UNIVERSITY OF CALIFORNIA, SAN DIEGO
BERKELEY  DAVIS  IRVINE  LOS ANGELES  MERCED  RIVERSIDE  SAN DIEGO  SAN
FRANCISCO
Wouter J. den Haan
Department of Economics - 0508
(858) 534-0762 (-7040 fax)
[email protected]
UCSD
SANTA BARBARA  SANTA
CRUZ
9500 GILMAN DRIVE
LA JOLLA, CALIFORNIA 92093-0508
August 12th 2002
Professor Harold Uhlig
Dept. of Economics
Humboldt University
Spandauer Str. 1
10178 Berlin
Dear Harold,
Enclosed is the revision of my paper with Steven Sumner “The comovement between real
activity and prices in the G7,” 2001-039. We thank you and the referees for the constructive comments.
Several of your concerns were caused by a communication failure. For example, your main concern
seems to be a lack of standard errors. To avoid clutter we had used a somewhat unusual approach (open
and filled-in symbols) to indicate the significance levels instead of the usual error bands. The revised
text and the new graphs hopefully reveal more directly that many of the negative correlation coefficients
found are overwhelmingly significant.
One of the three referees1 seems very assertive. It is clear that when you write a paper on a topic
like the correlation between prices and real activity you are bound to step on someone’s toes, even if you
tread carefully. Being clear in the revision about the purpose of the paper has hopefully alleviated an
important part of this referee’s concern. But this referee also takes issue with using an “aggregate
approach” with which we presume he means the popular procedure to evaluate dynamic stochastic
models by comparing key moments of the model to their sample counterparts. The referee’s statement
that “…, an aggregated approach as taken in the paper does not reveal anything about a theory on
business cycle fluctuations [emphasis added by us]” basically makes all papers that try to match real
business cycle moments or other moments, for example, the Sharpe ratio, irrelevant. We think our
empirical findings are interesting whether or not they are explicitly used to evaluate models. The
possibility of using the proposed statistics for the purpose of evaluating models is worth pointing out,
however, since Den Haan (2000) shows that the negative correlation of forecast errors does provide
powerful identifying information. We, therefore, respond to this referee’s concern expressed in part 1.d,
but if the frequent use of this procedure in the literature has not convinced him then we doubt whether
we will change his views.
1
The referee whose report starts with “The paper studies … .”
Another troubling issue with this referee is the following. We clearly point out in the paper that
the economic motivation behind the proposed statistics can be found in Den Haan (2000). We find it,
therefore, somewhat insulting to be told by the referee that “… the authors know … little about
economics” and we are actually somewhat surprised you passed this report along without a modifier,
especially since the referee doesn’t bother to address any of the issues raised in Den Haan (2000).
We are grateful that you put in the effort to find two new energetic referees when the first-round
referees were not responding and for then promptly making a decision yourself. Since Steve is on the job
market this coming year, it would be great if the EER could beat the first-round turnover time.
Sincerely,
Wouter J. den Haan
PS After December 1st 2002 my address will be
Department of Economics
London Business School
Regent's Park
London
NW1 4SA
UK
The Comovements between Prices and Economic Activity in the G7
Response to the Editor
I. VAR specification: You seem concerned with pretesting for unit roots (and possibly
also with using model selection criteria). We definitely agree with you that the point of
our method is that it is a simple one and works regardless of the degree of integration or
whether cointegration is present. Although we don’t think of what we do as “bizarre”, we
agree that it may seem illogical to implement this procedure as careful econometricians
using established techniques to find a specification that will provide the most precise
estimates. We, therefore, now present in the paper the results based on a VAR in levels
with simply one year worth of lags, a linear trend, and a quadratic trend. In the
accompanying note we also show the results when you impose a unit root and when you
use AIC to choose a more parsimonious VAR specification. You’ll be happy to see that
the results are virtually identical across specifications. Therefore, we have decided to
report the striking similarity in the paper but not to include the additional graphs in the
paper itself.2 You are probably correct that the results are much more convincing if
presented in this manner and we are grateful for your suggestion. Also, we have now
discussed in the text the details of the estimated VAR specification.
II. Standard errors: Again the news is good. Significant negative coefficients are found for
virtually every estimated VAR. To avoid clutter we had used a somewhat unusual
approach (open and filled-in symbols) to indicate the significance levels and apparently
not given the significance levels enough emphasis in the text. Now, the significance
levels are given more emphasis in the text and the legends in the graphs reveal directly
the meaning of the symbols and the significance of the negative coefficients.
