② The McG econometrics. Fourth Regression Analysis CHAPTER ONE: THE NATURE OF REGRESSION ANALYSIS 31 natural ordering (ascending or descending) of the values along the scale Therefore, comparisons such as X2< X1 or X2>X1 are meaningful. Most economic variables belong to this category. Thus, it is meaningful to ask how big is this year's GDP compared with the previous years GDP. nterval Scale An interval scale variable satisfies the last two properties of the ratio scale variable but not the first. thus the distance between two time periods, say(2000-1995)is meaningful, but not the ratio of two time Ordinal Scale A variable belongs to this category only if it satisfies the third property of the ratio scale (i.e, natural ordering). Examples are grad ing systems(A, B, C grades)or income class (upper, middle, lower). For these variables the ordering exists but the distances between the categories cannot be quantified. Students of economics will recall the indifference curves between two goods, each higher indifference curve indicating higher level of utility, but one cannot quantify by how much one indifference curve is higher than the others Nominal Scale Variables in this category have none of the features of the ratio scale variables Variables such as gender(male, female) and mari al status(married, unmarried, divorced, separated) simply denote cate gories. Question: What is the reason why such variables cannot be expressed on the ratio, interval, or ordinal scales? As we shall see, econometric techniques that may be suitable for ratio scale variables may not be suitable for nominal scale variables. Therefore, it is important to bear in mind the distinctions among the four types of mea surement scales discussed above 1. 8 SUMMARY AND CONCLUSIONS 1. The key idea behind regression analysis is the statistical dependence of one variable, the dependent variable, on one or more other variables, the explanatory variables 2. The objective of such analysis is to estimate and/or predict the mean or average value of the dependent variable on the basis of the known or fixed values of the explanatory variables 3. In practice the of regression analysis depends on the avail ability of the appropriate data. This chapter discussed the nature, sources, and limitations of the data that are generally available for research, espe cially in the social sciences 4. In any research, the researcher should clearly state the sources of the data used in the analysis, their definitions, their methods of collection, and any gaps or omissions in the data as well as any revisions in the data. Keep n mind that the macroeconomic data published by the government are often revised
Gujarati: Basic Econometrics, Fourth Edition I. Single−Equation Regression Models 1. The Nature of Regression Analysis © The McGraw−Hill Companies, 2004 CHAPTER ONE: THE NATURE OF REGRESSION ANALYSIS 31 natural ordering (ascending or descending) of the values along the scale. Therefore, comparisons such as X2 ≤ X1 or X2 ≥ X1 are meaningful. Most economic variables belong to this category. Thus, it is meaningful to ask how big is this year’s GDP compared with the previous year’s GDP. Interval Scale An interval scale variable satisfies the last two properties of the ratio scale variable but not the first. Thus, the distance between two time periods, say (2000–1995) is meaningful, but not the ratio of two time periods (2000/1995). Ordinal Scale A variable belongs to this category only if it satisfies the third property of the ratio scale (i.e., natural ordering). Examples are grading systems (A, B, C grades) or income class (upper, middle, lower). For these variables the ordering exists but the distances between the categories cannot be quantified. Students of economics will recall the indifference curves between two goods, each higher indifference curve indicating higher