Innovation in Durable Goods

Summary

We develop a model of R&D competition between an incumbent and a potential entrant with network externalities and durable goods. We show that the threat of entry eliminates the commitment problem that an incumbent may face in its R&D decision due to the goods durability. Moreover, a potential entrant over-invests in R&D and an established incumbent might exhibit higher, equal or lower R&D investments in comparison with the social optimum. In our model, the incumbent’s commitment problem and the efficiency of its R&D level is determined by the extent of the network externalities.

Introduction
 

An industry exhibits network externalities when the benefit that consumers enjoy from purchasing one or several of its goods depends on the number of other consumers that use the same and/or compatible products. For the firms in those sectors (e.g. software, telecommunications, consumer electronics, etc.), the presence of network externalities implies that the attractiveness of their products is a function of their quality-adjusted prices and the potential benefit attached to their expected network sizes (i.e. installed bases).

Those products (i.e. network goods) tend to be characterized by two features closely related. Durability and rapid technological progress. 2 Durability implies that network goods tend to ”wear out” not as a result of physical deterioration, but as a consequence of technical obsolescence; a feature due to technological progress. For example, a given software (or mobile phone, or video game, etc.) can be functional for a long time. However, the utility derived by its use tend to be dissipated due to new (and actually very frequent) developments that are more closely related to consumers needs and tastes.

This paper considers a stylized network industry where these two features, durability and technological progress, are analyzed together. In particular, we propose a model of R&D competition between an incumbent and a potential entrant and consider the implications of the durability of network goods. Our main objective is to isolate the role of network externalities and analyze the social efficiency of the R&D incentives of the firms in this industry.

We depart from the current literature by considering, simultaneously, an oligopolistic setup, endogenous R&D processes and durable goods. Therefore, this paper is not only closely related to the literature on durable goods and to the literature on technological progress in network industries, but represents a first step in bridge them together.

The economic literature has highlighted the role that durability plays in the evolution of a market dominated by a monopolist. In particular, the conventional problem for the monopolist is that, having sold a durable good, there is an incentive to reduce price later to bring into the market those consumers that would not pay the initial high price. However, consumers realize that the monopolist has such an incentive to reduce price once they have purchased and those that value the good less highly will withhold their purchase until price falls. For this reason the monopolist is unable to extract as much money from the market as would be possible with a pre-commitment of ”no future price reductions”. The fact that in the absence of commitment the monopolist may act against his own profitability implies a ”time-inconsistency” problem (i.e. choices that maximize current profitability might not maximize overall profitability).

This notion was first discussed by Coase (1972) and has been labelled as the ”Coase Conjecture”. 3 Since its formulation, the Coase Conjecture has been theoretically devel-oped in several papers that consider the robustness of the basic observation. 4

The essential problem is that the monopolist’s actions in the future provide competi-tion for the company in the present market. 5 If the monopolist is able to lease the good, distort technology or implement buy back procedures then more profit can be extracted from the market since these strategies restrict the aftermarket. 6 Failing this the monopo-list has an incentive to reduce durability or make the good obsolete after a period of time. 7 The existing analysis of durability in the presence of network externalities has intended,as the main literature on durability, to verify the validity of the Coase Conjecture. 8 However, the implications of durability are much broader than the pricing commitment

problem considered in the analysis of the Coase Conjecture. In particular, the result that a monopolist in the absence of commitment may affect its own overall profitability applies in several contexts. In fact, as pointed out by Waldman (2003), any present and future action that affects the future (relative) value of the monopolist’s used goods might be subject to the ”time-inconsistency” described above. One leading case of such actions is a firm’s R&D expenditures which, by definition, affect the (relative) value of used (or previously sold) goods. 9

In the presence of network externalities, the similar analysis of introduction of new durable goods has been analyzed. 10 However, this literature is focused on a monopolistic setup and considers the production of new technologies as exogenous. Hence, and to the best of our knowledge, there is no analysis that consider explicitly the process of endogenous R&D processes in the presence of network externalities and durable goods.

The paper presented by Ellison and Fudenberg (2000) is the closest to ours and is ac-tually our departure point.  In that paper, the authors consider a monopoly that operates in a two-period framework and produces durable network goods.  In the first period the monopoly  produces  a  good  with  a  given  low  quality  and,  subsequently,  has  the  choice of introducing an improved version in the second period.   Network externalities play a role because the improvement of the old good implies backward compatibility.  That is, consumers of the new good enjoy network benefits from the entire population, while con-sumers of the old good only enjoy network benefits from consumers of the same good. 11 In their model, there is an inflow of new consumers in the second period and, with consumer homogeneity, the paper shows that the monopolist has the incentive to introduce the improved good, even though the monopolist’s overall profits (and social surplus) is reduced. That is, in the absence of commitment the monopolist’s choice that maximizes current (second period) profits does not maximize overall profitability.

We present a model that extends that of Ellison and Fudenberg (2000) by introducing and endogenous R&D process in the production of the new technology, and consider the role of a potential entrant. We show results not present in the Ellison and Fudenberg (2000) analysis. In particular, we consider a two-period framework with an incumbent, a potential entrant and an inflow of new consumers. Consumers are homogeneous and participate in a market with durable network goods.

In the first period, there is a first group of consumers that buy a network good from the established incumbent. Before the second period starts, a potential entrant appears in the market and, jointly with the incumbent, decides on an investment level that will allow him to compete in the second period. This R&D process is stochastic. By investing a certain amount, both firm determine the probability that in the second period they are able to produce a new product that is quality-improved relative to the existing good produced by the incumbent. Conditional on the success or failure of the innovation process, both firms compete in price in the second period when a new group of consumers arrive.

We analyze the incentives to innovate for both firms, we compare it to the social opti-mum and investigate the role of the network externalities.  With our simplified approach, we are able to isolate the impact of network externalities and reach three main results. 12 First, the threat of entry reverses the commitment problem that a monopolist (without such threat) may face in its R&D decision given good durability. This result is not present in the current literature and follows from the role that R&D incentives play in deterring entry.  In our case, the monopolist’s commitment problem arises only due to the presence of network externalities.

Second, the levels of R&D determined by market outcome might differ from the so-cially optimal levels. In particular, a potential entrant always over-invests (as an entry strategy) and an established incumbent might exhibit higher, lower or equal R&D levels in comparison with the social optimum. This result suggests that successful entry takes place too often in comparison with the social optimum.

And third, the extent of network externalities is the crucial parameter in the efficiency of the incumbent R&D level. In fact, it is only the presence of network externalities that permits, potentially, to the established incumbent to provide an efficient level of innovation. Without network externalities (or very low network effects), it is shown that the incumbent firm always under-invests in R&D efforts. This result sheds some light on the debate whether a dominant incumbent in a network industry provides sufficient innovation to the society.

The paper is organized as follows. The next section presents the model. Section 3 presents the analysis of its equilibrium. Section 4 computes the social optimum and compares it with the results of the market outcome. Finally, section 5 concludes and discusses some areas of further research.

The Model
 

We consider a model of a network industry with durable goods based on that of Ellison and Fudenberg (2000). 13 There are two periods denoted by t = 1 and t = 2 with a group of homogeneous consumers arriving in each period. In period 1 there is a monopolist incumbent that is challenged in period 2 by a potential entrant. In period 2, firms compete in prices with quality differentiated products. Quality is determined through endogenous and stochastic R&D processes carried out in period 1.

Supply Side and R&D Process

In period 1, an incumbent monopolist, I, produces a durable network good with quality level q1 (i.e. stand-alone value). The good lasts two periods after which it vanishes. We consider the case of product innovations where, subject to R&D expenditures, the incumbent might be able to produce a network good of better quality to be introduced in period 2. In our model, this process of innovation is carried out at the end of period 1. In addition, we assume that the outcome of the R&D process is stochastic with two possible outcomes, success or failure. This outcome is realized at the beginning of period 2.

Demand Side and Expectation Formation Process

The demand side represents the core of the model. In each period there is a group of Nt homogeneous consumers arriving in the market and, for convenience, we normalize N1 + N2 = 1. Consumers exhibit a per-period unitary demand for a network good and buy as soon as they reach the market. This implies that the N1 consumers make a purchase decisions in period 1 and in period 2. Given durability, this is not a trivial implication.

To see this, note that the price charged to the N1 consumers in period 1 tries to extract period 1 and 2 surpluses (i.e. the good is durable). However, period 2 surplus is affected by the outcome of the R&D processes, the prices of the two firms in period 2 and the N1 and N2 consumers’ choices. Therefore, the willingness to pay of the N1 consumers in period 1 depends on their beliefs on how the firms are going to behave in period 2. This gives rise to the commitment problem discussed in the introduction.

Conclusions


We presented a model of R&D competition between an incumbent and a potential entrant in market with durable goods and network externalities. In particular, we analyzed the market outcome and the social efficiency of the incentive to innovate in the presence of uncertain innovation processes. The robustness of the presented results with respect to the assumed functional forms is the objective of current work.

We found three main results. First, the threat of entry reverses the commitment problem that a monopolist (without such threat) may face in its R&D decision given the durability of the network goods. This result is not present in the current literature on R&D and follows from the role that R&D incentives play in deterring entry. In our case, the monopolist’s commitment problem arises only due to the presence of network externalities.
 

 

The Effect Of Durable Goods On The Growth Globally

The present System of National Accounts (SNA93) treats durable consumption goods as

consumption goods rather than investment although rentals for owner occupied households is imputed into GDP. We argue that households de facto treat the purchase of durable goods as investments and thus, the treatment of durables as capital assets conceptually does not differ from the present treatment of owner occupied dwellings. This is not captured by the economic analysis based on current statistical conventions.

The purpose of this paper is to estimate the effect of durable goods and ICT on euro area economic growth and productivity change; when expenditure on consumer durables is recorded as capital investment. The capitalization of consumer durables impacts both the levels and growth rates of the capital stock, productivity and GDP. Our growth accounting computations demonstrated that the capital services of durables contributed one-tenth of economic growth and one-eight of labour productivity growth in 1995-2004. ICT's impacts were larger, i.e., one-fifth of GVA growth and one-sixth of labour productivity growth.