Also note that, unlike Den Haan (2000), we do not calculate correlation
coefficients from the actual forecast errors but use the moments that are implied by the
estimated VAR. This means that your concern about a small number of overlapping
intervals is less critical. For example, the unconditional covariance of two stationary
series corresponds to the covariance of the infinite-horizon forecast errors. A finite
sample doesn’t even contain one single infinite-year-period. Nevertheless, it is still
possible that the estimate of the covariance of the infinite-horizon forecast errors implied
by the estimated VAR is very accurate.
III. Robustness: In the accompanying note we show that the results are robust for different
VAR specifications for all 7 countries. We also show that the results are robust when you
include the wage rate or when you use the producer price index instead of the consumer
price index. Since the results are so similar and the note is made available on the web, we
just discuss the similarity in the text and do not include the graphs. Moreover, in my JME
paper I show (for the US) that the results are robust when you estimate a VAR that also
includes an interest rate, total reserves, and the ratio of non-borrowed to borrowed
reserves.
IV. Data and subsample stability: Both for quarterly and for monthly data we now report
the results for the sample period from 1980 to 2001 and the results are similar. The
monthly data used are slightly updated to include the most recent data. For the quarterly
2
We mention in the paper that the note with the additional results is available on the web.
data we now report the results for the US and the UK. This has several advantages. First,
the US and the UK are the only two countries for which quarterly GDP data over the
period from 1960 are readily available to the public. In the earlier version we had used for
some countries data we received directly from staff members at the IMF. The data on the
most recent IMF data CD, however, had been revised and didn’t match the earlier data. If
you are concerned that any of the claims made above in I, II, or III doesn’t hold for our
old data set, then feel free to contact us and we’ll send you the results. Second, it
simplifies the exposition while with the monthly data we still make clear that the results
are robust across countries.
V. Frequency domain filters: We have drastically reduced the discussion on frequencydomain filters. However, we feel it is important enough to warrant a very short (one-page)
discussion on the appropriateness of frequency-domain filters when the underlying series
are integrated. We have done this for the following reasons.
1. I am not aware of any paper in the literature that shows that frequency-domain
filters also take out the appropriate frequencies when the series are integrated.
Note that the point is not to show that the filtered series are stationary, which is
trivial. The point is to show that for integrated time series, the filtered series also
have a spectrum equal to zero for frequencies outside the chosen band and a
spectrum equal to the original spectrum for frequencies inside the chosen band.
Given that the series used in our paper are clearly integrated it seems unscientific
not to explain why the properties of frequency-domain filters carry over to this
case.
2. This is especially important since as pointed out by one referee “… this clearly
has confused the profession” and we feel the need to defend ourselves against the
claims sometimes found in the literature that frequency-domain filters can not be
used for integrated series. We agree with you that this is a side issue in our paper,
but we also agree with the other referee that there is some methodological
contribution that is worthwhile for the profession. For example, our analysis
shows that the transfer functions plotted in the working paper version of your
paper with Morten Ravn on adjusting the HP-filter are still valid when the
underlying series are integrated.
I have searched long and hard in the literature without finding a discussion on this
issue. Nevertheless, I don’t think the idea in our paper of using limits to show the results
carry over to integrated series is completely unknown. I have spoken extensively with
Clive Granger about this issue and he thinks he has seen it somewhere else before,
although he doesn’t know where. Given that there is some confusion in the literature,
however, it seems to us that it would be useful to have a reference for this result in the
literature. If you still think the discussion takes too much space, maybe you will consider
letting us put it in the appendix.
VI. Canova-de Nicolo: We now reference this paper. We don’t think the paper relates
closely to our work however, because their paper still imposes theory-based restrictions to
compute correlation coefficients. Canova and de Nicola suggest that their restrictions are
very weak but I am not so sure about that. For example, if the responses for prices are
hump-shaped the predictions for inflation wouldn’t necessarily be consistent with the
intuition you obtain from the standard undergraduate textbook. Canova and de Nicola
study a simplified version of the shopping time model from my 1990 JME and 1995
JEDC paper, but I know the properties of this model well enough to know that there is no
way this model can replicate the statistics reported in our paper when “demand” shocks
dominate “technology” shocks. One other concern we have with this paper is that except
for Japan the authors only use one lag in the estimated VAR. It is hard to believe that with
monthly data you can capture the dynamics accurately with only one lag.
