Imane El Ouadghiri
email: imane.elouadghiri@u-paris10.fr

Valérie Mignon
email: valerie.mignon@u-paris10.fr.

Nicolas Boitout
email: nicolas.boitout@marketscience.fr

On the impact of macroeconomic news surprises on Treasury-bond yields *

Keywords: JEL Classification: G14, G12, E44, C22 bond market, event study, macroeconomic news

This paper investigates the impact of surprises associated with monthly macroeconomic news releases on Treasury-bond yields, by paying particular attention to the moment at which the information is published in the month. Implementing an event study on intraday data, we show that (i) the main bond market movers are based on economic activity and inflation indicators, (ii) long-maturity bonds are slightly more impacted by surprises than short-maturity ones, and (iii) the bond market is more sensitive to bad news than to good announcements. Finally, we evidence an empirical monotonic relationship between the surprises' impact and their corresponding news' publication date and/or their sign.

Introduction

A vast literature is devoted to the analysis of financial markets' responses to macroeconomic news announcements, 1 with pioneering studies 2 that have been implemented to investigate the efficient capital market hypothesis. Since the beginning of the 1980s, researches 3 have focused on whether the impact of macroeconomic news releases on financial assets is of the same nature and amplitude whatever the type of announcements, with the aim of identifying the economic indicators to which market participants are most sensitive. While the first studies (see, e.g. [START_REF] Schwert | The Adjustment of Stock Prices to Information About Inflation[END_REF]) were based, at the best, on daily data, the increasing availability of high-frequency series has lead to a renewed interest in the literature in assessing the reaction of return series to macroeconomic news few minutes or seconds after their publication. 4 Our paper falls into this strand of the event-study literature, considering the case of Treasury markets.

Basically, two kinds of information may affect asset prices. The first category is observed and interpreted homogeneously by all market participants, and is considered as "common knowledge news". The second category-"non-common knowledge news"-concerns information that is not observed by all market participants and gives way to different interpretations. 5 Being pre-scheduled with publication dates well known in advance by all market participants, expected macroeconomic news announcements can be considered as "common knowledge news". In this paper, we focus on such public news and aim at investigating the responses of Treasury-bond yields to those releases of scheduled macroeconomic announcements.

Information and economic statistics released by newspapers, news channels and international news agencies are generally published once per year, quarter, month or week. Organized according to a predetermined schedule known to all, these macroeconomic figures provide information about the current state of the economy and its future evolution through consensus forecasts published by professional forecasters. Public information concerns all economic fields, central banks policies, household sentiments, corporate profits, etc., and the publication of these figures and associated forecasts plays a key role for financial analysts. Such information indeed constitutes a decision-making tool allowing them to take positions on the market. As shown by [START_REF] Andersen | Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange[END_REF], [START_REF] Laakkonen | The Impact of Macroeconomic News on Exchange Rate Volatility[END_REF], [START_REF] Lee | Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics[END_REF], and [START_REF] Lahaye | Jumps, cojumps and macro announcements[END_REF] among others, the arrival of some of the most important expected macroeconomic news-such as the consumer price index, ISM (Institute of Supply Management) manufacturing index, consumer confidence index, retail sales, producer price index, non-farm payrolls and news related to the labor market to name a few-generate significant variations in asset returns and trading activities on financial markets, and often leads to large changes in market volatility, thereby causing discontinuities-commonly called "jumps" in the price process. These findings can be explained by the fact that traders change their positions in response to the arrival of new information on the market, such a flow of orders causing a sudden adjustment.

