Appendix 1
In this appendix, we solve the longrun equilibrium of the model presented in Sect. 3. We also derive the effect of export taxes on real factor remuneration in the short, medium and long terms.
The longrun equilibrium
Let Υ denote the degree of comparative advantage of the secondary sector and π denote the international price of the agricultural good relative to the manufacturing good, i.e., the terms of trade:
$$\varUpsilon = \frac{M}{A}\frac{{L^{1  \beta } K^{\beta  \alpha } }}{{T^{1  \alpha } }},$$
$$\pi = \frac{{p_{\text{a}} }}{{p_{\text{m}} }}.$$
Moreover, let
$$\lambda = \frac{{L_{\text{m}} }}{L},$$
$$\kappa = \frac{{K_{\text{m}} }}{K}.$$
That is, λ is the share of workers employed in the manufacturing sector and κ is the share of units of capital employed in that sector. We seek to characterize the steadystate ratios κ and λ as functions of the technological and preference parameters, factor endowments and exogenous variables: terms of trade π and the ad valorem tax rate on exports τ.
Since land is used only in the primary sector, its outside opportunity cost is zero. Given our technological assumptions, the marginal product of the first infinitesimal unit of capital employed in the primary sector is infinite; therefore κ < 1, i.e., the primary sector always employs some capital.
The demand for capital in the primary sector solves the following firstorder condition for profit optimization of the representative firm in the sector:
$$\alpha \left( {\frac{1}{1  \kappa }} \right)^{1  \alpha } p_{\text{a}}^{d} = \frac{{r_{\text{a}} K}}{{K^{\alpha } T^{1  \alpha } A}},$$
(1)
where \(p_{\text{a}}^{d}\) is the domestic price of the agricultural good and r
_{a} is the return to capital in the primary sector. Similarly, the demand for land in the primary sector, given the land rental rate, q, is given by:
$$\left( {1  \alpha } \right)\left( {1  \kappa } \right)^{\alpha } p_{\text{a}}^{d} = \frac{qT}{{K^{\alpha } T^{1  \alpha } A}}.$$
(2)
If some capital is also employed in the secondary sector, then the demand for capital in the secondary sector satisfies:
$$\beta \left( {\frac{\lambda }{\kappa }} \right)^{1  \beta } \varUpsilon p_{\text{m}}^{d} = \frac{{r_{\text{m}} K}}{{K^{\alpha } T^{1  \alpha } A}},$$
(3)
where \(p_{\text{m}}^{d}\) is the domestic price of the manufactured good and r
_{
m
} is the return to capital in the secondary sector. The demand for labor in the sector is given by:
$$(1  \beta )\left( {\frac{\kappa }{\lambda }} \right)^{\beta } \varUpsilon p_{\text{m}}^{d} = \frac{Lw}{{K^{\alpha } T^{1  \alpha } A}},$$
(4)
where w is the wage rate.
The Cobb–Douglas utility function that we use to represent the preferences of consumers implies that the share of each good in total expenditure is constant. Let ϕ
_{a}, ϕ
_{m} be the shares of the agricultural and manufactured goods, respectively. Naturally, 1 − ϕ
_{a} − ϕ
_{m} is the share of the service good. The aggregate demand for each good (c
_{a}, c
_{m} and c
_{s}) satisfies the following maximizing condition:
$$\frac{{c_{\text{m}} p_{\text{m}}^{d} }}{{\phi_{\text{m}} }} = \frac{{c_{\text{a}} p_{\text{a}}^{d} }}{{\phi_{\text{a}} }} = \frac{{\left( {1  \lambda } \right)Lw}}{{1  \phi_{\text{a}}  \phi_{\text{m}} }},$$
(5)
where we have already imposed the market equilibrium condition in the nontradable sector:
$$c_{\text{s}} = \left( {1  \lambda } \right)Lw.$$
(6)
In an open economy without international capital markets, trade is balanced in each period. Therefore,
$$\kappa^{\beta } \lambda^{1  \beta } \varUpsilon + \pi \left( {1  \kappa } \right)^{\alpha } = \frac{{c_{\text{m}} + \pi c_{\text{a}} }}{{K^{\alpha } T^{1  \alpha } A}}$$
(7)
If the country is trading internationally, the domestic price of the agricultural good is \(p_{\text{a}}^{d} \,=\, \left( { 1  \tau } \right)p_{\text{a}}\). Due to the Lerner symmetry theorem, we assume that the import tax is zero. Therefore, we have \(p_{\text{m}}^{d} = p_{\text{m}}\).
The following subsections solve the different types of steadystate equilibria that might exist. First, we study the autarky equilibrium. We derive the shares λ
_{aut} and κ
_{aut} and the autarky relative domestic price p
_{aut}. This price has to be such that π(1 − τ) ≤ p
_{aut} ≤ π: it is not profitable to export or import goods. Second, we study the equilibrium under specialization in the production of primary goods. We derive the input prices w and r and then obtain the marginal cost of producing the manufactured good. This marginal cost has to be higher than the international price of the manufactured good. Third, we study the equilibrium under diversification and trade. We derive the shares λ and κ and the exports of primary goods. All of these three variables have to be positive in equilibrium. Finally, we derive the equilibrium under reversal of the pattern of trade. We proceed in the same way as in the case of diversification and trade, but now we set τ = 0 and we require the exports of the manufactured good to be positive.
Autarky equilibrium
We now solve the model for autarky by imposing that the consumed quantities equal the produced quantities for each of the three goods:
$$\begin{aligned} \frac{{c_{\text{m}} }}{{K^{\alpha } T^{1  \alpha } A}} \,= \kappa^{\beta } \lambda^{1  \beta } \varUpsilon , \hfill \\ \frac{{c_{\text{a}} }}{{K^{\alpha } T^{1  \alpha } A}} = \left( {1  \kappa } \right)^{\alpha } . \hfill \\ \end{aligned}$$
(8)
Using 1, 2, 4, 5, 6 and 8, we derive the following values for λ