The Comovements between Prices and Economic Activity in the G7
Response to the referee whose report start with “The paper studies”
1a. Purpose: The purpose of our paper is to show that a particular set of statistics, that we
believe has powerful identifying information, has very similar values for different
countries.3
1b. Usefulness: The usefulness of this set of statistics has, in our opinion, been shown in
the 2000 JME paper of Den Haan. The argument in that paper is the following. Cooley
and Ohanian (1991) show that the correlation between HP-filtered prices and real activity
is negative in the postwar period. In response, several papers including Ball and Mankiw
(1994) and Chadha and Prasad (1993), Judd and Trehan (1995) argue that this empirical
finding is consistent with a popular model of sticky prices that only has demand shocks.
Den Haan (2000), however, shows that this model with only demand shocks is not
consistent with the observed negative correlation between price and output forecast
errors.
We want to point out that our statistics provide a description of the data just as
statistics like, for example, the observed equity premium and the Sharpe ratio. The
relevant question is whether a model is consistent with the particular values of the
statistics or not. We don’t see why the possibility that the statistics are “contaminated by
other factors” reduces the need for any proposed theory to match these observed finding.
1c. Need for theory and intuition: In our opinion, the proposed statistics only provide
explicit implications on business cycle fluctuations if one also writes down a model. But
conditional on a model they provide very powerful information, as was shown in Den
Haan (2000). We, therefore, do not agree with the referee’s statement that “…, an
aggregated approach as taken in the paper does not reveal anything about a theory on
business cycle fluctuations” [emphasis added by us]. In addition, we think that the
proposed statistics are intuitive in the sense that they can suggest important insights to the
researcher who wants to develop models that fit the data better. For example, unlike the
traditional statistics, the VAR methodology does reveal some positive correlations for
several samples.
1d.Using “stylized facts” to evaluate models: The referee says the following: “The wage
explosion in the late 1960’s and the beginning of the 1970’s generated stagflation. In the
real business cycle framework this would have been interpreted as a negative technology
shock although the source of the shock was a series of adverse supply shocks. Hence, an
aggregated approach as taken in the paper does not reveal anything about a theory on
business cycle fluctuations.” First of all we want to point out that our empirical findings
are interesting whether or not they are explicitly used to evaluate models. As pointed out
above, they are a description of the data and provide useful information to anybody who
takes data seriously. If the referee means that it is possible that two theories can have the
same implications for a particular set of correlation coefficients then that is, of course,
possible. That is not only possible for the statistics proposed here but is true in general
when one uses the standard practice of matching a limited set of moments. But as we
3
Moreover, these estimates are robust across different VAR specifications and across different subsamples.
pointed out in the earlier version, maximum likelihood estimation techniques are typically
not feasible for dynamic stochastic equilibrium models.4 In fact, part of the motivation of
the proposed statistic is to alleviate this problem also recognized by Hansen and
Heckman, who in their 1996 Journal of Economic Perspectives article point out that by
considering a full set of statistics that captures the dynamics of the time series the
identifying power increases.
Of course, there may be a better alternative to evaluate dynamic stochastic
macroeconomic models. As Geweke (1999) points, however, the desire in modern
dynamic macro economics to incorporate the effects of stochastic shocks on agents’
policy rules, makes it ridiculous to just add regression error terms to the theoretical
behavior rules, which in turn means that maximum likelihood estimation is not possible.
Testing models using over-identifying restrictions with GMM estimation techniques also
hasn’t been very successful. Some progress has been made with Bayesian methods but
these are not that simple to implement.
More importantly, there is a solution to the problem the referee brings up.
Standard procedure in such a case is to look at additional statistics. In this particular
example about wage inflation, the obvious statistics to look at are the correlations
between real wages and output and the correlations between real wages and prices. The
results of these additional statistics are reported in Figure A3.2 in the accompanying note.
The graph shows that the correlation between real wages and output is positive and the
correlation between real wages and the price level is negative! We were actually stunned
by these findings ourselves. In fact, I investigated this issue in a version of the matching
model used in the 2000 AER paper with Garey Ramey and Joel Watson. In this model an
increase in the bargaining weight leads to an increase in real wages and a decrease in
output. A reduction in money demand would then lead to an increase in the price level.
