Idiosyncratic Shocks and the Role of Nonconvexities in Plant and Aggregate Investment Dynamics

We examine a model of lumpy investment wherein establishments face persistent shocks to common and plant-specific productivity, and nonconvex adjustment costs lead them to pursue generalized (S,s) investment rules. We allow persistent heterogeneity in both capital and total factor productivity alongside low-level investments exempt from adjustment costs to develop the first model consistent with available evidence on establishment-level investment rates. Reassessing the implications of lumpy investment for aggregate dynamics in this setting, we find that they remain substantial when factor supply considerations are ignored, but are quantitatively irrelevant in general equilibrium. The substantial implications of general equilibrium extend beyond the dynamics of aggregate series. While the presence of idiosyncratic shocks makes the time-averaged distribution of plant-level investment rates largely invariant to market-clearing movements in real wages and interest rates, we show that the dynamics of plants' investments differ sharply in their presence. Thus, model-based estimations of capital adjustment costs involving panel data may be quite sensitive to the assumption about equilibrium. Our analysis also offers new insights about how nonconvex adjustment costs influence investment at the plant. When establishments face large and weakly persistent idiosyncratic productivity shocks consistent with existing estimates, we find that nonconvex costs do not cause lumpy investments, but act to eliminate them(S,s) policies, lumpy investment, quantitative general equilibrium

Idiosyncratic shocks and the role of nonconvexities in plant and aggregate investment dynamics

The authors study a model of lumpy investment wherein establishments face persistent shocks to common and plant-specific productivity, and nonconvex adjustment costs lead them to pursue generalized (S,s) investment rules. They allow persistent heterogeneity in both capital and total factor productivity alongside low-level investments exempt from adjustment costs to develop the first model consistent with the cross-sectional distribution of establishment investment rates. Examining the implications of lumpy investment for aggregate dynamics in this setting, the authors find that they remain substantial when factor supply considerations are ignored, but are quantitatively irrelevant in general equilibrium. ; The substantial implications of general equilibrium extend beyond the dynamics of aggregate series. While the presence of idiosyncratic shocks makes the time-averaged distribution of plant-level investment rates largely invariant to market-clearing movements in real wages and interest rates, the authors show that the dynamics of plants' investments differ sharply in their presence. Thus, model-based estimations of capital adjustment costs involving panel data may be quite sensitive to the assumption about equilibrium. Their analysis also offers new insights about how nonconvex adjustment costs influence investment at the plant. When establishments face idiosyncratic productivity shocks consistent with existing estimates, they find that nonconvex costs do not cause lumpy investments, but act to eliminate them.Investments

Idiosyncratic shocks and the role of nonconvexities in plant and aggregate investment dynamics.

We solve equilibrium models of lumpy investment wherein establishments face persistent shocks to common and plant-specific productivity. Nonconvex adjustment costs lead plants to pursue generalized (S,s) decision rules with respect to capital; as a result, their individual investments are lumpy. In partial equilibrium, this yields substantial skewness and kurtosis in aggregate investment, though with differences in plant-level productivity, these nonlinearities are far less pronounced. Moreover, nonconvex costs, like quadratic adjustment costs, greatly increase the persistence of aggregate investment rates, yielding a better match with the data. ; In general equilibrium, aggregate nonlinearities disappear, and investment rates are very persistent, regardless of capital adjustment costs. While the aggregate implications of lumpy investment change substantially in equilibrium, the inclusion of fixed costs or idiosyncratic shocks yields an average distribution of plant investment rates that, in contrast, is largely unaffected by market-clearing movements in real wages and interest rates. Nonetheless, we find that to understand the dynamics of plant-level investment requires general equilibrium analysis.Investments ; Productivity

Idiosyncratic shocks and the role of nonconvexities in plant and aggregate investment dynamics

We solve equilibrium models of lumpy investment wherein establishments face persistent shocks to common and plant-specific productivity. Nonconvex adjustment costs lead plants to pursue generalized (S, s) rules with respect to capital; thus, their investments are lumpy. In partial equilibrium, this yields substantial skewness and kurtosis in aggregate investment, though, with differences in plant-level productivity, these nonlinearities are far less pronounced. Moreover, nonconvex costs, like quadratic adjustment costs, increase the persistence of aggregate investment, yielding a better match with the data. In general equilibrium, aggregate nonlinearities disappear, and investment rates are very persistent, regardless of adjustment costs. While the aggregate implications of lumpy investment change substantially in equilibrium, the inclusion of fixed costs or idiosyncratic shocks makes the average distribution of plant investment rates largely invariant to market-clearing movements in real wages and interest rates. Nonetheless, we find that understanding the dynamics of plant-level investment requires general equilibrium analysis.Capital investments ; Business enterprises ; Investments

Quantization as Histogram Segmentation: Optimal Scalar Quantizer Design in Network Systems

An algorithm for scalar quantizer design on discrete-alphabet sources is proposed. The proposed algorithm can be used to design fixed-rate and entropy-constrained conventional scalar quantizers, multiresolution scalar quantizers, multiple description scalar quantizers, and Wyner–Ziv scalar quantizers. The algorithm guarantees globally optimal solutions for conventional fixed-rate scalar quantizers and entropy-constrained scalar quantizers. For the other coding scenarios, the algorithm yields the best code among all codes that meet a given convexity constraint. In all cases, the algorithm run-time is polynomial in the size of the source alphabet. The algorithm derivation arises from a demonstration of the connection between scalar quantization, histogram segmentation, and the shortest path problem in a certain directed acyclic graph

Cognitive Beamforming for Multiple Secondary Data Streams With Individual SNR Constraints

In this paper, we consider cognitive beamforming for multiple secondary data streams subject to individual signal-to-noise ratio (SNR) requirements for each secondary data stream. In such a cognitive radio system, the secondary user is permitted to use the spectrum allocated to the primary user as long as the caused interference at the primary receiver is tolerable. With both secondary SNR constraint and primary interference power constraint, we aim to minimize the secondary transmit power consumption. By exploiting the individual SNR requirements, we formulate this cognitive beamforming problem as an optimization problem on the Stiefel manifold. Both zero forcing beamforming (ZFB) and nonzero forcing beamforming (NFB) are considered. For the ZFB case, we derive a closed form beamforming solution. For the NFB case, we prove that the strong duality holds for the nonconvex primal problem and thus the optimal solution can be easily obtained by solving the dual problem. Finally, numerical results are presented to illustrate the performance of the proposed cognitive beamforming solutions.Comment: This is the longer version of a paper to appear in the IEEE Transactions on Signal Processin