## _wp0646

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---

### I. Introduction and motivation
- Home (household) production is quantitatively large: empirical studies suggest the value of home production is between 40 and 50 percent of measured GNP in most industrialized countries.
- Incorporating household production into stochastic dynamic business cycle models improves fit to business cycle features (example: Greenwood, Rogerson, and Wright (GRW, 1995)).
- A key data problem: time series on home production do not exist; many studies rely on identifying assumptions to infer home productivity shocks from parameterized models.

### IKS "theory for measurement" approach
- Ingram, Kocherlakota, and Savin (IKS, 1997) use Euler equations from a dynamic stochastic model with a home production sector to map observable market data to unobservable home-sector series.
- Using U.S. market hours, market consumption, and output, IKS derive series for:
  - home output,
  - hours spent in home production,
  - hours spent at leisure.
- The approach avoids reliance on ad hoc assumptions for home-sector productivity shocks by deriving home-sector series from observable market data.

### Research questions and data scope
- Main questions:
  - Are home-sector business cycle properties similar across comparable industrialized economies?
  - Are cyclical fluctuations in the home sector related across countries?
  - Do home production models produce home-sector features consistent with the IKS-derived series?
- Intended sample: G-7 countries; data limitations restrict analysis to Canada, the United States, Germany, and Japan.
- Data: seasonally adjusted quarterly IFS data:
  - 1970:1–2003:4 for Canada, Japan, United States.
  - 1970:1–1997:4 for Germany.
- Series used: consumption (ct), investment (it = gross capital formation + inventory adjustments), net exports (nxt = exports − imports), output yt = ct + it + nxt.
- Conversion: real per capita using CPI (1995 prices) and population from IFS.
- Employment and weekly average hours (nonagricultural) from OECD; total hours nt = weekly hours × employment rate normalized by weekly time endowment 168.
- No filtering applied before feeding into the model (raw series later logged/HP filtered for business-cycle statistics as specified).

### Model (small open-economy BRW variant and mapping)
- Representative agent with period utility: Cobb-Douglas in leisure and CES combination of market consumption (mt c) and home-produced consumption (nt c).
- Time endowment constraint: 1 = mt h + nt h + t l.
- Sector production functions (Cobb-Douglas):
  - mt y = mt A (mt k)^{mα} (mt h)^{1−mα}
  - nt y = nt A (nt k)^{nα} (nt h)^{1−nα}
- Market output can be consumed, invested, or exported; home output is consumed only.
- Capital depreciates at rate δ and is freely mobile across sectors.
- Key mapping expressions (from observables to unobservables):
  - Home hours relation (as stated in source; see equation (3) in original): nt h = ( (mt c / nt c)^{ρ−1} * (γm / (1−γm)) )^{1/ρ}
  - Leisure and home hours solved from observable market consumption and hours using model first-order conditions ((5)–(7) in source).
- Intertemporal dynamics (capital law of motion, foreign asset accumulation) do not affect the static mapping from market observables to home-sector unobservables.

### Parameter calibration (benchmark and alternatives)
- Benchmark parameters (based on IKS):
  - mα = 0.28 (market labor income share = 0.72)
  - nα = 0.14
  - mγ = 0.4
  - lγ = 0.73 (IKS; panel data suggests mean home hours ≈ 85% of market hours; authors’ data consistent with lγ = 0.71)
  - ρ (elasticity parameter): benchmark ρ = 0.5; alternative considered ρ = −1.5
- Sensitivity experiments include alternative mα (e.g., 0.36), varying nα within [0, 0.28], and varying lγ (example: to 0.5).

### Time-series behavior (benchmark)
- Trends by country:
  - United States and Canada: home hours declined (notably since 1983); market hours increased relative to 1970 levels; leisure rises slightly because fall in home hours > increase in market hours (U.S.).
  - Japan and Germany: home hours have not declined; market hours decreased.
- Recession behavior:
  - Leisure rises in each recession.
  - Home hours often rise during recessions (time out of employment increases both leisure and home hours).
- Home consumption is sensitive to ρ:
  - ρ = 0.5 versus ρ = −1.5 produce markedly different home-consumption series.

