From Mercantilism to Free-Trade:
A History of Fiscal Capacity Building ∗
Didac Queralt†
September 2013
Abstract
Historically, rulers have resorted to mercantilist practices when they were short
of revenue and the fiscal capacity of the state was limited. This paper evaluates the
conditions under which mercantilist practices are adopted as a temporary solution in
a long-term path to free trade and high fiscal capacity. To this end, I evaluate the
inter-temporal dilemmas of institutional investment in fiscal capacity as a function of
political capture, the stock of fiscal capacity and the technology distance between the
protected industry and potential competitors. An endogenous switch from a mercantilist equilibrium to a free-entry equilibrium characterized by high-fiscal capacity and
competitive industry is possible only if the initial stock of fiscal capacity is sufficiently
large. On the contrary, early adoption of mercantilist policy might guide an economy
into a long-term poverty trap. The paper suggests that fiscal capacity drives industrial
productivity and, in turn, economic growth. Altogether, I propose a theory of endogenous fiscal institutions in which optimal trade policy (protection vs. free-entry) is
driven by the accumulation of fiscal capacity. The model predictions are examined using a statistical analysis of fiscal capacity building and technology adoption in Western
Europe.
∗
I gratefully acknowledge Luz Marina Arias, Neal Beck, Pablo Beramendi, Christian Dippel, Avner Greif,
Horacio Larreguy, Isabela Mares, Adam Przeworski, David Stasavage and Jeff Timmons for their comments
and suggestions as well as participants at the Political Economy Seminar at Duke University and the Political
Economy of State Capacity Conference at the Juan March Institute.
†
Juan March Institute; Center For Advanced Studies in the Social Sciences, Castelló 77, 28006 Madrid;
[email protected]
1
1
Introduction
High fiscal capacity is a dream-come-true for any political ruler whose survival depends
on public spending: major education, health or infrastructure programs are feasible only
when the state can secure a large and stable stream of revenue (Lindert, 2004). High fiscal
capacity is however a rare phenomenon in history. Urged by the need to satisfy social
demands, rulers have had to devise alternative strategies to raise revenue. Among these,
institutional investment in fiscal capacity is the most ambitious one (Acemoglu, 2005; Besley
and Persson, 2011). This strategy expands permanently the stream of tax revenue, but it
also requires patience: the returns of institutional investment are hardly realized in the shortrun. Time might be a luxury in politics. Rushed by immediate political needs, often times
rulers have resorted to less elegant revenue-generating strategies (Levi, 1988). Among these,
protectionist policy is the paradigm. The history is swamped of examples of new tariffs
being adopted or artificial monopolies being created for purely revenue purposes. This is
exemplified by the mercantilist era in Europe (Ekelund and Tollison, 1981, 1997), where
restrictions on trade and licensing were responsible for a significant increase in tax revenue.
Recognizing the pervasive use of protectionist barriers as a revenue-generating policy, this
paper evaluates how mercantilist revenue was managed. Specifically, I identify the conditions
under which mercantilist practices might inhibit or be conducive to institutional investment
in fiscal capacity.
Mercantilist Europe stands out as a case in which revenue raised through protectionist
policy was partially reinvested in institutional investment in fiscal capacity. The capacity to
tax private income steadily grew over centuries, accelerating in the late nineteenth century
(Cardoso and Lains, 2010). Mercantilist practices became gradually unnecessary across
the continent and free-trade policy was ultimately embraced (Findlay and O’Rourke, 2007;
Reinert, 2007). The British brewing industry perfectly exemplifies this transition. In early
eighteenth century, the British Parliament bargained with major brewers the adoption of
entry barriers to French wine competitors in exchange for higher tax compliance by the
2
protected industry (Nye, 2007). The deal was sealed. Excise yields rose up to 24% of British
revenue at the turn of the century. Protection, however, did not stifle investment in fiscal
capacity. Throughout the period, the government strengthened the tax administration,
specifically the capacity to monitor the brewing industry (Brewer, 1988; O’Brien, 2000).
Eventually, protection became unnecessary to guarantee effective excise collection, and entry
barriers were dropped in 1830. By that time, beer producers had become productive enough
to compete against French wine producers. The British economy endogenously switched
from a mercantilist agreement with low fiscal capacity and uncompetitive firms to a freemarket equilibrium with high fiscal capacity and a strongly competitive industry. Not only
the state reinvested a share of the mercantilist-generated revenue, but the protected industry
seized the regulatory shelter to catch-up with foreign competitors.
The British experience should not be interpreted as the norm. Mercantilist agreements
might fail to stimulate innovation or improve fiscal capacity. Bolivia exemplifies this other
outcome. Starting in 1930 the Bolivian government decided to use export quotas as a
stick-and-carrot mechanism to promote tax compliance by tin producers (Gallo, 1988). The
strategy proved successful: tax yields from the tin sector doubled in ten years. In 1942, it
accounted for 62% of total revenue (Gallo, 1988; Peres Cajı́as, 2010). Despite the massive
entry of new resources, Bolivia did not reinvest even a small share to improve its poor tax
administration. The latter remained flawed organized and tax officials ill trained. Indeed, it
still lacked the basic capacity to tax land or its products (Gallo, 1997; Whitehead, 1975). So
bad was the state of its tax administration that Bolivia ranked second from the bottom in a
fiscal capacity survey conducted by the IMF across 49 developing economies in the early 1960s
(Bahl, 1972). The stagnation of the tax administration was accompanied by the absence of
significant productivity achievements in the tin industry. Domestic producers did not take
advantage of the regulatory shelter to improve productivity. Firms rarely reinvested the
profit, and the capitalization of the mines declined over the period (Gallo, 1988; Klein, 1986).
3
Major technical challenges for the future of the industry remained unattended.1 Instead, tin
producers focused on lobbying the government to maximize export quotas (Hillman, 2002).
As a result, by the end of two mercantilist decades, Bolivia’s world share of tin production
had declined by three percent, from 22.3 to 19.4% (Ayub and Hashimoto, 1985)
The British and Bolivian examples illustrate opposite usages of mercantilist-derived revenue. In the British case, surplus revenue was funneled in fiscal capacity building; in Bolivia,
all revenue was spent in present consumption. These examples also suggest that the incentives to catch-up with foreign competitors might depend on the evolution of fiscal capacity.
This paper evaluates both decisions: investment in fiscal capacity and technology adoption.
On the one hand, it is argued that institutional investment might affect the path of innovation of the protected industry. The credibility of an eventual drop of protection drives the
decision to catch up with foreign competitors. This way, productivity growth is argued to be
endogenous to fiscal capacity building. On the other hand, institutional investment in fiscal
capacity is evaluated as a dynamic optimization problem of a ruler who seeks to maximize
long-term political survival. The inter-temporal trade-offs behind the investment decision
are conditioned by the effect of protection on current wages and public spending, the initial
stock of fiscal capacity, the extent of policy capture, and the technology differential between
the protected industry and foreign competitors. Ultimately, the theoretical model proposed
in this paper suggests that the current stock of fiscal capacity would guide investment decisions under mercantilist regimes. If the initial stock of fiscal capacity is very low to begin
with, a ruler seeking to maximize political survival might never invest in fiscal capacity.
The present forgone consumption would be too large for institutional investment to take
place. In this cases, mercantilism becomes a steady equilibrium, driving the economy into a
low fiscal capacity, low income trap. Only if the stock of fiscal capacity is intermediate at
the time mercantilist policy is adopted, mercantilist-derived revenue might be reinvested in
fiscal capacity building. Anticipating an eventual drop of entry barriers, domestic industry
1
Tin mines in Bolivia were hardly accessible and were ill communicated, what increased the production
costs relative to Malaysia, the world leader in tin production and main competitor.
4
seizes protection to catch-up with superior competitors. Eventually, protection is no longer
preferred and the economy switches from a mercantilist society equilibrium characterized
by low-fiscal capacity and uncompetitive firms to a free-trade equilibrium characterized by
high-fiscal capacity and competitive industry.
Altogether, I present a theory of endogenous fiscal and trade institutions which emphasizes the inter-temporal trade-offs of institutional investment. The theory evaluates under
what conditions rulers seeking to maximize political survival would reinvest part of the shortrun protectionist-generated revenue in institutional investment in fiscal capacity. As far as
I am aware of, this is the first paper that evaluates the interaction of short- and long-run
revenue-producing strategies (Levi, 1988).
This paper speaks to different literatures. The theoretical model suggests that institutional underinvestment does not need of political instability or ethnic conflict (Besley and
Persson, 2011). The mere short-term opportunity costs of fiscal capacity investment (i.e.,
lower levels of public good consumption) might push a ruler to underinvest in fiscal capacity
institutions even in a frictionless society. The results also speak to the infant-industry protection literature (Harrison and Rodrı́guez-Clare, 2010). Particularly, it sheds light on the
effect of tariff protection on long-term economic growth (Tena-Junguito, 2010; Irwin, 2000;
Lehmann and O’Rourke, 2011). These works find heterogenous effects of tariff protection
depending on the initial income level and political institutions. This paper qualifies this debate by conditioning the path of technology innovation to the initial stock of fiscal capacity
when mercantilist practices are implemented. Depending on this value, rulers face different
incentives to reinvest tariff revenue in fiscal capacity building, which determines, in turn, the
incentives to innovate among protected industry. Lastly, the results in this paper also speaks
to the barriers to technology adoption literature (Mokyr, 1991; Acemoglu, 2008; Parente and
Prescott, 2000; Comin and Hobijn, 2009a). These works characterize technology traps as the
result of rent-seeking by government. The theoretical model qualifies this debate by pointing
out the incentives that even a well-intended (non-corruptible) ruler might have to stick to a
5
mercantilist policy. When fiscal capacity is poor, institutional investment in fiscal capacity
does not pay off. As a direct consequence, protected industry lacks the proper system of
incentives to innovate.
The rest of the paper is organized as follows: Section 2 provides a stylized model of
mercantilism to which I refer as Protection-for-Tax-Compliance. Departing from Ekelund
and Tollison (1981), the static model characterizes the decision to exchange protection for tax
compliance as a function of the stock of fiscal capacity, relative wages and public spending.
In other words, the theoretical model derives conditions under which we should expect a
given country to adopt a mercantilist strategy in order to generate revenue in the first
place. Sections 3 evaluates the conditions under which the tax proceeds derived from a
Protectionist-for-Tax-Compliance mercantilist agreement are reinvested in expanding the
stock of fiscal capacity. Two scenarios are considered: one in which the ruler’s preferences
are fully aligned with labor’s, and another in which the ruler is open to political giving from
domestic producers. The theoretical section is followed by a (still preliminary) empirical
analysis in Section 4. In particular, I exploit within-region variation in late 19th and early
20th century Europe to evaluate an empirical implications of the model: provided the ruler
and labor are aligned and the stock of fiscal capacity is intermediate, we should expect
positive rates of technology adoption by protected firms. A brief Conclusion follows the
empirical section.
