House Prices and Vacancies after Hurricane Katrina: Empirical Analysis of a Search & Matching Model

Transcription

1 House Prices and Vacancies after Hurricane Katrina: Empirical Analysis of a Search & Matching Model S. Aneeqa Aqeel* University of Michigan November 7, 2009 Abstract This paper examines the housing market effects of Hurricane Katrina. I develop a dynamic structural equilibrium matching model of housing vacancies and residential investment. The model is used to analyze the impact of Hurricane Katrina on house prices, ownership vacancies and investment for 57 MSAs within a 550 mile radius of New Orleans. Using disaggregated data, I utilize the exogenous variation in housing stock due to the Hurricane to obtain an estimate of the elasticity of flow supply in housing. Data show that in metro areas closest to the epicenter of the Hurricane, prices rise by 7 percent immediately after Katrina. Across MSAs in which one or more counties were declared disaster zones by FEMA, residential building permits rise by 19 percentage points in 2006 over the previous year. The ownership vacancy rate in New Orleans metro area increases from 2.2 percent in 2005 to 4 percent in Using the matching model for each MSA, I generate artificial dynamic paths for prices, ownership vacancies and investment in response to the observed actual reduction in housing stock and the migration dynamics after Katrina. I compare the predictions of the model with actual data and find that house prices tend to quantitatively overshoot in the model, while new investment in housing reacts similarly to actual residential investment. The ownership vacancy rate in the model also substantially overshoots compared to the data for Hurricane-impacted areas. * I am indebted to my advisors Christopher House, Matthew Shapiro and Jeffrey Campbell for their immense support and guidance. I am grateful to Michael Elsby for helpful discussion. I also thank participants at the University of Michigan Macro Lunch and the Chicago Fed Economic Research Department lunch seminar for helpful comments and suggestions. Contact: saaqeel@umich.edu

2 1. Introduction This paper presents a dynamic structural equilibrium search and matching model of housing vacancies and investment. Hurricane Katrina provides a natural experiment to evaluate the performance of the model, by causing a sharp unanticipated reduction in the stock of housing and a consequent increase in the demand for residential investment. I analyze the movement in house prices, ownership vacancies and new residential investment for Metropolitan Statistical Areas (MSAs) affected by the Hurricane. I use a calibrated version of the model to simulate dynamic paths of these variables in response to the exogenous reduction in housing stock and the migration dynamics actually observed. I then compare the simulated data from the matching model to the actual data. House prices tend to quantitatively overshoot by a lot in the model in response to an exogenous shock mimicking Hurricane Katrina, while new investment in housing reacts similarly to actual residential investment. The ownership vacancy rate in the model also substantially overshoots compared to the data for Hurricane-impacted areas. A successful model of the market for owner-occupied housing should account for the behavior of vacancies over time. Despite the co-existence of searching buyers and available houses for sale, many houses remain vacant for long periods of time. Persistent vacancies are thus an important and readily observable feature of the housing market. A dynamic matching framework is a natural approach to modeling a market with equilibrium vacancies because it introduces a real friction that impedes market clearing even with flexible prices. The model I present here is based on models in the labor search literature (Dale T. Mortensen 1970; Christopher A. Pissarides 1985). The friction take the mechanical form of stochastic rationing (Pissarides, 2000), allowing searchers to match with available vacant houses at a Poisson rate each period. The rationale behind it is to introduce a delay before a household s needs and requirements are satisfied by an available vacant house for sale. In the model, interaction between structural vacancies and supply of new housing units also reflects the stock-flow nature of housing supply whereby even a small shock to housing stock can lead to large, persistent adjustments of flow investment in new housing. This feature makes the model particularly well-suited to studying the impact of Hurricane Katrina, which rendered between 25 and 38 percent of the housing stock severely damaged or uninhabitable in the metropolitan areas of New Orleans, Louisiana; Gulfport-Biloxi and Pascagoula in Mississippi; and Beaumont-Port Arthur in Texas. 2

3 The model analyzes a market for owner-occupied housing in a single metropolitan area. Here, potential buyers and sellers of homes meet in a decentralized market to trade houses. The meetings are governed by an exogenous matching technology. The technology implies that any buyer faces a positive probability of simply not meeting a seller each period, and vice versa. Therefore, despite buyers being present and actively searching, some houses remain vacant in equilibrium due to the matching friction. Profit-maximizing firms construct new homes for sale each period. Potential buyers do not distinguish between new and existing homes, so construction of new homes depends only on the total number of vacant houses already on the market and this determines sellers expected surplus from a sale. In this way, the existing stock of housing directly impacts the flow of new housing. The flow supply of housing responds to price changes and allows the stock of housing to adjust to exogenous shocks. I adopt the standard assumption that prices are negotiated through Nash bargaining by each buyer-seller pair. Given their outside options, each pair agrees on a mutually acceptable division of trade surplus from a successful sale in the current period, rather than waiting to find another transaction opportunity. Thus, when a buyer-seller pair meets it results in a sale, and a match refers to both a meeting and a successful transaction. I model Hurricane Katrina as an unanticipated shock. The shock moves the market out of its steady state equilibrium with a sudden reduction in the housing stock and an outward migration from metropolitan areas lying in the path of the Hurricane. While there is a positive correlation between destruction of a housing unit and emigration by its owner, I assume that not all owner-occupiers whose houses are destroyed in the model emigrate from an affected city. Moreover, some affected areas have no outmigration at all. Since not all former owner-occupiers leave affected cities, demand for ownership housing rises after the shock, bidding up house prices and stimulating new investment. While looking for a house to buy, searchers who have lost their homes are frictionlessly absorbed by an exogenous rental market. The model also allows emigrants to sell their existing homes on the market if they have not been destroyed, predicting a rise in vacancies as residents move away. Due to the matching friction, slow-moving vacancies have a propagating effect on prices and investment. For Hurricane-affected MSAs that experience sustained in-migration after the initial shock, vacancies continue to fall for several years. For other affected MSAs, relative 3

4 supply of vacancies to searchers rises slowly within a year or two as new construction replaces destroyed housing units. In MSAs which experienced the largest proportions of destroyed housing units, prices rise sharply. As the number of available housing units recovers, prices gradually decline towards steady state in the model. Hurricane Katrina occurred on August 29, Data show that in metro areas closest to the epicenter of Hurricane Katrina, house prices rose by almost 7 percent in 2005Q4 and have continued to rise steadily till 2008Q4. The ownership vacancy rate doubled between 2005 and 2007 in New Orleans MSA. Across MSAs in which one or more counties were declared disaster zones by FEMA, residential new building permits rose by 19 percent in 2006 over the previous year. Movement in cities near the epicenter of the Hurricane is more pronounced. For these near MSAs, I take the ratio of the difference-in-differences estimates of the change in house prices and permits from before and after the Hurricane to obtain a flow supply elasticity. I use this estimated elasticity to calibrate the model. In quantitative application of the model, the effect of the shock is carried through a moving average process assumed for in- and out-migration and calibrated to match actual migration data since the Hurricane Katrina. To study the impact of the Hurricane, I generate artificial data for 57 MSAs, matching actual housing-stock damage and migration patterns across MSAs. I generate observations by MSA for 12 quarters each to compare against the 3 years of actual data available following Katrina. Substituting these artificial observations for actual data in the time series per MSA, I re-estimate the pooled cross sectional regressions used for the actual data and compare the estimates from the simulated data with the estimates from the actual data. The model successfully predicts a rise in prices for disaster areas but overshoots in magnitude compared to actual data. Across all affected cities, the average predicted quarterly price increase in simulated data is 39 percent from 2005Q3 to 2005Q4, compared to 3.4 percent in actual data. In actual data, prices in the affected metro areas continue to rise after the Hurricane while prices decline towards steady state in the model. Not surprisingly, the model also predicts that residential investment increases after the Hurricane but again predicts somewhat larger magnitudes of change. For affected MSAs, permits rise by 33 percent in a year in simulations while they rise by 19 percent in the data. 4

5 While in actual data, building permits rise by 36 percentage points from 2005 to 2006 for MSAs within 100 miles of New Orleans, in the model the change in flow housing investment is about 49 percent. Finally, like the response of prices and investment, the response of ownership vacancies predicted by the model exceeds the response in the actual data. For in-fema areas, the vacancy rate falls by 24 basis points after the Hurricane, while in the model the vacancy rate declines by 2 percent. The next section presents the search and matching model of housing. Section 3 presents regression analysis of the Hurricane s effect on net migration, house prices, residential building permits and ownership vacancies in the affected areas. Section 4 presents the model calibration and simulation results. Section 5 discusses related literature and Section 6 concludes. 2. Matching in the Housing Market Market Technology I consider a dynamic market for non-rental housing with a fixed population of N households and a finite number of firms that produce new houses. In this paper, the market represents a single MSA but the model can also be applied to other levels of aggregation without any substantial changes. Let H denote the existing total stock of houses. The market for non-rental housing is driven by a match technology that dictates whether an available buyer and seller will meet and transact in any period. Prices are determined by Nash bargaining between each buyer and seller pair. The match technology is assumed to be a Cobb-Douglas function. Matches per period, M, are determined by the function, =, where S is the number of households searching for a house, V is the number of ownership vacancies (i.e. houses for sale) on the market and γ is the elasticity of total matches with respect to the number of searchers. As is usual in matching models, the technology causes market non-clearing because it imposes that not all potential buyer-seller pairs will meet, which is captured by the matching parameter <1. If =1 and γ = 0.5 each potential buyer would meet and transact with a potential seller and the market would clear completely with no unmatched vacancies or searchers remaining. If the 5

