Correlated Shocks, Hysteresis, and the Sacrifice Ratio: Evidence from India

TLDR: In an emerging market with frequent shocks output sacrifice from disinflation depends not only on the Phillips curve slope but also on shifts in demand and supply as discussed by the authors, introducing shocks and correlatio...

Abstract: In an emerging market with frequent shocks output sacrifice from disinflation depends not only on the Phillips curve slope but also on shifts in demand and supply. Introducing shocks and correlatio...

Figures

Table A.5: : Equations of the Model

Table A.2: : Unit root test - ADF and PP test for Q, PROD, i and core inflation

Table A.1: Unit root test - ADF and PP test for Log-output, core inflation and food inflation

Table 7: Summarized results of simultaneous equation model

Table 1: Episode-based estimate of sacrifice ratio for India (annual data)

Table 2: Episode-based estimate of sacrifice ratio for India (quarterly data)

Full text

WP-2019-026
Correlated Shocks, Hysteresis, and the Sacrifice Ratio: Evidence from
India
Ashima Goyal and Gagan Goel
Indira Gandhi Institute of Development Research, Mumbai
August 2019

Correlated Shocks, Hysteresis, and the Sacrifice Ratio: Evidence from
India
Ashima Goyal and Gagan Goel
Email(corresponding author): ashima@igidr.ac.in
Abstract
In an emerging market subject to frequent shocks output sacrifice from disinflation depends not only on
the Phillips curve slope but also on shifts in demand and supply. Introducing shocks and correlations
between shocks in a Kalman filter based estimation, the slope flattens, correlation between permanent
output shocks (supply) and output gap (demand) shocks is negative and a new decomposition of output
between trend and output gap shocks is obtained. The flat supply curve is robust to parameter changes,
and business cycle turning points are tracked well, but the decomposition varies. More stable inflation
expectation and rise in forward-looking behaviour increases volatility of trend growth and reduces the
output gap. Inflation targeting had such effects in India. Estimated sacrifice ratio varies with the period
and method, but it rises to 6.7 over 2011-17 if such hysteresis is included. Simultaneous equation
estimation corroborates the results. In the estimation period, inflation targeting affected expectations
but not inflation.
Keywords: Sacrifice ratio; Phillips curve slope; correlated demand and supply shocks; hysteresis
JEL Code: E32, E52, E31
Acknowledgements:
The paper further develops Gagan Goel’s IGIDR M.Phil thesis. Helpful comments from annonymous referees, Jayati Sarkar,
Subrata Sarkar and Abhishek Kumar and secretarial assistance from Reshma Aguiar are acknowledged.

Correlated Shocks, Hysteresis, and the Sacrifice Ratio:
Evidence from India
August 8, 2019
1 Introduction
Low and stable inflation has been part of monetary policy goals all over the world. But disinflationary
policy to reduce inflation is expected to have costs in the form of lower output and employment.
The sacrifice ratio (SR) is defined as the short-run output loss due to reducing inflation.
A trade off between output and inflation in the short run is empirically observed primarily in
advanced economies. The aggregate supply or Phillips curve (PC) gives the rise in unanticipated
inflation (expected inflation subtracted from actual inflation), as a function of the difference of
output from its potential level. The SR depends on the slope of the Phillips curve. For advanced
economies, there is some evidence the PC has flattened (IMF 2013) raising the SR.
In emerging economies, supply-side constraints imply frequent shifts in the PC
1
. Correlated
demand shifts can occur if forward-looking behaviour adjusts private demand or if policy responds
to supply shocks. This can further impact supply. Our objective is to estimate the SR in the presence
of such correlations in demand and supply shocks that can affect trend output and therefore have
persistent effects. Sacrifice ratio is then measured on an adjustment path consisting of a series of
shifting equilibria from one long run equilibrium to another (Zhang, 2005 and Hofsetter, 2008).
Emerging economies growth is volatile compared to advanced economies. So it requires more
careful disentangling of trend output from the cyclical component. If the cycle affects the trend,
demand shocks can create persistent effects or hysteresis. In the literature, generally Hodrick and
Prescott (HP) or Band-Pass filters are used to disentangle these components. These filters smooth
out either the trend component or the cyclical component of output. Potential or trend output
and expected inflation are not observed time series but they are required for estimating the PC and
SR accurately. Trend and cyclical component are unobservable components of observed output. A
Kalman filter (KF) allows a stochastic trend, correlation between trend and cycle, as well as other
unobservables to be extracted using available data. We therefore estimate the SR using the KF
technique, following BN (Basistha and Nelson, 2007).
Figure 1 shows the output sacrifice for a pure demand shock and for a demand shock in the
presence of a supply shock. The top panel shows a large output sacrifice from a fall in demand if
1
There is evidence of a flat aggregate supply curve with multiple supply shocks for India (Goyal and Tripathi,
2015; Goyal 2011).
1

