Working Paper Abstracts – 1988

Working Paper Abstracts – 1988

no abstract

no abstract

no abstract

no abstract


There is some empirical evidence that high tax bracket investors hold the equity of unlevered firms while law tax bracket investors hold levered firms. It has been suggested that an extension of the Miller model can provide a theory which is consistent with this observation. However, it has been stated elsewhere that this separation arises only for some sequences of shareholder voting and trading. We show that clienteles exist irrespective of the sequence of events. However, the relationship between firm value and capital structure depends on whether a group with a tax rate equal to the corporate rate exists.


Various tax policies provide consumers with forms of insurance. Social security has the payoff characteristics of an annuity. Income tax provides consumers with a degree of income insurance because the government shares part of the individual’s income risk. Redistributive taxes can be used to spread aggregate income risks across different generations. The effects of these and other tax policies are shown to depend crucially on the nature of existing private insurance arrangements.


When several investors with different risk aversions trade competitively in a capital market, the allocation of wealth fluctuates randomly between them and acts as a state variable against which each market participant will want to hedge. This hedging motive complicates the investors’ portfolio choice and the equilibrium in the capital market. Although every financial economist is aware of this difficulty, to our knowledge, this issue has never been analyzed in detail. The current paper features two investors, with the same degree of impatience, one of them being logarithmic and the other having an isoelastic utility function. They face one risky constant-return-to-scale stationary production opportunity and they can borrow and lend to and from each other. The behaviors of the allocation of wealth and of the aggregate capital stock are characterized, along with the behavior of the rate of interest and that of the security market line. The two main results are: (1) given the particular menu of assets under consideration, investors in equilibrium do revise their portfolios over time so that some trading takes place, (2) when the two investors ‘disagree’ about whether the economy should be expanding or contracting, it is possible for the allocation of wealth and the capital stock to admit steady-state distributions. It is also possible for these to randomly oscillate between two extreme attracting points. This is in contrast to the certainty case, where aggregate wealth becomes either very large or very small and one investor in the long run holds all the wealth. The existence of trading opens the way to a theory of capital flows and market trading volume.

no abstract


Recent work on the price behavior of French common stocks concluded that the evidence is consistent with equity pricing according to the Capital Asset Pricing Model (CAPM). In this paper we re-examine the evidence on the risk-return characteristics of French equity and show that the estimated parameters of the risk-return relationship exhibit strong seasonality. The risk- return relationship is not linear and portfolio size affect equity pricing during January. These results cast some doubt on the validity of the CAPM as a descriptor of French equity returns.


We re-examine the pricing of common stocks on the Belgium Stock Exchange in light of two related phenomena recently reported in the literature: the size effect and risk–premia seasonality. When these two phenomena are ignored we cannot reject the hypothesis that the behavior of common stock prices conform to the CAPM. However, when size and seasonality are accounted for in the stochastic process that generates stock returns, the hypothesis that the CAPM describes (and explains) the pricing of common stocks must be rejected, even during the month of January despite the presence of a positive systematic risk premium and the absence of an unsystematic risk premium during that month.

no abstract


Transferring physical capital and transferring production and sales activities from one country to the other typically entails large adjustment costs. The model of this paper features two homogeneous stocks of physical capital located in two different countries separated by an ‘ocean.’ The two physical stocks are optimally invested in a random production process yielding real returns, consumed by local residents, or transferred abroad. Retro-fitting, transferring and re-building capital equipment, and increasing production and sales abroad either takes time (during which capital is idle) or consumes real resources. As a result, the price of capital-consumption goods located in one place is not equal to that of goods located in the other place. The stochastic process for this deviation from the Law of One Price (LOP) is obtained. By construction, this process is compatible with financial market efficiency and with the possibility of (costly) trade in commodities. Whereas empirical studies have found no evidence against the hypothesis that LOP deviations follow a martingale, the theoretical process which I find, exhibits mean reversion (as well as a fair degree of conditional hetero-scedasticity) when investors are risk averse.


Many analyses of debt policy assume exogenous government expenditures. Instead, we use an optimizing model in which the government selects values of taxes, spending, and debt to maximize welfare. If demand for publicly provided goods is elastic, a debt-financed tax cut increases consumption, because individuals rationally expect some reduced government spending in future. Even though future taxes rise, they do not offset the expansionary effect of the current tax cut on consumption. Depending on preferences, the marginal propensity to consume out of tax cuts can take any value between zero and the marginal propensity out of ordinary income.


