Journal of Housing Economics 18 (2009) 1–12

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Journal of Housing Economics journal homepage: www.elsevier.com/locate/jhec

Housing demand in Mexico q Matías Fontenla a, Fidel Gonzalez b,* a b

Department of Economics, University of New Mexico, Albuquerque, NM 87131, USA Department of Economics and Intl. Business, Sam Houston State University, Huntsville, TX 77341, USA

a r t i c l e

i n f o

Article history: Received 19 September 2007 Available online 10 September 2008

JEL classification: R21 R58 Keywords: Housing demand Mexico

a b s t r a c t This paper analyzes the components of housing demand in Mexico in the context of developing and developed nations. The case of Mexico is particularly interesting given that population and income dynamics, as well as current housing shortages, suggest that the demand for housing will significantly increase in the near future. We use micro-level data from market-based mortgages that originated during the period of 2002 to 2004 for 21 metropolitan areas in Mexico. We find the price elasticity of housing demand to be 0.3, lower than previous studies for developed countries and within the range for developing countries. Permanent income is a major component of housing demand, with an elasticity of 0.8. In contrast, temporary income has a very low elasticity of 0.04. The mortgage rate elasticity for 25-year mortgages is 0.39. We believe these results provide important information to policy makers and practitioners in Mexico and other developing nations. Ó 2008 Elsevier Inc. All rights reserved.

1. Introduction Numerous studies have researched housing demand for developed countries, but applied research for developing countries is still scarce. As noted by Malpezzi (1999), while housing market behavior across countries has been similar, developing countries present important distortions in land and credit markets, urban infrastructure, and regulation and law enforcement, among others. Also, many of the largest and fastest growing urban centers are located in developing nations. Mexico, like most developing countries, suffers a significant shortage of housing. The National Housing Commission (Conafovi) concluded in 2000 that Mexico required 1.8 million new housing units and major improvements in 2.5 million existing units given their severe level of deteq We would like to thank the editor and an anonymous referee for excellent comments and suggestions, David Drukker and Jayme Meyer for helpful comments, and Sociedad Hipotecaria Federal personnel for all their support. The views expressed in this paper are those of the authors and do not necessarily reflect the views of SHF. * Corresponding author. Fax: +1 936 294 3488. E-mail address: fi[email protected] (F. Gonzalez).

1051-1377/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jhe.2008.08.001

rioration. Population and income dynamics will continue to exacerbate this housing shortage in coming years. The National Population Council (Conapo) estimates the number of households will increase from 26.1 million in 2005 to 36.9 million in 2021, with an average of 673,484 new households each year (see Conapo, 2005). In addition, the size and income of the middle class are expected to increase (see Skelton 2006). Durand and Massey (2004) use the Mexican Migration Project dataset to reveal that the number one reason Mexicans migrate to the United States is to generate enough savings to purchase or build a home back in Mexico. Thus, it is possible that significant improvements in Mexican housing markets may actually affect migration patterns to the United States. This paper analyzes the different components of housing demand in Mexico. We use data from market-based mortgages that originated during the period 2002–2004. To our knowledge, there are no previous studies that estimate housing demand in Mexico.1 Previous work on the Mexican housing sector focused on the mortgage market 1 This paper follows up on the preliminary analysis of Fontenla et al. (2007).

2

M. Fontenla, F. Gonzalez / Journal of Housing Economics 18 (2009) 1–12

and the 1995 crisis (see Pickering, 2000a; Lea and Bernstein, 1996). Gonzalez (1997) estimates the tenure choice of households and their expenditure in housing related services which includes in one variable spending in rent, maintenance, water, electricity, gas, and other services, using the Income Expenditure Survey (ENIGH) for three metropolitan areas of Mexico. Our analysis differs in that we estimate the actual quantity of housing demanded and do not consider spending in related services such as water and electricity. Moreover, we use real market transactions that cover 21 metropolitan areas in 16 of the 32 states of Mexico. Previous studies for developing countries are carefully reviewed in Malpezzi (1999). Most studies use a logarithmic or linear approach, differentiate by tenure, and housing payment for owners is obtained as an imputed rent value. In terms of data, most of the studies are cross-sectional and use household surveys, generally for a particular city or urban area. The key results in terms of price and income elasticities are the following: (1) Income elasticity is divided into owners and renters and in some cases between permanent and temporary income. Most income elasticities are between 0.4 and 0.8 for renters and 0.6 to 1.2 for owners. Permanent income elasticities tend to be higher than temporary income elasticities. (2) Price elasticity is not commonly reported and presents a high degree of variation. However, when it is provided, housing demand is price-inelastic. Estimates vary from close to zero for the Follain et al. (1980) study of South Korea, to almost 1 for Malpezzi and Mayo (1987a,b). In general, price elasticities tend to be lower in absolute value than income elasticities. Other papers for developing countries published after Malpezzi’s (1999) review also confirm these main results. Tiwari and Parikh (1999) estimate the demand for Mumbai, India using a cross-section semi-logarithmic single equation OLS model by tenure. Price elasticities are -0.85 for owners and 1.02 for renters. Halicioglu (2007) follows an Auto Regressive Distributed Lag approach using macroeconomic data for Turkey from 1964 to 2004. The income elasticity is close to one and the price elasticity is 0.2. The literature on developed countries is extensive. The studies range from estimation at the national level, to specific age or race groups. Mayo (1981) and Ermisch et al. (1996) provide a review of results and methodologies. Ermisch et al. (1996) locates the income elasticity of demand between 0.8 and 1.0 and the permanent income elasticity of demand between 0.76 and 0.87. For the latter, Mayo (1981) presents a range of 0.36–0.87 for owners when disaggregated data are used. Regarding the price elasticity of demand, Mayo (1981) reports that it varies depending on how housing prices are obtained and the model used. Using hedonic price indexes similar to the approach in our paper, the price elasticity is 0.53. Moreover, Ermisch et al. (1996) reports a range between 0.5 and 0.8. We contribute to the existing literature by estimating the parameters of housing demand of 21 metropolitan areas in Mexico and comparing our results to previous estimates for developed and developing countries. The approach in our paper differs from previous work for developing countries in the following ways: (a) we use

