A Small Dynamic Stochastic General Equilibrium Model of the Economy of Kazakhstan
Bulat Mukhamediyev
Al-Farabi Kazakh National University
The oil price dynamics has a significant impact on economic development of both oil-importing
and oil exporting countries. In recent years the price of oil has risen above $ 100 a barrel and
remains above this level even in the face of the continuing economic crisis caused by the
economic slowdown in developed countries. The increase of oil prices in a developed economy
puts pressure on domestic prices due to rising production costs and loss of productivity. And for
an oil producing country contraction of economic activity in partner countries leads to a
reduction in demand for hydrocarbons and a decrease of income countries that export resources.
But even in favorable conditions for the country providing oil to the world market, there is a risk
of Dutch disease and uncontrolled growth of domestic prices for goods and services due to
excessive oil revenues.
In Kazakhstan after the global economic crisis favorable period from 2000 to 2007with high
GDP growth rates was replaced by a period of moderate growth. According to estimates of
monetary policy rules, performed by the author, the National Bank of Kazakhstan concentrated
its focus on inflation targeting after the surge of prices up to 18.7 percent in 2008 and on
stabilization of the exchange rate. In this article an analysis of the different options of monetary
policy for a small model of the dynamic stochastic general equilibrium was performed. The
model estimation results reveal that an increase of the share of oil revenues allocated to current
consumption has a debilitating effect on the consequences from shocks on oil price and global oil
demand rise to economic indicators of the country.
Model
A small model of the dynamic stochastic general equilibrium in an open economy which is
based on the standard model of an open economy and its development and takes into account
the specific characteristics of the economy of Kazakhstan is presented. The structure of the
model corresponds to an approach developed in the work of Gali & Monacelli (2005) , Gunter
(2009), Obstfeld & Rogoff (2001), Silveira (2006) and is based on their proposed designs. The
model takes into account the specific features associated with oil production, accumulation and
use of oil revenues in the economy of Kazakhstan.
Domestic Households
It will be convenient to start a description with a presentation of a model of two countries. It is
assumed that all households in each country have identical preferences and have equal
conditions. In the country named Home (H) a continuum of households indexed as j ∈ [0, n)
resides. And in another country named Foreign (F), j ∈ [n, 1] households inhabit. The so-called
new model of a small open economy can be considered as a limit case of the model of two
countries when n tends to zero.
Each household is an owner of monopolistically competitive firm that produces a diversified
commodity i ∈ [0, n) in the country H or a commodity i ∈ [n, 1] in the country F. It is assumed
that the law of one price for all goods is in place, and all goods are traded.
A representative household seeks to maximize the utility function
𝑡
∑∞
𝑡=0 𝛽 𝐸0 {
𝑗
𝑠𝑗 1+𝜑
𝑗
(𝐶𝑡 − 𝜂𝐶𝑡−1 )1−𝜎
1−𝜎
−
𝑁𝑡
1+𝜑
},
(1)
under the sequence of budget constraints
𝑃𝑡 𝐶𝑡 + 𝐸𝑡 [𝑄𝑡,𝑡+1 𝐷𝑡+1 ] ≤ 𝐷𝑡 + 𝑊𝑡 𝑁𝑡 + 𝑇𝑡 ,
(2)
𝑠𝑗
where φ, φ> 1, is the inverse of the wage elasticity of the labor supply 𝑁𝑡
and σ, σ > 0, is the
𝑗
inverse of the elasticity of intertemporal substitution of consumption 𝐶𝑡 , 𝐷𝑡+1 – nominal
payments for a securities portfolio at the end of period t, 𝑄𝑡,𝑡+1 − a stochastic discount factor for
nominal payments for a period ahead to a household in the country. Coefficient β is an
intertemporal discount factor, 0 < β < 1, 𝑊𝑡
𝑗
- wages, and term 𝜂𝐶𝑡−1 is an external habit
formation.
A solution to the optimization problem of the household gives the first order condition in the
aggregated form:
𝑃𝑡
(𝐶𝑡 − 𝜂𝐶𝑡−1 )−𝜎 = 𝛽 (𝑃
𝑡+1
) (𝐶𝑡+1 − 𝜂𝐶𝑡 )−𝜎 ,
𝜂
𝑁𝑡
(𝐶𝑡 − 𝜂𝐶𝑡−1 )−𝜎
=
𝑊𝑡
𝑃𝑡
(3)
.