_{aut}, κ
_{aut} and the autarky relative domestic price p
_{aut}:
$$\begin{aligned} \kappa_{\text{aut}} = & \frac{{\phi_{\text{m}} \beta }}{{\phi_{\text{m}} \beta + \phi_{\text{a}} \alpha }}, \\ \lambda_{\text{aut}} = & \frac{{\phi_{\text{m}} (1  \beta )}}{{\phi_{\text{m}} (1  \beta ) + \left( {1  \phi_{\text{a}}  \phi_{\text{m}} } \right)}}, \\ p_{\text{aut}} = & \frac{{\beta^{\beta } }}{{\alpha^{\alpha } }}\left( {\phi_{\text{m}} \beta + \phi_{\text{a}} \alpha } \right)^{\alpha  \beta } \phi_{\text{a}}^{1  \alpha } \left( {\frac{(1  \beta )}{{\left( {\left( {1  \phi_{\text{a}}  \beta \phi_{\text{m}} } \right)} \right)}}} \right)^{1  \beta } \varUpsilon . \\ \end{aligned}$$
(9)
For autarky to be a steadystate equilibrium, p
_{aut} has to satisfy
$$\pi \left( {1  \tau } \right) \le p_{\text{aut}} \le \pi .$$
Otherwise, there are arbitrage opportunities for exporting and importing goods.
Equilibrium under specialization
A specialized economy imports the secondary good and produces and exports the agricultural good. The economy is specialized in the primary sector if there is no capital or labor employed in the secondary sector; therefore: κ = λ = 0. For this to be an equilibrium, the wages and capital rental rate paid in the other sectors of the economy must be greater than what can be profitably paid by the secondary sector.
$$mc_{\text{m}} = \left[ {\left[ {\frac{1  \beta }{\beta }} \right]^{\beta } + \left[ {\frac{\beta }{1  \beta }} \right]^{1  \beta } } \right]r^{\beta } w^{1  \beta } M^{  1} \ge p_{\text{m}}^{d} .$$
(10)
Using 1, 5, 7 and 10, setting λ = κ = 0, \(p_{\text{m}}^{d} = p_{\text{m}}\) and \(p_{\text{a}}^{d} = (1  \tau )p_{\text{a}}\), we obtain that specialization is an equilibrium if
$$\varUpsilon \le \left[ {\left[ {\frac{1  \beta }{\beta }} \right]^{\beta } + \left[ {\frac{\beta }{1  \beta }} \right]^{1  \beta } } \right]\alpha^{\beta } \left[ {\frac{{\left( {1  \phi_{\text{a}}  \phi_{\text{m}} } \right)}}{{\left( {\phi_{\text{m}} \left( {1  \tau } \right) + \phi_{\text{a}} } \right)}}} \right]^{1  \beta } \left( {1  \tau } \right)\pi .$$
Otherwise, there will be diversification. Naturally, ceteris paribus, for favorable enough terms of trade, the economy will specialize in the production of primary goods.
Diversification and trade
Using 1,2, 4,5, 7 and imposing \(p_{\text{m}}^{d} = p_{\text{m}}\) and \(p_{\text{a}}^{d} = (1  \tau )p_{\text{a}}\), we solve for the endogenous variables κ and λ.
From the conditions 1 and 2, we obtain λ as an increasing function of κ:
$$\lambda = \left[ {\frac{\alpha }{\beta }\left( {\frac{1}{1  \kappa }} \right)^{1  \alpha } \left( {1  \tau } \right)\frac{\pi }{\varUpsilon }} \right]^{{\frac{1}{1  \beta }}} \kappa .$$
From 4, 5 and 7 we deduce:
$$\frac{\lambda }{{\left( {1  \lambda } \right)}} + \left( {\frac{\pi }{\varUpsilon }} \right)^{{\frac{\beta }{1  \beta }}} \frac{{\left( {1  \kappa } \right)^{{\frac{\alpha  \beta }{1  \beta }}} }}{{\left( {1  \lambda } \right)}}\left[ {\frac{\alpha }{\beta }\left( {1  \tau } \right)} \right]^{{\frac{\beta }{1  \beta }}} = \frac{{\phi_{\text{m}} + \frac{{\phi_{\text{a}} }}{{\left( {1  \tau } \right)}}}}{{1  \phi_{\text{a}}  \phi_{\text{m}} }}(1  \beta ).$$
(11)
If β > α, then the lefthand side of the former expression is increasing in κ, whereas the righthand side is constant. Thus, there is at most one value of κ that satisfies this expression; λ*and κ* denote the shares that satisfy Eq. 11.
Proposition 1
In the diversification and trade equilibrium, an improvement in the terms of trade or a reduction in the export tax will lead to lower values of λ* and κ*.
The solution is a steadystate equilibrium if the country exports the primary good and, at the same time, produces a positive amount of the manufactured good. The conditions for diversification were explained in Sect. 7.1.2.
Positive exports of the agricultural good implies:
$$\frac{{c_{\text{a}} }}{{K^{\alpha } T^{1  \alpha } A}} \le \left( {1  \kappa } \right)^{\alpha } .$$
In terms of the exogenous variables, this condition becomes:
$$\frac{{\phi_{\text{a}} (1  \beta )}}{{\left( {1  \phi_{\text{a}}  \phi_{\text{m}} } \right)\left( {1  \tau } \right)}}\frac{\varUpsilon }{\pi } \le \frac{{\left( {1  \kappa^{ * } } \right)^{\alpha } }}{{\left( {1  \lambda^{ * } } \right)}}\left( {\frac{{\lambda^{ * } }}{{\kappa^{ * } }}} \right)^{\beta } .$$
Reversal of the pattern of trade
Using the same approach as in Sect. 7.1.3 but setting τ = 0, we solve for the endogenous variables. In this case, the solution is a steadystate equilibrium if the exports of the manufacturing good are positive, i.e., if c
_{a}(K
^{α}
T
^{1−α}
A)^{−1} > (1 − κ)^{α}. In terms of the exogenous variables, this condition becomes:
$$\frac{{\phi_{\text{a}} (1  \beta )}}{{\left( {1  \phi_{\text{a}}  \phi_{\text{m}} } \right)}}\frac{\varUpsilon }{\pi } > \frac{{\left( {1  \kappa^{ * } } \right)^{\alpha } }}{{\left( {1  \lambda^{ * } } \right)}}\left( {\frac{{\lambda^{ * } }}{{\kappa^{ * } }}} \right)^{\beta } .$$
Graphical representation
Given a set of parameters Υ, ϕ
_{a}, ϕ
_{m}, α and β with β > α ,0 < ϕ
_{a}, 0 < ϕ
_{m} and ϕ
_{m} + ϕ
_{a} < 1, we can map each pair (π, τ) to one of the steady states above. Assuming β > α, Fig. 1 in Sect. 3.1 shows the different regions in the (π, τ) space. The frontier between the reversal of trade and autarky regions is given by the autarky price equation:
