Journal of the Japanese and International Economies 14, 304–326 (2000) doi:10.1006/jjie.2000.0451, available online at http://www.idealibrary.com on

Output-Inflation Trade-Off at Near-Zero Inflation Rates Kenji Nishizaki Research and Statistics Department, Bank of Japan

and Tsutomu Watanabe1 Institute of Economic Research, Hitotsubashi University Received February 11, 2000; revised August 3, 2000

Nishizaki, Kenji, and Watanabe, Tsutomu—Output-Inflation Trade-Off at Near-Zero Inflation Rates The purpose of this paper is to provide new evidence about the cost of near-zero inflation using Japanese data. We test the hypothesis that the short-run Phillips curve becomes flatter as the rate of inflation approaches zero. In implementing the test, we pay special attention to how to control for other factors affecting the rate of inflation. First, we use the skewness of the distribution of relative-price changes as a measure of supply shocks. Second, we use information contained in the cross-prefecture Phillips curve to control for changes in the expected rate of inflation. Through a series of empirical analyses, we find evidences consistent with the hypothesis. In particular, we find that the estimated slope in the 1990s is smaller than before. J. Japan. Int. Econ., December 2000, 14(4), pp. 304–326. Research and Statistics Department, Bank of Japan and Institute of Economic Research, Hitotsubashi University. °c 2000 Academic Press Journal of Economic Literature Classification Numbers: E31, E50. Key Words: short-run Phillips curve; output–inflation trade-off; near-zero inflation; downward rigidity of nominal wages; menu costs.

We thank Larry Ball, Christopher Carroll, Fumio Hayashi, Steve Kamin, Nikolas Panigirtzoglou, Eric Rosengren, Katsunori Watanabe, and a referee for helpful discussions and comments. The views expressed herein are those of the authors and not necessarily those of the Bank of Japan or Hitotsubashi University. 1 Correspondence should be addressed to Institute of Economic Research, Hitotsubashi University, Kunitachi, Tokyo 186-8603, Japan. Fax: 81-42-580-8333; E-mail: [email protected]. 304 0889-1583/99 $30.00

c 2000 by Academic Press Copyright ° All rights of reproduction in any form reserved.

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1. INTRODUCTION The Japanese economy has been experiencing disinflation since the beginning of the 1990s when the bubble in stock and land prices burst. For example, yearto-year inflation rates measured by the Consumer Price Index have been gradually declining since the first quarter of 1991. CPI inflation rates were negative in the second and third quarters of 1995, and were in the narrow range of 0 to 1% in 1996 and 1997.2 More recently, year-to-year CPI inflation rates have been negative since the third quarter of 1998. In addition, the rate of wage inflation has been negative since early 1998. Looking back at the movements of the Japanese CPI inflation rates in the postwar period, we find that near-zero inflation rates are a very rare phenomenon. During only three years were the inflation rates negative, namely 1950, 1955, and 1958. For these three years, however, it was commonly observed that inflation rates increased again soon after they recorded negative values. The present situation is different from these instances in that inflation rates have been staying at a near-zero level for about five years and there are no indications of it increasing. Moreover, it is difficult to find a comparable example in the experiences of other industrial countries during the postwar period. For example, the German economy experienced negative rates of inflation at the final stage of the hyperinflation, but it was just a one-year event.3 Researchers often point out that the Japanese inflation rates are too low. Their argument is based on the following cost–benefit analysis of low inflation.4 That is, it is no doubt that high inflation, say 100% a year, deteriorates the national welfare. In such a situation, a reduction in the rate of inflation to, say 10%, would significantly improve the national welfare. However, applying the same argument to the case of reducing inflation from 3% to zero is misleading. This is because the marginal benefit of reducing inflation is decreasing as the starting rate of inflation becomes lower. For instance, the shoe-leather costs in an economy with 3% inflation are negligible and significant reductions cannot be expected, even if the inflation rate were reduced to zero. On the other hand, there is enough reason to believe that the marginal cost of disinflation increases as the starting rate of inflation becomes lower. For example, if downward rigidity in nominal wages exists, the slope of the short-run Phillips curve becomes smaller as the inflation rate approaches zero. Combining the two, the marginal cost of reducing inflation exceeds the marginal benefit at some positive rate of inflation, and therefore,

2

CPI inflation rates increased in April 1997, when the consumption tax rate was increased by 2%. The description in the text is based on the figure that is adjusted for this effect. See the Bank of Japan monthly report for adjusted figures. 3 Going back to the interwar period, persistent near-zero inflation was an everyday event; even persistent declines in the price level, deflation, were not a rare phenomenon. Given the difference in the currency system, particularly the international currency system, however, a simple comparison would be misleading. 4 See, for example, Fischer (1996), Krugman (1996), and Akerlof et al. (1996).

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near-zero inflation is not worth pursuing.5 The above argument is not easy to accept by central bank officials with strong beliefs that the price stability is, by definition, zero inflation.6 Moreover, the discussion continues about whether zero inflation is worth pursuing or not.7 In many empirical studies, it is interesting that the cost and benefit of nearzero inflation is attempted to be measured without using data obtained from the economy when near-zero inflation exists. Some relationship between inflation and other variables is sought using the data of high- or medium-inflation periods, from which it is inferred what would happen if the inflation rate approaches zero.8 Given that industrial countries except Japan have never experienced periods of near-zero inflation, such an approach is inevitable but not recommended. The purpose of this paper is to provide new information about the cost and benefit of zero inflation using Japanese data from 1970 to 1997. The 1990s is not a shining period for the Japanese economy, but it might be a very important period from the viewpoint of constructing a data set suitable for the cost–benefit analysis of zero inflation. Our interest in this paper is in the costs of disinflation at near-zero inflation. More specifically, we are interested in whether the relationship between the rate of inflation and the slackness of the economy, the short-run Phillips curve, depends on the level of inflation rates. We would like to test the hypothesis that the short-run Phillips curve becomes flatter as the rate of inflation approaches zero. Figure 1 compares the sacrifice ratio, defined by the cumulative deviation of real GDP from trend divided by the cumulative declines in CPI inflation, in three periods of disinflation: mid-1970s, early 1980s, and 1990s. The sacrifice ratio of the 1990s is clearly much larger than the ratios of the other two periods. This evidence is consistent with the above hypothesis that the short-run Phillips curve becomes flatter as the rate of inflation approaches zero, but how strongly does this support the hypothesis? One of the most important procedures in implementing the above test is to properly control for other factors affecting the rate of inflation. For example, the fluctuations of oil prices must be controlled for. Another example is an increase in the Japanese imports of labor-intensive products from the east-Asian economies in the first half of the 1990s. Inflow of these goods led to a change in their relative prices in the Japanese markets and, consequently, to a decline in the Japanese CPI 5

