## ANNEX I. SUMMARY STATISTICS (wpiea2019271-print-pdf)

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### Introduction, scope, and data coverage
- Objective: systematic cross-country analysis of the impact of digitalization on inflation using national price indexes and a new proxy for digitalization (IP addresses).
- Sample and frequency:
  - Cross-country econometric analysis conducted in a sample of 36 economies.
  - Panel regressions include period January 1990–December 2017.
  - Monthly frequency; total observations: 9019.

### Measurement: digitalization proxy and construction
- Proxy: number of IP addresses per country (IPv4 and IPv6), monthly series.
- Rationale and advantages:
  - Captures penetration, use, and interconnectedness associated with digitalization.
  - Global coverage, monthly frequency, public availability.
  - Correlates with Networked Readiness Index (NRI) as robustness indicator.
- IP protocol facts preserved:
  - IPv4: 32 bits, total space 4,294,967,296 (2^32).
  - IPv6: 128 bits, space 2^128 (approximately 340 undecillion).
  - IPv6 launched on June 6, 2012; 24-hour test on June 8, 2011.
- Digitalization index construction (Eq. (8)):
  - Di,t = αi,tIPv4 · gi,tIPv4 + αi,tIPv6 · gi,tIPv6
  - αi,tIPv4 and αi,tIPv6 weights are country-specific penetration weights based on per-capita allocations relative to global per-capita allocations; αi,tIPv6 = 1 − αi,tIPv4.
- Caveats:
  - Allocation ≠ active usage; address translation (NAT) and allocation practices imply imperfect 1:1 mapping to devices.
  - Zero in series does not imply zero digitalization.

### Theoretical framework and transmission channels (Section III)
- Three broad channels through which digitalization affects prices/inflation:
  - (i) Direct channel: declining prices of ICT-related goods and services.
  - (ii) Market-structure/competition channel: lower entry barriers, e-commerce, easier price comparisons, emergence of superstar firms.
  - (iii) Productivity channel: enhanced productivity lowers operational/marginal costs.
- Price-setting formalization (selected equations and implications preserved):
  - Eq. (1): 휋t = 훼휋t∗ + 휷E t 휋t+1, with 휋t = ∆pt and 휋t∗ = pt∗ − pt−1.
  - Optimal price: pt∗ = μt + mct (Eq. (3)), with μt(d) = 1/휖X,t(d).
  - Marginal cost: mct(d) = vt(d) + wt(d) − mpt(d) (Eq. (4)).
  - Under Cobb-Douglas, mpt(d) = lnφ + at(d)/φ − (1 − φ)/φ yt(d) (Eq. (5)).
  - Combined inflation relation (Eq. (7)):
    - 휋t(d) = (1 − 휷/(1 − 훼))휋(d) + 휷/(1 − 훼)E t 휋t+1(d) + 훼(1 − φ)/(1 − 훼)/φ ỹt(d) − 훼(1 − 훼)/φ ãt(d) + 훼(1 − 훼)/φ (w̃t(d) − p̃t(d)) + 훼(1 − 훼)[μt(d) + vt(d)].
- Model implications highlighted:
  - Digitalization can affect inflation via expectations, Phillips-curve slope, and marginal-cost channels.
  - Parameters: 훼 is Cobb-Douglas elasticity of factor (labor) demand; 휷 is intertemporal discount factor.

### Empirical approach and controls (Section V and Annex regressions)
- Main methods:
  - Panel Phillips-curve estimation with two-way fixed effects and clustered standard errors.
  - Principal component analysis (PCA) on de-meaned standardized inflation vectors to extract common factors.
  - Johansen cointegration tests (3 lags baseline) to test long-run relations between second principal component and global proxies (digitalization, GVC, China PPI).
  - Rolling 60-month regressions to detect structural breaks (e.g., IPv6 introduction).
- Key macro controls and data sources:
  - Inflation, unemployment, NEER, bilateral exchange rates: IMF IFS.
  - One-year-ahead inflation expectations, annual output gap: WEO.
  - Energy and food inflation: World Bank Commodity Price Index.
  - China’s PPI: Haver Analytics Ltd.
  - GVC integration: OECD database (foreign value added divided by exports).
- Unemployment gap computed using HP filter with λ = 129,600.

### Main econometric findings (Panel: January 1990–December 2017)
- Benchmark panel estimates (N = 9019; R2 = 0.983; adj. R2 = 0.983):
  - Lagged inflation 훿1b = 0.866***.
  - Inflation expectations 훿2f = 0.167***.
  - Unemployment gap 훿3g ≈ -0.364** (Column 1) to -0.366* (Column 4).
  - NEER coefficient 휽1neer ≈ -0.002*.
  - Energy inflation 휽2ener = 0.441***.
  - Food inflation 휽2food = -0.347* (sign switches when time FE excluded).
- Digitalization — cost-productivity channel:
  - Lagged coefficient 훽1IP = -0.006* (standard error 0.003) (both raw and standardized specifications reported).
  - Contemporaneous coefficient 훽2IP generally small and not robustly significant (examples: -0.002 with s.e. 0.003–0.005; Alternative specs show occasional -0.005* (0.003)).
  - Interpretation: a one-percentage increase in the digitalization index reduces inflation by 0.006 percent (short-run panel estimate).
- Additional digitalization channels:
  - Phillips-curve slope interaction 훽4IP small and not consistently significant in full-sample panel estimates.
  - Expectation channel 훽3IP not statistically significant (coefficient reported as -0.000 to -0.001).
- Standardized results mirror raw-coefficient findings (e.g., standardized 훽1IP ≈ -0.003 to -0.004 with significance in several specs).

