Lecture 12 Preview: Model Specification and Model Development Model Specification: Ramsey REgression Specification Error Test (RESET) RESET Logic Model.

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Presentation transcript:

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: H 0 :  Esty2 = 0 The artificial model uses the same information in a different form. New form of the information adds NO explanatory power New form of the information adds explanatory power Consider the following null and alternative hypotheses: Original Model: y t =  Const +  x x t + e t Estimated or “fitted” values of y: Esty = b Const + b x x Prob[Results IF H 0 True] small  Unlikely H 0 is true  Might it be prudent to consider a new model that uses the information in a difference form? Prob[Results IF H 0 True] large  Likely H 0 is true  Is there a compelling reason to consider a new model that uses the information in a different form? Regression: b Const and b x 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: YesNo H 1 :  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: Q Explanatory Variable(s):EstimateSEt-StatisticProb P  I ChickP Const Number of Observations24 Ordinary Least Squares (OLS) Dependent Variable: Q Explanatory Variable(s):EstimateSEt-StatisticProb P I  ChickP  EstQSquared 5.79E E Const  Number of Observations24 RESET Application: Linear Demand Model for Beef Original Model: Q t =  Const +  P P t +  I I t +  CP ChickP t + e t Artificial Model: Generate the variables:EstQ EstQSquared = EstQ  EstQ Critical Regression Result: The EstQSquared coefficient estimate is 5.79E-05, The estimate does not equal 0; the estimate is from 0. This evidence suggests that the new form of the information adds explanatory power. H 0 :  EstQ2 = 0  New form of the information adds NO explanatory power H 1 :  EstQ2  0  New form of the information adds explanatory power  EViews  EViews Estimated Equation: EstQ = 159,032  549.5P I ChickP

Ordinary Least Squares (OLS) Dependent Variable: Q Explanatory Variable(s):EstimateSEt-StatisticProb P I  ChickP  EstQSquared 5.79E E Const  Number of Observations24 H 0 :  EstQ2 = 0  New form of the information adds NO explanatory power H 1 :  EstQ2  0  New form of the information adds explanatory power Prob[Results IF H 0 True]: What is the probability that the estimate of  EstQ2 from one regression would be at least from 0, if H 0 were true (that is, if  EstQ2 actually equaled 0, if the different form of the information added no explanatory power)? Prob[Results IF H 0 True] small  Unlikely H 0 is true  Unlikely that the new form of the information adds NO explanatory power Prob[Results IF H 0 True] =.0276 Question: At the “traditional” significance levels of 5 or 10 percent (.05 or.10) : What does Prob[Results IF H 0 True] equal? b EstQ2 t-distribution.0276/ /  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 Test Dependent Variable: Q Explanatory Variable(s):EstimateSEt-StatisticProb P I  ChickP  C  Fitted^25.79E E Number of Observations24 Critical Result: The Fitted^2 coefficient estimate is 5.79E  05, The estimate does not equal 0; the estimate is 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 H 0 True] =.0276 Artificial Model: H 0 :  EstQ2 = 0  New form of the information adds NO explanatory power H 1 :  EstQ2  0  New form of the information adds explanatory power Estimate of  EstQ2 = 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 H 0. 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 2008 VotePartyDem t Percent of popular vote received by the Democratic candidate in year t VotePartyRep t Percent of popular vote received by the Republican candidate in year t VotePartyThird t 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. PresPartyR1 t 1 if incumbent President is Republican in year t; 0 if Democrat PresIncum t 1 if incumbent President is a candidate in year t, 0 otherwise PresPartyTerms t Number of consecutive terms the incumbent President’s party has held the Presidency in year t UnemCurrent t Unemployment rate in year t (percent) RealGdpCurrent t Real GDP in year t RealGdpGrowth t Real GDP growth rate in year t (percent) PriceCpiCurrent t Price level in year t (CPI) InflCpiCurrent t Inflation rate in year t based on the CPI (percent) PriceGdpCurrent t GDP price deflator in year t InflGdpCurrent t Inflation rate in year t based on the GDP price deflator (percent) We need to generate a new variable.