Another argument against zero inflation is that it weakens the ability of central banks to stimulate an economy by creating a negative real interest rate. See Summers (1996) for this argument. The zero lower bound on nominal interest rates is studied further by Orphanides and Wieland (1998) and Reifschneider and Williams (1999), among others. 6 For example, Kunio Okina, Director at the Bank of Japan, mentions the fact that “consumer prices have been stable” as one of the reasons why he is against the adoption of a positive inflation targeting in Japan (Okina, 1999). Given that year-to-year CPI inflation rates at the time of his writing were 0.3 (1999:2Q) and 0.0% (1999:3Q), it seems that he defines price stability as zero inflation, as measured by the CPI. 7 Yates (1998) provides a good summary of the discussion. 8 As far as we know, an exception is Yates (1998), which studies the shape of the Phillips curves in the United Kingdom and other countries, using data from 1800.

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FIG. 1. Sacrifice ratio.

inflation rates. These are the examples of supply shocks that should be controlled for when estimating the Phillips curve. In previous studies, particularly those on the Japanese economy,9 researchers have used import-price inflation as a proxy for supply shocks. Import-price inflation is a good proxy for supply shocks if they come from foreign economies, but fails to work properly when shocks originate domestically. For example, some researchers point out that the inflow of laborintensive products has improved the productivity of Japanese firms through price competition with the east-Asian firms, thereby contributing to disinflation in the mid-1990s. This type of supply shock is hard to detect as long as we use importprice inflation. In this paper, following the proposal by Ball and Mankiw (1995), we use the skewness of the distribution of relative price changes as an alternative measure of supply shocks. Changes in the expected rate of inflation are also an important factor causing shifts in the short-run Phillips curve. Given the lack of an explicit measure for expected inflation, however, it is hard to control for this directly. Our empirical strategy for this problem is to use a panel data set of inflation rates and active opening rates. The latter rate is defined as the ratio of job offers to applicants, which is observed for 46 prefectures from 1971 to 1997. First, we transform the observed values of these two rates by subtracting the appropriate national averages. 9

Yoshikawa (1995) provides a useful survey of empirical studies on the short-run Phillips curve in Japan.

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In this way, we remove the effects of nationwide shocks, which include changes in expectations about the future course of monetary policy conducted by the central bank. By using the transformed panel data, the estimated slope of the short-run Phillips curve should be free from any bias caused by uncontrolled nationwide disturbances. The rest of the paper is organized as follows: Section 2 provides brief overviews of theories and empirical evidences about the relationship between the slope of the short-run Phillips curve and the level of inflation rates. Sections 3 and 4 explain the data and our empirical strategy. Section 5 shows the results of the empirical investigation. Using data on the CPI and wage inflation rates, as well as active opening rates, we find that the slope of the short-run Phillips curve becomes flatter as the rate of inflation approaches zero. This relationship holds even when we control for supply shocks and expected inflation. Section 6 presents our conclusion.

2. THEORIES AND EVIDENCE OF A NONLINEAR SHORT-RUN PHILLIPS CURVE 2.1. Two Theories of a Nonlinear Short-Run Phillips Curve Two sets of theories are related with the hypothesis that the slope of the shortrun Phillips curve becomes smaller as the rate of inflation approaches zero. The first set involves several theories concerning the so-called downward rigidity of nominal wages. For example, Keynes argues that if individual workers sought to maximize their returns relative to others (not just their own returns), workers would not accept a wage cut if they were uncertain whether other workers would face similar cuts. There are numerous studies based on this idea, including Tobin (1972). If nominal wages are downwardly rigid, then disinflation that starts from a low rate of inflation requires greater increases in unemployment. Therefore, the short-run Phillips curve becomes flatter as the rate of inflation approaches zero. The second line of theoretical research starts with Ball et al. (1988).10 They consider an economy where firms face a menu cost of price adjustments. In this economy, the higher average inflation is, the more often firms must adjust their prices to keep up with the price level. This implies that when there is an aggregate demand disturbance, firms can pass it into prices more quickly. Thus, its real 10 The Lucas imperfect-information model is also related with our interests. The Lucas model predicts that output-inflation trade-off is negatively related with the variance of aggregate demand shocks; namely, the slope of the short-run Phillips curve is steeper in an economy where the variance of aggregate demand shocks is greater. If a high inflation environment tends to accompany large variance of aggregate demand shocks, the Lucas model implies a positive correlation between the average inflation rate and the slope of the short-run Phillips curve. See Lucas (1973) for cross-country evidence of this model.

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effects are smaller. On the other hand, at near-zero inflation rates, the interval between price adjustments is longer because firms are reluctant to pay even small costs of adjustments. In this situation, an immediate consequence of a negative demand shock appears as a reduction in outputs, with almost no effect on prices. In other words, the short-run Phillips curve is flatter at near-zero inflation rates. Ball et al. (1988) test this prediction using a cross-section of 43 countries and find a statistically significant negative relationship between output–inflation trade-off and average inflation. Defina (1991) and Yates and Chapple (1996) confirm the robustness of the Ball et al. result. The above two items of research differ in two important respects. First, according to the hypothesis of downward nominal wage rigidity, nonlinearity of the Phillips curve is observed in wage inflation as well as price inflation. On the other hand, the Ball et al. hypothesis says that nonlinearity should be observed only in price inflation. Second, the hypothesis of downward nominal wage rigidity implies that nonlinearity of the Phillips curve is observed only in the neighborhood of zero inflation. In contrast, the Ball et al. hypothesis implies that nonlinearity should exist everywhere and that the slope of the Phillips curve should continuously decrease as the rate of inflation approaches zero. 2.2. Empirical Evidences of a Nonlinear Short-Run Phillips Curve Nonlinearity (or linearity) of the short-run Phillips curve has been the focus of numerous empirical studies. For example, Clark et al. (1996) find that the U.S. inflation-output is nonlinear, using quarterly data from 1964 to 1990. Also, Laxton et al. (1995) show that if one assumes that the Phillips curve is identical in each of the G-7 economies, then there is fairly strong evidence of nonlinearity. However, relaxing this identification restriction, Turner (1995) concludes that the Phillips curve is nonlinear in the United States, Japan, and Canada but linear in the other four countries. In addition, Gordon (1994) claims that there is no evidence of nonlinearity in the U.S. data. In addition to the above studies, there are a few empirical works focusing on the nonlinearity of the short-run Phillips curves in low inflation economies. Card and Hyslop (1997), looking at the cross-state Phillips curve using U.S. data, find that the Phillips curve is steeper when inflation is high, but that this relationship is imprecisely estimated and thus statistically insignificant. Additionally, de Kock and Ghaleb (1996) provide evidence from across-country comparison that lowering inflation from moderate levels is proportionately more costly than lowering it from higher levels.

