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
Solow residual correlations across countries and industries
Costello(1993)JPE
<quote>
I find that aggregate output growth is correlated across countries, but aggregate productivity growth is only weakly correlated across countries. At the industry level, productivity growth is significantly correlated across industries within a country but is less correlated across countries for any individual industry. In the error-components framework, the estimated nation effects are as important as, and sometimes more important than, industry effects.
The evidence suggests that short-run productivity growth is more similar across industries in one nation than across countries for a particular industry. The results are consistent with the presence of labor hoarding if labor hoarding is truly a national occurrence. The results are also consistent with observing nation-specific technology shocks to the extent that they represent excluded factors such as human capital or the infrastructure in a country.
<unquote>
<quote>
I find that aggregate output growth is correlated across countries, but aggregate productivity growth is only weakly correlated across countries. At the industry level, productivity growth is significantly correlated across industries within a country but is less correlated across countries for any individual industry. In the error-components framework, the estimated nation effects are as important as, and sometimes more important than, industry effects.
The evidence suggests that short-run productivity growth is more similar across industries in one nation than across countries for a particular industry. The results are consistent with the presence of labor hoarding if labor hoarding is truly a national occurrence. The results are also consistent with observing nation-specific technology shocks to the extent that they represent excluded factors such as human capital or the infrastructure in a country.
<unquote>
2013年9月28日土曜日
Convergence or non-convergence in output across countries
Cheung and Pascual (2004) Oxford Economic Papers
- it cannot be determined by statistical methods in common use.
- it depends on the null hypothesis of convergence or no convergence.
<quote>
The study of cross-country output dynamics from both viewpoints gives an equal opportunity for both convergence and no convergence to be validated by the data as the null hypothesis.
Our empirical results suggest that the inference about output convergence can be dictated by the choice of a null hypothesis. A conclusion of no output convergence can be reached just because no convergence is considered as the null hypothesis. Further, the no-convergence result reported in previous studies pursuing the time- series definition may be attributed to the low power of the test procedures being used. While short output data series or the use of univariate unit root procedures yields very limited support for the convergence hypothesis, the combination of long sample and efficient panel procedures delivers a more favorable result for the same hypothesis.
<unquote>
- it cannot be determined by statistical methods in common use.
- it depends on the null hypothesis of convergence or no convergence.
<quote>
The study of cross-country output dynamics from both viewpoints gives an equal opportunity for both convergence and no convergence to be validated by the data as the null hypothesis.
Our empirical results suggest that the inference about output convergence can be dictated by the choice of a null hypothesis. A conclusion of no output convergence can be reached just because no convergence is considered as the null hypothesis. Further, the no-convergence result reported in previous studies pursuing the time- series definition may be attributed to the low power of the test procedures being used. While short output data series or the use of univariate unit root procedures yields very limited support for the convergence hypothesis, the combination of long sample and efficient panel procedures delivers a more favorable result for the same hypothesis.
<unquote>
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9月24日火曜日
Habit Formation
Abel1990AER
<quote>
This paper introduces a utility function that nests three classes of utility functions: 1) time-separable utility functions; 2) "catching up with the Joneses" utility functions that depend on the consumer's level of consumption relative to the lagged cross-sectional average level of consumption; and 3) utility functions that display habit formation. Incorporating this utility function into a Lucas (1978) asset pricing model allows calculation of closed-form solutions for the prices of stocks, bills and consols under the assumption that consumption growth is i.i.d. Then equilibrium asset prices are used to examine the equity premium puzzle.
Panel C presents the unconditional expected rates of return under habit formation. The expected rates of return on both long-lived assets (stocks and consols) are extremely sensitive to the value of ALPHA (coefficient of risk averesion). Under logarithmic utility (ALPHA = 1), the expected rates of return are the same as under time-separable preferences and relative consumption. However, with ALPHA = 1.14, the expected rates of return on stocks and consols are both greater than 35 percent.
<unquote>
<quote>
This paper introduces a utility function that nests three classes of utility functions: 1) time-separable utility functions; 2) "catching up with the Joneses" utility functions that depend on the consumer's level of consumption relative to the lagged cross-sectional average level of consumption; and 3) utility functions that display habit formation. Incorporating this utility function into a Lucas (1978) asset pricing model allows calculation of closed-form solutions for the prices of stocks, bills and consols under the assumption that consumption growth is i.i.d. Then equilibrium asset prices are used to examine the equity premium puzzle.
Panel C presents the unconditional expected rates of return under habit formation. The expected rates of return on both long-lived assets (stocks and consols) are extremely sensitive to the value of ALPHA (coefficient of risk averesion). Under logarithmic utility (ALPHA = 1), the expected rates of return are the same as under time-separable preferences and relative consumption. However, with ALPHA = 1.14, the expected rates of return on stocks and consols are both greater than 35 percent.
<unquote>
Catching up with the Joneses
Abel(1990)AER
<quote>
"catching up with the Joneses" utility functions that depend on the consumer's level of consumption relative to the lagged cross-sectional average level of consumption.
<unquote>
Abel(1999)JME
<quote>
The catching up with the Joneses feature of the utility function was originally
introduced to help account for the high average value of the equity premium
observed empirically. However, when this form of the utility function was
specified to imply a realistic value of the equity premium in Abel (1990), the
model produced a riskless rate of return that was far too volatile. Campbell and
Cochrane (1994) developed a form of catching up with the Joneses preferences
that yielded, as in actual data, a large equity premium and low variability of the
riskless rate. They achieved this low variability of the riskless rate by specifying
a complicated recursive function for the determination of the benchmark level of
consumption. Here I adopt a simpler formulation of the benchmark level of
consumption that produces, with the inclusion of leverage, low variability of the
riskless rate along with a large equity premium.
