Imperfect Financial Markets and Investment Inefficiencies: Albagli, Hellwig & Tsyvinski (2023)

What this is. The paper’s core theoretical results, the partial and general equilibrium models with their defining equations, and the empirical-relevance discussion: enough to understand the mechanism and all six propositions without reading all 32 pages. To replicate or extend it, read the full article at doi.org/10.1257/aer.20170725.

TL;DR

Incumbent shareholders who sell a fraction of their equity before dividends are realized have a rent-seeking motive: by distorting investment, they can move the market price in their favor. With upside risk in cash flows (positive return asymmetry), they overinvest to inflate expected prices; with downside risk, they underinvest to avoid price deflation. The magnitude of the distortion scales with three parameters: the percentage return wedge between market-implied and fundamental returns ($\Delta$), the fraction of shares traded ($\alpha$), and the inverse scalability of investment ($\chi^{-1}$). In general equilibrium, the shareholders’ collective attempts to boost their firms’ share prices lower aggregate dividends, creating an externality that dampens overinvestment with upside risk but amplifies underinvestment with downside risk. A corrective tax implements the efficient allocation in both settings.

Core results

Propositions reference the paper’s own numbering; locators point into the source PDF.

#	Result	Locator	Magnitude
R1	Partial equilibrium investment distortion: overinvestment for upside risk ($\alpha\Delta > 0$), underinvestment for downside risk ($\alpha\Delta < 0$); log distortion approximately $\alpha\Delta\chi^{-1}$	Proposition 1, pp. 2333-2334	$\hat{K}/K^* = (1+\alpha\Delta)^{1/\chi}$; dividend losses $V(\hat{K})/V(K^*) = (1+\alpha\Delta)^{1/\chi}(1-\alpha\Delta\chi^{-1})$
R2	Negative expected dividends arise when upside risk and high scalability combine: the firm overinvests so severely that it destroys value in expectation	Proposition 1(iv), eq. 4, p. 2333	Condition: $\alpha\Delta\chi^{-1} > 1$
R3	Partial equilibrium corrective tax implements efficient investment by offsetting the return wedge	eq. 5, p. 2336	$\tau = 1 - \frac{1}{1+\alpha\Delta}$
R4	General equilibrium unique solution; investment is lower than in partial equilibrium ($K_{GE} < K_{PE}$); with upside risk overinvestment is dampened ($K_{PE} > K_{GE} > K^*$); with downside risk underinvestment is amplified ($K_{GE} < K_{PE} < K^*$)	Proposition 2, p. 2342	$K_{GE}/K^* = \bigl(1 + \alpha\Delta \cdot Q/\hat{Q}\,/\,(1-\alpha+\alpha Q/\hat{Q})\bigr)^{1/\chi}$
R5	Limiting behavior for highly scalable investments ($\chi \to 0$): upside distortions are bounded ($K_{GE}/K^* \to e^\alpha$); downside distortions are unbounded ($K_{GE}/K^* \to 0$ as investment collapses; GE surplus vanishes relative to PE surplus)	Proposition 3, p. 2342	Upside: $\lim_{\chi \to 0} V(K_{GE})/V(K^*) = (1-\alpha)e^\alpha < 1$; Downside: $\lim_{\chi \to 0} V(K_{GE})/V(K_{PE}) = 0$
R6	Information feedback (price-contingent investment) merges both mechanisms: investment is positively correlated with prices (excess sensitivity to market signals), and higher investment predicts lower future equity returns	Proposition 4, pp. 2348-2349	$\text{cov}(\hat{K}(z), P(z)) > 0$; $\hat{K}(z)/K^*(z)$ increasing in $z$; $\text{cov}\bigl(\hat{K}(z),\,(V(z)-P(z))/P(z)\bigr) < 0$

Overall (paper’s conclusion). Even small departures from market efficiency can produce large aggregate investment distortions when investments are highly scalable, and these distortions are compounded by the price externality in general equilibrium. The paper provides a rationale for regulating financial risk-taking by publicly traded firms even when equity markets operate near efficiency.

Theory / model

The model has three stages and is developed first in partial equilibrium (Section I) and then embedded in general equilibrium (Section II).

