Empirical Methods Of Economics

Empirical Methods of Economics

1. Use RTDE and QTDE to obtain a time series of a price index, P, for UK domestic expenditure. 2 marks

1963 to 1994 on UK real domestic expenditure(RTDE), nominal domestic expenditure(QTDE), a nominal interest rate (INT; note this is 100+the interest rate expressed as a percentage) and a measure of money holdings (M4)

P=RTDE/QTDE

year

RTDE

QTDE

INTL

1963

1/180

Empirical Methods of Economics

288.56

30.814

1.053

14.969

9.364575

1964

307.559

34.037

1.058

16.106

9.03602

2/180

Empirical Methods of Economics

1965

312.417

36.256

1.0643

17.616

8.616974

1966

317.366

38.395

1.0691

18.757

8.265816

3/180

Empirical Methods of Economics

1967

329.964

40.985

1.068

21.158

8.050848

1968

341.032

44.39

1.0754

22.964

4/180

Empirical Methods of Economics

7.682631

1969

341.179

46.853

1.0905

24.123

7.281903

1970

349.045

51.27

1.0921

5/180

Empirical Methods of Economics

27.009

6.807977

1971

357.267

57.323

1.0885

31.4

6.232524

1972

372.979

64.466

6/180

Empirical Methods of Economics

1.089

38.674

5.78567

1973

402.565

76.242

1.1071

47.119

5.280095

1974

393.599

7/180

Empirical Methods of Economics

88.949

1.1477

52.197

4.424996

1975

386.71

108.923

1.1439

58.383

3.550306

1976

8/180

Empirical Methods of Economics

397.225

129.328

1.1443

64.97

3.071454

1977

396.143

146.204

1.1273

74.595

2.709522

9/180

Empirical Methods of Economics

1978

411.909

167.515

1.1247

85.77

2.458938

1979

426.915

197.906

1.1299

98.131

10 / 180

Empirical Methods of Economics

2.15716

1980

414.792

227.537

1.1378

114.923

1.822965

1981

408.223

249.322

1.1474

11 / 180

Empirical Methods of Economics

138.363

1.637332

1982

417.916

274.649

1.1288

154.909

1.521637

1983

438.768

302.895

12 / 180

Empirical Methods of Economics

1.108

175.299

1.448581

1984

450.949

326.498

1.1069

198.93

1.381169

1985

464.316

13 / 180

Empirical Methods of Economics

354.291

1.1062

224.794

1.31055

1986

487.33

388.179

1.0987

258.304

1.255426

1987

14 / 180

Empirical Methods of Economics

513.083

428.721

1.0947

304.948

1.196776

1988

553.461

488.953

1.0936

358.233

1.131931

15 / 180

Empirical Methods of Economics

1989

569.719

537.279

1.0958

426.322

1.060378

1990

566.238

1.1108

477.138

16 / 180

Empirical Methods of Economics

1991

548.532

581.897

1.0992

504.133

0.942662

1992

549.543

605.295

1.0912

517.883

17 / 180

Empirical Methods of Economics

0.907893

1993

561.346

638.4

1.0787

544.055

0.879301

1994

580.092

675.164

1.0805

18 / 180

Empirical Methods of Economics

567.157

0.859187

2. Use the data on P to calculate RM4, the real money supply. 2 marks RM4 = (M4) P

The real money supply is equal to money holding M4 multiplied by the price index P.