The issue of dynamic efficiency is central to analyses of capital accumulation and economic growth. Yet the question of what characteristics should be examined to determine whether actual economies are dynamically efficient is unresolved. This paper develops a criterion for determining whether an economy is dynamically efficient. The criterion, which holds for economies in which technological progress and population growth are stochastic, involves a comparison of the cash flows generated by capital with the level of investment. Its application to the United States economy and the economies of other major OECD nations suggests that they are dynamically efficient.


The effects on asset prices of changes in risk are studied in a general equilibrium model in which the conditional risk evolves stochastically over time. The savings decisions of consumers take account of the fact that conditional risk is a serially correlated random variable. By restricting the specification of consumers’ preferences and the stochastic specification of dividends, it is possible to obtain an exact solution for the prices of the aggregate stock and diskless one-period bonds. An increase in the conditional risk reduces the stock price if and only if the elasticity marginal utility is less than one.


Several recent studies have suggested that empirical rejections of the permanent income/life cycle model might be due to the existence of liquidity constraints. This paper tests the permanent income hypothesis against the alternative hypothesis that consumers optimize subject to a well specified sequence of borrowing constraints. Implications for consumption in the presence of borrowing constraints are derived and then tested using time series/cross section data on families from the Panel Study of Income Dynamics. The results generally support the hypothesis that an inability to borrow against future labor income affects the consumption of a significant portion of the population.


This paper investigates the dynamics of real interest rates and inflation in the context of an equilibrium asset pricing model. Formulas for bond prices and optimal forecasts of inflation are shown to form a state space system. The model’s parameters are estimated by maximum likelihood, using a Kalman filter to compute the likelihood function. The estimation uses time series data on Treasury bill prices of various maturities and survey forecasts of inflation. The results suggest chat the stochastic processes for real interest rates and expected inflation are mutually dependent; innovations in the processes display significant negative correlation while expected changes in each variable are significantly positively related to the level of the other variable. There is evidence that over the past decade inflation and real interest rates have displayed somewhat less mean reversion than previously. Distinguishing real rates from expected inflation is likely to lead to gains in interest rate modelling.



A commercial loan sale or secondary loan participation is a contract under which a bank sells the cash stream from a loan to a third party, usually without recourse. In accordance with accepted accounting procedures, this no–recourse contract allows removal of the underlying loan from the balance sheet of the bank, so that the funding of the loan is not subject to capital or reserve requirements. Since commercial banks are thought to specialize in the origination of non-marketable claims on borrowing firms, the apparent ability of banks to sell these assets seems paradoxical. The paradox could be explained if loan sales contracts contained implicit guarantees in the form of options by loan buyers to sell the loans back to the bank if the underlying borrower performs worse than anticipated. If such guarantees exist, then loans which are sold represent contingent liabilities, and a rationale for increasing capital requirements may exist. As an indirect test of the existence of this guarantee, we investigate whether loan sales and commercial paper prices contain a risk premium for the default of the selling bank. The empirical evidence supports the hypothesis of implicit guarantees.


The paper makes a case for foreign currency debt as a hedging device in an open economy subject to stochastic shocks to output. A government can reduce uncertainty in net wealth and in consumption by issuing foreign or domestic currency debt, if unexpected domestic and foreign inflation are negatively correlated with domestic output.

Foreign currency debt is desirable in comparison to domestic currency debt, if growth rates of output of both countries are closely related and if domestic inflation is relatively uncertain. In addition, foreign currency debt replaces domestic currency debt as hedge, whenever issuing domestic debt is prevented or discouraged by incentive problems.

It also shows that time-consistency problems may motivate capital controls or taxes on international borrowing.

no abstract


In this paper, option pricing theory is used to value and analyze many performance-based fee contracts that are currently in use. A potential problem with some of these contracts is that they may induce portfolio managers to adversely alter the risk of the portfolio they manage. This paper is prescriptive, in that it derives conditions for contract parameters that provide proper risk incentives for classes of investment strategies. For buy-and-hold and rebalancing strategies, adverse risk incentives are avoided when the penalties for poor performance outweigh the rewards for good performance.