6 matching parameter is less than 1, the probability that any one buyer or seller is matched is less than 1 and the market does not clear immediately. New and existing houses are bought and sold in the market without distinction. For the sellers, the probability of selling a vacant house in any period depends on the total number of vacancies in the market. The probability of selling is = =, where = is the relative supply of vacant houses. As relative supply increases, the probability of selling a house falls. Households searching for a house to buy face a positive probability of not meeting a seller in a given period. This mechanically captures the delay experienced by a household before it finds a house suitable for its needs in the real world. The probability of buying a house is = = and depends on the relative number of searchers and vacancies. As relative supply increases, the probability of successfully purchasing a house rises. Timing The model is in discrete time. The sequence of events within a period is described by the timeline below. Period t begins with an existing stock of housing H t, vacancies V t and searchers S t. The period begins by matching vacancies with searchers. Unmatched buyers and sellers wait until the next period to try to match again. Households who are successfully matched become owner-occupiers, earning an expected imputed rent. Unmatched searchers rent until the next period. Matching & Bargaining in the Housing Market Own & Occupy Exogenous Separation Depreciation New Construction Following the payoffs, a fraction λ of owner-occupiers are exogenously separated from their existing houses. These households become searchers next period and their houses enter the pool of vacancies. A fraction of owners that are not separated may still have to search next period because their house has depreciated. Depreciation renders a house uninhabitable and beyond repair, so a depreciated house cannot be resold. The assumption is made mainly for tractability and allows 6

7 the model to incorporate destruction of housing units, as occurred after Hurricane Katrina. This type of depreciation process implies that old houses and new houses are perfect substitutes and thus house prices are independent of the age of the house. At the end of the period, construction firms make investment in new houses for sale, X t,. New houses augment the stock of vacant non-rental housing available for sale next period, V t+1, and add to the stock of housing in the market H t+1. Similarly, existing houses that are separated from their current owners enter the stock of vacancies for next period. Population, Searchers, Vacancies & Housing Stock The population N t of the MSA varies according to exogenous migration into and out of the MSA. The law of motion for population is given by equation [1]. = + [1] The evolution of searchers in the market depends on the match and separation probabilities as well as net migration. Given the timeline above, the number of searchers satisfies equation [2]. = [2] The total number of searchers entering the market at the start of period t+1 is the sum of unmatched searchers from the previous period and new immigrants into the city. Further, all matched owner-occupier households in the total population who are forced to move due to a separation or depreciation shock also enter the body of searchers. Due to the sequence of events, a house that is matched at the start of period t can subsequently depreciate or be separated from its owner later in the [t, t+1] time interval, forcing the new owner to reenter the stream of searchers in t+1. Emigration is an outflow from the total number of searchers. Specifically, σem emigrants are searchers who leave the city instead of continuing to look for a house in the city. The remaining emigrants are all owner-occupiers, of whom are those who have experienced destruction of their houses and would have been searchers next period if they had remained in the city. Total vacancies at the start of period t+1 include unmatched vacancies from last period net of depreciation and existing houses put up for sale by owner-occupiers who experience the 7

8 move-shock but not depreciation in interval [t, t+1]. X t, which is new construction, also increases vacancies. Finally, ω is the fraction of owner-occupier emigrants who have not experienced depreciation of their homes who sell their houses when the market meets at t+1. Equation [3] expresses the law of motion for vacancies in the market. = [3] The housing stock at t+1 is the sum of existing houses after depreciation and new construction, as in equation [4]. = 1 + [4] To achieve stable equilibrium in the model, new housing investment and prices play the role of jump variables. The ratio of total vacancies to total searchers,θ, jumps by the degree that new investment jumps when an exogenous shock occurs. The model incorporates aggregate uncertainty through the separation rate λ t, which follows an AR (1) process and also through rents, which are assumed to be exogenous but can vary over time. A special case of this is when both λ t and rent are constant, which is the assumption maintained for the remainder of the paper. All asset value equations, however, are written including an expectations operator due to the potential of the model to incorporate aggregate uncertainty. To model the shock to the stock of housing from Hurricane Katrina, the rate of depreciation varies from its fixed value δ if a binary event variable, κ t that denotes the occurrence of the Hurricane takes the value 1. The coefficient on κ t measures the percentage of housing units destroyed by the shock in the depreciation expression = +. Simultaneously with the reduction in housing stock, the Hurricane event κ t also causes migration out of cities that are hit directly. Cities that are not in the Hurricane s path receive immigrants. Thus, there is also exogenous variation in population due to the shock event. Asset Value Equations The expected payoff (in monetary units) of being an owner-occupier, a searcher or a seller is expressed in the form of a dynamic recursive asset value equation. Households and firms are 8

9 homogenous, risk-neutral, forward-looking utility- and profit-maximizers, respectively. Their expected payoffs from searching or transacting at t are based on the underlying incentive constraints of searchers, buyers and sellers. These value equations are used to determine the surplus created for a buyer-seller pair by a successful match, which is divided between the two parties during price-setting. While in aggregate the number of households separated from their existing housing units each period is deterministic given a constant rate of separation λ in any period; at the individual level, the move event is random and occurs at a Poisson rate. The searching household has a choice between matching with a house today and continuing to search for a better match next period. A household that becomes a searcher in the interval [t, t+1] must wait until the start of t+1 to receive an opportunity to match. Hence, the value of searching, L t, is discounted at the risk-free rate, r, and defined as the probabilityweighted sum of the expected value earned by an owner-occupier net of the expected purchasing price, and the value of remaining in the search state next period. This is expressed as equation [5]. = [ + 1 ] [5] While a household is in the search state, it is absorbed without friction by the rental market. The rental market is assumed to be exogenous to the ownership housing market. The flow rental payment by searchers is the opportunity cost of not owning, and it is here included in the value of owning a house in equation [6] as imputed rent. Note that a household may only own one house at a time. = [6] The value equation [6] states that an owner-occupier in period t earns the current rent R t which is stochastic and exogenous, as well as a utility gain associated from owning a home which is identical across households. This joy of ownership in monetary terms, b, can be thought of as a benefit of owning arising from the ability to customize one s residence. If the owner-occupier experiences involuntary separation from his existing house and the house does not depreciate in the same time interval, he will also earn the expected return of a seller, A t, which is explicitly written in equation [8]. If there is involuntary separation or the existing house depreciates, the household becomes a searcher and earns expected return L t. Finally, if the 9

10 household escapes separation and depreciation it earns the present discounted continuation value of being an owner-occupier in t+1. Construction firms have convex costs of production. The optimal production level requires that the marginal cost of production equals the expected marginal benefit of a vacancy. Rising marginal costs imply an upward sloping flow supply curve for new housing units. Since the firm can only sell a new vacancy in the period after construction, the decision to construct a new house rests on the expected asset value of a vacancy for sale. Thus, is the expected sales value of a house and denotes investment in new housing in equation [7]. The elasticity of supply is denoted while α is a stochastic cost-shifter term that captures changes in production technology. = In the timing of the model, houses newly constructed in period t can only be sold when the market meets in t+1. Hence, the cost of new construction is essentially a sunk cost for the firm. If a newly built house is not sold right away and enters the stock of vacancies, firms may make positive profits on these intra-marginal units despite the zero profit condition that applies to the latest marginal unit produced. The cost incurred by waiting to sell a house is depreciation. I assume that the market does not distinguish between new and old houses, so V t+1 in equation [3] is the total supply of vacant homes available for purchase at t+1. Therefore, the expected sales value of a house is the same regardless of its age and its seller s identity. Whether an existing homeowner or a firm, a seller has three available choices at the start of period t when the matching market meets. The first is to accept the negotiated price P t and sell the vacancy immediately. The second is to leave the house vacant till the next period and receive expected sales value after depreciation in t+1. Finally, sellers have an outside option in the rental market, analogous to searchers. The third choice for a seller is to convert the house into a rental property permanently and pay some >0 in one-off transaction costs at t, incurred in selling the property to a rental management company or taking on the burden of rental management oneself. Rental houses are assumed to depreciate at a higher rate than ownership properties, R δ > δ. This is formalized in equation [8]. [7] 10

11 = 1 1+ [ max, 1, Γ + 1 max 1, Γ ] The current expected value of a vacancy, A t, is based on the two possible outcomes a seller faces next time the matching market meets: with probability the seller will meet a buyer and have the choice to sell the vacancy at price, given the outside options to wait another period or convert the unit to a rental house permanently. With probability 1, the seller will fail to meet a buyer in the market and will choose between waiting another period to sell the vacancy and converting it into a rental house forever. The expected stream of payments from converting the house into a rental unit is summarized by Γ = + Γ. [8] Price Determination When the market pairs a buyer and seller together, they negotiate over how to divide total surplus generated from the match, which is the sum of net returns for buyer and seller from transacting right away. I assume that this negotiation takes the form of Nash bargaining. Equation [9] defines the bargained sales prices of a vacancy, where ϕ denotes the buyer s bargaining weight. Since all buyers and sellers are homogeneous, the market price is the same for each matched buyer-seller pair. For max 1, Γ and 1 > Γ, = max 1 [9] Equilibrium and the Steady State Equilibrium requires determination of price and relative supply that satisfy equations [1] through [9]. The equilibrium sales price of a house is determined under the condition that a seller, if matched, weakly prefers an immediate sale over waiting an additional period; and, if unmatched, strictly prefers to wait an additional period to sell rather than permanently convert a vacancy into a rental unit. This imposes that 1 >Γ and > 1 in equation [8]. Given the equilibrium price, the exogenous separation and depreciation rates and exogenous rent, firms decide how much flow investment to undertake in equilibrium, per equations [7] to [9]. 11

