Simple New Keynesian macroeconomic models work well for analyzing the impact of various types of shocks on small open economies and emerging markets. The models are a bit more complex than those for large economies, because one must consider the exchange rate, terms-of-trade and financial pressure. Yet understanding some basic connections between market factors and the overall economy already supports intuition for macro trading strategies. Moreover, the analysis of the effect of various shocks is possible in simple diagrams.

Evan Tanner (2017), “The Algebraic Galaxy of Simple Macroeconomic Models: A Hitchhiker’s Guide”, IMF Working Paper, May 2017, WP/17/123.

The post ties in with this sites’ lecture on systematic value through macro trends, particularly the part on best practices for tracking macro trends. The post is a sequel to the post “Simple macroeconomics for trading”.

The below are excerpts from the paper. Emphasis and cursive text have been added to explain key points from the angle of macro trading. Formulas and their explanations have been modified for easier reading. The post contains nevertheless a lot more formal equations than we would usually permit. This is a one-off deviation from the rules of this site, for a worthy cause.

A (relatively) simple macro model

“A New Keynesian model for a closed economy consists of three core equations: the IS curve [Investment-Savings curve, representing the relation between aggregate goods demand and the real interest rate], a monetary policy reaction function [in form of a Taylor rule for the short-term interest rate], and an aggregate supply or Phillips curve relationship [representing the relation between the economy’s output gap and inflation].”

“The… [simple static] New Keynesian model…may be extended to show the impacts that internal and external shocks will have on a small open economy…We assume the economy to be small relative to the rest of the world. It faces an external rate of interest (including a risk premium) that it has no influence over. Importantly, the model can help us understand in a straightforward way how externally-based shocks, in addition to domestic shocks, will affect the economy’s short-run equilibrium…Such effects will be transmitted through to the markets for exports and imports.”

Exchange rates, terms of trade and financial pressure

“The traditional definition of the real exchange rate, a key price in any open economy model, is…[the ratio of external to domestic prices in common currency]. The level of external prices…may be written as a (geometric) weighted average of export and import prices.”

Q[t] = (S[t] × WP[t]) / LP[t]
with WP[t] = WPX[t]v × WPM[t](1-v)

Q[t] is the real exchange rate as domestic currency units per world currency unit,
adjusted by the ratio of external to internal prices,
(increase means domestic currency depreciation)
S[t] is the nominal exchange rate as domestic units per world currency unit,
WP[t] is the level of external prices of all goods and services in world currency units,
LP[t] is the local-currency price for all goods and services,
WPX[t] is the world currency price for exported goods and services,
WPM[t] is the world currency price for imported goods and services,
v is the relative importance of local exports versus imports (0 < v < 1)

Terms of trade of a small economy are represented by the ratio of world currency prices of its exports versus the world currency prices of its imports:

ToT[t] = WPX[t] / WPM[t]

ToT[t] is the local economy’s terms of trade, i.e the ratio of export to import prices in international markets,
WPX[t] is the world currency price for exported goods and services,
WPM[t] is the world currency price for imported goods and services.

“The natural rate of interest [of the small open economy] is…assumed to be the sum of the natural external rate of interest and a baseline risk premium. Importantly, the natural rate of interest is a steady-state construct.”

RN = RXN + LRP

RN is the domestic natural rate of interest of an open economy,
RXN is the external natural rate of interest,
LRP is the long-term risk premium charged on local assets.

“In any economy, open or closed, the steady state natural interest rate converges to the steady state marginal product of capital net of depreciation… In an open economy, the steady state marginal product of capital net of depreciation converges to an exogenous value, namely the natural external rate of interest and a baseline risk premium thorough net capital accumulation.”

“We may discuss changes in foreign monetary and financial conditions as deviations from that steady state. Tighter foreign monetary policy implies that the external rate of interest is above its steady state. An idiosyncratic revision to investor perceptions of a country will be reflected its risk premium: a capital flight scenario would imply that the risk premium is above its steady state. Jointly, external financial pressures reflect the divergence between the external interest rate plus risk premium from their baseline values.”

XFP[t] = (RX[t] + RP[t]) – (RXN + LRP)

XFP[t] is the external financial pressure in period t
RX[t] is the external interest rate in period t
RP[t] is the risk premium charged on local assets in period t,
RXN is the external natural rate of interest,
LRP is the long-term risk premium charged on local assets.

