Searcharxiv⌕ Search

arXiv subjects

Ngoc-Sang Pham

Publications and source records attributed to Ngoc-Sang Pham.

11 recordsLinked to original sources
arXiv2026

To Bubble or Not to Bubble: Asset Price Dynamics and Optimality in OLG Economies

We study an overlapping generations (OLG) exchange economy with an asset that yields dividends. First, we derive general conditions, based on exogenous parameters, that give rise to three distinct scenarios: (1) only bubbleless equilibria exist, (2) a bubbleless equilibrium coexists with a continuum of bubbly equilibria, and (3) all equilibria are bubbly. Under stationary endowments and standard assumptions, we provide a complete characterization of the equilibrium set and the associated asset price dynamics. In this setting, a bubbly equilibrium exists if and only if the interest rate in the economy without the asset is strictly lower than the population growth rate and the sum of per capita dividends is finite. Second, we establish necessary and sufficient conditions for Pareto optimality. Finally, we investigate the relationship between asset price behaviors and the optimality of equilibria.

q-fin.CP↗
arXiv2026

Global Characterization of Equilibria in Tirole's (1985) Model with a Dividend-Paying Asset

We revisit Tirole's classic paper "Asset Bubbles and Overlapping Generations" (1985, Econometrica) in the case of a dividend-paying asset. Recently, Pham and Toda (2026) constructed a counterexample to Proposition 1(c), showing that Tirole's equilibrium classification is incorrect as stated and that long-run outcomes can depend on initial capital. This paper characterizes the entire set of equilibrium initial asset prices under capital over-accumulation. Exactly one of three regimes occurs: (i) a unique bubbleless equilibrium with capital converging to zero (capital collapse), (ii) a unique asymptotically bubbly equilibrium converging to a positive steady state (bubble necessity), or (iii) a continuum of equilibria with different long-run bubble behavior (indeterminacy). We further derive a threshold for initial capital under the bubble necessity condition, establish preference-free sufficient conditions for capital collapse, and show that the continuum in the pure bubble model survives sufficiently small dividend perturbations. Closed-form examples illustrate the possible long-run outcomes.

econ.TH↗
arXiv2026

A note on first-order and transversality conditions in infinite-horizon continuous-time optimal control models

We provide simple and easily verifiable necessary and sufficient conditions for infinite-horizon continuous-time optimal control problems. Under standard concavity and integrability assumptions, we show that optimal paths are fully characterized by first-order conditions together with a transversality condition. Importantly, the transversality condition is derived as a consequence of the model's structure rather than imposed a priori. Our results apply directly to standard economic models, including optimal growth and consumption--saving problems.

math.OC↗
arXiv2026

FDI versus R\&D in an endogenous growth model

We investigate the role of foreign direct investment (FDI) and research and development (R\&D) in the transitional dynamics of host countries using an optimal growth model. FDI may benefit the host country's GNP by enabling multinational enterprises to hire local workers. However, if the host country focuses solely on FDI, it may fall into a middle-income trap. Most importantly, we show that if the host country invests in R\&D, its economy can reach sustained growth. In this case, FDI benefits the host country, but only in the early stages of its development process.

q-fin.GN↗
arXiv2026

The relationship between general equilibrium models with infinite-lived agents and overlapping generations models, and some applications

We prove that a two-cycle equilibrium in a general equilibrium model with infinitely-lived agents (GEILA) constitutes an equilibrium in an overlapping generations (OLG) model. Conversely, an equilibrium in an OLG model that satisfies additional conditions is part of an equilibrium in a GEILA model. Our framework, which includes three assets (physical capital, a Lucas tree, and fiat money), encompasses both exchange and production economies. As an application, we demonstrate that equilibrium indeterminacy and rational asset price bubbles can arise not only in OLG models but also in GEILA models.

q-fin.GN↗
arXiv2026

Comment on 'Asset Bubbles and Overlapping Generations'

Tirole (1985) studied an overlapping generations model with capital accumulation and showed that the emergence of asset bubbles solves the capital over-accumulation problem. His Proposition 1(c) claims that if the dividend growth rate is above the bubbleless interest rate (the steady-state interest rate in the economy without the asset) but below the population growth rate, then bubbles are necessary in the sense that there exists no bubbleless equilibrium but there exists a unique bubbly equilibrium. We show that this result (as stated) is incorrect by presenting an example economy that satisfies all assumptions of Proposition 1(c) but its unique equilibrium is bubbleless. We also restore Proposition 1(c) under the additional assumptions that initial capital is sufficiently large and dividends are sufficiently small. We show through examples that these conditions are essential.

econ.TH↗
arXiv2025

Governance, productivity and economic development

This paper explores the interplay between transfer policies, R\&D, corruption, and economic development using a general equilibrium model with heterogeneous agents and a government. The government collects taxes, redistributes fiscal revenues, and undertakes public investment (in R\&D, infrastructure, etc.). Corruption is modeled as a fraction of tax revenues that is siphoned off and removed from the economy. We first establish the existence of a political-economic equilibrium. Then, using an analytically tractable framework with two private agents, we examine the effects of corruption and evaluate the impact of various policies, including redistribution and innovation-led strategies.

q-fin.CP↗
arXiv2025

Wariness and Poverty Traps

We investigate the effects of wariness (defined as individuals' concern for their minimum utility over time) on poverty traps and equilibrium multiplicity in an overlapping generations (OLG) model. We explore conditions under which (i) wariness amplifies or mitigates the likelihood of poverty traps in the economy and (ii) it gives rise to multiple intertemporal equilibria. Furthermore, we conduct comparative statics to characterize these effects and to examine how the interplay between wariness, productivity, and factor substitutability influences the dynamics of the economy.

q-fin.CP↗
arXiv2025

(Non-Monotonic) Effects of Productivity and Credit Constraints on Equilibrium Aggregate Production in General Equilibrium Models with Heterogeneous Producers

We show that, in a market economy, the aggregate production level depends not only on the aggregate variables but also on the distribution of individual characteristics (e.g., productivity, credit limit, ...). We prove that, due to financial frictions, the equilibrium aggregate production may be non-monotonic in both individual productivity and credit limit. We provide conditions (based on exogenous parameters) under which this phenomenon happens. By consequence, improving productivity or relaxing credit limit of firms may not necessarily be beneficial to economic development.

q-fin.CP↗
arXiv2025

Equilibrium with non-convex preferences: some insights

We study the existence of equilibrium when agents' preferences may not beconvex. For some specific utility functions, we provide a necessary and sufficientcondition under which there exists an equilibrium. The standard approach cannot be directly applied to our examples because the demand correspondence of some agents is neither single-valued nor convex-valued.

q-fin.CP↗