the aggregate supply curve (or PC) is flat. The bottom panel shows the output sacrifice would be
even larger if a supply shock follows a demand shock or a demand shock follows a supply shock,
while the change in inflation depends on the size of the supply shock. If consumption is reduced
after an adverse supply shock, output falls while prices rise. This could happen if forward looking
agents reduce demand following a supply shock, or if monetary or fiscal policy contracts. Growth
rates could also be affected, as supply contracts further.
A leftward shift of aggregate demand (AD) following contractionary policy to reduce inflation
after a cost shock would add to a contraction in demand from forward-looking households. A
negative correlation between AD and aggregate supply (AS) shocks follows. Moreover, firms may
expect higher interest rates from contractionary monetary policy and thus higher input cost, which
induces further leftward shift of the AS curve. So, forward-looking behaviour would accentuate
correlations between inflation, trend and output gap. This was the Indian experience after external
shocks in the 1970s, 2011 and in 2018. Temporary supply shocks triggered sustained periods of
lower growth. Goyal and Kumar (2018) show policy induced demand shocks shifted the AS curve
to the left in 2011
2
.
Therefore a SR calculated only using slopes and not shifts in the AS and AD curves would be an
underestimate. Taking account of shifts and correlations, or using a simultaneous equation structure
rather than a single equation PC, would give a more correct estimate of the SR or change in output
accompanying a fall in inflation
3
.
Emerging economies differ from advanced economies in many aspects of their economic structure.
We take account of two major differences that can be expected to affect the SR—frequent supply
shocks and their correlation with demand shocks. Second, how this affects the volatility of trend
growth and therefore persistence of demand shocks.
Results from the KF estimations are: The slope of the PC flattens, the correlation between
permanent output (supply) shocks and output gap (demand) shocks is estimated to be negative
and a new decomposition of output between trend and output gap shocks is obtained. While the
flat supply curve is robust to parameter changes and business cycle turning points are tracked well,
the level of the output gap changes. A fall in volatility of inflation expectations and rise in forward-
looking behaviour increases the volatility of trend growth and reduces the output gap. There are
indications of such effects after monetary-fiscal policy tightened in 2011 and inflation targeting was
adopted in 2013. The output sacrifice from an estimate that includes persistent growth effects
is larger (6.7 over 2011-17) for the post global financial crisis (GFC) disinflation compared to the
literature and our own initial episode based estimates. The implication for policy is that structural
reforms, such as the adoption of inflation targeting, that impose large demand shocks, should be
carefully implemented to minimize such shocks. The analysis implies demand shocks will have
more persistent effects to the extent forward-looking behaviour increases and inflation expectations
become less volatile.
2
They allow for multiple high and low growth equilibria. Persistent low growth shifts the long-run AS leftward.
Shifts in AS and AD are due to lagged endogenous variables, expectations as well as policy shocks. The correlation
between all three components is negative. BN also estimate a negative correlation between permanent and gap
shocks for the UK.
3
Just as Goyal and Tripathi (2015) find correctly measuring supply shocks reduces the AS slope.
2

Figure 1: Impact of demand and supply shocks on output and inflation
AD-AS: Disinflationary Monetary Policy and a Supply Shock
3

Frequently asked questions

Q1. What is the advantage of the hybrid method?