(4)
The following notation will clarify the remaining variables. The composite index of consumption
1
𝑗 1−𝛿
1
𝑗
1
𝛿
𝑗 1−𝛿
]𝛿−1
1
𝐶𝑡 = [(1 − 𝛼)𝛿 𝐶𝐻,𝑡
+ 𝛼 𝛿 𝐶𝐹,𝑡
is determined on the basis of the consumption index
1
𝑗
1
𝜀
𝑛
1
1−
𝜀
𝑗
𝐶𝐻,𝑡 = [(𝑛) ∫0 𝐶𝐻,𝑡 (𝑖)
1
𝑗
1
𝜀
𝑛
𝜀
𝜀−1
𝑑𝑖]
1
1−
𝜀
𝑗
𝐶𝐹,𝑡 = [(1−𝑛) ∫0 𝐶𝐹,𝑡 (𝑖)
,
(5)
𝜀
𝜀−1
𝑑𝑖]
(6)
𝑗
𝑗
of domestic and foreign goods, respectively and the values 𝐶𝐻,𝑡 (𝑖) for 𝑖 ∈ [0, 𝑛) and 𝐶𝐹,𝑡 (𝑖) for
𝑖 ∈ [𝑛, 1] as well represent consumption levels of domestic and foreign goods, respectively. Here
ε is the elasticity of intratemporal substitution among goods produced in a same country, ε> 0.
And δ is the elasticity of intratemporal substitution between a bundle of Home goods and a
bundle of Foreign goods. The value α determines the share of imported goods in the domestic
consumption of the household. Similar formulas hold for the country F.
The solution to the optimization problem of minimization
𝑛
𝑗
∫ 𝑃𝐻,𝑡 (𝑖)𝐶𝐻,𝑡 (𝑖)𝑑𝑖
0
𝑗
for 𝐶𝐻,𝑡 (𝑖) under the constraint (5) and the minimization problem
𝑛
𝑗
∫ 𝑃𝐻,𝑡 (𝑖)𝐶𝐻,𝑡 (𝑖)𝑑𝑖
0
under the constraint (6), where
1
𝑃𝐻,𝑡 =
𝑛
1−𝜀
(𝑛 ∫0 𝑃𝐻,𝑡 (𝑖)1−𝜀 𝑑𝑖 )
1
1
, 𝑃𝐹,𝑡 =
1
1−𝜀
(1−𝑛 ∫𝑛 𝑃𝐹,𝑡 (𝑖)1−𝜀 𝑑𝑖 )
1
,
provides the optimal allocation of consumption between domestic and foreign goods:
𝑃𝐻,𝑡 −𝛿
𝑗
С𝐻,𝑡 = (1 − 𝛼) (
𝑃𝑡
)
𝑗
𝑃𝐹,𝑡 −𝛿
𝑗
𝐶𝑡 ,
С𝐹,𝑡 = 𝛼 (
)
𝑃𝑡
𝑗
𝐶𝑡 .
Here 𝑃𝑡 is an index of consumer prices in the country H:
1
1−𝛿
1−𝛿 1−𝛿
𝑃𝑡 = [(1 − 𝛼)𝐶𝐻,𝑡
+ 𝛼𝐶𝐹,𝑡
] .
Also, we have the formulas for the consumer price indices of domestic and foreign goods:
𝑃𝐻,𝑡 −𝛿
С𝐻,𝑡 (1 − 𝛼) (
𝑃𝑡
)
𝐶𝑡 ,
С𝐹,𝑡 𝛼 (
𝑃𝐹,𝑡 −𝛿
𝑃𝑡
)
𝐶𝑡 .
All similar formulas hold for the country F. For it all variables are marked with a superscript (*).
Given the existence of a representative agent in each economy and the condition (4), we can
present the function of aggregate labor supply for both countries:
𝑁𝑡𝑠
𝑁𝑡∗𝑠
=
=
𝑛 𝑠𝑗
∫0 𝑁𝑡 𝑑𝑗
𝑛 ∗𝑠𝑗
∫0 𝑁𝑡 𝑑𝑗
1+
= 𝑛
𝜎
𝜑
1
𝑊 𝜑
( 𝑡)
𝑃𝑡
1+
= (1 − 𝑛)
𝜎
𝜑
−
𝐶𝑡
𝜎
𝜑
,
1
𝑊𝑡∗ 𝜑
( 𝑃∗ ) 𝐶𝑡∗
−
(7)
𝜎
𝜑
.
