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In a closed economy context, Krusell and Smith (1998) show that heterogeneity in household discount factors is important for their incomplete markets model with idiosyncratic uncertainty to match U.S. data.
Readers who are familiar with Ghironi (2000) may wish to review the main assumptions below and move directly to Section III.
We use logarithmic utility for analytical tractability and, more importantly, because we intentionally choose to be conservative on the importance of wealth effects. These are amplified when steady-state assets are not zero, and they would be even stronger if the elasticity of intertemporal substitution were lower than 1. Assuming logarithmic utility allows us to focus more explicitly on the effect of tilts in consumption profiles generated by heterogeneous discounting.
We allow for monopolistic competition in production of goods in Ghironi, İşcan, and Rebucci (2003). There, households trade also shares in firms (though only domestically). However, price flexibility and monopoly offsetting subsidies imply that equilibrium dividends and share prices are zero in all periods, and the relevant equilibrium conditions are the same as in the model described here.
For simplicity, we will often refer to the representative member of generation ν as the “representative consumer” below. Strictly speaking, though, the model we set up is not a representative consumer one, as representative agents of different generations may behave differently.
Given that individuals are born owning no financial wealth, because they are not linked by altruism to individuals born in previous periods,
Because all firms in the world economy are born at t = –∞, after which no new firms appear, it is not necessary to index output and labor demands by the firms’ date of birth.
Where necessary for clarity, we use a “hat” to differentiate the aggregate level of a variable from the aggregate per capita level.
Although all firms in each country demand the same amount of labor in equilibrium, we leave the i superscript on labor demand to differentiate labor employed by an individual firm from aggregate per capita employment, which will be denoted by dropping the superscript.
Substituting yt = wtLt into (13) and using the resulting equation and its foreign counterpart in conjunction with (14) yields
We will consider the consequences of shocks to home and foreign productivity starting from initial steady-state levels
We assume that labor does not move across countries. Given a steady-state real wage differential, we motivate absence of long-run labor flows by appealing to the presence of prohibitive costs of relocating abroad that more than offset the welfare differential implied by differences in real wages.
If α =1 and
For the reasons discussed above, the functions are such that, if α= 1, it is
Even if consumption is increasing and labor effort is decreasing relative to the previous period for each individual home household in steady state, and opposite tilts characterize foreign households, the entry of new households with no assets in each period ensures that aggregate per capita consumption and labor effort are constant.
In the representative agent model with n= 0, the consumption differential across countries is a random walk, and all shocks have permanent consequences via wealth redistribution regardless of their temporary or permanent nature.
Ghironi (2000) shows that the log-linear model has a unique solution when α= 1 and steady-state productivities are equal across countries. While we cannot verify determinacy analytically when the steady state is asymmetric, we do not find an excessive number of stable roots when solving the model numerically.
Ghironi (2000) shows that lower (higher but finite) values of ω reduce (amplify) the elasticities of cross country differentials to net foreign asset accumulation in the symmetric version of the model. Consistent with Cole and Obstfeld (1991) and Corsetti and Pesenti (2001), there is no role for asset accumulation if ω = 1 and steady-state assets are zero.
Although the average rate of quarterly population growth for the United States between 1973:01 and 2000:03 has been 0.0025, extending the model to incorporate probability of death as in Blanchard (1985) would make it possible to reproduce the dynamics generated by n = 0.01 with a lower rate of entry of new households by choosing the proper value of the probability of death. The choice of n = 0.01 thus mimics the behavior of a more complicated, yet largely isomorphic setup.
The interested reader can find theoretical and empirical impulse responses to transitory, country-specific shocks in Ghironi, İşcan, and Rebucci (2003).
In the case of a permanent asymmetric shock – say, to home productivity – net foreign assets do not move, as home agents still find it optimal to consume the entire value of the shock in all periods without changing their labor effort. However, consumption and GDP increase by less than the shock, because the terms of trade of the home economy deteriorate due to the relative increase in the supply of home goods. See Ghironi (2000) for details.
We show in Ghironi, İşcan, and Rebucci (2003) that, if α is close to 1 and steady-state home labor effort is close to foreign (a condition that is satisfied in our example), the solution for the risk-free, world interest rate can be written approximately as
Notice that this does not detract from the observation we made in the Introduction that endogeneity of the interest rate is among the features that differentiate our model from small open economy models that assume heterogeneous discounting but an exogenous world interest rate. This is so because, even if the interest rate remains at its steady-state level after permanent shocks, the steady-state interest rate is endogenous and such that
We have also analyzed Germany and Japan as the empirical “home” economy. We do not report these results to conserve space. See footnote 36 for a brief discussion. Notice that, in Section IV, we thought of the foreign economy in the model as the United States. In this section, we label the United States. as the “home” economy of the empirical model, and we argue that its behavior is consistent with the relatively impatient (foreign) economy of the theoretical model.
Note that such a shock does not necessarily increase measured labor productivity in both countries by the same amount, on impact or during adjustment. Both the numerator and denominator of our empirical labor productivity measure (business sector output per hour worked) are endogenous in the theoretical model and respond differently across countries to a permanent, worldwide productivity shock when discount rates are asymmetric.
We rescaled the data on B by a positive number to ensure that its logarithm is always well defined.
For the period 1995–97, in fact, U.S. labor productivity and net foreign assets exhibit unusual behavior compared to the rest of the sample. At the same time, our full sample ends in 1997:Q4, which prevents us from testing and treating this last period as a different regime.
Estimated VAR equations are not reported but are available on request.
Notice that, in the absence of cointegration between home and foreign productivity, these economies would diverge over time. Productivity convergence within the G7 is also empirically defensible (see below). Furthermore, it is not uncommon to have a degree of statistical weakness in applied cointegration analysis. For instance, both King et al. (1991) and Mellander et al. (1992) encounter such statistical weakness in their cointegration tests, nevertheless implement the common trend analysis. (In their cases, they find the right number of cointegration vectors, but the data reject the identification restrictions they impose from economic theory.)
All coefficients in the system (23) should be positive (negative, in Table 2, panel B, because reported on the left-hand side of the cointegration relation), except, possibly,
Notice that our benchmark calibration is consistent with these estimates of the long-run relation between domestic and foreign productivity, which point to the United States as more productive than the rest of the G7 economies.
We followed Mellander et al. (1992) to estimate the VAR model in common trend representation and used the RATS code written by Anders Warne.
When we estimate the system with Japan as the empirical home economy and the rest of the G-7 excluding Japan as the foreign economy, the response of foreign assets to productivity has the opposite sign to that of the United States system, while the responses of both foreign assets and consumption are considerably smaller than those in the U.S. in absolute value. These results reinforce our evidence for qualitative cross-country differences in responses of foreign assets and consumption to permanent, worldwide productivity shocks, and also suggest that Japan may be an important counterpart to the U.S. case we analyzed (i.e., the more patient country). Our results for Germany, instead, are more mixed. We report these results in Ghironi, İşcan, and Rebucci (2003).
The OECD defines the business sector as “the institutional sector whose primary role is the production and sale of goods and services. This sector consequently corresponds to the aggregation of the corporate, quasi-corporate and unincorporated enterprises including public enterprises.” We should note that the OECD created this business sector data base with “the specific purpose of comparing […] economic performance in the OECD member countries. By focusing only on market agents and sectors [the business sector data] facilitate and enhance data comparability across countries” (Meyer zu Schlochtern and Meyer zu Schlochtern, 1994).