Christiano, L. J. and M. Eichenbaum. 1990. "Unit Roots in Real Gnp: Do We Know, and Do We Care?" Carnegie-Rochester Conference Series on Public Policy
---<quote>---
Macroeconomists have traditionally viewed movements output as representing temporary fluctuations about a deterministic trend. According to this view, innovations to real gross national product (GNP) should have no impact on long-run forecasts of aggregate output. Increasingly, however, this view of aggregate fluctuations has been challenged, Following the provocative work of Nelson and Plosser (1982), numerous economists have argued that real GNP is best characterized as a stochastic process that does not revert to a deterministic trend path. Under these circumstances, innovations to real GNP should affect output forecasts into the indefinite future. In pursuing this interpretation of the data, various researchers have tried to measure the long-run response of real GNP to a shock. Estimates of this response are often referred to as the persistence of shocks to real GNP.
---<unquote>---
2013年11月29日金曜日
2013年11月27日水曜日
Trading Costs in IRBC
Backus, D. K.; P. J. Kehoe and F. E. Kydland. 1992. "International Real Business Cycles." Journal of Political Economy
---<quote>---
A surprising feature of these two experiments is that a small trading cost produces most of the properties of autarky. A possible explanation comes from Cole and Obstfeld (1991): if the gains from trade are small, then a small cost may have a large effect on the quantity of trade in goods and assets. To investigate this for our model, we measure the gains from trade by comparing equilibria in the benchmark (free-trade) economy to those in the autarky economy. We express the welfare gain as the percentage increase in the consumption path under autarky necessary to reach the same level of welfare attained with free access to international markets. Welfare in each case is estimated as the mean value of discounted utility over the 50 replications of 100 periods each. We find that consumption in autarky must be increased only 0.3 percent to make consumers as well off as they are when international markets are open. The welfare gains from trade in our theoretical economies stem solely from trade across states and dates. As in similar calculations by Cole and Obstfeld, the gains are remarkably small, which may help to account for the large effect of a small trading cost on the model's equilibria.
---<unquote>---
---<quote>---
A surprising feature of these two experiments is that a small trading cost produces most of the properties of autarky. A possible explanation comes from Cole and Obstfeld (1991): if the gains from trade are small, then a small cost may have a large effect on the quantity of trade in goods and assets. To investigate this for our model, we measure the gains from trade by comparing equilibria in the benchmark (free-trade) economy to those in the autarky economy. We express the welfare gain as the percentage increase in the consumption path under autarky necessary to reach the same level of welfare attained with free access to international markets. Welfare in each case is estimated as the mean value of discounted utility over the 50 replications of 100 periods each. We find that consumption in autarky must be increased only 0.3 percent to make consumers as well off as they are when international markets are open. The welfare gains from trade in our theoretical economies stem solely from trade across states and dates. As in similar calculations by Cole and Obstfeld, the gains are remarkably small, which may help to account for the large effect of a small trading cost on the model's equilibria.
---<unquote>---
2013年11月26日火曜日
Complete vs. Incomplete Market (1)
Baxter, M. and M. J. Crucini. 1995. "Business Cycles and the Asset Structure of Foreign-Trade." International Economic Review
---<quote>----
The within-country correlation between saving and investment is slightly lower in the bond economy compared with the complete markets economy. This might seem surprising, since one's intuition is that closing asset markets, thus forcing individualsto bear more country-specificrisk, would act to increase within-country saving-investment correlations. However, this "basic saving measure" (defined as output minus consumption) need not be a good measure of true saving in an open economy, as discussed by Obstfeld (1986) and Stockman and Svensson (1987).
---<unquote>----
---<quote>----
The within-country correlation between saving and investment is slightly lower in the bond economy compared with the complete markets economy. This might seem surprising, since one's intuition is that closing asset markets, thus forcing individualsto bear more country-specificrisk, would act to increase within-country saving-investment correlations. However, this "basic saving measure" (defined as output minus consumption) need not be a good measure of true saving in an open economy, as discussed by Obstfeld (1986) and Stockman and Svensson (1987).
