The demographic boom and the rise of informal employment

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Motivating facts: Evidence from the National Transfer Accounts

The National Transfer Accounts (NTA), launched in the early 2000s, disaggregates economic flows seen in the System of National Accounts (SNA) into various ages. In doing so, it allows for a better understanding of how people earn, consume, share and save their income across time, on a macroeconomic level. This can be useful in shedding more light on intergenera-tional (re)allocations and various transfers.
Based on lifecycle theory, the NTA quantifies the lifecycle deficit (or surplus) for each age, which is the difference between consumption and labor income. Children, for example, have lifecycle deficits because they do not earn any labor income, whereas working-age adults often have lifecycle surpluses. At each age, an individual can bridge (reallocate) this deficit (surplus) through three main channels: (1) public transfers, both cash and in-kind; (2) private transfers, within and between households (which exclude the inheritance flows introduced in the paper); and (3) asset-based reallocations such as financial income and savings (NTA Manual (2013)). This can be seen through the NTA Identity below: Ca,t − La,t = Ta,t+public − Ta,t−public + Ta,t+private − Ta,t−private + Aa,t+ − Aa,t−net public transfers net private transfers asset based reallocations where a denotes age, t denotes time, + stands for received and − stands for given. Net transfers and reallocations are the difference between what is received and what is transferred.
Public transfers in the NTA includes what individuals give in terms of taxes and what they receive in various subsidies and social security support, for instance. Private transfers include what is transmitted for purposes such education, healthcare, imputed rent3 and all other types of consumption. Asset-based reallocations are largely intertemporal and can be divided into capital income and property income, both public and private.4 These various flows are calculated using administrative records, household surveys and various other surveys that may be country- and time-specific (United Nations (2013)).
Due to the growing use of the NTA methodology across countries, the database can offer some unique perspectives on how people earn, consume, and reallocate their resources (d’Albis and Moosa (2015) and Lee and Mason (2011)). In France, for example, the NTA data show that the age profile of per capita consumption, in real terms, has not changed drastically between 1979 and 2011, while the age profile of labor income shifted towards higher ages, in line with increasing years of education (d’Albis et al. (2015)).
However, more relevant to the purposes of this paper is the magnitude and trend of private transfers, which have often been difficult to quantify on an aggregate level prior to the NTA. These private transfers, more specifically, include two categories: (1) Intrahousehold transfers, i.e. those given and received within one household, which often mean a family; (2) Interhoushold transfers, i.e. between households, which include “regular” and “occasional” cash transfers, as well as “in-kind” transfers. Some of these transfers are estimated using survey data, but the majority are calculated as a residual after estimating the consumption of the individuals in the household and their incomes.
For children, who are the primary recipients of these transfers as will be shown below, these transfers come to bridge the gap between their private consumption and their (lack of) labor income. In France, the sweeping majority of children’s private consumption are in areas other than private education expenditures and private healthcare (refer to Figure 1.13 in Appendix 1.7). Consequently, these transfers effectively serve to support children’s food, shelter, clothing and everything else.
The data show that “interhousehold” transfers as captured by the NTA are generally small, making up at most a tenth of the total intra- and interhousehold transfers during the period 1979-2011. For ease of reference, they are dropped from the following analysis, where we focus on intrahousehold transfers and inheritance flows.
The NTA France database was also able to provide age-profiles of bequest and inter-vivo gifts, referred to here as “inheritance”, utilizing estimates from a series of works on France by Thomas Piketty (Piketty (2011), Piketty et al. (2014) and Piketty (2014)). While they can also be categorized as “interhousehold”, they are not typically included in the NTA database for various reasons, including a lack of data. The availability of this data for France allows us to expand the analysis and incorporate more holistically all (monetary) intergenerational flows.
The trend and composition of these two types of private transfers show several important trends. The first is that the sum of these flows has remained a relatively stable share of Gross National Income in France, from about 25% in 1979 to a little over 22% in 2011, with a small dip in the late 1990s, as shown in Figure 1.1.
The second is that despite their relatively stable share, the composition of these transfers has changed over time, with a decrease in the share of intrahousehold transfers in overall private transfers. Consequently, the ratio of intrahousehold transfers-to-inheritance has declined, from about 3.6 in 1979 to less than 1 in 2011, as seen in Figure 1.2. This is a ratio of great interest to the purposes of this paper as it captures the change in the composition over time, which we can explain through the theoretical model.
The NTA data also point to the directionality of intrahousehold transfers and inheritance. The working-age population, which is defined conservatively here as those 20-59 years old, is an important net giver of intrahousehold transfers, contributing an average of 93% between 1979 and 2011. Net recipients of these transfers are the younger age groups, mostly those that 0-19 years old, as shown in Figure 1.3. This directionality does not change if we look at net transfers in terms of per capita of each group to account for demographic changes of the groups (as shown in Figure 1.14).5 The oldest age group, 60+ is a minor net giver of intrahousehold transfers.
Figure 1.3: Net intrahousehold transfers by broad age-group (billion real euros)
Source: NTA (France)
Inheritance, on the other hand, has been mostly received over the years by both the “working-age” population, in addition to a smaller share received by the oldest generation that is 60+ years old, as shown in Figure 1.4. In fact, over the years, the working-age population has received an average of about 80% of inheritance. The NTA profiles also show that the highest value of received inheritance has not only increased over time, but has also been delayed over time. This means that individuals are now receiving more money at later ages (the age profile of inheritance can be seen in Figure 1.15 in Appendix 1.7). This is in line, of course, with rising life expectancy. This does not change if we look at flows in terms of per capita of the recipient (as shown in Figure 1.16 in Appendix 1.7).6 Figure 1.4: Received inheritance by broad age-group (billion real euros)
Source: NTA (France)
The final stylized fact that we make use of relates to the evolution of wealth inequality in France over time. Data from the World Inequality Database (WID) show that the Gini coefficient of wealth inequality has increased during the period that we consider in this paper, from 0.66 in 1979 to 0.7, with some variation in between, as shown in Figure 1.5. The share of wealth by the top decile and the top percentile of the population has increased. This is a fact that we exploit in the theoretical model in the following section, where we link private intergenerational transfers to wealth inequality.

