## From Servers to Rates: AI, ICT Capital, and the Natural Rate — Working Paper No. WP/2025/224 ## Source details **Canonical URL:** [From Servers to Rates: AI, ICT Capital, and the Natural Rate — Working Paper No. WP/2025/224](https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025224-source-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2025/english/wpiea2025224-source-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2025/english/wpiea2025224-source-pdf.pdf.json) --- ### Features Related to ICT Investment - Overview and motivation - Digital investment has entered a new phase fueled by the rapid rise of generative artificial intelligence (AI). - In 2024, U.S. corporations already allocated over four percent of GDP to information- and communication-technology (ICT) assets, including high-performance servers, specialized software, and advanced network infrastructure. - The paper develops a dynamic stochastic general equilibrium (DSGE) model à la Smets and Wouters (2007) to investigate: - How AI-driven ICT capital influences aggregate output, inflation, and the natural rate of interest. - How alternative future trajectories of AI-related ICT investment shape macroeconomic outcomes and affect the conduct of monetary policy. - Key model features: - Separation of ICT from non-ICT capital. - Distinct adjustment costs for ICT investment. - Flexible degree of substitutability between ICT capital and labor. - Model estimation sample: U.S. quarterly data from 1980Q1 to 2024Q2. - Main qualitative result - Macroeconomic consequences of AI adoption—and implications for monetary policy—depend critically on whether ICT capital complements or substitutes for labor. - Historical estimates point to mild gross substitutability between ICT capital and labor. - Counterfactual simulations highlight: - Easier substitution leads to higher ICT investment but smaller employment and wage gains. - Stronger complementarity dampens investment but strengthens employment, wage and consumption, thus pushing up the natural rate of interest. - Quantitative scenario outcomes (five-year horizon) - Across scenarios, the paper reports: - Annual GDP growth rises by 0.1 to 0.9 percentage point. - Inflation rises by 0.1 to 0.8 percentage point. - The natural rate of interest increases by up to 0.7 percentage point. - Caveats - The model abstracts from a direct ICT/AI impact on TFP, despite evidence that ICT—particularly with AI—may exert a direct impact on TFP with ambiguous implications for inflation. - The analysis focuses on aggregate macroeconomic outcomes and does not capture heterogeneous effects across worker groups. - Policy implications (summary) - Central banks should monitor both the volume of ICT investment and how it interacts with labor markets as AI-related ICT investment accelerates. - The degree of complementarity between labor and new technologies is central in shaping wage dynamics, inflation pressure, and the trajectory of the natural rate. - Risks: - If ICT adoption boosts labor demand and policymakers do not recognize a structural rise in the natural rate, an overly accommodative stance could fuel persistent inflation. - If ICT tends to displace labor, excessive monetary tightening may unnecessarily slow the economy. - Model structure — households and ICT investment (laws of motion and FOCs) - Households own both ICT and non-ICT capital and rent them to intermediate goods producers. ICT investment is denoted I_ICT and non-ICT investment I_t. The law of motion for the ICT capital stock, K_ICT_t, is given by: - K_ICT_t = (1→ω_ICT) K_ICT_{t→1} + exp(e x_ICT_t) (1→S_ICT) I_ICT_t / I_ICT_{t→1} .(1) - ω_ICT denotes the depreciation rate of ICT capital. - e x_ICT_t is a shock to the marginal efficiency of ICT investment. - S_ICT(·) represents the adjustment cost function with properties: S_ICT(1) = S_ICT↑(1) = 0, and S_ICT↑↑ = ε_ICT > 0. - First-order conditions for ICT capital: - Q_ICT_t = θ E_t [ (β_{t+1}/β_t) (R_ICT_{t+1} + Q_ICT_{t+1} (1→ω_ICT) ) ] ,(2) - 1 = Q_ICT_t exp(e x_ICT_t) (1→S_ICT( I_ICT_t / I_ICT_{t→1} )) → S_ICT↑( I_ICT_t / I_ICT_{t→1} ) & (I_ICT_t / I_ICT_{t→1}) + E_t [ (β_{t+1}/β_t) Q_ICT_{t+1} exp(e x_ICT_{t+1}) S_ICT↑( I_ICT_{t+1} / I_ICT_t ) & (I_ICT_{t+1} / I_ICT_t)^2 ] / 2 .(3) - Q_ICT_t denotes Tobin’s Q for ICT capital; R_ICT_{t+1} is the real gross rental rate for ICT capital. - Production technology and factor demand - Production nests ICT capital and labor in a CES aggregator E_t, used alongside non-ICT capital K_t in a Cobb-Douglas form: - Y_t = exp(e a_t) K_t^{ω} E_t^{1→ω} ,(4) - E_t = [ π_ICT (K_ICT_t)^{(ω→1)/ω} + π_L (L_t)^{(ω→1)/ω} ]^{ω/(ω→1)} ,(5) - Notation: - Y_t: output. - e a_t: TFP shock. - π: non-ICT capital share of income. - ρ (rho) is the elasticity of substitution between ICT capital and labor. - π_ICT and π_L are distribution parameters. - CES cases: - Cobb-Douglas when ρ ↑ 1. - Leontief (fixed proportions) when ρ ↑ 0. - Linear (perfect substitutes) when ρ ↑ ↓. - When 0 < ρ < 1, ICT capital and labor are gross complements. - When ρ > 1, they are gross substitutes. - Factor-demand conditions from cost-minimization: - R_k_t = μ_t π Y_t / K_t ,(6) - W_t = μ_t (1→π) π_L Y_t E_t^{ω→1)/ω} L_t^{1/ω} ,(7) - R_ICT_t = μ_t (1→π) π_ICT Y_t E_t^{(ω→1)/ω} (K_ICT_t)^{1/ω} ,(8) - μ_t denotes the Lagrange multiplier (marginal cost), R_k_t is the rental rate of non-ICT capital, and W_t is the nominal wage. - Parametrization note - CES distribution parameters can be re-parametrized based on steady-state income shares S_{K_ICT} and S_L and the elasticity of substitution ρ: - π_ICT = S_{k_ICT} (1→ω) [ E K_ICT ]^{(ω→1)/ω} and π_L = S_L (1→ω) [ E L ]^{(ω→1)/ω} , where E, K_ICT and L represent steady-state