• Established a macroeconomic framework where the concept of the firm had a mean- ing while the model was tractable and amenable to a variety of exercises. In this framework it is possible to think about trade liberalization and firms in GE.
• Explicitly modeled the importance of reallocation of production through the death of the least productive firms.
The Melitz (2003) model provides the backbone for many of the major trade papers writ- ten in the past years. Here we note just a few. Helpman, Melitz, and Yeaple (2004) endo- genizes a firm’s decision whether to export or to pursue foreign direct investment (FDI). Melitz and Ottaviano (2008) derive a version of the model with linear demand (instead of CES) to analyze how mark-ups endogenously respond to trade liberalizations. Helpman, Melitz, and Rubinstein (2008) discuss how the model (with a bounded distribution of pro- ductivity) can be used to explain the zero trade flows observed in bilateral trade data and what it suggests for the estimation of empirical gravity models. Helpman, Itskhoki, and Redding (2010) incorporate labor market frictions into a Melitz (2003) framework. Arko- lakis (2010) extends the Melitz (2003) framework to incorporate market penetration costs. Eaton, Kortum, and Kramarz (2011) us
The Eaton and Kortum (2002) model remains the primary framework for the study of trade in perfectly competitive markets (especially agriculture). However, because of a lack of a real concept of a firm, it has proven less popular than the Melitz (2003) model for the study of firm-level data. In Bernard, Eaton, Jensen, and Kortum (2003), the authors did extend the framework to one where there is Bertrand competition between firms. The basic idea is straightforward: the price charged by the single firm that exports a variety is the marginal cost of the second best firm. While this allows for endogenous (non-constant)
markups, the extension required somewhat more complicated probability tools and has turned out to be slightly less tractable than Melitz (2003) extensions such as Melitz and Ottaviano (2008), where there are endogenous markups due to non-CES preferences.
4.7
Homeworks
1. General properties of gravity trade models. Consider the model developed in section 4.3-4.5.
(a) Argue that in all these models profits are a constant fraction of production. (b) Argue that in the model consider in Section (4.5) payments to fixed costs are a
constant fraction of production.
2. The Frechet distribution. For all n ∈ {1, ...,N}, suppose that the random variable
zn ≥0 is distributed according to the Frechet distribution, i.e.:
Pr{zn≤z}=exp
−Tnz−θ
,
whereTi >0 andθ >0 are known parameters. Define the random variablepn= cznn.
Calculate: πin ≡Pr pn≤min k6=n pk
3. The Pareto distribution. Suppose that the random variablezn ∈ [bn,∞)is distributed
according to the Pareto distribution, i.e.:
Pr{zn ≤z}=1− bn z −θ ,
Chapter 5
Closing the model
In order to determine the solution of the endogenous variables of the models we con- structed above in the general equilibrium. The individual goods markets are already as- sumed to clear since we replaced the consumer demand directly in the sales of the firm for each good.
In this section we will make use of three general assumption.Consider the
Aggregate profits are a constant share of revenues. LetΠj denote countryj’s aggregate
profits gross of entry costs (if any). The first macro-level restriction states thatΠj must be
a constant share of countryj’s total revenues:
R1For any country j,Πj/Yj = π¯ whereζ ≥0.
Under perfect competition, R1 trivially holds since aggregate profits are equal to zero. Under monopolistic competition with homogeneous firms, R12 also necessarily holds be- cause of Dixit-Stiglitz preferences; see Krugman (1980). In more general environments, however, R2 is a non-trivial restriction.
R2 For any country pair,i, j,the share of spending on fixed exporting cost to bilateral sales is constantγij =γ¯ whereγ¯ ≥0.
The third restriction is that the value of imports of goods must be equal to the value of exports of goods:
R3For any country j∑kXkj =∑kXjk
In general, total income of the representative agent in country jmay also depend on the wages paid to foreign workers by countryj’s firms as well as the wages paid by foreign firms to country j’s workers. Thus, total expenditure in countryj,Xj ≡ ∑iXij, could be
different from countryj’s total revenues,Yj ≡∑ni=1Xji. R1 rules out this possibility.
5.1
General Equilibrium
We now show how we can determine the wages,wi, and spending,Xi that solve for the
model’s general equilibrium (income,yi, can be written always as a straightforward func-
tion of spending in the cases we will analyze). It turns out that under the technologi- cal distributions and demand structures that we introduced above, we can first solve for wages and spending and all the rest of the variables can be written as simple functions of these two variables. To create a formal mapping to the data, where trade deficits are a commonplace, we can also allow for exogenous transfer payments to countries,Di, (fol- lowing Dekle, Eaton, and Kortum (2008)) which in a static model will imply an equal amount of trade deficit. Of course, these trade deficits have to sum up to zero across countries,∑iDi =0.
i) the budget constraint of the representative consumer
∑
k Xki =∑
k λkiXi =Xi ≡wiLi+πi+Di, (5.1)whereπi is total profits earned by firms from countryinet of fixed marketing costs (if
any),
ii) and the current account balance (there are no capital flows) that consists of exports, imports and related payment to labor for fixed marketing costs but can be equivalently written as total expenditure equals total income and transfers
0=
∑
k6=i Xik | {z } exports −∑
k6=i Xki | {z } imports +∑
k6=i γkiXki−∑
k6=i γikXik | {z }net foreign income
+Di =⇒ 0=
∑
k Xik−∑
k Xki+∑
k γkiXki−∑
k γikXik+Di =⇒ Xi =∑
k Xki =∑
k Xik+∑
k γkiXki−∑
k γikXik+Di, (5.2)whereγij is the share of bilateral sales from ito j that accrues to labor for payments of
fixed marketing costs, and trade flowsXij.
These set of equations can be used to solve forwi, Xi using an additional normaliza- tion. Notice that is straightforward to show that with the CES demand we assume budget balance is equivalent to the CES price index. In particular,