Endogenous labour supply with several occupational categories in a bi-regional Computable General Equilibrium (CGE) model

Decaluwé B., Lemelin A. and Bahan D. Endogenous labour supply with several occupational categories in a bi-regional computable general equilibrium (CGE) model, Regional Studies. To make labour supply endogenous in the Québec Finance Ministry Québec–Rest-of-Canada bi-regional computable general equilibrium (CGE) model, household utility functions include as many types of leisure as there are occupational categories. Each household is modelled as a group of individuals who maximize utility independently, while sharing identical preferences for goods. Therefore, the consumption of goods is the same as in a standard linear expenditure system (LES), but cross-elasticity of supply of any labour category relative to another's wage rate is zero. Marginal income tax rates represent not only personal income taxes, but also implicit taxation of income through transfer reduction. Model behaviour is consistent with analytical expectations. Decaluwé B., Lemelin A. et Bahan D. L'offre de travail endogène du modèle bi-régional Québec-Reste-du-Canada du Ministère des finances du Québec dérive de fonctions d'utilité avec autant de types de loisir que de catégories professionnelles. Chaque ménage est constitué d'individus maximisant leur utilité indépendamment, ayant néanmoins des préférences identiques pour les biens. Résultat: la consommation de biens est comme dans un SLD standard, mais l'élasticité-prix croisée de l'offre entre les catégories de travail est nulle. Les taux marginaux d'imposition du revenu représentent les impôts personnels, mais aussi la taxation implicite du revenu résultant de la réduction des transferts. Le modèle se comporte conformément aux prédictions théoriques. Modèle d'équilibre général bi-régional Offre de travail ménagère Decaluwé B., Lemelin A. und Bahan D. Endogenes Angebot an Arbeitskräften in mehreren Berufssparten in einem biregionalen berechenbaren allgemeinen Gleichgewichtsmodell (CGE-Modell), Regional Studies. Um das Angebot an Arbeitskräften im biregionalen berechenbaren allgemeinen Gleichgewichtsmodell (CGE-Modell) des Finanzministeriums von Québec für die Region Québec und das übrige Kanada endogen zu gestalten, werden bei den Haushaltsnutzenfunktionen ebenso viele Freizeitarten wie Berufssparten berücksichtigt. Jeder Haushalt wird als Gruppe von Personen modelliert, die den Nutzen unabhängig voneinander maximieren und dabei identische Güterpräferenzen aufweisen. Der Güterverbrauch ist daher derselbe wie bei einem herkömmlichen linearen Ausgabensystem (LES), wobei sich jedoch die Kreuzelastizität des Angebots einer Arbeitskraftkategorie in Bezug auf den Lohnsatz einer anderen Kategorie auf Null beläuft. Die marginalen Einkommenssteuersätze beziehen sich nicht nur auf die privaten Einkommenssteuern, sondern auch auf die implizite Einkommensbesteuerung durch Transferreduktion. Das Verhalten des Modells entspricht den analytischen Erwartungen. Berechenbares allgemeines Gleichgewicht (CGE) Arbeitskraftangebot von Haushalten Decaluwé B., Lemelin A. y Bahan D. La oferta endógena de trabajo con varias categorías laborales en un modelo de equilibrio general computable bi-regional, Regional Studies. Para que la oferta de trabajo sea endógena en el modelo de equilibrio general computable bi-regional del Québec y el resto del Canadá empleado por el Ministerio de Hacienda, se tienen en cuenta las funciones de utilidad con tantos tipos de ocio como categorías laborales. Cada hogar se modela como un grupo de individuos que maximizan la utilidad de modo independiente a la vez que comparten preferencias idénticas de bienes. Por consiguiente, el consumo de bienes es el mismo que en un sistema lineal de gastos pero la elasticidad cruzada de la oferta de cualquier categoría laboral relativa a la tasa salarial de otra categoría es nula. Las tasas marginales del impuesto sobre la renta representan no sólo los impuestos sobre la renta de las personas físicas sino también el impuesto implícito de la renta mediante la reducción de transferencias. El comportamiento del modelo corresponde a las expectativas analíticas. Equilibrio computable general Oferta laboral de los hogares

Keywords: Computable general equilibrium (CGE); Household labour supply

This paper focuses on the specification of endogenous labour supply in computable general equilibrium (CGE) models with several categories of labour, when each representative household is an aggregate of dissimilar households that supply labour in different occupational categories. A novel approach has been applied in the Ministère des Finances du Québec bi-regional CGE of the Province of Québec and the rest of Canada, where micro-founded labour supply is combined with a wage-curve-equilibrating mechanism. A simulation experiment illustrates the workings of the model.

The standard microeconomic model of labour supply assumes that leisure is a normal good with an opportunity cost equal to the wage rate.[1] An increase in the wage rate has income and substitution effects. On the one hand, it raises the opportunity cost of leisure and induces the consumer to work more (take less leisure), that is the substitution effect. On the other hand, the rise in the wage rate augments full income, which increases the consumption of all normal goods, including leisure, that is the income effect. The total effect on labour supply (leisure demand) often takes the form of a backward-bending labour supply curve:[2] at lower wage rates, the substitution effect is greater than the income effect, and the consumer reacts to a rise by reducing leisure and increasing labour time; at higher rates, the income effect is the stronger, and the supply curve 'bends backwards'. However, even though individual labour supply curves may be backward-bending, it is reasonable to expect that the aggregate labour supply curve may not be. Therefore, when the consumer-worker is a 'representative agent', a positively sloped supply curve is expected and generally assumed in CGE models.

Explicit modelling of the labour supply behaviour of households is, of course, not a new idea in the CGE literature.[3] De Melo and Tarr[14], for example,[4] introduced labour–leisure choice in their CGE model calibrated with United States data to study welfare and sectoral effects of removing quotas on textiles, automobiles, and steel. The central value of the income elasticity of labour supply used was –0.12, and the resulting elasticity with respect to the real wage was 0.055. They found that the worker–consumer substitutes leisure for commodity consumption and benefits less from quota removal, since he or she consumes less of the formerly protected goods. The welfare effects with endogenous labour supply are not very different from those obtained with a fixed labour supply. The income effect dominates because the low elasticity of labour supply to the real wage leads to a small decline in hours worked.

In a previous study, Tarr[28] used an alternate technique to incorporate endogenous labour supply in his United States model. Tarr assumed a three-stage budgeting programme where, at the first stage, the consumer chooses between leisure and aggregate consumption. Tarr concluded that the welfare effects (gains or losses) fall with higher values of the income elasticity of labour supply, the latter being the worker–consumer valuation of leisure relative to consumption goods.

On the other hand, Ballardet al.[4] used a constant elasticity of substitution (CES) function representing imperfect substitutability between leisure and the consumption of goods. They used another calibration procedure, based on the assumption that the time available to the worker–consumer is 40 out of a possible 70 hours per week. They noted that their results depended heavily on the calibration procedure.[5]

Decaluwéet al.[15] and Annabi[1] evaluated a tariff-reduction policy with a small open economy model. The introduction of an endogenous labour supply implies that some of the adjustment to reduced labour demand (employment) is absorbed by a reduction in labour supply (an increase in leisure demand), so that wage rates fall less than in the case of exogenous labour supply. Substituting leisure for commodity consumption reduces the gains from tariff removal. The greater the elasticity of labour supply with respect to income, the less the increase in commodity consumption relative to leisure, and the lower the benefits from liberalization. These results are consistent with the literature.

As shown by the literature reviewed above, the set of consumption goods must be extended to include leisure in order to make labour supply endogenous in a model. But how can that be done in a CGE with several categories of labour, where each representative household is in fact an aggregate of very diverse households which supply labour in different occupational categories? (For instance, the household type 'Married couple with two children, age under 35, with income CA$15 000–24 999' includes farmers as well as professionals.)

The novelty of the present approach is to assume that each household is endowed with several time-budgets, one per occupational category, to be allocated between work and leisure. This may seem hard to imagine if one thinks of a real-life household. However, it must be kept in mind that although household behaviour is derived from consumer utility maximization, each household in the CGE is a 'representative' household, made up of a large number of households, whose members belong to different occupational categories. It is simply impossible to model representative household behaviour entirely as if it were a single real household of, say, a man and a woman.

True, there are households with more than one worker. But even if, by adjusting members' shares of domestic tasks, one member's leisure can be substituted to another's to a certain extent, it is reasonable to think that, mainly, each working member of the household consumes his or her own leisure time. Indeed, this is in agreement with microeconomic labour supply models of households with more than one worker (Blundell and Macurdy, [10]).

With this in mind, and depending on the view one holds concerning substitution possibilities between types of leisure, there are two possible approaches. According to the first, the representative household is treated as an integrated decision unit with respect to leisure consumption, just as it is with respect to the consumption of goods: labour supplies are represented as if resulting from joint decisions by household members. This leads to non-zero cross-price labour supply elasticities, since different types of leisure are substitutes. Which is why the second approach is preferred, where each household is treated as if it were made up of as many members as there are occupational categories, and where each member maximizes his or her own utility regardless of what the other members do. By analogy, this hypothesis is called 'Coloc', from the French word 'colocataire', meaning roommate (or cotenant).

Formally, each of the above approaches can be related to one of two rival models in the literature on household labour supply: the integrated decision unit hypothesis leads to a specification equivalent to the unitary model of labour supply; the 'Coloc' approach can be viewed as a particular case of the collective labour supply model (Chiappori, [12]; Fortin and Lacroix, [22]; Chiapporiet al., [13]).

Chiappori[12] showed that, in the particular case where the preferences of household members are 'egoistic', the utility maximization problem is equivalent to a multistage process: at the first stage, non-labour income is shared among household members; at the second stage, each maximizes his or her utility independently of others, subject to the budget constraint resulting from the sharing rule. It will be shown below that, in addition, the 'Coloc' approach assumes that the sharing rule is a constant share allocation, which makes it a special case.

However, it must be pointed out that despite the formal similarities between the specifications under consideration for the CGE model on the one hand and the microeconomic household labour supply models on the other hand, their application contexts are radically different. The theoretical investigation of household labour supply aims at characterizing microeconomic behaviour which results from an interaction between members of a household, more specifically between a husband and a wife in a couple. The specifications under consideration here are intended to represent the aggregate behaviour of a group of households by way of a representative agent. But what is actually being modelled is the behaviour of a group of households made up of a large number of individual households, some of which include more than one labour market participant. In this context, it is difficult to imagine what an altruistic utility function, or a 'caring agent' (Becker, [6]), could mean. Only a micro-simulation model could make it possible to represent both the solidarity between members within a household and the independence between households.

The rest of the paper is organized as follows. The second section presents the general structure of the Ministère des Finances du Québec bi-regional CGE model. The third section describes the wage-curve labour market-equilibrating mechanism. The fourth section develops the micro-founded household labour supply specification, which is the core contribution of this paper. The fifth section illustrates the model's workings by analysing a simulation scenario involving household labour supply behaviour. Concluding comments complete the article.

The Ministère des Finances du Québec CGE model is a static, multi-sector model adapted to the specific characteristics of the Québec economy, in the Canadian and world contexts. The model is therefore a bi-regional model where not only the Québec economy, but also that of the rest of Canada are explicitly modelled, including their mutual relations and international linkages. Thus, it is possible to take into account feedback effects between the two economies. Moreover, in addition to representing direct effects of federal and provincial policies, thanks to its bi-regional structure the model takes into account their indirect effects, that is, effects on Québec of the direct effects of federal or other government policies on the rest of Canada, and vice versa. The model's bi-regional structure and the federal organization of the Canadian economy are reflected in the existence of supra-regional accounts:[7] interest and dividend pool accounts; a single rest-of-the-world account for the two regions; a 'consolidated' federal government account, which accepts surpluses or deficits from federal activities within Québec (in addition to recording federal government receipts and expenditures in the rest of Canada), and a common accumulation (savings–investments) account.

There are four categories of agents in the model: firms, households, governments, and the rest of the world. All agents are price-takers. But while the first two are optimizers, the latter are not. Nonetheless, all agents must satisfy their budget constraints. The model is highly detailed, and the level of detail is as fine for the rest of Canada as it is for Québec, except for governments. In the case of governments, the subdivision of the rest of Canada into provinces and territories is ignored, so that the nine other provincial governments are aggregated into a single agent, as are all local and regional governments outside Québec. In each of the two regions there are fifty-six industries, 121 categories of goods and services, and forty-eight personal consumption expenditure categories. Investments are distributed among thirteen categories of investment goods. There are 150 types of households in Québec, and 155 in the rest of Canada; these are defined according to household composition, income level, and age group.[8] Such a fine classification makes it possible to evaluate social impacts of fiscal policies, following the representative agent approach, in which all agents of a given category are supposed to have identical characteristics and to behave identically (this implies in particular that intra-group income variance is assumed to be zero). Labour demand in each region is divided into eleven occupational categories, and household labour supply is endogenous. Labour supply is modelled in an innovative way, which departs somewhat from the conventional representative agent assumption (see below). Finally, the model has two types of capital, corresponding to corporations and unincorporated businesses. Depending on the structure of their capital in terms of the categories of investment goods, firms face different tax rates. Capital taxation follows the marginal effective tax rate (METR) approach, and capital is partially mobile:[9] it is assumed, first, that capital is mobile between industries and regions, but not between types; and, second, that only part of the capital stock is mobile. Such partial mobility is characterized by the fraction of capital, set at 0.95, which is non-mobile ('captive') relative to the initial state (a value of zero would imply perfect mobility, and a value of one corresponds to industry- and region-specific capital). Capital supply of each type to a given industry in a given region is then constrained to be no less than the stock of non-mobile capital. The geographic mobility of capital is not contained within national borders: the net influx of foreign capital of each type increases with the ratio of the rental rate of mobile capital in Canada over the international rate. Overall, capital mobility, in whichever dimension, is very limited, reflecting the fact that the model is not a long-run model. Actually, being static, and highly disaggregated, the model is better suited to short- to medium-term simulations, which is what the Ministère des Finances was initially interested in.

Absent from the model, however, is factor accumulation (capital stock growth, and demographic changes which affect labour supply): dynamic and inter-temporal phenomena are not accounted for in agent behaviour. The model is, therefore, basically static, although partial capital mobility does introduce an implicit time dimension.

Apart from the special features already mentioned, the general structure of the model is relatively standard. For each region, the model reproduces the classic circular flow of income and expenditure. Production factors (labour and capital) are used in the production of goods and services, which are either sold locally or exported to the other region or abroad. Supply and demand on factor markets jointly determine wage rates and the rental rate of capital, in other words, factor payments. Factor payments translate into agents' incomes: once transfers between agents (including income taxes) and savings are taken into account, incomes are transformed into final demand, which, together with intermediate demand, constitutes domestic demand. Domestic demand interacts with supply from local producers, from the other region, and from the rest of the world. Thus are determined prices and quantities of goods and services purchased locally and imported, which closes the circular flow. Therefore, the model is authentically a CGE model: equilibrium prices and quantities are determined by the interaction of supply and demand on markets.

Production functions follow a standard CGE specification. In every industry, a constant returns-to-scale production technology uses labour, capital, and intermediate inputs. Production is a two-level process. On the lower level, value added is produced with the two types of capital and with labour from different occupational categories, according to a Cobb–Douglas technology. In the absence of specific information on substitution elasticities, the Cobb–Douglas form is 'neutral' in that it maintains constant distributive shares. On the upper level, value added and intermediate consumption are combined according to a Leontief function to produce output. The intermediate consumption of each industry is a Leontief function of goods and services. The choice of Leontief functions is a conservative one insofar as it is certain not to overestimate the substitution effects of tax changes.

Output is an aggregate of the various industry products, which are directed towards the domestic market or towards the export market, either in the other region or in the rest of the world. Two-level constant elasticity-of-transformation (CET) functions capture the imperfect substitutability in production, first of the various products, then of goods directed towards different markets. On the first level, the industry's composite output is a combination of its various products, while on the second level each product is an aggregate of similar goods directed towards the three different outlet markets: the domestic market, exports to the other region (the rest of Canada for Québec, and vice versa), and international exports. At each stage, the composition of the aggregate maximizes the representative firm's sales revenue, given component prices.

Household income comes from wages and salaries, dividends and interests, and net transfers from the governments and from abroad. Labour income generated by productive activities is distributed among households according to their supplies of labour (see below). On the other hand, even if households are the ultimate owners of businesses, they do not receive capital income from corporations directly: corporate capital income is first received by firms that pay dividends and interests to the corresponding supra-regional accounts; it is from these supra-regional accounts that investment income is distributed, in fixed shares, to households.

The spending behaviour of each type of household in each region is modelled following the representative agent approach (the present paper departs from that approach, however, when it comes to modelling labour supply; see below). The model represents the way households dispose of their income in several stages:

• • After income taxes have been paid, a fixed share of disposable income is dedicated to savings.[10]
• • Transfers made by households, including the transfer component of interest paid on consumer debt, are exogenous fixed amounts.
• • The rest is the household's consumption budget.
• • Each representative household then distributes its consumption between personal expenditure categories so as to maximize its utility following a Stone–Geary utility function (demand functions thus form a linear expenditure system – LES).
• • Finally, consumption demand for each personal expenditure category is summed over all households in a given region, and this demand is translated into the optimal mix of goods and services, following a constant elasticity-of-substitution (CES) function.

Domestic absorption of each good is the sum of quantities demanded by households, firms, and governments for final private and public consumption, investment, and intermediate consumption. Most goods and services are supplied by more than one domestic producing industry, and may also be imported from the other region or from the rest of the world. It is assumed that from the buyer's point of view, goods and services supplied by different domestic industries are perfect substitutes.

Such is not the case, however, of domestically produced goods and services versus imports from the other region or from the rest of the world. The quantity demanded of each good is a composite of domestic production and imports. Demand allocation between the three competing supply sources is determined by a CES aggregation function. The hypothesis that imports and domestic products are not perfect substitutes translates into an elasticity that is less than infinite, following the widespread Armington[2] approach. Therefore, the shares of the three supply sources are determined by minimizing the acquisition cost of the composite good; thanks to the homotheticity of the CES function, the price of the composite follows. One advantage of this approach is the possibility of applying different taxes on goods and services depending on their origin (such as import duties, which are levied only on international imports).

Particular care was taken when representing fiscal instruments. Each tax applies to a flow that represents the corresponding tax base as closely as possible. Such is the case, in particular, of indirect taxes, which are applied, so to speak, in successive layers, one over the other. Moreover, effective tax rates may be different, according to whether they apply to household consumption expenditures, investment spending, or intermediate consumption. Also, capital taxation and household income taxation follow the marginal effective tax rate (METR) approach pioneered by Fullerton and Gordon[23].

In a short- to medium-term model, a realistic representation of the labour market cannot but take into consideration the fact of unemployment. Therefore, labour market equilibrium in the model does not conform to its strict micro-theoretic definition. Rather, at the wage rate that prevails in the model solution, quantities of labour supplied and demanded are not equal. The solution is nevertheless an 'equilibrium' in a broader sense, in that the resulting unemployment rate must be compatible with the level of the wage rate.

Compatibility between the rate of unemployment and the wage rate is represented by a 'wage curve' (Blanchflower and Oswald, [8]; Card, [11]). The wage curve concept, widely accepted today, comes from a series of empirical studies based on data from several countries[11] showing a negatively sloped relationship between the unemployment rate and the local real wage rate (in the model, a 'local' labour market is the labour market for a given professional category in a given region). The wage curve is the locus of pairs of compatible values of the unemployment rate and of the wage rate. Fig. 1 illustrates the shape of the wage curve as it was developed by Blanchflower and Oswald[8], and it shows how the wage rate and the rate of unemployment are jointly determined.

Graph: Fig. 1 Determination of the wage rate and unemployment rate according to a wage curve

The algebraic formulation of the wage curve is:

Graph

where lnw represents the natural logarithm of the real wage rate w; lnTCHO represents the natural logarithm of the rate of unemployment; ϵ is the (negative) slope of the curve in logarithmic form – therefore, ϵ is the (negative) elasticity of the wage rate with respect to the rate of unemployment; and ξ represents 'fixed effects' related to regional economic conditions or to industry characteristics, as well as to the set of relevant attributes of workers (when parameters are estimated with micro-data, those attributes may include age, sex, education, etc.).

According to Blanchflower and Oswald[8] and Card[11], the overall conclusion of research conducted in several countries is that the wage curve is 'virtually identical from one country to the next, and stable in time', with an elasticity, ϵ, generally close to –0.1 (Blanchflower and Oswald, [8], p. 156; Card, [11], pp. 1, 32–35). For Canada specifically, Blanchflower and Oswald found a global elasticity equal to –0.09, an estimate based on data for the period 1972–1987. The wage curve elasticities in the model have been estimated by Danielle Bilodeau and Laurence Bargaud of the Institut de la statistique Québec (ISQ), using micro-data from Statistics Canada's Survey of Consumer Finances for 1981–1997, and from the Survey of Labour and Income Dynamics for 1997–2001 (Table 1).

Table 1. Estimated wage curve elasticities by region and by occupation in the general equilibrium model of the Ministère des Finances du Québec (MEGFQ)

Before presenting the model of labour supply, the price of leisure must be examined. In a simple theoretical model, it is simply equal to the wage rate, w. But in the general equilibrium model of the Ministère des Finances du Québec (MEGFQ), the price of leisure is:

Graph

where PCTLl,hh,rg is the price of type l leisure[12] for household hh in region rg; ψhh is the marginal propensity to save of household hh; is the marginal rate of income taxation of household hh by government gvt; is the implicit marginal rate of taxation on household hh's income due to the reduction of type pr transfers by government gvt; prr is an index that runs over transfers that are reducible as a function of income; TCHOl,rg is the unemployment rate of occupational category l in region rg; and wl,rg is the wage rate of occupational category l in region rg.

The opportunity cost of leisure for member l,rg of household hh is, therefore, equal to the mathematical expectation of the wage rate of occupational category l, net of income taxes and savings.[13] The mathematical expectation of the wage rate is defined as the product of the wage rate by the probability of being employed, the latter being the complement of the unemployment rate of occupation l in region rg (1 – TCHOl,rg); thus, it is assumed that unemployment in labour market l,rg affects all households offering that type of labour proportionately. The marginal propensity to save and marginal tax rates are assumed to be the same for all members of a household.

Replacing labour income by its mathematical expectation is analogous, as it were, to assuming rational expectations: the consumer maximizes utility knowing that a fraction of his or her labour supply may not find employment. From a different point of view, unemployment can be seen as having the same effect on household behaviour as a tax on wages: it creates a gap between, on the one hand, the price before taxes (gross wage rate) on the basis of which employers make their hiring decisions, and, on the other hand, the after-tax price (mathematical expectation of the wage rate) on the basis of which workers decide on their supply of labour.

To clarify ideas, the 'Coloc' model is presented in a simplified form, without the cumbersome notation of the full model.

According to the 'Coloc' approach, each member of the household supplies a single type of labour and maximizes his or her utility independently from other members. To define the maximization problem of member i of the household with a Stone–Geary utility function, it is necessary to divide the cost of minimum consumption and non-labour income y between members. Let ωi be the share of member i (that parameter is calibrated from social accounting matrix (SAM) data: it is equal to the share of the household's total labour income from occupational category i). Of course:

Graph

It will be shown below that this distribution parameter plays an important role in the solution.

Then the maximization problem of member i in the household is:

Graph

subject to:

Graph

where Ui is member i's utility; Cih is the consumption of commodity h by member i; is the minimum consumption of commodity h by the household; Ti is the endowment of type i time; TNTi is type i leisure (non-labour) time; is type i minimum leisure (non-labour) time; Y is non-labour income; ph is the price of commodity h; is the price of type i leisure (=net wage of type i labour); and αih and γi are parameters of the utility function of household member i, with:

Graph

Hence, linear expenditure system (LES) demand functions:

Graph

Graph

where:

Graph

with:

Graph

where YINTi is member i's full income; and SUPINTi is member i's full supernumerary income, that is, with a Stone–Geary utility function, the surplus of full income over the cost of minimum consumption of commodities and leisure.

Labour supply is derived from leisure demand. Let TTi be the supply of type i labour. By definition:

Graph

That is fine, but commodity demand (5) and labour supply (8) are functions of non-observable full supernumerary income. It can be demonstrated, however, that:

Graph

where:

Graph

is conventional supernumerary income, defined as the surplus of actual income over the cost of minimum consumption of goods.

One can now rewrite member i's demand functions:

Graph

Graph

and type i labour supply function:

Graph

The own-price elasticity of type i labour supply is positive, provided that CSUPi >  TTi, that is, provided that:

Graph

or, equivalently:

Graph

In other words, labour supply own-price elasticity is positive for all household members, provided that non-labour income be sufficient to cover the household's minimum consumption; in the opposite case, the elasticity is negative for all household members.[14] Since the value of CSUPi depends on member i's share ωi in the representative household, so does the member's own-price elasticity of labour supply.

As for the cross-price elasticity, it is obviously zero, given the form of the supply function, where CSUPi does not depend upon wage rates other than wi. Therefore, the model makes it possible to take into account that, for example, a change in the wage rate of physicians in household category 'Couple with two children' has no impact on the labour supply of farmers in the same household category.

Commodity demand by the household as a whole is:

Graph

The additional hypothesis is made that whatever their marginal budget share of leisure γi, all members of the household divide their discretionary consumption of ordinary goods in identical proportions. That translates into the condition that the ratio:

Graph

be equal for all members i of the household.

Under these conditions:

Graph

where:

Graph

Commodity demand by the household as a whole is the same as under the integrated decision unit hypothesis, provided it is assumed that while their preferences for leisure may be different, all members of the household nevertheless share identical preferences in terms of commodity consumption. The authors think that the present approach is preferable to what is found in the literature on CGEs with the representative household hypothesis and endogenous labour supply. The present approach permits one to describe correctly the labour supply behaviour of households, without assuming that their consumption behaviour depends on members' occupational categories.[15] This new approach could be applied in any context where the criteria defining household categories are different from those defining labour market categories.

To illustrate the model's workings, this section will analyse the results of a simulation that will specifically show the impact on household labour supply of an exogenous shock, namely a 10% proportional reduction in effective tax rates on household income in Québec.[16] Income taxes and transfers that are reducible as a function of income are best visualized as linear functions of income, the former with a positive slope and the latter with a negative slope; the absolute values of the slopes are the corresponding METRs. The simulation involved a 10% reduction in the intercepts, as well as in the slopes.

Detailed results are presented in Tables 2–5.

Table 2. Impact on household labour supply (percentage change from base values)

Table 3. Impact on wage rates and labour supply and demand in Québec, by occupation (percentage change from base values)

Table 4. Impact on selected indicators (percentage change from base values)

Table 5. Impact on real gross domestic product (percentage change from base values)

Before commenting on the results, a few remarks are in order concerning the model's macro-closure for this simulation: The current account balance (foreign savings) is fixed, government expenditures are fixed in real terms, and fiscal parameters are exogenous, so that government savings are endogenous. Since household and firm savings are also endogenous, investments are endogenously determined by the savings–investment balance. This 'savings-driven' approach is a rather common closure in the literature.[17] The fixed current balance assumption avoids the 'free lunch' situation in which foreign savings automatically replace any drop in domestic savings, allowing for fixed investment. For, if foreign borrowing is available at no cost, the 'optimal' approach is to increase foreign borrowing indefinitely. Also, it is definitely appropriate that government expenditures be determined exogenously when simulating the impact of government budget scenarios. Letting investment adjust to the savings–investment equality can be interpreted as recognizing the possibility that public expenditures may 'crowd out' investment. Letting private consumption adjust instead – tantamount to a so-called Kaldorian closure – would be rather unusual (although it has been used by some).

The impact of a reduction of effective income tax rates on disposable income, consumption, savings, and investment will be first examined. The reduction increases the real disposable income (0.703%), consumption (0.633%), and savings of Québec households. However, this increase in household savings does not necessarily translate into a greater level of real investment since, with fixed real government spending, the tax reduction lowers government revenue and ultimately savings. In the end the impact on aggregate savings and, consequently, on investment is negative both in Québec (–0.320%) and in the rest of Canada (–0.313%), which can be interpreted as a 'crowding-out' effect. When reading the results regarding investment, it should be kept in mind that this is a static model: investment demand for goods is not linked to capital formation, capital demand or rates of return; increases in the stock of capital that would result from investment are not defined in the model, let alone attributed to specific industries, as they would in a dynamic model. Nominal investment expenditures are determined by endogenous domestic savings and the fixed current account balance (fixed foreign savings), in accordance with the model closure discussed above. Investment expenditures are first distributed in fixed proportions between regions and commodities; then the demand for goods and services for investment purposes in each region is pooled with demand for other purposes and allocated between producing regions and imports following the Armington constant elasticity-of-substitution (CES) imperfect substituability model.

Initially, the reduction in Québec personal income tax has two effects on household behaviour. On the one hand, the reduction in marginal rates (METRs) creates a substitution effect by increasing the after-tax real wage, and thus the opportunity cost of leisure for households that pay income taxes or receive transfers that are reducible as a function of income. So, the substitution effect tends to decrease the demand for leisure, and therefore increase the supply of labour. On the other hand, the reduction in marginal tax rates creates an income effect, which operates through what microeconomic theory calls full income (that is, the income that the household could earn if it were to set its supply of labour at its upper bound). This income effect increases the demand for leisure and reduces the labour supply of all households.

But there is another income effect associated with the reduction in the initial amounts of both income taxes paid and transfers received (the intercepts, which do not depend on income variations). The sign of this income effect on household labour supply depends on the fiscal situation of a household. If a household is a net taxpayer regarding the initial amounts of income taxes and transfers,[18] the reduction in the initial amount of income taxes increases its disposable income, and therefore its demand for leisure, that is, it decreases its labour supply. But if a household is a net beneficiary regarding the initial amounts of income taxes and transfers,[19] the reduction in initial transfers reduces its disposable income, and consequently its demand for leisure. These various effects are illustrated in Fig. 2.

Graph: Fig. 2 Consumer equilibrium – labour supply

Starting with an initial equilibrium at E0, the change in METRs modifies the price of leisure and creates a substitution effect (E0 → E1) and an income effect (E1 → E2) for all households. For net beneficiaries regarding the initial amounts of income taxes and transfers, the reduction in the initial amount received creates an additional income effect, which is negative (E2 → E3); on the contrary, for net taxpayers regarding the initial amounts of income taxes and transfers, the reduction in the initial amount of income tax creates a positive income effect (E2 → E4).

The net effect on labour supply depends on the respective magnitudes of these effects. The numbers in Table 2 for Québec households show that, overall, the substitution effect dominates in all income groups, and it is bolstered by the initial transfer reduction effect in the case of lower-income households. Moreover, it is clear that the higher the initial level of marginal tax rates, the larger the substitution effect. Now, households with a total income of CA$15 000 or less face METRs that are considerably higher than average because, as net beneficiaries, the transfers they receive are sharply reduced as their labour income increases. All these factors result in a labour supply increase of 9.929%, much higher than that of other groups.

Looking at occupational categories, the biggest rise in labour supply is in the service category (0.666%). This is no surprise, since that professional category includes many minimum-wage workers belonging to households with a total income of CA$15 000 or less. At the opposite end of the spectrum, the weakest increase in labour supply is in the managerial and professional categories (0.155%). Overall, labour supply rises by 0.286% and labour demand by 0.130%.

What are the consequences of this increase in labour supply on wage rates? If one refers to Fig. 1, an increase in labour supply corresponds to a rightward shift of the labour supply curve in the right-hand-side supply-and-demand graph. This will also displace the excess labour supply curve down and to the right in the left-hand-side graph. Because of the negative elasticity of the wage curve, one expects that since labour supply increases, real wage rates will drop, and unemployment will increase.[20] Indeed, real wage rates fall (compare nominal wage rate increases in Table 4, 0.027% in total, with the 0.120% increase in consumer prices), and the unemployment rate rises by 0.961%.

Nonetheless, there is an increase in employment (0.130%), which is greater than the fall in real wage rates, so that real disposable income (0.703%), consumption (0.633%), and household savings increase in Québec.

The effect on consumer prices is consistent with the changes in the labour market just described. They increase as a result of two phenomena. First, the rise in disposable income drives up consumer demand for goods and services (0.633%) and creates upward pressure on prices. Second, the increase in nominal wage rates (and also in after-tax capital rental rates – see below) inflate firms' production costs. Since producers equalize marginal cost and marginal revenue, the increase in marginal cost is partly compensated, through the supply–demand interaction, by an increase in consumer and producer prices (0.076%).

