Samuelson Model Research Articles

Oscillatory and Property Conditions for Third Order Difference Equation with Negative Middle-Term

This paper presents a detailed analysis of the oscillation and Property A conditions for third-order advanced difference equations with negative middle terms. The authors employ the generalized Riccati transformation technique and summation by parts to establish sufficient criteria for the solutions to be oscillatory or have Property A. The main results and their proofs are presented clearly and concisely. The difference equations have been a topic of interest in various scientific fields such as economics, physics, and mathematical biology. The results presented in this paper can be used to inform the development of more accurate models for real-world problems in various scientific fields. Additionally, this paper explores the economic theory of business cycles and its mathematical foundations, specifically Samuelson's model, which outlines five potential trajectories or trends that economic activity can follow based on different combinations of the marginal propensity to consume multiplier parameter(α) and the accelerator coefficient (β).

Modifications of the Samuelson Economic Cycle Model

Abstract The paper presents an analysis of modifications of the standard discrete Samuelson model with determination of the stability of the equilibrium point. The stability region of the equilibrium point depending on the parameters contained in each model is determined using the Schur-Cohn stability criterion.

Модель Хекшера-Оліна-Самуельсона: теоретичний базис і умови застосування

The Heckscher – Ohlin – Samuelson model provides a mathematical proof of the possibility of equalizing the relative and absolute prices for production factors in international trade with certain assumptions. However, in practice, these assumptions are not followed. Therefore, there is a need to adjust the parameters of the model by calculating the indicators of cost estimation and the use of production factors. Therefore, the purpose of the research is to generalize the theoretical provisions of the Heckscher – Ohlin – Samuelson model in order to find the possibilities of its application in the conditions of the post- war economic recovery of Ukraine. The main research methods were theoretical generalization, economic and statistical analysis, multivariate linear regression. In the process of the research, several partial tasks were performed: 1) systematizing the views of scientists regarding methods of adjusting the parameters of the Heckscher – Ohlin –Samuelson model; the existence of a statistical relationship between the factor saturation of the economies of individual countries with the indicators of their foreign trade and changes in the prices of production factors; recommendations for the application of the Heckscher – Ohlin – Samuelson model in the conditions of the post-war economic recovery of Ukraine. A comparison of the volumes of available labor and capital investment were made for 2020. And it proves that industrialized countries are excessively capital-saturated, but the calculation of K/L ratios still does not explain the structure of their international trade. At the same time, for some relatively developed countries, including Ukraine, the K/L ratio is “paradoxical”. The results of the regression analysis of production factors and foreign trade indicators of 30 countries, of the largest volume of capital investments, prove the existence of a relatively close connection of K/L ratios with indicators of export-import and their growth, in condition of the involving of correction coefficients into the basic Heckscher – Ohlin – Samuelson model. The main condition for applying the tools of the Heckscher – Ohlin – Samuelson model in modern practice is the mitigation of its assumptions regarding the homogeneity of production factors, their full use, and the limitation of their international mobility. In addition, it is necessary to ensure the identity of the measurement parameters of production factors in different statistical systems, taking into account the time factor and exchange rate differences. The practical significance of the study is that in the conditions of the post-war economic recovery of Ukraine, most of the assumptions of the Heckscher – Ohlin – Samuelson model are nullified. Its explained by situation that state will have to introduce strict restrictions on the movement of production factors and international trade for some time. This allows to form real statistics on the use of production factors and, on its basis, to carry out programming of Ukraine's international trade.

The Impact of Trade Liberalization on Income Inequality: Does the Direction of Trade Matter?

Recent trends in inequality have raised concerns among researchers and policymakers globally. The role of globalization, one of the leading forces driving this trend, continues to be intensely debated in academic and policy circles. Invoking standard trade theory, this paper analyses whether and the extent to which trade liberalization has contributed to the recent trends in inequality. The approach and findings of the paper are novel: previous studies of trade liberalization’s impact on inequality do not explicitly control the direction of trade. The empirical results show that trade liberalization is associated with decreasing income inequality overall, but contingent on the direction of trade, it has opposing effects: North–North and South–South trade are inequality-reducing while North–South trade is inequality-increasing. Simply put, liberalizing trade between countries of similar developmental levels does not raise inequality. This paper affirms, using recent data, that trade with developing countries raises inequality in developed countries. Additionally, it finds that North–South trade (particularly imports from high-income to low-income countries) may also raise inequality in developing countries, contrary to Heckscher–Ohlin–Stolper–Samuelson model predictions. Skill-biased technical change, a consequence of trade liberalization between North and South, is the main mechanism driving inequality increases in developing countries.

