2.1 Overview

The core model on which we build is the EAGLE model, which is a multi-country dynamic general equilibrium model of the euro area within the world economy, see Gomes et al. (Reference Gomes, Jacquinot and Pisani2010) and Gomes et al. (Reference Gomes, Jacquinot and Pisani2012). The model shares the same theoretical setup as the ECB’s New Area Wide model, (Christoffel et al. Reference Christoffel, Coenen and Warne2008) or the IMF Global Economy Model, GEM (Laxton and Pesenti, Reference Laxton and Pesenti2003). It is a large scale micro-founded model of a monetary union that consists of an open economy version of the New Keynesian paradigm. Given the purpose of our analysis, the version used here includes a significantly expanded and micro-founded labour market block, which we describe in detail in Section 2.4.

In the model, the world economy consists of three blocs. Two blocs are members of a monetary union, the euro area (EA). Thus, these two blocs (Home and the Rest of the euro area, REA) have a common nominal exchange rate and a common nominal interest rate. Regarding the monetary authority, the central bank sets the domestic short-term nominal interest rate according to a Taylor-type rule, by reacting to consumer price inflation, and unemployment gap, both defined at the euro area level. In the simulations we use alternative monetary policy rules for the euro area that are described in Section 3. The remaining bloc, the rest of the world (RW), has its own nominal interest rate and nominal exchange rate. The monetary authorities in this bloc set the domestic short-term nominal interest rate according to a Taylor-type rule that reacts to domestic variables (inflation and output growth). In all blocs, fiscal policy is conducted at the country level. All regions trade with each other at the levels of intermediate goods, with a matrix of bilateral trade flows based on recent historical averages. International asset trade is limited to non-contingent nominal bonds denominated in US dollars. We provide the key model equations below and the full model equations in Online Appendix F.

2.2 Firms

In each country there are two types of firms. One type produces final non-tradable goods under perfect competition using domestic tradable goods, imported tradable goods and non-tradable goods. Final goods can be used for private consumption ( $Q_{C,t}$ ) and for private investment ( $Q_{I,t}$ ). They are assembled from tradable goods, $TT_{h,t}$ and non-tradable goods, $NT_{h,t}$ , with $h \in [C, \ I]$ using the constant elasticity of substitution technology. There is also a final public good that is fully biased towards domestic non-tradable intermediate goods. In the case of consumption goods ( $h=C$ ):Footnote ³

(1) \begin{equation} Q_{C,t} =\left [ \nu _{C}^{\frac {1}{\mu _{C}}} TT_{C,t}^{\frac {\mu _{C}-1}{\mu _{C}}} + \left (1-\nu _{C}\right )^{\frac {1}{\mu _{C}}}NT_{C,t}^{\frac {\mu _{C}-1}{\mu _{C}}}\right ]^{\frac {\mu _{C}}{\mu _{C-1}}}, \end{equation}

where:

(2) \begin{equation} TT_{C,t} =\left [ \nu _{TC}^{\frac {1}{\mu _{TC}}}HT_{C,t} ^{\frac {\mu _{TC}-1}{\mu _{TC}}} + \left ( 1-\nu _{TC}\right ) ^{\frac {1}{\mu _{TC}}}IM_{C,t}^{\frac {\mu _{TC}-1}{\mu _{TC}}}\right ]^{\frac {\mu _{TC}}{\mu _{TC-1}}}. \end{equation}

Similarly, tradable goods are a composite bundle of of domestic tradable goods, $HT_{C,t}$ , and imports, $IM_{C,t}$ , which, in turn, are also a composite of imports from other regions.Footnote ⁴ Parameters $\mu _C$ , $\mu _{TC}$ (and $\mu _{IMC}$ in the case of the import bundle) are intratemporal elasticities of substitution between the inputs in the production functions, while $\nu _C$ and $\nu _{TC}$ ( $\nu _{IM_C}$ in the case of the import bundle) are weights (quasi-shares) of the inputs into the production functions.

