## 2. Permanent World Productivity Shock, Alternative Parameterizations ## Source details **Canonical URL:** [2. Permanent World Productivity Shock, Alternative Parameterizations](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp0582.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp0582.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp0582.pdf.json) --- ### Theoretical framework and key mechanism - Model structure: - Two-country, dynamic general equilibrium model with overlapping generations and heterogeneous household discount factors. - Domestic households discount factor: =0=99. - Foreign households discount factor: =0=9999 (so foreign discount factor is 0=9899). - Heterogeneous discounting generates tilted steady-state individual consumption profiles: upward tilt in the relatively patient country, downward tilt in the relatively impatient country. - Main mechanism: - Tilted individual consumption profiles induce countries to engage in asset trade after worldwide productivity shocks even when both countries experience the same permanent productivity increase. - In response to a permanent, worldwide productivity increase: - Households in the relatively more patient country accumulate assets; aggregate per capita consumption reaches the new, higher steady state from below. - Households in the relatively more impatient country accumulate debt; aggregate per capita consumption reaches the new, higher steady state from above. - Channel absent in symmetric models with equal discount factors where consumption jumps immediately to the new steady state and net foreign assets do not move. ### Benchmark parameterization and impulse-response intuition - Benchmark parameter values (quarters): - =0=99, =0=9999, $=3, =0=33, d==5, q=0=01, ]=1, ]W=1=29. - Calibration choices and implications: -  chosen close to 1 because small differences generate large steady-state net foreign asset positions; value chosen so that the long-run ratio of debt to quarterly GDP for the foreign economy is approximately 35percent on an annualized GDP basis. - Representative experiment: a 1percent permanent increase in productivity at home and abroad (!=1). - Predicted dynamics under the benchmark: - Home (patient) economy accumulates net foreign assets over time; foreign economy accumulates debt. - No long-run effect on the risk-free world real interest rate for the permanent worldwide shock in the benchmark. - Relative prices move: the relative price of home goods falls on impact and then returns to steady state as labor effort and prices adjust. - Consumption responses: both countries’ consumption increase immediately, but the patient country’s consumption rises over time toward the new steady state (from below) while the impatient country’s consumption declines toward its new steady state (from above). - Sensitivity (four alternative parameterizations): - Scenario 1: ]=]W=1 (remove steady-state productivity differential). - Scenario 2: ]=1, ]W=1=29, =0=999 (lower heterogeneity). - Scenario 3: =0=9999, ]=1, ]W=1=29, $=1=5 (lower substitutability). - Scenario 4: =0=9999, ]=]W=1, $=1=5. - Qualitative pattern of impulse responses is the same across scenarios; Scenario 2 deviates most quantitatively (stronger tilts when  is lower). Results are robust to assumptions on initial steady-state productivity and substitutability. ### Empirical strategy and identification - Empirical counterpart: - Constructed a six-variable VAR in levels (log): home and foreign productivity, net foreign assets, risk-free real interest rate, home consumption, foreign consumption. - Minimum state vector motivated by the theoretical solution: predetermined states are net foreign assets and the risk-free interest rate; exogenous states are domestic and foreign productivity. - Data: - Quarterly sample for G-7: primary sample 1977:Q1–1997:Q4; VAR estimation window (with seasonal dummies) 1980:Q1–1994:Q4. - Sources: OECD Analytical Database (business-sector output, consumption, employment, hours), quarterly net foreign assets constructed by Christopher Baum based on Lane and Milesi-Ferretti (2001), and IMF IFS. - Labor productivity measured as business-sector real output per hour worked; consumption and net foreign assets expressed in per capita PPP U.S. dollar terms; net foreign asset series rescaled to ensure positivity before taking logs. - Identification of a permanent worldwide productivity shock: - Follow King et al. (1991) and Mellander et al. (1992): use the common stochastic trend in the VAR levels representation; interpret the innovation to the unique common trend as the permanent worldwide productivity shock. - Long-run identifying assumptions: - (i) home and foreign labor productivity levels are cointegrated (common stochastic trend). - (ii) four additional cointegration relations tie the remaining variables to the productivity ratio, motivated by the model’s steady-state