The purpose of this paper is to estimate the effect of durable goods and ICT on euro area (EA) GDP growth and productivity change from 1995 to 2004. In this exercise expenditure on consumer durables is recorded as capital investment. This impacts both the levels and growth rates of the capital stock, productivity and GDP. The advantage of this treatment is that it makes the treatment of consumer durables symmetric to that used in the Systems of National Accounts to account for owner occupied dwellings. As we also account for the effect of ICT the true proximate sources of growth are highlighted.

We argue that households de facto treat the purchase of durable goods as investments. However, this is not captured by the economic analysis based on current statistical conventions. The present System of National Accounts (SNA93) treats consumer durables as a part of private consumption, whereas Dale Jorgenson consistently treats consumer durables as capital inputs both on the output and the input sides. Charles Hulten recently defined investments as such expenditures that are made at the expense of current consumption in order to increase or maintain future consumption.

The results of this paper also show that the new treatment of consumer durables increases annual GVA growth by 0.08 percentage points and labour productivity growth by 0.07 percentage points as the new growth of gross value added (GVA) is two and labour productivity growth is 1.2 per cent. Furthermore, our growth accounting computations demonstrated that the capital services of durables contributed one-tenth of economic growth and one-eight of labour productivity growth. It was no surprise that ICT's impacts were larger, i.e., one-fifth of GVA growth and one-sixth of labour productivity growth.

The combined contribution of ICT and durable capital deepening is the most important component of EA labour productivity growth. The role of other capital deepening is nearly as big. Previously we thought that the deepening of other capital carried by far the largest contribution.

As the outcome of this paper is that the alternative treatment of durable goods as well ICT has a considerable effect on economic growth and productivity, it is not difficult to find a policy recommendation or justification for this paper. This paper emphasises that in fiscal as well as ECB.

The reclassification of durable goods has an effect on GDP. The reallocation of consumer durables to gross fixed capital formation (instead of private consumption) increases output (and possibly intermediate consumption), since investment from the output approach point of view provides a service flow to production. From the income approach point of view this treatment affects two components: operating surplus and consumption of fixed capital. Together these effects are by definition exactly the same size as the service flow effect of the output approach. From the expenditure point of view, durable goods should first be re-classified from private consumption to investment. Second, the value of the service flow has

to be classified as private consumption.

The capitalisation of durable goods has also been suggested to be considered during the currently ongoing SNA update. The proposal was rejected because “consumer durables are not regarded as assets in the system because the services they provide are not within the production boundary”. However, the Inter-Secretariat Working Group on National Accounts proposed to record capitalised consumer durable goods in satellite accounts. Moreover the group recommended showing consumer durable goods as a memorandum item in the balance sheet but not in the totals of non-financial assets.

There are five sources of labour productivity growth. The first one is durable goods' capital deepening, i.e., the share weighted increase of durable good capital services per hour worked. The second source is the share weighted deepening of ICT capital. The third source is the share weighted deepening of other capital. The fourth component is the improvement in labour quality, which is defined as the difference between the growth rates of labour services and hours worked, multiplied by labour’s income share. The fifth component is a general advance in multi-factor productivity, which increases labour productivity point for point.

The EA aggregate is a simple aggregation of available EA Member States (EA-MS).

However, the EU KLEMS database does not include data for all the EA-MS, i.e. Greece, Ireland, Cyprus, Luxembourg, Malta, Portugal and Slovenia do not have any data available in the database. Since Slovenia is a member of the EA only since 2007, and Cyprus and Malta since 2008, it is not necessary to include them in the analysis. Thus, Greece, Ireland and Luxembourg are the only countries for which no data is available and they represent approximately five percent of the EA-GDP in 2006. Therefore, levels in this paper are underestimated by approximately five percent.

The private consumption data is the so-called “Table 5 data” of the ESA 95 transmission programme. This data is available for almost all of the MS. The detail of the data is the two-digit level of the COICOP classification. As discussed later this data is broken down in more detail to estimate the share of durable goods. Unfortunately, more detailed data than 2-digit level data is not available from the international databases. The data is not PPP corrected and therefore, we had to perform the PPP correction ourselves. This has been explained in more

details in the following sub-section.

Stocks of consumer durables

Private consumption can be divided into services and goods that can be classified durable, semi-durable or non-durable. Owing to the lack of detailed expenditure data on durables, we used the same annual shares of consumer durables in each two-digit COICOP consumption group as in our previous work (see table 1) and multiplied these shares with the national two-digit current price consumption expenditure figures of the EA countries.

Estimation of output and value added

In this paper, consumer durables are treated in the same way as imputed rents in the national accounts. In principle, the logic of capitalising durable goods follows exactly the same logic as imputed rents. The SNA postulates that heads of households who own the dwellings that the households occupy are formally treated as owners of unincorporated enterprises that produce housing services consumed by those same households. As well-organised markets for rented housing exist in most countries, the output of own-account housing services can be valued using the prices of the same kinds of services sold on the market, in line with the

general valuation rules adopted for goods or services produced on one’s own account. In other words, the output of housing services produced by owner-occupiers is valued at the estimated rental that a tenant would pay for the same accommodation, taking into consideration factors such as location, neighbourhood amenities, and so forth, as well as the size and quality of the dwelling itself.

The weights of alternative rates of return for durable goods have been calculated from the annual Monetary Union Financial Accounts (MUFA). Three different categories of assets have been used in the calculation: currencies and deposits, shares, and debt securities (including mutual funds). The returns of the currencies and deposits were calculated by using one-month Euribor (Euro Interbank Offered Rate). The returns of shares were calculated by using the Dow Jones Euro STOXX price index, and finally, the returns of debt securities were calculated by using the three-year EA Government benchmark bond yield.

Treating consumer durables as investments has a surprisingly large impact on the level of EA gross value added. The ratio of the output of consumer durables to unrevised GVA (both at current prices) varies between 6.45 and 9.64 per cent annually. On average it is 8.03 per cent in the years 1995-2004 (table 3). The GVA impact is lessening towards the end of the period since the output of consumer durables only stayed level although nominal GVA increased by a quarter in the decade we are observing. The impact of consumer durable assets on the EA

capital stock cannot yet be estimated since the capital stocks underlying the capital service calculations have not been released in the EU KLEMS database.According to the growth accounting results published by the EU KLEMS consortium in November 2007 the EA gross value added (GVA) grew in volume terms on average by 1.92 per cent annually in the years 1995-2004 (table 4). This growth stemmed nine-tenths from the combined effect of the inputs and the rest was attributed to multi-factor productivity (MFP) . One third of economic growth came from labour services and almost sixty per cent from capital services (of which twenty percentage points was related to ICT capital services). Capitalising durables does not radically alter our general perception of the proximate sources of EA economic growth. The relative contributions of the inputs and the

residual remain similar. There are, however, important differences. Economic growth was actually faster than previously perceived (2.00 per cent annually and not. Furthermore, the capital services of durable goods were one-tenth of economic growth. This naturally implies that the contributions of the other inputs were lower.

Another way of looking at economic growth is to decompose it into the impacts of labour input and labour productivity (table 5). Hours worked increased in the observation period at the brisk rate of 0.79 per cent per annum. The new treatment of consumer durables boosted economic growth by 0.08 percentage points annually and labour productivity growth by 0.07 percentage points. Using equation 4 we found that of the new labour productivity growth estimate of 1.20 per cent annually as much as 0.15 percentage points, or one-eighth, was attributed to the share weighted increase of durable good capital services per hour worked by our calculations. One-sixth of labour productivity growth stemmed from ICT capital deepening. Again, the contributions of the other inputs turned out to be lower than earlier

thought. The residual remained unchanged.

Conclusions

The purpose of this paper was to estimate the effects of ICT and durable goods, when they are treated as investments, on EA GDP and productivity growth. The increasing use of technology and the breakthrough of home/entertainment technology in the past few decades emphasises the importance of this kind of analysis. Capitalising consumer durables has a surprisingly large impact on the level of EA economic growth. In relation to unrevised GVA the share is around 8 per cent on average in the years 1995-2004.

Various Factors Influencing the Growth of Durable Goods

The Role Of Superstars

Our calibration of the persistence of the superstar shock is guided by the Gini index for wealth we want to match. However, we cannot estimate this persistence from standard data sets. This is not the case for the process governing regular households’ shocks, which is very close to the idiosyncratic component of the earnings process estimated by Storesletten, Telmer, and Yaron 2004) using data from the PSID. What is the contribution of superstars in shaping the overall level

of wealth inequality? To answer this question, we eliminate the superstar shock and recalibrate all economies so that they still produce the same aggregates. The results are shown in Table 5. The Gini index for wealth falls to 0.645, whereas in the benchmark economy with superstars the Gini index for regular households is 0.75 (its counterpart in the data is 0.77, see Table 1). Importantly, wealth inequality is slightly lower in the benchmark economy than in the one-asset economy and the difference in the Gini indices is about the same magnitude as in the specification with superstars. Thus, adding the superstars not only helps us bring the overall Gini coefficient for wealth closer to that of the data, but it also helps us obtain the implied level of wealth inequality for households outside the top 1 percent of the earnings distribution. Eliminating superstars, however, does not change our main result: the existence of illiquid assets and credit frictions mitigate somewhat the effect of uninsurable idiosyncratic labor risk on wealth inequality resulting in slightly lower inequality.