### Magnitude, timing, and rolling-window evidence
- Estimated average impact since mid-2012:
  - Digitalization process contributed on average to reduce annual inflation by 0.05 percentage points since mid-2012.
  - Cumulative impact on the price level about 0.5 percent between mid-2012 and end-2017.
- Rolling 60-month regressions (starting January 2009) show:
  - Cost-productivity channel becomes statistically significant in early-2011 (contemporaneous) and late-2012 (lagged).
  - Evidence of Phillips-curve flattening since 2012: unemployment-gap coefficient declines since mid-2010 and becomes statistically significant after late-2011; interaction (unemployment gap × digitalization index) becomes significant after early-2011 with increasing positive coefficient.
  - Expectation channel remains generally insignificant except briefly starting late-2011.

### Common-factor (PCA) and long-run (cointegration) results
- PCA results:
  - First three principal components explain on average 68.9 percent of inflation variation in the sample.
  - Share explained by first three PCs rose to 79.1 percent post-GFC; increase driven mainly by first PC.
  - First PC correlation with oil price changes: 0.6.
  - Third PC correlation with U.S. dollar index (DXY) post-GFC: about -0.4.
  - Second PC explains about 12 percent of domestic inflation variation (about 20 percent pre-GFC; 15 percent post-GFC).
- Johansen cointegration (baseline and subsamples):
  - Baseline cointegration vector coefficients:
    - Digitalization proxy = -1.904***.
    - Global Value Chains (GVC) = -2.159***.
    - Constant = 51.556.
    - China PPI not significant in baseline (coefficient example reported 0.073 in some specs).
  - Sub-sample 2009–2014: Digitalization proxy = -5.626***; GVC = -2.264***.
  - Emerging Markets sub-sample: Digitalization proxy = -22.432***; GVC = -6.462***.
- Interpretation:
  - A one percentage point increase in the digitalization proxy is associated with a 1.9 percentage point decline in the second principal component of inflation in the long run.
  - Since the second principal component explains about 12 percent of inflation variation, this implies substantial long-run structural effects of digitalization on trend inflation.
  - GVC integration also negatively associated with the structural (second) principal component.

### Summary statistics (Monthly sample, January 1990–December 2017; N = 9019)
- Digitalization Index:
  - Mean: 1.26
  - S.D.: 2.74
  - Min: -16.91
  - P5: 0.00
  - P25: 0.02
  - P50: 0.31
  - P75: 1.32
  - P95: 5.82
  - Max: 29.25
- Inflation:
  - Mean: 3.05
  - S.D.: 4.63
  - Min: -6.54
  - P5: -0.59
  - P25: 1.06
  - P50: 2.16
  - P75: 3.60
  - P95: 9.02
  - Max: 78.66
- Unemployment gap:
  - Mean: 0.00
  - S.D.: 0.11
  - Min: -0.48
  - P5: -0.19
  - P25: -0.06
  - P50: 0.00
  - P75: 0.06
  - P95: 0.16
  - Max: 0.51
- Inflation expectation:
  - Mean: 2.99
  - S.D.: 3.47
  - Min: -2.62
  - P5: 0.78
  - P25: 1.70
  - P50: 2.28
  - P75: 3.10
  - P95: 7.46
  - Max: 123.33
- NEER:
  - Mean: 100.80
  - S.D.: 56.37
  - Min: 53.71
  - P5: 77.52
  - P25: 93.42
  - P50: 98.40
  - P75: 101.93
  - P95: 119.75
  - Max: 1635.65
- Energy inflation:
  - Mean: 0.65
  - S.D.: 7.07
  - Min: -28.36
  - P5: -11.35
  - P25: -3.35
  - P50: 0.90
  - P75: 4.76
  - P95: 11.36
  - Max: 134.30
- Food inflation:
  - Mean: 0.31
  - S.D.: 3.73
  - Min: -22.10
  - P5: -5.02
  - P25: -1.99
  - P50: 0.16
  - P75: 2.58
  - P95: 5.84
  - Max: 114.50

### Challenges, limitations, and robustness
- Measurement challenges:
  - Digitalization is multidimensional; no consensus on a single working definition or perfect cross-country measure.
  - Existing indexes have limited coverage, short spans, and low frequency.
  - National price indexes may be distorted by inadequate quality adjustment for digital goods and services, handling of new products, and measurement difficulties in new markets (e.g., e-commerce, sharing economy).
- Proxy limitations:
  - Allocated IP addresses do not ensure active usage; NAT and other practices distort mapping to devices.
  - Aggregating internet-traffic and address measures by country is complex.
- Identification and sample constraints:
  - Sample restricted by availability of high-frequency macro indicators.
  - Paper does not quantify biases that digitalization may imply for national price indexes.
- Robustness statements:
  - Results robust across standardized and raw coefficient specifications; rolling regressions confirm timing of effects; PCA and cointegration analyses provide complementary long-run evidence.

### Conclusions and policy implications
- Two primary conclusions:
  - Digitalization is a key determinant of the global trend/structural component of inflation.
  - Digitalization has contributed to reducing short-term inflation, particularly since 2012, mainly through a direct cost/mark-up (cost-productivity) channel and, to a lesser extent, by altering price-setting behavior (evidence of Phillips-curve flattening since 2012).
- Quantitative magnitudes:
  - Short-run panel estimate: a one-percentage increase in the digitalization index reduces inflation by 0.006 percent.
  - Since mid-2012 average annual inflation reduced by 0.05 percentage points; cumulative price-level effect about 0.5 percent between mid-2012 and end-2017.
  - Long-run cointegration: a one percentage point increase in the digitalization proxy associated with a 1.9 percentage point decline in the second principal component of inflation.
- Policy recommendations:
  - Central banks should monitor digitalization’s effects on price dynamics and traditional relationships (e.g., Phillips curve).
  - Recalibration of policy responses may be needed to reflect structural changes from the digital economy.
  - Immediate policy response is complicated by digitalization’s structural and gradual nature.

