The market price of risk and the equity premium: A legacy of the Great Depression?

By positing learning and a pessimistic initial prior, we build a model that disconnects a representative consumer's subjective attitudes toward risk from the high price of risk that a rational-expectations econometrician would deduce from financial market data. We follow Friedman and Schwartz [1963. A Monetary History of the United States, 1857-1960. Princeton University Press, Princeton, NJ] in hypothesizing that the Great Depression heightened fears of economic instability. We use a robustness calculation to elicit a pessimistic prior for a representative consumer and let him update beliefs via Bayes’ law. Learning eventually erases pessimism, but while it persists, pessimism contributes a volatile multiplicative component to the stochastic discount factor that a rational-expectation econometrician would detect. With sufficient initial pessimism, the model generates substantial values for the market price of risk and equity premium and predicts high Sharpe ratios and forecastable excess stock returns.     

Adjustment costs,durables, and aggregate consumption

Previous tests of the permanent-income hypothesis (PIH) have focused on either non-durables or durables expenditures in isolation. This paper studies consumer purchases of non-durables and durables as the outcome of a single optimization problem. It is shown that, with non-separability in utility, the presence of adjustment costs of changing durables stocks may affect the time series properties of both components of expenditure. An econometric test of the PIH based on the model developed in the paper is both more efficient and less prone to bias than those in some previous studies; however, this test confirms earlier rejections of the PIH in aggregate quarterly data.     

Generalizing the permanent-income hypothesis: Revisiting Friedman's conjecture on consumption

Friedman's contribution to the consumption literature goes well beyond the seminal permanent-income hypothesis. He conjectured that the marginal propensity to consume out of financial wealth shall be larger than out of “human wealth”, the present discounted value of future labor income. I present an explicitly solved model to deliver this widely noted consumption property by specifying that the conditional variance of changes in income increases with its level. A larger realization of income not only implies a higher level of human wealth, but also signals a riskier stream of future labor income, inducing a higher precautionary saving, and thus giving rise to Friedman's conjecture. Appropriately adjusting human wealth for income risk, I show that Friedman's conjecture may be formulated as a “generalized” permanent income hypothesis. I further show that Friedman's conjecture captures the first-order effect of stochastic precautionary savings. Finally, I propose a natural decomposition of the optimal saving rule to formalize various motives for holding wealth as emphasized in [Friedman, M., 1957. A Theory of the Consumption Function. Princeton University Press, Princeton].     

Optimality of the Friedman Rule in an Overlapping Generations Model with Spatial Separation

Recent models with spatial separation and limited communication suggest that the Friedman rule may not be optimal. This is important in light of the disparity between theory and practice concerning optimal monetary policy. We take a close look at these models and show that intergenerational transfers are key to the suboptimality of the Friedman rule. The Friedman rule is a necessary condition for achieving the efficient allocation in equilibrium. We also show that the Friedman rule is chosen whenever agents can implement mutually beneficial arrangements.     

The Friedman rule and inflation targeting

We use concepts from the financial economics discipline – and in particular the methods of continuous time finance – to develop a monetarist model under which the rate of inflation evolves in terms of a first-order mean reversion process based on a ‘white noise’ error structure. The Fokker–Planck (i.e. the Chapman–Kolmogorov) equation is then invoked to retrieve the steady-state (i.e. unconditional) probability distribution for the rate of inflation. Monthly data for the UK Consumer Price Index (CPI) covering the period from 1988 until 2012 are then used to estimate the parameters of the probability distribution for the UK inflation rate. The parameter estimates are compatible with the hypothesis that the UK inflation rate evolves in terms of a slightly skewed and highly leptokurtic probability distribution that encompasses non-convergent higher moments. We then determine the Hamilton–Jacobi–Bellman fundamental equation of optimality corresponding to a monetary policy loss function defined in terms of the squared difference between the targeted rate of inflation and the actual inflation rate. Optimising and then solving the Hamilton–Jacobi–Bellman equation shows that the optimal control for the rate of increase in the money supply will be a linear function of the difference between the current rate of inflation and the targeted inflation rate. The conditions under which the optimal control will lead to the Friedman rule are then determined. These conditions are used in conjunction with the Fokker–Planck equation and the mean reversion process describing the evolution of the inflation rate to determine the probability distribution for the inflation rate under the Friedman rule. This shows that whilst the empirically determined probability distribution for the UK inflation rate meets some of the conditions required for the application of the Friedman rule, it does not meet them all.     

