To what extent does Helpman (1998)
explain US regional price differences?
An empirical validation of the parameter estimates of Helpman’s price equation for USregional data in the period between 2008 and 2014.
Author: Henco Ouwendijk
Student number: S2201720
Contact: h.c.ouwendijk@student.rug.nl
Supervisor: B. Los
Co-assessor: D. Soudis
MSc. International Economics & Business – University of Groningen
Abstract
Recent developments in the new economic geography (NEG) literature increased the theoretical understanding of the problem of agglomeration. However, most theoretical findings are currently not validated by much empirical evidence. Price effects are one of the factors that play a significant role in the explanation of the spatial distribution of economic activity and population. This paper provides an empirical test of the structural parameters estimates of the price equation of Helpman’s (1998) model. It examined the explanatory power of his model using regional price index data for tradable goods and housing of 358 metropolitan statistical areas (MSAs) in the United States between 2008 and 2014. With the use of econometric techniques, this paper concludes that the empirics do not correspond perfectly with Helpman’s parameter predictions. Most parameter estimates indeed show the right signs, but none had the expected magnitude. Moreover, data do not support Helpman’s mechanisms that determine price index levels.
Keywords: Regional price indices - NEG - Helpman (1998) – empirical validation – parameter estimates
Contents
Abstract ... 2
List of Tables and Figures ... 3
Introduction ... 4
Literature Review ... 6
Krugman’s core-periphery model ... 7
Helpman’s basic model ... 9
Regional price indices ... 12
Previous results ... 15 Methodology ... 19 Estimation issues ... 22 Data ... 27 Analysis ... 31 Discussion ... 36 Conclusion ... 38 Reference list ... 41 Appendix ... 43
Appendix A: Graphs and Figures ... 43
Appendix B. Equilibrium equations of Helpman (1998): ... 46
List of Tables and Figures
TABLE 1: Discussed NEG core-periphery models ... 11TABLE 2: Moran’s I test statistics ... 25
FIGURE 1: Overall Regional Price Parities by MSA in 2014 (US=100) ... 27
TABLE 3: Descriptive statistics ... 30
TABLE 4: Estimation results of pooled regression of price index model of equation 9, 11 and 12, using cluster-robust standard errors ... 32
TABLE 5: Estimation results of fixed effects regression model of equation 13 and 17 ... 34
TABLE 6: Estimation of the spatial lag model (Equation 16) ... 36
TABLE A1: Correlation matrix (N = 2506) ... 43
TABLE A2: size classes of municipalities ... 44
TABLE A3: estimation results of pooled regression analysis (Equation 9 & 12) ... 45
Introduction
The average US citizen spent in 2014 over 42 hours in traffic jams – the equivalent of an entire week of work. More than 139 million people traveled a daily average of 52 minutes between their neighborhood and work (Ingraham, 2016). Those congestion problems have an enormous economic impact. Inefficient traffic situations cost the US economy approximately $160 billion in 2014, mainly due to wasted time and fuel – more than $1000,- per commuter urban mobility scorecard report, 2015). And this figure have not included the negative consequences of missed meetings, longer delivery times, business relocations, draining economic growth and other congestion-related effects. And it is getting worse in the near future if current policies are not changed. The urban mobility scorecard report (2015) forecasts the average traffic congestion torise at an annual growth rate between 2% and 4% (Schrank, Eisele, Lomax, and Bak, 2015).
Traffic congestion is not a problem in itself, but one of the symptoms of a big underlying issue: the clustering of people. US cities include more than 70% of US population, and 85% of economic activity1, but cover only 3.5% of US land area. (Manyika, Remes, Dobbs, Orellana, & Schaer, 2012). Literature contains several theoretical explanations for the concentration of people and economic activity. New economic geography (NEG) is one of them. This line of literature descends from Krugman (1991) and tries to include location choices into the mainstream economic models. It explains the highly uneven distribution of economic activity and people with a tension between agglomerating and spreading forces. One of the key models is developed by Helpman (1998). With his paper, he provides a fresh look at the problem of agglomeration and tries to explain the distribution of economic activity and population in more developed economies. His model includes two regions with a housing sector and a manufacturing sector. The manufacturing sector fosters agglomeration, while it supplies differentiated products that are traded between regions against shipping costs. Firms cluster and locate close to their customers to avoid transportation costs. In his model, the availability of housing operates as the key dispersing force. Helpman assumes the housing product is exogenous determined and fixed per region, which makes it more costly to use in agglomerated areas. Individuals move to more dispersed areas to save housing costs. His model consists of three principal equations that interact2. In this paper, the price equation receives the primary interest, because price difference could be one of the reasons why congestion exist. If so, inverse price policies could be a structural solution for the current congestion problems.
Nevertheless, the empirical validation of those NEG models lags behind for two reasons. Firstly, the combination of non-linear structure and multiple equilibria make empirical validation complicated.
1 Areas are defined as US city if they include more than 150.000 residents. This paper uses the relative percentage of 2 In line with Krugman (1991), Helpman’s model consists of a wage equation, an income equation and a price index
Secondly, insufficient regional price data is available. However, validation is crucial to understand the relevance of NEG theory for economic policy. On of the few exceptions is Hanson (1998, 2001, 2005). He provides direct tests for the parameter estimates of the spatial wage equation of Helpman (1998) and found questionable results. The demand linkages that underlie Helpman’s model are of limited geographical scope. Brakman, Garretsen, & Van Marrewijk (2009) confirmed Hanson’s results. Empirical validation studies of price equations are even more scarce. To my notice, only Kosfeld et al. (2008) executed a validation test of the price index equation of Helpman (1998). He used price index data of only 21 Bavarian countries of 2002, but did not find strong empirical evidence that supported the Helpman model. I extent their empirical analysis and validate the structural parameters of Helpman’s price equation, using data of a different geographical level in a different nation for a different time period. This paper offers the first analysis of Helpman’s price equation for country-wide data, by using regional price index data of a sample of 358 metropolitan statistical areas (MSAs) in the United States between 2008 and 2014 and answers the following research question: To what extent does the Helpman-model (1998) explain the variance in US
regional price parities (RPPs) in the period between 2008 and 2014? This paper uses
log-linearization techniques and several other econometric technics to simplify and fit the price index equations of non-tradeable housing goods and tradeable goods for proper econometric analysis and bypasses the impact of four urgent estimation errors.