The Role Of the Persistence Of the Earnings Process

Our benchmark model with illiquid assets and credit frictions delivers just slightly lower wealth inequality than the standard one-asset economy used in the literature. This result is obtained using an earnings process with very high persistence (consistent with the empirical evidence). To determine if our result is robust to this specification, we simulate our model economy using a different transition matrix for the earnings process holding the earnings shocks and the stationary distribution constant. In particular, we keep the probability of becoming a superstar unchanged but assume the probability of being one of the six regular types is the same for all types. The transition matrix is shown in Table 6. We recalibrate the relevant parameters so that aggregate statistics remain the same (the parameter values are in the notes to Table 7). We call this economy

the volatile benchmark economy. With lower persistence in the earnings process, wealth inequality is much lower than before (the Gini index is 0.635 in the volatile bechmark case). Houses are more equally distributed (the Gini coefficient is 0.256) and financial assets are less concentrated (the Gini coefficient is 0.863). Housing wealth as a fraction of total wealth decreases in all quintiles – since earnings shocks are not persistent, households accumulate proportionally more liquid assets. As with the persistent earnings

process, housing wealth as a fraction of total wealth decreases with wealth but the differences across quintiles are less extreme. In the one-asset economy, wealth is also less concentrated (the Gini index is 0.676). Importantly, inequality is still higher in the volatile one-asset economy than in the volatile benchmark economy. Moreover, the difference is now more pronounced. In order to understand why this is the case, it is useful to construct a measure of permanent earnings in our model. Since we abstract from aggregate uncertainty, for any household whose earnings shock in period t is e, we can write permanent earnings, e, as the sum of current and future earnings: The (normalized) permanent earnings shocks with the volatile process and the original process are: {1.00, 1.01, 1.01, 1.02, 1.04, 1.09, 7.38} and {1.00, 1.22, 1.49, 1.84, 2.32, 3.04, 13.07}, respectively. Regular households are much more similar with the more volatile earnings process, they save less, which leads to lower inequality. For the same reason, houses are more similar across households, which results in less differences in wealth composition across quintiles. Furthermore, with less savings, more households are likely to be affected by the frictions of our model, which explains the larger difference in inequality between the benchmark economy and the one-asset economy in this case. However, the difference in wealth inequality across models is still modest in magnitude.

This calibration allows us to illustrate further the predictions of our model regarding the distribution of houses. Table 8 presents key distributional statistics for homeowners in the data (first panel) and in the model with both persistent and volatile earnings (second panel and third panels respectively). With persistent earnings, the Gini index for earnings is lower in the model than in

the data (0.408 vs. 0.479 in the data). This implies lower levels of inequality for any dimension of wealth but, nevertheless, the model with persistent earnings captures the remarkable similarity of the distributions of earnings and houses observed in the data. This feature of the data is not specific to 1998 as shown in Table 9 (although houses are becoming slightly more concentrated than earnings in the recent years). In our model, houses cannot be more unequally distributed than earnings for homeowners because the return to owner occupied housing falls with the size of the house. Note that with volatile earnings, the Gini coefficient for houses is less than half the coef-ficient for earnings (0.179 vs. 0.449).14 What causes this difference? The distributions of earnings and houses are quite close with persistent earnings in our model because permanent earnings and current earnings are highly correlated and households acquire houses according to their permanent income.15 While permanent income still guides house purchases with volatile earnings, current earnings in this case are not highly correlated with permanent income and the distributions are not

alike. In summary, high persistence is necessary to obtain a Gini index for wealth close to the one observed in the data. Nevertheless, earnings persistence cannot be estimated directly using the Survey of Consumer Finances.16 Our analysis in this section suggests that the distribution of houses might be used to discriminate among earnings processes that differ in their persistence. That is, the distribution of houses gives us indirect evidence of the persistence of the earnings process. Changes in the down payment and the adjustment cost Over the last few decades, there has been a significant reduction in the down payment required by

financial institutions as well as a proliferation of home equity loans. In our model, a decrease in the parameter θ captures these financial changes (although we cannot disentangle one from the other). We analyze the effects of financial liberalization on aggregate ratios and on the wealth distribution by simulating our model economy for different values of the down payment requirement (keeping all other parameters constant). A decrease in the down payment requirement relaxes the borrowing constraint. Thus, fewer households are constrained and their purchases of houses increase. Therefore, inequality in houses should decrease (see Table 10). However, because a decrease in θ implies higher borrowing in the economy, financial assets become more concentrated and overall, wealth inequality worsens. In general, the observed effects tend to be small. This is because changes in the down payment affect mainly liquidity constrained households, who are concentrated at the bottom of the wealth distribution.

Since their asset holdings amount to a very small fraction of aggregate wealth, the effect of changing the down payment on total wealth is not large. For instance, the Gini of wealth with no down payment is 0.81, while with a 20 percent down payment it is 0.801. When the down payment is 100 percent, the Gini coefficient for wealth is substantially lower, 0.736. Table 10 demonstrates that the distribution of financial assets across quintiles is significantly more concentrated for lower down payments. The counterpart to this result is in Table 11, where we show that the portfolio of poor households becomes substantially more illiquid as down payments fall. Table 11 also indicates that with lower down payments, the housing stock increases, the capital stock decreases and the interest rate rises (from 3.473 for a 100 percent down payment to 3.996 for no down payment).

With a rental market, as down payments decrease, homeownership increases (results not tabulated for brevity). For example, with a down payment of 50 percent, homeownership is only 49 percent, while with a 5 percent down payment the rate is 83 percent. As a result, inequality in housing decreases considerably more than without a rental market (the corresponding Gini coefficients for housing for a 50 percent and a 5 percent down payment are 0.68 and 0.55 respectively). As before, because there is more borrowing, financial assets become more concentrated with lower down payments. The effect on overall inequality is even smaller in this case and can be non-monotonic in the down payment. For example, going from a 50 percent to a 20 percent down payment leads to less inequality (the Gini index for wealth goes from 0.8116 to 0.809), while going from a 20 percent to a 5 percent down payment increases inequality slightly (the Gini index increases from 0.809 to 0.8121). However, with or without a rental market, when down payments decrease the housing stock increases, the capital stock decreases and the interest rate rises (the equilibrium interest rate in the choice economy with a 50 percent down payment is 3.87 percent while the interest rate is 3.95 percent with a 5 percent down payment).

We also investigate the effect of changes in the degree of illiquidity of houses. In Table 10, we report aggregates with a higher adjustment cost, with no adjustment costs and for an economy with liquid houses and no down payments (ρ = 0, θ = 0). As before, all remaining parameters are kept at their benchmark values. For a given down payment, lowering ρ makes the durable more attractive for households of all wealth levels, which leads to an important increase in the housing stock. Thus, the change in aggregate wealth composition seems more dramatic than the effect of lowering down payments. Since the housing stock increases, the capital stock decreases and the interest rate sharply rises (from 3.71 to 4.25 when going from 10 percent to 0 percent in transaction costs). However, the effect on the wealth distribution is negligible. In terms of wealth composition (see Table 11), decreasing the degree of illiquidity increases the housing wealth to total wealth ratio substantially for the lower quintiles.

Final Comments

In this paper, we explicitly model the existence of illiquid houses that serve as collateral for loans in the context of a heterogenous agents model with uninsurable earnings risk. Our goal is to asses whether the availability of houses mitigates the effect of uninsurable idiosyncratic labor risk on wealth inequality. In our model, households can save in the form of a liquid asset and in the form

of illiquid houses that can be purchased on credit (minus a down payment). Our economy delivers slightly less wealth inequality than the one-asset economy analyzed in the literature. We show that the standard model is indeed equivalent to an economy with liquid houses, a zero down payment and a perfect rental market. The difference in terms of wealth inequality between both economies is small because the frictions of our model (required down payments and adjustment costs) mainly affect the poor who only account for a small fraction of aggregate wealth. Importantly, our two-asset economy has one main advantage over the standard one-asset framework:it allows us to study wealth composition issues. Our model is able to reproduce all main patterns of the U.S. distribution: (1) wealth is more concentrated than earnings, (2) financial assets are more concentrated than wealth, (3) households’ portfolios become more liquid as wealth increases, and (4) the distribution of houses and earnings for homeowners are very similar. A fairly persistent earnings process is necessary to obtain the latter result. We also show that the easing of collateral credit has an important effect on the portfolios of the relatively poor.In this study, we abstract from some important issues that remain topics for future research. The most obvious and potentially important one, is the omission of life-cycle effects. In the data,a household’s portfolio composition varies with age and it would be interesting to analyze whether or not the model can account for the life-cycle patterns of wealth holding and wealth composition. Also, some of the aggregate effects discussed in this paper may be amplified when including life cycle considerations. An further extension could deal with the interaction between collateral credit and earnings ability. For example, access to collateral credit could increase the probability of becoming a superstar.

Role Of Housing Market and House Size In the Evoulution of Durable Goods

In our benchmark economy, houses have a very similar distribution to that of earnings. In the data, however, houses are much more concentrated. In the model, the Gini indices for earnings and houses are 0.499 and 0.483, respectively, whereas in the data they are 0.497 and 0.649. This discrepancy may be explained by the fact that we are abstracting from a housing rental market. Thus, the question we address here is whether the existence of a rental market has an impact on the level of wealth inequality.

To investigate this possibility, we consider an alternative economy with an explicit rental market. Households can obtain housing services either by purchasing them in the market or by buying housing stock. We proceed as in Gervais (2002) and assume there is a financial intermediary that buys housing stock and sells housing services in the market. Our main simplification is that the financial intermediary is not subject to adjustment costs when transacting the housing stock. As commonly used in the tenure choice literature (see Henderson and Ioannides 1983), we assume rental units depreciate at a higher rate than owner-occupied units to capture possible moral hazard problems in the rental market. We have labeled this economy the choice economy (we provide a more detailed description, as well as an equilibrium concept in Appendix B). Importantly, the economy is calibrated so that it produces the same aggregates as both the one-asset and the benchmark economy (parameters shown in Table 3). When calibrating the model we have one extra target, the homeownership rate (roughly 69 percent in the U.S.) and one more parameter, the additional depreciation of rental units, δf . An incremental depreciation of 0.6 percent allows us to obtain our target. The bottom panel of Table 4 presents the comparable wealth distribution measures.

The role of the housing rental market

Without a rental market, all households must buy some housing stock. Therefore, they are forced to keep some savings in the form of the required down payment. However, this wealth is illiquid. Since poor households face more fluctuations in their income than relatively rich households (uncertain earnings are a higher proportion of total income for them), they feel more compelled to build a buffer stock of liquid assets to smooth their nondurable consumption. With a rental market, poor households can rent instead instead of owning a house and they do not need to accumulate extra savings, and as a result, wealth inequality is slightly higher than in the one-asset economy (the Gini index for total wealth increases from 0.801 to 0.809). The effect on total wealth inequality is small because the introduction of the rental market affects mainly the poor who account for just a small fraction of total wealth. However, the effect on the distribution of houses is significant.

The Gini coefficient for houses rises from 0.483 to 0.585, closer to the number in the data, 0.649. In summary, inequality in houses substantially increases when a rental market is introduced but the overall level of wealth inequality rises just slightly.

