Understanding the Backus–Smith puzzle: It's the (nominal) exchange rate,stupid

Backus, Kehoe and Kydland (BKK 1992) demonstrated that if international capital markets are complete, consumption growth correlations across countries should be higher than their corresponding output growth correlations. In stark contrast to the theory, however, in actual data the consumption growth correlation is lower than the output growth correlation. By assuming trade imperfections due to non-traded goods, Backus, D.K., Smith, G.W. [1993 Consumption and real exchange rates in dynamic economies with non-traded goods. Journal of International Economics 35(3–4), 297–316] showed that there is an additional impediment at work that can lower the consumption growth correlation. While their argument was successful in partially explaining the puzzlingly low cross country correlation of consumption growth rates, it contributed to generating another puzzle because the data forcefully show that consumption growth is negatively correlated with the real exchange rate, which is also a violation of the theory. Using data for OECD countries, we decompose real exchange rate growth into its nominal exchange rate growth and inflation differential components, and find that nominal exchange rate movements are the main source for the Backus-Smith puzzle. We demonstrate the robustness of this finding by examining sub-samples of the data, by allowing for imperfect risk sharing due to ‘rule of thumb’ consumers, and by examining intranational data across the U.S. states where the nominal exchange rate is fixed.     

Discretionary monetary policy and inflation persistence

Rational expectations models of staggered price/wage contracts have failed to replicate the observed persistence in inflation and unemployment during disinflationary periods. The current literature on this persistency puzzle has focused on augmenting the nominal contract model with imperfect credibility and learning. In this paper, I re-examine the persistency puzzle by focusing on the discretionary nature of monetary policy. I show that when the central bank is allowed to re-optimize a quadratic loss function each period, imperfect credibility and learning, even in the absence of staggered contracts, can generate a significant amount of inflation persistence and employment losses during a disinflationary period.     

Rethinking the liquidity puzzle: Application of a new measure of the economic money stock

Historically, attempts to solve the liquidity puzzle focus on narrowly defined monetary aggregates, such as non-borrowed reserves, the monetary base, or M1. Many of these efforts fail to find a short-term negative correlation between interest rates and monetary policy innovations. More recent research uses sophisticated macroeconomic and econometric modeling. However, little research has investigated the role measurement error plays in the liquidity puzzle, since in nearly every case, work investigating the liquidity puzzle has used one of the official monetary aggregates, which have been shown to exhibit significant measurement error. In this paper, we examine the role that measurement error plays in the liquidity puzzle by (i) providing a theoretical framework explaining how the official simple-sum methodology can lead to a liquidity puzzle, and (ii) testing for the liquidity effect by estimating an unrestricted VAR.     

Money,Asset Prices,and the Liquidity Premium

This paper examines the effect of monetary policy on the market value of the liquidity services that financial assets provide, known as the liquidity premium. The theory predicts that money supply and nominal interest rates have positive effects on the liquidity premium, but asset supply has a negative effect. The empirical analysis with U.S. data confirms the theoretical predictions. The theory also proposes that the liquidity properties of assets can cause negative nominal yields when the money holding cost is low and liquid assets are scarce. The suggestive empirical findings in Switzerland to support this theoretical result are presented.     

Liquidity,default, taxes,and yields on municipal bonds

We examine the effects of liquidity, default and personal taxes on the relative yields of Treasuries and municipals using a generalized model with liquidity risk. The municipal yield model includes liquidity as a state factor. Using a unique transaction dataset, we estimate the liquidity risk of municipals and its effect on bond yields. Empirical evidence shows that municipal bond yields are strongly affected by all three factors. The effects of default and liquidity risk on municipal yields increase with maturity and credit risk. Liquidity premium accounts for about 9–13% of municipal yields for AAA bonds, 9–15% for AA/A bonds and 8–19% for BBB bonds. A substantial portion of the maturity spread between long- and short-maturity municipal bonds is attributed to the liquidity premium. Ignoring the liquidity risk effect thus results in a severe underestimation of municipal bond yields. Conditional on the effects of default and liquidity risk, we obtain implicit tax rates very close to the statutory tax rates of high-income individuals and institutional investors. Furthermore, these implicit income tax rates are quite stable across bonds of different maturities. Results show that including liquidity risk in the municipal bond pricing model helps explain the muni puzzle.     

Wealth Distribution, Inflation Tax, and Societal Benefits of Illiquid Bonds

Illiquid nominal government bonds are shown to have two opposing effects on welfare. First, the relatively poor choose to top-up money balances for future consumption by purchasing nominal bonds at a discount. The wealth distribution becomes more centered with a smaller consumption deviation from the first best. Second, the higher inflation tax on monetary wealth to finance interest payments makes money less valuable, so that the quantity of output produced in exchange for money decreases. The trade-off between the welfare-enhancing effect on wealth distribution and the distortionary effect on output implies the socially optimal discount rate and liquidity.     