Agents do not automatically react to the value of macroeconomic figures itself, but more frequently to the distance that separates it from its forecast, i.e. to the surprise corresponding thus to the unanticipated component of news releases. 6 This characteristic explains why investors are willing to expend considerable resources in macroeconomic forecasting services in order to improve their decision-making process. As a consequence, a growing number of institutions conduct market participants' surveys and provide forecasts of upcoming macroeconomic news announcements. These institutions calculate the surprise component linked to the macroeconomic announcement, which is crucial in investigating the impact of such news on market returns and volatility (see [START_REF] Silvia | Ranking Professional Forecasters in an Unbalanced Panel: A New Approach[END_REF] among others). The choice of the forecasting institution is thus a key issue. Specifically, there are currently five main forecast data providers, namely Bloomberg, Briefing.com, Dow Jones, International Money Market Services (MMS), and Reuters. MMS data have been used for a long time in several previous event studies. Considering various scheduled macroeconomic announcements provided by MMS, [START_REF] Ederington | How Markets Process Information: News Releases and Volatility[END_REF] find that some of them affect the volatility of the three considered futures markets-Treasury bond, Eurodollar and Deutsche Mark-5 minutes after their announcement. [START_REF] Balduzzi | Economic News and Bond Prices: Evidence from the U.S. Treasury Market[END_REF] investigate the effects of scheduled macroeconomic news also provided by MMS on bond prices, trading volume and bid-ask spreads, showing that 17 public news releases have a significant impact. Studying as well the influence of macroeconomic news announcements on interest rates using MMS consensus forecasts, [START_REF] Andersen | Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange[END_REF] and [START_REF] Gürkaynak | The Sensitivity of Long-Term Interest Rates to Economic News: Evidence and Implications for Macroeconomic Models[END_REF] provide empirical evidence that long-term nominal forward rates are excessively sensitive to monetary policy shocks. Given that MMS ceased to provide its survey services in 2003 since its acquisition by Informa, recent studies essentially rely on data from Bloomberg, Dow Jones and Briefing.com. [START_REF] Dungey | Empirical Evidence on Jumps in the Term Structure of the US Treasury Market[END_REF] use the Bloomberg survey to link the surprises to jumps and co-jumps in the U.S. term structure, and [START_REF] Jiang | Information Shocks, Liquidity Shocks, Jumps, and Price Discovery: Evidence from the U.S. Treasury Market[END_REF] rely on both Bloomberg and Briefing.com forecasts to examine the importance of surprises versus market liquidity in explaining the jumps observed in the U.S. Treasury market. They find that jumps mainly occur at the time when macroeconomic news are released, and that announcements preceding liquidity shocks-such as changes in the bid-ask spread and market depth-have significant predictive power for explaining those jumps. In all cases, the surprises are shown to have large and significant impact on financial asset prices.

More generally, the properties of forecasting surveys and comparisons between agencies' forecasts have been the subject of some investigations in the literature. [START_REF] Pearce | Stock Prices and Economic News[END_REF] examine the accuracy of MMS forecasts and put forward a significant bias in industrial production expectations. [START_REF] Balduzzi | Economic News and Bond Prices: Evidence from the U.S. Treasury Market[END_REF] find little evidence that MMS forecasts are biased predictors of the considered announcements, and no evidence of expectation revisions during the time interval between the survey release and the news publication. Some studies seeking to compare the quality of forecasting surveys highlight the superiority of Bloomberg over other agencies. Considering a sample of 51 announcements, [START_REF] Noel | An empirical examination of Bloomberg's macroeconomic forecasts of the G-7 nations[END_REF] shows that MMS forecasts are more volatile than Bloomberg's ones. Examining the U.S. equity futures markets' reaction to announcement surprises provided by both Bloomberg and Briefing.com, Chen, Jiang, and Wang (2013) also find that Bloomberg forecasts are overall more accurate and display smaller prediction errors than Briefing.com. 7 In line with these findings, we focus in this paper on the impact of macroeconomic reports extracted from the Bloomberg terminal.

