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Learning and equilibrium selection in a monetary overlapping generations model with sticky prices
(2003)
We study adaptive learning in a monetary overlapping generations model with sticky prices and monopolistic competition for the case where learning agents observe current endogenous variables. Observability of current variables is essential for informational consistency of the learning setup with the model set up but generates multiple temporary equilibria when prices are flexible and prevents a straightforward construction of the learning dynamics. Sticky prices overcome this problem by avoiding simultaneity between prices and price expectations. Adaptive learning then robustly selects the determinate (monetary) steady state independent from the degree of imperfect competition. The indeterminate (non-monetary) steady state and non-stationary equilibria are never stable. Stability in a deterministic version of the model may differ because perfect foresight equilibria can be the limit of restricted perceptions equilibria of the stochastic economy with vanishing noise and thereby inherit different stability properties. This discontinuity at the zero variance of shocks suggests to analyze learning in stochastic models.
This paper considers a sticky price model with a cash-in-advance constraint where agents forecast inflation rates with the help of econometric models. Agents use least squares learning to estimate two competing models of which one is consistent with rational expectations once learning is complete. When past performance governs the choice of forecast model, agents may prefer to use the inconsistent forecast model, which generates an equilibrium where forecasts are inefficient. While average output and inflation result the same as under rational expectations, higher moments differ substantially: output and inflation show persistence, inflation responds sluggishly to nominal disturbances, and the dynamic correlations of output and inflation match U.S. data surprisingly well.
This paper compares Bayesian decision theory with robust decision theory where the decision maker optimizes with respect to the worst state realization. For a class of robust decision problems there exists a sequence of Bayesian decision problems whose solution converges towards the robust solution. It is shown that the limiting Bayesian problem displays infinite risk aversion and that decisions are insensitive (robust) to the precise assignment of prior probabilities. This holds independent from whether the preference for robustness is global or restricted to local perturbations around some reference model.
We study optimal nominal demand policy in an economy with monopolistic competition and flexible prices when firms have imperfect common knowledge about the shocks hitting the economy. Parametrizing firms´ information imperfections by a (Shannon) capacity parameter that constrains the amount of information flowing to each firm, we study how policy that minimizes a quadratic objective in output and prices depends on this parameter. When price setting decisions of firms are strategic complements, for a large range of capacity values optimal policy nominally accommodates mark-up shocks in the short-run. This finding is robust to the policy maker observing shocks imperfectly or being uncertain about firms´ capacity parameter. With persistent mark-up shocks accommodation may increase in the medium term, but decreases in the long-run thereby generating a hump-shaped price response and a slow reduction in output. Instead, when prices are strategic substitutes, policy tends to react restrictively to mark-up shocks. However, rational expectations equilibria may then not exist with small amounts of imperfect common knowledge.
Ignoring the existence of the zero lower bound on nominal interest rates one considerably understates the value of monetary commitment in New Keynesian models. A stochastic forward-looking model with lower bound, calibrated to the U.S. economy, suggests that low values for the natural rate of interest lead to sizeable output losses and deflation under discretionary monetary policy. The fall in output and deflation are much larger than in the case with policy commitment and do not show up at all if the model abstracts from the existence of the lower bound. The welfare losses of discretionary policy increase even further when inflation is partly determined by lagged inflation in the Phillips curve. These results emerge because private sector expectations and the discretionary policy response to these expectations reinforce each other and cause the lower bound to be reached much earlier than under commitment. JEL Klassifikation: E31, E52
We determine optimal monetary policy under commitment in a forwardlooking New Keynesian model when nominal interest rates are bounded below by zero. The lower bound represents an occasionally binding constraint that causes the model and optimal policy to be nonlinear. A calibration to the U.S. economy suggests that policy should reduce nominal interest rates more aggressively than suggested by a model without lower bound. Rational agents anticipate the possibility of reaching the lower bound in the future and this amplifies the effects of adverse shocks well before the bound is reached. While the empirical magnitude of U.S. mark-up shocks seems too small to entail zero nominal interest rates, shocks affecting the natural real interest rate plausibly lead to a binding lower bound. Under optimal policy, however, this occurs quite infrequently and does not require targeting a positive average rate of inflation. Interestingly, the presence of binding real rate shocks alters the policy response to (non-binding) mark-up shocks. JEL Klassifikation: C63, E31, E52 .