Asset Prices,Liquidity, and Monetary Policy in an Exchange Economy

I formulate a model in which money coexists with equity shares on a risky aggregate endowment. Agents can use equity as a means of payment, so shocks to equity prices translate into aggregate liquidity shocks that disrupt the mechanism of exchange. I characterize a family of optimal monetary policies and find that the resulting equity prices are independent of monetary considerations. I also study a perturbation of the family of optimal policies that targets a positive constant nominal interest rate and find that in this case the real equity return includes a liquidity return that depends on monetary considerations.     

The “price puzzle” reconsidered

A large literature has employed structural vector autoregressive (SVAR) models to investigate the empirical effects of U.S. monetary policy. Many of these models regularly produce a “price puzzle”—a rise in the aggregate price level in response to a contractionary innovation to monetary policy—unless commodity prices are included. Conventional wisdom maintains that commodity prices resolve the price puzzle because they contain information that helps the Federal Reserve forecast inflation. I examine a number of plausible alternative indicator variables and find little correlation between an ability to forecast inflation and an ability to resolve the price puzzle. Additionally, a sub-sample investigation reveals that evidence of a price puzzle is associated primarily with the 1959-1979 sample period, and that most indicators—including commodity prices—cannot resolve the puzzle over this period.     

Insured uncovered interest parity

The current literature suggests that uncovered interest parity (UIP) does not hold because of differences in risk in holding different currency denominated debt. We test whether this risk is related to sovereign credit risk in government bonds. We consider an insured uncovered interest parity relationship – that is, one where debt is insured with credit default swap (CDS) contracts. CDS rates help explain the UIP puzzle but have no predictive power for carry trade returns and currency movements.     

Money as stock

The fiscal theory determines the price level from the value of nominal government debt as a claim to government primary surpluses, just as private stock is valued as a claim to corporate profits. Valuation equations are not constraints, so this theory does not mistreat the government's intertemporal budget constraint. I anchor the analysis in a simple cash in advance model. When money demand falls to zero, I show that the price level can still be determined by the government debt valuation equation.     

Distortionary Taxation, Debt, and the Price Level

This paper compares the determinacy of equilibria under exogenous interest rates in an economy with a cash constraint, in which taxation is lump-sum or distortionary. Under passive fiscal policies lump-sum taxes generate nominal indeterminacy, while with distortionary taxes indeterminacy can be real, but not purely nominal. In general, under distortionary taxation uniqueness of the equilibrium allocation depends on monetary and fiscal policy interactions through taxes, debt, and interest rates. To illustrate this principle, we consider balanced-budget policies under distortionary income taxation and show that a unique equilibrium allocation prevails if interest rates are set consistent with long-run deflation. A separate section extends the analysis to endogenous interest rates.     

Inflation targeting: What inflation rate to target?

In an economy with nominal rigidities in both an intermediate good sector and a finished good sector, and thus with a natural distinction between CPI and PPI inflation rates, a benevolent central bank faces a tradeoff between stabilizing the two measures of inflation, a final output gap and, unique to our model, a real marginal cost gap in the intermediate sector, so that optimal monetary policy is second-best. We discuss how to implement the optimal policy with minimal information requirement and evaluate the robustness of these simple rules when the central bank may not know the exact sources of shocks or nominal rigidities. A main finding is that a simple hybrid rule under which the short-term interest rate responds to CPI inflation and PPI inflation results in a welfare level close to the optimum, whereas policy rules that ignore PPI inflation or PPI sector shocks can result in significant welfare losses.     

A re-examination on dissecting the purchasing power parity puzzle

The purpose of this paper is to examine the source of a real exchange-rate adjustment based on the impulse-response function constructed from local projections when the true data-generating process (DGP) is unknown. This work extends the local-projection method proposed by Jordà [2005. Estimation and inference of impulse responses by local projections. American Economic Review 95, 161-182] to allow for variables that are I(1) and exhibit cointegration. Our paper shows that nominal exchange-rate adjustments dominate in the reversion toward PPP regardless of a nominal exchange-rate shock or a price shock. It is also shown that the half-life of real exchange rates is close to that of nominal exchange rates. Since these results are consistent with those of Cheung et al. [Cheung, Y.W., Lai, K.S., Bergman, M., 2004. Dissecting the PPP puzzle: the unconventional roles of nominal exchange rate and price adjustments. Journal of International Economics 64, 135-150], we therefore conclude that their main findings are robust to possible misspecifications in the true DGP.     