Partial equilibrium baseline (§I.A, pp. 2326-2330). A single firm. At stage 1, incumbent shareholders choose investment $k \geq 0$. At stage 2, they sell a fraction $\alpha \in (0,1]$ of shares to outside investors. At stage 3, dividends $\Pi(\theta, k) \equiv R(\theta)k - C(k)$ are paid to final shareholders, where $\theta \sim \mathcal{N}(0, \lambda^{-1})$ is a stochastic fundamental and $C(k) = k^{1+\chi}/(1+\chi)$ with $\chi \geq 0$. The parameter $\chi^{-1}$ captures the scalability of investment. Ex ante efficient investment $K^*$ maximizes $E[\Pi(\theta,k)]$.

At stage 2, informed investors (mass 1) each observe private signal $x_i \sim \mathcal{N}(\theta, \beta^{-1})$; noise traders place a random demand $\alpha\Phi(u)$ with $u \sim \mathcal{N}(0, \delta^{-1})$ independent of $\theta$. In the unique noisy rational expectations equilibrium, the sufficient statistic for the price signal is $z \equiv \theta + (1/\sqrt{\beta}) \cdot u$, and the Lemma (p. 2327) gives the market-clearing price (eq. 1):

P(z, k) = E\!\left[\Pi(\theta, k) \mid x = z, z\right] \tag{1}

The price equals the expected dividend of the marginal informed trader, who observes both private signal $x = z$ and the public signal embedded in the price (also $z$). This double-conditioning places excess weight on $z$ relative to its true precision as a public signal, generating a systematic bias: the market-implied prior is $\mathcal{N}(0, \hat{\lambda}^{-1})$ with $\hat{\lambda}^{-1} > \lambda^{-1}$, so prices overweight tail realizations of $\theta$. Denote $\hat{E}[\cdot]$ as the expectation under this market-implied prior.

At stage 1, incumbent shareholders maximize (eq. 2, p. 2329):

\max_{k \geq 0} \; E\!\left[\alpha P(z;k) + (1-\alpha)\Pi(\theta,k)\right] \tag{2}

$= \max_{k \geq 0}\left\{ E[\Pi(\theta,k)] + \alpha E\!\left[P(z;k) - \Pi(\theta,k)\right] \right\}$

The term $\alpha E[P(z;k) - \Pi(\theta,k)]$ is the rent accruing to incumbent shareholders from the price bias. In equilibrium, the distorted investment $\hat{K}$ satisfies (eq. 3, p. 2330):

C'(\hat{K}) = E[R(\theta)] + \alpha\!\left(\hat{E}[R(\theta)] - E[R(\theta)]\right) \tag{3}

Defining the return wedge $\Delta \equiv \hat{E}[R(\theta)]/E[R(\theta)] - 1$, the investment ratio is (p. 2332):

$\frac{\hat{K}}{K^*} = (1 + \alpha\Delta)^{1/\chi}$

When $R(\cdot)$ has upside risk (gains exceed losses at fixed distances from the mean), $\hat{E}[R(\theta)] > E[R(\theta)]$ so $\Delta > 0$ and $\hat{K} > K^*$ (overinvestment). When $R(\cdot)$ has downside risk, $\Delta < 0$ and $\hat{K} < K^*$ (underinvestment). For upside risk with high scalability, expected dividends can turn negative when $\alpha\Delta\chi^{-1} > 1$ (eq. 4, p. 2333) as the firm pursues negative-NPV overinvestment to capture rent.

The Grossman and Stiglitz (1980) noisy REE framework underpins the price characterization: prices aggregate private information but the market-clearing condition introduces a systematic bias that shareholders exploit through their investment decision.

General equilibrium (§II, pp. 2337-2345). A unit measure of firms indexed $i$, each with idiosyncratic fundamental $\theta_i \sim \mathcal{N}(0, \lambda^{-1})$. Incumbent shareholders sell an endogenous (and symmetric) fraction $s$ of shares. Final shareholders invest through mutual funds (acting as noise traders) and hedge funds (acquiring noisy private information about each firm). Let aggregate market value $T = \int P_i \, di$ and aggregate dividends $V = \int \Pi_i \, di$. With log preferences $v_I(C^I_2) + u_I(C^I_3) = \alpha\ln C^I_2 + (1-\alpha)\ln C^I_3$ for incumbent shareholders (ensuring $s = \alpha$ is exogenous), the aggregate intertemporal MRS satisfies (eq. 6, p. 2337):

\frac{T}{V} = Q^{-1} = \frac{u'_I((1-s)V)}{v'_I(sT)} = u'_F(sV) \tag{6}

The GE equity price for firm $i$ is (eq. 7, p. 2339):

