Documento de Investigación. DI. N° 01-2022. Julio 2022
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Documento de Investigación. DI. N°1, 2022
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Rethinking Fiscal Rules
Luis Carranza Ugarte
1
Julián Díaz – Saavedra
2
José Galdón – Sánchez
3
1
Universidad de San Martín de Porres, Lima, Perú
2
Universidad de Granada, Andalucía, España
3
Universidad Pública de Navarra, Navarra, España
Agradecimientos
A Jonathan Heathcote, Alberto Barreix, Mikel
Casares y Renzo Mini por sus valiosas sugerencias
y comentarios. José E. Galdón – Sánchez, agradece
el soporte financiero del Ministerio de Ciencia,
Innovación y Universidades (Proyecto DGCT, No.
PGC2018093542BI00). Julián Díaz – Saavedra,
agradece el soporte financiero a la Agencia Estatal
de Investigación (Proyecto PID2019 – 110783GB –
I00/AEI/10.13039/501100011033).
Correspondencia
Oficina de Investigación, Acreditación y Calidad,
Instituto de Gobierno y de Gestión Pública,
Universidad de San Martín de Porres, Jr. Martín
Dulanto # 151, Lima, Perú.
Correo: oiac_iggp@usmp.pe
Abstract
The Covid 19 pandemic has caused both a decrease in tax
revenues and an increase in public spending, forcing
governments to increase fiscal deficits to unprecedented
levels. Given these circumstances, it is foreseeable that fiscal
rules will play a predominant role in the design of many
countries’ recovery policies. We develop a general
equilibrium, overlapping generations model for a small,
open economy in order to study the impact of several fiscal
rules upon welfare, public expenditures and growth. We
calibrate the model to the Peruvian economy. In this
economy, fiscal rules have been widely used and, unlike in
other Latin American countries, they have been relatively
successful. We find that fiscal rules will generate better
results in terms of output and welfare if, in addition to
maintaining control over the fiscal result, they also eliminate
the bias in favor of current expenditure. We also find that
the performance of economies that implement structural
rules tends to be better than the performance of economies
that implement rules based on current results.
KEYWORDS: Fiscal policy, Infrastructure, Public spending,
Public Deficit, Debt limits
JEL classification: E62, H54, O23
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1. Introduction
The Covid-19 pandemic has generated an unprecedented crisis in the global economy. The estimated world
GDP [Gross Domestic Product] contraction for 2020 is 4.4%, in accordance with the IMF [International
Monetary Fund] World Economic Outlook of October 2020 (IMF, 2020).
1
Governments have responded with
massive fiscal and monetary public policy decisions. The fall in tax revenues resulting from the recession,
as well as direct measures adopted in order to expand public spending, in combination with the extensions
for tax payments which have been applied in most countries, will increase fiscal deficits to unprecedented
levels, which will therefore impact the amounts of indebtedness. Faced with this situation, the countries
which were applying fiscal rules when the pandemic arose have proceeded to suspend the limits imposed
by these rules. Fiscal rules are intended to avoid discretion in the management of the fiscal policy.
Their primary objective is to achieve macroeconomic stability by eliminating or reducing fiscal deficit bias.
This objective is equivalent to target an optimal level for the amount of public debt. In order to achieve this
objective, fiscal rules must address two issues related to debt management. First, they should determine the
optimal level of public debt that generates interest rates low enough not to affect the optimal path of private
investment and growth, allowing for the implementation of countercyclical fiscal policies in times of
recession. Second, given the existing imperfections in the credit market and taking into account the initial
conditions of the economy (for example, the initial size of its debt or its infrastructure gap), they should
facilitate convergence to the level of public debt determined to be optimal.
If the output recovery is slow, those countries which were previously implementing fiscal rules will likely
need to consider having a transition period before implementing them again. This implies that, once sanitary
conditions are normalized, additional fiscal measures will be required in the future in order to stimulate
demand. This is true to an even greater extent for countries where fiscal rules are applied according to levels
rather than flows.
The need for adaptation of the fiscal rules provides an opportunity to study their complete redesign. This is
even more the case given the high levels of indebtedness that most countries will have subsequently. In
particular, Latin American countries will need to rethink their structural objectives regarding the reduction
of infrastructure gaps. This is so since the implementation of fiscal rules also generally affects the optimal
composition of public spending, in favor of current spending (which tends to be unproductive or has little
impact on growth) and limiting capital spending (which tends to positively affect productivity). In this vein,
Blanchard and Giavazzi (2004) find that the way to reduce public spending is through a reduction in
infrastructure spending.
Ardanaz and Izquierdo (2021) and Ardanaz et al. (2020) find asymmetric public spending responses during
different stages of the economic cycle. During periods of economic expansion, when tax revenues increase,
public spending also increases mainly explained by current expenditures. On the contrary, during periods
of recession, when tax revenues fall, the public spending reduction is mainly explained by a reduction in
capital expenditure. This asymmetric behavior is associated with the political nature of spending decisions,
which is so dependent on the political cycle, and which is generally carried out by governments with finite
time horizons. Moreover, this behavior is accentuated when the economy approaches elections (see Rogoff,
1990). Given the role that infrastructure plays in an economy’s production capacity and productivity, this
negative bias on infrastructure spending tends to negatively affect long-term growth (Aschauer, 1989;
Easterly and Rebelo, 1993; Arslanalp et al., 2010, and Carranza et al., 2014).
In our study, we are not interested in a problem of discretion versus commitment, but we rather present a
proposal for rethinking fiscal rules which have the objective of optimizing the fiscal policy response to the
1
In the case of Latin America, the IMF estimates a GDP contraction of approximately 8.1%. Moreover, the expected fiscal deficit will be on average
7.5% of GDP and fiscal requirements (financing of debt plus fiscal deficit) will amount to more than 11% of GDP.
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apparent dilemma between growth and stabilization. Our starting point is that fiscal rules are better than
dicretionary fiscal policy. We also assume that countries, once output starts recovering, will redisign and
implement fiscal rules again. As in Dovis and Kirpalani (2021), the assumption ... “is that society can
credibly impose rules on policy makers and that policy makers can commit to follow these rules.”
To carry out our analysis, we build a dynamic, general equilibrium, overlapping generations model
economy to study the long term aggregate and welfare consequences of implementing various fiscal rules.
In our model economy, the households differ in age and decide how much to optimally work, consume, and
save. Production is carried out by a neoclassical representative firm that behaves competitively in its product
and factor markets, where production factors are labor, and private and public capital (infrastructure). We
also model a government, which runs a pay-as-you-go pension system financed with payroll taxes, and
which uses consumption, capital and income taxes to finance the provision of a government public
consumption good, public investment, and interest payments on public debt. We compute the solution for
both the Social Planner and the decentralized economy where we explicitly assume a government that faces
a static maximization problem. In other words, the government mainly cares about current public
consumption. We also assume imperfections in the financial markets, due to both the economy's default
risks and its own limits on indebtedness.
Since we aim to assess the relative success of various fiscal rules, we calibrate our theoretical model to a
typical Latin American economy such as that of Peru.
2
Justification for this selection is provided in section
3. Next, we introduce and simulate the impact of four different fiscal rules. The first two stabilize the current
and structural fiscal deficits, respectively; while the third and fourth rules add a restriction on the
composition of public spending which prevents the government from favoring current spending to the
detriment of investment in infrastructure. We want to analyze which rule best solves the dilemma between
stability and growth, and which rule generates greater well-being over the long term. Similarly, we analyze
the performance of the economy under the aforementioned four rules when it is affected by various shocks.
