Writing Papers

Writing Papers

William Thomson. A Guide for the Young Economist

Notation and De�nitions

Writing PapersNotation

Bad notation can make an otherwise well-written paperimpossible 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 Ri is agent i�s preference relation, then agent j�s preferencerelation is...

Do not designate just any quantity by ε

Writing PapersNotation

Choose the abbreviation of your assumptions carefully (Mon,Cont, Con)

A common way to introduce an abbreviation for a condition isto 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

Writing PapersNotation

Respect the hierarchy of the di¤erent parts of a paper

Do not refer in the main text to terms, ideas or derivationsintroduced in a footnote or in a remark.

Footnotes should contain only information that is notessential 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 forinstance, certain northern European countries such as Germany mayfeel some disappointment from observing that many othersignatories do not carry out their promises as they should.

Footnote: Existing evidence suggests that only 15 out of the 41countries included in Annex I of the Kyoto protocol have ful�lledtheir commitments in Article 3.

Writing PapersNotation

For instance if you use M and M 0, make them play exactly theroles they play in the de�nition.

Ex. if in the de�nition M 0 > M, avoid M > M 0 in yourapplication.

Writing PapersNotation

Example

Consider a common pool resource (CPR) where an incumbentinitially exploits the CPR and an entrant analyzes whether ornot to enter

Writing PapersNotation

The initial stock of the CPR is either low or high,θK = fθL, θHg

Writing PapersNotation

Example

Assume a two-stage complete information gameFirst stage, the incumbent is the only �rm in the areaSecond stage of the game the entrant decides whether or notto join the incumbent.Agents have to select an e¤ort level xi (�rst stage) and ei andej (second Stage)

Writing PapersNotation

Example

The incumbent exerts an e¤ort level of x1 > 0, with anassociated cost of c(x1)

where marginal cost of e¤ort is positive, cx � 0 and convexcxx � 0.The total amount of resource appropriated by the incumbentis f (x1, θK ), which increases in the initial stock, fθ > 0, andin the e¤ort level, fx � 0but exhibits decreasing marginal returns to e¤ort, fxx � 0Assume that the marginal product of e¤ort increases in theinitial stock, fxθ � 0.The incumbent enjoys the following monopoly pro�tsMK1 (x1) � f (x1, θK )� c(x1).

Writing PapersNotation

Example

Minimum Wages and Employment: A Case Study of theFast-Food Industry in NJ and PA

Writing PapersNotation

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 ormore

Wave 2: stores in PA and stores in NJ paying less than $5.00

Xi 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 tomeet the new minimum rate.

Writing PapersNotation

De�nitions

Do not assume Readers familiarity with your terms

Many Studies have analyzed the problem of the commons using thePrisoner�s dilemma game (Muhsam, 1973), chicken or assurancegames (Ostrom et al. 1994), and in�nitely repeated games (Balandand Platteau 1996). The prevention of the Tragedy of the commonshas been demonstrated using di¤erent models, from theconsideration of asymmetric players to the change in the structureof the game (for a comprehensive review of these studies see Faysee,2005)

Writing PapersNotation

When you �rst use a term, make it immediately clear that it isindeed new.

Example: The function f exhibits decreasing marginal returns

We use Di¤erence-in-Di¤erence (DD) analysis to compare thechange in outcomes for the experimental states to the changein outcome for the non-experimental states.

"An allocation rule is e¢ cient if for all preference pro�le Rand all allocations z that it selects for R, there is noallocation z 0 that all agents �nd at least as desirable as z andthat at least one agent prefers"