The Price Puzzle

The Price Puzzle: Theories and Further Empirical
Evidence
Edorta Rojí ∗
Department of Economics, LSE
May 6, 2009
Abstract: This paper reviews the recent literature on one of the main puzzles of monetary
policy: the positive reaction of prices to a tightening monetary policy shock. The
different explanations of the phenomenon are divided into three groups: the misspecified
view, the cost channel acceptance and the indeterminacy path. Giordani’s (2004) suggestion
of including output gap instead of output in a three variable VAR to eliminate the puzzle is
then checked for a battery of different measures of output gap. We find that, for quarterly
U.S. data, the output is not enough to avoid the problem. Furthermore, for the pre-Volcker
sub-sample, output gap does not eliminate the puzzle at all.
Keywords: Price puzzle; Monetary Policy; VAR; Output gap; Misspecification; Cost
channel; Indeterminacy.
JEL Classification Numbers: E31, E52.
∗ E-mail: e.roji@lse.ac.uk. The author is grateful to the Fundación Ramón Areces for his generous financial
support.
1

1 Introduction
Although the phenomenon of an increase in the level of prices following a tightening
in the monetary conditions of an economy is an event that has occurred in industrialized
countries several times in the postwar period, it was not until the beginning of the nineties
when the first empirical study about the effects of monetary policy shocks appeared (Sims,
1992). Using the vector autoregressive (VAR) methods on postwar data for the U.S., Japan
and three European countries, Sims noted that the initial response of prices to interest rate
shocks were, contrary to what could be expected by the theory, significantly positive (and,
in some countries, even persistent). 1
Sims also noted that this result 2 (called the ‘price puzzle’ by Eichenbaum, 1992) was
mitigated by the inclusion of commodity prices in the VAR, so he claimed that this was
due to the fact that the committee in charge of managing monetary policy was looking to
more variables than the included in his model in order to predict future inflation. Thus,
if we have an omitted variables problem, we could wrongly identify as monetary policy
shocks endogenous movements in the interest rates that the authorities develop in response
to movements in these so-called ‘information variables’. This explanation provoked that the
price puzzle was seen by many authors as an evidence of having a misspecified model, and
that adding commodity prices in the VAR has become the standard practice to avoid the
problem (Christiano et al., 1999).
However, in light of the doubts cast on the ‘information variable solution’ (Hanson,
2004), there are many other alternative explanations of the phenomenon. Balke and
Emery (1994) showed that there is also evidence of the price puzzle using the Romer
1 It is now generally accepted that the interest rate targeted by the monetary authorities is a better
measure of monetary policy than the different variables of quantity of money. See, e.g., Bernanke and
Blinder (1992).
2 Before Sims’ paper, the relation between inflation and interest rates had been studied by many authors.
See, e.g., Sargent (1973).
2

and Romer (1989) way of identifying monetary policy contractions by examining the
historical records of the Federal Reserve meetings (the ‘narrative approach’).
They also
argued that the puzzle is more evident for the postwar period previous to 1979 and even
that the inclusion of commodity prices in the VAR does not eliminate it for this sub-sample. 3
Other studies suggest that the price puzzle may be due to the non-distinction between
transitory and permanent monetary policy shocks (Bache and Leitemo, 2008) or even that
the evidence could be remarkably different if we use monthly or quarterly data (Kapinos,
2007). A relatively new and strong explanation of the event is that it can appear if
the authorities carry the monetary policy in a passive way (Boivin and Giannoni, 2002,
Castelnuovo y Surico, 2006, Dueker, 2006 and Belaygorod and Dueker, 2007).
On the
other hand, Barth and Ramey (2001) and Gaiotti and Secchi (2006), among others, try
to explain the increase of prices following a contractionary monetary policy shock with
what has been called the ‘cost channel’ of transmission of monetary policy.
Giordani
(2004) shows that the use of output gap instead of output in a three variable VAR
that includes output, inflation and federal funds rate can solve the price puzzle for quarterly
data and explain why the inclusion of commodity prices help to reduce the phenomenon.
This dissertation has two objectives:
to present a rather extensive survey of the
different explanations of the price puzzle among the literature and to modestly study
further the robustness of the results of Giordani (2004). The paper is organized as follows.
The next section is dedicated to the literature review, divided by the main different
streams in studying the phenomenon.
Section 3 discusses the robustness of including
the output gap in the VAR methodology for the U.S. data, examining different mea-
3 A large number of studies that divide the postwar data in two sub-samples tend to use 1979 or 1982
as the separation year. This is because Paul Volcker was appointed Chairman of the Board of Governors of
the Federal Reserve in the third quarter of 1979 and stated as a main objective the fight against inflation.
However, for the 1979-82 period, the Fed explicitly targeted non-borrowed reserves. See Bernanke and Mihov
(1998).
3

