Chapter 12: Model Specification and Development

Transcription

1 Chapter 12: Model Specification and Development Chapter 12 Outline Model Specification: Ramsey REgression Specification Error Test (RESET) o RESET Logic o Linear Demand Model o Constant Elasticity Demand Model Model Development: The Effect of Economic Conditions on Presidential Elections o General Theory: It s the economy stupid. o Generate Relevant Variables o Data Oddities o Model Formulation and Assessment: An Iterative Process o Specific Theories: Model 1: Past Performance Theory Model 2: Present Performance Theory Model 3: Present Trend Theory I Model 4: Present Trend Theory II Chapter 12 Prep Questions 1. Consider a multiple regression model. When a particular explanatory variable has no effect on the dependent variable, what does the actual value of its coefficient equal? 2. The 1992 Clinton Presidential campaign focused on the economy and made the phrase It s the economy stupid famous. Bill Clinton and his political advisors relied on the theory that voters hold the President and his party responsible for the state of the economy. When the economy performs well, the President s party gets credit; when the economy performs poorly, the President s party takes the blame. It s the Economy Stupid Theory: The American electorate is sensitive to economic conditions. Good economic conditions increase the vote for the President s party; bad economic conditions decrease the vote for the President s party. Consider the following model: VotePresParty t = β Const + β UnemPriorAvg UnemPriorAvg t + e t where VotePresParty t = Percent of the popular vote received by the incumbent President s party in year t UnemPriorAvg t = Average unemployment rate in the three years prior to election, that is,

2 2 three years prior to year t a. Assuming that the It s the Economy Stupid Theory is correct, would β UnemPriorAvg be positive, negative or zero? b. For the moment assume that when you run the appropriate regression, the sign of the coefficient estimate agrees with your answer to part a. Formulate the null and alternative hypotheses for this model. 3. Again focus on the on the It s the Economy Stupid Theory. Consider a second model: VotePresParty t = β Const + β UnemCurrent UnemCurrent t + e t where UnemCurrent t = Unemployment rate in the current year, year t a. Assuming that the theory is correct, would β UnemCurrent be positive, negative or zero? b. For the moment assume that when you run the appropriate regression, the sign of the coefficient estimate agrees with your answer to part a. Formulate the null and alternative hypotheses for this model. 4. Again focus on the on the It s the Economy Stupid Theory. Consider a third model: VotePresParty t = β Const + β UnemTrend UnemTrend t + e t where UnemCurrent t = Unemployment rate change from previous year; that is, the unemployment rate trend in year t (NB: If the unemployment rate is rising, the trend will be a positive number; if the unemployment rate is falling, the trend will be a negative number.) a. Assuming that the theory is correct, would β UnemTrend be positive, negative or zero? b. For the moment assume that when you run the appropriate regression, the sign of the coefficient estimate agrees with your answer to part a. Formulate the null and alternative hypotheses for this model. 5. The following table reports the percent of the popular vote received by the Democrats, Republicans, and third parties for every Presidential election since Year VotePartyDem VotePartyRep VotePartyThird

3 Focus your attention on the vote received by third party candidates. a. Which election stands out as especially unusual? b. What were the special political circumstances that explain why this particular election is so unusual? Model Specification: Ramsey REgression Specification Error Test (RESET) We have introduced two different models of demand: the linear demand model: Q t = β Const + β P P t + β I I t + β CP ChickP t + e t the constant elasticity demand model: LogQ t = c + β P LogP t + β I LogI t + β CP LogChickP t + e t Project: Assess the specification of the demand models.