Therefore, simulations of the most common shocks faced by Latin American economies such as commodity
price shocks, increased variability of product given the dependence on primary activities, and financial
stress will be computed.
The use of an overlapping generations model within the literature of fiscal rules constitutes a novelty. Our
choice is due to the following reason. Peru, like many other countries, is undergoing a demographic
transition process, or more precisely, a process of population aging. Consequently, this economy will
experience significant changes in the age distribution of its population. That is, over the next decades, the
demographic dependency ratio will increase. According to the Peruvian Instituto Nacional de Estadística e
Informática, (INEI [National Institute of Statistics and Informatics]), the ratio of the number of people aged
65 and over on the number of people aged between 20 and 64, will go from the current 13 percent to 27
percent in 2050. This population aging has mainly two consequences, which are not reflected in the
quantitative results presented by previous literature. First, the change in the age distribution of the
population affects the potential output of the economy, a relevant variable within the literature. Specifically,
the future population aging should reduce the expected potential output over the next few decades. Second,
and despite the low coverage of social spending in Latin American countries, this aging implies an increase
in public spending for the retirement and health systems during the next decades, for which the
implementation of the fiscal rules carry an additional benefit in terms of lower income taxes and higher
wages.
We obtain three main results. First, we find strong evidence that introducing fiscal rules improves welfare
in the economy, especially over the long term. Second, designing rules which address not only the bias for
fiscal deficit, but also take into account the bias for current expenditure, is of critical importance in order to
2
Overall, and despite calibrating the model to Peruvian data and the Peruvian institutional setting, our findings can be generalized to other Latin
American countries.
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induce a public expenditure composition which is closer to optimal. Put differently, protecting public
investment is a key policy objective. And third, we also find that the gap in output between economies with
and without fiscal rules raises when there are commodity price shocks and increases in volatility that affect
the economies.
To the best of our knowledge, our paper is the first attempt to facilitate the debate related to the long term
welfare gains or losses derived from the implementation of fiscal rules, and how their potential negative
effects can be mitigated. At the same time, our work is placed in a literature that analyzes the effects of fiscal
rules on fiscal outcomes (e.g., Dahan and Strawczynski, 2013, Hallerberg et al., 2009, Fabrizio and Mody,
2006, and Neyapti, 2013), interest rates (e.g., Iara and Wolff, 2014), output volatility (e.g., Fatás and Mihov,
2006), or welfare (e.g. Alfaro and Kanczuk, 2019). Our paper is also related with those papers that analyze
fiscal rules under external shocks (e.g., Halac and Yared, 2014, and Fernández-Villaverde et al., 2011). Our
work has also connections with the literature that assesses the permanent negative effects of fiscal
consolidations on long term output (e.g. Blanchard and Leigh, 2013, Fatás and Summers, 2018, and House
et al., 2020). However, our paper does not consider the possibility of default (as it is the case in Alfaro and
Kanczuk, 2019, or Hatchondo and Roch, 2017), nor in our model economy fiscal rules arise because the
government intend to signal its type (e.g., Dovis and Kirpalani, 2020).
In Section 2 of the paper, we analyze the reasons why fiscal rules are necessary. Section 3 describes the
Peruvian economy, its experience with the implementation of various fiscal rules, the analysis of how the
fiscal result evolved, and the composition of public spending under the various rules implemented. Our
model and the solutions for both the social planner and a decentralized economy are presented in Section 4.
Section 5 is devoted to the calibration of our model economy. The policy experiments, the demographic and
fiscal scenarios in which the experiments take place, the simulation of the optimal and benchmark model
economies, and the different fiscal rules studied appear in Section 6. In Section 7, we present the results of
simulating our model economy under these fiscal rules. Section 8 concludes.
2. The Need for Fiscal Rules as an Instrument of Fiscal Policy
During the last decade, an increasing number of countries have incorporated fiscal rules in the managing of
their fiscal policies in order to improve transparency and control of the fiscal deficit (Eyraud et al., 2018).
Faced with the need to respond to the economic crisis caused by the pandemic, most of these countries have
been forced to abandon the objectives set by the fiscal rules that they were implementing. However, it is
predictable that once the effects of the crisis pass, the countries will return to the implementation of fiscal
rules, having to re-analyze the corresponding transition and objectives. It seems important, therefore, to
discuss the reasons why countries have been adopting fiscal rules in the first place.
Fiscal rules, understood as quantitative restrictions on either the level or the rate of growth of specific fiscal
variables (usually current debt or fiscal deficit, or with some adjustment for the economic cycle), are
intended to avoid discretion in the management of the fiscal policy.
3
Discretion generates a significant
increase in public spending, which in turn causes debt size to increase over time as well. Moreover, the need
to address higher financial expenses in the future makes debt more persistent. This bias towards increasing
fiscal deficits (deficit bias) has been widely discussed in the economic literature (Alessina and Drazen, 1991;
or Persson and Tabellini, 2000, among others). There are two fundamental reasons for the existence of this
fiscal deficit bias:
(i) The short-term incentives for policymakers, which intensify during the elections period, i.e.
the so-called political spending cycle (Alessina and Tabellini, 1990), and are related to the
fact that administration periods are finite.
3
For a definition of fiscal rules and their typology, see Kopits and Symansky (1998).
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(ii) The existence of the “common pool problem”, which occurs when interest groups compete
for increased public spending without internalizing the negative effects of higher future
taxes, generating the so called “voracity effect” (Tornell and Lane, 1999).
The effects of this fiscal deficit bias are very detrimental for the economy. First, the excessive size of public
debt ends up negatively affecting long-term growth. Reinhart and Rogoff (2010) find that debt-to-GDP levels
over 90% negatively affect the growth of countries. The mechanism through which higher levels of debt
translate into lower growth is the presence of higher interest rates (Haugh et al., 2009; Baldacci and Kumar,
2010; or Schuknecht et al., 2010). Higher interest rates end up negatively affecting private investment and,
ultimately, long run growth (Blanchard and Perotti, 2002, and Fatas and Mihov, 2003, among others). This
line of thinking includes the hypothesis proposed by Giavazzi and Pagano (1990), according to which, a
contraction of public spending can be expansive if interest rates are reduced. The studies of Bertola and
Drazen (1993), and Alessina and Perotti (1996) have confirmed this hypothesis. However, Perotti (2013) finds
that a fiscal contraction is expansive if it is accompanied by both a real depreciation of the exchange rate and
an expansive monetary policy. Similarly, Baldacci et al. (2015) find that a contractive fiscal policy is
expansive as long as the credit restrictions in the economy are not severe.
Second, in the presence of a shock, it is not possible to implement an anti-cyclical fiscal policy if there are
high levels of indebtedness. In their seminal contribution, Gavin and Perotti (1997) show that fiscal policy
tends to be pro-cyclical. This would be the result of increasing expenses when cyclical revenues rise (in times
of expansion) and decreasing expenses when cyclical revenues diminish (in times of recession), since there
is no room to increase the deficit due to the excessive size of the public debt and the imperfections of the
credit market (Riascos and Vegh, 2003). The impossibility of implementing an anti-cyclical fiscal policy is
even more serious because the fiscal multipliers tend to be greater in times of recession (Baum et al., 2012).
Finally, and derived from the aforementioned characteristics, we observe that, prior to discretionary fiscal
policy results in pro-cyclical behavior, the fiscal policy tends to amplify economic cycles by inducing greater
volatility, further weakening the structural vulnerabilities of the economy either in terms of the structure of
the tax revenues (Talvi and Vegh, 2005) or external factors (Radelet and Sachs, 1998).