12 This condition for equilibrium rules out other possible configurations. For instance, if net sales price of a house falls below the expected rental stream, it is possible that all houses are converted to rental units and the market for ownership unravels. This occurs when 1 <, implying that market price undervalues ownership relative to expected rental returns, i.e. <. Another possibility is that a seller will always choose to convert to a rental unit if he cannot sell the house right away. This occurs if the expected value of waiting to sell is below that of converting to a rental unit, but the market price is overvalued relative to expected rental returns from the house, i.e. >. Another degenerate solution is possible when waiting is preferable both to renting out a vacancy and selling it at t+1. This implies that a seller will simply choose to wait forever. The steady state is characterized by a constant ratio of vacancies to searchers, θ, constant population size and a constant level of the housing stock. Both immigration and emigration are assumed to be zero in steady state when total population takes its steady state value N. Moreover, the values of owning, selling and searching for a house are also constant in the steady state. Substituting these values into the Nash bargaining solution yields the steady state bargainedprice which can be simplified and written as a decreasing function of steady state θ, as expressed in [10] where <0. = + [10] Flow supply in steady state also depends on the condition that selling today is always preferable to waiting or converting to a rental unit. The steady state flow supply curve for new houses in P-θ space is expressed in equation [11], where h >0. =h [11] Thus, equations [10] and [11] can be solved to yield steady state price and relative supply, as a function of the parameters of the model. A lower bound on market price is given by the outcome where a seller is indifferent between selling today, waiting to sell and renting out the vacancy. This is the case where = 1 =Γ. By no arbitrage, the minimum possible sales price that will allow a market for ownership to exist is one at which the steady state return to a seller from permanently renting out a housing unit is equal to that from selling it today. This is the price = =. 12

13 Section 4 presents the results of the model after a shock to housing stock and migration, with discussion of the dynamic implications of the model. 3. Stylized Facts and Data This section discusses data sources and presents difference-in-differences regression analysis of net migration, prices, residential building permits and ownership vacancies across affected areas and a comparison group. The regression analysis is used to establish a set of facts regarding the impact of Hurricane Katrina on key housing market variables. In the next section, these facts are compared to predicted patterns for prices, investment and ownership vacancies in the model when shocks to housing stock and migration taken from actual data are fed into the matching model. Data Hurricane Katrina made landfall in Plaquemines Parish in southern New Orleans, Louisiana (see Map 1) on the morning of 29 August 2005, continuing over Mississippi and Alabama. It damaged and destroyed between 25 and 38 percent of the housing stock in the metropolitan areas of New Orleans, Louisiana; Gulfport-Biloxi and Pascagoula in Mississippi; and Beaumont-Port Arthur in Texas. These cities saw massive outmigration immediately following the Hurricane, and rents and prices went up in affected areas. I use estimates of housing stock destroyed and damaged produced by the Federal Emergency Management Agency (FEMA) at the country level, across Texas, Louisiana, Mississippi and Alabama. These estimates do not include damaged vacant or seasonal housing and also exclude second homes. I combine estimates of major and severe damage to calculate the percentage of housing units destroyed by the Hurricane. Major damage refers to flooding of up to 2 feet or where less than 50 percent of a house is damaged and requires extensive repair work for future occupancy. Severely damaged housing units are either completely destroyed or with flooding of 2 or more feet. Out of a total of 117 counties affected by the Hurricane, the highest concentration of destruction of housing units occurred in 11 counties along the Louisiana and Mississippi coastlines. These counties mostly comprise New Orleans-Metairie-Kenner, LA and Gulfport- Biloxi, MS MSAs and are listed in Table 1. The table also shows detailed county-level damage 13

14 estimates. Worst hit in New Orleans MSA were Orleans, St. Bernard and Plaquemines Parishes, which lost between 35 and 50 percent of their housing stocks in the flooding from Katrina. In Gulfport MSA, Hancock County was worst affected and lost almost 20 percent of its housing stock. In Table 2, I aggregate county level estimates to show estimated loss of housing stock at the MSA level for affected areas that are included in my regression sample (see below for details). The complete destruction of housing stock is clearly the worst in New Orleans, MSA where the breaking of the levees rendered 80 percent of the city underwater, with water rising up to 20 feet high in places. Table 2 also provides data on total housing stock, number of occupied units, population in occupied units and occupancy by tenure for affected MSAs. These data are from the American Community Survey 2005 and the Census Bureau. Commensurate with the shock to occupied housing units, New Orleans-Metairie-Kenner MSA witnessed a massive outflux of population following Katrina. Approximately 40 percent of its population in occupied housing units moved from the metro area during September-December 2005 and was absorbed in large part by neighbouring MSAs. The American Community Survey produced special summary estimates for September-December 2005, which show that of post- Katrina movers, only 28.4 percent relocated within New Orleans MSA, while 14.5 percent moved to Houston, TX metropolitan area and 11.6 percent to the remainder of Texas. 8.1 percent of movers from New Orleans MSA moved to Baton Rouge, LA MSA and 20.6 percent moved to the remainder of the U.S. (excluding Gulf Coast states) (Koerber, 2006). Next, I use MSA level data on ownership vacancies from the Housing Vacancy Survey (HVS) at the Census Bureau, which maintains longer time series for New Orleans and Houston than are available from the ACS. The disadvantage to using HVS data is that only two in-fema MSAs are available, because the HVS surveys only the top 75 MSAs. The ownership vacancy rate is defined as all vacant houses for sale divided by the sum of owner-occupied houses, forsale houses and houses sold but not occupied. The ownership vacancy rate in New Orleans MSA rose from 0.9 percent in 2004 to 2.2 percent in 2005, and continued to rise thereafter. Figure 1 plots the annual vacancy rate for New Orleans MSA from 1990 onwards; the vertical line marks the year 2005 when Hurricane Katrina occurred. Note that MSA definitions used by the HVS changed in 1995 and The sharp increase in the ownership vacancy rate in 2000 to 3.4 percent, coincides with recessionary pressure on Louisiana s economy from the oil industry. The 14

15 rate of unemployment in Louisiana rose from 4.5 percent in 2000 to 5.4 percent in By comparison, the average rate of unemployment in Louisiana for September- December 2005, after Hurricane Katrina, is estimated at 8.8 percent. Figure 2 plots the OFHEO House Price Index (HPI) for New Orleans MSA normalized by U.S. HPI. The vertical line at 2005Q3 marks the quarter in which Hurricane Katrina occurred. The picture is quite stark: house prices fall steadily between 2000Q1 to 2005Q3. From 2005Q4, the price index swings up and continues to climb, showing a clear reversal of the earlier trend. Finally, Figure 3 displays residential building permits for single family homes in New Orleans MSA relative to single family residential permits for the U.S. The vertical line marks the year 2005 when Hurricane Katrina occurred. Permit issuance is a signal of anticipated new housing starts, not a direct count of new houses constructed. While the relative rate of permit issuance seems to have slowed in New Orleans in 2003, new investment in residential single family homes has been rising steadily since Hurricane Katrina. Regression Analysis Although there are a total of 38 MSAs identified with one or more Hurricane-hit counties, not all MSAs are followed in data series on prices and vacancy rates. These data are typically restricted to the largest 75 MSAs in the U.S., which limits the number of in-fema MSAs that can be included in my regression sample. Therefore, the treatment group in my sample consists of 13 MSAs that were directly hit by Hurricane Katrina, the maximum for which price data are available. The sample period is 2000 to I use annual net migration and new residential investment (as proxied by building permits for residential single-family units) for MSAs from the Census Bureau. Due to sample size restrictions, the Census does not produce estimates of starts for geographies below the Census Regions. However, since permits are the fundamental series on which Census estimates of housing starts are formed, they provide a second-best estimate of residential building activity even though they cannot be interpreted directly as housing starts. Permits data are not survey based estimates and instead provide a complete count of intended new residential building activity in the U.S. The Census notes that only about 2.5 percent of housing starts in the United States are built in non-permit areas. Building permits are issued only for new construction and do not include remodeling or repair to existing houses. The 15

