## 1.     Inflation,     1990–2005

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### Introduction
- Inflation rates in many emerging and industrialized countries declined substantially for a number of years; several countries, such as Japan and China, have experienced deflation.
- Two opposing views about China’s role:
  - China exporting deflation: excess manufacturing capacity pressuring manufactured goods’ prices downward and China’s exchange rate linkage to the United States dollar leading to cheaper exports.
  - China exporting inflation: as deflation ended in 2003, China’s surging import demand argued to raise global prices for commodities and goods.
- China’s world export share noted as “around 6 percent in 2003.”
- Paper focus: whether China is exporting general deflation or inflation to the United States and Japan, motivated by China’s rising integration and substantial exports to the United States and Japan.

### Trade shares (Table 1: Sources and Destinations of Imports, 2002)
- Destination: China — from U.S.: 8.8 percent; from Japan: 16.1 percent.
- Destination: U.S. — from China: 11.1 percent; from Japan: 10.4 percent.
- Destination: Japan — from China: 18.2 percent; from U.S.: 17.4 percent.
- Source: DOTS.

### Theoretical underpinnings
- Imported intermediates models (Kollmann, 2001; Bergin, 2003): foreign price increases can raise domestic marginal costs; calibrations often show little impact on domestic prices.
- Imported final goods models (Clarida, Gali, and Gertler, 2002): possible inflation spillovers if central banks set policy cooperatively; non-cooperative policy can insulate domestic inflation.
- Three channels for China’s prices to affect foreign consumer prices (Kamin, Marazzi, and Schindler, 2004):
  - Direct effect: cheaper final goods exports lower the foreign price index.
  - Cost channel: lower foreign inflation depresses foreign nominal wages, lowering production costs.
  - Demand channel: China’s cheaper exports can harm foreign producers’ markets and profits, reducing foreign demand and prices.
- Indirect channels:
  - China’s cheap exports to third countries could lower nominal wage growth there and indirectly affect other countries’ prices.
  - Rising Chinese demand for metals could raise global marginal costs for metals, increasing costs in downstream industries worldwide.
  - Potential to export can prompt domestic producers in trading partners to lower prices to maintain market share.

### Empirical results — overview
- Focus on links between inflation rates (not price levels) in China, the United States, and Japan.
- Cointegration tests do not find cointegration between aggregate price indices in China and the United States.
- Cointegration tests find 1 cointegration equation between China and Japan; adjustment coefficients imply prices in Japan influence China but not vice versa (ECM China = -0.04 (t = -3.59); ECM Japan = 0.01 (t = 1.47)).

### Cointegration test results (Table 2: Cointegration Tests on Price Levels)
- China and the United States (Max-eigen tests):
  - Hypothesized None: Eigenvalue 0.10; Max-Eigen Statistic 8.89; 0.05 Critical Value 14.26; Probability 0.30.
  - Hypothesized At most 1: Eigenvalue 0.00; Max-Eigen Statistic 0.36; 0.05 Critical Value 3.84; Probability 0.55.
  - Note: Max-eigenvalue test indicates no cointegration at the 0.05 level.
- China and Japan (Max-eigen tests):
  - Hypothesized None: Eigenvalue 0.18; Max-Eigen Statistic 16.21; 0.05 Critical Value 14.26; Probability 0.02.
  - Hypothesized At most 1: Eigenvalue 0.04; Max-Eigen Statistic 3.16; 0.05 Critical Value 3.84; Probability 0.08.
  - Note: Max-eigenvalue test indicates 1 cointegration equation at the 0.05 level.
- Adjustment coefficients in ECM:
  - ECM for Inflation in China: -0.04 (-3.59)
  - ECM for Inflation in Japan: 0.01 (1.47)
- Source: Authors’ calculations. Test: Unrestricted Cointegration Rank Test (Maximum Eigenvalue).

### Granger causality and simple VAR results
- Data: seasonally adjusted annualized quarterly inflation rates from Q2 1984; retail prices used for China.
- Lag lengths: 3 for the United States model; 4 for the Japanese model (Akaike Information Criteria).
- Bivariate Granger causality test results (Table 3):
  - US Inflation excluding Chinese Inflation: Chi-sq 6.00; d.f. 3; Probability 0.11.
  - Chinese Inflation excluding US Inflation: Chi-sq 11.58; d.f. 3; Probability 0.01.
  - Japan Inflation excluding Chinese Inflation: Chi-sq 7.79; d.f. 4; Probability 0.10.
  - Chinese Inflation excluding Japan Inflation: Chi-sq 1.65; d.f. 4; Probability 0.80.
- Interpretation:
  - Chinese inflation does not Granger cause inflation in the United States or Japan at the 5 percent level; some statistics are near the 10 percent boundary (US-China 0.11; Japan-China 0.10).
  - United States inflation Granger causes inflation in China (Probability 0.01).
- VAR impulse response:
  - A temporary 1 standard error unanticipated increase in inflation in China (about 5 percentage points) would lead to a small 0.3 percentage point increase in United States inflation after three quarters.