2
Set Up
Suppose there are three agents in the economy: the political ruler, the incumbent pro-
ducer and a potential entrant.
The Ruler. The ruler decides over the tax rate τ ∈ [0, 1], and entry regulation. The latter
consists of regulation allowing (banning) entry of superior competitors. Initially, the ruler
is assumed to maximize the utility of a representative wage-earner. This assumption, later
6
relaxed, suffices to prove that the lack of investment in fiscal capacity does not necessarily
result from economic elites opposing investment, but from the dynamic dilemmas faced by
labor.
Consistent with the assumption, the ruler’s indirect utility is a linear combination of
wages, ω, and per capita public spending, Ḡ = G/L, where L denotes the total number of
wage-earners. Altogether,
V = ω + ρḠ
(1)
where ρ > 1 denotes the extra-weight conferred to public spending. Public spending is pureconsumption, and is funded by tax revenue T . Taxes are raised from a sales tax. Total tax
revenue is T = τ px, with price p, and sales x. The ruler does not keep any additional share
of T for self-consumption. All tax proceeds are funneled to public spending. Accordingly,
an identity between spending G and tax revenue T is assumed (i.e., G ≡ T ).
Initially, the tax rate (and hence, tax revenue T ) is upper bounded by the fiscal capacity
endowment, τo . This parameter denotes the maximum share of private income that can
be taxed by the state. Fiscal capacity can be expanded with costly investments in tax
administration (Besley and Persson, 2011). However, as it is examined below, Protectionfor-Tax-Compliance may achieve the same levels of fiscal capacity by means of extorting
domestic industry.
Production. The economy has a fixed number L of people, who have no demand for
leisure, and offer their labor inelastically.2 All labor is hired in the final market sector. Final
output is produced under perfect competition, using labor and a flow of intermediate product
x of low (high) quality Aj ∈ {Al , Ah }
Y =
2
1
(Aj L)1−α xα
α
The structure of the economy is borrowed from Aghion and Howitt (2009).
7
(2)
and constant returns (i.e., α ∈ (0, 1)). The final good Y is the numeráire (i.e., its unit price
is one). Wage in the final sector equals the marginal productivity of labor
ω=
(1 − α)Aj 1−α xα
αLα
(3)
which is increasing in Aj , the quality of the intermediate product.
The intermediate product is produced monopolistically using a flow of final product, one
for one.3 The monopolist seeks to maximize profit
π = (1 − τ )px − x
(4)
where τ denotes the sales tax rate, which is imposed on intermediate good sales only.4
The quality of the intermediate product Aj in the final market depends on the technology
vintage operated by the intermediate sector monopolist. Initially, the intermediate market is
operated by an old firm which supplies the market with an input of low quality Al . A more
competitive firm might enter the intermediate market. In case of entry, the new entrant
supplies the final market with an intermediate product of high quality Ah > Al .5
Action Set. The ruler sets entry policy and tax policy. Entry regulation consists of costless
regulation allowing (banning) entry of the new, superior competitor. Licenses, technical
restrictions, price markups, or credit constraints are examples of this kind of restrictive
entry regulation. Tax policy consists of a sales tax τ imposed on intermediate good sales
only.
As the historical examples reviewed in the introduction suggest, entry barriers might be
3
One might suspect that the existence of a monopoly might already denote high fiscal capacity. Nonnatural monopolies are hard to enforce. However, working with intermediate monopolistic sector is just a
simplifying assumption. I prove elsewhere that the results hold if this assumption is relaxed and an oligopoly
is assumed instead (Queralt, 2013).
4
Expression (4) implicitly implies that the intermediate producer does not hire any labor, and that the
marginal cost of production is 1.
5
Results do not depend on the source of heterogeneity between intermediate producers. The results hold
if they are assumed to produce inputs of the same quality but at different marginal costs.
8
adopted conditional on higher tax abidance by the protected firms. Here, specifically, the
Protection-for-Tax-Compliance bargain consists of exchanging entry regulation for higher
tax compliance, τp > τo , where τp denotes the tax rate in the protectionist regime. If barriers
are not raised, a new competitive firm enters with certainty. The new producer, already
competitive, does not need protection from competitors. Thus, the tax rate can only be set
from within the fiscal capacity range τe ∈ [0, τo ], with subscript e standing for entry.
So far this is a one-period static game with an extensive structure:
• First, the ruler decides whether to adopt entry barriers.
• If barriers are adopted, the old producer stays in and complies with τp > τo .
• If barriers are not raised, entry takes place, intermediate good producers compete, and
abide by τe ≤ τo .
• Given entry and tax policy, tax revenue, wages and profit follow.
Commitment problems in case of protection are ruled out by assumption. Repeated interaction between government and domestic producers is expected to solve any credibility
issues.6
What follows seeks to identify the conditions under which the ruler would prefer to raise
entry barriers despite keeping the unproductive firm “in”.
2.1
Analysis
The static model is solved by backwards induction. We have to analyze the ruler and producers’ equilibrium payoffs in case of free-entry and protection separately, and then examine
when the ruler prefers to adopt entry barriers instead of free-entry.
6
VAT collection tends to be implemented monthly, and protectionist policy (such as licenses) can be
easily declined. Such flexibility, combined with the extinction payoffs upon entry (presumably, minus infinite)
should be sufficient to prevent any deviation by the incumbent producer.
9
2.1.1
Free-Entry Regime
Suppose free-entry is adopted. Then a new firm enters the intermediate market. Since
Ah > Al , the old producer instantaneously drops as a result of Schumpeterian competition.7
Given τe , the new-entrant’s problem is
max πh = (1 − τe )ph xh − xh
x
(5)
where subscript h refers to prices and production associated to input of high quality Ah .
Since the intermediate producer supplies a competitive market, price ph must equal the
marginal productivity of input xh . Taking this into account, the maximization problem
yields equilibrium demand
x∗h = Ah L(α(1 − τe ))1/(1−α)
(6)
with equilibrium price
1
α(1 − τe )
(7)
1−α
Ah (α(1 − τe ))α/(1−α)
α
(8)
p∗h =
and market-clearing wage
ωh∗ =
Given x∗h , p∗h and ωh∗ , the ruler problem reduces to
max V =
τe
ωh∗ + ρ
h
τe p∗h x∗h
L
i
(9)
s.t. τe ≤ τo
In words, the ruler’s maximization problem is constrained by the endowment of fiscal capacity
of the economy τo . Since ωh∗ is decreasing in τe , concavity is assured. The solution to the
7
Schumpeterian market competition itself may be modeled. In that case, we would allow the two intermediate producers to differ in the marginal cost of production (instead of the productivity of the intermediate
input). Results in that case are identical, as proved in Queralt (2013).
10
Lagrangian depends on whether the fiscal constraint bites.
τe∗ =
"
#



 (1 − α) 1 − ρ1
if λ = 0


 τ
o
if λ > 0
If fiscal capacity endowment is sufficiently large (i.e., the fiscal constraint is not binding),
the ruler adopts her ideal or unconstrained tax rate. For future reference, let
"
1
τ (λ = 0) ≡ (1 − α) 1 −
ρ
#
(10)
which implies that the unconstrained (or ideal) tax rate increases in the preference for public
spending, ρ > 1. Expression (10) also implies that the equilibrium tax rate has an upper
bound, τe∗ < 1 − α. That is, not even a labor agent in office with full fiscal capacity (i.e.,
λ = 0) would confiscate all income from the wealthy. The reason lies in the effect that taxes
exert on prices (∂p/∂τ > 0) and wages (∂ω/∂τ < 0). Thus, in a free-entry regime, it is in
the best interest of wage-earners to allow the producer to gain positive profit.
So far we have assumed that the fiscal constraint did not bind (λ = 0). This might
be too much of an optimistic assumption in many economies, especially among those still
developing.8 When the constraint in (9) bites, the ruler adopts the maximum tax rate that
the endowment of fiscal capacity allows. That is, τe∗ (λ > 0) = τo . This is true because
the ruler utility function is a strictly increasing function in τe ∈ [0, τ (λ = 0)]. Proposition 1
summarizes this result.
Proposition 1. Suppose free entry of a more productive firm is allowed, and that the fiscal
constraint in (9) is binding. Then the ruler sets τe∗ = τo and raises revenue T p∗h , x∗h , τe∗ |Ah ,
with equilibrium price and wage given by (7) and (8), respectively, the old producer drops
and the new entrant gains positive profit πh (τe∗ , Ah ) > 0.
Intuitively, Proposition 1 states that the ruler sets the equilibrium tax rate to exhaust
8
Brautigam, Fjeldstad, and Moore (2008); Gillis (1989); Thirsk (1997) offer a comprehensive survey of
developing economies with poor fiscal capacity.
11
fiscal capacity if she allows for free-entry. Likewise, Proposition 1 implies that when fiscal
capacity is limited (i.e., the fiscal constraint bites), the equilibrium tax rate paid by the new
firm is sub-optimal for wage-earners.
2.1.2
Protectionist Regime
When the intermediate monopolist is obsolete, the ruler can induce the old firm to abide
by a higher tax rate τp > τo in exchange for protection from superior competitors. Otherwise,
barriers are not adopted and the incumbent producer is eventually phased out of the market
by the new entrant. Notice that the ruler cannot implement the same extortion mechanism
when the new firm enters. The new producer, already competitive, is in no need of protection
from superior competitors. In other words, Protection-for-Tax-Compliance is only effective
among old, obsolete producers.
For the sake of simplicity, assume that the ruler conditions entry barrier to the domestic
producer’s abidance to τ (λ = 0), as defined in (10). By agreeing to the ruler’s terms, the
domestic firm receives the necessary protection for survival though at a high cost: abiding
by a higher tax rate than the fiscal capacity endowment, τ (λ = 0) > τo . Accordingly, the
equilibrium prices become
p∗l =
1
α(1 − τp )
(11)
equilibrium demand is set to
x∗l = Al L(α(1 − τp ))1/(1−α)
(12)
and equilibrium wages are
ωl∗ =
1−α
Al (α(1 − τp ))α/(1−α)
α
Proposition 2 summarizes the results of this sub-game.
12
(13)
Proposition 2. Suppose entry barriers are raised. Then the ruler sets τp∗ > τo , with τp∗ =
τ (λ = 0), the optimal tax rate had the fiscal capacity constraint not bidden. Accordingly, the
ruler raises tax revenue T p∗l , x∗l , τp∗ |Al ), with p∗l and x∗l given by (11) and (12); wages are
set to (13); and the incumbent firm gains profit πl (τp∗ , Al ) > 0.
2.1.3
Protection-for-Tax-Compliance Equilibrium
We now focus on the comparison between the protectionist and the free-entry regimes
when the fiscal capacity constraint binds (λ > 0 in (9)). If barriers are not raised, a new
firm enters the market with certainty. In this case, wages increase (because Ah > Al ) but
tax revenue remains constrained to the fiscal capacity endowment, τe∗ (λ > 0) = τo . On the
contrary, if barriers are raised, wages remain low but the tax rate achieves the ruler’s ideal
rate (i.e., the fiscal capacity constraint becomes slack). Given these alternatives, the ruler
must choose between wages or tax revenue. Both cannot rise simultaneously.