The role of the minimum house size

In our computation strategy so far, we have not imposed any minimum house size available to consumers. Households can buy or rent whatever size house they desire. In absence of a rental market, imposing a minimum size for the houses individuals can purchase would produce a lower wealth inequality than in the benchmark economy. Without a rental market, households are forced to save more to accumulate the down payment if the house they must purchase is bigger. Poor households, who are most likely affected, have to increase their savings proportionally more than wealthier ones. Also, by increasing the minimum size we are compressing the variance of the housing distribution. As a result, wealth inequality must be lower.

In the choice economy, however, the result would be the opposite. The larger the smallest house available, the higher the earnings of the household who is indifferent between renting and buying, and the higher the fraction of households who rent. Therefore, the fraction of households whose portfolio return is equal to the interest rate is higher, and wealth inequality must be larger the larger the house minimum size. Nevertheless, inequality is never larger than in the one-asset economy, the case in which all households get the same portfolio return. The reason is the following. Consider the extreme case in which the minimum house size is so large that all households rent (and the economy is calibrated to produce the same aggregates). Further, assume that there is no moral hazard problems (i.e., the depreciation rate of owner occupied units and rental units is the same). In this economy, housing services are produced by a financial intermediary nd households only hold liquid financial assets. The financial intermediary decides what proportion of financial assets is rented out to the firm as capital and what proportion is sold to household as housing services (in equilibrium both returns are the same). In the one-asset economy, a household’s wealth is composed of financial assets and houses but both are equally liquid so the two economies are equivalent. This can be seen by comparing the second and fourth panels in below: the one-asset economy and the high minimum size economy just described produce identical distributions.

Technology and Durable Goods

We need to construct measures of output, capital, the stock of houses (Y , K, H), and their investment counterparts according to an appropriate criterion. We use data from the National Income and Product Accounts (henceforth NIPA) and the Fixed Assets Tables (henceforth FAT), both from the Bureau of Economic Analysis. We define capital as the sum of non-residential private fixed assets plus the stock of inventories plus consumer durables. Investment in capital, Ik, is defined accordingly. H is private residential stock and Ih is private residential investment. Finally, we need a measure of output, Y . In our benchmark economy, output consists of labor income plus income from non-residential capital: Y = F(K,L) = wL+rK = C +Ik+Ih. Thus, output is measured as GDP minus housing services.6 We proceed as Cooley and Prescott (1995) to calculate the capital share of our economy. We do not make any imputation to output for government owned capital since are focus is on privately held wealth. The implied share of capital in output is 0.26. The capital-output ratio is 1.64 and the housing-output ratio is 1.07.7 We set the depreciation rate of capital so that it matches the investment-capital ratio, 0.12. The implied steady state interest rate

is 3.91 percent.8 Finally, we need a measure of GDP in our model economy. GDP is simply output, Y , plus housing services. We follow Cooley and Prescott (1995) and set GDP=Y + iH, where i = r + δh is the implicit rental price for housing services. The resulting capital-GDP ratio is 1.51 and the corresponding housing-GDP ratio is 0.98. The aggregate ratio (K + H)/GDP is 2.49. The share of capital income to GDP in our model, once we impute housing services, is 31 percent, slightly lower than that estimated by Prescott (1986). For preferences over consumption of the nondurable good and housing services, we follow Luengo-

Prado (2006) and use the separable utility function u(c, s(·)) = c1−σ 1−σ + γ s(·)1−σ 1−σ . We assume that housing services are proportional to the housing stock and set the constant of proportionality to one. σ, the risk aversion parameter is 2. The calibration of γ and δh is not straightforward due to the presence of adjustment costs. In the steady state, Ih is δh H plus the aggregate adjustment cost. We choose values for γ and δh to jointly match the ratio of housing to nondurable consumption and the housing-output ratio in NIPA (H/C = 1.40 and H/Y = 1.07, respectively). This implies γ = 0.166 and δh = 0.0367. The discount factor, β = 0.9006, is such that the net interest rate in the steady state is 3.91 percent.

We use a down payment of 20 percent, slightly below the 25 percent average down payment for the period 1963-2001 reported by the Federal Housing Finance Board. Thus, individuals can borrow up to 80 percent of the value of the durable.9 While in reality households may be able to acquire houses with lower down payments, it is also the case that these households face higher marginal borrowing costs (including a higher interest rate and the purchase of mortgage insurance). To keep the model tractable, the down payment parameter is the same for all consumers and the borrowing rate is not a function of θ. We report results for higher and lower down payments in section 5 to assess the robustness of our results.

We consider non-convex costs of adjustment in the market for houses, which result in infrequent changes of the residential stock. We assume households pay the adjustment cost every time the value of the stock changes. The idea underlying this assumption is that a household can buy a house of any desired size, but once it has been bought the stock is illiquid. In order to change the house, the household needs to sell the stock and selling it entails transaction costs. We assume that right after consuming housing services the stock depreciates at the rate δh, and that if a household lets the house depreciate, the household must pay the adjustment cost (i.e., we force households to do maintenance of the stock).10 In particular, the specification of the adjustment cost is:τ (h , h) = Iρ(1 − δh) h, (9)where I = 0 if h = h, and 1 otherwise. This cost can be seen as a loss in the selling price when changing the housing stock. Note that once the household decides to change the stock, the adjustment cost is proportional to the inherited level of residential assets, ρ (1 − δh) h. With this specification, the transaction cost does not quickly diminish in importance as households become wealthier, as with a purely fixed cost. In our benchmark case, we set ρ equal to 5 percent (the typical fee charged by real estate brokers in the U.S. economy is around 6 percent). Computational details on how to compute the model are given below.

In an economy with no transaction costs, a zero down payment, and a perfect rental market, the return to financial assets is the same as the market return for housing. Therefore, the household portfolio composition cannot be determined. Additionally, the consumption of housing services is not tied to the household’s holdings of residential assets. Households can acquire additional housing

services or sell housing services to others in the rental market. In this case, the price of housing services affects the composition of the consumption basket (nondurable consumption vs. housing services) but not the savings decision. Thus, the household problem can be written in terms of two state variables, earnings and total assets (a + h). More details are given in Appendix A. Our calibration strategy is such that both the benchmark economy and the one-asset economy produce the same capital-output, housing-output and housing-nondurable ratios. The parameter in the utility function, γ = 0.161, is chosen to match the ratio of residential stock to nondurable consumption in the data, H/C = 1.40.11 The depreciation rate of houses, δh, is set so that it matches the housing investment-stock ratio in the data, 0.043. The discount factor, β = 0.904 is chosen so that the ratio of total wealth to GDP, (K + H)/GDP is equal to 2.49. The share of capital and the depreciation rate of capital do not change. Table 3 summarizes the calibration parameters for both the benchmark economy and the one-asset economy (the other rows in the The wealth distribution Table 4 shows wealth distribution and wealth composition statistics for the benchmark economy that we can compare to the ones from the data summarized in Table 1. Wealth is unequally distributed with a Gini index of 0.801 (this is because of our calibration strategy). In our model as in the data, houses are more equally distributed than financial assets. The Gini coefficient for houses is 0.483 (0.649 in the data), while the Gini coefficient for financial assets is 0.93 (0.945 in the data).12 Also, houses represent a smaller proportion of wealth for the rich (as in the data). Since the return to housing is the marginal utility of the services it renders and marginal utility is decreasing, this is not surprising. The model fares remarkably well in the wealth-composition dimension given that we abstract from several factors that may affect the composition of a household’s portfolio,such as taxes, house price changes and life-cycle effects. For instance, our model predicts that households in the bottom 40 percent of the wealth distribution hold, on average, 339 percent of their wealth as houses, whereas this number is 280 percent in the data. For the top quintile, the predicted ratio in the model is 24, while it is 27 in the data. Next, Table 4 presents wealth distribution statistics for the one-asset economy. In this case, we cannot distinguish between financial assets and houses and concentrate on total wealth. The Gini index for wealth is slightly lower in the benchmark economy than in the one-asset economy, 0.801 and 0.816, respectively. Inequality is lower in the benchmark economy (which does not allow for a rental market) because all households have some wealth in the form of the required down payment. The difference between both economies is small because the frictions of our model (down payments and adjustment costs) mainly affect the poor who only account for a small fraction of aggregate wealth. In the one-asset economy, both the down payment and the adjustment cost are zero (as opposed to 20 and 5 percent,respectively, in the benchmark case). That is, there is more credit and more liquidity in the one-asset economy than in the benchmark economy. Lowering the down payment only affects households who are constrained at the margin, typically poor households. Moreover, the larger the house a individual owns, the higher the possible loan. That is, collateralized loans of this type provide more credit to households who may need it less. In addition, wealthy households do not need to change their houses as often as less wealthy ones, the reason being thatthe variance of their income is lower than that of poor households because earnings represent a lower fraction of their income. Aside from houses being illiquid, we have made two assumptions that may be important for understanding the differences between the benchmark economy and the one-asset economy. The first is the absence of a housing rental market. The second is the minimum house size that a household can purchase. We analyze each in turn.

Wealth Distribution and Durable Goods

In the United States, wealth is significantly more unequally distributed than earnings. Models with uninsurable idiosyncratic labor risk have been used widely to study the determinants of wealth inequality across households and to try to understand this fact. In these models, wealth inequality arises because a market to insure specific earnings risks does not exist and households self-insure by accumulating an asset (assumed to be perfectly liquid) that is used to smooth consumption over time. Our contribution is to quantitatively study the determinants of wealth inequality in economies where households not only accumulate liquid financial assets, but can also save in the form of illiquid assets such as a house. In reality, houses also provide collateral for loans. The question that we address is whether the inclusion of illiquid assets that serve as collateral amplifies or mitigates the effect of uninsurable idiosyncratic labor risk on wealth

inequality. 