$$p_{\text{aut}} = \frac{{\beta^{\beta } }}{{\alpha^{\alpha } }}\left( {\phi_{\text{m}} \beta + \phi_{\text{a}} \alpha } \right)^{\alpha  \beta } \phi_{\text{a}}^{1  \alpha } \left( {\frac{(1  \beta )}{{\left( {\left( {1  \phi_{\text{a}}  \beta \phi_{\text{m}} } \right)} \right)}}} \right)^{1  \beta } \varUpsilon .$$
The autarky region and the diversification and trade region are delimited by the level of τ that makes exports equal to zero:
$$\tau = 1  \frac{{p_{\text{aut}} }}{\pi }.$$
The specialization and diversification regions are separated by the points at which the marginal firm is indifferent to producing the first unit of the manufactured good or not:
$$\pi = \frac{{\left[ {\frac{{\left( {\phi_{\text{m}} \left( {1  \tau } \right) + \phi_{\text{a}} } \right)}}{{\left( {1  \phi_{\text{a}}  \phi_{\text{m}} } \right)}}} \right]^{1  \beta } \varUpsilon }}{{\left[ {\left[ {\frac{1  \beta }{\beta }} \right]^{\beta } + \left[ {\frac{\beta }{1  \beta }} \right]^{1  \beta } } \right]\alpha^{\beta } }}\frac{1}{{\left( {1  \tau } \right)}}.$$
The political economy of protectionism
The tax rate τ affects the prices and resource allocation of the economy. As we show below, the real remuneration of some factors of production increases with τ, while the real remuneration of other factors decreases. Therefore, unless all economic agents are equally endowed, changes in the level of protectionism could have major distributional consequences. In this section, we derive the preferences of the different economic groups with regard to the policy variable τ under the main assumption that each economic agent has only one source of income. In our analysis, we consider three time horizons: the short, medium and long terms. In the short run, no reallocation of factors takes place. In the medium run, only labor is allowed to move between the secondary and the tertiary sector. In the long run, all mobile factors can be reallocated and the economy can fully adjust to its new equilibrium. Although we may assume that inputs are fixed within a sector, they are mobile across different firms within that sector. Thus, competition among different firms within a sector drives input prices to equalize the value of their marginal product.
While we do not set up a formal model of political competition that determines the evolution of the policy variable τ, we do stress the political tensions that this model generates. We use these results to articulate our discussion on the rise and fall of protectionism in Argentina and the underlying distributional conflict.
Under autarky, or when the patterns of trade are such that the country exports manufactured goods, the tax on exports of primary goods has no effect whatsoever. We might think that the government could also tax the exports of manufactured goods. However, we do not delve into those issues simply because we do not think that they will shed any light on the main topic of this paper. So, we assume that the economy is always in one of the two other possible scenarios in which τ matters: either close to a steady state in which the economy specializes in the production of primary goods, or close to a steady state in which there is diversification of production and the country exports primary goods.
The demand for protectionism
In this section, we derive the effects of protectionism and changes in the terms of trade on the real remunerations of the factors of production. We loglinearize the model to derive the effect of protectionism in the short and medium run. The loglinearization is around an initial allocation. This initial allocation might be a steadystate equilibrium, in which case it is determined by π and τ; however, the argument follows through for any initial allocation determined also by κ and λ.
The zero profit condition in the primary sector implies:
$$a_{\text{a}} = (1  \alpha )t + \alpha k_{\text{a}} ,$$
where \(a_{\text{a}} = dp_{\text{a}}^{d} /p_{\text{a}}^{d}\) is the percentage variation in the domestic price of the agricultural good, t = dq/q denotes the percentage variation in the rent of the land and k
_{a} = dr
_{a}/r
_{a} is the percentage variation in the return to capital in the primary sector. Since, in the short and medium run, capital is not mobile between sectors, it will be useful to employ different notations for the capital invested in the primary and secondary sectors. Finally, α is the share of capital in the total cost of production in the primary sector. Homotheticity of the production function implies that α is a function only of input prices. Moreover, under the assumption of a Cobb–Douglas technology, α is invariant. Similarly, in the manufacturing sector, we have:
$$m_{\text{m}} = l_{\text{m}} (1  \beta ) + k_{\text{m}} \beta ,$$
where \(m_{\text{m}} = dp_{\text{m}}^{d} /p_{\text{m}}^{d}\) is the percentage variation in the domestic price of the manufactured good, l
_{m} = dw
_{m}/w
_{m} denotes the percentage variation in wages and k
_{m} = dr
_{m}/r
_{m} is the percentage variation in the return to capital in the secondary sector. As before, β is the share of capital in the total cost of production. We continue to assume that β ≥ α; that is, we assume that capital is used more intensively in the secondary sector. Though this last assumption is not crucial, it will help us to solve some ambiguities later on. Finally, for the service sector, we have:
where n and l
_{n} = dw
_{n}/w
_{n} are the respective percentage variations in the prices of the service good and the wages paid in that sector.
