2.1 Aggregate Demand

The home economy resource constraint is expressed as a share-weighted average of home consumption c_t, government spending g_t, and “net exports” (the difference between exports $$m_{c,t}^{*}$$ and imports m_c,t) weighted by the (steady-state) trade share m_y

Imports expand as domestic consumption rises and fall in response to an increase in their relative price, so that import demand is given by

where $${\gamma }_t^{m,c}=p_{m,t}-p_{c,t}$$ is the price of a bundle of imported goods relative to that of a consumption basket comprising both domestically-produced and imported goods. This relative price reduces to the consumption-based real exchange rate $q_{ct}=p_t^{*}+s_t-p_{c,t}$ under the assumption of full pass-through $(p_{m,t}=p_t^{*}+s_t)$ from exchange rates to import prices.

Similarly, export demand $m_{c,t}^{*}$ rises with foreign consumption $c_t^{*}$ and falls with the relative price of exported goods (produced by home exporters) to that of their foreign competitors, ${\gamma }_t^{x,*}=p_{x,t}-p_t^{*}$,

When foreign currency prices of home products move one-to-one with the exchange rate, we have ${\gamma }_t^{x,*}=p_t-s_t-p_t^{*}$ and the real exchange rate is given by $q_{p,t}=s_t+p_t^{*}-p_t$.

Consumption demand is determined by the consumption Euler equation linking the marginal utility of consumption λ_c,t to future marginal utility of consumption and short-term real interest rates faced by consumers r_b,t,

The marginal utility of consumption varies inversely with current consumption, but rises with past consumption, with the latter reflecting habit persistence in consumption,

Taken together, these equations imply that consumption demand depends on a long-term real interest rate $$r_{b,t}^L$$, but with an important caveat that this borrowing rate depends on a discounted sum of future short rates:

The inclusion of discounting is in the spirit of the behavioralist New Keynesian model of Gabaix (2016) and it implies that future short term real interest rates have muted effects on current consumption demand.²

In addition to allowing for discounting, our model departs from the standard New Keynesian setup by assuming that the borrowing rate facing home consumers includes a time-varying “private borrowing spread” Ψ_t:

where $$r_t^L$$ is the long-term real interest rate on government bonds, and the interest rate spread Ψ_t is a discounted sum of future gaps between the nominal borrowing rate and policy rate, i.e.,

The private borrowing spread is assumed to rise when the real exchange rate depreciates

capturing a balance sheet channel of transmission, whereby an exchange rate depreciation may cause debt and debt-servicing costs to jump and financial conditions to tighten, particularly when a substantial part of borrowing represents unhedged foreign currency debt. More specifically, the function f(q_c,t) is upward sloping and locally convex, which allows for the possibility that depreciations above a certain threshold may exert large nonlinear effects on financial conditions even while small depreciations may have only minimal effects.

We assume that uncovered interest parity (UIP) does not hold in the short run. The aggregate demand block of the model thus includes a risk-augmented UIP equation and an equation for the evolution of the home economy’s net foreign liabilities. The UIP equation is specified as

and implies that the real exchange rate depreciates (i.e., q_c,t rises) when the foreign real interest rate rises relative to the domestic interest rate, or if the UIP risk premium Φ(•) rises; conversely, it appreciates in response to a tax on capital outflows τ_t. The time-varying UIP risk premium Φ(•) implies that investors require significantly higher expected returns if the home economy’s net foreign liabilities d_t rise relative to a threshold level of $${\overline{d}}_t$$ and in times of market stress. The government may reduce this UIP risk premium directly by using foreign exchange intervention. Foreign exchange sales (- b_t) strengthen the demand for home currency and thus may reduce the foreign exchange risk-premium under conditions detailed in Section 4.1.

