# Quantitative Methods for Political Economy Pencil Problem Set

Quantitative Methods for Political Economy Pencil Problem Set

# Guidelines (Please, read them carefully)

- This problem set is due on 11th December 2020 before 3.00 pm.
- Please note that questions and queries regarding this assignment will beanswered only via KEATS.
- You have two options to submit your work:
- If you are in Campus – You can hand in a handwritten document containing the answer for all the questions. The document containing your answers will be handed in at the Administrators o¢ ce of the Department of Political Economy (7th Floor NE Bush House). Upon submission of your problem set you will be asked to signed o⁄ your assignment in a list. Please, make sure that you sign up the list. Failure to do so will be interpreted as a nonsubmission of this assignment. Also, note that this option may not be available at the time of submission if new closures or travel restrictions are imposed by the government.
- If you are not in Campus or want to minimise non-essential travelling – You can upload your work into KEATS. You can do this by scanning your work and using a format that can be upload into KEATS. An alternative, which I strongly encourage, is that you use LaTex to generate a document containing your answers to the problems. Further information about LaTex options will be given on KEATS.

- The document containing your answers is expected to be well organisedand easy to read. This implies presenting the solutions in a tidy and ordered manner. For example, every answer is expected to start in a separate page. Failing to do so for any question will result in losing up to 20% of the total marks assigned to such question.
- Please, make sure that the solution is properly highlighted. Likewise makesure that all relevant information needed to understand the solution is also properly displayed.
- If you submit your work in person, please avoid using big folders or plasticenvelopes. The best way to present your work is by submitting your paper sheets stapled together.
- You may work in groups but note that all the answers must be the result ofyour individual judgment. You may also be tempted to use some software to calculate your answer. This is ne, except that for an answer to be fully valid it will need to show all the di⁄erent calculations leading up to such result. Please note, that If you answer any question just by showing the value of a particular statistics (like a mean, or a ) the answer will not be considered valid and will receive a mark of 0.

# F Exercise 1 (35%)

We are interested in explaining whether being nancially monitored by the EU has any e⁄ect on the electoral support to establishment parties. By establishment parties, it is meant parties that before 2008 either were the main opposition platform in parliament or were the main party in goverment. Our hypothesis is that nancial monitoring will have a negative relationship with the support to such parties. The model we want to estimate is

*V ote *= _{0 }+ _{1}*Monitoring *+ *u*

where *Vote *is the vote share received by establishment parties in a particular country and election and *Monitoring *is a binary variable indicating that a country was nancially intervened or not in a particular year.

Using the data in Table 1 below, please perform the following tasks:

- Draw a suitable graph where you show how
*Vote*changes depending on a country being or not monitored. (5%) - Calculate
_{0 }and_{1 }(5%) - Explain the meaning of
_{0 }and_{1}*:*How is*Vote*related to*Monitoring*?

(5%).

- Calculate coe¢ cient of determination (R-square) using the following formula. Provide a meaningful explanation of this statistics. (5%)
- Calculate the t-value of
_{1}*:*What is its level of statistical signi cance? How con dent would you be in rejecting the null hypothesis? (5%) - Calculate a 95% CI containing the prediction of
*Vote*for a country when*Monitoring*= 0 and*Monitoring*= 1*:*(5%) - Assess the validity of your model generally. Are you con dent with thesample of data used? Justify your answers. (5%)

Table 1: Support to establishment parties and nancial monitoring.

Country | Year | Monitoring | Vote |

Ireland | 2002 | No monitoring | 74.80 |

Ireland | 2007 | No monitoring | 79 |

Ireland | 2011 | Financial Monitoring | 72.90 |

Greece | 2000 | No monitoring | 86.50 |

Greece | 2004 | No monitoring | 85.90 |

Greece | 2007 | No monitoring | 79.90 |

Greece | 2009 | No monitoring | 77.40 |

Greece | 2012 | Financial Monitoring | 42 |

Greece | 2015 | Financial Monitoring | 34.38 |

Spain | 2000 | No monitoring | 78.69 |

Spain | 2004 | No monitoring | 80.30 |

Spain | 2008 | No monitoring | 83.80 |

Spain | 2011 | Financial Monitoring | 73.29 |

Spain | 2015 | Financial Monitoring | 50.71 |

Portugal | 1999 | No monitoring | 76.30 |

Portugal | 2002 | No monitoring | 78 |

Portugal | 2005 | No monitoring | 76 |

Portugal | 2009 | No monitoring | 67.69 |

Portugal | 2011 | Financial Monitoring | 69.50 |

Portugal | 2015 | Financial Monitoring | 69.18 |

# F Exercise 2 (10%)

You want to improve the previous model and conclude that more variables are needed in order to make sure that the e⁄ect of Monitored is properly captured. One possible variables is to the e⁄ect of the nancial crisis that a⁄ected these countries since 2009. This is captured by a binary variable that takes the value 1 if year is equal or greater than 2009 and 0 for the rest of observations. Your new model is the following.