*Source: wpiea2019271-print-pdf - ANNEX I. SUMMARY STATISTICS*

### ANNEX I. SUMMARY STATISTICS _____________________________________________________________ 32

### ANNEX I. SUMMARY STATISTICS

### Introduction and scope
- The digitalization process has transformed production, distribution, financial and payments systems, and economic behavior over the past 25 years.
- The macroeconomic implications of digitalization, particularly its impact on inflation and monetary policy, are not well understood and the literature is in its infancy.
- This paper conducts a systematic cross-country analysis of the impact of digitalization on inflation using national price indexes and a new proxy for digitalization.

### Measurement: digitalization proxy and data coverage
- Proxy proposed: the number of IP addresses per country, which:
  - Captures the degree of penetration, use, and interconnectedness associated with digitalization.
  - Has global coverage and is available on a monthly basis for all countries in the world since the early 1990s.
- Empirical sample and frequency constraints:
  - Cross-country econometric analysis conducted in a sample of 36 economies.
  - Panel regressions referenced include the period January 1990–December 2017 (Table listing).

### Empirical approach
- Main methods:
  - Estimation of Phillips curves using panel regressions to assess the role of digitalization in domestic inflation developments.
  - Principal component analysis to decompose inflation dynamics into orthogonal factors.
  - Cointegration analysis to test long-run relationships between principal components of inflation and the digitalization proxy, controlling for other global factors (e.g., global value chains, China’s role).
- Key econometric tests and listings referenced: Panel regressions for inflation, Johansen cointegration test, cointegration analysis, principal component variance shares.

### Main findings and quantitative results
- Digitalization has been a statistically significant driver of domestic inflation and has contributed to lowering it since 2012.
- Estimated impact on inflation:
  - Since mid-2012 the digitalization process has contributed on average to reduce annual inflation by 0.05 percentage points.
  - A one-percentage point increase in the digitalization proxy leads to a 1.9 percentage point decline in the second principal component of inflation in the long run.
- Principal component decomposition:
  - Inflation can be decomposed into three well-defined factors that explain over two-thirds of the variance of inflation in the cross-country sample.
  - The second principal component captures structural dynamics of inflation and explains more than 10 percent of inflation variation in the sample.
- Transmission channels:
  - The impact of digitalization on inflation mainly operates through a direct and indirect cost/competition channel (e.g., lowering costs of production and distribution, increased competition, productivity effects).
  - No conclusive evidence that digitalization affects inflation through expectations formation.
- Relation to other global factors:
  - Analysis controls for global value chains and China’s role; results suggest digitalization acts as a global force that lowers inflation across the world.
- Interpretation and magnitude:
  - The estimated average reduction of 0.05 percentage points since mid-2012 is consistent with country studies finding that changes in information and communication technology and e-commerce account for a small share of inflation developments, but cumulative effects on price levels are non-negligible.

### Challenges and limitations noted
- Measurement challenges:
  - Digitalization is a multidimensional and dynamic concept without a fully agreed working definition and no consensus on measurement.
  - Existing cross-country indicators have limited coverage and are often annual and short-span.
  - National price indexes may be distorted due to inadequate quality adjustments for digital goods and services, handling of new products, and measurement difficulties in new markets (e.g., e-commerce, sharing economy).
- Identification and sample constraints:
  - The sample is mainly restricted by the availability of adequate high-frequency data.
  - The paper does not address the challenges of measuring distortions or biases that digitalization may imply for existing national price indexes.

*Source: wpiea2019271-print-pdf - ANNEX I. SUMMARY STATISTICS*

### Section III lays out a simple set up to rationalize the transmission channels through which

### wpiea2019271-print-pdf - Section III lays out a simple set up to rationalize the transmission channels through which

### Structure and scope of the paper
- Section III: sets up a simple framework to rationalize transmission channels through which digitalization can affect prices and inflation.
- Section IV: defines and measures digitalization and motivates using IP addresses as a proxy.
- Section V: presents econometric analysis of how digitalization affects inflation, including panel Phillips-curve estimates, channels, common factors, and comparison of the IP proxy with other global factors.
- Final section: concludes.

### Key findings from the literature review (Section II)
- Microeconomic studies focus on online price formation and comparisons with offline prices (Gorodnichenko et al., 2018; Cavallo and Rigobon, 2016; Cavallo, 2017, 2018a).
- Online price data enable new high-frequency price indexes that mitigate measurement biases in traditional CPI construction (Cavallo and Rigobon, 2011; Cavallo et al., 2014, 2015; Cavallo, 2018a, 2018b).
- Empirical regularities documented:
  - Online prices often show less dispersion than offline markets (Gorodnichenko et al., 2018).
  - Online platforms tend to have lower price levels and inflation than offline markets (Goolsbee and Klenow, 2018).
  - Online prices are more flexible, display greater exchange-rate pass-through, faster convergence, and have spillover effects on offline markets reducing price dispersion (Gorodnichenko et al., 2018; Cavallo, 2018a).
  - Online prices still exhibit imperfections: price stickiness and large cross-sectional dispersion (Cavallo, 2017; Gorodnichenko et al., 2018).
  - Online prices are often unresponsive to aggregate demand shocks and closely follow individual demands (Gorodnichenko et al., 2018).
- Cross-country macroeconomic evidence on digitalization’s impact on inflation is scarce; a few scattered studies show a negative correlation between digitalization and inflation (e.g., Yi and Choi (2005) find a 1 percent increase in internet users reduces inflation by 0.04-0.13 percentage points).