In this context, the institutional response to mitigate fiscal policy deficit bias has been the implementation
of fiscal rules. This implementation can be seen as: (i) commitment device, imposing direct restrictions on
governments (Alessina and Tabellini, 1990); (ii) signaling device, sending information to the market in order
to reduce uncertainty in decision making (Debrun and Kumar, 2007); and (iii) coordination device,
facilitating the establishing of coalitions to reduce the common pool problem (Cordes et al., 2015). A broad
debate has arisen in the economic literature regarding the effectiveness of fiscal rules at achieving the
objectives of macroeconomic stability and the reduction of deficit bias. This debate has placed the emphasis
on institutional factors (coverage, flexibility, simplicity, budgetary institutions, etc.) in order to determine
when fiscal rules are most effective (Eyraud et al., 2018). However, there is little debate so far related to the
long run welfare gains or losses derived from the implementation of such fiscal rules, and how their
potential negative effects can be mitigated. Facilitating this debate is the objective of this paper.
3. Fiscal Rules: The Peruvian Case
Peru is an interesting case of the application of fiscal rules. The first fiscal rule was implemented in late 1999,
when the country was facing the negative effects of both the Russian crisis (late 1998) and the Brazilian debt
crisis (January 1999). These exogenous shocks negatively affected growth and fiscal results. According to
the INEI, the year 1999 ended with a fiscal deficit of 3.4% of GDP and a level of public debt of 51.4% of GDP.
In order to ensure the return to macroeconomic stability, the fiscal rule established a ceiling for the fiscal
deficit at 1% of GDP, capping the real growth of non-financial government spending, which was established
at 2% per year. Despite successive modifications to the fiscal rule, Peru’s fiscal history has been successful
in terms of achieving macroeconomic stability. As shown in Figure 1, debt to GDP reached 21.6% in 2011
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and finished 2019 at 26.8%, with Peru being one of the countries with the lowest debt levels in the Latin
American region.
However, in terms of the composition of spending, the story was not homogeneous, and the fiscal rule
underwent significant modifications. In this regard, there have been three important milestones during the
whole period affecting not only the behavior of the fiscal deficit and the debt to GDP ratio, but also the
behavior of current spending and public investment. A first period (from 2000 to 2006) in which, as already
mentioned, there were two rules: a limit to the current fiscal deficit of 1% of GDP and a ceiling of 2% for the
annual growth of real non-financial government spending. A second period (from 2007 to 2011) in which
the limit for fiscal deficit remained at 1% of GDP, but the limit of the real rate of growth for government
spending was restricted only for current spending and set at 3%. A third period (from 2012 to 2019) in which,
initially, in 2012 the current spending rule was suspended and, finally, in 2013 both rules for the fiscal deficit
and for the public spending were replaced by a limit of 1% of GDP for the structural fiscal deficit.
4
What is relevant to highlight here is that during the period 2007-2011 there was no direct restriction on
public investment, only on current spending, while through the fiscal deficit there was an indirect restriction
on public investment. However, in the other two periods, there was no distinction between current and
capital expenditure.
The Peruvian experience reflects two important stylized facts. First, when fiscal rules do not distinguish
between current spending and capital expenditure (public investment), there is a pre- dominance of current
expenditure over public investment, i.e. government preferences clearly opt for higher current expenditure.
As we observe in the figures 2A and 2B, only in the period 2007-2011 when public investment ceases to have
a direct restriction in the fiscal rule, we observe a strong growth of public investment in relation to GDP
while current spending remains stable against GDP.
5
In the period 2000-2006, current expenditure remained
relatively constant to GDP, with the fiscal deficit rule being restrictive, forcing a smooth convergence to the
maximum deficit of 1%. On the other hand, in the period 2012-2019 there is a decreasing trend in public
investment in terms of GDP, while current spending soared in growth rate and relative to GDP, and then
remained relatively stable.
4
In 2003 and 2008, minor changes were introduced to the spending growth limit and, in 2009 and 2020; the rules were suspended due to the
international financial crisis and the COVID-19 crisis, respectively.
5
In 2009, the suspension of the fiscal rule due to the international financial crisis generated an increase in current spending as part of the fiscal
stimulus for the recovery of aggregate demand.
Figure 1. Peru: Debt to GDP ratio, 2000-2019 (%)
55
50
45
40
35
30
25
20
15
2000 2004 2008 2012 2016 2020
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Second, the Peruvian case also shows that governments with finite time horizon have a bias towards current
spending and against public investment. The reason is simple: there is more pressure from politicians in
favor of current spending because the impact on voters is more visible in the short-term, while in the case
of public investment the impact is materialized in the long term. This is the reason why, when there are
budget constraints, it is of crucial importance to protect public investment
6
.
Overall, these facts give us an intuition of what a hypothetical government objective function would look
like, with public consumption and public investment expenditures as arguments. See section 4.3 for a more
detailed description of such objective function.
4. Model Economy
We build a general equilibrium overlapping generations model economy with imperfect credit markets in
a small open economy. In our model, each period corresponds to one year. The economy is populated by
households, firms, and a government that we will describe below
7
.
Once we set up the model, we will proceed as follows. First, we will specify the solution for a centralized
economy, i.e. the Social Planner. Then we will establish an economy where agents take decisions in a
decentralized way. Into this economy, we will introduce a government elected for every period which has
a defined preference function and a budget constraint. As we will see, the differences between the solutions
of a centralized economy and a decentralized economy vary in conjunction with two factors: (i) the efficiency
losses resulting from the distortions that appear when taxes are introduced and (ii) the bad decisions of the
government, which translate into high indebtedness and a greater bias towards current spending given the
government’s preferences.
The objective of the paper is to explain precisely how fiscal rules can help reduce both the bias to increase
the deficit and the bias to increase current expenditures.
8
6
The changes experienced by the composition of government spending in the Peruvian case are in line with what has been found in Blanchard and
Giavazzi (2004), Ardanaz and Izquierdo (2021) and Ardanaz et al. (2020).
7
As it has been already mentioned in the introduction, the use of a model of overlapping generations makes it possible to incorporate the
population dynamics of Peru during the next decades. This is important because the simulation results show the sustained increase in pension
spending due to population aging.
8
From the point of view of the endogenous growth theory, other channels for macroeconomic stability positively affecting long-term growth
(greater financing for innovation, greater public investment that generates increasing returns to scale, greater private investment that generates
learning-by-doing, etc.) can be noted. However, in this paper, we want to focus exclusively on the channels for reducing both deficit biases and
current spending exhibited by the economies.
Figure 2A. Peru: Current Expenditure to GDP,
2000-2019 (%)
16.5
16.0
15.5
15.0
14.5
14.0
13.5
13.0
12.5
12.0
2000 2004 2008 2012 2016 2020
Figure 2B. Peru: Public Investment to GDP,
2000-2019 (%)
7
6
5
4
3
2
1
0
2000 2004 2008 2012 2016 2020
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4.1. Environment
Demographics. The economy is populated by overlapping generations of individuals of measure
who
enter the economy at age and live until the maximum of years. Parameter
denotes the
conditional probability of surviving from age to age at period .
Employment Status. Individuals in our economy are either workers or retirees, and every individual enters
the economy as a worker. Once an individual has reached the mandatory retirement age,
, she leaves the
labor market and becomes a retiree.
Endowments. Workers receive an endowment of efficiency labor units every period. This endowment
depends on the household’s age, and we use it to characterize the earnings life-cycle profile. We model this
profile using the following quadratic function:
(1)
where
is the deterministic productivity profile of households at age , and letters
denote parameters. We choose this functional form because it allows us to represent the life-cycle profile of
the productivity of workers in a very parsimonious way.
