Greenwood-Hercowitz-Huffman(1988)AER
<quote>
Fluctuations in investment played a key role in Keynes' view of the trade cycle. There, shifts in the marginal efficiency of investment impact on investment, aggregate demand and therefore, given the disequilibrium in the labor market, employment and output. The quintessential case of this type is when there is an increase in the marginal efficiency of newly produced capital that does not affect the productivity of the capital stock already on line. When a shock of this type occurs in a standard neoclassical model, employment and output also tend to rise, but the mechanism is very different. The increase in the rate of return on investment stimulates current labor effort and output through an intertemporal substitution effect on leisure. A potential problem with this mechanism, as discussed by Robert Barro and Robert King (1984), is that intertemporal substitution which induces individuals to postpone leisure, also works to cut consumption. This effect would tend to make consumption move countercyclically, which contradicts the evidence. Labor productivity would tend to move in the " wrong" direction, too. An expansion of labor effort, given the fixed supply of capital in the short run, causes labor's productivity to decline.
In contrast to the intertemporal substitution effect mentioned above, the transmission mechanism of the investment shocks works in the present model through the optimal utilization of capital and its positive effect on the marginal productivity of labor. As will be seen, an important aspect of such a change in labor productivity is that it creates intratemporal substitution, away from leisure and toward consumption, generating procyclical effects on consumption and labor effort. Additionally, average labor productivity responds procyclically to these shocks.
That is, labor effort is determined independently of the intertemporal consumption-savings choice, which is very convenient in obtaining results from the model. As a consequence, the intertemporal substitution effect on labor effort, a central ingredient in many macroeconomic models, is eliminated. Rather than being a drawback, this implication of the utility function has the advantage of emphasizing the alternative transmission of investment shocks being studied here. When analyzing fluctuations in labor effort, this framework stresses shifts in the productivity of labor brought about by changes in the optimal rate of capacity utilization, as opposed to intertemporal substitution effects stressed by others.
<unquote>
2013年9月30日月曜日
2013年9月26日木曜日
Basic Small Country IRBC Model
Mendoza(1991)AER
- They use Canadian data.
- Basic model has no adjustment costs of capital stock.
- Trade Balance is not negatively correlated with output in case relative risk aversion is high (GAMMA = 2). In case of GAMMA = 1.001, the correlation becomes negative, but the number is small. Further, if including capital adjustment costs, the correlation of them can be close to the actual data.
- Savings is not highly correlated with investments, but if including capital adjustment costs, the correlation of them can be close to the actual data.
Benchmark Model
<quote>
In general, the benchmark model is capable of mimicking the ranking of variability of the actual aggregates, and it is also consistent with some of the coefficients of autocorrelation and correlation with domestic output. Of special interest is the fact that the model mimics the absence of comovement between GDP and foreign interest payments or the trade-balance:output ratio (TB/ Y). This contrasts with the less favorable results obtained in previous empirical studies of intertemporal-equilibrium models of the current account (e.g., Ahmed, 1986; Hercowitz, 1986b).
The low correlation between S and I in the benchmark model is not related to the degree of international capital mobility. Instead, it follows from the low degree of serial autocorrelation of the shocks used to calibrate the model. With RHO = 0.36, the productivity shocks are not persistent enough to cause sufficient divergence between the expected marginal productivity of capital and the world's real interest rate to produce a stronger correlation between S and I. If, for instance, RHO is increased to 0.99, the degree of correlation between savings and investment reaches 0.8. Thus, although the benchmark model cannot mimic simultaneously the stylized facts of GDP and the correlation between savings and investment, it does support the argument presented by Obstfeld (1986) and Finn (1990), claiming that the intensity of the comovement between S and I in economies with perfect capital mobility depends on the degree of persistence of the underlying technological disturbances.
<unquote>
Adjustment Cost Model
<quote>
Perhaps the most significant result produced by these simulations is that the adjustment-cost model is capable of mimicking the two striking empirical regularities of open economies mentioned in the Introduction. Regardless of the value assigned to GAMMA, this model mimics the variability and GDP-correlation of the ratio of the trade balance to output, as well as the correlation between savings and investment. In fact, the comovement between S and I is slightly higher in both artificial economies than in the data, and this occurs without affecting the perfect international mobility of financial capital.
The introduction of moderate adjustment costs increases the persistence of the disturbances needed to calibrate the model, and with more permanent shocks investment tends to move closer together with savings, as Obstfeld (1986) suggested. Moreover, in line with the findings of Dooley et al. (1987), the perfect mobility of financial capital proves to be consistent not only with the correlation between S and I, but also with adjustment costs that prevent fast changes in physical capital.