sures of output gap constructed by using distinct variables and checking if the price puzzle
disappears for the pre-Volcker period. Finally, concluding remarks are presented in section 4.
2 Literature review
As was mentioned in the introduction, the price puzzle literature started with Sims (1992)
and the answer of Eichenbaum (1992). Since then we have had different studies about the
topic, from the rather common misspecified view to the indeterminacy literature and the
total acceptance of the puzzle by the cost channel defenders.
2.1 The misspecified view
The forward-looking monetary authorities theory of Sims has been widely accepted.
As Balke and Emery (1994) remark, an alternative but quite similar explanation of the
phenomenon is that the Central Banks react to negative supply shocks. Under this view,
a non-persistent negative supply shock can increase prices and real interest rates if the
authorities reaction to the shock is to increase interest rates but the response is not enough
to avoid the inflation raising. 4
Eichenbaum (1992), who sucessfully labelled the term as the ‘price puzzle’, suggests that
Sims’ findings may be due to the fact that interest rate innovations are not a good measure
of monetary policy shocks.
Instead, he proposes monetary aggregates or non borrowed
reserves as alternative variables for capturing monetary policy disturbances and shows
that innovation to non borrowed reserves produce small and positive, but not persistent,
increases in the price level. The author ends claiming that further research should point to
examine accurately the way monetary policy is managed in each country, something that
4 Note that this last point is also present in Sims’ explanation.
4

has been extensively done for the U.S.
While Eichenbaum’s critique of the interest rate innovations being used as good measure
of monetary policy has been overcome by an extensive literature showing the opposite, 5 the
non borrowed reserves suggestion has been shown very productive in solving the other main
puzzle of monetary policy research: the liquidity puzzle (Christiano et al., 1996, 1999).
Leeper and Roush (2003) also claim that the price puzzle may be due to the incorrect
separation between money demand shocks and monetary policy in recursive identification
schemes (i.e., using the Choleski identification) and show that correctly including money in
the VAR can help solve the puzzle.
The fact is that this misspecified view has become quite popular, and including
commodity prices in the VAR to avoid the puzzle is viewed as a standard practice.
However, Hanson (2004) presents convincing results that question this view.
First, he
builds a model of what he called the ‘conventional view’ of the price puzzle, showing that
it implies that the variables with more forecasting power should behave better in reducing
or completely eliminating the presence of the puzzle, and that the phenomenon should
be more pronounced the higher the response of monetary authorities to inflationary pressures.
When confronting these two implications with the data, he finds that the evidence of a
positive relation between forecasting power and ability to solve the puzzle is not conclusive.
Indeed, he suggests not only that predictive power seems not enough to avoid the presence
of the phenomenon, but also that commodity prices can be interpreted as a type I error in
a standard hypothesis relating forecasting power and the reaction of prices. In addition,
the second implication does not hold either, because he obtains, as many other authors,
that the price puzzle in the U.S. is much more pronounced in the years prior to 1980, a
5 In particular, for the case of the U.S., arguing that the federal funds rate target by the Federal Reserve
is in fact a good measure of monetary policy actions.
5