year

RTDE

QTDE

INTL

19 / 180

Empirical Methods of Economics

RM4

1963

288.56

30.814

1.053

14.969

9.364575

140.1783

1964

307.559

20 / 180

Empirical Methods of Economics

34.037

1.058

16.106

9.03602

145.5341

1965

312.417

36.256

1.0643

17.616

8.616974

21 / 180

Empirical Methods of Economics

151.7966

1966

317.366

38.395

1.0691

18.757

8.265816

155.0419

1967

329.964

40.985

22 / 180

Empirical Methods of Economics

1.068

21.158

8.050848

170.3398

1968

341.032

44.39

1.0754

22.964

7.682631

176.4239

23 / 180

Empirical Methods of Economics

1969

341.179

46.853

1.0905

24.123

7.281903

175.6613

1970

349.045

51.27

1.0921

27.009

24 / 180

Empirical Methods of Economics

6.807977

183.8767

1971

357.267

57.323

1.0885

31.4

6.232524

195.7013

1972

372.979

25 / 180

Empirical Methods of Economics

64.466

1.089

38.674

5.78567

223.755

1973

402.565

76.242

1.1071

47.119

5.280095

26 / 180

Empirical Methods of Economics

248.7928

1974

393.599

88.949

1.1477

52.197

4.424996

230.9715

1975

386.71

108.923

27 / 180

Empirical Methods of Economics

1.1439

58.383

3.550306

207.2775

1976

397.225

129.328

1.1443

64.97

3.071454

199.5524

28 / 180

Empirical Methods of Economics

1977

396.143

146.204

1.1273

74.595

2.709522

202.1168

1978

411.909

167.515

1.1247

85.77

29 / 180

Empirical Methods of Economics

2.458938

210.9031

1979

426.915

197.906

1.1299

98.131

2.15716

211.6843

1980

414.792

30 / 180

Empirical Methods of Economics

227.537

1.1378

114.923

1.822965

209.5006

1981

408.223

249.322

1.1474

138.363

1.637332

31 / 180

Empirical Methods of Economics

226.5462

1982

417.916

274.649

1.1288

154.909

1.521637

235.7152

1983

438.768

302.895

32 / 180

Empirical Methods of Economics

1.108

175.299

1.448581

253.9348

1984

450.949

326.498

1.1069

198.93

1.381169

274.756

33 / 180

Empirical Methods of Economics

1985

464.316

354.291

1.1062

224.794

1.31055

294.6037

1986

487.33

388.179

1.0987

258.304

34 / 180

Empirical Methods of Economics

1.255426

324.2816

1987

513.083

428.721

1.0947

304.948

1.196776

364.9544

1988

553.461

35 / 180

Empirical Methods of Economics

488.953

1.0936

358.233

1.131931

405.495

1989

569.719

537.279

1.0958

426.322

1.060378

36 / 180

Empirical Methods of Economics

452.0626

1990

566.238

1.1108

477.138

1991

548.532

581.897

37 / 180

Empirical Methods of Economics

1.0992

504.133

0.942662

475.2269

1992

549.543

605.295

1.0912

517.883

0.907893

470.1823

38 / 180

Empirical Methods of Economics

1993

561.346

638.4

1.0787

544.055

0.879301

478.3883

1994

580.092

675.164

1.0805

567.157

39 / 180

Empirical Methods of Economics

0.859187

487.2938

3. Use the series P to calculate PI, the rate of inflation for UK 1964-1993. Why can’t this series begin in 1963?

(Hint: the rate of inflation is the proportionate or percentage rate of increase of prices:

See last year’s exercises in CIT.) 2 marks

The rate of inflation will be given by the percentage increase in price, we use the previous year as the base year and because the data for 1962 does not exist we can’t calculate the inflation rate of the year 1963.

