# «Elena Loutskina University of Virginia, Darden School of Business & Philip E. Strahan Boston College, Wharton Financial Institutions Center & NBER ...»

Since the intrinsic volatility of a particular market may play a role in this entry decision, the relationships observed in the fixed effects OLS estimate of Equation (2) could be biased by reverse causality. For example, if out-of-state banks prefer to enter safe markets, the coefficient on financial integration would tend to be biased downward in OLS. To eliminate this potential source of bias, we also estimate Eq. (2) using an instrumental variable model, where the instrument for the In-CBSA ratio equals the index of restrictions on interstate branching described in Section II. This index ranges from zero to four, where four represents the highest level of barriers to entry by out-of-state banks. Since this index varies mainly across states, rather than within states over time, we do not have strong identification in the fixed effects model. Hence, we report OLS with and without CBSA fixed effects but only report the IV model without these effects. (All models include time effects.) Measuring Integration by CBSA-year pairs To measure integration between pairs of CBSAs, we build the Common CBSA Ratio. For each CBSA pair, we sum up all deposits with a common ownership link, add these across the two markets, and then divide by the total amount of deposits in the two CBSAs. Higher values of Common CBSA Ratio indicate a greater degree of shared financial resources – greater integration – between CBSAs.

since each observation represents a pair of CBSAs, the instrument equals the sum of the branching restrictions index in the states where the two CBSAs are located. Hence, we again report both the fixed effects OLS model as well as the IV model.8 Table 1 reports summary statistics for our volatility and integration measures. Panel A reports the CBSA-year level means and standard deviations for house-price volatility and the four integration measures; Panel (B) reports these statistics for the two pair-wise interrelatedness measures and the pair-wise integration measure. The In-CBSA ratio average 81.4% (Panel A), indicating that in the typical CBSA-year the majority of deposits are owned by banking companies with deposits elsewhere. This variable has substantial variation – mainly in the cross section – with a standard deviation of 15.3%. The average house-price growth shock equals 4.56%, suggesting substantial CBSA-specific shocks to local markets after removing trends in overall housing price appreciation. The pair-wise data tell a similar story, with an average difference in growth residuals between pairs of CBSAs of 4.07 percentage points. Almost 40% of market pairs have some ownership links, with an average Common CBSA ratio of 8.28%.

Volatility increases with integration Table 2 reports our estimation of Equation (2), linking financial integration to total house-price growth volatility, along with the first-stage model for the In-CBSA Ratio. All models include time fixed effects to take out aggregate trends as well as the national business cycle. In addition, we control in all models for the share of employment across the following different industry segments: construction, mining and logging; finance; education and health

## 8 We include the pair-wise fixed effects even in the IV model. Since the instrument depends on branching in two areas rather than one, a change in the branching index in either locality’s state generates within-CBSA variation over time. Thus, we get strong identification in the first-stage model, even including the pair-wise fixed effects.

and business services and other services.9 In some models, we also incorporate CBSA-level fixed effects to capture time invariant market-level characteristics that may be correlated with volatility. In every case, we cluster data at the CBSA level to build our standard errors.

The results strongly suggest, first, that financial integration is greater in CBSAs located in states with fewer restrictions on interstate branching (Table 2, column 1). An increase in the branching index from 0 to 4 – from least to most restrictive – comes with a decline in the InCBSA ratio of about 5%, which is large relative to the variation in this variable (σ = 15.3% - see Table 1). The branching restrictions index has strong explanatory power in the first stage as well, with a t-statistic above 3. The F-statistic for the first stage regression equation is 10.3, which confirms that we have a well-identified model and pass the weak instruments test of Stock and Yogo (2005).

Second, financial integration is associated with greater volatility of housing prices (columns 2 & 3). In-CBSA ratio has a positive and significant effect on volatility in OLS without the CBSA effects (column 2); in this OLS model, however, the economic magnitude of integration is small. As noted, however, endogenous entry by banks may bias the coefficient on integration downward (that is, toward zero), and this notion is supported by the IV model, where the coefficient rises in magnitude substantially. In this model (column 3), a standard deviation

increase relative to the dispersion in house-price volatility (σ = 2.8% - see Table 1).

Interrelatedness across markets falls with integration Table 3 reports the estimation of Equation (3a), along with the first stage model linking integration between pairs of CBSA markets (Common CBSA ratio) to the sum of the branching restrictions index in the two states. In these pair-wise models, the dependent variable equals the negative of the absolute value of the difference in house-price growth shocks in a given year (recall Equation (3b) above). As noted, all of the models include time fixed effects and a separate fixed effect for every unique pair of CBSAs – a total of 65,508 unique fixed effects.

These fixed effects remove factors such as geographical distance that may affect the similarity of housing markets between two CBSAs. We also include a variable capturing the ‘distance’ or similarity of the industry mix between pairs, equal to the sum of squared difference in industry shares (i.e. the Euclidean distance). This pair-wise factor will capture variation over time in the differences in industry mix between markets. We also group our data into clusters for each CBSA to build standard errors. So, although the models are built from nearly one million observations, there are just 362 independent clusters.