The Friedman Rule in a Model with Endogenous Growth and Cash‐in‐Advance Constraint

This paper introduces money into an overlapping‐generations model with endogenous growth. The main message of the paper is that as long as the modified golden rule is attained, the Friedman rule is optimal. The result holds regardless of the ability of the government to internalize the externality and control the level of human capital. Other results include: (i) violation of the Friedman rule for a different second‐best environment wherein human capital accumulation is controlled but not physical capital accumulation and (ii) existence of a negative relationship between money growth rate and the economy’s endogenous growth rate.     

The paradox of interest rates of the Greenback Era: A reexamination

The two leading explanations for the counterintuitive behavior of interest rates during the Greenback Era (1862-1878) - the resumption expectations model of Calomiris (1988) and the capital flow argument of Friedman and Schwartz (1963) - are inconsistent with each other in terms of their treatment of financial arbitrage. A methodology to identify unexploited arbitrage opportunities in financial data is proposed. Observable returns strongly suggest that the money market of the Greenback Era did not systematically admit arbitrage, except possibly around the times of the Gold Corner of 1869 and the Panic of 1873, which implies that Calomiris provides a more plausible explanation.     

Seigniorage,inflation, and reputation

This paper derives a reputational equilibrium for inflation in a model in which the sovereign obtains valuable seigniorage by issuing fiat money in exchange for real resources. With contemporaneous perception of actual sovereign behavior and immediate adjustment of real cash balances to new information, the Friedman elasticity solution for maximal seigniorage is a reputational equilibrium. More generally, the objective of maximal seigniorage produces an equilibrium inflation rate equal either to a generalization of the Friedman elasticity solution or to the rate at which the sovereign discounts future seigniorage adjusted for the growth rate, whichever is larger. The model formalizes the conjecture that inflation rates in excess of the Friedman solution are attributable to high discount rates for future seigniorage.     

Sticky information and sticky prices

In the U.S. and Europe, prices change at least once a year. Yet nominal macro shocks seem to have real effects lasting well beyond a year. “Sticky information” models, as posited by Mankiw and Reis [2002. Sticky information versus sticky prices: a proposal to replace the new Keynesian Phillips curve. Quarterly Journal of Economics 117, 1295–1328], Sims [2003. Implications of rational inattention. Journal of Monetary Economics 50(3), 665–690], and Woodford [2003. Princeton University Press: Princeton, NJ], can reconcile micro flexibility with macro rigidity. We simulate a sticky information model in which price setters update information on macro shocks less frequently than information on micro shocks. We then examine price changes in the micro data underlying the U.S. CPI. Empirical price changes react to old information, just as sticky information models predict.     

习惯形成下的最优货币政策

著名的弗里德曼规则指出,最优货币政策可以通过设置名义利率等于0来实现。本文构造了基于习惯形成的最优货币政策模型,并使用主方法求解了模型。本文的研究表明,当家庭的效用函数偏好具有习惯形成的特点时,弗里德曼规则仍然成立。     

The Friedman rule: Old and new

In overlapping generations models, money growth creates intergenerational wealth effects and leads to the breakdown of the Friedman rule; the rule can be restored via lump-sum tax and transfers that neutralize these wealth transfers. Additionally, and in contrast to money-in-the-utility-function models, the Friedman rule is not the unique first-best solution in cash-in-advance-constraint models of money: a continuum of combinations of money growth rates and consumption taxes implement the first-best allocation. This paper traces through the intellectual origins of the first (old) result, which was recently restated in Bhattacharya, et al. [2005. Monetary policy, fiscal policy, and the inflation tax: equivalence results. Macroeconomic Dynamics 7, 647-669.] and formally demonstrates the second (new) result.     

Bootstrap Tests for Multivariate Event Studies

Statistical tests for multivariate event studies—exact or asymptotic—are derived based on multivariate normality. As it has been previously documented that the performances of these tests are not satisfactory, because stock returns are far from normally distributed (especially for daily returns), this paper proposes the use of bootstrap methods, which are free from any specific distributional assumption, to provide better approximations to the sampling distributions of test statistics in multivariate event studies. The Monte Carlo experiments based on real daily returns data show that the bootstrap tests outperform the traditional tests by having close rejection rates to the nominal significance levels. The traditional tests, in contrast, tend to reject the null hypotheses too often.     