This project is motivated by the fact that houses comprise almost 40 percent of the total wealth held by households in the U.S. economy. Moreover, according to the Survey of Consumer Finances, 92 percent of all available credit to consumers is collateral credit. Collateral debt accounts for 15.5 percent of aggregate household net worth and the average ratio of collateral credit to total debt across households is roughly 79 percent.In this post, we build a general equilibrium model economy of ex-ante identical households who face uninsurable idiosyncratic shocks to their labor endowments. Households have two means of

saving: liquid financial assets and illiquid houses. We model houses as assets that can be adjusted to any level at a given non-convex cost. Furthermore, houses can be financed (minus a down payment) and can be used as collateral for home equity loans. For simplicity, we allow no other form of credit. In our model, households derive utility from consumption of a nondurable good and durable goods from housing services. We assume there is no rental market for houses so households obtain housing services by purchasing residential stock. We calibrate the model economy so that its steady state statistics match selected aggregate statistics of the U.S. economy and data on the earnings distribution. In particular, we construct an earnings process that is a mixture of a process estimated directly from the data plus an extra shock that allows us to jointly match the observed level of earnings and wealth inequality. We assume there are two types of households, regular households and superstars.

The process that governs the earnings of regular households is calibrated using data for households outside the top 1 percent of the earnings distribution of households with positive earnings in the 1998 Survey of Consumer Finances (SCF-98), and is very similar to the idiosyncratic component of the earnings process estimated by Storesletten, Telmer, and Yaron (2004) using the Panel Study

of Income Dynamics (PSID). We calibrate the superstar shock level and its persistence so that the overall Gini index for earnings and wealth match those observed in the data. Our goal is to assess the role of illiquid assets in explaining the wealth distribution. To this end, we must compare our benchmark economy to the standard economy without illiquid assets considered in the literature. This comparison is not straightforward. We show that, in fact, Aiyagari’s (1994) economy is equivalent to an economy with liquid houses, no down payments, home equity loans with a loan-to-value ratio of 1, and a perfect rental market. We call this economy the one-asset economy. Using the same earnings process, we calibrate the one-asset economy to produce the same aggregates as our benchmark economy. We find that with illiquid assets and limited collateral loans wealth inequality is just slightly lower than in the one-asset economy. Wealth inequality is lower because the credit restriction implies that all households must hold some wealth in the form of the required down payment (this is not the case in the one-asset economy). The difference is small because the frictions of our model (required down payments and adjustment costs) mainly affect poor households that only account for a small fraction of aggregate wealth. Eliminating the superstars, introducing a rental market, or imposing a minimum size for the houses that households can purchase does not change our conclusions. However, when we lower the persistence of the earnings process, the frictions of our model have a larger effect because more households are affected by them.

 

In summary, the standard one-asset economy analyzed in the literature implicitly allows for collateral loans and the fact that one asset is illiquid does not have much of an effect over the wealth distribution. Nevertheless, our richer model allows us to study other dimensions of wealth inequality. For example, financial assets are more concentrated than total wealth, while residential assets are less concentrated than total wealth. Our model can replicate and explain these facts easily. Furthermore, we document that the earnings and the housing distributions are remarkably similar in the United States. Our model can account for this fact as long as the earnings process is fairly persistent. Finally, we can use our framework to analyze how changes in down payment requirements and the availability of home equity loans affect the economy. We find that as collateral credit expands, total wealth decreases, the interest rate increases and wealth inequality—measured by the Gini index—may worsen (more details are given throughout the paper). Furthermore, the easing of credit has a significant effect on the portfolios of poor households.

Merging With Durable Goods

Merger analysis requires an assessment of the extent to equipment was not likely to sustain collective dominance).The market for tractors provides a good illustration of the constrained after the merger. In durable good industries, significance of durability. First, the rate of depreciation is an important factor can be the potential for the existing relatively low for tractors: our econometric estimates based stock of used machines to act as a constraint on the on new and used equipment prices suggested an average behaviour of new equipment manufacturers. Should we depreciation rate of only about 8% in Europe. Second, data worry less about a merger when the product is “durable” - used to forecast the sale of used tractor parts indicated that is, when it has a long useful life. Third, the demand for new tractors has been in long-term decline (tractor sales in the Durable products stay around a long time. Much machinery EU have declined from over 300,000 units per year in the and industrial equipment is designed to last, and its useful late 1970s to around 175,000 in 1998). The long-term life can often be stretched through increased maintenance. decline in the demand for new tractors is expected to Many products have a lively second-hand market. What continue, suggesting there will be ample availability of used would happen if manufacturers of durable new equipment.

Against this background, we estimated that the value of key characteristic of durable goods is that they provide stock of used equipment in service is large relative to new a stream of services over an extended period of time, often equipment, even when such calculations are based on the long after the sale. It is these services which their buyers depreciated value of used equipment (not simply the ultimately value - a machine allows a flow of production number of pieces of equipment in service). Taking into services over time; a vehicle gives a flow of transport account age and depreciation rate, we found that the services, etc. Once a durable good has been sold, the depreciated value of the stock of used tractors in Europe is supplier has very limited control over the services which a large multiple (as much as 11 times) that of new tractor that good produces (essentially only through its spare parts sales. This large stock of available used equipment

policy). In future years, these services will effectively suggests that attempts to increase the price of new tractors provide competition to the sales of new durable goods - would require a very large reduction in sales - basically, future buyers can decide whether to purchase a new because new tractor sales account for only a small machine, or whether to achieve the same (or similar) effect proportion of the total “stream of services” derived from by making use of an existing machine which is already in tractor use each year. The greater the required output the market (at least if there is no major technical change)restriction in order to achieve a given price rise, the less likely the price rise is to be profitable. If the price of the new good rises, customers may be able to use their existing equipment more intensively,Further, tractors are not used very intensively in

extend its life, perhaps by spending more on maintenance.The average annual usage is 750 hours, which suggests Customers who would previously have considered buying a considerable scope for more intensive use. There is also new good might instead buy a slightly less new, second- clear evidence that demand is very sensitive to farm hand one. The existence of a stock of used goods - income, which suggests that the timing of purchases is not whether in operation or sitting on dealers’ lots - can thus driven purely by the age of the equipment, but rather that increase the elasticity of the demand facing new equipment farmers have considerable discretion in choosing when to manufacturers, and reduce the attraction of post-merger buy a new tractor (our estimates suggest that a 1% decline price increases. This has the potential to reduce the

in real net income per farm is associated with a 2.5% market power enjoyed by durable goods suppliers, and 1decline in sales of new equipment) hence may affect the merger analysis.Markets for second-hand tractors are well developed, and the case of agricultural equipment sales of second-hand tractors in each year are between the recent New Holland/Case merger (Case No. IV/M. and 3 times sales of new tractors. Moreover, there are 1571) between producers of agricultural equipment is an relatively few customers in this market with strong example of a market where the constraining effects of an preferences for new goods. 

Information on a sample of the existing stock of goods were highly plausible, although the sales of new and used tractors between 1996-98 for which European Commission’s Merger Task Force cleared the financing was obtained, suggest that relatively few farmers merger on more conventional grounds (it concluded that exclusively purchase new equipment. Among farmers who the market share distribution in the supply of new purchased multiple tractors between 1996-98, including at least one new tractor, nearly 60% also purchased a used tractor. Significantly, the price of new and used tractors were also highly correlated, suggesting that they compete in the same market.

1. The pricing of durable goods in general - whether by a monopolist or by competing suppliers - has been extensively analysed.

2. Economic literature (much of it focusing on suppliers’ and customers’ New Holland and Case ranked respectively in first and fourth place

incentives for making a sale/purchase today, as opposed to waiting). in the sale of tractors in Europe.

The need for pragmatism A contrast: commercial aircraft

However it would be wrong to infer from this example that It is instructive to compare the case of agricultural the stock of consumer durable goods will always be able to constrain equipment with the 1997 Boeing/McDonnell Douglas new good prices. There are circumstances in which the merger in commercial aircraft. The durable good argument used stock clearly is not equivalent to a competitive supply. was advanced at the time by the merging parties, but in Sometimes the stock is almost completely utilised and the our view a close empirical analysis showed that the ability to extend its life or use it more intensively is limited. conditions under which the stock of a durable good can do.Under these circumstances, the supply elasticity of the constrain the price of a new good were not met.Used stock may be close to zero - i.e. if the merged parties For example, the supply elasticity of used aircraft was were to raise prices, the extent to which the output found to be virtually zero: only a small fraction of the stock extracted from existing stock could be increased would be of surplus used (parked) aircraft could economically be very limited. And if in addition entry is unlikely to occur, and returned to service (only 180 estimated units world-wide, demand is growing fast, then durability cannot prevent the against new demand for 16,000 new aircraft required over exercise of market power. the following 20 years). This was unlikely to constrain the Whether the existence of a used stock has any effect on price of new aircraft given also the high average age of the the market power of new equipment suppliers is entirely an world-wide fleet and rapid anticipated demand growth (the empirical question, determined by the facts of the particular fleet of 9,000 was to be almost entirely replaced, and its case. It is important for policy to be able to identify in size almost doubled, over the same period). Bringing the practice the circumstances under which durability can or parked aircraft into service could have deferred at most cannot constrain the prices charged by new goods 30% of the first year’s expected purchases of new aircraft.

As a first step towards this, a simple checklist further, airlines work their equipment hard and have only can be applied at least to screen cases where the limited ability to use their existing stock of aircraft more constraining effect of used equipment is plausible from intensively to obviate the need for a new plane. The ability cases where it is not to defer retirement of existing aircraft was also limited, and even if retirement of existing aircraft could have been reduced by 5-10% this would have resulted in an increase Used equipment will be more likely to provide a constraint in the aircraft stock of only 20-40 units in each year.on post-merger incentives to increase price if:Unlike agricultural equipment, there were no third party (a) it is economical to use the stock more intensively suppliers of parts and services. It was plausible that

and/or the useful life of the equipment can be Boeing could have been able to render the stock of extended if the price of the new good rises, thereby McDonnell Douglas or older Boeing aircraft obsolete and reducing the demand for new equipment; thereby make it more difficult for airlines to extend the

(b) there is no substantial fraction of consumers with a useful life of the stock strong preference for new goods (especially if manufacturers can price-discriminate between those These factors suggested that the durable nature of aircraft who do and those who do not value newness); could at most increase slightly the elasticity of industry (c) goods do not depreciate rapidly, and technical change demand for new aircraft, but not make it large. Hence is not too fast, so existing products are reasonable durability was unlikely to eliminate any anti-competitive substitutes for new products; impact of the merger.(d) demand growth is slow, so it is more likely that customers can meet their demand by using the stock 

Enforcement agencies have been traditionally resistant sales of new equipment are not high relative to the durable goods arguments because of the potentially far-existing stock, so new goods suppliers would have to reaching implications for the analysis of mergers. However decrease their sales substantially to have any there are good economic reasons why durability can appreciable upward effect on prices; constrain future price increases for new equipment. manufacturers do not control the maintenance of the stock, so owners should have no problem obtaining The effectiveness of this constraint will of course depend parts and service and manufacturers cannot on the specific industry circumstances. Certainly the accelerate its obsolescence; likelihood that used tractors constrain the price of new goods are sold rather than leased, so that the tractors does not extend automatically to other durable remaining “stream of services” embodied in the goods. For example, the rate of depreciation of tractors is existing stock of equipment is controlled by customers low relative to durable goods such as cars and trucks(or second hand re-sellers), and not by the new goods (which typically have much shorter lifetimes). 

