lecture 12 preview: model specification and model development model specification: ramsey regression...

Lecture 12 Preview: Model Specification and Model Development

Model Specification: Ramsey REgression Specification Error Test (RESET)RESET Logic

Model Development

Model 3: Present Trend Theory I

Model 4: Present Trend Theory II

Model 2: Present Performance Theory

Linear Demand Model for Beef

General Theory: “It’s the economy stupid.”

Model Formulation and Assessment – An Iterative Process

Model 1: Past Performance Theory

Specific Models

Data Oddities

The Effect of Economic Conditions on Elections

Model Specification: Ramsey REgression Specification Error Test (RESET)

Artificial Model:

H0: Esty2 = 0The artificial model uses the same information in a different form.

New form of the information adds NO explanatory powerNew form of the information adds explanatory power

Consider the following null and alternative hypotheses:

Original Model: yt = Const + xxt + et

Estimated or “fitted” values of y: Esty = bConst + bxx

Prob[Results IF H0 True] small

Unlikely H0 is true

Might it be prudent to consider a

new model that uses the information in a difference form?

Prob[Results IF H0 True] large

Likely H0 is true

Is there a compelling reason to

consider a new model that uses the information in a different form?

Regression: bConst and bx estimate Const and x

Since Esty is derived solely from the information used to estimate the original model, the artificial model includes no new information.

RESET Question: Is the model using the available information in the “best” way?

Critical Points:

Yes No

H1: Esty2 0

Unlikely that the new form of the

information adds NO explanatory power

Likely that the new form of the information adds NO explanatory power

Likely that the new form of the information adds explanatory power

Why is this called an artificial model? By itself, it doesn’t make causal sense.

Ordinary Least Squares (OLS)Dependent Variable: QExplanatory Variable(s): Estimate SE t-Statistic Prob

P 549.4847 130.2611 -4.218333 0.0004I 24.24854 11.27214 2.151192 0.0439ChickP 287.3737 193.3540 1.486257 0.1528Const 159032.4 61472.68 2.587041 0.0176

Number of Observations 24


P 13431.05 5861.208 2.291515 0.0335I 593.4581 259.1146 -2.290330 0.0336ChickP 7054.644 3082.373 -2.288706 0.0337EstQSquared 5.79E-05 2.42E-05 2.385742 0.0276Const 1085301. 524497.0 -2.069223 0.0524


RESET Application: Linear Demand Model for BeefOriginal Model: Qt = Const + PPt + IIt + CPChickPt + et

Artificial Model:

Generate the variables: EstQ EstQSquared = EstQ EstQ

Critical Regression Result: The EstQSquared coefficient estimate is 5.79E-05, .0000579. The estimate does not equal 0; the estimate is .0000579 from 0. This evidence suggests that the new form of the information adds explanatory power.

H0: EstQ2 = 0 New form of the information adds NO explanatory power H1: EstQ2 0 New form of the information adds explanatory power

EViews

EViews

Estimated Equation: EstQ = 159,032 549.5P + 24.25I + 287.4ChickP

http://www3.amherst.edu/~fwesthoff/MITLinks/PP-BeefDemand-1985-1986-Reset.wf1



P 13431.05 5861.208 2.291515 0.0335I 593.4581 259.1146 -2.290330 0.0336ChickP 7054.644 3082.373 -2.288706 0.0337EstQSquared 5.79E-05 2.42E-05 2.385742 0.0276Const 1085301. 524497.0 -2.069223 0.0524


H0: EstQ2 = 0 New form of the information adds NO explanatory power H1: EstQ2 0 New form of the information adds explanatory power Prob[Results IF H0 True]: What is the probability that the estimate of EstQ2 from one regression would be at least .0000579 from 0, if H0 were true (that is, if EstQ2 actually equaled 0, if the different form of the information added no explanatory power)?

