Money, Interest Rates, and Exchange Rates with Endogenously Segmented Markets

Households must pay a fixed real cost g each time they transfer cash between the goods market and the asset market, and this fixed cost makes it optimal for most households to trade only occasionally rather than every period. In any period, the economy divides into “active” households – those with real balances high or low enough that paying the fixed cost and adjusting is worthwhile – and “inactive” households in a middle “zone of inactivity” who simply spend whatever real balances they currently hold (Sec. I). Which households are active, and how many, is determined endogenously each period by a cutoff rule (eq. [8]) rather than fixed exogenously, which is why the authors call the resulting segmentation “endogenous.”

Because only active households are “on the other side” of an open-market operation, a money injection is absorbed exclusively by them, raising their current consumption and lowering their marginal utility, while inactive households simply suffer the inflation tax on the real balances they are holding. This channel – the “segmentation effect” – enters the Fisher equation alongside the ordinary expected-inflation effect (eq. [17] vs. [16]): real interest rates fall whenever the segmentation effect dominates the expected-inflation effect, which the model shows happens whenever money growth is sufficiently mean-reverting and the elasticity parameter φ (how responsive active households’ marginal utility is to a money shock) is large enough relative to the persistence of money growth (condition [18]).

The model generates a negative relation between expected inflation and real interest rates, matching the pattern documented by Barr and Campbell (1997) using indexed and nominal U.K. bonds, because a mean-reverting money injection raises expected inflation while simultaneously lowering active households’ marginal utility and hence the real rate. In a standard cash-in-advance model without segmentation, by contrast, persistent money injections raise expected inflation but leave real interest rates completely unaffected, so no such relation can arise at all.

Yes: with moderate amounts of segmentation the model produces nominal interest rate responses to a money shock that decay only gradually (at the persistence rate of the money-growth process itself), because the fraction of the money stock absorbed by currently active households remains elevated for several periods after the shock, not just the period of impact (Sec. IV). Under a first-order autoregressive money-growth process with persistence ρ=.5, the authors show the model matches a liquidity effect if φ≥1, and under their calibration (curvature parameter σ=2 to 8, with one-fifth to one-half of households inactive at a time) φ of around 2 is readily attainable (eq. [19] and surrounding discussion).

Under a long-memory moving-average process for money growth (one whose coefficients decline quickly at first and then more slowly), the segmentation effect dominates at short horizons while the expected-inflation effect dominates at longer horizons, so a money injection lowers the short-term nominal rate on impact, steepens/twists the yield curve, and the short rate subsequently rises back toward – and briefly above – its mean (Sec. IV.B, Fig. 4), a pattern the authors note resembles the dynamic responses estimated by Cochrane (1998). Because the term structure in the model satisfies the expectations hypothesis with a constant risk premium, this impulse-response pattern for the short rate fully characterizes the response of the whole yield curve.

Unlike Grossman and Weiss (1983) and Rotemberg (1984, 1985), who study exogenously segmented markets with incomplete asset trade (limiting their analysis to one-time, deterministic shocks), and unlike Lucas (1990) and its extensions (Fuerst 1992; Christiano and Eichenbaum 1992, 1995), where households split cash between markets before the money shock is known and so only unanticipated shocks have real effects and liquidity effects last only one period, this paper’s households trade a complete set of state-contingent bonds subject only to the fixed-cost friction, so the model is fully stochastic, segmentation is endogenous, and – because markets are otherwise complete – “all the results can be derived with paper and pencil.” The authors note this lets their model generate persistent liquidity effects from anticipated as well as unanticipated shocks, a property Christiano-Eichenbaum-style models achieve only by adding further ad hoc adjustment costs.

In the two-country cash-in-advance extension, when inflation is low enough that asset markets remain segmented, money injections have a substantial impact on the real exchange rate, so nominal and real exchange rates move together with similar volatility and persistence – matching patterns the authors document for Canada, France, Germany, Italy, Japan, and the United Kingdom (Table 1: nominal/real volatility ratios of roughly .96-1.10, nominal-real correlations of .93-.99, and real-rate serial correlation around .76-.79). As steady-state inflation rises, however, Proposition 2 shows that above some threshold all households find it worth paying the fixed cost every period, so φ falls to zero, segmentation disappears, and money injections affect only the nominal exchange rate – which the authors show matches the pattern, in a sample of up to 49 countries using IMF data for 1970:1-1999:3, that nominal exchange-rate volatility substantially exceeds real exchange-rate volatility in high-inflation countries (Fig. 7) but not in low-inflation ones.

The authors are explicit that the model abstracts from goods-market frictions such as sticky prices, that the two-country version has no trade in goods across countries (households consume only their own country’s good), and that generating volatile real exchange rates in a fully realistic setting “needs frictions in both the goods and asset markets” (citing Chari, Kehoe, and McGrattan), so this paper’s asset-market-only mechanism is presented as a complement to, not a substitute for, goods-market-friction models such as Obstfeld and Rogoff (1995). They also note that constructing examples with a smoothly declining segmentation parameter as inflation rises is possible but that a fuller quantitative match to the exchange-rate data would require adding real shocks, which they do not pursue.

The model “breaks the links between either asset prices or the real exchange rate and aggregate consumption,” which the authors present as a potential resolution of the consumption-real exchange rate anomaly – the fact that standard representative-agent international models predict a near-one correlation between the real exchange rate and relative consumption across countries, whereas in the data (citing Backus and Smith 1993) that correlation is small and sometimes near zero. Because in this model only the subset of households currently active in the asset market determines asset prices and the exchange rate, aggregate consumption need not move in lockstep with the real exchange rate the way it does in representative-agent models.