Based on these data, our paper aims at investigating the impact of surprises associated with monthly macroeconomic news releases on Treasury-bond returns, by paying particular attention to the moment at which the information is published in the month. While various factors may be at play in explaining the impact of news releases on returns, such as the type of news and the economic context that prevails at the time of publication, the publication date itself may indeed be of crucial importance, possibly influencing the other news and leading to mimetic phenomena. One may thus expect that the earlier the news is published during the month, the more important will be its impact. We investigate this hypothesis in the present study. Our analysis complements the existing studies in several ways. First, we focus on the Treasury-bond market and retain two maturities-namely 2-year and 10-year-allowing us to compare the news' impact at different horizons, and to test the hypothesis that long-term bonds are more volatile than short-term bonds. Second, instead of focusing on one specific country, we consider a sample of five countries by investigating the effect of macroeconomic news announced in the United States, the United Kingdom, China, Germany and Japan on bond yields of the three former economies. The choice of those three countries can be justified by the fact that (i) U.S. and U.K. forecasting institutions are usually seen as robust and enough "mature" to attract the interest of global markets, and (ii) the increasing role played by China, whose trade balance figures have become a key indicator of world economic health. Third, to avoid masking intraday effects when dealing with daily data, we use intraday data-the frequency being 15 minutes for U.S. data, and 5 minutes for U.K. and China. We also consider a longer and more recent period compared to the existing event studies, starting in January 2007 and ending in March 2013, thus including major topical events such as the world financial crisis as well as the European debt crisis. Fourth, from a methodological viewpoint and to our best knowledge, our contribution is the first to establish a link between the strength of the impact of macroeconomic news and the corresponding publication date in the month and/or the sign of the associated surprises.

Our main findings can be summarized as follows. The time at which the news is published in the month strongly matters. Specifically, information released in mid-month generates very few surprises contrary to the news published at the beginning or the end of the month. Regarding the type of announcements, the main market movers are based on economic activity and inflation related indicators. Our event study also evidences that (i) not only U.S. surprises have a significant impact on bond yields, but also German and Japanese news, (ii) bad news have a greater effect than good announcements, as expected, and (iii) long-maturity bonds are slightly more sensitive than short-maturity ones to the arrival of new information, in accordance with the liquidity preference theory.8

The rest of the paper is organized as follows. Section 2 describes the data. Section 3 presents some preliminary results regarding the forecasting surveys' accuracy, and the importance of the news' publication date. Section 4 is devoted to the event study, and Section 5 concludes the paper.

Data description

Macroeconomic news and bond price data are respectively extracted from Bloomberg and Reuters terminals.

Macroeconomic news announcements

According to [START_REF] Fleming | Price Formation and Liquidity in the U.S. Treasury Market: The Response to Public Information[END_REF], [START_REF] Balduzzi | Economic News and Bond Prices: Evidence from the U.S. Treasury Market[END_REF], [START_REF] Andersen | Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange[END_REF] and [START_REF] Andersen | Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange[END_REF], bond yields respond significantly to announcements about employment, inflation, output, housing, consumer (CPI) and producer (PPI) price indexes. [START_REF] Chen | Market Reaction to Information Shocks. Does the Bloomberg and Briefing.com Survey Matter?[END_REF] also evidence that markets strongly react to inflation news (CPI and PPI announcements) and negative shocks in housing prices, personal spending, and retail sales. [START_REF] Dungey | Empirical Evidence on Jumps in the Term Structure of the US Treasury Market[END_REF] retain CPI, PPI, retail sales, housing starts, GDP, durable goods and non-farm payrolls as the most important news items for bond markets. These macroeconomic figures that are considered as key factors are known in the event-study literature as "market mover indicators" and naturally include activity, employment and inflation indicators. Other variables can also be retained, depending on data availability. Following the afore mentioned previous studies, as well as [START_REF] Lahaye | Jumps, cojumps and macro announcements[END_REF]Neely (2011), Jiang, Lo, and[START_REF] Jiang | Information Shocks, Liquidity Shocks, Jumps, and Price Discovery: Evidence from the U.S. Treasury Market[END_REF] and [START_REF] Erdemlioglu | Econometric modeling of exchange rate volatility and jumps[END_REF], we consider a wide set of news items including the subsequent monthly announcements' categories for our five considered countries: activity indicators (industrial production, durable goods orders, factory orders, ISM manufacturing index...), consumption and employment indicators (consumer confidence index, consumer credit index, retail sales, new home sales, non-farm payrolls, unemployment rate...), inflation indicators (consumer price index, producer price index...) and foreign trade indicators (trade balance). These announcements are based on a total of 17 items for the U.S. market, 8 for the U.K., 4 for China, 10 for Germany, and 9 for Japan (see Tables 7 to 11 in Appendix).