### Framework of transmission channels (Section III)
- Three broad channels through which digitalization affects prices/inflation (Charbonneau et al., 2017):
  - (i) Direct channel: prices of ICT-related goods and services decline due to technological change.
  - (ii) Market-structure/competition channel: lower barriers to entry, emergence of superstar firms, rise of e-commerce, easier price comparisons.
  - (iii) Productivity channel: enhanced productivity lowers operational costs.
- Formalization in price-stickiness models:
  - Eq. (1): 휋t = 훼휋t∗ + 휷E t 휋t+1, where 휋t = ∆pt and 휋t∗ = pt∗ − pt−1.
  - Forward-looking solution rewritten as Eq. (2): ∆pt = −(1 − 휷/(1 − 훼))휋 + 훼/(1 − 훼)(pt∗ − pt−1) + 휷/(1 − 훼)E t ∆pt+1. (Intercept −(1 − 휷/(1 − 훼))휋 included to ensure a long-run solution.)
  - Optimal prices as markup over marginal cost: Eq. (3): pt∗ = μt + mct.
  - Markup μt is inverse of price elasticity of demand 휖X,t(d), with dependence on digitalization d (μt(d) = 1/휖X,t(d)).
  - Marginal cost expressed as function of labor mark-up vt ≅ 1/휖D,t(d), nominal wage wt, and marginal product of labor mpt: Eq. (4): mct(d) = vt(d) + wt(d) − mpt(d).
  - Under Cobb-Douglas, marginal product of labor: Eq. (5): mpt(d) = lnφ + at(d)/φ − (1 − φ)/φ yt(d), where φ is demand elasticity of substitution across varieties.
  - Combining yields optimal price: Eq. (6): pt∗(d) = −lnφ + μt(d) + vt(d) + wt(d) − at(d)/φ + (1 − φ)/φ yt(d).
  - Combining Eqs. (2) and (6) gives inflation as function of past and expected inflation, output gap, technology, real returns to factors, and cost-push shocks (markups and labor mark-up): Eq. (7):
    - 휋t(d) = (1 − 휷/(1 − 훼))휋(d) + 휷/(1 − 훼)E t 휋t+1(d) + 훼(1 − φ)/(1 − 훼)/φ ỹt(d) − 훼(1 − 훼)/φ ãt(d) + 훼(1 − 훼)/φ (w̃t(d) − p̃t(d)) + 훼(1 − 훼)[μt(d) + vt(d)].
- Implications: digitalization can influence inflation via:
  - Inflation expectations.
  - Changing slope of the Phillips curve (altering price response to output gap).
  - Affecting marginal costs through technology, factor costs, and competition/mark-ups.
- Parameters noted: 훼 is Cobb-Douglas elasticity of factor (labor) demand; 휷 is intertemporal discount factor.
- Specification embeds standard price-setting models (Taylor overlapped contracts, Calvo, Rotemberg).

### Measuring digitalization and motivation for an IP-address proxy (Section IV)
- Conceptual definition: digitalization = process of converting any information into a digital format (string of zeros and ones), encompassing generation, processing, sharing, and transactions of information; involves infrastructure, networks (internet, platforms), IT services, and digital goods and services.
- Characteristics of digitalization: pervasiveness, continued improvement, declining costs of use, innovation-spawning; transforms behavior and market structures.
- Existing country-level/comprehensive digitalization indexes (examples summarized in Table 1; selected indicators and coverage):
  - Networked Readiness Index (NRI) — World Economic Forum — country level, 139 countries, 2012–16.
  - Digital Economy and Society Index (DESI) — European Commission — 28 European countries, 2014–18.
  - The Digitization Index — Katz et al. (2014) — 184 countries, 2004–11 (selected countries 1995–11).
  - DiGiX — Cámara and Tuesta (2017) — 100 countries, year 2015.
  - Digital Adoption Index (DAI) — World Bank — 171 countries, year 2016 only.
  - MGI Industry Digitization Index — McKinsey Global Institute (2015) — 22 US sectors, year 1997, 2005, 2013.
  - ICT Development Index (IDI) — ITU — 176 countries, 2009–17.
  - US occupation-specific digital scores — Muro et al. (2017, Brookings) — 545 occupations, 23 industry groups, 2002–16.
  - China Internet-plus Index — Tencent Research Institute (annual since 2015).
- Limitations of many indices: limited country/regional coverage, small time spans, low frequency (often annual).
- Proposed high-frequency proxy: number of Internet Protocol (IP) addresses.
  - IP address: numerical label assigned to each device connected to a network using Internet Protocol; identifies every device (computer, cellphones, cameras, printers, etc.) connected to the Internet.
  - Rationale: every device connecting to the internet needs an identifier; IP addresses capture extent and penetration of infrastructure and access/usage of connected devices; available for all countries at monthly frequency.
- IP protocol versions used:
  - IPv4 and IPv6 (formats summarized in Table 2).
  - IPv4: length 32 bits (4 bytes). Dot-decimal notation xxx.xxx.xxx.xxx with 0<=xxx<=255. Supports total space of 4,294,967,296 or 2^32 addresses. Example loopback address: 127.0.0.1. Example public-form address: 192.0.2.53.
  - IPv6: length 128 bits (16 bytes). Hexadecimal string format with eight groups. Space is 2^128 (approximately 340 undecillion addresses). Example: 2001:0db8:582:ae33::29.
- Deployment facts and dates:
  - IPv4 has been in place since the 1980s and is most widely used.
  - IPv6 was developed between 1993 and 1998 and tested on June 8, 2011 by over 400 major web companies (24-hour test).
  - IPv6 was launched on June 6, 2012.
  - IPv6 provides a much larger address space and different routing features; not interoperable with IPv4 without translator gateways.
- Data sources and coverage for IP proxy:
  - IPv4 addresses data from Asia-Pacific Network Information Centre (APNIC): 193 countries and regions between 1990 and 2018.
  - IPv6 data from same source, similar country coverage, available since 2009. IPv6 indicator uses number of prefixes (48 prefixes) proportional to total addresses.
  - Figures show penetration dynamics and correlation with Networked Readiness Index (NRI).
- Advantages of IP-address proxy:
  - Global coverage, high frequency (monthly), public availability.
  - Effective proxy for digitalization indicated by correlation with NRI.
- Caveats and operational issues:
  - Allocation is highly but not perfectly correlated with usage of addresses; allocation does not imply active use.
  - Allocated addresses may not map 1:1 to connected devices due to network address translators (especially in IPv4).
  - A zero in the data does not imply zero digitalization.
  - Aggregating internet-traffic measures by country is intrinsically difficult.