### Key takeaways from Granger/VAR analyses
- Empirical evidence points to only weak transmission of Chinese inflation to inflation in the United States and Japan during the sample period.
- Asymmetric adjustment between China and Japan: Japan’s price level influences China’s but not vice versa (ECM for China: -0.04 (-3.59); ECM for Japan: 0.01 (1.47)).
- Granger causality: United States inflation Granger causes Chinese inflation (Chi-sq 11.58; d.f. 3; Probability 0.01); evidence that Chinese inflation Granger causes US or Japan inflation is weak (US: Probability 0.11; Japan: Probability 0.10 and 0.80 depending on direction).
- Back-of-the-envelope calculation:
  - Imports ≈ 12 percent of U.S. GDP and around 14 percent of that comes from China; therefore, a 1 percent increase in Chinese inflation would, ceteris paribus, lead to an expected increase in U.S. inflation of about 0.02 percentage point via direct import share (excluding other channels).

### VAR models and identification (Models 1 and 2)
- Two larger VARs estimated for both the United States and Japan, loosely based on McCarthy (1999) “distribution chain” model.
- Identification and ordering assumptions:
  - Commodity shocks (commp) and United States output shocks (us_gdp) contemporaneously affect all other variables.
  - Model 1 (United States): United States inflation could be affected contemporaneously by ch_rpi and usd_rmb, but not vice versa. US import prices contemporaneously affect US consumer prices. Producer prices excluded.
  - Model 2: Treats the United States as more exogenous; US import price inflation and US consumer price inflation can affect contemporaneously Chinese retail price inflation. Model 2 includes Chinese industrial production growth (ch_ip) contemporaneously affecting Chinese inflation.
- Mathematical form:
  - Model 1: Y1_t = A(L) Y1_{t-1} + e1t ; Y1 = [commp, us_gdp, ch_rpi, usd_rmb, us_ipi, us_cpi]
  - Model 2: Y2_t = B(L) Y2_{t-1} + e2t ; Y2 = [commp, us_gdp, usd_rmb, us_ipi, us_cpi, ch_ip, ch_rpi]
- Variables are quarter-on-quarter seasonally adjusted annualized growth rates (except exchange rate). Two lags used in estimations.

### Impulse response qualitative summary
- United States inflation responds positively to positive shocks to import prices and output growth.
- United States import prices respond positively to increases in world commodity prices.
- Inflation in Japan increases in response to higher output and import prices; import prices increase with higher commodity prices.
- Renminbi (usd_rmb) is suggested to depreciate in response to an increase in Chinese inflation (based on a period with large simultaneous fluctuations in the renminbi and China’s inflation rate).

### Variance decomposition (8 quarter horizon) — selected exact figures from Table 4
- Model 1 U.S. (rows show contributions to each variable in order COMMP US_GDP CH_RPI USD_RMB US_IPI US_CPI Total)
  - COMMP: 81.8 5.3 1.6 1.9 4.6 4.8 100.0
  - US_GDP: 14.5 73.6 1.7 4.7 5.3 0.3 100.0
  - CH_RPI: 7.7 9.9 76.3 4.1 1.2 0.8 100.0
  - USD_RMB: 2.5 9.2 16.5 65.4 3.2 3.2 100.0
  - US_IPI: 19.4 1.5 3.8 0.5 67.4 7.5 100.0
  - US_CPI: 8.8 29.8 5.5 1.5 34.2 20.3 100.0
- Model 2 U.S. (preserved as in source)
  - COMMP: 80.3 4.8 2.1 4.5 5.0 0.5 2.9 100.0
  - US_GDP: 13.8 72.5 3.0 5.6 0.4 2.8 1.8 100.0
  - USD_RMB: 2.5 9.3 78.9 3.3 3.0 1.5 1.5 100.0
  - US_IPI: 19.3 1.3 1.0 70.0 0.7 4.0 0.1 100.0
  - US_CPI: 8.4 29.5 2.9 35.6 20.0 1.6 2.0 100.0
  - CH_IP: 3.0 7.8 11.8 1.8 8.2 66.0 1.2 100.0
  - CH_RPI: 8.4 12.4 3.1 5.3 6.0 13.0 30.0 0.0 100.0  (row preserved as in source)
- Model 1 Japan
  - COMMP: 78.5 7.7 1.8 4.7 1.4 5.9 100.0
  - JP_GDP: 9.9 79.3 2.7 2.4 2.4 3.3 100.0
  - CH_RPI: 10.8 3.5 74.6 8.9 2.0 0.3 100.0
  - YEN_RMB: 7.1 3.9 4.5 81.8 0.7 1.9 100.0
  - JP_IPI: 3.3 5.6 2.9 39.1 47.9 1.2 100.0
  - JP_CPI: 1.9 10.7 3.3 3.2 7.3 73.5 100.0
- Model 2 Japan (preserved as in source)
  - COMMP: 78.1 7.5 5.0 1.5 6.4 0.5 1.0 100.0
  - JP_GDP: 9.7 79.0 3.0 3.0 3.1 0.9 1.4 100.0
  - YEN_RMB: 7.1 3.9 85.4 0.9 1.7 0.2 0.7 100.0
  - JP_IPI: 3.1 6.5 3.7 47.1 47.9 1.0 1.2 3.2 100.0  (row preserved as in source)
  - JP_CPI: 2.0 10.9 2.9 8.5 73.3 0.4 1.9 100.0
  - CH_IP: 2.4 2.0 6.7 5.0 2.5 78.5 2.8 100.0
  - CH_RPI: 10.8 4.3 20.5 1.5 0.9 19.4 42.7 100.0  (row preserved as in source)
- Table label: Table 4. Variance Decomposition of Models 1 and 2 (8 quarter horizon)

### Interpretation from VAR/variance decomposition
- Chinese price developments have only a small direct effect on United States import and consumer prices; commodity prices and United States domestic factors are far more important for U.S. import and consumer price variability.
- United States economic activity (us_gdp) explains more than 10 percent of Chinese inflation variability; United States inflation’s contribution to Chinese inflation variability is very small.
- Chinese developments contribute less than 4 percent of the variability in Japanese import and consumer prices.
- Exchange rate developments (usd_rmb and yen/rmb) are moderately important in cross-country price variability and transmission.