period when the reaction of the Federal Reserve to inflation was smaller, 6
as have been
documented by, e.g., Clarida et al. (2000)
For the purpose of this article, it is worth noting that Hanson also studied the incremental
forecasting power of the variable capacity utilization (which is the one that, for
the manufacturing sector, Giordani (2004) uses as a proxy for the output gap to solve
the price puzzle or, at least, to improve the results from misspecification), and he finds
that it exhibits a small incremental forecasting power and that it reduces the duration of
the puzzle.
Furthermore, the inclusion of capacity utilization in the VAR provokes that
output increases and capacity utilization itself initially reacts positively to a contractionary
monetary policy disturbance, though the effect is small and quite brief.
Finally, a recent paper by Bache and Leitemo (2008) argues that the identification of
monetary policy shocks should distinguish between permanent and transitory disturbances.
They define permanent shocks as the ones that affect the inflation target and present a model
in which both types of shocks have different effects in output and inflation. Then, failure
to separate the two could spuriosly generate the price puzzle. The authors also present a
simulation that shows that their explanation does not imply any other problem, i.e., it avoids
the rise of output in response to a negative monetary policy shock. While the presence of
a price puzzle but not of an output puzzle can cast some doubts about their hypothesis,
this new explanation of the puzzle seems quite promising and, as Bache and Leitemo claim,
further research should be dedicated to find an identification scheme that incorporates the
opposite propagation mechanisms of the two disturbances.
6 The relation that this has with the price puzzle will be covered in detail in section 2.3.
6

2.2 Accepting the puzzle: The cost channel
A totally different way of confronting Sims’ results is to accept that the level of prices
does increase after a contractionary monetary policy shock and hence try to create a theory
that explains why this occurs. The best way to do this is through the supply effects and this
branch is generally called the cost channel of transmission of monetary policy. Intuitively,
this view introduces interest rates into the cost function of the firms, so when a negative
monetary disturbance raises interest rates, the firm’s marginal cost, through the effect of
working capital in the production process, also increases. Initially, the firms increase their
prices in response to the increase in their costs, but the fall of the aggregate demand finally
reduces the price level.
Barth and Ramey (2001) important contribution emphasizes that the supply-side (or
cost-side) effects of monetary policy on real variables in the short run 7 should also be taking
into account. Examining data on manufacturing industries, they show that prices increase
(and output falls) after an unanticipated monetary contraction, and these results are robust
after controlling for the price puzzle and the effects of oil shocks. Interestingly, they also
found that these cost channel effects were more significant for the pre-Volcker period, i.e.,
during those years more industries reacted to a contractionary monetary shock by increasing
their prices.
This last point is, as noted before, consistent with the findings among the
literature of the price puzzle being greater in the first part of the postwar period and not
solved in that sub-sample using commodity prices.
Furthermore, Gaiotti and Secchi (2006) examine the data of nearly 2.000 manufacturing
Italian firms through a fourteen years period, finding that the cost channel is indeed
important and significance. The way they model the cost channel is rather typical among
7 As Gaiotti and Secchi (2006) point out, in the long run the demand effects dominate, which is consistent
with monetary neutrality.
7

the literature and is by assuming that the inputs of the firm must be paid in advance, so
the production of the firm and the interest rate of the financing are directly related. Under
this setting, they find robust evidence on the fact that monetary policy also works through
the supply side, although the payment in advance assumption seems to be less important
than the role of working capital on the production of the firm.
However, at a macroeconomic level, Rabanal (2007) estimate, using Bayesian methods,
a dynamic stochastic general equilibrium (DSGE) model including a cost channel and
finds that the elasticity of inflation to changes in the nominal interest rate is quite low,
ultimately resulting in having a zero probability of observing a rise in prices following a
monetary policy contraction.
In addition, he also shows that, in his setup, the presence
of the cost channel in all firms is not enough to generate a positive response of inflation
to a monetary policy contraction, but needs also to include other more restrictive conditions.
The results of Rabanal contradict the findings of Christiano et al. (2005) and Ravenna
and Walsh (2006), who find that the cost channel of transmission of monetary policy is more
important and can generate an increase of inflation following a monetary policy tightening.
Beyond this diverse results, more research is needed in this area taking into account what
Barth and Ramey (2001) initially remark: that even if we accept that the demand effects of
monetary policy actions dominate, the supply side should also be taken into account. In that
sense, to construct a general equilibrium model that clearly separates demand and supply
effects is a future challenge to be overcome. Explain why commodity prices help to solve the
price puzzle is also a question to be answered in the future by the cost channel defenders.
2.3 The indeterminacy path
In the last few years several papers have appeared with a new and strong explanation
of the puzzle: that the phenomenon can appear in periods of indeterminacy. Traditionally
8