year

RTDE

QTDE

INTL

40 / 180

Empirical Methods of Economics

RM4

1963

288.56

30.814

1.053

14.969

9.364575

140.1783

41 / 180

Empirical Methods of Economics

1964

307.559

34.037

1.058

16.106

9.03602

145.5341

-32.8555

1965

312.417

36.256

1.0643

42 / 180

Empirical Methods of Economics

17.616

8.616974

151.7966

-41.9046

1966

317.366

38.395

1.0691

18.757

8.265816

155.0419

43 / 180

Empirical Methods of Economics

-35.1158

1967

329.964

40.985

1.068

21.158

8.050848

170.3398

-21.4968

1968

341.032

44 / 180

Empirical Methods of Economics

44.39

1.0754

22.964

7.682631

176.4239

-36.8217

1969

341.179

46.853

1.0905

24.123

7.281903

45 / 180

Empirical Methods of Economics

175.6613

-40.0728

1970

349.045

51.27

1.0921

27.009

6.807977

183.8767

-47.3926

1971

46 / 180

Empirical Methods of Economics

357.267

57.323

1.0885

31.4

6.232524

195.7013

-57.5453

1972

372.979

64.466

1.089

47 / 180

Empirical Methods of Economics

38.674

5.78567

223.755

-44.6855

1973

402.565

76.242

1.1071

47.119

5.280095

248.7928

-50.5575

48 / 180

Empirical Methods of Economics

1974

393.599

88.949

1.1477

52.197

4.424996

230.9715

-85.5099

1975

386.71

108.923

49 / 180

Empirical Methods of Economics

1.1439

58.383

3.550306

207.2775

-87.469

1976

397.225

129.328

1.1443

64.97

3.071454

50 / 180

Empirical Methods of Economics

199.5524

-47.8852

1977

396.143

146.204

1.1273

74.595

2.709522

202.1168

-36.1932

1978

51 / 180

Empirical Methods of Economics

411.909

167.515

1.1247

85.77

2.458938

210.9031

-25.0584

1979

426.915

197.906

1.1299

98.131

52 / 180

Empirical Methods of Economics

2.15716

211.6843

-30.1778

1980

414.792

227.537

1.1378

114.923

1.822965

209.5006

-33.4195

53 / 180

Empirical Methods of Economics

1981

408.223

249.322

1.1474

138.363

1.637332

226.5462

-18.5633

1982

417.916

274.649

54 / 180

Empirical Methods of Economics

1.1288

154.909

1.521637

235.7152

-11.5696

1983

438.768

302.895

1.108

175.299

1.448581

253.9348

55 / 180

Empirical Methods of Economics

-7.30555

1984

450.949

326.498

1.1069

198.93

1.381169

274.756

-6.74119

1985

464.316

56 / 180

Empirical Methods of Economics

354.291

1.1062

224.794

1.31055

294.6037

-7.06195

1986

487.33

388.179

1.0987

258.304

57 / 180

Empirical Methods of Economics

1.255426

324.2816

-5.51238

1987

513.083

428.721

1.0947

304.948

1.196776

364.9544

-5.865

58 / 180

Empirical Methods of Economics

1988

553.461

488.953

1.0936

358.233

1.131931

405.495

-6.48451

1989

569.719

537.279

1.0958

59 / 180

Empirical Methods of Economics

426.322

1.060378

452.0626

-7.15526

1990

566.238

1.1108

477.138

60 / 180

Empirical Methods of Economics

-6.03783

1991

548.532

581.897

1.0992

504.133

0.942662

475.2269

-5.73383

1992

549.543

61 / 180

Empirical Methods of Economics

605.295

1.0912

517.883

0.907893

470.1823

-3.47688

1993

561.346

638.4

1.0787

544.055

0.879301

62 / 180

Empirical Methods of Economics

478.3883

-2.85915

1994

580.092

675.164

1.0805

567.157

0.859187

487.2938

-2.01146

63 / 180

Empirical Methods of Economics

4. Use PI to calculate (100 plus) the real interest rate, RINT= INT-PI. 2 marks year

RTDE QTDE INTL M4 p RM4

PI RINT

1963

288.56

64 / 180

Empirical Methods of Economics

30.814

1.053

14.969

9.364575

140.1783

1.053

1964

307.559

34.037

1.058

65 / 180

Empirical Methods of Economics

16.106

9.03602

145.5341