### Variable Coefficient Models — setup and identification
- Objective: Allow coefficients to be stochastic and vary with trade to address potential understatement of Chinese inflation’s impact when using two-decade samples.
- Signal equation (United States, final parsimonious specification):
  - us_cpi_t = a0 + a1 us_cpi_t-1 + a2 us_cpi_t-2 + a4 commp_t + a5 commp_t-1 + a6 commp_t-2 + a7 us_gdp_t + a8 us_gdp_t-1 + a9 us_gdp_t-2 + a10 usd_rmb_t + a11 usd_rmb_t-1 + a12 usd_rmb_t-2 + a13 us_ipi_t + a14 us_ipi_t-1 + a15 us_ipi_t-2 + b_t ch_rpi_t-1 + e_1t
  - bt = c0 + c1 trade_us_ch_t + e_2t ; e_2t ~ (0, V_t)
  - V_t = exp(c1 trade_us_ch_t-1 + c2 ch_rpi_t-1)
  - trade_us_ch = share of imports from China in total United States imports.
- Estimation: State space model and the Kalman filter. Variables quarter-on-quarter seasonally adjusted growth rates (except trade share).

### Key estimation results — United States, Japan, China (Table 5)
- United States (us_cpi equation) — parsimonious estimates (absolute value of z-Statistics in parenthesis):
  - us_cpi_t = 0.44 – 0.01 commp_t + 0.77 us_gdp_t + 0.30 us_gdp_t-1 + 0.11 us_ipi_t + b1t ch_rpi_t-1
    - (0.78) (2.26) (4.78) (2.03) (4.45)
  - b1t = – 0.001 – 0.003 trade_us_ch_t + e1t
    - (0.04) (0.47)
  - e1t ~ (0, exp(-0.58 ch_rpi_t-1))  — (9.35)
  - Log likelihood: 17.56; Akaike Information Criterion: -0.23
- Japan (jp_cpi equation):
  - jp_cpi_t = 0.50 – 0.18 jp_cpi_t-1 + 0.50 jp_cpi_t-2 + 0.05 jp_ipi_t-1 + b2t ch_rpi_t-1
    - (0.95) (0.22) (4.39) (1.93)
  - b2t = 0.11 – 0.01 trade_jp_ch_t + e2t
    - (0.95) (0.80)
  - e2t ~ (0, exp(-0.50 ch_rpi_t-1))  — (3.03)
  - Log likelihood: -197.33; Akaike Information Criterion: 5.01
- China (ch_rpi equation):
  - ch_rpi_t = -5.02 + 0.53 ch_rpi_t-1 + 0.17 ch_rpi_t-2 + 0.22 ch_ip_t + 0.14 ch_ip_t-1 + b3t us_cpi_t-1
    - (6.31) (5.11) (1.94) (6.38) (3.31)
  - b3t = 0.56 – 0.01 trade_ch_us_t + e3t
    - (1.80) (1.52)
  - e3t ~ (0, exp(-0.13 us_cpi_t-1))  — (1.32)
  - Log likelihood: -218.13; Akaike Information Criterion: 5.56

### Interpretation of variable coefficient results
- United States:
  - Increasing US–China trade share does not uncover a stronger China→US inflation link: coefficient on trade share is negative and statistically insignificant.
  - Average estimated variable coefficient is zero, implying an average impact of Chinese inflation on US inflation of zero.
  - High Chinese inflation around 1994 had no impact on US inflation: both coefficient estimate and its variance approach zero in that period.
  - Variable coefficient positive for short periods (notably during China’s deflationary period in 2001 and in 2003) but effects are short-lived (one quarter) and not persistent.
- Japan:
  - Results broadly similar to the United States; variable coefficient often not statistically different from zero during lower inflation/deflation periods.
- China:
  - b3t (US inflation’s impact on China) has a statistically significant and positive mean (0.56), suggesting US inflation effects on China are longer lasting than China→US effects.

