Sparse Vector Autoregressive Modeling

The vector autoregressive (VAR) model has been widely used for modeling temporal dependence in a multivariate time series. For large (and even moderate) dimensions, the number of AR coefficients can be prohibitively large, resulting in noisy estimates, unstable predictions and difficult-to-interpret temporal dependence. To overcome such drawbacks, we propose a 2-stage approach for fitting sparse VAR (sVAR) models in which many of the AR coefficients are zero. The first stage selects non-zero AR coefficients based on an estimate of the partial spectral coherence (PSC) together with the use of BIC. The PSC is useful for quantifying the conditional relationship between marginal series in a multivariate process. A refinement second stage is then applied to further reduce the number of parameters. The performance of this 2-stage approach is illustrated with simulation results. The 2-stage approach is also applied to two real data examples: the first is the Google Flu Trends data and the second is a time series of concentration levels of air pollutants.Comment: 39 pages, 7 figure

Land-price dynamics and macroeconomic fluctuations

We argue that positive comovements between land prices and business investment are a driving force behind the broad impact of land-price dynamics on the macroeconomy. We develop an economic mechanism that captures the comovements by incorporating two key features into a DSGE model: we introduce land as a collateral asset in firms' credit constraints, and we identify a shock that drives most of the observed fluctuations in land prices. Our estimates imply that these two features combine to generate an empirically important mechanism that amplifies and propagates macroeconomic fluctuations through the joint dynamics of land prices and business investment.

Land-price dynamics and macroeconomic fluctuations

We argue that positive co-movements between land prices and business investment are a driving force behind the broad impact of land-price dynamics on the macroeconomy. We develop an economic mechanism that captures the co-movements by incorporating two key features into a DSGE model: We introduce land as a collateral asset in firms’ credit constraints and we identify a shock that drives most of the observed fluctuations in land prices. Our estimates imply that these two features combine to generate an empirically important mechanism that amplifies and propagates macroeconomic fluctuations through the joint dynamics of land prices and business investment.Real property

Do credit constraints amplify macroeconomic fluctuations?

Previous studies on financial frictions have been unable to establish the empirical significance of credit constraints in macroeconomic fluctuations. This paper argues that the muted impact of credit constraints stems from the absence of a mechanism to explain the observed persistent comovements between housing prices and business investment. We develop such a mechanism by incorporating two key features into a dynamic stochastic general equilibrium model: We identify shocks that shift the demand for collateral assets and allow productive agents to be credit-constrained. A combination of these two features enables our model to successfully generate an empirically important mechanism that amplifies and propagates macroeconomic fluctuations through credit constraints.

The Space of Closed G2G_2-Structures. I. Connections

In this article, we develop foundational theory for geometries of the space of closed $G_2$-structures in a given cohomology class as an infinite-dimensional manifold. We introduce Sobolev-type metrics, construct their Levi-Civita connections, formulate geodesic equations, and analyse the variational structures of torsion free $G_2$-structures under these Sobolev-type metrics.Comment: 51 page