Preferences. Each period individuals derive utility from consumption and leisure. Specifically, we assume
(2)
where
is the share of time at age in period that individuals devote to labor market activities.
Consequently,
, is leisure at age in period , is the relative utility weight on leisure, and is the
elasticity of marginal utility regarding leisure. Finally, consumption at age in period ,
, is given by the
Cobb-Douglas function
, where
is the consumption of the private good and
is
the consumption of the public good provided by the government. The utility function in (2), a separable
preference defined over consumption in log and leisure, is commonly used in the real business cycle
literature (see, for example, Campbell 1994).
Technology. The economy produces an internationally tradable composite commodity. Firms choose optimal
quantities of labor and private capital taking factor prices and public capital as given. The technology is
represented by a standard Cobb-Douglas production function. Consequently, the production of output at
period ,
, requires labor input,
, private capital,
, and public capital (infrastructures),
. We also
assume that both goods and factor markets are perfectly competitive. The technology used by the
representative firm is given by:
(3)
where
is a productivity shock, whose law of motion is given by
, and
. And
denotes a deterministic exogenous labor-augmenting productivity factor whose law of
motion is
Parameters and are the respective output elasticities to private capital,
labor, and public capital. We also assume constant returns to scale, that is
. Finally, we also assume that both types of capitals depreciate geometrically at a constant rate
.
Credit Market. In our model economy, we assume imperfections in the financial markets, due to both the
economy’s default risks and its own limits on indebtedness. Specifically, we assume that the interest rate
faced by domestic agents,
, is increasing in the ratio of public foreign debt, , to domestic output, . That
is, the domestic interest rate is given by
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CARRANZA, DÍAZ – SAAVEDRA y GALDÓN - SÁNCHEZ
(4)
where
denotes the world interest rate, is a parameter that reflects the country-specific interest
premium,
is the beginning of period public foreign debt, and
is output at period .
Finally, we also assume that there is a maximum level of public debt to output ratio given by the parameter
. This additional restriction on the sensitivity of the interest rate to the level of debt is due to the fact that,
when a country reaches excessive levels of indebtedness, the financial markets stop lending and therefore
the country can only access out-of-market placements, through bilateral debt or the multilateral
development banks.
9
4.2. Social Planner Problem
In this economy, a benevolent central planner takes decisions to maximize social welfare. Specifically,
(5)
where is the time preference discount factor, and
are net financial assets. This maximization is carried
on subject to the feasibility constraint:
(6)
and
(7)
and
(8)
where
and
are investment in private and public physical capital respectively. Moreover, for the
interest rate, we have that:
(9)
where
evolves in accordance with the credit market imperfections given the domestic net foreign asset
position.
4.3. Decentralized Economy (Benchmark Model Economy)
An alternative setting to the Social Planner Problem is the competitive market environment, in which each
agent makes her own decisions in order to maximize her respective objective function. Let’s now consider
the characterization of this decentralized economy.
Individual's problem. In our benchmark model economy, individuals maximize the expected discounted
lifetime utility,
(10)
9
For simplicity, we choose
for the debt-output ratio.
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In addition, individuals are subject to the following period constraint
(11)
Where
(12)
(13)
(14)
(15)
(16)
and where
is the wage rate,
denotes the interest rate given by expression (4),
is total taxes,
is the
income tax rate,
is the consumption tax rate,
is the capital income tax rate,
is the payroll tax rate,
is the retirement pension,
are firm's profits,
is total income,
is capital income,
is labor income,
is total income (net of payroll and capital income taxes), and
is the amount of assets at the beginning
of the period. We also assume that net assets are constrained as being non negative, and that
10
. Notice that, in our economy, every household can earn capital income, only workers can earn labor
income, and only retirees can receive retirement pensions
11
.
Firms. The Firm's maximization problem can be stated as
where
are profits, and
is the gross interest rate at period . The First Order Conditions of this
static problem are:
that is, prices are the factor marginal productivities of private capital and labor.
Government. The government has two roles in our model economy. It establishes the fiscal policy and runs
a public pension system, which we describe in turn.
Fiscal policy. In order to determine how the government allocates total revenues between the public
consumption good and infrastructure, we assume that the government's objective function is given by:
(17)
Equation (17) obviously depends on the expenditure variables of the Government. As we have seen on both
the Section 3, where we discuss the Peruvian case, and the evidence presented by Ardanaz and Izquierdo
(2021), there is a clear bias towards current spending by politicians in addition to the overwhelming
empirical evidence of deficit bias (Alessina and Drazen, 1991, and Persson and Tabellini 2000). In this way,
we present a simplification of the government's preferences, leaving aside taxes, which tend to show
marginal changes, unless the country is in a severe fiscal crisis.
10
We assume that households receive the same rental rate as the one faced by the government in the international market due to arbitrage
conditions.
11
For the experiments that we perform, we maintain the tax rates for capital and total income as constant. The payroll tax is adjusted to balance the
pension system, and the consumption tax rate may change according to the implemented fiscal rule. See below.
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This is basically a static maximization problem that must be solved for every period . Furthermore, it is
straightforward to note from this maximization problem, that the shares of public revenues allocated to the
provision of the public consumption good and infrastructure are and (1-) respectively. Therefore, if the
government has a bias towards current spending on the public consumption good, measured by the
parameter , the economy would tend to have a low level of public capital in comparison to its private
capital.
On the other hand, the government in our model economy collects tax revenues using a proportional tax on
total income, a proportional tax on capital income, and a proportional tax on consumption. It also issues one
period real foreign debt. For simplicity, we also assume that the government confiscates unintentional
bequests. The government uses these revenues to finance spending in infrastructure, which raises total factor
productivity. It also makes transfers to households in the form of a public consumption good and repays
the principal plus the interest on the endogenous stock of public debt. Therefore, government spending
must be equal to its revenue:
(18)
where
,
, and
are total tax collections from the total income, capital income, and consumption
taxes respectively,
is unintentional bequests,
is the beginning of period stock of foreign public debt,
is the flow of the public good, and
is the spending on infrastructure.
12
In addition to the credit imperfection introduced in equation (4), we incorporate two additional restrictions.
First, an 80% limit for the public debt indebtedness to output ratio, reflecting cases like Argentina in which
access to capital markets is severely limited after a certain level is reached and the spread in the secondary
market tends to grow exponentially, discounting a greater probability of default.
13
Second, we assume that
the maximum limit for the fiscal deficit is 5% of GDP per year, up to the limit of 80% of the debt-to-GDP
ratio.
Pension System. To complete the specification of our model economy we must describe its pay-as-you-go
pension system. The system imposes a payroll tax,
, over gross labor income, and it also delivers a
retirement pension,
, to all households aged
or older. The budget constraint for the pension system is
defined as:
(19)
where
is total pension payments, and
is gross labor income.
5. Calibration
As it has been mentioned, our baseline economy is calibrated to the Peruvian economy. In what follows, we
fully characterize our model economy and evaluate the calibration results obtained.
5.1. Parameters and Targets
To fully characterize our model economy, we must choose the values of a total of 24 parameters. Of these
parameters, 4 describe household preferences, 3 describe the labor efficiency units allocation process, 9
describe the production technology, and 8 describe the remaining components of the fiscal and pension
12
We assume that the income and capital income tax rates remain constant during our quantitative exercises, in their initial steady state value. The
rationality is that the fiscal rules we study in this paper primarily address the fiscal aggregates (debt, deficit, and expense). Fiscal rules on public
revenues only appear when there are exceptional fiscal revenues.
13
For developed countries, Reinhart and Roggoff (2010) consider a limit of 90% in the debt to output ratio, above which the growth of the countries
is seriously affected. In the case of emerging economies, the IMF (2002) recommends debt limits of 40% to avoid affecting long-term growth due to
the volatility of tax revenues.