3. DATA Our data set consists of three measures of inflation rates and a measure of the slackness of the economy. Inflation rates are measured by (i) year-to-year inflation

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rates of the CPI, (ii) year-to-year inflation rates of nominal wages per worker, and (iii) year-to-year inflation rates of nominal wages per hour. By looking at both price inflation and wage inflation, we hope to be able to identify the cause of the nonlinearity in the Phillips curve, if it is detected. The series of the CPI we use is the 1995-base index calculated by the Management and Coordination Agency of the Japanese government. The series of wages, both per-worker and per-hour, are taken from the Monthly Labor Survey, conducted by the Ministry of Labor.11 We use total cash earnings, the sum of scheduled cash earnings, and special cash earnings as a measure of wages and total hours worked as a measure of working hours. Slackness of the economy is measured by the active opening rate, which is the ratio of job offers to applicants. The data on the active opening rate used in this paper are part of the Employment Referral Statistics, which are collected by about 600 public employment security offices, intermediaries between employers and job applicants, located all over the country, and released by the Ministry of Labor. The active opening rate captures cyclical movements in labor markets better than the unemployment rate, which is significantly affected by changes in structural unemployment (i.e., unemployment caused by a technological change or a shift in people’s tastes toward new products). In terms of the statistical coverage, however, the unemployment rate is preferable to the active opening rate. We use the active opening rate as a measure of the slackness of the economy because alternative measures, such as the unemployment rate, are not available by prefecture. We denote the CPI inflation rate in prefecture i at time t by πit ,12 inflation rates of wage per person by ω1it , inflation rates of wage per hour by ω2it , and the active opening rate by xit . We have balanced panels for these four variables for 46 prefectures,13 from 1971 to 1997. Table 1 presents descriptive statistics for our data. Several things are noteworthy. First, the standard deviation of inflation rates over time (0.053) is larger than that over cross-sections (0.005). Second, the standard deviations of wage inflation over cross-sections are much larger than those for CPI inflation. The standard deviations of ω1 and ω2 are, on average, 0.020 and 0.021, while the corresponding value for π is 0.005. This may reflect the difference in the degree of arbitrage across prefectures. That is, a large part of the components of the CPI are tradable goods; therefore arbitrage across prefectures works well, while the mobility of workers across prefectures is limited, at least in the short run. Third, there exists a tendency, for all of the four variables, in which the standard deviation is large in a year when the mean is high. Thus, the coefficient of variation, the standard deviation divided by the mean, is stable over time. 11 The survey covers about 16,700 establishments with 30 or more regular employees, and the sample is replaced every three years. 12 To be more precise, π represents the CPI inflation rate in the city with prefectural government it of prefecture i. 13 Excluding Okinawa prefecture, for which complete data, from 1971 to 1997, are not available.

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TABLE I Descriptive Statistics, 46 Prefectures, 1971–1997

CPI inflation Standard deviation

Wage inflation (per worker) Mean

Wage inflation (per hour)

Active opening rates

Standard Standard Standard deviation Mean deviation Mean deviation

Year

Mean

1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997

0.060 0.046 0.121 0.244 0.116 0.091 0.079 0.037 0.036 0.082 0.049 0.024 0.018 0.023 0.021 0.004 −0.002 0.005 0.022 0.031 0.033 0.015 0.011 0.005 −0.004 −0.001 0.018

0.007 0.007 0.009 0.013 0.010 0.005 0.005 0.005 0.004 0.006 0.005 0.004 0.004 0.004 0.003 0.004 0.003 0.004 0.004 0.003 0.004 0.004 0.003 0.003 0.004 0.004 0.003

0.151 0.158 0.194 0.271 0.147 0.131 0.094 0.069 0.049 0.064 0.059 0.027 0.030 0.043 0.028 0.030 0.028 0.014 0.049 0.043 0.038 0.025 −0.008 0.021 0.019 0.021 0.021

0.014 0.014 0.038 0.025 0.023 0.028 0.015 0.012 0.024 0.010 0.010 0.026 0.013 0.008 0.021 0.013 0.011 0.034 0.011 0.017 0.028 0.013 0.031 0.018 0.018 0.036 0.017

0.163 0.161 0.201 0.317 0.168 0.112 0.094 0.067 0.040 0.067 0.063 0.029 0.028 0.033 0.036 0.033 0.025 0.013 0.060 0.063 0.056 0.048 0.020 0.025 0.019 0.018 0.029

0.013 0.015 0.041 0.025 0.023 0.029 0.016 0.013 0.026 0.011 0.009 0.028 0.015 0.008 0.025 0.012 0.010 0.035 0.013 0.013 0.030 0.011 0.031 0.018 0.018 0.042 0.032

1.194 1.254 2.009 1.318 0.621 0.666 0.574 0.578 0.726 0.757 0.681 0.606 0.596 0.667 0.694 0.628 0.685 0.988 1.223 2.088 1.584 1.257 0.910 0.781 0.755 0.817 0.838

0.845 0.833 1.385 0.807 0.263 0.296 0.242 0.239 0.308 0.326 0.291 0.259 0.254 0.304 0.318 0.268 0.273 0.377 0.457 0.767 0.552 0.422 0.288 0.251 0.236 0.240 0.255

Across-year values Mean 0.044 Standard 0.053 deviation

0.005 0.002

0.067 0.066

0.020 0.009

0.074 0.071

0.021 0.010

0.944 0.419

0.421 0.276

4. EMPIRICAL STRATEGY The Phillips curve equation we will estimate in the next section is defined by πit = (n t + ri ) + βxit + γ sit + u it ,