level of utility, but one cannot quantify by how much one indifference curve is higher than the others. Nominal Scale Variables in this category have none of the features of the ratio scale variables. Variables such as gender (male, female) and marital status (married, unmarried, divorced, separated) simply denote categories. Question: What is the reason why such variables cannot be expressed on the ratio, interval, or ordinal scales? As we shall see, econometric techniques that may be suitable for ratio scale variables may not be suitable for nominal scale variables. Therefore, it is important to bear in mind the distinctions among the four types of measurement scales discussed above. 1.8 SUMMARY AND CONCLUSIONS 1. The key idea behind regression analysis is the statistical dependence of one variable, the dependent variable, on one or more other variables, the explanatory variables. 2. The objective of such analysis is to estimate and/or predict the mean or average value of the dependent variable on the basis of the known or fixed values of the explanatory variables. 3. In practice the success of regression analysis depends on the availability of the appropriate data. This chapter discussed the nature, sources, and limitations of the data that are generally available for research, especially in the social sciences. 4. In any research, the researcher should clearly state the sources of the data used in the analysis, their definitions, their methods of collection, and any gaps or omissions in the data as well as any revisions in the data. Keep in mind that the macroeconomic data published by the government are often revised
1. The Nature of ② The McG Econometrics. Fourth Regression Analysis 32 PART ONE: SINGLE-EQUATION REGRESSION MODELS 5. Since the reader may not have the time, energy, or resources to track down the data, the reader has the right to presume that the data used by the researcher are properly gathered and that the computations and analysis EXERCISES 1.1. Table 1.2 gives data on the Consumer Price Index(CPI) for seven industri- alized countries with 1982-1984= 100 as the base of the index a. From the given data, compute the inflation rate for each country. 6 b. Plot the inflation rate for each country against time (i. e, use the hori zontal axis for time and the vertical axis for the inflation rate.) c. What broad conclusions can you draw about the inflation experience in the seven countries Which country's inflation rate seems to be most variable? Can you offer explanation? TABLE 1.2 CPI IN SEVEN INDUSTRIAL COUNTRIES, 1973-1997(1982-1984= 100) Year Canada France Germany U. K 197340.80000346000062.8000020.6000047.9000027.9000044.40000 197445.20000 24.6000059.00000 49.30000 197550.10000 288000065.90000 53.80000 197653.90000 6.90000 的感: 6060000 72.60000 240000 22000075.40000 87900 90.90000 97.1000087.70000 9650000 1983100.40001004000100.300010 998000099.60000 1984104.7000108.1000 1:0 102.1000104.800 03.9000 1985109.00001144000 104.1000111.1000107.6000 1986 1200 1173000 104.8000114.9000109.6000 21.1000 104.8000119.7000113.6000 1244000 1056000125.6000118.3000 50.4000108.1000135.3000 24.0000 990135.5000 596000111.4000148.2000130.7000 1698000115.0000156.90001362000 19921453000 8.8000116.9000162.7000140.3000 9931479000143.5000127.60001864000118.4000165.3000144.5000 99414820001458000131.1000193.7000119.3000169.40001482000 1995151.40001484000133.5000204.1000119.1000175.10001524000 996153.80001514000135.50002120000119.3000179.4000156.9000 19971563000153.2000137.8000215.7000121.3000185.0000160.5000 Subtract from the current years CPI the CPI from the previous year, divide the differ- ence by the previous years CPI, and multiply the result by 100. Thus, the inflation rate for Canada for1974is[(45.2-40.8)/40.8]×100=10.78%( approx.)
