The Long-run Effects of Lockdown in Ceará Economy Through Productivity
An Recursive CGE Approach
Heitor Gabriel S. Monteiro1
Christiano Modesto Penna2
20 setembro, 2021
Abstract
We estimate the effects that the Lockdown will cause in Ceará’s economy through the productivity of labor, measured as instruction-level of supplied labor, making adaptations of the Ceará CGE model: Mares-CE. We make three families owners of low-skilled, middle-skilled, and high-skilled labors each one; an investment sector with law motions to recursivity; and, among the laws, the rates of growth to each population’s family, used as a key to the simulation of the counterfactual and lockdown scenarios, considering the pattern find in Kuznets Curve for Education to Ceará. We find that the lockdown scenario will cause a low-skilled labor specialization, which means a growing and cheaper Industry’s output and dependence on imports of Services expensive commodity, wish is intensive in high-skilled labor. The real GDP ends 8.75% smaller than the base scenario. In the remuneration Laspeyres index, the middle-skilled family felt the greatest difference: the remuneration ends 176.09% higher than the base scenario. In the cost of living Laspeyres index, the high-skilled family felt a major difference: your perceived inflation is 15.76% higher than the base scenario. The government plays an important role in social security, improving 33.29% of the low-skilled family endowment; and in the investment sector, decreasing your dissavings and opening space to bigger domestic savings, 5.04% higher than the counterfactual scenario.1 Introduction
We calculate the long-run impacts of Covid-19 Pandemics in Ceará’s economy considering the different effects of lockdown on the education process and so on the productivity of labor. To find this impacts, we modify the Ceará’s CGE-model3 expanding the household’s representation in three different agents by education level (low, middle, and high), and therefore your respective supply of labor; put time recursion in the model; and simulating a counterfactual scenario without pandemic and other with pandemic’s chock. This chock is on the growth rate of three families during a discrete-time. To find the measures of growth rates we estimate the schooling Kuznets Curve for Ceará to show us what stage of distribution of education the labor market is in and where this distribution will move.
Therefore, this paper brings a methodological novelty in the literature by considering the impact of the change from the pandemic in the economic environment through time with the interaction of heterogeneous households. For example, we don’t expect that the sensibility of wages to education should be the same after the entire workforce offers differently less education. So, to estimate the new income level, we should consider the interaction in the labor market, and this is what CGE models do.
The CGE-instrumental is largely used for considerate holistic aspects of chocks in the economy. In the national context, Domingues (2002) uses the SPARTA multicountry model to analyze the sectoral impacts of trade openness of Alca in São Paulo. Cury, Coelho, and Corseiul (2005) construct a model that divides the families by urbanization (urban and rural), categories of per capita income (poor, average, and high), and households head characteristics (active and non-active) with involuntary unemployment gave by an empirical Wage Curve to analyze distributional aspects of fiscal policies. Haddad and Domingues (2001) develop the EFES model: a Johansen-type recursive model4 for Brazil that forecasts changes in exports and technological progress of sectors for 1999 to 2004. They use the expected return of capital in the next period to allocate the capital in the present period using deterministic equations and a single-family representation.
The Ceará’s government and academy have attention to use general equilibrium models to guide public policies decisions. Lucio, Garcia, and C. Pereira (2020) uses a recursive CGE applied to Ceará to analyze the efficiency in tax collection as a way to overcome the fiscal problem arising from the COVID-19 pandemic, focused on the revenue structure of government argent. Paiva (2019) build a dynamic CGE model to analyze the permanent and temporary effects of public investment in Ceará and its effectiveness in the long-run term, attempting to the marginal return of the public capital stock. Paiva and Neto (2021) proposed a wide CGE model used to advise state decisions, called MARES-CE, with a single-family, many sectors openness, and foreign trade with rest-of-the-Brazil and world. This model will be modified in this work to our aims.
In our proposed model, we have three types of families, each one indexed by a level of education. This permits that families with different structures of instruction have different structures of consumption. As Michael (1975) points out, the level of formal education directly influences consumer behavior independently of its effect on money income, and this effect of education is not a random or erratic one, but is systematically related to the changes in consumption patterns attributable to differences in levels of income. So, we believe that this structure is able to explain much better the consumption decision of the families and thus brings more realism to the model.
Consider schooling as development of the productivity of labor, or human capital, is well established in literature such as Schultz (1963) and Hanushek (2002) that that links labor productivity, income and economic growth to the quality of education systems. This brings the importance that Ceará’s government gives to education, Carneiro and Irffi (2017) highlights Ceará as a pioneer state, since 1996, in encouraging cities to improve their levels of educational coverage and quality in external exams using transfer funds. Which results in leaders of the state in the rank of the Basic Education Development Index (IDEB)5 of the country. Our work intends to provide to policy makers a possibles that what will happen with schooling levels of labor due to Lockdown using the Educational Kuznets Curve pattern.
Separate households by schooling is also a good representation of the unequal private and public conditions that face the students, and the Educational Kuznets Curve considers it by assumption of pattern between average and variance of the quantity of the groups analyzed. Cavalcante, Komatsu, and Filho (2020) says that “the Covid-19 pandemic will impact educational inequality among students” and Henares, Komatsu, and Filho (2021) finds that students whose parents have superior education have a note 43% higher than others students in standardized math and writing tests. It suggests a high correlation between family environments with high education levels and a needed structure for make new high-skilled labor family.
Consider the long-term in this aim is important by contemplating the maturing-time of results in human capital through education, this level of education brings consequences for entire labor-life. According to OECD,6 Brazil is above average in time of closed-school and projections show that it will affect the worldwide economy until the end of the century.
To cite other jobs that estimate the impact of school-closure in the economy, Barros (2020) estimate a loss of national GDP of 5.3% or 23% if we delay in a year the conclusion of the studies but ensuring that the Brazilian students will learn well or if we allow them to advance through the school year without ensuring that they learned well during the lockdown, respectively. He takes, for the first scenario, the present value of the mean of the income loss if the students delay a year your entry into the labor market, keeping constant the reported years of study; and, for the second scenario, the contracting firm considers one year of study less than the years reported. In addition, González and Capilla (2020) reported that the Spanish youngers would be the wages reduced by 0.5 p.p. during their lives if remotes classes during one year of lockdown have half of the efficacy of the presential classes. They apply to Spain an empirical estimate of Jaume and Willén (2019) for Argentine, where finds that 88 days of the teachers strike reduced the wages of males and females students of the primary school by, respectively, 3.2% and 1.9% for ten years starting at the ages of 30, this is a loss in annual aggregate earnings of labor of 2.99%.
2 Methodology
2.1 The CGE Recursive Model
We use the Ceará’s CGE-model, called MARES-CE, published for Paiva and Neto (2021) and modify them according the structure of Hosoe, Gasawa, and Hashimoto (2010), and recusiveness in Hosoe (2013). The proposed model is schematized as follows in Figure .
Representative Scheme of Proposed Model. Own elaboration.
As schematized, there is three different labor factors (\(L^1\), \(L^2\), \(L^3\)) divided by instruction level7, that belongs to each family, \(l = (F^1, F^2, F^3)\), respectively. Together with capital (\(K\)) are inputs in first aggregation using an Cobb–Douglas function to results the aggregated-factor (\(Y\)). In the next step, an Leontief function joins the aggregated-factor (\(Y\)) with intermediate inputs of the firms (\(X^{int}\)) to make the gross domestic output (\(Z\)).
Now, we enter in the trade with foreign. The gross domestic output is separated to domestic market (\(Q^s\)), exports to world (\(E^w\)), and to rest-of-the-Brazil (\(E^{br}\)) using an CET8 function. The goods to domestic market (\(Q^s\)) is joined with imports from world (\(M^w\)) and the rest-of-the-Brazil (\(M^{br}\)) using an CES9 function to forms the Ceará’s aggregate supply (\(Q^f\)). In the balance of payments of the foreign trade, we have also net savings from world (\(S^{w}\)) and rest-of-the-Brazil (\(S^{br}\)).
