The theoretical model highlights that in developing countries, infrastructure accumulation depends on the attractiveness of the informal sector. The baseline model shows that an increase in taxation has heterogeneous effects on high-skilled and low-skilled workers. I show that under the informal regime, increasing taxation does not affect the net income of the low-skilled while the dynamic impact on the high-skilled wage depends on its effect on the infrastructure accumulation and on the skill premium. The effects for high-skilled workers are amplified in the model with endogenous brain drain. Moreover, in this extended model, a developing countries may switch from informality to the formal regime by accumulating larger stocks of infrastructure and human capital. The short-run and long-run responses to a fiscal shock depends on the parameters of the model.
Hence, in this section, I quantitatively assess the impact of policy reforms affecting the tax base or the tax rate. I first describe my parametrization strategy which is common to both variants of the model. I calibrate the model on 60 developing countries at the year 2000.27 One period lasts 25 years and I assume
each country is at its steady state in the year 2000. As informality is observed in all countries, the steady state belongs, by construction, to the informal region. The parametrization strategy is designed so as to perfectly match, for each developing country, the data on the evolution of the size and structure of the labor force between 1975-2000, on the size of the formal sector, on the size of the labor force in the informal sector, and on the skill premium. The first Subsection explains my data sources and my calibration strategy. Then, the other Subsections discuss the results of my policy experiments.
2.4.1
Calibration Strategy
In the set of parameters, I distinguish between common (structural) elasticities and country-specific characteristics. The set of structural parameters is (ε, φ, n, µ). A key elasticity is ε, which links the level
27The quantitative appendix reports the list of countries, see Subsection 2.6.3.1. The same table report the country code
of total factor productivity to the stock of infrastructure per worker. As IMF (2014), I use the value computed by Bom and Ligthart (2014), who find an average elasticity of output to core infrastructure of 0.17. Another important elasticity is φ, which captures the education externality. I follow de la Croix and Docquier (2012), who use an elasticity of 0.277. They obtain this value by regressing the level of total factor productivity on the skill ratio using a sample of 142 developing countries in the year 2000.28
As in de la Croix and Docquier (2012), I also set the fertility differential n to 0.605 in all countries.29
The last structural parameter is µ, the scale parameter of the distribution of migration taste shocks. As outlined in Section 2.3.9, I set it to unity. This choice implies an elasticity of the high-skilled emigration rate to the ratio of net wages equal to one.
As far as country characteristics are concerned, data on income tax rate are taken from Dobbs (2013). He provides estimates on public infrastructure investments as a percentage of GDP for the period 1992- 2001. This variable is computed for some countries and for most regions of the world.30 According to
Figure 9, the country that invested the highest share of its GDP in infrastructure is China, where the average investment rate in public infrastructure was equal to 8.5% of GDP between 1992 and 2001. Much smaller levels are obtained for Africa and the Middle East, where average investments in infrastructure were equal to 3.6% of GDP.
Figure 9: Income taxes devoted to public infrastructure (1992-2001)
China Developed Countries East Europe/Eurasia European Union India Japan Latin America
Middle East and Africa United States 0 1 2 3 4 5 6 7 8 9
Average Investments on Infrastructure between 1992-2001
Country/Region
Data on average investments on infrastructure (as a % of GDP) for the period 1992-2001 comes from Dobbs (2013). The tax rate borne by formal sector workers matches these estimates.
28Following the same paper, I recall that there is still a debate about the size of the education externality. For instance,
Acemoglu and Angrist (2001) find no effect of schooling on productivity, whereas Iranzo and Peri (2009b) find a value of 0.44 for the US States.
29They use data on on fertility rates from Kremer and Chen (1999) and then compute the differential fertility for the
period 1985-1989 and for 26 developing countries. They find that the correlation between country-specific levels of the fertility differential and the human capital of women is small. On this basis, they assume that the fertility differential is independent of the level of development.
Some other country-specific parameters and endogenous variables,31
nl,j, nh,j, αj, mj, mj, zss,j, zss,f,j for each country j,32are calibrated by combining various data sources
and to match some moments. From Defoort (2008) and Docquier et al. (2009), I use data on the size and education structure of the labor force in the years 1975 and 2000. This allows me to compute the gross growth rate of the workforce, g2000,j. Furthermore, Docquier et al. (2009) provide data on emigration
rates by education level for each source country. I use them as proxies for m2000,j and m2000,j.33 Using
g2000,j, n, and the skill-specific emigration rates, I identify the low-skilled fertility rate, nl,j, as the solution
of Eq. (40). I also obtain nh,j after dividing nl,j by n.
