Question

Problem 2: Please, can you help to solve the following problem for me I have hard time to solve it.

The following table uses OLS to analyze the correlates of state legislators voting yes on a compromise proposal that moved the state gas tax half way to their preferred alternative. The dependent variable is 1 if the legislator voted for the proposal and 0 if they did not. The independent variables are defined as follows:

Voter retribution: Respondents were asked “In general, if you were to make compromises on policy, how much retribution would you face from voters in your district?” Response options were none, some, and lot. This is treated as two dummy variables for some and a lot.

Moral treatment: 1 if arguments for the bill included language making a moral claim about the issue and 0 if not.

Party of the sponsor: the sponsors of the bill were randomized to be two members from the same party as the legislator, two from the opposing party, or one Democrat and one Republican. This is treated as two dummy variables for opposition and bipartisan sponsors.

Future power: Respondents were asked for their perception of how much power legislators who share their view on this issue would have in the legislative chamber in the future. Respondents had five options for the amount of future power: a lot more, a little more, the same amount of power, a little less, and a lot less. This is treated as a continuous variable.

Majority: 1 if legislator is in the majority party, 0 otherwise.

Republican: 1 if legislator is a Republican, 0 otherwise.

Woman: 1 if legislator is female, 0 otherwise.

Distance to SQ: distance between most preferred gas tax (in cents) and the status quo.

Dependent Variable=Vote for Compromise (1)

High voter retribution -0.211* (0.124) Some voter retribution -0.002 (0.055) Moral treatment 0.044 (0.050) Opposition Sponsors 0.056 (0.062) Bipartisan Sponsors 0.065 (0.060) Future Power 0.005 (0.030) In majority -0.195* (0.052) Republican -0.243* (0.054) Woman 0.030 (0.057) Distance to SQ -0.003 (0.003) Constant 0.945* (0.112) Observations 257 R-squared 0.173 Note: standard errors in parentheses. *p<0.05

a)  What is the interpretation of the coefficient on Republican?

b) What is the interpretation of the coefficient on high voter retribution?

c) Calculated the predicted value of Y for the following values of the independent variables: voter retribution (=some), moral treatment (=0), opposing party sponsors, future power (=2), majority (=0), Republican (=1), woman (=0), distance to the status quo (=10). Interpret this predicted value of Y.

d) Describe two limitations of using OLS when you have a binary dependent variable.

Answer 1

a)

The coefficient on Republican is - 0.243

This means that the probability of a Republican to vote for the proposal is 0.243 less than a non-Republican legislator.

b)

The coefficient on high voter retribution is -0.211

This means that the probability of a legislator who thinks that if they were to make compromises on policy, they would face high retribution from voters in their district, to vote for the proposal is 0.211 less than a legislator who thinks that if they were to make compromises on policy, they would face no retribution from voters in their district.

c)

voter retribution (=some), moral treatment (=0), opposing party sponsors, future power (=2), majority (=0), Republican (=1), woman (=0), distance to the status quo (=10)

Then

Y = - 0.002 + 0 + 0.056 + 0.005 * 2 + 0 - 0.243 + 0 - 0.003 * 10 + 0.945

= 0.736

This means that the probability of this legislator to vote for the proposal is 0.736

d)

1. Nonconforming Predicted Probabilities: Probabilities must logically be between 0 and 1, but the OLS can predict probabilities outside this range.
2. Heteroskedastic by construction (always use robust standard errors)