P_i(z_i, k_i) = \frac{1}{\hat{Q}} \, E\!\left[\Pi(\theta_i, k_i) \mid x = z_i, z_i\right] \tag{7}

where $\hat{Q}$ is the threshold return on equity required by hedge funds in equilibrium. Aggregating across firms and combining with $E[P_i] = T = VQ^{-1}$, the equilibrium $\hat{Q}$ satisfies (eq. 8, p. 2340):

\hat{Q} = Q \cdot \frac{\hat{E}[\Pi(\theta,K)]}{E[\Pi(\theta,K)]} \tag{8}

The ratio $Q/\hat{Q}$ is the GE wedge that adjusts the PE rent-seeking incentive. Each firm’s incumbents maximize (eq. 10, p. 2340):

\max_{k_i \geq 0} \left\{ \alpha \frac{Q}{\hat{Q}} \hat{E}[\Pi(\theta_i, k_i)] + (1-\alpha) E[\Pi(\theta_i, k_i)] \right\} \tag{10}

The GE investment ratio and the intertemporal wedge jointly satisfy (eqs. 11 and 13, pp. 2340-2341):

\frac{K_{GE}}{K^*} = \left(1 + \alpha\Delta \cdot \frac{Q/\hat{Q}}{1-\alpha+\alpha Q/\hat{Q}}\right)^{1/\chi} \tag{11}

\frac{Q}{\hat{Q}} = \frac{\chi + 1 - (K_{GE}/K^*)^\chi}{(1+\chi)(1+\Delta) - (K_{GE}/K^*)^\chi} \tag{13}

With upside risk ($\Delta > 0$), overinvestment by all firms lowers aggregate dividends $V$ and thus $Q$, making $Q < \hat{Q}$ (i.e. $Q/\hat{Q} < 1$): the GE wedge attenuates the PE overinvestment, so $K_{PE} > K_{GE} > K^*$. With downside risk ($\Delta < 0$), underinvestment raises $Q > \hat{Q}$: the GE wedge amplifies underinvestment, so $K_{GE} < K_{PE} < K^*$. This externality arises because individual shareholders do not internalize that their collective rent-seeking reduces aggregate dividends $V$, thereby lowering $Q$ and ultimately feeding back to distort the intertemporal incentive of all firms.

Method

The model is solved analytically throughout. The solution strategy builds on noisy-rational-expectations for the price characterization and dynamic-general-equilibrium for the fixed-point analysis.

Price characterization. The noisy REE price (eq. 1) is derived using the Gaussian signal structure: the market-clearing condition with informed and noise traders yields the sufficient statistic $z = \theta + (1/\sqrt{\beta})\cdot u$ (Lemma, p. 2327). Compounding normal distributions implies $E[P(z;k)] = \hat{E}[\Pi(\theta,k)]$ under a market-implied prior with inflated variance $\hat{\lambda}^{-1}$ (p. 2330). This representation holds for general (nonlinear) payoff functions $R(\cdot)$, as shown in the companion paper Albagli, Hellwig and Tsyvinski (forthcoming), making the results robust to the specific return functional form.

Partial equilibrium investment. The FOC for investment (eq. 3) follows from differentiating eq. 2 and noting $E[\partial P(z;k)/\partial k] = \hat{E}[R(\theta)]$. The power cost structure $C(k) = k^{1+\chi}/(1+\chi)$ yields the closed-form investment ratio $\hat{K}/K^* = (1+\alpha\Delta)^{1/\chi}$. Comparative statics follow from first-order approximations around the efficient level $K^*$; the dividend-loss formula $V(\hat{K})/V(K^*) = (1+\alpha\Delta)^{1/\chi}(1-\alpha\Delta\chi^{-1})$ is derived by a second-order expansion of $\ln(V(\hat{K})/V(K^*))$ around zero (pp. 2332-2333).

General equilibrium fixed point. Proposition 2 (existence and uniqueness) is proved by showing that equations (11) and (13) have a unique solution $(K_{GE}/K^*, Q/\hat{Q})$ via continuity arguments and monotone comparative statics (Appendix, pp. 2351-2353). The limiting results in Proposition 3 follow by taking $\chi \to 0$ and establishing boundary behavior of the ratio using L’Hopital-type arguments.