-32.8555

33.91349

1965

312.417

36.256

1.0643

17.616

8.616974

151.7966

66 / 180

Empirical Methods of Economics

-41.9046

42.96889

1966

317.366

38.395

1.0691

18.757

8.265816

155.0419

-35.1158

36.18489

67 / 180

Empirical Methods of Economics

1967

329.964

40.985

1.068

21.158

8.050848

170.3398

-21.4968

22.5648

1968

341.032

68 / 180

Empirical Methods of Economics

44.39

1.0754

22.964

7.682631

176.4239

-36.8217

37.89706

1969

341.179

46.853

1.0905

24.123

69 / 180

Empirical Methods of Economics

7.281903

175.6613

-40.0728

41.16333

1970

349.045

51.27

1.0921

27.009

6.807977

183.8767

70 / 180

Empirical Methods of Economics

-47.3926

48.48466

1971

357.267

57.323

1.0885

31.4

6.232524

195.7013

-57.5453

58.63379

71 / 180

Empirical Methods of Economics

1972

372.979

64.466

1.089

38.674

5.78567

223.755

-44.6855

45.77445

1973

402.565

76.242

72 / 180

Empirical Methods of Economics

1.1071

47.119

5.280095

248.7928

-50.5575

51.6646

1974

393.599

88.949

1.1477

52.197

73 / 180

Empirical Methods of Economics

4.424996

230.9715

-85.5099

86.65756

1975

386.71

108.923

1.1439

58.383

3.550306

207.2775

-87.469

74 / 180

Empirical Methods of Economics

88.61292

1976

397.225

129.328

1.1443

64.97

3.071454

199.5524

-47.8852

49.02952

1977

75 / 180

Empirical Methods of Economics

396.143

146.204

1.1273

74.595

2.709522

202.1168

-36.1932

37.32047

1978

411.909

167.515

76 / 180

Empirical Methods of Economics

1.1247

85.77

2.458938

210.9031

-25.0584

26.18313

1979

426.915

197.906

1.1299

98.131

2.15716

77 / 180

Empirical Methods of Economics

211.6843

-30.1778

31.30765

1980

414.792

227.537

1.1378

114.923

1.822965

209.5006

-33.4195

78 / 180

Empirical Methods of Economics

34.55734

1981

408.223

249.322

1.1474

138.363

1.637332

226.5462

-18.5633

19.71066

1982

79 / 180

Empirical Methods of Economics

417.916

274.649

1.1288

154.909

1.521637

235.7152

-11.5696

12.69837

1983

438.768

302.895

1.108

80 / 180

Empirical Methods of Economics

175.299

1.448581

253.9348

-7.30555

8.413552

1984

450.949

326.498

1.1069

198.93

1.381169

81 / 180

Empirical Methods of Economics

274.756

-6.74119

7.848093

1985

464.316

354.291

1.1062

224.794

1.31055

294.6037

-7.06195

8.168145

82 / 180

Empirical Methods of Economics

1986

487.33

388.179

1.0987

258.304

1.255426

324.2816

-5.51238

6.611083

1987

513.083

83 / 180

Empirical Methods of Economics

428.721

1.0947

304.948

1.196776

364.9544

-5.865

6.959698

1988

553.461

488.953

1.0936

84 / 180

Empirical Methods of Economics

358.233

1.131931

405.495

-6.48451

7.578111

1989

569.719

537.279

1.0958

426.322

1.060378

452.0626

85 / 180

Empirical Methods of Economics

-7.15526

8.251057

1990

566.238

1.1108

477.138

-6.03783

7.148631

86 / 180

Empirical Methods of Economics

1991

548.532

581.897

1.0992

504.133

0.942662

475.2269

-5.73383

6.833033

1992

549.543

87 / 180

Empirical Methods of Economics

605.295

1.0912

517.883

0.907893

470.1823

-3.47688

4.568083

1993

561.346

638.4

1.0787

544.055

88 / 180

Empirical Methods of Economics

0.879301

478.3883

-2.85915

3.937847

1994

580.092

675.164

1.0805

567.157

0.859187

487.2938

89 / 180

Empirical Methods of Economics

-2.01146

3.091957

5. The model will be specified in logs. Variable names in lower case correspond to the logs of the upper case versions. So rm4=ln (RM4) and rint=ln (RINT)