For equilibrium values for G(τ ∗ ) and ω(Aj , τ ∗ ) in both sub-games (summarized in Propositions 1 and 2 ), we seek to assess whether the ruler would ever prefer raising barriers to
allowing for free-entry of a superior competitor. The answer depends on the technology
distance between the new and the old producer, the fiscal capacity endowment (i.e., how far
it is from the ruler ideal tax rate), and the valuation of public spending.
Proposition 3. (Protection-for-Tax-Compliance) Suppose the fiscal capacity constraint in
(9) bites, and
1
1 − α(1 − ρ) 1−α
Ah
<ρ
Al
ρ
(14)
Then, there exists a τ̂ < τ (λ = 0) such that, for all τo ∈ [0, τ̂ ], a unique SPNE exists in
which the ruler prefers to adopt entry-barriers to free-entry. In this equilibrium, the ruler
sets τp∗ = τ (λ = 0), tax revenue increases up to T (τp∗ ) > T (τe∗ ) but wages decrease to
ω(τp∗ ) < ω(τe∗ ); the incumbent firm stays “in” and makes profit πl (τp∗ ) < πl (τo ); and the
would-be entrant remains “out”.
13
Proof. See Appendix.
Proposition 3 states that a labor-friendly ruler finds Protection-for-Tax-Compliance preferable to free-entry when fiscal capacity endowment is sufficiently low despite protection blocks
entry of superior technology and pushes equilibrium wages down. That is, the ultimate combination of lower wages but higher tax compliance by the obsolete incumbent producer is
preferred to the alternative scenario with higher wages but lower tax compliance by the new
producer. But this is only true as long as fiscal capacity endowment τo is sufficiently low (i.e.,
τo ≤ τ̂ ), and the productivity differential between the old and new producer is not excessively
large (i.e., satisfies expression (14)). When these conditions are met, the ruler’s marginal
gain of an unit increase of per capita public spending Ḡ(τp∗ ) is greater than the marginal loss
in wages ω(τp∗ ). By the same token, when fiscal capacity endowment is sufficiently large (i.e.,
τo > τ̂ ), the relative magnitude of these two marginal effects flip, and free-entry is preferred
instead. This result has immediate implications: when fiscal capacity is high, protection is
granted for reasons other than inducing tax compliance (e.g., rent-seeking by government).
Expression (14) in Proposition 3 implies that the Protection-for-Tax-Compliance equilibrium may only arise when the technology differential between the incumbent and would-be
entrant is not too large. This is consistent with the historical survey of technology adoption
conducted by Comin and Hobijn (2009a). When the benefits of a new technology are too
large, no barrier can prevent it from entering. True also, these circumstances are exceptional. Finally, it is worth mentioning that right-hand side of expression (14) is increasing in
the valuation of public spending ρ. That is, the more public funded-consumption is valued
by labor, the easier expression (14) is met. This result anticipates the long-term perils of
Protection-for-Tax-Compliance. The more valued public spending, the more likely protectionist policy might be adopted to induce higher tax abidance. As it argued below, this may
cause perverse effects in the long-run.
Figure 1 depicts the SPNE defined in Proposition 3 provided (14) is satisfied. The
horizontal axis represents the fiscal capacity endowment τo (or, if preferred, the tax rate at
14
Equilibrium Tax (𝜏*) 1
free-entry
PFTC
𝜏*(λ=0)
0
45˚
𝜏ˆ
𝜏(λ=0)
1
Fiscal Capacity
Endowment ( 𝜏o )
Figure 1: Equilibrium Tax Rate and ruler’s Optimal Strategy along Fiscal Capacity Endowment (provided expression (14) is satisfied)
the beginning of the game). Recall, this parameter denotes the maximum share of fiscal
capacity that can be taxed without extortion. The vertical axis represents the equilibrium
tax rate (or, if preferred, the final tax rate).
Figure 1 depicts three distinct segments (solid line). Two of them are horizontal; and
these are separated by a diagonal line. When fiscal capacity endowment falls to the right of
τ (λ = 0), the unconstrained fiscal capacity, the equilibrium tax rate is τ (λ = 0) itself. That
is precisely why it can be interpreted as the ideal tax rate of the ruler.9 From Proposition
1, moreover, we know that the ideal tax rate is smaller than 1. When the fiscal capacity
endowment is above this ideal value, free-entry is always adopted, since tax compliance by
the old producer upon protection does not outweigh the boost in wages following entry of
the new firm. However, the interesting scenario is limited to the interval of fiscal capacity
endowment between 0 and τ (λ = 0). For these states of the world, the fiscal capacity
9
Since the tax administration is costly, we should observe no economy with a fiscal capacity endowment
above the ideal point. But this segment is plotted for completeness
15
constraint bites. Here, we can distinguish two sub-intervals: by Proposition 3, for τo ≤ τ̂
the ruler prefers to raise entry barriers and, in exchange, sets τp∗ equal to her ideal value,
τ (λ = 0). That is why we observe a horizontal line at τ ∗ = τ (λ = 0) for τo ∈ [0, τ̂ ]. Instead,
for τo ∈ (τ̂, τ (λ = 0)], the ruler allows for free-entry. By Proposition 1 she sets τe∗ = τo (i.e.,
the equilibrium tax rate is set to exhaust fiscal capacity). This explains why the equilibrium
tax rate for this range of fiscal capacity endowment falls along the 45◦ line.
Altogether, Protection-for-Tax-Compliance offers a unique mechanism of institutional
extortion of domestic producers. When the latter are uncompetitive and fiscal capacity
is weak, rulers may still resort to this regulatory mechanism to induce tax compliance by
domestic firms.10
3
The Long Run
Protectionist-for-Tax-Compliance might be a convenient policy in the short run even
for a ruler advancing labor interests. Wages decrease but they are fully compensated by
the increase in tax revenue raised from domestic industry. Still this institutional solution
might produce perverse effects in the long-run if it perpetually impedes the adoption of
superior technology or discourages the investment in fiscal capacity. The Bolivian mercantilist experience exemplifies the risks derived from this form of protectionist policy. The
British experience, on the other hand, suggests that mercantilism might be a temporary
solution while fiscal capacity expands enough. Next, we explore the conditions under which
Protection-for-Tax-Compliance is a means to a higher equilibrium of high fiscal capacity or
the beginning of a poverty trap.
10
Elsewhere I proved that the existence of the Protection-for-Tax-Compliance equilibrium exists even if
the ruler attaches a non-negative weight to domestic producers’ welfare (Queralt, 2013).
16
3.1
Mechanics
This extension assumes that Protection-for-Tax-Compliance is already in place, and evaluates the conditions under which it is replaced by free-entry. The initial state of fiscal capacity is low. In terms of the benchmark model, this implies that τo < τ̂ . From Proposition
3 the technological distance between Al and Ah cannot be excessive for Protection-for-TaxCompliance to be an equilibrium. Thus, we also assume that condition (14) is satisfied.
Now we add a second period, t = {1, 2}. Suppose fiscal capacity endowment can move
from τ1 = τo up to τ2 = τ (λ = 0) at a cost σT , with σ < 1.11 That is, the economy can
evolve from constrained to unconstrained fiscal capacity from period 1 to period 2 if a share
σ of tax revenue T is invested in fiscal capacity. Denote I ∈ {1, 0} the Ruler investment
decision in fiscal capacity. Then,
τ2 =



if I = 0
τ1

 τ (λ = 0)
(15)
if I = 1
where τ1 = τo , the fiscal capacity endowment in period 1. For the sake of simplicity,
assume σ is independent of the distance between τo and τ (λ = 0).12
The producer is now allowed to innovate too. He might adopt technology Ah . Technological adoption takes a full period to materialize, and it is costly. The intermediate producer
must funnel a share 1 − δ of its own intermediate good output into R&D activities. Hence,
when the intermediate producer innovates, only a share δ of intermediate good xl reaches the
final market. The magnitude of δ < 1 can be related to the technological distance between
11
Alternatively, the goal of the investment decision could be τ2 = τ̂ , as defined in Proposition 3. This
possibility is evaluated in the Appendix. Results do not change. Nevertheless, since τ̂ is not explicitly
defined, the algebra becomes cumbersome. For that reason, I stick to τ2 = τ (λ = 0) in the main text.
12
One would suspect the investment
cost σ to be an increasing function of the distance between these
two magnitudes, σ = Φ τ (λ) − τo . Since none of them are a function of τ1 , we can solve inter-temporal
problem assuming an exogenous value of σ. Then, we make use of comparative statics to evaluate how the
distance between τo and τ (λ = 0) (i.e., smaller or bigger σ) might condition investment in fiscal capacity or
technological innovation.
17
Ah and Al , but it can also be interpreted as the quality of the capital market (the lower
the δ, the harder to obtain funds to invest in R&D), or even the strength of property right
protection (the lower the δ, the more resources have to be funneled to guarantee the same
outcome).
Given τo < τ̂ , the order of play becomes
• At the beginning of period 1, the ruler decides whether to invest σT in fiscal capacity,
and sets period 1 entry policy and sales tax rate.
• The producer decides whether to adopt technology Ah at a cost (1 − δ)xl , and chooses
period 1 profit-maximizing output xl .
• In Period 2, given the stock of fiscal capacity τ2 , the rules sets period 2 tax rate and
entry policy.
• The producer (old or new) chooses period 2 profit-maximizing production, and the
game ends.
Once we allow the ruler to invest in fiscal capacity and the producer to adopt the superior
technology, we can envision four possible strategies profile. These are depicted in Table 1.
However, two of them are unlikely and are disregarded in the analysis. First, if the ruler does
invest in fiscal capacity in period 1, by expression (15) and Proposition 3 she drops barriers
in period 2. This implies that period 1 obsolete producer will compete with the superior
firm in period 2. The only way he can inhibit entry is by innovating himself (i.e., invest in
technology adoption in period 1). If the incumbent does not adopt the superior technology,
by Schumpeterian competition he is dropped following entry of the new firm in period 2.
Thus, as long as extinction payoff is sufficiently low (as one would presume), investment in
fiscal capacity by the ruler should always be followed by adoption of the higher technology
by the incumbent producer. That I call, induced-innovation. Second, if the ruler does not
invest in fiscal capacity, it is unlikely that the incumbent producer innovates. Since adoption
18
PRODUCER
Invest, Adopt
Invest, Not adopt
RULER
Not invest, Adopt Not invest, Not adopt
Table 1: Strategy profiles: Investment in Fiscal Capacity vs. Adoption of Higher Technology.
is costly and fiscal capacity endowment is (and will remain) sufficiently low in period 2 as
to sustain the Protection-for-Tax-Compliance equilibrium, the incumbent producer has no
incentive to innovate once the ruler decides not to invest. Altogether, next section considers
only two of the four strategy profiles in Table 1: that on the top left corner, {invest, adopt};
and that on the bottom right corner, {not invest, not adopt}.