Using the Samuelson Model to Assess the French Economy's Business Cycle: A Mathematical Study

The business cycle is considered one of the essential and replenishable topics. It represents one of the flaws of the capitalist economic system and several adjectives that give it this importance. Therefore, economists gave it the necessary attention. Perhaps the most well-known of them is Samuelson, credited with being one of the first economists to study and model the market cycle. It attempted to quantify and forecast the market cycle by integrating two concepts: the multiplier and the compressor. The tools of this model were applied in our research on the French economy over the period (1985-2018). The study could determine the business cycles that it has gone through in a precise and objective way, totaling five business cycles (for the studied period), including the start and end dates (except the last cycle, which has not ended yet).

The Outlines of a Possible Pension System Funded with Human Capital

The broadly used pay-as-you-go (PAYG) pension system is intrinsically wrong. The essence of the problem is that the PAYG system distributes the yield of raising children, i.e., of human capital investment (which is essentially the pension contribution), in such a way that it disregards the extent to which individuals have contributed to this, and even whether it has occurred at all. This error can be corrected if we take the pension contribution to be the yield on an investment of human capital, and as such use this to pay back the costs and expenses of the raising of the contribution payer—overall to those who paid these costs and expenses at the time. Accordingly, the central question of my study is whether it is possible to construct a consistent pension system based on the above foundations, and how my ideas may be inserted into the Diamond–Samuelson model. The method of the study was logical analysis and the construction of a theoretical mathematical model. The results of the study show that it is possible to construct a public pension system that operates according to a different logic than today’s system, a system which is free from the effects of demographic fluctuations, which does not motivate the refusal to have children, and which will remain self-sufficient under all circumstances. The study achieves this by presenting a possible pension system of this kind in detail. Via the suitable modification of the Diamond–Samuelson model, I have succeeded in showing that the pension system I am proposing increases the willingness to have children up to the social optimum, in contrast to the fully (but traditionally) funded and PAYG systems. This system currently only exists in theory and may be regarded as a major theoretical innovation, which naturally has certain (although not particularly extensive) antecedents. Its introduction could enable the resolution of the contradictions of existing pension systems and could also provide a solution to the as yet unsolved problem of the increasingly expensive regeneration of human capital, and as such, its potential practical implications are immeasurable.

Unemployment effects of trade with a low‐wage country: A minimum‐wage model with sector‐specific factors

AbstractContrary to conventional wisdom, this paper shows that a high‐wage economy can paradoxically reduce its level of aggregate unemployment by engaging in international trade with a low‐wage country. We demonstrate this possibility after introducing a minimum wage into the basic specific‐factor model (with immobile capital and mobile labor), even though the opposite result is known to arise in the longer‐run framework of the standard Heckscher–Ohlin–Samuelson model (with both inputs mobile). Our result provides a cautionary note for public‐policy discussions that promote trade barriers as a way to reduce unemployment.

A Nonsmooth Extension of Samuelson’s Multiplier-Accelerator Model

Dynamical-systems approaches have historically been used in business-cycle theory to generate sustained oscillations in macroeconomic variables. We aim to contribute to this literature by extending the original Samuelson multiplier-accelerator model with a discontinuous stabilization policy in terms of government expenditure. We show that the nonsmoothness yields dynamics in terms of periodic orbits and irregular fluctuations, not found in the original Samuelson model. We also note with particular interest that our model is able to generate localized nonstationary dynamics, which is in contrast to the most standard models found in the literature.

Trade, Inequality and Distribution-neutral Fiscal Policy

Gains from trade and inequality do not feature prominently in trade theory. The standard criterion of Pareto efficiency indicates nothing about inequality when applied to the redistribution of gains from trade. Yet, trade-induced inequality has become a talking point and extremely contentious issue worldwide. In a Heckscher–Ohlin–Samuelson (HOS) model of trade, we consider tax-transfer policies that do not decrease the absolute income of any group, as suggested by the standard Pareto rule and keep the pre-trade degree of inequality between skilled and unskilled workers unchanged. Such a fiscal policy exists and is independent of whether the tax is progressive or proportional. We show that the aggregate gain in real income due to trade can be distributed to make everyone better off without increasing inequality. A generalization of the basic result shows that any Pareto efficient allocation can be transformed into a distribution-neutral allocation through appropriate fiscal policy. JEL Codes: F11, J31, D63, H20, H23