(1)

where n t and ri represent factors determining the location of the short-run Phillips curve, sit represents a measure of supply shocks, and u it is the disturbance term,

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assumed to be i.i.d. We call n t , which takes the same value across prefectures, the nationwide factor, and ri the regional factor. In the conventional interpretation of the short-run Phillips curve, the nationwide factor includes the so-called core inflation as an important component. Moreover, the core inflation is mainly determined by the expected inflation, which must be identical across prefectures because it is determined by the future course of monetary policy conducted by the central bank. Our task is to investigate the relationship between the level of inflation rates and the value of β. In particular, we are interested in whether or not the value of β declined in the 1990s when the rate of inflation approached zero. A problem we confront in estimating the relationship is that supply shifters, n t , ri , and sit , are not easy to observe. This is a serious problem because the estimator for β is biased unless these variables are controlled properly. It is the core of our empirical strategy to provide a remedy for this estimation bias. 4.1. Supply Shocks In the sample period, 1971 to 1997, oil prices and exchange rates were important determinants of the CPI inflation rates, so that import-price inflation could be a good proxy for this type of supply shocks. Other types of supply shocks that had significant downward pressure on the CPI inflation rates in the first half of the 1990s were: (i) inflow of labor-intensive products from the east-Asian economies; (ii) improvements in the efficiency of the Japanese distribution system; and (iii) a series of deregulations, such as the abolition of barriers to beef imports. These aggregate supply shocks had negative impacts on the CPI inflation rate in the period from 1992 to 1995, when the active opening rates, xit , were improving. This suggests the possibility that the variables sit and xit are negatively correlated. If this is the case, the estimated value of β would be biased toward zero, when estimated without controlling for these supply shocks. Our strategy to cope with these supply shocks is to use the skewness of the relative-price changes as a measure of aggregate supply shocks, following the proposal of Ball and Mankiw (1995). Suppose, for example, the inflow of laborintensive products from the east-Asian economies gives downward pressure on the relative prices of these goods. In this case, the actual distribution of relative prices is skewed to the left, and, consequently, measures of skewness have negative values. Measuring the skewness of the distribution in this way can be interpreted as a generalization of measuring changes in relative prices of particular goods, such as food or energy. In the next section, we use the following three measures for the skewness of relative price changes. The first measure is Z Skew =

∞

−∞

ν3 h(ν) dν, σ3

where ν is a relative price change in a specific product (that is, the rate of inflation

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in that product minus the overall CPI inflation rate), h(ν) is the density function for ν, and σ is the standard deviation of ν. The second measure is Z AsymX =

−x −∞

Z

∞

νh(ν) dν +

νh(ν) dν

x

which measures the mass in the upper tail of the distribution of relative price changes minus the mass in the lower tail. The tails are defined as relative price changes greater than X% or smaller than −X%. Note that AsymX is zero for a symmetric distribution, positive when the right tail is larger than the left tail, and negative when the left tail is larger. The third measure is: Z Q=

∞

−∞

|ν| · νh(ν) dν.

Note that the weight given to relative price changes increases linearly with the size of adjustments, while AsymX gives full weight to price changes above a cutoff and zero weight to other smaller price changes. Also note that Q is zero for a symmetric distribution, positive when the distribution is skewed to the right, and negative when it is skewed to the left. 4.2. Expected Inflation The conventional way to control for expected inflation, or more broadly n t , is to use a proxy. For example, we could use past inflation or long-term nominal interest rates as a proxy (see, for example, Clark et al. (1996) and Yates (1998)). The first half of the next section follows this line of research, but the rest adopts a different approach that takes full advantage of the panel data set, which is summarized below. We transform the observations of πit and xit as follows. First, we take the average over i for each term of Eq. (1) to get π¯ t = n t + r¯ + β x¯ t + γ s¯t + u¯ t ,

(2)

where variables with the overbar represent national averages. Next, by subtracting (2) from (1), we get πˆ it = rˆi + β xˆ it + γ sˆit + uˆ it ,

(3)

where πˆ it = πit − π¯ t , rˆi = ri − r¯ , xˆ it = xit − x¯ t , sˆit = sit − s¯t , and uˆ it = u it − u¯ t . The variables πˆ it , xˆ it , and sˆit represent the deviations of the current inflation rate, the active opening rate, and the supply shock, in prefecture i, from the corresponding national averages, respectively. Equation (3) tells us how much the inflation rate in prefecture i changes, relative to the national average, when the active opening rate in that prefecture deviates from the national average.

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An important point to note here is that n t does not appear in Eq. (3), so we do not have to worry about the observability of nationwide factors. In Eq. (3), we are looking at the movements of π and x only around the respective national averages, and therefore we are allowed to neglect the movements of nationwide factors themselves. To give an intuitive understanding about what is going on here, suppose there exist two types of shocks that determine the movements of π and x: nationwide shocks and regional shocks. Calculating the deviations of the two variables from their respective national average is equivalent to removing the movements of the two variables due to nationwide shocks. Thus, πˆ it and xˆ it in Eq. (3) represent responses of the two variables to regional shocks, and Eq. (3) describes the relationship between these responses. The methodology used here is the same as that used in the analysis of panel data to eliminate the estimation bias caused by the existence of omitted variables that are correlated with explanatory variables. That is, if the omitted variables fluctuate over time, but are constant over cross-sections, we can eliminate the estimation bias by either adding time-dummies or differencing the sample observations. In our example, the omitted variable is the nationwide factor, n t , which is unobservable and therefore omitted. Subtracting the national average from the observed variables has the same effects as the operation of differencing the sample observations.14

5. EMPIRICAL RESULTS In this section, we estimate the short-run Phillips curve following the empirical strategy described above. Depending on the focus of the analysis we will use three different kinds of data sets: aggregated time-series data, original panel data, and transformed panel data (i.e., all variables are expressed as deviations from the appropriate national averages). 5.1. Aggregated Time-Series Data As a point of departure, we try to control for supply shocks using aggregated time-series data. We regress CPI inflation rates, πt , on lagged CPI inflation rates, πt−1 , lagged active opening rates, xt−1 , and a measure of supply shock. To allow for the nonlinearity of the Phillips curve, we add lagged active opening rates multiplied by a dummy variable that takes the value one when the CPI inflation rate is below 3% and zero otherwise. If the short-run Phillips curve is nonlinear in that the slope depends on the inflation rates, the coefficient of the dummy term (lagged active opening rates multiplied by the dummy variable) should be different from zero. We use quarterly data from 1971:1 to 1997:4. 14

See Chapter 9 of Hsiao (1986) for more details on this methodology. Also, see Debelle and Lamont (1997) for an application of this idea in macroeconomics. An alternative way to estimate Eq. (1) is to use SUR (seemingly unrelated regressions), regarding n t + u it as a disturbance term with interprefecture correlation.