This seems consistent with the view of the author. But as documented in the graphs and
to our surprise, this story is not consistent with the data. In fact, the data seem to be
consistent with a standard RBC model in which an increase in productivity increases
wages and output while putting downward pressure on prices. We are not sure whether
these results are robust or whether we used the best wage series, but since the two
theories imply different correlations, there apparently is important identifying information
in the type of aggregate statistics used.
1.e Summary: We hope to have alleviated the referee’s concerns by being more clear in
the revision about (i) the purpose of our paper and (ii) the identifying power of statistics
like ours, that carefully incorporate dynamic aspects of time series.
2. Stability: The referee writes: “The recent low inflation suggests that we may have
entered a new era where output and prices may start to be positively related. I therefore
feel that it is not a general economic law that has been found in the paper.” We agree
that no general economic law has been found and we now point out in the paper that the
time series behavior of prices and output was substantially different in the prewar period.
When we repeat our exercise for the period from 1980 to 2001, however, we still
typically find negative and significant correlations between forecast errors, both for
quarterly and monthly data. The correlation between filtered prices and output is
We followed one of the other referee’s suggestion to take the discussion on this issue out because it is in his opinion well known. See
Geweke (1999) for a detailed discussion.
4
somewhat less negative in some countries. Note that the productivity increases observed
during the 1990’s are often believed to have increased output and kept inflation low,
which could be the cause for a continued negative relationship. If the referee has any
empirical evidence that we have entered a new era where output and prices may start to
be positively related then, of course, we would be interested in receiving this.
3. More on purpose: We have rewritten the introduction to be hopefully more clear about
the purpose of our paper. The referee says that it is not entirely clear which casual
relationship is of interest—is it the influence of output on prices or vice versa? Obviously
it would be nice to have statistics that reveal everything. Given that the proposed set of
statistics is already capable of showing that a particular set of models previously believed
to be consistent with the data is not consistent with the data, the proposed statistics
already provide some useful information even if they don’t reveal everything we would
like to know.
4. We agree that the statement “any theory in which procyclical prices figure crucially in
accounting for postwar business cycle fluctuations is doomed to failure” is somewhat
harsh and we have eliminated it even though we don’t see how the presence of often
insignificant positive coefficients at some short forecast horizons should not be a warning
against models in which procylical prices figure “crucially”.
5. We would love to include more economic intuition but agree with the editor that it is
better to focus on the novel contributions. We make it clear in the paper that more
economic intuition and motivation can be found in Den Haan (2000). Therefore, we find
it somewhat insulting that the referee writes that ‘… the authors know … little about
economics,” especially since the referee doesn’t bother to address any of the issues raised
in Den Haan (2000). 5
6. In the accompanying note we show that the results are very similar when producer
prices are used instead of consumer prices and we mention this finding in the current
version.
7. The Cogley and Nason reference is now complete.
Reference:
Geweke, J.F., 1999, Computational experiments and reality, manuscript, University of Iowa.
5
Given that with 608 downloads it was in 2000 the second most-requested paper on Elseviers electronic journal database this article
cannot be too bad.
The Comovements between Prices and Economic Activity in the G7
Response to the referee whose report start with
“The paper makes two contributions …”
1. We have now included some more traditional information on the comovement
between prices and output in Section 2.
2. The advantage of using correlation coefficients is that the actual value is easy to
understand. The disadvantage is that it doesn’t make clear whether the comovement is
quantitatively important. We now also provide some information on the covariances,
which makes it possible to compare the levels at different forecast horizons.
The Comovements between Prices and Economic Activity in the G7
Response to the referee whose report start with
“This paper examines …”
Main concerns.
1. Length:
 As you can see, we have drastically reduced the length of the paper. At the
suggestion of the editor, we have not followed your advice to spend 2-3 pages on
frequency domain filters and non-stationary series, but have instead shortened this
discussion to 1 page. We have eliminated the section on stability.
 Den Haan (2000) gives a detailed comparison between the method used in our
paper and the multivariate Beveridge-Nelson approach used in the 1996 JME
article of Rotemberg (and the 1996 AER article of Rotemberg and Woodford), so
we have chosen not to repeat this discussion. Den Haan (2000) documents the
limitations of Rotemberg’s approach with the following example. Below we have
reproduced Figure 1 from Den Haan (2000) that presents the impulse response
functions of prices and output in economy 1 and economy 2. For simplicity
assume that in both economies the analyzed shock is the only stochastic driving
process. The two statistics considered by Rotemberg are then identical in both
economies, while the procedure used here clearly would reveal the crucial
differences between the two economies.