### Stylized business-cycle findings — volatility (benchmark)
- Preprocessing for statistics: variables (except net exports) logged and HP filtered; net exports normalized by output then HP filtered.
- Market-variable regularities:
  - Consumption is less volatile than output.
  - Investment roughly three times more volatile than output on average.
  - Net exports volatility lies between investment and output except in Japan where net exports is most volatile.
  - Market hours less volatile than output; relative standard deviation on average close to consumption.
- Home-sector regularities (benchmark):
  - Home hours volatility slightly larger than market hours in each country.
  - Leisure is the least volatile: standard deviation of leisure ≈ 9 percent as large as that of output.
  - Relative volatility of home hours ≈ 80 percent.
  - Home output more volatile than market output: home vs market output volatility ranges from 1.9 (United States) to 3.6 (Germany).
- Selected row means and standard deviations reported (from Table 1):
  - Market Consumption: mean 0.68, Std. Dev. 0.09
  - Market Hours: mean 0.70, Std. Dev. 0.12
  - Investment: mean 2.70, Std. Dev. 0.39
  - Net Exports: mean 2.29, Std. Dev. 1.25
  - Home consumption (output): mean 2.58, Std. Dev. 0.72
  - Home hours: mean 0.78, Std. Dev. 0.16
  - Leisure: mean 0.09, Std. Dev. 0.02
  - Market Labor Productivity: mean 0.76, Std. Dev. 0.17
  - Market Solow Residual: mean 0.89, Std. Dev. 0.03
  - Home Labor Productivity: mean 1.85, Std. Dev. 0.55
  - Home Solow Residual: mean 2.47, Std. Dev. 0.70
- Solow residuals:
  - Home Solow residual volatility exceeds market Solow residual volatility and output volatility (range 1.3 to 2.61 across countries).

### Persistence
- Output autocorrelation: mean = 0.82 (range 0.78 in Germany to 0.88 in United States).
- Market consumption, market hours, investment, net exports: quite persistent.
- Home variables are less persistent than market variables:
  - Home consumption autocorrelation lower than market consumption in all countries.
  - Home hours exhibit less inertia than market hours in all countries.
- Leisure is highly persistent: average autocorrelation coefficient = 0.74.

### Comovement (contemporaneous correlations with market output)
- Selected correlations with market output (country examples and panel means):
  - Market consumption: procyclical; correlations: 0.91 (United States), 0.78 (Canada), 0.86 (Germany), 0.84 (Japan); mean 0.85, Std. Dev. 0.05.
  - Market hours: procyclical; mean 0.67, Std. Dev. 0.17.
  - Investment: procyclical; mean 0.88, Std. Dev. 0.05.
  - Net exports: countercyclical; mean −0.24, Std. Dev. 0.21.
  - Home consumption (output): low/no clear correlation with market output; range −0.14 (United States) to 0.12 (Germany); mean 0.05, Std. Dev. 0.13.
  - Home hours: on average negatively correlated with market output; range −0.47 (United States) to −0.11 (Germany); mean −0.25, Std. Dev. 0.15.
  - Leisure: highly countercyclical in all countries; average correlation with output −0.79, Std. Dev. 0.07.
- Lead/lag behavior:
  - Leisure and home hours are countercyclical at all leads and lags.
  - Average contemporaneous correlation between home and market hours = −0.67.
  - Average contemporaneous correlation between leisure and market hours = −0.79.
  - Decrease in market hours is offset by increases in both leisure and home hours; leisure volatility small relative to the other time uses.

### Driving processes (productivity shocks)
- Productivity shock process assumed Markov: A_{t+1} = π A_t + ε_{t+1} where A′ = [ln(mt A), ln(nt A)] and ε_t ~ N(0, Σ).
- Empirical findings (Table 4 summary):
  - Persistence coefficients ≈ 0.94–0.95 (mean 0.95) — both market and home productivity shocks are highly persistent.
  - Sectoral feedback coefficient small in absolute value (technological spillovers between market and home sectors mostly negligible).
  - Standard deviation of home productivity disturbance ≈ three times that of market disturbance.
  - Contemporaneous correlation between market and home productivity shocks positive and large across countries; empirical estimates lower than some prior assumptions (example: empirical ~0.33 vs BRW assumed 0.67).
- Mean variance-covariance entries reported (panel mean from Table 4):
  - Variance-covariance Σ (mean): market variance 0.014, home variance 0.038, off-diagonal 0.021 (as presented in source table format).