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policies. To choose the values of these 24 parameters we need 24 equations or calibration targets which we
describe below. The values of these 24 parameters are reported in Table 1.
Table 1: Parameter values
Parameter
Value
Earnings Life-Cycle
1.1276
0.0468
0.0007
Preferences
Curvature
4.0000
Time preference
0.9815
Utility weight on leisure
1.0000
Private consumption share
0.8000
Technology
Private capital share
0.2500
Public capital share
0.0800
Labor share
0.6700
Depreciation rate
0.1000
Labor Productivity growth
0.0040
Long run value TFP
1.0000
Autoregressive coefficient
0.9500
Mean (TFP shock)
0.0000
Standard deviation (TFP shock)
0.0076
Fiscal Policy
Capital Income Tax rate
0.2771
Total Income Tax Rate
0.1115
Consumption Tax Rate
0.1894
Government consumption share
0.8000
Interest rate premium
0.0500
Maximum Debt-Output ratio
0.8000
Pension Policy
Mandatory retirement age
65
Payroll tax rate
0.0440
The life-cycle profile of earnings. We estimate the values of the 3 parameters of the quadratic function that we
describe in expression (1), using the five-year age groups distribution of monthly wages in 2015 reported by
the INEI. We represent this function in Figure 3. This procedure allows us to identify the values of those 3
parameters directly. The parameters
,
, and
take values 1.1276, 0.0468, and 0.007 respectively.
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Preferences. To determine the household's preferences, we must establish the values of four parameters. First,
we assume that the discount factor is = 0.9815, such that the value for the risk-free world interest rate is
= 0.0188. We also assume that is 4.0, as it is standard in the literature. This choice implies that the
Intertemporal Elasticity of Substitution (IES) varies over the life-cycle as a function of leisure relative to work
hours.
14
We also assume that the share of consumption of the private good is = 0.8. The rationale for this
choice is that, according to the statistics of the Central Reserve Bank of Peru (BCRP [Banco Central de
Reserva del Perú]), for the years 2014-2018, private consumption in Peru had a participation rate of around
0.8 with respect to total consumption.
Finally, for simplicity, we assume that the scale parameter used to replicate the average share of time
dedicated to labor market activities, , is one. The rationale behind this assumption has to do with the fact
that Peru, like many other Latin American countries, has a high degree of informality in its labor market,
which makes it difficult to know the average number of effective hours worked in the economy.
15
We could
assign different values to that parameter, however, it will not change the essence of the main results that we
obtain in our exercises.
Technology. To fully describe technology in our model economy, we must establish the values of 9
parameters. Following Castillo and Rojas (2014), we assume = 0.25, = 0.67 and = 0.08. These coefficients
are also consistent with the values reported by the BCRP. Consequently, we assume that the economy is
subject to constant returns to scale, such that firms will produce extraordinary profits of the magnitude
.This is the reason why we include these positive profits in the households’ budget constraint. This is also
the approach followed by Cassou and Lansing (1998). For the depreciation rate we assume a value of = 0.1,
a value that is standard in the literature. The constant growth rate for labor augmenting productivity is set
in = 0.004, a value that is consistent with the average growth rate of labor productivity in the Peruvian
economy for the 1995-2015 period according to the INEI. Finally, we must establish the values that
characterize the stochastic process for the total factor productivity
. Following Montoro and Moreno
(2007), we assume
= 1,
= 0,
= 0.0076, and = 0.95.
Government. To characterize the government sector in our model economy, we must set the values for 8
parameters. Regarding the fiscal policy, we target the output shares of
,
and
such that they
replicate the GDP shares corresponding to Sales and Gross Receipt Taxes, Corporate Profit Taxes, and
Individual Income taxes. According to the INEI, the average numbers for the period 2007-2015 were 8.56,
4.19, and 1.66 percent of GDP, respectively. These numbers directly establish the values for
,
, and
.
We also assume that the maximum level for the Public debt to output ratio is
= 0.8. This number can be
14
The IES is given by
.In the initial steady state of our model economy, the value for the average IES is 0.76.
15
According to a report by the National Chamber of Commerce, Production, Tourism and Services of Peru [Cámara Nacional de Comercio,
Producción, Turismo y Servicios de Perú], labor informality was 71.1% in 2019.
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seen as an average of those observed for a sample of Latin American countries before the COVID-19 crisis.
For example, Ecuador, with a public debt to GDP ratio of around 50 percent in 2019, did not had access to
international credit markets by that year until it reach an aggrement with the International Monetary Fund
(IMF). On the other hand, Brazil had access to these markets despite having a public debt to GDP ratio of
almost 90 percent that same year.
The weight of public consumption in the government's objective function is another key parameter since it
determines the average level of public capital under-accumulation in the benchmark economy. As already
mentioned, since 2000, in Peru, 3 periods are clearly distinguished in relation to the fiscal rules implemented.
First, from 2000 to 2006, a period in which a limit is imposed on the current fiscal deficit of 1% of GDP and
a rule for the annual growth of real general government spending of no more than 2%. Second, between
2007 and 2011, where an annual growth of the real central government consumption is established not
greater than 3% but maintaining the limit to the current fiscal deficit of 1% of GDP. Third, between 2012 and
2019, where the rule that limited the growth of the central government's real consumption is eliminated and
the current deficit rule is replaced by a structural deficit rule less than or equal to 1% of GDP. When fiscal
rules do not distinguish between consumption and capital expenditure (public investment), there is a
predominance of public consumption over public investment, that is, the government's preferences clearly
favor higher current spending. This is the case during the periods 2000 to 2006 and from 2012 to 2019.
Specifically, and in these periods, the share of government current spending within the total government
consumption was around 80% of total government expenditure, according to the the BCRP statistics.
Consequently, we impose that the share of public consumption in the government's objective function is =
0.8. Finally, and for the parameter that reflects the country-specific interest premium, we choose a value of
= 0.05, since this number falls within the 0.03-0.09 range, which is standard in the literature.
The remaining two parameters define the public pension system of our model economy. First, we assume
that the mandatory retirement age is
= 65, since this number is standard in life-cycle models where the
retirement decision is exogenous. Second, we target the output share of
, so that it replicates the GDP share
of public pension payments. According to the Economy and Finance Ministry of Peru, the average of this
share for the period 2000 to 2010, was 2.7 percent. This value directly determines the value for the payroll
tax rate,
5.2. Calibration Results
We begin this section by showing the calibration results related to the main aggregates and ratios of the
Peruvian economy. Subsequently, we consider the life-cycle profiles generated by our model economy in
the initial steady state.
Macroeconomic Aggregates and Ratios. In Table 2 we report selected macroeconomic ratios in Peru and in the
benchmark model economy. We find that the benchmark model economy does a good job in replicating
most of the values for the reported ratios. Specifically, the model exactly replicates the ratios related to tax
collection. This was expected, given that these ratios were calibration targets. The model also almost exactly
replicates the ratio of private physical capital to output. We find this result very encouraging since we did
not target explicitly this statistic in our calibration procedure. Finally, the model underestimates the ratio of
public capital to output by 12 percentage points. As in the previous case, we did not target explicitly this
statistic in our calibration procedure.
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Table 2: Macroeconomic Ratios in Peru and in the Benchmark Model Economy* (%)
Spain
8.56
4.19
1.66
2.7
1.67
0.56
Model
8.56
4.19
1.66
2.7
1.68
0.44
*Variable Y* denotes GDP at market prices. The Peruvian data for the tax collections is taken from the INEI. The
Peruvian data for the capital stock is taken from the IMF (Investment and Capital Stock Dataset, 1960-2017), and
correspond to the year 2017.