The aggregate demand block of the model is completed with the equation describing the evolution of net foreign liabilities. As the home economy is assumed to be restricted to borrowing (or lending) abroad in the foreign currency, its net foreign liabilities (as a share of GDP) evolve according to:

In a standard linearized setup with a zero steady-state debt, the term (1 + r_dt) simply equals to the steady-state gross real interest rate (1 + r_d). Accordingly, small variations in other variables, including the exchange rate, do not trigger any endogenous feedback on debt service costs. However, in the nonlinear specification of the model considered in Section 4, the real interest rate r_d,t is determined by

This expression highlights how the domestic real interest rate is influenced by the foreign interest rate, domestic inflation, the change in the nominal exchange rate, as well as the previous period risk-premium $\Phi (d_{t-1},{\overline{d}}_{t-1},b_{t-1})$. Ceteris paribus, a higher foreign nominal interest rate increases debt service costs, as does a depreciation of the domestic currency; whereas higher domestic inflation lowers it.

2.2 Aggregate Supply

Turning to the supply side, the price-setting equation takes the form of a modified New Keynesian Phillips Curve:

This specification is based on Calvo-style price setting, with the sensitivity of inflation π_t (on domestically produced goods) to marginal cost m_ct determined by the slope coefficient κ_mc, which itself varies inversely with the mean duration of price contracts. The Phillips Curve is assumed to embed some structural persistence that is determined by the indexation parameter ι_d. This persistence may be interpreted as reflecting dynamic indexation (as in Christiano et al., 2005) or inflation expectations with an adaptive component (as in Clarida et al., 1999). Our preferred interpretation is along the latter lines, as it highlights the role of imperfect central bank credibility and the ability of the central bank to anchor inflation expectations. Either interpretation is consistent with cost shocks exerting highly persistent “second round” effects on inflation. In addition, and as in the “IS Curve” (eq. 4) discussed above, we allow for discounting δ_π that damps the influence of future marginal cost on current inflation. We also retain the assumption of full indexation of prices in the non-stochastic formulation of our model, which implies that the steady-state embeds no price distortions.

Marginal cost mc_t rises with an increase in the producer real wage ξ_t, and falls with a decline in the marginal product of labor mpl_t

The marginal product of labor is based on a Cobb-Douglas production function:

Turning to labor supply, the marginal rate of substitution mrs_t between consumption and leisure – which determines the cost of working an additional hour in terms of consumption goods – is given by

and hence rises as hours worked increase or as the marginal utility of consumption declines. To highlight how exchange rate depreciation can put upward pressure on (product) wages and hence firm marginal costs, it’s helpful to consider the special case in which wages are fully flexible and there is full passthrough of exchange rate changes to consumer prices (i.e, producer currency pricing). In this case, the product real wage facing firms can then be expressed as

Thus, exchange rate depreciation boosts the relative price of imported goods, causing households to demand a higher real wage in terms of the home produced good ξ_t to keep their purchasing power intact (as required to induce them to work the same number of hours and leave their mrs_t unchanged). The extent of upward pressure on firms’ costs rises with the openness of the economy, but is damped if passthrough from exchange rates to import prices is muted (as in our benchmark calibration which assumes local currency pricing).

In our baseline specification, nominal wages are sticky and set in Calvo-style wage contracts and the wage Phillips curve takes the following form

hence, nominal wage inflation ω_t depends on future wage inflation and the gap between the marginal cost of work and the consumption real wage. This setup allows for a flexible specification of wage indexation in which the relevant inflation measure indexing wages is a long moving average of either past realized inflation, or of exchange rate changes:

The dependence of wage inflation on past exchange rate changes allows for substantial second round effects through a wage channel. The product real wage is determined by the identity:

with the consumption real wage given by equation (16).