16 average lag between issuance of permit and start of construction for new residential buildings is 0.8 months, for Over , no construction has been started by end of year (regardless of month of issue) for approximately 9.5 percent of residential permits issued. I use MSA-level quarterly OFHEO Housing Price Index (HPI) from the Federal Housing Finance Authority (FHFA) website. The HPI is a repeated-sales index and records the sales prices of only those houses that have been sold at least twice over. An MSA can only be reported in a quarter if it has at least 10 qualifying transactions in that quarter. Finally, data on vacancy rates are even less extensive than other time series. Vacancy data are available from 1986 onwards from the Housing Vacancy Survey for only 2 in-fema MSAs. See the Appendix for a list of the MSAs followed by the HVS. Data from the HVS suffer from varying sample size at quarterly frequencies, so I use annual observations only. I also correct for varying MSA definitions over the sample period by calculating heteroskedasticityrobust standard errors in the vacancy rate regressions. To select a comparison group, I include all MSAs for which the HPI is available in a 550 mile radius around New Orleans (excluding those in Florida). See Map 2 for a visual representation of all included MSAs. Altogether, a total of 57 MSAs are included in my sample, which are also listed, together with distance in miles from New Orleans, in the Appendix. With a panel data set for net migration, prices and permits for the full sample of 57 MSAs, I estimate the following difference-in-differences regressions for each series by pooled OLS 1. Equations [12] and [13] are cross-sectional representations of the estimating equations for a single MSA i. = + + [12] = [13] are time dummies, j=2000, 2001,, In equation [12], FEMA interacted with time is a binary variable that takes value 1 if MSA i lies in the FEMA sub-sample of MSAs and the date is j; it takes value 0 otherwise. In equation [13] an MSA lies at Near distance to the epicenter of the Hurricane if it lies within 100 miles of New Orleans. An MSA lies at Medium 1 I do not undertake fixed effects estimation because it is unlikely that area-fixed effects are correlated with the regressors, namely distance interacted with time and disaster-status (in-fema MSA) interacted with time. Nevertheless, preliminary work including fixed effects for prices and permits shows that whilst including area-fixed effects improves efficiency, it does not alter estimated treatment effects from the pooled regression. For purposes of inference, it is important to take area-fixed effects into account, but inference is not the goal of the empirical work undertaken here. 16

17 distance if it is between 100 and 200 miles away from New Orleans. The interaction variables Near*Time and Medium*Time take value 1 if an MSA is Near or Medium respectively and the date is j. In both specifications, the time trend captures the average time path for the comparison group of MSAs that are either non-fema or further than 200 miles from New Orleans city, respectively. The FEMA interaction terms isolate the impact of the Hurricane in excess of the trend, for all affected MSAs identified by FEMA as eligible for receiving public and individual assistance. Near and medium dummies similarly measure impact in excess of the trend on areas close to the epicenter of the storm. I expect to see that the lower the proximity to New Orleans MSA, the less of an estimated deviation there will be for a particular group from the average trend, i.e. > for all j. Since the FEMA group comprises MSAs at varying distances from New Orleans, I also expect that > for all j. Regressions are estimated by pooled OLS or Prais-Winsten regression if there is serial correlation in the residuals. Variance estimates are corrected for panel-heteroskedasticity and serial correlation in the residuals where appropriate. I do not allow contemporaneous correlation in the errors across MSAs. Figure 4 plots estimated FEMA and distance coefficients, for the dependent variable annual net migration as a percentage of total MSA population. Migration estimates are made from mid-year to mid-year and the vertical line in both panels is drawn at mid This corresponds to estimated migration from mid-2005 to mid-2006, thereby including the effect of the Hurricane. Plots of the estimated FEMA and NEAR effects tell the same story. MSAs that bore the brunt of Hurricane Katrina roughly follow the trend prior to the Hurricane. Between 2005 and 2006 in-fema MSAs clearly experience a statistically significant outflux of population, which is estimated at 9.7 percent in NEAR MSAs and 3.8 percent across FEMA metro areas. Point estimates plotted for MEDIUM cities are statistically significant. Selected point estimates and panel-corrected standard errors for both specifications for relative net migration are presented in Table 3. Figure 5 presents estimated FEMA and distance coefficients for the housing price index. NEAR and MEDIUM plotted estimates are normalized to zero in 2000Q1, so the lower panel in Figure 5 can be interpreted as change in price in percentage points. The estimated time trend is again identical for both variations of the regression but is not plotted here. FEMA coefficient 17

18 estimates before 2005Q3 illustrate the similarity of MSAs included in the sample, in that house prices in FEMA cities pre-katrina were consistently between only 2 and 4 index points above the trend for the comparison group. Thus, the subsequent change in trend for in-fema cities was sparked by the only completely unpredictable event that occurred after 2005Q2. Had the shock been foreseeable, the pre-2005q2 pattern suggests that prices across the whole sample would have moved in concord. There is a clear and statistically significant positive effect on prices for in-fema and NEAR MSAs after Hurricane Katrina struck, starting in 2005Q4. Prices in FEMA MSAs increase by 3 percent from 2005Q3, while the jump is 7 percent for NEAR MSAs. As expected, there is a much smaller increase in MEDIUM cities of 1 percent right after the Hurricane. In NEAR MSAs prices continue to rise, peaking at 24 percentage points above their 2005Q2 level at the end of Figure 5 clearly bears out the hypothesis that the closer an MSA lies to the epicenter of the Hurricane, the higher the house price increase it experiences after its occurrence. Selected point estimates for these regressions are presented in Table 4. Next, I analyze the effects of the shock on log residential building permits for singlefamily homes. Figure 6 plots selected coefficient estimates for both specifications. As with prices, distance coefficient estimates for 2000 are normalized to zero so the plots can be interpreted as percent change in log permits over the previous year. The bottom panel of Figure 6 shows that NEAR MSAs saw an increase of 35 percent from 2005 to 2006, while permits issued in-fema MSAs increased by 19 percent. Selected point estimates and standard errors from these regressions are presented in Table 5. The estimated change in prices and permits after the Hurricane provide an instrumental variables estimate of the flow elasticity of supply for areas near the epicenter of the Hurricane. The Hurricane s destruction of housing stock provides an instrument for a shift in flow demand of housing along a stable flow supply curve. For conformity, I re-estimate equation [13] for log prices at annual frequency and construct the ratio of the change in log permits from 2004 to 2006 to the change in log prices over the same period. This yields an estimated flow supply elasticity of 2. Turning finally to data on the ownership vacancy rate by MSA, Figure 7 illustrates clearly that there is a statistically significant rise in vacancy rates in New Orleans MSA in 2007 and Even though the estimated coefficient for NEAR2005 is not statistically significant, 18

19 the difference between NEAR2004 and NEAR2005 is significantly different from zero, with a χ 2 (1) value of (p-value of 0). In-FEMA point estimates show a decline in the ownership vacancy rate after 2005, but coefficient estimates are never significantly different from zero. The plot is an average of the ownership vacancy rate between Houston (where the vacancy rate fell as Houston experienced immigration from New Orleans) and New Orleans (where the vacancy rate rose after the Hurricane). Table 6 reports regression results for data on ownership vacancy rates. All standard errors are corrected for panel-heteroskedasticity to address the issue of changing MSA boundary definitions in vacancy data. These regressions have been run on a panel dataset for 8 MSAs over , of which two are in-fema MSAs (Houston and New Orleans metro areas), and one is within 100 miles of the Hurricane s center - New Orleans MSA itself. The NEAR coefficient therefore isolates the effect on the ownership vacancy rate for New Orleans. Vacancy rates are the average of quarterly rates, recorded at the end of the calendar year, so the vacancy rate in both 2005 and 2006 will show the effects of the Hurricane on the ownership housing market. To emphasize the effect of large fractions of the stock of housing being destroyed by the Hurricane on vacancies, I also re-estimate the regressions after adjusting all in-fema observations for the percentage damage incurred. Since non-fema MSAs experience no damage to housing stock, observations for log permits are multiplied by a factor of 1 (i.e. included without adjustment); for in-fema MSAs, observations are multiplied by a factor (1+η), where η > 0 is the percentage of occupied housing units destroyed. Thus, the more damage an MSA experienced, the more weight its observations have in the regression across all years. Results for actual weighted data in Table 6 show a positive and statistically significant FEMA coefficient in Moreover, all estimated coefficients for specification 2 are statistically significant and reinforce the suggestion that vacancy rates rose in New Orleans MSA after Hurricane Katrina given the high level of destruction in the housing stock. To summarize these findings, metro areas that lie in the path of Hurricane Katrina have experienced higher prices, higher vacancy rates and higher residential permit since Disaster-hit metro areas experienced a large emigration of their resident population which has only been partially reversed thus far. I now proceed to calibrate the model and present simulation results for the full sample of MSAs given shocks that are taken from the data. 19

20 4. Calibration and Simulation Results For the quantitative exercise, I solve the matching model using the Anderson-Moore algorithm. For all MSAs, I choose baseline parameter values from US aggregate data, as detailed in Table 7. There are a few assumptions worth noting. The searcher s Nash bargaining weight is set equal to the searcher s Cobb-Douglas weight in the matching function per the Hosios (1990) condition, which is sufficient for the decentralized equilibrium price and number of vacancies per searcher to be equal to the social planner s solution. This assumes firstly that the social planner s solution is achievable and desirable for the housing market. Secondly, the searcher s match elasticity value of 0.5 implies that one vacancy is created per searcher in the market. Finally, I set the value of exogenous rent in the steady state as 4 percent per annum of sales value, which is in line with estimates by Davis et al (2007) that real rent is between 3.5 and 5.5 percent of sales value in U.S. data. 2 In steady state, price and relative supply are normalized to equal 1 and searchers and vacancies are 5.8 percent of the total population and housing stock respectively. I also apply the post-disaster estimate of flow elasticity of supply of 2 in calibration of the model. I model Hurricane Katrina as a shock variable κ that takes value 1 at the beginning of time in the simulation and is zero thereafter. When κ takes the value 1, depreciation of the housing stock rises by η percent above the steady state level. I calibrate η from actual data for all Hurricane-hit MSAs and set it to zero for all comparison MSAs. The effect of the shock is also carried through emigration and immigration, which are calibrated to actual migration data and this reproduces the actual path of population by construction for each MSA. Since the model does not recognize permanent renters, it is important to make additional adjustments for emigration from New Orleans MSA, for which the designation of emigrants by tenure is available. In total, 32 percent of the total population of New Orleans emigrated after the Hurricane. The number of owner-occupiers who left amounted to 7.6 percent of the pre- Hurricane population. Since the matching model has no place for permanent renters, it is important to account for the large percentage of renters that comprise the total emigration from the city. I therefore mimic the number of owner-occupiers leaving New Orleans in the model to actual data and force all searchers (who are renters) to leave when the shock hits. In the benchmark calibration of the model, I set migration patterns for all MSAs except New Orleans to 2 Time series data on median rents at the MSA level have recently come to my attention, which have not yet been incorporated into the paper. This will follow in a revised version, but at present the maintained assumption for simulations is that rents are exogenous and constant. 20

21 equal actual data exactly. Migration into and out of New Orleans in the model, however, is net of permanent renters and set to 42 percent of actual migration. I check for the robustness of model results under this assumption by setting model migration patterns for all MSAs at 42 percent of actual data and will report those results later in this section. Running the model also requires an assumption about the fraction of emigrants whose houses are destroyed in Hurricane-hit MSAs. This requires choosing a value for the parameter in equation [2]. If is zero, the correlation between destruction of housing and emigration is zero, which is unreasonable. For equal to 1, all owner-occupier emigrants have their houses destroyed. For the benchmark calibration, I set to 0.5 and present robustness checks later in this section. Under these assumptions, I run 57 replications of the model, using the 57 MSA-specific individualized calibrations and generate artificial data for my sample for the 13 quarters following Hurricane Katrina. I will first consider the implications of the shock for a single MSA and then proceed to summarize findings for all MSAs through regression analysis. Figure 8 displays impulse responses for New Orleans for the benchmark calibration, to illustrate the dynamic behavior of the model. When the shock hits the city, the housing stock and population fall by the calibrated amount. While emigration implies a decline in the number of searchers next period, the increase in demand for housing due to the magnitude of destruction of housing stock far outweighs this negative effect. Consequently searchers increase by 600 percent relative to steady state. Vacancies initially rise a mere 16 percent above steady state when the shock occurs, but plummet after that even though new investment rises. Essentially, the matching friction induces inertia in the evolution of housing demand as captured by the number of searchers. Excess demand bids up price and the likelihood of selling a vacant house increases almost fourfold. Flow investment only increases by enough in this forward-looking model to produce the number of housing units the market will match each period, rather than the number of total searchers looking for a house. This eliminates the stock of vacant housing upfront and raises the probability of selling a house over threefold. Since the matching technology does not allow immediate reallocation of housing units across searchers, the effects on price and investment are perpetuated as long as housing demand persists away from the steady state level. 21

22 The behavior of price in relation to the likelihood of selling is important to illustrate a more general point about the model s mechanisms. All else equal, the lower is the hazard rate for a vacant house, the longer its duration of vacancy, and the lower the bargained price it will receive. In the impulse responses here, the ratio of vacancies to searchers falls on impact and slowly rises over time. Thus, the duration of vacancy for available housing units falls and the price a house is able to fetch rises dramatically. The model is therefore able to capture the effect of time-on-market on sales prices in a dynamic aggregate equilibrium framework. To summarize the results of the Monte Carlo simulations and illustrate the predictive capability of the model, I create a combination panel dataset for prices, investment and the vacancy rate. Per MSA, I combine artificial data generated by the model for 13 quarters following the shock (2005Q4 to 2008Q4) with actual data for that MSA for the sample period before Katrina. Using these combination series for the whole panel of MSAs, I re-estimate the regressions for prices, vacancy rates and log investment. I plot the simulated-data estimation results against actual results for prices, permits and vacancy rates in Figures 9 to 11, maintaining the convention that estimates based on actual data alone are represented by solid lines while simulated data estimates are represented by dotted lines. For the FEMA specification in each figure, I also present results from robustness checks in the simulations. These plots are stacked and are read as follows. The line labeled Simulated FEMA BM lies directly above the line labeled Actual FEMA. For example, the point estimate for Simulated FEMA BM for 2005Q4 is equal to the vertical distance between the Simulated FEMA BM line and data point directly below it on the Actual FEMA line at 2005Q4. For ease of comparison, relevant point estimates for 2005 and 2006 for each calibration are also labeled in figures to show the jump predicted by the model on impact of the Hurricane. Since point estimates prior to the Hurricane are identical for all specifications and simulations, by construction, the figures only plot coefficient estimates from simulated and actual data after 2005(Q3). Bottom panels in Figures 9-11 plot NEAR and MEDIUM point estimates for simulated and actual data sets. Figure 9 presents point estimates for prices. In actual data, in-fema MSAs experience a 3.4 percent increase in 2005Q4 over the previous quarter. In contrast, prices in the model overshoot, increasing by 39 percent for in-fema MSAs in the benchmark calibration. The overshooting is even more pronounced in NEAR MSAs, where prices rise by 68 percent in the 22

23 model, compared to about 7 percent in the data. The model seems to perform better for MEDIUM MSAs. This overshooting behavior is due to the size of the shift in demand for housing after the Hurricane. Even though a fraction of former homeowners leave affected cities after the shock, the remaining former owner-occupiers push up demand up to sevenfold because the destruction of housing stock is so large. The top panel in Figure 9 shows that the overshooting behavior of price in FEMA MSAs is robust to any assumption about the correlation of emigration and destruction of housing (captured by ). By construction, the model returns to steady state after a shock, so simulated prices decline over time in Figure 9. In actual data, by contrast, prices in the affected metro areas continue to rise after the Hurricane. Figure 10 similarly compares simulation and actual results for log permits. Here too, the change in permits predicted by the model between 2005 and 2006 is higher than that seen in the data. For in-fema MSAs permits rise by 33 percent in simulations while they rise by 19 percent in the data. In NEAR MSAs, the overshooting is more pronounced, but the model performs relatively well for MEDIUM cities. These effects are robust to any value chosen for. Once more, however, permits in the model start to decline towards steady state, while they are seen to continue to rise above trend in actual data. Finally, Figure 11 shows that vacancy rates also tend to overshoot in the model relative to the data in that FEMA vacancy rates fall by a more than in actual data. For in-fema areas, the vacancy rate falls by 24 basis points after the Hurricane, while in the model the vacancy rate declines by 2 percent. For New Orleans alone, as summarized by the NEAR point estimates, the prediction of the model is counterfactual altogether. The top panels in Figures 9 to 11 also show the effect of assuming lower magnitude of migratory flows in all MSAs than in the benchmark model. Specifically, I restrict migration shocks to be 40 percent of actual size, which reflects the split between renters and owneroccupiers in emigrants from New Orleans. In this case, denoted =0.42 in the figures, prices and permits overshoot by a couple of percentage points more in FEMA areas, while the vacancy rate overshoots by less than the benchmark model, compared to actual data. This illustrates the incremental effect of migration on the housing market, in addition to that of destruction of housing units. Specifically, the lower is reallocation of households across MSAs, the more upward pressure there is on prices and permits to respond to higher demand for housing. More 23

24 houses are produced for sale and sales from the stock of vacancies are replaced at a higher rate in affected MSAs because investment jumps to meet higher demand. The impulse responses and Monte Carlo simulation exercise discussed in this section illustrate the dynamic behavior of the model in response to a completely unforeseen shock to housing flow demand at the start of time. The model propagates the effects of the shock over time through slow moving searchers and vacancies which are restricted in their speed of adjustment by the match friction. Therefore the burden of adjustment in response to the large demand shock lies on jump variables, namely prices and investment, which tend to overshoot relative to actual movement in the data. Since all homeowners who lose a house in the Hurricane are assumed to be immediately searching for another house to purchase, demand increases by several orders of magnitude in affected MSAs in the model. In actual data, it is likely that the demand for ownership housing units is moderated by financial or other constraints on households that are not incorporated here. 5. Related Literature There are a number of empirical studies and theoretical asset-pricing analyses of the housing market that utilize the search and matching framework (Albrecht, et al, 2007; Krainer & LeRoy, 2002; Williams, 1995). These papers tend to focus on the negative correlation between time-onmarket and sales price observed in the housing market, as well as on price premia in ownership or rental vacancies. In the paper that is perhaps closest in spirit to this one, Wheaton (1990) presents a static search model that incorporates structural long-run vacancies but holds the number of vacant ownership homes fixed in the short run with no new net demand. All demand and short run supply is generated from unit switching, given a pre-existing level of vacancies. Holding vacancies fixed, Wheaton shows that longer expected matching times are inversely related with final sales price. The matching model contributed by this paper is dynamic and incorporates aggregate uncertainty. Agents in the model are forward looking and firms decide how many new housing units to produce per period. Aggregate demand for housing shifts in response to migration, rent and move shocks in general. In the natural experiment analyzed here, the model is incorporates a shock to aggregate demand through the destruction of housing stock. Finally, the model also 24