The results of our analysis do not correspond perfectly with Helpman’s parameter predictions. Most parameter estimates are significant and have right signs, but have a smaller magnitude than Helpman predicted. Furthermore, the goodness of fit of the model was smaller than the goodness of fit of other empirical tests. Moreover, some doubts could be raised by Helpman’s price mechanisms and assumptions.
This implies that Helpman could explain the real-world distribution of price index levels, but that those predictions should be treated with appropriate concerns. Spatial planning policy may benefit from econometric research on the determinants of regional price parities, but more research must be done before clear policies could be recommended.
Literature Review
This section briefly discusses the theoretical models of Krugman (1991) and Helpman (1998) and outlines their main differences. Furthermore, it provides Helpman’s major expectations for regional price index levels. In addition, this section discusses some other papers that include an empirical validation of one of the main equations of Helpman (1998).
The concept of agglomeration is frequently discussed in economic literature. Neoclassical models explain the uneven distribution of economic activity across space with ‘first nature geography differences’. ‘First nature’ refers to interregional differences in physical geography, like climate and resource endowments. NEG neglects this exogenous determined first nature differences, but includes second nature geography in their models. ‘Second nature’ refers to the location of economic agents relative to the site of other agents in space (Redding, 2009). Fujita, Krugman, and Venables (1999) surveyed relevant NEG literature and developed the principal structure for the new economic geography (NEG) school. It explains the highly uneven distribution of economic activity with a tension between agglomerating and spreading forces. NEG models assume that the productivity level of firms (supply-side) in agglomerated areas exceeds the productivity level of firms that are located in more dispersed areas, due to the existence of external increasing returns to scale (IRS).
Marshall (1920) identified three sources of productivity benefits due to externalities: the first reason refers to productivity benefits due to the pooled labor market. The labor market in agglomerated areas is thicker and contains more specialized and better-trained workers. Secondly, firms in agglomerated areas benefit from input sharing of non-tradeable specialized products. Finally, urban firms benefit from spillovers that exist due to better sharing-, matching- and learning opportunities. Beside firms, consumers also prefer to agglomerate (demand-side). Agglomerated areas are attractive for individuals, while more job opportunities are available in agglomerated areas. Moreover, consumers have more choice of varieties in agglomerated areas, while agglomerated areas produce more manufacturing varieties. Finally, agglomerated areas possess more and better public goods and services than dispersed areas.
On the other hand, also spreading forces exist. One of the primary dispersing forces is congestion. “Congestion refers to all costs that originate from market failure caused by urban agglomeration: e.g. limitations in space, heavy usage of roads, communications errors, limited local resources, environmental pollution and transportation costs” (Brakman et al. 2009).
Krugman’s core-periphery model
Krugman (1991) developed a framework that uses the concepts of increasing returns to scale, transportation costs, and factor mobility to explain the development of agglomeration. His core-periphery model is a variant of the monopolistic competition framework developed by Dixit & Stiglizt (1977) and includes two regions with two sectors: each area contains a manufacturing sector and an agricultural sector. The manufacturing sector produces an aggregate of differentiated varieties under increasing returns to scale (monopolistic competition), while this production requires some fixed costs. Firms show profit-maximizing behavior, and locate in the area with the lowest production costs. The agricultural sector produces a homogeneous good under constant returns to scale (perfect competition). The homogeneous good is determined as a numeraire3. Farmers are immobile and unable to move to other regions, because their factor of production, land, sticks to that particular area4. Both farmers and manufacturing workers maximize utility by consuming a combination of agricultural good and the aggregate of manufacturing varieties.5. Those manufacturing varieties are traded across regions because consumers obtain more utility from consuming the whole variety of products than they obtain from the consumption of one single variety. This utility benefit is negatively related to the level of transportations costs. For both sectors, two features are important:
Firstly, Krugman assumes that only the manufacturing workers can relocate and move between regions. Secondly, Krugman believes that individuals could trade both the homogeneous agricultural good and the varieties of the manufacturing between areas. In Krugman’s (1991) model, it is costless to transport both agricultural and manufacturing goods within regions. The absence of (physical) distance between goods, people and information within regions eliminates transportation costs. Furthermore, it is also free of charge to transport the agricultural good between regions. However, the interregional trade of the manufacturing goods requires a transportation fee. Those shipping costs for manufacturing products increase with distance according to the so-called
‘Samuelson iceberg-principle’, which implies that a portion of the transported good is eaten as
compensation for moving it. Manufacturing firms are assumed to produce only one single variety, which require one factor of production, namely labor.6 Individuals are both workers and consumers
3 Economic agents base their decisions on relative price levels and not on absolute price levels. This allows Krugman
(1991) to use the price of the agricultural good as a reference to express the prices of other goods relative to the agricultural good. To makes thinks not unnecessary complicated, the price of agricultural goods is set equal to one.
4 Krugman assumes the relative amount of agricultural workers to be exogenously determined. 5 Krugman assumes the utility function of individuals to look like: 𝑈 = 𝐶
!!𝐶! (!!!)
, with CA = consumption of
agricultural good, Cm = consumption of manufacturing aggregate, and 𝜇 = share of expenditure spend on manufacturing
aggregate. Cm is defined by [ !!!!𝑐(!!!)/!]!/(!!!), with 𝜎 as elasticity of substitution and N the number of
manufacturing varieties.
at the same time, which optimize utility by relocation to the area with a higher real wage. A following paragraph will discuss the relation of wage premiums with agglomeration and the reasons for those wage differences.
Krugman determines the combination of positive transport costs and economies of scale (fixed production costs) as the main agglomerating forces. Firms minimize the number of production facilities to save fixed costs. It is beneficial for firms to locate in agglomerated areas, because they can serve the customers in that area without additional transportation costs. When the demand of farmers is dispersed between the two regions, it creates an incentive for manufacturing firms to disperse as well. Farmers are not allowed to relocate to other regions, which mean that their regional demand is fixed. Manufacturing firms extend production to the more dispersed areas, if total transportation costs exceed the fixed costs that are required to build a new firm.
The Krugman-model consists of three equations that interact: price index, real wage and real income (Appendix B). For the purpose of this paper, the discussion of the equations is limited to the price mechanism. For a more extensive discussion, I refer to Fujita et al. (1999). The equation of the price index for manufacturing goods in region R (Pr) is defined as:
𝑃! = [𝜆!(𝑇!!")!!!𝑊
!!!!]!!!!