relations (forms given in the text as linearized relations (18)–(23)). ### Cointegration and specification results - Estimation and tests (1980:Q1–1994:Q4): - Six-variable VAR estimated in levels with two lags plus seasonal dummies. - Johansen procedure (productivity entered endogenously) indicates a single common stochastic trend (one eigenvalue close to zero / five stationary components). Trace tests reported in Table 2, Panel A (trace statistics and p-values as reported). - Overidentifying restrictions implied by the five cointegration relations cannot be rejected: LR test Chi^2 (3) = 2.1357 [0.5447]. - When productivity is entered exogenously in a four-variable VAR, the Johansen test suggests full rank for that system (Panel C). - Interpretation: - Evidence supports treating domestic and foreign productivity as sharing a common stochastic trend (economically plausible as technology diffusion and long-run growth processes). - Estimated cointegration vectors (Table 2, Panel B) have economically sensible signs and statistical significance for the relations imposed. ### Empirical impulse-response findings - Responses to a one-standard-deviation innovation to the common stochastic productivity trend: - Net foreign assets: - U.S. net foreign assets respond strongly and negatively to the permanent worldwide productivity shock (U.S. increases foreign indebtedness). - Rest of the G-7 accumulates net foreign assets. - Consumption: - U.S. consumption increases on impact and then moves toward its new steady state from above. - Rest-of-G-7 consumption increases on impact and moves to its new steady state from below. - Asymmetric consumption dynamics consistent with the model’s prediction when the United States is interpreted as the relatively impatient economy and the rest of the G-7 as the patient economy. - Real interest rate: - Estimated responses show an initial positive point estimate for the U.S. real interest rate but standard errors indicate it is not statistically different from zero; consistent with the theoretical prediction that permanent worldwide productivity shocks need not affect the world risk-free real rate materially in the benchmark. - Consistency with prior literature: - Results align with other empirical findings that current accounts and net foreign assets respond asymmetrically across countries to worldwide productivity shocks. ### Main substantive findings and implications - Heterogeneous discounting across countries (even if differences are small) can generate substantial steady-state net foreign asset positions and qualitatively different transitional dynamics following permanent worldwide productivity shocks. - Permanent, symmetric increases in world productivity can lead to asymmetric net foreign asset accumulation: the relatively patient economy becomes a net creditor; the relatively impatient economy becomes a net debtor. - Consumption tilting (upward tilt in patient country, downward tilt in impatient country) is a key channel: it drives asset trade and the observed asymmetric responses of consumption and net foreign assets without requiring a change in the world risk-free real interest rate. - Empirical VAR evidence for the G-7 (U.S. as home, aggregate of remaining G-7 as foreign) is broadly consistent with the theoretical model: - Sample and estimation: 1977:Q1–1997:Q4 data; VAR estimated over 1980:Q1–1994:Q4. - Estimated long-run relation between domestic and foreign productivity supports the common-trend identification. - Estimated impulse responses match model predictions: U.S. net foreign assets decline after a permanent worldwide productivity innovation while rest-of-G-7 net foreign assets rise; consumption dynamics mirror theoretical tilting. ### Research implications and suggestions for extensions - Structural interpretation of long-run asset positions matters for interpreting transitional dynamics; models that exogenously impose long-run net foreign asset levels (e.g., via bond-adjustment costs or exogenous interest-premium functions) lack this structural link. - Model limitations and avenues for future work: - Current model focuses on heterogeneity in subjective discount factors as the source of asymmetry; other structural heterogeneities (demographics, technology, credit constraints, production differences) could also be important and deserve exploration. - Extensions could include investment in physical capital, richer production asymmetries, and explicit demographic heterogeneity. *Italic source: _wp0582 - 2. Permanent World Productivity Shock, Alternative Parameterizations (PDF chapter), canonical URL as provided in the input* ### References ### _wp0582 - References ### References - .....................................................................................................................26 ### Tables - 1. The Benchmark Solution...............................................................................................29 - 2. Cointegration Analysis...................................................................................................30 ### Figures - 1. Permanent World Productivity Shock, Benchmark..................................................31 *Source: _wp0582 - References* ### 2. Permanent World Productivity Shock, Alternative Parameterizations.....................32 ### 2. Permanent World Productivity Shock, Alternative Parameterizations ### Theoretical framework and key mechanism - Two-country, dynamic general equilibrium model with overlapping generations and heterogeneous household discount factors: - Domestic households discount factor: =0=99. - Foreign households discount factor: =0=9999 (so foreign discount factor is 0=9899). - Heterogeneous discounting generates tilted steady-state individual consumption profiles: upward tilt in the relatively patient country, downward tilt in the relatively impatient country. - Main economic mechanism: - Tilted individual consumption profiles induce countries to engage in asset trade after worldwide productivity shocks even when both countries experience the same permanent productivity increase. - In response to a permanent, worldwide productivity increase: - Households in the relatively more patient country accumulate assets; aggregate per capita consumption reaches the new, higher steady state from below. - Households in the relatively more impatient country accumulate debt; aggregate per capita consumption reaches the new, higher steady state from above. - This channel is absent in symmetric models with equal discount factors where consumption jumps immediately to the new steady state and net foreign assets do not move. ### Benchmark parameterization and impulse-response intuition - Benchmark parameter values (quarters): - =0=99, =0=9999, $=3, =0=33, d==5, q=0=01, ]=1, ]W=1=29. - Calibration choices and implications: -  chosen close to 1 because small differences generate large steady-state net foreign asset positions; value chosen so that the long-run ratio of debt to quarterly GDP for the foreign economy is approximately 35percent on an annualized GDP basis. - Representative experiment: a 1percent permanent increase in productivity at home and abroad (!=1). - Predicted dynamics under the benchmark: - Home (patient) economy accumulates net foreign assets over time; foreign economy accumulates debt. - No long-run effect on the risk-free world real interest rate for the permanent worldwide shock in the benchmark. - Relative prices move: the relative price of home goods falls on impact and then returns to steady state as labor effort and prices adjust. - Consumption responses: both countries’ consumption increase immediately, but the patient country’s consumption rises over time toward the new steady state (from below) while the impatient country’s consumption declines toward its new steady state (from above). - Sensitivity: - Four alternative parameterizations considered: - Scenario 1: ]=]W=1 (remove steady-state productivity differential). - Scenario 2: ]=1, ]W=1=29, =0=999 (lower heterogeneity). - Scenario 3: =0=9999, ]=1, ]W=1=29, $=1=5 (lower substitutability). - Scenario 4: =0=9999, ]=]W=1, $=1=5. - Qualitative pattern of impulse responses is the same across scenarios; Scenario 2 deviates most quantitatively (stronger tilts when  is lower). Results are robust to assumptions on initial steady-state productivity and substitutability. ### Empirical strategy and identification - Empirical counterpart: - Constructed a six-variable VAR in levels (log): home and foreign productivity, net foreign assets, risk-free real interest rate, home consumption, foreign consumption. - Minimum state vector motivated by the theoretical solution: predetermined states are net foreign assets and the risk-free interest rate; exogenous states are domestic and foreign productivity. - Data: - Quarterly sample for G-7: primary sample 1977:Q1–1997:Q4; VAR estimation window (with seasonal dummies) 1980:Q1–1994:Q4. - Sources: OECD Analytical Database (business-sector output, consumption, employment, hours), quarterly net foreign assets constructed by Christopher Baum based on Lane and Milesi-Ferretti (2001), and IMF IFS. - Labor productivity measured as business-sector real output per hour worked; consumption and net foreign assets expressed in per capita PPP U.S. dollar terms; net foreign asset series rescaled to ensure positivity before taking logs. - Identification of a permanent worldwide productivity shock: - Follow King et al. (1991) and Mellander et al. (1992): use the common stochastic trend in the VAR levels representation; interpret the innovation to the unique common trend as the permanent worldwide productivity shock. - Long-run identifying assumptions: - (i) home and foreign labor productivity levels are cointegrated (common stochastic trend). - (ii) four additional cointegration