### Data construction and econometric approach (Section V)
- Sample:
  - 36 advanced and emerging market economies (sample list referenced; sample selection determined by availability of monthly macro indicators).
  - Longest sample possible: January 1990–December 2017, monthly frequency.
  - Use of high-frequency data allows exploration of structural breaks (e.g., introduction of IPv6) using 60-month rolling regressions.
- Construction of a monthly digitalization index by country, Di,t:
  - Di,t = αi,tIPv4 · gi,tIPv4 + αi,tIPv6 · gi,tIPv6  (Eq. (8))
  - Weights αi,tIPv4 and αi,tIPv6 are country-specific penetration weights equal to the country-specific penetration of IPv4 or IPv6 relative to their global penetration in per-capita terms:
    - αi,tIPv4 = [IPv4i,t / popi,t] / [ Σi IPv4i,t / Σi popi,t ] ÷ ( [IPv4i,t / popi,t] / [ Σi IPv4i,t / Σi popi,t ] + [IPv6i,t / popi,t] / [ Σi IPv6i,t / Σi popi,t ] )
    - αi,tIPv6 = 1 − αi,tIPv4
  - Index uses weighted average of growth rates gi,tIPv4 and gi,tIPv6.
- Macroeconomic and control data sources:
  - Monthly inflation, unemployment, nominal effective exchange rate, bilateral exchange rates (vis-à-vis the U.S. dollar): IMF International Financial Statistics (IFS).
  - One-year-ahead inflation expectations and annual output gap: World Economic Outlook (WEO) database.
  - Country-specific monthly energy and food inflation: World Bank Commodity Price Index.
  - China’s PPI: Haver Analytics Ltd. database.
  - Global value chains (GVCs) integration: foreign value added divided by exports from OECD database.
  - Absolute penetration of digitalization: log of the number of IP addresses (country rankings noted: U.S. and Japan among most digitalized; Croatia, Slovakia, Uruguay among lowest).
- Empirical strategy highlights:
  - Panel estimates of the Phillips curve to test how digitalization affects inflation via expectations, Phillips curve slope, and marginal-cost channels.
  - Complementary analysis exploring common factors driving inflation and whether these are explained by the IP proxy versus other global factors.
  - Rolling-regression analysis (60-month windows) to detect structural breaks associated with digitalization milestones (e.g., IPv6 introduction).

*Source: wpiea2019271-print-pdf - Section III lays out a simple set up to rationalize the transmission channels through which*

### Annex I, and a plot of our digitalization index is presented in Annex II.

### Annex I

### A. Does Digitalization Influence Inflation in the Short Run?
- Empirical framework: Eq. (9) models inflation rate 휋i,t as function of:
  - Backward-looking inflation component 훿1b and forward-looking component 훿2f;
  - Economic slack Yigap with parameter 훿3g;
  - Controls Xj,i,t−1 capturing commodity prices (energy, food) and nominal effective exchange rate NEERi,t with coefficients 휃jz for z = neeer, ener, food;
  - Country fixed-effects 훼i and time fixed-effects dt.
- Digitalization index Dij,t enters in growth rates to capture channels:
  - Cost-productivity: lagged (훽1IP) and contemporaneous (훽2IP) effects.
  - Expectations formation: (훽3IP).
  - Phillips-curve slope (interaction with demand slack): (훽4IP).
- Expectations for signs:
  - Cost-productivity: negative sign for 훽1IP and 훽2IP.
  - Phillips-curve flattening: positive sign for 훽4IP.
  - More forward-looking price formation: positive sign for 훽3IP.
- Unemployment gap computed using Hodrick–Prescott filter with λ = 129,600; specifically the ratio of (unemployment − HP filtered series) to the filtered series.
- Model estimated with monthly data using two-way fixed-effects.

### B. Econometric Results (Panel: January 1990–December 2017)
- Summary of key coefficient estimates (Table 3):
  - Lagged inflation 훿1b = 0.866***
  - Inflation expectations 훿2f = 0.167***
  - Unemployment gap 훿3g = -0.364** (Column 1) to -0.366* (Column 4)
  - NEER coefficient 휽1neer = -0.002*
  - Energy price inflation 휽2ener = 0.441***
  - Food price inflation 휽2food = -0.347* (switches to positive when time FE excluded)
  - Digitalization — cost-productivity channel:
    - Lagged 훽1IP = -0.006* (standard error 0.003)
    - Contemporaneous 훽2IP = -0.002 (standard error 0.003–0.005)
  - Digitalization — Phillips-curve slope 훽4IP = 0.001 (not statistically significant)
  - Digitalization — expectation channel 훽3IP = -0.000 (not statistically significant)
  - Sample size N = 9019; R2 = 0.983; adj. R2 = 0.983
  - Clustered standard errors reported; significance: * p < 0.10, ** p < 0.05, *** p < 0.01
- Main findings:
  - Standard NKPC components display expected signs; sum of coefficients close to 1 suggesting inflation expectations formed by both backward and forward-looking components.
  - Digitalization has on average a negative impact on inflation, primarily via the cost-productivity channel (negative and significant lagged coefficient 훽1IP across specifications).
  - Magnitude: a one-percentage increase in the digitalization index reduces inflation by 0.006 percent.
  - Estimated observed penetration implies average annual inflation declined by about 0.05 percent since mid-2012; cumulative impact on the price level about 0.5 percent between mid-2012 and end-2017.
  - No robust evidence that digitalization flattened the Phillips curve over the full sample (훽4IP not significant in Table 3).
  - No evidence that digitalization affects inflation through the expectations channel (훽3IP not significant; positive sign).