values. ### Linearized Model Equations - Households: equilibrium conditions and shocks - Households maximize lifetime utility U_t(·)=ln(C_t →h C_{t-1})→ L_t^{1+ε}/(1+ε) with habit parameter h and inverse Frisch elasticity ς. - Key log-linearized conditions: - Consumption Euler equation links ˆC_t to past and expected future consumption, the real interest rate (nominal rate ˆR_t minus expected inflation E_t[ˆπ_{t+1}]), and risk-premium shock e^b_t. - Wage-setting condition under Calvo-style nominal rigidity with indexation; real wage ˆW_t and hours ˆL_t feature with wage-stickiness parameters ω_w and ω_wi and wage mark-up shock e^w_t. - Investment dynamics: - Non-ICT investment: ˆI_t responds gradually with adjustment-cost parameter ε and Tobin’s Q ˆQ_t; shock e^x_t (IST shock). - ICT investment: ˆI_{ICT,t} with adjustment-cost parameter ε_{ICT} and Tobin’s Q_{ICT} ˆQ_{ICT,t}; shock e^{x}_{ICT,t}. - Capital accumulation: - Non-ICT: ˆK_{t+1}=(1→ω)ˆK_t+ω ˆI_t+ε e^x_t (equation 13) with depreciation rate ω. - ICT: ˆK_{ICT,t+1}=(1→ω_{ICT})ˆK_{ICT,t}+ω_{ICT} ˆI_{ICT,t}+ε_{ICT} e^{x}_{ICT,t} (equation 14) with depreciation rate ω_{ICT}. - Tobin’s Q equations for non-ICT and ICT capital depend positively on expected future rental rates and values, negatively on expected real interest rate, and include risk premium disturbance e^b_t. - Interpretation of shocks: - e^b_t: risk-premium shock raising required asset return, reducing consumption and investment, lowering value of capital. - e^x_t and e^{x}_{ICT,t}: IST shocks capturing variations in marginal efficiency of investment. - e^w_t: wage mark-up shock affecting wage-setting power. - Firms: production, factor demand, and price-setting - Output ˆY_t linked to technology shock e^a_t and inputs per equation (17); CES aggregator and composite-input definitions summarized in equation (18). - Factor prices and rental rates: - ICT rental rate (equation 19): ˆR_{ICT,t} is a function of the ratio of ICT capital to labor and the real wage ˆW_t. - Non-ICT rental rate (equation 20): ˆR_{k,t} depends on ratio between traditional and ICT capital, composite input, and ˆR_{ICT,t}. - Price-setting: - New Keynesian Phillips curve (equation 21) under Calvo pricing with indexation: - Price stickiness parameter ω_p and price indexation parameter ω_pi. - Inflation responds to expected and lagged inflation, marginal cost (function of output, CES input, labor, real wage), and price mark-up shock e^p_t. - Classification of shocks: - Shocks to ICT and non-ICT IST, risk premium, government spending, and monetary policy behave as demand shocks. - Shocks to TFP, price and wage mark-ups exhibit supply-shock dynamics. - Central bank rule, resource constraint, and exogenous processes - Taylor rule: - ˆR^n_t = ⇀i ˆR^n_{t-1} + (1→⇀i) [ ⇀θ ˆπ_t + ⇀y (ˆY_t → ˆY^n_t) + ⇀!y (change in output gap) ] + e^r_t. - Policy parameters: ⇀i (interest-rate smoothing), ⇀θ (inflation responsiveness), ⇀y (output-gap responsiveness), ⇀!y (changes in output gap responsiveness). - ˆY^n_t is potential output from a flexible-price/wage model; natural rate R^n_t computed similarly. - e^r_t: monetary policy shock. - Resource constraint: - ˆY_t = (C/Y) ˆC_t + (I/Y) ˆI_t + (I_{ICT}/Y) ˆI_{ICT,t} + (G/Y) e^g_t, with government spending shock e^g_t. - Exogenous processes: - Eight exogenous variables e^π_t with π ∈ {a, b, g, p, r, x, x_{ICT}, w} follow AR(1) with autoregressive parameters ⇀π and i.i.d. shocks ↽π with standard deviations ↼π, except price and wage mark-up shocks which follow ARMA(1,1) with MA coefficients μ_p and μ_w. - Data, measurement equations, and sample - Sample: quarterly data from 1980Q1 to 2024Q2; alternative samples include 2005Q1–2024Q2 and 1980Q1–2019Q4 (pre-COVID). - Rationale: start when ICT investment / GDP > 2 percent; ratio reaches about 4 per cent by end of sample. - Observables: (i) real GDP, (ii) real non-ICT investment, (iii) real ICT investment, (iv) real private consumption, (v) hours worked, (vi) GDP deflator, (vii) real wage, (viii) shadow nominal interest rate. - Shadow nominal interest rate from Wu and Xia (2016), complemented by federal funds rate prior to 1990Q1 and after 2023Q2. - Transformations: - GDP, consumption, non-ICT investment, ICT investment, real wage, GDP deflator: logged and first-differenced. - Shadow nominal interest rate: quarterly terms. - Hours worked: logged and demeaned. - Measurement equation linking observables to model variables reported (equation 24), with common quarterly trend growth rate ̄γ, average hours ̄L, steady-state inflation ̄φ and interest rate ̄r^n. - Calibration, priors and posterior estimates (selected) - Calibrated parameters: - Discount factor θ = 0.99 (targets annual risk-free rate of 4 percent). - Non-ICT capital depreciation rate ω = 0.025 (10 percent p.a.). - Labor share S_L = 0.67 (two thirds of income). - Elasticities of substitution in goods and labor, ↽ and ↽_w = 6 (targets gross steady-state mark-up of 1.20). - Government spending to GDP g_y = 0.2. - ICT capital depreciation rate ω_{ICT} = 0.057. - ICT capital share S_{k,ICT} = 0.067. - Estimation details: - Two Metropolis-Hastings chains, each with 500,000 draws. - Priors: Inverse Gamma for shock standard deviations (loose prior, 2 degrees of freedom); Beta for parameters in [0,1]; Normal for unbounded parameters. - Prior mean of ICT investment adjustment costs set equal to non-ICT investment; prior for elasticity of substitution between labor and ICT capital centered at 1 with standard deviation 0.50. - Selected posterior means and 95 percent credible intervals: - Calvo prices π_p: posterior mean 0.85 [0.83;0.88] - Calvo wages π_w: posterior mean 0.81 [0.76;0.86] - Price indexation