Prob[Results IF H0 True] small

Unlikely H0 is true

Unlikely that the new form of

the information adds NO explanatory power

Prob[Results IF H0 True] = .0276 Question: At the “traditional” significance levels of 5 or 10 percent (.05 or .10) :What does Prob[Results IF H0 True] equal?

bEstQ2

t-distribution

.0276/2

.00005790

.0276/2

.0000579.0000579

Might it be prudent to consider

a new model that uses the information in a different form?

Likely that the new form of the information adds explanatory

power

Yes

Question: Can we use the tails probability?

Yes

Ramsey RESET TestDependent Variable: QExplanatory Variable(s): Estimate SE t-Statistic Prob

P 13431.11 5861.274 2.291499 0.0335I 593.4412 259.1094 -2.290311 0.0336ChickP 7054.195 3082.207 -2.288683 0.0337C 1085437. 524557.3 -2.069244 0.0524Fitted^2 5.79E-05 2.43E-05 2.385725 0.0276

Number of Observations 24Critical Result: The Fitted^2 coefficient estimate is 5.79E05, .0000579. The

estimate does not equal 0; the estimate is .0000579 from 0. This evidence suggests that the new form of the information adds explanatory power.

Let us see how statistical software can do the work for us.

Prob[Results IF H0 True] = .0276

Artificial Model:

H0: EstQ2 = 0 New form of the information adds NO explanatory power H1: EstQ2 0 New form of the information adds explanatory power

Estimate of EstQ2 = .0000579 These are the same results as before.Software is automatically doing what we did “by hand.”

Summary: At the “traditional” 5 or 10 percent (.05 or .10) significance level, we reject H0.Reject the notion that the new form of the information adds no explanatory power.

EViews

Getting started in EViews: Run the original regression;Click View, Stability Diagnostics, Ramsey RESET Test; Enter the number of artificial variables to include (1 by default);Click OK.


1992 Election: Bill Clinton versus George Bush (George W.’s father)Clinton’s Mantra: “It’s the economy stupid.”General Theory: The American electorate is sensitive to economic conditions; Americans

hold the President and his party responsible for the state of the economy.

Question: How can we test that theory?

Data: 1890 to 2008VotePartyDemt Percent of popular vote received by the Democratic candidate in year tVotePartyRept Percent of popular vote received by the Republican candidate in year tVotePartyThirdt Percent of the popular vote received by third party candidates in year t

Good economic conditions increase the vote for the President’s party; Bad economic conditions decrease the vote for the President’s party.

PresPartyR1t 1 if incumbent President is Republican in year t; 0 if DemocratPresIncumt 1 if incumbent President is a candidate in year t, 0 otherwisePresPartyTermst Number of consecutive terms the incumbent President’s party has held the Presidency in year t UnemCurrentt Unemployment rate in year t (percent)RealGdpCurrentt Real GDP in year tRealGdpGrowtht Real GDP growth rate in year t (percent)

PriceCpiCurrentt Price level in year t (CPI)InflCpiCurrentt Inflation rate in year t based on the CPI (percent) PriceGdpCurrentt GDP price deflator in year tInflGdpCurrentt Inflation rate in year t based on the GDP price deflator (percent)

We need to generate a new variable.

Data OdditiesThird Parties

1912 President Election: Third parties garnered more than a third of the vote.How might we account for 1912 and the other “odd” years?

Ignore 1912 (and perhaps the other unusual elections also).

VotePresPartyTwot Percent of popular vote received by the President’s party based on the two major parties (ignoring third parties)

Year VotePartyDem VotePartyRep VotePartyThird1912 41.8 23.2 35.01924 28.5 54.0 17.51968 42.7 43.4 13.91992 43.3 37.7 19.0

Two of many possibilities:

VotePresPartyt = PresPartyR1tVotePartyRept + (1PresPartyR1t)VotePartyDemt

VotePresPartyt Percent of popular vote received by the President’s party in year tGenerate a New Variable

When President’s party is Rep: PresPartyR1t = 1 VotePresPartyt = VotePartyRept

When President’s party is Dem: PresPartyR1t = 0 VotePresPartyt = VotePartyDemt

VotePresPartyTwot =

EViews

PresPartyR1t Dummy variable: 1 if Republican incumbent, 0 if Democrat

VotePresPartyt

VotePartyRept + VotePartyDemt

100

http://www3.amherst.edu/~fwesthoff/MITLinks/PP-PresElections-1890-2008.wf1

Model Development: Model Formulation and Assessment – An Iterative Process

Keep in mind two important points:

There is no “cookbook” procedure we can follow.