The real interest parity requires that a currency appreciates in real terms in accordance with its interest rate differential over the other currency and the risk premium charged on the other currency. Thereby future expected depreciation compensates of the differences in remuneration and risk.

q[t] = (RX[t] – R[t]) + RP[t]

q[t] is the real appreciation of the world currency over its long-term norm,
RX[t] is the external interest rate in period t,
R[t] is the local interest rate in period t,
RP[t] is the risk premium charged on local assets in period t.

“The real interest parity condition that tells us the short run deviation of the real exchange rate from its long-run baseline value. This condition implies impacts of domestic monetary policy and external financial pressures on the real exchange rate that are symmetric: a domestic monetary tightening causes the real exchange rate to appreciate; this reduces relative prices of both exports and imports. By contrast, an increase in external financial pressures will bring about a depreciation of the real exchange rate; this increases relative prices of both exports and imports.”

The IS curve

The IS curve describes the relation between an economy’s output gap and its real interest rate. It is based on the economy’s goods market equilibrium.

The goods market equilibrium requires real consumption, investment, government spending and net exports (exports minus imports) to be equal to the output of the economy:

Y[t] = C[t] + I[t] + G[t] +EX[t] – IM[t]

Y[t] is aggregate output of the economy,
C[t] is aggregate consumption in period t
I[t] is aggregate investment in period t,
G[t] is aggregate real government spending in period t,
EX[t] is exports of goods and services in period t,
IM[t] is imports of goods and services in period t.

The assumptions and functions for aggregate consumption, investment and government spending have been explained in a previous post (view here).

“The level of exports is assumed to comprise two elements: a long-run component, which is expressed as a constant fraction of potential output, and a short-run component which is linked to deviations of the relative price of exports from its long run norm.”

EX[t] = (x + dx × rpx[t]) × YP

EX[t] is exports of goods and services in period t,
x is the long-term share of exports to potential GDP,
rpx[t] is the percent deviation of the relative price of exports from the long-run norm,
dx is the sensitivity of exports to export price increases (dx > 0),
YP is the potential output of the economy.

“The relative price of exports is defined as the world currency [USD] price of exports converted to domestic currency by the nominal exchange rate and divided by domestic price level… We may thus think of [the relative price of exports]…as a real exchange rate that applies specifically to exporters.”

RPX[t] = (S[t] × WPX[t]) / LP[t]

RPX[t] is the relative price of exported goods and services,
S[t] is the nominal exchange rate as domestic units per world currency unit,
(increase means domestic currency depreciation)
WPX[t] is the world currency price for exported goods and services,
LP[t] is the local-currency price for all goods and services.

“The corresponding equation for imports is structured much like that of exports but also includes a term for the output gap.”

IM[t] = (im + ims × gap[t] – di × rpm[t]) × YP

IM[t] is imports of goods and services in period t,
im is the long-term share of imports to potential GDP,
gap[t] is the output gap, i.e. the difference between actual and potential in % of potential
ims is the short-term marginal propensity to import out of temporary real income,
rpm[t] is the percent deviation of the relative price of imports from the long-run norm,
di is the sensitivity of imports to import price increases (di > 0),
YP is the potential output of the economy.

“We may think of the relative price of imports as a real exchange rate that applies specifically to import markets.”

RPM[t] = (S[t] × WPM[t]) / LP[t]

RPM[t] is the relative price of imported goods and services,
S[t] is the nominal exchange rate as domestic units per world currency unit,
(increase means domestic currency depreciation)
WPM[t] is the world currency price for imported goods and services,
LP[t] is the local-currency price for all goods and services.

“An open economy is vulnerable to shocks that originate externally. Such shocks will have first order impacts on exports and imports. The model highlights the fact that shocks—both domestic and external—are transmitted to the economy through their impacts on the relative prices of imports and exports.”

Expressing relative price levels as logarithms or approximate percent deviations, one can decompose relative export and import price deviations into real depreciation and terms of trade deviations:

rpx[t] = q[t] + (1-v) × tot[t]

rpm[t] = q[t] – v × tot[t]

rpx[t] is the percent deviation of the relative price of imports from the long-run norm,
rpm[t] is the percent deviation of the relative price of imports from the long-run norm,
q[t] is the real appreciation of the world currency over its long-term norm,
tot[t] is the percent increase in terms-of-trade over its long-term norm,
v is the relative importance of local exports over imports.