The model mimics the variability and GDP correlation of TB/ Y because, in the presence of adjustment costs, the shocks that enable the model to mimic the stylized facts are expected to last long enough for the pro-borrowing effect, caused by an expected expansion of future output, to compensate for the pro-saving effect induced by a raise in contemporaneous output. These simulations suggest, therefore, that the intertemporal-equilibrium approach to the current account can be consistent with the empirical regularities of the business cycle.
The simulations also shed some light on a problem confronted by some empirical models of adjustment costs. As pointed out by Sargent (1978), these models generally produce reduced-form autoregressions in which highly persistent shocks cannot be distinguished from significant adjustment costs. Similarly, in the model studied here the variability of investment can be reduced by increasing the serial autocorrelation of the shocks, RHO, instead of introducing the adjustment costs. An increase in RHO reduces the probability of moving to the opposite state of productivity and lessens the chances of adjusting the capital stock, thereby reducing the variability of investment. However, the resulting persistence of the disturbances is too high and causes the model to exaggerate the actual moments. For instance, with GAMMA = 2 and PHI = 0, if RHO is set to 0.9 the variability of I falls to 5.4 percent, but the variability of GDP rises to 5 percent, and its serial autocorrelation is almost perfect. Thus, the simulations establish the relevance of adjustment costs relative to highly persistent shocks by showing that the latter are not consistent with the business cycle.
<unquote>
Appendix
<quote>
The model studied here also differs from the standard real-business-cycle prototypein its use of an endogenous rate of time preference to determine a well-defined stationary equilibrium for the holdings of foreignassets. This approach was introduced by Obstfeld (1981), following the principles formulated by Hirofumi Uzawa (1968), to analyze current-account dynamics in a deterministic model of a small open economy.
<unquote>
- They use Canadian data.
- Basic model has no adjustment costs of capital stock.
- Trade Balance is not negatively correlated with output in case relative risk aversion is high (GAMMA = 2). In case of GAMMA = 1.001, the correlation becomes negative, but the number is small. Further, if including capital adjustment costs, the correlation of them can be close to the actual data.
- Savings is not highly correlated with investments, but if including capital adjustment costs, the correlation of them can be close to the actual data.
Benchmark Model
<quote>
In general, the benchmark model is capable of mimicking the ranking of variability of the actual aggregates, and it is also consistent with some of the coefficients of autocorrelation and correlation with domestic output. Of special interest is the fact that the model mimics the absence of comovement between GDP and foreign interest payments or the trade-balance:output ratio (TB/ Y). This contrasts with the less favorable results obtained in previous empirical studies of intertemporal-equilibrium models of the current account (e.g., Ahmed, 1986; Hercowitz, 1986b).
The low correlation between S and I in the benchmark model is not related to the degree of international capital mobility. Instead, it follows from the low degree of serial autocorrelation of the shocks used to calibrate the model. With RHO = 0.36, the productivity shocks are not persistent enough to cause sufficient divergence between the expected marginal productivity of capital and the world's real interest rate to produce a stronger correlation between S and I. If, for instance, RHO is increased to 0.99, the degree of correlation between savings and investment reaches 0.8. Thus, although the benchmark model cannot mimic simultaneously the stylized facts of GDP and the correlation between savings and investment, it does support the argument presented by Obstfeld (1986) and Finn (1990), claiming that the intensity of the comovement between S and I in economies with perfect capital mobility depends on the degree of persistence of the underlying technological disturbances.
<unquote>
Adjustment Cost Model
<quote>
Perhaps the most significant result produced by these simulations is that the adjustment-cost model is capable of mimicking the two striking empirical regularities of open economies mentioned in the Introduction. Regardless of the value assigned to GAMMA, this model mimics the variability and GDP-correlation of the ratio of the trade balance to output, as well as the correlation between savings and investment. In fact, the comovement between S and I is slightly higher in both artificial economies than in the data, and this occurs without affecting the perfect international mobility of financial capital.
The introduction of moderate adjustment costs increases the persistence of the disturbances needed to calibrate the model, and with more permanent shocks investment tends to move closer together with savings, as Obstfeld (1986) suggested. Moreover, in line with the findings of Dooley et al. (1987), the perfect mobility of financial capital proves to be consistent not only with the correlation between S and I, but also with adjustment costs that prevent fast changes in physical capital.