! (Equation 1)
Where 𝜆! stands for the regional share of total manufacturing labor force L in region S. WS
represent the regional nominal wage in region S and 𝜎 the elasticity of substitution for manufacturing goods and 𝑇!!" the transportation fee to move a unit of a manufacturing variety from region R to region 𝑆7. In Krugman (1991), the price index for manufacturing varieties (Pr) is
identical to the overall regional price index, while agricultural good is set as a numeraire. This is justified, while no transportation costs for agricultural goods exist, and the production of agricultural products is described by constant returns to scale. It is not only beneficial for firms to locate in agglomerated areas but also for individuals. Consumers benefit in two ways from dwelling in agglomerated areas. Firstly, agglomerated areas produce more varieties, which can be purchased without transportation fee (Overman & Venables, 2005). Secondly, workers in agglomerated areas are better paid. The nominal wage rate is higher in agglomerated areas due to the Marshallian productivity benefits, which allow firms in agglomerated areas to pay their employees better. These two facts are the main reason why Krugman concludes that the price index is lower in agglomerated areas. This is displayed in the price index equation, which shows a positive relation between the price index (Pr) and both the nominal wage rate (W) and the transportation fee (𝑇). Krugman’s
model predicts lower cost-of-living in agglomerated central area and higher in the dispersed remote
7 Krugman’s modeling restrictions only allow the transport cost parameter (T
rural area, assuming that price indices for manufacturing goods are identical to cost of living indices.
The core-periphery model of Krugman (1991) is in general not suitable for empirical validation, because of their limited number of long-run equilibrium outcomes. Krugman’s model (1991) is only able to predict either one region with all economic activity (full agglomeration) in the case of low transportation costs, or two regions with the same number of manufacturing firms in the case of zero or high shipping costs (identical dispersion). Other outcomes are not possible under Krugman’s assumptions. However, this does not correspond to current and past distributions of economic activity and population for the United States or any other developed country. The US consists of multiple locations with a significant variation in population and economic activity. Helpman (1998) model suits better for empirical validation, while his model is able to predict more realistic long-run equilibria with unequally dispersed distributions of population and economic activity. This means his model could generate 2 regions with an unequal amount of economic activity and population in the long term. Compared to Krugman, Helpman’s model has two other main advantages. Firstly, his model obtains more realistic stable long-run equilibria for developed countries like the US. Secondly, his model incorporates more realistic predictions for the price levels of non-tradeable goods and services.
Helpman’s basic model
Helpman (1998) modified the core-periphery model of Krugman and replaced the agricultural sector for a housing sector. In his paper, Helpman aims to discover the main determinants of the distribution of people across space. He argues that the Krugman model succeeded to implement geography in economic models. However, Krugman’s predictions particular apply to countries with a huge agricultural sector. Predictions are less suitable for the distribution of economic activity in developed western nations with a smaller agricultural sector. The absence of a big agricultural sector negatively impacts the strength of the dispersing force. With his modifications, Helpman obtains results that better match to urban economic models8 and that are closer to the current distribution of economic activity and population in western countries.
Both models have an identical set-up. Krugman’s assumptions for the manufacturing sector hold for Helpman’s manufacturing sector (tradable goods) as well. Manufacturing firms could optimize utility by relocating to another region. Also Helpman’s housing sector has the same structure as the
8 Urban economic models (UE) descend from the Alonso-Muth-Mills variant of the Von Thünen monocentric model,
agricultural sector in Krugman’s model; it is characterized by constant return to scale and perfect competition. The suppliers of housing are immobile to move between regions, like the farmers in Krugman. Helpman assumes regions to have a fixed and exogenous determined stock of housing. Workers work in the same area as they live. This means that the population determines the labor supply and the number of manufacturing variety.9 Consumers spend their entire income on the consumption of a combination of the manufacturing and the housing (not agricultural) goods. However, two significant differences with Krugman (1991) exists:
1) Helpman replaces the homogeneous agricultural good for a homogeneous housing good. In contrast to Krugman (1991), Helpman assumes that the homogeneous good of housing could not be traded across regions and sticks in the region where it is located.
2) Krugman assumes demand of farmers (producers homogeneous good) is tied to the location. Agricultural workers spend their entire income in the region where they live and work. However, in Helpman (1998), are housing owners allowed to spend the income they obtained from their housing good on imported products from other regions as well. This means that a growth of the regional housing income in region R also generates demand in other regions. Helpman assumes this demand is proportional to the relative number of residents in a region.
Helpman’s results reflect the impact of these two different assumptions. His second different assumption allows population differences between regions with identical housing supply, which is not possible in Krugman (1991). This enables Helpman’s model to obtain also other and more stable dispersed long-run equilibrium outcomes than a dispersed equilibrium with similar regions with the same economic activity and population. Besides more long-run equilibrium possibilities, this second assumption also alters the relation between the degree of transport costs and agglomeration. Krugman’s model predicted agglomeration to happen in the case of low transportation costs, while high transportation costs lead to dispersion in the long run. In contrast to Krugman, Helpman (1998) predicts stable agglomerating equilibriums in the case of high transportation costs and stable dispersing equilibria exist in the case of low transportation costs. Secondly, Helpman obtained different predictions for the distribution of price index levels. Helpman (1998) demonstrated in his paper that Krugman’s predictions of cost-of-livings accounts for tradeable goods, but not for non-tradeable goods like housing. Non-tradeable goods are more expensive in agglomerated areas, while the fixed amount of housing creates scarcity. Agglomerated areas show high grow figures which lead to a growth in the demand for housing. While the supply of housing is fixed, this extra demand results in higher prices in agglomerated areas. This creates a
tension for utility-maximizing individuals between the desire to move to agglomerated areas for a better variety choice, but desire to move to dispersed areas for lower housing prices. In equilibrium, the gains and losses of those two forces balance. Overall, his model implies core areas to be slightly more expensive to live in than rural areas, which corresponds better to current reality according to Suedekum (2006).
Like Krugman’s model, manufacturing sector is, due to the existence of positive transport costs and increasing returns to scale a driving agglomerating force. Contrary to Krugman (1991), the supply of housing functions as the main dispersing force and not the dispersed demand for manufacturing varieties. He argues that the higher housing prices in agglomerated areas push people to move to the cheaper remote areas. As result of the tension between those two forces, manufacturers prefer to locate close to areas with a large number of houses in order to minimize costs. For some manufacturing firms it is economically better to stay in dispersed areas to serve the people that live in that neighborhood.