π_pi: posterior mean 0.20 [0.08;0.32] - Wage indexation π_wi: posterior mean 0.68 [0.49;0.87] - Habit parameter h: posterior mean 0.21 [0.16;0.26] - Inverse Frisch elasticity ρ: posterior mean 2.91 [2.33;3.50] - Non-ICT investment adjustment costs ς: posterior mean 3.12 [2.18;4.02] - ICT investment adjustment costs ς_{ICT}: posterior mean 7.20 [5.39;8.99] - Elasticity of substitution φ (between labor and ICT capital): posterior mean 1.51 [0.94;2.07] - Inflation - Taylor rule coefficient ⇀ω: posterior mean 1.92 [1.73;2.11] - Output - Taylor rule coefficient ⇀y: posterior mean 0.04 [0.02;0.06] - Taylor rule changes in y ⇀!y: posterior mean 0.16 [0.12;0.21] - Taylor rule smoothing ⇀i: posterior mean 0.81 [0.78;0.85] - Trend ̄γ: posterior mean 0.34 [0.29;0.38] - Inflation steady state ̄φ: posterior mean 0.59 [0.47;0.72] - Interest rate steady state ̄R: posterior mean 0.94 [0.72;1.15] - Hours steady state ̄L: posterior mean 0.06 [-0.27;0.39] - Exogenous processes posterior highlights: - Technology persistence ↼a: posterior mean 0.97 [0.96;0.99] - Price mark-up persistence ↼p: posterior mean 0.99 [0.97;1.00] - Price mark-up MA μ_p: posterior mean 0.79 [0.70;0.88] - Wage mark-up persistence ↼w: posterior mean 0.48 [0.17;0.78] - Wage mark-up MA μ_w: posterior mean 0.50 [0.21;0.78] - ICT investment persistence ↼x_{ICT}: posterior mean 0.98 [0.97;1.00] - Non-ICT investment persistence ↼x: posterior mean 0.98 [0.97;1.00] - Preference shock persistence ↼b: posterior mean 0.88 [0.84;0.92] - Government spending persistence ↼g: posterior mean 0.92 [0.89;0.95] - Key interpretations: - Posterior mean φ = 1.51 [0.94;2.07] favors moderate gross substitutability between labor and ICT capital, though Cobb-Douglas (ρ=1) is not ruled out. - ICT investment adjustment costs ς_{ICT} (mean 7.20) substantially exceed non-ICT ς (mean 3.12), suggesting large implementation frictions for ICT adoption. - Habit persistence low (h = 0.21), yet output and consumption impulse responses are smooth, indicating endogenous persistence beyond habit. - Taylor rule: strong response to inflation (1.92), weak response to output gap (0.04), notable response to changes in the output gap (0.16); interest-rate smoothing 0.81. - Most shocks are highly persistent except wage mark-up and monetary policy shocks. - Robustness: - Estimates for 2000Q1–2024Q2 and pre-COVID 1980Q1–2019Q4 show deep parameters similar to full sample; ICT-specific parameters used in simulations are very similar across samples. - IRFs to all shocks exhibit expected signs and shapes with relatively narrow 95-percent confidence bands. ### Variance Decomposition - Key findings on variance decomposition - At a 1-year horizon, demand shocks account for two thirds of output fluctuations, with risk premium shocks playing the largest role. - ICT IST shocks increase in importance over time, explaining 15.5 percent of output movements in the longer run. - The role of government and monetary policy shocks decays over time. - ICT IST shocks play a larger role for the variance of output than for the variance of inflation. - On impact, supply shocks—specifically the price mark-up shock—play a dominant role in affecting inflation dynamics; in the medium-to-long run, demand disturbances are the main drivers of inflation. - Fluctuations in the natural rate of interest are driven primarily by the risk premium shocks both in the short and in the medium-to-long term. - TFP shocks are more relevant in the short run and their importance decays over time, contrary to the ICT and non-ICT IST shocks, the importance of which increases over time. - Price mark-up, wage mark-up and monetary policy shocks have zero contributions by construction. - Quantitative and historical magnitudes (model-implied natural rate) - The model-implied natural rate of interest reached a peak of 8.4 percent in 1981. - The natural rate followed a persistent downward trend and hit -5.2 percent in 2020. - The natural rate moved back above zero and reached an estimated 2.3 percent in 2023. - The estimated natural rate is a short-run equilibrium concept and is more volatile than medium-term estimates from semi-structural or statistical models. - Interpretation of drivers of the natural rate - Risk premium shocks account for a sizable share of deviations of the natural rate from its steady state, with negative contributions during periods of heightened uncertainty. - Shifts in households’ preferences on savings (precautionary savings or preference for safe assets) are relevant for explaining movements in the natural rate of interest. - TFP shocks display variability and partially offset or amplify the effects of risk premium shocks across historical episodes (e.g., negative TFP contributions in the mid 1980s; positive in the early 1990s with IT rise; negative in early 2000s and post-global financial crisis). - ICT investment contributions are consistently positive but modest relative to non-ICT investment because ICT remains a smaller fraction of total investment. - Non-ICT IST shocks produce larger contributions to the natural rate owing to the larger non-ICT component of investment, with patterns that: - bolstered the natural rate in the early 1980s amid robust capital deepening; - turned negative in the 1990s and early 2000s as manufacturing offshored and slowed; - returned positive in the late 2010s alongside renewed capital spending. - Government spending shocks show more sporadic effects, reflecting their role as a residual category in the closed-economy DSGE framework. ### Evolution of ICT Investment and Scenarios - Recent trends and context - Deloitte survey (Raskovich et al., 2024): in 2024 U.S. firms allocated 7.5 percent of revenue to