The model mimics the variability and GDP correlation of TB/ Y because, in the presence of adjustment costs, the shocks that enable the model to mimic the stylized facts are expected to last long enough for the pro-borrowing effect, caused by an expected expansion of future output, to compensate for the pro-saving effect induced by a raise in contemporaneous output. These simulations suggest, therefore, that the intertemporal-equilibrium approach to the current account can be consistent with the empirical regularities of the business cycle.
The simulations also shed some light on a problem confronted by some empirical models of adjustment costs. As pointed out by Sargent (1978), these models generally produce reduced-form autoregressions in which highly persistent shocks cannot be distinguished from significant adjustment costs. Similarly, in the model studied here the variability of investment can be reduced by increasing the serial autocorrelation of the shocks, RHO, instead of introducing the adjustment costs. An increase in RHO reduces the probability of moving to the opposite state of productivity and lessens the chances of adjusting the capital stock, thereby reducing the variability of investment. However, the resulting persistence of the disturbances is too high and causes the model to exaggerate the actual moments. For instance, with GAMMA = 2 and PHI = 0, if RHO is set to 0.9 the variability of I falls to 5.4 percent, but the variability of GDP rises to 5 percent, and its serial autocorrelation is almost perfect. Thus, the simulations establish the relevance of adjustment costs relative to highly persistent shocks by showing that the latter are not consistent with the business cycle.
<unquote>
Appendix
<quote>
The model studied here also differs from the standard real-business-cycle prototypein its use of an endogenous rate of time preference to determine a well-defined stationary equilibrium for the holdings of foreignassets. This approach was introduced by Obstfeld (1981), following the principles formulated by Hirofumi Uzawa (1968), to analyze current-account dynamics in a deterministic model of a small open economy.
<unquote>
2013年8月8日木曜日
2012年3月29日木曜日
Dunlop Tarshis Observation
The correlation between hours worked and the real wage is close to zero.
Christiano and Eichenbaum 1992 "Current Real-Business-Cycle Theories and Aggregate Labor-Market Fluctuations"
http://ideas.repec.org/a/aea/aecrev/v82y1992i3p430-50.html
Christiano and Eichenbaum 1992 "Current Real-Business-Cycle Theories and Aggregate Labor-Market Fluctuations"
http://ideas.repec.org/a/aea/aecrev/v82y1992i3p430-50.html
2012年3月28日水曜日
Recursive Competitive Equilibrium
"Formally, a Recursive Competitive Equilibrium (RCE) is characterized by time invariant functions of a limited number of ‘state variables’, which summarize the effects of past decisions and current information.
These functions (decision rules) include
(a) a pricing function,
(b) a value function,
(c) a period allocation policy specifying the individual’s decision,
(d) period allocation policy specifying the decision of each firm and
(e) a function specifying the law of motion of the capital stock."
Mehra 2005 "Recursive Competitive Equilibrium"
www.academicwebpages.com/preview/mehra/pdf/REC Nov 9.pdf
These functions (decision rules) include
(a) a pricing function,
(b) a value function,
(c) a period allocation policy specifying the individual’s decision,
(d) period allocation policy specifying the decision of each firm and
(e) a function specifying the law of motion of the capital stock."
Mehra 2005 "Recursive Competitive Equilibrium"
www.academicwebpages.com/preview/mehra/pdf/REC Nov 9.pdf
2012年3月23日金曜日
RBC: Impulse/ Amplification/ Propagation Mechanism
1. Impulse Mechanism
Exogenous variables in RBC models.
In the standard RBC models, the technology shock is only considered for impulse mechanisms. The standard RBC models generate the high correlation between productivity and labor; however, in the data this correlation is close to zero. In response to this problem, the introduction of government expenditure shocks, household production shocks, distortionary tax shock, etc. are considered.
Only technology shock means that in the labor market the labor demand is only affected by the shock, which generates the high correlation between productivity and labor. In order to weaken the correlation, some shocks which affect the labor supply is needed.
2. Amplification Mechanism
Typically the labor response but also could include variable capacity utilization of capital.
Hansen 1985 Indivisible Labor and the Business Cycle
"Unlike previous equilibrium models of the business cycle, this economy displays large fluctuations in hours worked and relatively small fluctuations in productivity."
http://www.sciencedirect.com/science/article/pii/030439328590039X
3. Propagation Mechanism
Typically the consumption and investment response to smooth the consumption path.