year

RM4

RINT

rm4

rint

1963

140.1783

90 / 180

Empirical Methods of Economics

1.053

4.942915

0.051643

1964

145.5341

33.91349

4.980411

3.523813

1965

151.7966

42.96889

91 / 180

Empirical Methods of Economics

5.022542

3.760476

1966

155.0419

36.18489

5.043695

3.588642

1967

170.3398

22.5648

5.137795

92 / 180

Empirical Methods of Economics

3.116391

1968

176.4239

37.89706

5.17289

3.634874

1969

175.6613

41.16333

5.168558

3.717548

93 / 180

Empirical Methods of Economics

1970

183.8767

48.48466

5.214265

3.881247

1971

195.7013

58.63379

5.276589

4.071311

1972

94 / 180

Empirical Methods of Economics

223.755

45.77445

5.410552

3.823726

1973

248.7928

51.6646

5.51662

3.944773

1974

230.9715

95 / 180

Empirical Methods of Economics

86.65756

5.442294

4.461964

1975

207.2775

88.61292

5.334059

4.484278

1976

199.5524

49.02952

96 / 180

Empirical Methods of Economics

5.296077

3.892423

1977

202.1168

37.32047

5.308846

3.619542

1978

210.9031

26.18313

5.351399

97 / 180

Empirical Methods of Economics

3.265115

1979

211.6843

31.30765

5.355096

3.443863

1980

209.5006

34.55734

5.344727

3.54262

98 / 180

Empirical Methods of Economics

1981

226.5462

19.71066

5.422949

2.98116

1982

235.7152

12.69837

5.462624

2.541474

1983

99 / 180

Empirical Methods of Economics

253.9348

8.413552

5.537078

2.129844

1984

274.756

7.848093

5.615883

2.060271

1985

294.6037

100 / 180

Empirical Methods of Economics

8.168145

5.685631

2.100242

1986

324.2816

6.611083

5.781612

1.888747

1987

364.9544

6.959698

101 / 180

Empirical Methods of Economics

5.899773

1.940136

1988

405.495

7.578111

6.005109

2.025264

1989

452.0626

8.251057

6.113821

102 / 180

Empirical Methods of Economics

2.110341

1990

477.138

7.148631

6.167806

1.966921

1991

475.2269

6.833033

6.163792

1.921769

103 / 180

Empirical Methods of Economics

1992

470.1823

4.568083

6.15312

1.519094

1993

478.3883

3.937847

6.170423

1.370634

1994

104 / 180

Empirical Methods of Economics

487.2938

3.091957

6.188867

1.128804

6. Use Excel’s regression command to regress rm4 on a constant and rintl for the period 1964 to 1994. All subsequent regressions should be performed on this sample.

I.e. the Population model RM4t=

To do this use the regression facility in Data Analysis 4 marks

rm4 = K +M rint where K is a constant.

M= -0.32849

K= 6.137936

105 / 180

Empirical Methods of Economics

Therefore rm4 = 6.137936 – 0.32849 rint

7. Explain the economic interpretation of the estimated coefficient of rint.

Comment on the statistical significance of the coefficients. 4 marks

The function rm4 = 6.137936 – 0.32849rint means that the real money supply is a function of the existing interest rates in an economy, the autonomous money supply is 6.137936 billion pounds. An increase in interest rate by one unit will reduce the real money supply by 0.32849 billion pounds.

8. Now extend your model to include real domestic total expenditure.

Write the population model and the estimated model and explain the economic interpretation of the estimated coefficients.

Use a t-test to test the hypothesis that real interest rates do not influence the demand for money. 8 marks

106 / 180

Empirical Methods of Economics

rm4 = K + B1 rint + B2 RTDE

multiple regression model

rm4 = K + B1 rint + B2 RTDE

107 / 180

Empirical Methods of Economics

1 2

2 2

108 / 180

Empirical Methods of Economics

X 2

year

RTDE

rint

rm4

rint

RTDE

RTDE (rint)

rm4 (rint)

109 / 180

Empirical Methods of Economics

rm4(RTDE)