The model

We consider an economy of overlapping generations in discrete time, akin to Diamond (1965). Economic growth is endogenous and driven by human capital accumulation. Generations are linked to each other through altruism for various transfers, and they make up “dynasties.” Production, on the other hand, is made through a representative firm, which operates in perfect competition and produces with constant returns to scale. Below, we set-up the model and show its main conclusions.

Model set-up

The individual

Each individual in this model lives for three periods: childhood, adulthood and old-age. For ease of notation, we assume that children are born at time (t − 1). However, decisions are taken by adults for their children and their old-age at time (t).
There exists in each period two types of dynasties in the economy indexed by i = {1, 2}, which differ in their desire for bequest. Dynasty i = 1, which makes up a fixed proportion p of the population, where p ∈ (0, 1), is egoistic and, therefore, does not make any bequest, whereas dynasty i = 2, with a proportion 1 − p of the population, has a desire to bequeath. This heterogeneity in the desire to bequeath is also found in the data, pioneered by Laitner and Juster (1996), who found this heterogeneity when examining a sample of pension holders in the U.S. Kopczuk and Lupton (2007), using a similar method but a different dataset, also found this heterogeneity, with about three-quarters of the elderly population having a bequest motive that caused them to reduce their consumption and transfer inheritance to the following generation.7
We assume, for further simplicity, no population growth, and thus population size is nor-malized to 1 over time.
Besides decisions pertaining to consumption and savings, individuals also make decisions regarding two kinds of intergenerational transfers. The first are transfers in the form of inheritance, denoted (b), which are made at old age to the middle age-group (adulthood).
The second are intrahousehold transfers made by adults for children, denoted (m). These transfers are used solely for the development of children’s human capital, and they should be positively correlated with the child’s future labor income.
We assume, however, that the human capital of the individual does not only depend on these parental intrahousehold transfers, which are specific to dynasty i, but also on the average stock of human capital in society. This assumption is in line with the “external effect” argued originally by Lucas Jr (1988) and later integrated into models as in Tamura (1991) and Bovenberg and van Ewijk (1997). These models suggest that the average stock of human capital in society does not only affect the individual’s own human capital, but also by extension the productivity of all factors of production.8 It is also in line with the idea that individuals do not start with a clean slate, or zero human capital, when they are born, but that they are endowed from the beginning with a certain level of human capital that is best approximated by the average human capital in the economy (see, for example, Glomm and Ravikumar (1997) and de la Croix and Michel (2007)).
Therefore, the human capital, H, of an adult at time t of dynasty i can be expressed as a function of the previous period’s average human capital and the intrahousehold transfers received at childhood, as the following: Hi,t = mi,tλ−1Ht1−−1λ, λ ∈ (0, 1) (1.1) where λ is the elasticity of human capital accumulation with respect to intrahousehold trans-fers – a crucial parameter in our model.