in the models, indeterminacy is reached when the monetary authorities do not respond
to inflation strongly enough, i.e., when the parameter that measure the reaction of the
monetary policy rule to inflation is less than one, and hence the so-called ‘Taylor principle’
is not satisfied. The situation is called indeterminate because we then do not have a unique
rational expectations equilibrium.
It has not been until very recently that Lubik and Schorfheide (2003) have shown how
to empirically estimate monetary DSGE models under indeterminacy based on likelihood
methods.
Belaygorod and Dueker (2007) use their results to obtain that indeterminacy
in the U.S. occurred between 1972 and 1982, and that during that period the impulse
response function of inflation to an interest rate shock shows a sustained positive response,
opposite to what they find for the posterior determinacy period. Note that these results
are consistent with the findings, documented in many articles, of the price puzzle being
stronger and not fully solved using commodity prices in the pre-Volcker period.
Boivin and Giannoni (2002) suggest that the response of the economy to interest rates
movements has changed over time and confirm that the puzzle is also present in the years
previous to 1980. Furthermore, they perform a counterfactual exercise and obtain that the
intuitive response of inflation to interest rates is achieved by imposing the post-1980 policy
to the pre-1980 sub-sample and vice versa, i.e., the price puzzle in the post-1980 period is
obtained imposing the pre-1980 policy on it. 8
On the other hand, Castelnuovo and Surico (2006) use Lubik and Schorfheide findings
to simulate data, estimate structural VARs and obtain that the puzzle only appears for the
pre-1979 period. However, their results are aimed to show that the puzzle is indeed and artificial
result that appears in the periods of passive monetary policy due to misspecification.
8 They find similar results dividing the sample in 1984 instead of 1980. See charts 2 and 3 of their paper.
9

In particular, they use a New Keynesian model incapable of producing a positive response
of prices to contractionary monetary policy shock in either period and use simulations to
show that the model can account for the pre-1979 sub-sample puzzle results spuriously if
expected inflation is omitted from the VAR. This occurs because the persistence of expected
inflation is higher under indeterminacy and hence a variable capturing this point should be
added to the VAR for that sub-sample.
Interestingly for the purpose of this paper, Castelnuovo and Surico use in their paper
different measures of output gap in a three variable VAR similar to the one used by Giordani
(2004) 9 and find that the price puzzle does not disappear for the period previous to 1979
and that this conclusion is independent of using different measures of output gap. Before
finishing this section, note also that the indeterminacy view is not consistent with the way
Hanson (2004) models his conventional view of the puzzle (because it implies that the
phenomenon should be greater the stronger is the reaction of authorities to inflation), and
hence is consistent with Hanson’s results because he finds that this second implication of
the standard view does not hold.
3 Reexamining empirically Giordani’s results
As was mentioned in the introduction, Giordani (2004) shows how the use of output
gap (which he proxies using the capacity utilization in the manufacturing sector) instead
of output in a three variable VAR can solve the price puzzle. Hence his view can belong
to the misspecified common path though his type of omitted variable bias is different.
Furthermore, the author explains why commodity prices help to solve the puzzle, which is
mainly because they are correlated with the output gap. However, in his article, Giordani
notes that the puzzle is not resolved with monthly data and he attributes this fact to the
9 Including output gap, inflation and nominal interest rates.
10

