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New Monetarist Economics  

Chao Gu, Han Han, and Randall Wright

This article provides an introduction to New Monetarist Economics. This branch of macro and monetary theory emphasizes imperfect commitment, information problems, and sometimes spatial (endogenously) separation as key frictions in the economy to derive endogenously institutions like monetary exchange or financial intermediation. We present three generations of models in development of New Monetarism. The first model studies an environment in which agents meet bilaterally and lack commitment, which allows money to be valued endogenously as means of payment. In this setup both goods and money are indivisible to keep things tractable. Second-generation models relax the assumption of indivisible goods and use bargaining theory (or related mechanisms) to endogenize prices. Variations of these models are applied to financial asset markets and intermediation. Assets and goods are both divisible in third-generation models, which makes them better suited to policy analysis and empirical work. This framework can also be used to help understand financial markets and liquidity.


Q-Factors and Investment CAPM  

Lu Zhang

The Hou–Xue–Zhang q-factor model says that the expected return of an asset in excess of the risk-free rate is described by its sensitivities to the market factor, a size factor, an investment factor, and a return on equity (ROE) factor. Empirically, the q-factor model shows strong explanatory power and largely summarizes the cross-section of average stock returns. Most important, it fully subsumes the Fama–French 6-factor model in head-to-head spanning tests. The q-factor model is an empirical implementation of the investment-based capital asset pricing model (the Investment CAPM). The basic philosophy is to price risky assets from the perspective of their suppliers (firms), as opposed to their buyers (investors). Mathematically, the investment CAPM is a restatement of the net present value (NPV) rule in corporate finance. Intuitively, high investment relative to low expected profitability must imply low costs of capital, and low investment relative to high expected profitability must imply high costs of capital. In a multiperiod framework, if investment is high next period, the present value of cash flows from next period onward must be high. Consisting mostly of this next period present value, the benefits to investment this period must also be high. As such, high investment next period relative to current investment (high expected investment growth) must imply high costs of capital (to keep current investment low). As a disruptive innovation, the investment CAPM has broad-ranging implications for academic finance and asset management practice. First, the consumption CAPM, of which the classic Sharpe–Lintner CAPM is a special case, is conceptually incomplete. The crux is that it blindly focuses on the demand of risky assets, while abstracting from the supply altogether. Alas, anomalies are primarily relations between firm characteristics and expected returns. By focusing on the supply, the investment CAPM is the missing piece of equilibrium asset pricing. Second, the investment CAPM retains efficient markets, with cross-sectionally varying expected returns, depending on firms’ investment, profitability, and expected growth. As such, capital markets follow standard economic principles, in sharp contrast to the teachings of behavioral finance. Finally, the investment CAPM validates Graham and Dodd’s security analysis on equilibrium grounds, within efficient markets.


Reduced Rank Regression Models in Economics and Finance  

Gianluca Cubadda and Alain Hecq

Reduced rank regression (RRR) has been extensively employed for modelling economic and financial time series. The main goals of RRR are to specify and estimate models that are capable of reproducing the presence of common dynamics among variables such as the serial correlation common feature and the multivariate autoregressive index models. Although cointegration analysis is likely the most prominent example of the use of RRR in econometrics, a large body of research is aimed at detecting and modelling co-movements in time series that are stationary or that have been stationarized after proper transformations. The motivations for the use of RRR in time series econometrics include dimension reductions, which simplify complex dynamics and thus make interpretations easier, as well as the pursuit of efficiency gains in both estimation and prediction. Via the final equation representation, RRR also makes the nexus between multivariate time series and parsimonious marginal ARIMA (autoregressive integrated moving average) models. RRR’s drawback, which is common to all of the dimension reduction techniques, is that the underlying restrictions may or may not be present in the data.


Sparse Grids for Dynamic Economic Models  

Johannes Brumm, Christopher Krause, Andreas Schaab, and Simon Scheidegger

Solving dynamic economic models that capture salient real-world heterogeneity and nonlinearity requires the approximation of high-dimensional functions. As their dimensionality increases, compute time and storage requirements grow exponentially. Sparse grids alleviate this curse of dimensionality by substantially reducing the number of interpolation nodes, that is, grid points needed to achieve a desired level of accuracy. The construction principle of sparse grids is to extend univariate interpolation formulae to the multivariate case by choosing linear combinations of tensor products in a way that reduces the number of grid points by orders of magnitude relative to a full tensor-product grid and doing so without substantially increasing interpolation errors. The most popular versions of sparse grids used in economics are (dimension-adaptive) Smolyak sparse grids that use global polynomial basis functions, and (spatially adaptive) sparse grids with local basis functions. The former can economize on the number of interpolation nodes for sufficiently smooth functions, while the latter can also handle non-smooth functions with locally distinct behavior such as kinks. In economics, sparse grids are particularly useful for interpolating the policy and value functions of dynamic models with state spaces between two and several dozen dimensions, depending on the application. In discrete-time models, sparse grid interpolation can be embedded in standard time iteration or value function iteration algorithms. In continuous-time models, sparse grids can be embedded in finite-difference methods for solving partial differential equations like Hamilton-Jacobi-Bellman equations. In both cases, local adaptivity, as well as spatial adaptivity, can add a second layer of sparsity to the fundamental sparse-grid construction. Beyond these salient use-cases in economics, sparse grids can also accelerate other computational tasks that arise in high-dimensional settings, including regression, classification, density estimation, quadrature, and uncertainty quantification.