The other type of firms produces intermediate goods, which are produced by an array of firms under monopolistic competition. A set of intermediate goods firms produces tradable goods and another set produces non-tradable goods, using domestic labour and capital, combined according to a Cobb–Douglas technology. For the case of tradable goods:Footnote ⁵

(3) \begin{equation} Y_{T,t} = z_{T,t}K_{T,t}^{\alpha _{T}}N_{T,t}^{1-\alpha _{T}}-\psi _{T}, \end{equation}

where $\psi _{T}$ is a fixed cost. The inputs are homogenous capital services, $K_{T,t}$ , and labour services, $N_{T,t}$ . Capital services are supplied by domestic households under perfect competition, yielding that demand for capital is determined by its marginal product being equal to the rental rate, while labour demand is determined by the marginal product of labour at intermediate goods firm being equal to the cost of labour determined by labour packers, as described below. $z_{T,t}$ is a sector-specific productivity shock. The market power implies that firms set nominal prices and charge a markup over marginal costs. Nominal prices are sticky (see Online Appendix F for the definition of the corresponding price indices).

2.3 Households

There are two types of infinitely-lived households in each country, Ricardian ( $s=i$ ) and HtM ( $s=j$ ). Households gain utility from consuming and suffer disutility from working. Households maximise lifetime utility:

(4) \begin{equation} E_{t}\left [ \sum \limits _{k=0}^{\infty }\beta ^{k}\left ( \frac {1-\kappa }{1-\sigma }\left ( \frac {c_{s,t+k} -\kappa C_{s,t+k-1}}{1-\kappa }\right ) ^{1-\sigma }-\frac {1}{1+\zeta }h_{s,t+k}^{1+\zeta }\right ) \right ], \end{equation}

where $c_{s,t}$ is consumption, $\beta$ is the discount rate, $\sigma$ is the inverse of the intertemporal elasticity of substitution and $\zeta$ is the inverse of the elasticity of hours worked, $h_{s,t}$ , with respect to the real wage. $\kappa$ is the degree of habit formation in consumption of each type of households, where the habit depends on the aggregate consumption of the type, $C_{s,t}$ .

Ricardian households have access to financial markets, where they buy and sell domestic government bonds and internationally traded bonds denominated in US dollars (as well as an euro denominated bond traded within euro area blocs), accumulate physical capital, rent their services to firms, supply labour and hold money for transaction purposes. HtM households have only access to money balances, which means that their ability to intertemporally smooth consumption is limited.

2.4 Labour market

The labour market features search frictions as in Mortensen and Pissarides (Reference Mortensen, Pissarides, Mortensen and Pissarides1999), but adds sticky wages by means of staggered wage setting, and a potential to distinguish wage stickiness of new hires and existing workers. This approach follows broadly Bodart et al. (Reference Bodart, de Walque, Pierrard, Sneessens and Wouters2006) and de Walque et al. (Reference de Walque, Pierrard, Sneessens and Wouters2009). In addition, we distinguish between labour market segments for Ricardian and HtM households, each of which can have their own unemployment, hours worked, wage setting, and different . wage rigidities for new hires and existing workers.

The aim of this relatively complex structure is to capture the labour market more realistically in an otherwise two-agent model, in particular the fact that it is likely that wages for new hires are more volatile than wages for existing workers (see e.g. Haefke et al. (Reference Haefke, Sonntag and Van Rens2013) and Lydon and Lozej (Reference Lydon and Lozej2018)) and that it is likely that poorer households are often those for whom employment outcomes are more susceptible to business cycle fluctuations than for richer households. This is in line with the evidence for several countries (see Cairó and Cajner (Reference Cairó and Cajner2018) for the US, Broer et al. (Reference Broer, Kramer and Mitman2022) for Germany, and Herman and Lozej (Reference Herman and Lozej2023) for a selection of European countries).

More volatile employment outcomes for a particular segment of wealth distribution are not important in a representative-agent framework, where income fluctuations can be smoothed by risk sharing among the households. However, as outlined in the above papers, labour market at the bottom of the income distribution is different than at the top. This is why we need this relatively complex setup of the labour market to be able to capture the more volatile properties of the labour market for HtM households. This has broader implications, because the fluctuations in this labour market, due to the inability to smooth consumption, affect aggregate consumption and aggregate fluctuations.

