Improvements to photometry. Part 1: Better estimation of derivatives in extinction and transformation equations

Atmospheric extinction in wideband photometry is examined both analytically and through numerical simulations. If the derivatives that appear in the Stromgren-King theory are estimated carefully, it appears that wideband measurements can be transformed to outside the atmosphere with errors no greater than a millimagnitude. A numerical analysis approach is used to estimate derivatives of both the stellar and atmospheric extinction spectra, avoiding previous assumptions that the extinction follows a power law. However, it is essential to satify the requirements of the sampling theorem to keep aliasing errors small. Typically, this means that band separations cannot exceed half of the full width at half-peak response. Further work is needed to examine higher order effects, which may well be significant

Explicit Evidence on an Implicit Contract

We offer the first direct evidence of an implicit contract in a goods market. The evidence we offer comes from the market for Coca-Cola. We demonstrate that the Coca-Cola Company left a substantial amount of written evidence of its implicit contract with its consumers—a very explicit form of an implicit contract. The contract represented the promise of a five cent (nominal) price and adherence to the “Secret Formula”. In general, the implicit nature of such contracts makes observation difficult. To overcome this difficulty, we adopt a narrative approach. Based on the analysis of a large number of historical documents obtained from the Coca-Cola Archives and other sources, we offer evidence of the Coca-Cola Company both acknowledging and acting on this implicit contract. We also make another unique contribution by exploring quality as a margin of adjustment available to Coca-Cola. The implicit contract included a promise not only of a constant nominal price but also a constant quality (i.e., 6.5 oz. of the Secret Formula). During a period of over 70 years, we find evidence of only a single case of true quality change. By studying the margin of adjustment the Coca-Cola Company chose in response to changes in market conditions, we demonstrate that the perceived costs of breaking the implicit contract were large. We argue that one piece of direct evidence on the magnitude of these costs is the aftermath “New Coke’s” introduction in 1985.Implicit Contract, Explicit Contract, Invisible Handshake, Customer Market, Long- Term Relationship, Price Rigidity, Nickel Coke, Coca-Cola

Re-measuring labor's share

Measuring labor's share of an economy's aggregate income seems straightforward,at least in principle. Count up wage and salary income, along with the value of benefitsprovided to employees, and divide it by total income. However, one fundamentalconcept of labor's share in macroeconomic theory is not the amount of aggregate incomepaid out to labor. Rather, it is the share of aggregate production that is attributable to"raw" units of labor. Or, otherwise stated, it is the share of aggregate income that wouldhave been paid to laborers if they had no accumulated stocks of human capital.1 Thisshare corresponds to an aggregate production function parameter: the elasticity of outputwith respect to physical (i.e. non-augmented or raw) units of labor (Robert Solow, 1957).In this paper we estimate annual raw labor´s share for the US, 1949 to 1996.Labor's Share, Factor Shares, Development, Biased Technical Change, Capital Intensity

Labor's shares - aggregate and industry: accounting for both in a model of unbalanced growth with induced innovation

The relative stability of aggregate labor's share constitutes one of the great macroeconomic ratios. However, relative stability at the aggregate level masks the unbalanced nature of industry labor's shares - the Kuznets stylized facts underlie those of Kaldor. We present a two-sector - one labor-only and the other using both capital and labor - model of unbalanced economic development with induced innovation that can rationalize these phenomena as well as several other empirical regularities of actual economies. Specifically, the model features (i) one sector ("goods" production) becoming increasingly capital-intensive over time; (ii) an increasing relative price and share in total output of the labor-only sector ("services"); and (iii) diverging sectoral labor's shares despite (iii) an aggregate labor's share that converges from above to a value between 0 and unity. Furthermore, the model (iv) supports either a neoclassical steady-state or long-run endogenous growth, giving it the potential to account for a wide range of real world development experiences.Labor's Share, Factor Shares, Development, Biased Technical Change, Capital Intensity