digital transformation, with 5.4 percent directed specifically through IT departments—nearly double the share from just four years earlier. - Gartner (2025) projection: worldwide IT spending to grow by 9.8 percent in 2025, reaching U.S. $5.6 trillion, with U.S. firms contributing disproportionately to this expansion. - Narrative: rapid uptake of generative AI and renewed corporate digital-transformation efforts have driven a clear uptick in ICT investment since 2023, suggesting a potential new phase of ICT capital deepening comparable in macroeconomic importance to the 1990s surge. - Historical: ICT-investment-to-GDP ratio rose steeply in the 1990s, peaking at approximately 4.5 percent of GDP in 2000, declined after the dot-com crash, then trended upward with a distinct uptick since 2023. - Scenario definitions and projected paths (2025–2029) - Conservative scenario: - Extends the linear trend observed since 2003. - ICT-investment-to-GDP ratio reaches 4.3 percent by 2029. - Corresponds to average nominal ICT investment growth of approximately 6.3 percent per year (IMF WEO April 2025 used for nominal GDP). - After adjustment for inflation and population, implies real per capita ICT investment growth of approximately 3.3 percent per year. - Ambitious scenario: - Assumes industry momentum translates into a steeper trajectory. - ICT-investment-to-GDP ratio reaches 5.0 percent by 2029, surpassing historical high. - Requires nominal ICT investment growth of about 9.4 percent annually. - After adjustment implies real per capita ICT investment growth of 6.4 percent annually. - Simulation design and calibration - ICT investment paths are held constant across calibrations and the sequence of ICT IST shocks is adjusted to replicate these paths in real per capita terms. - Nominal growth rates converted to real per capita using IMF WEO GDP deflator projections and recent U.S. population growth averages. - Elasticity of substitution calibrations: - Baseline calibration: ρ = 1.51 (posterior mean). - Greater factor complementarity: ρ = 0.50. - Greater factor substitutability: ρ = 3.00. - Mechanism: - With stronger complementarity, delivering the same ICT investment path requires proportionally larger increases in labor input → larger ICT IST shocks and stronger macro impulses. - With greater substitutability, ICT capital can more readily replace labor → smaller IST shocks and muted aggregate effects. - Quantitative macroeconomic impacts (average annual impact over a five-year horizon; percentage points) - Conservative Scenario - Baseline calibration: GDP Growth 0.13 ; Inflation 0.12 ; Nat. Rate 0.01 - Greater factor complementarity: GDP Growth 0.44 ; Inflation 0.44 ; Nat. Rate 0.37 - Greater factor substitutability: GDP Growth 0.11 ; Inflation 0.09 ; Nat. Rate -0.02 - Ambitious Scenario - Baseline calibration: GDP Growth 0.25 ; Inflation 0.23 ; Nat. Rate 0.02 - Greater factor complementarity: GDP Growth 0.86 ; Inflation 0.85 ; Nat. Rate 0.73 - Greater factor substitutability: GDP Growth 0.22 ; Inflation 0.17 ; Nat. Rate -0.03 - Aggregate ranges highlighted: - Annual GDP growth rises by 0.1-0.9 percentage point. - Inflation rises by 0.1-0.8 percentage point. - The natural rate rises by up to 0.7 percentage point. - Model experiment insights - Complements (low ρ) imply the same ICT investment trajectory delivers: - Larger labor demand, stronger upward pressure on wages, inflation, and aggregate demand. - A materially higher natural rate (example: ambitious + complementarity → natural rate up 0.73 percentage point). - Substitutes (high ρ) imply: - Easier labor displacement, eased capacity constraints, dampened wage and price pressures. - Marginal or negative movement in the natural rate in some calibrations. - Policy implications and considerations - The labor-technology elasticity crucially determines inflationary pressure and the level of the natural rate; identical ICT investment paths may warrant very different policy responses depending on ρ. - Accurate assessment of the natural rate trajectory in the AI era requires judgment on the nature of technological change, not only real-time output and inflation data. - Risks of misjudgment: - Underestimating complementarity risks falling behind a rising natural rate (operating closer to the effective lower bound). - Overestimating complementarity when substitutability prevails risks needlessly restraining the economy. - Directions for future research: - Incorporate potential TFP effects of AI (explicitly excluded from these simulations). - Extend analysis to include international spillovers, firm heterogeneity in adoption, and coordinated fiscal measures to smooth transition to an AI-intensive production landscape. *Source: wpiea2025224-source-pdf — From Servers to Rates: AI, ICT Capital, and the Natural Rate — Working Paper No. WP/2025/224* ### 2.1 Features Related to ICT Investment . . . . . . . . . . . . . . . . . . . . . . .9 ### 2.1 Features Related to ICT Investment ### Overview and motivation - Digital investment has entered a new phase fueled by the rapid rise of generative artificial intelligence (AI). - In 2024, U.S. corporations already allocated over four percent of GDP to information- and communication-technology (ICT) assets, including high-performance servers, specialized software, and advanced network infrastructure. - The paper develops a dynamic stochastic general equilibrium (DSGE) model à la Smets and Wouters (2007) to investigate: - How AI-driven ICT capital influences aggregate output, inflation, and the natural rate of interest. - How alternative future trajectories of AI-related ICT investment shape macroeconomic outcomes and affect the conduct of monetary