3.2
Analysis
For fiscal capacity endowment τ2 as defined in (15), period 2 strategies and payoffs are
characterized by Proposition 3. We only have to analyze the investment decisions in period
1 to fully characterize the SPNE in the whole game. Period 1 best responses are solved by
backwards induction within the period.
The producer In period 1, the ruler decides whether to adopt the high technology Ah .
Given τo ≤ τ̂ , the producer only innovates if he is induced to; that is, if and only if the ruler
decides to invest in period 1. If the ruler does not invest in fiscal capacity, the producer
does not innovate. His payoffs are then defined by Proposition 3. If the ruler invests in
fiscal capacity instead, the producer is induced to innovate -as previously argued. In order
to adopt the superior technology, (1 − δ) units of intermediate output x are lost in period
1. This share represents the cost of technology adoption. The profit function (upon the
investment decision of the ruler) becomes
π1 (I = 1) = (1 − τ1 )p1 δx1 − x1
19
(16)
That is, the producer still produces x1 units of intermediate good, but only a share δ of it
reaches to the final market. The other share (1 − δ) is invested in technology adoption.
The equilibrium price p1 is still determined by the marginal productivity of input x in the
final market, p = ∂Y /∂x, with Y defined by (2). Given p1 , the producer problem becomes
max π1 (I = 1) = (1 − τ1 )(Al L)1−α δxα1 − x1
x
(17)
which is maximized for
1
x∗1 (I = 1) = Al L(αδ(1 − τ )) 1−α
(18)
Notice that the costs of innovation, (1 − δ)x, translate into lower equilibrium production in
comparison to the Protection-for-Tax-Compliance equilibrium without investment in fiscal
capacity (characterized by Proposition 3 ). Accordingly, equilibrium prices rise to
p∗1 (I = 1) =
1
αδ(1 − τ1 )
(19)
Altogether, induced-innovation depresses production and increases prices compared to the
alternative scenario without any investment in fiscal capacity.
The Ruler The ruler decides whether to invest in fiscal capacity, I ∈ {0, 1}, anticipating
the effects of period 1 production and prices upon investment. Investment also consumes
a share σ of period 1 tax revenue T . Since public spending G is also funded by taxation,
fiscal capacity investment reduces per capita public spending in period 1. The exact level of
public spending is determined by
max V1 (I = 1) =
τ1
ω1∗
+ρ
h (1 − σ)T i
1
L
(20)
with
T1 = τ1 p∗1 x∗1
20
(21)
and p∗1 , x∗1 given by (18) and (19), and equilibrium wage
ω1∗ =
α
1−α
Al (δα(1 − τ1 )) 1−α
α
(22)
Given all the primitives, the ruler problem is solved for
h
τ1∗ = (1 − α) 1 −
i
1
ρ(1 − σ)
(23)
Expression (23) implies that the equilibrium tax in period 1 is a decreasing function of σ,
the cost of investing in fiscal capacity. The reason lies in how the investment costs inclines
the underlying trade-off between wages and public spending in favor of the former. Fiscal
capacity investment not only reduces the magnitude of public spending but also, due to the
induced-innovation costs (1 − δ), pushes wages down. This additional effect reduces the
ruler preference for higher tax rates. In turn, this explains why the equilibrium tax rate in
(23) is lower than that in the benchmark case. Against all intuitions, when tax revenue is
most needed (i.e., the ruler needs taxation to fund public spending and investment in fiscal
capacity), the ruler has the weakest incentives to raise taxes. These are lowest when σ → σ̄,
with
σ̄ = 1 −
1
ρ
(24)
When σ → σ̄ the investment cost of fiscal capacity is so large that wages are given full
priority in (20) and the equilibrium tax is set to 0 - thus precluding any expansion in fiscal
capacity at all -.13
From now on, we assume σ < σ̄.
Lemma 1. Suppose the ruler invests in fiscal capacity in period 1 at a cost σT . Then, the
13
If σ is said to increase in the distance between the constrained and unconstrained fiscal capacity,
expression (23) implies traps are more likely for states with weaker state capacity. These economies, despite
having the highest σs and need of higher fiscal capacity investments, are those facing weaker incentives to
expand fiscal capacity.
21
producer is induced to adopt technology Ah at a cost (1 − δ)x1 . Provided that
δ < δ̄ =
1−α
ρ
1−α
ρ(1−σ)
α+
α+
<1
(25)
then ω(I = 1) < ω(I = 0) and G(I = 1) < G(I = 0), with ω(I = 0) and G(I = 0) defined in
Proposition 2.
Proof. See Appendix.
Condition (25) guarantees that the cost of induced-technological innovation is significant
enough as to push period 1 equilibrium wages down.14 Lemma 1 defines a prototypical
consumption inter-temporal dilemma. Both elements in the ruler utility function, wages and
per capita public spending, decrease in period 1 whenever the ruler invests in fiscal capacity.
The benefits of investment in fiscal capacity materialized in period 2 must be sufficiently
large as to offset period 1 utility loss.
Period 2 payoffs are given by Proposition 3. If the ruler invests in fiscal capacity in t = 1,
τ2 = τ (λ = 0), and free-entry is preferred. A new firm enters, wages rise and firms are
taxed at the unconstrained tax rate. On the contrary, if the ruler does not invest in t = 1,
τ2 = τ1 < τ̂ and Protection-for-Tax-Compliance is still preferred in period 2. Specifically,
the two-period ruler payoffs are
Vt =



i
h
l ,I=0)
2 × ωt (V = 0) + ρ Tt (AL

 ω1 (I = 1) + (1 − σ)ρ T1 (I=1) ) + ω2 (Ah , τ (λ = 0)) + ρ T2 (Ah ,τ (λ=0)) )
L
L
if I = 0
(26)
if I = 1
Proposition 4. (Perpetual Protection-for-Tax-Compliance) Suppose Contition (25) in Lemma
1 is met; fiscal capacity endowment τ1 < τ̂ , as defined in Proposition 3; induced-technology
14
Wages depend negatively on δ but positively on σ -since the latter reduces the equilibrium tax rate.
Only when δ is sufficiently low, the first effect dominates and ω1 (I = 1) < ω1 (I = 0).
22
adoption cost (1 − δ)x1 , with δ ∈ (0, 1); and investment cost in fiscal capacity σT with
σ ∈ (0, σ̄) and σ̄ defined in (24). Then
α
• If Ah < 2 − δ 1−α , investment in fiscal capacity in period 1 is never a SPNE.
• If Ah > 2, investment in fiscal capacity in period 1 is always a SPNE.
α
• If 2 − δ 1−α < Ah < 2, there is a σ̂ < σ̄ such that for all σ̂ < σ ≤ σ̄ investment in fiscal
capacity is never a SPNE.
Proof. See Appendix
Proposition 4 states that the ruler invests in fiscal capacity whenever the boost of future
technology is very high (Ah > 2). This is consistent with Comin and Hobijn (2009a) findings,
which prove that no major technology innovation can be perpetually blocked. True also,
major innovations are rare. When innovations are incremental (Ah < 2), investment depends
on the innovation cost δ and the institutional investment cost σ. As δ approaches 0 (i.e.,
induced-innovation costs grows), the parameter space of fiscal investment shrinkages. The
future gains derived from the new technology do not compensate the foregone consumption
in the present (that is, lower wages and lower public spending in t = 1). Provided δ > 0
(i.e., induced-innovation costs are not extreme), there exists an intermediate interval of
fiscal capacity cost σ ∈ [0, σ̂] in which institutional investment takes place despite the future
technology is just incremental. That is, fiscal capacity investment only takes place under
very restrictive conditions: not only the institutional investment cost must be low, as one
would presume, but induced-innovation costs must be low too. Otherwise, investment in
fiscal capacity would be too painful in the present. Wages and tax revenue would shrink too
much in the short-run to justify future returns. If these two conditions are not simultaneously
met, a labor-friendly ruler would prefer to stick to the status quo, that is, Protection-forTax-Compliance.
We already know that fiscal capacity building in peacetime requires political stability and
low ethnic conflict (Besley and Persson, 2011). Proposition 4 adds a less intuitive prediction:
23
even if the political arena is perfectly stable (parameter γ = 0 in Besley and Persson (2011))
and ethnic divisions are frictionless (parameter θ = 1/2, ibid.) rulers might still lack the
incentives to invest in fiscal capacity. The mere inter-temporal dilemma of institutional
investment might suffice to discourage even a labor-friendly ruler from strengthening the tax
administration.15 In other words, the high opportunity costs of investment might prevent the
ruler from improving the capacity to tax the wealthy more severely in the future. Given those
constraints, a labor-friendly ruler might prefer to stick to the status quo (i.e. Protection-forTax-Compliance) despite it perpetuates poor fiscal capacity and low wages.
3.3
Vested Interests
Proposition 4 states that when the cost of fiscal capacity investment is small, the ruler
might opt for investing in period 1 and deviate from Protection-for-Tax-Compliance in period
2. We now explore the possibility of political giving. The pockets of producers are usually
full of money. Under some circumstances, they might prefer to bribe the ruler in order
to keep the status quo (i.e., Protection-for-Tax-Compliance) rather than adopting a new
technology.16
Specifically, this section explores the possibility that vested interests use contributions
(or bribing) in order to inhibit fiscal capacity investment when investment cost is low (i.e.,
σ < σ̂). To this end, a new stage at the very beginning of period 1 is required. In this stage,
the incumbent producer evaluates whether he bribes the ruler to keep the status quo (i.e.,
Protection-for-Tax-Compliance). Commitment problems are ruled out by assumption.
15
Besley and Persson (2011) do not reach this result because they separate the institutional investment
decision, F(τ2 −τ1 ), from the policy decision, τ . In that set up, investment affects current utility by reducing
the flow of public goods, but does not affect the current tax rate. That modeling strategy is convenient for
extending the core model in several ways, as they do. However, one would suspect that the tax rate is prone
to increase when investment costs are to be funded on top of public spending (still necessary for political
survival). Their approach, meritorious for many reasons, seems to omit part of the core inter-temporal
dilemma by arbitrarily separating the institutional investment from the policy decision.
16
Elsewhere, I evaluate the possibility that producers buy-off protection while keeping taxes low (Queralt,
2013). Consistent with Grossman and Helpman (1994), I prove that producers can use contributions to
receive protection while still paying low taxes (even below the state’s fiscal capacity). However, when fiscal
capacity endowment is sufficiently low, the tax associated to contribution-induced protection is still larger
than the fiscal capacity endowment. In other words, Protection-for-Tax-Compliance is bribing-proof.
24
3.3.1
Analysis
The producer has an incentive to bribe whenever the profit following innovation is lower
than the profit in the status quo, or
2
X
Πt (I = 0) ≥
2
X
t
Πt (I = 1, δ)
(27)
t
Lemma 2. (Producer Participation Constraint) There exists a δ̃ < δ̄, with δ̄ defined in (25)
such that, for all δ ≤ δ̃, the producer has an incentive to bribe the ruler in order to keep the
status quo.