### Subcomponents of CPI — motivation and findings
- Motivation: Aggregate null results could mask offsetting sectoral effects (e.g., falling household appliance prices vs. rising food prices in China during 2003–04).
- CPI weights (Table 6):
  - Food weights: United States 14.4 percent; Japan 27.3 percent; China 33.6 percent.
  - Household items weights: United States 4.5 percent; Japan 3.7 percent; China 6.5 percent.
- United States — subcomponents (Table 7):
  - Food prices:
    - us_cpi_food_t = 2.57 + 0.32 us_cpi_food_t-1 – 0.42 us_cpi_food_t-2 + b1t ch_cpi_food_t-1
      - (4.96) (2.52) (3.29)
    - b1t = – 0.20 + 0.04 trade_us_ch_t + e1t
      - (5.05) (10.02)
    - e1t ~ (0, exp(-0.20 ch_cpi_food_t-1))  — (7.15)
    - Log likelihood: -133.96; Akaike Information Criterion: 4.86
    - Finding: Changes in Chinese food prices help explain US food price movements, with statistically significant variable coefficients during several periods (examples include 1991, 1996, and 2003).
  - Household furnishings:
    - us_cpi_hhf_t = 1.26 + 0.03 us_cpi_hhf_t-1 – 0.21 us_gdp_t-1 + b2t ch_cpi_hhf_t-1
      - (1.30) (0.07) (0.35)
    - b2t = – 0.14 + 0.04 trade_us_ch_t + e2t
      - (0.12) (0.27)
    - e2t ~ (0, exp(-1.03 ch_cpi_hhf_t-1))  — (2.94)
    - Log likelihood: -87.74; Akaike Information Criterion: 4.51
    - Finding: Weaker evidence, but indicates increased linkage in 2002–03 when household furnishing prices declined in China while trade grew rapidly.
  - Implication: Offsetting movements in food and household furnishing prices can reduce visibility of aggregate links.
- Japan — subcomponents (Table 8):
  - Food prices:
    - jp_cpi_food_t = –0.55 + b1t ch_cpi_food_t-1
      - (1.22)
    - b1t = –0.31 + 0.03 trade_jp_ch_t + e1t
      - (1.75) (1.99)
    - e1t ~ (0, exp(-0.17 ch_cpi_food_t-1))  — (4.29)
    - Log likelihood: -170.79; Akaike Information Criterion: 6.06
    - Finding: Coefficient on trade variable in the food price system is statistically significant and has the expected sign; variable coefficient appears statistically significant and positive in 2004 (small magnitude).
  - Household furnishings:
    - jp_cpi_hhf_t = –1.55 – 0.23 jp_cpi_hhf_t-1 + b2t ch_cpi_hhf_t-1
      - (0.76) (0.30)
    - b2t = –2.10 + 0.18 trade_us_ch_t + e2t
      - (0.71) (0.87)
    - e2t ~ (0, exp(-0.16 ch_cpi_hhf_t-1))  — (1.02)
    - Log likelihood: -108.51; Akaike Information Criterion: 5.45
    - Finding: Broadly similar to US; some evidence of evolving linkages by subcomponent.

### Overall conclusions and interpretation (Section IV)
- Aggregate result: Chinese prices have a fairly small and temporary impact on United States and Japanese prices; result robust across a variety of model specifications.
- Sector-specific evidence: Some sector-specific linkages exist between China and the United States, especially at the final manufactured goods level; aggregated evidence is weaker or breaks down.
- Possible explanations for weak aggregate link:
  - China functioning as a production hub: increased trade may reflect routings of exports from Asia through China, exaggerating China’s direct impact on importing-country prices.
  - Other global factors: simultaneous declines in inflation across countries may reflect central bank behavior and common shocks rather than China’s increasing global role.
- Recommendations for further work:
  - Examine East Asia as a region to assess whether regional effects have a larger impact on US and Japanese prices than China alone.
  - Conduct event studies or global market analysis for specific sectors (e.g., drought-driven food price shocks) to disentangle direct vs. indirect channels.

*Source: _wp0636 - 1.     Inflation,     1990–2005 (PDF chapter/section).*

### 1.     Inflation,     1990–2005 ........................................................................................

### 1.     Inflation,     1990–2005

### Introduction
- Inflation rates in many emerging and industrialized countries declined substantially for a number of years; several countries, such as Japan and China, have experienced deflation.
- Debates highlighted two opposing views about China’s role:
  - China exporting deflation: argued to result from excess manufacturing capacity pressuring manufactured goods’ prices downward and China’s exchange rate linkage to the United States dollar leading to cheaper exports.
  - China exporting inflation: as deflation ended in 2003, China’s surging import demand was argued to raise global prices for commodities and goods.
- China’s world export share noted as “around 6 percent in 2003” in the discussion of potential global impact.
- The paper focuses on whether China is exporting general deflation or inflation to the United States and Japan, motivated by China’s rising integration and substantial exports to the United States and Japan (see Table 1).

### Trade shares (Table 1: Sources and Destinations of Imports, 2002)
- Destination: China — from U.S.: 8.8 percent; from Japan: 16.1 percent.
- Destination: U.S. — from China: 11.1 percent; from Japan: 10.4 percent.
- Destination: Japan — from China: 18.2 percent; from U.S.: 17.4 percent.
- Source: DOTS.

### Theoretical underpinnings
- Models where imports are intermediate goods (Kollmann, 2001; Bergin, 2003) imply foreign price increases can raise domestic marginal costs and, given price stickiness, may be passed to households, but calibrations often show little impact of foreign price shocks on domestic prices.
- Models allowing imported final goods (Clarida, Gali, and Gertler, 2002) show possible inflation spillovers if central banks set policy cooperatively; non-cooperative policy can insulate domestic inflation.
- Kamin, Marazzi, and Schindler (2004) identify three channels for China’s prices to affect foreign consumer prices:
  - Direct effect: cheaper final goods exports lower the foreign price index.
  - Cost channel: lower foreign inflation depresses foreign nominal wages, lowering production costs.
  - Demand channel: China’s cheaper exports can harm foreign producers’ markets and profits, reducing foreign demand and prices.
- Indirect channels discussed:
  - China’s cheap exports to third countries could lower nominal wage growth there and indirectly affect prices in other countries.
  - Rising Chinese demand for metals could raise global marginal costs for metals, increasing costs in downstream industries worldwide.
  - The potential to export (not only actual exports) can prompt domestic producers in trading partners to lower prices to maintain market share.