Our model allows for deviations from the law of one price in both the import and export sector. Thus, there are Phillips curves that are relevant for determining import prices and export prices, with both derived from Calvo-style pricing assumptions. Specifically, the price-setting for both consumer-goods imports (m) and domestic exports (x) sectors are given by

where π_j,t, j ∈ {m,x}, denotes the deviation in quarter t of the log of gross inflation from its steady state (π_j,t ≡ dΠ_j,t /Π_j, where Π_j,t = P_j,t/P_j,t-1 is gross inflation, P_j,t is the price level, and Πj is the steady-state gross inflation rate in sector j); ι_j and ξ_j are parameters (ξ_j is the Calvo price-stickiness parameter); mc_t denotes the real marginal cost of firms in sector j; and ϱ j,t denotes a time-varying markup in sector j, assumed to be i.i.d. and TV $$N(0,{\sigma }_{{\mathrm{\varrho }}_j}^2)$$. Firms in sector j that do not optimize their price in a given quarter are assumed to index them to the previous quarter’s inflation in the sector and the steady state inflation target according to ι_jΠ_j,t−1 + (1 − ι_j)Π_j so the parameter ι_j is an indexation parameter reflecting the weight on dynamic (lagged) inflation component. Firms’ marginal costs are further defined as

where the two relative prices ${\gamma }_t^{x,*}and{\gamma }_t^{m,d}$ are given by

Finally, consumer price inflation is defined as

where m_c = m_y(1 — g_y), i.e. we assume that there is only trade in private consumption goods, and π_m,t denotes the local currency price of imported goods. In the special case of full pass-through, equation (25) simplifies to π_c,t π_t + m_c∆q_c,t. Notably, our modeling of imperfect pass-through of exchange rate movements to export and import prices nests both local, producer and dominant currency pricing as special cases.

2.3 Monetary and Fiscal Policy

The central bank is assumed to follow a Taylor-style policy rule

where i is the steady-state nominal interest rate (since variables are measures relative to steady state levels, ι_t = —i implies that the policy rate reaches its assumed lower bound of zero). The rule specifies that the central bank considers both the expected and current four quarter change in the core CPI inflation rate, noting that ${\overline{\pi }}_{c,t}=({\overline{\pi }}_{c,t}+{\overline{\pi }}_{c,t-1}+{\overline{\pi }}_{c,t-2}+{\overline{\pi }}_{c,t-3})/4$. It also takes domestic output (measured as deviation from its trend path) into account. Our assumption that the central bank responds to core CPI inflation in essence means that the central bank puts some weight on responding to import price inflation π_m,t The parameter γ_i allows for interest rate smoothing and e_i,t is an interest rate shock.

Government expenditure g_t in eq. (1) is assumed to follow an exogenous AR(1) process (see below for more details). The steady-state level of g is financed by labor income taxes, but any variations in government spending around its steady state are assumed to be paid for via lump-sum taxes. This simplifying assumption allows us to abstract from the dynamic aspects of fiscal policy.

2.4 Calibration

We calibrate our model at a quarterly frequency using fairly standard parameter values. For tractability, the calibration is identical for advanced and emerging market economies with two key exceptions. First, we allow the parameters governing price and wage formation to differ, to capture less-well anchored inflation expectations in EMEs relative to AEs. Second, the EME formulation of the model allows for two key nonlinear balance sheet channels (via an endogenous UIP risk premium $$\mathrm{\Phi }(d_t,{\overline{d}}_t,b_t)$$ in eq. (9) and an endogenous private borrowing spread Ψ in eq. (7)).

The responsiveness of inflation to marginal cost and of wages to the labor market wedge plays a key role in determining how monetary policy actions affect output and inflation, as well as the extent to which medium-term inflation expectations respond to shocks. The calibration for the AE economy relies on findings in the literature on estimated DSGE models (see Linde et al., 2016; Del Negro et al., 2013; Campbell et al., 2012), specifically the low slopes of the price and wage curves (i.e. κ_p and κ_w) and that structural persistence in price and wage inflation is also low (i.e. ι_p and ι_w are small). In line with the literature, we use κ_p = .005 and κ_w = .02 and ι_v = .5 and ι_w = 0 as our “AE calibration.”³ For the EMEs, we set the parameters capturing the degree of structural persistence in inflation and wages (ip and L_W) to 0.75, to capture the greater degree to which inflation expectations depend on realized inflation and wages. The slope of the price and wage Phillips curves (n_p and κ_w) are also set notably higher than in the AE case (.02 and .03, respectively) .⁴