*V ote *= _{0 }+ _{1}*Monitored *+ _{2}*Crisis *+ *u*

- Are you con dent with this new estimation? Answer your questions in as much detail as you can.

# Exercise 3 (10%)

Given that

*u*^*i *= *y**i **y*^*i *= *y**i *^0 ^1*x**i*

The logic of OLS results when the following expression is minimised

^ ^ *x**i*)2

_{0 1}

Using basic calculus one can obtain the partial derivative of the expression above with respect to ^_{0 }and ^_{1 }resulting in the following two equations:

^0 ^1*x _{i}*) = 0

and

^0 ^1*x _{i}*) = 0

Using these two equations and basic algebra, prove that the sum of the squared errors in a bivariate regression is minimised when:

0 = *y *1*x*

and

(Hint: You will need summations properties #5 and #6 )

# Exercise 4 (10%)

Suppose that you have a sample of size n on three variables, *y*, *x*_{1 }and *x*_{2}*: *You are interested in the e⁄ect of *x*_{1 }on *y: *^{Let }~_{1 }be the coe¢ cient of *x*_{1 }from the simple regression and ^1 the coe¢ cient of *x*1 from the regression of *y *on *x*1 and *x*_{2}*: *The standard errors reported by your software is:

*se*(~_{1}) = ^{~}

P(*x _{i }x*)

and

*se*(^_{1}) = P ^{^ }p*V IF*_{1}

(*x _{i }x*)

where ~ is the standard regression error (SER) from the simple regression, ^ is the SER from the multiple regression, and is the

R-squared from the regression of *x*_{1 }on *x*_{2}*:*

Using this information answer the following questions in as much as detail as possible:

- Which regression parameter ~
_{1 }or ^_{1 }would you use in your analysis? (5%) - Compare
*se*(~_{1}) and*se*(^_{1}) and explain why*se*(^_{1}) can be smaller or larger than*se*(~_{1})*:*(5%)

# Exercise 5 (10%)

Using the le Armigeonetal2015.pdf, calculate the following:

- Using model 3 in table 4, calculate the expected level of SWD for a countrywhere the change in the Units per Labour Cost (
*ULC*) decreases from 20 to -10 in intervals of 10 units depending on whether a country belongs to the Eurozone or not. In doing these calculations, hold the remaining control variables xed. Fill in the following table with the relevant values.(5%)

Table 2: SWD conditional on EMU membership and values of ULC

- Using model 3, calculate the expected level of SWD for a country wherethe change in
*Unemployment*decreases from 6 to -6 in intervals of 4 units depending on whether a country belongs to the Eurozone or not. In doing these calculations, hold the remaining control variables xed. Fill in the following table with the relevant values.(5%)

Table 3: SWD conditional on EMU membership and unemployment levels

# Exercise 6: Essay (500 words max) (25%)

You are interested in studying what causes economic growth. You think that an important part of the explanation may be related to the quality of institutions. In particular, you think that respect for property rights is essential to understand how countries developed di⁄erently. After developing your theory you test your hypotheses using the following model:

*Development *= _{0 }+ _{1}*PropertyRights *+ * _{i}Controls *+

*u*

where *Development *indicates the level of economic development in a given country, Property Rights is an index re ecting the capacity of government to expropriate and the parameter * _{i }*refers to a vector of relevant controls variables.

Write a short essay (500 words max) where you discuss the following questions (Note: You can write the essay using a text editor and attach it to your hand written results) :

- What is the main problem in this estimation model? Why should you becautious about the coe¢ cient of
*PropertyRights*? (5%) - Theoretically, how would you x this problem? What would you need to observe to make sure the estimation is correct? (5%)
- Propose and develop an empirical solution to x this problem. Make sure that you provide su¢ cient justi cation to support your strategy. (15%)