Gujarati: Basic Econometrics, Fourth Edition I. Single−Equation Regression Models 1. The Nature of Regression Analysis © The McGraw−Hill Companies, 2004 32 PART ONE: SINGLE-EQUATION REGRESSION MODELS 16Subtract from the current year’s CPI the CPI from the previous year, divide the difference by the previous year’s CPI, and multiply the result by 100. Thus, the inflation rate for Canada for 1974 is [(45.2 − 40.8)/40.8] × 100 = 10.78% (approx.). 5. Since the reader may not have the time, energy, or resources to track down the data, the reader has the right to presume that the data used by the researcher are properly gathered and that the computations and analysis are correct. EXERCISES 1.1. Table 1.2 gives data on the Consumer Price Index (CPI) for seven industrialized countries with 1982–1984 = 100 as the base of the index. a. From the given data, compute the inflation rate for each country.16 b. Plot the inflation rate for each country against time (i.e., use the horizontal axis for time and the vertical axis for the inflation rate.) c. What broad conclusions can you draw about the inflation experience in the seven countries? d. Which country’s inflation rate seems to be most variable? Can you offer any explanation? TABLE 1.2 CPI IN SEVEN INDUSTRIAL COUNTRIES, 1973–1997 (1982−1984 = 100) Year Canada France Germany Italy Japan U.K. U.S. 1973 40.80000 34.60000 62.80000 20.60000 47.90000 27.90000 44.40000 1974 45.20000 39.30000 67.10000 24.60000 59.00000 32.30000 49.30000 1975 50.10000 43.90000 71.10000 28.80000 65.90000 40.20000 53.80000 1976 53.90000 48.10000 74.20000 33.60000 72.20000 46.80000 56.90000 1977 58.10000 52.70000 76.90000 40.10000 78.10000 54.20000 60.60000 1978 63.30000 57.50000 79.00000 45.10000 81.40000 58.70000 65.20000 1979 69.20000 63.60000 82.20000 52.10000 84.40000 66.60000 72.60000 1980 76.10000 72.30000 86.70000 63.20000 90.90000 78.50000 82.40000 1981 85.60000 81.90000 92.20000 75.40000 95.30000 87.90000 90.90000 1982 94.90000 91.70000 97.10000 87.70000 98.10000 95.40000 96.50000 1983 100.4000 100.4000 100.3000 100.8000 99.80000 99.80000 99.60000 1984 104.7000 108.1000 102.7000 111.5000 102.1000 104.8000 103.9000 1985 109.0000 114.4000 104.8000 121.1000 104.1000 111.1000 107.6000 1986 113.5000 117.3000 104.7000 128.5000 104.8000 114.9000 109.6000 1987 118.4000 121.1000 104.9000 134.4000 104.8000 119.7000 113.6000 1988 123.2000 124.4000 106.3000 141.1000 105.6000 125.6000 118.3000 1989 129.3000 128.7000 109.2000 150.4000 108.1000 135.3000 124.0000 1990 135.5000 133.0000 112.2000 159.6000 111.4000 148.2000 130.7000 1991 143.1000 137.2000 116.3000 169.8000 115.0000 156.9000 136.2000 1992 145.3000 140.5000 122.1000 178.8000 116.9000 162.7000 140.3000 1993 147.9000 143.5000 127.6000 186.4000 118.4000 165.3000 144.5000 1994 148.2000 145.8000 131.1000 193.7000 119.3000 169.4000 148.2000 1995 151.4000 148.4000 133.5000 204.1000 119.1000 175.1000 152.4000 1996 153.8000 151.4000 135.5000 212.0000 119.3000 179.4000 156.9000 1997 156.3000 153.2000 137.8000 215.7000 121.3000 185.0000 160.5000
1. The Nature of ② The McG econometrics. Fourth Regression Analysis CHAPTER ONE: THE NATURE OF REGRESSION ANALYSIS 3 1. 2. a. Plot the inflation rate of Canada, France, Germany, Italy, Japan, and the United Kingdom against the United States inflation rate b. Comment generally about the behavior of the inflation rate in the six countries vis-a-vis the U.S. inflation rate c. If you find that the six countries' inflation rates move in the same direc- tion as the U.S. inflation rate, would that suggest that U.S. inflation causes"inflation in the other countries? Why or why not? 1.3. Table 1.3 gives the foreign exchange rates for seven industrialized countries for years 1977-1998. Except for the United Kingdom, the exchange rate is defined as the units of foreign currency for one U.S. dollar; for the United Kingdom, it is defined as the number of U.S. dollars for one U. K pound. ehavior of the exchange rates over the given time penn the general a. Plot these exchange rates against time and comment b. The dollar is said to appreciate if it can buy more units of a foreign y. Contrarily, it is said to depreciate if it buys fewer units of a foreign currency. Over the time period 1977-1998, what has been the on macroeconomics or international economics to find out what facila K general behavior of the U.S. dollar? Incidentally, look up any textbo determine the appreciation or depreciation of a currency 1. 