Elasticity Of Substitution Research Articles

Poor Substitutes? Counterfactual Methods in IO and Trade Compared

Abstract Constant elasticity of substitution (CES) demand for monopolistically competitive firm-varieties is a standard tool for models in international trade and macroeconomics. Inter-variety substitution in this model follows a simple share proportionality rule. In contrast, the standard toolkit in industrial organization (IO) estimates a demand system in which cross-elasticities depend on similarity in observable attributes. The gain in realism from the IO approach comes at the expense of requiring richer data and greater computational challenges. This paper uses the data generating process of Berry, Levinsohn and Pakes (1995), BLP, who established the modern IO method, to simulate counterfactual trade policy experiments. We use the CES model as an approximation of the more complex underlying demand system and market structure. Although the CES model omits key elements of the data generating process, the errors are offsetting, allowing it to fit BLP-based predictions closely. For aggregate outcomes, it turns out that incorporating non-unitary pass-through matters more than fixing over-simplified substitution patterns.

Technology of Input–Output Analysis with CES Production: Application for Studying the Kazakhstan Supply Chain during the COVID-19 Pandemic

Input–output analysis finds widespread application in estimating the shock effects on production networks within both local and global economies. We are developing a new technology for intersectoral analysis that takes into account the substitution of production factors within a complex supply network triggered by external or internal shocks. This technology is based on the explicit solution of a pair of convex programming problems: the resource allocation problem under the assumption of Constant Elasticity of Substitution (CES) technologies and the special dual Young problem. Solving these problems, we can ascertain the equilibrium inputs and price indexes of goods within the production network. In this paper, we apply this technology to analyze the economy of Kazakhstan in the context of the COVID-19 pandemic. Our calculations provide us with the means to discuss the macroeconomic responses of the multi-sectoral production network in Kazakhstan to both external and internal shocks stemming from the pandemic.

A dynamic quantile model for distinguishing intertemporal substitution from risk aversion

This paper uses a dynamic quantile model to estimate the elasticity of intertemporal substitution (EIS) and risk attitude using large disaggregated data from the NielsenIQ Consumer Panel. This data is transactional at the consumption purchase level, which minimizes measurement error, and the final sample contains more than two million observations. In the quantile model, the risk attitude is captured by the quantile and is, therefore, separable from the EIS. To estimate the parameters of interest we use the Euler equation along with instrumental variables quantile regression. First, we estimate the model across different levels of risk attitude. Empirical results document evidence of monotonically decreasing EIS along quantiles. For large risk aversion, the EIS is greater than one, whereas for small risk aversion it descends into negative values. Subsequently, we estimate the risk attitude and the EIS simultaneously. The results substantiate a risk attitude close to the median, with EIS consistently positive and smaller than one.

Factor substitution, long-run equilibrium, and convergence speed in the Lucas model

We study the effect of factor substitution on long-run equilibrium in the Lucas model with CES production. The long-run growth rate does not depend on the elasticity of substitution. However, there is a negative (positive) relationship between the elasticity of factor substitution and the convergence speed if the baseline ratio of physical capital to effective labor is below (above) its steady-state value.

Joint elicitation of elasticity of intertemporal substitution, risk and time preferences

AbstractThe elicitation of the elasticity of intertemporal substitution (EIS), discount factor and risk attitude parameters in dynamic models is of central importance to economics, finance and public policy. This paper suggests an alternative method to jointly elicit and estimate these three parameters using experimental data. We employ a new model based on dynamic quantile preferences, where individuals maximize the stream of future ‐quantile utilities, for . These preferences are simple, dynamically consistent and monotonic. In the quantile model, the risk attitude is captured by the quantile of the payoff distribution, while the EIS and the discount factor are related to the utility function describing individual's intertemporal behaviour, hence allowing for complete separability between risk, EIS and discount factor. The estimation of the parameters of interest uses a structural maximum likelihood method. Individual's risk aversion is estimated below the median. The discount factor is marginally smaller than estimates reported in the literature, and the EIS is slightly larger than one, which suggests that utility over time is concave. The estimates for the elasticity contrast with those reported by the existing studies using observational disaggregated data, which in general find an elasticity smaller than one.

