parish council to remove the handle of the Broad Street pump. Cholera deaths in Soho subsided soon after, though Snow noted that death rates in his Broad Street treatment zone were already declining... In an 1855 revision of his essay, Snow reported death rates by district and water source for various parts of London. He noted that many of the high-death-rate districts in South London were supplied by one of two companies, the Southwark and Vauxhall Company or the Lambeth Company. In 1849, both companies drew water from the contaminated Thames in central London. Starting in 1852, however, the Lambeth Company drew from the river at Thames Ditton, an uncontaminated water source upstream. Snow showed that between 1849 and 1854 deaths from cholera fell in the area supplied by the Lambeth Company but rose in that supplied by the Southwark and Vauxhall Company. Use the description above and Table XII from Snow below to answer this question. a) (1) In Gertler et al (2016)'s notation, what are Y and P in this question? b) (1) What are the two groups in the difference-in-differences analysis? c) (1) Interpret John Snow's concern from the first paragraph in the language of Gertler et al. (2016) d) Draw the typical difference-in-differences graph, labeling points using data from Table XII. There is more than one right way to do this. You should: i. (1) Show the treated group trend. ii. (1) Show the comparison group trend. iii. (1) Show the counterfactual trend for the treated group. e) (1) What is your difference-in-differences estimate of the effect of P on Y from part a)? There is more than one correct answer. f) (1) What assumption do you have to make for your estimate in e) to be causal? Do you believe the assumption? TABLE XII. Deaths Deaths from Sub-Districts. Cholera in 1849. from Cholera in 1854. Water Supply. St. Saviour, Southwark. 283 371 St. Olave 157 161 St. John, Horsleydown 192 148 St. James, Bermondsey. 249 362 St. Mary Magdalen 259 244 Leather Market 226 237 Rotherhithe* 352 282 Wandsworth. Battersea 97 59 Southwark & Vaux- hall Company only. 111 171 8 9 235 240 92 174 Putney. Camberwell Peckham Christchurch, Southwark 256 113 Kent Road 267 174 Borough Road 312 270 London Road 257 93 Trinity, Newington 318 210 St. Peter, Walworth 446 388 St. Mary, Newington 143 92 Waterloo Road (1st) 193 58 Waterloo Road (2nd) 243 117 Lambeth Church (1st) 215 49 Lambeth Church (2nd). 544 193 Kennington (1st) . 187 303 Kennington (2nd) 153 142 Brixton 81 48 . Clapham 114 165 St. George, Camberwell 176 132 Norwood Streatham Lambeth Company, and Southwark and Vauxhall Compy. 2 10 154 15 Lambeth Company Dulwich 1 Sydenham 5 12 only. 12 First 12 sub-districts 2261 2458 Southwk.& Vauxhall. Next 16 sub-districts . 3905 2547 Both Companies. Last 4 sub-districts 162 37 Lambeth Company. A small part of Rotherhithe is now supplied by the Kent Water Company.