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TABLE II Nonlinear Phillips Curve Dependent variable = πt Independent variables Constant Active opening rates Dummy × active opening rates Import-price inflation

1 −0.0121 (−2.3117) 0.0298 (5.0305) −0.0129 (−2.9314)

Skewness

2

3

1. Threshold = 3% −0.0069 −0.0119 (−1.8731) (−2.2230) 0.0215 0.0300 (5.5165) (4.9398) −0.0097 −0.0127 (−2.8748) (−2.8652) 0.0355 (5.3269) 0.0998 (1.4310)

Asym 15

4

5

−0.0138 (−3.5344) 0.0269 (6.5471) −0.0087 (−2.3558)

−0.0142 (−2.8252) 0.0305 (5.4136) −0.0105 (−2.4867)

0.7944 (3.2262)

Q πt−1 R¯ 2 Constant Active opening rates Dummy × active opening rates Import-price inflation

0.8168 (17.9780) 0.8905 −0.0147 (−2.6825) 0.0270 (4.4342) -0.0081 (−1.7094)

Skewness

0.7921 (25.3834) 0.9498

0.8074 (17.3267) 0.8862

2. Threshold = 2% −0.0089 −0.0148 (−1.8646 (−2.6641) 0.0206 0.0271 (4.0303) (4.3835) −0.0058 −0.0071 (−1.3814) (−1.4545) 0.0406 (4.7910) 0.0909 (1.2391)

Asym15

0.8380 (26.6048) 0.9418

4.2172 (3.6944) 0.8010 (18.5750) 0.9010

−0.0160 (−4.0827) 0.0248 (6.0606) −0.0041 (−1.0426)

−0.0168 (−3.3050) 0.0278 (4.9987) −0.0050 (−1.1107)

0.8714 (3.5003)

Q πt−1 R¯ 2

0.8498 (18.9969) 0.8775

0.7893 (19.8113) 0.9133

0.8446 (18.5972) 0.8730

0.8659 (29.2315) 0.9393

4.4401 (3.7922) 0.8355 (20.5425) 0.8966

Note. (1) Quarterly data, 1971:1-1997:4. (2) Dummy takes the value one when inflation rates are below 2% and zero otherwise. (3) Numbers in parentheses are t-statistics. (4) Estimated by OLS or Cochrane–Orcutt method.

Column 1 of Table II, part 1 presents, as a benchmark, the regression result when the supply-shock variable is not included. The estimated coefficient of xt−1 is 0.0298 and that of the dummy term is −0.0129. In other words, the slope of the short-run Phillips curve is 0.0298 when the rate of inflation is above 3% but

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decreases to 0.0169 when it is below 3%. The coefficient of the dummy term is negative and significantly different from zero, supporting the hypothesis that the slope of the short-run Phillips curve becomes smaller as the rate of inflation decreases. As explained in the previous section, the coefficient of xt−1 is biased unless supply shocks are properly controlled for. Column 2 of Table II, part 1 shows the regression result when we add import-price inflation as a measure of supply shocks. The coefficient of x t−1 becomes smaller, decreasing from 0.0298 to 0.0215, which is consistent with the fact that a substantial decline in the rate of import-price inflation in the early 1980s contributed to CPI disinflation. The coefficient of the dummy term becomes smaller in absolute value but is still significantly different from zero. Namely, the nonlinearity of the short-run Phillips curve is weaker than before, but still remains. We next measure relative-price changes using the methodology proposed by Ball and Mankiw (1995). We use the CPI components at the subgroup level. For example, food is disaggregated into cereals, fish and shellfish, meat, dairy products and eggs, vegetables and seaweed, and so on. The number of subgroups is 45. Using the series of subgroup indexes, as well as the weight of each subgroup in 1995, we calculate the three variables defined in the previous section (Skew, AsymX, and Q) for each prefecture.15 Figure 2 shows the movements of the national averages of these three variables. As seen in Fig. 2, the three variables commonly take negative values in the periods of 1986–87, 1992–93 and 1995–96, which suggests that relative prices of some goods and services declined in these periods.16 Taking into consideration that (i) the inflation rates were below 3% in these periods; (ii) active opening rates were increasing at a slow pace in the periods, 1992–93 and 1995–96, we should expect that, by adding one of the three variables, the coefficient of the dummy term would be smaller, in absolute value, than with no supply-shock variable. Columns 3, 4, and 5 of Table II, part 1 show that coefficients on the dummy term are indeed smaller in absolute value than those in the case of no supply-shock variable. However, they are still significantly different from zero, which indicates that the nonlinearity of the short-run Phillips curve does not disappear even when we control for supply shocks using various measures of relative price changes. In Table II, part 2, the threshold, at which the short-run Phillips curve kinks, is changed from 3 to 2% to check the sensitivity of the results. The regression results indicate that the coefficient of the dummy term is negative as before, but not significantly different from zero. This suggests the possibility that a kink of the short-run Phillips curve occurs around 3%, rather than 2%. To examine the linearity (or nonlinearity) of the short-run Phillips curve in a more formal way, we conduct a likelihood ratio (LR) test assuming a generalized 15 Other studies that calculate relative price change in Japan include Fukuda et al. (1991), whose main interest is in the second moment of relative price distribution rather than its third moment. 16 We note that both Skew and Q stay at near-zero value in 1974 when inflation increased significantly. We fail to find any remarkable change in relative prices in 1974. This may be evidence against the argument that high inflation in 1974 was due to the oil price hike.