In these industries would therefore be less effective in constraining the price of new equipment. Similarly, rapid the more of these conditions are satisfied, the more technological changes in durable goods such as computer plausible it is that durable goods will constrain the ability of and telecommunications equipment make these types of new equipment manufacturers to raise price following a used goods less effective in constraining the price of new merger. Furthermore, the durable nature of goods makes equipment. Only an extensive empirical assessment can oligopolistic coordination (‘collective dominance’) establish whether the existing stock of used equipment can significantly more difficult to achieve. indeed provide a credible competitive constraint which will prevent prices from rising.

Production Capacity and Competition For Durable Goods

The basic theory concerns a monopolist with no threat of competition facing identical consumers, and abstracts from the learning curve, substitute products and other features of durable goods manufacturing and sales, many of which work to slow market penetration relative to the rate predicted by the theory. The main conclusion of the theory is that, for common interest rates and other parameters, we should expect full market penetration to require ten to twenty years or more. Moreover, when the goods are imperfectly durable, full penetration can require fifty years or so. The theory suggests that penetration requires a long time relative to the actual rate of penetration of cellular phones, VCRs, camcorders, palm computing devices and other imperfectly-durable consumer durables. In such cases, the crash is small, while fast penetration necessarily requires that a significant crash occurs around the time of full market penetration, when the market

switches from new sales to replacement sales.

The basic theory has the feature that market penetration is efficient, for the intuitive reason that the monopolist is capturing all the of the value of production, and thus desires to maximize that value and hence chooses an efficient capacity. Thus, the long times to market penetration are a feature of efficiency as well as monopoly. The time to market penetration is decreasing in the durability of the good, and tends to be U-shaped in the interest rate. For low interest rates, there is little gain from fast penetration, because everyone is patient, and thus it pays to use capacity over longer times to satiate the market. For very high interest rates, the profitability of the market is reduced, and the firm slows market penetration in response, converging to an infinite time to market penetration for a finite interest rate that makes the production unprofitable.

Does competition speed up market penetration? We will show that in one sense, the answer is yes – the more firms there are, the faster is the market penetration. However, this increase in speed will not be adequate to overturn the conclusions of the basic theory. The basic theory considered a seller who did not undercut itself over time, even when the market reached saturation. With competition, such a path becomes implausible, and prices will tend to converge to marginal costs over time, a feature of the theory known as the Coase conjecture. It turns out that while competition accelerates market penetration, penetration converges to the basic theory solution as the number of firms goes to infinity. This is quite sensible: a monopolist that can capture all the value of its sales produces efficiently, as does the perfectly competitive industry; an imperfectly competitive industry is slower to saturate the market as a means of propping up the price. The case of monopoly divides into two types – the efficient monopolist and the monopolist who competes, imperfectly, with future incarnations of itself. The former is efficient, the latter the slowest to market of all. Most relevant economic theory has been focused on Ronald Coase’s wonderful 1972 conjecture that a monopolist of a durable good will have an incentive to cut the price, and when the monopolist can cut the price sufficiently rapidly, the monopolist will price near marginal costs. For example, Gul, Sonnenchein and Wilson (1986) demonstrate that the Coase conjecture is a feature of stationary equililbria. Kahn (1986) demonstrates that increasing marginal costs insure that even the continuous time limits of discrete time games have positive profits, although these profits are lower than those which would arise on the commitment path. By positing a fixed, albeit endogenous, initial capacity, we sidestep the Coase conjecture, because the seller cannot sell the large quantities required by the Coase path. In one sense the Compaq ipaq story is unusual because Compaq did not price the 3600 series to capture the high prices created by the shortage. Consequently, an important part of the analysis of pricing concerns the optimal price path. We are used to the rapid decline in prices of consumer electronics. Prices may start high, but rapidly fall to a small fraction of their initial levels as mass production and competition take hold.

A Basic Model of Monopoly

Consider the introduction of a new durable product by a monopolist. The product’s durability, d, is the rate at which the product fails; this is modeled for convenience as an exponential, so that a product sold at time t is still operating at time s with probability e -d(s-t). Let r be the rate at which future profits are discounted, so that profits received by the firm at time t have a present value of e -rt.

Conclusion

This paper presents a theory of manufacturing capacity choice for a durable good. The remarkable conclusion is that efficient production may entail ten to fifty years before full market saturation is reached. The time to market saturation is increased as the good becomes less durable, and the size of the crash when saturation is reached falls as the durability decreases. The monopoly seller is efficient provided he doesn’t ever undercut himself, a feature of some equilibria of the “gap” case, where demand exceeds marginal costs. With competition, either on the Coase path for a monopolist, or with multiple producers, market penetration may arrive only in the limit as time diverges, with sellers producing only the amount that replaces a satiated market. This situation arises only if the depreciation rate of the good is larger than the interest rate, and may not arise when the number of competitors exceeds two, depending on the cost of capacity. In such a case, there is no crash, only a soft landing as the market is satiated, with a growth rate converging to zero. Increases in the number of competitors speed product introduction, converging to the efficient level as the number of competitors goes to infinity. In addition, increases in the depreciation rate of the good also tend to increase the time to market saturation.

Durable Goods - Understanding Volatility In Global Trade Of Durable Goods - Part 2

Here we present some descriptive statistics on trade flows that help to motivate our model of trade in durables. We use our 25 OECD country data from NBER-UN World Trade Data and use the latest available data (year 2000) to calculate the share of durable goods in international trade. The original data are at 4-digit SITC levels. We aggregate them into 1- and 2-digit levels for each country. Then we use the information of the SITC classifications to classify imports and exports into durable and nondurable goods. At the 1-digit SITC level, there are 10 categories (0-9). Categories 0 (FOOD AND LIVE ANIMALS), 1 (BEVERAGES AND TOBACCO), and 4 (ANIMAL AND VEGETABLE OILS, FATS AND WAXES) are obviously nondurable goods. It is also straightforward that category 7 (MACHINERY AND TRANSPORT EQUIPMENT) belongs to durable goods. Category 2 is raw materials that exclude fuels such as petroleum. Category 3 contains energy products such as coal, petroleum, gas, etc. The remaining categories however are difficult to classify. This is particularly true for category 5 (CHEMICALS AND RELATED PRODUCTS, N.E.S.). Even if we go down to the 3-digit level, it is still unclear which categories belong to durable goods.

We find that this category includes many nondurable goods, such as fertilizers, medicines, cleaning products, etc. To avoid exaggerating the share of durable goods, we put the whole category 5 into nondurable goods. But we note that this category does include some durable goods, such as plastic tubes, pipes, etc.
For categories 6, 8 and 9, we go down to the SITC 2-digit levels for more information about the durability of goods. Category 6 (MANUFACTURED GOODS CLASSIFIED CHIEFLY BY MATERIALS) classifies goods according to their materials. We assume that goods produced from leather, rubber, or metals are durables (61-62 and 66-69). Goods produced from wood (other than furniture), paper, or textile (63-65) are nondurables. Category 8 includes other manufactured products that are not listed in categories 6 and 7. We assume that construction goods (81), furniture (82), professional instruments (87), photographic equipments
(88) are durable goods. Travel goods (83), clothing (84), footwear (85) and remaining goods (89) are classified as nondurables. Category 9 includes products that are not classified elsewhere. In this category, we assume that coins and gold (95-97) are durables. All remaining products are classified as nondurables.
It reports the share of durable goods in imports and exports in our 25 OECD country dataset.An average durable goods account for about 60% of total imports and exports in these countries. If we exclude raw materials (SITC 2) and energy products (SITC 3), the share increases to 70% . We find that about three quarters of trade is in durable goods in the US if we exclude energy products, which is in line with the finding of Erceg, Guerrieri, and Gust (2006). We note some outliers for exports. More than 50% of exports in Australia and New Zealand are in categories zero (FOOD AND LIVE ANIMALS) and two (CRUDE MATERIALS, INEDIBLE, EXCEPT FUELS). 65% of exports in Iceland are FOOD AND LIVE ANIMALS. Norway exports a significant amount of energy products. After we exclude
raw materials and energy products, Australia and Norway become close to our sample mean. Iceland and New Zealand still export a much lower share of durable goods than other OECD countries. But our overall results confirm that durable goods account for a large portion of international trade for OECD countries. In particular, category 7 (MACHINERY AND TRANSPORT EQUIPMENT) on average accounts for more than 40% of trade for OECD countries.

A Two-country Benchmark Model

There are two symmetric countries in our model, Home and Foreign. We depart from the standard models that were once used in performing these calculations, by having two production sectors in each country: the nondurable good and durable good sectors. All firms are perfectly competitive with flexible prices. Nondurable goods can only be used for domestic consumption. Durable goods are traded across countries and used for durable consumption and capital accumulation. Because of the symmetry between these two countries, we describe our model focusing on the Home country.