Efficiency improvement from restricting the liquidity of nominal bonds

In a monetary search model with nominal bonds, agents face matching/taste shocks but they cannot insure, borrow or trade against such shocks. A government imposes a legal restriction that prohibits bonds from being used to buy a subset of goods. I show that this legal restriction can increase the society's welfare. In contrast to the literature, this efficiency role persists in the steady state and even when the households cannot trade assets after receiving the shocks. Moreover, it can exist when the Friedman rule is available and when the restriction is only obeyed by government agents.     

Credit lines as monitored liquidity insurance: Theory and evidence

We propose a theory of credit lines provided by banks to firms as a form of monitored liquidity insurance. Bank monitoring and resulting revocations help control illiquidity-seeking behavior of firms insured by credit lines. The cost of credit lines is thus greater for firms with high liquidity risk, which in turn are likely to use cash instead of credit lines. We test this implication for corporate liquidity management by identifying exogenous shocks to liquidity risk of firms in corporate bond and equity markets. Firms experiencing increases in liquidity risk move out of credit lines and into cash holdings.     

Real Balance Effects,Timing, and Equilibrium Determination

By assuming that money balances at the beginning instead of at the end of the period provide transaction services, standard results on nominal and real determinacy in monetary models are overturned. The key is that predetermined real money balances can be a state variable. Whereas the determination of the absolute price level typically depends on fiscal policy under an exogenous interest setting, nominal determinacy is now achieved even when fiscal policy is Ricardian. Also, in contrast to the Taylor principle, the interest rate policy should respond passively to changes in inflation, thus ensuring nonoscillatory and locally stable equilibrium sequences.     

Co-integrating currencies and yield differentials

This study investigates the relationship between currencies and interest rates of different maturity horizons. The real exchange rate is found to depend both on short-term real domestic and foreign interest rate difference and on long-term real domestic and foreign interest rate difference. Co-integrating regressions of contemporaneous currency rates generate negative and significant coefficients for long-term rate differentials, consistent with uncovered interest parity. Therefore, the expectations hypothesis holds for long horizons. On the other hand, positive coefficients for real short-term interest rate differentials reveal the forward premium puzzle: the failure of uncovered interest parity for short-horizons. Results are partly driven by the very different risk characteristics of short-term bonds and foreign bonds.     

Trend inflation, wage and price rigidities, and productivity growth

What are the steady-state implications of inflation in a general-equilibrium model with real per capita output growth and staggered nominal price and wage contracts? Surprisingly, a benchmark calibration implies an optimal inflation rate of -1.9 percent. The analysis also shows that trend inflation has important effects on the economy when combined with nominal contracts and real output growth. Steady-state output and welfare losses are quantitatively important even for low values of trend inflation. Further, nominal wage contracting is found to be quantitatively more important than nominal price contracting in generating the results. This conclusion does not arise from price dispersion per se, but from an effect of nominal output growth on the optimal markup of monopolistically competitive labour suppliers. Finally, accounting for productivity growth is found to be important for calculating the welfare costs of inflation. Indeed, the presence of 2 percent productivity growth increases the welfare costs of inflation in the benchmark specification by a factor of four relative to the no-growth case.     

On the (in)feasibility of covered interest parity as a solution to the forward bias puzzle

This paper examines Pippenger's (2011) proposed solution to the forward bias puzzle, which is based on the covered interest parity (CIP) condition. It is argued that the CIP-based approach does not solve this well known and long-standing puzzle in international finance in a meaningful way. Moreover, it is shown that empirical results from such an approach follow mechanically from the identity-like nature of the theory of covered interest parity, which, aside from small deviations due to transaction costs, is assumed to hold in all periods (as if it were an identity). We show that rather than leading to new insights, the simple reconfiguration of CIP to solve for the time t + 1 spot exchange rate leads to tautological expressions that, when estimated, might appear to successfully explain the forward bias, but in actuality are trivial. Results from simple simulation exercises further illustrate the inconclusiveness of the proposed solution method.     

The Liquidity Effect in the Federal Funds Market: Evidence at the Monthly Frequency

In this paper, we argue that much of the research into the link between money and interest rates suffers from misspecification. The measure of money and the measure of interest rates are not always well matched. In examining the transmission of monetary policy, we show that using an appropriate measure of money, Federal Reserve balances, and the appropriate interest rate, the federal funds rate, a clear liquidity effect exists. Furthermore, we explain how a lack of a clear institutional understanding may have contributed to the finding of a "liquidity puzzle" in the past.