### Cross-country correlations
- Cross-country regularities:
  - Cross-country output correlations typically larger than consumption correlations (quantity anomaly).
  - Investment correlations positive and generally smaller than those of output.
  - Market hours positively correlated across countries.
  - Net exports correlations mixed; most are negative.
  - Market Solow residual correlations positive across pairs.
- Home-sector cross-country correlations:
  - Home consumption correlations smaller than market consumption correlations; four of six pairwise correlations low and negative, others low and positive.
  - Home hours correlations smaller than market hours in all cases.
  - Leisure series exhibit much higher cross-country correlation than home hours; all leisure correlation pairs positive.
  - Home productivity correlations mostly negative or low; lower than market productivity correlations.
  - Home Solow residual correlations are low and lower than market Solow residual correlations.

### Sensitivity analysis (high level)
- Principal findings robust to parameter variation; detailed results available on request (as stated).
- Examples of parameter effects:
  - Increasing mα to 0.36 (from 0.28) → small increases in relative volatilities: home consumption to 2.27 (from 1.90), home hours to 0.86 (from 0.67); minor changes in correlations.
  - Varying nα over feasible range has modest effects on leisure properties; U.S. leisure SD robust in range 0.0652 to 0.0663.
  - Decreasing lγ to 0.5 → home consumption on average 1.57 times as volatile as market output; home hours become less volatile; correlations shift (home output correlation with market output increases; home hours correlation with market output becomes more negative).
  - Changing ρ:
    - With ρ = 0.5 (benchmark), average home output volatility = 2.58 times market output.
    - With ρ = −1.5 (complements), average home output volatility = 1.34 times market output.
    - Comovement differences:
      - With ρ = 0.5: average correlations of home output with market output and market consumption = 0.05 and −0.17 respectively.
      - With ρ = −1.5: average correlations = 0.54 and 0.77 respectively.

### Conclusion (Section VI summary)
- Model-based mapping from observable market aggregates yields comparable time series on home production (home hours, home consumption, leisure) across Canada, the United States, Germany, and Japan.
- Robust cross-country regularities:
  - Home production is more volatile than market production in all studied countries.
  - Market and home sector hours have similar volatility.
  - Leisure is much less volatile than other time uses and is highly countercyclical in all countries.
  - Home hours are countercyclical in all countries.
  - Home production variables are less persistent than market variables.
  - Home production is not highly correlated with market output; cross-country correlations for home production are lower than for market production.
- Comparison with prior studies:
  - Earlier studies tend to underestimate home-sector productivity shock volatility and overestimate correlation between home and market productivity shocks.
  - Despite quantitative differences, there are significant qualitative similarities with previous simulation-based results, supporting robustness of some earlier modeling assumptions.
- Caveats and suggested extensions:
  - Results depend on model and parameter choices; sensitivity analysis mitigates but does not eliminate model-dependence.
  - Future work: analyze fiscal and monetary policy roles in home/market sector interactions; extend analysis to developing countries where household production is a larger fraction of aggregate output.

*Source: _wp0646 (IMF Working Paper excerpt).*

### 1.         Hours         ...............................................................................................

### Hours

### I. Introduction and Motivation
- A large part of economic activity occurs in the home; empirical studies suggest the value of home (household) production is between 40 and 50 percent of measured GNP in most industrialized countries.
- Because of this quantitative importance, understanding fluctuations in household production strengthens understanding of aggregate economic fluctuations.
- Incorporating household production into stochastic dynamic business cycle models has improved the models' ability to match business cycle features (e.g., Greenwood, Rogerson, and Wright (GRW, 1995)).
- A key empirical weakness: time series on home production do not exist, so many studies rely on assumptions to identify home productivity shocks in parameterized dynamic stochastic models and then evaluate only market-sector artificial data against observed data.

### IKS "Theory for Measurement" Approach
- Ingram, Kocherlakota, and Savin (IKS, 1997) develop an alternative that uses the Euler equations from a dynamic stochastic model with a home production sector to map observable market data to unobservable home sector data.
- Using U.S. data on market hours, market consumption, and output, IKS derive series for:
  - home output,
  - hours spent in home production,
  - hours spent at leisure.
- The approach avoids reliance on simplifying identifying assumptions for home-sector productivity shocks by deriving home-sector series from observable market data.

### Research Questions Addressed
- Whether business cycle properties of the home sector are similar across comparable industrialized economies.
- Whether cyclical fluctuations in the home sector are related across countries (cross-country correlations).
- Whether home production models produce home-sector business cycle features consistent with series derived via the IKS approach.