measurement error present in the monthly data.
Kapinos (2007) questioned Giordani’s results showing the differences between two measures
of the output gap (percentage deviation of capacity utilization and the linearly detrended
log index of industrial production) and remarking that the price puzzle is still present
for both types of measures and for both monthly and quarterly data. The rest of this paper is
dedicated to extend Kapinos’s results in order to find if the solution proposed by Giordani’s
is really robust to use different measures for the output gap.
3.1 The model
In order to make the results comparable with those of Giordani (2004), we are going to
use the following structural model:
⎛
A
⎜
⎝
y g t
π t
⎞ ⎛
⎟
⎠ = C(L) ⎜
⎝
y g t−1
π t−1
⎞ ⎛
⎟
⎠ + B ⎜
⎝
v y t
v π t
⎞
⎟
⎠
(1)
i t
i t−1
v i t
where y g t
is the measure of output gap, π t is the level of inflation, i t is the interest rate (the
Federal funds rate), A is a 3×3 upper-triangular matrix that describes the contemporaneous
relations between the three variables, C(L) is a matrix of finite order lag polynomial, B is a
3×3 diagonal matrix that relates the variables with the structural shocks and
⎛
⎞
v t ≡
⎜
⎝
v y t
v π t
⎟
⎠
(2)
v i t
is the vector of orthogonal structural shocks assumed to be white noise with zero mean and
unit variance. Note that this last point combines with the facts that A is upper-triangular
and B is a diagonal matrix means we are using a Choleski decomposition, i.e., a recursive
11

identification scheme.
As the structural shocks are not observed in the data, to correctly estimate this model
we must estimate his reduced-form version:
⎛
⎞
⎛
⎞
⎛
⎞
⎜
⎝
y g t
π t
⎟
⎠ = A−1 C(L)
⎜
⎝
y g t−1
π t−1
⎟
⎠ + A−1 B
⎜
⎝
v y t
v π t
⎟
⎠
(3)
i t
i t−1
v i t
Calling A −1 Bv t = u t the vector of reduced form errors that is indeed observed in the data,
we can get the variance-covariance matrix of it:
E(u t u ′ t) = A −1 BE(v t v ′ t)B ′ A −1 = A −1 BIB ′ A −1 (4)
where the last equality comes from the fact that we have assumed that the variance of the
structural shocks is one.
Then, substituting population moments with sample moments in equation (4) and provided
that the system is identified, we can estimate A −1 and B, hence obtaining the initially
unobserved structural shocks and the impulse response functions of the variables to the
shocks. 10
3.2 Empirical evidence using U.S. data
Giordani (2004) uses capacity utilization in the manufacturing sector as a proxy for
output gap. Following the literature, as in Clarida et al. (2000) or Castelnuovo and Surico
(2006), we have calculated a battery of proxies for the output gap. It will be easier to list
them:
10 The objective of this section was to briefly explain how the VAR works. See Christiano et al. (1999)
and Favero (2001) for more details.
12

• Capacity utilization: Not only for the manufacturing sector (CU), but also for the total
industry (TCU).
• Deviation of (log) real GDP from fitted linear and quadratic trends.
• Difference between (log) real GDP and the measure of real potential GDP (in logs)
estimated by the Congressional Budget Office (CBO).
• Deviation of (log) real GDP from a HP filter trend. 11
• Deviation of (log) civilian employment from fitted linear and quadratic trends.
• Deviation of (log) industrial production: electric and gas utilities (IP: E&G Utilities)
from fitted linear and quadratic trends.
• Deviation of (log) all employees of total private industries (Empl. Priv. Ind.) from
fitted linear and quadratic trends.
• Deviation of the civilian unemployment rate (Unempl. Rate) from fitted linear and
quadratic trends.
• Deviation of the NAIRU from fitted linear and quadratic trends.
All the series have been obtained from FRED except that of the last point, which comes
from the CBO. Note that, for the last two variables, the sign has to be changed when
calculating the output gap in order to make the results comparable.
The following table shows the correlation between some of the built measures of output
gap and capacity utilization in the manufacturing sector:
where CU is capacity utilization in the manufacturing sector (Giordani’s variable), TCU is
capacity utilization in the total industry, GDPPot is the measure of output gap constructed
11 As Giordani (2004) and Castelnuovo and Surico (2006) point out, the HP filter is two sided, so the
filtered data may lead to inconsistent estimates. We use it here for the sake of comparison.
13