mortgage data with households’ socioeconomic information, mortgage terms, and physical characteristics of the housing unit, (b) housing values come from real market transactions, and (c) we consider a Box-Cox transformation to allow the data to determine the degree of nonlinearity in the model. Regarding the results, we find the price elasticity of housing demand to be 0.3, which is lower than the range for owners in developed countries and within the range for developing countries. This low price elasticity may be explained by the lack of close substitutes to owning a housing unit in Mexico, relative to developed countries. For instance, rental markets are underdeveloped because of strong regulatory and legal deficiencies. Moreover, the aforementioned need of 1.8 million new housing units also tends to decrease the price elasticity of demand. Permanent income is also an important factor in the demand with an elasticity of 0.8. This is within the range for developed and developing countries. Temporary income has a small effect on housing demand with an elasticity of 0.04, which is low compared to previous studies. We find the final mortgage interest rate elasticity for 25-year mortgages to be 0.39, suggesting that lower mortgage rates can play an important role in housing demand. Regarding the demographic characteristics of the household, male heads of household demand 4% less than females, and married households demand 2% more than their unmarried counterparts. Finally, head of household age and number of dependents decrease the amount of housing demanded. The rest of the paper is organized in five sections. In the next section we present the theoretical framework and the three-step empirical model used in this paper. Section 3 discusses the data. In Section 4 we perform the empirical estimations and present the main results. We offer some concluding remarks in Section 5. 2. Theoretical framework and empirical specification 2.1. Theoretical framework The theoretical framework follows the work of Goodman (1988) and Zabel (2004). We consider the problem faced by household i in market j whose utility function depends on the amount of the housing unit (q) and other goods consumed (C). Households have the same utility function but differ in their demographic characteristics (A). The vector A includes variables such as head of household age, gender, and education.

U i;j ¼ Uðqi;j ; C i;j ; Ai Þ

ð1Þ

Assuming a static setting the household’s problem is to maximize utility subject to their income (m) and the price (p) of housing and other goods.

Max Uðqi;j ; C i;j ; Ai Þ qi;j C i;j

s:t:

ð2Þ

C i;j þ pj qi;j ¼ mi;j where the price of C is the numeraire and set equal to one. We allow housing prices to be different across markets.

M. Fontenla, F. Gonzalez / Journal of Housing Economics 18 (2009) 1–12

The previous maximization will yield the household’s demand function for housing:

qi;j ¼ qðpj ; mi;j ; Ai Þ

ð3Þ

Estimating the implicit parameters of Eq. (3) is the main purpose of this paper. We usually observe the value of the housing unit rather than the quantity. Thus, qi;j has to be estimated in order to obtain Eq. (3). This is achieved by noting that an important feature of housing markets is that the physical and surrounding characteristics of the housing units are important and vary widely across housing units. Define Hn as the vector that represents housing characteristics (such as lot size, distance to amenities, construction size and number of bedrooms, among others) for housing unit n. Similarly, bj is defined as the parameter vector, which is allowed to vary across markets, for each of the housing unit characteristics in Hn . Thus, the value v of a housing unit n in market j consumed by household i is given by the following expression:

vin;j ¼ vðHn ; bj Þ

ð4Þ vin;j

If the characteristics Hn and the value of each housing unit are known, then it is possible to estimate bj using a hedonic price model. In addition, defining Hn as the standard unit we can compute the price index pj as follows:

pj ¼ 100 

vðHn ; bj Þ vðHn ; b1 Þ

ð5Þ

where the market for which pj ¼ 100 is j ¼ 1.2 The value of the housing unit n in market j consumed by the household i can be expressed as vin;j ¼ qi;j  pj .3 Therefore, the quantity of housing is obtained as follows:

qi;j ¼

vin;j pj

ð6Þ

Finally, once qi;j is obtained from Eq. (6) and pj , mi;j and Ai are known, then it is possible to estimate Eq. (3).

characteristics (such as number of bedrooms, bathrooms, built square meters and location) and neighborhood characteristics. The hedonic estimation allows us to construct a price index for each metropolitan area per year. Following Eq. (6), the price index is used to obtain the housing quantity demanded per household. Finally, we estimate the housing demand Eq. (3), using socioeconomic characteristics of the buyer, including temporary and permanent income, and the housing price index. Note that Eq. (7) is substituted into Eq. (3). We use a Box-Cox transformation across all specifications in each step. Box-Cox obtains the maximum likelihood estimates of the parameters according to

X xk  1 X yh  1 bk k ¼ aþ þ dj zj þ e h k

ð8Þ

where e  Nð0; r2 Þ and h; k 2 ð1; þ1Þ. The dependent variable y is transformed by the parameter h, and each of the independent variables xk is transformed by the same parameter k. The transformed variables must be strictly positive to be defined for all values of h and k. Thus, variables that have negative values or contain zeros, such as dummy variables, are not transformed. We denote these non-transformed independent variables by zj . Since Box-Cox embeds several standard functional forms, estimating h and k allows us to test these functional forms without imposing them a priori on the data. In particular, when h ¼ k ¼ 1, then Eq. (8) becomes linear. When h ¼ k ! 0, the transformed elements of (8) become log-linear. Finally, when h ¼ k ¼ 1, the transformed elements of the regression become the multiplicative inverse specification. We perform these tests on all our estimations. Another benefit of the Box-Cox transformation is that it makes the residuals more closely normal and less heteroskedastic. Note that the coefficients in a nonlinear model are not equal to the slopes with respect to the variables. In fact, the derivatives of the dependent variable with respect to the independent variables are the following4

oy ¼ bk xkk1 y1h oxk

2.2. Empirical specification

3

ð9Þ

The econometric estimation of the model outlined above follows three steps. First, we follow previous literature by dividing income (mi ) into two components, permanent (mpi ) and temporary (mti ):

and

mi ¼ mpi þ mt i

and thus the elasticities for the transformed independent variables are

ð7Þ

This is achieved by running a household income regression using household demographic characteristics. The fitted value of the regression provides permanent income, while temporary income is calculated as the residual. Second, in order to obtain pj of Eq. (5), we undertake a hedonic price regression using Eq. (4). Specifically, we estimate the price of housing by decomposing its constituent