Table 3 reports the results for specifications using the continuous measure of integration (Common CBSA ratio = the fraction of commonly owned deposits), and using a dummy variable equal to one for markets that have some degree of commonly owned bank deposits. The latter model is somewhat easier to interpret and also may be more robust to outliers. Columns (1) and (2) report the first stage models, where for both the continuous and dummy variable approaches we have very strong identification (t-stat 10 for the branching restrictions instrument). For

(most open) to 8 (least open) would come with a 16% increase in the probability that the two CBSAs have some common ownership in deposits (column 2).

Consistent with Table 2, we find that markets that are more integrated with each other have less commonality in growth shocks, and we also find that magnitudes increase when we instrument for integration with branching restrictiveness (columns 3-6). For example, the indicator variable model suggests that markets that share bank deposits have house-price growth shocks that are 4.4% less similar, which is large relative to the overall variation of these differential shocks (σ = 4.13% - see Table 1). The results support the idea that capital flows affect collateral values. In markets that are financially connected, markets with high credit demand (e.g. high house prices) can draw on financial capital from markets with lower demand, thereby reducing the correlatedness of collateral values between the two markets. In markets that share financial resources, housing price growth rates become less similar. This result is strong evidence that financial integration amplifies credit-demand shocks; capital flowing between these markets lowers the similarity in shocks to the value of collateral.

## IV. THE EFFECTS OF HOUSING PRICES ON ECONOMIC GROWTH

In this section we ask two questions. First, did the increase in housing-price volatility lead to greater business-cycle instability? Second, did financial integration strengthen the link from housing prices to overall economic performance, thus further raising overall volatility? The first question is motivated by the trend toward greater housing price volatility (recall Figure 1).The second question is suggested by theories of financial integration, which imply that more

prices, or more generally, the value of collateral – and economic output.

To answer these questions, we trace out the causal impact of shocks to housing prices on overall economic output by CBSA-year (Yi,t), measured by personal income growth, employment growth, employment growth without sectors directly affected by housing (construction and finance) and GDP growth. Specifically, we estimate panel regressions with the following

**structure:**

and Yi,t = αyt + γyi + βy1 House-Price Growthi,t + βy2 Financial Integrationi,t (4b) + βy3Financial Integrationi,t * House-Price Growthi,t + Other Control Variables + εi,t.

We estimate Equations (4a) and (4b) for our CBSA-year panel dataset from 1994 to 2006, including both year and CBSA fixed effects. The year effects remove trends as well as the national business cycles, while the CBSA effects take out long-run differences in average economic growth rates.

To test how financial integration affects links from house price shocks (or, more generally, collateral shocks), we interact House-Price Growthi,t with In-CBSA ratio, using the branching restrictions index as the instrument for In-CBSA ratio, as in Table 2. If changes in housing prices raise borrower debt capacity and, in turn, raises consumer demand and firm investment, then βy1 0 (4a); if financial integration, by allowing capital to flow in from external markets, strengthens this effect, then βy3 0 in (4b). In order to estimate the overall

and then estimate models with the interaction term in (4b).

As additional controls variables, we include the share of employment across industry sectors as before; three measures of the strength and health of the local banking sector: the average capital-asset ratio, the log asset size of banks operating in the CBSA, and the average growth rate of assets of local banks; and, in some specifications, one lag of the dependent variable.10 GSE Housing-Finance Subsidies as a Source of Instruments for Housing Price Growth Shocks to the overall economy will both affect and be affected by the value of housing, as well as the value of real estate and collateral more generally. Our aim is to trace out the causal impact of shocks to housing on the overall economy; hence, we need instruments that move housing prices (and so are sufficiently powerful) but otherwise remain unrelated to fundamental drivers of economic growth (and so meet the exclusion restriction for valid instruments). We use subsidies in housing-finance from the GSEs to build such instruments.11 Potential home buyers receive a financing subsidy through the activities of the GSEs, who stand ready to buy mortgages that fall below the jumbo-loan cutoff and meet a set of credit-worthiness underwriting criteria.12 The cut-off is binding on borrowers, as is evident from the histogram of loan applications and loan approval rates presented in Figures 2A and 2B (adapted from Loutskina and Strahan (2009)). The large spike in loan applications and approval rates just

## 10 Industry shares are from the Bureau of Labor Statistics. Bank characteristics are taken from the Bank Call Reports; CBSA-level averages equal the weighted average of banks operating in the CBSA based on the share of deposits held in a given CBSA by each bank.

11 Adelino, Schoar and Severino (2011) use a similar strategy at the transaction level to trace out how GSE subsidies affect the price per square foot of housing.

12 For evidence about the size of this subsidy, see Loutskina and Strahan (2010).

jumbo loan cut-off. The cutoff is the same everywhere (except Alaska and Hawaii), and it increases annually based on a mechanical formula linked to changes in national housing prices.

The increase in the jumbo-loan cutoff thus raises the subsidy to some potential home buyers, but the increase, crucially, is not dependent on conditions in the local area (CBSA).