Cobb–Douglas preferences ensure that the percentage increase in expenditures of the three goods are the same: a
_{a} + c_{a} = m
_{m} + c
_{m} = c
_{n} + n, where c
_{
i
} denotes the percentage variation in the consumption of good i. For any agent, the indirect utility function is given by:
$$\ln w  \sum\limits_{i = 1}^{3} \phi_{i} \ln p_{i}^{d} ,$$
where w denotes the income of the individual. Notice that we can construct an exact “price index” to account for the effect of price changes in total utility. We use this price index to deflate all the nominal variables of the economy.
$$p = a_{c} \phi_{a} + m_{c} \phi_{m} + n_{n} \left( {1  \phi_{a}  \phi_{m} } \right).$$
In our model, the government changes domestic relative prices by taxing trade. The domestic price of the agricultural good is then given by \(p_{\text{a}}^{d} = p_{\text{a}} \left( { 1  \tau } \right)\).Taking logs and denoting t
_{a} = dτ
_{a}/(1 − τ
_{a}), we obtain:
$$a_{\text{a}} = a_{i}  t_{\text{a}} .$$
For the manufactured good, its domestic price is given by m
_{m} = m
_{
i
}. The economy budget constraint is: p
_{m}
Y
_{m} + p
_{a}
Y
_{a} = p
_{m}
C
_{m} + p
_{a}
C
_{a}. Loglinearizing this equation around the initial values, we have:
$$\left( {m_{i} + y_{m} } \right)\left( {1  \chi_{a} } \right) + \left( {a_{i} + y_{a} } \right)\chi_{a} = \left( {c_{m} + m_{i} } \right)\left( {1  \gamma_{a} } \right) + \left( {a_{i} + c_{a} } \right)\gamma_{a} ,$$
where y
_{
i
} = dY
_{
i
}/Y
_{
i
} and γ
_{a} is the share of the agricultural good in total expenditure on tradable goods, evaluated at international prices. The parameter χ
_{a} is the share of the production of the agricultural good in the total value of the domestic production of tradable goods at international prices. If the country exports the primary good, then χ
_{a} > γ
_{a}.
The variable γ
_{a} can be rewritten in terms of parameters of the model:
$$\begin{aligned} \gamma_{\text{a}} = & \frac{{p_{\text{a}} C_{\text{a}} }}{{p_{\text{m}} C_{\text{m}} + p_{\text{a}} C_{\text{a}} }} \\ = & \frac{{\phi_{\text{a}} }}{{\left( {1  \tau } \right)\phi_{\text{m}} + \phi_{\text{a}} }}. \\ \end{aligned}$$
Similarly, for χ
_{a},
$$\chi_{\text{a}} = \frac{1}{{1 + \frac{{\lambda^{1  \beta } \kappa^{\beta } }}{{\pi \left( {1  \kappa } \right)^{\alpha } }}\varUpsilon }}.$$
We now consider the adjustment of the economy to changes in international prices and taxes, assuming different speeds of adjustment for the mobile factors of production.
Short run
In the short run, all factors of production are reallocated only within the sector where they were previously employed. Given the Cobb–Douglas production function and the zero profit condition, we know that the flow of earnings accruing to landlords is equal to a fraction of the value of the total production of the primary sector. Given that land is not reallocated, the percentage increase in the rental rate for land is equal to:
$$t = a_{\text{a}} + y_{\text{a}} .$$
Since, in the short run, the allocation of capital in the primary sector does not change, the following capital rent equation holds:
$$k_{\text{a}} = a_{\text{a}} + y_{\text{a}} .$$
Similarly, in the manufacturing sector, the following capital rent and wage equations hold:
$$k_{\text{m}} = m_{\text{m}} + y_{\text{m}} ,$$
$$l_{\text{m}} = m_{\text{m}} + y_{\text{m}} .$$
Finally, total expenditure on services has to equal the total wages paid in the sector. Noting that the production of services has to equal consumption, we find that:
$$l_{\text{n}} = c_{\text{n}} + n_{\text{n}} .$$
Let us now consider the effects of an increase in the international price of the primary good. Given that there is no factor reallocation, the output of the three goods remains constant. Without government intervention, the domestic price of the primary good and the return to the factors employed in the primary sector increase in proportion to the increase in the terms of trade. Since the agents owning those resources are wealthier, they increase their demand for services, which drives up wages in the tertiary sector. Workers in the service sector enjoy an increase in their nominal wages that is proportional to the economy’s degree of specialization: χ
_{a}. Finally, the factors employed in the manufacturing sector do not receive any increase in their remunerations. The consumer price index rises, since the prices of both the primary and the tertiary goods increase. Proposition 2 summarizes these results.
Proposition 2
In the short run, an increase in the international price of the agricultural good (i.e., an improvement in the terms of trade) raises the real remuneration received by landowners, capitalists in the primary sector and service workers. However, it reduces the real remuneration of workers and capitalists in the manufacturing sector.
Notice that the real effects of an increase in the international price of the agricultural good are identical to those of a decrease in the international price of the manufactured good. Agents may demand policies that will protect them from changes in international prices. Proposition 3 deals with the effects of taxes on exports.
Proposition 3
In the short run, protectionist policies reduce the real remuneration of landowners, capitalists in the primary sector and service workers. If ϕ_{a} > 0, protectionist policies will raise the real remuneration of workers and capitalists in the secondary sector.
Medium run