2 In the case of where a Box-Cox transformation is used, as in this study, the numerator in the fraction on the right-hand side of Eq. (5) is raised to 1 hj and the denominator to h1 j¼1 , where hj is the Box-Cox transformation of the housing value variable of each market j. 3 This assumes that the household i consumes only the housing unit n, which allows us to simplify notation.

oy ¼ dj y1h ozj

gx 

oy xk ¼ bk xkk yh ; oxk y

ð10Þ

ð11Þ

and for the non-transformed independent variables

gz 

oy zj ¼ dj zj yh : ozj y

ð12Þ

We report the elasticities, where applicable, in all our estimations. Since elasticities for dummy variables have no meaningful economic interpretation, we report the average percent change that the specific category adds to the dependent variable. That is, 4

Taking logs to Eq. (8) and using the result oy=ox ¼ ðo ln y=oxÞy.

4

oy=ozj ¼ dj yh y

M. Fontenla, F. Gonzalez / Journal of Housing Economics 18 (2009) 1–12

ð13Þ

3. Data We obtained information for 20,979 Federal Mortgage Society (SHF) loans originated between October 2002 and June 2004. SHF is a Mexican second floor government development bank that provides funding to commercial and non-bank banks. The latter are also known as SOFOLES.5 The SHF loans used in this study are double-index mortgages (DIMs) originated and administrated by SOFOLES. The main feature of these loans is that the principal is indexed to a price-level-adjusting unit of account (UDI) and the mortgage payment is adjusted according to the federal minimum wage. The difference between the borrower payment and the amortization is covered by an UDI-Minimum Wage Swap provided by SHF.6 The dataset has information on the physical attributes of the housing unit, socioeconomic characteristics of the household, and the financial conditions of the mortgage in 112 municipalities in Mexico. This is the first time that such detailed data has been collected for market-based mortgages in Mexico. 3.1. Metropolitan areas Our original dataset is at the municipal level. We use Conapo’s (2007) delimitation of metropolitan areas (MAS) in Mexico to assign 70 municipalities in our dataset to 36 MAS. The remaining 42 municipalities are allocated to their corresponding metropolitan area by using SNIM (2007). SNIM (2007) provides detailed information on all the municipalities in the country and the city where they are located. Each of these 42 municipalities is the only municipality in its corresponding city. Thus, we assign the observations at the municipal level to that city. The next step is to reduce the dataset for which we have a certain minimum of observations per year for each MAS. Since we only have data for the last three months of 2002, only 12 MAS have 50 or more observations for this year. In order to incorporate more MAS in our estimations, we group the observations for the last three months of 2002 together with the observations of 2003. Zabel (2004) uses 100 as a lower bound for observations per city and year. Given the characteristics of our data, we set the threshold at 49 observations per year. This provides us with 21 MAS and a total of 18,975 observations.7 Thus, we are able to ob-

5 A second floor development bank is a financial institution that provides credit to other financial intermediaries that in turn lend these funds to the public in sectors of the economy that are either underserved or considered particularly important. Non-bank banks are financial institutions that offer credit to the public but do not receive deposits from them and are usually concentrated in one sector of the economy. Pickering (2000b) provides a good overview of mortgage SOFOLES in Mexico. 6 See Lea and Bernstein (1996) and Lipscomb et al. (2003) for a complete explanation of UDIs in the Mexican housing sector context. 7 Table B.1 in Appendix B shows the number of observations by MAS and time period.

tain 42 prices (21 urban areas for two time periods), which is essential to identifying the demand equation. The 21 MAS in our dataset are a good sample of Mexican metropolitan areas. The combined population of these cities represents about 40% of the country’s total population. They include the four largest metropolitan areas in Mexico, each with a population of over 2.5 million. In addition, we have three cities with populations between 1 and 2.5 million, eight medium size cities with populations between 0.5 and 1 million, and six small cities with populations between 100,000 and 500,000. In terms of geographic distribution, six are located in the northwest, two in the north center, four in the northeast, two in the west, five in the center, and two in the southeast. 3.2. Housing unit, household, and mortgage characteristics Our dataset includes information for only new housing units. This is a reflection of the scarce financing for purchases of used houses in Mexico. Official government statistics report no mortgages for used housing in 2002 and 2003 and just 62 for the entire country in 2004 (see Conafovi 2002–2004).8 The used housing sector has suffered from a lack of financing, unclear valuation rules, the preference for new housing by consumers and developers, and the dire situation of the public property registry in many states of the country. Table 1 shows the descriptive statistics of relevant variables in our dataset.9 Mortgage terms in our dataset range from 5 to 25 years, the latter representing 92% of total loans. The average loan to value is 0.86, which indicates an average down payment of 14%. According to the SHF rules during this time period, the housing value cannot exceed 500,000 UDIs at the time of origination (around $157,000 USD). Household monthly income ranges from $647 to $13,874 USD with an average of $2,203 USD and a median of $1,850 USD. According to the Household Income Expenditure Survey (ENIGH) of 2004 the average monthly urban household income for the sixth decile was the equivalent to $647 USD. Thus, our income data covers between 30% and 40% of the richest urban households. These are the households that are able to obtain a mortgage given the market conditions.10 Moreover, the average in our dataset is four times the average urban household income of $534 USD. The value of the housing unit represents about 1.49 years of household income. This is a low number compared to the United States where the National Association of Realtors (2007) data reports an average ratio of 3.6 in 2004. However, interest rates in Mexico are

8 Unofficial figures from CIDOC (2005) estimate that in 2004 about 9% of total mortgages were for used housing. Even this upper-bound estimate is very low compared to developed countries. 9 Appendix A presents the definitions of all the variables and the descriptive statistics of the variables not included in Table 1. 10 Mexican households with monthly income from the formal sector between $300 and $700 USD obtain subsidized mortgages from mainly two institutions: infonavit (a tripartite organization of the government, employers and workers available only to formal private workers) and Fovissste (federal government sponsored loans for workers in the public sector). Formal and informal households with monthly income less than $300 USD receive housing finance mostly from the federal government through Fonhapo.