The aggregate supply is divided among the consumption of each families (\(C_{f1}\), \(C_{f2}\), \(C_{f3}\)), consumption of the government (\(G^f\)), intermediate inputs of the firms (\(X^{int}\)), and good-of-investment (\(X^{inv}\)). Each family and the government also have saving in your balance of payments (\(S^p_l\) and \(S^g\), respectively). All savings are summed and divided by the price of capital-commodity (\(p^{III}\)) to make the real-amount of capital available in economy (\(III\)) that will be used in two things: as output of the good-of-investment (\(X^{inv}\)) function and shared for each sector as investment (\(II\)), to form the capital of each firm (\(K\)). The equations will be detailed in next section.
We reduce the SAM10 make by Paiva and Neto (2021) to Ceará’s economy as in Table 5.1, in Appendix 1. To the divisions between families, we apply rates for new SAM to Ceará following what is proposed in Section 2.1.9.
2.1.1 Firm
We make three firms that represents the three commodities that will be marketed: agriculture, industry, and services. So, for each period, \(t\), each firm, \(i\), needs four inputs, \(h\), to maximize the profits:
\[\begin{equation} \tag{2.1} Max_{(Y_{i,t},F_{h,t})} \ \ \ \Pi_{i,t} = p^{Y}_{i,t} Y_{i,t} - \sum_{h}p^{F}_{h,i,t}F_{h,i,t} \end{equation}\]
Where \(\Pi_{i,t}\) is the profit of each firm in each period; \(p^Y_{i,t}\) is the price of each output of firms; \(p^{F}_{h,i,t}\) is the price of each factor by each firm in time; and \(F_{h,i,t}\) is the factor needed for each firm in time. This profit-equation is subjected to production function:
\[\begin{equation} \tag{2.2} Y_{i,t} = b_{i,t} \prod_{h} F^{\beta_{h,i}}_{h,i,t} \end{equation}\]
In which \(b_{i,t}\) is the TPF11 that change in time; and \(\beta_{h,i}\) is the elasticity of production. Resulting this demand for factor:
\[\begin{equation} \tag{2.3} F_{h,i,t} = \left( \frac{p^{Y}_{i,t}\beta_{h,i}} {p^{F}_{h,i,t}} \right) Y_{i,t} \end{equation}\]
2.1.2 Intermediate Inputs
In this step, each firm uses each one final-commodities as intermediate input. It is make with a profit maximization:
\[\begin{equation} \tag{2.4} Max_{(Z_{i,t}, Y_{i,t} X^{int}_{i,t})} \ \ \ \Pi_{i,t} = p^{Z}_{i,t} Z_{i,t} - ( p^{Y}_{i,t} Y_{i,t} + \sum_{j}p^{Q^f}_{j,t} X^{int}_{j,t}) \end{equation}\]
In which \(i \equiv j\); \(p^{Z}_{i,t}\) is the price of each gross domestic output in time (\(Z_{i,t}\)); and \(p^{Q^f}_{j,t}\) is the price of each final-commodity supplied in Ceará. Subject to a Leontief:
\[\begin{equation} \tag{2.5} Z_{i,t} = min \left( \left[ \frac{X^{int}_{j,i,t}}{ax_{j, i}} \right]_{j}, \frac{Y_{i,t}}{ay_i} \right) \end{equation}\]
Where \(ax_{j, i}\) and \(ay_i\) are the proportion of final-commodity \(X^{int}_j\) and \(Y_{i,t}\), respectively. That are used as intermediate input for gross domestic output (\(Z_{i.t}\)). What results in equations for demand of intermediate inputs:
\[\begin{equation} \tag{2.6} X^{int}_{j,i,t} = ax_{j,i} Z_{i,t} \end{equation}\] \[\begin{equation} \tag{2.7} Y_{j,i,t} = ay_{j,i} Z_{i,t} \end{equation}\]
With a price-formation12 of \(Z_{i,t}\):
\[\begin{equation} \tag{2.8} p^{Z}_{i,t} = ay_{j,i}p^{Y}_{i,t} + \sum_{j}(ax_{j,i}p^{Q^f}_{j,i,t}) \end{equation}\]
2.1.3 Foreign Trade
First, we have an maximization that represents the optimal choice between exports and sell for domestic demand:
\[\begin{equation} \tag{2.9} Max_{(E^{w}_{i,t}, E^{br}_{i,t}, Q^s_{i,t}, Z_{i,t})} \ \ \ \Pi_{i,t} = (p^{E^{w}}_{i,t}E^w_{i,t} + p^{E^{br}}_{i,t}E^{br}_{i,t} + p^{Q^{s}}_{i,t}Q^s_{i,t}) - (1-\tau^{Z}_{1,i}-\tau^{Z}_{2,i}) p^{Z}_{i,t} Z_{i,t} \end{equation}\]
Where \(p^{E^{w}}_{i,t}\) and \(p^{E^{br}}_{i,t}\) are, respectively, the price in domestic currency of exported commodities to world and to rest-of-the-Brazil. The domestic prices are endogenous while the two foreign prices are exogenous because Ceará is an price-taker of the world and of the rest-of-the-Brazil. So, the exchange rates is substituted to more broader variables: the external and the internal margin of commerce (\(Mg^w\), \(Mg^{br}\)), both endogenous too. \(p^{Q^{s}}_{i,t}\) is the price of commodities that stay in Ceará; \(\tau^{Z}_{1,i}\) is tax on the circulation of goods and services, called ICMS; and \(\tau^{Z}_{2,i}\) is others taxes rate. Subject to:
\[\begin{equation} \tag{2.10} Z_{i,t} = \theta_{i} (\xi_1 (E^w_{i,t})^{\phi} + \xi_2 (E^{br}_{i,t})^{\phi} + \xi_3 (Q^s_{i,t})^{\phi})^{\frac{1}{\phi}} \end{equation}\] \[\begin{equation} \tag{2.11} \sum^3_{s=1} \xi_s = 1 \end{equation}\] \[\begin{equation} \tag{2.12} 0 \leq \xi_s \leq 1 \ \ \forall s \end{equation}\]
Where \(\theta_i\) is scale parameter; \(\xi_s\) is share coefficients; and \(\phi\) is an parameter defined by the elasticity of transformation13 .That results in demand equations:
\[\begin{equation} \tag{2.13} E^w_{i,t} = \left[ \frac{\theta^{\phi}_{i} \xi_1 (1+\tau^{Z}_{1,i} + \tau^{Z}_{2,i}) p^{Z}_{i,t}}{p^{E^w}_{i,t}} \right] ^ {\frac{1}{1-\phi}} Z_{i,t} \end{equation}\] \[\begin{equation} \tag{2.14} E^{br}_{i,t} = \left[ \frac{\theta^{\phi}_{i} \xi_2 (1+\tau^{Z}_{1,i} + \tau^{Z}_{2,i}) p^{Z}_{i,t}}{p^{E^{br}}_{i,t}} \right] ^ {\frac{1}{1-\phi}} Z_{i,t} \end{equation}\] \[\begin{equation} \tag{2.15} Q^s_{i,t} = \left[ \frac{\theta^{\phi}_{i} \xi_3 (1+\tau^{Z}_{1,i} + \tau^{Z}_{2,i}) p^{Z}_{i,t}}{p^{Q^s}_{i,t}} \right] ^ {\frac{1}{1-\phi}} Z_{i,t} \end{equation}\]
In second stage, is jointed what stay in Ceará with imports from world and rest-of-the-Brazil to form the aggregate supply of the territory in an maximization-problem:
\[\begin{equation} \tag{2.16} Max_{(M^{w}_{i,t}, M^{br}_{i,t}, Q^{f}_{i,t}, Q^{s}_{i,t})} \ \ \ \Pi_{i,t} = p^{Q^f}_{i,t}Q^{f}_{i,t} - [(1-\tau^{M^w}_i) p^{M^{w}}_{i,t} M^{w}_{i,t} + p^{M^{br}}_{i,t} M^{br}_{i,t} + p^{Q^s}_{i,t}Q^s_{i,t}] \end{equation}\]
Where \(p^{M^{w}}_{i,t}\) and \(p^{M^{br}}_{i,t}\) are, respectively, the price in domestic currency of imports commodities from world and from rest-of-the-Brazil; \(p^{Q^{f}}_{i,t}\) is the price of commodities that are the aggregate supply in Ceará; and \(\tau^{M^w}_i\) is rate tax on international imports. Subject to:
\[\begin{equation} \tag{2.17} Q^f_{i,t} = \vartheta_{i}(\delta_1 (M^w_{i,t})^{\eta} + \delta_2 (M^{br}_{i,t})^{\eta} + \delta_3 (Q^s_{i,t})^{\eta})^{\frac{1}{\eta}} \end{equation}\] \[\begin{equation} \tag{2.18} \sum^3_{s=1} \delta_s = 1 \end{equation}\] \[\begin{equation} \tag{2.19} 0 \leq \delta_s \leq 1 \ \ \forall s \end{equation}\]