Empirical literature remains divided over the consequence of the tension between agglomerating and dispersing forces for the cost of living. We have seen two contradicting NEG models. Helpman’s (1998) predictions seem more intuitive than the predictions of Krugman (1991). City life is in general more expensive due to scarcity on housing markets. Land scarcity and additional TABLE 1: Discussed NEG core-periphery models
Krugman (1991) Helpman (1998) Suedkum (2006)
Sectors 1. Homogeneous and mobile agricultural sector (PC); 2. Heterogeneous and mobile manufacturing sector (IRS);
1. Homogeneous and immobile housing sector (PC);
2. Heterogeneous and mobile manufacturing sector (IRS);
1. Homogeneous and mobile agricultural sector (PC); 2. Homogeneous and immobile housing sector; 3. Heterogeneous manufacturing sector (IRS); Assumptions accounting for all models
- Producing manufacturing goods require some fixed and variable costs;
- Distributing manufacturing variety to other regions than regions of production require transportation costs according to the Samuelson’ iceberg-principle;
- Workers (M) optimize utility by migrating to the region with higher wages; farmers/house owners are not able to relocate across regions.
Assumptions that differ between models:
- Agricultural good freely (≠TC) tradeable across regions
- Demand of farmers is tied to location
- Housing good not tradeable across regions
- Demand of house owners generate some supply in all regions in proportion to relative population
- Agricultural goods freely (≠TC) tradeable across regions, - Housing good not tradeable across regions.
Results - Urban Pr < rural Pr
- Stable agglomeration à TC = low - Stable dispersion à TC = high - Urban Pr > rural Pr - Stable agglomeration à TC = high
- Stable dispersion à TC = low
- Urban Pr > rural Pr
- Stable agglomeration à TC = low
demand for housing boost urban prices. The major part of empirical studies indeed provides evidence for this (DuMond, Hirsch, & MacPherson, 1999; Tabuchi, 2001, Suedekum, 2006 etc.)
Regional price indices
This paragraph will briefly discuss the price equation of Helpman (1998) and the adjustments done by Kosfeld et al. (2008). With a few exceptions, the price index equation for tradeable goods retains the same structure of the price equation of manufacturing in Krugman (1991). Fujita et al.s (1999) defined this relation as follows:
𝑃!,! = [𝑁!(𝑃!! ∗ 𝜏 !")!!!] ! (!!!) ! !!! r = 1,2, …., n, (Equation 2)
Where Ns represents the number of varieties of tradeable goods in region S10. 𝑃!! stands for the
uniform price paid for manufacturing goods by consumers in region S. τ!" represents the ad-valorem ‘iceberg’ cost of shipping goods from region S to R and 𝜎 denotes the elasticity of substitution between varieties11. Equation 2 shows that it is more expensive for individuals to purchase a manufacturing variety from a different region than purchasing products that are produced in their own region, while importing manufacturing products from other regions require additional transportation costs. The price of manufacturing variety I produced in regions S and consumed in region R, equals the price of manufacturing variety I in region S (𝑃!,!! ) times a
transportation premium function, which increases with distance (𝑒!!!"). 𝑃!,!! = 𝑃
!,!! 𝑒!!!" (Equation 3)
Smaller regions produce fewer varieties themselves and therefore need to import manufacturing varieties from other regions against transportations costs. If utility-optimizing individuals in smaller areas want to consume the same basket of goods as individuals in larger regions, they have to pay more, because it requires more transportations costs. Helpman’s model predicts a lower price index of manufacturing or tradeable goods in agglomerated areas, just like Krugman (1991). Individuals obtain a utility benefit if they move from a dispersed area to an agglomerated area, because they could buy more goods and services with the money they save from using less transportation services.
Dispersion arises from the costs of housing. Helpman assumes the stock of housing (Hr) could not
be traded to other regions. Both the housing stock and the share of income spent on manufacturing varieties (µ) are exogenously determined in Helpman (1998). The model expects the total regional housing income is identical to regional total housing expenditures in an equilibrium situation, because Helpman does not permit housing ownership by residents from other regions in his model.
10 While every firm produces only 1 variety N
Therefore, regional housing prices (PH,r) is a product of three variables: the share of expenditures
consumed on manufacture products (𝜇), regional income (Yr) and the regional housing stock (Hr):
𝑃!,! = (1 − 𝜇)!!
!! r = 1,2, …., n, (Equation 4)
Equation 4 shows that the housing prices of agglomerated areas to exceed housing prices in dispersed areas. In this case, regions attract more immigrants (both firms and consumers), regional total income (Yr) increases12. The relation in equation 4 provides that in case of a higher income,
the housing price must increase if income grows. In line with Krugman (1991), income is a function of wages and labor supply (Appendix B) and wages increase with agglomeration due to agglomeration benefits. This means that new individuals pay more for housing in agglomerated areas. Utility maximizing consumers will move to the cheaper dispersed areas.
Previously, this paper showed that the overall price level depends on the relative tension between agglomeration and dispersing forces. Furthermore, Helpman predicts a positive relation between housing prices and agglomeration and a negative relation between manufacturing prices and agglomeration. Helpman (1998) rearranged this Cobb-Douglas function and obtained the following overall price index equation for region R (PA,r):
𝑃!,! = 𝑃!,!! 𝑃!,!(!!!) r = 1,2, …., n, (Equation 5) Where 𝑃!,!! stands for the price index for tradeable goods in region R, 𝑃!,!!!! represents the price index for non-traded housing goods in region R, and with 𝜇 as the parameter that represents the share of expenditures that is spent on manufacturing product varieties in region R. Unlike Krugman (1991), the overall price index (Pr) is not only determined by the price index for tradeable goods
(PT), but also by the price index for housing, because regional housing prices do not equalize
through interregional trade. Krugman assumes identical prices of agricultural good, while this could be traded freely between regions without transportation costs. In Helpman (1998), interregional mobility of the housing goods is not present.
In line with Kosfeld et al. (2008) equation 2 could be rearranged. The regional share of the total manufacturing labor force (λs) and the manufacturing nominal wage (𝜔! ) of region S are
implemented instead of the number of varieties (Ns) and manufacturing price (𝑃!!). This is justified,
while Helpman (1998) assumes, like Krugman (1991), that all firms produce a single variety with the use of one unit of labor. The costs of labor are identical to the nominal wage in region S, while
12 𝑌
!= 𝜆!𝐿 (𝜔!+ ℎ!), where L is the total labor amount, 𝜔! the nominal wage and ℎ! the income derived from a
labor is the only input factor present in his model. Therefore, the price of manufactures equals the regional nominal wage:
𝑃!,! = ! [𝜆!(𝜔! 𝜏!")!!!]!(!!!)