We assume a continuum of labour firms in each labour market segment, with each labour firm employing one worker. Labour firms pay labour taxes, bargain with households over wages, and post vacancies at a per-period fixed cost. If they find a worker, they sell homogeneous labour services to a labour packer, which aggregates labour from the Ricardian and HtM labour market segments and sells aggregated labour services to intermediate goods firms.

The flows on the labour market are as follows. The number of workers in segment $s$ (recall that $s=i$ for Ricardian and $s=j$ for HtM households) that are employed after the matching process has been completed, $nde_{s,t}$ , evolves as follows:

(5) \begin{equation} nde_{s,t}=(1-\delta _{x,s})\ nde_{s,t-1} + M_{s,t}, \end{equation}

where $M_{s,t}$ is the number of new matches formed in a period, and $\delta _{x,s}$ is the fraction of existing employment relationships that have (exogenously) separated in each period. The number of matches $M_{s,t}$ is defined according to the following matching function:

(6) \begin{equation} M_{s,t}=\phi _{s,M}(un_{s,t})^{\mu _s}(vac_{s,t})^{1-\mu _s}=p_{s,t}^{W} un_{s,t}=p_{s,t}^{F} vac_{s,t}, \end{equation}

where $\phi _{s,M}$ is matching efficiency, $un_{s,t}$ is the number of searching workers, $vac_{s,t}$ is the number of vacancies, $p_{s,t}^{W}$ is the matching probability for workers of each type, $p_{s,t}^{F}$ is the matching probability for firms, and $\mu _s$ is the elasticity of the matching function with respect to unemployment in each segment.

The probability for a searching worker to find a job is

(7) \begin{equation} p_{s,t}^W=\frac {M_{t}}{un_{s,t}}=\phi _{s,M}(\frac {vac_{s,t}}{un_{s,t}})^{1-\mu _s} \end{equation}

and the probability of a firm finding a worker is

(8) \begin{equation} p_{s,t}^F=\frac {M_{s,t}}{vac_{s,t}}=\phi _{s,M}(\frac {vac_{s,t}}{un_{s,t}})^{-\mu _s} .\end{equation}

The number of unemployed workers who search for work at the beginning of period t (i.e., the number of workers who enter the matching process, $un_{s,t}$ ) is equal to those who were unemployed at the end of period $t-1$ after the $t-1$ matching has been completed (i.e., $une_{s,t-1}$ ), plus the newly separated workers (i.e., $\delta _{x,s}nde_{s,t-1}$ ):

(9) \begin{equation} un_{s,t}=une_{s,t-1}+\delta _{x,s} nde_{s,t-1}. \end{equation}

These workers are the ones who receive unemployment benefits. The population of each bloc in the model is standardised to 1, and so is the mass of households in each segment, so that the number of unemployed at the end of the period in a segment $s$ is $une_{s,t}=1-nde_{s,t}$ . Total unemployment in a bloc is a weighted unemployment across labour market segments, where $\omega$ is the share of HtM households: $une_{t} = \omega \, une_{j,t} + (1-\omega ) une_{i,t}$ .

2.4.1 Value functions

We will require two sets of value functions. One set of value functions is for wages that have been renegotiated in the current period, and one set of values for wages that have not been renegotiated. We assume that wages that have not been renegotiated are indexed to inflation. The notation follows closely the notation used in Bodart et al. (Reference Bodart, de Walque, Pierrard, Sneessens and Wouters2006) and de Walque et al. (Reference de Walque, Pierrard, Sneessens and Wouters2009).

Value functions for a labour firm

Let $A^F(w^*_{s,t})$ denote the value of a job for a firm employing a worker from household type $s \in [i, \ j]$ , where $w^*_{s,j}$ is the renegotiated wage. Following Bodart et al. (Reference Bodart, de Walque, Pierrard, Sneessens and Wouters2006), it will be convenient to use this value in marginal utility terms, so we define ${\mathcal{A}}^F(w^*_{s,t}) \equiv u'(c_{s,t}) A^F(w^*_{s,t})$ , where $u'(c_{s,t})$ is the marginal utility of consumption of household $s$ . The value of a job with a renegotiated wage for a labour firm can then be written as