The other parameters are the same for both AE and EME economies. The term $${\pi }_{c,t}^L$$ capturing the “trend inflation” rate to which wages are indexed assumes that Φ = .05 and ξ = 1, which implies that this trend inflation measure is a long distributed lag of past inflation. This parametrization is identical for both AEs and EMEs. A discount factor of β = 0.995 implies a steady-state real interest rate of 2 percent (at an annualized rate). With an annualized steady-state inflation rate of 2 percent (i.e., π = 0.005), the steady-state annualized nominal interest rate equals 4 percent (so i = 0.01). We set the intertemporal substitution elasticity σ to 1, which is consistent with log utility.⁵ The habit parameter κ_c is set to 0.8. The Frisch elasticity of labor supply of $$\frac{1}{\chi }=0.5$$ and capital share of α = 0.3 are in the typical range specified in the literature. The government share of steady state output is set to 20 percent (g_y = 0.2). In the spirit of Gabaix (2016), we allow for discounting in the consumption euler, UIP, and price-setting equations by setting δ_π = 0.95, and 5,1- = 0.92.

In the baseline calibration of the parameters in the monetary policy rule (26), we set γ_π = 1.5, γ_π = .0625, and γ_i = 0. The coefficient on the output gap, which is 0.25 at an annual rate, is modestly lower than in the standard Taylor rule (0.50).

Turning to trade, we assume that import and export prices are consistent with “local currency pricing” so that both are sticky in the local currency. Our calibration implies that import and export prices are more responsive to marginal costs in EMEs relative to AEs, and structural persistence also noticeably higher.⁶The parameter ε_c determining the sensitivity of imports to the real exchange rate is set to 0.8, as is its export counterpart $${ϵ}_c^{*}$$. These values are consistent with evidence about trade price elasticities for a large set of both advanced and emerging market economies. We further assume a 20 percent import share, i.e. we set m_y equal to 0.2.⁷

The exogenous shocks $$s_t=\{g_t,{ϵ}_{c,t},e_{i,t},c_t^{*},r_t^{*},{\overline{d}}_t,b_t,{\tau }_{i,t},{\tau }_{o,t}\}$$ are assumed to follow AR(1) processes

where the persistence ρ_s and standard deviation of each shock (σ_s) process will be described when they are used in the analysis.

Finally, we solve the model using Dynare, documented in Adjemian et al. (2011).

3.1 UIP Risk Premium Shock Transmission: AEs vs EMEs

In this section, we assess the effects of an investor risk tolerance shock $${\overline{d}}_t$$ that causes investors to be less willing to hold bonds issued by the home economy and is tantamount to a UIP risk premium shock. In particular, investors demand a higher expected return on the bonds issued by home agents relative to those issued by foreign residents (inclusive of expected currency appreciation).

The shock is assumed to follow an AR(1) process with $${\rho }_{\overline{d}}=0.9$$ and is scaled so that the real exchange rate depreciates by 10 percent in the AE economy (Figure 1).

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Transmission of Risk-Premium Shocks in Advanced and Emerging Markets

Citation: IMF Working Papers 2020, 122; 10.5089/9781513549668.001.A001

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For the AE, the shock does not pose a major policy challenge (blue lines). The exchange rate depreciation stimulates net exports, causing output to rise. The combination of higher output and higher import prices causes inflation to rise, but with well-anchored inflation expectations monetary policy can “look through” the transient rise in inflation and focus on output. All told, the shock looks very similar to a “standard” aggregate demand shock, notwithstanding the transient initial boost in inflation.

The same shock, by contrast, generates a more difficult policy tradeoff in the EME economy (red dotted line). While the depreciation boosts real net exports, inflation expectations are less well anchored than in the AE, and the exchange rate depreciation has large and persistent effects on inflation. This induces the central bank to raise real (and nominal) interest rates, which crowds out domestic demand. Output contracts slightly on balance, while inflation rises substantially – clearly highlighting the problems that exchange rate depreciations may pose for economies with these characteristics. Had our simulation allowed for a balance sheet channel in which the exchange rate depreciation increased private borrowing spreads, output would contract even more.