4 4 RESET Logic Both models use the same information to explain the quantity of beef demanded: the price of beef (the good s own price), income, and the price of chicken. The models use this information differently, however. That is, the two models specify two different ways in which the quantity of beef demanded is related to the price of beef (the good s own price), income, and the price of chicken. We shall now explore how we might decide whether or not a particular specification of the model can be improved. The RESET test is designed to do just this. In the test, we modify the original model to construct an artificial model. An artificial model is not designed to test a theory, but rather it is designed to assess the original model. To explain the RESET test we begin with the general form of the simple linear regression model: y is the dependent variable and x is the explanatory variable: y t = β Const + β x x t + e t We use the ordinary least squares (OLS) estimation procedure to estimate the model s parameters: b Const estimates β Const. b x estimates β x. The parameter estimates can be used to estimate the value of y: Esty= b Const + b x x The estimated value of y is sometimes called the fitted value of y. Now, we come to the RESET test. We specify an artificial model which adds an explanatory variable to the original model. The new explanatory variable is the estimated value of y squared: 2 yt = γconst + γ xxt + γesty2estyt + εt The artificial model looks just like the original model with one addition: the square of the estimated value for the original model s dependent variable, Esty 2. Esty is calculated from the information used to estimate the original model. Consequently, the artificial model adds no new information. The artificial model uses the same information as the original model, but uses it in a different way. This is the rationale behind the RESET test: Critical Point: The artificial model adds no new information. It is just using the same information in a different form. Question: Can this new form of the information in the artificial model help us explain the dependent variable significantly better? The coefficient of Esty 2 provides the answer to this question. If γ Esty2, the coefficient of Esty 2, equals 0, the new form of the information is adding no explanatory power; if γ Esty2 does not

5 5 equal 0, the new form adds power. We now construct the appropriate null and alternative hypotheses: H 0 : γ Esty2 = 0 New form of the information adds NO explanatory power H 1 : γ Esty2 0 New form of the information adds explanatory power Prob[Results IF H 0 True] small Prob[Results IF H 0 True] large Unlikely that H 0 is true Likely that H 0 is true Reject H 0 Do not reject H 0 Unlikely that the new form of the information adds no explanatory power Likely that the new form of the information adds no Likely that the new form of the information adds explanatory power There is reason to consider a new model that uses the information in a different form. explanatory power There is no compelling reason to consider a new model that uses the information in a different form. Linear Demand Model We shall now consider the linear model of beef demand to illustrate the RESET test: Original Model: Q t = β Const + β P P t + β I I t + β CP ChickP t + e t [Link to MIT-BeefDemand wf1 goes here.]

6 6 First, run the regression to estimate the parameters of the original model: Ordinary Least Squares (OLS) Dependent Variable: Q Explanatory Variable(s): Estimate SE t-statistic Prob P I ChickP Const Number of Observations 24 Estimated Equation: EstQ = 159, P I ChickP Table 12.1: Beef Demand Regression Results Linear Model Now, construct the artificial model: 2 Artificial model: Qt = γconst + γ PPt + γ IIt + γcpchickpt + γestq2estqt + εt EstQ is the estimated value of Q based on the original model: EstQ = 159, P I ChickP Step 1: Collect data, run the regression, and interpret the estimates. After generating EstQ, we square it to generate EstQSquared: EstQSquared = EstQ 2 Then we use the ordinary least squares (OLS) estimation procedure to estimate the model s parameters: Ordinary Least Squares (OLS) Dependent Variable: Q Explanatory Variable(s): Estimate SE t-statistic Prob P I ChickP EstQSquared 5.79E E Const Number of Observations 24 Critical Result: The EstQSquared coefficient estimate is The estimate does not equal 0; the estimate is from 0. This evidence suggests that the new form of the information adds explanatory power. Table 12.2: Beef Demand Regression Results Artificial Model