On the capital front, the pressure of demand and the increase in consumer and producer prices allow the after-tax rental rate of capital to rise, increasing the supply of capital in Québec and reducing it in the rest of Canada. The combined positive impacts on labour and capital demand result in a 0.213% increase in Québec's real gross domestic product and a (very) small reduction in the rest of Canada's (–0.044%). The lower capital demand in the rest of Canada is essentially due to a reallocation of capital from the rest of Canada to Québec. The small positive impact on total capital demand in Canada (0.002%) represents a displacement of capital from the rest of the world to Canada in response to the relative appreciation of the rental rate of capital in Canada. At first sight, it might seem surprising that, for Canada as a whole, the increase in gross domestic product is greater than either the increase in capital demand or the increase in employment. But that apparent paradox is easily resolved. First, it can be verified that the change, for Canada as a whole, of capital demand, labour demand, and real gross domestic product is a weighted average of Québec and the rest of Canada, with the weight of Québec in the 20–22% range, depending on which variable is under consideration. It can also be verified that the change in real gross domestic product for Québec, as well as for the rest of Canada, is an intermediate value between the change in labour demand and the change in capital demand. But in Québec, the implicit weight of capital in the real gross domestic product change, relative to that of labour, is larger than in the rest of Canada. Partial mobility has allowed a displacement of capital from the rest of Canada to Québec, where its productivity is higher, due to a lower initial capital-to-labour ratio. That reallocation of capital accounts for the fact that, for the whole of Canada, the increase in gross domestic product is outside the range defined by the rates of change of capital and labour. Table 6 illustrates the above argument.

Table 6. Analysis of the impact on capital, labour, and real gross domestic product

Finally, what are the implications of a reduction of Québec METRs on interregional and international imports and exports? Because of the impact on consumer and producer prices, a greater share of goods and services are now imported due to a reduction in the competitiveness of Québec's goods. The results show increases in imports from the rest of Canada (0.091%) and from the rest of the world (0.248%). Moreover, the rise in producer prices also has an impact on the competitiveness of Québec goods and services on other markets. This translates into a reduction of Québec exports to the rest of Canada (–0.025%) and to the rest of the world (–0.040%).

This paper focused on the specification of endogenous labour supply in computable general equilibrium (CGE) models with several categories of labour, when each representative household is an aggregate of dissimilar households that supply labour in different occupational categories. It presented the novel approach applied in the Ministère des Finances du Québec CGE, a large, multisector, bi-regional CGE model of Québec and the rest of Canada.

Labour supply is made endogenous by including leisure in the households' Stone–Geary utility functions. The model distinguishes as many types of leisure as there are occupational categories of labour. However, in order to prevent non-zero cross-price elasticities of labour supply between different occupational categories, each representative household is modelled as a group of individuals who maximize their utility independently, while sharing identical preferences for goods. The result is a model where household consumption demand is the same as it would be in a standard linear expenditure system (LES) model, while the labour supply of each category by a given household is independent from the wage rate of other categories.

The marginal effective tax rate (METR) approach, applied to personal income taxes, is taken into account in the determination of labour supply. Marginal tax rates represent not only personal income taxes, but also the implicit taxation of income through the reduction of certain transfers. Thus, the model can simulate the work incentive effect of some transfer payment programmes, such as social welfare. Labour market equilibrium is achieved through a wage-curve-equilibrating mechanism allowing for the presence of unemployment. A simulation experiment illustrates the workings of the model.

In the simulation, a 10% cut in all income tax parameters (marginal rates and intercepts) influences household labour-supply behaviour in several ways. First, the reduction in marginal rates (METRs) increases the after-tax real wage, and thus the opportunity cost of leisure for households that pay income taxes or receive transfers that are reducible as a function of income; this creates a substitution effect tending to decrease the demand for leisure, and therefore increase the supply of labour. Second, the reduction in marginal tax rates creates an income effect by raising full income, thus increasing the demand for leisure and reducing the labour supply of all households. Finally, there is another income effect on household labour supply. It is associated with the reduction in the initial amounts (intercepts) of both income taxes paid and transfers received, and its sign depends on the fiscal situation of a household regarding those initial amounts: those who are initially net taxpayers diminish, while those who are initially net beneficiaries of transfers increase their labour supply.

This simulation experiment demonstrates the feasibility of the novel specification presented here, and illustrates its usefulness in taking into consideration aspects of labour supply that are highly relevant for policy-making, but that other models tend to ignore. One such aspect is the work-incentive impact of changes in the implicit taxation of public transfers. The 'policy implication' one draws, therefore, is that whenever fiscal proposals are expected to have implications on the labour supply through the incentive to work, policy-makers and model builders should consider the possibilities offered by the type of model discussed in this paper.