Proof. See Appendix.
Lemma 2 defines the producer participation constraint for bribing. It is a function of
the cost of the induced technology adoption. As expected, when the innovation cost is big
(small δ) the producer has a stronger incentive to bribe the ruler to prevent the latter from
investing in fiscal capacity. δ can be associated to the cost of innovating (i.e., the distance
between the high and low technology); but it can also reflect the strength of property right
protection (the lower the δ, the lower the returns of the innovation process); or even the
quality of the financial market (the lower δ, the more difficult to fund R&D activity).
When δ < δ̃, the producer has an incentive to bribe. But it does not necessarily mean that
the ruler would accept the bid. This is the case whenever the maximum feasible contribution
(at least) matches the ruler indirect utility derived from investing in fiscal capacity, Vt (I = 1).
Definition 1. The maximum feasible contribution is
cmax =
2
X
Πt (I = 0) −
t
2
X
Πt (I = 1, δ)
(28)
t
Expression (28) defines the maximum contribution the producer would ever give. It is
equal to the difference between his utility under the status quo and upon innovating.
25
Definition 2. The Ruler Incentive Constraint is defined by
cmax ≥
2
X
Vt (I = 1) −
2
X
t
Vt (I = 0)
(29)
t
Expression (29) defines the ruler incentive constraint, that is, the contribution that would
make her stick to the status quo (i.e., Protection-for-Tax-Compliance) despite σ < σ̂. The
interpretation is straightforward: the ruler would only keep the status quo if the bribe is
large enough to outbid the utility derived from expanding the fiscal capacity of the state.
Proposition 5. (Perpetual Protection-for-Tax-Compliance with Bribing) Suppose Lemma 2
α
and Ah ∈ (2 − δ 1−α , 2) are satisfied. Then, there exists a σ̃ ∈ (0, 1), σ̃ < σ̂ such that, for
all σ ∈ [σ̃, σ̂), there exists a unique SPNE in which the producer has an incentive to bribe
2
2
P
P
and the ruler always accepts the contribution c∗ =
Vt (I = 1) − Vt (I = 0); in exchange,
t
t
the ruler keeps the status quo (i.e., Protection-for-Tax-Compliance) despite the low wages
ωt (I = 0) and low fiscal capacity τ2 = τ1 = τo < τ̂ , as defined in Proposition 3. The obsolete
producer remains “in”, makes profit πl (c∗ |δ ≤ δ̃) ≥ 0, and the new entrant stays “out”.
Proof. See Appendix.
Proposition 5 states that when the costs of innovation are sufficiently big (δ ≤ δ̃), the
producer offers a bribe to the ruler, and the ruler accepts it whenever the cost of fiscal
capacity investment σ is moderately low (σ ∈ [σ̃, σ̂)). More importantly, the range of σs for
which the ruler would invest in fiscal capacity is now smaller than the one in which bribes
were not allowed. This implies the producer is able to align the ruler interests with his
thanks to political giving. As a direct consequence, the status quo (i.e., mercantilism) can
be preserved in states of the world in which it would be optimal to invest in fiscal capacity
for a labor-friendly ruler (i.e., σ ∈ [σ̃, σ̂)). Figure 2 plots the parameter space for which
fiscal capacity investment takes place once the producer is responsive to bribing. Compared
to the labor-friendly ruler in Proposition 4, a contribution-responsive ruler would invest in
fiscal capacity in fewer states of the world. Specifically, the producer is able to buy-off
26
investment
by a ruler
responsive to contributions
no investment (s.q.)
investment by a labor agent in office
0
∼
𝜎
no investment (s.q.)
𝜎^
𝜎¯
𝜎
1
Figure 2: Equilibrium investment by the cost of fiscal capacity investment and ruler type.
favorable policy whenever σ ∈ [σ̃, σ̂). A labor agent in office would invest in fiscal capacity
if σ falls in this range. On the contrary, the bribe-responsive ruler would prefer to take
the money and keep the status quo despite the perpetuation of low wages, low productivity
and weak fiscal capacity. In other words, obsolete producers can induce the ruler to stick to
Protection-for-Tax-Compliance even when this equilibrium is detrimental for wage-earners.17
Proposition 4 stated that a low productivity, low fiscal capacity equilibrium might arise
even in presence of a ruler who seeks to maximize labor welfare. Proposition 5 emphasizes
the increased risk of falling in this kind of poverty traps when government is ruled by rentseeking politicians. Both Propositions 4 and 5 illustrate how easy is to perpetuated a status
quo in which taxation falls on a reduced group, the incumbent producers, who in exchange
of their cooperation get to determine policy in their own benefit and against labor. The
perpetuation of a weak states incapable of taxing the economy gives them economic and
political advantage which, in turn, might be used to perpetuate their privilege. Protectionfor-Tax-Compliance might be a second-best policy in the short-term as long as it helps to
collect the resources required to expand fiscal capacity. However, under the circumstances
identified in Proposition 5, Protection-for-Tax-Compliance can be utilized by producers to
17
Proposition 5 also states that the producer stays “in” and makes positive profit despite the contribution
cost, c∗ . Only when Lemma 2 is met at equality, δ = δ̃, the producer would remain “in” but make competitive
profit only.
27
perpetuate an inefficient equilibrium.
4
Empirical Implications
Protectionist barriers are said to stifle innovation. The theoretical model challenges this
overwhelmingly accepted statement. Specifically, the model predicts that technology innovation might take place under protection whenever the ruler funnels the proceeds of mercantilist
protection to expand the stock of fiscal capacity. In anticipation of an eventual drop of entry
barriers, protected firms would take advantage of the regulatory shelter to catch-up with
superior competitors. That I called, induced innovation. However, by Propositions 3 to 5
we also know that the ruler would only expand the stock of fiscal capacity if the latter is not
too low to begin with and the ruler is not captured by vested interests (i.e., the protected
industry). Altogether, if the ruler and labor preferences are sufficiently aligned (as compared
to an scenario in which the ruler is captured by domestic industry) and the stock of fiscal
capacity is sufficiently large, mercantilist practices such as Protection-for-Tax-Compliance
might induce technology adoption by protected firms.
This section tests this theoretical implication for a set of countries and a time period,
Western Europe 1865-1950, in which protection was still significant (Reinert, 2007), fiscal
capacity was not to too low to begin with (Cardoso and Lains, 2010), and rulers were
(partially) accountable to labor through elections (Przeworski, 2010).18 If the theoretical
model is right, under such conditions we should expect mercantilist practices to induce
adoption of superior competitors by protected industry.
Certainly, protection in the late 19th century in Western Europe was lower than used
to be. Still, as we can observe in Figure 3, the average import duty was twice as high as
current values all over the period. The analysis exploits these relatively high values to test
whether technology adoption took place under a protectionist scenario.
18
Data constraints limit the sample to eight cases: Austria-Hungary (later Austria), Denmark, France,
Germany, Italy, Norway, Sweden and the United Kingdom.
28
.15
.1
Import Duty
.05
0
1860
1880
1900
1920
1940
1960
1980
2000
year
Figure 3: Average Import Duty in Western Europe before and after 1950. Source: Clemens
and Williamson (2004).
Fiscal capacity in Western Europe grew over the considered period (Aidt and Jensen,
2009; Barnes, 2011; Scheve and Stasavage, 2010). Figure 4 plots the evolution of the share
of income tax over total revenue for the considered sample. The income tax is said to be the
maximum exponent of fiscal capacity (Tilly, 1990) and, as such, is seems to be a reasonable
10
% income tax to total revenue
15
20
25
30
proxy for the stock of fiscal capacity.
1865
1885
1905
year
1925
1945
Figure 4: Average Share of Income Tax over Total Tax Revenue in Western Europe between
1865 and 1950. Source: Flora (1983)
This section investigates whether the expansion of fiscal capacity propelled the adoption
of newer technologies among protected economies conditional on the ruler-labor preference
alignment. To proxy for technology adoption, the dependent variable, I measure measure
29
Table 2: Data availability for the two dependent variables
Austria-Hungary
Austria
Denmark
France
Germany
Italy
Norway
Sweden
United Kingdom
Rail Freight Tons per Km
Energy Production per Person
first
1875
1925
1893
1865
1865
1885
1867
1898
1920
first
1920
1920
1901
1900
1895
1920
1901
1896
last
1912
1950
1950
1950
1938
1950
1950
1950
1950
last
1950
1950
1950
1944
1950
1950
1950
1950
the intensive use of two of major technologies in the industrial revolution: rail freight tons
per km and energy production per capita. The data is drawn from the Comin and Hobijn
(2009b) Cross-country Historical Adoption Technology Dataset dataset. The coverage of the
data by country differs by technology. Table 2 reports the first and last year for which
information exists by country. The analysis will consider Austria and Austria-Hungary as
being different countries. Overall, the rail freight data has a broader coverage in time except
for the United Kingdom.
The ruler-labor preference alignment is proxied by the level of enfranchisement in a given
point of type. I work under the premise that in the late 19th and early 20th century Europe,
workers’ interests were better upheld whenever they could hold the ruler accountable for
her actions at election day. Moreover, franchise correlates with elements of a free society
(e.g. free press) which make exposure more likely (Treisman, 2000). The main sources of
the franchise variable are Caramani (2000), Flora (1983) and Nohlen and Stöver (2010).
All models include some additional controls: real GDP, which is drawn from Maddison
(2007), and primary education enrollment, post mail usage and military size, which are
drawn from Banks and Wilson (2012). These controls capture the capacity and the necessity
of investing in fiscal capacity building. Adopting the income tax requires a strong and
costly state apparatus. The capacity to build it is proxied by the real GDP, the education
enrollment and post mail usage. These are all proxies of state capacity. Still, the expansion
30
of fiscal capacity might be a consequence of war. To account for this possibility, all models
account for the size of the military. The size of military not only captures increases due to
war but also preparation for war.
The two dependent variables are serially correlated. Accordingly, standard OLS assumptions are not satisfied. In order to eliminate serial correlation, I work with Lagged Dependent
Variable (LDV) and Autoregressive Distributive Lag (ADL) models (Beck and Katz, 2011).
ADL models include the first lag of the dependent and all independent variables. Additionally, I fit a battery of time fixed effects to account for any (non-monotonic) time trend and
a battery of country fixed effects (to cope with unobserved heterogeneity).19 Once all these
elements are considered, serial correlation almost disappears.
4.1
Results
For technology adoption to occur, the theoretical prediction requires three conditions to
be satisfied simultaneously: the ruler and labor must be aligned, import protection should
be effective, and fiscal capacity has to be low. In order to test this prediction, a threeway interaction is in order. We have two measures for the dependent variable, technology
adoption: rail freight ton per km and energy production per capita. And also proxies for
the three-way interaction components: on the one hand, import protection is proxied by the
level of import duties and ruler-labor alignment by the franchise level. On the other hand,
low fiscal capacity is proxied by the share of tax revenue not derived from the income tax.
