Fiscal and monetary interactions when wage-setters are large: is there a role for corporatist policies?

Abstract

This paper studies the macroeconomic consequences of alternative policy regimes in a closed economy where a central bank, a fiscal authority and a monopoly union interact via their effects on output and inflation. The analysis compares macroeconomic outcomes in a non-cooperative setting, where players may move sequentially or simultaneously, and in a regime of cooperation between the government and wage-setters. The cooperative regime captures a climate of accord among social parties that is finalised at common macroeconomic targets in the tradition of corporatism, as in the recent experience of “social pacts” in many European countries. The paper makes two main contributions. First, it shows that macroeconomic outcomes are suboptimal in the non-cooperative regime and may deliver extreme (undesirable) results even when all players share common ideal targets for output and inflation. All players would be better off with a less extreme value for output or inflation, yet they fail to reach a more advantageous allocation as long as there is an inherent conflict among their further objectives. Moreover, the result is robust to a change in the degree of central bank’s conservatism. Second, I find that cooperation between the government and the monopoly union towards common ideal targets for inflation, output and taxes enhances social welfare even in the absence of explicit coordination with the central bank.

Appendix

1.1 The model

The economy is populated by a continuum of agents of unit mass, j ∈ (0, 1), and a continuum of monopolistically competitive firms defined on the unit interval i ∈ (0, 1). Each agent consumes a basket of goods that comprises all varieties produced in the economy and supplies its own type of labour services. Any pair of varieties of goods and labour services has a constant elasticity of substitution.

As in Lippi (2003) output, Y, is produced using differentiated labour inputs according to a constant return to scale technology:

$$ Y_{i} = \left[ {\int\limits_{0}^{1} {L_{ij}^{{{\frac{\varphi - 1}{\varphi }}}} {\text{d}}j} } \right]^{{_{{{\frac{{^{\alpha \varphi } }}{\varphi - 1}}}} }} $$

(22)

where $L_{j}$ is labour supplied by worker j, φ > 1 measures the elasticity of substitution among labour types and α ∈ (0, 1) is a return to scale parameter. Let W _j represent the nominal wage of worker j. Then, the price index for labour inputs, defined as the minimal nominal cost of producing a unit of output, is given as follows:

$$ W = \left[ {\int\limits_{0}^{1} {W_{j}^{{\left( {1 - \varphi } \right)}} {\text{d}}j} } \right]^{{_{{{\frac{{^{1} }}{1 - \varphi }}}} }} $$

(23)

Cost minimisation implies that the demand for each type of labour is decreasing in the relative wage, as indicated in the expression below:

$$ L_{ij} = \left( {{\frac{{W_{j} }}{W}}} \right)^{ - \varphi } Y_{i}^{{{\frac{1}{\alpha }}}} $$

(24)

In a symmetric equilibrium with W _j  = W, it is easy to derive aggregate employment as follows:

$$ L = \left( {{\frac{W}{\alpha P}}} \right)^{{ - {\frac{1}{1 - \alpha }}}} $$

(25)

Note that the expression above coincides with equilibrium employment under wage bargaining since agents are willing to provide any amount of labour that is demanded in the economy at the wage rate negotiated by the monopoly union.

Agents derive utility from consumption, C, and dislike labour effort. In order to keep algebraic complexity at a bare minimum, utility is assumed to be additively separable in the two arguments:

$$ U_{j} = \ln C_{j} - {\frac{\kappa }{2}}L_{j}^{2} $$

(26)

with consumption given by the Dixit–Stiglitz aggregator:

$$ C = \left[ {\int\limits_{0}^{1} {\left( {C_{i} } \right)^{{{\frac{\theta - 1}{\theta }}}} {\text{d}}i} } \right]^{{{\frac{\theta }{\theta - 1}}}} $$

(27)

where $\theta > 1$ captures the elasticity of substitution among varieties. It is easy to show that firms in the goods market face the following demand:

$$ Y_{i}^{d} = \left( {{\frac{{P_{i} }}{P}}} \right)^{ - \theta } C $$

(28)

where $P_{i}^{{}}$ is the price of variety i and P is the consumer-price index defined as follows:

$$ P = \left[ {\int\limits_{0}^{1} {\left( {P_{i} } \right)^{1 - \theta } {\text{d}}i} } \right]^{{{\frac{1}{1 - \theta }}}} $$

(29)

Each firm will set the price for its own variety so as to maximize profits given market demand (28), yielding:

$$ {\frac{{P_{i} }}{P}} = \left( {{\frac{\theta }{{\alpha \left( {\theta - 1} \right)}}}} \right)^{{{\frac{\alpha }{\Updelta }}}} \left( {{\frac{W}{{P\left( {1 - t} \right)}}}} \right)^{{{\frac{\alpha }{\Updelta }}}} \left( C \right)^{{{\frac{1 - \alpha }{\Updelta }}}} $$

(30)

with $\Updelta \equiv \alpha + \theta \left( {1 - \alpha } \right)$.