This paper presents a simple model that provides insights about various measures of portfolio performance. The model explores three criticisms of these measures: (i) the inability to identify an appropriate benchmark portfolio; (ii) the possibility of overestimating risk because of market timing ability; and (iii) the failure of informed investors to earn positive risk-adjusted returns because of increasing risk aversion. The paper argues that these are not serious impediments to performance evaluation. In particular, it shows (i) that the appropriate benchmark portfolio is the unconditional mean-variance efficient portfolio of the evaluated investor’s tradable assets, even when the investor does not optimally hold the mean-variance efficient portfolio; (ii) that the market timing risk-adjustment problem can be overcome with new measures; and (iii) that informed investors display negative risk-adjusted returns only for pathological preferences that treat risky assets as Giffen goods.


Previous studies of mutual fund performance have analyzed the net returns of funds, which have fees, expenses, and other transactions costs subtracted from them, or have added an estimate of transaction costs to the net returns to obtain an estimate of gross returns. In addition, these studies analyzed samples that were subject to survivorship bias. This paper employs the quarterly portfolio holdings of a large sample of mutual funds to construct an alternative estimate of gross returns. This samples, which is not subject to survivorship bias, is used in conjunction with a sample that contains the actual (net) returns of mutual funds, which is subject to survival bias. In addition to allowing us to estimate the bias in measured performance that is due to the survival requirement, (less than 0.5% per year for the average fund), and total transaction costs, (about 2.5% per year), the sample is used to test for the existence of abnormal performance. The tests indicate that the risk-adjusted gross returns of some funds were significantly positive in the 1975-84 time period.


No economic event on or about October 19, 1987 can explain the record collapse of equity prices that occurred on that day. In the summer of 1987 equity valuations were at a historically high levels based on current and projected earnings and the real interest rates available in the bond market.

This paper constructs a theoretical index of stock prices based on the range of actual forecasts of future corporate profits made during 1987. The dispersion of these profit forecasts increased markedly prior to the crash and the actual level of stock prices reached in the summer of 1987 could be justified by only the 10% most optimistic forecasters. Some reasons for the divergence between the actual level of stock prices and the level based on the mean forecasts of corporate profits are analyzed. These include the effects of the unprecedented five-year bull market in stocks, changes in the equity risk premium, and investors’ misjudgment of the market impact of portfolio insurance.

The divergence between the theoretical and actual stock market levels may have made stocks extremely vulnerable to any negative shocks. The stock market decline appeared to be a related response of investors to rising real interest rates, which reached their peak on the morning of October 19th. Evidence is presented which suggests that the deteriorating US trade deficit was the most important source of the rising dollar interest rates prior to the crash. Increasing inflationary expectations played only a small role in the rate rise and the Federal Reserve assumed a neutral or only moderately tight stance during most of 1987. It is shown that, despite much public opinion to the contrary, there is little evidence to suggest that investors’ perceptions of the US budget deficit worsened prior to the crash and were a factor in the fall of equity prices.


This paper presents a mean-variance framework for likelihood ration tests of asset pricing models. A pricing model is tested by examining the position of one of more reference portfolios is sample mean-standard-deviation space. Included are tests of both single-beta and multiple-beta relations, with or without a riskless asset, using either a general or a specific alternative hypothesis. Tests with factors that are not portfolio returns are also included. The mean-variance framework is illustrated by testing the zero-beta CAPM, a two-beta pricing model, and the consumption-beta model.


We investigate the cross-sectional relation between dividend yield and expected return and attempt to include various effects of changing risk measure and changing risk premiums. A stock’s risk is measured by its sensitivities to two factors, a market factor and a changing-risk-premium factor. After analyzing dividend-related changes in risk measures, we investigate the presence of dividend effects in expected returns using four methods, each imposing a different structure on the temporal behavior of risk measures and risk premiums. For each method, we find no reliable cross-sectional relation between dividend yield and risk-adjusted expected return.


The paper explores how the structure of government debt affects the budget in a stochastic environment. In the theoretical part, I present two models that motivate why governments should care about the risk inherent in its choice of liabilities. The models are based on tax-smoothing and risk aversion of taxpayers, respectively. Debt should be structured to hedge against macroeconomic shocks that affect the government budget, in particular against shocks to aggregate output. The optimal structure of government liabilities generally includes some “risky” securities which are state contingent in real terms.