### Empirical results — overview
- Focus: links between inflation rates (rather than price levels) in China, the United States, and Japan.
- Cointegration tests do not find cointegration between aggregate price indices in China and the United States (Table 2).
- Cointegration tests find 1 cointegration equation between China and Japan (Table 2); however:
  - Adjustment coefficient in the error correction mechanism for the price level in Japan is not statistically significant.
  - Adjustment coefficient for the error correction mechanism for the price level in China is reported as -0.04 (t = -3.59), significantly different from zero, suggesting prices in Japan influence China but not vice versa.

### Cointegration test results (Table 2: Cointegration Tests on Price Levels)
- China and the United States (Max-eigen tests):
  - Hypothesized None: Eigenvalue 0.10; Max-Eigen Statistic 8.89; 0.05 Critical Value 14.26; Probability 0.30.
  - Hypothesized At most 1: Eigenvalue 0.00; Max-Eigen Statistic 0.36; 0.05 Critical Value 3.84; Probability 0.55.
  - Note: Max-eigenvalue test indicates no cointegration at the 0.05 level.
- China and Japan (Max-eigen tests):
  - Hypothesized None: Eigenvalue 0.18; Max-Eigen Statistic 16.21; 0.05 Critical Value 14.26; Probability 0.02.
  - Hypothesized At most 1: Eigenvalue 0.04; Max-Eigen Statistic 3.16; 0.05 Critical Value 3.84; Probability 0.08.
  - Note: Max-eigenvalue test indicates 1 cointegration equation at the 0.05 level.
- Adjustment coefficients in ECM:
  - ECM for Inflation in China: -0.04 (-3.59)
  - ECM for Inflation in Japan: 0.01 (1.47)
- Source: Authors’ calculations. Test: Unrestricted Cointegration Rank Test (Maximum Eigenvalue).

### A simple model of inflation — Granger causality and VAR
- Data: seasonally adjusted annualized quarterly inflation rates from Q2 1984; retail prices used for China.
- Bivariate Granger causality tests (Table 3) — chosen lag lengths: 3 for the United States model, 4 for the Japanese model (based on Akaike Information Criteria).
- Granger causality test results (Table 3):
  - US Inflation excluding Chinese Inflation: Chi-sq 6.00; d.f. 3; Probability 0.11 (probability that Chinese Inflation does not Granger Cause US Inflation).
  - Chinese Inflation excluding US Inflation: Chi-sq 11.58; d.f. 3; Probability 0.01 (probability that US Inflation does not Granger Cause Chinese Inflation).
  - Japan Inflation excluding Chinese Inflation: Chi-sq 7.79; d.f. 4; Probability 0.10.
  - Chinese Inflation excluding Japan Inflation: Chi-sq 1.65; d.f. 4; Probability 0.80.
- Interpretation of Granger results:
  - Tests suggest Chinese inflation does not Granger cause inflation in the United States or Japan at the 5 percent level; some statistics are close to the 10 percent boundary (e.g., US-China at 0.11; Japan-China at 0.10).
  - United States inflation Granger causes inflation in China (probability 0.01), consistent with historical transmission from the reserve country during periods with a fixed exchange rate component in the sample.
- Vector Autoregression impulse responses:
  - A temporary 1 standard error unanticipated increase in inflation in China (about 5 percentage points) would lead to a small 0.3 percentage point increase in United States inflation after three quarters (impulse response reported in text).

### Key takeaways from this content unit
- Empirical evidence in the analyzed models and tests points to only weak transmission of Chinese inflation to inflation in the United States and Japan during the sample period.
- Cointegration and ECM results suggest asymmetric adjustment between China and Japan: Japan’s price level influences China’s but not vice versa (ECM for China: -0.04 (-3.59); ECM for Japan: 0.01 (1.47)).
- Granger causality tests indicate United States inflation Granger causes Chinese inflation (Chi-sq 11.58; d.f. 3; Probability 0.01), while evidence that Chinese inflation Granger causes US or Japan inflation is weak (US: Probability 0.11; Japan: Probability 0.10 and 0.80 depending on direction).
- A back-of-the-envelope calculation highlighted in the discussion:
  - Imports constitute around 12 percent of U.S. GDP and around 14 percent of that comes from China; therefore, a 1 percent increase in Chinese inflation would, ceteris paribus, lead to an expected increase in U.S. inflation of about 0.02 percentage point via direct import share, excluding other channels.