(10) \begin{equation} \begin{split} {\mathcal{A}}_t^F(w^*_{s,t}) &= u'(c_{s,t}) \left (h^{\alpha _H}_{s,t}x_{s,t} - h_{s,t}w^*_{s,t}(1+\tau _t^{wf})\right ) \\ &+ \beta (1-\delta _{x,s})\left [(1-\xi _{w,s}){\mathcal{A}}_{t+1}^F(w^*_{s,t+1}) + \xi _{w,s}{\mathcal{A}}_{t+1}^F(w^*_{s,t}) \right ] \end{split}_. \end{equation}

Here the term $h^{\alpha _H}_{s,t}$ denotes the effective hours that a labour firm produces from hours $h_{s,t}$ supplied by the worker from household $s$ .Footnote ⁶ $x_{s,t}$ is what the labour packer pays for such unit of labour. The first term in the brackets on the right-hand side of equation (10) therefore measures earnings of the labour firm from selling hours worked. But for these hours it has to pay to the household hourly wage, which is in this case newly renegotiated, $w^*_{s,t}$ . Because we assume that labour firms pay some labour taxes (social security contributions), the cost for the labour firm is increased by taxes paid, at the rate $\tau _t^{wf}$ . In the next period, if the firm and the worker do not separate, which occurs with probability $(1-\delta _{x,s})$ , two cases can arise. In the first case, which occurs with the probability $(1-\xi _{w,s})$ , wages are renegotiated and the value of the worker for the labour firm is again the value of a worker with a renegotiated wage, just in the next period, ${\mathcal{A}}_{t + 1}^F(w^*_{s,t + 1})$ . With probability $\xi _{w,s}$ wages are not renegotiated and the firm is in next period stuck with the next period’s worker value at the current wage, ${\mathcal{A}}_{t + 1}^F(w^*_{s,t})$ .

Free entry condition

A firm posting a vacancy for household type $s$ must pay a per-period constant cost $\psi _s$ for having a vacancy open. If $\kappa _{w,s}$ denotes the probability that a firm cannot renegotiate the wage for a newly hired worker from household type $s$ , then the value of employing a new worker is, in monetary terms (recall, ${\mathcal{A}}^F(w^*_{s,t}) \equiv u'(c_{s,t}) A^F(w^*_{s,t})$ , and the same for the value at average wage), equal to the weighted average of the value of a worker at a newly-renegotiated job and the value of a worker hired at average wage. The free-entry condition is therefore:

(11) \begin{equation} \psi _s = p^F_t \beta \frac {u'(c_{s,t + 1})}{u'(c_{s,t})} \left [(1-\kappa _{w,s}){\mathcal{A}}_t^F(w^*_{s,t + 1}) + \kappa _{w,s} {\mathcal{A}}_t^F(w_{s,t + 1})\right ]. \end{equation}

Value functions for a worker

Similarly as for labour firms, we can define value functions for workers. Again we have two types of value functions, one for a newly-renegotiated wage and one for the average wage, for each type of household. The value of a job, net of the value of unemployment, for a worker with newly-renegotiated wage is

(12) \begin{equation} \begin{split} {\mathcal{A}}_t^H(w^*_{s,t}) &= u'(c_{s,t}) \left (h_{s,t}w^*_{s,t}(1-\tau ^{wh}_{t}) - b_{s,t}\right ) - \chi \frac {h_{s,t}^{1+\varphi }}{1+\varphi } \\ &+ \beta (1-\delta _{x,s})\left [(1-\xi _{w,s}){\mathcal{A}}_{t+1}^H(w^*_{s,t+1}) + \xi _{w,s}{\mathcal{A}}_{t+1}^H(w^*_{s,t}) \right ] \\ &- \beta p^W_{s,t} \left [(1-\kappa _{w,s}){\mathcal{A}}_{t+1}^H(w^*_{s,t+1}) + \kappa _{w,s}{\mathcal{A}}_{t+1}^H(w_{s,t+1}) \right ]. \end{split} \end{equation}

The first line of equation (12) denotes, in utility terms, first the net gain of having a job, which is hours worked times wage net of taxes paid by the household, at a rate $\tau ^{wh}_{t}$ and net of opportunity cost of having a job, which are unemployment benefits, $b_{s,t}$ .Footnote ⁷ The second term in the first line is the disutility of hours worked.Footnote ⁸ The second line represents the value of having a job in the next period, which occurs with the probability $(1-\delta _{x,s})$ . This job can be either at the newly renegotiated wage or at the current wage. The last row of equation (12) is the opportunity cost of having a job, which is the value of being unemployed. If a worker is unemployed, then there is a probability $p^W_{s,t}$ to find a job, which can be either at a newly-renegotiated wage with probability $(1-\kappa _{w,s})$ , or at an average wage, with probability $\kappa _{w,s}$ .

