The model presented in this paper builds on interesting contributions in the field of dynamic general equilibrium modeling, like those of [30–35–36–37]. However, it differs from some of these models in its treatment of expectations, since households and firms are myopic in their decision making. Our model is thus a recursive dynamic general equilibrium that can then be viewed as a sequence of successive static general equilibria linked by adjusting the level of capital and labor stocks. The Seychelles is treated as a small open economy that takes world prices as given. The whole structure and equations of the model are described in [31]. The assumptions about the reference case are specified in Table A1 (Appendices) to avoid a tedious presentation in the core of the text. Four types of economic agents are considered: firms, households, the government, and the rest of the world. The model considers the linkages between firms, households, and the government in the domestic economy, as well as the economy's linkages with the rest of the world, considering resource constraints. The main economic agents in the model respond to changes in relative prices. The model considers the presence of taxes levied by the government on transactions of goods and services and primary factor incomes. It also considers the government's ability to invest in public infrastructure, which affects the productivity of private primary factors.
The model assumes an exogenous growth rate for the labour force in the economy. In the reference situation, the model provides projections for various sectoral and macroeconomic variables based on IMF projections for real GDP growth rates and the values of exports of goods (Table A1)2. Based on the growth rate of the labour force and the evolution of physical capital, the model determines the underlying growth rates of total factor productivity, which are consistent with the growth rates of GDP.
The calibration of the model is based on the 2019 social accounting matrix (SAM) of the Seychelles, built using the coefficients of the 2014 SUT and 2019’s actual levels for aggregate variables from the national accounts, balance of payments, and government financial operations statistics [31]. The Seychelles Industrial Classification of 23 industries and 35 products was aggregated into nine sectors3 to simplify the presentation of results. The ‘fish industry’ group encompasses fishing and fish processing activities.
Firms
In each industry, production requires a combination of labor, capital, and intermediate inputs. The production technology features constant returns to scale and provides managers with various options for substituting inputs in response to changes in relative prices. The productivity of private primary factors is influenced by the level of public capital stock provided by the government. Firms pay taxes and invest in physical capital, which increases their capital stock.
The optimal level of inputs is determined by a cost minimization rule and the Shephard lemma. Since firms are not endowed with an intertemporal behaviour in the model, the level of investment is determined in an ad hoc manner, based on the rental rate of capital and the price of capital goods. Gross output is transformed into goods using a fixed-proportion rule, and the same good produced by different industries is aggregated using a CES function. The representative firm receives transfers from the government and retains a fixed share of the return on capital for saving.
Households
Households have preferences for leisure and for domestically produced and imported goods. Over time, their total time endowment grows at the same rate as the constant growth rate of the population. They allocate their time between labour and leisure and derive their income from the returns to labour and physical capital, transfers received from the government, and net transfers from the rest of the world. They pay income taxes to the government and other taxes, such as sales taxes on goods, levied by the government.
In each period, the representative household maximizes its utility, subject to a budget constraint, to determine the optimal level of labour supply and consumption of goods. A two-level nested utility function is used to represent the preferences of representative households, where utility is a logarithmic function of total consumption and leisure at the top level and total consumption is a CES function of various goods at the second level. A two-step optimization process is used to solve the representative household problem. At the optimum, an increase in the relative price of a good reduces affects relative quantity demanded.
The government
The government consumes goods and invests in public capital, which increases the productivity of private factors. It finances its expenditures through taxes and bond issuance. Government spending includes consumption spending, public investment spending, transfers to households and firms, and interest payments on government debt. A fixed proportion rule is used to allocate the total expenditure of each category among the various commodities. The government's total outlays minus its total revenue represents its balance. When this is negative, the government finances the deficit through bonds purchased by domestic households and non-residents. The government pays interest on its outstanding debt to domestic and foreign residents. Government spending on capital goods increases the public capital stock and affects the productivity of private primary factors such as private capital and labour. Public investment affects the economy both on the traditional demand side through the demand for capital goods and on the supply side through its impact on the productivity of private factors.
Relations with the rest of the world
The domestic economy relates to the rest of the world through exports, imports, transfers to households and the government, and net capital inflows to finance investment. On the supply side, total production of each good in the domestic economy is sold or exported. A constant elasticity of transformation (CET) function is used to capture the transformation of the composite into sales in both markets. A revenue maximization rule is used to determine the optimal level of sales in each market.
On the demand side, total demand for each commodity by domestic agents includes demand from households, the government, firms for intermediate uses, and for investment by the private sector and the government. Investment demand by sector of destination is a different concept from investment demand, which we discussed earlier. Total investment by sector of destination is a composite of investment demand by sector of origin. A Cobb-Douglas aggregator is used to combine investment by sector of origin to form total investment demand by sector of destination. A cost minimization rule is used to determine the composition of the composite and its dual price. The aggregate demand for each good is a composite of domestically produced goods and imports. A CES aggregator is used to capture the imperfect substitutability between the goods of the two origins.
Equilibrium and dynamics
The model assumes that all economic agents respect their budget constraints, and that market equilibrium is achieved through price adjustment. The wage rate adjusts to clear the labour market, and the price of each domestically produced good adjusts to supply and demand. Capital is industry-specific, and investment flows move between industries in response to differences in rates of return. There is a macroeconomic equilibrium between savings and investment in which total investment must be financed by total savings, i.e., the sum of foreign and domestic savings.
To avoid a Ponzi game, the model incorporates a closure rule in which the ratio of foreign savings to current GDP follows an exogenous path each period. The model is closed by adjusting in each period the saving rate of households to achieve equilibrium between savings and investment. The model's dynamics are driven by the evolution of the labour force, private and public capital, and public debt.
[2] https://www.imf.org/external/datamapper/NGDP_RPCH@WEO/OEMDC/ADVEC/WEOWORLD/SYC
[3] Agriculture, Fish industry, Manufacturing, Utilities, Construction, Finance and real estate, Tourism, Information and communications, and Other services. The 23 industries and 35 products are included in the model; aggregation into nine sectors is done only for the presentation of the model results.