The advantage of their hybrid method is that variables that were endogenous could be modelled with the full VAR lag structure, but exogenous, dummy and other context specific variables could also be introduced. 

Q2. What is the effect of the flat supply curve on the output gap?

While the flat supply curve is robust to parameter changes and business cycle turning points are tracked well, the level of the output gap changes. 

Q3. What are the commonly used methods of calculating the SR?

The most frequently used methods of calculating the SR are broadly: Variants of a PC model, including extensions to SVAR, and the disinflation episode method. 

Q4. What is the reason for the large actual growth fluctuations of this period?

One reason for the large actual growth fluctuations of this period could be demand contractions in the context of better anchoring of inflation expectations since their analysis suggests this would increase the impact of demand shocks on potential output. 

Q5. What is the effect of more forward looking behaviour and fall in inflation expectation volatility?

More forward looking behaviour and fall in inflation expectation volatility increases the volatility of trend growth and reduces that of the output gap. 

Q6. What is the inverse relation of p and g in the simulations?

The negative ρpg and inverse relation of σp and σg in the simulations suggest demand contractions reduce supply, lowering potential output. 

Q7. What is the effect of the simultaneous equation estimation of the Phillips curve?

A simultaneous equation estimation of the Phillips curve corroborates the dominance of supply shocks, reduction in AS slope under better estimation and the correlation between the output gap and productivity. 

Q8. What is the reason for the growth loss in India?

Some of this growth loss was due to prolonged tight financial conditions as IT was adopted while the country was on a fiscal deficit reduction path under fiscal responsibility legislation. 

Q9. What can the authors do to assess the effects of structural shocks on the model variables?

Only after decomposing forecast errors into structural shocks that are mutually uncorrelated and have an economic interpretation can the authors assess the causal effects of these shocks on the model variables. 

Q10. What is the effect of inflation targeting on growth?

Inflation targeting may have increased forward-looking behaviour, thus increasing the growth loss from tighter policy, even if it did not have an appreciable impact on inflation itself in the period of estimation, after controlling for supply shocks. 

Q11. What is the proxy for inflation in india?

Low per capita incomes and a large share of food in the consumption basket in India during this period made food inflation a good proxy for inflation expectations. 

Q12. What is the cost of falling output gaps from sustained tightening?

The cost in falling output gaps from sustained tightening over Q3 2011 to Q1 2017 was 6% from BII, which sends all the stochastic variations to the output gap but fall in trend growth also has to be added to the SR. 

Q13. What is the correlation between the slope of the PC and the output gap?

The slope of the PC flattens, the correlation between permanent output (supply) shocks and output gap (demand) shocks is estimated to be negative and a new decomposition of output between trend and output gap shocks is obtained. 

Q14. What are the main shortcomings of the HP filter?

Additional shortcomings specific to the HP filter are: (i) it is difficult to identify the appropriate value of the detrending parameter λ and (ii) this technique is susceptible to what is often referred to as end-point bias caused by the asymmetry inherent in the filter at the extreme points of a time series. 

Q15. What are the main assumptions that are imposed on the model responses?

Structural interpretations of VAR models impose additional identifying assumptions based on institutional knowledge, economic theory or other extraneous constraints on the model responses. 

Q16. What is the effect of adding more relevant variables to the KF model?

The introduction of additional relevant variables than can be added in the minimal unobserved component model, served as a further robustness check on the KF results and gives more insights on the SR. 

Q17. What is the difference between the output gap and the inflation shock?

Since the volatility of trend output is higher in the lower panels with unconstrained ρs, the changes in output gap are smaller, but more frequent especially in the post 2012 period of demand contractions that harmed supply conditions.