“aggregate” shock hitting the productivity of all firms. Although this paper does not provide a theory of the time variation of the distribution of firms’ productivity, there is little reason to suppose that this distribution is stable over time. On the empirical side, Bloom et al. (2009) provide evidence sug- gesting that the variance of establishment, firm and industry level shocks in the U.S. is countercyclical. Bachman and Bayer (2009), using a panel of public and private German firms in manufacturing and retail, find that the variance of innovations to firms’ productivity increases in recessions. In this paper, we provide evidence that the variance of the distribution of firms productivity in Spanish manufacturing sectors varies sensibly over time. It follows that the interaction between a time varying productivity distribution and an **elasticity** of **substitution** different from one provides a source of fluc- tuations in aggregate productivity without the need to assume a common (aggregate) shock to the productivity of all firms, or an input-output matrix that transmits sectoral shocks across sectors.

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There is a dramatic change of the effects of an in- creased interest rate when the technical progress becomes endogenous and variable. Firstly, the expected lifetime of the investment will not decrease but increase at a certain level of the **elasticity** of **substitution**. Secondly, the pro- ductivity of labour and the capital intensity at the cur- rent period will be increasing in the interest rate when the substitutability between labour and capital becomes smaller.

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Diﬀerently from most of the literature, this investigation employs a speciﬁcation with both labor- and capital-augmenting technical change. While for labor input we keep the traditional constant growth rate representation, for capital we impose a particular structure with capital playing a key role. In this exercise we do not calibrate the parameters of the production function but use our previous estimated values. Besides, the esti- mated **elasticity** of **substitution** is less than 1, a value by now well-grounded in the recent literature (see for instance León-Ledesma 2010; for a critical discussion of the traditional methodology in estimating the **elasticity** of sub- stitution, see Federici and Saltari 2014). The data on Italian economy refers to the period 1981:Q4—2005:Q2. 1

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In this paper we build on the dynamic model of the Italian economy of Saltari et al. (2012, 2013). The main result of those papers is that the weakness of the Italian economy in the last two decades has been the total factor productivity ( ) slowdown. The aim of this paper is to investigate the roots of this slowdown. The analysis focusses on the speciﬁc pattern of technical progress in determining the dynamics. Of course, this analysis can not be done with the Cobb-Douglas technology, where technical progress is only Hicks neutral, but requires a production function which allows to distinguish between the direction and the bias of technical progress. Diﬀerently from most of the literature, this investigation employs a speciﬁcation with both labor- and capital-augmenting technical change. While for labor input we keep the traditional constant growth rate representation, for capital we impose a particular structure with capital playing a key role. Moreover, in this exercise we do not calibrate the parameters of the production function but use our estimated values. It should be noted that the estimated **elasticity** of **substitution** is less than 1. Such as a value is by now well-grounded in the empirical literature (see for instance León- Ledesma 2010; for a critical discussion of the traditional methodology in estimating the **elasticity** of **substitution**, see Federici and Saltari 2014). On theoretical grounds, a 1 implies that any amount of output can be pro- duced with either zero amount of capital or zero amount of labor, which is clearly absurd (note that the Cobb Douglas almost shares this last property). The data on Italian economy refers to the period 1981:Q4—2005:Q2. 1

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DOI: 10.4236/jamp.2017.511178 2186 Journal of Applied Mathematics and Physics based solely on a Cobb-Douglas production function model may not be realistic because the Cobb-Douglas production function (2) has the unitary **elasticity** of **substitution** and as [23] has shown, it is not suitable to model the US economy with the **elasticity** of **substitution** equal to 1 (also, it is not known whether we can realistically assume that the **elasticity** of **substitution** is 1 for all the other countries involved in that study). So, it would be of significant interest to estimate the economic growth for various countries using the same data but for a more general setting involving the CES production function model for a range of values of the parameter γ in (1) with α = 0.3 , and then to estimate an optimal value of γ to fit the data set.