Variables TCU GDPPot GDP-HP UnempR-qt
CU 0.99 0.66 0.70 0.69
Table 1: Correlations between the output gap used
by Giordani and other measures of output gap.
using the real potential GDP estimated by the CBO, GDP-HP is the one built using the
HP filter trend and UnempR-qt is the one using the unemployment rate with a quadratic
trend. The other measures of output gap constructed as remarked in the previous list have
all a positive correlation greater than 0.43 with the variable used by Giordani except the
two filtered variables using the NAIRU, which have a very small but negative coefficient.
This is because the NAIRU provided by the CBO is quite rigid, i.e., does not change much
over time, and hence the filtered data is not very accurate. Thus, we can use the different
measures of output gap in the described three variables VAR to see if output gap really
solves, or at least relieves, the puzzle.
Figure 1 shows the impulse responses of inflation to a contractionary monetary policy
shock in the three variable VAR described above. Note that the variable at the description
of each graph informs just about how the output gap was calculated and not about the
nature of the impulse response function, which is common for all charts (response of inflation
to a monetary policy shock). Furthermore, the graphs has been ordered (from left to right
and up and down) using the correlation that each measure of the output gap has with the
variable that Giordani (2004) uses. Therefore the graph of the top left corner shows the
result that Giordani obtained using capacity utilization in the manufacturing sector (i.e.,
corr(CU,CU) = 1).
14

Figure 1. Impulse responses of INF to a tightening monetary policy shock under different measures of
output gap. The words in brackets indicate if the measure of output gap was calculated using a linear trend
(lt), quadratic trend (qt) or the Hodrick-Prescott (HPt) filter.
Examining carefully Figure 1, we can see that the price puzzle remains with every single
measure of the output gap though the increase in the level of inflation is significant just in
approximately half of the cases, with the other half divided between the cases where the
response is not significant (four or five cases) and the cases where the signicance is doubtful.
In addition to that, the increase in prices seems to be highly persistent, with a duration
that generally lasts from 2-3 to 8-10 quarters. Note also that the reaction of prices when the
15

output gap is calculated using the potential GDP estimated by the CBO, which is probably
one of the best measures of output gap that can be obtained and is highly correlated with
the CU variable used by Giordani (as shown in Table 1), is clearly significant and rather
persistent.
Figure 2 shows, in this order, the impulse responses for a three variable VAR using (log)
real GDP, and for a four variable VAR including, besides inflation and interest rates (placed
the last), combinations of (log) real GDP, capacity utilization in the manufacturing sector
and a commodity price index. If we compare the results of Figures 1 and 2 we can inferred
several results: First, as Giordani claims, it seems true that including a measure of output
gap in the model instead of output helps to reduce the magnitude and persistence of the
price puzzle, as no impulse response graph in Figure 1 gives a response of prices so positive
as the one given in the left corner of Figure 2. Besides, including commodity prices in a four
variable VAR with output, inflation and federal funds rate (in this order, and commodity
prices placed second) reduces the puzzle in a similar way as including the output gap in
it. Finally, including commodity prices and output gap together in the four variable VAR
reduces further the magnitude of the puzzle to the point where the response of prices is
initially almost zero.
Figure 2.
Impulse responses of INF to a tightening monetary policy shock under a three variable VAR
with GDP, a four variable VAR with GDP and commodity prices, a four variable VAR with GDP and
capacity utilization in the manufacturing sector and a four variable VAR with capacity utilization in the
manufacturing sector and commodity prices.
16

However, the second conclusion emerges from the fact that we are using the measure of
output gap that helps to reduce the puzzle the most, i.e., the one Giordani (2004) used. If
we try instead to include in the four variable VAR the other measures of output gap (i.e.,
do the same as for the third graph of Figure 2 but with the other measures of output gap),
we find that (not shown) the reaction of prices is in general signicantly positive and more
persistent, in line with the results of Figure 1. Hence we conclude that although it seems
certain that including output gap in the model helps to alleviate the problem, it does not
solve it. Furthermore, the inclusion of commodity prices continues to be useful to solve the
problem, and containing useful information of the output gap, as Giordani (2004) claims,
does not seem to be the reason for it.
3.2.1 Sub-sample analysis
We have already mentioned several times that various papers have pointed out that
the price puzzle is stronger and not solved even using commodity prices in the pre-Volcker
period. 12
Therefore, studying how the different measures of output gap behave in that
period is a natural next step.
12 See, e.g., Balke and Emery (1994), Barth and Ramey (2001), Hanson (2004), Castelnuovo and Surico
(2006) and Belaygorod and Dueker (2007).
17