### C. Rolling Regression Analysis (60-month window starting January 2009)
- Confirms cost-productivity channel as the main transmission mechanism; contemporaneous and lagged impacts become statistically significant in early-2011 and late-2012, respectively.
- Evidence that digitalization has slightly flattened the Phillips curve particularly since 2012:
  - Unemployment gap coefficient declines since mid-2010 and becomes statistically significant after late-2011.
  - Interaction term (unemployment gap × digitalization index) becomes significant after early-2011 with increasing positive coefficient → response of inflation to unemployment gap has weakened with digitalization.
- Expectation channel remains generally insignificant apart from a brief period starting late-2011.
- Conclusion: cost-productivity impact of digitalization gained importance in recent years; Phillips-curve flattening evident over time.

### D. Is Digitalization a Key Global Driver of Trend Inflation?
- Methodology:
  - Principal component analysis (PCA) on de-meaned standardized inflation vectors Πt to extract common factors f t and loadings Λ.
  - Cointegration analysis (Johansen tests with 3 lags for baseline; lag selection reported) to assess long-run relationships between the second principal component and proxies: China PPI (PPIusd), GVC index, and digitalization proxy.
  - Digitalization proxy for long-run analysis uses weighted average of level of digitalization in per-capita terms (notation D i,t l).
- PCA results:
  - First three principal components explain on average 68.9 percent of inflation variation in the sample.
  - Share explained by first three PCs increased over time, peaking post-GFC at 79.1 percent; increase mainly due to rising contribution of first PC.
  - First PC highly correlated with oil price changes (correlation coefficient 0.6).
  - Third PC shows negative comovement with U.S. dollar index (DXY), correlation about -0.4 post-GFC.
  - Second PC explains about 12 percent of domestic inflation variation (about 20 percent pre-GFC and 15 percent post-GFC).
- Cointegration and long-run results (Table 5 / Johansen test):
  - Baseline and sub-sample 2009–2014 show presence of two cointegration vectors; Emerging Markets sample shows one cointegration vector.
  - Cointegration vector coefficients (baseline):
    - Digitalization proxy = -1.904*** (significant at 1 percent)
    - Global Value Chains (GVC) = -2.159*** (significant at 1 percent)
    - China PPI (USD) not significant (coefficient reported 0.073 in some specifications)
    - Constant = 51.556
  - Sub-sample 2009–2014: Digitalization proxy = -5.626***; GVC = -2.264***.
  - Emerging Markets: Digitalization proxy = -22.432***; GVC = -6.462***.
- Interpretation:
  - Digitalization proxy and GVC index are negatively correlated with the structural (second) principal component of inflation.
  - A one percentage point increase in the digitalization proxy is associated with a 1.9 percentage point decline in the second principal component of inflation in the long run; the second principal component explains 12 percent of the sample countries’ inflation variation.
  - Robustness: results hold for a wider sample of 36 emerging market economies; China’s PPI not a significant explanatory variable in examined sample.

### E. Global Drivers of Inflation — Synthesis
- Cyclical drivers:
  - Energy prices (first principal component) and changes in the dollar valuation (third principal component) largely explain cyclical variation in headline inflation.
- Structural drivers:
  - Digitalization proxy and Global Value Chains index negatively associated with long-run (structural) component of inflation.
  - Greater integration of production processes (GVC) and deepening digitalization correlate with lower inflation in the long run.

### F. Conclusions and Policy Implications
- Two main takeaways:
  - Digitalization is a key determinant of the global trend/structural component of inflation.
  - Digitalization has contributed to reducing short-term inflation, particularly since 2012, mainly through a direct cost/mark-up channel (productivity improvements or increased competition), and to a lesser extent by altering price-setting behavior (flattening the Phillips curve in recent years).
  - No conclusive evidence that digitalization affects inflation via the inflation expectations channel.
- Policy implications:
  - Digitalization’s structural features make immediate central bank responses difficult.
  - If digitalization contributes to lowering trend inflation, central bankers should monitor its impact on price dynamics and established relationships (e.g., with output gaps).
  - Central banks may need to recalibrate policy responses to reflect the realities of the digital economy where necessary.