(8)
𝑡
Firms
There is a continuum of firms i ∈ [0, n) producing a variety of final goods, using labor 𝑁𝑡𝑖 and oil
𝑂𝑡𝑖 . They apply identical technologies
𝑌𝐻,𝑡 (𝑖) = 𝐴𝑡 min{𝑁𝑡𝑖 ,
1
𝜁
𝑂𝑡𝑖 },
(9)
i.e. expend labor and oil in fixed proportions. Parameter 𝐴𝑡 stands for the total factor
productivity. Its dynamics is described by first-order autoregressive process AR (1):
𝑙𝑛𝐴𝑡 = 𝜌𝐴 𝑙𝑛𝐴𝑡−1 + 𝜀𝐴,𝑡 ,
where 𝜌𝐴 ∈ [0,1), and the random variable 𝜀𝐴,𝑡 is independently and identically distributed with
a zero mean and a final standard deviation 𝜎𝐴 . Since in reality a firm will not spend excessive
amounts of resources, we can assume that the condition of conformity of oil used by the quantity
of labor: 𝑂𝑡 = ζ𝑁𝑡 .
Oil Sector
In the Home country there is a firm producing oil. Part of the oil 𝑂𝑡 is consumed by domestic
firms for the production of final goods, and the rest 𝑂𝑡∗ goes abroad to foreign producers. Oil
producing firm takes the price of oil 𝑃𝑡𝑂 and wage rate 𝑊𝑡 as given. The volume of oil 𝑂𝑡𝑆 is
determined by the amount of labor used 𝑁𝑡𝑂 . The firm maximizes its profits in each period:
𝑚𝑎𝑥[𝑃𝑡𝑂 𝑂𝑡𝑆 − 𝑊𝑡 𝑁𝑡𝑂 ]
𝜈
under constraint 𝑂𝑡𝑆 = 𝑍𝑡 𝑁𝑡𝑂 ,
(12)
where the parameter 0 <ν <1, which reflects the diminishing returns to labor in the production
technology of oil. A factor 𝑍𝑡 determines the performance, and changes in accordance with the
process of autoregression
𝑙𝑛𝑍𝑡 = 𝜌𝑍 𝑙𝑛𝑍𝑡−1 + 𝜀𝑍,𝑡 ,
where 𝜌𝑍 ∈ [0,1), and the random variable 𝜀𝑍,𝑡 are independently and identically distributed
with a zero mean and a final standard deviation 𝜎𝑍 . By substituting 𝑂𝑡𝑆 from condition (12) into
the profit function and by differentiating it by 𝑁𝑡𝑂 we obtain the first order condition for the oil
producing firm’s problem
ν𝑍𝑡 𝑃𝑡𝑂 𝑁𝑡𝑂
𝜈−1
= 𝑊𝑡 .
(13)
Equilibrium
In the model of markets of final goods, labor and oil are presented. In equilibrium at each of
them clearing should take place, i.e. the supply must be equal to the demand:
∗
𝑌𝐻,𝑡 = 𝐶𝐻,𝑡 + 𝐶𝐻,𝑡
,
(14)
𝑁𝑡𝑠 = 𝑁𝑡𝑂 + 𝑁𝑡 ,
(15)
𝑂𝑡𝑆 = 𝑂𝑡 + 𝑂𝑡∗ .
(16)
Here, the demand for labor by firms producing final goods 𝑁𝑡 as well as the demand for oil 𝑂𝑡
is determined by summing over all firms. We also use the international risk sharing condition
𝐶𝑡 =
1⁄
𝑛
1−𝑛
𝜗𝑄𝑡 𝜎 𝐶𝑡∗
(17)
Log-linearization of this equation around the steady state at 𝜗 = 1 gives the equation:
𝑛
𝑐𝑡 = 𝑙𝑛 (1−𝑛) +
1
𝜎
𝑞𝑡 + 𝑐𝑡∗ .
Here with small letters except n deviations of the logarithms of the corresponding variables in
the logarithms of these variables in a stable condition are marked. So 𝑥 = 𝑙𝑛𝑋𝑡 − 𝑙𝑛𝑋 for
any variable X, but for rate of inflation 𝜋𝑡 = 𝑙𝑛𝑃𝑡 − 𝑙𝑛𝑃 , where X, P are values of
corresponding variables in steady state.