M. Fontenla, F. Gonzalez / Journal of Housing Economics 18 (2009) 1–12 Table 1 Descriptive statistics Mean

Std. dev.

Head of household age 36.05 8.68 Household monthly 2203.17 1354.92 income Dependents 1.24 1.32 Housing value 39362.41 17523.42 Credit 33601.48 14371.45 LTV 0.86 0.09 Mortgage term 24.37 2.28 Final mortgage rate 13.51 1.09 Bedrooms 2.45 0.65 Full baths 1.28 0.49 Half baths 0.47 0.50 2 116.62 64.57 Lot size (m ) 2 73.43 28.51 Built size (m ) Assigned parking 0.76 0.59 spaces Observations 18975 Average exchange rate MX$/USD = 10.8111

Min

Max

20.00 647.48

66.00 13874.63

0.00 12134.42 7177.51 0.18 5.00 10.71 1.00 1.00 0.00 41.29 26.81 0.00

12.00 156910.58 125528.39 0.98 25.00 19.26 4.00 3.00 2.00 1038.00 737.73 2.00

approximately double those of the US, making the mortgage payment around 20% of income, which is similar to that of the US. The final mortgage rate is an all-inclusive rate, which includes the interest rate on the loan, origination fee, insurance (life, housing, and mortgage), servicing, UDI-Minimum wage swap, and maintenance payment. The mortgages considered in our dataset do not have penalties for partial or full prepayments. Finally, monetary data is originally in Mexican pesos (MXP) or UDIs and it is transformed to USD in Table 1 for exposition purposes, using the period’s average exchange rate. All regressions are performed using pesos. 4. Estimation 4.1. Permanent income Household income is particularly important in the demand for housing. Previous studies show the importance of distinguishing between permanent and temporary income on housing demand (see Lee 1968 and Goodman and Kawai 1982). We consider two specifications for our permanent income regression. The first transforms the dependent variable income by h and the independent variable age by k. To be exact, 7 mh  1 agek  1 X dj gradej þ d8 Dmale ¼aþb þ h k j¼2

þ d9 Dmarried þ d10 DzoneA þ d11 DzoneB þ d12 Dsal þ d13 Dprof þ d14 Dinformal þ d15 Dothinc þ d16 Dð2002&03Þ þ e

ð14Þ

The right hand side of Eq. (14) shows head of household’s age, dummy variables for each education level (2, elementary school; 3, middle school; 4, high school; 5, technical school; 6, college and 7, graduate school), gender (Dmale), civil status (Dmarried) and sources of income, as well as minimum wage dummies for regions A (DzoneA) and B (DzoneB) and a time period dummy (D2002&03). The federal government categorizes all the municipalities

5

and metropolitan areas in the country into three minimum wage zones that reflect the cost of living and are correlated with degrees of development. Zone A has the highest cost of living and comprises the most developed zones of the country, followed by zones B and C. Regarding the source of income, individuals are classified in the following exclusive categories according to their main source of income: salaried (Dsal); professional services such as lawyers, architects, doctors (Dprof); informal (Dinformal) and others (Dothinc). The dummy variable D2002&03 is the time period dummy for the observations that took place in the last three months of 2002 and all 2003. The omitted categories are no education, unmarried, female, minimum wage zone C, business owners, and year 2004. The second specification is identical to Eq. (14), except that it forces k ¼ 1 and includes age squared on the right hand side. Table 2 shows the results. The estimate for the h equals 0.4 across specifications, while the exponent k for age is 2.32 for Model I. Likelihood-ratio tests show that the linear, log-linear and multiplicative inverse specifications are strongly rejected across both specifications. This provides compelling support for using the Box-Cox model, rather than imposing a particular specification from the outset. When age is transformed in Model I, it exhibits a positive elasticity of 0.363. For Model II, the impact of an extra year of age on annual income is USD 274.6.11 Also, both specifications show strict concavity of income as a function of age. Specifically in Model II, income increases with age at a decreasing rate, and then declines, providing support for the life-cycle income theory. The parameter estimates imply that income reaches its highest level at age 49 and then declines, all else equal.12 Table 3 also shows a clear premium on income for head of households with college degrees and graduate studies, the latter earning 38% more relative to individuals with no formal education. Lower education levels show no significant effect on income relative to no education, except for middle-school, which affects income negatively. This supports the idea that the labor market does not distinguish among lower education levels. In addition, male head of households earn about 5.7% higher than females, and married head of households earn 8.9% more than their unmarried counterparts. As expected, we found that incomes in zone A are 5.9% higher than zone C. The minimum wage zone B does not have a statistically significant impact on income relative to zone C. This suggests that minimum wage zones B and C are relatively similar. The negative sign on all estimated parameters for income sources indicates that households where the head is a business owner have the highest income, with salaried and informal workers earning the least on average. Households for which the head of household is a professional worker earn 8% less than when the head of household is a business owner.

This is E½mjagetþ1   E½mjaget , where E½m ¼ ½ðbXÞh þ 11=h . Maximizing Eq. (15) (with k = 1 and including age squared) with respect to age, we have om=oage ¼ ðbage þ 2oage2 Þm1h ¼ 0. Thus, we have age ¼ bage =ð2oage2 Þ. Applying the parameter estimates of Table 3, we obtain 48.56 years as the age where income is at its maximum. 11 12

6

M. Fontenla, F. Gonzalez / Journal of Housing Economics 18 (2009) 1–12

Table 2 Determinants of income—Box-Cox Income

Model I Coeff.