Tables 7 to 11 in Appendix display an overview of the considered announcements released on the Bloomberg terminal during the January 2007 to March 2013 period, together with their main characteristics. U.S. macroeconomic figures are almost always released at expected times, mainly around 13:30 and 15:30 GMT (8:30 and 10:30 EST). More specifically, among the 17 regularly scheduled news releases, 10 are published at 13:30 GMT (08:30 EST), covering all inflation and employment indicators, trade balance, personal spending and durable goods orders. Five of the announcements are published at 15:00 GMT (10:00 EST), including new home sales, consumer confidence index, ISM manufacturing index, Philadelphia FED and factory orders; the remaining two announcements-industrial production and consumer credit-being published at 14:15 GMT (09:15 EST) and 20:00 GMT (15:00 EST) respectively. Most U.K. figures are released at 09:30 GMT (4:30 EST), except GfK's consumer confidence index. German figures are published around 07:00 GMT (2:00 EST) and 11:00 GMT (6:00 EST), Japanese ones around 23:30 GMT (18:30 EST) and 00:50 GMT (19:50 EST), and Chinese ones mostly around 01:30 and 10:30 GMT (20:30 and 05:30 EST).

Regarding the definition of the surprises, we follow the previous literature by standardizing the surprise of each news announcement (see [START_REF] Balduzzi | Economic News and Bond Prices: Evidence from the U.S. Treasury Market[END_REF] among others). Let S it be the forecast error related to news announcement i at time t, we have:

S it = A it -F it σi (1)
where A it is the released value for announcement i at time t, F it the median of the Bloomberg forecast survey, 9 and σi the standard deviation of the difference A it -F it . S it is thus a measure of the unexpected component of the released information, i.e. the surprise.

Bond price data

Turning to bond price data, two maturities are considered, namely 2 and 10 years. 2Y denotes the two-year maturity, 10Y the ten-year maturity.

As shown in Table 1, average intradaily returns are globally close to zero, as expected. They are notably negative for the U.S., which may be explained by the major recent events that have strongly affected the world, and especially the U.S., such as the global financial crisis, but also by the downward trend in U.S. nominal interest rates since the mid-1980s. Finally, as it is frequently the case with financial data, bond price returns are skewed and display high kurtosis values, which means that the empirical returns distribution is more peaked and has fatter tails than the normal density.

Data preliminary analysis

We first examine whether consensus forecasts of monthly news announcements from Bloomberg surveys have a tendency to be systematically biased. Then, we study the relationship between macroeconomic news' forecast errors and their corresponding publication dates.

The consensus "dilemma"

The dilemma lies in the fact that if consensus data represent the mean (or median) market sentiment, the smoothing process induced by the averaging (or median) operation may generate biased forecasts. However, as stressed above, it is not the published value in itself that is important, but its distance from the expected value. Hence, the reaction of market participants to macroeconomic figures should not be apprehended in absolute but rather in relative terms.