That is,
Low Fiscal Capacity = 100 − %
income tax
total revenue
(30)
The estimates of the three-way interaction are reported in Table 3. The dependent variable
in Models 1 to 4 is the log of Rail Freight tons to km and in Models 5 and 8 it is the log
of Energy Production per capita. Models 1, 3, 5 and 7 include the lag of the dependent
19
The fixed effects are correlated with the lag of the dependent variable. However, the bias is of order
1/T , with T̄ = 45.
31
variable (LDV models). Models 2, 4, 6 and 8 also include the first lag of all independent
variables (ADL models).20
We are mainly interested in the coefficient of the three-way interaction. For each of the
two basic specifications (Models 1 and 2, and 5 and 6), the three-way interaction estimate
holds a positive sign, consistent with the model prediction. That is to say, when fiscal
capacity is low and ruler and labor are aligned, positive protection does not stifle innovation,
but the contrary.
The coefficients for import duty protection are strangely large. The reason lies on the
skewed distribution of this variable. In order to check whether the results are driven by the
presence of a few outliers in this variable, I apply a logarithmic transformation to protection
and re-run the main specification. Models 3, 4, 7 and 8 report the new results for both
the LDV and ADL specifications, respectively. The new estimates are virtually identical to
the initial ones, except for the magnitude of the coefficients (which is a function of the new
variable range). Altogether, the results suggest that the initial estimates were not driven by
any outlier case in the protection variable.
To better understand what these coefficients mean, Figure 5 plots the marginal effect of
protection on the level of rail freight ton per km for several values of fiscal capacity. Fiscal
capacity is lowest when the share of taxes not stemming from the income tax is largest (right
extreme of the horizontal axis). Fiscal capacity is highest when all revenue stems from the
income tax. This never happens in the real world. The highest value in the sample is 60%,
which corresponds to the left extreme of the horizontal axis. In order to test the modifying
effect of fiscal capacity on protection we need to fix the third variable in the interaction to
some meaningful value. In particular, the simulation fixes franchise to two extreme values:
0 and 70% of total population enfranchised, respectively. The former value is associated
with a fully autocratic regime, and the latter to a fully democratic polity. Figure 5 plots
the marginal effect of protection on the level of rail freight per km for several values of
20
Due to space constraints, the lags are not reported in the results tables.
32
Marginal Effect of Protection on Rail Freight
-1
-.5
0
.5
1
40
60
80
100
Non-Income Tax Revenue
franchise=0
franchise=.7
Figure 5: Marginal Effect of Protection on Rail Freight per KM for Different values of Fiscal
Capacity and two values of Franchise. Estimates drawn from Model 3 in Table 3. 90% CI
fiscal capacity weakness and two values of franchise. When protection is adopted in an
autocratic regime (blue curve), its effect on rail freight declines as fiscal capacity weakens.
This result is consistent with the theoretical model. When fiscal capacity is low and the
ruler and labor preferences are not aligned, fiscal capacity investment is not expected to
follow and, accordingly, the producer lacks any incentive to adopt superior technologies.
Under such circumstances, the status quo (i.e., mercantilism) should prevail. The effect of
protection flips in a fully democratic regime (red curve), where the ruler and labor interests
should be somehow aligned. When fiscal capacity is high (left extreme in the horizontal
axis), protection stifles innovation. However, as the stock of fiscal capacity decreases (we
move rightwards along the horizontal axis), the effect of protection on technology adoption
approaches 0 and, at the extreme, it even turns positive, consistent with the theory. That is
to say, if fiscal capacity is low but the ruler and labor are aligned, protected industry would
catch up with foreign competitors in anticipation of an eventual drop of protection caused
by an improved stock of fiscal capacity. That is how induced innovation operates.
Table 4 includes different robustness tests. Models 1 and 2 re-run the main specification
replacing the size of the military for the occurrence of war. Wars and the use of railroads
are said to be mutually dependent (Gaetano Onorato, Scheve, and Stasavage, 2013), but
33
34
yes
no
440
.996
Lagged Dependent Variable
Lagged Independent Variables
Observations
R-squared
yes
yes
434
.996
-.036***
(.013)
2.585**
(1.005)
.013**
(.007)
.978***
(.217)
2.987
(2.685)
1.506
(2.268)
.028
(.033)
-1.203*
(.729)
-.158***
(.057)
-22.479***
(8.205)
12.522***
(4.444)
.294***
(.107)
(2)
Freight/km
ADL
yes
no
440
.996
1.243***
(.472)
-2.820***
(1.002)
-.017***
(.006)
.083***
(.030)
-6.552***
(2.398)
-.038***
(.014)
.411***
(.098)
.283
(.476)
.405
(.662)
.031*
(.019)
2.527*
(1.360)
.037***
(.013)
(3)
Freight/km
LDV
yes
yes
434
.996
1.166***
(.444)
-2.328**
(.906)
-.014**
(.006)
.066**
(.028)
-5.178**
(2.249)
-.036***
(.014)
1.000***
(.212)
3.251
(2.727)
.735
(2.258)
.022
(.033)
2.491*
(1.309)
.030***
(.011)
(4)
Freight/km
ADL
yes
no
294
.998
-.020***
(.007)
1.396***
(.495)
.011***
(.004)
-.099*
(.058)
.501
(.473)
-.800
(.556)
.042**
(.017)
-3.475***
(.917)
-.132***
(.031)
-14.158***
(4.172)
9.922***
(2.307)
.188***
(.056)
(5)
Energy/cap
LDV
Table 3: Testing for Induced Innovation.
All models include a battery of country and year fixed effects. Robust standard errors in parentheses. *** p<0.01, **
p<0.05, * p<0.1
Intercept
Military Size
Primary Education Enrollment
Mail
ln(GDP)
Low Fiscal Capacity
Franchise
-.042***
(.014)
3.018***
(1.141)
.020***
(.008)
.432***
(.103)
.356
(.508)
.095
(.648)
.044**
(.019)
-1.930**
(.803)
-.191***
(.062)
-28.021***
(9.100)
14.272***
(4.862)
.366***
(.118)
(1)
Freight/km
LDV
Franchise×Low Fiscal Capacity
ln(Protection)×Low Fiscal Capacity
ln(Protection)×Franchise
ln(Protection)
Protection
Protection×Franchise
Protection×Low Fiscal Capacity
ln(Protection)×Franchise×Low Fiscal Capacity
Protection×Franchise×Low Fiscal Capacity
Dependent Variable →
Model Type →
yes
yes
290
.998
-.022***
(.008)
1.433**
(.557)
.014***
(.004)
.215*
(.110)
-.622
(1.187)
.845
(1.497)
.023
(.027)
-3.322***
(.917)
-.144***
(.036)
-15.620***
(4.873)
1.755***
(2.816)
.210***
(.066)
(6)
Energy/cap
ADL
yes
no
294
.998
.858***
(.250)
-1.072**
(.443)
-.011***
(.003)
.035**
(.014)
-2.626**
(1.082)
-.029***
(.008)
-.059
(.060)
.630
(.449)
-.457
(.527)
.032*
(.017)
-.766
(1.323)
.015**
(.006)
(7)
Energy/cap
LDV
yes
yes
290
.998
.895***
(.283)
-1.196**
(.497)
-.012***
(.004)
.039**
(.015)
-2.985**
(1.209)
-.029***
(.009)
.237**
(.108)
-.298
(1.217)
-.032
(1.417)
.027
(.027)
-.576
(1.414)
.016**
(.007)
(8)
Energy/cap
ADL
they also expand the stock of fiscal capacity (Tilly, 1990). To account for this source of
endogeneity, I replace the military size variable for a war indicator variable based on Ghosn,
Palmer, and Bremer (2004). The results with the new control are virtually identical to
the previous estimates although the three-way interactive coefficient for Energy per Capita
does not achieve standard levels of statistically significance. Models 3 and 4 explore an
alternative proxy for ruler-labor alignment. Instead of franchise, a dichotomous variable
indicating democratic status is used. This variable is drawn from Boix, Miller, and Rosato
(2013). Again, the three-way interaction remains statistically significant. Finally, Models 5
and 6 use an alternative proxy for the stock of fiscal capacity. Instead of using income tax
revenue (a particular type of direct taxation), I use all revenue stemming from direct taxes
as a proxy for fiscal capacity. Among others, this new proxy includes property, business,
window or land tax revenue. For the sake of interpretation, I also reverse this variable
to measure low fiscal capacity (see (30) for clarification). Once this other proxy of fiscal
capacity is considered, the estimates of the three-way interaction remain virtually identical
to previous models.
Overall, the results suggest that technology growth is not necessarily incompatible with
protection of domestic industry. However, for that to be the case, protected industry must
believe protection is only temporary, which requires of institutional investment in fiscal
capacity to begin with. And that may only happen if fiscal capacity is not too low and the
ruler and labor preferences are (partially) aligned. When these two conditions are satisfied,
protection might not prevent but induce technology adoption. Indeed, the experience of
these eight European economies suggests that an endogenous transition from a mercantilist
society characterized by low fiscal capacity and low productivity to a free-trade economy
characterized by high-fiscal capacity and high-productivity might be possible.
35
36
440
.996
2.439*
(1.368)
-.065*
(.038)
.433***
(.100)
.328
(.479)
.962
(.636)
.080***
(.030)
-.017***
(.006)
-.039***
(.014)
1.276***
(.486)
-2.722***
(.986)
-6.243***
(2.347)
.036***
(.012)
(1)
Freight/km
294
.998
4.158***
(1.272)
-.045*
(.024)
.136**
(.056)
.451
(.419)
.328
(.483)
.014
(.014)
-.008**
(.003)
-.020**
(.009)
.617**
(.262)
-.539
(.440)
-1.204
(1.080)
.007
(.006)
(2)
Energy/cap
440
.995
.415***
(.100)
-.281
(.556)
.623
(.682)
.006
(.020)
.511
(1.052)
-1.828*
(1.077)
-.829*
(.448)
.023*
(.013)
-.008*
(.005)
-.018
(.011)
.618
(.379)
.010*
(.005)
(3)
Freight/km
294
.998
-.020
(.065)
-.174
(.467)
-.767
(.508)
.031*
(.016)
-1.350
(1.211)
-1.296**
(.640)
-.602**
(.261)
.017**
(.008)
-.010***
(.003)
-.025***
(.007)
.794***
(.236)
.008**
(.003)
(4)
Energy/cap
419
.997
.274***
(.091)
.021
(.438)
-.192
(.604)
.024
(.018)
.142
(.896)
-.012**
(.006)
-.005**
(.002)
.031**
(.015)
.267*
(.146)
-.825**
(.353)
-1.921**
(.950)
.014**
(.005)
(5)
Freight/km
290
.998
-.080
(.058)
.573
(.483)
-.564
(.547)
.035*
(.018)
-1.522
(1.001)
-.016***
(.004)
-.007***
(.002)
.022***
(.008)
.434***
(.109)
-.628***
(.212)
-1.265***
(.484)
.011***
(.003)
(6)
Energy/cap
Table 4: Robustness Checks.
