Data and empirical model

The main goal is to estimate the effect of dismissals of public-sector employees on the shadow economy. To this end, we exploit the impact of policy-induced public-sector dismissals introduced by IMF conditionality programmes. Typically, IMF programmes include several conditions regarding the size of public-sector employment. Once a country borrows from the IMF, its government agrees to initiate a series of reforms to correct the underlying inefficiencies of its economy. Programme conditions focus on macroeconomic, financial, and monetary issues; however, several programmes include structural reforms in areas like the labour and product market. In this respect, one condition typically included in several programmes is reducing public-sector employment or the total public-sector wage bill. Besides improving government finances, this condition is expected to affect the wage and employment structure in the labour market (Adam, Reference Adam2020; Malley and Moutos, Reference Malley and Moutos1996). According to the database of IMF conditionality (Kentikelenis et al., Reference Kentikelenis, Stubbs and King2016), in the period from 1990 to 2018, out of the 185 total IMF programmes initiated in all countries, only 42 programmes involved a condition to reduce the number of civil servants, whereas 48 programmes had a policy prescription of lowering the total public-sector wage bill.Footnote ²

To estimate the effect of public-sector dismissal, we develop a dynamic model in the spirit of Angrist et al. (Reference Angrist, Jordi and Kuersteiner2018), Jordà and Taylor (Reference Jordà and Taylor2016), and Kuvshinov and Zimmermann (Reference Kuvshinov and Zimmermann2019). More specifically, we compare the change in the share of the shadow economy from year 0, that is, 1 year before a programme that involved reductions in public-sector employment, to year h = 1,2,3,4,5. As the control group, we use all countries under an IMF programme. However, IMF programmes are non-random policy events; therefore, we use the inverse probability weighting method to mimic randomisation.Footnote ³

This method has a series of advantages. First, it estimates the dynamic effect of IMF public-sector employment reduction programmes on the outcome variable. Second, it allows for non-linearities in the time response of the outcome (i.e. the share of the shadow economy) to the treatment (i.e. public-sector employment reductions). Third, we extend the empirical model to allow for the local projection of the shadow economy by estimating a two-stage model that relies on the inverse probability weighting and the regression adjustment method (Jordà et al., Reference Jordà, Schularick and Taylor2016; Jordà and Taylor, Reference Jordà and Taylor2016). This latter model has the significant advantage that it requires only one of both stages, ordinary least squares (OLS) or probit, to be correctly specified to derive correct estimates for the effect of treatment, that is, public-sector layoff programmes. In addition, neither method relies on any exclusion restrictions, and thus, all variables can be considered endogenous in our dataset (Kuvshinov and Zimmermann, Reference Kuvshinov and Zimmermann2019). As a result, our analysis effectively takes into account the endogeneity.

To be more specific, we assume that the following probit model gives the estimated probability of having an IMF programme that reduces public-sector employment:

(1) $$\widehat {P{V_{i,t}}} = \Phi \left( {\mathop \sum \limits_{j = 1}^2 {S_{i,t - j}},{X_{i,t}},\, \hat {\!\beta} } \right)$$

where $\widehat {P{V_{i,t}}}$ is the predicted probability of a public-sector employment reduction programme in country i at time t + 1, $\Phi $ is the cumulative distribution function of the standard normal distribution, ${S_{i,t - j}}$ is the lagged value of shadow economy as a share of GDP at j years before the programme is enacted, ${X_{i,t}}$ is a vector of control variables, and finally, ${\hat {\!\beta}} $ is the vector of estimated coefficients.Footnote ⁴ Then, the average treatment effect (ATE) of the treatment for each h, that is, public-sector employment reduction under the Augmented Inverse Probability Weighting Scheme, is given by

(2) $$\eqalign{ \Lambda _{AIPW}^h = & {1 \over n}\sum\limits_i {\sum\limits_t {\left\{ {\left[ {{{{D_{i,t}}\left( {{S_{i,t + h}} - {S_{i,t}}} \right)} \over {\widehat {P{V_{i,t}}}}} - {{(1 - {D_{i,t}})\left( {{S_{i,t + h}} - {S_{i,t}}} \right)} \over {\widehat {1 - P{V_{i,t}}}}}} \right]\;} + \left[ {m_1^h\left( {X_{i,t}^{},\hat \theta _1^h} \right) - m_0^h\left( {X_{i,t}^{},\hat \theta _0^h} \right)} \right]\right.}} \cr & - \left[ {{{{D_{i,t}}m_1^h\left( {X_{i,t}^{},\hat \theta _1^h} \right)} \over {\widehat {P{V_{i,t}}}}} - {{(1 - {D_{i,t}})m_0^h\left( {X_{i,t}^{},\hat \theta _0^h} \right)} \over {\widehat {1 - P{V_{i,t}}}}}} \right] \Bigg\} }$$

where ${\rm{m}}_1^{\rm{h}}\left( {{\rm{X}}_{{\rm{i}},{\rm{t}}}^{},{\rm{\hat \theta }}_1^{\rm{h}}} \right)\;{\rm{and}}\;{\rm{m}}_0^{\rm{h}}\left( {{\rm{X}}_{{\rm{i}},{\rm{t}}}^{},{\rm{\hat \theta }}_0^{\rm{h}}} \right)$ are the conditional mean of a regression of $\left( {{{\rm{S}}_{{\rm{i}},{\rm{t}} + {\rm{h}}}} - {{\rm{S}}_{{\rm{i}},{\rm{t}}}}} \right)$ on $X_{i,t}^{}$ and ${{\rm{D}}_{{\rm{i}},{\rm{t}}}}$ is the dummy that separates the treatment and control group.

Note that (2) is estimated for each time horizon h=1,…, 5; thus, we compute the change in the share of the shadow economy for each period h after the treatment.Footnote ⁵ Then, for each period after that, we examine the associated change compared to the value at t. We follow Jordà and Taylor (Reference Jordà and Taylor2016) and use cluster robust methods to compute the estimated coefficients’ standard errors.

To measure the size of the shadow economy, we use the dynamic general equilibrium (DGE) estimates of the share of the shadow economy of Elgin et al. (Reference Elgin, Kose, Ohnsorge and Yu2021). The main advantage of this method is that it covers a wide range of countries over a considerable period. In the present paper, we use the available estimates for our sample of countries over the 1990–2018 period. To ensure that our results are not driven by the choice of the DGE model estimates, for robustness, we also use the Multiple Indicators Multiple Causes (MIMIC) model-based estimates provided by the same authors.Footnote ⁶

Vector X _i,t includes a series of macroeconomic controls to model the selection into treatment. These are the current account balance as a share of GDP, the government budget balance as a share of GDP, a dummy that takes the value of 1 when a country is a democracy, the log of GDP per capita, the growth rate of GDP per capita, the number of years that the country has spent under an IMF programme, the unemployment rate, the degree of public-sector corruption, the share of the urban population, and finally, the labour force participation rate.Footnote ⁷

The role of institutions

An extensive literature on the determinants of the size of the informal sector shows the importance of institutions (Gërxhani and Cichocki, Reference Gërxhani and Cichocki2023; Khan and Rehman, Reference Khan and Rehman2022). When institutional quality and government efficiency are low, we expect it will be easier for unemployed workers to find a job in the shadow economy.

In Table 3, we examine the role of institutions regarding the effect of policy-induced public-sector layoffs on the share of the shadow economy. All results are obtained using the first model of Table 1 as the baseline case. First, we examine the underlying relationship depending on the level of institutional quality since political and economic institutions are expected to influence the ease with which workers and firms can relocate between the formal and informal sectors. In economies with a weak institutional environment, the expansion of the informal sector will be largely unhindered; thus, we should expect a higher reallocation towards the shadow economy compared to countries with a better institutional environment. We expect that a similar rationale will also apply if one differentiates countries according to political regimes since in authoritarian political systems, institutions such as the tax authorities, various regulatory bodies, the judiciary, and law enforcement are mere instruments of autocratic rule, without the autonomy required to be effective guardians of compliance with existing laws and regulations.

Table 3.

The role of institutions

Notes: See Table 2.

The results in the first four models of Table 3 indicate this is the case. First, we differentiate between democratic and autocratic countries using the dichotomous democracy variable (Bjørnskov and Rode, Reference Bjørnskov and Rode2020). The positive effect of public-sector layoffs on the share of the shadow economy is more pronounced in autocracies, where all effects are statistically significant for all years after the programme’s initiation. Furthermore, the point estimates are more than double in magnitude than in the case of democracies. Moreover, as the first line indicates, the ATEs for democracies are much lower in size and statistically significant only for 4 and 5 years after treatment.

A similar picture emerges when we split our sample into countries with high and low institutional quality. A country is classified as one of high (low) institutional quality when the International Country Risk Guide indicator of Quality of Government (taken from Teorell et al., Reference Teorell, Dahlberg, Holmberg, Rothstein, Alvarado Pachon and Axelsson2020) is above (below) the variable’s median value. The results indicate that the effect of public-sector employment reductions is more pronounced in countries with low institutional quality. All point estimates, except for time t when they are statistically the same, are more than twice in magnitude in countries with low institutional quality.

Finally, in models (5) and (6), we replicate the same analysis regarding the effect of institutions as in models (3) and (4); however, this time, we use the government effectiveness index (as taken from the World Bank Governance Indicators). Countries with higher government efficiency are expected to be able to limit the size of the shadow economy. Thus, we should expect that policy-induced public-sector layoffs will not result in many workers ending up in the shadow economy as the government will control the expansion of the informal sector. Countries are classified as ones with high (low) government effectiveness if the average government effectiveness index is above (below) the (sample) median value. The results in models (5) and (6) replicate the results obtained so far.

Overall, the empirical results show a robust positive, non-mechanical relationship between public-sector dismissal programmes and the size of the shadow economy. Moreover, this relationship appears to persist over time; thus, it is not due to a temporary adjustment process until the laid-off workers find a job in the formal sector but suggests a change in the economy’s structure. Countries with a low-institutional-quality environment, where shifting to the unregulated informal sector is easier, are more prone to this change.

Sectoral specification

Agrarian sector

The agrarian good is produced using informal labour and a factor in fixed supply. The factor in fixed supply is provided by landowners (land), and we normalise its supply to unity. The labour used by the agrarian sector is denoted by L _A.

The agrarian sector’s production function displays diminishing returns:

(3) $$A = \gamma {L_A} - {\delta \over 2}L_A^2$$

where A denotes output, with both $\gamma$ and $\delta $ positive.

Denoting the (informal) wage rate as $w$ , and using the agrarian good as the numeraire (P _A =1), the sector’s profit-maximising demand for labour is

(4) $${L_A} = {{\gamma - w} \over \delta }$$

The resulting aggregate profits of agrarian sector producers are equal to

(5) $$\Pi = {\delta \over 2}{\left( {{{\gamma - w} \over \delta }} \right)^2}$$

We assume that profits are equally distributed among the landowners, whose number equals T.

The modern sector

The modern sector comprises two distinct sub-sectors: the formal sector and the informal sector. What distinguishes the two sectors is that the formal sector produces a high-quality variety of the VDP, whereas the informal sector produces a low-quality variety. The VDP is produced only with labour. Quality is measured by an index $Q,$ $0 \lt Q \lt 1$ , and there is complete information regarding the quality index. We assume that there exists a ‘cottage’ technology available to all for producing low-quality varieties of the VDP and a modern technology allowing the production of high-quality varieties. Low-quality varieties are defined as those for which $Q \lt \bar Q$ , whereas high-quality varieties are identified with $Q \gt \bar Q$ . Firms with access to the technology that allows the production of high-quality varieties belong to the formal sector, whereas the rest are informal. We may think that production technology is such that formal firms have access to excludable public inputs, allowing them to produce high-quality goods at a lower cost than informal firms (e.g. access to electricity at subsidised prices). Moreover, this categorisation of firms is motivated by the fact that consumers of high-quality, high-priced items are more likely to demand after-sales services (guarantees, repairs, etc.) to which only formal sector firms can credibly commit to (and be legally responsible).

For informal firms to be able to produce the low-quality variety at a lower cost than formal firms, we need to assume that the difference in productivity between formal and informal producers is small when quality is low – since then, any wage advantage of informal firms (explained below) could offset their productivity disadvantage (see Fotoniata and Moutos (Reference Fotoniata and Moutos2013) for applications of this idea in other contexts). Rauch (Reference Rauch1991) suggested that the inferior technological capability of informal firms is the reason for their inability to compete on an equal footing with formal firms, thus forcing them to operate in the informal sector where the ability to avoid some costs related to regulation allows them to survive. Our assumption that modern technology is available to a subset of firms that hire only formal workers is used as a convenient shortcut to concentrate on the implications of the interactions between the structure of product demand, the informal sector, and government employment.

As long as the informal producers’ productivity disadvantage gets larger as quality increases, there will be a quality threshold after which formal producers will have lower costs than informal ones. Our assumption that modern technology is available only to a subset of firms starkly manifests this idea.

This simple formulation captures two fundamental features of a typical dual developing economy: (1) the quality gap between sectors and (2) the limited access of the informal sector to public services.

Formal firms face labour market regulation in having to pay a (binding) minimum wage, $\overline w$ . In addition to labour market regulations, formal firms have to incur a cost, F, per physical unit of output. We may consider this cost the ‘price of formality,’ representing the burden of various taxesFootnote ¹⁵ imposed on formal firms or the costs of complying with various environmental, health, or work-safety regulations. Informal firms do not comply with any of the above regulations and pay their workers the (market-clearing) informal wage rate $w$ . We assume that the minimum-wage rate, $\overline w$ , is higher than the informal wage rate, $w \lt \overline w$ .

Following Flam and Helpman (Reference Flam and Helpman1987) and Banerji and Jain (Reference Banerji and Jain2007), we assume that average costs depend on quality and that, for any given quality level, average cost is independent of the number of physical units produced. Perfect competition ensures that prices will equal average (and marginal) costs. We write the average cost functions (as functions of quality) for formal and informal firms as,

(6) $$AC\left( {{Q_F}} \right) = P\left( {{Q_F}} \right) = \overline w{Q_F} + F$$

(7) $$AC\left( {{Q_I}} \right) = P\left( {{Q_I}} \right) = w{Q_I}$$

Since $\overline w \gt w\;$ and ${Q_F} \gt {Q_I}$ , it follows that the price of formal firms will be higher than of informal firms:

$$P\left( {{Q_F}} \right) \gt \;P\left( {{Q_I}} \right).$$

This specification of average costs implies that as quality increases, more units of labour are required to produce each physical unit of the VDP product. This assumption is consistent with the fact that increases in quality – for a given state of technological capability – involve the employment of a larger number of personnel not only for the production of a higher number of features attached to each good that directly absorb labour but also to the development and refinement of these features as well.

Households

The economy is populated by a fixed number of landowners (T) and identical working households (L), each endowed with one unit of labour, which they offer inelastically. For simplicity, we assume that the landowning households do not supply any labour.

Following Flam and Helpman (Reference Flam and Helpman1987), we treat the homogeneous good as divisible, while the VDP is assumed to be indivisible, and households can consume only one unit of it. A convenient characterisation of household preferences over the consumption of goods (for either landowners or working households) is given by the following utility function for household i:

(8) $${U_i} = {\theta _i}lnQ + ln{A_i}$$

In equation (8), Q stands for the quality (either Q _F or Q _I ) level of the VDP, ${A_i}$ is the quantity of the homogeneous good (agricultural) consumed by agent i, and θ _i is a parameter that differentiates the intensity of household preferences for the quality level of the VDP.

To conform to empirical observations on the economic environment of developing economies, we first assume that all households working in the informal (either modern or agrarian) sector have the same preferences, with taste parameter ${\theta _I} = 1,\;\;$ and always decide to consume the low-quality, informally produced VDP (Q _I ). The budget constraint of these households is

$$w = P\left( {{Q_I}} \right) + {A_I} = w{Q_I} + {A_I},$$

where ${A_I}$ is the consumption of the homogeneous good and $w{Q_I}$ is the price of the low-quality variety offered by informal firms. Given the above preferences, the utility-maximising demand for the homogeneous good A_IN is

(9) $${A_I} = w - w{Q_I}$$

Figure 2 displays the choices of a household receiving the informal wage. The two quality levels of the VDP are depicted on the horizontal axis, and the quantity of the homogeneous good (as well as household income given that P _A = 1) is depicted on the vertical axis. The household’s income determines the budget constraint, which, since only two quality levels of the VDP are available, comprises just points 1 and 2.

Figure 2.

Consumption behaviour of formal-sector and informal-sector households.

Low-income households select between these points, the one giving them the highest utility, which in Figure 2 is point 1 – the one associated with consumption of the informally produced, low-quality variety of the VDP.

For households earning the minimum wage, we assume that there are differences in their intensity of preferences over the quality level, implying the willingness to pay for the high-quality Q_F. For this income group, we assume that the taste parameter is distributed according to a continuous uniform distribution in the interval $\left[ {1,\;\varepsilon \;} \right]$ and its cumulative density function is given by

(10) $$D( \theta ) = \cases{ { 0 \quad\quad\quad {\hskip-3pt {\rm if} \quad\hskip18pt\theta \lt 1}} \cr {{{\varepsilon - \theta } \over {\varepsilon - 1}}}\quad\quad {{\rm if} \quad 1 \le \theta \le \varepsilon } \cr 1 \quad\quad\hskip7pt {{\rm if} \quad\hskip18pt \theta \gt \varepsilon}}$$

For simplicity and without much loss of generality, we assume that changes in households’ employment status will be associated with changes in their preference structure; that is, households switching from informal to formal employment will acquire the preference traits (through peer pressure or social osmosis) of formal-sector households.

In Figure 2, we depict the formal-sector households with income equal to the minimum wage; their budget constraint comprises points 3 and 4. Among these households, the one with the highest value of $\theta \left( { = \varepsilon } \right)$ has a map of ‘steep’ indifference curves (one of which is denoted by $\theta = \varepsilon $ ₎ and achieves maximum utility by consuming bundle 4. As a result, the utility-maximising demand for the homogeneous good is

(11) $${\rm A}_F^H = \overline w - P\left( {{Q_F}} \right) = \overline w - \left( {\overline w{Q_F} + F} \right)$$

To ensure that this household purchases both goods, we assume that $\overline w\left( {1 - {Q_F}} \right) \gt F$ , which can be the case only if ${Q_F} \lt 1$ . In contrast, the household with the lowest value of θ is represented by indifference curve θ=1 and chooses to consume bundle 3, that is, the informally produced good. The demand for good A by this household is

(12) $${\rm A}_F^L = \overline w - P\left( {{Q_I}} \right) = \overline w - \overline w{Q_I}$$

Equations (11) and (12) imply that for a formal-sector household with θ = θ _i, the indirect utility function takes the form:

(13) $$V_F^H = {\theta _\iota }ln{Q_F} + {\rm{ln}}\left( {\overline w - \overline w{Q_F} - F} \right){\rm{, if\ it\ consumes\ the\ high - quality\ good}}$$

(14) $$V_F^L = {\theta _\iota }ln{Q_I} + \ln \left( {\overline w - \overline w{Q_I}} \right){\rm{, if\ it\ consumes\ the\ low - quality\ good}}$$

Let θ* denote the value of θ for which a household is indifferent between consuming one unit of quality ${Q_F}$ at price $P\left( {{Q_F}} \right)$ and one unit of quality ${Q_I}$ at price $P\left( {{Q_I}} \right)$ . For this household, it must hold that $V_F^H = V_F^L$ , which implies

(15) $${\theta ^*}\ln {Q_F} + \ln (\bar w - \bar w{Q_F} - F) = {\theta ^*}\ln {Q_I} + \ln (\bar w - w{Q_I}).$$

Solving equation (12) for θ*, we find

(16) $${\theta ^*} = {{\ln \left( {\overline w - w{Q_I}} \right) - \ln \left( {\overline w - \overline w{Q_F} - F} \right)} \over {{\rm{ln}}{Q_F} - {\rm{ln}}{Q_I}}}.$$

As expected, equation (16) implies that ${{d{\theta ^*}} \over {dw}} \lt 0$ since a rise in the informal wage would increase the cost of the (low-quality) informal variety and induce more households to purchase the (high-quality) formal variety.

A formal-sector household with θ = θ ^* is depicted in Figure 2 as possessing the indifference curve passing from points 3 and 4.

Using the specification of the uniform distribution adopted above, we find that the number of formal-sector households that consume the high-quality variety (i.e. those with θ ≥ θ*) is equal to $\left( {{{\varepsilon - {\theta ^*}} \over {\varepsilon - 1}}} \right){L_F}$ , where L_F is employment in the formal sector.

We assume that landowners earn significantly more than minimum-wage earners so that they always choose to consume the high-quality variety of the VDP, produced in the formal sector, implying that their consumption of homogeneous good, A_T , is

$${A_T} = {{{\pi _A}} \over T} - P\left( {{Q_F}} \right) = {{\left( {1 - \alpha } \right)BL_A^\alpha } \over T} - \left( {{W_M}{Q_F} + F} \right),$$

where ${{\left( {1 - \alpha } \right)BL_A^\alpha } \over T}$ is the profits accruing to each of the T landowners.

Government sector

In addition to setting (and enforcing) the minimum wage, the government is assumed to employ workers to produce basic public services (e.g. law and order, national defence), paying these workers the minimum wage. The number of these workers is denoted by ${L_G}$ . We assume that these workers have the same preferences as formal-sector workers who also receive the minimum wage, that is, ( ${U_i} = {\theta _i}lnQ$ + $ln{A_i}$ ), with the distribution of the taste parameter $\theta $ being also given by equation (10). This implies that the number of government-employed households consuming the high-quality variety (i.e. those with θ ≥ θ*) equals to $\left( {{{\varepsilon - {\theta ^*}} \over {\varepsilon - 1}}} \right){L_G}$ .

Analysis

To examine the effects of reductions in government employment, we assume that workers are mobile across sectors, and thus, should they fail to find employment either in the government sector or in the formal (modern) sector at the minimum wage, they offer their services in the informal (modern plus agrarian) sectors at the market-clearing wage, $w$ .

The demand for labour by formal-sector firms arises from the demand for high-quality varieties registered by two groups of households. The first group belongs to the formal-sector and government-sector households that choose to purchase the high-quality variety of the VDP; the size of this group is equal to $\left( {{{\varepsilon - {\theta ^*}} \over {\varepsilon - 1}}} \right)({L_F} + {L_G})$ . The second group consists of all landowning households (T). Thus, the demand for labour by formal-sector firms is equal to $\left( {{{\varepsilon - {\theta ^*}} \over {\varepsilon - 1}}} \right)({L_F} + {L_G}){Q_F} + T{Q_F}$ . Adding government employment to this, we get the (aggregate) demand for formal employment ( $L_F^D)$ , that is,

(17) $$L_F^D = \left( {{{\varepsilon - {\theta ^{\rm{*}}}} \over {\varepsilon - 1}}} \right)({L_F} + {L_G}){Q_F} + T{Q_F}+ {L_G}.$$

Since ${{d{\theta ^*}} \over {dw}} \lt 0$ (i.e. equation (16)), we conclude that the demand for formal labour is an increasing function of the informal-sector wage rate.

The demand for labour by informal firms in the modern sector arises from the consumption of the low-quality variety of the VDP by households (working) in both the formal and informal sectors. The number of formal-sector plus government-sector households consuming the low-quality variety is equal to $\left( {{{{\theta ^*} - 1} \over {\varepsilon - 1}}} \right)({L_F} + {L_G})$ . The number of informal and agrarian households is equal to $L - ({L_F} + {L_G})$ , where L is the total number of workers/households. Thus, the demand for informal labour by low-quality producers of the VDP is equal to $\left( {{{{\theta ^*} - 1} \over {\varepsilon - 1}}} \right)({L_F} + {L_G}){Q_I} + \left( {L - ({L_F} + {L_G}} \right)){Q_I}$ . Adding to this the demand for labour by the agrarian sector (see equation (4)), we get that the aggregate demand for informal labour is

(18) $$L_I^D = \left( {{{{\theta ^*} - 1} \over {\varepsilon - 1}}} \right)({L_F} + {L_G}){Q_I} + \left( {L - ({L_F} + {L_G}} \right)){Q_I} + {{\gamma - w} \over \delta }.$$

We note that the aggregate demand for informal labour is decreasing in the informal wage rate, w, not only because the demand for labour in the agrarian sector is a negative function of the wage rate but also because an increase in w reduces the proportion of formal-sector and government-sector households purchasing the low-quality variety of the VDP.

Under the assumption of inter-sectoral labour mobility, the wage rate in the agrarian and informal sectors will be determined by the requirement that the number of labour units demanded in the informal and agrarian sectors equals the relevant labour supply. Since the latter is equal to the workers not employed in the formal and government sectors ( $\;{L_I} = L - ({L_F} + {L_G}))$ , and assuming that workers prefer to find employment either in the formal or government sector (so that $L_F^D = {L_F}\;$ ), we can state the labour market-clearing condition for workers in the informal and agrarian sectors as

(19) $$L - ({L_F} + {L_G}) = \left( {{{{\theta ^*} - 1} \over {\varepsilon - 1}}} \right)({L_F} + {L_G}){Q_I} + \left( {L - ({L_F} + {L_G}} \right)){Q_I} + {{\gamma - w} \over \delta }.$$

Equation (19), along with equations (16) and (17), can be used to solve for the market-clearing wage rate w, ${\theta ^*}$ , and ${L_F}$ . Employment in the agrarian sector can then be determined by equation (4), which further allows to determine informal employment in the modern sector as the difference between total informal employment (= $L - ({L_F} + {L_G}))$ and employment in the agrarian sector.

We now provide a diagrammatic representation of the equilibrium allocation of employment across sectors.Footnote ¹⁶ In Figure 3, the size of the horizontal axis ${O_I}{O_F}$ is equal to the total labour supply, $L$ , which is divided between (total) formal employment (= ${L_F} + {L_G})\;$ and (total) informal employment ( ${L_I}$ = $L - ({L_F} + {L_G})).$ Informal employment is measured rightwards from the origin A, whereas formal employment is measured leftwards from the origin B $.$ The demand curve for informal labour, drawn with respect to the origin A, is depicted as the downward-sloping curve $L_I^D$ (equation (15)), whereas the demand curve for formal labour is drawn with respect to the origin $B$ and is depicted as the upward-sloping curve $\;L_F^D$ (equation (17)). The latter curve is drawn assuming that the (exogenous) number of government employees is measured by the line segment βΓ.Footnote ¹⁷

Figure 3.

Effects of reductions in government employment on labour allocation across sectors.

The initial, full-employment, equilibrium allocation of labour across sectors is determined at the intersection of the $L_I^D$ and $L_F^D$ curves at point α, with total informal employment being equal to Α $I\;$ and private formal-sector employment being equal to IΓ. The informal wage rate is equal to ${w_0}$ .

Consider now a reduction in government employment to ${B}\Delta $ . As a result, the $L_F^D$ curve shifts to the right ( $L_F^{D'})$ , and the new equilibrium informal wage rate drops to ${w_1}$ - as determined by point b, whereas there is an expansion of informal employment by $IH$ units, to ΑΗ $.$ Note that informal employment (modern plus agrarian) expands by more than the reduction in government employment. This happens because private employment in the formal-sector contracts is also due to the switch in demand towards the low-quality variety of the VDP produced by informal producers as a result of the drop in the informal wage rate. Thus, the informal sector’s size (both employment and output) increases not only in relationship to the total size of the formal sector (i.e. the sum of the formal private sector plus the government sector) but also in relationship to the formal private sector.

Our framework can also be used to analyse the effects of a reduction in the public-sector wage bill without public-sector layoffs – that is, a reduction in public-sector wages. This reduction in the income of public-sector employees would induce some to switch from consuming the high-quality varieties (produced by formal firms) to the low-quality varieties offered by informal firms, thus inducing a reallocation of economic activity in the private sector from formal to informal producers.