Where \(\vartheta_i\) is scale parameter; \(\delta_s\) is share coefficients; and \(\eta\) is an parameter defined by the elasticity of substitution14 .That results in demand equations:
\[\begin{equation} \tag{2.20} M^{w}_{i,t} = \left[ \frac{\vartheta^{\eta}_{i} \delta_1 p^{Q^f}_{i,t}}{(1+\tau^{M^w}_i)p^{M^w}_{i,t}} \right]^{\frac{1}{1-\eta}} Q^f_{i,t} \end{equation}\] \[\begin{equation} \tag{2.21} M^{br}_{i,t} = \left[ \frac{\vartheta^{\eta}_{i} \delta_2 p^{Q^f}_{i,t}}{p^{M^{br}}_{i,t}} \right]^{\frac{1}{1-\eta}} Q^f_{i,t} \end{equation}\] \[\begin{equation} \tag{2.22} Q^s_{i,t} = \left[ \frac{\vartheta^{\eta}_{i} \delta_3 p^{Q^f}_{i,t}}{p^{Q^s}_ {i,t}} \right]^{\frac{1}{1-\eta}} Q^f_{i,t} \end{equation}\]
That are restricted by the national and international balance of payments, respectively:
\[\begin{equation} \tag{2.23} S^{br}_t = (Mg^{br})^{-1} \sum_i (p^{M^{br}}_{i,t}M^{br}_{i,t} - p^{E^{br}}_{i,t}E^{br}_{i,t}) \end{equation}\] \[\begin{equation} \tag{2.24} S^{w}_t = (Mg^{w})^{-1} \sum_i (p^{M^{w}}_{i,t}M^{w}_{i,t} - p^{E^{w}}_{i,t}E^{w}_{i,t}) \end{equation}\]
2.1.4 Government
In MARES-CE, all three levels (national, state, and municipal) of the State are represented in a single locally acting agent. The government have revenue based in households income taxation, production taxation, and international imports taxation as follows:
\[\begin{equation} \tag{2.25} T^D_{t} = \sum_h \sum_l \sum_i \tau^D_{l,h} p^{F}_{h,i,t} FF_{h,l,t} \end{equation}\] \[\begin{equation} \tag{2.26} T^Z_{t} = \sum_i (\tau^{Z}_{1,i} + \tau^{Z}_{2,i}) p^{Z}_{i,t} Z_{i,t} \end{equation}\] \[\begin{equation} \tag{2.27} T^{M^w}_{t} = \sum_i \tau^{M^w}_i p^{M^w}_{i,t} M^{w}_{i,t} \end{equation}\]
Where \(T^D_{t}, T^Z_{t},\) and \(T^{M^w}_{t}\) are the amount of revenue from income, production, and importation, respectively. \(\tau^D_h\) is the tax rate on the endowments of the families; and \(FF_{h,l,t}\) is the endowments of the families. And have the demand-behavior:
\[\begin{equation} \tag{2.28} G^{f}_{i,t} = \frac{\mu_i}{p^{Q^f}_{i,t}} (T^D_{t} + T^Z_{t} + T^{M^w}_{t}) \end{equation}\]
Where \(\mu_i\) is the share of expenditure with each final-commodity. Restricted by:
\[\begin{equation} \tag{2.29} \sum_i G^{f}_{i,t} = (1-ss^g) (T^D_{t} + T^Z_{t} + T^{M^w}_{t} - \sum_l TF_{l,t}) \end{equation}\] \[\begin{equation} \tag{2.30} \sum_i \mu_i = 1 \end{equation}\]
In which \(ss^g\) is the rate of the government savings and \(TF_l\) are direct transfers to each family, all exogenously given.
2.1.5 Heterogeneous Households
Consuming the final-commodities (\(Q^f_{i,t}\)), each family maximize the felicity-function:
\[\begin{equation} \tag{2.31} Max_{C^f_l} \ \ UU_{l,t} = a_l \prod_i (C^f_{l,i,t})^{\alpha_{l,i}} \end{equation}\]
Where \(UU_{l,t}\) is an consumption measure; \(a_l\) is a scale parameter; and \(\alpha_{l,i}\) is a share parameter of consumption. Restricted by:
\[\begin{equation} \tag{2.32} \sum_i p^{C^f}_{i,t} C^f_{l,i,t} = \sum_h \sum_i (1-ss^p_l-\tau^D_{l,h}) p^{F}_{h,i,t} FF_{h,l,t} + TF_{l,t} \end{equation}\] \[\begin{equation} \tag{2.33} \sum_i \alpha_{l,i} = 1 \end{equation}\]
That result in a demand function:
\[\begin{equation} \tag{2.34} C^f_{l,i,t} = \frac{\alpha_{l,i}}{p^{C^f}_{i,t}}[\sum_{h} \sum_i ((1-ss^p_l-\tau^D_{l,h}) p^{F}_{h,i,t} FF_{h,l,t}) + TF_{l,t}] \end{equation}\]
Therefore, the model maximizes the Benthamite Social Welfare Utility Function (\(SWU\)), that is neutral among families:
\[\begin{equation} \tag{2.35} Max_{UU_{l,t}} \ \ SWU = \sum_l \sum_t \frac{UU_{l,t}}{(1+ ror)^{t-1}} \end{equation}\]
Which \(ror\) is the rate of return of the capital stock to capital service used by firms.
2.1.6 Savings and Investment
We have three fonts of savings: the foreign sectors (Equations (2.23) and (2.24)); the government (Equation (2.36)); and the families (Equation (2.37)).
\[\begin{equation} \tag{2.36} S^g_t = ss^g (T^D_{t} + T^Z_{t} + T^{M^w}_{t} - \sum_l TF_{l,t}) \end{equation}\] \[\begin{equation} \tag{2.37} S^p_{l,t} = ss^p_l \sum_h \sum_i [p^{F}_{h,i,t} FF_{h,l,t}] - TF_{l,t} \end{equation}\]
The aggregate saving forms the total investment in each period (\(III_t\)):
\[\begin{equation} \tag{2.38} III_t = \frac{ \sum_l S^p_{l,t} + S^g_t + (Mg^{br})S^{br}_t + (Mg^{w})S^{w}_t }{p^{III}_t} \end{equation}\]
Will be used as output of the good-of-investment production-function and their demand, as follows respectively:
\[\begin{equation} \tag{2.39} III_t = \Lambda \prod_i (X_{i,t}^{inv})^{\lambda_i} \end{equation}\] \[\begin{equation} \tag{2.40} X_{i,t}^{inv} = \lambda_i \left( \frac{p^{III}_t}{p^{Q^f}_{i,t}} \right) III_t \end{equation}\]
Where \(\Lambda\) is the scale parameter of production-function and \(\lambda_i\) is the share coefficient of production. This total investment is shared for each sector with:
\[\begin{equation} \tag{2.41} II_{i,t} = \left( \frac{(p^{F}_{h=K,j,t})^{\zeta} F_{h=K,j,t}}{ \sum_{i} (p^{F}_{h=K,i,t})^{\zeta} F_{h=K,i,t}} \right) III_t \end{equation}\]
Therefore:
\[ \sum_j \left( \frac{(p^{F}_{h=K,j,t})^{\zeta} F_{h=K,j,t}}{ \sum_{i} (p^{F}_{h=K,i,t})^{\zeta} F_{h=K,i,t}} \right) = 1 \ \ \ \rightarrow \ \ \ \sum_i II_{i,t} = III_t \]
In which \(\zeta\) is an sensitivity-parameter of allocations to marginal rate of return of the investment, i.e., the price paid for capital. The higher \(\zeta\), greater will be the investment in better payers sectors, the less the size of the sectors will matter. Each investment destined to sector will update your capital stock (\(KK_{i,t}\)), that is immobilized in the sector once installed. The capital stock of the sector also forms the capital used by an rate (\(ror\)) as follows:
\[\begin{equation} \tag{2.42} F_{h=K,i,t} = ror KK_{i,t} \end{equation}\]
2.1.7 Dynamics and Market-clearing Condictions
To dynamics, there is an law motion of capital; growth of the three family-labor types; and technological progress, respectively:
\[\begin{equation} \tag{2.43} KK_{i, t+1} = (1+dep) KK_{i, t} + II_{i,t} \end{equation}\] \[\begin{equation} \tag{2.44} FF_{h,l, t+1} = (1 + pop_{l}) FF_{h,l,t} \end{equation}\]
Where \(dep\) is rate of depreciation of the capital stock; \(pop_{l}\) is the growth rate of each endowments of each family.