---<unquote>----
2013年11月18日月曜日
2013年11月17日日曜日
Role of EIS and Risk Aversion
http://www.lse.ac.uk/finance/prospectiveStudents/phdFinance/files09/Job_Market_Paper_Aytek_Malkhozov.pdf
Malkhozov and Samloo (2009) "Asset Prices in a News Driven Real Business Cycle Model"
<quote>
Lets first consider a Lucas-tree economy. A positive shock to expected consumption growth (or a negative shock to uncertainty) increases wealth to consumption ratio, which adjusts through movements in wealth since consumption is exogenous. This adjustment depends on the size of the elasticity of intertemporal substitution. If the substitution effect dominates the wealth effect, i.e. elasticity of intertemporal substitution is greater than one, the agent would like to hold more of the asset, thus driving prices up. Otherwise (when elasticity of intertemporal substitution is less than 1) the agent prefers bringing the increase in consumption forward, depressing prices.
How does this matter for risk premia? Shocks to expected consumption growth affect expected future returns to wealth. The agent with relative risk aversion greater than 1 wants to hedge against these changes in the investment opportunity set (and bet on them if relative risk aversion is less than one). Notice that relative risk aversion and inverse of the elasticity of intertemporal substitution are comparable measures of propensity to smooth consumption across states and time respectively. Therefore if the two are equal (CRRA case) the changes in wealth-consumption ratio exactly offset the hedging demand. With Epstein-Zin preferences there can be a wedge between relative risk aversion and the inverse of the elasticity of intertemporal substitution which will translate into premia. As an example, consider an agent with both elasticity of intertemporal substitution and relative risk aversion greater than 1, exposed to a positive shock to expected consumption growth. The intertemporal substitution effect drives up asset prices. The hedging demand effect would imply that the agent wants his portfolio to depreciate. Therefore a premium is required for the agent to hold the asset in equilibrium. If consumption and dividends are correlated the results for the pricing of aggregate risk carry forward to the risk premium for the claim on aggregate dividends. Recursive preferences are crucial for this mechanism.
<unquote>
Malkhozov and Samloo (2009) "Asset Prices in a News Driven Real Business Cycle Model"
<quote>
Lets first consider a Lucas-tree economy. A positive shock to expected consumption growth (or a negative shock to uncertainty) increases wealth to consumption ratio, which adjusts through movements in wealth since consumption is exogenous. This adjustment depends on the size of the elasticity of intertemporal substitution. If the substitution effect dominates the wealth effect, i.e. elasticity of intertemporal substitution is greater than one, the agent would like to hold more of the asset, thus driving prices up. Otherwise (when elasticity of intertemporal substitution is less than 1) the agent prefers bringing the increase in consumption forward, depressing prices.
How does this matter for risk premia? Shocks to expected consumption growth affect expected future returns to wealth. The agent with relative risk aversion greater than 1 wants to hedge against these changes in the investment opportunity set (and bet on them if relative risk aversion is less than one). Notice that relative risk aversion and inverse of the elasticity of intertemporal substitution are comparable measures of propensity to smooth consumption across states and time respectively. Therefore if the two are equal (CRRA case) the changes in wealth-consumption ratio exactly offset the hedging demand. With Epstein-Zin preferences there can be a wedge between relative risk aversion and the inverse of the elasticity of intertemporal substitution which will translate into premia. As an example, consider an agent with both elasticity of intertemporal substitution and relative risk aversion greater than 1, exposed to a positive shock to expected consumption growth. The intertemporal substitution effect drives up asset prices. The hedging demand effect would imply that the agent wants his portfolio to depreciate. Therefore a premium is required for the agent to hold the asset in equilibrium. If consumption and dividends are correlated the results for the pricing of aggregate risk carry forward to the risk premium for the claim on aggregate dividends. Recursive preferences are crucial for this mechanism.
<unquote>
2013年11月16日土曜日
2013年11月3日日曜日
GARCH/ Stochastic Volatility Model
http://mitizane.ll.chiba-u.jp/metadb/up/AN10005358/09127216_26-3_129.pdf
http://faculty.washington.edu/ezivot/econ589/ch4.pdf
GARCH <- 単一の不確実性
SV <- 複数の不確実性
例）リターン／ボラティティのモデル化
GARCH <- リターンへのショック（イノベーション）のみが確率過程のドライバー
SV <- リターンとボラティリティそれぞれへのショック（イノベーション）を考慮
http://faculty.washington.edu/ezivot/econ589/ch4.pdf
GARCH <- 単一の不確実性
SV <- 複数の不確実性
例）リターン／ボラティティのモデル化
GARCH <- リターンへのショック（イノベーション）のみが確率過程のドライバー
SV <- リターンとボラティリティそれぞれへのショック（イノベーション）を考慮
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