We determine optimal monetary policy under commitment in a forwardlooking New Keynesian model when nominal interest rates are bounded below by zero. The lower bound represents an occasionally binding constraint that causes the model and optimal policy to be nonlinear. A calibration to the U.S. economy suggests that policy should reduce nominal interest rates more aggressively than suggested by a model without lower bound. Rational agents anticipate the possibility of reaching the lower bound in the future and this amplifies the effects of adverse shocks well before the bound is reached. While the empirical magnitude of U.S. mark-up shocks seems too small to entail zero nominal interest rates, shocks affecting the natural real interest rate plausibly lead to a binding lower bound. Under optimal policy, however, this occurs quite infrequently and does not imply positive average inflation rates in equilibrium. Interestingly, the presence of binding real rate shocks alters the policy response to (non-binding) mark-up shocks.
Earlier studies of the seigniorage inflation model have found that the high-inflation steady state is not stable under adaptive learning. We reconsider this issue and analyze the full set of solutions for the linearized model. Our main focus is on stationary hyperinflationary paths near the high-inflation steady state. The hyperinflationary paths are stable under learning if agents can utilize contemporaneous data. However, in an economy populated by a mixture of agents, some of whom only have access to lagged data, stable inflationary paths emerge only if the proportion of agents with access to contemporaneous data is sufficiently high. JEL Klassifikation: C62, D83, D84, E31
Motivated by the observation that survey expectations of stock returns are inconsistent with rational return expectations under real-world probabilities, we investigate whether alternative expectations hypotheses entertained in the asset pricing literature are consistent with the survey evidence. We empirically test (1) the notion that survey forecasts constitute rational but risk-neutral forecasts of future returns, and (2) the notion that survey fore- casts are ambiguity averse/robust forecasts of future returns. We find that these alternative hypotheses are also strongly rejected by the data, albeit for different reasons. Hypothesis (1) is rejected because survey return forecasts are not in line with risk-free interest rates and because survey expected excess returns are predictable. Hypothesis (2) is rejected because agents are not al- ways pessimistic about future returns, instead often display overly optimistic return expectations. We speculate as to what kind of expectations theories might be consistent with the available survey evidence.
Optimal trend inflation
(2017)
We present a sticky-price model incorporating heterogeneous Firms and systematic firm-level productivity trends. Aggregating the model in closed form, we show that it delivers radically different predictions for the optimal inflation rate than canonical sticky price models featuring homogenous Firms:
(1) the optimal steady-state inflation rate generically differs from zero and,
(2) inflation optimally responds to productivity disturbances.
Using micro data from the US Census Bureau to estimate the inflation-relevant productivity trends at the firm level, we find that the optimal US inflation rate is positive. It was slightly above 2 percent in the year 1986, but continuously declined thereafter, reaching about 1 percent in the year 2013.
We analytically characterize optimal monetary policy for an augmented New Keynesian model with a housing sector. In a setting where the private sector has rational expectations about future housing prices and inflation, optimal monetary policy can be characterized without making reference to housing price developments: commitment to a 'target criterion' that refers to inflation and the output gap only is optimal, as in the standard model without a housing sector. When the policymaker is concerned with potential departures of private sector expectations from rational ones and seeks to choose a policy that is robust against such possible departures, then the optimal target criterion must also depend on housing prices. In the empirically realistic case where housing is subsidized and where monopoly power causes output to fall short of its optimal level, the robustly optimal target criterion requires the central bank to 'lean against' housing prices: following unexpected housing price increases, policy should adopt a stance that is projected to undershoot its normal targets for inflation and the output gap, and similarly aim to overshoot those targets in the case of unexpected declines in housing prices. The robustly optimal target criterion does not require that policy distinguish between 'fundamental' and 'non-fundamental' movements in housing prices.
In the secondary art market, artists play no active role. This allows us to isolate cultural influences on the demand for female artists’ work from supply-side factors. Using 1.5 million auction transactions in 45 countries, we document a 47.6% gender discount in auction prices for paintings. The discount is higher in countries with greater gender inequality. In experiments, participants are unable to guess the gender of an artist simply by looking at a painting and they vary in their preferences for paintings associated with female artists. Women's art appears to sell for less because it is made by women.
In this paper, we develop a state-dependent sensitivity value-at-risk (SDSVaR) approach that enables us to quantify the direction, size, and duration of risk spillovers among financial institutions as a function of the state of financial markets (tranquil, normal, and volatile). Within a system of quantile regressions for four sets of major financial institutions (commercial banks, investment banks, hedge funds, and insurance companies) we show that while small during normal times, equivalent shocks lead to considerable spillover effects in volatile market periods. Commercial banks and, especially, hedge funds appear to play a major role in the transmission of shocks to other financial institutions. Using daily data, we can trace out the spillover effects over time in a set of impulse response functions and find that they reach their peak after 10 to 15 days.
Credit boom detection methodologies (such as threshold method) lack robustness as they are based on univariate detrending analysis and resort to ratios of credit to real activity. I propose a quantitative indicator to detect atypical behavior of credit from a multivariate system - a monetary VAR. This methodology explicitly accounts for endogenous interactions between credit, asset prices and real activity and detects atypical credit expansions and contractions in the Euro Area, Japan and the U.S. robustly and timely. The analysis also proves useful in real time.