*Source: Annex I (wpiea2019271-print-pdf).*

### Annex I. Summary Statistics

### Annex I. Summary Statistics

### Summary statistics (Monthly Sample, January 1990–December 2017)
- Observations: 9019 for all series listed.
- Digitalization Index
  - Mean: 1.26
  - S.D.: 2.74
  - Min: -16.91
  - P5: 0.00
  - P25: 0.02
  - P50: 0.31
  - P75: 1.32
  - P95: 5.82
  - Max: 29.25
- Inflation
  - Mean: 3.05
  - S.D.: 4.63
  - Min: -6.54
  - P5: -0.59
  - P25: 1.06
  - P50: 2.16
  - P75: 3.60
  - P95: 9.02
  - Max: 78.66
- Unemployment gap
  - Mean: 0.00
  - S.D.: 0.11
  - Min: -0.48
  - P5: -0.19
  - P25: -0.06
  - P50: 0.00
  - P75: 0.06
  - P95: 0.16
  - Max: 0.51
- Inflation expectation
  - Mean: 2.99
  - S.D.: 3.47
  - Min: -2.62
  - P5: 0.78
  - P25: 1.70
  - P50: 2.28
  - P75: 3.10
  - P95: 7.46
  - Max: 123.33
- NEER
  - Mean: 100.80
  - S.D.: 56.37
  - Min: 53.71
  - P5: 77.52
  - P25: 93.42
  - P50: 98.40
  - P75: 101.93
  - P95: 119.75
  - Max: 1635.65
- Energy inflation
  - Mean: 0.65
  - S.D.: 7.07
  - Min: -28.36
  - P5: -11.35
  - P25: -3.35
  - P50: 0.90
  - P75: 4.76
  - P95: 11.36
  - Max: 134.30
- Food inflation
  - Mean: 0.31
  - S.D.: 3.73
  - Min: -22.10
  - P5: -5.02
  - P25: -1.99
  - P50: 0.16
  - P75: 2.58
  - P95: 5.84
  - Max: 114.50

### Annex II. Digitalization Indicators Across Countries

### Penetration of digitalization (IPv4 addresses, log scale)
- Figures present time series by country with x-axis ticks at: 1990m1, 2000m1, 2010m1, 2020m1.
- Countries shown include: Austria, Belgium, Brazil, Bulgaria, Canada, Chile, Colombia, Croatia, Cyprus, Czech Republic, Denmark, Finland, France, Germany, Greece, Hong Kong SAR, Hungary, Ireland, Israel, Italy, Japan, Latvia, Malaysia, Netherlands, Norway, Poland, Portugal, Romania, Russian Federation, Slovakia, Spain, Sweden, Switzerland, United Kingdom, United States, Uruguay.
- Source stated: Author’s calculations based on IP data set.

### Penetration of digitalization (IPv6 addresses, log scale)
- Figures present time series by country with x-axis ticks at: 2009m6, 2013m6, 2017m6.
- Countries shown mirror the IPv4 set: Austria, Belgium, Brazil, Bulgaria, Canada, Chile, Colombia, Croatia, Cyprus, Czech Republic, Denmark, Finland, France, Germany, Greece, Hong Kong SAR, Hungary, Ireland, Israel, Italy, Japan, Latvia, Malaysia, Netherlands, Norway, Poland, Portugal, Romania, Russian Federation, Slovakia, Spain, Sweden, Switzerland, United Kingdom, United States, Uruguay.
- Source stated: Author’s calculations based on IP data set.

### Digitalization Index (country time series)
- Figures show Digitalization Index with y-axis range from -20 to 30 and x-axis ticks at: 1990m1, 2000m1, 2010m1, 2020m1.
- Country panels replicate the country list used for IPv4/IPv6 figures.
- Source stated: Author’s calculations based on IP data set. For calculations see text.

### Annex III. Panel Regressions for Inflation — Key Results

### Table A2: Panel Regressions for Inflation, 1990.1 to 2017.12 (Digitalization Index)
- Sample size: N = 9019 for all specifications.
- Reporting: Benchmark Specification and Alternative Specification across four columns each: OLS, Month FE, Country FE, Both FE. Dependent variable: Inflation.
- Core coefficient estimates (standard errors in parentheses). Significance levels: * p < 0.10, ** p < 0.05, *** p < 0.01.

Key coefficient estimates (Benchmark Specification / Alternative Specification):

- Lagged inflation (휹1 풃)
  - OLS: 0.846*** (0.051)
  - Month FE: 0.871*** (0.038)
  - Country FE: 0.843*** (0.050)
  - Both FE: 0.866*** (0.038)
  - Alternative: 0.846*** (0.052), 0.871*** (0.039), 0.842*** (0.050), 0.866*** (0.038)

- Inflation expectations (휹2 풇)
  - Benchmark:
    - OLS: 0.203*** (0.071)
    - Month FE: 0.156*** (0.050)
    - Country FE: 0.212*** (0.069)
    - Both FE: 0.167*** (0.050)
  - Alternative:
    - OLS: 0.202*** (0.068)
    - Month FE: 0.156*** (0.048)
    - Country FE: 0.211*** (0.066)
    - Both FE: 0.167*** (0.047)

- Unemployment gap (휹3 품)
  - Benchmark:
    - OLS: -0.618*** (0.153)
    - Month FE: -0.354* (0.185)
    - Country FE: -0.632*** (0.152)
    - Both FE: -0.366* (0.184)
  - Alternative:
    - OLS: -0.622*** (0.156)
    - Month FE: -0.354* (0.178)
    - Country FE: -0.638*** (0.156)
    - Both FE: -0.366** (0.177)

- Digitalization — Cost-productivity channel (휷1 I P)
  - Benchmark and Alternative identical reporting:
    - OLS: -0.008** (0.003)
    - Month FE: -0.006* (0.003)
    - Country FE: -0.008** (0.003)
    - Both FE: -0.006* (0.003)

- Digitalization — second term (휷2 I P)
  - Benchmark:
    - OLS: -0.002 (0.007)
    - Month FE: -0.002 (0.004)
    - Country FE: -0.001 (0.007)
    - Both FE: -0.002 (0.005)
  - Alternative:
    - OLS: -0.005* (0.003)
    - Month FE: -0.002 (0.003)
    - Country FE: -0.005* (0.003)
    - Both FE: -0.002 (0.003)

- Digitalization — expectation channel (휷3 I P)
  - Benchmark reported:
    - OLS: -0.001 (0.002)
    - Month FE: 0.000 (0.002)
    - Country FE: -0.001 (0.002)
    - Both FE: -0.000 (0.002)
  - Alternative: corresponding entries shown where applicable; standard errors (0.002).