Our modeling strategy is motivated by the empirical regularities discussed below. As we have noted, in order to explain the high volatility of imports and exports, it is not promising to rely on the response of these variables to price changes. That would tend to make imports and exports negatively correlated, but in fact they are positively correlated. Instead, we note that changes in capital stocks can be very volatile in response to persistent changes in productivity. It is well known that investment is very volatile and pro-cyclical. However, it would be unrealistic to attribute all of the movements in imports and exports to trade in capital goods. In order to match the movements in trade volumes, we would need to ascribe an unrealistically high share of trade to trade in capital goods. Instead, we add trade in durable consumption goods to the model. This is a plausible avenue to explore, because Baxter (1995) has shown that about two-thirds of trade is in either capital goods or durable consumption goods. We suspect that in fact this is an underestimate of the share of durables, since many goods that have characteristics of durables - such as clothing - are classified as nondurables. It is intuitive.We list all equilibrium conditions for both countries in developed as well as underdeveloped categories and that a large fraction of trade is in durables. Nondurable goods are typically more perishable, and thus more expensive to ship than durables.The standard RBC models are able to capture the pro-cyclicality of imports and exports, and the countercyclicality of the trade balance by introducing capital goods. But they are unable to match the volatility because most trade is in consumption goods, so the fraction of trade accounted for by investment goods is too small to account for the overall volatility of trade volumes. However, recognizing that much of trade in consumption goods is trade in consumer durables, we are able to simultaneously reconcile the volatility and cyclical behavior of imports and exports. We are able to match the business cycle facts on trade without giving up realism in other dimensions, particularly in the characteristics of consumption behavior over the business cycle. That is because we recognize that a large fraction of consumption is in services, which we model as a nondurable nontraded good.

Trade in capital goods and consumer durables would introduce too much volatility in trade if we did not allow for some sort of installation cost. This is a well-known feature of international RBC models. But this also allows us to build a model consistent with another widely-recognized fact: that trade elasticities
are higher in the long run in response to persistent shocks than they are in the short run. In our model, home and foreign durable consumption and capital goods are close substitutes, but the sensitivity over the business cycle to relative price changes is low because of these costs of adjustment. In addition, we introduce an iceberg cost of trade. Here, we want to capture the idea that there is “home bias” in consumption of durables, as well as in the use of capital goods in production. Especially for large economic areas such as the US or the European Union, imports are a relatively small component of the overall consumption basket, or mix of inputs used in production. Because we model traded goods as being highly substitutable in the long run, it does not seem natural to simultaneously introduce home bias directly into the utility function or production function. Instead, and consistent with much of the recent literature in trade, we posit that there are costs to trade which lead to this home bias even in the long run.We note that there is a tension in modeling the behavior of trade volumes over the business cycle. Imports and exports are pro-cyclical and their standard deviation (in logs) is much larger than that of GDP.At the same time, they are apparently not very responsive in the short run to price changes. The model of consumer durables and investment goods captures these features for reasonable parameter values. We discuss the calibration in below, after the theoretical presentation of the model.

We calibrate our model such that in the steady state, the structure of the economy is the same as in below. Details about how to solve the steady state can be found below. In our benchmark economy,
nondurable goods account for 60% of total output and durable goods account for the remaining 40%. Among the durable goods, half of them are used for consumption (equivalent to 20% of total output) and the other
half are used for investment (equivalent to 20% of total output).17 Among durable consumption goods, 65% are used for domestic consumption (equivalent to 13% of total output) and 35% are used for exports (equivalent to 7% total output). Among durable investment goods, 70% are used for domestic investment
(equivalent to 14% of total output) and 30% are used for exports (equivalent to 6% of total output). In this economy, the investment accounts for 20% of total output and the consumption (durable plus nondurable) accounts for the remaining 80%. The trade share of output is 13%. Those features match the US data
closely. It shows parameter values that we use to match our benchmark model with the described economy structure. We set the shares of home goods in capital ( ) and durable consumption ( ) at 50%. That is, there is no home bias exogenously built in our economy structure. Instead, we generate the observed low
trade share from the iceberg trade cost . We will discuss this more later. As in Backus, Kehoe, and Kydland (1992), the capital share in production  is set to 36%, and the subjective discount factor is set to 0.99, which gives a 4% annual real interest rate. The depreciation rate of durable consumption  is set
to 0.05, which implies a 20% annual depreciation rate for consumption durables. A similar depreciation rate has been used in Bernanke (1985) and Baxter (1996).

Given those parameters, we choose other parameters to match the economy structure as discussed below. We first choose the preference parameter μ and the depreciation rate of capital  jointly to match the relative size of durable and nondurable good sectors, and the size of investment in durable goods. μ is set to 0.23 and
 is set to 0.013 such that 1. the durable good sector accounts for 40% of total output and, 2. the investment accounts for 50% of durable goods, or equivalently 20% of total output. Consumption durables account for the remaining 50% of durable goods, or equivalently 20% of total output. The trade cost ( ) and the elasticity of substitution between the home and foreign goods are calibrated to match two empirical findings:

1. The trade share of total output is about 13%;

2. The long-run elasticity of substitution between the home and foreign goods is high. In our calibration, the long-run elasticity of substitution between the home and foreign capital () is set to 9.1. The elasticity of substitution between the home and foreign durable consumption  is set to 6.85. In the steady state, the trade in capital goods (durable consumption goods) accounts for 46% (54%) of total trade. The above calibration of and  implies an overall elasticity of 7.9, which is the same as in Head and Reis (2001).18 The trade cost ( ) is calibrated to 0.1, that is, 90% of goods arrive in their destination countries in the international trade. For given and , this trade cost generates a trade share of 13%.We use different values for and  to generate different home bias levels for capital and durable consumption.

Capital is more biased towards home goods than durable consumption (70% vs 65%). For given trade cost, the degree of home bias increases with the elasticity of substitution. So we assign a higher elasticity of substitution to capital goods. Alternatively, we can assume the same elasticity of substitution, but higher trade cost for capital goods. In either method, capital can have a higher level of home bias than durable consumption. We used the first method because it matches a pattern observed in the data. For given decrease in trade cost, the first method predicts that the share of investment goods in international
trade increases relative to the share of durable consumption. Intuitively, the investment goods are more substitutable across countries than durable consumption under this setup. So when the trade cost decreases, there is more substitution for investment goods than for durable consumption. As a result, the share of
investment goods in the trade increases. We then plot this prediction from the model. The same pattern is also found in the US data: from 1994 to 2006, the share of capital goods except automotive in total export
goods increased from 34.4% to 45.1%.19 The preference parameters and  are set to their standard levels used in the GHH utility function. The parameter is chosen such that the labor supply is one third in the steady state. We assume that the elasticity of substitution between the durable and nondurable consumption is low. The adjustment cost parameters of durable consumption (1) is chosen to match the volatility of durable consumption, which is about three times as volatile as output in the data. The adjustment cost of capital stock (2) is calibrated to match the volatility of investment, which is about three times as volatile as output in the data.

We follow Erceg and Levin (2007) in calibrating the productivity shocks in the durable and nondurable goods sectors. However, there is no information about the cross-country spillovers of those shocks in their closed-economy model. Empirical findings usually suggest small cross-country spillovers. For instance,
Baxter and Crucini (1995) find no significant international transmission of shocks, except for possible transmission between US and Canada. In Kollman’s (2004) estimate between the US and three EU countries, the spillover is 0.03. In Corsetti, Dedola, and Leduc (forthcoming), the spillover is −0.06 for traded goods and 0.01 for nontraded goods. We will first set those spillovers at zero and then choose some values used in the literature to check whether our results are robust under different shock structures.

Performance of Benchmark Model

The model is solved and simulated using the first-order perturbation method. The model’s artificial time series are logged (except for net exports) and Hodrick-Prescott (H-P) filtered with a smoothing parameter of 1600. The reported statistics in this section are averages across 100 simulations. Our benchmark model
performs well in three broad categories. First, the model can match the observed IRBC statistics, including the “trade volatility” and “positive comovement” of imports and exports as documented in a suervey. Second, the model can replicate the elasticity puzzle in the trade literature. Finally, our model can replicate
the Backus-Smith puzzle and offers some new insights on this puzzle.

International RBC Statistics

It shows simulation results for four models. In the benchmark model, we assume that there is no spillover of productivity shocks across sectors and countries. But innovations in durable good sector are positively correlated across countries. In the model of High Correlation, the correlation of innovations is
set to a higher level as in Corsetti, Dedola, and Leduc (forthcoming). Models High Spillover and Medium Spillover allow spillover of productivity shocks across countries. In the model High Spillover, the spillover coefficients is set to 0.088, which has been used by BKK. In the literature, smaller values have also been
used. So in the model of Medium Spillover, we set this parameter to 0.044. All of these models can match data fairly well in the following respects:

1. The models can replicate the volatility (relative to that of GDP) of aggregate variables such as consumption, investment, durable consumption, and labor.

2. Real imports, exports and net exports are as volatile as in the data. That is, our model can successfully replicate the excessive volatility of imports and exports.

3. Both imports and exports are pro-cyclical and positively correlated with each other. Net exports are
counter-cyclical.

4. The CPI-based real exchange rate is about twice as volatile as GDP.

A noticeable difference between our benchmark model and the models with cross-country correlation of technology shocks is that the volatility of imports and exports decreases when we allow spillovers. This result is consistent with BKK’s finding that net exports become less volatile when cross-country spillovers
increase. But even when we set the spillover coefficient at 0.088, which is relatively large in the literature,imports and exports are still about two times as volatile as output. If we set the spillover coefficient to a moderate level of 0.044, the simulation results are very close to our benchmark results.In all of our calibrations, we note the following shortcomings: As in almost all RBC models, real exchange rate volatility is still lower than in the data. However, our model does quite well relative to the literature. The
standard deviation of the real exchange rate in our benchmark model is roughly 50% of the standard deviation in the data. Across all specifications, our model produces somewhat lower correlations of real imports with GDP than appear in the data. And, perhaps as a consequence, net exports are not as negatively correlated
with GDP as in the data. Cross-country output correlation is nearly zero in the standard IRBC models, though this correlation is usually large in the data.24 Our model provides little insight on this issue. We find that the cross-country correlation of output increases if we allow innovations to be correlated across countries. For instance, if we set cross-country correlation of innovations to 0.258 for both durable good and nondurable good sectors in the model of Medium Spillover, the cross-country output correlation increases from −0.01 to 0.1. However, it is still far less than it in the data. Kose and Yi (2003) find that their model can generate stronger cross-country correlations for pairs of countries that trade more. But the increased correlation still falls far short of the empirical findings.