*Source: _wp0636 - 1.     Inflation,     1990–2005 (PDF chapter/section).*

### 0.5 percentage point increase in inflation in Japan after a year. Consistent with the Granger

### _wp0636 - 0.5 percentage point increase in inflation in Japan after a year. Consistent with the Granger

### Key empirical findings
- A 0.5 percentage point increase in inflation in Japan after a year.
- Consistent with the Granger causality test results, a temporary 1 standard error increase in inflation in the United States (about 1.3 percentage points) would lead to 1 percentage point increase in inflation in China.
- The model finds no significant impact of Chinese inflation on inflation or import prices in the United States.
- Chinese retail price shocks explain 3.8 and 5.5 percent of the variability of United States import and consumer prices in Model 1.
- More than 10 percent of the variation in Chinese inflation is explained by changes in United States GDP; the contribution of United States inflation to Chinese inflation variability is very small.
- Chinese developments contribute less than 4 percent of the variability in Japanese import and consumer prices.
- The quarterly data in this paper spans Q1 1984 – Q2 2005.

### VAR models and identification
- Two larger VAR models (Model 1 and Model 2) are estimated for both the United States and Japan, loosely based on the recursive “distribution chain” model developed by McCarthy (1999).
- Assumptions and ordering:
  - Commodity shocks (commp) and United States output shocks (us_gdp) capture supply and demand shocks that can contemporaneously affect all other variables.
  - Model 1 (for the United States): United States inflation could be affected contemporaneously by inflation in China (ch_rpi) and the renminbi exchange rate (usd_rmb), but not vice versa. United States import prices contemporaneously affect United States consumer prices. Producer prices are excluded.
  - Model 2: Treats the United States as more exogenous; United States import price inflation and United States consumer price inflation can affect contemporaneously Chinese retail price inflation. Model 2 also includes the growth rate of Chinese industrial production (ch_ip) contemporaneously affecting Chinese inflation.
- Mathematical representation:
  - Model 1: Y1_t = A(L) Y1_{t-1} + e1t
  - Model 2: Y2_t = B(L) Y2_{t-1} + e2t
  - Y1 = [commp, us_gdp, ch_rpi, usd_rmb, us_ipi, us_cpi]
  - Y2 = [commp, us_gdp, usd_rmb, us_ipi, us_cpi, ch_ip, ch_rpi]
- All variables used in the VAR are quarter-on-quarter seasonally adjusted annualized growth rates (except the exchange rate). For each country, quarterly output growth is used rather than an output gap.
- Lag selection: employed sequential modified likelihood ratio test, final prediction error test, AIC, Schwartz Criterion, and Hannan-Quinn Criterion. Tests were not uniform; two lags were used in estimations to minimize the chance of insufficient lags.
- Impulse response functions are computed as responses to Cholesky one S.D. innovations ± 2 S.E.

### Impulse response summary (qualitative)
- United States inflation responds positively to positive shocks to import prices and output growth.
- United States import prices respond positively to increases in world commodity prices.
- Inflation in Japan increases in response to higher output and import prices; import prices increase with higher commodity prices.
- The renminbi (usd_rmb) is suggested to depreciate in response to an increase in Chinese inflation (noted that this is based on a period with large simultaneous fluctuations in the renminbi and China’s inflation rate).

### Variance decomposition (8 quarter horizon) — selected rows from Table 4 (exact figures preserved)
- Model 1 U.S. (rows show contributions to each variable in order COMMP US_GDP CH_RPI USD_RMB US_IPI US_CPI Total)
  - COMMP: 81.8 5.3 1.6 1.9 4.6 4.8 100.0
  - US_GDP: 14.5 73.6 1.7 4.7 5.3 0.3 100.0
  - CH_RPI: 7.7 9.9 76.3 4.1 1.2 0.8 100.0
  - USD_RMB: 2.5 9.2 16.5 65.4 3.2 3.2 100.0
  - US_IPI: 19.4 1.5 3.8 0.5 67.4 7.5 100.0
  - US_CPI: 8.8 29.8 5.5 1.5 34.2 20.3 100.0
- Model 2 U.S.
  - COMMP: 80.3 4.8 2.1 4.5 5.0 0.5 2.9 100.0
  - US_GDP: 13.8 72.5 3.0 5.6 0.4 2.8 1.8 100.0
  - USD_RMB: 2.5 9.3 78.9 3.3 3.0 1.5 1.5 100.0
  - US_IPI: 19.3 1.3 1.0 70.0 0.7 4.0 0.1 100.0
  - US_CPI: 8.4 29.5 2.9 35.6 20.0 1.6 2.0 100.0
  - CH_IP: 3.0 7.8 11.8 1.8 8.2 66.0 1.2 100.0
  - CH_RPI: 8.4 12.4 3.1 5.3 3.6 1.0 13.0 30.0 0.0 100.0  (table row formatting indicates CH_RPI row: 8.4 12.4 3.1 5.3 6.0 13.0 ? — preserved as in source text: "CH_RPI8.412.431.53.61.013.030.0100.0")
- Model 1 Japan
  - COMMP: 78.5 7.7 1.8 4.7 1.4 5.9 100.0
  - JP_GDP: 9.9 79.3 2.7 2.4 2.4 3.3 100.0
  - CH_RPI: 10.8 3.5 74.6 8.9 2.0 0.3 100.0
  - YEN_RMB: 7.1 3.9 4.5 81.8 0.7 1.9 100.0
  - JP_IPI: 3.3 5.6 2.9 39.1 47.9 1.2 100.0
  - JP_CPI: 1.9 10.7 3.3 3.2 7.3 73.5 100.0
- Model 2 Japan
  - COMMP: 78.1 7.5 5.0 1.5 6.4 0.5 1.0 100.0
  - JP_GDP: 9.7 79.0 3.0 3.0 3.1 0.9 1.4 100.0
  - YEN_RMB: 7.1 3.9 85.4 0.9 1.7 0.2 0.7 100.0
  - JP_IPI: 3.1 6.5 3.7 47.1 47.9 1.0 1.2 3.2 100.0  (preserved as in source: "JP_IPI3.16.537.147.91.01.23.2100.0")
  - JP_CPI: 2.0 10.9 2.9 8.5 73.3 0.4 1.9 100.0
  - CH_IP: 2.4 2.0 6.7 5.0 2.5 78.5 2.8 100.0
  - CH_RPI: 10.8 4.3 20.5 1.5 0.9 19.4 42.7 100.0  (preserved as in source: "CH_RPI10.84.320.51.50.919.442.7100.0")
- Source table label: Table 4. Variance Decomposition of Models 1 and 2 (8 quarter horizon)