7 7 Step 2: Play the cynic and challenge the results; construct the null and alternative hypotheses. Cynic s view: Despite the results, the new form of the information adds no explanatory power. The coefficient EstQ 2, γ EstQ2, actually equals 0. H 0 : γ EstQ2 = 0 Cynic is correct: New form of the information adds NO explanatory power; there is no compelling reason to consider a new specification of the original model. H 1 : γ EstQ2 0 Cynic is incorrect: New form of the information adds explanatory power; there is reason to consider a new specification of the original model. Step 3: Formulate the question to assess the cynic s view and the null hypothesis. Generic Question: What is the probability that the results would be like those we actually obtained (or even stronger), if the cynic is correct the new form of the information adds NO explanatory power? Specific Question: The regression s estimate of γ EstQ2 was What is the probability that the estimate of γ EstQ2 from one regression would be at least from 0, if H 0 were true (that is, if γ EstQ2 actually equaled 0, if the different form of the information did not improve the regression)? Answer: Prob[Results IF H 0 True] The size of this probability determines whether we reject the null hypothesis: Prob[Results IF H 0 True] small Prob[Results IF H 0 True] large Unlikely that H 0 is true Likely that H 0 is true Reject H 0 Do not reject H 0 Steps 4 and 5: The tails probability reported in the regression results is the probability that we need: Prob[Results IF H 0 True] = We would reject the null hypothesis at the 5 percent significance level. This suggests that it may be prudent to investigate an alternative specification of the original model.

8 8 Fortunately, statistical software provides a very easy way to run a RESET test by generating the new variable automatically. Getting Started in EViews After running the unrestricted regression: Click View, Stability Diagnostics, Ramsey RESET Test. Enter the number of fitted terms to include, 1 in this case (we want one fitted term, EstQ 2 ). Click OK. Ramsey RESET Test Dependent Variable: Q Explanatory Variable(s): Estimate SE t-statistic Prob P I ChickP C Fitted^2 5.79E E Number of Observations 24 Critical Result: The Fitted^2 coefficient estimate is The estimate does not equal 0; the estimate is from 0. This evidence suggests that the new form of the information adds explanatory power. Table 12.3: Beef Demand Regression Results Linear Model RESET Test Our calculations and those provided by the statistical software are essentially the same. The slight differences that do emerge result from the fact that we rounded off some decimal places from the parameter estimates of the original model when we generated the estimated value of Q, EstQ. Summarizing the RESET logic: EstQ 2 adds no additional information; it is just using the same information in a different form. In the case of our linear demand model, including EstQ 2 in the artificial regression improves the results significantly suggesting it may be prudent to investigate an alternative specification of the original model.

9 9 Constant Elasticity Demand Model Next, consider a different specification of the model, a constant elasticity demand model: Original model: LogQ t = c + β P LogP t + β I LogI t + β CP LogChickP t + e t We then estimate its parameters using the ordinary least squares (OLS) estimation procedure: [Link to MIT-BeefDemand wf1 goes here.] Ordinary Least Squares (OLS) Dependent Variable: LogQ Explanatory Variable(s): Estimate SE t-statistic Prob LogP LogI LogChickP Const Number of Observations 24 Estimated Equation: EstLogQ = LogP +.51LogI +.12LogChick Table 12.4: Beef Demand Regression Results Constant Elasticity Model Now, let us construct the artificial model: 2 LogQt = γconst + γplogpt + γ ILogIt + γcplogchickpt + γ EstQ2EstLogQt + εt Step 1: Collect data, run the regression, and interpret the estimates. We shall estimate the artificial model using statistical software: Ramsey RESET Test Dependent Variable: Q Explanatory Variable(s): Estimate SE t-statistic Prob LogP LogI LogChickP Const Fitted^ Number of Observations 24 Critical Result: The Fitted^2 coefficient is The estimate does not equal 0; the estimate is 10.7 from 0. This evidence suggests that the new form of the information adds explanatory power. Table 12.5: Beef Demand Regression Results Constant Elasticity Model RESET Test