This paper investigates the risk channel of monetary policy on the asset side of banks’ balance sheets. We use a factoraugmented vector autoregression (FAVAR) model to show that aggregate lending standards of U.S. banks, such as their collateral requirements for firms, are significantly loosened in response to an unexpected decrease in the Federal Funds rate. Based on this evidence, we reformulate the costly state verification (CSV) contract to allow for an active financial intermediary, embed it in a New Keynesian dynamic stochastic general equilibrium (DSGE) model, and show that – consistent with our empirical findings – an expansionary monetary policy shock implies a temporary increase in bank lending relative to borrower collateral. In the model, this is accompanied by a higher default rate of borrowers.
We find that on average consumers chose the contract that ex post minimized their net costs. A substantial fraction of consumers (about 40%) still chose the ex post sub-optimal contract, with some incurring hundreds of dollars of avoidable interest costs. Nonetheless, the probability of choosing the sub-optimal contract declines with the dollar magnitude of the potential error, and consumers with larger errors were more likely to subsequently switch to the optimal contract. Thus most of the errors appear not to have been very costly, with the exception that a small minority of consumers persists in holding substantially sub-optimal contracts without switching. Klassifikation: G11, G21, E21, E51
The reaction of consumer spending and debt to tax rebates – evidence from consumer credit data
(2008)
We use a new panel dataset of credit card accounts to analyze how consumer responded to the 2001 Federal income tax rebates. We estimate the monthly response of credit card payments, spending, and debt, exploiting the unique, randomized timing of the rebate disbursement. We find that, on average, consumers initially saved some of the rebate, by increasing their credit card payments and thereby paying down debt. But soon afterwards their spending increased, counter to the canonical Permanent-Income model. Spending rose most for consumers who were initially most likely to be liquidity constrained, whereas debt declined most (so saving rose most) for unconstrained consumers. More generally, the results suggest that there can be important dynamics in consumers’ response to “lumpy” increases in income like tax rebates, working in part through balance sheet (liquidity) mechanisms.
Even as online advertising continues to grow, a central question remains: Who to target? Yet, advertisers know little about how to select from the hundreds of audience segments for targeting (and combinations thereof) for a profitable online advertising campaign. Utilizing insights from a field experiment on Facebook (Study 1), we develop a model that helps advertisers solve the cold-start problem of selecting audience segments for targeting. Our model enables advertisers to calculate the break-even performance of an audience segment to make a targeted ad campaign at least as profitable as an untargeted one. Advertisers can use this novel model to decide whether to test specific audience segments in their campaigns (e.g., in randomized controlled trials). We apply our model to data from the Spotify ad platform to study the profitability of different audience segments (Study 2). Approximately half of those audience segments require the click-through rate to double compared to an untargeted campaign, which is unrealistically high for most ad campaigns. Our model also shows that narrow segments require a lift that is likely not attainable, specifically when the data quality of these segments is poor. We confirm this theoretical finding in an empirical study (Study 3): A decrease in data quality due to Apple’s introduction of the App Tracking Transparency (ATT) framework more negatively affects the click-through rate of narrow (versus broad) audience segments.
DESPITE AMPLE EVIDENCE THAT CUSTOMERS EXHIBIT HIGHER DISCOUNT RATES THAN FIRMS, IT IS NOT CLEAR HOW DIFFERENCES IN DISCOUNT RATES AFFECT OPTIMAL PRICES, PROFITS, AND WELFARE OF COMPLEMENTARY PRODUCTS (WHICH COULD BE GOODS OR SERVICES). WE SHOW FOR COMPLEMENTARY PROUCTS THAT HIGHER DISCOUNT RATES OF CUSTOMERS DO NOT INCREASE PROFIT OR CONSUMER SURPLUS. FIRMS, INCLUDING BANKS, WOULD BE ADVISED TO SEEK TO REDUCE EXCESSIVE DISCOUNT RATES AMONG CONSUMERS.
Modeling short-term interest rates as following regime-switching processes has become increasingly popular. Theoretically, regime-switching models are able to capture rational expectations of infrequently occurring discrete events. Technically, they allow for potential time-varying stationarity. After discussing both aspects with reference to the recent literature, this paper provides estimations of various univariate regime-switching specifications for the German three-month money market rate and bivariate specifications additionally including the term spread. However, the main contribution is a multi-step out-of-sample forecasting competition. It turns out that forecasts are improved substantially when allowing for state-dependence. Particularly, the informational content of the term spread for future short rate changes can be exploited optimally within a multivariate regime-switching framework.