1963

288.56

0.051643

4.942915

24.43241

0.002667

83266.87

14.90210408

0.25526696

1426.3276

110 / 180

Empirical Methods of Economics

1964

307.559

3.523813

4.980411

24.80449

12.41726

94592.54

1083.780402

17.550037

1531.7702

1965

111 / 180

Empirical Methods of Economics

312.417

3.760476

5.022542

25.22593

14.14118

97604.38

1174.83663

18.8871486

1569.1275

1966

317.366

3.588642

112 / 180

Empirical Methods of Economics

5.043695

25.43886

12.87835

100721.2

1138.912957

18.1000157

1600.6973

1967

329.964

3.116391

5.137795

113 / 180

Empirical Methods of Economics

26.39694

9.711893

108876.2

1028.29684

16.0113781

1695.2874

1968

341.032

3.634874

5.17289

26.75879

13.21231

114 / 180

Empirical Methods of Economics

116302.8

1239.60835

18.8028034

1764.121

1969

341.179

3.717548

5.168558

26.71399

13.82016

116403.1

115 / 180

Empirical Methods of Economics

1268.349309

19.2143625

1763.4034

1970

349.045

3.881247

5.214265

27.18856

15.06408

121832.4

1354.729859

20.2378504

116 / 180

Empirical Methods of Economics

1820.0131

1971

357.267

4.071311

5.276589

27.84239

16.57557

127639.7

1454.545067

21.4826348

1885.1511

117 / 180

Empirical Methods of Economics

1972

372.979

3.823726

5.410552

29.27407

14.62088

139113.3

1426.1695

20.6884684

2018.0223

1973

118 / 180

Empirical Methods of Economics

402.565

3.944773

5.51662

30.4331

15.56123

162058.6

1588.027543

21.7618136

2220.7981

1974

393.599

4.461964

119 / 180

Empirical Methods of Economics

5.442294

29.61856

19.90912

154920.2

1756.224568

24.2833199

2142.0815

1975

386.71

4.484278

5.334059

120 / 180

Empirical Methods of Economics

28.45219

20.10875

149544.6

1734.115145

23.9194034

2062.734

1976

397.225

3.892423

5.296077

28.04843

15.15096

121 / 180

Empirical Methods of Economics

157787.7

1546.167726

20.6145719

2103.7342

1977

396.143

3.619542

5.308846

28.18385

13.10108

156929.3

122 / 180

Empirical Methods of Economics

1433.856227

19.2155911

2103.0622

1978

411.909

3.265115

5.351399

28.63747

10.66098

169669

1344.930255

17.4729331

123 / 180

Empirical Methods of Economics

2204.2894

1979

426.915

3.443863

5.355096

28.67705

11.86019

182256.4

1470.236773

18.442217

2286.1708

124 / 180

Empirical Methods of Economics

1980

414.792

3.54262

5.344727

28.56611

12.55016

172052.4

1469.450435

18.9343368

2216.95

1981

125 / 180

Empirical Methods of Economics

408.223

2.98116

5.422949

29.40838

8.887315

166646

1216.978079

16.1666786

2213.7725

1982

417.916

2.541474

126 / 180

Empirical Methods of Economics

5.462624

29.84026

6.45909

174653.8

1062.122648

13.8831169

2282.918

1983

438.768

2.129844

5.537078

127 / 180

Empirical Methods of Economics

30.65923

4.536235

192517.4

934.5073922

11.7931124

2429.4926

1984

450.949

2.060271

5.615883

31.53814

4.244717

128 / 180

Empirical Methods of Economics

203355

929.0771472

11.5702409

2532.4768

1985

464.316

2.100242

5.685631

32.3264

4.411016

215589.3

129 / 180

Empirical Methods of Economics

975.1759645

11.941201

2639.9294

1986

487.33

1.888747

5.781612

33.42704

3.567365

237490.5

920.4430755

10.9200023

130 / 180

Empirical Methods of Economics

2817.553

1987

513.083

1.940136

5.899773

34.80732

3.764128

263254.2

995.4507993

11.446362

3027.0732

131 / 180

Empirical Methods of Economics

1988

553.461

2.025264

6.005109

36.06133

4.101694

306319.1

1120.904639

12.1619311

3323.5936

1989

132 / 180

Empirical Methods of Economics

569.719

2.110341

6.113821

37.37881

4.453539

324579.7

1202.301364

12.9022471

3483.16

1990

566.238

1.966921

133 / 180

Empirical Methods of Economics

6.167806

38.04183

3.868778

320625.5

1113.745413

12.1315871

3492.4461

1991

548.532

1.921769

6.163792

134 / 180

Empirical Methods of Economics

37.99233

3.693196

300887.4

1054.151793

11.8453844

3381.0372

1992

549.543

1.519094

6.15312

37.86089

2.307647

135 / 180

Empirical Methods of Economics

301997.5

834.807474

9.34716767

3381.404

1993

561.346

1.370634

6.170423

38.07412

1.878638

315109.3

136 / 180

Empirical Methods of Economics

769.3999134

8.45739156

3463.7423

1994

580.092

1.128804

6.188867

38.30207

1.274198

336506.7

654.81017

6.98601783

137 / 180

Empirical Methods of Economics

3590.1122

total

13656.74

91.50895

176.6878

980.4113

298.7944

6071102

37311.01556

497.426594

76472.452

138 / 180

Empirical Methods of Economics

B1=

0.3950299

B2=

0.0101684

139 / 180

Empirical Methods of Economics

K= rm4-B1rint-B2 RTDE

1.9883166

140 / 180

Empirical Methods of Economics

rm4 =1.9883166+0.3950299rint+1.9883166RTDE

Interpretation:

141 / 180

Empirical Methods of Economics

The model indicates that the autonomous real money supply is 1.9883166 billion pounds, it further indicates that when the rate of interest is increased by one unit there is an increase in the money supply amounting to 0.3950299 billion pounds and also that if the real domestic expenditure increases by one unit the real supply for money increases by 1.9883166 billion pounds.

9. Extend the model in part 6 again to include pi, the log of the rate of inflation. Write the Population model you are now considering.

Explain the economic interpretation of the coefficient of pi.

Be careful to explain the role of the other right hand variables in its interpretation. 8 marks

rm4 = K + B1 rint + ln P

142 / 180

Empirical Methods of Economics

143 / 180

Empirical Methods of Economics

1 2

2 2

X 2

144 / 180

Empirical Methods of Economics

YX 2

year

rm4

rint

ln pi

rint 2

ln pi 2

rint(ln pi)

rm4(rint)

rm4(ln pi)

145 / 180

Empirical Methods of Economics

1963

4.942915

0.051643

1964

4.980411

146 / 180

Empirical Methods of Economics

3.523813

32.8555

3.492119

12.41726

12.1949

12.30557489

17.550037

17.392189

1965

5.022542

3.760476

147 / 180

Empirical Methods of Economics

41.9046

3.735396

14.14118

13.95318

14.04686553

18.8871486

18.761181

1966

5.043695

3.588642

35.1158

3.558651

148 / 180

Empirical Methods of Economics

12.87835

12.664

12.77072506

18.1000157

17.948751

1967

5.137795

3.116391

21.4968

3.067904

9.711893

149 / 180

Empirical Methods of Economics

9.412035

9.560788685

16.0113781

15.762262

1968

5.17289

3.634874

36.8217

3.606087

13.21231

13.00387

13.10767313

150 / 180

Empirical Methods of Economics

18.8028034

18.653893

1969

5.168558

3.717548

40.0728

3.690698

13.82016

13.62125

13.72034622

19.2143625

151 / 180

Empirical Methods of Economics

19.075586

1970

5.214265

3.881247

47.3926

3.858466

15.06408

14.88776

14.97565997

20.2378504

20.119065

152 / 180

Empirical Methods of Economics

1971

5.276589

4.071311

57.5453

4.052572

16.57557

16.42334

16.49928285

21.4826348

21.383759

1972

5.410552

153 / 180

Empirical Methods of Economics

3.823726

44.6855

3.799649

14.62088

14.43733

14.52881692

20.6884684

20.558199

1973

5.51662

3.944773

154 / 180

Empirical Methods of Economics

50.5575

3.923111

15.56123

15.3908

15.47578354

21.7618136

21.642314

1974

5.442294

4.461964

85.5099

4.448632

155 / 180

Empirical Methods of Economics

19.90912

19.79033

19.84963654

24.2833199

24.210764

1975

5.334059

4.484278

87.469

4.471284

20.10875

156 / 180

Empirical Methods of Economics

19.99238

20.05048247

23.9194034

23.850095

1976

5.296077

3.892423

47.8852

3.868806

15.15096

14.96766

15.05903132

157 / 180

Empirical Methods of Economics

20.6145719

20.489497

1977

5.308846

3.619542

36.1932

3.588871

13.10108

12.88

12.99007024

19.2155911

158 / 180

Empirical Methods of Economics

19.052765

1978

5.351399

3.265115

25.0584

3.221209

10.66098

10.37619

10.51761815

17.4729331

17.237975

159 / 180

Empirical Methods of Economics

1979

5.355096

3.443863

30.1778

3.407107

11.86019

11.60838

11.7336082

18.442217

18.245383

1980

5.344727

160 / 180

Empirical Methods of Economics

3.54262

33.4195

3.50914

12.55016

12.31406

12.43154799

18.9343368

18.755393

1981

5.422949

2.98116

161 / 180

Empirical Methods of Economics

18.5633

2.921187

8.887315

8.533331

8.708524386

16.1666786