policy. - Key model features: - Separation of ICT from non-ICT capital. - Distinct adjustment costs for ICT investment. - Flexible degree of substitutability between ICT capital and labor. - Model estimation sample: U.S. quarterly data from 1980Q1 to 2024Q2. ### Main qualitative result - The macroeconomic consequences of AI adoption—and the resulting implications for monetary policy—depend critically on whether ICT capital complements or substitutes for labor. - Historical estimates point to mild gross substitutability between ICT capital and labor. - Counterfactual simulations highlight that: - Easier substitution leads to higher ICT investment but smaller employment and wage gains. - Stronger complementarity dampens investment but strengthens employment, wage and consumption, thus pushing up the natural rate of interest. ### Quantitative scenario outcomes (five-year horizon) - Across scenarios, the paper reports: - Annual GDP growth rises by 0.1 to 0.9 percentage point. - Inflation rises by 0.1 to 0.8 percentage point. - The natural rate of interest increases by up to 0.7 percentage point. ### Caveats highlighted in the paper - The model abstracts from a direct ICT/AI impact on TFP, despite evidence that ICT—particularly with AI—may exert a direct impact on TFP with ambiguous implications for inflation. - The analysis focuses on aggregate macroeconomic outcomes and does not capture heterogeneous effects across worker groups. ### Policy implication summary - As AI-related ICT investment accelerates, central banks should monitor both the volume of investment and how it interacts with labor markets. - The degree of complementarity between labor and new technologies is central in shaping wage dynamics, inflation pressure, and the trajectory of the natural rate. - Risks: - If ICT adoption boosts labor demand and policymakers do not recognize a structural rise in the natural rate, an overly accommodative stance could fuel persistent inflation. - If ICT tends to displace labor, excessive monetary tightening may unnecessarily slow the economy. ### Model structure — households and ICT investment (laws of motion and FOCs) - Households own both ICT and non-ICT capital and rent them to intermediate goods producers. ICT investment is denoted I_ICT and non-ICT investment I_t. The law of motion for the ICT capital stock, K_ICT_t, is given by: K_ICT_t = (1→ω_ICT) K_ICT_{t→1} + exp(e x_ICT_t) (1→S_ICT) I_ICT_t / I_ICT_{t→1} .(1) - Here: - ω_ICT denotes the depreciation rate of ICT capital. - e x_ICT_t is a shock to the marginal efficiency of ICT investment. - S_ICT(·) represents the adjustment cost function with properties: S_ICT(1) = S_ICT↑(1) = 0, and S_ICT↑↑ = ε_ICT > 0. - First-order conditions (Tobin’s Q and investment Euler-type) for ICT capital: Q_ICT_t = θ E_t [ (β_{t+1}/β_t) (R_ICT_{t+1} + Q_ICT_{t+1} (1→ω_ICT) ) ] ,(2) 1 = Q_ICT_t exp(e x_ICT_t) (1→S_ICT( I_ICT_t / I_ICT_{t→1} )) → S_ICT↑( I_ICT_t / I_ICT_{t→1} ) & (I_ICT_t / I_ICT_{t→1}) + E_t [ (β_{t+1}/β_t) Q_ICT_{t+1} exp(e x_ICT_{t+1}) S_ICT↑( I_ICT_{t+1} / I_ICT_t ) & (I_ICT_{t+1} / I_ICT_t)^2 ] / 2 ,(3) - Where Q_ICT_t denotes the Tobin’s Q for ICT capital, and R_ICT_{t+1} is the real gross rental rate for ICT capital. ### Production technology and factor demand - Production function nests ICT capital and labor in a CES aggregator E_t, used alongside non-ICT capital K_t in a Cobb-Douglas form: Y_t = exp(e a_t) K_t^{ω} E_t^{1→ω} ,(4) E_t = [ π_ICT (K_ICT_t)^{(ω→1)/ω} + π_L (L_t)^{(ω→1)/ω} ]^{ω/(ω→1)} ,(5) - Notation and interpretation: - Y_t: output. - e a_t: TFP shock. - π: non-ICT capital share of income. - ρ (rho) is the elasticity of substitution between ICT capital and labor. - π_ICT and π_L are distribution parameters. - CES cases described: - Cobb-Douglas when ρ ↑ 1. - Leontief (fixed proportions) when ρ ↑ 0. - Linear (perfect substitutes) when ρ ↑ ↓. - When 0 < ρ < 1, ICT capital and labor are gross complements. - When ρ > 1, they are gross substitutes. - Cost-minimization by intermediate goods producers yields factor-demand conditions: R_k_t = μ_t π Y_t / K_t ,(6) W_t = μ_t (1→π) π_L Y_t E_t^{ω→1)/ω} L_t^{1/ω} ,(7) R_ICT_t = μ_t (1→π) π_ICT Y_t E_t^{(ω→1)/ω} (K_ICT_t)^{1/ω} ,(8) - Where μ_t denotes the Lagrange multiplier (marginal cost), R_k_t is the rental rate of non-ICT capital, and W_t is the nominal wage. ### Parametrization note - CES distribution parameters can be re-parametrized based on steady-state income shares of ICT capital and labor, S_{K_ICT} and S_L, and the elasticity of substitution ρ, so that: π_ICT = S_{k_ICT} (1→ω) [ E K_ICT ]^{(ω→1)/ω} and π_L = S_L (1→ω) [ E L ]^{(ω→1)/ω} , where E, K_ICT and L represent steady-state values. *Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025224-source-pdf.pdf* ### 2.2 Linearized Model Equations ### 2.2 Linearized Model Equations ### Households: equilibrium conditions and shocks - Households maximize lifetime utility U_t(·)=ln(C_t →h C_{t-1})→ L_t^{1+ε}/(1+ε) with habit parameter h and inverse Frisch elasticity ς. - Key log-linearized conditions: - Consumption Euler equation (equation 9) linking ˆC_t to past and expected future consumption, the real interest rate (nominal rate ˆR_t minus expected inflation E_t[ˆπ_{t+1}]), and risk-premium shock e^b_t. - Wage-setting condition under Calvo-style nominal rigidity with indexation (equation 10); real wage ˆW_t and hours ˆL_t feature with wage-stickiness parameters ω_w and ω_wi and wage mark-up shock e^w_t. - Investment dynamics: - Non-ICT investment (equation 11): ˆI_t responds gradually with adjustment-cost parameter ε and Tobin’s Q ˆQ_t; shock e^x_t (IST shock). - ICT investment (equation 12): ˆI_{ICT,t} with adjustment-cost parameter ε_{ICT} and