From Docquier et al. (2009), I compute the skill ratio in year 2000, zss,j. I combine this variable with
data on the size of the informal sector labor force. Such data were compiled in Schneider (2012), after exploiting OECD and World Bank data. In particular, Schneider (2012) provides estimates of the level of informal employment for 60 developing and transition countries and for the year 1998. The sample include 33 African countries (average proportion of informal workers equal to 54.2% of the labor force), 12 Asian countries (average proportion equal to 46.5%), 9 Latin American countries (average proportion equal to 46.5%), and 6 European transition economies (average proportion equal to 50.0%).34 This allows me to identify the skill ratio in the formal sector, zss,f,t, one of the key variables of my model, using:
zss,f,j =
H2000,j
L2000,j(1 − sj)
, (47)
where sj is the size of the informal labor force in country j as reported in Schneider (2012) for the year
1998, H2000,j and L2000,j are the stocks of high-skilled and low-skilled workers reported in Docquier et al.
(2009).
Then, I calibrate α, the elasticity of official GDP to the stock of high-skilled, so as to match data on the skill premium. From Section 2.3.1, the wage ratio between high-skilled and low-skilled workers in the formal sector is equal to W R = (1−α)zα
f,t. Hendricks (2004) provides Mincerian measures of
returns per year of schooling for 54 countries around the year 2000. From Barro and Lee (2013) I can assess the difference in years of schooling between a high-skilled and a low-skilled worker.35 In the following, M R2000,j, means the Mincerian return in country j, while DY2000,j stands for the difference
in years of schooling between high-skilled and low-skilled workers. Therefore, the wage ratio is given by W R2000,j = (1 + M R2000,j) DY2000,j. I determine α as following: αj = W R2000,jzss,f,j 1 + W R2000,jzss,f,,j , (48)
I also assume that α is time invariant. Finally, a last set of country-specific parameters and the value of
31The subscript ss stands for steady state. 32m
2000,j is endogenous in the second variant, in such a case the right notation requires the drop of the year from the
subscript, namely mss,j.
33They define as high-skilled workers all individuals aged 25 and over with at least one year of college education. 34A key assumption made on estimating the informal sector labor force is that its magnitude in cities is at least as high
as in rural areas, which is clearly a conservative assumption.
35For some countries, data on Mincerian returns or on years of education are not available. In such cases, I proxy
the wage ratio as in Delogu et al. (2014), who predicted wage ratios using a simple OLS regression, ln (W R2000,j) =
0.25 − 0.131 ln h j 1−hj with R2= 0.57.
infrastructure per capita at the steady state are calibrated,
A0,,j, qj, γj, w∗j, kss,j, are calibrated using the assumption that the year 2000 is a steady state (the
subscript ss stands for steady state). I need to calibrate A0,j and γj, the formal and informal scale
parameters, qj the fraction of children receiving higher education in low-skilled families, and kss,j, the
stock of infrastructure per worker. Furthermore, when brain drain is endogenous I also calibrate w∗j, the high-skilled net wage abroad. I identify the level of these variables by numerically solving a non- linear system at the steady state. In the exogenous brain drain case (A0,j, qj, kss,j, γss,j) are determined
simultaneously, solving numerically (for each country considered) the non-linear system delineated by Eqs. (25), (35), (49), (53).36 I use data on GDP in USD dollars for the year 2000 from World Bank (2012). For the extended model with endogenous brain drain, I add the equation which governs the brain drain, Eq. (46), and then I solve for A0,j, qj, kss,j, γj, wj∗. The equations defining the steady state levels
of the skill ratio and the stock of infrastructure change as well. I numerically solve a new system which includes Eqs. (57) and (59) instead of Eq. (49) and Eq. (53).37 Figure 10 shows the calibrated values
of the stock of infrastructure per worker for all countries considered. A table in Subsection 2.6.3.1 of the Appendix reports the list of the countries with the associated code and the calibrated value of the stock of infrastructure per worker.