2.4.2 Wages and hours

Assuming standard (efficient) Nash bargaining between households and labour firms, every period, wages and hours worked are determined by maximising the following expression, where $eta_s$ measures the bargaining power of workers of type $s$ :

(13) \begin{equation} \max _{w^*_{s,t},h_{s,t}} \left (A_t^H(w^*_{s,t})\right )^{\eta _s} \left (A_t^F(w^*_{s,t})\right )^{1-\eta _s}. \end{equation}

The result is that wages are split according to the Nash sharing rule:

(14) \begin{equation} \eta _s (1-\tau _{t}^{wh})A_t^F(w^*_{s,t})=(1-\eta _s)(1 + \tau _{t}^{wf}) A_t^H(w^*_{s,t}). \end{equation}

The intuition for the above rule is that households and labour firms bargain over each other’s matching surpluses, where the surplus of the firm is the value of the worker (because in equilibrium the value of the vacancy is zero), and for the household the value of the match is the net gain from being employed (relative to being unemployed), both evaluated at the currently-negotiated wage. The above equation thus determines $w^*_{t,s}$ .

The average wage is a weighted average of the average wage from the previous period and the wages of new hires, where the weights are the share of workers who have kept their employment and wage from the previous period in total current employment, $\frac {(1-\delta _{x,s})nde_{s,t-1}}{nde_{s,t}}$ , and the share of newly hired workers at the new wage, $\frac {M_{s,t}}{nde_{s,t}}$ . Note that only a fraction $\xi _{w,s}$ of workers that have kept their jobs are able to index wages to trend inflation. The average wage is therefore determined as follows:

(15) \begin{equation} \begin{split} w_{s,t} &= \frac {(1-\delta _{x,s})nde_{s,t-1}}{nde_{s,t}}\left [\xi _{w,s} \frac {1 + \overline {\pi }}{1 + \pi _{t-1}}w_{s,t-1} + (1-\xi _{w,s})w^*_{s,t} \right ] \\ & + \frac {M_{s,t}}{nde_{s,t}}\left [\kappa _{w,s}w_{s,t} + (1-\kappa _{w,s})w^*_{s,t} \right ], \end{split} \end{equation}

where the first row is the average wage of existing workers and the second row is the average wage of new hires, with the number of new matches $M_{s,t}$ counting the number of new hires.Footnote ⁹

Similarly, hours worked are determined by per-period Nash bargaining, and after taking into account the wage decision (equation 14), hours worked expression is:

(16) \begin{equation} \alpha _{H}x_{s,t}(h_{s,t})^{\alpha _{H-1}}=\frac {\chi }{u'(c_{s,t})}\frac {(1 + \tau _{t}^{wf})}{(1-\tau _{t}^{wh})}(h_{s,t})^{\varphi }. \end{equation}

The term on the left is the marginal revenue from labour services brought about by an additional hour worked and the term on the right is the marginal disutility of having to work an additional hour, in after-tax consumption terms.

Note that throughout our notation we have assumed that hours worked do not depend on wages. Equation (16) shows that under the assumption of efficient Nash bargaining, this is indeed the case.Footnote ¹⁰

2.4.3 labour packer

Labour from Ricardian and HtM households is aggregated by a labour packer using a CES technology, as follows:

(17) \begin{equation} n_t^{1-\frac {1}{\eta _L}} = \left [(1-\omega )^{\frac {1}{\eta _L}} \left (nde_{i,t}h_{i,t}^{\alpha _H} \right )^{1-\frac {1}{\eta _L}} + \omega ^{\frac {1}{\eta _L}} \left (nde_{j,t}h_{j,t}^{\alpha _H} \right )^{1-\frac {1}{\eta _L}} \right ], \end{equation}

where $n_t$ are aggregate labour services and $nde_{s,t}h_{s,t}^{\alpha _H}$ are total labour services provided by labour firms in household segment $s$ . Parameter $\omega$ measures the share of HtM households in the economy and $\eta _L$ the degree of substitution between Ricardian and HtM households.