For every efficient unit of labor, an adult receives a wage wt that entails a gross labor income of wtHi,t, as well as bequest from the older generation, βi,t. From this inflow of income, he/she decides to consume ci,t, to save si,t and to invest in children mi,t. At old age, the individual allocates from his/her capitalized savings, Rt+1si,t, how much to consume, (di,t+1), and how much to bequeath to the adult generation, bi,t+1.
We denote Vti the utility of an adult of dynasty i and assume that it is a logarithmic function.
The individual, therefore, maximizes the utility function, Vti, as the following: max ln(ci,t) + θ ln(mi,t) + β ln(di,t+1) + βγi ln(bi,t+1) (1.2) ci,t,mi,t,di,t+1,bi,t+1
where θ captures the preference to give intrahousehold transfers, β captures time preference, and γi captures the intergenerational degree of altruism of dynasty i. We assume that γ1 = 0 for the egoistic dynasty, and γ2 = γ ∈ (0, 1) for the altruistic dynasty. Note that this formulation expresses the inheritance motive as a “joy of giving,” as proposed by Yaari (1964). This is a common expression for altruism in the literature due to its tractability (Abel and Warshawsky (1987)).
The budget constraints for a type i individual are as follows:
ci,t + si,t + mi,t ≤ wtHi,t + bi,t (1.3)
di,t+1 + bi,t+1 ≤ si,tRt+1 (1.4)
where Rt and wt are the rate of return on capital and wage per effective labor unit, respec-tively. We assume that at time 0, si,0 and Hi,0 are given.
From the first-order conditions we can derive optimal consumption, savings, intra-household transfers and inheritance for type i at time t as follows:
ci,t = 1 (wtHi,t + bi,t) (1.5)
1 + θ + β(1 + γi)
mi,t = θ
(wtHi,t + bi,t) (1.6)
1 + θ + β(1 + γi)
di,t+1 = βRt+1 (wtHi,t + bi,t) (1.7)
1 + θ + β(1 + γi)
bi,t+1 = βγiRt+1 (wtHi,t + bi,t) (1.8)
1 + θ + β(1 + γi)
Given differences in the preference to bequeath, optimal inheritance for each dynasty can be more clearly expressed as the following:
b1,t+1 = 0 (1.9a)
b2,t+1 = βγRt+1 (wtH2,t + b2,t) (1.9b)
Note that given the logarithmic utility function, optimal inheritance and intrahousehold transfer will always be an interior solutions. This means that the set-up of the model does not allow for negative bequest and transfer.
The savings function for each dynasty can be derived as follows:
s1,t = 1 + β + θ wtH1,t
β(1 + γ)
s2,t = 1 + θ + β(1 + γ)(wtH2,t + b2,t)
Due to our logarithm utility function, it is no surprise that the optimal level of our control variables is always proportional to the agent’s wealth, (wtHi,t + bi,t). Additionally, note that that:
β(1 + γ) > β
1+θ+β(1+γ) 1+β+θ
which implies that the rate of savings of the altruistic household is always higher than that of the egoistic one.

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Production in the economy, denoted by F (Kt, Ht), occurs through a representative firm that operates according to constant returns to scale and uses two inputs: the aggregate stock of capital in the economy, Kt, and the aggregate stock of human capital, Ht, expressed as the following:
Yt = KtαHt1−α (1.12) where α is the output elasticity of capital in the production function. To simplify the analysis, we assume that capital is fully depreciated after each period t.
We define new variables Yt ≡ Ht and Kt ≡ Ht the output and capital per effective worker, respectively. Then in intensive form, the production function can be written as Yt = Kt . In equilibrium, factors are paid their marginal products:
˜ α−1 (1.13)
Rt = αKt
˜ α (1.14)
wt = (1 − α)Kt

