The question: estimate of difference in difference is required. Consider the model with regression discontinuity. Compare regression discontinuity and difference in difference in the context of the model. please see below for details

1. The impact of gender quotas in electoral lists To address the scarcity of women in politics, in recent years many countries have adopted gender quotas in candidate lists requiring the presence of a minimum share of female candidates. By construction, these quotas increase the share of female candidates. However, it remains an empirical question whether they also lead to an increase in the share of women getting elected or reaching top political positions. Let us focus in the case of local elections in Spain. Within a proportional representation electoral system with closed lists, a quota requiring the presence of at least 40% of candidates of each gender on the ballot was implemented in 2007 in municipalities with more than 5,000 inhabitants. (a) One could use a difference-in-differences (DID) strategy to analyse the impact of these quotas on the probability that a woman is elected as mayor. Explain briefly how would you do it: write down the equation that you would estimate for a simple DID and define all its terms. Explain also briefly what are the key requirements that would make the DID strategy adequate in this context and potential threats to its validity. (3 marks) (b) Let us consider the possibility of using a regression discontinuity design (RDD) to estimate how quotas affect the probability that a woman becomes mayor. Explain briefly what are the key requirements that would make the RDD strategy adequate in this particular context. (3 marks) (c) Let us now compare the RDD and the DID estimates. Do they identify the impact of the treatment on the same type of municipalities? Which one is likely to provide more precise estimates? Which one is likely to provide more consistent estimates? (4 marks)