In the medium run, labor is allowed to move across industries, so wages equalize across sectors. Loglinearizing the market clearing condition for labor, we have:
$$\lambda \left( {m_{\text{m}} + y_{\text{m}} } \right) + (1  \lambda )\left( {n_{\text{n}} + y_{\text{n}} } \right) = l.$$
This equation and the condition that l
_{m} = l
_{n} = l replace the two equations of wage determination obtained for the case of the shortrun equilibrium. Now, the shortrun effects of an improvement in the terms of trade include an increase in the production of services and a decrease in the total production of manufactures. Since there is no factor adjustment in the primary sector, the remuneration of capital and land increase by the same proportion as the terms of trade. This generates an upward shift in the demand for services which is met both by an increase in its equilibrium price and by a displacement of labor from the secondary to the tertiary sector. The manufacturing sector uses less labor, and the return to capital in this sector therefore falls. Overall, consumption of the primary good decreases, and consumption of the manufactured and service goods increases.
Proposition 4
In the medium run, an improvement in the terms of trade increases the real remuneration received by landowners and capitalists in the primary sector. It harms capitalists in the manufacturing sector. The real wage increases if and only if:
$$\chi_{\text{a}} (1  \lambda ) > \frac{{\phi_{\text{a}} }}{{\left( {\phi_{\text{m}} \beta + \alpha_{\text{a}} } \right)}}.$$
Higher demand for services increases wages in that sector and attracts workers from the manufacturing sector, raising wages across the economy. However, the equilibrium increase in wages may fall short of compensating the negative welfare effect of the increase in the price of the agricultural good. The more specialized the economy in the primary and tertiary sector (i.e., a higher χ
_{a} and a lower λ), the more likely is it that real wages will increase in the medium run. This is because, in such cases, the upward shift in demand for labor in the service sector is stronger. Thus, notice that, if the economy is already industrialized, an increase in the terms of trade may harm workers even in the medium run.
Proposition 5
In the medium run, protectionist policies reduce the real remuneration of landowners and capitalists in the primary sector. If ϕ
_{a} > 0, protectionist policies increase the real remuneration of capitalists in the manufacturing sector. If ϕ
_{a} > 0, workers’ welfare increases if and only if:
$$(1  \lambda )\left[ {\left( {1  \beta } \right)\chi_{\text{a}} + \beta \frac{{\phi_{\text{a}} + \phi_{\text{m}} }}{{\phi_{\text{a}} + \left( {1  \tau } \right)\phi_{\text{m}} }}} \right] \le 1.$$
Workers’ welfare increases with protectionism if the economy is beyond a given level of industrialization. In this case, workers may ally with capitalists in the secondary sector to demand protectionist policies. If τ = 0, this condition is satisfied as soon as the economy starts producing in the secondary sector. A higher tax rate implies that the condition will be met for higher λ and lower χ
_{a}. In Fig. 3, we find the pairs (π, τ), such that workers are indifferent to whether there is more or less protection, since movement in either direction will improve workers’ welfare in the medium run.
Moreover, we expect that, the more industrialized the economy is, the larger the share of workers who will be employed in the secondary sector and, hence, by virtue of Proposition 2, the larger the share of workers who will also benefit from protectionist policies in the short run.
Long run
In the long run, the economy will tend toward a new steady state. Therefore, it is useful to analyze the effects of protectionism based on the results obtained in Sect. 7.1.
A full analysis of the longrun solution for this economy is fairly complicated. Nevertheless, the two propositions set out below suffice for our purposes in this paper. We focus only on the preferences for protectionism of landlords and workers, since we assume that capitalists are concerned only with policies in the short and medium run, when their capital is sunk in one particular activity. We assume that the economy is initially in the specialization and trade or in the diversification and trade regions (i.e., it exports the primary good). Otherwise, changes in the export tax rate would not have any effect.
Proposition 6
In the long run, landlords benefit from an improvement in the terms of trade and from a reduction in export taxes.
Proposition 7
If the economy is specialized, then, in the long run, workers benefit from an improvement in the terms of trade and from a reduction in export taxes. There is always a π
^{*} high enough so that workers are better off at τ = 0.
Constantelasticityofsubstitution (CES) preferences and technology in Autarky
In this appendix, we derive a loglinearization around the autarky equilibrium for a CES economy. The results of this section are referred to in Sect. 3.4.
The production functions of the agricultural and manufactured goods are, respectively:
$$A\left( {\xi_{T} T^{{\rho_{1} }} + \xi_{{K,{\text{a}}}} K_{A}^{{\rho_{1} }} } \right)^{{1/\rho_{1} }} ,$$
$$M\left( {\xi_{L} L_{M}^{{\rho_{2} }} + \xi_{{K,{\text{m}}}} K_{M}^{{\rho_{2} }} } \right)^{{1/\rho_{2} }} ,$$
where A and M are productivity parameters, \(\xi^{\prime}_{i} s\) are share parameters and (1 − ρ
_{
i
})^{−1} for i ϵ {1, 2} are the elasticity of substitution. Notice that:
ρ
_{
i
}