Cogley and Nason 1995 Output Dynamics in Real-Business-Cycle Models
"Many RBC models have weak internal propagation mechanisms and must rely
on external sources of dynamics to replicate both facts. Models that incorporate
labor adjustment costs are partially successful. They endogenously generate
positive autocorrelation in output growth, but they need implausibly large
transitory shocks to match the trend-reverting component in output."
"Robert E. Lucas and Thomas J. Sargent (1981) noted that capital accumulation and costs of adjustment could turn serially uncorrelated shocks into serially correlated movements in output. Although RBC theorists have explored this idea in great detail, the propagation mechanisms embodied in current models do not generate the right kind of output dynamics. Our results suggest that RBC theorists ought to devote further attention to modeling internal sources of propagation."
http://ideas.repec.org/a/aea/aecrev/v85y1995i3p492-511.html
Exogenous variables in RBC models.
In the standard RBC models, the technology shock is only considered for impulse mechanisms. The standard RBC models generate the high correlation between productivity and labor; however, in the data this correlation is close to zero. In response to this problem, the introduction of government expenditure shocks, household production shocks, distortionary tax shock, etc. are considered.
Only technology shock means that in the labor market the labor demand is only affected by the shock, which generates the high correlation between productivity and labor. In order to weaken the correlation, some shocks which affect the labor supply is needed.
2. Amplification Mechanism
Typically the labor response but also could include variable capacity utilization of capital.
Hansen 1985 Indivisible Labor and the Business Cycle
"Unlike previous equilibrium models of the business cycle, this economy displays large fluctuations in hours worked and relatively small fluctuations in productivity."
http://www.sciencedirect.com/science/article/pii/030439328590039X
3. Propagation Mechanism
Typically the consumption and investment response to smooth the consumption path.
Cogley and Nason 1995 Output Dynamics in Real-Business-Cycle Models
"Many RBC models have weak internal propagation mechanisms and must rely
on external sources of dynamics to replicate both facts. Models that incorporate
labor adjustment costs are partially successful. They endogenously generate
positive autocorrelation in output growth, but they need implausibly large
transitory shocks to match the trend-reverting component in output."
"Robert E. Lucas and Thomas J. Sargent (1981) noted that capital accumulation and costs of adjustment could turn serially uncorrelated shocks into serially correlated movements in output. Although RBC theorists have explored this idea in great detail, the propagation mechanisms embodied in current models do not generate the right kind of output dynamics. Our results suggest that RBC theorists ought to devote further attention to modeling internal sources of propagation."
http://ideas.repec.org/a/aea/aecrev/v85y1995i3p492-511.html
2012年3月22日木曜日
Cyclical Properties of Real Data and RBC (Hansen Wright 1992)
Cyclical Properties of U.S. and Model-Generated Time Series (Hansen Wright 1992)
Type of Data or Model σy σc/σy σi/σy σh/σy σw/σy σh/σw cor(h,w)
U.S. Time Series*
Output 1.92 .45 2.78
Hours Worked:
1. Household Survey .78 .57 1.37 .07
(All Industries)
2. Establishment Survey .96 .45 2.15 -.14
(Nonag. Industries)
Models**
Standard 1.30 .31 3.15 .49 .53 .94 .93
Nonseparable Leisure 1.51 .29 3.23 .65 .40 1.63 .80
Indivisible Labor 1.73 .29 3.25 .76 .29 2.63 .76
Government Spending 1.24 .54 3.08 .55 .61 .90 .49
Home Production 1.71 .51 2.73 .75 .39 1.92 .49
·U.S. data here are the same as those in Table 2; they are 101 the longer time period: 1947:1-1991:3.
http://minneapolisfed.org/publications_papers/pub_display.cfm?id=242
Type of Data or Model σy σc/σy σi/σy σh/σy σw/σy σh/σw cor(h,w)
U.S. Time Series*
Output 1.92 .45 2.78
Hours Worked:
1. Household Survey .78 .57 1.37 .07
(All Industries)
2. Establishment Survey .96 .45 2.15 -.14
(Nonag. Industries)
Models**
Standard 1.30 .31 3.15 .49 .53 .94 .93
Nonseparable Leisure 1.51 .29 3.23 .65 .40 1.63 .80
Indivisible Labor 1.73 .29 3.25 .76 .29 2.63 .76
Government Spending 1.24 .54 3.08 .55 .61 .90 .49
Home Production 1.71 .51 2.73 .75 .39 1.92 .49
·U.S. data here are the same as those in Table 2; they are 101 the longer time period: 1947:1-1991:3.
http://minneapolisfed.org/publications_papers/pub_display.cfm?id=242
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