Given that prediction quality is obviously related to the number of forecasters included in the panel of experts, we assess the accuracy of Bloomberg consensus forecasts by considering the number of forecasters who participate to the survey. For important news announcements, such as those related to industrial production, retail sales and consumer price index, the number of professional forecasters submitting their forecasts to Bloomberg prior to a variable release announcement can reach up to 80 (source: Bloomberg). However, the number of forecasters varies depending on the type of macroeconomic news announcements, and also from month to month. To assess if there are enough panelists so that we can estimate the mean or median surveys with sufficient accuracy, we construct a test allowing us to estimate the significance of the distance between the mean of the responses from forecasters and the mean of the market, the latter being given by the actual realization of the macroeconomic news release. The underlying idea of our test is based on the definition of consensus forecasts as the median of individual forecasts made by the experts. Specifically, if the panel comprises a sufficient number of experts, the median of individual forecasts tends to its asymptotic value and, in turn, constitutes a good proxy for the consensus. If this is not the case, the corresponding value has to be eliminated from the considered series. Assuming that mean and median are approximately the same because of the symmetry of the distribution, the distance is thus defined as:

dist = μF -μA (2)
where μF is the mean of forecasters' responses, and μA denotes the mean of the market. To estimate the standard deviation of the mean of forecasters' responses, we consider the usual formula:

sdev(μ F ) = σF √ N ( 3
)
where N is the number of forecasters from which we compute the mean, and σF is the empirical standard deviation of the forecasters' responses. Therefore, we build a t-test that divides the distance between the mean of surveys and the mean of the market by the standard deviation of the mean of forecasters' responses:

T dist = dist sdev(μ F ) = μF -μA σF × √ N (4)
T dist is distributed as a Student with (T -K) degrees of freedom, T being the number of observations included in the calculation of the distance and K the number of estimated variables. Applying this test on our data has allowed us to clean our database by eliminating all values that were non-significant at the usual 95% confidence level. Finally, note that we have checked that all our considered series-macroeconomic figures announced, consensus forecasts, and bond price returns-are stationary.12 3.2 Relationship between the publication date and surprise's nature

The amount of macroeconomic news published every month is constantly growing, whose importance differs according to the considered market. This importance may also be different, depending on the time at which the news is published in the month. One key issue is thus to identify the given moment at which macroeconomic news starts to be considered by investors as a market mover indicator.

It seems reasonable to think that all markets tend to react immediately when a typical figure is of primary importance for market participants. An emblematic example is U.S. non-farm payrolls, available each first Friday of the month at 13:30 GMT. It is the subject of intense scrutiny by market participants, and therefore market post-releases reactions are immediate. While this is a very typical case, we can however expect that the date at which the news is published in the month (beginning, end, mid) matters regarding the surprises size, and, in turn, the market impact. For a given type of news, if the first information published is associated with the strongest market reaction, one may expect a "rush" to publication. In the recent period, private institutions publishing macroeconomic news rushed to release their figures quite early during the month. An example is provided by the Markit PMI, which is published the first day of each month and generates a very strong market reaction.

Figure 1 provides a first insight by displaying the number of zero surprises (y-axis) together with the corresponding macroeconomic announcements' date (i.e. day in the month, x-axis).

With the exception of China, 13 Figure 1 exhibits a similar pattern for the four other countries: news published at the beginning or the end of the month are associated with the highest number of non-zero surprises (i.e., expectations that differ from published values). In other words, the news published in mid-month generate very few surprises, making them more easily predictable. Turning to information type, CPI and unemployment related news are associated with the highest number of zero surprises. 14 Various possible explanations could be proposed regarding the importance of the publication date. The first one is the fact that psychological phenomena are more at play at the beginning or the end of the month, leading to more anticipation errors (i.e., surprises). Such psychological phenomena could take the form of mimetic and/or overreaction behaviors due to the quite important amount of information provided at the beginning or the end of the month. Similarly, the very few surprises associated with the news published in mid-month could be explained by the existence, at the beginning of the month, of specific information related to those mid-month scheduled news allowing for more accurate predictions. The second explanation could stem from the nature of the news published at the considered time. As previously mentioned, some of the news published at the beginning of the month constitute indicators to which market participants are highly sensitive and for which post-releases reactions are thus important. Finally, a more "practical" explanation could be that large traders, who have to report at the end of each month to their supervisor, somehow balance their portfolio at the end of month and have thus more liquidity to invest at the beginning of the following month. Let us now provide an in-depth analysis of these first results through the impact study.