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Douglas being strongly rejected. Klump et al. (2008) estimated a long-run supply model for the euro area over the period 1970-2005 and they found an aggregate **elasticity** of **substitution** below unity (around 0.7). Mallick (2012) obtained the **elasticity** parameters for 90 countries by estimating the CES production function for each country separately using respective country time series spanning for the period 1950—2000. The mean value for all 90 countries is 0.338. The mean values for the East Asia and Sub-Saharan African countries are 0.737 and 0.275, respectively. For the countries the mean is 0.340. A clear pattern is evident, he concludes, that, on average, the value of **elasticity** increases secularly with the growth rate of per capita . One problem with interpreting these cross-study results is that the various analyses are not all measuring the same thing: the results found are generally sensitive to sample size and estimation techniques. La Grandville (1989), Klump and La Grandville (2000) emphasize the role of normalization of the CES production function because it makes more consistent cross-study estimates of the **elasticity** parameter.

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The price transmission from the international market to the domestic market of tunas was investigated in the present research. For this purpose, the **elasticity** of **substitution** between tuna imports with goods produced in Iran (Armington **Elasticity**) was calculated. Armington **elasticity** reflects a degree of **substitution** between commodities produced domestically and those produced abroad. A greater **elasticity** indicates that buyers did not discriminate between domestic and foreign produced commodities and the buyers considered them the same. Therefore, any policy to influence the price of imported commodities will be effective in regulating the prices of commodities produced domestically. In the present study, in order to calculate Armington **elasticity**, the annual data for the year between 1974 and 2014 were used along with the technique of maximum entropy (ME). In addition to Armington **elasticity**, the least square estimated and vector error correction model (ECM) was estimated using entropy maximization. The results showed that Armington tension in the long-term was greater than that in the short-term. Even though this means the product has been imported, it serves as an alternative for domestically produced commodities; therefore, buyers do not see any difference between them. Additionally, the prices of these products have been affected by global prices and the swings in global prices can be transported more easily to the internal market for these products in the long-term than in the short-term.

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It is well known for a Cobb-Douglas production function that the **elasticity** of a factor demand is the inverse of the share of output going to the other fac- tors. Since Cobb-Douglas has a unit **elasticity** of **substitution**, the demand **elasticity** trivially equals the ratio of the **elasticity** of **substitution** to the share of output going to the other factor. I show here that this result can be genera- lized to any constant returns to scale production function. As a result, if a factor is known to be a substitute for (complement of) other factors, the in- verse of the share of output going to other factors will be a lower (upper) bound for the factor’s **elasticity** of demand.

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The **elasticity** of **substitution** introduced by Hicks (1932) was reformulated by Lerner (1933) as the degree to which the marginal rate of **substitution** between two inputs varies as the ratio of the quantity of those inputs varies while output is held constant. Assuming integrability (Hicks and Allen, 1934b), Hicks and Allen (1934a) proposed the following formula:

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The **elasticity** of intertemporal **substitution** is a crucial parameter in …nance and macroeconomics, yet its estimation remains elusive. We show, based on Fisher’s relation and the expectations theory of the term structure, that the EIS is the inverse of the product of the average term to maturity of debt instruments and the consumption-output ratio. Therefore, the EIS need not be estimated but can be calibrated from observable data.

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We show that the Hotelling-Lau **elasticity** of **substitution**, an extension of the Allen-Uzawa **elasticity** to allow for optimal output-quantity (or utility) responses to changes in factor prices, inherits all of the failings of the Allen-Uzawa **elasticity** identified by Blackorby and Russell [1989 AER]. An analogous extension of the Morishima **elasticity** of **substitution** to allow for output quantity changes preserves the salient properties of the original Hicksian notion of **elasticity** of **substitution**.