!!! r = 1,2, …., n, (Equation 6)
The transport costs are measured as a function of distance (𝑒!!!"). Based on Krugman's (1991) third equilibrium condition long run real wages (𝜔!"#$) are assumed to equalize across regions13. This allows me to arrange the price index for tradeable goods in region R as following:
𝑃!,! = 𝛾 𝑌!(!!!)/!𝐻!(!!!)/!𝜔!"#$!/! r = 1,2, …., n, (Equation 7) 𝛾 represents the constant that depends on the equilibrium real wage rate (𝜔!"#$). Krugman’s fourth equilibrium condition states that regional income is a sum of income derived from agricultural sector (in Helpman’s model substituted by housing) and labor. This and the fact that regional housing income equals regional housing expenditures, allow us to simplify the price index equation: 𝑃!,! = 𝜑𝑌!𝐻!!!!/! r = 1,2, …., n, (Equation 8) with 𝜑 as constant.
Kosfeld et al. (2008) view equations (4) and (8) as the main equations for respectively the non-tradeable or rent price index and non-tradeable goods price index. Income (Yr) positively impacts the
price index in both the equation of tradeable manufacturing good as housing good. Therefore, this paper generates the following hypothesis:
δPT,r / δYr > 0 (equation 8) (Hypotheses 1)
δPH / δYr, > 0 (equation 4). (Hypothesis 2)
The mathematical conditions of the log-linearization restrict Yr to equal one, but this will be
discussed in the methodology part. Furthermore, equation 8 denotes the housing stock (Hr) to
impact the price index for tradeable goods (PT) positively. Equation 4 reveals that the housing stock
has a negative impact on the price index for housing (PH), which is in line with microeconomic
theory. This results in the following hypotheses:
δPT,r / δHr: > 0 (equation 8) (Hypothesis 3)
δPH,r / δHr :< 0 (equation 4). (Hypothesis 4)
Income is positively related to the price index for tradeable goods (PT,r) and the regional price index
for housing stocks (PH,r). Hypothesis 3 is in line with microeconomic theory, while a positive shift
13 In long run !!"#$,!
in supply has a negative effect on the price of that product if all other factors remain equal. The combination of hypothesis 3 and 4 determines the overall price index (PA) together:
δPA,r / δYr > 0 (equation 5) (Hypothesis 5)
Both Kosfeld et al. (2008) and Hanson (2005) state that net gain due to the fall in prices of manufacturing goods (eq. 7) compensates the negative impact of scarcer houses (eq. 4) on price levels. Therefore, the housing stock parameter mathematically drops out of the Cobb-Douglass overall pricing index. We expect changes in the housing stock should not be reflected in the price index changes:
δPA,r / δHr : = 0 (equation 5) (Hypothesis 6)
Log linearization limits the impact of Housing stock (Hr) on the price index for tradeable goods (PT)
to (1 − 𝜇)/𝜇 and PH,r to -1, but also this will be discussed in the methodology part. Previous results
Kosfeld et al. (2008) have examined the validity of the Helpman model, by estimating and testing the structural parameters of the price index equation for 21 regional areas in Germany for non-tradeable goods, non-tradeable goods, housing and the overall consumer price index (CPIo) for 2002
data. Using the same econometric techniques as this paper, they show that empirics do not support the crucial features of the price mechanism of Helpman. The parameter estimates of their primary explanatory variable, income (Yr) had the predicted positive sign for all four price indices, although
the relative impact was lower than they expected. The magnitude of all four parameter estimates of income (βY) was below 0.1 instead the predicted magnitude of 1. Furthermore, as expected, they
found a negative relation between the housing stock and the price index of non-tradeable goods and the price index of housing goods, although with a lower magnitude than they expected. However, in contrast to their expectations, the sign of housing stock parameter estimate for their overall consumer price index was not neutral but negative. The parameter estimate of the housing stock in the price index equation for tradeable goods was not positive but negative. Empirical evidence supports Helpmans predictions to a limited extend. Therefore, they concluded that Helpman could explain the real-world distribution of price index levels to a certain extent and that policy measures based on his model should be treated with appropriate concerns
between regional wages and market potential14 for 3075 countries in the US between 1970 and
1990, by using a simple market potential function. They compared the results of this test of the simple market potential regression to the results of the augmented function of market potential based on Helpman (1998). His results show a significant association between variation in market proximity and regional wages. The parameter estimates were consistent with the theory. However, his data rejected the hypothesis that the augmented market-potential based on Helpman (1998) was favorable over the simple market potential function. Brakman, Garretsen, & Schramm (2004) also verified the significance of the key model parameters of the wage equation of the Helpman model. They found for German data some estimated parameters had incorrect signs. Distance, for example, was positively related to economic dependence, which contradicts intuition.
More recent literature criticized Helpman for his expectations for the level of transportation costs. As discussed before, Krugman (1991) and Helpman (1998) differ in the prediction at which level of transportation costs agglomeration is stable. Krugman (1991) predicts agglomeration to happen in the case of low transportation costs and dispersion in the case of zero and high transportation costs, where Helpman’s model predicts agglomeration in the case of high costs of transportation. According to Suedekum (2006), this expectation does not correspond to reality. Krugman showed in his model that the relative real wage increases in the case of low transportation costs and decreases if transportation costs are high. When regional wages diverge, agglomeration happens, while people could earn a much higher wage when they migrate to the agglomerated area. When wages converge, dispersion seems much more stable. Therefore, low transport costs and dispersion is not realistic, according to Suedekum (2006). Fact checking proves that western countries are more agglomerated than developing and low income countries and that transportation between rural and urban countries is more expensive in poor dispersed countries than in the agglomerated western nations (Worldbank, 2013).15 Suedekum solved this problem by adding a non-tradeable housing sector, instead of replacing the agricultural sector for a housing sector. This enabled Suedekum (2006) to obtain the same realistic predictions for a positive relation between agglomeration and price index levels, but with maintaining Krugman’s’ essential assumptions. To prove the rightness of his model he regressed nominal wage, regional population and the regional income with a cost-of-living index for 208 US MSAs in 2000. The regression results supported his model.