Life-cycle profiles. Figure 4 shows life-cycle profiles of consumption, assets, and hours worked as a percentage
of disposable time. We find that hours worked are mainly in the range of 20 and 30% of disposable time.
Consumption shows the usual increasing profile at the beginning, then decreases, and finally remains
constant because it is entirely financed by pensions as well as the public consumption good.
Figure 4 also displays the usual patterns of average asset holdings over the life cycle. The figure shows not
only that agents begin to accumulate assets late in the working lifetime, but also that these assets are almost
totally consumed as soon as the agents reach 80 years old. Put differently, households in our model economy
have little incentive to save, and the reasons are: (i) households are not altruistic, so they do not leave
voluntary inheritances; (ii) there is no uncertainty in the income received by households, so they do not have
a precautionary reason to save; (iii) the government assured them a flow of consumption with the provision
of the public consumption good, during the different stages of the life cycle; and (iv) during the time of
retirement, the government pays retirement pensions.
6. Policy Experiments, Scenarios, and Fiscal Rules
In this section, we describe both the experiments, and the demographic and fiscal scenarios that we use in
our simulations. We also simulate the optimal and the benchmark model economies. Finally, we define the
four fiscal rules that we are going to use in our final simulations.
6.1. Experiments
All the simulations that we describe below, involve the computation of an initial and final steady state, and
the transition path between them. Additionally, all simulations share the following features. The initial
steady state ( ) is characterized by a public debt to output ratio of 60 percent, such that the domestic
interest rate is 4.88 percent. Moreover, in this initial steady state, total public revenues (net of public debt
interest payments) are split between public consumption and investment in infrastructure according to the
government preferences. From period to , all model economies are exposed to the same
productivity shocks. Subsequently, we assume that the productivity shock reaches its long-term mean value
. Figure 5 plots the realization of this productivity shock between periods to .
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6.2. Scenarios
All of the model economies we are going to study share the demographic and fiscal scenarios that
we now describe.
Demographics. We take the measure
for all = {20,21,...,100} directly from the demographic
projection (middle hypothesis) of the Peruvian INEI, for the period 2000 to 2050. After this last
year, we assume that this measure remains constant at its 2050 value. We also take the conditional
probabilities of surviving
between 2017 and 2050 from the INEI. We assume that between
2000 and 2016, these probabilities are those estimated for the year 2017. We also assume that these
probabilities remain constant at their 2050 value after that same year.
16
In Figure 6A, we plot the
implied old-age dependency ratio, which we define as the number of people with 65+ years old
to the number of agents aged 20 to 64. In Figure 6B, we plot the age-dependent survival
probabilities for both 2000 and 2050.
Pension Policy. Recall that, in our model economy, the pension system budget constraints is:
16
The Peruvian INEI reports the population projection for five-year age groups: 20-24 years, 25-29 years, etc. We assume, within each age group,
that there is the same number of people at each age. Similarly, this demographic projection is done for 5-year intervals. In this case, we perform a
linear interpolation, for each age group, between two immediately consecutive periods.
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(20)
In all model economies, the payroll tax rates vary across the economies because we change them
to finance pensions. Every other variable in these expressions also varies in time and varies across
economies because they are all endogenous.
6.3. Optimal and Benchmark Model Economies
In what follows, we simulate the optimal and the benchmark model economies, following the simulation
strategy mentioned in subsection 6.1.
The Optimal Model Economy (Social Planner Problem). In the Optimal Model Economy (as stated in equations
(5) to (9)), the optimal allocations of public and private capital given the maximization problem faced by the
benevolent social planner are
(21)
where
and
are the marginal productivities of both private and public capital. Note also that
public investment in infrastructure for period can be obtained from the law of motion of public capital
(22)
On the other hand, the optimal allocations for both the private and public consumption goods imply that at
any age ,
(23)
The Benchmark Model Economy. Our benchmark model economy assumes that the mix of public expenditures
is set according to the government’s preferences. Moreover, we assume that between periods and
, the government runs a fiscal deficit of 5 percent of output, such that at the end of period , the ratio
Public Debt to output becomes 80 percent (the maximum allowed value for this ratio), and it remains
constant at this same value throughout the transition path.
If we compare the evolution of output during the transition path both in the Social Planner economy and in
the Benchmark case, we note significant differences (see Figure 7). Specifically, and with both economies
starting from the same initial conditions, output under the Social Planner grows significantly from the
outset, while Benchmark case output remains at relatively stable levels, although slightly below its initial
value. The latter is, in turn, due to the increase in domestic interest rates (caused by the increase in public
indebtedness) which reduces the accumulation of capital. On the contrary, the sustained increase in output
under the social planner is a consequence of the substantial increase in public capital, motivated by the
optimality conditions between both types of capital, and by increased private capital. In other words, the
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investment in infrastructure in the case of the Social Planner's problem is substantially higher.
There is a significant difference in output performance between the Social Planner economy and the
Benchmark economy with imperfect financial markets and one-period Government. The primary
explanation for such a difference is the bias towards large fiscal deficits, which results in high interest rates
affecting private capital accumulation and, therefore, economic growth. In order to correct for this problem,
institutional arrangements were implemented during the last two decades, primarily imposing restrictions
on the level of debt and/or the level of the fiscal deficit, with a large amount of research devoted to
addressing the convenience of targeting current or structural fiscal deficits (Wyplosz, 2013; Eyraud et al.,
2018). However, in recent years, after achieving macroeconomic stability and keeping both fiscal deficits
and total public debt under control, significant dissatisfaction has arisen among policy makers related to
output performance given the strong bias towards public consumption and the limited reduction in the debt
to output ratio observed in most countries (Ardanaz and Izquierdo, 2021, and Ardanaz et al., 2020).
6.4. Fiscal Rules
In what follows, we define the fiscal rules that we are going to use in our final simulations. We introduce
four different rules. The first two deal with the problem of deficit bias, imposing a current deficit rule equal
to zero and a structural deficit equal to zero. The other two rules incorporate an additional expenditure rule
into both the current deficit rule and the structural deficit rule, imposing that public capital spending be
aligned with the optimality condition given by equation (21). In other words, for the first two rules we alter
the budget constraint, while for the latter two rules the government’s preference function is also altered.
17
Fiscal Rule I (FR1). This rule implies a balanced current fiscal budget for every period, i.e. the current fiscal
deficit is equal to zero. In this model economy, we continue to assume that the government runs a fiscal
deficit of 5 percent of output between periods and However, and once the Public Debt to output
ratio reaches 80 percent, the government runs a primary fiscal surplus to pay the interest of public debt. This
assumption has two consequences. First, the nominal amount of government debt at the end of period
remains constant along the transition path. Second, the public debt to output ratio varies during the
transitional dynamics. In fact, and once the productivity shock reaches its long run mean value
, this
ratio decreases because the output grows. Specifically, the government budget constraint becomes:
(24)
Fiscal Rule II (FR2). This rule implies a balanced structural fiscal budget for every period. As in the
Benchmark model economy, the government runs a fiscal deficit equivalent to 5 percent of output between
17
There are multiple possibilities to impose fiscal rules. For simplicity, we choose a canonical rule giving by the optimality conditions in order to
illustrate the differences.
