Unusable Models

Date Probability of Expansion

2004.01 0.8900436

2004.02 0.8529418

2004.03 0.8958149

2004.04 0.9889716

2004.05 0.9779222

2004.06 0.9596789

2004.07 0.9537724

2004.08 0.9124027

2004.09 0.905971

2004.10 0.9785185

2004.11 0.9806106

2004.12 0.9501554

ePr 1

1 e

t

t

z

t zy

Variable Definition

yt1 if the economy is in expansion in month t, 0 otherwise.

α Constant term.

CPIt-12Percentage growth in CPI from month t-1 to t.

PRIt-12Change in Prime Lending Rate from month t-1 to t.

AUTOt-12

Percentage change in Auto & Light Truck Sales (units) from t-1 to t.

UNEMPt-12 Unemployment Rate from t-1 to t.

James

Pr(Expansion) < 0.5 Pr(Expansion) > 0.5

Expansion = 0 0.90% 14.03%Expansion = 1 1.49% 83.58%

Regressor Estimate (standard error)

α 1.143723 (.9417604)

CPIt-12 -324.3699 (58.59455)

PRIt-12 4.270071 (24.76497)

AUTOt-12 .9219443 (1.544931)

UNEMPt-12 38.7216 (16.10947)

Insignificant regressor

Insignificant regressor

Date Probability of Expansion

2004.01 0.996768

2004.02 0.997384

2004.03 0.997272

2004.04 0.997833

2004.05 0.997856

2004.06 0.997612

2004.07 0.997613

2004.08 0.997321

2004.09 0.997399

2004.10 0.997336

2004.11 0.9984

2004.12 0.998653

ePr 1

1 e

t

t

z

t zy

Variable Definition

yt1 if the economy is in expansion in month t, 0 otherwise.

xt

Percentage growth in the CPI from month t – 1 to t. Used first difference percentage change to correct for nonstationarity.

vtFederal funds rate in month t.

wt Unemployment rate in month t.

Kandrack & Marchand

Pr(Expansion) < 0.5 Pr(Expansion) > 0.5

Expansion = 0.034 .083

Expansion = 1.024 .857

Regressor Estimate (standard error)

xt-12 -21.47994 (92.2867)

vt-12 -62.40843 (9.582975)

wt-12 121.6263 (26.1079)

Model: 1976.01-2003.12

Insignificant regressor

ePr 1

1 e

t

t

z

t zy

Variable Definition

yt1 if the economy is in expansion in month t, 0 otherwise.

x1t

Percentage growth in the CPI from month t – 1 to t. Used first difference to correct for non-stationarity.

X2t

Change in the Federal Funds Rate from month t – 1 to t. Used first difference to correct for non-stationarity.

X3tUnemployment change from month t – 1 to t.

Lyle

Pr(Expansion) < 0.5 Pr(Expansion) > 0.5

Expansion = 01.5%

12.7%

Expansion = 11.5% 84.3%

Regressor Estimate (standard error)

x1t 41.69

x2t 1.17

x3t 10.82

Date Probability of Expansion

2004.01 0.9250919

2004.02 0.9322258

2004.03 0.8952298

2004.04 0.8487291

2004.05 0.9537538

2004.06 0.9458787

2004.07 0.9278827

2004.08 0.908724

2004.09 0.9327555

2004.10 0.9335673

2004.11 0.9682772

2004.12 0.9583349

Do not use numeric identifiers unless there is some relationship among the variables. E.g., Inflation, Inflation squared, etc. Even then, the variables should be listed as X1, X2, etc. Putting the number in the subscript confuses the interpretation of t.

Estimates without standard errors are useless.

Date Probability of Expansion

2004.01 0.146

2004.02 0.141

2004.03 0.158

2004.04 0.239

2004.05 0.222

2004.06 0.213

2004.07 0.199

2004.08 0.153

2004.09 0.178

2004.10 0.225

2004.11 0.223

2004.12 0.203

Variable Definition

Ct-12Percentage growth in the CPI from month t – 1 to t.

Pt-12

% change in prime lending rate

Ft-12% change in the Federal Funds rate

Tt-12% change in truck sales

Et-12% change in unemployment

yt-121 if the economy is in expansion in month t, 0 otherwise.

Peck, Petrovich, Redshaw, Steckel

Pr(Expansion) < 0.5 Pr(Expansion) > 0.5

Expansion = 0 .0681 .086

Expansion = 1 .3095 .536

Regressor Estimate (standard error)

Ct-12 -6.11 (0.0)

Pt-12 0.81 (0.416)

Ft-12 -1.5 (0.133)

Tt-12 .99(.323)

Et-12 1.07(.287)

1 12 2 12 3 12 4 12 5 12t t t t t ty C P F T E

Pr( 1)1

t

t

y

t y

ey

e

What is this?

What is this?

What is this?

Let t = 2004.06Ct-12 = Inflation from 2004.05 to 2004.06?