### Data Scope and Countries
- Intended focus: Group of Seven (G-7) countries, but data limitations restrict the study to Canada, the United States, Germany, and Japan.
- These economies are similar in industrialization and broadly similar business cycle features in observable data, though they have known structural differences in labor markets.

### Stylized Business Cycle Findings (robust across the four countries)
- Home production is more volatile than market production.
- Volatility of hours spent in home production is close to the volatility of market hours.
- Leisure is much less volatile than any other series.
- Home production variables are less persistent than market variables.
- Leisure hours and home hours are both countercyclical.
- Home production has no strong correlation with market production.

### Cross-Country Correlations and Tradeability
- Since home production is not tradable, cross-country correlations for home series are expected to be lower than for market series; the evidence shows this holds in nearly every case.
- For home consumption, cross-country correlations are mostly negative.

### Comparison with Existing Literature and Model Validation
- Although actual home-sector series are unobservable, the IKS-derived series allow comparison:
  - Business cycle properties found robustly across countries appear in home-series generated by other studies, indicating considerable consistency.
  - Some of the identifying assumptions used by other studies to extract home-sector shocks are empirically supported: the processes assumed by some studies are largely consistent with those derived via the IKS mapping.
  - There are differences between assumptions in the literature and the derived processes; these differences are noted but not detailed in this excerpt.

### Contextual and Empirical Notes
- Survey and time-use diary data provide spotty direct evidence on home production activities (e.g., Juster and Stafford (1991); Gronau and Hamermesh (2006)).
- Empirical references cited for household time use:
  - A typical married U.S. couple spends 25 percent of their time working at home while allocating 33 percent of their time to market activities (Juster and Stafford (1991)).
  - Bonke (1995) finds women allocate as much as 57 percent and men as much as 21 percent of their time to home production.
  - Greenwood, Rogerson, and Wright (1995) document that investment in household capital is larger than in market capital.
- The IKS “theory for measurement” approach has parallels in other applications that back out unobserved series using model-implied mappings from observed data (examples: IKS 1994a/1994b; Baxter and King (1998); Smith and Zin (1997); Blankenau, Kose, and Yi (2001); Beauchemin (2000)).

### Paper Organization (as far as presented)
- Section II: model and empirical methodology.
- Section III: data sources.
- Section IV: model calibration.
- Section V: results.

*Source: _wp0646 - 1.         Hours         ..............................................................................................., IMF Working Paper (excerpt).*

### conclusion and a summary of the results are in Section VI.

### _wp0646 - conclusion and a summary of the results are in Section VI.

### Model
- Small open economy version of Benhabib, Rogerson, and Wright (BRW, 1991) with an infinitely lived representative agent deriving utility from home produced goods (nt c), market produced goods (mt c), and leisure (t l).
- Period utility: Cobb-Douglas in leisure and CES combination of mt c and nt c.
- Restrictions: β, γm, γl, ρ ∈ [0,1] and γl > .5 sufficient for tnt l h >.
- Sector production (Cobb-Douglas):
  - mt y = mt A (mt k)^{mα} (mt h)^{1−mα}
  - nt y = nt A (nt k)^{nα} (nt h)^{1−nα}
- Time endowment: 1 = mt h + nt h + t l. (Equation (1))
- Market output can be consumed, invested, or exported; home output is consumed only. (Equation (2))
- Capital depreciates at rate δ and moves freely across sectors.
- Key derived expressions (mapping observables to unobservables):
  - Home output-consumption relation: nt h = ( (mt c / nt c)^{ρ−1} * (γm / (1−γm)) )^{1/ρ}  (see equation (3) in source)
  - Leisure and home hours solved from observables using (5)–(7); business-cycle properties depend on parameter combinations such as 1/(1−nα)−1/(1−mα) and 1/(1−lγ)−1/(1−mγ) as described in text.
- Intertemporal dynamics (capital law of motion, foreign asset accumulation) do not affect the mapping from market observables to home-sector unobservables.

### Data
- Seasonally adjusted quarterly data from IMF’s International Financial Statistics (IFS):
  - 1970:1–2003:4 for Canada, Japan, United States.
  - 1970:1–1997:4 for Germany (series end with euro introduction).
- Series: consumption (ct), investment (it = gross capital formation + inventory adjustments), net exports (nxt = exports − imports), output yt = ct + it + nxt.
- Converted to real per capita using CPI (1995 prices) and population from IFS.
- Employment and weekly average hours (nonagricultural) from OECD; total hours nt = weekly hours × employment rate normalized by weekly time endowment 168.
- No filtering applied before feeding into model.

