The inflation risk premium in the term structure of interest rates bis quarterly Review, part 3, September 2008

The inflation risk premium and the macroeconomy 

In order to gain some insight into what the underlying drivers of inflation risk 

premia are, it is useful to investigate how they evolve in response to changes in 

the macroeconomic state variables. Ultimately, all time variation in the 

estimated premia will be due to movements in these variables. It turns out that 

two of the state variables are the main drivers of inflation premia in the United 

                                                      

17

   The same result holds for five-year forward break-even rates five years ahead, a common 

indicator of market inflation expectations for distant horizons. For the United States, the 

premium-adjusted version of this forward break-even rate has differed little from the raw 

version, while in the case of the euro area the adjustment has generally resulted in a 

significantly lower level compared to the raw series (see BIS (2008, pp 112–13)).  

… are close to 

survey inflation 

expectations 

---

 

 

 

BIS Quarterly Review, September 2008  

35

 

States as well as in the euro area: the output gap and inflation. Broad 

movements in the 10-year inflation risk premium largely match those of the 

output gap, while higher-frequency fluctuations in the premium seem to be 

aligned with changes in the level of inflation. 

Movements in the output gap and in inflation are due to combinations of 

the structural shocks in the model, so, to better understand the ultimate 

determinants of premia, it is necessary to examine their reaction to such 

shocks. One of the advantages of the modelling strategy adopted here is that it 

makes it possible to compute impulse response functions of yields and 

associated premia to the underlying macro shocks. Graphs 5 and 6 show US 

and euro area responses of inflation risk premia and expected inflation to 

demand and supply shocks. The left-hand panels refer to a two-year horizon 

and the right-hand panels to a 10-year horizon. These graphs show that the 

responses of inflation premia to demand shocks (ie shocks to the output gap in 

equation (3)) are much more persistent than responses to supply shocks 

(ie shocks to inflation in equation (4)). Intuitively, this reflects the fact that the 

effects on inflation and output from demand shocks are substantially longer-

lasting than those from supply shocks. 

Looking at the results in more detail, a positive shock to US aggregate 

demand, corresponding to a 1 percentage point increase in the shock to the 

output gap in equation (3), pushes up the 10-year inflation premium by around 

13 basis points (Graph 5, right-hand panel), possibly reflecting perceptions of a 

higher risk of upside inflation surprises as the output gap widens. A positive 

demand shock also raises the average expected inflation rate by about 7 basis 

points, resulting in an overall increase in the 10-year break-even rate (ie the 

sum of the two responses) of some 20 basis points. At the two-year horizon 

(Graph 5, left-hand panel), the effect on the break-even rate from a demand 

shock is even larger, at around 35 basis points on impact, but now the bulk of 

the response is due to rising inflation expectations, while the inflation premium 

US impulse responses

 

In per cent 

Two-year responses 

Ten-year responses 

–0.1

0

0.1

0.2

0.3

0

10

20

30

40

50

60

Inflation risk premium response 

to demand shock

Expected inflation response 

to demand shock

 

–0.04

0

0.04

0.08

0.12

0

10

20

30

40

50

60

Inflation risk premium 

response to supply shock

Expected inflation 

response to supply shock

The demand shock corresponds to a 1 percentage point increase in the shock to the output gap in 

equation (3), while the supply shock is a 1 percentage point increase (in annualised terms) in the shock to 

inflation in equation (4). Horizontal axis measures the horizon of the responses in months. 

Source: Author’s calculations. 

Graph 5 

… with demand 

shocks having 

persistent effects … 

Inflation and output 

movements drive 

developments in 

inflation premia … 

---

 

 

 

36 

BIS Quarterly Review, September 2008

 

response is similar to the 10-year case. Demand shocks therefore seem to 

induce parallel shifts in the inflation premium, while inflation expectations react 

much more strongly for short maturities than for long.  

The responses to supply shocks in Graph 5 (corresponding to a 

1 percentage point increase in the shock to inflation in equation (4)) are clearly 

less pronounced and less persistent than for demand shocks. Nonetheless, the 

short-term reaction of both expected inflation and inflation risk premia at the 

two-year horizon is sizeable. This suggests that investors become more averse 

to inflation risk as inflation rises.  

As in the United States, a positive demand shock also raises expected 

inflation in the euro area, and more so at the two-year horizon than at the 

10-year horizon (Graph 6). However, in contrast to the US case, the inflation 

premium response is uniformly negative, albeit small. In terms of the response 

of euro area break-even inflation to demand shocks, the two effects largely 

cancel out. Given that the inflation risk premium accounts for a sizeable portion 

of the overall term premium, this negative response of the inflation premium to 

demand shocks appears to be in line with evidence from Germany prior to the 

introduction of the euro, as documented in Hördahl et al (2006), where term 

premia reacted negatively to positive demand shocks. A possible explanation 

for this finding could be that investors become more willing to take on risks – 

including inflation risks – during booms, while they require larger premia during 

recessions.

18

 

With respect to euro area responses to a supply shock, the results in 

Graph 6 are qualitatively similar to those for the United States. A 1 percentage 

point upward shock to aggregate supply raises the two-year break-even rate by 

around 40 basis points on impact, an effect that quickly wears off. Most of this 

                                                      

18

   Such effects have been found elsewhere. Piazzesi and Swanson (2008), for example, report 

strongly countercyclical risk premia based on estimates on federal funds futures prices.  

Euro area impulse responses

 

In per cent 

Two-year responses 

Ten-year responses 

–0.1

0

0.1

0.2

0.3

0

10

20

30

40

50

60

Inflation risk premium response 

to demand shock

Expected inflation response 

to demand shock

 

–0.04

0

0.04

0.08

0.12

0

10

20

30

40

50

60

Inflation risk premium response 

to supply shock

Expected inflation response 

to supply shock

The demand shock corresponds to a 1 percentage point increase in the shock to the output gap in  

equation (3), while the supply shock is a 1 percentage point increase (in annualised terms) in the shock to 

inflation in equation (4). Horizontal axis measures the horizon of the responses in months. 

Source: Author’s calculations. 

Graph 6 

… while the impact 

of supply shocks is 

short-lived 

---

 

 

 

BIS Quarterly Review, September 2008  

37

 

increase is due to a higher two-year inflation premium (over 30 basis points). At 

the 10-year horizon, the break-even response is similarly short-lived and 

substantially smaller at around 10 basis points, predominantly due to the 

inflation premium.  

Conclusion 

This article estimates inflation risk premia using a dynamic term structure 

model based on an explicit structural macroeconomic model. The identification 

and quantification of such premia are important because they introduce a 

wedge between break-even inflation rates and investors’ expectations of future 

inflation. In addition, inflation risk premia per se may provide useful information 

to policymakers with respect to market participants’ aversion to inflation risks 

as well as to their perceptions about such risks.  

The results show that inflation risk premia in the United States and in the 

euro area are on average positive, but relatively small. Moreover, the estimated 

premia vary over time, mainly in response to changes in economic activity, as 

measured by the output gap, and inflation. The estimates suggest that 

fluctuations in output drive much of the cyclical variation in inflation premia, 

while high-frequency premia fluctuations are mostly due to changes in the level 

of inflation. 

References 

Ang, A, G Bekaert and M Wei (2008): “The term structure of real rates and 

expected inflation”,