To macro-closures, join with the Equations (2.23), (2.24), (2.29), (2.32), and (2.42):
\[\begin{equation} \tag{2.45} Q^{f}_{i,t} = \sum_l C^f_{l,i,t} + G^{f}_{i,t} + X_{i,t}^{inv} + \sum_j X^{int}_{j,i,t} \end{equation}\] \[\begin{equation} \tag{2.46} \sum_i F_{h,i,t} = FF_{h,l,t} \ \ \ \forall h=(L^1, L^2, L^3) \end{equation}\] \[\begin{equation} \tag{2.47} p^{F}_{h,i,t} = p^{F}_{h,j,t} \ \ \ \forall h=(L^1, L^2, L^3) \end{equation}\]
Notice that, in Equations (2.46) and (2.47), the equality don’t cover the factor demanded, endowments, and price when \(h=K\). This happen because the formation of the capital-factor follows Equation (2.42) and endowments follows the population growth rate \(pop_l\) in Equation (2.44); and differences between capital stocks, gave by Equation (2.43), leads to different prices of capital-factor. This is the center of capital-immobility installed in sector.
2.1.8 Adjustment of Assumed Capital Growth
Until now, we have two different motions of capital: one attached by growth of families, gave by Equation (2.44), that is, the capital-endowment; and other attached by growth of the capital stock, gave by Equation (2.43) and (2.42), the capital-factor. Given these two movements, we have adjust the good-of-investment (\(X^{inv}\)) to the desired growth of the economy, following the growth of the capital-endowment:
\[\begin{equation} \tag{2.48} II^{ASS}_t = \sum_l \left( \frac{pop_l + dep}{ror} \right) FF_{h=K, l, t} \end{equation}\]
The ratio of this lack, \(adjust = \frac{II^{ASS}}{II^{SAM}}\), is used to record for the new good-of-investment in the SAM:
\[\begin{equation} \tag{2.49} X_{i,t=00}^{inv} = adjust X_{i,t=00}^{inv, SAM} \end{equation}\]
To maintain the equality between the sums of the rows and columns of the SAM, we apply the difference in exports of the rest-of-the-Brazil:
\[\begin{equation} \tag{2.50} E^{br}_{i,t=00} = E^{br, SAM}_{i,t=00} - (X_{i,t=00}^{inv} - X_{i,t=00}^{inv, SAM}) \end{equation}\]
So, we have a new formation of foreign saving:
\[\begin{equation} \tag{2.51} S^{br}_{t=00} = \sum_i (M^{br,SAM}_{i,t=00} - E^{br}_{i,t=00}) \end{equation}\]
The values of the SAM, \(t=00\), will be used to calibrate the parameters of the model.
2.1.9 Modiffing the SAM
To modify the SAM of the Table 5.1, we use the Continuous National Household Sample Survey15 of 2013 to divide the amount of the aggregated wages between instruction levels. To identify and divide the consumption, private savings, and capital remuneration between families, we use the Consumer Expenditure Survey16 of 2008.
In addition, we use the data of the Siconfi17 to divide the amount transferred directly and indirectly from the government to families, following your weight share in population. To divide the share of the amount paid to income tax, we use the data of the tax income, by levels of income, from Federal Revenue Service Agency18 of 2013. The transfer and the income tax are also residually used to balance the sum of the SAM rows and columns. The results will be described in the next section.
2.2 Modelling the Schock
The Lockdown will impact the productivity of labor in the long-term through the education process during the school closing. This impact will change the rates of growth of the groups of instruction, \(pop_l\). But where were these rates going and where are they going? To answer, Langoni (1973) and Barros and Mendonça (1995) finds a pattern of development in the labor market of many countries, in the distribution of instruction.
Starting from a minimum level of education, while the average of education grows, the inequality in education level also grows. And it happens until a maximum level of inequality, forming an inverted-U-shaped curve between average and variance, called Kuznets Curve of Education, as shown in Figure .
Evolution of the Level of Inequality in Instruction of Labor Force of the Brazil by Average of Years of Education, 1995-2007, Barros et al. (2010) .
This pattern modeled to Ceará will lead us to new distributions of the families’ population by find in what stage of labor market Ceará lies. The rates of growth and decrease of the population will be used as counterfactual and Lockdown’s chock scenarios, respectively.
3 Results
3.1 The Ceará’s Labor Market
Figure 3.1: Share of the Families in Labour Market of the Ceará. 1995-2015. Own Elaboration
Figure 3.1 shows what happens with the instructions group supplied in Ceará’s labor market: a transition from low to the middle level of instruction. While the average growth rate of all periods to \(F^1\) is -0.35%, to \(F^2\) is 8.71%, and 8.04% to \(F^3\). As result, the average of instruction has a mean of the annual growth rate of 3.86% The reduction of discrepancy is clear, as shown in the Kuznets Curve of Education, in Figure 3.2.
Figure 3.2: Ceara’s Kuznets Curve for Education, 1995-2015. Average of the Years of Instruction by Variance of the Count of the Groups of Familie. Own Elaboration
The year of the SAM is 2013, on this point, in Figure 3.2, any increase in the average of instruction leads to a smaller variance, and any reduction of average will move to greater variance. The rates of increase and decrease, starting in 2013, will be used in the simulation of scenarios of the model, as show the Table 3.1.
| Counterfactual | Lockdown | |
|---|---|---|
| \(pop_{F^1}\) | -0.04342 | 0.04539 |
| \(pop_{F^2}\) | 0.03855 | -0.03712 |
| \(pop_{F^3}\) | 0.03435 | -0.03321 |
| Source: Own elaboration. |
3.2 The New SAM
The new SAM used to model is in Table 5.2, in Appendix 1. The shares to expand the amounts of SAM in Table 5.1 is detailed in Table 3.2 bellow.
| Variables | Family 1 | Family 2 | Family 3 |
|---|---|---|---|
| Consumption of Goods | |||
| Agriculture | 0.3773 | 0.3261 | 0.2967 |
| Industry | 0.3202 | 0.2915 | 0.3883 |
| Services | 0.2925 | 0.3013 | 0.4062 |
| Saving | |||
| Invesment | 0.0506 | 0.1473 | 0.8022 |
| Factors Remuneration | |||
| Agriculture | 0.8685 | 0.1117 | 0.0198 |
| Industry | 0.6193 | 0.3067 | 0.0741 |
| Services | 0.2451 | 0.2992 | 0.4557 |
| Capital | 0.0512 | 0.1701 | 0.7787 |
| Government | |||
| Income Tax | 0.0043 | 0.0248 | 0.9709 |
| Transfers | 0.6052 | 0.3601 | 0.0347 |
| Source: Own elaboration. | |||
To better understand the scenario around these shares, the economically active population is composed of 55.64% of the Family 1, with low education level; 30.12% of the Family 2, with middle instruction; and 14.24% of the Family 3, with high instruction. Despite this participation, Family 1 is the owner of 32.17% of the wage mass while Family 2 and Family 3 are the owner of 29.41% and 38.42%, respectively.
The offer of public education, public security, and public health represents purchases from the families to sectors that are possible due to transfers from government to families. We see the redistribution nature of the government activity, for example: while the direct tax of the total income is 19.33% to the Family 3, to Family 1 is 0.17%; and while the direct transfers from the government represent 0.78% of the revenue of the Family 3, represents 27.57% of the revenue of the Family 1.