Common sense and inventiveness play critical roles in model development.

Model Formulation:Formulate a specific model

describing the general theory.

Model Assessment:Apply econometric techniques

to assess the specific model

Incorporate insights from the assessment to refine the

specific model describing the general theory.

Art and science.

Ordinary Least Squares (OLS)Dependent Variable: VotePresPartyTwoExplanatory Variable(s): Estimate SE t-Statistic Prob

UnemPriorAvg 0.331914 0.319360 1.039310 0.3079Const 49.70180 2.595936 19.14600 0.0000


Specific ModelsVoting Model 1: Past Performance – The electorate is sensitive to how well the economy has performed in the three years prior to the election.

UnemPriorAvgt Average unemployment rate in the three years prior to election

Model: VotePresPartyTwot = Const + UnemPriorAvgUnemPriorAvgt + et

Theory: UnemPriorAvg < 0

Interpretation: We estimate that a 1 percentage point increase in the average unemployment rate during the three years prior to the election increases the vote the President’s party receives by .33 percentage points.

Is this good or bad news? What should we do?

Step 1: Collect data, run the regression, and interpret the estimates.

Step 0: Construct a model reflecting the theory to be tested

Critical Result: The coefficient estimate for UnemPriorAvg equals .33. The positive sign of the coefficient estimate suggests that an increase in the average unemployment rate in the three years prior to the election increases the votes received by the President’s party.

Bad news.

EViews

Back to the “drawing board.”

UnemPriorAvgt = UnemCurrentt (1) + UnemCurrentt (2) + UnemCurrentt (3)

3

A high average unemployment rate will decrease the votes for the President’s party.A low average unemployment rate will increase the votes for the President’s party.









Possible Insight: Perhaps the electorate is myopic. Perhaps the electorate is not interested in what occurred three years ago or two years ago or even

one year ago.

Perhaps the electorate is only concerned with what is going

on right now.


UnemCurrent 0.124858 0.294305 -0.424247 0.6746Const 52.70895 2.414476 21.83039 0.0000


Voting Model 2: Present Performance – The electorate is sensitive to how well the economy is performing during the election year.

Model: VotePresPartyTwot = Const + UnemCurrentUnemCurrentt + et

Theory: UnemCurrent < 0

Step 2: Play the cynic and challenge the results; construct the null and alternative hypotheses Cynic’s View: Despite the results the current unemployment rate has no effect on votes for the President’s party.

Interpretation: We estimate that a 1 percentage point increase in the election year unemployment rate decreases the vote the President’s party receives by .12 percentage points.

H0: UnemCurrent = 0 UnemCurrent has no effect on VotePresPartyTwo

H1: UnemCurrent < 0 Higher UnemCurrent reduces VotePresPartyTwo

Is this good or bad news?

Step 1: Collect data, run the regression, and interpret the estimates.

Step 0: Construct a model reflecting the theory to be tested

Critical Result: The coefficient estimate for UnemCurrent equals .12. The negative sign of the coefficient estimate suggests that a higher unemployment rate in the election year decreases the votes received by the President’s party.

Good news – the evidence lends support to the theory.

EViews

A high unemployment rate will decrease the votes for the President’s party.A low unemployment rate will increase the votes for the President’s party.



UnemCurrent 0.124858 0.294305 -0.424247 0.6746Const 52.70895 2.414476 21.83039 0.0000


Generic Question: What is the probability that the results would be like those we actually obtained (or even stronger), if the cynic were correct?