5.1 Contractionary demand shock

We pick the monetary policy shock as a ”representative” demand shock because it has the advantage that it illustrates the properties of the model in response to a shock that is widely studied in both theoretical and empirical literature. Moreover, it helps to understand what monetary policy reaction does when we discuss the responses to a supply shock in the next subsection. The shock size is standardised to achieve a 1 p.p. maximum decrease in inflation (annualised) under the benchmark rule (IT) with a positive weight on unemployment, and this size of the shock is kept fixed across simulations with different monetary policy rules.Footnote ¹⁵

Figure 1.

Contractionary demand shock: area-wide demand components.Notes: Horizontal axes: quarters; vertical axes: percent deviations from the steady state. All variables are in real terms.

Figures 1 and 2 show the euro-area-wide variables for the three interest rate rules, one in each column, and for different weights placed on unemployment. The full black line shows the case when the central bank responds to the unemployment rate and the dashed red line shows the case where the central bank does not respond to unemployment. For the ASUT rule the case where the weight on unemployment is zero always corresponds to the strict inflation targeting rule, i.e., to dashed red lines in the leftmost column of the figure, which is why we show as an alternative the ASUT rule with stronger response to unemployment ( $\phi _u$ =3).Footnote ¹⁶

Figure 2.

Contractionary demand shock: area-wide variables.Notes: Horizontal axes: quarters; vertical axes: percentage point deviations from the steady state, except wages, which are in precent deviations. Interest rates and inflation are annualised.

Two observations stand out. First, fluctuations in all variables are more pronounced when the weight on unemployment in the monetary policy rule is zero or small. These fluctuations are longer-lasting for real variables, while inflation returns to its initial level faster, especially considering the fact that it falls more initially. The latter happens because forward-looking firms anticipate lower demand in the future, which implies lower wages and lower marginal costs, which translates in faster and stronger initial fall in inflation, but also to its faster return to initial level. When the central bank rule responds to unemployment, it counteracts the decline in unemployment, which means that after the initial shock, interest rates endogenously tighten somewhat less due to the increase in unemployment. Because the increase in unemployment is persistent, the central bank returns its interest rate to the initial level faster compared to the case with no unemployment in the monetary policy rule (this is the most evident for the AIT case in Figure 2). This causes a lower and less persistent tightening of the real interest rate, which counters the reduction of economic activity. Note that the losses in output, employment, and consumption are the lowest in the case of the ASUT with the strongest response to unemployment (dotted red line in Figure 1).

Figure 3.

Contractionary demand shock: country-specific demand components.Notes: Horizontal axes: quarters; vertical axes: percent deviations from the steady state. All variables are in real terms.

Second, fluctuations tend to be more pronounced under the AIT rule, even when the rule does include a response to unemployment. The reason is that the AIT rule is relatively slow to react, so interest rates endogenously respond more slowly and more persistently to economic developments, which delays the return of the interest rate to the initial level (the nominal interest rate for AIT returns to the initial level only after around 12 quarters, whereas for the other cases this happens about four quarters earlier, see bottom-right chart in Figure 2). This is reflected in the longer-lasting elevated level of the real rate, with the corresponding negative consequences for the aggregate consumption and demand. Including the response to unemployment helps alleviate this persistence, but does not undo this property of the AIT rule.

Figure 4.

Contractionary demand shock: country-specific variables.Notes: Horizontal axes: quarters; vertical axes: percent deviations from the steady state, except unemployment, which is in percentage point deviations. All variables are in real terms.

Figure 5.

Contractionary demand shock: country-specific variables.Notes: Horizontal axes: quarters; vertical axes: percent deviations from the steady state, except job finding probabilities and relative consumption, which are in p.p. deviations. All variables are in real terms.