Transformed age Not transformed _constant Elementary school Middle school High school Technical school College Graduate school Dummy male Dummy married Dummy Zone A Dummy Zone B Dummy salaried Dummy professional Dummy informal Dummy other income D2002&03

Table 3 Relevant Box-Cox hedonic regression elasticities

26.31516 (0.000) 8.887427 0.000147 (0.777) 0.003342 (0.000) 0.000785 (0.099) 0.000075 (0.877) 0.004041 (0.000) 0.006727 (0.000) 0.001001 (0.000) 0.001562 (0.000) 0.001047 (0.000) 0.000037 (0.834) 0.003960 (0.000) 0.001436 (0.000) 0.003641 (0.000) 0.004050 (0.000) 0.000327 (0.016)

Model II Perc. chg.

Coeff.

Perc. chg.

0.363a

0.008 0.189 0.044 0.004 0.229 0.381 0.057 0.089 0.059 0.002 0.224 0.081 0.206 0.229

0.019

Age Age2

2.435585 0.000122 (0.815) 0.003396 (0.000) 0.000774 (0.108) 0.000073 (0.881) 0.004139 (0.000) 0.006844 (0.000) 0.001026 (0.000) 0.001585 (0.000) 0.001059 (0.000) 0.000042 (0.811) 0.004014 (0.000) 0.001484 (0.000) 0.003688 (0.000) 0.004086 (0.000) 0.000348 (0.011) 0.000874 (0.000) 0.000009 (0.000)

0.007

Lot size Built size Bedrooms Full baths Half baths Parking D2002&03 a

Median elasticity

Std. dev.

% of times significant (p < 0.05)

0.28 0.77 0.19 0.16 0.07 0.03 0.07a

0.15 0.42 0.17 0.22 0.06 0.12 0.07

81 100 57 57 57 90 95

Percentage change with respect to average housing value.

0.190 0.043 0.004

Finally, the predicted values stemming from Model I are interpreted as the permanent income component, while the residuals are considered temporary income.

0.232 0.383 0.057 0.089 0.059 0.002 0.225 0.083 0.206 0.229

0.019

Coeff.

P > |z|

Coeff.

P > |z|

k h

2.320822 0.400596

0.000 0.000

0.399354

0.000

Observations LR v2 P > v2

18,975 3244.81 0.000

18,975 3623.25 0.000

Test HO:

P > v2

Test HO:

P > v2

h = k = 1 h=k=0 h=k=1

0.000 0.000 0.000

h=1 h?0 h=1

0.000 0.000 0.000

P > v2 in parenthesis. a Elasticity.

The 2002–2003 year dummy shows that incomes in the last three months of 2002 and all 2003 are 1.9% higher than incomes in 2004. The macroeconomic conditions for 2002, 2003 and 2004 do not seem to explain this income change since real GDP actually increased during that period. In fact, the 2002–2004 time period represents the recovery from the mild 2001 recession. Therefore, we do not have a definite intuitive explanation for this effect.

4.2. Hedonic regressions In order to estimate vðHn ; bj Þ in Eq. (4) we utilize a hedonic price model using the Box-Cox transformation of Eq. (4). Since each MAS represents a separate housing market, we estimate a separate hedonic regression for every MAS. We pool the observations across time given that coefficients are unlikely to change over our short time period, and include the time-period dummy. We are unable to use neighborhood characteristics because confidentiality issues allow us only to identify observations at the municipal level. We do not use municipality characteristics since 14 of the 21 MAS in our dataset have only one municipality. Therefore, we follow Zabel (2004) and use owner’s characteristics to proxy for neighborhood characteristics. In particular we use the permanent income (mp) obtained from Eq. (14), age (age), schooling level (education), gender dummy (Dmale) and a dummy for marital status (Dmarried). Thus, the explanatory variables for the hedonic regression of each MAS are a set of physical characteristics of the housing unit, the aforementioned set of owner’s characteristics and the 2002–2003 dummy variable. The hedonic regression for each MAS is the following: k

k

vh  1 lotsize  1 builtsize  1 mpk  1 ¼ a þ b1 þ b2 þ b3 h k k k agek  1 þ d1 bedrms þ d2 fbath þ d3 halfbath þ b4 k þ d4 park þ d5 education þ d5 Dmarried þ d5 Dmale ð15Þ þ d5 D2002&03 þ e where the dependent variable is the housing unit’s value (v) transformed by h, the other independent variables are lot size (lotsize) and building size (builtsize) in square meters, owner’s permanent income (mp), number of bedrooms (bedrms), full baths (fbath), half baths (halfbath), assigned parking spaces (park), an index of the owner’s education level (education) and the 2002–2003 dummy (D2002&03). As mentioned in the data section, we do not include the age of the housing unit, since all units are new. The omitted categories are female, unmarried owners, and year 2004. We estimate the elasticities for the physical characteristics of the housing unit and the percentage change for the