### Parameter calibration (benchmark and alternatives)
- Benchmark (based on IKS):
  - mα = 0.28 (implying market labor income share = 0.72)
  - nα = 0.14
  - mγ = 0.4
  - lγ = 0.73 (IKS; panel data suggests mean home hours ≈ 85% of market hours; in authors’ data this holds with lγ = 0.71)
  - ρ (elasticity parameter): benchmark ρ = 0.5; alternative considered ρ = −1.5
- Sensitivity experiments:
  - Alternative mα values (e.g., 0.36) considered.
  - Range for nα constrained to [0, 0.28] when market production is more capital-intensive.

### Results — Time series behavior (benchmark)
- United States and Canada:
  - Home hours declined, most notably since 1983.
  - Market hours increased from 1970 levels; in the United States fall in home hours > increase in market hours → leisure rises slightly.
- Japan and Germany:
  - Home hours have not declined; market hours decreased.
- Recessions:
  - Leisure rises in each recession; home hours often rise during recessions, implying time out of employment increases both leisure and home hours.
- Home consumption behavior depends critically on ρ:
  - ρ = 0.5 (substitutes) vs ρ = −1.5 (complements) produce markedly different home-consumption series (Figure 3).

### Stylized features of business-cycle dynamics — Volatility
- Preprocessing: all variables (except net exports) logged and HP filtered; net exports normalized by output then HP filtered.
- Market-variable regularities:
  - Consumption less volatile than output.
  - Investment roughly three times more volatile than output on average.
  - Net exports volatility lies between investment and output except Japan where net exports is most volatile.
  - Market hours less volatile than output; relative standard deviation on average close to consumption.
- Home-sector series (benchmark):
  - Home hours volatility slightly larger than market hours in each country.
  - Leisure is the least volatile: standard deviation of leisure ≈ 9 percent (stated as “roughly 9 percent as large as that of output”).
  - Relative volatility of home hours ≈ 80 percent.
  - Home output more volatile than market output: home vs market output volatility ranges from 1.9 (United States) to 3.6 (Germany).
- Table 1 (selected row means and std. dev. from source):
  - Market Consumption: mean 0.68, Std. Dev. 0.09
  - Market Hours: mean 0.70, Std. Dev. 0.12
  - Investment: mean 2.70, Std. Dev. 0.39
  - Net Exports: mean 2.29, Std. Dev. 1.25
  - Home consumption (output): mean 2.58, Std. Dev. 0.72
  - Home hours: mean 0.78, Std. Dev. 0.16
  - Leisure: mean 0.09, Std. Dev. 0.02
  - Market Labor Productivity: mean 0.76, Std. Dev. 0.17
  - Market Solow Residual: mean 0.89, Std. Dev. 0.03
  - Home Labor Productivity: mean 1.85, Std. Dev. 0.55
  - Home Solow Residual: mean 2.47, Std. Dev. 0.70
- Solow residuals (log formulas given in text); home Solow residual volatility > market Solow residual volatility and > output volatility (range 1.3 to 2.61 across countries).

### Persistence
- Table 2 (selected averages and ranges):
  - Output autocorrelation mean = 0.82 (range 0.78 in Germany to 0.88 in United States).
  - Market consumption, market hours, investment, net exports: quite persistent.
  - Home variables less persistent than market variables:
    - Home consumption autocorrelation lower than market consumption in all countries.
    - Home hours exhibit less inertia than market hours in all countries.
  - Leisure is highly persistent: average autocorrelation coefficient = 0.74.

### Comovement (contemporaneous correlations with output)
- Table 3 (selected correlations with market output — country range and mean):
  - Market consumption: procyclical; correlations: 0.91 (United States), 0.78 (Canada), 0.86 (Germany), 0.84 (Japan); mean 0.85, Std. Dev. 0.05.
  - Market hours: procyclical; mean 0.67, Std. Dev. 0.17.
  - Investment: procyclical; mean 0.88, Std. Dev. 0.05.
  - Net exports: countercyclical; mean −0.24, Std. Dev. 0.21.
  - Home consumption (output): low/no clear correlation with market output; range −0.14 (United States) to 0.12 (Germany); mean 0.05, Std. Dev. 0.13.
  - Home hours: on average negatively correlated with market output; range −0.47 (United States) to −0.11 (Germany); mean −0.25, Std. Dev. 0.15.
  - Leisure: highly countercyclical in all countries; average correlation with output −0.79, Std. Dev. 0.07.
- Lead/lag behavior:
  - Leisure and home hours are countercyclical at all leads and lags.
  - Average contemporaneous correlation between home and market hours = −0.67; between leisure and market hours = −0.79.
  - Decrease in market hours is offset by increases in both leisure and home hours; leisure volatility small relative to the other time uses.