- Digitalization and the Slope of the Phillips Curve (휷4 I P)
  - Benchmark:
    - OLS: 0.007 (0.025)
    - Month FE: 0.002 (0.019)
    - Country FE: 0.007 (0.024)
    - Both FE: 0.001 (0.019)
  - Alternative:
    - OLS: 0.011 (0.023)
    - Month FE: 0.002 (0.002) [table shows 0.002 (0.002) for month FE]
    - Country FE: 0.011 (0.022)
    - Both FE: 0.001 (0.018)

- Other controls
  - NEER (휽1 넬)
    - Coefficients roughly: -0.002 (0.001) across specifications; some marked as -0.002* (0.001)
  - Energy inflation (휽2 에너)
    - Benchmark:
      - OLS: 0.015*** (0.002)
      - Month FE: 0.484*** (0.148)
      - Country FE: 0.014*** (0.002)
      - Both FE: 0.441*** (0.152)
    - Alternative similar: 0.015*** (0.002), 0.483*** (0.153), 0.014*** (0.002), 0.441*** (0.159)
  - Food inflation (휽2 푸드)
    - Benchmark:
      - OLS: 0.027** (0.011)
      - Month FE: -0.387** (0.164)
      - Country FE: 0.027** (0.011)
      - Both FE: -0.347** (0.168)
    - Alternative similar: 0.027** (0.011), -0.386** (0.169), 0.027** (0.011), -0.347* (0.176)

- Goodness of fit
  - R2: 0.980 (OLS), 0.983 (Month FE), 0.980 (Country FE), 0.983 (Both FE) — identical across Benchmark and Alternative.
  - adj. R2: 0.980, 0.982, 0.980, 0.983 correspondingly.

- Note: Clustered standard errors in parentheses. Significance levels: * p < 0.10, ** p < 0.05, *** p < 0.01.

### Table A3: Panel Regressions for Inflation, 1990.1 to 2017.12 (Digitalization Index – Standardized Coefficients)
- Sample size: N = 9019 for all specifications.
- Core standardized coefficient estimates (standard errors in parentheses). Significance levels as above.

Selected standardized estimates:

- Lagged inflation (휹1 풃): 0.846*** (0.051); 0.871*** (0.038); 0.843*** (0.050); 0.866*** (0.038) — same across Benchmark and Alternative columns reported.
- Inflation expectations (휹2 풇):
  - OLS: 0.121*** (0.042)
  - Month FE: 0.093*** (0.030)
  - Country FE: 0.127*** (0.041)
  - Both FE: 0.100*** (0.030)
  - Alternative: 0.120*** (0.040), 0.093*** (0.029), 0.126*** (0.039), 0.100*** (0.028)
- Unemployment gap (휹3 품):
  - OLS: -0.011*** (0.003)
  - Month FE: -0.006* (0.003)
  - Country FE: -0.012*** (0.003)
  - Both FE: -0.007* (0.003)
  - Alternative: similar with last cell -0.007** (0.003)
- Digitalization — Cost-productivity channel (휷1 I P):
  - OLS: -0.004** (0.002)
  - Month FE: -0.003* (0.002)
  - Country FE: -0.004** (0.002)
  - Both FE: -0.003* (0.002)
- Digitalization — second term (휷2 I P):
  - OLS: -0.001 (0.003)
  - Month FE: -0.001 (0.002)
  - Country FE: -0.001 (0.003)
  - Both FE: -0.001 (0.002)
  - Alternative shows small significant entries: -0.002* (0.001) in OLS and Country FE columns.
- Digitalization — expectation channel (휷3 I P):
  - OLS: -0.002 (0.007)
  - Month FE: 0.000 (0.005)
  - Country FE: -0.003 (0.007)
  - Both FE: -0.000 (0.005)
- Digitalization and the Slope of the Phillips Curve (휷4 I P): coefficients ~0.000–0.001 with standard errors (0.001).
- Other controls (standardized)
  - NEER (휽1 넬): -0.023 (0.014); -0.019 (0.012); -0.024* (0.014); -0.021* (0.012)
  - Energy inflation (휽2 에너): 0.018*** (0.002); 0.589*** (0.181); 0.017*** (0.002); 0.538*** (0.185)
  - Food inflation (휽2 푸드): 0.017** (0.007); -0.247** (0.105); 0.017** (0.007); -0.222** (0.107)
- R2 and adj. R2: 0.980 / 0.980 (OLS), 0.983 / 0.982 (Month FE), 0.980 / 0.980 (Country FE), 0.983 / 0.983 (Both FE).

### Key analytical takeaways from the reported tables and figures
- The Digitalization Index exhibits wide cross-country/time variation: Min = -16.91, Max = 29.25, Mean = 1.26, S.D. = 2.74 (N = 9019).
- Regression results consistently show:
  - A large, highly significant coefficient on lagged inflation (p < 0.01) across all specifications (coefficients about 0.84–0.87).
  - Inflation expectations enter positively and significantly in all specifications.
  - The unemployment gap enters negatively and significantly in most specifications.
  - The Digitalization Index, via the cost-productivity channel (휷1 I P), has a small negative and statistically significant effect on inflation in both raw and standardized coefficients (e.g., -0.008** raw; -0.004** standardized in OLS).
  - Other digitalization-related terms (휷2, 휷3, 휷4) are generally small and not consistently significant, with occasional marginal significance for 휷2 in the Alternative Specification.
  - Energy inflation exhibits a positive and significant association with headline inflation; food inflation coefficients vary in sign across fixed-effects specifications.

*Source: wpiea2019271-print-pdf - Annex I. Summary Statistics*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019271-print-pdf.pdf_