relations tie the remaining variables to the productivity ratio, motivated by the model’s steady-state relations (forms given in the text as linearized relations (18)–(23)). ### Cointegration and specification results - Cointegration tests (1980:Q1–1994:Q4): - Six-variable VAR estimated in levels with two lags plus seasonal dummies. - Johansen procedure (productivity entered endogenously) indicates a single common stochastic trend (one eigenvalue close to zero / five stationary components). Trace tests reported in Table 2, Panel A (trace statistics and p-values as reported). - Overidentifying restrictions implied by the five cointegration relations cannot be rejected: LR test Chi^2 (3) = 2.1357 [0.5447]. - When productivity is entered exogenously in a four-variable VAR, the Johansen test suggests full rank for that system (Panel C). - Interpretation: - Evidence supports treating domestic and foreign productivity as sharing a common stochastic trend (economically plausible as technology diffusion and long-run growth processes). - Estimated cointegration vectors (Table 2, Panel B) have economically sensible signs and statistical significance for the relations imposed. ### Empirical impulse-response findings - Estimation of impulse responses to a one-standard-deviation innovation to the common stochastic productivity trend (Figure 3): - Net foreign assets: - U.S. net foreign assets respond strongly and negatively to the permanent worldwide productivity shock (U.S. increases foreign indebtedness). - Rest of the G-7 accumulates net foreign assets. - Consumption: - U.S. consumption increases on impact and then moves toward its new steady state from above. - Rest-of-G-7 consumption increases on impact and moves to its new steady state from below. - These asymmetric consumption dynamics are consistent with the model’s prediction when the United States is interpreted as the relatively impatient economy and the rest of the G-7 as the patient economy. - Real interest rate: - Estimated responses show an initial positive point estimate for the U.S. real interest rate but standard errors indicate it is not statistically different from zero; consistent with the theoretical prediction that permanent worldwide productivity shocks need not affect the world risk-free real rate materially in the benchmark. - Consistency with prior literature: - Results align with other empirical findings that current accounts and net foreign assets respond asymmetrically across countries to worldwide productivity shocks (for example, Gregory and Head (1999); Nason and Rogers (2002)). ### Main substantive findings and implications - Heterogeneous discounting across countries (even if differences are small) can generate substantial steady-state net foreign asset positions and qualitatively different transitional dynamics following permanent worldwide productivity shocks. - Permanent, symmetric increases in world productivity can lead to asymmetric net foreign asset accumulation: the relatively patient economy becomes a net creditor; the relatively impatient economy becomes a net debtor. - Consumption tilting (upward tilt in patient country, downward tilt in impatient country) is a key channel: it drives asset trade and the observed asymmetric responses of consumption and net foreign assets without requiring a change in the world risk-free real interest rate. - Empirical VAR evidence for the G-7 (U.S. as home, aggregate of remaining G-7 as foreign) is broadly consistent with the theoretical model: - Sample and estimation: 1977:Q1–1997:Q4 data; VAR estimated over 1980:Q1–1994:Q4. - Estimated long-run relation between domestic and foreign productivity supports the common-trend identification. - Estimated impulse responses match model predictions: U.S. net foreign assets decline after a permanent worldwide productivity innovation while rest-of-G-7 net foreign assets rise; consumption dynamics mirror theoretical tilting. ### Research implications and suggestions for extensions - Structural interpretation of long-run asset positions matters for interpreting transitional dynamics; models that exogenously impose long-run net foreign asset levels (e.g., via bond-adjustment costs or exogenous interest-premium functions) lack this structural link. - Model limitations and avenues for future work: - Current model focuses on heterogeneity in subjective discount factors as the source of asymmetry; other structural heterogeneities (demographics, technology, credit constraints, production differences) could also be important and deserve exploration. - Extensions could include investment in physical capital, richer production asymmetries, and explicit demographic heterogeneity. *Italic source: _wp0582 - 2. Permanent World Productivity Shock, Alternative Parameterizations (PDF chapter), canonical URL as provided in the input* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp0582.pdf_