25 incorporates a dynamic aggregate inverse relationship between time-on-market for a vacancy and selling price. 6. Conclusion This paper contributes a new model of the housing market to macroeconomic literature and provides evidence of its predictive capability. The model is a dynamic quantitative matching model for the housing market that forecasts the path of prices, vacancies and flow investment after an unforeseen shock to the housing stock from Hurricane Katrina. It propagates the effects of the shock over time through slow moving searchers and vacancies which are restricted in their speed of adjustment by the matching technology. The burden of adjustment therefore lies on jump variables, namely prices and investment. These variables tend to overshoot relative to actual movement in the data for MSAs affected by Hurricane Katrina.. The overshooting behavior in the model is due to the size of the shift in demand for housing after the Hurricane. Even though a fraction of former homeowners leave affected cities after the shock, the remaining former owner-occupiers push up demand dramatically because the fraction of the housing stock destroyed is so large. Since all homeowners who lose a house in the Hurricane are assumed to be immediately searching for another house to purchase in the model, demand increases by several orders of magnitude in affected MSAs. In actual data, the demand for ownership housing units is likely tempered by financial or other constraints on households. Furthermore, the model s performance also hinges on the assumption of constant rent. This last assumption is clearly counterfactual. Future work will explicitly consider the consequences of endogenous changes in rent. Considering simulation results for New Orleans as a case study of the worst-affected city in the sample, a number of important observations can be made about the model s dynamics. New Orleans experienced both the highest fraction of loss of housing stock and population due to Hurricane Katrina. While emigration implies a decline in the number of searchers in the model, the increase in demand for housing due to the magnitude of destruction of housing stock far outweighs this negative effect. Excess demand bids up price and the likelihood of selling a vacant house increases almost fourfold. The behavior of price in relation to the likelihood of selling illustrates a more general point about the model s mechanisms. All else equal, the higher is the hazard rate for a vacant house, the lower its duration of vacancy, and the higher the 25

26 bargained price it will receive. When demand rises after the shock, relative supply of vacancies and hence the duration of vacancy for available units both fall and the price a house is able to fetch rises dramatically. The model is therefore able to capture the effect of time-on-market on sales prices in a dynamic aggregate equilibrium framework. After the shock, the matching friction induces inertia in the evolution of housing demand as captured by the number of searchers. Flow investment only increases by enough in this forward-looking model to produce the number of housing units the market will match each period, rather than the number of total searchers looking for a house. Since the matching technology does not allow immediate reallocation of housing units across searchers, the effects on price and investment are perpetuated as long as housing demand persists away from the steady state level. The model in this paper does not analyze the effects of movement in the rental price of houses. Since rental prices must also rise after a reduction in the stock of housing, it is likely that incorporating a rental market would cause prices to further overshoot in the model. However, it is also possible that former owner-occupiers might switch to rental units rather than search for a new house to purchase in the aftermath of the shock. The result would depend on the individual household s choice between renting and buying a house. This provides a rich set of questions for future work that will build on the present matching model of housing. 26

27 References Albrecht, James, Axel Anderson, Eric Smith and Susan Vroman, "Opportunistic Matching In The Housing Market," International Economic Review, vol. 48(2), p , May. Davis, Morris A., Andreas Lehnert and Robert F. Martin, The Rent-Price Ratio for the Aggregate Stock of Owner-Occupied Housing, Review of Income and Wealth, 2008, vol. 54 (2), p Hosios, Arthur J, "On the Efficiency of Matching and Related Models of Search and Unemployment," Review of Economic Studies, vol. 57(2), p , April. Koerber, Kin, Migration Patterns and Mover Characteristics from the 2005 ACS Gulf Coast Area Special Products, U.S. Census Bureau, Housing and Economic Household Statistics Division, November. Available online at Krainer, John & Stephen F. LeRoy, "research articles : Equilibrium valuation of illiquid assets," Economic Theory, Springer, vol. 19(2), p Mortensen, Dale T, "Job Search, the Duration of Unemployment, and the Phillips Curve," American Economic Review, American Economic Association, vol. 60(5), p , December. Mortensen, Dale T., "Job search and labor market analysis," Handbook of Labor Economics, in: O. Ashenfelter & R. Layard (ed.), Handbook of Labor Economics, edition 1, volume 2, chapter 15, p , Elsevier. Pissarides, Christopher A, "Short-Run Equilibrium Dynamics of Unemployment, Vacancies, and Real Wages," American Economic Review, Vol. 75, (4), pp , September. Pissarides, Christopher A., Equilibrium Unemployment Theory, 2nd Edition, MIT Press Books, The MIT Press, January. U.S. Department of Housing and Urban Development s Office of Policy Development and Research, Current Housing Unit Damage Estimates Hurricanes Katrina, Rita and Wilma February 12, 2006 (Revised April 7, 2006) Available on the internet at Wheaton,William, Vacancy, Search and Prices in a Housing Market Model, Journal of Political Economy 98 (1990), p Williams, J., Pricing Real Assets with Costly Search, Review of Financial Studies 8 (1995), p

28 Appendix American Community Survey The ACS produced a special set of event estimates for the U.S. Gulf Coast immediately after Hurricane Katrina which are used in this paper to identify migration patterns (Koerber 2006). These are summary profiles of Alabama, Louisiana, Mississippi and Texas, at the state, selected county, selected MSA, in-fema areas and balance-of-state designations. The Special Product includes annualized estimates of housing units, tenure and occupancy status as well as migration and population counts for 2005 in two batches: January to August 2005, and September to December Estimates are not controlled to independent population or housing unit counts, but are otherwise made in a manner identical to the regular ACS products 3. The Special Product uses the same national sample selected at the beginning of 2005 for the standard 2005 Survey, which comprises about 1,945,000 addresses for the 8-month estimates and 977,000 addresses for the 4-month estimates 4. These can be accessed on the web at Tropical Cyclone Reports on Hurricanes Katrina and Rita are available on the web at and FEMA Damage Estimates by Tenure According to FEMA, percent of the total occupied housing units in Louisiana suffered major or severe damage and 5.66 percent in Mississippi. Amongst this, 5.6 percent of Louisiana s owner-occupied housing stock was damaged and almost 8% of its renter-occupied housing units. Appendix Table A2 shows the breakdown of damage estimates by tenure, at the state level. The percentages of housing units destroyed or damaged are with respect to the count of 3 Usually, estimates published by the ACS are controlled to independent population estimates by the Census, as of July 1 of that year. Since the population counts of July 1,2005 would not reflect the effects of Katrina, this step was omitted in the Special Product. 4 The sampling frame and sampling rates were not adjusted for the ACS 2005 Special Product. Further, since sample selection occurred well before Hurricane Katrina struck, temporary shelters and group quarters were not included in the Survey. 28

29 occupied housing units estimated in the American Community Survey Calculating the percentages of units damaged this way gives an indication of how much of the displaced population from these states had to move location due to destruction of housing stock. For instance, Louisiana was clearly the worst hit state, where 5.6 percent of owner-occupied housing units and almost 8 percent of renter-occupied housing units were destroyed by the Hurricane. In the main paper, damage estimates are presented as a percentage of total housing stock and those are the numbers used to calibrate the matching model. FEMA inspections lasted until 12 February 2006, so these estimates include damage from Hurricane Rita. Hurricane Rita occurred on 24 September 2005 and caused repeated flooding of areas affected by Katrina. For the use of FEMA estimates in this paper, this does not pose an issue since other data series used are annual (or, in case of price data, quarterly). Having damage estimates for the third quarter of 2005 makes them more consistent with the rest of the analysis. 29

30 Appendix Table A1 Sample for Empirical Analysis CBSA Code MSA Name Miles to New Orleans HVS Sub- Sample New Orleans-Metairie-Kenner, LA 0.00 Yes Houma-Bayou Cane-Thibodaux, LA Gulfport-Biloxi, MS Baton Rouge, LA Pascagoula, MS Hattiesburg, MS Lafayette, LA Mobile, AL Jackson, MS Alexandria, LA Lake Charles, LA Monroe, LA Beaumont-Port Arthur, TX Tuscaloosa, AL Montgomery, AL Shreveport-Bossier City, LA Dothan, AL Birmingham-Hoover, AL Yes Pine Bluff, AR Houston-Sugar Land-Baytown, TX Yes Longview, TX Auburn-Opelika, AL Texarkana, TX-Texarkana, AR Columbus, GA-AL Tyler, TX Little Rock-North Little Rock-Conway, AR Anniston-Oxford, AL Memphis, TN-MS-AR Yes Hot Springs, AR Florence-Muscle Shoals, AL Decatur, AL Gadsden, AL Albany, GA College Station-Bryan, TX Huntsville, AL Jackson, TN Jonesboro, AR Valdosta, GA

31 Appendix Table A1 (Contd.) Sample for Empirical Analysis CBSA Code MSA Name Miles to New Orleans Rome, GA Warner Robins, GA HVS Sub- Sample Atlanta-Sandy Springs-Marietta, GA Yes Victoria, TX Macon, GA Waco, TX Dallas-Plano-Irving, TX (MSAD) Yes Dalton, GA Chattanooga, TN-GA Austin-Round Rock, TX Yes Corpus Christi, TX Nashville-Davidson--Murfreesboro--Franklin, TN Yes Cleveland, TN Gainesville, GA Athens-Clarke County, GA Brunswick, GA Brownsville-Harlingen, TX Augusta-Richmond County, GA-SC Savannah, GA Notes: This table displays the list of metropolitan statistical areas (MSAs) that comprise the sample for empirical analysis in this paper, sorted by Miles to New Orleans. The first column shows the CBSA code the standard geographic identifier for each MSA per November 2007 MSA definitions. The last column indicates with entry Yes if the MSA is in the sub-sample for which ownership vacancy rates are available from the Housing Vacancy Survey. 31

