Intertemporal substitution and durable goods: long-run data

In this paper, we use long-run annual data to estimate the intertemporal elasticity of substitution while accounting for the intra-temporal substitution between nondurable consumption goods and durable consumption goods. We apply a two-step procedure that combines a cointegration approach to preference parameter estimation with Generalized Method of Moments.

Long-run real exchange rate changes and the properties of the variance of k-differences

Engel (1999) computes the variance of k-differences for each time horizon us- ing the method of Cochrane (1988) in order to measure the importance of the traded goods component in U.S. real exchange rate movements. The importance of traded goods should decrease as the horizon increases if the law of one price holds for traded goods in the long run. However, Engel ?nds that the variance of k-di¤erences decreases only initially and then increases as k approaches the sample size. He interpets the increasing variance as evidence of an increase in the long-run importance of the traded goods component. By contrast, we show that the variance of k-di¤erences tends to return to the initial value as k approaches the sample size whether the variable is stationary or unit root nonstationary. Our results imply that the increasing variances for k-values close to the sample size cannot be inter- preted as evidence of an increase in the importance of the traded goods component in the long run. We ?nd that our test results regarding the variance of k-di¤erences are consistent with smaller importance of the traded goods component in the longer run.Real exchange rate, Variance ratio, Traded and nontraded goods

Purchasing Power Parity and the Taylor Rule

In the Kehoe and Midrigan (2007) model, the persistence parameter of the real exchange rate is closely related to the measure of price stickiness in the Calvo-pricing model. When we employ this view, Rogo's (1996) 3 to 5 year consensus half-life implies that rms update their prices every 18 to 30 quarters on average. This is at odds with most estimates from U.S. aggregate data when single equation methods are applied to the New Keynesian Phillips Curve (NKPC), or when system methods are applied to Dynamic Stochastic General Equilibrium (DSGE) models that include the NKPC. It is well known, however, that there is a large degree of uncertainty around the consensus half-life of the real exchange rate. To obtain a more efficient estimator, this paper develops a system method that combines the Taylor rule and a standard exchange rate model to estimate half-lives. We use a median unbiased estimator for the system method with nonparametric bootstrap confidence intervals, and compare the results with those from the single equation method typically used in the literature. Applying the method to the real exchange rates of 18 developed countries against the U.S. dollar, we nd that most of the half-life estimates from the single equation method fall in the range of 3 to 5 years with wide confidence intervals that extend to positive infinity. In contrast, the system method yields median-unbiased estimates that are typically shorter than one year with much sharper 95% confidence intervals, most of which range from 3 quarters to 5 years. These median unbiased estimates and the lower bound of the confidence intervals for the half-lives of real exchange rates are consistent with most estimates of price stickiness using aggregate U.S. data for the NKPC and DSGE models.Purchasing Power Parity, Calvo Pricing, Taylor Rule, Half-Life of PPP Deviations, Median Unbiased Estimator, Grid-t Confidence Interval

Purchasing Power Parity for Traded and Non-traded Goods: A Structural Error Correction Model Approach

When univariate methods are applied to real exchange rates, point estimates of autoregressive (AR) coefficients typically imply very slow rates of mean reversion. However, a recent study by Murray and Papell (2002) calculates confidence intervals for estimates of half-lives for long-horizon and post-1973 data, and concludes that univariate methods provide virtually no information regarding the size of the half lives. This paper estimates half-lives with a system method based on a structural error correction model for the nominal exchange rate, a domestic price index, a foreign price index, and a monetary variable. The method is applied to estimate half lives of real exchange rates based on producer price indices, consumer price indices, and GDP implicit deflators. The idea is that the traded component of the producer price index (PPI) is proportionately larger than that of the consumer price index (CPI). If the convergence rate is faster for traded goods prices than that for non-traded goods prices, half-lives for the real exchange rate based on the PPI should be shorter than those for the real exchange rate based on the CPI and that on the GDP implicit deflator. Our empirical results are consistent with this view.

The Effects of Japanese Monetary Policy Shocks on Exchange Rates: A Structural Vector Error Correction Model Approach

This paper investigates the effects of shocks to Japanese monetary policy on exchange rates and other macroeconomic variables, using structural vector error correction model methods with long-run restrictions. Long-run restrictions are attractive because they are more directly related to economic models than typical recursive short-run restrictions that some variables are not affected contemporaneously by shocks to other variables. In contrast with our earlier study of U.S. monetary policy with long-run restrictions in which the empirical results were more consistent with the standard exchange rate model than those with short-run restrictions, our results for Japanese monetary policy with long-run restrictions are less consistent with the model than those with short-run restrictions.

Decreasing Relative Risk Aversion and Tests of Risk Sharing

The relative risk aversion (RRA) coefficient of a household whose consumption is close to the subsistence level may be very high. For example, if consumption is exactly at the subsistence level, the household may not be willing to bear any risk. If this is the case, then the RRA coefficient must be a decreasing function of wealth for poor households. Therefore we should allow the possibility of decreasing RRA (DRRA) in testing the full risk sharing hypothesis. However, existing tests in the empirical literature are derived using preferences that exhibit either increasing or constant RRA even when they are applied to data containing low-income households. We therefore use a Hyperbolic Absolute Risk Aversion (HARA) utility, which implies increasing, constant, and decreasing RRA as special cases, to test full risk-sharing hypothesis. Using the International Food Policy Research Institute (IFPRI) and the International Crops Research Institute of the Semi-Arid Tropics (ICRISAT) household level data sets, we find evidence in support of the DRRA hypothesis, along with evidence favoring full risk-sharing hypothesis at the village level, and evidence against the hypothesis at the inter-village level. When RRA is restricted to be constant, we replicate the previous results in the literature: reject the full risk-sharing hypothesis at both levels. Our tests, however, reject this restriction and favor DRRA in almost all cases. These results suggest that it is important to allow for DRRA in testing the full risk-sharing hypothesis when data containing low-income households are investigated.

Measuring intertemporal substitution: The role of durable goods

As pointed out by Hall (1988), intertemporal substitution by consumers is a central element of many modern macroeconomic and international models. For example, many of the policy implications of an endogenous growth model studied by Barro (1990) depends on the assumption that the intertemporal elasticity of substitution is positive. In estimating the intertemporal elasticity of substitution (IES), however, Hall (1988) fmds that when time aggregation is taken into account, his point estimates are small and not significantly different from zero. Hall concludes that ti:e elasticity is unlikely to be much above 0.1 and may well be zero. We argue that Hall's estimator for the IES is downward biased because the intra-temporal substitution between nondurable consumption goods and durable consumption goods is ignored and because the changes in real interest rates affect user costs of durable goods. We use a two-step procedure that combines a cointegration approach to preference parameter estimation with Hansen and Singleton's (1982) Generalized Method of Moments approach in order to take these effects into account. In contrast to Hall's result, our estimates for the IES are positive and significantly different from zero even when time aggregation is taken into account.consumption durable goods real interest rates saving