The analysis of leverage arises naturally from the formulation of the canonical
asset introduced in this paper. The payoff in period t on the canonical asset is
specified to be proportional to yt^LAMBDA, where yt is an observable random variable and LAMBDA is a constant. I use this formulation in order to include fixed-income securities and equities as special cases.
Rather than proceed with separate derivations for the prices and rates of
return for different assets such as equity, short-term bills and long-term bonds,
I will introduce a canonical asset that includes all of these assets as special cases.
The canonical asset introduced here includes equities and fixed-income securities
of all maturities.
<unquote>
<quote>
"catching up with the Joneses" utility functions that depend on the consumer's level of consumption relative to the lagged cross-sectional average level of consumption.
<unquote>
Abel(1999)JME
<quote>
The catching up with the Joneses feature of the utility function was originally
introduced to help account for the high average value of the equity premium
observed empirically. However, when this form of the utility function was
specified to imply a realistic value of the equity premium in Abel (1990), the
model produced a riskless rate of return that was far too volatile. Campbell and
Cochrane (1994) developed a form of catching up with the Joneses preferences
that yielded, as in actual data, a large equity premium and low variability of the
riskless rate. They achieved this low variability of the riskless rate by specifying
a complicated recursive function for the determination of the benchmark level of
consumption. Here I adopt a simpler formulation of the benchmark level of
consumption that produces, with the inclusion of leverage, low variability of the
riskless rate along with a large equity premium.
The analysis of leverage arises naturally from the formulation of the canonical
asset introduced in this paper. The payoff in period t on the canonical asset is
specified to be proportional to yt^LAMBDA, where yt is an observable random variable and LAMBDA is a constant. I use this formulation in order to include fixed-income securities and equities as special cases.
Rather than proceed with separate derivations for the prices and rates of
return for different assets such as equity, short-term bills and long-term bonds,
I will introduce a canonical asset that includes all of these assets as special cases.
The canonical asset introduced here includes equities and fixed-income securities
of all maturities.
<unquote>
2013年9月23日月曜日
Roll's critique
http://en.wikipedia.org/wiki/Roll%27s_critique
Epstein-Zin(1991)JPE
<quote>
The nominal return on the optimal portfolio is measured with the value-weighted index of shares traded on the New York Stock Exchange. A number of issues arise from the use of this measure, but the primary concern for our purposes is whether it is sufficiently broad to capture the relevant part of actual holdings of wealth; that is, Roll's (1977) critique of CAPM is relevant here. If stochastic wages are a large factor in the wealth constraint of the typical agent, then, as discussed in Section II, the return on the optimal portfolio of the agent should reflect the shadow return of the agent's human capital. Rather than attempt a lengthy analysis of this issue at this time, we shall simply assume that factors that may not be properly measured by the value- weighted index of stock returns do not affect the empirical analysis in an appreciable way. The appropriateness of this assumption, vis-a-vis the empirical results below, remains an open question.
<unquote>
Campbell(1996)JPE
<quote>
In response to the Roll (1977) critique, I extend the Campbell (1993) model to allow for human capital as a component of wealth. I impute the return on human capital from data on aggregate labor income and asset returns. Finally, I develop an econometric frame- work in which the model can be confronted with historical data.
The asset pricing model developed in Section II is empirically testable only if one can measure the return on the market portfolio. Financial economists commonly proxy the market portfolio by a value-weighted index of common stocks, but this practice is questionable. Even if the stock index return captures the return on financial wealth, as argued by Stambaugh (1982), it may not capture the return on human wealth. Approximately two-thirds of gross national product goes to labor and only one-third to capital, so human wealth is likely to be about two-thirds of total wealth and twice financial wealth. This suggests that the omission of human wealth may be a serious matter.
Increases in expected future labor income cause a positive return on human capital, but increases in expected future asset returns cause a negative return on human capital because the labor income stream is now discounted at a higher rate and is therefore worth less today.
<unquote>
Epstein-Zin(1991)JPE
<quote>
The nominal return on the optimal portfolio is measured with the value-weighted index of shares traded on the New York Stock Exchange. A number of issues arise from the use of this measure, but the primary concern for our purposes is whether it is sufficiently broad to capture the relevant part of actual holdings of wealth; that is, Roll's (1977) critique of CAPM is relevant here. If stochastic wages are a large factor in the wealth constraint of the typical agent, then, as discussed in Section II, the return on the optimal portfolio of the agent should reflect the shadow return of the agent's human capital. Rather than attempt a lengthy analysis of this issue at this time, we shall simply assume that factors that may not be properly measured by the value- weighted index of stock returns do not affect the empirical analysis in an appreciable way. The appropriateness of this assumption, vis-a-vis the empirical results below, remains an open question.
<unquote>
Campbell(1996)JPE
<quote>
In response to the Roll (1977) critique, I extend the Campbell (1993) model to allow for human capital as a component of wealth. I impute the return on human capital from data on aggregate labor income and asset returns. Finally, I develop an econometric frame- work in which the model can be confronted with historical data.
The asset pricing model developed in Section II is empirically testable only if one can measure the return on the market portfolio. Financial economists commonly proxy the market portfolio by a value-weighted index of common stocks, but this practice is questionable. Even if the stock index return captures the return on financial wealth, as argued by Stambaugh (1982), it may not capture the return on human wealth. Approximately two-thirds of gross national product goes to labor and only one-third to capital, so human wealth is likely to be about two-thirds of total wealth and twice financial wealth. This suggests that the omission of human wealth may be a serious matter.
Increases in expected future labor income cause a positive return on human capital, but increases in expected future asset returns cause a negative return on human capital because the labor income stream is now discounted at a higher rate and is therefore worth less today.
<unquote>
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