The Power of Substitution: The Great German Gas Debate in Retrospect

ABSTRACT: The Russian attack on Ukraine in February 2022 laid bare Germany's dependence on Russian energy imports and ignited a heated debate on the costs of a cutoff from Russian gas. While one side predicted economic collapse, the other side (ours) predicted "substantial but manageable" economic costs due to households and firms adapting to the shock. Using the empirical evidence now at hand, this paper studies the adjustment of the German economy after Russia weaponized gas exports by cutting Germany off from gas supplies in the summer of 2022. We document two key margins of adjustment. First, Germany was able to replace substantial amounts of Russian gas with imports from third countries, underscoring the insurance provided by openness to international trade. Second, the German economy reduced gas consumption by about 20 percent, driven mostly by industry (26 percent) and households (17 percent). The economic costs of demand reduction were manageable with the economy as a whole only experiencing a mild one-quarter contraction in the winter of 2022–2023 and then stagnating. Overall industrial production decoupled from production in energy-intensive sectors (which did see large drops) and declined only slightly. We draw a number of key lessons from this important case study about the insurance offered by access to global markets and the power of substitution, specifically that supply shocks have dramatically smaller costs when elasticities of substitution are very low (but nonzero) compared to a truly zero elasticity.

A generalization of the Symmetric Translog functional form

Feenstra and Weinstein introduced a special case of the translog cost function, the Symmetric Translog (ST) Cost Function, which replaced all of the second order parameters which are present in the Translog functional form by a single positive parameter. The ST functional form is useful in the context of estimating consumer preferences over related products and provides an alternative to the use of Constant Elasticity of Substitution (CES) preferences in this context. The ST functional form has a potential advantage over the CES functional form that it produces finite estimates for reservation prices for missing products whereas the CES reservation prices are always infinite. The present paper proposes a Generalized Symmetric Translog Cost Function which also generates finite reservation prices but is more flexible than the ST functional form.

Subsidy Policies of Agricultural Producer Service and Wage Inequality in Developing Economy

This study examines the effects of subsidy policies of agricultural producer service on wage disparity while taking into account the modernization of small-scale farming in developing nations. Due to small-scale operations, agriculture needs an intermediary sector-an agricultural producer service sector-to help modernization by facilitating the entry of non-agricultural intermediate inputs. Main conclusions are wage subsidy policy on skilled labor expands it in the short term. In the long run, the results of wage subsidy of skilled labor depend on the elasticity of substitution among varieties in service sector. When the elasticity of substitution is relatively small (large), subsiding skilled labor narrows down (expands) the wage inequality.

Is green growth possible and even desirable in a spaceship economy?

There seems to be a consensus among many growth and resource economists that perpetual growth can be ensured if it gets increasingly resource-efficient and if growth focuses on creating values, a result derived by models using production functions that allow asymptotically complete decoupling of the economy from its resource base by substituting natural resources through physical and knowledge capital. This growth process can be called green growth. The following paper attempts to show, within the framework of an semi-endogenous growth model using a linear-exponential production function (Linex function) with bounded resource efficiency, that the accumulation of physical and knowledge capital to substitute natural resources cannot guarantee green growth. As the population grows, per capita income decreases, and the economy’s capital base decays. In addition, an ecological displacement effect resulting from the biophysical embeddedness of the economy further exacerbates the result. Physical capital pushes back the natural spaces necessary to regenerate natural services and resources and can, therefore, not be accumulated endlessly. A comparison with standard resource models shows that this displacement effect also limits growth for models with production functions with low elasticities of substitution. Finally, the analysis of transitory dynamics addresses aspects of intergenerational equality in a limited biosphere.

Consensus manipulation in social network group decision making with value-based opinion evolution

Opinion evolution is a common phenomenon in social network group decision-making (SNGDM), where the key issue is modelling trust weights among individuals. In social and economic networks, the links among individuals represent trust relationships that can offer value. However, extant studies on trust weight distribution have failed to consider individual network values. Moreover, in some scenarios, the external stakeholder may want to manipulate the opinion evolution process to achieve the desired consensus outcome. Therefore, this study proposes value-based opinion evolution and discusses consensus manipulation in SNGDM. First, we measured the total value of an individual in a network, which consisted of two parts: intrinsic value and network value. Notably, we used the constant elasticity of substitution from economics as an operator to aggregate intrinsic and network values. Based on this, we described value-based opinion evolution and established an optimisation-based consensus manipulation model for SNGDM with value-based opinion evolution (CM-VBOE). Furthermore, we conducted some sensitive analyses, which indicate that an individual’s value in the network increases with the decay factor and decreases with the elasticity of substitution, and provide a comparative analysis, which expands on the importance of accounting for the decay factor and elasticity of substitution when modelling value-based opinion evolution. Finally, a hypothetical application for crowdfunding project selection is presented to illustrate the applicability of the proposed CM-VBOE.