Figure 3. Impulse responses of INF to a tightening monetary policy shock under different measures of
output gap. The words in brackets indicate if the measure of output gap was calculated using a linear trend
(lt), quadratic trend (qt) or the Hodrick-Prescott (HPt) filter. Sample goes from 1949Q1 to 1979Q4, but
some variables start after 1949.
Figure 3 shows the same impulse responses as Figure 1 but for the pre-Volcker subsample
(1949Q1 to 1979Q4). The results confirm that output gap in the three variable VAR does
not solve the price puzzle as the increase in prices after the contractionary monetary policy
shock is significantly positive for all the measures of output gap except the ones built with
capacity utilization and industrial production: electric and gas utilities. However, the series
for these four variables do not start until 1970 (1972Q1 for CU and IP: E&G utilities (lt
18

and qt), and 1967Q1 for TCU), so their impulse responses could be affected by the small
number of observations. Therefore, Giordani’s suggestion is not enough to solve the puzzle.
When checking similar combinations to the VAR specifications of Figure 2 (not shown),
we confirm that the price puzzle also emerges for this period even including commodity
prices in the VAR. In addition, two further results emerge.
First, that including output
gap instead of output improve the impulse responses making the positive reaction
of prices less strong and persistent.
And, more important, that the inclusion of both
commodity prices and output gap seems to improve further the response of prices (using
capacity utilization as output gap, the results are similar to the ones for the entire
sample, i.e, similar to the fourth graph of Figure 2).
This suggests that, for the time
being and from the misspecified point of view, the best way a researcher has to avoid the
price puzzle is to include in his VAR specification both commodity prices and the output gap.
Finally, when analysing the 1980Q1 to 2008Q4 sub-sample, we find (again not shown
here, but available upon request) that the price puzzle, as Giordani (2004) claims is generally
solved by including output gap in the VAR. Interestingly, using capacity utilization the
reaction of prices is barely positive (and not significant), but using some of the other
measures of output gap the initial response of inflation is negative.
4 Conclusion
This paper has surveyed the price puzzle (i.e., the positive reaction of inflation to a
tightening monetary policy shock), an important stylized fact discovered by Sims (1992).
From the large number of ways proposed to solve the phenomenon, we have clasified them
in three groups: the misspecified view, the cost channel explanation and the indeterminacy
19

path, and reviewed the main and latest papers of each.
Inside the misspecified explanation of the puzzle, Giordani (2004) has proposed a new
way to solve it: to include in the VAR the output gap instead of output.
To check the
robustness of his results, we have constructed up to sixteen different measures of output
gap and have obtained that, although including the output gap rather than the output is a
good practice (which should be done just because it is implied by the theory), it does not
completely solve the puzzle. Furthermore, commodity prices still seem to be a good variable
to include in the VAR if we want to mitigate the problem, and, for the pre-1979 period, the
puzzle is reduced, but does not disappear at all.
Hence, our findings strongly suggest three things: one is that include output gap instead
of output in the empirical models should become a standard practice in studying monetary
policy and its effects. In addition, including both commodity prices and a measure of output
gap in the VAR specification seems to be the best way we have to avoid the problem. On
the other hand, the price puzzle seems to be a fact still present and hence further research
is needed. Commodity prices, as now the output gap, are variables that help to mitigate the
problem, but does not make it disappear, so the misspecified view should try to find out why
this occurs and how it can be solved analytically and empirically. The indeterminacy path
seems to be a good way to follow, but, as the advocators of the cost channel solution, they
should explain why commodity prices help to solve the puzzle. This last point is important,
as the role that commodity prices plays in theoretical models has not been well explained
yet. Finally, the Bache and Leitemo (2008) proposition of distinguish between permanent
and transitory shocks seems also to be a good framework for future research.
20

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