Figures 3 to 5 show country-specific outcomes in the euro area for the three monetary policy rules. Home is shown with red lines and the rest of the euro area with black lines. Note the considerable differences between the responses of the two regions regardless of the monetary policy rule. This reflects in part the differences in the labour markets, but also differences in the structure of the economy. One such difference between the EA blocs is in terms of the import-content of investment, where Home imports a much bigger share of investment goods than the REA, and are therefore more affected by the euro appreciation that follows monetary tightening. This is part of the reason why imports in Home decrease as much as in the REA even though investment and consumption decrease by less. Another reason for the differences is the export orientation of the two euro-area blocs. Home is much more open to the RW, while the REA is more closed. This leads to a different degree of exposure to the euro exchange rate and therefore different fluctuations in exports, as can clearly be seen in Figure 3.

Differences in labour market structure also lead to some divergence between countries. For instance, while Home’s output decreases by about a two thirds as much as the REA output, unemployment of both types of households increases by half as much or less than in the REA. Figure 5 explains where among the households this dampening of unemployment occurs. In Home, most of the dampening of unemployment is among the poor HtM households. There, the job finding probability decreases the least, compared with the Ricardian households. This is not the case in the REA, where most of the adjustment in employment and job finding is on the side of the poor HtM households. This holds across all the rules and regardless of whether the central bank attaches some weight to unemployment or not.

Interestingly, if the central bank does not react to unemployment after an expansionary shock, consumption level of the poor households in both EA regions decreases by more than the consumption level of richer Ricardian households and therefore leads to an increase in consumption inequality. Here it is useful to recall the statement of Chairman Powell (Reference Powell2020) that we cited in the Introduction, namely the “… appreciation of a strong labour market, particularly for many in low- and moderate-income communities …”. In the case of a contractionary demand shock, this line of thinking implies that central banks seeking to reduce inequality in consumption should allow for somewhat less persistent tightening in response to a weak labour market. This is akin to the asymmetric unemployment targeting rule, which would ignore unemployment whenever it decreased below its steady-state value (or respond less to its increase), as displayed in the middle panel of the figure.Footnote ¹⁷

Figure 6.

Inflationary supply shock: area-wide demand components.Notes: Horizontal axes: quarters; vertical axes: percent deviations from the steady state. All variables are in real terms.

Another important takeaway from the cross-country comparison is that the divergence between two intra-EA regions tends to be the strongest when fluctuations are large in absolute terms, which happens when monetary policy does not respond to unemployment. Similarly, the inequality in consumption within countries also increases more strongly when the central bank does not react to unemployment, see bottom panels of Figure 5.

Figure 7.

Inflationary supply shock: area-wide variables.Notes: Horizontal axes: quarters; vertical axes: percentage point deviations from the steady state, except wages, which are in precent deviations. Interest rates and inflation are annualised.

5.2 Inflationary supply shock

We now investigate the performance of monetary policy rules under the shock scenario that induces a trade-off between stabilising inflation and unemployment. To achieve this, we simulate a symmetric and equal increase in markups in tradable and non-tradable sectors in both blocs of the euro area.Footnote ¹⁸ As before, the size of the shock is calibrated to achieve a 1 p.p. maximum increase in the euro-area-wide inflation under the benchmark rule and the size of the shock is kept the same across policy rules.

Figures 6 and 7 show the euro area-wide outcomes. The supply shock generates an increase in inflation and a negative impact on economic activity. The fluctuations in (un)employment, aggregate demand and its components are again stronger if the central bank pays no attention to unemployment, while in this case inflation shows a much milder increase (figure 8, figure 9).

Figure 8.

Inflationary supply shock: country-specific demand components.Notes: Horizontal axes: quarters; vertical axes: percent deviations from the steady state. All variables are in real terms.

Compared to the other two rules, AIT tends to attenuate or even neutralise the negative real impact of the shock in the first few quarters when the central bank reacts to unemployment, mainly because this rule stipulates a slower increase followed by a reduction in the nominal rate, which results in a stronger drop in real interest rate and hence an increase in Ricardian households’ consumption in the short run. Recall that these households represent 75% of all households and that their consumption level is about a quarter higher than consumption of HtM households, so that Ricardian households have a strong influence on aggregate consumption. This effect on Ricardian households’ consumption due to a lower real rate is present for all rules and can also be observed for the more aggressive ASUT rule in the middle column. Moreover, in the case of the AIT rule this effect is sufficiently strong that it prevents the short-run increase in unemployment, which shields the income and consumption of HtM households in the short run (these effects can most clearly be seen by looking at full lines in the bottom row of Figure 10).