10 10 Step 2: Play the cynic and challenge the results; construct the null and alternative hypotheses. Cynic s view: Despite the results, the new form of the information adds no explanatory power. The coefficient EstQ 2, γ EstQ2, actually equals 0. H 0 : γ EstQ2 = 0 Cynic is correct: New form of the information adds NO explanatory power; there is no compelling reason to consider a new specification of the original model. H 1 : γ EstQ2 0 Cynic is incorrect: New form of the information adds explanatory power; there is reason to consider a new specification of the original model. Step 3: Formulate the question to assess the cynic s view and the null hypothesis. Generic Question: What is the probability that the results would be like those we actually obtained (or even stronger), if the cynic is correct the new form of the information adds NO explanatory power? Specific Question: The regression s estimate of γ EstQ2 was What is the probability that the estimate of γ EstQ2 from one regression would be at least 10.7 from 0, if H 0 were true (that is, if γ EstQ2 actually equaled 0, if the different form of the information did not improve the regression)? Answer: Prob[Results IF H 0 True] The size of this probability determines whether we reject the null hypothesis: Prob[Results IF H 0 True] small Prob[Results IF H 0 True] large Unlikely that H 0 is true Likely that H 0 is true Reject H 0 Do not reject H 0 Steps 4 and 5: The tails probability reported in the regression results is the probability that we need: Prob[Results IF H 0 True] =.0598 Using the traditional significance levels of 1 or 5 percent, we do not reject the null hypothesis and conclude that there is no compelling reason to specify a new model.

11 11 Model Development: The Effect of Economic Conditions on Presidential Elections General Theory: It s the economy stupid. The 1992 Clinton Presidential campaign focused on the economy and made the phrase It s the economy stupid famous. Bill Clinton and his political advisors relied of the theory that voters hold the President and his party responsible for the state of the economy. When the economy performs well, the President s party gets credit; when the economy performs poorly, the President s party takes the blame: It s the Economy Stupid Theory: The American electorate is sensitive to economic conditions. Good economic conditions increase the vote for the President s party; bad economic conditions decrease the vote for the President s party. Project: Assess the effect of economic conditions on presidential elections. Clearly, we need data to test this theory. Fortunately, we have already collected some data. Data from 1890 to 2008 can be easily accessed: Presidential Election Data: Annual time series data of U. S. Presidential election and economic statistics from 1890 to 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 (minor) party candidates in year t PresPartyR1 t 1 if incumbent President is Republican in year t; 0 if Democrat in year t 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 RealGdpCurrent t RealGdpGrowth t PriceCpiCurrent t InflCpiCurrent t PriceGdpCurrent t InflGdpCurrent t Unemployment rate in year t (percent) Real GDP in year t Real GDP growth rate in year t (percent) Price level in year t (CPI) Inflation rate in year t based on the CPI (percent) GDP price deflator in year t Inflation rate in year t based on the GDP price deflator (percent)

12 12 [Link to MIT-PresElections wf1 goes here.] Generate Relevant Variables First, note that the data does not include the variable that we are trying to explain: the vote received by the incumbent President s party: VotePresParty t Percent of popular vote received by the President s party in year t Fortunately, we can generate it from the variables that we have. We have data reporting the percent of the popular vote received by the Democratic and Republican candidates, VotePartyDem t and VotePartyRep t. Also, another variable indicates the incumbent President s party, PresPartyR1 t. Focus attention on these three variables: VotePartyDem t VotePartyRep t PresPartyR1 t Percent of popular vote received by the Democratic candidate in year t Percent of popular vote received by the Republican candidate in year t 1 if the President is a Republican in year t, 0 if Democrat in year t We can use the following equation to generate the variable VotePresParty: VotePresParty t = PresPartyR1 t VotePartyRep t + (1 PresPartyR1 t ) VotePartyDem t To show that this new variable indeed equals the vote receive by the President s party consider the two possibilities: When the Republicans are occupying the White House: PresPartyR1 t = 1 and 1 PresPartyR1 t = 0 The new variable VotePresParty t will equal the vote received by the Republican candidate: VotePresParty t = PresPartyR1 t VotePartyRep t + (1 PresPartyR1 t ) VotePartyDem t = 1 VotePartyRep t + 0 VotePartyDem t = VotePartyRep t On the other hand, when the Democrats are occupying the White House: PresPartyR1 t = 0 and 1 PresPartyR1 t = 1 The new variable VotePresParty t will equal the vote received by the Democratic candidate: VotePresParty t = PresPartyR1 t VotePartyRep t + (1 PresPartyR1 t ) VotePartyDem t = 0 VotePartyRep t + 1 VotePartyDem t = VotePartyDem t