Figure 10: Calibrated stock of infrastructure per worker (by continent)
AGOBENBFA BWA CIVCMR COG ETH GAB GHAGIN GMBKEN LBR LSO MDGMLI MRT MWI NAM NER NGARWASDNSEN
SLETCDTGO TUN TZAUGA ZAR ZWE 0 20 40 60 80 100 120 140 Infrastructure Africa BGR GEO HRV ROM RUS SVN 0 50 100 150 200 250 300 350 400 Infrastructure Europe ARM CHN IDN IND KAZ KGZ LKA MNG NPL PAK PHL YEM 0 20 40 60 80 100 Infrastructure Asia BOL BRA CHL COL ECU GTM PER PRY SLV 0 10 20 30 40 50 60 70 80 Infrastructure South-Central America
This figure reports the calibrated values of infrastructure, kss. In the appendix, Section 2.6.3.1 provides the association between
countries codes’ and countries’ names.
36In Section 2.6.1.1 of the Technical Appendix, I report Eqs. (49), (53) which set, respectively, the skill-ratio and
infrastructure- levels at the steady state for the model with exogenous brain drain.
37In Section 2.6.1.3 of the Technical appendix, I report Eqs. (57) and (59). These equations define the skill ratio and
Figure 10 shows that the calibrated value of kss reaches its greatest value in Slovenia. Among Asian
countries, China is the country where the index reaches its greatest value, in spite of the fact that it looks evidently too small when compared to some European and African countries.
I validate the parametrization strategy by computing correlations between the calibrated values of kss
and physical measures of infrastructure. Table 4 shows that the calibrated infrastructure index exhibits strong correlations with actual measures of infrastructure.
Table 4: Correlation between kss and official proxies for infrastructure
Var (year 2000) k00
Paved roads (%) 0.49
Kwh per capita 0.69
Telephone Lines 0.74
Electricity Losses -0.20
Data Source: World Bank (2010)
The first row shows that kss is positively correlated with the percentage of paved roads (69%). Im-
portantly, the correlations between kss and the production of Kwh per capita (69%) or the number of
telephone lines (74%) are large. Finally, the last row shows that infrastructure is negatively correlated with a measure of electric power transmission and distribution losses.
2.4.2
Simulations
I now use the calibrated model to simulate the country-specific responses to three policy reforms, which affect either the tax base or the income tax rate. I simulate the effects of these reforms on the trajectory of the stock of infrastructure per worker (kt), of wages (wh,tand wl,t), and of the high-skilled emigration
rate ( ¯mt). In all cases, the shock occurs in the year 2025 and is assumed to be permanent. I study its
short- and long-run effects (abusing the standard terminology, I refer to the year 2100 when describing the long-run effects), considering both variants, namely with exogenous and endogenous emigration rates. In the first numerical experiment, labeled as “Removing informality”, I simulate the effect of a total ban of the informal sector. The shock consists in setting γ = 0, so that all low-skilled workers are forced to join the formal sector, then paying taxes and contributing to the funding of public infrastructure. The informal sector is usually described as a heterogeneous sector including registered firms activities hidden from the state, wage employment or self-employment in unregistered small-scale business units, and sometimes home production. A total ban of informality is neither a feasible option (as part of it involves home production) nor a desirable option (informality serves a subsistence sector for many workers) in developing countries. This experiment must only be considered as a thought experiment that illustrates the effect of the informal sector on the marginal productivity and income of workers at low level of development. Results are discussed in Subsection 2.4.2.1.
In the second numerical experiment, labeled as “Taxing informality ”, I allow the government to tax informal workers at the same rate as the formal ones. A large share of informality (including the overwhelming share that involves market transactions) is tolerated by the State in developing countries. The reasons are multiple, such as the incapacity of the State to develop or maintain social programs, its incapacity to manage unemployment, the fear of a bankruptcy of the economy, the fear of social tensions, etc. I disregard the political implications of changing the tax base, and consider this scenario as another thought experiment illustrating the role of tax evasion. Contrary to the first experiment, which induces a drastic fall in the marginal productivity of low-skilled workers (due to their massive inflow in the formal sector), this shock induces smaller effects on their marginal productivity. However, it implies that all low-skilled workers become fiscal contributors. Results are discussed in Subsection 2.4.2.2.
The third numerical experiment, labeled as “Fiscal policy”, considers a 1 percentage point increase in the tax rate borne by formal workers. This scenario can be considered as a feasible policy reform. It allows understanding the dynamic implications of an expansive fiscal policy for infrastructure accumulation, human capital accumulation, brain drain and development. Results are discussed in Subsection 2.4.2.3.