### Driving processes (productivity shocks)
- Productivity shocks assumed Markov: A_{t+1} = π A_t + ε_{t+1} where A′ = [ln(mt A), ln(nt A)] and ε_t ~ N(0, Σ).
- Table 4 (selected empirical findings and summary statistics):
  - Persistence coefficients ≈ 0.94–0.95 (mean 0.95) — both market and home productivity shocks highly persistent.
  - Sectoral feedback coefficient small in absolute value → technological spillovers between market and home sectors mostly negligible.
  - Standard deviation of home productivity disturbance ≈ three times that of market disturbance.
  - Contemporaneous correlation between market and home productivity shocks positive and large across countries; empirical estimate ~0.33 (U.S. example) vs BRW assumed 0.67.
- Numerical entries from Table 4 (mean panel):
  - Persistence π (mean): 0.95    0.03 / 0.10    0.85 (table presents block format; standard errors in parentheses).
  - Variance-covariance Σ (mean): matrix with variances 0.014 (market) and 0.038 (home) and off-diagonal 0.021 (correlation representation in table).

### Cross-country correlations
- Table 5 (summary):
  - Cross-country output correlations typically larger than consumption correlations (quantity anomaly).
  - Investment correlations positive and generally smaller than those of output.
  - Market hours positively correlated across countries.
  - Net exports correlations mixed; most are negative.
  - Market Solow residual correlations positive across pairs.
  - Home-sector cross-country correlations:
    - Home consumption correlations smaller than market counterparts; four of six correlations low and negative, others low and positive.
    - Home hours correlations smaller than market hours in all cases.
    - Leisure series exhibit much higher cross-country correlation than home hours; all leisure correlation pairs positive.
    - Home productivity correlations mostly negative or low; lower than market productivity correlations.
    - Solow residual correlations of home sector are low and lower than those of market sector.

### Sensitivity analysis (high level)
- Principal findings robust to parameter variation; detailed results available upon request.
- Effects of varying parameters:
  - Increasing mα to 0.36 from 0.28 → small increases in relative volatilities of home consumption (to 2.27 from 1.90) and home hours (to 0.86 from 0.67) and minor changes in correlations.
  - Varying nα over feasible range has modest effects on leisure properties; leisure SD for U.S. robust in range 0.0652 to 0.0663.
  - Decreasing lγ to 0.5 → home consumption on average 1.57 times as volatile as market output; home hours become less volatile; correlations change (home output correlation with market output increases; correlation of home hours with market output becomes more negative).
  - Changing ρ:
    - With ρ = 0.5 (benchmark), average home output volatility = 2.58 times market output.
    - With ρ = −1.5 (complements), average home output volatility = 1.34 times market output.
    - Comovement: average correlations of home output with market output and market consumption:
      - With ρ = 0.5: 0.05 and −0.17 respectively.
      - With ρ = −1.5: 0.54 and 0.77 respectively.

### Conclusion (Section VI summary and overall findings)
- Comparable time series on home production are generated via the model-based mapping from observable market aggregates to unobservables (home hours, home consumption, leisure).
- Cross-country regularities:
  - Home production is more volatile than market production in all countries studied.
  - Market and home sector hours have similar volatility.
  - Leisure is much less volatile than other uses of time (home and market hours).
  - Leisure is highly countercyclical in all countries; home hours are countercyclical in all countries.
  - Home production variables exhibit less persistence than market variables.
  - Home production is not highly correlated with market output; cross-country correlations for home production are lower than for market production.
- Differences with earlier studies:
  - Earlier studies underestimate the volatility of home-sector productivity shocks and overestimate the correlation between home and market productivity shocks.
  - Despite some quantitative differences, there are significant qualitative similarities with previous simulation-based results, supporting the robustness of earlier modeling assumptions.
- Caveats and future research:
  - Results depend on the choice of model and parameters; sensitivity analysis mitigates but does not eliminate model-dependence.
  - Extensions: study roles of fiscal and monetary policies in interactions between home and market sectors; analyze home production dynamics in developing countries where household production comprises a larger fraction of aggregate output.