Since export and import prices are determined by [1] terms-of-trade and [2] the real exchange rate and, hence, by interest rate and risk premium conditions, the equations for export and import demand can be re-written to reflect the influence of these financial market conditions. In particular, real exports increase with easier local monetary policy, external financial pressure, and better terms-of-trade.

EX[t] = (x – dx × (R[t] – RN) + dx × XFP[t] + dx × (1 – v) × tot[t]) × YP

EX[t] is exports of goods and services in period t,
x is the long-term share of exports to potential GDP,
dx is the sensitivity of exports to export price increases (dx > 0),
R[t] is the local real interest rate in period t,
RN is the local natural real rate of interest
XFP[t] is the external financial pressure in period t
tot[t] is the percent increase in terms-of-trade over its long-term norm,
v is the relative importance of local exports over imports.
YP is the potential output of the economy.

Real imports increase in times of a positive output gap, easier monetary conditions, external financial pressure and worse terms-of-trade.

IM[t] = (im + ims × gap[t] – di × (R[t] – RN) + di × XFP[t] – di × v × tot[t]) × YP

IM[t] is imports of goods and services in period t,
im is the long-term share of imports to potential GDP,
gap[t] is the output gap, i.e. the difference between actual and potential in % of potential
ims is the short-term marginal propensity to import out of temporary real income,
di is the sensitivity of imports to import price increases (di > 0),
R[t] is the local real interest rate in period t,
RN is the local natural real rate of interest,
XFP[t] is the external financial pressure in period t,
tot[t] is the percent increase in terms-of-trade over its long-term norm,
v is the relative importance of local exports over imports.
YP is the potential output of the economy.

The IS curve generally describes the goods market equilibrium from the demand side, as a relation between output gap and the local real interest rate. For an open economy, the closed-economy IS curve, which is based in consumption, investment and government spending only (and has been shown in a previous post here) can be enhanced, by considering the export and import demand equations to see the influence of external financial conditions.

R[t] = RN – (c1 × gap[t] + gp[t] + dxi × XFP[t] + sdxi × tot[t]) / (ar + dxi)

R[t] is the local real interest rate in period t,
RN is the local natural rate of interest,
gap[t] is the output gap in period t,
c1 is a structural and typically positive constant,
gp[t] is the government spending ‘shock’ in period t, in % of potential output
dxi is the difference between export and import price sensitivity (dx – di > 0)
sdxi is the weighted sum of export and import price sensitivity ((1-v) × dx + v × di > 0),
ar is the sensitivity of investment with respect to the real interest (absolute value)

Note that the IS curve is typically downward sloped. It shifts to the right (higher output for same real interest rate) in the presence of a government spending shock, external financial pressure and an elevation of terms-of-trade.

The RR curve

The RR curve represents the monetary policy and inflation side of the economy and is complementary to the IS curve.

“Regarding monetary policy in an open economy, since the natural rate of interest depends on the external rate of interest plus a risk premium, we add external financial pressures to the monetary reaction function.”

NR[t] = RN + PE + bp × (P[t] – PT) + bg × gap[t] + RD[t] + XFP[t]

NR[t] is the nominal short-term interest rate,
PE is expected long-term inflation,
P[t] is the current rate of inflation,
PT is the central bank’s inflation target,
bp is the sensitivity of the short-term interest rate to excess inflation,
gap[t] is the current output gap,
bg is the sensitivity of the short-term interest rate to the output gap,
RD[t] is a discretionary deviation of the policy rate from the rule (“monetary tightening shock”),
XFP[t] is the external financial pressure in period t.

“Finally, inflation in the open economy [determined by Phillips curve] differs from the closed economy expression insofar as a fraction of external financial pressures, which have impacts on the real exchange rate, are also passed through to the domestic economy.”

P[t] = PE + cg × (gap[t] – ss[t]) + cf × XFP[t]

PE is expected long-term inflation,
ss[t] is a supply shock,
gap[t] is the current output gap,
cg is the sensitivity of inflation to excess demand,
XFP[t] is the external financial pressure in period t,
cf is the sensitivity of inflation to external pressure (“exchange rate pass-through”).