"The Real Thing:" Nominal Price Rigidity of the Nickel Coke, 1886-1959

We report that the price of a 6.5oz Coke was 5¢ from 1886 until 1959. Thus, we are documenting a nominal price rigidity that lasted more than 70 years! The case of Coca-Cola is particularly interesting because during the 70-year period there were substantial changes in the soft drink industry as well as two World Wars, the Great Depression, and numerous regulatory interventions and lawsuits, which led to substantial changes in the Coca-Cola market conditions. The nickel price of Coke, nevertheless, remained unchanged. We find that this unusual rigidity is best explained by (1) a contract between the Company and its parent bottlers that encouraged retail price maintenance, (2) a single-coin vending machine technology, which limited the Company's price adjustment options due to limited availability and unreliability of the existing flexible price adjustment technologies, and (3) a single-coin monetary transaction technology, which limited the Company's price adjustment options due to the customer "inconvenience cost." We show that these price adjustment costs are of a different nature than the standard menu cost, and their estimates exceed the existing estimates by an order of magnitude. A possible broader relevance of the nickel Coke phenomenon is discussed in the context of Nickel and Dime Stores, which were popular in the US in the late 1800s and the early 1900s.Sticky Prices, Cost of Adjustment, Menu Cost, Retail Price Maintenance, Single-Coin Vending Machine, Customer Inconvenience Cost, Coca-Cola, Coke, Nickel Coke, Pepsi, Nickel and Dime Stores

Heterogeneous Convergence

We use U.S. county-level data containing 3,058 cross-sectional observations and 41 conditioning variables to study economic growth and explore possible heterogeneity in growth determination across 32 individual states. Using a 3SLS-IV estimation method, we find that all statistically significant convergence rates (for 32 individual states) are above 2 percent, with an average of 8.1 percent. For 7 states the convergence rate can be rejected as identical to at least one other state’s convergence rate with 95 percent confidence. Convergence rates are negatively correlated with initial income. The size of government at all levels of decentralization is either unproductive or negatively correlated with growth. Educational attainment has a non-linear relationship with growth. The size of the finance, insurance and real estate, and entertainment industries are positively correlated with growth, while the size of the education industry is negatively correlated with growth. Heterogeneity in the effects of balanced growth path determinants across individual states is harder to detect than in convergence rates.Economic Growth, Conditional Convergence, County Level Data

Sigma Convergence Versus Beta Convergence: Evidence from U.S. County-Level Data

This note outlines (i) why σ-convergence may not accompany β-convergence; (ii) cites evidence of β-convergence in the U.S.; (iii) demonstrates that σ-convergence does not hold across the U.S., or within most U.S. states; and (iv) demonstrates the robustness of this finding to increases in mean income. The distributions of shocks appear important towards accounting for income disparity.σ-convergence, β-convergence, Solow growth model, speed of convergence

Heterogeneity in Convergence Rates and Income Determination across U.S. States: Evidence from County-Level Data

We utilize county-level data to explore growth determination in the U.S. and possible heterogeneity in growth determination across individual states. The data includes over 3,000 cross-sectional observations and 39 demographic control variables. We use a consistent two stage least squares estimation procedure. (We report OLS estimates as well.) The estimated convergence rate across the U.S. is about 7 percent per year – higher than the 2 percent normally found with OLS in cross-country, U.S. state, and European region samples. Estimated convergence rates for 32 individual states are above 2 percent with an average of 8.1 percent. For 29 states the convergence rate is above 2 percent with 95 percent confidence. For seven states the convergence rate can be rejected as identical to at least one other state’s convergence rate with 95 percent confidence. In examining the determinants of balanced growth path heights, we find that government at all levels of decentralization is negatively correlated with economic growth. Educational attainment of a population has a non-linear relationship with economic growth according to our estimates: growth is positively related to high-school degree attainment, seemingly unrelated to obtaining some college education, and then positively related to four-year degree or more attainment. Also, finance, insurance and real estate industry and entertainment industry are positively correlated with growth, while education industry is negatively correlated with growth. Heterogeneity in the effects of balanced growth path determinants across individual states is much harder to detect (or dismiss) than in convergence rates.Economic Growth, Income Convergence, Solow Growth Model, Balanced Growth Path, Heterogeneity in Convergence, Education and Growth, Size of Government and Growth, Consistent Estimation, County-Level Data

Evidence of induced innovation in US sectoral Capital´s shares

We use annual data on capital´s share and relative factor prices from 35 US industriesfrom 1960 to 2005 to test the induced innovation hypothesis. We derive, from a productionfunction framework, testable implications for the effect of contemporaneous and lagged factorprice ratios on capital´s share of production. The predicted effect is positive or negativedepending on the elasticity of substitution between labor and capital. From panel regressions, theestimated effect of the contemporaneous factor price ratio implies an elasticity of substitutionthat is less than unity, consistent with the consensus from the literature. Based on this, ournegative estimated effects for lagged price ratios are both statistically significant and consistentwith the induced innovation hypothesis.induced innovation, biased technical change, capital´s share, labor´s share, elasticityof substitution