Maths-QA450

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Question 1

 

The regression output reflects an analysis conducted on the determinants of crime reduction. The dependent variable in this model is the number of crimes committed per month. The independent variables are as follows:

 

  • Police= Average number of police patrolling per month

 

  • Unemployment rate= Percent of unemployed residents

 

  • Poverty= Percent of city residents living below the federal poverty level

 

  • Curfew= Does the city have a curfew for citizens under 18 (1=Yes/0=No)

 

 BetaStd. ErrorStand BetaP-value
     
Constant506109.2 .00
     
Police-15.2513.945.99.00
     
Unemployment50.4614.8.797.00
     
Poverty20.988.14,27.00
     
Curfew-75.2.24.18.00
     

 

 

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  1. Interpret the output for each variable in the model. Since you know how each variable is measured, be sure to discuss specific unit changes.

 

  1. On average, how many crimes would a city expect to see under the following conditions

 

  1. 20 officers

 

  1. 7% unemployment

 

  1. 25% of population living below poverty level

 

  1. No curfew

 

  1. How many crimes would a city expect to see if that city increased the number of officers from 20 to 50 and added a curfew (unemployment and population living below poverty is the same as #2)?
  2. Assume that your city wants to reduce the number of crimes by 20%. The average number of crimes committed per month is 506. Unemployment and population living below poverty is the same as #2? How many officers would be needed with and without a curfew?

 

 

Question 2

 

Below is a regression output estimating factors that impact city revenues. The data used for this model span over 40 years. The dependent variable is the actual revenues (in millions and adjusted for inflation). The independent variables used in the model are as follows:

 

  • Unemployment=Average yearly unemployment rate measured as a percentage

 

  • Population Growth=Percent increase from the previous year

 

  • Per Capita Income=Per capita income (in dollars and adjusted for inflation)

 

 BetaStd. ErrorP-value
    
Constant95.473.11.00
    
Unemployment-8.14.244.00
    
Pop Growth.523.162.00
    
Per Cap Income.026.006.00
    

 

  1. What is the estimated revenue for the city if unemployment is 3%, the city’s population is expected to grow by 1.35%, and per capita income is expected to rise by $30,000?

 

  1. How much less revenue would the city expect to bring in if we overestimated population growth noted in question A by .05%?

 

  1. Knowing that unemployment, population growth and per capita income all impact the amount of revenues brought in by a city, members on the city council are wondering what is the best strategy to increase the city’s revenues without raising taxes. To this end, the city is exploring three different economic development strategies. Unfortunately, the city only has the capacity to pursue one of the strategies in the near future. The three strategies are listed below. Currently, the unemployment rate is 4%, population growth is 1%, and per capita income is $25,000.

 

  1. Plan 1: decrease the unemployment rate by 1%

 

  1. Plan 2: increase the population growth by 4%

 

  1. Plan 3: increase per capita income by $10,000

 

 

Question 3

 

Like individuals, many governments amass “rainy day” savings in case of emergencies. A sudden decrease in revenue means the governments must consider cutting services, raising taxes, or borrowing money. None of these actions are desirable. Thus, a rainy day fund can help alleviate emergencies by providing a cushion of money to help offset any short-term revenue shortages.

 

While a “rainy day” fund seems like a fiscally prudent action, many believe these funds have been co opted for political purposes. There is anecdotal evidence that suggests this might be true. For example, Republican governments will use the rainy day fund to cover lost revenue from tax cuts. Democratic lead governments have been accused of dipping into the rainy day fund to cover increased costs. And, in cases of divided government (e.g. when one party controls the legislature and the other party controls the executive branch), the rainy day fund is used to settle budget disagreements.

 

Another issue that has come to light is that many governments have placed tax and expenditure limitations on themselves. A tax limitation means that a government is limited on how much it can raise taxes in a given time period. An expenditure limitation limits the amount of expenditure growth in a given year. It is argued that the rainy day fund allows lawmakers to circumvent these rules by dipping into savings to get money to pay for new programs or services.

 

Below is a logistic regression output that explores the likelihood that a state will tap into its rainy day fund based on a host of independent variables. The variables in the model are as follows

 

 

Dependent variable

 

  1. A state accesses its rainy day fund (1=taps the fund 0=does not tap the fund)

 

Independent variables

 

  1. Real Income Growth: measured as a five year running average of real personal income growth

 

  1. Revenue Limit: A state has a tax limit (1=state has the limit 0=state does not)

 

  1. Expenditure Limit: A state has a expeture limit (1=state has the limit 0=state does not)

 

  1. Democratic Control: Democrats control both the legislature and governor (1=dem control 0=Republican control

 

  1. Divided government: One party holds power in legislature and one party holds power in Governor (1=divided government 0= not divided government)

 

  1. Citizen Ideology: Measures how liberal or conservative a state is. Measured on a scale between 0 and 100 where 0= all citizens are conservative and 100=all citizens are liberal)

 

 

 

Answer the following questions

 

  • Interpret the results below.

 

  • What is the probability that a state will tap their rainy day fund under the following

 

conditions:

 

  • Real income growth= 3%

 

  • A state has a revenue limit

 

  • A state does not have an expenditure limit

 

  • Republicans control both the legislature and governor

 

  • Citizen ideology= 42

 

 

 

 

 Coeff.S.E. 
Real Income Growth-18.7310.93***
Revenue Limit0.250.25**
Expenditure Limit-0.320.23 
Democratic Control0.560.27*
Divided Government0.500.27*
Citizen Ideology-0.020.01*
_cons0.760.83**

 

 

01*** .05** .10*

 

 

N=840

 

 

 

Pseudo R2 = 0.28

 

 
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