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FIG. 2. Relative price changes.

version of the short-run Phillips curve, B(πt ) = a0 + a1 xt−1 + a2 st + a3 πt−1 + εt ,

(4)

where B(.) is the Box–Cox transformation, defined by B(π) = (π λ − 1)/λ. Note that by transforming the dependent variable in this way, we allow the slope of the short-run Phillips curve, ∂π/∂ x, to depend on the rate of inflation. If λ = 1 then B(π) = π − 1, which means that the linear Phillips curve is a special case of the above specification. We estimate λ as well as ai (i = 0, 1, 2, 3) by

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NISHIZAKI AND WATANABE TABLE III Tests for Linearity B(πt ) = a0 + a1 xt−1 + a2 st + a3 πt−1 + Et

λˆ Standard error Log-Likelihood λ = λˆ λ=1 LR test statistic p-value

No supplyshock variable [1]

Import-price inflation [2]

Skewness [3]

Asym15 [4]

Q [5]

0.7736 (0.0488)

0.8326 (0.0537)

0.7486 (0.0489)

0.7522 (0.0453)

0.7313 (0.0457)

354.47 342.99 22.96 0.0000

363.79 356.59 14.40 0.0002

357.50 343.81 27.40 0.0000

367.10 350.79 32.61 0.0000

370.82 351.76 38.13 0.0000

Note. B(π) ≡ (π λ − 1)/λ. The parameters ai (i = 0, 1, 2, 3) and λ are estimated by the maximum likelihood method. Standard errors of λˆ are computed from the covariance of analytic first derivatives (BHHH).

the maximum-likelihood method using the quarterly data 1971:1 to 1998:3.17 Table III reports estimates of λ as well as LR test statistics for the null hypothesis that the Phillips curve is linear (i.e., λ = 1). Estimates of λ range from 0.73 to 0.83, depending on what supply-shock variable is used. Combined with a positive coefficient of x t−1 (which is not shown in the table), this is consistent with the hypothesis that the slope of the short-run Phillips curve is an increasing function of the rate of inflation. As shown on the final row of the table, we reject the null hypothesis, at the 0.1% significance level, in all of the five cases. 5.2. Original Panel Data To control for expected inflation, we estimate Eq. (3) using the transformed panel data. Before proceeding further, we estimate, as a preliminary step, a simpler model using the original panel data. We assume, for the moment, that n t in Eq. (1) is time-invariant. Then Eq. (1) is simplified to πit = ri + βxit + γ sit + u it ,

(5)

where n t is assumed to be not only constant, but also zero, for simplicity. An important point to note is that β does not depend on i. To check whether the original panel data support this assumption, we compare the model described by Eq. (5) with the following model, πit = ri + βi xit + γ sit + u it ,

(6)

17 To transform π by B( ), π must be strictly positive. But π takes negative values five times in the sample period: −0.002 in 86:04, −0.008 in 87:01, −0.006 in 95:04, −0.004 in 96:01, and −0.002 in 98:03. To accommodate this problem, we used B(π + 0.01) and B(π + 0.05) as dependent variables, but no significantly different results were found.

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where both intercepts and slopes of the Phillips curve are assumed to be different across prefectures. Note that the model described by (5) is a special case of that of (6) and that a stronger restriction on β is imposed in (5), as compared with (6). To test whether this restriction is appropriate, we estimate both models using the same panel data and compare the residual sums of squares. The column labeled “Slope is homogeneous?” in Table IV part 1 presents the results of F-tests. We use π, ω1 , and ω2 as measures of annual inflation rates and Skew as a measure of supply shocks. The regression results are shown for the full sample, 1971–97, as well as for the subsamples: 1971–79, 1980–89, and 1990–97. For all of the 12 cases, the restriction on β is not rejected at the 5% significance level. If we interpret the relationship between π (or ω) and x in the time-series dimension as mainly reflecting the responses of these variables to nationwide shocks, while the relationship in the cross-prefecture dimension is seen as reflecting the responses to regional shocks, the results of F-tests imply that the responses of π (or ω) and x to these shocks are almost identical, irrespective of whether they are nationwide or regional ones. Having concluded that the restriction on β is not rejected by the data, in the next step we proceed to check whether or not we can impose an additional restriction that ri is invariant across prefectures. πit = r + βxit + γ sit + u it

(7)

If this is the true structure, the number of coefficients to be estimated is reduced from 47 (r1 , . . . , r46 and β) to 2 (r and β) and the efficiency of estimation would be improved. To check the appropriateness of this restriction, we estimate both models and compare the residual sums of squares. The column labeled “Both slope and intercept are homogeneous?” in Table IV, part 1 presents the results of the F-tests, which indicate that the additional restriction is not rejected for 11 of the 12 cases. The above results indicate that the appropriate model is that described by (7) for the 11 cases and that described by (6) for the 12th case. Estimates of β are shown on the column labeled “trade-off parameter” in Table IV, part 1. In 11 of the 12 cases, they have the expected sign and are significantly different from zero. The subsample estimates seem to suggest that the coefficients for the 1970s are larger than those for the 1980s or 1990s. For example, the estimate of β when we use ω1 as the dependent variable is 0.0300 in the subsample of 1971–79, but declines to 0.0065 in the subsample of 1980–89, and 0.0113 in the subsample of 1990–97. To check whether these differences in subsample estimates are statistically significant or not, we calculate t-statistics for the hypothesis that the coefficient for the 1990s, denoted by β 1990 , is equal to that of the 1970s, β 1970 .18 The same statistics are calculated for the hypothesis of β 1990 being equal to β 1980 , as well as that of 18 Welch’s method is used to calculate t-statistics allowing for the standard deviation of β 1990 to be different from that of β1970 .

TABLE IV Estimates of Output-Inflation Trade-Off Measures of inflation

Slope is homogeneous?

Both slope and intercept are homogeneous?

Trade-off parameter, β

t-statistics

adj R2

1. Skewness of relative-price changes as supply-shock variable 1971–97 π ω1 ω2 1971–79 π ω1 ω2 1980–89 π ω1 ω2 1990–97 π ω1 ω2