The effects of carbon taxes on the welfare of households using multiple energy sources

Households use a variety of energy services by combining several sources of energy, such as electricity, gas, and kerosene. However, the effects of carbon taxes on the welfare of households using multiple energy sources have not yet been fully investigated. In this study, we propose a residential energy consumption model where the elasticity of substitution between energy sources is influenced by weather conditions and the relative evaluation of energy sources differs between households with different socioeconomic characteristics. We then conduct a household-level data analysis to estimate the elasticity of substitution, and the relative evaluation of electricity, city gas, LP gas, and kerosene. The empirical results show that the elasticity of substitution between energy sources increases as outside temperature drops, and households with different socioeconomic characteristics evaluate energy sources differently. Specifically, using the estimation results, we assess the impact of carbon taxation on household welfare. Assuming that total energy expenditure remains unchanged after carbon taxation, we compare the welfare impact of carbon taxation among households using different energy source combinations. The simulation results predict that households using electricity and kerosene in rural areas are most severely affected by carbon taxation.

Delay Solow Model with a Normalized CES Production Function

This study analyzes the relationship between the elasticity of substitution and the economic stability/instability. To this end, we adopt a CES production function that consistently involves all its variants and introduce two delays, called a gestation delay and a depreciation delay, into the Solow model. In the case of one delay, we find that the gestation delay is harmless, the depreciation delay has a destabilizing effect, and the two delays having the equal length possesses a stronger stabilizing effect than the destabilizing effect of the depreciation delay. In the case of two different delays, we analytically construct the stability switching curve that divides the parametric region into the stability and instability regions. We also demonstrate that the location of the stability switching curve depends not only on the elasticity of substitution but the baseline values of the CES function and the parametric values of the dynamic equation.

The Elasticity of Substitution Between Skilled and Unskilled Labor in Developing Countries: A Directed Technical Change Perspective

The Elasticity of Substitution Between Skilled and Unskilled Labor in Developing Countries: A Directed Technical Change Perspective

Exchange rates and monetary policy when tradable and nontradable goods are complements

This paper examines the implications of complementarity between tradable and nontradable goods for exchange rates and monetary policy in a two-country general equilibrium model. In doing so, it revisits well-known findings in the New Open Economy Macroeconomics literature that exchange rates are proportional to relative national money supplies and that optimal monetary policies respond only to domestic shocks. These results depend on a number of simplifying assumptions, including a unitary elasticity of substitution between tradable and nontradable goods. When this assumption is replaced by a more-realistic one of complementarity, exchange rates depend on relative productivity in addition to money supplies when prices are flexible. When prices are sticky, complementarity amplifies the effect of changes in relative money supplies on the exchange rate and creates additional spillover effects from changes in the foreign money supply to domestic consumption. With complementarity, optimal monetary policies respond to external as well as internal shocks.

The impact of trade on the elasticity of labor demand—Nonlinear analysis based on the perspective of human capital

Using the import and export trade data of 29 provinces and cities in China from 1997 to 2017, this paper studies the impact of trade on China’s labor demand elasticity, and whether the impact will be affected by the level of domestic human capital. The results show that: import is conducive to improving the labor demand elasticity, and export is conducive to reducing the labor demand elasticity. Moreover, with the improvement of domestic human capital level, the weakening effect of export on the labor demand elasticity is strengthened, and the improving effect of import on the labor demand elasticity is weakened. The reason is that the improvement of the level of human capital can reduce the demand elasticity of domestic and foreign consumers for domestic products by improving the cost performance of products, and can also reduce the factor substitution elasticity of labor force. Therefore, the improvement effect of import on the demand elasticity of labor force is weakened, and the weakening effect of export on the demand elasticity of labor force is strengthened. It can be seen that the improvement of domestic human capital level is conducive to the labor force to deal with the employment security problem in the trade liberalization.

Labor market distortion and its impact on wage inequality in the modernization of small‐scale agriculture

AbstractThis study investigates the impacts of labor market distortion on wage inequality by considering the modernization of small‐scale agriculture. Owing to small‐scale operations, agriculture requires an intermediate sector—an agricultural producer service sector—to facilitate the introduction of nonagricultural intermediate inputs and promote modernization. The basic model assumes perfect competition in the service sector and shows that if the elasticity of substitution between labor and services is sufficiently large (small), mitigating distortion widens (reduces) wage inequality between skilled and rural unskilled labor. In the extended model, we introduce a service sector with monopolistic competition and the main results of the basic model almost hold.