According to the approach of Calvo (1983) it is considered that each firm producing final
goods, sets a new price for the goods in period t with a probability 1-ξ and retains the same price
with a probability ξ. The new price of the company is determined by solving the maximization
problem:
𝑘
̅
∑∞
𝑘=0 𝜉 𝐸𝑡 [𝑄𝑡,𝑡+𝑘 𝑌𝐻,𝑡+𝑘 (𝑗)(𝑃𝐻,𝑡 (𝑗) − 𝑀𝐶𝑡+𝑘 )]
(18)
by 𝑃̅𝐻,𝑡 (𝑗) under the constraints
𝑌𝐻,𝑡+𝑘 (𝑗) = (
−𝛿
𝑃̅𝐻,𝑡+𝑘 (𝑗)
𝑃𝐻,𝑡+𝑘
)
∗
(𝐶𝐻,𝑡+𝑘 + 𝐶𝐻,𝑡+𝑘
)
(19)
For the model of optimal pricing in the article Gali & Monacelli (2005), the following formula
was received
𝜋𝐻,𝑡 = 𝛽𝐸𝑡 [𝜋𝐻,𝑡+1 ] + 𝜆𝑚𝑐
̂𝑡 ,
where 𝑚𝑐
̂ 𝑡 is the deviation of real marginal cost from its steady state, and the parameter 𝜆 =
1−𝛿
𝛿
(1 − 𝛽𝛿). Without oil production costs marginal costs of firms producing final goods are
the following:
𝑀𝐶𝑡 =
𝑊𝑡
(20)
𝐴𝑡 𝑃𝑡
After log-linearization around the steady state 𝑚𝑐
̂ 𝑡 can be written as
𝑚𝑐
̂ 𝑡 = (𝜑 + 𝜎)𝑦𝑡 − (𝜔 − 1)𝑠𝑡 .
(21)
Taking into account the production costs for the use of oil by firms producing final goods, then
(20) is changed to the following:
𝑀𝐶𝑡 =
𝑊𝑡 + 𝜁𝑃𝑡𝑂
(22)
𝐴𝑡 𝑃𝑡
Accordingly, the process of log linearization around a steady state instead of (22) leads to the
relationship
𝑚𝑐
̂ 𝑡 = (𝜑 + 𝜎)𝑦𝑡 − (𝜔 − 1)𝑠𝑡 + 𝜁(𝑝𝑡𝑂 − 𝑝𝑡 ).
(23)
With this clarification, associated with the use of oil revenues, New Keynesian Phillips Curve is
written as
𝜋𝐻,𝑡 = 𝛽𝐸𝑡 [𝜋𝐻,𝑡+1 ] + 𝜆(𝜑 + 𝜎)𝑦𝑡 + 𝜆(1 − 𝜔)𝑠𝑡 + 𝜆𝜁(𝑝𝑡𝑂 − 𝑝𝑡 ).
Revenue from the sale of oil abroad is 𝑃𝑡𝑂 𝑂𝑡∗ , and in real terms is
𝑃𝑡𝑂 𝑂𝑡∗
𝑃𝑡
(24)
. However, not the entire
oil revenues can be used for current consumption, but only part of it. The rest of revenues is
accumulated in the National Fund (a sovereign wealth fund). Let κ be the share of oil revenues
used for current consumption. This is equivalent to the current real income of the country with
the use of oil revenues on consumption is equal to
𝑌𝑡 + κ
𝑃𝑡𝑂 𝑂𝑡∗
𝑃𝑡
.
(25)
After log-linearization around the steady state (25) can be rewritten to
𝑦𝑡 + (𝑝𝑡𝑂 + 𝑜𝑡∗ − 𝑝𝑡 ) = 𝑐𝑡 +
𝜔−1
𝜎
𝑠𝑡 .
(26)
Taking into account equation (26) log-linearized equation of equilibrium on the market of goods
is reduced to
𝑂
∗ ]
𝑦𝑡 = 𝐸𝑡 [𝑦𝑡+1 ] + 𝐸𝑡 [𝛥(𝑝𝑡+1
− 𝑝𝑡+1 )] + 𝐸𝑡 [𝛥𝑜𝑡+1
−
𝜔−1
𝜎
𝐸𝑡 [𝑠𝑡+1 ] −
1
𝜎
(𝑟𝑡 − 𝐸𝑡 [𝜋𝑡+1 ] +
+ 𝑙𝑛𝛽) + (1 − 𝜅)(𝑝𝑡𝑂 + 𝑜𝑡∗ − 𝑝𝑡 ).
(27)
It is assumed that the monetary policy of central banks in the country and abroad follows the
Taylor rules:
𝑟𝑡 = 𝛿𝜋 𝜋𝑡 + 𝛿𝑦 𝑦𝑡 + 𝜀𝑀,𝑡 ,
(28)
∗
𝑟𝑡∗ = 𝛿𝜋∗ 𝜋𝑡∗ + 𝛿𝑦∗ 𝑦𝑡∗ + 𝜀𝑀,𝑡
,
(29)
∗
where each of the stochastic processes 𝜀𝑀,𝑡 and 𝜀𝑀,𝑡
represents a white noise.
