Question

3. Regressions. You are interested in analyzing whether states with higher banking regulation have higher unemployment rates than states with lower banking regulation. You have the following cross-sectional data on 4 states. unemployment_rate is the state's unemployment rate measured as a percent. regulation_index is a sum of dummy variables that describes the number of banking regulations implemented by the state state unemp rate ulation index 4 a) Estimate the coefficients (BoP1) of the linear model shown below using OLS and write the resulting regression equation. unemp rates-Po + β,Regulation Index, + Es b) c) d) Interpret each of the coefficients (A-A) in this regression. What sign would you expect to have? Explain your reasoning. Give one alternative explanation for B1 to be the opposite sign of what you answered in question 3c. (e.g. if you said you expect P1 to be negative, describe a scenario where the relation between regulation and unemployment rates is positive). e) Suppose you then think that states with higher unemployment rates may have different incentives to implement banking regulation than states with low unemployment rates. How would you modify the linear regression model in question 3.a to reflect this change? [Hint: Think about how dependent and independent variables appear in the regression model.] f) Estimate the coefficients of the linear model you specified in question 3.e g) Interpret the coefficients (Po. B1) in this new regression (from question 3.f) h) Calculate the prediction error for each state under each model Prediction errorPrediction error under model 3.a under model 3 state i) Which regression appears to generate more accurate predictions? Justify your answer

Answer 1

a. The regression equation using the above data can be written as : Y = 0.78 + 1.14 X + Error, where Y represents unemployment rate and X represents Regulation Index.

b. The intercept terms states that when the banking regulation in the country is zero, then unemployment rate in the country is equal to 0.78. The slope coefficient states that as banking regulation increases by one unit, keeping all other variables impacting unemployment rate as constant, then unemployment rate will increase by 1.14 units.

c. The slope coefficient will have a positive sign because it has been observed that as the banking regulation in the economy increases, the unemployment rate in the economy will also rise. Thus, Slope coefficient is positive.

d. The coefficient can be negative depending on the state of the economy. If the economy is currently facing a banking crisis, and the regulations on banking increases to improve overall banking situation in the economy, then it will lead to decline in unemployment rate.