32 Appendix Table A2 State-Level Estimated Damage to Occupied Housing Units in Hurricanes Katrina and Rita by Tenure Owner- Occupied Units Alabama Louisiana Mississippi Texas Renter- Occupied Units Owner- Occupied Units Renter- Occupied Units Owner- Occupied Units Renter- Occupied Units Owner- Occupied Units Renter- Occupied Units Flood Damage Major Damage 1, ,434 25,881 18,752 10, Severe Damage/Destroyed ,137 41,361 7,366 4, Wind Damage Major Damage ,589 13,182 12,137 4,602 7,700 2,292 Severe Damage/Destroyed ,432 1,721 2,252 1,285 1, Total Occupied Units 1,261, ,217 1,136, , , ,588 5,162,604 2,815,491 Severe Damage as Percentage of Occupied Units (%) Severe & Major Damage as Percentage of Occupied Units (%) Source: HUD Report (2006) ; American Community Survey 2005

33 Table 1 Estimated Number of Housing Units Damaged in Core Counties* Affected by Hurricane Katrina Major Damage Severe Damage Total Housing Units as of July 1, 2005 Percentage of Total Housing Stock Destroyed (%) Percentage of Total Housing Stock with Major or Severe Damage (%) Louisiana LAKE CHARLES MSA Cameron Parish 914 1,665 5, NEW ORLEANS-METAIRIE-KENNER MSA Jefferson Parish 29,643 4, , Orleans Parish 26,405 78, , Plaquemines Parish 1,190 3,994 11, St. Bernard Parish 5,938 13,748 27, St. Tammany Parish 15,948 1,682 88, ABBEVILLE MICROPOLITAN STATISTICAL AREA Vermilion Parish 2, , Mississippi GULFPORT-BILOXI MSA Hancock County 7,185 4,611 23, Harrison County 16,829 7,618 88, Stone County , PASCAGOULA MSA Jackson County 14,259 2,043 56, Notes:*Louisiana is divided into parishes, analogous to counties elsewhere. Counties are assigned to MSAs per November 2007 definitions by U.S. Office of Management & Budget (OMB). These estimates were finalized by February 12, 2006 & include storm surge damage from Rita. Hurricane Katrina hit New Orleans & Gulfport-Biloxi metro areas with unequaled force & most of this damage was initiated in September Lake Charles MSA lay directly in Rita s path & Rita also caused repeated flooding in areas previously hit by Katrina. Source: FEMA count of damaged units from HUD Report (2006); Estimated total housing units from Population Division, U.S. Census Bureau. 33

34 Table 2 Estimated Number of Housing Units Damaged in MSAs Affected by Hurricane Katrina Owner- Occupied Housing Units Renter- Occupied Housing Units Number of Housing Units with Major Damage Number of Housing Units with Severe Damage Total Number of Housing Units Damaged Major & Severely Damaged Houses as a Percentage of Occupied Housing Units (%) Total Damaged Houses as a Percentage of Occupied Housing Units (%) Baton Rouge, LA 190,591 83, , Beaumont-Port Arthur, TX 97,507 47,055 32,752 5, , Gulfport-Biloxi, MS 67,109 34,077 24,446 12,330 67, Hattiesburg, MS 31,822 16,806 1, , Houma-Bayou Cane-Thibodaux, LA 52,458 17,515 2, , Houston-Sugar Land-Baytown, TX 1,146, ,668 1, , Jackson, MS 131,145 62, , Lafayette, LA 65,859 29, , Lake Charles, LA 52,597 22,271 6,678 2,285 47, Mobile, AL 101,298 49,293 2, , New Orleans-Metairie-Kenner, LA 305, ,513 79, , , Pascagoula, MS 42,954 14,042 14,624 2,119 34, Tuscaloosa, AL 49,173 30, , Notes: Counties are assigned to MSAs per November 2007 definitions by U.S. Office of Management & Budget (OMB). Source: FEMA count of damaged units from HUD Report (2006); Estimated total housing units American Community Survey 2005, U.S. Census Bureau 34

35 Table 3 Pooled OLS Estimates for Net Migration as a Percentage of Population FEMA Specification Distance Specification FEMA Near Medium (0.9) (1.97) (0.28) (0.9) (1.97) (0.28) (0.9) (1.97) (0.28) *** -9.69*** 0.09 (0.9) (1.97) (0.28) (0.9) (1.97) (0.28) (0.9) (1.97) (0.28) Notes: Coefficient estimates are starred to indicate statistical significance: *** indicates significance at 1% level; ** indicates significance at 5%; and * indicates significance at 10% level. All estimates have panel-corrected standard errors in parentheses adjusted for panel-heteroskedasticity. This table displays selected coefficient estimates from the pooled cross sectional regression for net migration in my sample of 57 MSAs, which includes 13 in- FEMA metro areas. The estimated regression is of the form = + +, where i subscripts MSA. are time dummies, j=2000, 2001,, 2008 and are dummies capturing the effect of distance from New Orleans city in three different ways. The alternative specifications are as follows: 1) D i is a dummy identifying in-fema MSAs and is interacted with time. 2) D i is further divided into dummies indicating near distance (for an MSA that lies within 100 miles of New Orleans) or medium distance ( miles from New Orleans city) and interacted with time. See also Figure 4.

36 Table 4 Pooled OLS Estimation Results for the Housing Price Index FEMA Specification Distance Specification Date FEMA Near Medium 2005Q * (2.86) (5.28) (1.82) 2005Q ** (2.86) (5.28) (1.82) 2005Q ** 0.58 (2.86) (5.28) (1.82) 2005Q4 6.83** 18.55*** 1.55 (2.86) (5.28) (1.82) 2006Q1 8.8*** 20.88*** 3.13* (2.86) (5.28) (1.82) 2006Q *** 26.19*** 6.33*** (2.86) (5.28) (1.82) 2006Q *** 29.25*** 8.48*** (2.86) (5.28) (1.82) 2006Q *** 30.62*** 8.51*** (2.86) (5.28) (1.82) 2007Q1 15.8*** 33*** 8*** (2.86) (5.28) (1.82) 2007Q *** 32.41*** 8.63*** (2.86) (5.28) (1.82) 2007Q *** 32.92*** 9.85*** (2.86) (5.28) (1.82) 2007Q *** 35.11*** 9.76*** (2.86) (5.28) (1.82) 2008Q *** 35.07*** 10.42*** (2.86) (5.28) (1.82) 2008Q *** 34.3*** 10.4*** (2.86) (5.28) (1.82) 2008Q *** 30.54*** 9.81*** (2.86) (5.28) (1.82) 2008Q *** 31.99*** 9.5*** (2.86) (5.28) (1.82) Notes: Coefficient estimates are starred to indicate statistical significance: *** indicates significance at 1% level; ** indicates significance at 5%; and * indicates significance at 10% level. All estimates have panel-corrected standard errors in parentheses adjusted for panel-heteroskedasticity and for serial correlation in residuals. This table displays selected coefficient estimates from the pooled cross sectional regression for the house price index in my sample of 57 MSAs, which includes 13 in-fema metro areas. The estimated regression is of the form = + +, where i subscripts MSA. are time dummies, j=2000, 2001,, 2008 and are dummies capturing the effect of distance from New Orleans city in three different ways. The alternative specifications are as follows: 1) D i is a dummy identifying in-fema MSAs and is interacted with time. 2) D i is further divided into dummies indicating near distance (for an MSA that lies within 100 miles of New Orleans) or medium distance ( miles from New Orleans city) and interacted with time. See also Figure 5.

37 Table 5 Pooled Cross Section OLS Estimates for Log Residential Building Permits Actual Log Residential Building Permits Damage-Weighted Actual Log Residential Building Permits FEMA Specification Distance Specification FEMA Specification Distance Specification FEMA Near Medium FEMA Near Medium * ** 0.53** (-0.2) (-0.22) (-0.24) (-0.2) (-0.23) (-0.24) *** 0.68*** *** 0.89*** (-0.2) (-0.22) (-0.24) (-0.2) (-0.23) (-0.24) *** 0.55*** *** 0.76*** 0.08 (-0.2) (-0.22) (-0.24) (-0.2) (-0.23) (-0.24) *** 0.68*** *** 0.89*** 0.29 (-0.2) (-0.22) (-0.24) (-0.2) (-0.23) (-0.24) Notes: Coefficient estimates are starred to indicate statistical significance: *** indicates significance at 1% level; ** indicates significance at 5%; and * indicates significance at 10% level. All estimates have panel-corrected standard errors in parentheses adjusted for panel-heteroskedasticity. This table displays selected coefficient estimates from the pooled cross sectional regression for log permits in my sample of 57 MSAs, which includes 13 in- FEMA metro areas. The estimated regression is of the form = + +, where i subscripts MSA. are time dummies, j=2000, 2001,, 2008 and are dummies capturing the effect of distance from New Orleans city in three different ways. The alternative specifications are as follows: 1) D i is a dummy identifying in-fema MSAs and is interacted with time. 2) D i is further divided into dummies indicating near distance (for an MSA that lies within 100 miles of New Orleans) or medium distance ( miles from New Orleans city) and interacted with time. See also Figure 6.