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periods and . From period onwards, the government follows a structural fiscal budget rule,
aimed at eliminating the cyclic effects of output on the fiscal deficit. Therefore, an increase in the output
over its trend would lead to an increase in revenue without an increase in public spending, with the
consequent reduction in public debt. Stated differently, extraordinary tax revenues resulting from the
expansive phase of the cycle are saved for the time in which the output is in its recessive phase. Finally, as
in the previous simulations, once the productivity shock reaches its long run mean value
, this ratio
decreases because the output grows. In this case, the government budget constraint becomes:
(25)
where
is the structural tax revenues collected by the tax on Specifically,
(26)
Naturally, the changes in the age distribution that occur in the model during the path of transition to a final
steady state, modify labor force and savings, and therefore capital. In other words, the potential output of
the economy changes each period until the model converges asymptotically towards that final steady state.
Consequently, and to obtain the value of the potential output during the transition path, we proceed as
follows. We simulate the benchmark economy, but assume that total factor productivity remains at its long-
term value. This prevents the economy from being exposed to unexpected shocks that increase or decrease
output relative to the one observed in the absence of such disturbance. The rest of the scenarios, such as the
demographic and fiscal scenarios, remain exactly the same as those used in the benchmark economy.
Notice that with FR1 and FR2 we are imposing a stronger restriction on the Government’s problem, forcing
it not to increase the stock of debt (FR1) or forcing it to take debt only when current fiscal income is below
the structural fiscal income (FR2). However, under these two rules, the government continues to use its one-
period preferences to determine the expenditure composition between public consumption and public
investment. The next two rules deal with this issue.
We simulate two additional economies that resemble the two previous model economies, but with the
significant difference that the share of government expenditure allocated to public investment in
infrastructure follows the optimality condition described in the Optimal Model Economy. Specifically, the
optimality condition determines the amount of public investment in period , such that the public
consumption good is obtained residually from the government budget constraint. We also assume that this
is the rule followed by the government for every period .
Therefore, the next two fiscal rules are the following:
Fiscal Rule III (FR3). This rule is the FR1 to which an expenditure rule has been added.
Fiscal Rule IV (FR4). This rule is the FR2 to which an expenditure rule has been added.
Note that under the fiscal rules III and IV, the government behavior is restricted by equations (21) and (24).
The only difference is that public consumption is obtained residually from equation (24) under the Fiscal
Rule III, and from equation (25) under the Fiscal Rule IV. Put differently, under the last two fiscal rules, the
expenditure rule forces the government to decide first on public investment in order to achieve the optimal
ratio between private and public capital. Even though this expenditure rule must seem unrealistic, the idea
is to gain intuition about the “amount of protection” that public investment needs in order to avoid being
crowded out by public consumption, which can entail more benefits from the political point of view in the
short term.
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7. Results
In this section, we first introduce our simulations for the four different fiscal rules, comparing the results
obtained. Then, we study the performance of the economies adopting each of the four fiscal rules proposed
under three different shocks: commodity shock, higher output variability and financial stress.
18
7.1. Fiscal Rules's Performance
Figure 8A shows the output performance for the benchmark economy and the economies implementing the
four rules described in the previous section. It is not surprising that, in all cases, the output performance in
the economies with rules is better than in the economy with no rules (benchmark economy). Among the
economies with rules, the best performer is the economy implementing the FR4 and the worst performer is
the economy implementing the FR1. It is also interesting to notice that the FR3 tends to outperform the FR2,
clearly implying that having an expenditure rule protecting public investment is more useful than
addressing the shift from the current to the structural deficit.
Figure 8B shows the time series for the potential output. The evolution of the potential output during the
transition path is mainly determined by the population aging expected in Peru during the next decades.
Specifically, population aging reduces the workforce and increases the payroll tax needed to balance the
pension system budget. Additionally, the higher payroll tax reduces saving, and consequently, private
capital.
We are interested in the two channels available for improving output: the private channel, by lowering
interest rates and increasing private capital, and the public channel, by increasing public investment.
With respect to the private channel, Figure 9 shows that the debt to output ratio of the benchmark economy
remains constant at 80%. The public debt to product ratio has a well-differentiated behavior among the
economies that adhere to a zero-deficit rule as compared to those that follow a structural deficit rule. For
economies that have implemented rules based upon the current fiscal deficit (FR1 and FR3), the output ratio
slowly converges towards values close to 30% over the long term, primarily due to output growth. For
economies that have implemented rules based upon the structural fiscal deficit (FR2 and FR4), the ratio
converges to zero, more rapidly in the case of FR4 (because of the higher output) and more slowly in the
case of FR2. The interest rate follows the same pattern as the debt to output ratio (see Figure 10); affecting
investment decisions in the private sector (see Figure 11).
18
For every case, we present the de-trended Labor Augmenting Growth results.
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The main reason for this differentiated behavior in the ratio across economies is precisely the management
of public debt during those periods of time in which output departs from its potential level. If we take the
case of FR2, we see that until around period t = 130, output tends to be below its potential level almost every
period, which means that the ratio of public debt to output is at or near the maximum ratio, 80 percent.
Nonetheless, when the output of FR2 exceeds its potential value because of the sequence of positive
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exogenous shocks on TFP [Total-Factor Productivity] (see Figure 5), the government uses the additional tax
revenues to reduce public debt, which generates a sharp decline in the public debt to output ratio.
19
In the case of FR4 there is an additional effect. When the government goes into debt to offset the decline in
the tax revenues, which results from lower output as compared to potential output, a significant portion of
this new debt is aimed at financing investment in infrastructure, which translates into subsequent increases
in output due to a greater capitalization of the economy. Note that this is not the case for FR2, since the new
public debt generated by the government finances mostly the expenditure of the public consumption good.
In other words, and given the implementation of the spending rule, the output in FR4 quickly reaches and
exceeds potential output, which generates a rapid drop in the public debt to output ratio, all thanks to the
rule of structural deficit.
With respect to the second channel, the public one, we can note in Figure 12 that, for the economy
implementing FR4, the public capital to output ratio converges to its equilibrium level more rapidly. In this
case, given the expenditure rule imposed on the economy under FR3, the public capital to output ratio also
increases, although it does so at a slower pace than the economy under FR4. For economies under the FR1
and FR2, there is no substantial difference as compared to the benchmark economy.
20
When we study the ratio between private and public capital (see Figure 13), as it is anticipated by
construction, the economies under FR3 and FR4 rapidly converge to the optimal ratio provided by the
coefficients in the Cobb-Douglas production function. In contrast, the ratios obtained under the benchmark
economy and the economies implementing FR1 and FR2 are not optimal. In fact, those economies have too
much private capital given the level of public capital, because private capital is relatively large as compared
to the low level of public infrastructure. This is especially the case for the economy that is implementing FR2
when the interest rate is at its lowest level given that the public debt ratio is equal to zero.
19
Over the long run, the public debt to output ratio would tend towards zero under the FR1 and FR3 economies due to the growth of output.
However, and since this process is slow, it would force us to simulate a large number of periods to complete the transition path, until reaching a
stationary situation in the economy that would allow an asymptotic convergence towards the final steady state. To shorten the number of simulated
periods, we assume that the labor augmenting growth rate is 0 percent from period 250 onwards, hence the stabilization of the public debt to output
ratio going forward from that period.
20
Note that Figure 12 represents public capital in terms of output. In absolute terms, we observe a much larger increase under FR1 and FR2 relative
to the benchmark economy.
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It is interesting to note the evolution of the fiscal result for the various rules. By construction, in the case of
FR1 and FR3, the fiscal result is zero for each of the periods, while for FR2 and FR4 the current fiscal result
is something other than zero, but the structural result is zero (see Figure 14).
For the case of FR4, the economy converges more rapidly to the zero fiscal result, given the higher growth
and the faster decrease in debt. However, this result is obtained by way of increased volatility of the fiscal
result at the beginning. Thus, for the first 100 periods, the average result is 0.4% and the standard deviation
is 1.9, while for FR2, the average fiscal result is 0.2% and the standard deviation is 1.8.