14 Market potential is defined, “as the demand for goods produced in a location is the sum of purchasing power in other
locations, weighted by transport costs”. This means market potential is a function of regional income and distance.
15 In 2015 the urbanization ratio ((urban population/total population) x 100%) was 80% for high-income countries and
A significant gap in the literature exists. A considerable amount of empirical papers has shown that economic activity differs per location and geography impact economics. However, despite the prominent place of cost-of-living/price disparities in (new) economic geography, it is still grounded on minor empirical validation. Only a few papers attempt to estimate and test the structural parameters of models. Empirical research to validation of the parameter structure of NEG-models lags behind for two reasons. The first reason relates to the structure of most NEG NEG-models. Empirical validation of NEG models is relatively difficult, while it is complicated to insert a combination of a nonlinear structure and multiple equilibria into econometric equations. A second reason originates from data limitations. Most data are still gathered for national levels and not regional levels. Only a few official governments document regional price and cost-of-living indices on a broad scale. However, validation is crucial to understand the relevance of NEG theory for economic policy. Most papers focused on the validation of the parameters of the spatial wage equation of prominent NEG-models ( o.a. Brakman, Garretsen, & Schramm, 2004; Hanson, 2001), but to my notice only Kosfeld et al. (2008) provided some estimates test for the price equation parameters.
Moreover, this paper adds robustness by testing Kosfeld’s et al. (2008) methodology for a different country for panel data instead of a single time set. The dataset covers eight years instead of only one year (Kosfeld, 2008). This is a main benefit. Helpman’s model assumes a continuous interaction the between wages, income levels and price levels till a stable long equilibrium is obtained. Using a dataset that covers more than one year allows equalizing yearly corrections. Analyzing only data of 1 year makes it more likely that the parameter estimates are influenced by an exogenous event and do not approach true parameters value. Kosfeld et al. (2008) used for example only data of the year 2002. This is the first year after the dot.com crisis, which 1) could have an impact on the value of the parameters and 2) makes it discussable if the economy is in equilibrium. More important the used dataset is significantly larger than Kosfeld et al. (2008) used.
Empirical validation of Helpman’s (1998) is more robust while this paper analysis a different country with some significant differences. Germany and the US differ in numerous amenities. For example the countries possess different countries with a different climate and attitude. One difference could be important, while it could impact the housing market behavior of individuals. The USA is much more dispersed than Germany regarding geographical amenities and economic conditions. The range of the regional price index for rent services ranks from 48.00 to 200.70, while Kosfeld’s housing price index only ranges from 54.00 to 100.00. Using more data that shows more variety, results in general in more accurate test statistics and parameters estimates that approximate the true parameters better.
Methodology
This section outlines the methodology used to validate the structural parameter estimates of the Helpman model. Furthermore, it discusses four estimation errors that could bias the estimation results. Equations 5A and 8A represent the core of the price model. To validate the structural parameter estimates of Helpman’s price equation, these equations need to be converted to an econometric relation. However, nonlinearity is present in both the price equations for housing (equation 5) and tradeable goods (equation 8). I solved this problem with the use of log-linearization techniques. Log-log-linearization techniques introduce logarithms on both sides of the equation. This enables me to separate the combined effect of housing and income together into individual effects. The following log-linear models for both tradeable goods (5A) and housing (8A) are obtained:
𝑙𝑛 𝑃!,! = 𝑙𝑛 ( 1 − 𝜇) + 𝑙𝑛 𝑌!− 𝑙𝑛 𝐻!+ 𝜂!, (Equation 5A)
ln 𝑃!,! = 𝑙𝑛 𝜑 + ln 𝑌!+ !!!! 𝑙𝑛 𝐻!+ 𝜗! (Equation 8A)
where 𝜂! and 𝜗! stand for the residuals that contain the effects of unobserved influences. Conforming equation 3, PT and PH together determine the price index for all items in region R (PA).
The NEG-based pooled regression models of the three price indices (pi = Pt, PH and PA) have the
following structure:
𝑙𝑛 𝑃!",! = 𝛼 + 𝛽!𝑙𝑛 𝑌!",! + 𝛽! 𝑙𝑛 𝐻!",!+ 𝜀!",!, for t = 1,2, …, n, (Equation 9) where 𝛼 is the intercept for region R in year t, 𝛽! and 𝛽! the regression coefficient for respectively variable for income (Yr) and the variable for housing (Hr) and 𝜀!" as the error term. This is justified
in all 3 cases. For example, for the equation of the price index for tradeable goods (PT) hold if 𝛼
equals ln 𝜑, 𝛽! equals 1 and 𝛽! equals !!!! .
In the literature review, this paper denotes twelve hypotheses for the signs of the parameter estimates. However, in order to satisfy Helpman’s model, the parameters estimates should be tighter than some of these hypotheses. The mathematical consequences of the log-linearization technique restricted the hypotheses as follows:
For tradeable goods price index: (ln( 𝑃!,!): 𝛽!= 1; 𝛽!= (1 − 𝜇)/𝜇
For non-tradeable housing price index: (ln( 𝑃!,!): 𝛽!= 1; 𝛽!= −1
In order to satisfy this parameter constraints of Helpman, 𝛽! is restricted to 1 for both the tradeable
good price index (PT,r) and the housing price index (PH,r), while equation 5A and 8A show a positive
relation between income and price indices for all models. This implies that income elasticity is fully elastic for both tradeable goods and housing. The impact of non-tradeable housing on price indices is displayed by 𝛽!. The parameter estimates of housing (𝛽!) is restricted to -1 for the non-tradeable
housing price index equation (PH,r) and should equal 1-µ/µ in the price equation for tradeable goods
(PT,r). Therefore, the relation between the housing stock and non-tradeable housing goods is
perfectly negatively elastic, where the elasticity of housing stock with respect to tradeable goods equals the ratio of housing expenditures to manufacturing expenditures. The parameter estimates of income in the overall price index equation (PA, r) is restricted to 1, for the same reasons as for the
tradeable good price index (PT,r) and the housing price index (PH,r). The parameter estimates of
housing mathematically dropped out. Therefore, 𝛽! is equal to 0.