All models include a lagged dependent variable as well as battery of country and year fixed effects. Robust standard errors in parentheses.
*** p<.01, ** p<.05, * p<.1
Observations
R-squared
Intercept
Military Size
Primary School Enrollment
Mail
ln(GDP)
War
Franchise×Non-Direct-Tax Revenue
ln(Protection)×Non-Direct-Tax Revenue
Non-Direct-Tax Revenue
Democracy×Low Fiscal Capacity
ln(Protection)×Democracy
Democracy
Franchise
ln(Protection)×Franchise
ln(Protection)
Low Fiscal Capacity
ln(Protection)×Low Fiscal Capacity
Franchise×Low Fiscal Capacity
ln(Protection)×Franchise×Non-Direct-Tax Revenue
ln(Protection)×Democracy×Low Fiscal Capacity
ln(Protection)×Franchise×Low Fiscal Capacity
Dependent Variable →
5
Conclusions
The paper presents an theory of endogenous institutions where the accumulation of fiscal
capacity drives optimal trade policy. The theory is based on a practice originated back in
mercantilist Europe: when political survival depends on public spending but the capacity
to raise revenue through taxation is limited, rulers might grant protection from competition
to domestic producers in exchange for higher tax abidance. Proposition 3 to 5 identify the
conditions under which this strategy is optimal and those under which the revenue derived
from Protection-for-Tax-Compliance is reinvested in building fiscal capacity.
The initial endowment of fiscal capacity is proved to play a significant role in shaping
the incentives to reinvest the mercantilist revenue. When that stock is low to begin with,
mercantilist policy becomes a sticky equilibrium, either because the opportunity costs of
investment are too big, or because the ruler is captured by vested interests via political
giving. Either way, fiscal capacity building does not take place, not even if political stability
is guaranteed or ethnic divisions are frictionless (Besley and Persson, 2011). A premature
adoption of Protection-for-Tax-Compliance might be a second-best in the short-run, but
results detrimental in the long-term.
Only when the stock of fiscal capacity is intermediate to begin with, might mercantilist
policy be optimal in the short- and long-run. For this interval of the parameter space, tax
proceeds raised by Protection-for-Tax-Compliance are reinvested in expanding the stock of
fiscal capacity. Institutional investment itself induces technology adoption among incumbent
producers, who, anticipating an embracement of free trade as fiscal capacity expands, take
advantage of protection by catching-up with foreign competitors. Eventually, the stock of
fiscal capacity hits the point at which free-entry is optimal. The economy endogenously
switches from the protectionist equilibrium to a new one characterized by free-entry, high
fiscal capacity, competitive industry and high wages.
The mercantilist curse that results from premature adoption of Protection-for-Tax-Compliance
seems consistent with one of the two examples in the Introduction: Bolivia. This country
37
faced pressing social needs (large ρ) from 1930 to 1952.21 First the Chaco war, then the
appeasement of an increasingly militant labor movement called for an increase in public
spending. This demand was met. Revenue from tin taxes was spent in new welfare programs: they grew from 9% in the 1920s (before export licenses were used as sticks-andcarrot to induce tax compliance), to 16% in the 1930s and 25% in the 1940s (Gallo, 1988,
1997).22 Despite the emphasis on welfare programs, the precarious fiscal capacity remained
unattended. From Proposition 4 we know that rulers seeking to maximize a joint flow of
wages and public spending, as this was the case, face a strong inter-temporal dilemma when
present opportunity cost of institutional investment is too large. Under such circumstances,
even a ruler who only advances labor-interest might prioritize present consumption over fiscal capacity building. This might well explain what happened in 1930-1952 Bolivia. Social
needs were rampant and the stock of state capacity was very low. The foregone consumption
of institutional investment might had been too large even for a labor-friendly government.
The inter-temporal dilemma perpetuated protectionist policy as a means to induce tax compliance by tin producers. But at the same time, this institutional solution prevented further
institutional investments and productivity growth in the main sector of the economy. Eventually, the country was trapped in a low income, low fiscal capacity equilibrium. In stark
contrast to Bolivia, the European experience (illustrated by the cross-national analysis in
Section 5 ) suggests that an endogenous switch from mercantilism to free-trade is feasible as
long as the initial stock of fiscal capacity is not too low.
The results in this paper have two implications: first, no single policy fits all situations.
Optimal trade policy might differ significantly depending on the stock of state capacity, in
general, and fiscal capacity, in particular. Second, sudden trade liberalization might interrupt
what otherwise might be a path of endogenous development from mercantilist practices to
21
In 1952 a revolution took place and tin production was nationalized.
Between 1936 and 1946 three populist, labor-friendly government ruled Bolivia. These fulfilled significant reforms in tax and agricultural policy that benefited workers at the detriment of tin producers’ profits.
Conservative governments ruled from 1946 to 1952. They were certainly more friendly to the tin producers;
nevertheless, tax pressure on them was never relaxed. Political survival of conservative governments still
required expansive welfare programs (Gallo, 1988, 1997).
22
38
free-trade policy. Recent evidence suggests that a sudden deregulation of the terms of trade
leave countries unable to raise sufficient revenue from other sources (Baunsgaard and Keen,
2010). In terms of long-term labor welfare, early liberalization might be as detrimental as
perpetual mercantilism.
The results also speak to the barriers to technology literature (Mokyr, 1991; Acemoglu,
2008; Parente and Prescott, 2000; Comin and Hobijn, 2009a). The lack of technological adoption might be (involuntary) induced by a ruler who advances labor welfare only. When the
demand for public goods is high and fiscal capacity is low, Protection-for-Tax-Compliance
might alleviate immediate needs at a cost of long-term institutional underinvestment. Of
course, political giving might be responsible for inefficient policy. But, as we saw in Proposition 4, the mere inter-temporal dilemma of institutional investment might indirectly discourage technological adoption. From this point of view, technological obsolescence might
not only depend on the reluctance of producers to fund costly adoption, as the standard
argument goes, but also on the incapacity of the ruler to tax revenue from newer producers.
Finally, Propositions 4 sheds some light on the infant-industry debate, and particularly
on the effect of tariff protection on long-term economic growth (Tena-Junguito, 2010; Irwin,
2000; Lehmann and O’Rourke, 2011). The theoretical model suggests that the effect of tariff
protection on growth might be conditioned by the initial stock of fiscal capacity. If tariff
protection is adopted when fiscal capacity is too low to begin with, both the ruler and the
producers should lack incentives to invest and (thus) innovate. In absence of technology
adoption, long-term growth should not be expected. However, if protectionist tariffs are
raised when the stock of fiscal capacity is already intermediate, we might expect tariff revenue
being reinvested in fiscal capacity building. By the logic of induced innovation, institutional
investment would stimulate technology adoption. In turn, newer technologies would result
in endogenous growth (Romer, 1990).
Altogether, this work builds on the growing literature on state capacity building by
stressing the endogenous relationship between short- and long-term revenue production pol-
39
icy (Levi, 1988). We have studied how the satisfaction of current demand for public spending
might condition long-term institutional investment in fiscal capacity. In particular, depending on the initial stock of fiscal capacity, short-cuts to high fiscal capacity such as Protectionfor-Tax-Compliance might become a stepping stone to a high-tech, high-fiscal-capacity equilibrium or the downslide into a low-income, low-fiscal-capacity trap.
40
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6
Appendix
Proof of Proposition 3
Proof. Denote Ve (·) and Vp (·) the ruler utility under entry and protection, respectively. Ve (τo )
is an increasing monotone concave function in τo ∈ [0, τ (λ = 0)], with τ (λ = 0) being the
unconstrained tax rate. Given Al , Vp (τp∗ = τ (λ = 0)) defines a horizontal line in the V − τ
space. When τo → 0, as long as (14) is satisfied, Ve (τe∗ ) < Vp (τp∗ ). When τo → τ (λ = 0),
by Proposition 1, τe∗ = τ (λ = 0); since Ah > Al , then Ve (τe∗ ) > Vp (τp∗ ). Thus, by the
Intermediate Value Theorem, it must be true that there exists an unique τ̂, 0 < τ̂ < τ (λ = 0)
such that ∀τo ≤ τ̂ , Vp (τp∗ ) ≥ Ve (τe∗ ).
Proof of Lemma 1
The ruler utility is a function of wages and per capita public spending.
A sufficient condition for the existence of the ruler’s inter-temporal dilemma is G(I = 1) ≤
G(I = 0) and ω(I = 1) ≤ ω(I = 0). That is the case if δ̄ ≤ 1 + (1 − α)/ρ.
Proof. Per capita public spending is defined by (1 − σ)G/L, with G ≡ T = τ px. If no
investment in fiscal capacity takes place, σ = 0, and τ , p and x are defined by Proposition
3. If investment takes place, σ > 0, and τ , p and x are defined by (23), (18) and (19),
respectively. Upon substitution,
G∗ (I = 1) = (1 − σ)(1 − α −
G∗ (I = 0) = (1 − α −
1−α
)Al L[αδ(α
ρ(1−σ)
1−α
)Al L[α
ρ
+
+
1
1−α
)] 1−α
ρ(1−σ)
1
1−α 1−α
)]
ρ
(31)
For G(I = 1) < G(I = 0), it must be true that
"
(1 − σ)δ
α
1−α
α
# "
# 1−α
α + 1−α
ρ(1 − σ) − 1
ρ
<
1−α
ρ−1
α + ρ(1−α)
(32)
For all α ∈ (0, 1), δ < 1 and ρ > 1, the left-hand side of condition (32) is a negative convex
α
function of σ that cuts the vertical axis (σ = 0) at δ 1−α , and cuts the horizontal axis at σ = 1.
44
The right-hand side of condition (32) is a negative concave function that cuts the vertical
α
axis at 1 > δ 1−α , and the horizontal line at σ = 1. Thus, ∀σ ∈ (0, 1), G(I = 1) < G(I = 0).
Wages depend on δ and τ . When no technology innovation takes place, δ = 1; when
innovation takes place, δ < 1. Given τ (I = 1) and τ (I = 0), as defined by (23) and (10),
ω ∗ (I = 1) =
∗
ω (I = 0) =
α
1−α
1−α [α
(αδ)
α
α
1−α
1−α [α
(α)
α
+
α
1−α 1−α
]
ρ(1−σ)
(33)
α
1−α 1−α
]
ρ
+
For ω ∗ (I = 1) < ω ∗ (I = 0), it must be true that
δ < δ̄ =
1−α
ρ
1−α
ρ(1−σ)
α+
α+
(34)
Since σ ≤ 1 − 1/ρ, this implies δ̄ ≤ 1 + (1 − α)/ρ < 1. If innovation cost satisfies this
condition, wages following induced-innovation are lower than those without investment in
fiscal capacity.
