Competitive manufacturing with fluctuating demand and diverse technology: Mathematical proofs and illuminations on industry output-flexibility

I present an original model of competitive manufacturing with fluctuating demand and diverse technology with mathematical proofs. I discuss Aranoff's output-flexibility indicator, E(AC)-LRMC. I use the model to compute Aranoff's output-flexibility indicator to measure industry output-flexibility. I argue that a measure of industry output-flexibility is β_L(Q₂ − Q₁)/E(Q) I tie the demand-side discussion with the cost-side and show the degree of industry output-flexibility that will emerge under welfare and profit-maximizing pricing rules. I perform comparative statics of changes in technology, of demand, and of frequency of the high-peak state.     

Non-convexities in the adjustment of different capital inputs: A firm-level investigation

Recent developments in investment research have highlighted the importance of non-convexities and irreversibilities in firms’ adjustment of quasi-fixed inputs. Aggregation across capital goods may smooth out the discontinuities associated with the adjustment of individual assets. Lack of suitable data is one of the reasons why empirical work has typically relied on the assumption of capital homogeneity. In this paper we exploit a data set of 1539 Italian firms which allows us to disaggregate capital into equipment and structures, and purchases and sales of assets. We construct measures of fundamental Q to capture investment opportunities associated with each asset. We uncover the pattern of dynamic adjustment by using non-parametric techniques to relate each individual investment to its own fundamental Q.     

Investment options and the business cycle

This paper extends [R. Mehra, E.C. Prescott, Recursive competitive equilibrium: The case of homogeneous households, Econometrica 48 (1980) 1365-1380] to a production economy with two capital goods. It is an RBC model in which each unit of investment requires a new idea, an ‘option.’ When options are scarce, new capital is harder to put in place and the value of old capital rises. Thus the stock market and Tobin's Q are negative indexes of intangibles. During a boom, Q rises gradually, as options are used up. Because investment represents an exercise of options, it has an intertemporal substitution tradeoff that is absent from the adjustment-cost model. Equilibrium may be efficient even without markets for knowledge; the stock market may suffice.     

The (Q,S,s) pricing rule: a quantitative analysis

Are nominal prices sticky because menu costs prevent sellers from continuously adjusting their prices to keep up with inflation or because search frictions make sellers indifferent to any real price over some non-degenerate interval? The paper answers the question by developing and calibrating a model in which both search frictions and menu costs may generate price stickiness and sellers are subject to idiosyncratic shocks. The equilibrium of the calibrated model is such that sellers follow a (Q,S,s) pricing rule: each seller lets inflation erode the effective real value of the nominal prices until it reaches some point s and then pays the menu cost and sets a new nominal price with an effective real value drawn from a distribution with support [S, Q], with s < S < Q. Idiosyncratic shocks short-circuit the repricing cycle and may lead to negative price changes. The calibrated model reproduces closely the properties of the empirical price and price-change distributions. The calibrated model implies that search frictions are the main source of nominal price stickiness.     

A note on the global stability in dynamical economic systems

A simple set of sufficient conditions is given for utility functions to satisfy the Q-matrix condition of Brock and Scheinkman. Utility functions must be sufficiently concave but not excessively concave compared with the discount rate.     

The equity price channel in a New-Keynesian DSGE model with financial frictions and banking

This paper studies the role of the equity price channel in business cycle fluctuations, and highlights the equity price channel as a different aspect to general equilibrium models with financial frictions and, as a result, emphasizes the systemic influence of financial markets on the real economy. We develop a canonical dynamic general equilibrium model with a tractable role for the equity market in banking, entrepreneur and household economic activities. The model is estimated with Bayesian techniques using U.S. data over the sample period 1982Q01–2015Q01. We show that a dynamic general equilibrium model with an equity price channel well mimics the U.S. business cycle. The model reproduces the strong procyclicality of the equity price. The equity price channel significantly exacerbates business cycle fluctuations through both financial accelerator and bank capital channels. Our results support the increasing emphasis on common equity capital in Basel III regulations. This is beneficial in terms of financial stability, but amplifies and propagates shocks to the real economy.     

A behavioral characterization of plausible priors

Recent decision theories represent ambiguity via multiple priors, interpreted as alternative probabilistic models of the relevant uncertainty. This paper provides a robust behavioral foundation for this interpretation. A prior P is “plausible” if preferences over some subset of acts admit an expected utility representation with prior P, but not with any other prior Q≠P. Under suitable axioms, plausible priors can be elicited from preferences, and fully characterize them; also, probabilistic sophistication implies that there exists only one plausible prior; finally, “plausible posteriors” can be derived via Bayesian updating. Several familiar decision models are consistent with the proposed axioms.     

The quality effect: Does financial liberalization improve the allocation of capital?