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The present paper examines the role of factor substitution in a two-sector neoclassical growth model where investment goods and consumption goods are produced by use of diﬀerent technolo[r]

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price taker for all goods and services it produces and consumes. Also, the small open economy is affected by the second second-round effect of an increase in the commodity prices in the form of high foreign inflation and low world demand. Fourth, households and firms, both in the domestic economy and the rest of the world economy, use commodities for consumption and as a factor of production, respectively. In addition, the main behavioural parameters that the paper focuses on are the **elasticity** of **substitution** between government consumption and private consumption and the response of government consumption to fluctuations in the commodity prices. The former parameter is an indicator of the efficiency of government consumption and its effect on private consumption (crowding-in versus crowding-out), while the latter captures the behaviour and the stance of fiscal policy during booms and busts of commodity prices, along with the size of the commodity windfalls in the government’s revenue.

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We address a contention regarding capital deepening when the labor share of in- come declines and the **elasticity** of **substitution** is above unity between Karabarbou- nis and Neiman (2013) and Elsby et. al (2013). We demonstrate the incentive for technical change, which increases inequality and how investments in new technol- ogy create temporal misalignment between a decrease in the labor share of income and capital deepening. We show how the decline in the saving rate that occurred during the 80’s and 90’s may resolve the contention regarding capital deepening. We find that **elasticity** of **substitution** below unity is less consistent with the decline in the labor share of income.

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Discount factor Elasticity of intertemporal substitution Relative preference for leisure Relative preference for money holdings Share parameter in index of money holdings Elasticity of d[r]

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Description Discount Factor Depreciation Rate Share of Private Consumption in Utility Inverse Elasticity of Intertemporal Substitution Inverse Frisch Elasticity of Labor Supply Relative [r]

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In summary, our key contribution is to identify several important channels and their underlying determi- nants through which offshoring affects the domestic labor market. In particular, it identifies four channels which are crucial in determining the immediate and indirect effects of offshoring on employment and wages: On the one hand, the **elasticity** of task productivity schedules (indicating the relative comparative advan- tage) between medium-skill and low-skill worker, between offshore and medium-skill workers, and between high-skill and medium-skill workers. These elasticities capture the notion of how different type of workers are substitutable across the range of tasks. On the other hand, the **elasticity** of **substitution** between domestic and offshored tasks, which accounts for importance of production technology. These parameters are crucial in determining the immediate and indirect effects of offshoring on employment and wages. Moreover, these new insights can guide the empirical research by providing rationales why, for instance, the magnitude and the incidence of labor market polarization have been different between the advanced countries over the past recent decades.

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Abstract In this paper, we use long-run annual data to estimate the intertemporal elasticity of substitution while accounting for the intra-temporal substitution between nondurable consu[r]

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From this insight into the nature of the preferences, we can say that there are two dimensions of home bias in the gravity model (see eq. (24)). The first operates through the constant **elasticity** of **substitution** term ( θ >1), since the higher θ is, the higher the home bias gets as shown by Obstfeld and Rogoff. The second dimension operates through the Multilateral Resistance Terms because higher trade costs imply lower imports from every source. This implicitly makes consumption biased for home goods because countries tend to become autarkic in order to save on trade costs (we made this point clear at page 20). How these two dimensions interact and in what measure each of them contributes to determine the amount of foreign consumption is expressed in eq. (24).

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M RS indicates the marginal **substitution** relationship between good i and good j which corresponds to the slope of the indifference curve. At the opti- mum bundle, the slope of the indifference curve is equal to the price relation among the goods. The bigger the **elasticity** of **substitution** between good i and good j the more substitutional the goods (e.g. wine and beer) are. Opposite, if the **elasticity** of **substitution** approaches zero, the good i and j will be complementary goods (e.g. beer and pizza). The size of the **elasticity** of **substitution** determines the slope of the indifference curve: they converge towards a straight line when the **elasticity** of **substitution** approaches infinity (and the goods are sad to be perfect substitutes ), while the curve converges to- wards making a 90 degree kink when the **elasticity** of **substitution** approaches zero (and the goods are said perfect complements (Figure 1), while the IC are said Leontief ).

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