4. The data behind the MI money supply in Figure 1.5 are given in Table 1.4 Can you give reasons why the money supply has been increasing over the time period shown in the table? TABLE 1. 3 EXCHANGE RATES FOR SEVEN COUNTRIES: 1977-1998 Year Canada 19771.06330049161002323600268.62004.4802002.4065001.744900 19781.14050045091002.009700210.39004.5207001.7907001.918400 19791.1713004.2567001.834300219.020042893001.6644002.122400 801.1693004.2251001.817500226.63004.2310001.6772002.324600 9811.19900054397002263200220.63005.0660001.9675002.024300 19 1.2344006.579400242810024906006.2839002.0327001.748000 1.2325007.620400255390023755007.6718002.1007001.515900 1.2952008.7356002.845500237.46008.2708002.3500001.336800 195 13659008.9800002.942000238.47008.6032002.4552001.297400 13896006.9257002.170500168.35007.1273001.7979001467700 13259006.0122001.798100144.6000634690014918001.639800 199 1.2306005.9595001.757000128.170 1370001.4643001.781300 1.184200 802001.880800138.07006.4559001.6369001.638200 1.16680054467001.616600145.00005.9231001.3901001.784100 468001.661000134.590060521001.4356001.767400 921.20850052935001.561800126.78005.8258001.4064001.766300 931.2902005.6669001.654500111.08007.79560014781001.501600 1.621600102.180077161001.3667001.531900 1.43210093.960007.1406001.1812001.578500 1.504900108.78006.70820012361001.560700 9971 1734800121.06007.6446001.4514001.637600 981.48360058995001.759700130.99007.9522001.4506001.657300
Gujarati: Basic Econometrics, Fourth Edition I. Single−Equation Regression Models 1. The Nature of Regression Analysis © The McGraw−Hill Companies, 2004 CHAPTER ONE: THE NATURE OF REGRESSION ANALYSIS 33 1.2. a. Plot the inflation rate of Canada, France, Germany, Italy, Japan, and the United Kingdom against the United States inflation rate. b. Comment generally about the behavior of the inflation rate in the six countries vis-à-vis the U.S. inflation rate. c. If you find that the six countries’ inflation rates move in the same direction as the U.S. inflation rate, would that suggest that U.S. inflation “causes” inflation in the other countries? Why or why not? 1.3. Table 1.3 gives the foreign exchange rates for seven industrialized countries for years 1977–1998. Except for the United Kingdom, the exchange rate is defined as the units of foreign currency for one U.S. dollar; for the United Kingdom, it is defined as the number of U.S. dollars for one U.K. pound. a. Plot these exchange rates against time and comment on the general behavior of the exchange rates over the given time period. b. The dollar is said to appreciate if it can buy more units of a foreign currency. Contrarily, it is said to depreciate if it buys fewer units of a foreign currency. Over the time period 1977–1998, what has been the general behavior of the U.S. dollar? Incidentally, look up any textbook on macroeconomics or international economics to find out what factors determine the appreciation or depreciation of a currency. 