2.2 Basic Stylized Facts
2.3.2 Budget constraints and financial markets
This section highlights the key difference between my model and those of previ- ous authors who have studied optimal inflation targets. Households in the flexible price sector (food sector) do not have access to financial markets and they con- sume their wage income in each period.3 So these households are akin to “rule of
2This specification implies local labor markets for the sticky price and export sectors and perfect
risk-sharing among households in the nonfood sector (Ferrero, Gertler, and Svensson, 2010).
3Data in Demirg ¨uc¸-Kunt and Klapper (2012) show that, in less developed economies, access to
thumb” consumers.4 A representative household in the food sector maximizes its lifetime utility given by equation (2.1) subject to the budget constraint:
PtCtf +Pf,tC
∗=
Wf,tN f
t (2.6)
whereWf,t is the nominal wage in the food sector. The total expenditure to attain
a consumption indexCtf is given byPtC f t wherePt is defined as Pt =hγP1f−,tη+(1−γ)P1n−,tηi 1 1−η (2.7)
Pf,t denotes the price of food and Pn,t, the price index of nonfood goods, is
given by Pn,t = h ζP1m−,tξ+(1−ζ)P 1−ξ s,t i1−ξ1 (2.8) andPs,t is the Dixit-Stiglitz price index defined as
Ps,t = "Z 1 0 Xt(z)1−θdz #1−θ1 (2.9)
Households in the nonfood sector provide labor to firms in both the sticky price sector and the export sector. They can buy one-period nominal bonds and
areas. Basu and Srivastava (2005) document that 80 percent of individuals in India’s agricultural sector have no access to formal finance.
4There is no storage technology in the model. In addition to keeping the model tractable, this
could be seen as reflecting the constraints that rural households in emerging market economies face in getting access to the formal financial system for both borrowing and saving purposes.
foreign bonds to smooth their consumption. A representative household in this sector maximizes lifetime utility given by equation (2.1) subject to the following budget constraint PtCtn+Pf,tC∗+Bt+etB∗t + ψB 2 B ∗ t 2 ≤ Ws,t Rs 0 N s t(m)dm+Wx,t R1 s N x t(m)dm+Rt−1Bt−1+etR∗t−1B ∗ t−1+ Π s t (2.10)
where Bt and B∗t represents the quantity of one-period nominal risk free discount
bonds denominated in domestic and foreign currency, respectively. The gross nominal interest rates for those two types of bonds are denoted by Rt and R∗
t,
respectively.5 Wx
,t and Ws,t are the nominal wages in the export and sticky price
sectors andNx
t and N s
t are the labor supply in these two sectors. Π s
t is the profit
from firms in the sticky price sector.
2.3.3
Production
Each household in the food sector owns one firm and produces food using a linear technology in labor yf,t = Af,tN
f
t , subject to a common productivity shock Af,t.
Firms in this sector are price takers and, given a market pricePf,t, the zero profit
condition determines labor demand.
Similarly, firms in the sticky price sector use a linear technology in laborys,t(z)=
5I also include a small quadratic portfolio holding cost for foreign bond holdings, as suggested
As,tNts(z) and are subject to a common productivity shock As,t. Following Calvo
(1983), I assume that a fraction α ∈ (0,1) of firms cannot change their price in each period. Firms that are free to change the price at timetchoose a price Xt to maximize the discounted profit stream given by:
max Xt(z) Et ∞ X j=0 (αβ)jQt,t+j h yts,t+j(z)(Xt(z)− MC s t) i (2.11) whereQt,t+jis the stochastic discount factor,Xtis the price of the variety produced
by firmz, andys
t,t+j is the output of firm in periodt+ jwhen it has set its price in
periodt. Furthermore, the marginal cost is given byMCs t =
Wts As t .
Firms in the export sector also use a linear technologyyx,t = Ax,tNtx and face an
exogenous price level every period. Firms in this sector are assumed to be price takers. Import prices are exogenous and follow the law of one price. The terms of trade shock, which links import and export prices, determines the export price. Thus, Px,t = StPm,t, whereSt is the terms of trade. Given export prices, the firms’
cost minimization problem determines wages and, therefore, the labor demand in the sector.