The empirical part studies state-contingencies implemented by some specific securities. I find that nominal debt and long-term debt have desirable properties as hedges. This may motivate the current practice issuing non-indexed debt of various maturities. The argument justifying “risky” nominal and long-term debt suggests that the government may improve welfare by taking a short position in the stock market. This is strongly supported by the data. Finally, I find that issuing selected foreign currency bonds may be beneficial.


In this paper, we show the reason why the absence of asymptotic arbitrage opportunities in the sense of convergence in quadratic mean (ACQM) as defined in Huberman (1982) is only a necessary condition for an asset market equilibrium. For certain classes of risk-averting investors, a portfolio that is not an ACQM may sometimes provide infinitely blissful gratification. These investors would relentlessly explore such a portfolio and cause market disequilibrium. Consequently, the APT that is based on Huberman’s concept of arbitrage is not a valid description of the no-arbitrage pricing relation as other types of asymptotic arbitrage opportunities may exist in the economy. To resolve this inconsistency, we replace Huberman’s concept of asymptotic arbitrage (convergence in quadratic mean) with that of convergence in probability. We show that if the idiosyncratic risks of the linear K-factor structure are weakly dependent (or, more precisely, the sequence of the idiosyncratic risks in a lacunary system of order p for some p >1), the absence of the arbitrage opportunities in the sense of convergence in probability (ACP) implies an approximate linear pricing relation which is consistent with an asset market equilibrium for a broader class of preferences. However, there are still circumstances in which the absence of the ACP is not compatible with the asset market equilibrium. Finally, we claim that the absence of “asymptotically exact” arbitrage opportunities is consistent with asset market equilibrium for all risk-averting investors.


In this paper, we generalize the Arbitrage Pricing Theory (APT) to incorporate the cases where the idiosyncratic risks of the factor model are dependent and/or the second central absolute moments (variances) of the assets returns do not exist. A bound on the pricing errors, similar to the one derived in Ross (1976) and Huberman (1982), is derived in our generalized framework.

Specifically, it is shown that as long as the idiosyncratic risks are weakly dependent (or when the sequence of the idiosyncratic risks is a lacunary system), the approximate linear pricing relation holds in the absence of “arbitrage” in the sense of convergence in pth mean (ACPM). It can be demonstrated that the models in Huberman (1982), Ingersoll (1984) and Chamberlain and Rotschild (1983) are all special cases of this version of the APT. It is also established that, under suitable assumptions of the linear factor structure, the approximate linear pricing relation implies the nonexistence of asymptotic arbitrage opportunities. Thus the no-asymptotic-arbitrage position is a necessary and sufficient condition for the approximate linear pricing relation.


The three basic elements of the arbitrage pricing theory (APT) are the linear factor structure of asset returns, the nonexistence of asymptotic arbitrage opportunities, and the approximate linear pricing relation. This paper explores the necessary and sufficient conditions of the approximate linear pricing relation by systematically examining the associations among these three elements. The generalization evolves around various modes of stochastic convergence that characterize the nature of asymptotic arbitrage opportunities and around assorted assumptions about the idiosyncratic risks in the linear factor structure. This study is exhaustive in the sense that all modes of convergence are used in defining the asymptotic arbitrage opportunities. This study also allows researchers to know the trade-off between the linear factor structure and the no-asymptotic-arbitrage condition while keeping the approximate linear relation intact. Our generalization of the APT may enhance the understanding about the arbitrage pricing mechanism and the stochastic nature of the underlying economy.


The capital market is abound of mergers, spin-offs, sell-offs, and construction of mutual funds. All these activities impose linear or nonlinear transformations on the return generating process. The validity of the APT under linear transformations of asset returns has been discussed but not fully explored in the literature. The purpose of this paper is to examine the robustness of the APT with respect to arbitrary linear transformations. We show that the APT holds under any linear transformation as long as the product of the transformation matrix and its transpose is uniformly bounded.


Previous attempts to reject the hypothesis that real exchange rates follow a random walk have produced mixed results. This paper incorporates mean reversion and conditional heteroscedasticity into tests based on a theoretical model of deviations from the law of one price by Dumas (1988). The results indicate that once conditional heteroscedasticity is incorporated into the estimation significant mean reversion cannot be rejected. The tests also point to substantial differences between the real exchange rate behavior of countries which are in the European Monetary System and those which are not.