38 Table 6 Pooled Cross Section OLS estimates for Ownership Vacancy Rates Actual Ownership Vacancy Rate Damage-Weighted Actual Ownership Vacancy Rate FEMA Distance FEMA Distance Speciation Specification Specification Specification FEMA Near FEMA Near * 1.81*** *** 2.78*** (0.42) (0.23) (0.49) (0.24) (0.42) (0.23) (0.49) (0.24) ** -1*** * -0.79*** (0.42) (0.23) (0.49) (0.24) * -1.31*** *** (0.42) (0.23) (0.49) (0.24) *** *** (0.42) (0.23) (0.49) (0.24) ** 0.39* (-0.42) (-0.23) (-0.49) (-0.24) *** (-0.42) (-0.23) (-0.49) (-0.24) ** 1.21*** *** 2.34*** (-0.42) (-0.23) (-0.49) (-0.24) *** *** (-0.42) (-0.23) (-0.49) (-0.24) Notes: Coefficient estimates are starred to indicate statistical significance: *** indicates significance at 1% level; ** indicates significance at 5%; and * indicates significance at 10% level. All estimates have panel-corrected standard errors in parentheses adjusted for panel-heteroskedasticity. This table displays selected coefficient estimates from the pooled cross sectional regression for the ownership vacancy rate for a sample of 8 MSAs, which includes 2 in-fema metro areas. The estimated regression is of the form = + +, where i subscripts MSA. are time dummies, j=2000, 2001,, 2008 and are dummies capturing the effect of distance from New Orleans city in three different ways. The alternative specifications are as follows: 1) D i is a dummy identifying in-fema MSAs and is interacted with time. 2) D i is further divided into dummies indicating near distance (for an MSA that lies within 100 miles of New Orleans) or medium distance ( miles from New Orleans city) and interacted with time. See also Figure 7.

39 Table 7 - Calibrated Values for Parameters of the Matching Model Description Value Source Matching efficiency 0.82 per quarter γ Searchers elasticity in match function 0.5 Median search duration is 8 weeks for the U.S., National Association of Realtors Satisfies Hosios (1990) condition for efficient competitive equilibrium prices α Supply shifter 1-1 λ δ Elasticity of flow supply 2 Separation rate 0.2 per annum Depreciation rate per annum Nash bargaining weight of households 0.5 Coefficient estimates on FEMA2006 dummy from pooled cross sectional regressions for prices and log permits (annual data) in this paper Median length of stay in one house is 6 years for the U.S., National Association of Realtors Service life of a house is 80 years, Bureau of Economic Analysis (BEA), February 2008 Satisfies Hosios(1990) condition for efficient competitive equilibrium prices r R real discount rate Steady state exogenous real rental rate Percent of housing stock destroyed by Hurricane, varies by MSA i Fraction of emigrating owner-occupiers who sell their house 0.02 per annum Average real Federal Funds Rate, 1956Q1-2007Q Real rents lie between 3.5% and 5.5% of per annum the value of a house, Davis et al (2008) [0,0.381] HUD report (2006) 1 - Notes: This table shows the baseline values chosen for parameters and exogenous variables in the quantitative solution of the matching model.

40 Figure 1 Ownership Vacancy Rate for New Orleans MSA Percent Source: Housing Vacancy Survey, Census Bureau Notes: This figure shows the rate of vacant houses for sale relative to the total sum of owner-occupied houses, for-sale units and sold-but-not-occupied houses in New Orleans, MSA, Louisiana. The HVS is a supplement of the Current Population Survey. Until 1994, the HVS uses 1980 metropolitan area (MA) definitions; from it uses 1990 MA definitions and 2005 onwards it uses 2003 CBSA definitions. See HVS/Census Bureau website for information on how metropolitan areas are defined.

41 Figure 2 - Housing Price Index for New Orleans, MSA normalized by U.S. House Price Index Q1 2001Q1 2002Q1 2003Q1 2004Q1 2005Q1 2006Q1 2007Q1 2008Q1 2009Q1 Source: OFHEO/FHFA 41

42 Figure 3 - Single Family Residential Building Permits in New Orleans, MSA as a Percentage of US Single Family Building Permits Percent Source: Census Bureau Notes: This figure plots the level of annual residential building permits for single family houses issued in the New Orleans-Metairie-Kenner MSA as a percentage of total US single family residential permits since Building permits are issued for new construction only and do not reflect remodeling and repairs. All building permits issued are counted and only about 3 percent of housing starts in the U.S. are commenced without a permit. Permits are the primitive for Census estimates of housing starts (made only at the U.S. and regional levels of geography) but should not be interpreted directly as housing starts. 42

43 1 Figure 4 Net Migration as a Percentage of Total Population 0 Percent -1-2 FEMA Percent Near Medium Notes: This figure plots point estimates for FEMA, NEAR and MEDIUM dummies interacted with time from regressions for actual migration data. See Table 3 for regression results and details on estimation. 43

44 20 Figure 5 Estimation Results for Quarterly House Price Index (1995Q1=100) 15 Axis Title 10 FEMA Q1 2001Q1 2002Q1 2003Q1 2004Q1 2005Q1 2006Q1 2007Q1 2008Q1 Percent Q1 2001Q1 2002Q1 2003Q1 2004Q1 2005Q1 2006Q1 2007Q1 2008Q1 "Near" "Medium" Notes: This figure plots point estimates for FEMA, NEAR and MEDIUM dummies interacted with time from regressions for actual price data. See Table 4 for regression results and details on estimation. 44

45 Figure 6 Estimation Results for Log Residential Building Permits for Single-Family Units 0.75 Log Units FEMA Log Permits "Near" "Medium" Notes: This figure plots point estimates for FEMA, NEAR and MEDIUM dummies interacted with time from regressions for actual permits data. See Table 5 for regression results and details on estimation. 45

46 1 Figure 7 Estimation Results for Annual Ownership Vacancy Rate 0.5 Percent 0 FEMA Percent Near Notes: This figure plots point estimates for FEMA and NEAR dummies interacted with time from regressions for actual ownership vacancy rates. See Table 6 for regression results and details on estimation. 46

47 Figure 8 FEMA MSAs Simulated Impulse Responses to Katrina Shock % deviation % deviation % deviation Depreciation Years Years Investment Vacancies Years Housing Stock Years Price Years Searchers Years Population Years Probability of Selling Years Notes: This figure plots impulse responses from the model simulation for New Orleans MSA. The top panel shows the depreciation shock, which is equal to 38 percent of the housing stock by construction from the data. Also in the top panel is the shock to population, which falls 13.4 percent in New Orleans on impact of the Hurricane. The second and third panels plot the impulse response for 10 years following the Hurricane, for selected variables from the model. Note that actual data are only available for 3 y ears after the Hurricane, which occurred on 29 August 2005, for comparison with these simulations. 47

48 Figure 9 Estimation Results for Actual HPI and Simulated House Prices (Percentage) Q3 2006Q1 2006Q3 2007Q1 2007Q3 2008Q1 2008Q3 Simulated FEMA tau=0.42 Simulated FEMA psi=0.25 Simulated FEMA psi=1 Simulated FEMA BM Actual FEMA Q1 2001Q1 2002Q1 2003Q1 2004Q1 2005Q1 2006Q1 2007Q1 2008Q1 Actual NEAR Simulated NEAR Actual MEDIUM Simulated MEDIUM Notes: This figure plots regression results of actual versus artificial data on house prices. The dotted lines represent point estimates from artificial data. The top panel compares simulation results across different calibrations of the model and stacks each set of regression estimates one on top of the other. Hence the vertical distance between points at 2006Q1 for Actual FEMA and Simulated FEMA BM is the point estimate for Simulated FEMA BM. For the sake of graphical clarity, estimates prior to 2005Q3 are omitted in the top panel, because these are equal across actual and simulated data and across calibrations, by construction. 48

49 3.7 Figure 10 Estimation Results for Actual Log Permits and Simulated Flow Log Investment Simulated FEMA tau=0.42 Simulated FEMA psi=0.25 Simulated FEMA psi=1 Simulated "FEMA" BM Actual "FEMA" Actual "Near" Actual "Medium" Simulated "Near" Simulated "Medium" Notes: This figure plots regression results of actual versus artificial data on house prices. The dotted lines represent point estimates from artificial data. The top panel compares simulation results across different calibrations of the model and stacks each set of regression estimates one on top of the other. Hence the vertical distance between points at 2006Q1 for Actual FEMA and Simulated FEMA BM is the point estimate for Simulated FEMA BM. For the sake of graphical clarity, estimates prior to 2005Q3 are omitted in the top panel, because these are equal across actual and simulated data and across calibrations, by construction. 49

50 Figure 11 Estimation Results for Actual and Simulated Ownership Vacancy Rate 4 Percent Actual FEMA Simulated FEMA BM Simulated FEMA psi=1 Simulated FEMA tau= Percent Actual Near Simulated Near BM Notes: This figure plots regression results of actual versus artificial data on ownership vacancy rates. The dotted lines represent point estimates from artificial data. The top panel compares simulation results across different calibrations of the model and stacks each set of regression estimates one on top of the other. Hence the vertical distance between points at 2006Q1 for Actual FEMA and Simulated FEMA BM is equal to the numerical value of the point estimate for Simulated FEMA BM. For the sake of graphical clarity, estimates prior to 2005Q3 are omitted in the top panel, because these are equal across actual and simulated data and across calibrations, by construction. 50

51 Map 1 Louisiana Metropolitan Statistical Areas and Parishes Lake Ponchartrain Breton Sound 51

52 Map 2 Sample Selection for analysis of empirical data Source: Census Atlas of the United States, 52