Log-liner system
𝑤𝑡 − 𝑝𝑡 = 𝜑𝑛𝑡𝑆 +
𝜎
𝑐
1−𝜂 𝑡
−
𝜂𝜎
𝑐
1−𝜂 𝑡−1
,
𝑜𝑡𝑆 = 𝑧𝑡 + 𝜈𝑛𝑡𝑂 ,
𝑦𝑡 + (𝑝𝑡𝑂 + 𝑜𝑡∗ − 𝑝𝑡 ) = 𝑐𝑡 +
𝜔−1
𝜎
𝑠𝑡 ,
𝜋𝐻,𝑡 = 𝛽𝐸𝑡 [𝜋𝐻,𝑡+1 ] + 𝜆(𝜑 + 𝜎)𝑦𝑡 + 𝜆(1 − 𝜔)𝑠𝑡 ,
𝑂
∗ ]
𝑦𝑡 = 𝐸𝑡 [𝑦𝑡+1 ] + 𝐸𝑡 [𝛥(𝑝𝑡+1
− 𝑝𝑡+1 )] + 𝐸𝑡 [𝛥𝑜𝑡+1
−
𝜔−1
𝜎
+ 𝑙𝑛𝛽) + (1 − 𝜅)(𝑝𝑡𝑂 + 𝑜𝑡∗ − 𝑝𝑡 ) ,
𝑟𝑡𝑒 = (1 − 𝜃)
𝜎(1+𝜑)(𝜌−1)
𝜑+𝜎
𝑎𝑡 + 𝜃
𝜎(1+𝜑)(𝜌∗ −1)
𝜑+𝜎
𝑟𝑡 = 𝛿𝜋 𝜋𝑡 + 𝛿𝑦 𝑦𝑡 + 𝜀𝑀,𝑡 ,
∗ ]
𝜋𝑡∗ = 𝛽𝐸𝑡 [𝜋𝑡+1
+ 𝜆(𝜑 + 𝜎)𝑦𝑡∗ ,
∗ ]
𝑦𝑡∗ = 𝐸𝑡 [𝑦𝑡+1
−
𝑟𝑡∗𝑒 =
1
𝜎
∗ ]
(𝑟𝑡∗ − 𝐸𝑡 [𝜋𝑡+1
− 𝑟𝑡∗𝑒 ) ,
𝜎(1+𝜑)(𝜌∗ −1)
𝜑+𝜎
𝑎𝑡∗ − 𝑙𝑛𝛽 ,
∗
𝑟𝑡∗ = 𝛿𝜋∗ 𝜋𝑡∗ + 𝛿𝑦∗ 𝑦𝑡∗ + 𝜀𝑀,𝑡
,
𝑠𝑡 =
𝜎
𝜔
(𝑦𝑡 − 𝑦𝑡∗ ) ,
𝑤𝑡 − 𝑝𝑡 = 𝑧𝑡 + 𝑝𝑡𝑂 − 𝑝𝑡 + (𝜈 − 1)𝑛𝑡𝑂 ,
𝑜𝑡 = 𝑦𝑡 − 𝑎𝑡 ,
𝑛𝑡 =
𝑂
𝑜
𝜁𝑁 𝑡
𝑛𝑡𝑆 =
𝑁𝑆
𝑁
,
𝑁
𝑛𝑡 + (1 − 𝑁𝑆 )𝑛𝑡𝑂 ,
𝑎𝑡∗ − 𝑙𝑛𝛽 ,
𝐸𝑡 [𝑠𝑡+1 ] −
1
𝜎
(𝑟𝑡 − 𝐸𝑡 [𝜋𝑡+1 ] +
𝑂
𝑜𝑡𝑆 =
𝑂𝑆
𝑂
𝑜𝑡 + (1 − 𝑂𝑆 )𝑜𝑡∗ ,
𝑂
𝑝𝑡𝑂 − 𝑝𝑡 = 𝜌𝑝𝑜 (𝑝𝑡−1
− 𝑝𝑡−1 ) + 𝜀𝑝𝑜,𝑡 ,
∗
𝑜𝑡∗ = 𝜌𝑜∗ 𝑜𝑡−1
+ 𝜀𝑜∗,𝑡 ,
∗
𝑎𝑡∗ = 𝜌𝑎∗ 𝑎𝑡−1
+ 𝜀𝑎∗,𝑡 ,
𝑎𝑡 = 𝜌𝑎 𝑎𝑡−1 + 𝜀𝑎,𝑡 ,
𝑧𝑡 = 𝜌𝑧 𝑧𝑡−1 + 𝜀𝑧,𝑡 .
Here we use the following notations
𝜆=
1−𝛿
𝛿
(1 − 𝛽𝛿),
𝜔 = 1 + 𝛼̅(2 − 𝛼)(𝜎𝛿 − 1), 𝜃 =
𝜑(𝜔−1)
𝜑𝜔+𝜎
.