1.4. The data behind the M1 money supply in Figure 1.5 are given in Table 1.4. Can you give reasons why the money supply has been increasing over the time period shown in the table? TABLE 1.3 EXCHANGE RATES FOR SEVEN COUNTRIES: 1977–1998 Year Canada France Germany Japan Sweden Switzerland U.K. 1977 1.063300 4.916100 2.323600 268.6200 4.480200 2.406500 1.744900 1978 1.140500 4.509100 2.009700 210.3900 4.520700 1.790700 1.918400 1979 1.171300 4.256700 1.834300 219.0200 4.289300 1.664400 2.122400 1980 1.169300 4.225100 1.817500 226.6300 4.231000 1.677200 2.324600 1981 1.199000 5.439700 2.263200 220.6300 5.066000 1.967500 2.024300 1982 1.234400 6.579400 2.428100 249.0600 6.283900 2.032700 1.748000 1983 1.232500 7.620400 2.553900 237.5500 7.671800 2.100700 1.515900 1984 1.295200 8.735600 2.845500 237.4600 8.270800 2.350000 1.336800 1985 1.365900 8.980000 2.942000 238.4700 8.603200 2.455200 1.297400 1986 1.389600 6.925700 2.170500 168.3500 7.127300 1.797900 1.467700 1987 1.325900 6.012200 1.798100 144.6000 6.346900 1.491800 1.639800 1988 1.230600 5.959500 1.757000 128.1700 6.137000 1.464300 1.781300 1989 1.184200 6.380200 1.880800 138.0700 6.455900 1.636900 1.638200 1990 1.166800 5.446700 1.616600 145.0000 5.923100 1.390100 1.784100 1991 1.146000 5.646800 1.661000 134.5900 6.052100 1.435600 1.767400 1992 1.208500 5.293500 1.561800 126.7800 5.825800 1.406400 1.766300 1993 1.290200 5.666900 1.654500 111.0800 7.795600 1.478100 1.501600 1994 1.366400 5.545900 1.621600 102.1800 7.716100 1.366700 1.531900 1995 1.372500 4.986400 1.432100 93.96000 7.140600 1.181200 1.578500 1996 1.363800 5.115800 1.504900 108.7800 6.708200 1.236100 1.560700 1997 1.384900 5.839300 1.734800 121.0600 7.644600 1.451400 1.637600 1998 1.483600 5.899500 1.759700 130.9900 7.952200 1.450600 1.657300 Source: Economic Report of the President, January 2000 and January 2001
1. The Nature of ② The McG econometrics. Fourth Regression Analysis 34 PART ONE: SINGLE-EQUATION REGRESSION MODELS TABLE 1.4 SEASONALLY ADJUSTED M1 SUPPLY: 1959: 01-1999: 09(BILLIONS OF DOLLARS) 13889001393900 139.7400 1396900 140.6800 141.1700 141.7000141.9000141.0100140.4700140.3800139.9500 13998001398700139.7500139.5600139.6100139.5800 140.18 141.3100 141.1800 140.8600140.6900 141.0600141.6000141.8700 142.6600 428800 142.9200 14349 143.7800 144.7600 1452000 145.2400145.6600145.9600 146.5800 1464600146.57001463000 148.2600148.9000149.1700 151.3400 1519800 153.7400 154.4800 1553300 1568000157.8200158.7500 159.9600 50.710016094001614700162.0300161.7000 965:07 1630500163.6800164.8500165 166.7100 1690800169.6200170.51001718100171.33001 170.3100170.8100171.9700171.1600171.3800172.0300 178.13 79.7100180.6800181.6400 120 1854700 1894200 192.7400 196.0200 974100 000200 008100 3.5700 205.7500 211.8000 215.5400 18.7700 226.4700 227.7600 323200234.3000235.5800235.8900 243.1800 46.4100 2514700252.1500 251.6700 254.8900 2575400257.7600257.8600 269.2700 273.7100 74.2000 2792000 824300 870700 1976:01 288.4200 292.7000294.6600295.9300 1976:072972000299.0500299.6700302.0400303.5900306.2500 311.5400313.9400316.0200317.1900318.7100 1977:07 2.2700324 197 35.30003369600 344.8600346.8000 66003522600353.3 1979:013586000 3680500369.5900 1979:073772100378.8200379.2800380.8700380.8100381 1980:01385.8500389.7000388.1300 384.60003894600 1980:073949100400.0600 410.8300414.3800418.6900 424.4300 1981:07427.9000427.85 427.4600 430.8800 442.1300441.4900442.3700446.7800446.5300 4490900452.4900457.5000464.5700471.1200474.3000 1983:014766800483.8500490.18004927700499.7800504.3500 198307508.9600511.6000513.41 51721 520.7900 (Continued)
Gujarati: Basic Econometrics, Fourth Edition I. Single−Equation Regression Models 1. The Nature of Regression Analysis © The McGraw−Hill Companies, 2004 34 PART ONE: SINGLE-EQUATION REGRESSION MODELS TABLE 1.4 SEASONALLY ADJUSTED M1 SUPPLY: 1959:01–1999:09 (BILLIONS OF DOLLARS) 1959:01 138.8900 139.3900 139.7400 139.6900 140.6800 141.1700 1959:07 141.7000 141.9000 141.0100 140.4700 140.3800 139.9500 1960:01 139.9800 139.8700 139.7500 139.5600 139.6100 139.5800 1960:07 140.1800 141.3100 141.1800 140.9200 140.8600 140.6900 1961:01 141.0600 141.6000 141.8700 142.1300 142.6600 142.8800 1961:07 142.9200 143.4900 143.7800 144.1400 144.7600 145.2000 1962:01 145.2400 145.6600 145.9600 146.4000 