*Source: _wp0646 - conclusion and a summary of the results are in Section VI.*

### References

### References

### Household production, home production, and time allocation
- Backus, David K., Patrick J. Kehoe, and Finn E. Kydland, 1995, “International Business Cycles: Theory and Evidence,” in Frontiers of Business Cycle Research, ed. by Thomas Cooley (Princeton, New Jersey: Princeton University Press), pp. 331-57.
- Baxter, Marianne, 1996, “Are Consumer Durables Important for Business Cycles?” Review of Economics and Statistics, Vol. LXXVIII, pp. 147-55.
- Baxter, Marianne, and Urban J. Jermann, 1999, “Household Production and the Excess Sensitivity of Consumption to Current Income,” American Economic Review, Vol. 89, pp. 902-20.
- Bonke, Jens, 1992, “Distribution of Economic Resources: Implications of Including Household Production,” Review of Income and Wealth, Vol. 38, pp. 281-93.
- Bonke, Jens, 1995, “Education, Work and Gender: An International Comparison,” Working Paper EUF 95/4 (Florence: European University Institute).
- Gomme, Paul, Peter Rupert, and Finn Kydland, 2001, “Time-to-Build and Household Production,” Journal of Political Economy, Vol. 109, pp. 1115-31.
- Greenwood, Jeremy, and Zvi Hercowitz, 1991, “The Allocation of Capital and Time Over the Business Cycle,” Journal of Political Economy, Vol. 99, pp. 1188-1214.
- Greenwood, Jeremy, Richard Rogerson, and Randall Wright, 1995 “Household Production in Real Business Cycle Theory,” in Frontiers of Business Cycle Research, ed. by Thomas Cooley (Princeton, New Jersey: Princeton University Press), pp. 157-1745.
- Gronau, Reuben, 1986, “Home Production—A Survey,” in Handbook of Labor Economics, ed. by Orley Ashenfelter and Richard Layard (Amsterdam: North Holland), pp. 273-304.
- Gronau, Reuben, and Daniel S. Hamermesh, 2006, “Time vs. Goods: The Value of Measuring Household Production Technologies,” forthcoming in Review of Income and Wealth.
- Ingram, Beth, Narayana Kocherlakota, and N.E. Savin, 1997, “Using Theory for Measurement: an Analysis of the Cyclical Behavior of Home Production,” Journal of Monetary Economics, Vol. 40, pp. 435-56.
- Rogerson, Richard, Peter Rupert, and Randall Wright, 1995, “Estimating Substitution Elasticities in Models with Home Production,” Economic Theory, Vol. 6, pp. 179-93.
- Wrase, Jeff, 2001, “The Interplay Between Home Production and Business Activity,” Business Review of the Federal Reserve Bank of Philadelphia Q2, pp. 23-29.
- Parente, Stephen L., Richard Rogerson, and Randall Wright, 2000, “Homework in Development Economics: Household Production and the Wealth of Nations,” Journal of Political Economy, Vol. 108, pp. 680-87.
- Baxter, Marianne, and Robert G. King, 1998, “Productive Externalities and Business Cycles,” Working Paper (Charlottesville, Virginia: University of Virginia).
- Busato, Francesco, and Bruno Chiarini, 2004, “The Non-Market Sector in Europe and in the United States: Underground Activities and Home Production,” Working Paper (Naples: University of Napoli).
- Canova, Fabio, and Angel J. Ubide, 1998, International Business Cycles, Financial Markets and Household Production,” Journal of Economic Dynamics and Control, Vol. 22, pp. 545-72.
- McGrattan, Ellen, Richard Rogerson, and Randall Wright, 1997, “An Equilibrium Model of the Business Cycle with Household Production and Fiscal Policy,” International Economic Review, Vol. 38, pp. 267-90.