Data Oddities Third 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). VotePresPartyTwo t Percent of popular vote received by the President’s party based on the two major parties (ignoring third parties) YearVotePartyDemVotePartyRepVotePartyThird Two of many possibilities: VotePresParty t = PresPartyR1 t  VotePartyRep t + (1  PresPartyR1 t )  VotePartyDem t VotePresParty t Percent of popular vote received by the President’s party in year t Generate a New Variable When President’s party is Rep:PresPartyR1 t = 1VotePresParty t = VotePartyRep t When President’s party is Dem:PresPartyR1 t = 0VotePresParty t = VotePartyDem t VotePresPartyTwo t =  EViews PresPartyR1 t Dummy variable: 1 if Republican incumbent, 0 if Democrat VotePresParty t VotePartyRep t + VotePartyDem t  100

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: VotePresPartyTwo Explanatory Variable(s):EstimateSEt-StatisticProb UnemPriorAvg Const Number of Observations29 Specific Models Voting Model 1: Past Performance – The electorate is sensitive to how well the economy has performed in the three years prior to the election. UnemPriorAvg t Average unemployment rate in the three years prior to election Model: VotePresPartyTwo t =  Const +  UnemPriorAvg UnemPriorAvg t + e t 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.” UnemPriorAvg t = UnemCurrent t (  1) + UnemCurrent t (  2) + UnemCurrent t (  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.

Model Development: Model Formulation and Assessment – An Iterative Process 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. 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.

Ordinary Least Squares (OLS) Dependent Variable: VotePresPartyTwo Explanatory Variable(s):EstimateSEt-StatisticProb UnemCurrent  Const Number of Observations30 Voting Model 2: Present Performance – The electorate is sensitive to how well the economy is performing during the election year. Model: VotePresPartyTwo t =  Const +  UnemCurrent UnemCurrent t + e t 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. H 0 :  UnemCurrent = 0  UnemCurrent has no effect on VotePresPartyTwo H 1 :  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.

Ordinary Least Squares (OLS) Dependent Variable: VotePresPartyTwo Explanatory Variable(s):EstimateSEt-StatisticProb UnemCurrent  Const Number of Observations30 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 H 0 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 H 0 were actually true (if the actual coefficient,  UnemCurrent, equaled 0)? Hypotheses: H 0 :  UnemCurrent = 0 H 1 :  UnemCurrent < 0 Step 4: Calculate Prob[Results IF H 0 True]. Prob[Results IF H 0 True] = .34 About 1 chance in 3. At the “traditional” significance levels of 1, 5, or 10 percent (.01,.05, or.10) would you reject H 0 ? No.Is this good or bad news?Bad news. Step 5: Decide on the standard of proof, a significance level. b UnemCurrent Prob[Results IF H 0 True] 0 .12 Question: Can we use the tails probability? Yes

Model Development: Model Formulation and Assessment – An Iterative Process 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. 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.”

Ordinary Least Squares (OLS) Dependent Variable: VotePresPartyTwo Explanatory Variable(s):EstimateSEt-StatisticProb UnemTrend  Const Number of Observations30 Estimated 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. UnemTrend t Change in unemployment rate from the prior year UnemTrend t = UnemCurrent t  UnemCurrent t (  1) Model: VotePresPartyTwo t =  Const +  UnemTrend UnemTrend t + e t 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. H 0 :  UnemTrend = 0  UnemTrend has no effect on VotePresPartyTwo H 1 :  UnemTrend < 0  Rising unemployment reduces VotePresPartyTwo Prob[Results IF H 0 True] = =.098 Is 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.

Model Development: Model Formulation and Assessment – An Iterative Process 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. Possible Insight: It looks like the present trend approach has potential. Perhaps we should include some additional explanatory variables that describe the present trend.

Ordinary Least Squares (OLS) Dependent Variable: VotePresPartyTwo Explanatory Variable(s):EstimateSEt-StatisticProb UnemTrend  InflCpiCurrent  Const Number of Observations30 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. UnemTrendChange in unemployment rate from the prior year InflCpiCurrent Inflation rate in election year based on the CPI Model: VotePresPartyTwo t =  Const +  UnemTrend UnemTrend t +  InflCpiCurrent InflCpiCurrent t + e t Theory: Unemployment:  UnemTrend < 0 Inflation:  InflCpiCurrent < 0 b UnemTrend =  1.068: Rising unemployment rate leads to fewer votes for Pres’s party b InflCpiCurrent = .5855: Rising prices lead to fewer votes for Pres’s party H 0 :  UnemTrend = 0  UnemTrend has no effect H 1 :  UnemTrend < 0  Rising unemployment reduces Pres’s votes H 0 :  InflCpiCurrent = 0  InflCpiCurrent has no effect H 1 :  InflCpiCurrent < 0  Rising prices reduces Pres’s votes Unemployment Trend Prob[Results IF H 0 True] = .034 Inflation Prob[Results IF H 0 True] = .025 In each case, would you reject the null hypothesis at the “traditional” significance levels?  EViews Step 0: Step 1: Steps 2, 3, 4, and 5: