Extending working hours: why not work 42 h rather than 38?—a CGE analysis for Germany

Abstract

Faced with a record level of unemployment, the present debate in Germany is to extend the weekly hours of work. In this paper the employment effects of an economy-wide increase in weekly hours are quantified on the basis of a computable general equilibrium model for different specifications of the wage setting rule and the use of additional policy-induced public income. The simulation results back the argument of the opponents of longer working time that not more jobs will be created. However, when the higher tax revenues from GDP growth are used to reduce social security contributions, then the claim of the proponents that more jobs will be created can be supported.

Appendix: The GEM-E3 model

GEM-E3 is a multi-country computable general equilibrium model that was developed on behalf of the European Commission, Directorate-General for Research. A detailed presentation of the model structure and the empirical data basis is given in Capros et al. (1997) and Schmidt (1999). Each agent in GEM-E3 is a price-taker, in the sense that the market interactions, and not the agent, are setting the prices. Each agent is individually defining his supply or demand behaviour by optimising his own utility, profit or cost objectives.

A representative firm (at branch level) decides its supply of goods or services given its selling price and the prices of production factors. The firm supplies its output and selects a production technology so as to maximise its profit within the current year, given the fact that the firm cannot change the stock of productive capital within this period of time. The derived demands for inputs depend on the relative prices which are computed for all simultaneously interrelated markets by the model as a result of supply and demand interactions. In the single-country version for Germany 18 production sectors are included which are characterised by four-level nested CES production functions with labour, capital, and 18 intermediate inputs, including electricity, an input aggregate of three fossil fuel components (coal, oil, and gas), and an input aggregate of 14 nonenergy material components. Profit maximisation under constant returns to scale (in the long run) implies marginal revenues equal marginal costs, which explains the output price of domestic production in terms of a CES unit cost function. Labour is immobile across countries but mobile between sectors. The sectoral capital stock is quasi fixed for the current year at a level reached at the end of the previous year. Hence the demand function for capital is used to determine an endogenous ex post price of capital which clears the market for the fixed capital stock. It is used to calculate capital income, which is distributed among households (in form of interest payments from assets, dissemination of firms profits, entrepreneurs’ salary), firms, and the government. Given the ex ante price of capital, which depends on the price of investment goods, the rate of return on risk-free government bonds, and the rate of replacement, the factor demand function for capital can be employed to determine the desired stock of capital. The difference between the desired capital stock and fixed capital stock defines net investment.

The behaviour of the representative household is assumed to perform a two-stage budgeting procedure: an intertemporal allocation of lifetime wealth endowment between present and future consumption of goods and leisure and an intratemporal allocation of total consumption of goods between durable and non-durable goods. The representative household determines an allocation of its resources between present and future consumption by maximising an intertemporal utility function subject to an intertemporal budget constraint. Under myopic expectations and the assumption of constant and equal growth rates for both inflation and the nominal wage rate the Fisher relation can be used to derive demand functions for consumption and leisure. Labour supply is given by the residual between total time resources and leisure demand.

In the standard version of the GEM-E3 model with a neo-classical labour market, the wage rate serves to balance labour demand of firms and leisure demand of households. The savings of households are determined by the difference of disposable income and consumption expenditures. In the version which is used in this paper, the real net wage rate is exogenously fixed which leads to involuntary unemployment in equilibrium. Labour demand at the fixed wage rate determines employment. Involuntary unemployment is calculated as the difference between exogenously given time resources minus voluntary leisure minus labour demand.

The model distinguishes between two types of consumption expenditure: expenditure for non-linked, non-durable goods, which are allocated on the second stage of the consumer decision problem, and expenditure associated with the use of durable goods—covering capital user costs and demand for linked non-durable goods.

The government’s expenditure is exogenous in large parts while revenues are endogenous. Revenue categories are for example direct and indirect taxes, VAT, employers’ and employees’ social security contributions, export and production subsidies, or import duties.

The specification of Germany’s import demand for tradable commodities is based on the Armington model of national product differentiation. Expenditure is allocated between domestic demand of domestically produced goods and imports from the rest of the world. Thus, import demand is price elastic. The Armington assumption for German import demand implies that the German price level is not completely determined by (exogenous) world market prices. Domestically produced goods sold on the German market, however, are perfect substitutes for goods that are sold on foreign export markets. The rest of the world’s production and consumption behaviour is exogenous. The rest of the world supplies exports at fixed world market prices. The foreign import demand function is modelled in complete analogy to Germany’s import demand function (Armington). The Armington assumption for foreign import demand leads to a finitely price elastic import demand function of the rest of the world. Note that this specification allows for terms-of-trade effects: Higher prices of German exports can be partially shifted abroad (tax shifting effects towards the foreign sector). Both specifications modify the small-country assumption of exogenous world market prices.

In the model version used in this paper, asset markets and international capital flows are excluded, nominal exchange rates are fixed, and the balance-of-payments constraint for Germany is non-binding. Thus, a current account surplus or deficit has no feedback on the German economy. Since a flexible current account seems to be more reasonable in the short- or medium- than in the long-run, the simulations also reflect short- or medium-term results.

Since the demand system determines consumption goods by categories and the system of investment functions determines investment demand by destination, transition matrices are required to transform demand into deliveries from the industries. Therefore, the final demand is the result of the transition matrix of the type (branches categories) multiplied by the consumption categories. Similar to the matching of consumption categories to products, an investment matrix with fixed technical coefficients is used to calculate investment demand by origin (products) from investment demand by destination (branches).

The national accounting identity, which expresses that the private gross domestic production from both the flow of cost approach and the flow of product approach should be equal, is satisfied if and only if total saving, involving income distribution and fiscal policy relationships, equals total investment. Following Walras’ Law, this market is in equilibrium if an equilibrium price vector is found for the other markets (supposing that the demand, supply and price functions are specified according to the needs of an Arrow-Debreu economy). Therefore, the saving-investment identity and the corresponding global shadow price of capital (mobility of (new) capital between sectors but not across countries is assumed) is automatically given.