Case

Elasticity of substitution


−∞

Leontieff: perfect complements

0

0

Cobb–Douglas

1

1

Perfect substitutes

∞

The production function for services is still Y
_{N} = NL
_{N}, where N is a productivity parameter.
Consumer’s preferences are represented by:
$$\left( {\phi_{1} c_{A}^{{\rho_{d} }} + \phi_{2} c_{M}^{{\rho_{d} }} + (1  \phi_{1}  \phi_{2} )c_{\text{N}}^{{\rho_{d} }} } \right)^{{1/\rho_{d} }} .$$
We are interested in the effect of the exogenous variables (\(\hat{T},\,\hat{K},\,\hat{L},\,\hat{A},\,\hat{M},\,\hat{N}\), where \(\hat{T} = dT/T\)) on the capital and labor employment share \(\hat{\lambda }\) and \(\hat{\kappa }\). The following table shows the sign of these effects as a function of the elasticity of substitutions ρ
_{1}, ρ
_{2} and ρ
_{
d
}. For instance, the first row shows that the effect of an increase in the amount of land, \(\hat{T}\), on κ (i.e., \({\text{d}}\hat{\kappa }/{\text{d}}\hat{T}\)) has the same sign as ρ
_{1} − ρ
_{
d
}, whereas the effect on λ (i.e., \({\text{d}}\hat{\lambda }/{\text{d}}\hat{T}\)) has the same sign as −(ρ
_{2} − ρ
_{
d
})(ρ
_{1} − ρ
_{
d
}). The next rows show the sign of the effect for the other five exogenous variables.

\(d\hat{\kappa }\)

\(d\hat{\lambda }\)


\(d\hat{T}\)

ρ
_{1} − ρ
_{
d
}

−(ρ
_{2} − ρ
_{
d
})(ρ
_{1} − ρ
_{
d
})

\(d\hat{K}\)

(footnote)

ρ
_{
d
} − ρ
_{2}

\(d\hat{L}\)

ρ
_{
d
} − ρ
_{2}

ρ
_{2} − ρ
_{
d
}

\(d\hat{A}\)

− ρ
_{
d
}

(ρ
_{2} − ρ
_{
d
})ρ
_{
d
}

\(d\hat{M}\)

ρ
_{
d
}

ρ
_{
d
}

\(d\hat{N}\)