“By combining the open economy monetary policy rule and the Phillips curve we obtain the equilibrium real rate of interest in the open economy [RR curve].”

R[t] = RN + bp × (PE – PT) + b1 × gap[t] – b2 × ss[t] + RD[t] + b3 × XFP[t]

b1 = bg + cg × (bp -1) > 0,
b2 = cg × (bp – 1) > 0,
b3 = 1 + cf × (bp – 1) > 0

R[t] is the real interest rate in period t,
RN is the natural rate of interest,
gap[t] is the output gap,
ss[t] is a supply shock
RD[t] is a discretionary deviation of the policy rate from the rule,
XFP[t] is the external financial pressure in period t,
bp is the sensitivity of the interest rate to excess inflation (> 1, for hawkish central banks),
cg is the sensitivity of inflation to excess demand,
bg is the sensitivity of the short-term interest rate to the output gap,
cf is the sensitivity of inflation to external pressure (“exchange rate pass-through”).

Like the IS curve, the RR curve describes a relation between the real interest rate and the output gap. However, it is upward sloping for inflation-averse or ‘hawkish’ central banks, meaning that a higher output gap is typically associated with a higher real interest rate. Note also that the following “shocks” push that curve to the left (i.e. higher real interest rate for same output gap): negative supply shock, monetary tightening shock and external financial pressure.

Overall macroeconomic equilibrium for this closed economy

The macroeconomic equilibrium of this open economy is [1] the real interest rate and output gap pair for which both the IS and RR curve conditions are met and [2] the external trade balance (net exports) and real exchange rate pair that is consistent with the real interest rate conditions.

Formally, we would have to set the solutions for the real interest rate equal and subsequently solve for the equilibrium output gap, real interest rate, inflation, exchange rates and so forth. Since the resulting terms are large and take some time to interpret, a more practical analysis for macro traders can make use of three simple graphs.

  • We draw into the real rate/ output gap diagram the downward sloping IS curve and the upward sloping RR curve. Their intersection marks the equilibrium in terms of real rate and output.
  • We draw into the inflation/ output gap diagram the upward sloping Phillips curve. The inflation rate that corresponds to the equilibrium output gap is the equilibrium inflation rate. Note also that the equilibrium nominal interest rate is the sum of the real interest rate and the inflation rate.
  • Finally, we draw into the net export real exchange rate (depreciation) diagram an upward sloping net export curve. The upward slope means that the higher the real exchange rate (the more depreciated the local currency) the larger the net exports. External and financial conditions affect the real exchange rate and hence mean that we move along the curve. Positive shocks to terms-of-trade and declines in the output gap (as per IS-RR diagram) push the curve to the right.

The practical use of the model and this representation is that we can simulate various types of shocks that can be observed in the economy and the market, by shifting the IS/RR curves accordingly (first graph below). Thereupon we can infer the stylized consequences for the real and nominal interest rates from the changed equilibrium by looking at the inflation/output gap (second graph below). Finally, we can infer the impact on the real exchange rate by taking the change in the local real interest rate from the IS/RR diagram and insert it in the exchange rate equation:

q[t] = XFP[t] – (R[t] – RN)

XFP[t] is the external financial pressure in period t,
R[t] is the real interest rate in period t,
RN is the local natural rate of interest.

We can also derive the change in the trade balance from the net export curve (third graph below), but this is usually of secondary importance for macro trading.

The above example simulates the impact of a terms of trade deterioration and external financial pressure:

  • A terms-of-trade deterioration shifts the IS curve to the left and both the real interest rate and output gap decrease. The inflation rate would be reduced as well. The decrease in the local real interest rate leads to a rise in the real exchange rates, i.e. a real depreciation of the local currency.
  • A rise in external financial pressure shifts the IS curve to the right and the RR curve to the left. The key consequence is a rise in the local real interest rate. The impact on the output gap is less clear but numerical simulations suggest that it would be negative as well. The impact on the real exchange rate is uncertain, as the external pressure argues for depreciation, while the local interest rate response pushed the opposite way. Typically, the local policy response contains rather than prevents depreciation.