M. Fontenla, F. Gonzalez / Journal of Housing Economics 18 (2009) 1–12

time period dummy for each MAS. We do not compute the elasticities or percentage changes on the owner’s characteristics since these are just the instruments to proxy for neighborhood characteristics used to minimize bias in our estimates. The model is statistically significant in all the 21 hedonic regressions. Table 3 displays the median value and the standard deviation over the 21 MAS for the elasticities of the relevant variables. Complete results for each MAS are shown in Table B.1 in Appendix B. The median and standard deviations are computed over the elasticities for which the underlying regression coefficient is statistically significant at least 95% significance level (p-value < 0.05).13 In addition, the last column of Table 3 shows the percentage of times that each variable was statistically significant at least 95% significance level. For instance, Lot Size is statistically significant, at least 95% significance level, 81% of the time (17 of the 21 regressions for each MAS). Built Size shows the largest median effect on housing price and it is significant in all 21 regressions. Thus, a 1% increase in the built size of the housing unit produces a median 0.77% increase in housing price over the 21 MAS. The second biggest effect on housing value is Lot Size, with a median price elasticity of 0.28 and, as mentioned before, is statistically significant in 17 of 21 MAS. Number of Bedrooms has a median elasticity of 0.19, and is significant for 12 regressions. Also, bathrooms and half-bathrooms have median elasticities of 0.16 and 0.07, and both are significant for 12 MAS. The time period dummy is significant in 20 MAS, and indicates that homes sold in 2002–2003 were 6% more expensive relative to homes sold in 2004. The number of assigned parking spaces shows a negative median elasticity, perhaps counter-intuitively implying that increasing the number of assigned parking spaces actually reduces the price of housing. A possible explanation is that the assigned parking space variable may be capturing the impact that density has on price. That is, the assigned parking space may be positively correlated to population density, since the need for assigned parking spaces is lower for housing units located in less populated areas such as suburbs. Moreover, density is expected to be negatively correlated to house price given that other things equal, households prefer to live in less dense areas. Since our dataset does not have an indicator of density or suburb, then interpreting assigned parking spaces as a proxy for population density makes its negative sign intuitively right. We obtain vðHn ; bj Þ for each time period and MAS by calculating the average fitted value of the hedonic regression for the corresponding time period and MAS. The price index is then constructed following Eq. (5), where Mexico City in 2002–2003 is the value of the price index set equal to 100. Fig. 1 depicts the price index, which shows a significant variation in its values. This variation is an essential aspect of identifying the demand equation. Table B.1 in Appendix B also shows the values of the price index for each year and MAS. It has a standard deviation of 18.9, its highest value

13 The use of a p-value <0.05 to determine if a coefficient is statistically significant follows the convention in the literature.

7

being 160.2, corresponding to Los Cabos in 2004, a tourist area in the Northwest. The lowest price index is 66.7 for Ciudad Victoria in 2003, a metropolitan area in the Northeast.14 Following Eq. (6), we divide the housing value by the estimated relevant price index to obtain the quantity of housing (q) for each observation. 4.3. Housing demand estimation We compute the demand for housing using the estimated temporary and permanent income and other socioeconomic characteristics of the household and the mortgage final interest rate. The estimation is undertaken assuming the Box-Cox transformation of Eq. (3). We consider two different specifications which have the Box-Cox transformation of the house quantity (q) as the dependent variable but differ in the set of explanatory variables and the years of the mortgage term. In the first specification we consider two sets of explanatory variables. One set is the Box-Cox transformation of the housing price index (p), age, and permanent income. The second set of explanatory variables is the non-transformed temporary income (mt), number of dependents (dep) and categorical variables for married and male head of household. Consequently, the benchmark model is represented by the following equation:

qh  1 pk  1 mpk  1 agek  1 ¼ a þ b1 þ b2 þ b3 þ d1 mt h k k k þ d2 Dmarried þ d3 Dmale þ d4 dep þ e ð16Þ An important distinction with respect to previous studies is that we have information on the final mortgage rate paid by the owner. In our data, the final mortgage rate is the effective interest rate that borrowers actually pay. In addition to the mortgage rate, it also includes mortgage insurance, the minimum wage-UDI swap premium, and the servicing fee. Final mortgage rates usually vary across financial intermediaries (Sofoles), so that borrowers with similar characteristics may face different mortgages rates. Given that the final mortgage rate affects the owner’s monthly payment and the affordability of the housing unit, it may impact the quantity of housing demanded. Therefore, we include a second model to assess the importance of the final mortgage rate in the demand for housing. Since mortgage rates with shorter terms usually have higher annual rates, we eliminate this effect by considering only observations that have mortgage terms of 25 years.15 We use 25-year mortgages since they are the most popular and representative type of mortgage, comprising 92% of our dataset. Consequently, in the second model we add to the benchmark model the Box-Cox transformation of the final mortgage rate. In both Models I and II, the omitted variables are female and unmarried households.

14 The descriptive statistics of the price index are also shown in Table A.2 in Appendix A. 15 In our dataset the average final mortgage rates are 14.3%, 13.9%, 13.6%, 13.8% and 13.5% for mortgage terms of 5, 10, 15, 20 and 25 years, respectively.

M. Fontenla, F. Gonzalez / Journal of Housing Economics 18 (2009) 1–12

160

8

2004

Ag

ua

sc

al

ie nt C es aj e C me an C C hi u hu n a C d. hua J C ua d. re Vi z ct o C ria u G lia ua ca da n Ira l pu H aja e at r o− rm a Sa os la illo m Lo an s ca C ab M os e M xic ex a ic li o M Ci N on ty Pl uev terr ay o e L y a de are l C do ar m e Pu Pu n er e to b Va la l Q lart ue a re t R aro ey no s Ti a ju an a

60

80

100

Price Index

120

140

2002&2003

Fig. 1. Price index.

Table 4 presents the estimated coefficients, elasticities, and percent change for the two models. The likelihood-ratio tests indicate that the linear, log-linear and multiplicative inverse specifications are rejected for all specifications. All explanatory variables are statistically significant at the 99.9% level for both models. For Model I, price and permanent income are the two most important factors in our demand estimation. Zabel (2004) notes that estimates for price and income elasticity of demand tend to vary according to level of aggregation, measure of income, type of housing price and model estimation. We find the price elasticity of demand to be inelastic at 0.3. This is lower than the studies for developed countries, and in the lower bound for developing countries. For developed countries the reviews of Mayo (1981) and Ermisch et al. (1996) locates the elasticity of demand at 0.53 and in the 0.5 to 0.8 range, respectively. In the case of developing countries, Malpezzi (1999) shows that price elasticities have a great degree of variation from almost zero in the Follain et al. (1980) study for South Korea, to close to 1 in Malpezzi and Mayo (1987a,b) which includes several developing countries. We conjecture that our price elasticity is slightly lower than the range found for developed countries and within the range of developing countries because households in developing countries have few options in terms of housing. In Mexico the rental market is not fully developed and many households become owners through self-construction and progressive housing.16 This lack of good substitutes to owning reduces the price elasticity of demand. In addition, as mentioned in the introduction, the estimated

16

Progressive housing refers to the addition of new sections to a basic housing unit as income becomes available. JCHS (2004) provides a good overview of the rental market, progressive housing and self-construction in Mexico.

Table 4 Housing demand—Box-Cox Quantity of housing

Model I Coeff.