Calibration and parameters estimation
The model parameters can be divided into three groups. For the first group values of parameters
were taken as generally used in the literature. For the second group values of parameters were
taken by their rough estimate based on statistical data of the economy of Kazakhstan. So in the
calculations, the value of 𝛼̅ = 0.33 was used as an average ratio of import to GDP. And for the
third group estimation was taken by Bayesian estimation method using the Metropolis-Hastings
algorithm. The following table shows the values of parameters used in the model.
Parameter
Value
𝛼
0.33
𝜑
2.5
𝜎
0,95
𝜂
0.8006
𝜈
0.6996
𝛽
0.98
𝜅
0.12, 0.5
𝜁
0.5003
𝛿
1.5
𝛿𝜋
1.5
𝛿𝑦
0.5217
𝛿𝜋∗
1.5
𝛿𝑦
0.5
ON
1.0
NNS
0.4
OOS
0.4
OZOS
0.6
𝜌𝑝𝑜
0.7813
𝜌𝑜∗
0.9
𝜌𝑎
0.9524
𝜌𝑎∗
0.9975
𝜌𝑧
0.9
Numerical Analysis
Productivity shocks
Productivity shock reduces the marginal costs of firms, allowing them to reduce the price of
domestically produced goods (Fig.A.1). In terms of price rigidity a decline in real interest rates
happens, which in its turn moves the output and trade terms down before the rates go back to
the steady state values. The trade terms are reduced. As a consequence, there is a downward
slump in prices for goods produced in the country, as well as inflation (CPI). The real wage
increases dramatically, resulting in a decline in oil production, as well as in domestic use of oil
by producers. Accordingly, there is a decline in domestic consumption.
Productivity shock abroad has a similar effect on domestic economic performance of the
country, except for the terms of trade (Fig.A.2). Reduction in the marginal cost of foreign
producers leads to a slump in prices both abroad and in the Home country. There is a
temporary reduction in the interest rate, the output of final goods at home and abroad.
Monetary shocks
Impulse response functions for the Home country variables are shown in Fig. B.1. Due to the
monetary shock, leading to an increase of a short-term interest rate, there is a short-term
decline in inflation for goods produced in the country, and in the general level of inflation.
Negative shocks of output, the trade terms, oil production and employment in the oil sector
and consumption in the country Home are created. But there is an upswing in real wages,
which may explain the jumps up and then down of employment in the production sector of
final goods, total employment. Need to note that the effects of a short-term monetary shock
disappear relatively faster than in the case of an output shock.
The impact of an overseas monetary shock on economic indicators of Home country are
reflected in Fig. B.2. Monetary shock abroad boosts interest rates there, which leads to a
decline in production there and inflation. Positive jump in inflation of final-products reduces the
real wages in the country. This increases the demand for labor to firms and leads to an increase
in employment and output.
Oil Price Shocks
A short-term increase in oil prices, above all, leads to an increase in oil production and
employment growth in the oil sector of the Home country (Figure C.1). There is an outflow of
labor from the production of final goods. Interest rate and terms of trade increase. Real wage
is rising, stimulating domestic consumer demand and production of final goods. There is a
positive jump in inflation as on goods produced in the country, and on the CPI.
Differences between Fig. C.1 and C.2 are connected so that the first depicts impulse response
functions, when 12 percent oil revenues are used for current consumption, and the second case
- 50 percent. As can be seen, with a higher level of oil revenue use, changes of indicators occur
in the same directions as for using less of oil revenues, but their reaction to the positive jump in
oil prices are weaker.
Oil Demand Shocks
The sharp increase in oil consumption abroad causes a corresponding increase in its production
in the Home country (Figure D.1). An inflow of manpower to the oil sector is accompanied by its
outflow from industries producing final goods and, therefore, the decline of production in
them. The inflow of oil revenues causes the growth of inflation rate as CPI inflation, and on
goods produced in the country. The real interest rate increases. Here, the share of oil revenues,
which is used for current consumption, is equal to 12 percent. The implication of this is the
decline in real wages. The increase in oil revenues also explains the increase in consumption in
the country.
On Fig.D.2 a situation for which the share of oil revenues, which is used in the country for the
current consumption, is set at 50 percent is depicted. As you can see, all the deviations of
economic variables occur in the same directions as for the standard deduction of oil revenues
of 12 percent, but weaker.
Oil Production Productivity Shocks
A positive productivity shock in the oil sector reduces the need in labor (Fig.E). The outflow of
labor from the oil sector leads to their inflow into the sector of final goods. Throughout the
country real wages are increasing. A change in the share of oil revenue payments for current
consumption does not have any effect on the consequence of the shock in oil production.