15.841445

1982

5.462624

2.541474

11.5696

2.448381

162 / 180

Empirical Methods of Economics

6.45909

5.994569

6.222496573

13.8831169

13.374585

1983

5.537078

2.129844

7.30555

1.988634

4.536235

163 / 180

Empirical Methods of Economics

3.954667

4.235480903

11.7931124

11.011223

1984

5.615883

2.060271

6.74119

1.908236

4.244717

3.641366

3.931484255

164 / 180

Empirical Methods of Economics

11.5702409

10.716433

1985

5.685631

2.100242

7.06195

1.954721

4.411016

3.820935

4.105387599

11.941201

165 / 180

Empirical Methods of Economics

11.113824

1986

5.781612

1.888747

5.51238

1.706996

3.567365

2.913837

3.224084465

10.9200023

9.8691913

166 / 180

Empirical Methods of Economics

1987

5.899773

1.940136

5.865

1.769002

3.764128

3.12937

3.4321054

11.446362

10.436713

1988

6.005109

167 / 180

Empirical Methods of Economics

2.025264

6.48451

1.869416

4.101694

3.494717

3.786061444

12.1619311

11.226048

1989

6.113821

2.110341

168 / 180

Empirical Methods of Economics

7.15526

1.967848

4.453539

3.872425

4.15282979

12.9022471

12.031069

1990

6.167806

1.966921

6.03783

1.798045

169 / 180

Empirical Methods of Economics

3.868778

3.232965

3.536611832

12.1315871

11.089991

1991

6.163792

1.921769

5.73383

1.746384

3.693196

170 / 180

Empirical Methods of Economics

3.049856

3.356146094

11.8453844

10.764346

1992

6.15312

1.519094

3.47688

1.246135

2.307647

1.552853

1.892996718

171 / 180

Empirical Methods of Economics

9.34716767

7.6676203

1993

6.170423

1.370634

2.85915

1.050524

1.878638

1.103601

1.43988443

8.45739156

172 / 180

Empirical Methods of Economics

6.4821798

1994

6.188867

1.128804

2.01146

0.698861

1.274198

0.488406

0.788876896

6.98601783

4.3251567

173 / 180

Empirical Methods of Economics

totals

171.7449

91.45731

850.539

88.37408

298.7917

286.7004

292.4364825

497.171327

479.0889

174 / 180

Empirical Methods of Economics

B1=

16.847785

B2=

-15.51382

K= rm4-B1 rint – B2 ln p

-0.211921

175 / 180

Empirical Methods of Economics

rm4= -0.211921+ 16.847785 rint -15.51382 ln p

176 / 180

Empirical Methods of Economics

Interpretation:

our model portrays that the autonomous money supply is -0.211921 billion pounds, an increase in the interest rate by one unit will increase the supply of money by 16.847785 billion pounds, while an increase in the natural of inflation by one unit decreases the money supply by 15.51382 billion pounds.

10. Perform an F test to test the joint hypothesis that the coefficients of both pi and rint are zero and comment on the outcome. 8 marks

Null hypothesis

B1=B2=0

Alternative hypothesis

177 / 180

Empirical Methods of Economics

B1≠B2

Ess=

8855.3247

Tss=

955.9789

Rss=

178 / 180

Empirical Methods of Economics

-7899.346

4427.6624

-292.5684

179 / 180

Empirical Methods of Economics

-15.13377

References:

Badi Hani Baltagi (2002) Econometrics Springer publishers, USA

Michael H, C McKenna, J Livernois, Ray R and Thanasis S (2001) Mathematics for Economics MIT Press, USA

P. Schmidt (1976) Econometrics, Marcel Dekker publishers, USA

Sergio J. Rey (1956) Advances in Spatial Econometrics: methodology, tools and applications, Springer publishers, USA

180 / 180

Financial Model

The Bank Of England 2

Balance Of Payment Example

Economics By Adam Smith

Economic Problems Of Today

Statistical Analysis Example

Economic Presentation

Economics 5

References:

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