Tunneling or propping: Evidence from connected transactions in China

Friedman et al. (2003) develop a model in which, in equilibrium, controlling shareholders may choose either tunneling or propping of their listed companies depending on the magnitude of an adverse shock and the magnitude of the private benefits of control. In this paper, we employ connected transaction data from China to test the implications of their model. We hypothesize that, when listed companies are financially healthy (in financial distress), their controlling shareholders are more likely to conduct connected transactions to tunnel (prop up) their listed companies and the market reacts unfavorably (favorably) to the announcement of these transactions. Our empirical findings strongly support our hypotheses. We also find that all of the transaction types in our sample can be used for tunneling or propping depending on different financial situations of the firms. Finally, political connection is negatively associated with the announcement effect. Overall, our analysis supports Friedman et al.'s (2003) model by furnishing clear evidence for propping and tunneling to occur in the same company but at different times.     

Monetary Policy in a Schumpeterian Growth Model with Vertical R&D Sectors

We explore the growth and welfare effects of monetary policy in a Schumpeterian economy with cash-in-advance (CIA)-constrained research and development (R&D) investment in both the upstream and downstream sectors. We show that the nominal interest rate can have an inverted-U relation with economic growth due to its effects on labor allocations between manufacturing and R&D and between the R&D sectors. Furthermore, aggregate R&D overinvestment is generally sufficient but not necessary for the Friedman rule of zero nominal interest rates to be suboptimal. Calibrated using data from U.S. manufacturing firms, our model features a positive welfare-maximizing nominal interest rate despite aggregate R&D underinvestment.     

Response to Nelson and Schwartz

In responding to Nelson and Schwartz's [2008. The impact of Milton Friedman on modern monetary economics: setting the record straight on Paul Krugman's “Who was Milton Friedman?”. Journal of Monetary Economics 55, this issue] critique of my “Who Was Milton Friedman”, I focus on three central economic topics: (i) whether it is reasonable to claim that the Federal Reserve caused the Great Depression; (ii) whether monetary policy had the power to engineer an economic recovery after the onset of the depression; and (iii) whether monetarism succeeded or failed. On all these key points, I reject the criticisms of Nelson and Schwartz.     

Money and Output: Friedman and Schwartz Revisited

More than 50 years ago, Friedman and Schwartz examined historical data for the United States and found evidence of procyclical movements in the money stock, which led corresponding movements in output. We find similar correlations in more recent data; these appear most clearly when Divisia monetary aggregates are used in place of the Federal Reserve's official, simple‐sum measures. When we use information in Divisia money to estimate a structural vector autoregression, identified monetary policy shocks appear to have large and persistent effects on output and prices, with a lag that has lengthened considerably since the early 1980s.     

Optimality of the Friedman rule in economies with distorting taxes

We find conditions for the Friedman rule to be optimal in three standard monetary models. Our main contribution is to shed light on two issues in the literature. First, the conventional view maintains that when money is a final good, its services should be taxed. Moreover, if money demand is interest-inelastic, its services should be taxed heavily. We show that this view is incorrect. Second, there is an ongoing controversy about whether the optimality of the Friedman rule is connected to the intermediate goods result from public finance. We resolve this controversy by showing a deep connection between these results.     

In Old Chicago: Simons,Friedman, and the Development of Monetary‐Policy Rules

This paper examines the different policy rules proposed by Henry Simons, who, beginning in the mid‐1930s, advocated a price‐level stabilization rule, and by Milton Friedman, who, beginning in the late‐1950s, advocated a rule that targeted a constant growth rate of the money supply. Although both rules shared the objective of eliminating the policy uncertainty emanating from discretion, they differed because of the different views of Simons and Friedman about the stability of secular relationships. Simons’ rule relates to modern rules that emphasize the pursuit of price stability as representing optimal monetary policy.     

Four types of ignorance

This paper studies alternative ways of representing uncertainty about a law of motion in a version of a classic macroeconomic targetting problem of Milton Friedman (1953). We study both “unstructured uncertainty” – ignorance of the conditional distribution of the target next period as a function of states and controls – and more “structured uncertainty” – ignorance of the probability distribution of a response coefficient in an otherwise fully trusted specification of the conditional distribution of next period׳s target. We study whether and how different uncertainties affect Friedman׳s advice to be cautious in using a quantitative model to fine tune macroeconomic outcomes.