Finally, we follow Conesa and Krueger (1999) and compute the consumption equivalent variation measure
(CEV) for newborns before and after the fiscal reforms in the final steady states. Specifically, we compute
the welfare change of a reform for a newborn, by asking by how much this newborn's consumption has to
be increased in the benchmark steady state, holding leisure constant, so that her expected utility equals that
under the specific reform. Consequently, and given the form of the utility function, we compute
where and
are the value functions of a newborn under the benchmark and the reformed fiscal system,
respectively,
. For example, a of 0.01 implies that a newborn will enjoy an increase
in welfare equivalent to receive 1% higher consumption under the benchmark economy.
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In Table 3 we show the CEV, and we find that the adoption of a fiscal rule implies sizable welfare gains
relative to the absence of a rule. Furthermore, introducing rules which address not only the bias for fiscal
deficit, but also take into account the bias for current expenditure, seems to be of critical importance to
induce a public expenditure composition which is closer to optimal. Thus, the greater capitalization of the
economy under Fiscal Rule IV entails a significant increase in wages, and consequently, in consumption, so
that it translates in no minor welfare gains for newborn households. Our results are consistent with the
findings of Alfaro and Kanczuk (2019), who report significant welfare gains after introducing fiscal rules.
Table 3: Consumption Equivalent Variation for Newborns* (CEV, %)
CEV (%)*
Fiscal Rule I
8.07
Fiscal Rule II
7.68
Fiscal Rule III
7.33
Fiscal Rule III
10.65
*Relative to the Benchmark economy.
7.2. Fiscal Rules's Performance under Different Shocks
In what follows, we analyze the performance of the four fiscal rules described when exposed to three
different shock events: a commodity shock, increased output variability and financial stress.
7.2.1. Commodity Shock
We assume that there is a temporary commodity price increase for the domestically produced good which
increases domestic tax collections for each period. We model this shock as an exogenous increase in the
economy’s fiscal revenues during 5 periods (from period 6 to 10), and we assume three different scenarios:
a shock that increases fiscal revenues equivalent to 1, 3, and 5 percent of output for each period (see Figures
15, 16, and 17). These additional tax revenues are used for public expenditures under FR1 and FR3, but these
same extraordinary fiscal revenues are allocated to the reduction of public debt under FR2 and FR4.
We focus exclusively on the first 30 periods for the economies affected by the four fiscal rules studied in
order to emphasize the short-term responses of each economy to these three shocks. We find, as it was
anticipated, that there are no significant differences in output performance among these economies when
they are affected by the small shock representing 1% of output. However, the differences start to increase as
the shock rises.
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CARRANZA, DÍAZ – SAAVEDRA y GALDÓN - SÁNCHEZ
In general, fiscal rules that impose restrictions on current fiscal deficits tend to perform better during a
commodities shock, while the rules based on structural measures tend to reduce debt instead of increasing
public expenditure. During the medium term, the differences in favor of the structural based rules start to
increase. Figure 18 compares the differences in output performance between the FR4 and FR3 for the three
different shock scenarios. As can be noted, as time goes by, the impact of the temporary shock became
irrelevant.
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CARRANZA, DÍAZ – SAAVEDRA y GALDÓN - SÁNCHEZ
7.2.2. Higher GDP Variability
Next, we examine the performance of the rules when the TFP variability increases by a factor of 2. Under
this scenario, we must generate a new series of shocks with higher variability and compute the new output
performance for the economies. In this case, it is useful to compare the relative performance of the fiscal
rules described under two different regimes: a regime with low output volatility (
=0.0076) and a regime
with high output volatility (
=0.0152). This exercise is presented in Figure 19. Note that over the long term,
the difference in performance converges to the same value but, during the first 100 periods, the FR4 produces
significant better output performance as compared to the FR3. In short, the more volatile the economy
becomes, the more useful a structural based fiscal rule is.
7.2.3. Financial Stress
Finally, we investigate the case in which our economies are affected by financial stress. Using a simple OLS
regression of the spread (dependent variable) on the debt-to-output ratio (explanatory variable) for the Latin
American countries, we found that for the countries implementing fiscal rules, like Peru or Colombia, the
coefficient that reflects the country-specific interest premium is close to 0.05, which has been the number
that we have used in all our exercises. However, if we run the same regression for countries with high levels
of debt and no fiscal rules in place, like Argentina or Ecuador, we find coefficients between 0.25-0.30.
Based on the simple regressions described in this exercise, we will assume that the coefficient increases from
0.05 to 0.25, as an exogenous shock, then remains at that level. Although the general results stand, it is
interesting to note the relative performance of the fiscal rules under this scenario. Specifically, and for
obvious reasons, we will focus on the economies implementing FR1 and FR2. In Figure 20, we present the
performance for FR1 as compared to the benchmark economy under normal conditions and under a
financial stress situation. We find that, under financial stress, it is more relevant for an economy to
implement a fiscal rule because a higher interest rate will have a stronger negative impact on private capital
accumulation and therefore on the growth of output. Our results are related to the findings of Fernández-
Villaverde et al. (2011), who report that an increase in the interest rate volatility triggers a fall in output,
consumption, and investment. The same occurs when we perform this same exercise under the FR2. Figure
21 shows the results.
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CARRANZA, DÍAZ – SAAVEDRA y GALDÓN - SÁNCHEZ
Nonetheless, it is important to note that, when there is financial stress, the positive impact of implementing
a fiscal rule based on current fiscal results is relatively more significant than the positive impact of
implementing a fiscal rule based on structural fiscal results. The reason is that a structural rule includes the
structural output and, therefore under that scenario, it takes longer to reduce debt, something that it is not
relevant when the financial situation is not affected by any shock. When debt and spreads are high, fiscal
consolidation is of utmost importance. Stated differently, when the cost of taking external debt increases
very steeply, these external fiscal resources become very expensive because the high interest rate paid
greatly reduces the physical capital stock, and consequently, output.
8. Conclusions
Fiscal rules are useful instruments for achieving macroeconomic stability, this being understood as debt
levels that are sustainable over the medium-term. However, in terms of long-term growth, their
performance has not been so auspicious. Although it is true that, on the one hand, fiscal sustainability leads
to reduced financial costs, given fiscal stability, and therefore drives growth through private investment; on
the other hand, public investment is de-emphasized by the government, which, in the context of a restricted-
spending scenario, tends to favor the increasing of current spending. Hence, as we demonstrate with our
exercises, the fiscal rule will be more efficient if, in addition to maintaining control over the fiscal result, it
also eliminates the bias against public investment.
In this paper, we assume a spending rule that determines the level of public investment to be that which is
compatible with the optimal private capital ratio. Since this is clearly not implementable, simpler schemes,
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such as those applied by Peru for example, are required. As demonstrated in our simulations, protecting
public investment is a key policy objective.
It is interesting to note that the gap between economies with and without fiscal rules raises when there are
commodity price shocks and increases in volatility that affect the economies. Similarly, the results of
economies that implement structural rules tend to be better than the results of economies that implement
rules based on current results.
It is also interesting to note that when we compare a structural rule with a current rule, the structural rule
performs better. But, when economies face a scenario of financial stress, structural rules tend to reduce debt
less quickly, tolerating higher fiscal deficits for longer periods of time. This is clearly due to the manner in
which we have defined potential output and the structural fiscal result arising from this definition. The main
conclusion of our research is that it is critical that the Government does not use the structural results as and
excuse for delaying the necessary fiscal adjustments.
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