Figure 1 from Den Haan (2000): Two Economies with equal Rotemberg statistics.
A: Economy 1.
4
3.5
3
P
2.5
Y
2
1.5
1
0.5
0
0
2
4
6
8
10
time
12
14
16
18
20
B: Economy 2.
2
1.5
1
P
0.5
0
-0.5
Y
-1
-1.5
-2
0
2
4
6
8
10
12
14
16
18
20
time
2. Leads and Lags: The example in the referee’s report makes clear that there are
correlation measures of output and the price level that have positive values. Whether a
particular measure has a positive or negative value is in our opinion, however, of
secondary importance. The most relevant question is whether a particular statistic can do
a good job distinguishing between competing models. The sign of a comovement statistic
is obviously not completely unimportant because we are trained to intuitively associate a
particular sign with particular models or with the importance of particular types of
shocks.6 One has to be careful though to interpret the sign of a covariance when the series
has been filtered because it is difficult to understand how the trend removal affects the
dynamics of the residual. The first two panels of the following figure from Den
Haan (2000) plot the responses to a nominal demand shock for output and the price level
together with their HP trend levels using the sticky-price model of Den Haan (2000). The
bottom panel plots the deviations from trend.
6
A good example of a paper that uses this intuition is the paper by Canova and de Nicola (1999) that we now reference in the paper.
FIGURE 4 FROM DEN HAAN (2000): THE EFFECTS OF A NON-STATIONARY DEMAND SHOCK.
A: Impulse Response of the Price Level and its HP Trend.
1.6
1.4
1.2
1
HP-trend
0.8
0.6
0.4
0.2
0
0
5
10
15
20
25
30
25
30
time
B: Impulse Response of Output and the HP Trend Level.
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
5
10
15
20
time
C: Deviations from the HP Trend for Output and Prices.
0.80
0.60
0.20
Filtered Output (left-axis)
0.40
0.20
0.10
0.00
-0.20
-0.40
0.00
-0.10
Filtered Price Level (right-axis)
-0.60
-0.80
-0.20
0
5
10
15
20
25
30
time
Note: These figures plot the impulse response functions of the indicated variables in response to a demand shock when the demand shock is an integrated AR(1) with
2 = 0.5, the speed of adjustment parameter  = 0.05.
The referee writes the following: “It DOES seem to be the case that the maximum
absolute correlation is negative but this may not be strong evidence against the class of
models where prices do not react instantaneously to shocks to the economy. In particular,
the pictures [ in the referee report] may be consistent with a story where prices are
lagging output and where the length of the cycle is such that the contemporaneous
correlation between output and prices is negative.”
We absolutely agree with this statement. For example, if one would lead the price
response deviation from its trend in the lower panel one clearly gets a positive correlation.
But isn’t this just the point made by Ball and Mankiw (1994) and Chadha and Prasad
(1993) and Judd and Trehan (1995)? In fact these authors show that even negative
correlations of HP-filtered residuals are consistent with sticky-price models with only
demand shocks. The point made in Den Haan (2000) is that this class of model is not
consistent with a negative correlation of forecast errors since a negative correlation of
forecast errors means that the product of the accumulated response for output with the
accumulated response for the price level is negative.
Of course, if the VAR is misspecified and missing some important complicated
dynamics then the results may be misleading. Given that the results are so robust across
specifications, however, and that no researcher has ever found that VARs more
complicated than the ones we use are necessary to capture the data, we are confident that
our VARs correctly capture the time series behavior of prices and output.
Smaller Comments
a. See the discussion above on Rotemberg’s statistics.
b. We have used the terminology “short-run” and “long-run” less and have defined in a
footnote what we mean by these terms when the terms are first used.
c. We have drastically changed the way we present the results and hope that the current
graphs reveal better that we do report standard errors.
d. Done
e. Done
f. In response to your question how standard errors are calculated, we used Monte-Carlo
techniques to calculate the standard errors for the correlations of VAR forecast errors and
used the VARHAC procedure described in Den Haan and Levin (1997) to calculate
standard errors for the correlation coefficients of filtered data.