In the savings line of the SAM, we see, thanks to the dissaving of the government, the calibration of the saving share (\(ss^g\)) results in -0.6263 making a structurally indebted agent. The major endogenous font of savings is the Family 3 who owns, according to Table 3.2, 88.22% of all private investment and has \(ss^p_{l=F^3}\) = 0.2391, the major between the families. The capital-endowment is highly concentrated in this family too, that have 77.88% of the total of this remuneration. This shows us that \(pop_{F^3}\) may guide, through time, almost entire of domestic savings and, thus, the good-of-investment (\(X^{inv}_{i,t}\)) and the investment immobilized (\(II_{i,t}\))19.
The capital-remuneration of the Agriculture, Industry and Services are 83.92%, 47.03%, and 42.78%, of the total remuneration of the factors of each, respectively. So, Agriculture is most capital-intensive and Service is a high-skilled labor-intensive production process. Between the labor-force employed by each sector, we see in Table 5.3 high participation of \(L^1\) in the Industry production process. This gives us the sense that, under \(pop_{F^1}\) = -0.0434 of the counterfactual scenario, Industry will suffer more with this diminishing population, and Agriculture, because \(pop_{F^3}\) = 0.0343, will benefit from the increase of the savings and consequently increase of the investment immobilized. Additionally, 45.57% of the labor-remuneration of the Service is to high-skilled family; so, in Lockdown’s scenario, will suffer more with this diminishing population. This gives us a sense of what will happen with the factor-aggregation of each sector during the time in the simulations. The parameters from the calibration are shown in Appendix 2.
3.3 The Counterfactual Scenario
The main model result in counterfactual simulation is the power purchase of the different instruction levels analyzing side-by-side the Laspeyres index to perceived prices (Table 5.14) and to remuneration (Table 5.15)20. Because \(L^1\) becomes rare, reaching 9.69% of the labor market population, your remuneration grows up by 6.47% per year, in twenty years, and the remuneration of \(L^2\) and \(L^3\) decrease at 1.89% and 1.44% per year while the remuneration of the capital falls. As result, the Laspeyres remuneration index for families decrease to \(F^2\) and \(F^3\), in 28.09% and 23.56%, respectively. The Laspeyres price index for the three families are 0.18%, 0.39%, and 0.33%, respectively; it means that all families need a bit less money to keep the same living standard. We understand that the new set of factor remunerations decrease more than the price index to families \(F^2\) and \(F^3\), so these two families have decreasing power purchase; i.e., we can explain the growth of the \(F^2\) and \(F^3\) utilities only by populations growth. Let’s understand how this happens.
Despite the government dissaving, which grows up at 2.77% per period, the domestic savings is positive but diminishing at 0.23% per year. In the series beginning, domestic savings reached 12.99% of total savings; but foreign savings grew at 2.47% per year, becoming 91.74% in the simulation end. So, there was an average growth of \(III\) of 2.10% per year, as we see in Table 5.11, thanks to the foreign savings, which marks this importance to Ceará’s economy. The transformation from savings to investment became a bit more expensive: \(Mg^{br}/p^{III}\) and \(Mg^{w}/p^{III}\) decreased 0.04% and 0.15% per year, respectively. The \(III\) allocation to sector follows Figure 5.9, we find that Industry decreases its return to capital-factor while the marginal remuneration of capital in Services grows, as well as its receipt of new investments. With \(III\) growth, grows too \(X^{inv}\), as we see in Table 5.12.
As we see in Figure 5.1, maintaining the education growth level in Ceará would cause a reduction in low-skilled labor that implies a higher price for that factor, which is explained by the bargaining power mechanism21. The remuneration of \(L^2\) and \(L^3\) reduce by both Quantity Effect and Price Effect: greater quantity offered not only causes a decrease in remuneration, because of bargaining power, but also due to a lower premium sensibility for one higher instruction level. The diminishing price effect is largely found in developing economies22. Under these factors-price dynamics, the aggregated factor (\(Y_i\)) and gross production (\(Z_i\)) grew at the same average rate to Agriculture, Industry, and Service at 2.17%, 1.11%, and 2.23% per year, respectively. So, Agriculture benefits because is capital-intensive, Services benefits because is high-skilled labor-intensive between labors, and Industry grows less because is low-skilled labor-intensive. Indeed, by the cost Laspeyres index perceived by each firm23, in Table 5.16, Industry felt the higher increase costs. So, in this scenario, the nominal and real GDP24 grow at an average of 1.88% and 2.62% per year, respectively.
The prices received from gross domestic production (\(p^{Z}_{i,t}\)) represented in Figure 5.4, is used with \(p^{Q^s}_{i,t}\), \(p^{E^{br}}_{i,t}\), and \(p^{E^w}_{i,t}\), as in Figure 5.5 and 5.6, to decide how much stay in domestic market and how much is exported. We see that sell Industry to the internal market is more interesting because \(p^{Q^s}_{i,t}\) grow at 0.38% per year while the export price to world and rest-of-the-Brasil grows 0.01% and 0.11%, respectively. The decrease of \(p^{Q^s}_{i,t}\) to Agriculture and Service, at 0.42% and 0.22%, causes exportation grows more than what stays in the economy, as detailed in Table 5.12. On the other hand, the Industry’s \(p^{Q^s}_{i,t}\) growth rate also leads to imports growth rate higher than the domestic growth rate. Concluding the foreign relations, it comes to supply the internal need for industrial products.
The imports in total Ceará’s supply started with 18.13% and ends with 16.17%. Agriculture, Industry, and Service went from 4.18%, 47.82%, and 47.99% to 4.06%, 45.25%, and 50.69%, respectively, under the prices showed in Figure 5.10. With the fall of \(F^1\), the price of the Industry’s output increases, a pattern that we see in all model steps. So, happens a substitution from Industry to Services in agents consumption, as we see in Table 5.12. This scenario still results in an increase in welfare to all families, as we see in Table 5.13. Finally, the government increases your revenue through the market taxes and tax income from growing \(F^2\) and \(F^3\) while decreasing your transfers as \(F^1\) population decline too; so, your structural debt space grows at 2.77% per year, as in Table 5.11.
Concluding the counterfactual scenario, we saw a specialization of the economy in Services, with the high-skilled labor-intensive process, and Agriculture, which is capital-intensive; the foreign trade improves industrial product; and growth of utility to all families.
3.4 The Pandemic Chock
The lockdown simulation responds to the question: “what will happen if only the proportions of education levels change, even keeping the foreign savings inflow constant?” The main answer lies in the Government, which has an important role in growing your transfers to the growing low-skilled population, as we see in Table 5.13. In this scenario, with diminishing \(F^2\) and \(F^3\), our total tax revenue reached to be 82.13% of the total revenue in the counterfactual scenario at the end of the period’s simulation. On other hand, your total transfers reach 147.61% in the final period’s comparison with counterfactual. This difference implies a reduction in your debt capacity: your dissaving grown 0.15% per year and ended being 61.14% of the counterfactual debt. This open space to major domestic savings, which ends being 161.09% of the counterfactual. Let’s understand how this works.
The domestic savings growth causes a growth in total savings, that ends 105.04% of the counterfactual total. The transformation from foreign savings to investment (\(Mg^{br}/p^{III}\) and \(Mg^{w}/p^{III}\)) grow 0.28% and -0.24%, respectively. As result, the total investment grows and ends being 103.44% of the base scenario.
Occurs that Industry and Agriculture grow more because the economy is becoming low-skilled and capital abundant. Differing from counterfactual, the remuneration to capital-factor decreases faster and Agriculture becomes the better payer to this factor. As result, the nominal and real GDP grew at 1.33% and 2.13% per year, respectively. In comparison with Counterfactual, this GDP ends 8.75% smaller; the difference grows at an average of 13.91% per year.
The Ceará’s economy goes to the foreign market with expending Services and cheaper Industry and Agriculture. The higher fall speed to \(p^{Q^s}_{i,t}\) in comparison to \(p^{M^{br}}_{i,t}\) and \(p^{M^{w}}_{i,t}\) makes Agriculture exportation grow to world and rest-of-the-Brazil. The Industry exportation grows to both economies and especially more to the world. The import stage fills the need in the Services sector, with imports of the Services commodity from the rest-of-the-Brazil being the fastest growing in the period, at 3.73% per year, as shown in the Table5.12.