### International business cycles, open economy models, and trade
- Blankenau, William M., Ayhan Kose, and Kei-Mu Yi, 2001, “Can World Real Interest Rates Explain Business Cycles in a Small Open Economy?” Journal of Economic Dynamics and Control, Vol. 25, pp. 867-99.
- Christodoulakis, Nicos, Sophia P. Dimelis, and Tryphon Kollintzas, 1995, “Comparisons of Business Cycles in the EC: Idiosyncrasies and Regularities,” Economica, Vol. 62, pp. 1-27.
- Kim, Sunghyun H., and M. Ayhan Kose, 2003, “Dynamics of Open Economy Business Cycle Models: Understanding the Role of the Discount Factor,” Macroeconomic Dynamics, Vol. 7, pp. 263-90.
- Kose, M. Ayhan, 2002, Explaining Business Cycles in Small Open Economies,” Journal of International Economics, Vol. 56, pp. 299-327.
- Kose, M. Ayhan, Chris Otrok, and Charles Whiteman, 2003, “International Business Cycles: World Region, and Country Specific Factors,” American Economic Review, Vol. 93, pp. 1216-39.
- Kose, M. Ayhan, and Kei-Mu Yi, 2001, “International Trade and Business Cycles,” American Economic Review, Vol. 91, pp. 371-75.
- Zimmermann, Christian, 1995, “International Trade over the Business Cycle: Stylized Facts and Remaining Puzzles,” Working Paper No. 37, CREFÉ.

### Labor markets, institutions, and labor reallocation
- Benhabib, Jess, Richard Rogerson, and Randall Wright, 1991, “Homework on Labor Economics: Household Production and Aggregate Fluctuations,” Journal of Political Economy, Vol. 99, pp. 1166-87.
- Bertola, Giuseppe, and Richard Rogerson, 1997, “Institutions and Labor Reallocation,” European Economic Review, Vol. 41, pp. 1147-72.
- Genay, Hesna, and Prakash Loungani, 1997, “Labor Market Fluctuations in Japan and the U.S.: How Similar Are They?” Federal Reserve Bank of Chicago Economic Perspectives, Vol. 21, pp. 15-28.
- Juster, F. Thomas, and Frank P. Stafford, 1991, “The Allocation of Time: Empirical Findings, Behavioral Models, and Problems of Measurement,” Journal of Economic Literature, Vol. 29, pp. 471-522.
- Siebert, Horst, 1997, “Structural Change and Labor Market Flexibility: Experience in Selected OECD Countries” (Kiel: Institute fur Weltwirtschaft an der Universitat Kiel).
- Parente, Stephen L., Richard Rogerson, and Randall Wright, 2000, “Homework in Development Economics: Household Production and the Wealth of Nations,” Journal of Political Economy, Vol. 108, pp. 680-87.

### Methodology, estimation, and theoretical models
- Eichenbaum, Martin, and Lars P. Hansen, 1990, Estimating Models with Intertemporal Substitution Using Aggregate Time Series Data,” Journal of Business and Economic Statistics, Vol. 8, pp. 53-69.
- Ingram, Beth, Narayana Kocherlakota, and N.E. Savin, 1994a, “Explaining Business Cycles: A Multiple Shock Approach,” Journal of Monetary Economics, Vol. 34, pp. 415-28.
- Ingram, Beth, Narayana Kocherlakota, and N.E. Savin, 1994b, “Rational Expectations Shock Estimation” (unpublished; Iowa City, Iowa: University of Iowa).
- Smith, Grogor W., and Stanley E. Zin, 1997, “Real Business Cycle Realizations,” Carnegie-Rochester Series on Public Policy, Vol. 47, pp. 243-80.
- Rogerson, Richard, Peter Rupert, and Randall Wright, 1995, “Estimating Substitution Elasticities in Models with Home Production,” Economic Theory, Vol. 6, pp. 179-93.
- Ingram, Beth, Narayana Kocherlakota, and N.E. Savin, 1997, “Using Theory for Measurement: an Analysis of the Cyclical Behavior of Home Production,” Journal of Monetary Economics, Vol. 40, pp. 435-56.

### Public capital, fiscal policy, and structural change
- Beauchemin, Kenneth R., 2000, “Whither the Stock of Public Capital?” Working Paper (Albany, New York: State University of New York at Albany).
- McGrattan, Ellen, Richard Rogerson, and Randall Wright, 1997, “An Equilibrium Model of the Business Cycle with Household Production and Fiscal Policy,” International Economic Review, Vol. 38, pp. 267-90.
- Siebert, Horst, 1997, “Structural Change and Labor Market Flexibility: Experience in Selected OECD Countries” (Kiel: Institute fur Weltwirtschaft an der Universitat Kiel).

*Source: _wp0646 - References (PDF chapter/section).*

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