We document evidence of a “quality effect” of financial liberalization on allocative efficiency, as measured by dispersion in Tobin's Q across firms. We predict that financial liberalization, by equalizing access to credit, is associated with reduced variation in expected marginal returns. We test this prediction using a new financial liberalization index and firm-level data for five emerging markets: India, Jordan, Korea, Malaysia, and Thailand. We find robust evidence that financial liberalization, rather than financial deepening, is associated with improved allocative efficiency.     

Corporate finance side of the Q theory of investment

This paper presents a model of a firm under uncertainty in which the financial and investment decisions are simultaneously determined. If profits are small relative to investment, the firm finances a constant fraction of incremental investment by debt and the rest by retentions. If profits are large relative to investment, a constant fraction of marginal finance comes from debt and the rest from new shares. In these two financing regimes a one-to-one relationship between optimal investment and Q can be derived. No such relation exists in the third and intermediate regime in which incremental investment is entirely debt-financed.     

Financial frictions and investment: requiem in Q

Understanding the nature of financial frictions faced by firms is relevant for both monetary and fiscal policy experiments. Empirical investment studies commonly find that proxies for firms' internal funds are significant as explanatory variables, particularly in the Q-theory based regression framework. These findings are often interpreted as evidence of financial frictions. This paper investigates that inference by specifying and estimating a class of dynamic optimization models where imperfectly competitive firms face financial constraints. Market power induces the principal link between investment and internal funds. We find no evidence to support the argument that capital market imperfections contribute to the relationship between investment and profitability.     

Hayashi meets Kiyotaki and Moore: A theory of capital adjustment costs

Firm-level investment is lumpy and volatile but aggregate investment is much smoother and highly serially correlated. These different patterns of investment behavior have been viewed as indicating convex adjustment costs at the aggregate level but non-convex adjustment costs at the firm level. This paper shows that financial frictions in the form of collateralized borrowing at the firm level (Kiyotaki and Moore, 1997) can give rise to convex adjustment costs at the aggregate level yet at the same time generate lumpiness in plant-level investment. In particular, our model can (i) derive aggregate capital adjustment cost functions identical to those assumed by Hayashi (1982) and (ii) explain the weak empirical relationship between Tobin?s Q and plant-level investment.     

Influence and inefficiency in the internal capital market

I model inefficient resource allocations in M-form organizations due to influence activities by division managers that skew capital budgets in their favor. Corporate headquarters receives two types of signals about investment opportunities: private signals that can be distorted by managers, and public signals that are undistorted but noisy. Headquarters faces a tradeoff between the cost of attaining an accurate private signal and the value of the information the signal provides. In contrast to existing models of “socialism” in internal capital markets, I show that investment sensitivity to Tobin's Q is higher than first-best in firms where division managers hold equity (a result consistent with evidence presented in Scharfstein, 1998). When managers face high private costs from distorting information (equity holdings), headquarters may commit to investment contracts that place “too little” weight on private signals and “too much” weight on public signals (i.e. Q). This result has implications for managers in the design of capital budgeting processes and incentive compensation systems.     

Zero-sum condition: A necessary and sufficient condition for a transitive voting system

A simple and quick way to ascertain whether or not any given majority voting system can always produce a transitive social preference orderings without imposing any restriction on the distribution of diverse individual preference orderings is to examine whether all individual voting (preference) vectors satisfy the Addition Rule or not. This conclusion was obtained by first reformulating the voting mechanism into that of a linear mapping from T^m defined by q = Σp_i. It was found that the subset P of T that can accommodate all possible individual preference ordering profiles and such that every sum vector q = Σ p_i of its member vectors p_i is contained in T can be expressed as P = {p: p∈ T, s(p) = 0}. It was also pointed out that this is equivalent to the requirement that all individual preference (voting) functions must satisfy the Addition Rule. Finally, Borda's Rule and Saposnik's Contributive Rule were shown to be examples of transitive voting rules which satisfy these necessary and sufficient conditions.     

Transitive measurable utility

This paper continues a study of theories of preferences under risk that do not use the independence axiom of the von Neumann-Morgenstern theory. Unlike its predecessor, it assumes that preferences are transitive. The effects of transitivity are noted in two representations of preferences. The first, which also uses continuity and dominance axioms, involves a function u on a set P of probability measures for which u(p) > u(q) if and only if p is preferred to q. Although u might be nonlinear, it has other features of a von Neumann-Morgenstern linear utility function. The second representation has linear functions u and w on P, with w strictly positive except perhaps at preference-extreme measures—where it might vanish, such that u(p) w(q) > u(q) w(p) if and only if p is preferred to q. A symmetry axiom along with the axioms for the first representation are necessary and sufficient for the second representation.     