yes yes yes

yes yes yes

0.0130 0.0238 0.0312

6.0112 8.3503 10.1542

0.1061 0.0950 0.1017

yes yes yes

yes yes yes

0.0147 0.0300 0.0340

4.0195 8.0081 7.6237

0.0410 0.1608 0.1770

yes yes yes

yes yes yes

−0.0030 0.0065 0.0091

−1.1308 2.2977 2.9071

0.2323 0.0413 0.0556

yes yes yes

no yes yes

0.0143 0.0113 0.0186

15.4055 4.8094 7.2941

0.6253 0.0891 0.1817

2. Asym 15 as supply-shock variable 1971–97 π ω1 ω2 1971–79 π ω1 ω2 1980–89 π ω1 ω2 1990–97 π ω1 ω2

yes yes yes

yes yes yes

0.0034 0.0138 0.0197

3.7903 6.9732 10.2673

0.8477 0.5729 0.6559

yes yes yes

yes yes yes

0.0027 0.0214 0.0242

3.2110 8.9077 9.4084

0.9467 0.6499 0.7242

yes yes yes

yes yes yes

0.0012 0.0081 0.0110

0.6910 3.0578 3.7233

0.6449 0.1562 0.1567

no yes yes

— yes yes

— 0.0121 0.0198

— 5.3948 8.0790

— 0.0866 0.1805

3. Import-price inflation as supply-shock variable 1971–97 π ω1 ω2 1971–79 π ω1 ω2 1980–89 π ω1 ω2 1990–97 π ω1 ω2

yes yes yes

yes yes yes

0.0038 0.0153 0.0217

2.3673 5.9988 8.0895

0.5207 0.2976 0.3327

yes yes yes

yes yes yes

0.0023 0.0219 0.0250

1.0330 7.0693 6.8883

0.6441 0.4293 0.4631

yes yes yes

yes yes yes

−0.0059 0.0049 0.0074

−3.4801 1.8436 2.5214

0.6795 0.1543 0.1615

yes yes yes

no yes yes

0.0192 0.0123 0.0221

19.9759 5.6191 8.6634

0.5086 0.1132 0.1660

Note. Original panel data are used. Model selection is based on F-tests with the significance level of 5%. 320

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β 1980 being equal to β 1970 . The results of these t-tests are reported in column 1 of Table VI. These show that (i) β 1990 is significantly smaller than β 1970 , (ii) β 1990 is significantly greater than β1980 ,19 and (iii) β1980 is significantly smaller than β1970 . Taking into consideration that the average rate of inflation was the highest in the 1970s and the lowest in the 1990s, we find that both the first and the third findings are consistent with the hypothesis that the slope of the Phillips curve becomes smaller with the rate of inflation, but the second one is not. To check the sensitivity of these three findings, we estimate the same set of regressions using Asym15 and import-price inflation as the supply-shock variable in Tables IV, parts 2 and 3. As shown in these tables, and in columns 2 and 3 of table 6, we obtain almost the same results as before. 5.3. Transformed Panel Data We now proceed to the final step of our empirical analysis. Following the methodology described in Section 4.2, we control for expected inflation using the transformed panel data. As in the previous section, we conduct two sets of F-tests for Eq. (3). First, we test the restriction that β does not depend on i. The results of the corresponding F-tests when we use Skew as a supply-shock variable are reported on the second column of Table V, part 1. These results show that the restriction on β is not rejected for all 12 cases estimated. Next, we test the additional restriction that ri is invariant across prefectures. The third column of Table V, part 1 indicates that this restriction is not rejected for all 12 cases. Estimates of β are presented in the fourth column of Table V, part 1. They have the expected sign in all 12 cases, but some of them are not significantly different from zero. In particular, the estimates for the 1990s are very close to zero, irrespective of which measure of inflation is used. This is in sharp contrast with the results obtained from the original panel data. The different results obtained from the original panel data and the transformed panel data suggest the possibility that disinflation in the 1990s was substantially accelerated by declines in the expected inflation.20 That is, the coefficients β estimated using the original panel data have an upward bias because expected inflation is not controlled for properly. However, this bias is eliminated by using the transformed panel data. 19 Data support this statement when we use π or ω for the measure of inflation rates. However, 2 when we use ω for the measure of inflation rates, β1990 -β1980 is positive but not significantly different from zero. 20 Alternatively, one might interpret the two different results as reflecting differences in the responses of π ande x to nationwide and regional shocks. To illustrate this, suppose that the results from the original panel data mainly represent responses of the two variables to nationwide shocks, while those from the transformed panel data represent responses to regional shocks. Furthermore, suppose that the responses of π and x to nationwide shock are different from those to regional shocks. If this is the case, the coefficient β estimated using the original panel data would be different from that estimated using the transformed panel data. As shown in Section 5.2, however, the relationship between π and x for the time-series dimension is not significantly different from that for the cross-prefecture dimension. Therefore, we cannot reject the hypothesis that the responses of π and x to nationwide shocks are almost the same as those to regional ones.

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NISHIZAKI AND WATANABE TABLE V Estimates of Output-Inflation Trade-Off

Measures of inflation

Slope is homogeneous?

Both slope and intercept are homogeneous?

Trade-off parameter, β

t-statistics

adj R2

1. Skewness of relative-price changes as supply-shock variable 1971–97 π ω1 ω2 1971–79 π ω1 ω2 1980–89 π ω1 ω2

yes yes yes

yes yes yes

0.0005 0.0042 0.0061

1.4383 3.5132 4.6846

0.0213 0.0082 0.0160

yes yes yes

yes yes yes

0.0003 0.0042 0.0066

0.4999 2.6092 4.0042

−0.0023 0.0115 0.0329

yes yes yes

yes yes yes

0.0016 0.0084 0.0068

2.5226 3.2380 2.4605

0.0629 0.0185 0.0110

2. Asym 15 as supply-shock variable 1990–97 π ω1 ω2 1971–97 π ω1 ω2 1971–79 π ω1 ω2 1980–89 π ω1 ω2 1990–97 π ω1 ω2

yes yes yes

yes yes yes

0.0002 0.0023 0.0047

0.3555 0.7624 1.4028

0.1075 −0.0034 0.0002

no yes yes

— yes yes

— 0.0043 0.0061

— 3.5460 4.7008

— 0.0101 0.0169

no no yes

— — yes

— — 0.0066

— — 3.9938

— — 0.0345

no yes yes

— yes yes

— 0.0084 0.0073

— 3.2404 2.6341

— 0.0185 0.0126

yes yes yes

yes yes yes

0.0003 0.0023 0.0049

0.6852 0.7599 1.4535

0.0851 −0.0039 0.0011

Note. Transformed panel data are used. Model selection is based on F-tests with the significance level of 5%.

Comparing subsample estimates, we find that β 1990 is the smallest among the three estimates, β 1970 , β 1990 , and β 1990 . Given that the average rate of inflation was the lowest in the 1990s, this finding is consistent with the hypothesis that the slope of the Phillips curve becomes smaller with the rate of inflation.21 This contrasts 21

Although this finding is consistent with our hypothesis, we still cannot rule out the possibility that this is caused by other factors. For example, since early 1990s, many Japanese firms have been trying to reduce the number of workers as a part of business restructuring. This could be regarded as a structural change in firms’ behavior rather than a cyclical one. In this case, a sharp decline in the active opening rate would occur without accompanying significant disinflation.