The paper is concerned with time-consistency problems caused by monetary policy in an open economy. The temptation to generate surplus inflation is shown to depend positively on the amounts of nominal debt issued by the government or issued by individuals. Private debt matters, because inflationary money growth causes redistribution between domestic residents and foreigners. A government that cares about welfare of its residents will be tempted to inflate whenever it or its residents have issued nominal debt to foreigners. A net creditor position, however, may eliminate the time-consistency problem.

If money supply affects real exchange rates, foreign currency debt has similar incentive effects as nominal debt, but typically in the opposite direction. The time-consistency problem may be reduced or even eliminated by issuing foreign currency debt. To maximize the incentive effect, this debt should be sold to foreigners. Hence, international portfolio diversification may reduce welfare.

For the United States, these international considerations should become increasingly relevant as the country accumulates external deficits. My estimates indicate that the incentive to inflate more than doubled between 1982 and 1987. More than two-thirds of this increase was due to higher external debt, which was largely financed in nominal terms.


We model the demand for transactions services and liquidity in an economy with asymmetrically informed agents. It is shown that informed agents can systematically take advantage of agents who are relatively uninformed but who have unexpected needs to trade. This causes certain financial contracts to endogenously arise because they provide a type of “protection” to the uninformed agents. These contracts have the characteristics of creating a security with a safe return from underlying assets with certain returns. Intermediaries that resemble banks are examples of such a contract, and we provide a rationale for deposit insurance in this context. However, a commercial paper market in conjunction with intermediaries resembling money market mutual funds is another financial contract which provides this same transaction, service, and may well be preferred to the bank financial contract. Deposit insurance would not be needed in this later case, though the need for a government debt market may arise.


Secondary loan participations, or loan sales, are a recent innovation in banking. In a secondary loan participation, or loan sale, a bank makes a loan and then sells the cash stream from the loan without explicit contractual recourse, guarantee, insurance, or other credit enhancement, to a third party. Between the late 1970s and early 1988 this market grew from insignificant amounts to about $240 billion. In fact, in roughly the last four years the loans sales market has grown by 784 percent.

The development of the loan sales market is momentous. Bank loans hitherto were nonmarketable securities which could only be removed from the balance sheet by creating a contingent liability or by legally transferring the debtor-creditor relationship. Neither happened in significant volume. Whatever unique services were provided by banks, their production apparently required the bank to hold loans until maturity. Consequently, the recent practice of loan sales raises fundamental questions about the uniqueness of banks relative to markets as mechanisms for allocating capital. In particular, are banks continuing to perform unique services, such as enforcing loan covenants, or are these activities now performed by other economic agents, in markets? If banks are still performing these activities, what incentives to perform do they face if the loans can be sold without recourse?

This paper describes the evolution of the loans sales market and explains the legal, accounting, regulatory and economic issues raised by its growth. We present the available quantitative evidence on the growth of the loan sales market, the identity of buyers and sellers, the types of loans sold, the characteristics of the participation contracts, and the prices of loans which were sold. Qualitatively, loan participations are distinguished contractually from other bank asset contracts, and the prices of loans both legally and economically. The various contracts are defined and their legal implications discussed. A set of stylized facts about loan sales contracts, based on a sample of blank secondary loan participation contracts (and associated contracts with the underlying borrower), collected from money center banks, is presented.

Finally, we briefly consider possible explanations for how loans can be sold when this was not possible (in significant amounts) previously.


This paper develops distribution-specific theoretical constraints on relative prices of out-of-the-money European call and put options that are also valid for American options on futures. Systematic violations of these constraints by prices of American options on Deutschemark futures are found, indicating that distributions more asymmetric than standard models are necessary. An American option pricing model for jump-diffusion processes with asymmetric jump is developed. Estimates of parameters implicit in prices of options on Deutschemark futures indicate that throughout 1984-87, market participants perceived a remote chance of substantial crash in the dollar.


This paper derives the appropriate characterization of asset market equilibrium when asset prices follow jump-diffusion processes, and develops this general methodology for pricing options on such assets. Specific restrictions on distributions and preferences are imposed, yielding a tractable option pricing model that is valid even when jump risk is systematic and non-diversifiable. The dynamic hedging strategies justifying the option pricing model are described. Comparisons are made throughout the paper to the analogous problem of pricing options under stochastic volatility.