4 Impact study

Impact of macroeconomic news on bond returns

To analyze the impact of macroeconomic news on bond returns, we estimate the intra-daily response of bond yields at two maturities (2 and 10 years) to economic news releases using the standard event-study methodology. More specifically, we regress bond price changes from 5 minutes before to 15 minutes after the announcement (from 15 minutes before to 15 minutes after release for the U.S.) on the standardized surprise component of the macroeconomic news releases. The choice of this window can be justified by the fact that price variations are extremely rapid on the Treasury-bond market, with most of the impact occurring in the first five minutes after the release [START_REF] Balduzzi | Economic News and Bond Prices: Evidence from the U.S. Treasury Market[END_REF]). To ensure that all relevant price changes are fully captured, we thus retain a 15-minutes post-release interval. For each announcement i and each considered country, we run an OLS regression of the form:

R it = β 0i + β 1i S it + β 2i A it + 3 k=1 α ki R i,t-k + e it (5)
with:

14 All detailed results are available upon request to the authors. (P 15it -P -15it )/P -15it for the United States (P 15it -P -5it )/P -5it for others and:

A it = S it if S it < 0 0 if S it ≥ 0
where P 15it denotes the price 15 minutes after announcement i at time t,15 P -5it the price 5 minutes before the announcement i at time t, P -15it the price 15 minutes before the announcement i at time t, and S it the standardized surprise associated with announcement i at time t.

A it captures asymmetric effects by accounting for the sign of the surprise, β 1i measures the sensitivity of the bond price return to the announcement i and e it is an i.i.d. error term. The number of lags k included in the regressions is selected using the Schwarz information criterion.

Estimation results are presented in Table 2 for U.K. and U.S., and in Table 3 for China. For each surprise associated to announcement i (i = 1, ..., 48 for the U.S. and U.K., and i = 1, ..., 26 for China), those tables report the estimated value of the slope coefficient (β 1i ), the p-value corresponding to the asymmetry coefficient (β 2i ), and the value of the R-squared (R 2 ). As shown, some U.S. news releases have a significant impact on bond yields, as expected, but this is also the case of some German and Japanese surprises, particularly regarding activity and manufacturing indicators. By contrast, Chinese news surprises have very little effect. Various explanations may be suggested regarding this result. First, it could potentially reflect a weak confidence in figures published by the Chinese public institutions. Second, since bond prices reflect, among others, expectations regarding monetary policy, our result may be due to the weak reaction of China's monetary policy to Chinese news. Third, it could stem from the absence of portfolio reallocation after the news releases.

Interestingly, our results evidence that long-term maturity bonds are only slightly more reactive to news surprises than low-maturity ones. Turning to asymmetry coefficients, in most cases only the negative surprises have an impact on the returns, consistent with the wellknown result suggesting that bad news have a stronger effect than good announcements.

More in detail, some news surprises are significant for several bond yields, while others affect only one or two of them. The consumer price index is very present among the economic indicators significantly affecting bond returns, being the most widely followed monthly inflation indicator. The core CPI indicator (CPIC) is even more scrutinized by market participants due to its greater monthly stability. An increase in CPIC is associated with a decrease in bond returns, since declining interest rates (resulting from low inflation) tend to rise bond prices. The German business climate and PMI services indicators are also tracked by investors because they are early indicators of current economic conditions, the former representing busi-ness expectations and the latter referring to the private sector economy. Japanese tertiary industry, machine orders and unemployment rate indicators are also in the list of significant surprises. They represent respectively a measure of domestic activity, a leading indicator of production and a way for investors to gauge the tightness degree on the job market. If wage inflation threatens, interest rates are expected to rise, leading to a fall in bond prices. U.S. consumer confidence index, new home sales and non-farm payrolls provide information respectively on (i) the direction of the economy, the more confident consumers are about the economy, the more they are likely to spend; (ii) the housing market trend and, in turn, economic momentum; and (iii) the current level of economic activity. An increase in nonfarm payrolls translates into earnings that workers will spend on goods and services in the economy, leading to a decline in bond returns-rapid increases in employment causing fears of inflationary pressures suggesting a rise in interest rates.