13 13 After generating any new variable, it is important to check to be certain that it is generated correctly. The first few elections are reported below: Year VotePartyDem VotePartyRep PresPartyR1 VotePresParty Table 12.6: Checking Generated Variables Everything looks fine. When Republicans hold the White House (when PresPartyRI t equals 1), the new variable, VotePresParty t, equals the vote received by the Republican candidate (VotePartyRep t ). Alternatively, when Democrats hold the White House (when PresPartyR1 t equals 0), VotePresParty t equals the vote received by the Democratic candidate (VotePartyDem t ). Data Oddities Next, let us look at our voting data to investigate the possibility of data oddities. Year VotePartyDem VotePartyRep VotePartyThird

14 Table 12.7: Checking for Data Oddities In all but a handful of elections, third (minor) parties captured only a small percent of the total vote. In some years, third parties received a substantial fraction, however. The election of 1912 is the most notable example. In these elections, more than a third of votes are siphoned off from the Republicans and Democrats. How should deal with this? One approach is just to focus on those elections that were legitimate two party elections. In this approach, we might ignore all elections in which third (minor) parties receive at least 10 percent or perhaps 15 percent of the votes cast. If we were to pursue this approach, however, we would be discarding information. Econometricians never like to throw away information. Another approach would be to focus just on the two major parties by expressing the percent of votes just in terms of those votes casted just for the Republican and Democratic candidates. Let us call this variable VotePresPartyTwo t : VotePresPartyTwo t Percent of popular vote received by the incumbent President s party based on the two major parties (ignoring third parties) in year t We can generate this variable by using the following equation: VotePresPartyTwo = 100 VotePresParty/(VotePartyRep + VotePartyDem) As always, it is important to be certain that the new variable has been generated correctly: Year VotePres VotePartyDem VotePartyRep VotePresPartyTwo Table 12.8: Checking Generated Variables

15 15 Undoubtedly there are other ways to account for third parties. In this chapter, however, we shall do so by focusing on the variable VotePresPartyTwo. Model Formulation and Assessment: An Iterative Process Now, we shall illustrate the iterative process that that econometricians use to develop their models. There is no cookbook procedure we can follow. Common sense and inventiveness play critical roles in model development: Model Formulation: Formulate a specific model å Incorporate insights from describing the theory. the assessment to refine the specific model describing Model Assessment: the general theory. Apply econometric techniques ç to assess the model. Gradually, we refine the specific details of the model using an iterative process: model formulation and model assessment. In a real sense, this is as much of an art as a science. Specific Voting Models We shall describe specific models that attempt to explain the percent of the vote received by the President s party. In doing so, we shall illustrate how the iterative process of model formulation and model assessment leads us from one model to the next. We begin by observing that the unemployment rate is most frequently cited economic statistic. Every month the Bureau of Labor Statistics announces the previous month s unemployment rate. The announcement receives headline attention in the newspapers and on the evening news broadcasts. Consequently, it seems natural to begin with models that focus on the unemployment rate. Eventually, we shall refine our model by extending our focus to another important economic variable, inflation. Model 1: Past Performance Electorate is sensitive to how well the economy has performed in the three years prior to the election. The first model implicitly assumes that voters conscientiously assess economic conditions over the three previous years of the President s administration. If conditions have been good, the President and his party are rewarded with more votes. If conditions have been bad, fewer votes would be received. More specifically, we use the average unemployment rate in the three years prior to the election to quantify economic conditions over the three previous years of the President s administration.