This paper deviates from Kosfeld et al. (2008) and adds in line with Hanson (2005) market potential and coastal proximity to the model. Market potential refers to the phenomenon that demand for goods of a certain region is determined by purchasing power of other locations. Market potential is the main NEG variable according to Fingleton (2011). Coastal proximity is added in a numerous other studies that provide empirical test of NEG models (e.g. Fingleton, 2011; Hanson, 2005).
𝑙𝑛 𝑃!" = 𝛼 + 𝛽!𝑙𝑛 𝑌!"+ 𝛽!𝑙𝑛 𝐻!"+ 𝛽!"𝑀𝑃!" + 𝛽!"𝐶𝑃!" + 𝜀!" (Equation 10) Market proximity (MP) and geological benefits (CP) are both a dummy variable, which equals 1 when the MSA has respectively market proximity or coastal proximity or 0 in the case an MSA does not have market- or coastal proximity. This paper assumes MSAs to possess market potential when (1) they are located within 100 miles from one of the 10 major economic areas, or/and (2) if the area had more than 1 million residents in 2010 or (3) obtained a principal town with over 500.000 residents in 2010. This is in line with (Huang & Bocchi, 2009). However, stronger measures exist that are neglected for data limitation reasons.
Market potential of surrounding regions is expected to impact price levels in region R positively, because if regions have more purchasing power, the demand for manufacturing goods or region R increases and this will result in higher prices. Helpman assumes the housing good is not traded over regional borders. Therefore, the purchasing power of other regions would not impact the price levels of region R. Therefore, 𝛿!" should not differ significantly from 0. This defined the following hypothesis for market potential:
δPT,r / δMP > 0 (equation 9), (Hypotheses 7)
δPH,r / δMP = 0 (equation 9) (Hypothesis 9)
In line with Hanson (2005) we added coastal proximity as a dummy variable. Geological benefits are expected if MSAs are directly located on the coast or indirectly connected via one of the major rivers in the USA (Hudson, Ohio, Mississippi, Colorado and the Rio Grande). Other geological benefits, like fertile land or natural resources, are neglected mainly for data limitation reasons. Regions with coastal proximity have better access to other regions. Therefore, transportation from and to regions that have coastal proximity is cheaper. The markup for importing and exporting manufacturing goods is smaller for regions with coastal proximity than for regions without coastal proximity. Therefore, coastal proximity impact price level or regions negatively. Housing could not be traded to other regions in Helpman (1998). In line with this assumption coastal proximity does not impact the price of housing units:
δPT,r / δCPr > 0 (equation 9), (Hypothesis 10)
δPA,r / δCPr > 0 (equation 9), (Hypothesis 11)
δPH,r / δCPr = 0 (equation 9), (Hypothesis 12)
Helpman mentions in his paper something remarkable that could be of impact for my analysis. He assumed income from the housing by residents of a region is identical to the total income from housing is determined times the regional fraction of individuals (NMSA/Nusa). In the case that
preferences are described by a constant price elasticity, this fraction (NMSA/Nusa) also determines
prices of housing. In order to test if this holds for US data, we add relative population (Xr,t).
Latitude and longitude coordinates are added as control variables.
𝑙𝑛 𝑃!,!" = 𝛼 + 𝛽! 𝑙𝑛 𝑌!" + 𝛽!𝑙𝑛 𝐻!" + 𝛽!𝑙𝑛 𝑋!" + 𝛽!"𝑀𝑃!+ 𝛽!"𝐶𝑃!+ 𝑝!𝐿𝑎𝑡!+ 𝑝!𝐿𝑜𝑛!+ 𝜀!" (Equation 11) Equation 11 shows that the price of housing increases, if the supply of housing is fixed and relative population (Xr,t) rises. If a region grows faster than other regions, this means that more demand
push prices up. The following hypothesis is generated:
δPH,r / δXr, > 0 (equation 10), (Hypothesis 13)
Helpman did not discuss the effect of relative population on other price index estimates, so this paper does not include hypothesis for those other two price index estimates. To address biases caused by specific regional characteristics, the longitude and latitude coordinates are added to all regressions without fixed effects.
Estimation issues
To conduct proper econometric analysis, four estimation issues must be addressed. The first estimation error relates to unobserved heterogeneity in regional characteristics of MSAs. The US is a large country with substantial differences between locations. Those differences may influence the spatial distribution of price level indices. For example, Napa (California) and Sioux city (Iowa) had almost an identical regional GDP in 2008 of respectively $7329 billion and $7339 billion. Their housing stock of 53.000 and 58.000 was also not very different. Despite their identical regional income and housing stock, their price level index showed a huge gap. Napa’s price index for all goods was 120.40 in 2008, where Sioux City only had a price index of only 88.90. Napa was almost 40% more expensive than Sioux City that year. Differences like this could have been caused by numerous things. However, literature mentioned time-invariant location-specific amenities as the major explanation for price index differences between locations like Napa and Sioux City. In this example, Napa is located in sunny California close to the San Pablo Bay, while Sioux is located in cold and landlocked Iowa. The weather is a main reason why Napa is a popular destination for retiring people, that spend their money to enjoy the last moments of their life. This is reflected in the price index of Napa. Besides climate, numerous time-invariant location-specific amenities could bias cause regional price index differentials, e.g. large differences in the regional deposit of resources, differences in the average level of education, or differences in the regional taxes rate etc. Two methods that are widely used in previous literature to exclude the impact of exogenous time-invariant and location-specific amenities on price differences are fixed effects and first difference analysis. The parameter estimates of fixed effects and first differences regression analysis approximatethe real parameter more closely. This paper deals with this by including fixed effect in the regression model:
𝑙𝑛 𝑃!" = 𝛼!+ 𝛽!𝑙𝑛 𝑌!" + 𝛽!𝑙𝑛 𝐻!" + 𝑢!" (Equation 13)
Fixed effects regression analysis differs from a pooled regression analysis, while it allows for differences in the intercept parameter for each MSA. The fixed effects regression models omitted the variables of market potential (MPr) and coastal proximity (CPr), because both are
regional-specific time-invariant characteristics.