In this paper, we consider a model of dynamic stochastic general equilibrium for the economy
of Kazakhstan. The model is based on the standard model of an open economy and its
development till the model of two countries and takes into account the specific characteristics
of the economy of Kazakhstan. For firms producing final goods, a certain stiffness of
technologies is assumed, and for their descriptions production functions with fixed proportions
of resources are used.
Essential to the economic development of Kazakhstan is the flow of revenues from oil exports.
In order to prevent the growth of Dutch disease and inflation, the government does not use its
all oil revenues for current consumption, but only a small part of them. The rest of the oil
revenues is accumulated in the National Fund of Welfare.
In this paper the effects of production shocks, monetary shocks in the country and abroad, oil
price and demand for oil shocks abroad, performance shock in the oil production sector for
main economic indicators of the country are analyzed. It turns out that the increase in the
share of oil revenues allocated to current consumption has a debilitating effect on the
consequences from rising oil prices and global oil demand shocks.
References
Calvo, G. A. (1983). Staggered Prices in a Utility-Maximizing Framework, Journal of Monetary
Economics, 12:383-398.
Gali, J. & Monacelli, T. (2005). Monetary Policy and Exchange Rate Volatility in a Small Open
Economy. Review of Economic Studies, 72:707-734
Gunter, Ulrich (2009). Macroeconomic Interdependence in a Two-Country DSGE Model under
Diverging Interest-Rate Rules. Department of Economics, University of Vienna
Hohenstaufengasse 9, A-1010 Vienna, Austria.
Medina, Juan Pablo & Claudio Soto (2005). Oil Shocks and Monetary Policy in an Estimated
DSGE Model for a Small Open Economy. WP N.° 353 – Diciembre 2005, CENTRAL BANK OF
CHILE
Obstfeld, M. and K. Rogff (2001): Risk and Exchange Rates. Conference paper in honor of Assaf
Razin, Tel-Aviv University.
Silveira, Marcos Antonio (2006). Two-country new keynesian DSGE model: a small open
economy as a limit case. Rio de Janeiro, fevereiro de 2006
Appendices
A1. IR Functions for Home Variables to a Home Productivity, 𝜅 =0.12, 0.5
pih
y
s
0
0
0
-0.02
-0.005
-0.005
-0.04
10
20
30
40
-0.01
10
r
20
30
40
-0.01
re
0
2
-0.05
-0.02
1
10
20
30
40
-0.04
10
pi
20
30
40
0
0
-0.02
0.1
-0.5
20
30
0
40
10
20
30
40
20
30
40
30
40
no
0.2
10
10
wp
0
-0.04
20
a
0
-0.1
10
30
40
os
-1
10
20
o
0
0
-0.2
-1
-0.4
10
20
30
40
-2
10
ns
2
0.05
1
10
20
30
40
30
40
c
0
-0.005
-0.01
10
20
30
40
30
40
n
0.1
0
20
0
10
20
Fig. A.2: IR Functions for Home Variables to a Foreign Productivity Shock ,
pih
y
0
-0.02
𝜅 =0.12, 0.5
s
0
0.01
-0.01
0.005
-0.04
10
20
30
40
-0.02
10
r
20
30
40
0
re
0
0
-0.05
-0.02
-0.02
10
20
30
40
-0.04
10
piz
20
30
40
-0.04
0
-0.05
-0.01
-0.1
20
30
40
-0.02
10
rez
20
30
40
-0.2
az
0
-0.02
30
40
20
30
40