Date Probability of Expansion

2004.01 99.90%

2004.02 99.90%

2004.03 99.86%

2004.04 99.85%

2004.05 99.88%

2004.06 99.90%

2004.07 99.89%

2004.08 99.89%

2004.09 99.89%

2004.10 99.86%

2004.11 99.88%

2004.12 99.76%

ePr 1

1 e

t

t

z

t zy

Variable Definition

yt1 if the economy is in expansion in month t, 0 otherwise.

truckst-12Sales for trucks over 10,000 lbs from months t-12 to t.

fedfundt-12Interest rate banks charge each other for loans from months t-12 to t.

unempt-12Percent of the labor force that is unemployed from months t-12 to t.

Lauren Mondschein

Pr(Expansion) < 0.5 Pr(Expansion) > 0.5

Expansion = 06.02% 3.70%

Expansion = 1 9.03% 81.25%

Regressor Estimate (standard error)

truckst-12 -.0000618 (.0000256)

fedfundt-13 -61.83602 (7.487841)

unempt-12 100.3755 (18.80914)

Let t = 2004.06unempt-12 = unemployment rate from 2004.06 to 2005.05?

What does it mean, “unemployment from…”

Usable but Annoying Models

Micciulla, Barnes, Cocco

ePr 1

1 e

t

t

z

t zy

Pr(Expansion) < .5

Pr(Expansion) >.5

Expansion=0 3.42% 8.39%

Expansion=1 1.86% 86.34%

Date Probability of Expansion

2004.01 99.2%

2004.02 99.2%

2004.03 97.4%

2004.04 97.8%

2004.05 98.4%

2004.06 98.4%

2004.07 97.9%

2004.08 95.3%

2004.09 99.2%

2004.10 99.1%

2004.11 99.6%

2004.12 99.2%

The table is for definitions, not explanations.

You are not measuring to an accuracy of 1 part per 10 million, so do not report to an accuracy of 1 part per 10 million.

Do not use programming notation.

Date Probability of Expansion

2004.01 0.913

2004.02 0.876

2004.03 0.809

2004.04 0.985

2004.05 0.978

2004.06 0.972

2004.07 0.969

2004.08 0.948

2004.09 0.955

2004.10 0.968

2004.11 0.969

2004.12 0.938

Variable Definition

Yt1 if the economy is in expansion in month t, 0 otherwise.

CPItPercentage growth in the CPI from month t – 1 to t.

Unt Unemployment rate in month t

TretChange in 10-year treasury note rate (constant maturity) from month t-1 to t

PritChange in prime lending rate from month t-1 to t

Fedt Change in federal funds rate from month t-1 to t

Fitzpatrick

Pr(Expansion) < 0.5 Pr(Expansion) > 0.5

Expansion = 0 14/432=0.032 51/432=0.118

Expansion = 1 11/432=0.025 356/432=0.824

Regressor Estimate (standard error)

Constant -0.028 (0.577)

CPIt-12 -260.098 (43.195)

Unt-12 54.575 (11.195)

Trt-24 -152.622 (54.218)

Prit-18 -67.750 (27.158)

Fedt-12 -45.389 (24.560)

Subscript

This variable is not defined.

Single letters are preferable.

Date Probability of Expansion

2004.01 0.943420218

2004.02 0.946123803

2004.03 0.939171308

2004.04 0.930057196

2004.05 0.947771481

2004.06 0.94657743

2004.07 0.943593253

2004.08 0.941029462

2004.09 0.945876611

2004.10 0.945362815

2004.11 0.946811615

2004.12 0.947112725

ePr 1

1 e

t

t

z

t zy

Variable Definition

yt1 if the economy is in expansion in month t, 0 otherwise.

xtHousing Starts (single family, units)

wtPercentage growth in the CPI from month t – 1 to t.

Christy Werwie

Pr(Expansion) < 0.5 Pr(Expansion) > 0.5

Expansion = 0 0 14.2%

Expansion = 1 0 85.8%

Regressor Estimate (standard error)

xt-12 8.74e-07(6.08e-07)

wt-12 -1.8623 (.66909)

zt=α+β1xt-12+ β3wt-12+ut

Do not use programming notation.

Date Probability of Expansion

2004.01 99.90%

2004.02 99.90%

2004.03 99.86%

2004.04 99.85%

2004.05 99.88%

2004.06 99.90%

2004.07 99.89%

2004.08 99.89%

2004.09 99.89%

2004.10 99.86%

2004.11 99.88%

2004.12 99.76%

ePr 1

1 e

t

t

z

t zy

Variable Definition

Zt1 if the economy is in expansion in month t, 0 otherwise.

xtThe unemployment rate in month t.

TtTruck sales in month t.

FtFederal Funds Rate in month t.

Bowen

Pr(Expansion) < 0.5 Pr(Expansion) > 0.5

Expansion = 00.060185 0.090278

Expansion = 10.037037 0.8125

Regressor Estimate (standard error)

xt-12 100.3755(18.809)

Tt-12 -.0000618(0.000256)

Ft-12 -61.836(7.487)