Tobin’s Q_{ICT} ˆQ_{ICT,t}; shock e^{x}_{ICT,t}. - Capital accumulation: - Non-ICT: ˆK_{t+1}=(1→ω)ˆK_t+ω ˆI_t+ε e^x_t (equation 13) with depreciation rate ω. - ICT: ˆK_{ICT,t+1}=(1→ω_{ICT})ˆK_{ICT,t}+ω_{ICT} ˆI_{ICT,t}+ε_{ICT} e^{x}_{ICT,t} (equation 14) with depreciation rate ω_{ICT}. - Tobin’s Q equations for non-ICT and ICT capital (equations 15 and 16) depend positively on expected future rental rates and values, negatively on expected real interest rate, and include risk premium disturbance e^b_t. - Interpretation of shocks: - e^b_t: risk-premium shock capturing a wedge between policy rate and household asset return; raises required asset return, reduces consumption and investment, lowers value of capital. - e^x_t and e^{x}_{ICT,t}: IST shocks capturing variations in marginal efficiency of investment. - e^w_t: wage mark-up shock affecting wage-setting power. ### Firms: production, factor demand, and price-setting - Production and input aggregation: - Output ˆY_t linked to technology shock e^a_t and inputs per equation (17). - CES aggregator and composite-input definitions summarized in equation (18). - Factor prices and rental rates: - ICT rental rate (equation 19): ˆR_{ICT,t} is a function of the ratio of ICT capital to labor and the real wage ˆW_t. - Non-ICT rental rate (equation 20): ˆR_{k,t} depends on ratio between traditional and ICT capital, composite input, and ˆR_{ICT,t}. - Price-setting: - New Keynesian Phillips curve (equation 21) under Calvo pricing with indexation: - Price stickiness parameter ω_p and price indexation parameter ω_pi. - Inflation responds to expected and lagged inflation, marginal cost (function of output, CES input, labor, real wage), and price mark-up shock e^p_t. - Classification of shocks: - Shocks to ICT and non-ICT IST, risk premium, government spending, and monetary policy behave as demand shocks. - Shocks to TFP, price and wage mark-ups exhibit supply-shock dynamics. ### Central bank rule, resource constraint, and exogenous processes - Taylor rule (equation 22): - ˆR^n_t = ⇀i ˆR^n_{t-1} + (1→⇀i) [ ⇀θ ˆπ_t + ⇀y (ˆY_t → ˆY^n_t) + ⇀!y (change in output gap) ] + e^r_t. - Policy parameters: ⇀i (interest-rate smoothing), ⇀θ (inflation responsiveness), ⇀y (output-gap responsiveness), ⇀!y (changes in output gap responsiveness). - ˆY^n_t is potential output from a flexible-price/wage model; natural rate R^n_t computed similarly. - e^r_t: monetary policy shock. - Resource constraint (equation 23): - ˆY_t = (C/Y) ˆC_t + (I/Y) ˆI_t + (I_{ICT}/Y) ˆI_{ICT,t} + (G/Y) e^g_t, with government spending shock e^g_t. - Exogenous processes: - Eight exogenous variables e^π_t with π ∈ {a, b, g, p, r, x, x_{ICT}, w} follow AR(1) with autoregressive parameters ⇀π and i.i.d. shocks ↽π with standard deviations ↼π, except price and wage mark-up shocks which follow ARMA(1,1) with MA coefficients μ_p and μ_w. ### Data, measurement equations, and sample - Sample: quarterly data from 1980Q1 to 2024Q2; alternative samples include 2005Q1–2024Q2 and 1980Q1–2019Q4 (pre-COVID). - Rationale: start when ICT investment / GDP > 2 percent; ratio reaches about 4 per cent by end of sample. - Observables: (i) real GDP, (ii) real non-ICT investment, (iii) real ICT investment, (iv) real private consumption, (v) hours worked, (vi) GDP deflator, (vii) real wage, (viii) shadow nominal interest rate. - Shadow nominal interest rate from Wu and Xia (2016), complemented by federal funds rate prior to 1990Q1 and after 2023Q2. - Transformations: - GDP, consumption, non-ICT investment, ICT investment, real wage, GDP deflator: logged and first-differenced. - Shadow nominal interest rate: quarterly terms. - Hours worked: logged and demeaned. - Measurement equation linking observables to model variables reported (equation 24), with common quarterly trend growth rate ̄γ, average hours ̄L, steady-state inflation ̄φ and interest rate ̄r^n. ### Calibration, priors and posterior estimates (key calibrated values and posteriors) - Calibrated parameters (Table 1): - Discount factor θ = 0.99 (targets annual risk-free rate of 4 percent). - Non-ICT capital depreciation rate ω = 0.025 (10 percent p.a.). - Labor share S_L = 0.67 (two thirds of income). - Elasticities of substitution in goods and labor, ↽ and ↽_w = 6 (targets gross steady-state mark-up of 1.20). - Government spending to GDP g_y = 0.2. - ICT capital depreciation rate ω_{ICT} = 0.057. - ICT capital share S_{k,ICT} = 0.067. - Estimation details: - Two Metropolis-Hastings chains, each with 500,000 draws. - Priors: Inverse Gamma for shock standard deviations (loose prior, 2 degrees of freedom); Beta for parameters in [0,1]; Normal for unbounded parameters. - Prior mean of ICT investment adjustment costs set equal to non-ICT investment; prior for elasticity of substitution between labor and ICT capital centered at 1 with standard deviation 0.50. - Selected posterior means and 95 percent credible intervals (from Table 2): - Calvo prices π_p: posterior mean 0.85 [0.83;0.88] - Calvo wages π_w: posterior mean 0.81 [0.76;0.86] - Price indexation π_pi: posterior mean 0.20 [0.08;0.32] - Wage indexation π_wi: posterior mean 0.68 [0.49;0.87] - Habit parameter h: posterior mean 0.21 [0.16;0.26] - Inverse Frisch elasticity ρ: posterior mean 2.91 [2.33;3.50] - Non-ICT investment adjustment costs ς: posterior mean 3.12 [2.18;4.02] - ICT investment adjustment costs ς_{ICT}: posterior mean 7.20 [5.39;8.99] - Elasticity of substitution φ (between labor and ICT capital): posterior mean 1.51 [0.94;2.07] - Inflation - Taylor rule coefficient ⇀ω: posterior mean 1.92 [1.73;2.11] - Output - Taylor rule coefficient ⇀y: posterior mean 0.04 [0.02;0.06] - Taylor rule changes in y ⇀!y: posterior mean 0.16 [0.12;0.21] - Taylor rule smoothing ⇀i: posterior mean 0.81 [0.78;0.85] - Trend ̄γ: posterior mean 0.34 [0.29;0.38] - Inflation steady state ̄φ: posterior mean 0.59 [0.47;0.72] - Interest rate steady state ̄R: posterior mean 0.94 [0.72;1.15] - Hours steady state ̄L: posterior mean 0.06 [-0.27;0.39] - Exogenous processes posterior highlights (selected): - Technology persistence ↼a: posterior mean 0.97 [0.96;0.99] - Price mark-up persistence ↼p: posterior mean 0.99 [0.97;1.00] - Price mark-up MA μ_p: posterior mean 0.79 [0.70;0.88] - Wage mark-up persistence ↼w: posterior mean 0.48 [0.17;0.78] - Wage mark-up MA μ_w: posterior mean 0.50 [0.21;0.78] - ICT investment persistence ↼x_{ICT}: posterior mean 0.98 [0.97;1.00] - Non-ICT investment persistence ↼x: posterior mean 0.98 [0.97;1.00] - Preference shock persistence ↼b: posterior mean 0.88 [0.84;0.92] - Government spending persistence ↼g: posterior mean 0.92 [0.89;0.95] - Key interpretative findings: - Posterior mean of elasticity of substitution between labor and ICT capital φ = 1.51 with 95-percent credible interval [0.94;2.07]; posterior concentrated around values above unity, favoring moderate gross substitutability, though Cobb-Douglas (ρ=1) is not ruled out. - Adjustment costs: ICT investment adjustment costs ς_{ICT} (mean 7.20) are substantially higher than non-ICT ς (mean 3.12), suggesting large implementation frictions for ICT adoption (organizational restructuring, training, process reengineering). - Habit persistence low (h = 0.21), yet impulse responses of output and consumption are smooth, indicating endogenous persistence beyond habit. - Taylor rule estimates: strong response to inflation (1.92), weak response to output gap (0.04), and notable response to changes in output gap (0.16); interest-rate smoothing 0.81. - Most shocks are highly persistent except wage mark-up and monetary policy shocks. - Robustness and subsamples: - Estimates for 2000Q1–2024Q2 and pre-COVID 1980Q1–2019Q4 show deep parameters similar to full sample; ICT-specific parameters used in simulations are very similar across samples. - Impulse response functions (IRFs) to all shocks exhibit expected signs and shapes with relatively narrow 95-percent confidence bands; IRFs for ICT and non-ICT IST, risk premium, government spending and monetary policy act like demand shocks, while TFP, price and wage mark-ups act like supply shocks. *Source: wpiea2025224-source-pdf - 2.2 Linearized Model Equations* ### 3.3 Variance Decomposition ### 3.3 Variance Decomposition ### Key findings on variance decomposition - At a 1-year horizon, demand shocks account for two thirds of output fluctuations, with risk premium shocks playing the largest role. - ICT IST shocks increase in importance over time, explaining 15.5 percent of output movements in the longer run. - The role of government and monetary policy shocks decays over time. - ICT IST shocks play a larger role for the variance of output than for the variance of inflation. - On impact, supply shocks—specifically the price mark-up shock—play a dominant role in affecting inflation dynamics; in the medium-to-long run, demand disturbances are the main drivers of inflation. - Fluctuations in the natural rate of interest are driven primarily by the risk premium shocks both in the short and in the medium-to-long term. - TFP shocks are more relevant in the short run and their importance decays over time, contrary to the ICT and non-ICT IST shocks, the importance of which increases over time. - Price mark-up, wage mark-up and monetary policy shocks have zero contributions by construction. ### Quantitative and historical magnitudes (model-implied natural rate) - The model-implied natural rate of interest reached a peak of 8.4 percent in 1981. - The natural rate followed a persistent downward trend and hit -5.2 percent in 2020. - The natural rate moved back above zero and reached an estimated 2.3 percent in 2023. - The estimated natural rate is a short-run equilibrium concept and is more volatile than medium-term estimates from semi-structural or statistical models. ### Interpretation of drivers of the natural rate - Risk premium shocks account for a sizable share of deviations of the natural rate from its steady state, with negative contributions during periods of heightened uncertainty. - The results indicate that shifts in households’ preferences on savings (precautionary savings or preference for safe assets) are relevant for explaining movements in the natural rate of interest. - TFP shocks display variability and partially offset or amplify the effects of risk premium shocks across different historical episodes (e.g., negative TFP contributions in the mid 1980s; positive in the early 1990s with IT rise; negative in early 2000s and post-global financial crisis). - ICT investment contributions are consistently positive but modest relative to non-ICT investment because ICT remains a smaller fraction of total investment. - Non-ICT IST shocks produce larger contributions to the natural rate owing to the larger non-ICT component of investment, with patterns that: - bolstered the natural rate in the early 1980s amid robust capital deepening; - turned negative in the 1990s and early 2000s as manufacturing offshored and slowed; - returned positive in the late 2010s alongside renewed capital spending. - Government spending shocks show more sporadic effects, reflecting their role as a residual category in the closed-economy DSGE framework. *Source: wpiea2025224-source-pdf - 3.3 Variance Decomposition* ### 5.1 Evolution of ICT Investment and Scenarios ### 5.1 Evolution of ICT Investment and Scenarios ### Recent trends in ICT investment - Deloitte survey (Raskovich et al., 