When productivity shocks are persistent, it is well understood that investment will be volatile. Agents wish to change the capital stock quickly to take advantage of current and anticipated productivity shocks. This effect contributes to the high volatility our model produces for imports and exports, because capital
goods are traded. A positive productivity shock leads to a desire to increase Homes stock of domestically produced and foreign produced capital. This leads to the increase in demand for imports when there is a positive productivity shock. A positive productivity shock also increases the supply of Homes export good,
lowering its world price, and thus increasing exports. These effects are standard in RBC models, and explain why the models can generate procyclical imports and exports. However, if only investment goods are durable, and consumption goods are nondurable, the model does not produce sufficient volatility in imports and exports. For instance, if we change the depreciation rate of durable consumption ( D) to one and the adjustment cost to zero, the (relative) standard deviation of imports and exports decreases from 2.6 to 2.25 When we introduce a consumer durable sector, there is an additional source of volatility. Demand for consumer durables, like demand for investment goods, is forward looking. It is not expected productivity per second, but rather higher wealth from higher expected future income that leads to volatility in demand for durable consumer goods.

Consider the effect of a positive productivity shock in the production of durable goods. Because the shock is persistent, there is a significant wealth effect that pushes up demand for both home and foreign durable consumption goods. In addition, there is an increase in the relative price of nondurable goods, which leads to substitution from nondurables to durables. The price of home-produced durables relative to foreign-produced durables also increases, which leads to substitution toward home-produced durables. But overall, the wealth effect and the effect of the decline in the price of nondurables lead to an increase in import demand, despite the increase in the price of foreign durables relative to home durables. Indeed, total expenditure on imports increases more than the value of exports, leading to a decline in the trade balance.

However, part of that increase in import expenditure comes from the increased price of imports. But overall, the model still generates procyclical movements of import and export quantities. This shows the correlations between US GDP and real imports, exports and net exports at various leads and lags. As noted by Ghironi and Melitz (2007), the correlation between GDP and imports exhibits a tent-shaped pattern, while the correlations of exports and net exports with GDP are S-shaped.26 Our model captures these qualitative patterns well. Note in particular that the model captures the fact that, while current imports are positively correlated with GDP, imports are negatively correlated with lagged GDP at longer horizons. However, our model’s correlation of both imports and exports with lagged GDP declines quickly - too quickly - as the horizon increases. It appears especially that exports increase with a lagged response to a positive shock to GDP. It might be possible to capture this dynamic behavior by incorporating a lag between orders of durable goods and delivery.

Elasticity Puzzle

The elasticity of substitution between the home and foreign goods is defined as the percentage change of demand for imports relative to home goods, given a one percent change of the import price relative to the home-good price. Two methods have been used in the literature to estimate this elasticity. In the literature of
trade liberalization, studies investigate how much the demand for foreign goods increases after a permanent relative price change caused by tariff reduction. In the data, the trade share of output increases substantially over time after a small but permanent decrease in the tariff. This empirical finding suggests that the home
and foreign goods are highly substitutable. So the estimates from this strand of literature range from 6 to 15 with an average of 8. For instance, see Feenstra and Levinsohn (1995), Head and Ries (2001), Lai and Trefler (2002).
In another strand of literature, the same elasticity is estimated from transitory relative price changes at the business cycle frequency. We show with a simple example below that under a general setup used in the literature, those two methods are estimating the same parameter. However, estimates from business cycle frequency data are much smaller, in a range of 0.2 to 3.5. This result is robust for both disaggregate and aggregate data. For instance, see Reinert and Roland-Holst (1992), Blonigen and Wilson (1999), and Reinert and Shiells (1993) for studies on disaggregate data, and Heathcote and Perri (2002) and Bergin(2006) for estimates from aggregate data. These findings have been labeled as the “elasticity puzzle” in the trade literature.Several studies have offered explanations for this puzzle with a common feature that the long-run elasticity of substitution is high, but the short-run elasticity is low due to some market frictions.Our model is closely related. By the calibration of our model, the home and foreign goods are highly substitutable in the long run.

The short-run frictions in our model are adjustment costs of durable consumption and capital stocks. We calibrate those costs to match the volatility of investment and durable consumption. Under these conditions, we investigate whether adjustment costs can also deliver a reasonable short-run elasticity.

To calculate the short-run elasticity of substitution, we regress the (log) relative demand on the (log) relative price. We need the following variables in our regression: demand for foreign goods, domestic demand for home goods and the relative price. The demand for foreign goods is measured by real imports (RIMt).
The domestic demand for home goods is measured by domestic absorption (DAt), which is calculated by subtracting real imports from the sum of consumption and investment It is not surprising, of course, that we are able to generate an elasticity that is lower in the short run than in the long run by introducing costs of adjustment. Our point is simply that in a model in which trade is in durables, this is natural and accords with a long tradition in macroeconomics of modeling the gradual accumulation of capital. That is, the trade elasticity puzzle is easy to understand in a context in which trade is in durables which are accumulated slowly over time.Backus-Smith Puzzle Backus and Smith (1993) show in a model with nontraded goods that the real exchange rate should be perfectly correlated with cross-country relative consumption if households can trade a full set of contingent claims. This prediction is at odds with the data: the correlation of the real exchange rate and relative consumption among OECD countries is generally negative. Corsetti, Dedola, and Leduc (forthcoming) find the median of this correlation between the US and the remaining OECD countries is −0.42. These empirical findings are interpreted as lack of international risk sharing.31 However, Chari, Kehoe, and McGrattan (2002) show that incomplete financial markets are not sufficient: even a DSGE model with only bond markets implies a strong positive correlation. Some recent papers offer models to solve this puzzle. Corsetti, Dedola, and Leduc (forthcoming) find that if the elasticity of substitution between the home and foreign goods is small enough, the terms of trade improve, instead of deteriorate, in the face of a positive productivity shock it the home country. This could generate a negative correlation between the real exchange rate and relative consumption. Begnigo and Thoenissen (2007) show that even if the terms of trade deteriorate after a positive shock in the trade sector, the Balassa-Samuelson and wealth effects could be strong enough to generate a real appreciation in a model with nontraded goods. They argue that the price of nontraded goods increases after a positive shock in the tradable good sector, which calls for an appreciation of the real exchange rate.

This effect could dominate the deterioration of the terms of trade and induce a real appreciation. In this paper, we can also replicate the Backus-Smith empirical findings. The dynamics of consumption and the real exchange rate in response to a shock to productivity in the durable sector look very much like
those in Benigno and Thoenissen (2007). A positive shock lowers the price of the durable export, and because of home bias, that tends to work toward a real CPI depreciation. But that effect can be more than offset by the increase in the price of nondurable goods, which are not traded across countries. There are two forces working to push up the price of non-traded goods: First, there is the traditional Balassa-Samuelson effect. The increase in productivity pushes up the real wage, thus pushing up the relative price of non-tradables. In addition, overall consumption in the home country increases from a wealth effect, because higher productivity increases lifetime income for the home country. Even if there were no factors mobile between sectors, that would tend to push up the price of the nontradable goods, and help foster a real appreciation. We have that aggregate consumption is increasing, and under our calibrations, a real appreciation – these correspond to the data.However, our model also offers some new insight on this puzzle. The durable consumption measured in national accounts data is expenditures on new durable consumption goods. However, it is the service flow from the stock of durable consumption that enters the utility function. As emphasized by Obstfeld and Rogoff (2006), the consumer smooths the service flow from the stock of durable consumption, instead of the path of expenditures on durables.

Conclusion

The behavior of imports and exports is, of course, a key component of the linkages among economies. Our model confronts and, to a degree, successfully explains some strong empirical regularities. By modeling trade in durables, we can understand the high volatility of imports and exports relative to output. Trade in durables also offers a natural explanation for the trade elasticity puzzle – that the response of imports to changes in the terms of trade is low at business cycle frequencies, but is high when considering the long-run effect of permanent price changes. Our model performs well compared to other models, because it offers an
explanation that is also consistent with the observation that imports and exports are both procyclical, and positively correlated with each other, even when the terms of trade and real exchange rate are as volatile as
in the data. We believe the forward-looking nature of investment decisions and decisions to purchase consumer durables are a key feature of trade behavior. Our model noticeably fails to account for the high correlation of output across countries, which is a failure shared by essentially all rational expectations equilibrium models. However, we think that modeling trade as durables may still be a promising avenue for dealing with this puzzle as well, through channels that are not explored in this paper. One possibility is that while the common (across countries) component of productivity shocks may account for a small share of the variance of productivity, it may be that agents typically receive strong signals about the future common component. If news helps to drive business cycles (as in Beaudry and Portier, 2005), then perhaps news about the common component of productivity shocks helps contribute to the high correlation of business cyclesfailure shared by essentially all rational expectations equilibrium models. However, we think that modeling trade as durables may still be a promising avenue for dealing with this puzzle as well, through channels that are not explored in this paper. One possibility is that while the common (across countries) component of productivity shocks may account for a small share of the variance of productivity, it may be that agents typically receive strong signals about the future common component. If news helps to drive business cycles (as in Beaudry and Portier, 2005), then perhaps news about the common component of productivity shocks helps contribute to the high correlation of business cycles across countries. News about future productivity is especially important for durables, so the impact of news may be especially strong on the investment and consumer durables sectors. Another avenue that may deserve further exploration is a model with nominal price stickiness, as in DSGE models. Our model of durable trade creates large swings in demand for imports, which indeed is what allows it to account for trade volatility. But an increase in Home demand for Foreign output has only a small effect on Foreign’s output level. Instead, in our model, prices adjust so that more of Foreign’s output is channeled toward Home. In a model with sticky prices, changes in demand may lead to changes in aggregate output, and so create a channel for international spillovers. While these channels do exist in current DSGE models, they are not strong because the models do not account for large procyclical movements in imports and exports.It is an empirical fact that a large fraction of trade is in durables. Indeed, we view explaining this phenomenon - rather than assuming it, as we do in this study - to be another interesting topic for future research. What we have accomplished here is to demonstrate that trade in durables significantly alters the behavior of imports and exports in an RBC model in a way that can account for some striking empirical facts.