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TABLE VI Tests for Shifts in Estimated Trade-Off Parameter, β Original panel data

t-statistics β1990 -β1970 β1990 -β1980 β1980 -β1970

π ω1 ω2 π ω1 ω2 π ω1 ω2

Transformed panel data

Skewness as supply-shock variable [1]

Asym15 as supply-shock variable [2]

Import-price inflation as supply-shock variable [3]

Skewness as supply-shock variable [4]

Asym15 as supply-shock variable [5]

−35.1844∗∗∗ −4.2267 −2.9965 6.1432∗∗∗ 1.2820 2.3398∗∗ −33.1967∗∗∗ −4.9748 −4.5577∗∗∗

— −2.8179 −1.2501 — 1.1495 2.2833∗∗ −0.7619 −3.7050 −3.3685∗∗∗

6.9309∗∗∗ −2.5388 −0.8906 12.7991∗∗∗ 2.1228∗∗ 3.5454∗∗∗ −2.9367∗∗∗ −4.1416 −3.7343∗∗∗

−0.1635 −0.5859 −0.5091 −1.8383∗ −1.5544 −0.0043 1.5561 1.3533 0.0546

— — −0.4467 — −1.5546 −0.5466 — — 0.2198

Note. ∗∗∗,∗∗,∗ indicate that the hypothesis of no shifts in parameter β is rejected at the significance level of 1, 5, and 10%, respectively. t-statistics and corresponding degrees of freedom are calculated by Welch’s method. See Amemiya (1985) for details.

with the results obtained using the original panel data, where β 1990 is smaller than β 1970 but greater than β 1980 . Again, it is natural to interpret the difference as reflecting an upward bias in the estimate of β 1990 that is due to the failure to properly control for expected inflation. It is also important to note that the regularity we find holds for all three measures of inflation. This is consistent with the hypothesis of downward rigidity of nominal wages, but is not consistent with the Ball et al. hypothesis, suggesting that the nonlinearity of the Phillips curve comes from downward rigidity of nominal wages. To check the sensitivity of this result, Table V, part 2 repeats the same regression using Asym15 as a measure of supply shock. The subsample estimates, which are comparable only for the case when the dependent variable is ω2 , show that β 1990 is, again, the smallest among the three. Finally, we conduct a t-test for the hypothesis that β 1990 is the smallest among the three. The results, reported in columns 4 and 5 of Table VI, show that the differences among the three are not large relative to the corresponding standard errors of the estimators.

6. CONCLUSION In this paper, we tested the hypothesis that the slope of the short-run Phillips curve becomes flatter as the rate of inflation approaches zero. The regression analysis using the aggregated time-series data revealed that the Japanese data are consistent with the hypothesis and that the short-run Phillips curve kinks

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somewhere around 3%. The analysis using the transformed panel data also provided evidence consistent with the hypothesis, but less conclusive because the slope of the short-run Phillips curve is imprecisely estimated. To conclude the paper, we comment on the implications of a flatter short-run Phillips curve under low or near-zero inflation. First, our results provide additional evidence for the argument that central banks should aim at a positive, rather than a zero, rate of inflation. In interpreting this result, however, it should be kept in mind that economic systems evolve over time and reflect changes in their environments. In our context, this means that a smaller slope of the short-run Phillips curve at near-zero inflation rates might be a transitory phenomenon. Put differently, we cannot deny the possibility that the slope rises as the economic agents become accustomed to near-zero inflation rates. For example, the degree of downward rigidity of nominal wages is not independent from macroeconomic conditions, including the inflation rate. In this respect, recent movements toward the adoption of a new type of wage contracts, in which salaries of workers are determined reflecting their productivities, might be noteworthy. The spread of this type of wage contracts will surely enhance the flexibility of nominal wages, thereby weakening the nonlinearity of the short-run Phillips curve at near-zero inflation. Second, central banks find it difficult to conduct monetary policy, particularly fine-tuning policy, if they are watching only inflation rates. This is an immediate implication of a flatter short-run Phillips curve at near-zero inflation rates. To illustrate this, suppose an economy is hit by a negative demand disturbance that decreases nominal GDP. In a world with high inflation, where the short-run Phillips curve is steep, the consequence of a negative demand disturbance shows up as reduced inflation, having almost no effect on real GDP. On the other hand, in an economy with low inflation, where the short-run Phillips curve is flat, the consequence appears as a reduction in real GDP, having almost no effect on inflation rates (at least in the short run). An important point is that the rate of inflation is a sensitive variable in an economy with high inflation but not in one with low inflation. In other words, the inflation rate is not very informative in an economy with low inflation.22 Thus, it is dangerous if there is a heavy weight on inflation rates in the policy response function of a central bank in a low-inflation economy.23 22 Another aspect of low inflation rates is that a stable relationship between money supply and inflation rates is difficult to detect in a low-inflation economy. This is an immediate reflection of the flatter short-run Phillips curve. There is considerable evidence supporting this in the 1980s and 1990s in the Japanese economy. 23 Moreover, the insensitivity of inflation to various shocks creates a difficult problem for the management of monetary policy in a political environment. For example, some researchers, including Bernanke and Gertler (1999), argue that the Bank of Japan should have raised short-term interest rates in 1988 to prevent overheating of the economy. Responding to this argument, Yutaka Yamaguchi, Deputy Governor of the Bank of Japan, stated (Yamaguchi, 1999): “I don’t see how a central bank can increase interest to 8 or 10% when we don’t have inflation at all.”

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Yamaguchi, Y. (1999). Asset price and monetary policy: Japan’s experience, Remarks at a symposium sponsored by the Federal Reserve Bank of Kansas City in Jackson Hole, August 1999. Yates, A. (1998). “Downward Nominal Rigidity and Monetary Policy,” Bank of England Working Paper, No. 82. Yates, A., and Chapple, B. (1996). “What Determines the Short-Run Output-Inflation Trade-off?,” Bank of England Working Paper, No. 53. Yoshikawa, Hiroshi (1995). “Macroeconomics and the Japanese Economy,” Oxford University Press, Oxford.