### Interpretation and policy-relevant conclusions
- Chinese price developments have only a small direct effect on United States import and consumer prices; commodity prices and United States domestic factors are far more important for U.S. import and consumer price variability.
- United States economic activity (us_gdp) has a nontrivial effect on Chinese inflation variability (explaining more than 10 percent), with positive and statistically significant impulse responses to shocks to United States output and inflation.
- Chinese developments are unlikely to be a major contributor to Japanese deflation given their small contribution (less than 4 percent) to Japanese import and consumer price variability.
- Exchange rate developments (usd_rmb and yen/rmb) are moderately important in cross-country price variability and transmission.

*Source: Authors' calculations.*

### conclusions of Morimoto, Hirata, and Kato (2003), who suggest that increased supply

### _wp0636 - conclusions of Morimoto, Hirata, and Kato (2003), who suggest that increased supply

### Variable Coefficient Models — setup and identification
- Objective: Allow coefficients to be stochastic and vary with trade to address potential understatement of Chinese inflation’s impact on the United States and Japan when using two-decade samples.
- Focus: Inflation equation for the United States and Japan in Model 1; analogous equation estimated for China.
- Signal equation (United States, final parsimonious specification):
  - us_cpi_t = a0 + a1 us_cpi_t-1 + a2 us_cpi_t-2 + a4 commp_t + a5 commp_t-1 + a6 commp_t-2 + a7 us_gdp_t + a8 us_gdp_t-1 + a9 us_gdp_t-2 + a10 usd_rmb_t + a11 usd_rmb_t-1 + a12 usd_rmb_t-2 + a13 us_ipi_t + a14 us_ipi_t-1 + a15 us_ipi_t-2 + b_t ch_rpi_t-1 + e_1t
  - bt = c0 + c1 trade_us_ch_t + e_2t ; e_2t ~ (0, V_t)
  - trade_us_ch = share of imports from China in total United States imports.
- Variance specification:
  - V_t allowed to depend on China-specific factors: V_t = exp(c1 trade_us_ch_t-1 + c2 ch_rpi_t-1) (variance could increase with trade share and China inflation/deflation).
- Estimation method: State space model and the Kalman filter; the United States (and analogously Japan and China) inflation rate is the observed signal and the stochastic coefficient is the unobserved state variable.
- Data treatment: All variables except trade share are quarter-on-quarter seasonally adjusted growth rates. Parsimonious exclusion of insignificant regressors; contemporaneous vs. one-lag inclusion made no significant difference.

### Key estimation results — United States, Japan, China (Table 5)
- For the United States (us_cpi equation):
  - us_cpi_t = 0.44 – 0.01 commp_t + 0.77 us_gdp_t + 0.30 us_gdp_t-1 + 0.11 us_ipi_t + b1t ch_rpi_t-1
    - (0.78) (2.26) (4.78) (2.03) (4.45)  — absolute value of z-Statistics in parenthesis.
  - b1t = – 0.001 – 0.003 trade_us_ch_t + e1t
    - (0.04) (0.47)
  - e1t ~ (0, exp(-0.58 ch_rpi_t-1))  — (9.35)
  - Log likelihood: 17.56; Akaike Information Criterion: -0.23
- For Japan (jp_cpi equation):
  - jp_cpi_t = 0.50 – 0.18 jp_cpi_t-1 + 0.50 jp_cpi_t-2 + 0.05 jp_ipi_t-1 + b2t ch_rpi_t-1
    - (0.95) (0.22) (4.39) (1.93)
  - b2t = 0.11 – 0.01 trade_jp_ch_t + e2t
    - (0.95) (0.80)
  - e2t ~ (0, exp(-0.50 ch_rpi_t-1))  — (3.03)
  - Log likelihood: -197.33; Akaike Information Criterion: 5.01
- For China (ch_rpi equation):
  - ch_rpi_t = -5.02 + 0.53 ch_rpi_t-1 + 0.17 ch_rpi_t-2 + 0.22 ch_ip_t + 0.14 ch_ip_t-1 + b3t us_cpi_t-1
    - (6.31) (5.11) (1.94) (6.38) (3.31)
  - b3t = 0.56 – 0.01 trade_ch_us_t + e3t
    - (1.80) (1.52)
  - e3t ~ (0, exp(-0.13 us_cpi_t-1))  — (1.32)
  - Log likelihood: -218.13; Akaike Information Criterion: 5.56