(ρ
_{2} − ρ
_{
d
})ρ
_{
d
}

− ρ
_{
d
}

(footnote table) The sign of the effect of the endowment of capital on the share of capital employed in the manufacturing sector is the same as a quadratic function of ρ
_{1}, ρ
_{2} and ρ
_{
d
} that depends on parameters α, β and λ.
In Sect. 3.4.1, we analyze the effect of \(\hat{L}\) and \(\hat{A}\) (population growth and productivity growth in agriculture) on \(\hat{\kappa }\) and \(\hat{\lambda }\).
We notice that \({\text{d}}\hat{\lambda }/{\text{d}}\hat{L}\) has the same sign as ρ
_{2} − ρ
_{
d
}, i.e., population growth L will decrease λ if the elasticity of substitution in consumption is greater than in the production of manufactures (ρ
_{
d
} > ρ
_{2}). We also state that the effect on κ will be the opposite: \({\text{d}}\hat{\kappa }/{\text{d}}\hat{L}\) has the same sign as ρ
_{
d
} − ρ
_{2}.
Similarly, in the table we read that \({\text{d}}\hat{\lambda }/{\text{d}}\hat{A}\) has the same sign as (ρ
_{2} − ρ
_{
d
})ρ
_{
d
}, which corresponds with what was stated in Sect. 3.4.1: Higher productivity in the agricultural sector will decrease λ if the elasticity of substitution in consumption is greater than 1 and than that in the production of manufactures (i.e., ρ
_{
d
} > 0, ρ
_{
d
} > ρ
_{2}). Similarly, \({\text{d}}\hat{\kappa }/{\text{d}}\hat{A}\) will have the same sign as −ρ
_{
d
}: the share of capital, κ, will decrease if the elasticity of substitution in consumption is greater than 1.
Appendix 2
In this appendix, we provide evidence supporting our argument that trade policies are still a key component of electoral competition and that the coalitions vote as suggested by our model. We look at the developments of 2008, when the government’s attempt to increase export duties was met with a nationwide lockout by farming associations and mass demonstrations in urban centers. We also use the results of the 2007 presidential election and the 2009 legislative elections to compare how the incumbent party—Frente para la Victoria (FPV), a political coalition including the Justicialist Party—fared before and after it publicly confronted the proagriculture coalition.
Export duties were almost nonexistent during the 1990s, but were raised after the devaluation in 2002 to capture windfall profits from exporting firms. Over time, they became a reliable source of revenue for the federal government and a handy mechanism for keeping domestic food prices in check. For example, the tax rate on oilseeds exports was raised from 0.5% in 2001 to 17.5% in 2002.
The FPV is an electoral alliance that was founded in 2003 within the Justicialist (Peronist) Party by Néstor Kirchner, who ran for President the same year. The party won the election with an unimpressive 22% of the vote. However, in the legislative election of 2005, the FPV secured a majority in both houses of Congress, and in the presidential election of 2007, it obtained 45% of the vote—22% more than its nearest rival. In 2007 the FPV candidate was Mrs. Cristina Fernández de Kirchner, the incumbent president’s wife.
Up to 2008, the FPV government had increased export duties substantially. Export duties for oilseeds reached 32% during 2007. However, the government also kept the local currency undervalued, which benefitted exporting sectors.
In March 2008, the international price of oilseeds reached record levels. The government attempted to introduce a new slidingscale taxation system for soybean and sunflower exports that would raise duties to 44% of the prices of that time. The announcement was met by a nationwide lockout by farming firms. Government officials and governmentaffiliated labor unionists denounced the lockout as being staged by big farming companies and having no popular support. However, the proagriculture movement drew support from a large share of the middleclass population that gathered in urban centers to oppose the new tax scheme. After 4 months of political struggles that eroded the government’s approval ratings and fractured the cohesion among FPV members of Congress, the proposal was defeated in the Senate, despite the fact that the FPV had a majority in both houses of Congress. The legislative elections of 2009 mirrored the major setback suffered by the government the previous year. The FPV obtained 30% of the vote, 15% less than in the previous election, and lost its majority in both houses.
During the events of 2008, the FPV took a clear stance in the distributional conflict and appealed to the protectionist sentiment of its constituents. These appeals, which had been so effective during the second half of the twentieth century, resulted in a sharp reduction in approval ratings and votes.
Under the predictions of our model, agents with vested interests in the primary sector would be less likely to vote for the FPV after the party revealed its position concerning the distributional conflict. If agents voted according to their interests and trade policy was an important component of electoral competition, we should observe a sharper fall in FPV votes in districts where the majority of voters derive their income from the primary or the tertiary sector. We test that prediction by comparing the percentages of votes that the FPV received in 2007 and 2009 in different districts, or Partidos, of the Province of Buenos Aires.
For each of the 134 districts of Buenos Aires, we obtain a measure of the ratio of the population that should support free trade. Using 2001 census data, all individuals that derive their income from activities in the primary sector and all other individuals with some secondary schooling who are not employed in the manufacturing sector are classified as “free traders”. All individuals who derive their income from the manufacturing sector and those individuals who do not have at least some secondary schooling and are not employed in the primary sector are classified as “protectionists”.
In our model, we have abstracted from skill heterogeneity among workers. However, if skilled workers are employed more intensively in the tertiary sector, then we might expect them to support free trade. Similarly, if unskilled workers are employed intensively in the secondary sector, they should support protectionism (see Galiani et al. 2010). The inclusion of educational attainment in the classification captures such heterogeneity to some extent.
Suppose that, in district d, free traders and protectionists voted for FPV with probabilities π
_{
d,f
} and π
_{
d,p
}, respectively. Then, if the proportion of free traders in district d is f
_{
d
}, the total share of votes of FPV is: v
_{
d
} ≡ π
_{
d,p
} + (π
_{
d,f
} − π
_{
d,p
})f
_{
d
}. This identity holds for any classification of free traders. Now, we model π
_{
d,f
} = π(β
_{
f
}, ɛ
_{
d
}), i.e., the probability π
_{
d,f
} is equal to a monotonic function of a parameter β
_{
f
} and a disturbance ɛ
_{
d
} that is common to π
_{
d,f
} and π
_{
d,p
}. If we assume that π(β, ɛ) = β + ɛ and that E(ɛf) = 0, we can estimate β
_{
f
} and β
_{
p
} consistently by OLS, since v
_{
d
} = β
_{
p
} + (β
_{
f
} − β
_{
p
})f
_{
d
} + ɛ
_{
d
}. The parameters β
_{
i
} can be interpreted as the expected probability that an agent of type i votes for the FPV, where the expectation is taken across districts. The estimation results are shown below:

2007 Presidential election

2009 Legislative election


Coef.

SE

95% CI

Coef.

SE

95% CI


Free traders

0.205

0.042

0.122

0.288

− 0.086

0.041

− 0.167

− 0.005

Protectionists

0.858

0.058

0.742

0.974

0.774

0.057

0.660

0.888

Notice that both protectionists and free traders were less likely to vote for the FPV in 2009 than they were in 2007. However, the drop in the probability for free traders is more pronounced. To test the null hypothesis of an identical drop for both groups, we regress the difference in FPV votes between 2009 and 2007 on the share of free traders. Notice that
$$v_{d,09}  v_{d,07} = \left( {\beta_{p,09}  \beta_{p,07} } \right) + \left( {\beta_{f,09}  \beta_{f,07}  \beta_{p,09} + \beta_{p,07} } \right)f_{d} + \varepsilon_{d} .$$
We find some evidence against the hypothesis of an identical drop in probabilities: p value 0.067.
The negative coefficient for free traders in 2009 suggests that our linear specification of π(β, ɛ) may be incorrect. Therefore, we try a different specification: π(β, σ, ɛ) = Φ(β + σɛ), where Φ is the cumulative density function of a standard normal and σ is a parameter to be estimated. If we assume that ɛ is normally distributed, we can estimate β
_{
f
},β
_{
p
} and σ by maximum likelihood. Φ(β
_{
i
}) can be interpreted as the median probability that an agent of type i will vote for the FPV, where the median is taken over the distribution of probabilities π
_{
d,i
} across districts. The estimation results are shown below:

2007 Presidential election

2009 Legislative election


Coef β
_{
i
}

SE

Φ(β
_{
i
})

Coef β
_{
i
}

SE

Φ(β
_{
i
})


Free traders

− 1.030

0.142

0.152

− 2.567

0.336

0.005

Protectionists

1.437

0.288

0.925

0.385

0.051

0.650

Sigma

0.344

0.209
 
0.438

0.099
 
Now, we obtain that free traders voted for the FPV with positive probability. Moreover, it is still true that the probability of voting for the FPV drops more in the case of free traders.
The estimated probabilities seem too extreme, i.e., our classification seems to imply a strong negative correlation between the proportion of “free traders” and FPV votes by district. It may be the case that, irrespective of their classification, individuals in more agricultural districts are less likely to vote for the FPV, independently of their source of income. In that case, f
_{
d
} and ɛ
_{
d
} are negatively correlated and our results would be unable to distinguish between individual and districtlevel political attitudes. However, even if that is the case, the fact that the aggregate source of income affects political attitudes at the district level is also consistent with the predictions of our model: service workers will support policies that increase the aggregate income of their district and boost the demand for their services.
One might suspect that these differences in political attitudes are driven exclusively by the heterogeneity in educational attainment across districts. However, if we classify individuals solely on the basis of their educational attainment, we obtain strikingly different results. The estimated probability for unskilled individuals (no secondary education) falls drastically, while the probability for skilled workers remains almost constant. Unskilled individuals employed in the primary sector were less likely to vote for the FPV in 2009, while skilled individuals employed in the secondary sector partially compensated for the loss of votes from skilled individuals employed in the tertiary sector.

2007 Presidential election

2009 Legislative election


Coef.

SE

95% CI

Coef.

SE

95% CI


Skilled

0.318

0.031

0.257

0.379

0.288

0.037

0.215

0.360

Unskilled

0.662

0.036

0.590

0.733

0.253

0.043

0.169

0.337

For comparison purposes, we present the maximum likelihood results for the specification: Φ(β + σɛ). Notice how similar the estimated probabilities are in the two specifications.

2007 Presidential election

2009 Legislative election


Coef β
_{
i
}

SE

Φ(β
_{
i
})

Coef β
_{
i
}

SE

Φ(β
_{
i
})


Skilled

− 0.491

0.087

0.312

− 0.569

0.110

0.285

Unskilled

0.435

0.099

0.668

− 0.698

0.138

0.243

Sigma

0.207

0.073
 
0.262

0.062
 
This provides support for our claim that the source of income is a key determinant of individuals’ political attitudes. In particular, individuals with vested interests in the primary sector and skilled individuals in the tertiary sector support free trade policies. Individuals whose source of income is linked to the manufacturing sector support protectionist policies. Moreover, this exercise also suggests that individuals took into account the ideological and political stance of the FPV with respect to protectionism. Those who opposed protectionism were less likely to vote for the FPV in 2009 than in 2007.