Step 3: Formulate the question to assess the cynic’s view: Prob[Results IF H0 True]

Specific Question: The regression’s coefficient estimate was .12: What is the probability that the coefficient estimate in one regression would be .12 or less, if H0 were actually true (if the actual coefficient, UnemCurrent, equaled 0)?

Hypotheses: H0: UnemCurrent = 0 H1: UnemCurrent < 0

Step 4: Calculate Prob[Results IF H0 True].


2 .34 About 1 chance in 3.

At the “traditional” significance levels of 1, 5, or 10 percent (.01, .05, or .10) would you reject H0? No. Is this good or bad news? Bad news.

Step 5: Decide on the standard of proof, a significance level.

bUnemCurrent

Prob[Results IF H0 True]

0.12

Question: Can we use the tails probability? Yes








Possible Insight: We found some evidence, albeit weak, supporting the notion that the electorate is myopic.

Perhaps the electorate is concerned with the trend in the economy

whether economic conditions are getting better or getting worse at the

present time.

Perhaps the electorate does not want to “change horses in midstream.”


UnemTrend 0.752486 0.568784 -1.322973 0.1965Const 51.95260 1.325732 39.18785 0.0000

Number of Observations 30Estimated Equation: EstVotePresPartyTwo = 52.0 .75UnemTrend

Voting Model 3: Present Trend I – Electorate is sensitive to the current economic trend; more specifically, whether the unemployment rate is rising or falling in the election year.

UnemTrendt Change in unemployment rate from the prior yearUnemTrendt = UnemCurrentt UnemCurrentt (1)

Model: VotePresPartyTwot = Const + UnemTrendUnemTrendt + et

Theory: UnemTrend < 0

Interpretation: We estimate that a 1 percentage point rise in the unemployment rate from the previous year decreases the vote the President’s party receives by .75 percentage points.

H0: UnemTrend = 0 UnemTrend has no effect on VotePresPartyTwo H1: UnemTrend < 0 Rising unemployment reduces VotePresPartyTwo


2 = .098Is this good or bad news?

Critical Result: The UnemTrend coefficient estimate equals .75. The negative sign of the coefficient estimate suggests that deteriorating economic conditions as evidenced by a rising unemployment rate decreases the vote received by the President’s party.

Is this good or bad news? Good news – the evidence lends support to the theory.

Step 0:

Step 1:

Step 2:

EViews

Steps 3, 4, and 5:

A rising unemployment rate will decrease the votes for the President’s party.A falling unemployment rate will increase the votes for the President’s party.

Good news – kind of.









Possible Insight: It looks like the present trend approach has potential.

Perhaps we should include some

additional explanatory variables that describe the present trend.


UnemTrend 1.068160 0.560702 -1.905040 0.0675InflCpiCurrent 0.585465 0.286421 -2.044071 0.0508Const 53.57059 1.484912 36.07662 0.0000


Voting Model 4: Present Trend II –The electorate is sensitive not only to the current trend in the unemployment rate, but also the current trend in prices, the inflation rate in the election year.

UnemTrend Change in unemployment rate from the prior yearInflCpiCurrent Inflation rate in election year based on the CPI

Model: VotePresPartyTwot = Const + UnemTrendUnemTrendt + InflCpiCurrentInflCpiCurrentt + et

Theory: Unemployment: UnemTrend < 0 Inflation: InflCpiCurrent< 0

bUnemTrend = 1.068: Rising unemployment rate leads to fewer votes for Pres’s party

bInflCpiCurrent = .5855: Rising prices lead to fewer votes for Pres’s party

H0: UnemTrend = 0 UnemTrend has no effect H1: UnemTrend < 0 Rising unemployment reduces Pres’s votes

H0: InflCpiCurrent = 0 InflCpiCurrent has no effect H1: InflCpiCurrent < 0 Rising prices reduces Pres’s votes

Unemployment Trend


2 .034

Inflation


2 .025In each case, would you reject the null hypothesis at the “traditional” significance levels?

EViews

Step 0:

Step 1:

Steps 2, 3, 4, and 5:


lecture 12 preview: model specification and model development model specification: ramsey regression...

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