Transformed Price index Permanent income Age

1.2698 (0.000) 55.7545 (0.000) 0.2939 (0.000)

Model II Elast.

Coeff.

0.324 0.758 0.144

Final mortgage rate Not transformed _constant Temporary income Dummy married Dummy male Dependents

91.0896 0.000003 (0.000) 0.0059 (0.000) 0.0108 (0.000) 0.0046 (0.000)

0.043 a

0.022

0.040a 0.021

0.8107 (0.000) 21.1863 (0.000) 0.2175 (0.000) 0.3594 (0.000) 38.3903 0.000003 (0.000) 0.0061 (0.000) 0.0116 (0.000) 0.0047 (0.000)

Elast. 0.332 0.797 0.152 0.393

0.037 0.022a 0.042a 0.021

Coeff.

P > |z|

Coeff.

P > |z|

k h

0.565770 0.159750

0.000 0.000

0.461151 0.157110

0.000 0.000

Observations LR v2 P > v2

18,975 7719.62 0.000

17,317 7121.13 0.000

Test HO:

P > v2

P > v2

h = k = 1 h=k=0 h=k=1

0.000 0.000 0.000

0.000 0.000 0.000

P > v2 in parenthesis. a Percentage change with respect to the average housing quantity.

need of 1.8 million of new housing units also tends to decrease the price elasticity of demand.

M. Fontenla, F. Gonzalez / Journal of Housing Economics 18 (2009) 1–12

Permanent income is another important factor of housing demand in Mexico, with elasticities of 0.76 and 0.80. This is within the range found by Mayo (1981) of 0.36– 0.87 and Ermisch et al. (1996) of 0.76–0.87 for developed countries. It is also within the range of 0.6–1.2 for developing countries reported by Malpezzi (1999). This result implies that the demand for housing grows almost proportionally with economic growth and education in Mexico. In contrast, the elasticity for temporary income is close to zero at 0.04. This large difference between permanent and temporary income supports the procedure of dividing income by its different components. Mayo (1981) shows that results for demographic variables are ambiguous and difficult to compare across studies. The age of head of household elasticity of demand is negative at 0.14 and 0.15. Although age is initially expected to have a sizable impact on housing demand, our results show that when permanent and temporary income are accounted for, age has a relatively small negative effect. This indicates that the estimate for age represents variations in preferences. Our results also show that when the head of the household is married, average housing demand is 2.2% higher than for their unmarried counterparts. In addition, male heads of household demand 4% less than female heads of household. The effect of the number of dependents on the quantity demanded is small and negative, at 0.02 across models. The number of dependents can have two effects on the quantity of housing. On one hand, a higher number of dependents tends to increase the quantity demanded for housing to accommodate a larger household. On the other hand, more dependents reduce the amount of resources that the household can allocate to housing. In Mexico, the low development of the used housing sector makes it difficult for households to buy and sell their housing units to adjust for changes in household size. Thus, our results indicate that the overall effect of the reduction in disposable income of the household on the quantity demanded is more important than the possible adjustment for household size. In many cases, households build additional rooms onto existing housing units when the number of dependents increases. In Model II we find that the final mortgage rate can play an important role in the demand for housing, with an elasticity for 25-year mortgages of 0.39. The relative importance of the final mortgage rate provides some guidance to policy makers in the housing finance sector and explains public policy efforts to reduce mortgage rates. Since the mortgages used in this study are DIMs, which separate the loans’ payment rate (indexed to the minimum wage) to the accrual of principal (UDI interest rate), the final interest rate determines the size of the monthly payment, but not its growth rate. Castañeda (1995) shows that the relative low interest rate elasticity of demand for mortgage credit in Mexico between 1989 and 1993 is explained by the use of DIMs. Consequently, we conjecture that for peso-denominated mortgages, the final mortgage rate elasticity of demand should be greater than the elasticity we find for DIMs.

9

5. Conclusion Applied research on housing demand for developing countries is still scarce. A better understanding of housing demand in developing countries will allow policy makers to improve the design and implementation of housing policies. Mexico is an interesting case study in the context of developing nations as it is facing important challenges in the housing sector. The demand for housing in Mexico will soar in the immediate future due to an increase in the population in the household formation age, an expansion of the middle class, and a need to replace and improve existing units. Overall, we believe that the results in this paper further our understanding of housing demand in the context of developing countries. We estimate the housing demand in Mexico using a unique dataset that contains household socioeconomic information, mortgage terms, and physical characteristics of the housing unit. We include information for 21 metropolitan areas of different sizes and geographical location. Moreover, we provide a useful comparison of our results with previous research for developed and developing countries. We find that price elasticity of housing demand is lower than previous studies for developed countries and within the range of developing countries. Permanent income elasticities are also within the range of previous studies with values between 0.76 and 0.80. In contrast, temporary income elasticity is close to zero. The final interest rate elasticity for 25-year mortgages indicates that public policies designed to lower mortgage rates can play an important role in housing demand. Regarding the demographic characteristics of the household, we find that males demand less housing than females, and married heads of household demand more than their unmarried counterparts. Finally, head of household age and number of dependents decrease the amount of housing demanded. In the process of estimating housing demand we also find interesting results regarding socioeconomic characteristics of Mexican households. In particular, we find that lower education levels show no effect on income relative to no education. Also, male heads of household’s income is higher than females and married households earn more than unmarried households. We believe that the results in this paper are useful to policymakers in developing countries for three primary reasons. First, the design and implementation of urban policies depends to some degree on the estimation of the effective future housing demand. In these assessments demand elasticities are essential inputs. Second, the efficiency and costs calculations of housing subsidy programs are sensitive to the estimates of price and income elasticity. For example, Malpezzi and Mayo (1987) show that different assumptions about plausible values of the price elasticity of demand increase the cost of subsidies by 73%, and the deadweight loss to society by 400%. Moreover, in many countries, including Mexico, government or government-sponsored entities provide housing finance at interest rates lower than the market. The interest rate elasticity estimate in our study can allow these institutions to better assess the impact of

10

M. Fontenla, F. Gonzalez / Journal of Housing Economics 18 (2009) 1–12

these programs. Finally, policies aimed at increasing the affordability of housing without subsidies can also benefit from our study. In particular, our results indicate that price and interest rate elasticities of demand are similar. Thus, affordability policies can also be directed to reduce

mortgage interest rates. Mexico is a clear example in which the federal government has promoted the creation and development of mortgage-backed securities to reduce the intermediation costs and the final interest rate paid by the borrower.