16 16 Step 0: Formulate a model reflecting the theory to be tested. VotePresPartyTwo t = β Const + β UnemPriorAvg UnemPriorAvg t + e t where UnemPriorAvg t Average unemployment rate in the three years prior to election; that is, three years prior to year t Theory: A high the average unemployment rate during the three years prior to the election will decrease the votes for the incumbent President s party; a low average unemployment rate will increase the votes. The actual value of the coefficient, β UnemPriorAvg, is negative: β UnemPriorAvg < 0. Step 1: Collect data, run the regression, and interpret the estimates. After generating the variable UnemPriorAvg we use the ordinary least squares (OLS) estimation procedure to estimate the model s parameters: Ordinary Least Squares (OLS) Dependent Variable: VotePresPartyTwo Explanatory Variable(s): Estimate SE t-statistic Prob UnemPriorAvg Const Number of Observations 29 Estimated Equation: EstVotePresPartyTwo = UnemPriorAvg Interpretation of Estimates: b UnemPriorAvg =.33: 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. Critical Result: The coefficient estimate for UnemPriorAvg equals.33. The positive sign of the coefficient estimate suggests that a higher average unemployment rate in the three years prior to the election increases the votes received by the President s party. This evidence tends to refute the it s the economy stupid theory. Table 12.9: Election Regression Results Past Performance Model The coefficient estimate directly contradicts our theory. Accordingly, we shall abandon this model and go back to the drawing board. We shall consider another model.

17 17 Model 2: Present Performance Electorate is sensitive to how well the economy is performing during the election year itself. Our analysis of the first model suggests that voters may not have a long memory; accordingly, the second model suggests that voters are myopic; voters judge the President s party only on the current economic climate; they do not care what has occurred in the past. More specifically, we use the current unemployment rate to assess economic conditions. Step 0: Formulate a model reflecting the theory to be tested. VotePresPartyTwo t = β Const + β UnemCurrent UnemCurrent t + e t where UnemCurrent t Unemployment rate in the current year, year t Theory: A high unemployment rate in the election year itself will decrease the votes for incumbent President s party; a low unemployment rate will increase the votes. The actual value of the coefficient, β UnemCurrent, is negative: β UnemCurrent < 0. Step 1: Collect data, run the regression, and interpret the estimates. We use the ordinary least squares (OLS) estimation procedure to estimate the second model s parameters: Ordinary Least Squares (OLS) Dependent Variable: VotePresPartyTwo Explanatory Variable(s): Estimate SE t-statistic Prob UnemCurrent Const Number of Observations 30 Estimated Equation: EstVotePresPartyTwo = UnemCurrent Interpretation of Estimates: b UnemCurrent =.12: A 1 percentage point increase in the election year unemployment rate decreases the vote the President s party receives by.12 percentage points. 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 reduces the votes received by the President s party. This evidence lends support to the it s the economy stupid theory. Table 12.10: Election Regression Results Present Performance Model

18 18 This is good news. The evidence supports our theory. Now, we shall continue on to determine how confident we should be in our theory. 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 does not affect the votes received by the incumbent President s party. H 0 : β UnemCurrent = 0 Cynic is correct: Current unemployment rate has no effect on votes H 1 : β UnemCurrent < 0 Cynic is incorrect: High unemployment rate reduces votes for the incumbent President s party Step 3: Formulate the question to assess the cynic s view and the null hypothesis. Prob[Results IF H 0 True].12 0 Figure 12.1: Probability Distribution of Coefficient Estimate b UnemCurrent Generic Question: What is the probability that the results would be like those we actually obtained (or even stronger), if the cynic is correct and the current unemployment rate actually has no impact? 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, β UnemCurrent, equals 0)? Answer: Prob[Results IF H 0 True] The size of this probability determines whether we reject the null hypothesis: Prob[Results IF H 0 True] small Prob[Results IF H 0 True] large Unlikely that H 0 is true Likely that H 0 is true Reject H 0 Do not reject H 0