Sensitivity analysis for expected utility maximization in incomplete Brownian market models

We examine the issue of sensitivity with respect to model parameters for the problem of utility maximization from final wealth in an incomplete Samuelson model and mainly, but not exclusively, for utility functions of positive-power type. The method consists in moving the parameters through change of measure, which we call a weak perturbation, decoupling the usual wealth equation from the varying parameters. By rewriting the maximization problem in terms of a convex-analytical support function of a weakly-compact set, crucially leveraging on the work (Backhoff and Fontbona in SIAM J Financ Math 7(1):70–103, 2016), the previous formulation let us prove the Hadamard directional differentiability of the value function with respect to the market price of risk, the drift and interest rate parameters, as well as for volatility matrices under a stability condition on their Kernel, and derive explicit expressions for the directional derivatives. We contrast our proposed weak perturbations against what we call strong perturbations, where the wealth equation is directly influenced by the changing parameters. Contrary to conventional wisdom, we find that both points of view generally yield different sensitivities unless e.g. if initial parameters and their perturbations are deterministic.

Differential Representation of a Samuelson Model with a Telegraph Drift

Abstract In this paper we construct a system of three stochastic differential equations, which has a solution composed of a generalized telegraph signal process and a basic process. This system enabled us to find the escape probability of the basic process from an interval through its endpoint.

On the exponential stability of Samuelson model on some classes of times scales

We prove the remarkable property that the exponential stability of the Samuelson model is invariant under the times scales R and h Z whenever 0 < h ≤ 1 . We characterize the domains of stability for these time scales and we also give sufficient conditions for stability on a class of mixed times scale. We prove analogous results for the Samuelson model in an open economy. Our methods are based on a spectral characterization of exponential stability due to Potzsche, Siegmund and Wirth and a multiplier accelerator model on time scales due to Bohner, Gelles and Heim.

Beyond Balassa and Samuelson: real convergence, capital flows, and competitiveness in Greece

To better understand the convergence process prior and since the European financial and debt crisis, we scrutinize the role of capital flows for competitiveness in Greece and a set of six other euro area member countries (Portugal, Latvia, Estonia, Lithuania, Slovenia and the Slovak Republic). For this purpose the paper extends the seminal Balassa–Samuelson model by international capital markets with a particular focus on their impact on national wage policies. Capital flows are assumed to be able to invert the traditional direction of transmission of real wage increases from the tradable sector to the non-tradable sector and to make real wages increase beyond productivity increases. The augmented Balassa–Samuelson model is extended to trace cyclical deviations of real exchange rates from the productivity-driven equilibrium path. Panel estimations for the period from 1995 to 2013 reveal correlations in line with the Balassa–Samuelson effect, if Greece is excluded from the panel. For Greece, this in turn implies indication in favour of a credit-driven real wage increases beyond productivity increases what we call a “pseudo” Balassa–Samuelson effect.

On future drawdowns of Lévy processes

For a given Lévy process X=(Xt)t∈R+ and for fixed s∈R+∪{∞} and t∈R+ we analyse the future drawdown extremes that are defined as follows: D¯t,s∗=sup0≤u≤tinfu≤w<t+s(Xw−Xu),D¯t,s∗=inf0≤u≤tinfu≤w<t+s(Xw−Xu). The path-functionals D¯t,s∗ and D¯t,s∗ are of interest in various areas of application, including financial mathematics and queueing theory. In the case that X has a strictly positive mean, we find the exact asymptotic decay as x→∞ of the tail probabilities P(D¯t∗<x) and P(D¯t∗<x) of D¯t∗=lims→∞D¯t,s∗ and D¯t∗=lims→∞D¯t,s∗ both when the jumps satisfy the Cramér assumption and in a heavy-tailed case. Furthermore, in the case that the jumps of the Lévy process X are of single sign and X is not subordinator, we identify the one-dimensional distributions in terms of the scale function of X. By way of example, we derive explicit results for the Black–Scholes–Samuelson model.