2024): in 2024 U.S. firms allocated 7.5 percent of revenue to digital transformation, with 5.4 percent directed specifically through IT departments—nearly double the share from just four years earlier. - Gartner (2025) projection: worldwide IT spending to grow by 9.8 percent in 2025, reaching U.S. $5.6 trillion, with U.S. firms contributing disproportionately to this expansion. - Narrative: rapid uptake of generative AI and renewed corporate digital-transformation efforts have driven a clear uptick in ICT investment since 2023, suggesting a potential new phase of ICT capital deepening comparable in macroeconomic importance to the 1990s surge. ### Historical context and stylized facts - ICT-investment-to-GDP ratio history (1985–2024): rose steeply in the 1990s, peaking at approximately 4.5 percent of GDP in 2000, declined after the dot-com crash, then followed a slower upward trend through the 2000s and 2010s driven by cloud, mobile, and digital services, with a distinct uptick since 2023. ### Scenario definitions and projected paths (2025–2029) - Conservative scenario: - Extends the linear trend observed since 2003. - ICT-investment-to-GDP ratio reaches 4.3 percent by 2029. - Corresponds to average nominal ICT investment growth of approximately 6.3 percent per year (IMF WEO April 2025 used for nominal GDP). - After adjustment for inflation and population, implies real per capita ICT investment growth of approximately 3.3 percent per year. - Ambitious scenario: - Assumes industry momentum translates into a steeper trajectory. - ICT-investment-to-GDP ratio reaches 5.0 percent by 2029, surpassing historical high. - Requires nominal ICT investment growth of about 9.4 percent annually. - After adjustment implies real per capita ICT investment growth of 6.4 percent annually. ### Simulation design and calibration - Implementation: ICT investment paths are held constant across calibrations and the sequence of ICT investment-specific technology (ICT IST) shocks is adjusted to replicate these paths in real per capita terms. - Conversion note: nominal growth rates converted to real per capita using IMF WEO GDP deflator projections and recent U.S. population growth averages. - Elasticity of substitution calibrations (to capture uncertainty over AI’s labor role): - Baseline calibration: ρ = 1.51 (posterior mean of estimated model parameters). - Greater factor complementarity: ρ = 0.50. - Greater factor substitutability: ρ = 3.00. - Mechanism: with stronger complementarity, delivering the same ICT investment path requires proportionally larger increases in labor input → larger ICT IST shocks and stronger macroeconomic impulses; with greater substitutability, ICT capital can more readily replace labor → smaller IST shocks and muted aggregate effects. ### Quantitative macroeconomic impacts (average annual impact over a five-year horizon; percentage points) - Table 4 results summarized by scenario and calibration: - Conservative Scenario - Baseline calibration: GDP Growth 0.13 ; Inflation 0.12 ; Nat. Rate 0.01 - Greater factor complementarity: GDP Growth 0.44 ; Inflation 0.44 ; Nat. Rate 0.37 - Greater factor substitutability: GDP Growth 0.11 ; Inflation 0.09 ; Nat. Rate -0.02 - Ambitious Scenario - Baseline calibration: GDP Growth 0.25 ; Inflation 0.23 ; Nat. Rate 0.02 - Greater factor complementarity: GDP Growth 0.86 ; Inflation 0.85 ; Nat. Rate 0.73 - Greater factor substitutability: GDP Growth 0.22 ; Inflation 0.17 ; Nat. Rate -0.03 - Aggregate ranges highlighted in conclusions: - Across assumptions about scale of the ICT investment surge and labor-technology substitution: - Annual GDP growth rises by 0.1-0.9 percentage point. - Inflation rises by 0.1-0.8 percentage point. - The natural rate rises by up to 0.7 percentage point. ### Key model experiment insights - When ICT capital and labor are complements (low ρ), the same observable ICT investment trajectory implies: - Larger labor demand, stronger upward pressure on wages, inflation, and aggregate demand. - A materially higher natural rate of interest (example: ambitious + complementarity → natural rate up 0.73 percentage point). - When ICT capital and labor are substitutes (high ρ), the same ICT investment trajectory implies: - Easier labor displacement, eased capacity constraints, dampened wage and price pressures. - Marginal or negative movement in the natural rate of interest in some calibrations. ### Policy implications and considerations - Monetary policy sensitivity: - The labor-technology elasticity crucially determines inflationary pressure and the level of the natural rate; identical ICT investment paths may warrant very different policy responses depending on ρ. - Accurate assessment of the natural rate trajectory in the AI era requires judgment on the nature of technological change, not only real-time output and inflation data. - Risks of misjudgment: - Underestimating complementarity risks falling behind a rising natural rate (operating closer to the effective lower bound). - Overestimating complementarity when substitutability prevails risks needlessly restraining the economy. - Directions for future research (beyond scope of current simulations): - Incorporate potential TFP effects of AI (explicitly excluded from these simulations). - Extend analysis to include international spillovers, firm heterogeneity in adoption, and coordinated fiscal measures to smooth transition to an AI-intensive production landscape. *Source: 5.1 Evolution of ICT Investment and Scenarios (chapter/section content from the provided IMF source PDF).* ### References ### References ### Works on AI, technology, and growth - Acemoglu, D. 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