### Interpretation of variable coefficient results
- United States:
  - Incorporating the increasing US–China trade share does not uncover a stronger China→US inflation link: coefficient on trade share is negative and statistically insignificant.
  - The average estimated variable coefficient is zero, implying an average impact of Chinese inflation on US inflation of zero.
  - High inflation in China around 1994 had no impact on US inflation: both coefficient estimate and its variance approach zero in that period.
  - The variable coefficient becomes statistically positive for short periods (notably during China’s deflationary period in 2001 and during 2003 when Chinese inflation picked up), but these effects are short-lived (one quarter) and not persistent.
- Japan:
  - Results broadly similar to the United States.
  - During lower inflationary or deflationary periods, the variable coefficient is not statistically different from zero.
- China:
  - China’s estimated variable coefficient measuring US inflation’s impact on China, b3t, has a statistically significant and positive mean (0.56).
  - Suggests US inflation effects on China are longer lasting than China→US effects; consistent with inflation propagation from the reserve currency country to others.

### Subcomponents of CPI — motivation and findings
- Motivation: Aggregate null results could mask offsetting sectoral effects (e.g., falling household appliance prices vs. rising food prices in China during 2003–04).
- CPI weights (Table 6):
  - Food weights: United States 14.4 percent; Japan 27.3 percent; China 33.6 percent.
  - Household items weights: United States 4.5 percent; Japan 3.7 percent; China 6.5 percent.
  - Interpretation: Food price variations are more important for aggregate inflation than household appliance price variations due to larger weights.
- United States — subcomponents (Table 7):
  - Food prices:
    - us_cpi_food_t = 2.57 + 0.32 us_cpi_food_t-1 – 0.42 us_cpi_food_t-2 + b1t ch_cpi_food_t-1
      - (4.96) (2.52) (3.29)
    - b1t = – 0.20 + 0.04 trade_us_ch_t + e1t
      - (5.05) (10.02)
    - e1t ~ (0, exp(-0.20 ch_cpi_food_t-1))  — (7.15)
    - Log likelihood: -133.96; Akaike Information Criterion: 4.86
    - Finding: Changes in Chinese food prices help explain US food price movements, with statistically significant variable coefficients during several periods (link goes back to periods when trade was small; examples include 1991, 1996, and 2003).
  - Household furnishings:
    - us_cpi_hhf_t = 1.26 + 0.03 us_cpi_hhf_t-1 – 0.21 us_gdp_t-1 + b2t ch_cpi_hhf_t-1
      - (1.30) (0.07) (0.35)
    - b2t = – 0.14 + 0.04 trade_us_ch_t + e2t
      - (0.12) (0.27)
    - e2t ~ (0, exp(-1.03 ch_cpi_hhf_t-1))  — (2.94)
    - Log likelihood: -87.74; Akaike Information Criterion: 4.51
    - Finding: Evidence weaker (possibly due to shorter sample), but indicates an increased linkage in 2002–03 when household furnishing prices declined in China while trade grew rapidly.
  - Implication: Offsetting movements in food and household furnishing prices (e.g., 2003 food up, household furnishings down) can reduce the visibility of aggregate links.
- Japan — subcomponents (Table 8):
  - Food prices:
    - jp_cpi_food_t = –0.55 + b1t ch_cpi_food_t-1
      - (1.22)
    - b1t = –0.31 + 0.03 trade_jp_ch_t + e1t
      - (1.75) (1.99)
    - e1t ~ (0, exp(-0.17 ch_cpi_food_t-1))  — (4.29)
    - Log likelihood: -170.79; Akaike Information Criterion: 6.06
    - Finding: Coefficient on trade variable in the food price system is statistically significant and has the expected sign; variable coefficient appears statistically significant and positive in 2004 (small magnitude).
  - Household furnishings:
    - jp_cpi_hhf_t = –1.55 – 0.23 jp_cpi_hhf_t-1 + b2t ch_cpi_hhf_t-1
      - (0.76) (0.30)
    - b2t = –2.10 + 0.18 trade_us_ch_t + e2t
      - (0.71) (0.87)
    - e2t ~ (0, exp(-0.16 ch_cpi_hhf_t-1))  — (1.02)
    - Log likelihood: -108.51; Akaike Information Criterion: 5.45
    - Finding: Results broadly similar to US; some evidence of evolving linkages by subcomponent.

### Overall conclusions and interpretation (Section IV)
- Aggregate result: Chinese prices have a fairly small and temporary impact on United States and Japanese prices; result robust across a variety of model specifications.
- Sector-specific evidence: Some sector-specific linkages exist between China and the United States, especially at the final manufactured goods level; aggregated evidence is weaker or breaks down.
- Possible explanations for weak aggregate link:
  - China functioning as a production hub: increased trade may reflect routings of exports from Asia through China (Rumbaugh and Prasad (2003) argument), exaggerating China’s direct impact on importing-country prices.
  - Other global factors: Simultaneous declines in inflation across countries may reflect central bank behavior and common shocks rather than China’s increasing global role.
- Recommendation for further work:
  - Examine East Asia as a region to assess whether regional effects have a larger impact on US and Japanese prices than China alone.
  - Conduct event studies or global market analysis for specific sectors (e.g., drought-driven food price shocks) to disentangle direct vs. indirect channels.

*Source: Authors’ calculations.*

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