Appendix A. Description of variables and summary statistics Table A.1. Variable definitions Socioeconomic variables Head of household age Household monthly income Dependents Education Grade

Age in years of the head of household Gross household monthly income Number of dependents Highest education degree obtained by the head of household, 1, no education; 2, elementary school; 3, middle school; 4, high school; 5, technical school; 6, college; 7, graduate school 1 if the head of household is male, 0 otherwise 1 if the head of household is married, 0 otherwise Type of work that is the main source of income for the head of household 1 if main source of income comes from salaried work, 0 otherwise 1 if main source of income comes from professional work, 0 otherwise 1 if main source of income comes from informal work, 0 otherwise 1 if main source of income does not come from salaried, professional or informal work, 0 otherwise 1 if the household resides in the minimum wage zone A, 0 otherwise 1 if the household resides in the minimum wage zone B, 0 otherwise 1 if the household resides in the minimum wage zone C, 0 otherwise

Dummy male Dummy married Source of income Dummy salaried Dummy professional Dummy informal Dummy other income Dummy Zone A Dummy Zone B Dummy Zone C Mortgage variables Housing value Credit LTV Mortgage term Final mortgage rate D2002&03

Value of the housing unit as stated in the mortgage contract Monetary amount of the mortgage Loan to value (housing value/credit) Number of years the mortgage is scheduled to exist Effective fixed interest rate paid by the borrower 1 if the house was purchased during the last quarter of 2002 or all 2003, 0 otherwise

Housing unit variables Bedrooms Full baths Half baths Lot size Built size Assigned parking spaces

Number of bedrooms in the housing unit Number of full baths in the housing unit Number of half bath in the housing unit Total area of the lot in square meters Total area built in square meters of the housing unit Number of parking spaces assigned to the housing unit

Table A.2. Additional descriptive statistics Mean No education Elementary school Middle school High school Technical school College Graduate school Dummy male

0.018 0.055 0.102 0.139 0.115 0.517 0.053 0.645

Std. dev. 0.135 0.228 0.303 0.346 0.319 0.500 0.223 0.479

Min

Max 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

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M. Fontenla, F. Gonzalez / Journal of Housing Economics 18 (2009) 1–12

Table A.2 (continued) Mean Dummy married Dummy salaried Dummy professional Dummy informal Dummy other income Dummy Zone A Dummy Zone B Dummy Zone C D2002&03 Final 25-year mortgage rate

Std. dev.

0.544 0.799 0.036 0.022 0.030 0.382 0.452 0.166 0.709 13.48

Constructed variables Price index Housing quantity Permanent income Temporary income

Min

0.498 0.401 0.186 0.145 0.171 0.486 0.498 0.372 0.454 1.07

114.19 3731.40 20316.86 3501.86

18.90 1546.24 3827.72 13927.17

Max

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 11.00

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 19.00

66.71 980.79 10582.44 25014.29

160.25 18133.81 40324.05 136551.00

Appendix B. Hedonic elasticities, price index and observations by MAS Table B.1. Hedonic elasticties for p-value <0.05, price index and observations by MAS MAS

Aguascalientes Cajeme Can Cun Chihuahua Ciudad Juarez Ciudad Victoria Culiacan Guadalajara Hermosillo IrapuatoSalamanca Los Cabos Mexicali Mexico City Monterrey Nuevo Laredo Playa del Carmen Puebla Puerto Vallarta Queretaro Reynosa Tijuana

Elasticities

% Change

Price index

Observations

Lot size

Built size

Bedrooms

Full baths

Half baths

Parking

2002&03

2002&03

2004

2002&03

2004

0.74 0.29 0.49 0.28 0.28 —

0.54 0.08 0.44 0.58 0.85 1.07

0.32 0.10 0.38 — 0.05 —

0.17 — 0.08 0.11 0.10 —

0.13 0.14 0.05 0.05 0.21 —

0.06 0.10 0.02 0.02 0.07 0.35

0.07 0.38 0.04 0.03 0.13 0.01

92.8 72.0 130.2 116.0 146.0 66.7

108.2 93.4 123.4 124.0 154.2 71.8

296 301 749 893 1,108 99

135 73 242 492 470 49

0.35 0.41 0.30 0.06

1.01 0.68 0.78 0.76

— 0.05 — 0.14

— 0.17 — 0.13

0.08 — 0.07 —

0.03 0.08 0.06 0.09

0.11 0.07 0.13 0.05

145.0 106.2 123.5 90.1

108.9 82.9 102.9 96.6

141 865 592 177

158 437 403 95

0.25 0.28 — 0.26 0.26 0.16

1.34 0.84 1.02 0.61 0.03 1.89

0.09 0.39 — — 0.23 —

— — 0.04 0.20 0.24 —

— 0.08 0.02 0.04 0.02 —

— 0.03 0.02 0.06 0.00 0.35

0.09 0.07 0.13 0.12 0.01 0.03

144.6 119.1 100.0 130.6 113.9 99.8

160.2 136.3 123.2 114.7 84.2 81.3

343 1,152 1,511 1,398 119 204

129 442 346 393 294 72

0.23 — 0.13 0.39 —

0.48 0.77 0.99 0.54 0.86

— 0.50 0.28 0.16 —

0.89 — — 0.23 0.15

— — — — 0.13

0.04 — 0.05 0.02 0.05

0.08 0.14 0.08 0.05 —

92.2 96.1 108.2 115.4 101.5

87.2 67.9 115.5 86.4 114.4

254 76 328 422 2,421

58 79 148 103 908

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