I translate familiar concepts of discrete-time time-series to continuous-time equivalent. I cover lag operators, ARMA models, the relation between levels and differences, integration and cointegration, and the Hansen-Sargent prediction formulas

What are the shocks that drive economic fluctuations? I examine technology and money shocks in some detail, and briefly review the evidence on oil price and credit shocks. I conclude that none of these popular candidates accounts for the bulk of economic fluctuations. I then examine whether...

We measure monetary policy shocks as changes in the Fed funds target rate that surprise bond markets in daily data. These shock series avoid the omitted variable, time-varying parameter, and orthogonalization problem of monthly VARs, and do not impose the expectations hypothesis. We find...

Are individuals effectively insured against idiosyncratic shocks to income or wealth by either formal or informal mechanisms? This paper shows that under perfect insurance, marginal utility should grow at the same rate for all consumers, and that the distribution of measured consumption growth...

Financial innovation challenges the foundations of monetary theory, and standard monetary theory has not been very successful at describing the history of U.S. inflation. Motivated by these observations, I ask: Can we understand the history of U.S. inflation using a framework that ignores...

The fiscal theory says that the price level is determined by the ratio of nominal debt to the present value of real primary surpluses. I analyze long-term debt and optimal policy in the fiscal theory. I find that the maturity structure of the debt matters. For example, it determines whether news...

I show that a determinate, finite price level can be achieved in an economy with no monetary frictions, and no commodity standard or other explicit redemption commitment. I make one small modification to a standard cash in advance model: I reopen the security market at the end of the day. With...

This paper measures the expected return, mean, standard deviation, alpha, and beta of venture capital investments. The focus of the paper is correcting for the selection bias that is the central obstacle in evaluating such investments. Therefore, valuations are observed only when a firm goes...

I use the valuation equation of government debt to understand fiscal and monetary policy in and following the great recession of 2008-2009, to think about whether the US is headed for a fiscal inflation, and what that inflation will look like. I emphasize that a fiscal inflation can come well...