Proof of Proposition 4
Proof. Let σ ∈ (0, σ̄). Investment is preferred when
2
P
2
P
Vt (I = 1, δ) ≥
t
Vt (I = 0). After
t
some rearrangement, this implies
α
(1−α) 1−α
)
ρ(1−σ)
h
α
1−α 1−α
δ
α
(1−α)
ρ(1−σ)
i
+ ρ(1 − σ) 1 − α −
h
i
α
(1−α) 1−α 1−α + ρ 1 − α −
≥ (2Al − Ah )(α + 1−α
)
ρ
α
ρ
Al (α +
(35)
When σ → σ̄, τ ∗ (I = 1) → 0. Thus, there is no investment and no induced innovation.
For the right-hand-side of (35) to be greater than the left-hand side, all it is required is
Ah > 2Al . Normalize Al to 1, so Ah < 2.
When σ → 0,
Al (α +
h1 − α α
i
h
i
α
α
1 − α 1−α
1 − α 1−α
)
δ 1−α + (1 − α)(ρ − 1) ≥ (2Al − Ah ) (α +
)
+ (1 − α)(ρ − 1)
ρ
α
ρ
45
(36)
For the left-hand-side of (36) to be greater than the right-hand side, it must be the case
α
thatAh /Al > (2 − δ 1−α ). With Al normalized to 1,
α
Ah > (2 − δ 1−α )
α
α
Notice that δ 1−α < 1 and Ah > 1. Hence, (2 − δ 1−α ) < Ah < 2 is non-empty.
The LHS of expression (35) is a negative convex function of σ, whereas its RHS is a
α
horizontal line. If Ah ∈ [2 − δ 1−α ), 2], by the Intermediate Point Theorem there exists a
unique σ̂ ∈ (0, σ̄) such that ∀σ < σ̂ investment is preferred (LHS > RHS), and ∀σ ∈ [σ̂, σ̄),
no investment ever takes place (LHS ≤ RHS)
Proof of Lemma 2
Proof. Given ωt (I) and Gt (I) = τt pt xt as defined by Propositions 3 and 4,
2
P
Πt (I = 0) >
t
2
P
Πt (I = 1, δ) becomes
t
1
"
# 1−α
1 h
h1
i
i
1 − α 1−α
1
1 − α
(2Al − Ah ) α +
− 1 > Al δ α +
−1
ρ
ρ
ρ
δρ
(37)
The RHS of (37) is an increasing function of δ, while the LHS of (37) is independent of it.
To guarantee that both curves cut: (i) when δ → 0, LHS > RHS, which is straightforward;
and (ii) when δ → δ̄, as defined by (25), LHS < RHS. Notice that δ̄ is largest when σ = σ̄.
Plugging σ̄ into δ̄, and replacing δ for δ̄ in (37), we reach
(2Al − Ah )[
h
i
1
ρ
− 1] < Al
−1
α
α(1 + α(ρ − 1))
(38)
Since Al > 2Al − Ah , all we need is the element in brackets multiplying Al to be greater
than the one multiplying Al > 2Al − Ah , which is always satisfied.
46
Since LHS > RHS for lowest δ and LHS < RHS for highest δ = δ̄ (strict inequalities),
by the Intermediate Point Theorem, there exists δ̃ < δ̄ such that, ∀δ < δ̃ the producer has
an incentive to bribe, and none for δ ≥ δ̄.
Proof of Proposition 5
First, one needs to prove that a σ̃ < (0, 1) exists such that,
∀σ > σ̃, the status quo (i.e., Protection-for-Tax-Compliance) is preferred. Second, we have
to prove that σ̃ < σ̂:
Proof. The ruler incentive constraint can be re-expressed as
2 X
Πt (I = 0) + Vt (I = 0) − (Πt (I = 1) + Vt (I = 1)) ≥ 0
t
Plugging all equilibrium values in yields
α
(2Al − Ah ) α +
≥
(Al )δ
α
1−α
α+
(
(1−α) 1−α
ρ
1−α
ρ(1−σ)
α
1−α
α α+
1−α
α
L
1
α
+1 +
h
1−α
α
(
αδ α +
1−α
ρ(1−σ)
L
1
δα
−1 +
h
+ (1 − α)(ρ − 1)
1−α
α
i
)
+ (1 − α)(ρ(1 − σ))
)
i
(39)
Normalize L = 1.
Step 1. Let σ → σ̄, with σ̄ defined by (24). Then, τ ∗ = 0, which inhibits investment (i.e., τ2 =
τ1 = τo ) and, as a direct consequence, induced-innovation too (i.e., A1 = A2 = Al ). For
this constellation of parameters, the ruler would always prefers to stick to the status
quo (see Proposition 4 ). Let σ → 0; then for the right-hand side of expression (39) to
α
be bigger than the left-hand side, it suffices with Ah ≥ 2 − δ 1−α . By the Intermediate
Value Theorem, there exists a σ̃ ∈ (0, σ̄) such that, ∀σ > σ̃, the ruler always prefers
the status quo.
Step 2. Compare σ̂ (Proposition 4) and σ̃ (Proposition 5 ). σ̂ is implicitly defined in the Ruler
47
original problem
(α +
α
1−α 1−α
)
ρ
h
1−α
α
(2Al − Ah )(α +
+ρ 1−α−
α
1 − α 1−α
h
=
)
i
α
(1−α)
ρ(1 − σ)
+
ρ
1
−
α
−
Al δ 1−α 1−α
α
ρ
i
(1−α) ρ
and σ̃ is implicitly defined in the ruler incentive constraint in (39)
(α +
α
1−α
) 1−α
ρ(1−σ)
(2Al −Ah ) α+
=
α
(1−α) 1−α
(
α α+ 1−α
L
α
ρ
(
(Al
α
)δ 1−α
1−α
αδ α+ ρ(1−σ)
L
1
−1
δα
h
1
+1
α
h
+
+
i
)
1−α
+(1−α)(ρ−1)
α
i
(40)
)
1−α
+(1−α)(ρ(1−σ))
α
where the left-hand side is an increasing function of σ. On the contrary, none of the
two right-hand side expressions are a function of σ. Which curve does the left-hand
side cut first? Let
M=
1−α
α
+ (1 − α)(ρ − 1)
N=
1−α
α
+ (1 − α)(ρ(1 − σ))
X = (1 − α)(α +
Y =
1−α
)
ρ
(1 − δα)(α +
1−α
)
ρ(1−σ)
Given M, N, X, Y , σ̃ < σ̂ whenever
F1 =
X +M
M
>
= F2
Y +N
N
This is true if
h
i h
i
+ (1 − α)(ρ(1 − σ)) × (1 − α)(α + 1−α
)
ρ
i h
i
h
1−α
> 1−α
+
(1
−
α)(ρ
−
1)
×
(1
−
δα)(α
+
)
α
ρ(1−σ)
1−α
α
which is true for all σ ∈ [0, 1] and δ ∈ [0, 1] (thus, satisfying producer participation
48
constraint). Since F 2 is first-order dominated by F 1, σ̃ < σ̂ is always true.
Evaluation of an Alternative Investment Goal
Why is the investment goal is τ (λ = 0) and not τ̂ , as defined in Proposition 3 ? τ̂ is
not explicitly defined. That makes results less intuitive, but they do not change is esence.
ˆ ) for which investment takes place.
That is, there still exists a non-empty interval σ ∈ (0, σ̂
This Supplementary Section sketches the existence of this interval and compares it to the
one defined by Proposition 4.
By Proposition 3, τo < τ̂ ≤ τ (λ = 0). Since ∂τ ∗ /∂σ < 0, in case of investment, σ(τ̂ ) <
σ(τ (λ = 0)). Moreover, since σ = 0 when investment is null,
τ ∗ (I = 1|goal τ̂ ) < τ ∗ (I = 0)
(41)
This is a crucial result. It raises the same inter-temporal dilemma to that in the main text,
this time however for investment goal τ̂ . On the one hand, this inter-temporal dilemma is
responsible for the positive relationship of σ and period 1 wage, ω1 . In particular, since
σ(goal τ̂ ) < σ(goal τ (λ = 0)), by (23) τ ∗ (goal τ (λ = 0)) < τ ∗ (goal τ̂ ). Given ∂ω/∂τ < 0,
ω ∗ (goal τ̂ ) < ω ∗ (goal τ (λ = 0)). On the other hand, public spending utility G is increasing
in τ ∈ (0, τ (λ = 0). Since τ ∗ (goal τ̂ ) > τ ∗ (goal τ (λ = 0)). In sum, when the investment
goal is τ̂ instead of τ (λ = 0), period 1 equilibrium wage is lower but equilibrium per capita
public spending is higher.
1. Provided the investment goal is τ̂ , when is invested pursued by a benevolent ruler?
Suppose all Proposition 4 pre-conditions are met. Then, there exist a unique SPNE
ˆ and σ̂
ˆ ∈ (0, 1) investment is preferred. Proof similar to that of
such that for all σ < σ̂
Proposition 4.
ˆ exists, how does it compare to σ̂ defined in Proposition 4? Answer: σ̂
ˆ < σ̂
2. Provided σ̂
49
Proof. Let ωjt (I) and Gtj (I) be the indirect utility of wages and per capita public
spending following investing in fiscal capacity I ∈ {0, 1}, with goal j ∈ {l, h}, where
l denotes investment goal τ̂ and h investment goal τ (λ = 0), in period t ∈ {1, 2}.
Investment takes place whenever
ωl1 (I = 1) + G1l (I = 1) ≥
h
i h
i
2 ω(I = 0) + G(I = 0) − ωl2 (I = 1) + G2l (I = 1)
if goal is τ̂
(42)
ωh1 (I = 1) + G1h (I = 1) ≥
h
i h
i
2 ω(I = 0) + G(I = 0) − ωh2 (I = 1) + G2h (I = 1)
if goal is τ (λ = 0)
Notice that none of the right-hand side expressions in (42) depends on σ, the investment cost. On the contrary, both left-hand sides describe a monotone negative function
in σ. Now let Vjt (I = 1) be the total indirect utility per period. By Propisition 3,
Vjt (I = 1) is increasing in τ ∗ . Given goals τ̂ and τ (λ = 0), if investment takes place
Vh2 (I = 1) > Vl2 (I = 1). That implies
h
i
h
i
2
2 ω(I = 0) + G(I = 0) − Vh (I = 1) < 2 ω(I = 0) + G(I = 0) − Vl2 (I = 1)
(43)
Given (43), the left-hand side in (42) cuts the top right-hand side at earlier. That is,
ˆ < σ̂.
at a value σ = σ̂
This result implies that the parameter space of positive investment for the lower goal,
τ̂ , is smaller than the one for the higher goal, τ (λ = 0). The reason lies in the marginal
gain of period 1 investment. Since this is relatively smaller for the lower goal, the
incentives to invest also weaken. Altogether, focusing on the higher investment goal
τ (λ = 0) sets a more conservative scenario as it expands the parameter space of positive
investment.
50