The final supply reaches the end of the simulation’s period with 20.33% of imports and is composed of 5.30%, 54.11%, and 40.59% of Agriculture, Industry, and Services, respectively. As result, under the prices shown in Figure 5.10, the Laspeyres price index for three families grown -0.21%, 0.73%, and 1.23%, respectively. In comparison with the Laspeyres remuneration index, in Table5.15, we conclude that, excepting the population growth effects, the remuneration growth exceeds the growth of the costs only to families \(F^2\) and \(F^3\). This means that \(F^1\) depends on government transfers to at least keep your life standard, contributing with 33.29% of your budget in the end period.
Concluding the lockdown scenario, we saw Industry and Agriculture’s specialization, due to a low-skilled and capital abundance, with importation to meet the need for Services, with high-skilled labor intensity. The government plays an important role with transfers to \(F^1\) and fiscal discipline, which improve more domestic savings and good-of-investment.
4 Conclusions
The main objective of this work was to estimate the long-run impacts of lockdown in Ceará’s economy, as a sanitary response against Covid-19, through productivity translated in wages, considering productivity as developed human capital attained through the educational process. To do this, we built a regional model of general equilibrium with three representative families: \(F^1\), \(F^2\), and \(F^3\), categorized as low-skilled labor owner (\(L^1\)), middle-skilled labor owner (\(L^2\)), and high-skilled labor owner (\(L^3\)), respectively; domestic factor-aggregation and intermediary consumption step; foreign trade and savings inflow with rest-of-the-Brazil and world; one agent that represents the government; and a sector that transforms savings in investment and share it to firms. The model is recursively applied to discrete-time with some law motions and, among them, the growth rates of families, that is our key variable to represent the simulation of scenarios: a counterfactual-base scenario and a lockdown scenario; under the assumption that lockdown scenario makes Ceará’s labor supply structure return to previous levels of disparity along the educational Kuznets Curve for Ceará.
Is important to keep in mind some limitations that this parsimonious model has: the population growth is identically to active population and the labor offer by families is exogenous; we don’t consider monetary effects like interest rates; the marginal propensity to saving of the agents is fixed; there is one single agent to represent government; we maintain the foreign savings inflow constant between scenarios and not impose any change in international prices of the commodities; we not assume any change in rest-of-the-Brazil’s economy between scenarios. The aim is to select only the effects of changes of the populations in endogenous variables.
Finding the Ceará’s Kuznets Curve, we see that, since 2006, the growth of the educational level average of the labor market is accompanied by a decrease of inequality of the instruction. This traduces, following the theory and empirical findings, in lower marginal premium for more education. So, the geometric average of growth and decrease in families group around 2013 is used to extend the model’s population in scenarios, as shown in Table 3.1. The new SAM used in the model reveals, by calibration of parameters, that Agriculture is capital-intensive, Industry is low-skilled labor-intensive between the labors, and Services is a high-skilled labor-intensive process.
In the counterfactual scenario, the economy becomes high-skilled abundant, and domestic savings grow at decreasing rates thanks to the government, which can diminish your transfers to decreasing \(F^1\) and grow your goods consumption, increasing your dissaving. The remuneration to \(F^1\) grows 6.47% per year; it happens because \(L^1\) is becoming rare and your labor gains the power of bargaining, even in the same positions of jobs. So, Agriculture and Services grow faster and real GDP grows at an average of 2.62% per year. The final supply-demand match happens under decreasing prices to Agriculture and Services, so, the inflation perceived by each family, using Laspeyres index, fell 0.18%, 0.39%, and 0.33%, respectively. We conclude, considering also the remuneration index, that the utility of \(F^2\) and \(F^3\) grow only to the quantity growth of these families.
The first movement simulated to the pandemic scenario in our model is the growth of the low-skilled labor. In the real economy, this means a growth in the participation in the potential and traditional workforce25 population: working-age people, especially those who are financially vulnerable, that stop your studies and go to the labor market. The data to Ceará26, we see that the potential workforce grew at 5.77% per quarter from the beginning of 2020 until the second quarter of 2021, in accordance with the model. By the data to Brazil27 that can be divided by instruction levels, we see that \(F^1\), \(F^2\), and \(F^3\) diminished your participation in the workforce by a geometric average of 1.83%, 1.16%, and 0.94% per quarter in the same period, respectively. The smaller decrease on the participation of the high-skilled family possible indicates that the social security offered by the government can pay the reserve salary of some part of the low-skilled families and keep this share out of the labor market. In contrast, the high-skilled family has more to lose despite the adverse scenario. This means an inverse relationship between social security, transfers, and entry into the labor market. Indeed, The population with incomplete elementary education was declining before the pandemic and is declining much faster in the lockdown period. Some part of the population used the lockdown period to end the elementary school level. But this not happen with no instruction and incomplete high school population, who grew more faster than before the pandemic, in accordance with the model.
In the lockdown scenario, the economy becomes low-skilled abundant and ends with 5.44% more investment than the base scenario: the fall in government revenue joined with an increase in transfers coerce to decrease your dissavings, which results in more domestic savings and, thus, more investment. The Industry and Agriculture commodities grow faster and the Service’s output becomes more expensive, which too suffers with the higher cost, which increased 47.83% in simulation. The labors remuneration grow -3.17%, 5.20%, and 4.87%, respectively. As result, the real GDP grows at 2.13% per year and ends 8.75% smaller than the base scenario; the difference grows at an average of 13.91% per year. So, the inflation perceived by each family, using Laspeyres index, grow -0.21%, 0.73%, and 1.23%, respectively. So, the fall in remuneration of \(F^1\) is higher than the decrease in your price index, the growth of your utility is thanks to the quantity effect of the population growth. Indeed, the government transfers to \(F^1\) ends the simulation being 33.29% of its income, compared with 11.29% of the counterfactual.
This results of the lockdown scenario appoint to question raised by Lucio, Garcia, and C. Pereira (2020) in your model to analyze fiscal government activity, complementing the importance of alternatives against diminishing fiscal revenue such as efficiency in tax collection to Ceará state as a way to a solution. Also connects with Paiva (2019) results to Ceará about the trade-off of the government between rising current consumption and improve domestic capital stock, through savings in our model, to long-term production: a consumption-focused policy brings a sub-optimum scenario than a focus in a policy of domestic capital stock improvement. The government activity in the model also converges with the described spends by Lima et al. (2020) during the fists months of the lockdown, a higher spend at the municipal level in Ceará with social assistance.
Is clear the key role that government makes in the lockdown scenario, keeping assistance to the most vulnerable population and discipline to not choke the domestic savings through your debt space, more adverse scenario requires higher strategic public expends. In addition to taking care to reduce the trend of population increase that interrupts studies, i.e., break your productivity development due to lockdown.