On the investment implications of bankruptcy laws

Axiomatic analysis of bankruptcy problems reveals three major principles: (i) proportionality (PRO), (ii) equal awards (EA), and (iii) equal losses (EL). However, most real life bankruptcy procedures implement only the proportionality principle. We construct a noncooperative investment game to explore whether the explanation lies in the alternative implications of these principles on investment behavior. Our results are as follows (i) EL always induces higher total investment than PRO which in turn induces higher total investment than EA; (ii) PRO always induces higher egalitarian social welfare than both EA and EL in interior equilibria; (iii) PRO induces higher utilitarian social welfare than EL in interior equilibria but its relation to EA depends on the parameter values (however, a numerical analysis shows that on a large part of the parameter space, PRO induces higher utilitarian social welfare than EA).     

How to gamble against all odds

We compare the power of betting strategies (aka martingales) whose wagers take values in different sets of reals. A martingale whose wagers take values in a set A is called an A-martingale. A set of reals B anticipates a set A, if for every A-martingale there is a countable set of B-martingales, such that on every binary sequence on which the A-martingale gains an infinite amount at least one of the B-martingales gains an infinite amount, too.We show that for two important classes of pairs of sets A and B, B anticipates A if and only if the closure of B contains rA, for some positive r. One class is when A is bounded and B is bounded away from zero; the other class is when B is well ordered. Our results generalize several recent results in algorithmic randomness and answer a question posed by Chalcraft et al. (2012).     

Inter-district rice water productivity differences in Bangladesh: An empirical exploration and implications

While the bulk of research on crop water productivity (WP) focuses on static cross-section analysis, this research provides a spatio-temporal perspective. It estimates rice crop WP for 21 Bangladesh districts for 37 years; explores WP variations among districts; and investigates causality involving WP, intensification and technological variables; and groundwater irrigation and depth. It breaks new grounds by probing these significant but unexplored issues.Technological diffusion was the key factor explaining inter-district WP differences. The impact of agricultural intensification on rabi (dry season) and kharif (wet season) crop WPs was positive and negative respectively. Dummy variables typifying policy transition negatively impacted on WPs for both kharif and overall crops. While rabi and kharif rice WPs grew with time, overall crop WP recorded the strongest growth. Rabi and overall WPs were lower in salinity- and drought-prone districts covering 33% of Bangladesh's net cropped area (NCA).In 90% of Bangladesh's NCA districts, technological diffusion caused WP. Causality existed between groundwater irrigation and depth in 60% NCA. Despite significant potential to increase WP, increasing dependence on groundwater appears unsustainable. Widespread diffusion of HYVs in the kharif season, and development of salinity and drought-tolerant rice varieties could go a long way in sustaining rice WP.     

An efficiency theorem for incompletely known preferences

There are n agents who have von Neumann-Morgenstern utility functions on a finite set of alternatives A. Each agent i's utility function is known to lie in the nonempty, convex, relatively open set Ui. Suppose L is a lottery on A that is undominated, meaning that there is no other lottery that is guaranteed to Pareto dominate L no matter what the true utility functions are. Then, there exist utility functions ui∈Ui for which L is Pareto efficient. This result includes the ordinal efficiency welfare theorem as a special case.     

A progress report on Kelly's majority conjectures

LetC(m, n) be the proportion of n-voter profiles on m alternatives that have a majority winner. Jerry Kelly conjectured that C(m, n) > C(m + 1, n) for m ? 3 and n = 3 and n ? 5, and C(m, n) > C(m, n + 2) for m ? 3 and n ? 3. We prove these for special cases.     

Majority committees

Suppose an m-member committee is to be selected by a set of voters from a set X of M > m nominees. If A is an m-member committee, and if as many voters prefer A to B as prefer B to A for every other committee B of m nominees, then A is a majority committee of size m. Although the existence of majority nominees (m = 1) has been extensively analyzed, little attention has been given to conditions that imply the existence of majority committees of size m ? 2. Known restrictions on voters' preferences on X that guarntee the existence of a majority nominee could be applied directly to voters' preferences on m-member committees. However, this definitional exercise lacks intuitive appeal, and a different approach is taken in this paper. The paper presumes that profiles of voters' preferences on X are either dichotomous or single peaked. Both cases ensure the existence of a majority nominee. Independence-monotonicity assumptions are then used to connect voters' preferences on X to their preferences on committees of equal size. Although these assumptions guarantee the existence of majority committees when m = 1 and when m = M ? 1, they do not generally do so when 1 < m < M ? 1. The latter observation motivates additional restrictions on profiles. In the dichotomous case, we consider profiles in which all voters have the same number k of nominees in their preferred subsets, and show that this restriction guarantees the existence of a majority committee of size m for 1 < m < M ? 1 only when k = 1 or k = M ? 1. In the single-peaked case, we consider profiles in which all voters have the same most-preferred (peak) nominee, and prove that this guarantees the existence of a majority committee of size m for every m between 1 and M ? 1.