The institutional features of the Tokyo Stock Exchange allow tests that provide new insights into the determinants of stock return variances. When the exchange is open on Saturday, the weekend variance is roughly 60% higher than when it is closed. However, weekly variances are not increased by Saturday trading. The increase in weekend volume and variance caused by Saturday trading is offset by lower volume and variance on surrounding days. These results are consistent with the view that Saturday trading changes the timing of trades, and that variance is caused by private information revealed through trading. US stocks traded on Tokyo or Japanese stocks traded on the NYSE have increased trading hours, but trading of stock on a foreign exchange is typically light relative to domestic volume. The increased trading hours are not associated with an increase in stock return variance. This suggests that substantial volume is required for private information to be incorporated into stock prices and that there is no casual relation between trading hours and stock return variance.


This study analyzes the returns of NYSE stocks contained in the S&P 500 Index during the stock market decline on October 19 and October 20, 1987. The S&P stocks’ decline on October 19 was over 6% greater than the non-S&P stocks. In the first hour of trading on October 20, the S&P stocks recovered to the level of the non-S&P stocks. This study also finds a strong relation between order imbalances and stock price movements, both in time series and cross-sectional analyses. These results suggest that, in addition to the already know breakdown in the linkage between the prices of futures and the spot index on these two days, there were also breakdowns in the linkage among NYSE stocks.


The process of clearing and settling trades involves risks to both investors and the brokerage firms that represent them. Because of the International Organization of Securities Commissions (IOSCO) has appointed a technical committee to explore the problems of clearing and settlement in a global market. We argue for minimizing the length of the settlement cycle. This is a consideration that IOSCO should address.

In this paper we explore the nature of these risks, how they can b reduced; and we develop a way to estimate the size of these risks and their impact on transactions costs. We demonstrate that the risk brokerage firms face increases as the length of the settlement cycle increases. We provide a method to quantify some of the effects on transaction costs of changes in the settlement period. We discuss some strategies that brokerage firms may take to minimize the risk associated with clearance and settlement. And, as noted, we argue for minimizing the length of the settlement cycle.


There has been a long-running debate whether stock market prices are determined by fundamentals. To date no consensus has been reached. An important issue in this debate concerns the circumstances in which deviations from fundamentals are consistent with rational behavior. A continuous-time example where there are a finite number of rational traders with finite wealth is presented. It is shown that a finitely-lived security can trade above its fundamental.


Expected returns over long and short horizons are modeled using two approaches: an equilibrium asset pricing model and a vector autoregression (VAR). Empirical properties of returns that are consistent with the equilibrium model’s implications include (i) an annual “equity premium” of about six percent (ii) a U-shaped pattern of autocorrelations of returns with respect to investment horizon for the R-squared in projections of stock returns on predetermined financial variables. Parameters estimated in a monthly VAR for returns and these financial variables also imply autocorrelations, R-squared values, and conditional expected returns that are close to those computed with actual long-horizon returns. Simulations indicate that such a VAR is a reasonable approximation to the equilibrium model for representing the properties short- and long-horizon returns.

no abstract


Entry into a market seems to necessitate some investment into “marketing capital” (or distribution capital: advertising, dealerships, etc…). This form of investment has the property that, if it is unused for some time, it quickly becomes worthless. When entry into a market requires marketing investment, firms which are currently out of this market tend to delay entry until price vs. cost conditions have become extremely favorable. Conversely, firms which are in the market tend to delay exit until they can no longer bear large operating losses. This is because they know that, if they do exit, and if price vs. cost conditions later become favorable again, they will have to incur afresh the investment in marketing capital.

The purpose of the present paper is to produce a general-equilibrium model of capital formation in an economy subject to random shocks, when marketing capital (with the above properties) is used in distribution, in addition to the “normal” capital used in production.

We exhibit an analytical solution to the dynamic program representing the welfare optimum problem, along with the shadow prices corresponding to this program. These are also the prices which would support the general equilibrium of a decentralized market economy.

Our results pertain to the effect of entry costs, risk, risk aversion and productivity on the balance between marketing and productive capital, to the nature of growth paths in this economy and to the level of prices (such as the price of shares in the stock market, or the price of final goods) as well as the extent to which productivity shocks are passed through into these prices.

no abstract

no abstract