5 Appendix
5.1 Appendix 1: Social Accounting Matrices
| Agents | Agr | Ind | Srv | Inv | Cap | Lab | Fam | Gov | ICMS | Out | Im | RoW | Rob |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Agr | 332 | 2 650 | 416 | 879 | 4 200 | 6 | 272 | 773 | |||||
| Ind | 1 120 | 25 387 | 11 369 | 21 452 | 35 973 | 322 | 2 326 | 20 829 | |||||
| Srv | 307 | 9 283 | 19 183 | 3 585 | 43 270 | 27 952 | 510 | 4 508 | |||||
| Inv | 12 848 | -15 534 | 3 983 | 24 620 | |||||||||
| Cap | 4 095 | 9 099 | 30 223 | ||||||||||
| Lab | 785 | 10 249 | 40 420 | ||||||||||
| Fam | 43 416 | 51 453 | 12 054 | ||||||||||
| Gov | 10 634 | 6 903 | 8 621 | 4 900 | 645 | ||||||||
| ICMS | 226 | 7 321 | 1 075 | ||||||||||
| Out | 93 | 2 760 | 2 047 | ||||||||||
| Im | 22 | 617 | 6 | ||||||||||
| RoW | 866 | 6 175 | 50 | ||||||||||
| Rob | 1 683 | 45 238 | 3 810 | ||||||||||
| Source: Paiva and Neto (2021). Own elaboration. |
| Agents | Agr | Ind | Srv | Inv | Cap | L1 | L2 | L3 | F1 | F2 | F3 | Gov | ICMS | Out | Im | RoW | RoB |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Agr | 332 | 2 650 | 416 | 879 | 1 585 | 1 369 | 1 246 | 6 | 272 | 773 | |||||||
| Ind | 1 120 | 25 387 | 11 369 | 21 452 | 11 520 | 10 485 | 13 968 | 322 | 2 326 | 20 829 | |||||||
| Srv | 307 | 9 283 | 19 183 | 3 585 | 12 655 | 13 037 | 17 578 | 27 952 | 510 | 4 508 | |||||||
| Inv | 650 | 1 892 | 10 306 | -15 534 | 3 983 | 24 620 | |||||||||||
| Cap | 4 095 | 9 099 | 30 223 | ||||||||||||||
| L1 | 681 | 6 347 | 9 908 | ||||||||||||||
| L2 | 88 | 3 143 | 12 092 | ||||||||||||||
| L3 | 16 | 759 | 18 420 | ||||||||||||||
| F1 | 2 224 | 16 936 | 7 295 | ||||||||||||||
| F2 | 7 383 | 15 323 | 4 341 | ||||||||||||||
| F3 | 33 809 | 19 194 | 419 | ||||||||||||||
| Gov | 46 | 263 | 10 324 | 6 903 | 8 621 | 4 900 | 645 | ||||||||||
| ICMS | 226 | 7 321 | 1 075 | ||||||||||||||
| Out | 93 | 2 760 | 2 047 | ||||||||||||||
| Im | 22 | 617 | 6 | ||||||||||||||
| RoW | 866 | 6 175 | 50 | ||||||||||||||
| RoB | 1 683 | 45 238 | 3 810 | ||||||||||||||
| Source: Own elaboration. |
5.2 Appendix 2: Parameters From The Calibration
| Parameters | AGR | IND | SRV |
|---|---|---|---|
| Elasticities | |||
| K | 0.8392 | 0.4703 | 0.4278 |
| L1 | 0.1396 | 0.3280 | 0.1403 |
| L2 | 0.0180 | 0.1624 | 0.1712 |
| L3 | 0.0032 | 0.0392 | 0.2607 |
| TFP | |||
| b | 1.6695 | 3.1352 | 3.6378 |
| Source: Own elaboration. | |||
| Sector | AGR | IND | SRV |
|---|---|---|---|
| ax | |||
| AGR | 0.0500 | 0.1687 | 0.0462 |
| IND | 0.0468 | 0.4480 | 0.1638 |
| SRV | 0.0041 | 0.1119 | 0.1888 |
| ay | |||
| Zi | 0.7351 | 0.3414 | 0.6952 |
| Source: Own elaboration. | |||
| 1 Reads ‘from columm to line.’ | |||
| AGR | IND | SRV | |
|---|---|---|---|
| Qs | 0.1251 | 0.1719 | 0.0526 |
| Xc | 0.3204 | 0.2037 | 0.2352 |
| Xw | 0.5545 | 0.6244 | 0.7122 |
| TFP | 4.0564 | 3.3121 | 7.0392 |
| Source: Own elaboration. |
| AGR | IND | SRV | |
|---|---|---|---|
| Qs | 0.5300 | 0.4483 | 0.8236 |
| Mc | 0.2708 | 0.3923 | 0.1563 |
| Mw | 0.1992 | 0.1594 | 0.0201 |
| TFP | 2.5459 | 2.6636 | 1.4224 |
| Source: Own elaboration. |
| AGR | IND | SRV | |
|---|---|---|---|
| Elasticities | 0.0339234 | 0.827753 | 0.138324 |
| TFP | 1.72442 | ||
| Source: Own elaboration. |
| Products | F1 | F2 | F3 |
|---|---|---|---|
| Elasticities | |||
| AGR | 0.0615 | 0.0550 | 0.0380 |
| IND | 0.4472 | 0.4212 | 0.4259 |
| SRV | 0.4913 | 0.5238 | 0.5361 |
| TFP | |||
| a | 2.4123 | 2.3690 | 2.2751 |
| Savings Share | |||
| ss | 0.0246 | 0.0706 | 0.2391 |
| Source: Own elaboration. | |||
| AGR | IND | SRV | |
|---|---|---|---|
| Production.Tax | 0.0340 | 0.1292 | 0.0106 |
| Other.Tax | 0.0139 | 0.0487 | 0.0202 |
| Import.Tax | 0.0251 | 0.0999 | 0.1272 |
| Consumption | 0.0002 | 0.0114 | 0.9884 |
| Source: Own elaboration. |
5.3 Appendix 3: Visualization Results
Figure 5.1: Price of the Labor Factors. Own Elaboration
Figure 5.2: Price of the Capital-Factor for Sectors. Own Elaboration
Figure 5.3: Price of the Aggregated-Factor for Sectors. Own Elaboration
Figure 5.4: Price of the Gross Domestic Product for Sectors. Own Elaboration
Figure 5.5: Prices of the Exports. Own Elaboration
Figure 5.6: Prices of the Domestic Market. Own Elaboration
Figure 5.7: Prices of the Imports. Own Elaboration
Figure 5.8: Prices of the Investment. Own Elaboration
Figure 5.9: Investment Allocation Coefficients. Own Elaboration
Figure 5.10: Prices of the Internal Supply. Own Elaboration
5.4 Appendix 4: Tables Results
| Factor | Factor 0 AGR | Factor 0 IND | Factor 0 SRV | pf0 AGR | pf0 IND | pf0 SRV |
|---|---|---|---|---|---|---|
| K | 0.0329 | 0.0408 | 0.0303 | -0.0157 | -0.0225 | -0.0105 |
| F1 | -0.0451 | -0.0444 | -0.0425 | 0.0647 | 0.0647 | 0.0647 |
| F2 | 0.0363 | 0.0370 | 0.0391 | -0.0189 | -0.0189 | -0.0189 |
| F3 | 0.0316 | 0.0323 | 0.0344 | -0.0144 | -0.0144 | -0.0144 |
| Source: Own elaboration. |
| Scenarios | Sg | Sc | Sw | III | mgW | mgC | pIII | US |
|---|---|---|---|---|---|---|---|---|
| Counterfactual | 0.0277 | 0.0247 | 0.0247 | 0.0210 | 0.0001 | 0.0011 | 0.0016 | 0.0167 |
| Lockdown | 0.0015 | 0.0247 | 0.0247 | 0.0239 | -0.0027 | -0.0078 | -0.0054 | 0.0162 |
| Source: Own elaboration. |
| Variables | AGR 0 | IND 0 | SRV 0 | AGR 1 | IND 1 | SRV 1 |
|---|---|---|---|---|---|---|
| Y | 0.0217 | 0.0111 | 0.0223 | 0.0401 | 0.0240 | 0.0048 |
| Z | 0.0217 | 0.0111 | 0.0223 | 0.0401 | 0.0240 | 0.0048 |
| Qs | 0.0202 | 0.0129 | 0.0220 | 0.0361 | 0.0236 | 0.0057 |
| Xc | 0.0310 | 0.0075 | 0.0288 | 0.0560 | 0.0233 | -0.0248 |
| Xw | 0.0289 | 0.0054 | 0.0267 | 0.0670 | 0.0339 | -0.0146 |
| Mc | 0.0094 | 0.0184 | 0.0152 | 0.0165 | 0.0240 | 0.0373 |
| Mw | 0.0119 | 0.0208 | 0.0176 | -0.0047 | 0.0027 | 0.0156 |
| II | 0.0176 | 0.0113 | 0.0258 | 0.0325 | 0.0097 | 0.0283 |
| KK | 0.0329 | 0.0408 | 0.0303 | 0.0397 | 0.0400 | 0.0316 |
| shrII | -0.0033 | -0.0095 | 0.0047 | 0.0084 | -0.0138 | 0.0044 |
| Ti | 0.0182 | 0.0141 | 0.0202 | 0.0242 | 0.0163 | 0.0119 |
| To | 0.0182 | 0.0141 | 0.0202 | 0.0242 | 0.0163 | 0.0119 |
| Tm | 0.0120 | 0.0209 | 0.0177 | -0.0073 | 0.0000 | 0.0129 |
| Gf | 0.0305 | 0.0253 | 0.0299 | 0.0154 | 0.0087 | -0.0054 |
| Xinv | 0.0254 | 0.0202 | 0.0247 | 0.0325 | 0.0256 | 0.0113 |
| Qf | 0.0173 | 0.0159 | 0.0218 | 0.0287 | 0.0226 | 0.0071 |
| pxW | 0.0001 | 0.0001 | 0.0001 | -0.0027 | -0.0027 | -0.0027 |