Because the supply shock generates an increase in unemployment, it triggers a stronger monetary policy response whent he weight on unemployment gap is larger. For instance, the ASUT rule in its more aggressive version achieves a lower peak increase in unemployment than AIT that responds to unemployment. Therefore, the ASUT rule better mitigates the effect of the shock on unemployment but at the cost of higher inflation.

Figures 8 to 10 show the responses across countries, members of the euro area. Home is shown in black and the REA in red lines. Compared to the contractionary demand shock, the responses of both EA blocs to the shock are somewhat less divergent. The main reason for this is that production functions of Home and the REA do not differ as much as their structures of aggregate demand. Nevertheless, we still see some common properties of the monetary policy rules. First, we again observe a much stronger divergence between Home and the REA when monetary policy only responds to inflation (impulse responses shown with dashed lines tend to be more apart than impulse responses shown with full lines, with the exception of wages and consumption of HtM households). This holds across all three types of rules (IT, ASUT, AIT).

Figure 9.

Inflationary supply shock: country-specific variables.Notes:Horizontal axes: quarters; vertical axes: percent deviations from the steady state, except unemployment, which is in percentage point deviations. All variables are in real terms.

Second, we can see how the effect of lower real rate stimulates consumption of Ricardian households in the short run when central bank reacts to unemployment in Figure 10. Across the rules, but especially for ASUT and AIT, this temporary increase in aggregate demand increases job finding probability of HtM households, which for a short period of time protects their employment, income and consumption. The reason why there is an increase in job finding probability for HtM households is that their wages decrease by more than wages of Ricardian households, which shifts aggregate labour demand from firms more towards the now cheaper labour of HtM households. In this case we also observe that the divergence between Ricardian and HtM households’ consumption is limited (bottom panels of Figure 10). This is in stark contrast with the case where central bank only responds to inflation and where employment, wages, and job finding probabilities fall across the board already on impact. In this case, we also see a strong increase in inequality in terms of consumption in both EA blocs, as HtM households’ consumption decreases my much more than consumption of Ricardian households.

Figure 10.

Inflationary supply shock: country-specific variables.Notes: Horizontal axes: quarters; vertical axes: percent deviations from the steady state, except job finding probabilities and relative consumption, which are in p.p. deviations. All variables are in real terms.

5.3 Robustness checks

To make sure our results are robust, we perform a number of robustness checks with respect to the key choices. Our results remain unchanged, but the robustness checks offer some insights that we report in the main text. We relegate the more detailed explanation Online Appendices.

First, we investigate whether the slope of the wage Phillips curve matters for the trade-off between inflation and (un)employment. This is a natural question to ask in the context of an inflationary supply shock, which increases inflation and raises unemployment. While a detailed investigation of this question is outside the scope of this paper, we show in the Online Appendix D that more wage flexibility can alleviate the decline in employment after an inflationary supply shock and at the same time lead to lower inflation under all rules considered. It does, however, come at a cost of increasing within-country consumption inequality.

Second, it is not a priori clear that the bargaining power of Ricardian and HtM households is the same. In Online Appendix E we briefly discuss the mixed empirical evidence on this issue, and then conduct a robustness check for our main results for the case where the bargaining power of HtM households is lower than the bargaining power of Ricardian households. Lower bargaining power of HtM households makes their wages more flexible, causing them to fall by more in the case of an adverse shock. However, the loss of income due to wages is mostly offset by the lower increase in unemployment, so that our main results are not materially affected.

Finally, because a typical Taylor rule is more likely to feature the output gap rather than unemployment gap (even though this may not necessarily be the case, see e.g. Bundick and Petrosky-Nadeau (Reference Bundick and Petrosky-Nadeau2021)), we have checked if our results are robust to this modification. Our main results hold even if we consider the output gap in the rules. The reason is that the unemployment gap and the output gap are highly correlated in the model, even conditional on the chosen set of shocks.Footnote ¹⁹ The results are available upon request.