Corrective taxes. In partial equilibrium, the tax $\tau$ on payoff $R(\theta)k$ shifts the effective return so that the FOC yields $K^*$ (eq. 5, p. 2336):

\tau = 1 - \frac{1}{1+\alpha\Delta} \tag{5}

In general equilibrium, accounting for the intertemporal wedge $\hat{Q}/Q = 1 + (1+\chi^{-1})\Delta$ at the efficient level, the GE corrective tax is (eq. 14, p. 2345):

\tau = 1 - \frac{1 - \alpha + \alpha Q/\hat{Q}}{1 - \alpha + \alpha (Q/\hat{Q})(1+\Delta)} \tag{14}

This adjusts the PE formula by a Pigouvian correction for the aggregate externality through share prices.

Empirical specifications

Section III (pp. 2345-2350) studies the model’s empirical implications. The paper does not conduct original regressions; it shows that the PE model nests the predictions of two empirical literatures and discusses qualitative consistency with existing estimates.

Information feedback extension (§III.B, pp. 2346-2349). The PE model is extended to allow price-contingent investment $K(z)$: shareholders commit to an investment rule that the market anticipates. With $\alpha = 1$ (full share turnover), shareholders choose $\hat{K}(z)$ to satisfy $C'(\hat{K}(z)) = E[R(\theta)\mid x=z,z]$, so the equilibrium investment function is (p. 2348):

$\hat{K}(z) = \left[(1 + 1/\chi)\,P(z)\right]^{1/(1+\chi)}$

Expected equity returns decrease in investment and price:

$\frac{V(z)}{P(z)} - 1 = \frac{1+\chi}{\chi}\left(\frac{E[R(\theta)\mid z]}{E[R(\theta)\mid x=z,z]} - 1\right)$

Proposition 4 (pp. 2348-2349) establishes three predictions: (i) investment is increasing in share prices: $\text{cov}(\hat{K}(z), P(z)) > 0$; (ii) excess sensitivity relative to fundamentals: $\hat{K}(z)/K^*(z)$ is strictly increasing in $z$; (iii) higher investment leads to lower future equity returns: $\text{cov}(\hat{K}(z), (V(z)-P(z))/P(z)) < 0$.

Consistency with existing evidence (§III.A and §III.C, pp. 2346-2350). The model is consistent with three lines of external evidence:

• Diether, Malloy, and Scherbina (2002) find that stocks in the highest earnings-forecast-dispersion quintile earn about 0.62% per month (roughly 7% annualized) lower returns, consistent with overvaluation from upside-risk overinvestment.
• Polk and Sapienza (2009) estimate a positive relation between share overvaluation (proxied by discretionary accruals) and investment after controlling for Tobin’s Q, with stronger effects for firms with higher share turnover (the paper’s $\alpha$) and lower future returns for overinvesting firms: consistent with Proposition 4(i) and 4(iii).
• David, Hopenhayn and Venkateswaran (2016) calibrate a GE model with the same informational friction (but without the rent-seeking motive) and find it responsible for 20-50% of observed dispersion in the marginal revenue product of capital.

Datasets used

Dataset	Role in paper	Wiki page
Numerical simulations (Figures 1-5)	Synthetic data generated from model parameters to illustrate comparative statics on investment distortions and efficiency losses; no external dataset is used	No external data

Sample: none. The paper is theoretical; Figures 1-5 use calibrated parameter values (e.g., $\alpha = 0.5$, $\beta = 1$, $\lambda = 1$) without fitting to real data.

When to read the full paper

Read the original if you are: building on the model (the Appendix at pp. 2351-2353 contains full proofs of Propositions 1-3 and the GE existence-uniqueness argument); studying the optimal tax design in general equilibrium and its Pigouvian correction; extending the information-feedback model to dynamic or multi-period settings; or seeking the working paper version’s analysis of financial transaction taxes and additional policy instruments not covered in the published article.

Attribution and rights

Source: peer-reviewed, American Economic Review 113(9), September 2023. This distillation was extracted by an LLM on 2026-06-24 and is not human-verified or independently reproduced. The published article is paywalled; an author manuscript is available at hal.science/hal-04210328v1. Replication data are deposited at doi.org/10.3886/E185081V1.

Albagli, Elias, Christian Hellwig, and Aleh Tsyvinski. “Imperfect Financial Markets and Investment Inefficiencies.” American Economic Review 113, no. 9 (September 2023): 2323-2354. DOI: 10.1257/aer.20170725. Extract only; not licensed for reproduction.