Equilibrium in the economy

Given an initial capital for each dynasty Ki,0 and an initial human capital for each dynasty Hi,0, a competitive equilibrium for this economy implies a sequence of prices {Rt, wt}∞t=0 and quantities for dynasty-i variables {ci,t, di,t, si,t, mi,t, bi,t, Hi,t}∞t=0, together with aggregate variables {Yt, Ht, Kt}, such that:
(i) Households behave optimally, given by Equations (1.5)-(1.11).
(ii) Firms maximize their profit, given by Equations (1.13) and (1.14).
(iii) All markets clear.
The capital market clearing condition requires that the aggregate savings owned by members of both dynasties at time t are equal to the physical capital stock available at time t + 1:
K1,t = s1,t−1 (1.15a)
K2,t = s2,t−1 (1.15b)
Kt = pK1,t + (1 − p)K2,t = ps1,t−1 + (1 − p)s2,t−1 (1.15c)
The human capital market clearing condition requires that the aggregate human capital owned by both dynasties equals the human capital stock of the economy at time t:
Ht = pH1,t + (1 − p)H2,t = pm1λ,t−1Ht1−−1λ + (1 − p)m2λ,t−1Ht1−−1λ (1.16)
Finally, the goods market clearing condition, which results from the individual budget con-straints, requires that what is produced is consumed, shared or saved in the economy,9 such that:
p�c1,t + d1,t + m1,t + s1,t� + (1 − p)�c2,t + d2,t + m2,t + s2,t� = Yt (1.17)
From Equations (1.13) – (1.16), we can obtain the dynamic system which governs the equi-librium paths in the neighborhood of the steady state (K1, K2, H1, H2). We can easily see that this is a four-dimensional dynamic system with four pre-determined variables:
1+θ+β K1,t+1 = wtH1,t (1.18)
1+θ+β(1+γ) γ
K2,t+1 − RtK2,t = wtH2,t (1.19)
β(1 + γ) γ + 1
H1,t+1 = Ht1−λ( θ K1,t+1)λ (1.20)
H2,t+1 = Ht1−λ( θ K2,t+1)λ
β(1 + γ)
Ht = pH1,t + (1 − p)H2,t
Rt = α(pK1,t + (1 − p)K2,t )α−1
pH1,t + (1 − p)H2,t
wt = (1 − α)(pK1,t + (1 − p)K2,t )α
pH1,t + (1 − p)H2,t

Transitional dynamics and steady state

In order to examine the evolution of the economy in the short-term as well as its steady state in the long-term, we will transform in what follows all variables to the intensive form, i.e. per efficient unit of labor Ht. We will then denote the new variables with the symbol (∼) to mark this transformation. We define a new variable xt ≡ that captures the ratio of the capital intensity held by ˜ K2,t ˜ K2,t altruistic and egoistic dynasty, respectively, where K2,t ≡ Ht and K1,t ≡ Ht . We view capital, K, as the only form of measurable physical wealth in our model. Consequently, we exploit xt in later sections to measure wealth inequality in the economy. When this ratio is greater than 1, then wealth inequality appears in the sense that the altruistic family owns more capital than the egoistic one. When the ratio is less than 1, inequality still exists, but the egoistic family owns more capital than the altruistic one. Consequently, inequality increases when x moves further away from 1, in either the positive or the negative direction.
By dividing all variables of Equations (1.18)-(1.21) by the aggregate level of human capital, we can rewrite the equilibrium system in the intensive form which will then allow us to characterized the dynamic system of four dimensions (K1,t, K2,t, H1,t, H2,t) to the dynamics of only xt.10

Table of contents :

General introduction and summary 
1 Intrahousehold transfers, inheritance and implications on inequality 
1.1 Introduction
1.2 Motivating facts: Evidence from the National Transfer Accounts
1.3 The model
1.3.1 Model set-up
1.3.2 Equilibrium in the economy
1.3.3 Transitional dynamics and steady state
1.3.4 The intrahousehold transfers-inheritance ratio and wealth inequality
1.4 Comparative statics
1.5 Discussion
1.6 Concluding remarks
1.7 Appendix
2 The demographic boom and the rise of informal employment: The case for Egypt 
2.1 Introduction
2.2 The institutional context and motivating facts
2.3 The model
2.3.1 A simple static framework under pure competition
2.3.2 General set-up
2.3.3 Timing of events
2.3.4 Demographics, effort and matching
2.3.5 Workers’ value functions
2.3.6 Production
2.3.7 Equilibrium conditions
2.4 Numerical Analysis
2.4.1 Calibration
2.4.2 Simulations
2.5 Concluding remarks
2.6 Appendix
3 Exploring heterogeneity of micro and small enterprises in Morocco 
3.1 Introduction
3.2 Data and descriptives
3.2.1 The MSE Survey
3.2.2 Descriptive statistics
3.3 Empirical strategy
3.3.1 Defining top performers
3.3.2 Identifying potential gazelles and “others”
3.3.3 Exploiting the formality and informality of firms
3.4 Results
3.4.1 Identification of groups
3.4.2 Characteristic differences between the groups
3.4.3 Formal and informal firms
3.4.4 Choice of formality/informality
3.5 Robustness check: Expanding top performance identification
3.6 Discussion
3.7 Concluding remarks
3.8 Appendix


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