19 19 Steps 4 and 5: Use the EViews regression printout to calculate Prob[Results IF H 0 True]..6746/2.6746/ Figure 12.2: Probability Distribution of Coefficient Estimate b UnemCurrent The tails probability answers the following question: Question: If actual value of the coefficient were 0, what is the probability that the estimate would be at least.12 from 0? Answer: The probability of being in the left hand tail equals the tails probability divided by 2:.6746 Prob[Results IF H 0 True] =.34 2 This is not good news. By the traditional standards, a significance level of 1, 5, or 10 percent, this probability is large; we cannot reject the null hypothesis which asserts that the current unemployment rate has not effect on votes. Model 2 provides both good and bad news. The coefficient sign supports the theory suggesting that we are on the right track. Voters appear to have a short memory; they appear to be more concerned with present economic conditions than the past. The bad news is that the coefficient for the current unemployment rate does not meet the traditional standards of significance. Model 3: Present Trend Electorate is sensitive to the current trend, whether economic conditions are improving or deteriorating during the election year. The second model suggests that we may be on the right track by just focusing on the election year itself. The third model speculates that voters are concerned with the trend in economic conditions during the election year. If economic conditions are improving, the incumbent President s party is rewarded with more votes. On the other hand, if conditions are deteriorating, fewer votes would be received. We use the trend in the unemployment rate to assess the trend in economic conditions.

20 20 Step 0: Formulate a model reflecting the theory to be tested. VotePresPartyTwo t = β Const + β UnemTrend UnemTrend t + e t where UnemTrend t Unemployment rate change from previous year; that is, the unemployment rate trend in year t Theory: A rising unemployment rate during the election year will decrease the votes of the incumbent President s party; a falling unemployment rate will increase votes. The actual value of the coefficient, β UnemTrend, is negative: β UnemTrend < 0. Step 1: Collect data, run the regression, and interpret the estimates. After generating the variable UnemTrend we use the ordinary least squares (OLS) estimation procedure to estimate the model s parameters: Ordinary Least Squares (OLS) Dependent Variable: VotePresPartyTwo Explanatory Variable(s): Estimate SE t-statistic Prob UnemTrend Const Number of Observations 30 Estimated Equation: EstVotePresPartyTwo = UnemTrend Interpretation of Estimates: b UnemTrend = 0.75: A 1 percentage point rise in the unemployment from the previous year decreases the vote the President s party receives by.75 percentage points. On the other hand, a 1 percentage point fall in the unemployment rate increases the vote by.75 percentage points. 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 will decrease the vote received by the President s party. On the other hand, improving economic conditions as evidenced by a falling unemployment rate will increase the votes received by the President s party. This evidence lends support to the it s the economy stupid theory. Table 12.11: Election Regression Results Present Trend Model This is good news. It supports our theory. Now, we shall determine how confident we should be in our theory.

21 21 Step 2: Play the cynic and challenge the results; construct the null and alternative hypotheses. Cynic s view: Despite the results, the unemployment rate trend does not affect the votes received by the incumbent President s party. H 0 : β UnemTrend = 0 Cynic is correct: Unemployment rate trend has no effect on votes H 1 : β UnemTrend < 0 Cynic is incorrect: A rising unemployment rate (a positive value for UnemTrend) decreases the vote for the incumbent President s party; a falling unemployment rate trend (a negative value for UnemTrend) increases the vote. Steps 3, 4, and 5 We shall now calculate Prob[Results IF H 0 True]. We have done this several times now, we know that since we are conducting a one-tailed test, the Prob[Results IF H 0 True] equals half the tails probability:.1965 Prob[Results IF H 0 True] =.10 2 While this probability is still considered large at the 5 percent significance level, we appear to be on the right track. We shall shortly consider a fourth model which postulates that when judging economic conditions, the electorate considers not only the unemployment rate trend, but also the trend in prices, the inflation rate. Before moving on to Model 4, however, let us illustrate the subtle difference between Models 2 and 3 by using each to estimate the vote received by the President s party in For Model 2 we only need the unemployment rate for 2008 to calculate the estimate; for Model 3 we not only need the unemployment rate in 2008, but also the unemployment rate in the previous year, 2007: Unemployment Rate in 2008 = 5.81% Unemployment Rate in 2007 = 4.64% Model 2: In 2008, UnemCurrent = 5.81 EstVotePresPartyTwo = UnemCurrent = = = 52.0 Model 2 s estimate depends only on the unemployment rate in the current year, 2008 in this case. The unemployment rate for 2007 is irrelevant. The estimate for 2008 would be the same regardless of what the unemployment rate for 2007 equaled.