30
40
30
40
30
40
30
40
rz
0
10
10
yz
0
-0.1
20
pi
0
-0.1
10
2
2
1
1
10
20
-3
wp
10
20
x 10
-0.04
10
20
30
40
0
no
0
0
10
20
-3
os
x 10
30
40
o
0
-2
-0.005
0
-0.01
-4
-0.01
10
20
30
40
10
ns
20
30
40
-0.02
n
0.1
0
0.02
0.05
-0.01
10
20
30
40
0
10
20
20
c
0.04
0
10
30
40
-0.02
10
20
Fig. B.1: IR Functions for Home Variables to a Home Monetary Policy Shock ,
pih
y
s
0
0
0
-0.1
-0.5
-0.2
-0.2
10
20
30
40
-1
10
r
20
30
40
-0.4
0.1
0.2
0
0.05
20
30
40
-0.5
10
no
20
30
40
0
0
-0.2
-0.2
-0.5
20
30
40
-0.4
10
20
30
40
20
30
40
30
40
o
0
10
10
os
0
-0.4
20
wp
0.5
10
10
pi
0.4
0
𝜅 =0.12, 0.5
30
40
-1
10
20
ns
1
0
-1
5
10
15
20
25
30
35
40
25
30
35
40
25
30
35
40
n
5
0
-5
5
10
15
20
c
0
-0.2
-0.4
5
10
15
20
Fig. B.2: IR Functions for Home Variables to a Foreign Monetary Policy Shock ,
pih
y
s
0.04
0.1
0.4
0.02
0
0.2
0
10
20
30
40
-0.1
10
r
20
30
0
40
0.2
0
0
0
20
30
40
-0.2
10
yz
20
30
40
-0.2
0.5
10
20
30
0
40
10
20
30
30
40
40
-0.02
0
0
10
20
30
40
-0.05
10
o
0.5
0
0
20
30
40
-0.5
10
n
30
40
0.2
0
0
20
20
30
40
20
30
40
30
40
c
1
10
20
ns
0.1
10
10
os
0.05
-1
20
0
no
-0.1
40
0.02
0.1
-0.1
30
wp
-0.5
-1
10
rz
0
20
piz
0.2
10
10
pi
0.5
-0.5
𝜅 =0.12
30
40
-0.2
10
20
Fig. С.1: IR Functions for Home Variables to a Oil Price Shock, 𝜅
pih
y
1
s
0.5
0.4
0.5
0
0.2
10
20
30
40
0
10
r
20
30
0
40
2
1
0.5
1
20
30
40
0
10
wp
20
30
0
40
0.2
0.5
0.2
0.1
20
30
40
0
10
20
30
40
o
1
0.6
0
0.4
-1
0.2
-2
10
20
40
20
30
40
0
10
20
30
40
ns
0.8
0
30
os
0.4
10
10
no
1
0
20
pop
1
10
10
pi
2
0
= 0.12
30
40
-3
10
n
20
30
40
30
40
c
2
1.5
0
1
-2
0.5
-4
-6
10
20
30
40
0
10
20
Fig. С.2: IR Functions for Home Variables to a Oil Price Shock, 𝜅
pih
y
s
0.4
0.4
0.2
0.2
0.2
0.1
0
10
20
30
40
0
10
r
20
30
0
40
20
30
40
30
40
30
40
pop
0.5
2
0.5
1
10
20
30
40
0
10
wp
20
30
0
40
0.1
0.5
0.1
0.05
20
30
40
0
10
20
20
os
0.2
10
10
no
1
0
10
pi
1
0
= 0.5
30
40
o
0
10
20
ns
0.4
1
0.3
0
0.2
-1
0.1
0
10
20
30
40
-2
10
n
20
30
40
30
40
c
2
1.5
0
1
-2
0.5
-4
-6
10
20
30
40
0
10
20
Fig. D.1: IR Functions for Home Variables to a Oil Demand Shock,
pih
y
s
1
0.4
0.4
0.5
0.2
0.2
0
10
20
30
40
0
10
r
20
30
0
40
0
1
1
-0.2
20
30
40
0
10
oz
20
30
40
-0.4
1
1
1
0.5
20
30
40
0
10
20
30
40
20
30
40
30
40
os
2
10
10
no
2
0
20
wp
2
10
10
pi
2
0
𝜅 =0.12
30
40
o
0
10
20
ns
0.4
0
0.3
-1
0.2
-2
0.1
0
10
20
30
40
-3
10
n
20
30
40
30
40
c
0
1.5
-2
1
-4
0.5
-6
-8
10
20
30
40
0
10
20
Fig. D.2: IR Functions for Home Variables to an Oil Demand,
pih
𝜅 =0.5
y
s
1
0.4
0.2
0.5
0.2
0.1
0
10
20
30
40
0
10
r
20
30
0
40
pi
1
0
1
0.5
-0.2
10
20
30
40
0
10
oz
20
30
40
-0.4
1
1
0.5
0.5
20
30
40
0
10
20
30
40
20
30
40
30
40
os
1
10
10
no
2
0
20
wp
2
0
10
30
40
o
0
10
20
ns
0.4
0
0.3
-1
0.2
-2
0.1
0
10
20
30
40
-3
10
n
20
30
40
30
40
c
0
1.5
-2
1
-4
0.5
-6
-8
10
20
30
40
0
10
20
Fig. E: IR Functions for Home Variables to an Oil Production Productivity,
wp
z
2
2
1
1
0
10
20
30
40
0
10
no
1
-1
0.5
10
20
30
40
30
40
n
4
2
0
10
20
20
30
40
30
40
ns
0
-2
𝜅 =0.12, 0.5
0
10
20