Could the Lacking Absorption Capacity of the Inflowing Capital Be the Real Cause of the Resource Curse?—A Case Study of Transition Economies

The present study proposes an alternative explanation for the negative natural-resource-growth nexus. Based on the theoretical analysis, the study shows that a balanced capital–labor ratio plays an essential role in the absorption of complex capital goods. It estimates the parameters of the constant elasticity of the substitution production function in Mathcad using nonlinear least squares, i.e., an approximate Marquardt method of optimization. The empirical analysis is based on the time-series data of these countries for the time interval between 2000 and 2020. We conducted analyses by calculating the elasticity of substitution between capital and labor. Specifically, for these countries, the elasticity of substitution of capital and labor appeared to be less than one, which indicates a lack of labor, or, more precisely, a qualified labor force. Each of these countries receives windfall profits from the exploitation of natural resources, which greatly influences the import of capital-intensive products of complex technologies—in other words, the import of capital. However, the lack of an adequate labor force that could utilize the increased capital led to a decrease in the elasticity of capital and labor substitution. A comparison of the optimal and the observed capital–labor ratio coefficient shows that this coefficient is significantly higher than optimal in all three countries. Therefore, while keeping the wage fund in balance with fixed capital costs, investments in the knowledge economy and human capital appear to be the preferred areas for the efficient allocation of oil revenues.

Who pays for environmental protection? The impact of green tax reform on labor share in China

To cope with increasing environmental pollution, the Chinese government has introduced a nationwide Environmental Protection Tax Law (EPTL) policy, which encourages enterprises to step up pollution control efforts and optimize their production decisions. However, the “green cost” generated by the EPTL policy has received less attention in existing research. Based on the manually collected data on China's listed companies during 2013–2020, this paper innovatively calculates the substitution elasticity of green capital to labor. By regarding the EPTL policy as a quasi-natural experiment, the difference-in-difference (DID) model and other causal identification methods are further adopted to examine the real effect and influencing mechanism of green tax reform on labor share. The results indicate that the EPTL policy significantly reduces the labor share through two influencing paths: promoting green capital and squeezing out low-skilled labor. This finding demonstrates that the EPTL policy leads to green capital gains and human capital losses, and it is mainly low-skilled labor in enterprises that “pay for” environmental policy shocks. By decomposing the labor share, we find that the EPTL policy leads to a decrease in employees' average wages and an increase in labor productivity, which indirectly proves the rationality of the two mechanisms. Further analysis reveals that in capital-intensive and growth enterprises, and in enterprises that did not receive green subsidies from the government, the decrease in labor share caused by the EPTL policy is more pronounced. Finally, this paper proposes targeted policy recommendations for governments seeking to balance national welfare and green development.

Countercyclical Risks, Consumption, and Portfolio Choice: Theory and Evidence

Using a quantitative, calibrated life-cycle model, I show that countercyclical earnings risk affects individual consumption growth, reduces the share of wealth in stocks, and affects savings behavior. Using the Panel Study of Income Dynamics survey, I construct an empirical measure of countercyclical earnings risk and find evidence consistent with the model’s predictions. Specifically, larger downside earnings risk decreases consumption growth, increases left skewness in consumption growth, and reduces the share of wealth in stocks. Furthermore, the consumption effects are substantially more significant for stockholders than for nonstockholders, which arises through heterogeneity in the elasticity of intertemporal substitution. This paper was accepted by Tomasz Piskorski, finance. Supplemental Material: The data and online appendix are available at https://doi.org/10.1287/mnsc.2023.4837 .

Are working hours complements in production?

This paper studies the degree of complementarity in working hours among coworkers in production. Using matched employer-employee data, we first present facts on the within-establishment relationship between wages and hours worked that are consistent with the presence of complementarities in working hours. Next, we estimate the elasticity of substitution in working hours and find it to be 0.69 in the aggregate and between 0.52 and 1.03 across industries. We validate our elasticity estimates by showing that industries with higher elasticities exhibit greater flexibility in hours. Our results suggest that working hours are gross complements in production rather than perfect substitutes, as is typically assumed. An accounting exercise using our model estimations suggests that hours-wage penalties, due to complementarities in hours, can explain 5 to 30 percent of the gender wage gap over the life-cycle.