Ordering Results for Risk Bounds and Cost-efficient Payoffs in Partially Specified Risk Factor Models

Motivated by the problem of sharp risk bounds in partially specified risk factor models and by the method of cost-efficient payoffs with given payoff structure we introduce and describe some stochastic odering problems for conditionally comonotonic resp. antimonotonic random variables. The aim is to describe the influence of the specified dependence of the components of the random vector X with a benchmark Z on the risk bounds in a risk portfolio resp. on the gain of cost efficiency of the optimal payoffs. We obtain in particular explicit results in dependence on distributional parameters for elliptical models in the case of risk bounds and for the multivariate Samuelson model in the case of cost efficient payoffs.

Estimation of parameters of the Samuelson model with telegraph drift

We have constructed the estimates of unknown parameters of the Samuelson model with telegraph drift within the method of moments. We have proved the strong consistency of the estimates and obtained the asymptotic confidence regions for the unknown parameters.

Imperfect mobility of labor across sectors: a reappraisal of the Balassa–Samuelson effect

This paper investigates the relative price and relative wage effects of a higher productivity in the traded sector compared with the non traded sector in a two-sector open economy model with imperfect substitutability in hours worked across sectors. The Balassa–Samuelson (1964) model predicts that a rise in the sectoral productivity ratio by 1% raises the relative price of non tradables by 1% while leaving the non traded wage-traded wage ratio unchanged. Applying cointegration methods to a panel of fourteen OECD countries over the period 1970–2007, our estimates show that the relative price rises by only 0.78% and the relative wage falls by 0.27%. While our first set of empirical findings cast doubt on the quantitative predictions of the Balassa–Samuelson model, our second set of evidence highlights the role of imperfect labor mobility: the relative price responds more to a productivity differential between tradables and non tradables while the reaction of the relative wage is more muted in countries with higher intersectoral reallocation of labor. We show that the ability of the two-sector model to account for our evidence quantitatively relies upon two ingredients: i) imperfect mobility of labor across sectors, and ii) physical capital accumulation. Finally, our numerical results reveal that the model predicts the relative price response fairly well, and to a lesser extent the relative wage response.

Trade dynamics with sector-specific human capital

This paper develops a dynamic Heckscher Ohlin Samuelson model with sector-specific human capital and overlapping generations to characterize the dynamics and welfare implications of gradual labor market adjustment to trade. Our model is tractable enough to yield sharp analytic results, that complement and clarify an emerging empirical literature on labor market adjustment to trade. Existing generations that have accumulated specific human capital in one sector can switch sectors when the economy is hit by a trade shock. Nonetheless, the shock induces few workers to switch, generating a protracted adjustment that operates largely through the entry of new generations. This results in wages being tied to the sector of employment in the short-run but to the skill type in the long-run. Relative to a world with general human capital, welfare is improved for the skill group whose type-intensive sector shrinks. We extend the model to include physical capital and show that the transition is longer when capital is mobile. We also introduce nonpecuniary sector preferences and show that larger gross flows are associated with a longer transition.

A Partial Test of the Heckscher-Ohlin-Samuelson Model: US-Mexico Trade Relations and Labour in Mexico

Proponents of trade liberalization emphasize the role of trade and economic integration between less developed and more developed economies as an engine for development and improved standards of living. Nowhere is this argument more salient, and more controversial, than in the discussion of US-Mexico trade, and the North American Free Trade Agreement (NAFTA) specifically. As the Heckscher-Ohlin- Samuelson (HOS) model informs much of the rhetoric and policy surrounding the USMexico trade relationship, we attempt a partial test of the model and its assumptions regarding labour and employment in the case of the Mexican economy. Specifically, we focus on the Heckscher-Ohlin (HO) theorem and the Factor Price Equalization (FPE) theorem. We conclude that although economic analysts recognize that the model does not account the complexity of Mexico's domestic economy and international trade relationships, it continues to permeate rhetoric, remaining the dominant paradigm for proponents of NAFTA on both sides of the border.

Globalisation and Inter‐occupational Inequality: Empirical Evidence from OECD Countries

AbstractHow does globalisation affect inter‐occupational wage inequality within countries? This paper examines this by focusing on two dimensions of globalisation: openness to trade and openness to capital flows, using a relatively new data set on occupational wages. Estimates from a dynamic model for 15 OECD countries spanning the period 1983–2003 suggest that increased openness increases occupational wage inequality in poorer OECD countries as predicted by the Heckscher–Ohlin–Samuelson model, but for the more advanced OECD countries, we find no significant effect. The absence of the expected result for the latter category can be due to a rapid increase in the supply of skilled labour, to outsourcing of skilled jobs or because changes in the trade flows are too small to have any significant effect in those countries.