146.8400 146.5800 1962:07 146.4600 146.5700 146.3000 146.7100 147.2900 147.8200 1963:01 148.2600 148.9000 149.1700 149.7000 150.3900 150.4300 1963:07 151.3400 151.7800 151.9800 152.5500 153.6500 153.2900 1964:01 153.7400 154.3100 154.4800 154.7700 155.3300 155.6200 1964:07 156.8000 157.8200 158.7500 159.2400 159.9600 160.3000 1965:01 160.7100 160.9400 161.4700 162.0300 161.7000 162.1900 1965:07 163.0500 163.6800 164.8500 165.9700 166.7100 167.8500 1966:01 169.0800 169.6200 170.5100 171.8100 171.3300 171.5700 1966:07 170.3100 170.8100 171.9700 171.1600 171.3800 172.0300 1967:01 171.8600 172.9900 174.8100 174.1700 175.6800 177.0200 1967:07 178.1300 179.7100 180.6800 181.6400 182.3800 183.2600 1968:01 184.3300 184.7100 185.4700 186.6000 187.9900 189.4200 1968:07 190.4900 191.8400 192.7400 194.0200 196.0200 197.4100 1969:01 198.6900 199.3500 200.0200 200.7100 200.8100 201.2700 1969:07 201.6600 201.7300 202.1000 202.9000 203.5700 203.8800 1970:01 206.2200 205.0000 205.7500 206.7200 207.2200 207.5400 1970:07 207.9800 209.9300 211.8000 212.8800 213.6600 214.4100 1971:01 215.5400 217.4200 218.7700 220.0000 222.0200 223.4500 1971:07 224.8500 225.5800 226.4700 227.1600 227.7600 228.3200 1972:01 230.0900 232.3200 234.3000 235.5800 235.8900 236.6200 1972:07 238.7900 240.9300 243.1800 245.0200 246.4100 249.2500 1973:01 251.4700 252.1500 251.6700 252.7400 254.8900 256.6900 1973:07 257.5400 257.7600 257.8600 259.0400 260.9800 262.8800 1974:01 263.7600 265.3100 266.6800 267.2000 267.5600 268.4400 1974:07 269.2700 270.1200 271.0500 272.3500 273.7100 274.2000 1975:01 273.9000 275.0000 276.4200 276.1700 279.2000 282.4300 1975:07 283.6800 284.1500 285.6900 285.3900 286.8300 287.0700 1976:01 288.4200 290.7600 292.7000 294.6600 295.9300 296.1600 1976:07 297.2000 299.0500 299.6700 302.0400 303.5900 306.2500 1977:01 308.2600 311.5400 313.9400 316.0200 317.1900 318.7100 1977:07 320.1900 322.2700 324.4800 326.4000 328.6400 330.8700 1978:01 334.4000 335.3000 336.9600 339.9200 344.8600 346.8000 1978:07 347.6300 349.6600 352.2600 353.3500 355.4100 357.2800 1979:01 358.6000 359.9100 362.4500 368.0500 369.5900 373.3400 1979:07 377.2100 378.8200 379.2800 380.8700 380.8100 381.7700 1980:01 385.8500 389.7000 388.1300 383.4400 384.6000 389.4600 1980:07 394.9100 400.0600 405.3600 409.0600 410.3700 408.0600 1981:01 410.8300 414.3800 418.6900 427.0600 424.4300 425.5000 1981:07 427.9000 427.8500 427.4600 428.4500 430.8800 436.1700 1982:01 442.1300 441.4900 442.3700 446.7800 446.5300 447.8900 1982:07 449.0900 452.4900 457.5000 464.5700 471.1200 474.3000 1983:01 476.6800 483.8500 490.1800 492.7700 499.7800 504.3500 1983:07 508.9600 511.6000 513.4100 517.2100 518.5300 520.7900 (Continued )
1. The Nature of ② The McG econometrics. Fourth Regression Analysis CHAPTER ONE: THE NATURE OF REGRESSION ANALYSIS 35 TABLE 1.4 (Continued) 5365900 540.540 547.3200 575.0700 583.1700 611.8300 198601 20.4000 640.3500 520100 198607 6722000 695.2600 705.2400 729.3400 743.3900 46.0000 198707 7469600748.6600 198801 他物 757.0700761.1800 == 742200 810.3300 10m10mm。m二 88.84001004.34 1016.040 410 1047470 1066220 075610 1105430 11138001123.9001129310 1994011132200 11399101141.420 1142850 1145650 1152440 1150.410 1150440 1149.750 1149.480 1144.650 1144240 1124.5201116.3001115.470 1112.340 10825601080.490 1997011080.520 063370 1997071067570 1062.0 1067530 1073810 1080.650 8209 1078.170 1075.37010722101074.65010804001088.960 093350 1091.000109265011020101108.4001104.750 1999:071099.530 1102400 1093.460 Source: Board of Governors, Federal Reserve Bank, USA 1.5. Suppose you were to develop an economic model of criminal activities, say he hours spent in criminal activities(e. g, selling illegal drugs). What vari ables would you consider in developing such a model? See if your model matches the one developed by the Nobel laureate economist Gary Becke 6. Controlled experiments in economics: On April 7, 2000, President Clinton signed into law a bill passed by both Houses of the U. S Congress that lifted earnings limitations on Social Security recipients. Until then, recipients between the ages of 65 and 69 who earned more than $17,000 a year would lose 1 dollar's worth of Social Security benefit for every 3 dollars of income earned in excess of $17,000. How would you devise a study to assess the impact of this change in the law? Note: There was no income limitation for recipients over the age of 70 under the old law G S Becker, "Crime and Punishment: An Economic Approach, "Joumal of Political Econ- mvol.76,1968,pp.169-2
Gujarati: Basic Econometrics, Fourth Edition I. Single−Equation Regression Models 1. The Nature of Regression Analysis © The McGraw−Hill Companies, 2004 CHAPTER ONE: THE NATURE OF REGRESSION ANALYSIS 35 TABLE 1.4 (Continued) 1984:01 524.4000 526.9900 530.7800 534.0300 536.5900 540.5400 1984:07 542.1300 542.3900 543.8600 543.8700 547.3200 551.1900 1985:01 555.6600 562.4800 565.7400 569.5500 575.0700 583.1700 1985:07 590.8200 598.0600 604.4700 607.9100 611.8300 619.3600 1986:01 620.4000 624.1400 632.8100 640.3500 652.0100 661.5200 1986:07 672.2000 680.7700 688.5100 695.2600 705.2400 724.2800 1987:01 729.3400 729.8400 733.0100 743.3900 746.0000 743.7200 1987:07 744.9600 746.9600 748.6600 756.5000 752.8300 749.6800 1988:01 755.5500 757.0700 761.1800 767.5700 771.6800 779.1000 1988:07 783.4000 785.0800 784.8200 783.6300 784.4600 786.2600 1989:01 784.9200 783.4000 782.7400 778.8200 774.7900 774.2200 1989:07 779.7100 781.1400 782.2000 787.0500 787.9500 792.5700 1990:01 794.9300 797.6500 801.2500 806.2400 804.3600 810.3300 1990:07 811.8000 817.8500 821.8300 820.3000 822.0600 824.5600 1991:01 826.7300 832.4000 838.6200 842.7300 848.9600 858.3300 1991:07 862.9500 868.6500 871.5600 878.4000 887.9500 896.7000 1992:01 910.4900 925.1300 936.0000 943.8900 950.7800 954.7100 1992:07 964.6000 975.7100 988.8400 1004.340 1016.040 1024.450 1993:01 1030.900 1033.150 1037.990 1047.470 1066.220 1075.610 1993:07 1085.880 1095.560 1105.430 1113.800 1123.900 1129.310 1994:01 1132.200 1136.130 1139.910 1141.420 1142.850 1145.650 1994:07 1151.490 1151.390 1152.440 1150.410 1150.440 1149.750 1995:01 1150.640 1146.740 1146.520 1149.480 1144.650 1144.240 1995:07 1146.500 1146.100 1142.270 1136.430 1133.550 1126.730 1996:01 1122.580 1117.530 1122.590 1124.520 1116.300 1115.470 1996:07 1112.340 1102.180 1095.610 1082.560 1080.490 1081.340 1997:01 1080.520 1076.200 1072.420 1067.450 1063.370 1065.990 1997:07 1067.570 1072.080 1064.820 1062.060 1067.530 1074.870 1998:01 1073.810 1076.020 1080.650 1082.090 1078.170 1077.780 1998:07 1075.370 1072.210 1074.650 1080.400 1088.960 1093.350 1999:01 1091.000 1092.650 1102.010 1108.400 1104.750 1101.110 1999:07 1099.530 1102.400 1093.460 Source: Board of Governors, Federal Reserve Bank, USA. 1.5. Suppose you were to develop an economic model of criminal activities, say, the hours spent in criminal activities (e.g., selling illegal drugs). What variables would you consider in developing such a model? See if your model matches the one developed by the Nobel laureate economist Gary Becker.17 1.6. Controlled experiments in economics: On April 7, 2000, President Clinton signed into law a bill passed by both Houses of the U.S. Congress that lifted earnings limitations on Social Security recipients. Until then, recipients between the ages of 65 and 69 who earned more than $17,000 a year would lose 1 dollar’s worth of Social Security benefit for every 3 dollars of income earned in excess of $17,000. How would you devise a study to assess the impact of this change in the law? Note: There was no income limitation for recipients over the age of 70 under the old law. 17G. S. Becker, “Crime and Punishment: An Economic Approach,” Journal of Political Economy, vol. 76, 1968, pp. 169–217