3.2 Policy Tradeoffs in EMEs

Our simulations illustrate that EMEs may face difficult policy tradeoffs in the face of shocks that generate large exchange rate movements. Figure 2 compares the effects of the same-sized UIP risk premium shock as in the previous section under two policies. The red-dotted line shows the effects of the benchmark calibration (EME central bank follows a standard Taylor rule, same as in Figure 1) under a more accommodative policy. In this case, the central bank keeps output relatively stable but allows the exchange rate depreciation to have large and persistent effects on both CPI inflation and domestic inflation, potentially undermining monetary policy credibility. By contrast, tighter policy (blue lines) – in which the central bank responds more vigorously to both domestic and imported inflation – limits the size and persistence of the increase in inflation but generates a sharper output contraction of about 1.5 percent.

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Risk-Premium Shocks in Emerging Markets for Alternative Policy Rules

Citation: IMF Working Papers 2020, 122; 10.5089/9781513549668.001.A001

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These scenarios illustrate that conventional monetary policy performs rather poorly in simultaneously achieving a central bank’s inflation and output objectives if inflation expectations are not well-anchored. This provides a rationale for using additional policy instruments (FX intervention or capital controls) to reduce the risk of a de-anchoring of inflation expectations, and thereby allowing monetary policy to focus more on output stabilization and improving output-inflation trade-offs.

4.1 Modeling of Endogenous Risk-Premiums

We next provide an overview of how we parameterize the endogenous risk-premiums, Ψ_t = f(q_c,t) in eq. (8) and $$\mathrm{\Phi }(d_t/{\overline{d}}_t,{\phi }_t)$$ in eqs. (9) and (10). For Ψ_t, we specify the following logistic functional form

where ${\overline{q}}_t\equiv \overline{q}+{ϵ}_{\overline{q},t}$ is a threshold real exchange rate level $(E\left({\overline{q}}_t\right)=E(\overline{q}+{ϵ}_{\overline{q},t})=\overline{q})$ for which the endogenous risk premium becomes elevated, µ is the maximum one-period increase in the risk-premium Ψ_t, k_q is the logistic parameter which governs the extent to which the weaker real exchange rate elevates Ψ_t contemporaneously when the actual exchange rate approaches ${\overline{q}}_t$ The calibration of $\overline{q}=22.5$ implies that even a substantial real exchange rate depreciation relative to the steady state will not induce much of a rise in the private borrowing spread unless the stochastic risk appetite shock ${ϵ}_{\overline{q},t}$ is also sufficiently negative so that ${\overline{q}}_t\le q_{c,t}$. This feature helps match empirical evidence for EME corporate spreads which suggests that although large exchange rate depreciations make a sharp runup in private borrowing spreads (proxied empirically by corporate spreads) more likely, it is nevertheless often the case that the exchange rate may depreciate substantially without triggering a big increase in spreads.

We now turn to discuss the nonlinear formulation of the UIP risk premium. We assume that $\mathrm{\Phi }(d_t,{\overline{d}}_t,b_t)$ follows

where ${\overline{d}}_t\equiv \overline{d}+{ϵ}_{\overline{d},t}$, is a threshold net foreign liability level $(𝔼\left({\overline{q}}_t\right)=𝔼(\overline{q}+{ϵ}_{\overline{q},t})=\overline{q})$ for which the UIP risk premium becomes more sharply elevated, and the constant $\tilde{\phi }$ ensures that the UIP risk premium Φt equals 0 in the deterministic steady state.⁹ Foreign asset purchases by the central bank, b_t, follow an AR(1) process

Similarly, the debt appetite/limit, shock follows an AR(1) process satisfying:

As can be seen from comparing the two risk premium functions in Figure 3, two key differences between the specification of the private and UIP risk premiums are that the latter is associated with a non-zero slope even when d_t is zero and that Φ_t can be negative when the country accumulates foreign assets on net (so that d_t < 0). This feature of the UIP risk premium is required to ensure stationary net foreign liabilities, i.e. prevent the small open economy from accumulating infinite net foreign assets (see e.g. Schmitt-Grohe and Uribe, 2003).