2.4.2.1 Removing Informality
I start simulating the effect of a total ban of informal activities (setting γ = 0) from the year 2025 onward. In this counterfactual experiment, I prevent low-skilled workers from using the informal technology in developing countries, although they have incentives of doing so.38 As infrastructure is defined as a
stock variable (see Eq. (33)), the shock has gradual implications for the economy. When brain drain is exogenous, the stock of infrastructure per worker does not change in the short-run. Instead, when emigration rates are endogenous, the inflow of low-skilled workers in the formal sector increases the marginal productivity of high-skilled workers and reduces the brain drain. The stock of infrastructure per worker is then negatively affected in the short-run. However, a sizable impact on infrastructure is obtained in the long-run, after taxes have been invested. For each country in my sample, Figure 11 shows the long-run effect of banning informality on the stock of public infrastructure per worker, measured as percentage of deviation from the initial steady state. The grey bars show the effect obtained under exogenous brain drain, while the black bars show the additional gains obtained once emigration rates are endogenous.
The change in the stock of infrastructure per worker varies across countries. These variations are explained by the initial size of the informal sector, which is itself determined by the country-specific parameters of the model. As far as the exogenous migration scenario is concerned, it is possible to identify the exact equation that governs the percentage change in public infrastructure. This equation is reported in Subsection 2.6.3.2 of the appendix; it shows that the relative change in infrastructure is a function of a set of parameters and initial conditions (zss, kss, γ, α and τ ). To disentangle the sources
of variation across countries, I use the model with exogenous migration and compute the correlation between the change in public infrastructure per worker and each of these five determinants. Table 5
38On the contrary, high-skilled workers in developed countries have no incentive to work in the subsistence sector given
reports these correlations. I find that the relative change in public infrastructure is negatively correlated with each determinant. Consequently, countries starting with a lower initial level of infrastructure, with a smaller tax rate, with a less productive informal sector, or with a lower value of α experience larger effects on the public-infrastructure stock.
Table 5: Removing informality: determinants of the long-run change in public infrastructure (exogenous brain drain) Parameter/Variable Correlation γ -0.38 kss -0.30 zss -0.58 α -0.55 τ –0.17
The solution is more complex under the endogenous brain drain scenario. Figure 11 clearly illustrates that larger effects on infrastructure are obtained when the brain drain responds to the shock (see black bars). In this context, I compute the correlations between the extra-gain in public infrastructure gains and the high-skilled emigration rates in year 2000. Unsurprisingly, the size of the extra-gain is highly correlated with the current brain drain rate (the correlation is equal to 0.76). Banning the informal sector suddenly reduces the number of high-skilled emigrants. This effect materializes in the short-run, right after the shock. This is due to the rise in the domestic skill premium induced by the inflow of low-skilled workers in the formal sector. In subsequent periods, the brain drain rate slightly decreases due to gradual effect of the stock of public infrastructure on total factor productivity. Hence, the variations in the brain drain are correlated with the change in the stock of public infrastructure provided in Figure 11. Figure 12 illustrates the long-run change in the brain drain for a subset of countries (I only select countries where the high-skilled emigration rate exceeds 20% in the year 2000). It demonstrates that a large portion of the current brain drain can be explained by the existence of the informal economy in developing countries. Considering the extreme example of Gambia, a complete ban of informality reduces the brain drain from 70 to 30% in the long run.
Despite large long-run effects on the stock of public infrastructure, the model with exogenous brain drain predicts a negative effect on the GDP per capita, both in the short run and in the long run. This is due to the fact that low-skilled workers, the large majority of workers in poor countries, earn less. In the model with endogenous brain drain, banning informality increases human capital and productivity; the effect on GDP per capita becomes ambiguous. For ten developing countries (Gambia, Ghana, Kenya, Lesotho, Liberia, Malawi, Mali, Sierra Leone, Sri Lanka and Uganda), I predict a positive effect on GDP per capita in the long-run. In the other countries, the effect is negative: banning informality hurts low- skilled workers and benefits the highly skilled. The gains for the highly skilled are large and governed by three effects: a higher skill premium (due to the inflow of low-skilled workers in the formal sector), an uncertain effect on human capital in the formal sector (due to lower brain drain and the inflow of low-skilled workers), and a higher stock of infrastructure (due to greater tax base).
Endogenizing the brain drain has different implications for the low-skilled and high-skilled workers. When the brain drain decreases, total factor productivity is positively affected. However, the supply of human capital increases and this negatively affects the skill premium. The calibrated model shows