I assume that money is the sole financial asset and must be held at the beginning of each period in order to provide cash for nominal expenses:

$$ M_{j} \ge PC_{j} $$

(31)

Money is supplied by the central bank and distributed across agents as a rainfall:

$$ \overline{M} = \int\limits_{0}^{1} {M_{j} {\text{d}}j} $$

(32)

where $\overline{M}$ is the initial endowment.

The budget constraint for agent j is as follows:

$$ PC_{j} = WL_{j} + D_{j} $$

(33)

where D _j are nominal profits.

The government raises taxes on labour and utilises the proceeds to finance expenditures. As in Alesina and Perotti (1997), taxes on labour comprise a social security tax paid by the employer, at rate s, and an income tax, paid by workers at rate v. Denoting by GW the gross wage, a firm bears a per-worker cost of labour equal to GW(1 + s) while the worker receives a net wage W = GW(I − v). The cost of labour to the firm can therefore be written as W(1 − t) where (1 − t) ≡ (1 − v)/(1 + s) is the ratio between the net wage and the cost of labour. The government runs a balanced budget in each period:

$$ PG = {\frac{tW}{1 - t}} $$

(34)

where G is public expenditure in real terms. Note that the algebra of the model works equally well when labour taxes are negative, i.e. when labour is subsidized. In this case, G should be interpreted as a lump-sum tax.

1.2 The general equilibrium

I consider a symmetric equilibrium, where L _j  = L for any j and Y _i  = Y for all i. Equilibrium in the goods market implies that production does not fall short of aggregate demand:

$$ Y \ge C $$

(35)

where $Y = \int\nolimits_{0}^{1} {Y_{i} } {\text{d}}i$ is aggregate output. Aggregating the individual budget constraint across agents, gives the aggregate accounting identity $PC = WL + D = PY$, implying Y = C. Using the cash-in advance constraint, aggregate demand can easily be written as a function of real money balances:

$$ Y = {\frac{M}{P}} $$

(36)

In the symmetric equilibrium, the prices of different varieties are equalised, so that Eq. 30 implies:

$$ P = \left( {{\frac{\theta }{{\alpha \left( {\theta - 1} \right)}}}} \right)^{{{\frac{1}{\alpha }}}} \left( {{\frac{W}{{\left( {1 - t} \right)}}}} \right)^{\alpha } \overline{M}^{1 - \alpha } $$

(37)

1.3 The competitive benchmark

In the absence of tax distortions and with perfectly competitive markets for goods and labour, equilibrium is characterized as follows:

$$ \begin{aligned} \overline{L} = \, & \left( {{\frac{\alpha }{\kappa }}} \right)^{{{\frac{1}{2}}}} \\ \overline{Y} = \, & \overline{C} = \left( {{\frac{\alpha }{\kappa }}} \right)^{{{\frac{\alpha }{2}}}} \\ \overline{P} = \, & \overline{M} \left( {{\frac{\alpha }{\kappa }}} \right)^{{{\frac{ - \alpha }{2}}}} \\ \overline{W} = \, & \alpha \overline{M} \left( {{\frac{\alpha }{\kappa }}} \right)^{{{\frac{ - 1}{2}}}} \\ \end{aligned} $$

(38)

where a bar over a variable denotes the competitive level.

The competitive equilibrium is clearly a first best. In order to see why, rewrite agents’ utility (26) in terms of output using the identity Y = C and the production function in the symmetric equilibrium, obtaining $U = \ln Y - {\frac{\kappa }{2}}Y_{{}}^{{{\frac{2}{\alpha }}}}$. It is immediate to verify that the first derivative of the utility function relative to Y is nil for ${\text{Y}} = \left( {\alpha /\kappa } \right)^{{{\frac{\alpha }{2}}}}$ while the second derivative is always negative. This clearly shows that utility is maximized whenever output is at its competitive level.

1.4 A useful reduced-form

Consider the log-linear model where all variables are (log) deviations from the competitive standard. To this end, wages, money supply and the tax rate are first decomposed as follows:

$$ \begin{aligned} W = \, & \overline{W} \exp w \\ M = \, & \overline{M} \exp m \\ 1 - t = & \exp - \tau \\ \end{aligned} $$

(39)

where $\overline{M}$ and $\overline{W}$ are the competitive levels derived above while w, m and τ ≡ −log (1 − t) capture the deviation from the competitive benchmark. For ease of notation, lower-case letters denote the log deviation of the corresponding upper-case letter, so that w, for instance, is defined as $w \equiv \log \left( W \right) - \log \left( {\overline{W} } \right)$. The variable τ provides an obvious exception.

Taking logarithms of Eq. 37, disregarding constants and using Eq. 39 gives:

$$ p = \left( {1 - \alpha } \right)m + \alpha \left( {w + \tau } \right) $$

(40)

Equation (1) in the text is easily obtained from Eq. 40 after normalising the price level in the previous period to unity. Equation (2) simply obtains from taking logs of Eq. 36 and using Eq. 40 for substituting out p.