22 22 Model 3: In 2008, UnemTrend = = 1.17 EstVotePresPartyTwo = UnemTrend = = = 51.1 Model 3 s estimate depends on the change in the unemployment rate; consequently, the unemployment rates in both years are important. Model 4: Present Trend II Electorate is sensitive not only to the unemployment rate trend, but also the trend in prices, the inflation rate. The fourth model, like the third, theorizes that voters are concerned with the trend. If economic conditions are improving, the incumbent President s party is rewarded with more votes. If conditions were deteriorating, fewer votes would be received. The fourth model postulates that voters are not only concerned with the trend in the unemployment rate, but also the trend in prices. The inflation rate measures the trend in prices. A two percent inflation rate means that prices are on average rising by two percent; a three percent inflation rate means that prices are rising by three percent; etc. Step 0: Formulate a model reflecting the theory to be tested. VotePresPartyTwo t = β Const + β UnemTrend UnemTrend t + β InflCpiCurrent InflCpiCurrent t + e t where UnemTrend t Change in the unemployment rate in the current year, in year t InflCpiCurrent t Inflation rate based on the CPI in the current year, in year t Theory: A rising unemployment rate during the election year will decrease the votes of the incumbent President s party; a falling unemployment rate will increase votes. The actual value of the UnemTrend coefficient, β UnemTrend, is negative: β UnemTrend < 0. An increase in the inflation rate during the election year will decrease the votes of the incumbent President s party; a decrease in the inflation rate will increase votes. The actual value of the InflCpiCurrent coefficient, β InflCpiCurrent, is negative: β InflCpiCurrent < 0.

23 23 Step 1: Collect data, run the regression, and interpret the estimates. Ordinary Least Squares (OLS) Dependent Variable: VotePresPartyTwo Explanatory Variable(s): Estimate SE t-statistic Prob UnemTrend InflCpiCurrent Const Number of Observations 30 Estimated Equation: EstVotePresPartyTwo = UnemTrend.59InflCpiCurrent b UnemTrend = 1.07: A 1 percentage point rise in the unemployment rate from the previous year decreases the vote the President s party receives by 1.07 percent age points. b InflCpiCurrent =.59: A 1 percent rise in prices decreases the vote the President s party receives by.59 percent. Critical Result: The UnemTrend coefficient estimate equals The negative sign of the coefficient estimate suggests that deteriorating economic conditions as evidenced by a rising unemployment will decrease the vote received by the President s party. This evidence lends support to the it s the economy stupid theory. The InflCpiCurrent coefficient estimate equals.59. The negative sign of the coefficient estimate suggests that a rising prices decrease the votes received by the President s party. This evidence lends support to the it s the economy stupid theory. Table 12.12: Election Regression Results Present Trend Model Both coefficients suggest that deteriorating economic conditions decrease the votes received by the President s party. On the other hand, improving economic conditions increase the vote.

24 24 Step 2: Play the cynic and challenge the results; construct the null and alternative hypotheses. Cynic s view of unemployment rate trend: Despite the results, the unemployment trend has no effect. Cynic s view of inflation rate: Despite the results, the trend in prices has no effect. Unemployment Trend Hypotheses Inflation Hypotheses H 0 : β UnemTrend = 0 H 0 : β InflCpiCurrent = 0 H 1 : β UnemTrend < 0 H 1 : β InflCpiCurrent < 0 Steps 3, 4, and 5 Using the tails probabilities reported in the regression printout, we can easily compute Prob[Results IF H 0 True] for each of our theories: Unemployment Trend Inflation Prob[Results IF H 0 True] =.034 Prob[Results IF H 0 True] = At the 5 percent significance level, both of these probabilities are small. Hence, at the 5 percent significance level we can reject the null hypotheses that the unemployment trend and inflation have no effect on the vote for the incumbent President s party. This supports the notion that it s the economy stupid. This example illustrates the model formulation and assessment process. As mentioned before, the process is as much of an art as a science. There is no routine cookbook recipe that we can apply. It cannot be emphasized enough that we must use our common sense and inventiveness.