Optimal inflation to reduce inequality

Abstract

A popular argument in favor of price stability is that the inflation-tax burden would disproportionately fall on the poor because wealth is unevenly distributed and portfolio composition of poorer households is skewed towards a larger share of money holdings. We reconsider the issue in a DSGE model characterized by limited participation to the market for interest bearing assets (LAMP). We show that a combination of higher inflation and lower income taxes reduces inequality. When we calibrate the share of constrained agents to fit the wealth Gini index for the US, the optimal inflation rate is above 4%. This result is robust to alternative foundations of money demand equations.

Introduction

Over the last 30 years income and wealth inequality have increased in developed economies and the issue of wealth ownership concentration has come to the forefront (Saez and Zucman, 2014). Concern has also grown for the distributive effects of monetary policies (Galbraith et al., 2007, Coibion et al., 2012) and for the apparently adverse effects of Central Banks actions on inequality.³

A widely popular argument in favor of price stability is the asymmetric incidence of the inflation tax when wealth is unevenly distributed and portfolio composition of poorer households is skewed towards a larger share of money holdings, so that the inflation tax burden would disproportionately fall on the poor (Erosa and Ventura, 2002, Boel and Camera, 2009, Schmitt-Grohé and Uribe, 2011a). In fact, this is the key justification for endorsing price stability as a contribution to reducing inequality and poverty.⁴

In the paper we reconsider the issue of inflation optimality in a model where distributional issues arise because wealth holdings are concentrated in the hands of few households. We modify a standard DSGE model by introducing Limited Asset Market Participation (LAMP henceforth), in the form of a distinction between holders of interest bearing assets (unconstrained agents) and agents who only own money (constrained agents), as in Coenen et al. (2008).

Heterogeneity in the access to the market for interest bearing assets is a salient feature of the data. While the majority of US households (92.5%) own transaction accounts (including checking, savings, money market deposit accounts and money market mutual funds), only a small minority hold other financial assets, such as stocks, bonds, investment funds and other managed assets (which are held by less than the 20% of households).⁵ The major long term saving vehicle for US households are retirement accounts, held by the 50.4% of families. Excluding such important differences in wealth holdings from macroeconomic models implies that the distributional effects of policies and shocks are also ignored.

Assuming wealth inequality is not sufficient to identify a potential role for monetary policy and inflation. In principle, a redistributive scheme taxing wealth returns to subsidize constrained households should make monetary policy redundant. To obtain non-trivial results, we assume that the policymaker set of fiscal tools is incomplete. Further, in line with previous contributions on Ramsey-optimal monetary and fiscal policies, we posit that firms monopoly profits are not taxed. In representative agent models such as Schmitt-Grohé and Uribe (2004a) this assumption is made because distortionary taxation does not warrant an increase in the optimal inflation rate unless factor incomes are suboptimally taxed (see Schmitt-Grohé and Uribe, 2011a; and references cited therein). Maintaining this assumption here seems appropriate for several reasons. First, anecdotal evidence suggests that large multinationals such as Apple and Google are subject to a negligible tax burden on their worldwide profits (Fuest et al., 2013). This has become a primary concern for international agencies (OECD, 2013a, OECD, 2013b and European Commission, 2012). Second, a large literature documents that tax evasion and tax avoidance are related to firms rents.⁶ Third, emphasys on firms ability to escape profit taxation is particularly relevant in our context, where concern for inequality motivates the government's decisions.

Optimal inflation analysis crucially depends on underlying assumptions concerning economic incentives to hold money balances. The classical approach assumes that real money balances are proportional to consumption, so that money holdings and consumption should be equally distributed among households (Schmitt-Grohé and Uribe, 2004a).

Erosa and Ventura (2002) adopt instead a cash/credit-transaction approach, where a fraction of transactions are undertaken using a credit technology that exhibits economies of scale. In this case inflation increases inequality because poor households realize a larger percentage of cash transactions relative to rich households.

The classical approach implies that the distribution of money holdings replicates distribution of consumption levels, whereas the cash/credit-transaction approach implies that money holdings are more equally distributed than consumption because richer households consume more but hold less money balances. According to Ragot (2014), these results are in sharp contrast with empirical evidence in countries like the US and Italy, where the observed distribution of money across households is similar to the distribution of financial wealth, suggesting that the transaction motive for holding money plays a limited role relative to financial motives. In fact Ragot (2014) shows that the Gini indexes for money and financial wealth holdings are replicated in an heterogeneous agent model where consumption transactions are subject to a cash in advance constraint and financial transactions are subject to fixed costs à la Baumol–Tobin. We label this characterization of money demand as the infrequent trading approach. To assess the implications of the infrequent trading approach to money demand, we follow Alvarez et al. (2009), and assume that unconstrained agents can trade in financial markets only infrequently. Consistently with the facts discussed by Ragot (2014), this allows to obtain a distribution of money holding similar to that of financial wealth.

In our analysis, we compute the Ramsey steady state solution for our model. This adds to Schmitt-Grohé and Uribe (2004a) because the identification of the optimal financing mix (inflation and income tax) for a given level of public consumption takes into account the planner's concern for redistribution as a determinant of inflation. We take into account the alternative money demand specifications based on the consumption technologies discussed above, and account for unconstrained households' infrequent trading in the markets for interest-bearing assets.

We obtain the interesting result that, irrespective of the money demand specification adopted in the model, the planner chooses a steady state inflation rate which is higher than under the representative agent assumption. In fact we obtain optimal inflation rates which are always above $4\text{\%}$. In contrast with received wisdom, the fundamental reason underlying this result is that expected inflation shifts the fiscal burden towards asset holders. This happens because, even if inflation is a regressive tax that falls proportionally more on the wealth holdings of the poor, it allows to tax consumption out of monopoly profits by exploiting the fact that money holdings are larger for wealthier individuals, as implied by the Gini index for money holdings. Thus, shifting the financing mix towards higher inflation allows to shift the overall burden of taxation towards asset holders. For reasons explained in the text, our results are strengthened when we assume that the Planner can levy distinct labor and capital income taxes.

Our results are related to those of Jin (2009) that considers a growth model with inequality in both wealth and skill levels. Interestingly, that paper finds that inflation tends to reduce inequality when the latter depends on wealth inequality, a result compatible with ours. Another paper related to ours is Da Costa and Werning (2008), who analyse the optimality of the Friedman rule in a model in which agents have different private-knowledge labor productivities and the planner has access to non-linear labor income taxes. In that framework, zero inflation is always on the Pareto optimal frontier, which suggests that heterogeneity in non-labor incomes is necessary to introduce a role for inflation as a redistributive tool.

The rest of the paper is organized as follows. Section 2 presents the model. Section 3 defines the competitive equilibrium and the Ramsey optimal policy. Section 4 describes the results. Section 6 concludes.