Writing Papers. Writing Papers. William Thomson. A Guide for the Young Economist. Notation and De nitions

Transcription

1 Writing Papers William Thomson. A Guide for the Young Economist and De nitions

2 Bad notation can make an otherwise well-written paper impossible to read. Choose easily recognizable notation The best notation is notation whose meaning can be guessed: Y, W, F (X, L), U(X, Y ), Π, p, q, L, t If Z designates a set, call its members... If R i is agent i s preference relation, then agent j s preference relation is... Do not designate just any quantity by ɛ

3 Choose the abbreviation of your assumptions carefully (Mon, Cont, Con) A common way to introduce an abbreviation for a condition is to place it in parentheses. ex. Incentive Compatibility Condition (I.C ) Never put abbreviations in a section heading By C3 and C5 we conclude that there exist an equilibrium. Do not introduce notation you will use only once or twice

4 Respect the hierarchy of the di erent parts of a paper Do not refer in the main text to terms, ideas or derivations introduced in a footnote or in a remark. Footnotes should contain only information that is not essential to understanding your main arguments. Example: Second, regarding countries concern for each others ful llment of the IEA, we can also nd many real cases, where for instance, certain northern European countries such as Germany may feel some disappointment from observing that many other signatories do not carry out their promises as they should. Footnote: Existing evidence suggests that only 15 out of the 41 countries included in Annex I of the Kyoto protocol have ful lled their commitments in Article 3.

5 For instance if you use M and M 0, make them play exactly the roles they play in the de nition. Ex. if in the de nition M 0 > M, avoid M > M 0 in your application.

6 Example Consider a common pool resource (CPR) where an incumbent initially exploits the CPR and an entrant analyzes whether or not to enter

7 The initial stock of the CPR is either low or high, θ K = fθ L, θ H g

8 Example Assume a two-stage complete information game First stage, the incumbent is the only rm in the area Second stage of the game the entrant decides whether or not to join the incumbent. Agents have to select an e ort level x i ( rst stage) and e i and e j (second Stage)

9 Example The incumbent exerts an e ort level of x 1 > 0, with an associated cost of c(x 1 ) where marginal cost of e ort is positive, c x 0 and convex c xx 0. The total amount of resource appropriated by the incumbent is f (x 1, θ K ), which increases in the initial stock, f θ > 0, and in the e ort level, f x 0 but exhibits decreasing marginal returns to e ort, f xx 0 Assume that the marginal product of e ort increases in the initial stock, f x θ 0. The incumbent enjoys the following monopoly pro ts M K 1 (x 1) f (x 1, θ K ) c(x 1 ).

10 Example Minimum Wages and Employment: A Case Study of the Fast-Food Industry in NJ and PA

11 Example E i is the change in employment from wave 1 to wave 2 at store i Wave 1: stores in PA and stores in NJ paying $5.00 per hour or more Wave 2: stores in PA and stores in NJ paying less than $5.00 X i is a set of characteristics of store i, and NJ, is a dummy variable that equals 1 for stores in NJ. GAP is the proportional increase in wages at store i necessary to meet the new minimum rate.

12 De nitions Do not assume Readers familiarity with your terms Many Studies have analyzed the problem of the commons using the Prisoner s dilemma game (Muhsam, 1973), chicken or assurance games (Ostrom et al. 1994), and in nitely repeated games (Baland and Platteau 1996). The prevention of the Tragedy of the commons has been demonstrated using di erent models, from the consideration of asymmetric players to the change in the structure of the game (for a comprehensive review of these studies see Faysee, 2005)

13 When you rst use a term, make it immediately clear that it is indeed new. Example: The function f exhibits decreasing marginal returns We use Di erence-in-di erence (DD) analysis to compare the change in outcomes for the experimental states to the change in outcome for the non-experimental states. "An allocation rule is e cient if for all preference pro le R and all allocations z that it selects for R, there is no allocation z 0 that all agents nd at least as desirable as z and that at least one agent prefers"