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Risk Appetite and Risk Premiums

Citation: IMF Working Papers 2020, 122; 10.5089/9781513549668.001.A001

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We calibrate the parameters pertaining to the endogenous spread functions through the unconditional stochastic simulations reported in Section 4.3. This procedure, essentially a simulated method of moments exercise (see e.g. McFadden, 1989), enabled us to consider a constellation of the parameters ${\rho }_{\mathrm{\Phi }},k_d,\overline{d},\phi$, and the AR(1) process parameters ${\rho }_{\overline{d}}and{ϵ}_{\overline{d},t}$ which roughly matches a number of moments (unconditional persistence, unconditional and conditional volatilities, and mean and max values) for sovereign yield spreads on dollar denominated bonds for a selected set of emerging market economies. We adopt the same framework to pin down the key parameters (ρ_ψ, µ, $\overline{q}$, k_q) governing the evolution of private borrowing spreads, here proxied by corporate spreads from JP Morgan’s EMBI database, for the same set of EM economies. This procedure leads us to use the following parameter values for the UIP risk premium: ρ_Φ = .85, k_d = .4, $\overline{d}=12.5$, φ = .6, and ${\rho }_{\overline{d}}=.85and{\sigma }_{\overline{d}}=11$. For the private borrowing spread, we choose the parameters ρ_ψ, = .85, µ = .4, $\overline{q}=22.5$, k_q = 4. Even though the real exchange rate and net foreign liabilities are positively correlated in our model (ceteris paribus, countries with higher net foreign liabilities need a weaker exchange rate in order to maintain a persistent trade surplus which improves their external debt position), we allow the shock ${ϵ}_{\overline{q},t}$ in the private borrowing spread to be influenced by the debt limit shock ${ϵ}_{\overline{d},t}$ to strengthen the correlation between private and country borrowing spreads. Even so, the median correlation between corporate and sovereign spreads in our sample of EME countries is only about 0.4, and we therefore assume that the private debt limit shock ${ϵ}_{\overline{q},t}$ also has an idiosyncratic component, so that

where we set ρ_p = .85 and ${\sigma }_{\overline{d}}=4$.¹⁰

Finally, we motivate why our nonlinear formulation of these spreads plays a crucial role in our framework. One way to do this is to linearize the two risk premiums. The linearized representation of the private borrowing spread in eq. (28) is given by

and so, using the fact that q_c = 1 so $$E\left({ϵ}_{\overline{q}}\right)=0$$, and exploiting that Ψ = 0 so dΨ_t = ψ_t we arrive at

Comparing equations (28) and (33), we can observe that the effective coefficient on the real exchange rate in a linearized approximation of the nonlinear model, i.e. ${\rho }_q\equiv \mu \frac{e^{k_q\overline{q}}}{{(1+e^{k_q\overline{q}})}^2}{k}_q$, will be a very small number (under our calibration ρ_q ≈ 2e—5). One important implication is that capturing the empirically relevant nonlinearities of private borrowing spreads would seem infeasible in a standard linearized DSGE framework.

Turning to the country-specific UIP risk premium Φ_t in (29), total differentiation gives

As Φ = 0 we have that dΦ_t = φ_t and since db_t = b_t, dd_t = d_t and ${d\epsilon }_{\overline{d},t}={\epsilon }_{\overline{d},t}$, the above equation implies

where we have defined ${\varphi }_d=\varphi k_d[{\left(\frac{1}{1+e^{k_d\overline{d}}}\right)}^2{e}^{k_d\overline{d}}+\frac{1}{80}],{\varphi }_b=\varphi {\left(\frac{1}{1+e^{k_d\overline{d}}}\right)}^2{e}^{k_d\overline{d}}and{\varphi }_{{\epsilon }_{\overline{d}}}={\varphi }_b{k}_d.$.