| pmW | 0.0001 | 0.0001 | 0.0001 | -0.0027 | -0.0027 | -0.0027 |
| pxC | 0.0011 | 0.0011 | 0.0011 | -0.0078 | -0.0078 | -0.0078 |
| pmC | 0.0011 | 0.0011 | 0.0011 | -0.0078 | -0.0078 | -0.0078 |
| py | -0.0049 | 0.0062 | -0.0028 | -0.0191 | -0.0146 | 0.0093 |
| pz | -0.0034 | 0.0029 | -0.0020 | -0.0153 | -0.0075 | 0.0071 |
| pqs | -0.0042 | 0.0038 | -0.0022 | -0.0172 | -0.0076 | 0.0076 |
| pqf | -0.0027 | 0.0024 | -0.0021 | -0.0137 | -0.0071 | 0.0069 |
| Source: Own elaboration. |
| Scenarios | F1 | F2 | F3 |
|---|---|---|---|
| Counterfactual | |||
| shrK0 | -0.0739 | 0.0055 | 0.0014 |
| Ss0 | 0.0035 | 0.0236 | 0.0200 |
| Tdh0 | 0.0137 | 0.0208 | 0.0198 |
| trh0 | -0.0412 | 0.0365 | 0.0325 |
| UU0 | 0.0037 | 0.0239 | 0.0202 |
| Lockdown | |||
| shrK1 | 0.0728 | -0.0119 | -0.0079 |
| Ss1 | 0.0320 | 0.0043 | 0.0083 |
| Tdh1 | 0.0274 | 0.0095 | 0.0086 |
| trh1 | 0.0430 | -0.0352 | -0.0315 |
| UU1 | 0.0326 | 0.0045 | 0.0082 |
| Source: Own elaboration. | |||
| Index | F1 | F2 | F3 |
|---|---|---|---|
| Counterfactual | |||
| Laspeyres | -0.0019 | -0.0040 | -0.0034 |
| Paasche | -0.0037 | -0.0058 | -0.0052 |
| Fisher | -0.0028 | -0.0049 | -1.0043 |
| Lockdown | |||
| Laspeyres | -0.0021 | 0.0073 | 0.0123 |
| Paasche | -0.0227 | -0.0133 | -0.0075 |
| Fisher | -0.0124 | -0.0031 | 0.0024 |
| Source: Own elaboration. | |||
| Scenarios | F1 | F2 | F3 |
|---|---|---|---|
| Counterfactual | 2.0060 | -0.2809 | -0.2356 |
| Lockdown | -0.4421 | 0.9854 | 0.3059 |
| Source: Own elaboration. |
| Index | AGR | IND | SRV |
|---|---|---|---|
| Counterfactual | |||
| Laspeyres | 0.0954 | 0.5268 | 0.1280 |
| Paasche | -0.1710 | -1.0991 | -1.1348 |
| Fisher | -0.0471 | 0.1728 | -0.0121 |
| Lockdown | |||
| Laspeyres | -0.2836 | -0.0346 | 0.4783 |
| Paasche | -0.3188 | -0.3411 | -0.0202 |
| Fisher | -0.3014 | -0.2024 | 0.2035 |
| Source: Own elaboration. | |||
CAEN-UFC, Brazil. Contact by heitorgabriel.sm@gmail.com↩︎
Department of Economics in CAEN-UFC, Brazil. Contact by cmp@caen.ufc.br↩︎
Computable General Equilibrium↩︎
A wide-sector model with linearized equations of interaction among sectors, highly inspired in the Input-output matrix. Also called as Australian-tradition of CGE models. For more details, see Dixon, Koopman, and Rimmer (2013).↩︎
In the division by schooling for labeling families, \(L^1\) was considered people with incomplete high school to no education. For \(L^2\), complete high school, and for \(L^3\), complete or incomplete college education.↩︎
Constant Elasticity of Transformation↩︎
Constant Elasticity of Substitution↩︎
Social Accounting Matrix↩︎
Total Productivity of the Factors↩︎
We can’t find the optimal solution of an Leontief-type by differential coefficients. So, we apply the Equations (2.6) and (2.7) in zero-profit condition of perfect competitive market (\(\Pi_{i,t} =0\)) in Equation (2.4).↩︎
\(\phi = \frac{\psi + 1}{\psi}\) and \(\psi\) is the elasticity of transformation, was been considered equal to 1.5.↩︎
\(\eta = \frac{\sigma - 1}{\sigma}\) and \(\sigma\) is the elasticity of substitution, was been considered equal to 2.↩︎
Known as PNAD-C, in portuguese: Pesquisa Nacional por Amostra de Domicílios Contínua, from Brazilian Institute of Geography and Statistics (IBGE).↩︎
Known as POF, in portuguese: Pesquisa de Orçamentos Familiares, from Brazilian Institute of Geography and Statistics (IBGE).↩︎
Brazilian Public Sector Accounting and Tax Information System. Annual Balance of the Financial Statements Applied to the Public Sector, for Ceará, 2013.↩︎
Known as DIRPF, in portuguese: Grandes Números das Declarações do Imposto de Renda das Pessoas Físicas.↩︎
Rearranging the Equations (2.38) and (2.40), we see the relationship between savings and good-of-investment: \[ X_{i,t}^{inv} = \lambda_i \left( \frac{\sum_l S^p_{l,t} + S^g_t + S^{br}_t + S^{w}_t}{p^{Q^f}_{i,t}} \right) \] and rearranging the Equations (2.38), (2.41), (2.43), and (2.42) we see the relationship between savings and capital-factor: \[ F_{h=K,i,t+1} = ror \left[ (1+dep) KK_{i, t} + \left( \frac{(p^{F}_{h=K,i,t})^{\zeta} F_{h=K,i,t}}{ \sum_{j} (p^{F}_{h=K,j,t})^{\zeta} F_{h=K,j,t} } \right) \left( \frac{ \sum_l S^p_{l,t} + S^g_t + S^{br}_t + S^{w}_t }{p^{III}_t} \right) \right] \]↩︎
The Laspeyres perceived price index is: \[IP_{l} = \left( \frac{\sum_i p^{Q^f}_{i, t= 20} C^f_{l, i,t=1}}{\sum_i p^{Q^f}_{i, t= 1} C^f_{l, i,t=1}} \right) -1 \] And the Laspeyres remuneration index is: \[IR_{l} = \left( \frac{\sum_h \sum_i p^F_{h, i, t= 20} FF_{h, l, t=1}}{\sum_h \sum_i p^F_{h, i, t= 1} FF_{h, l, t=1}} \right) -1\] The reason to consider the Laspeyres index is to purge the quantity growth effect of the \(pop_l\) under endowments and the government transfers in the utility measure. In the model, the single representative family is receiving more transfers, paying more tax, and consuming more, as example. This means that the population is receiving, paying, and consuming a larger amount as it grows, not that every person in the population is receiving more net transfers or consuming more.↩︎
See Barufi, Haddad, and Nijkamp (2017) for more details and empirical finds to Brazil’s regions.↩︎
See Barros, Franco, and Mendonça (2007) for more details and empirical finds to Brazil.↩︎
\[IC_{i} = \left( \frac{\sum_h p^F_{h, i, t= 20} F_{h, i, t=1}}{\sum_h p^F_{h, i, t= 1} F_{h, i, t=1}} \right)\]↩︎
Gross Domestic Product, the total of remunerations: \(\sum_i \sum_h p^F_{h,i,t}F_{h,i,t}\). The real-value is \(\sum_i \sum_h p^F_{h,i,t=1}F_{h,i,t}\).↩︎
The definition used by IBGE: the group of people of appropriate age who are not in the traditional workforce (employed or looking for a job), but who had the potential to become the labor force. Composed of: 1) people who looked for work but were not immediately available to work; 2) people who did not look for work but would like to have a job and were available to work, including discouraged people: people outside the workforce who were available to take a job immediately but did not take action to get a job. We focus on the potential workforce because in the Lockdown the employment seeker cannot look for a job personally.↩︎
Available in the page of the IBGE.↩︎
As of the writing date, there was no publication of the statistics for the states. Collected from the IBGE: PNAD-COVID.↩︎