Another way to deal with the impact of time-invariant and location-specific externalities on price index levels, is a first difference regression analysis. This is shown in the following regression model:
(αr) disappears from the model. market proximity and coastal proximity do not change over the
years. Therefore, both the parameter estimates of market proximity and coastal proximity (∆δ!" and ∆δ!") are mathematically equal to zero. Literature states that a first difference regression analysis is more efficient and more valid when the error term urt is homoscedastic and not serially correlated, while fixed effects is more valid when urt follows a random walk , because the normal standard errors of the fixed effects estimator are understated in the presence of serial correlation (Bertrand, Duflo, & Mullainathan, 2004). However, in this situation strict exogeneity fails. Therefore, Bertrand et al. (2004) recommend to use a fixed effect estimator in combination with cluster-robust standard errors instead of the more preferable first difference estimator. I will come back to this endogeneity problem in the next paragraph. Beside time-invariant regional specific amenities, both methods also correct for heterogeneity in the regional distribution of expenditures and differences in inputs as well. This is in line with both Brakman et al. (2004) and Kosfeld et al (2008).
A second issue relates to the endogeneity problem. The endogeneity problem refers to the situation that an explanatory variable is correlated with the error term of the regression model. This violates the econometric condition that the independent and the error term should be uncorrelated. Several causes of endogeneity exist, however, in this case, endogeneity is the result of the presence of simultaneous causality. The Helpman-model consist of three equations that interact: the price index equation (Pr), the real wage equation (Wr) and real income equation (Yr)16. Helpman (1998) stated
that long-run equilibria are established due interaction between explains those three variables. The price index (Pr) is one of the determinants that explains the distribution of wages (Wr) and wage is
one of the determinants that explain the distribution of income. So, where income has a direct effect on prices, prices also indirectly affects the level of income, according to Helpman. However, our regression model tests the estimation parameters of the price index equation (Pr) with use of
regional income (Yr). This is called simultaneously causality. A shock or disturbance to either price
index or income would affect both the equilibrium of regional income (Yr) and the price index (Pr).
This endogeneity bias could lead to inconsistent ordinary least squares (OLS) and wrong test statistics. However, it is possible to remove the correlation of the disturbance term of our price index model with income with adequate econometric instruments.
Two solutions exist. An adequate solution to correct for an endogeneity bias is the use of exogenous variables or lagged variables that are uncorrelated with the error term instead of the endogenous variable income. However, removing income from the model and use different
explanatory variable would not be the most suitable solution, while agglomeration and income are crucial in the NEG models and are one of the reasons why regions attract workers and consumers. Another option to correct for endogeneity is the use of instrumental variables (IV). However, finding adequate instrumental variables is hard, while the instrumental variable should be correlated with the income variable and uncorrelated with the price variable. In line with Brakman et al. (2004), I used several instrumental variables, among them population, lagged population and the population density. However, none did fulfill the requirements for a good instrumental variable. Also lagged regional income and relative population (Xr) did not fulfill. However, results remain
close to normal fixed effects regression models. In line with Kosfeld et al (2008), I only provided the test statistics for the equation with lagged income and lagged relative population. With the use of a two-stage-least-square method (2SLS) to provide an adequate estimation technique which could for the inconsistent parameter estimates due to endogeneity problems:
ln 𝑌!" = 𝛼!+ 𝛾!𝑙𝑛 𝑍!"!! + 𝛾!𝑙𝑛 𝐻!" + 𝛾!𝑙𝑛 𝑋!" + 𝑣!" (Equation 17) Where Yr,t-1 and Xrt are the instrumental variables.
𝑙𝑛 𝑃!" = 𝛼!+ 𝛽!𝑙𝑛 𝑌!" + 𝛽!𝑙𝑛 𝐻!" + η!" (Equation 17’) The error term equals 𝜀!" = 𝑣!+ η!. Xrt stands for the relative population of the region R compared
to the total population(POP) of the USA (POPmsa, t/POPusa,t). Including a lagged variables income
separated the disturbance term into two parts: 𝑣! represent the unexplained variation in time and η! the disturbance that is not correlated with Yrt and Hrt.). Therefore, the parameter estimates of
income, β1, will approximate the true parameter of income.
The third issue relates to heteroscedasticity. This is related to the variance of the error term. If this error term systematically varies across the various MSAs the error term is not homoscedastic. The assumption that variance of the error is constant across observations is violated. This means that unobserved characteristics of a region that is present at each time period, e.g. climate, does not impact the error term of each period in time in the same way. Heteroscedasticity does not bias the parameter estimates, but affect the variance of the parameter estimators. This results in biased test statistics and confidence intervals. Results of the Breusch-Pagan test showed that the hypothesis that the test statistics are not influenced by heteroscedasticity could not be rejected17.
The impact of heteroscedasticity could be addressed with the use of robust cluster robust standard errors instead of normal standard errors. With the use of clustered robust standard errors, the parameter tests approach the significance of the true parameters better. This paper use those clustered robust standard errors to account for heteroscedasticity.
17 The Breusch-Pagan test is a specific test for linear forms of heteroscedasticity. This refers to situations that the error
The fourth issue relates to spatial effects. This refers to the situation that prices index for surrounding region do impact the level of a regional price index. Spatial effects could bias regression results if the delineation of spatial units is arbitrary. One of the spatial effects that is frequently present in empirical models that validate parameters of the NEG models is the modifiable areal unit problem (MAUP), which is discussed more comprehensively in the literature review. The US MSAs are unlike the
German NUTS-3 levels, not formal but functional areas. Functional areas are not prone to biases that exist because of the modifiable areal unit problem (MAUP), while the borders of functional areas are based on human interactions and not administrative borders.
Another spatial effects that frequently affects the spatial distribution of prices, is spatial autocorrelation. This refers to the phenomenon that spatial units are not totally independent but interact. Data values display the tendency of clustering/dispersion due to the existence of several spatial features. This means that a price index is more strongly related the price indices of regions than with distant price indices. For example, 9 of the top 12 locations in our dataset with the highest price indices were located in California, although their housing stock and regional income showed substantial variation. This could be the result of spatial autocorrelation. Autocorrelation causes underestimation of true variance. Therefore, the t-values are overestimated, which lead to incorrect hypothesis rejections. With use of Moran’s I spatial price autocorrelation could be detected. For the price index for housing (PH) and the overall price index (PA), significant positive Moran’s I’s were
found. Negative insignificant Moran’s I’s were found for the price index for tradeable goods (PT).
TABLE 2: Moran’s I test statistics
Moran I P-value
Overall price index (PA) 0.616 0.000*
Price index for tradeable goods (PT) -0.004 0.400
price indices for housing (PH) 0.580 0.000*
Income 0.001 0.340
Housing stock -0.001 0.440
Model (PA, = f( Yrt, Hrt, MP CP)) 69.558 0.000*