β 1i β 2i R 2 β 1i β 2i R 2 β 1i β 2i R 2 β 1i β 2i R 2 (p-

Relationship between macroeconomic surprises' impact and their publication date

To complement our preliminary analysis and the above event study, we now statistically seek for a potential monotonic relationship between the surprises' impact strength on bond returns and their corresponding publication date and/or their sign (number of negative, positive or zero surprises). Among the various measures that can apprehend such a relationship, the Kendall rank correlation coefficient-commonly referred to Kendall τ statistic-seems particularly appealing. 16We consider the Kendall τ b statistic, which is a non-parametric measure of association between two sets of ordinal variables, say x and y, when "tied" rankings are permitted. Its values vary from -1 for perfectly negative association to 1 for perfectly positive association, with τ b = 0 corresponding to the absence of association. The calculation of τ b is based on comparisons of pairs of joint rankings (x i , y i ) and (x j , y j ), i, j = 1, ..., N , N being the number of items. More specifically, we have:

x i,j =      +1 if x i < x j 0 if x i = x j -1 if x i > x j y i,j =      +1 if y i < y j 0 if y i = y j -1 if y i > y j
for i, j = 1, 2, ..., N and:

τ b = i,j x i,j y i,j i,j x 2 i,j i,j y 2 i,j (6)
We then have the following properties:

• (i) if x i < x j and y i < y j , or x i > x j and y i > y j , pairs are called concordant,

• (ii) if x i < x j and y i > y j , or x i > x j and y i < y j , pairs are called discordant.

Based on our previous results, we aim at establishing a link, a correspondence relationship between the coefficients' (β 1i ) t-statistics obtained in the impact study-representing the strength of the impact of each surprise on bond yields-and corresponding news release dates and / or surprises' sign.17 The null hypothesis is that the pairs (t-statistic, publication date)-or (t-statistic, number of zero surprises), (t-statistic, number of positive surprises) or (t-statistic, number of negative surprises)-are independent.

Tables 4, 5 and 6 report the results of the Kendall-based test. 18 The results are quite different for U.K. and U.S. 2-year bonds. Indeed, as shown in Table 4, the Kendall τ b is significant at the 10% level for the pair (t-statistic, negative surprises), meaning that there is a concordance between t-statistics' order and the number of negative surprises. For the U.S. (Table 5), the significance of the Kendall τ b statistic is obtained for the pairs (t-statistic, positive surprises). Consequently, macroeconomic news generating the largest number of negative surprises (i.e., a frequent overestimation of economic figures, causing forecast errors that are mostly negative) in U.K. and the largest number of positive surprises in U.S. are those that have the strongest impact on U.K. and U.S. bond returns, respectively. Turning now to long-term maturity bonds, Table 6 evidences that there is a concordance between t-statistics' order and publication dates: macroeconomic news published at the beginning or the end of the month are those that exert the strongest impact on bond returns.

On the whole, our findings evidence that the null hypothesis of mutual independence between the size of the impact on the one hand, and the ranking of news' publication by date or surprises' sign on the other hand, is rejected for 3 out of our 5 considered instruments. This supports our previous findings that investors tend to privilege news that are associated with both the largest number of non-zero surprises and publication dates planned at the beginning or the end of the month, rather than announcements with less surprises and planned midmonth.

Conclusion

The aim of this paper is to investigate the impact of surprises associated with monthly macroeconomic news releases on Treasury-bond yields, by paying particular attention to the moment at which the information is published in the month. Relying on intraday data, our event study globally shows that not only U.S. surprises have a significant effect on bond yields, but also German and Japanese ones. More in detail, we find that (i) the main market movers are based on economic activity and inflation indicators, (ii) long-term maturity bonds are slightly more impacted by surprises than short-maturity ones, and (iii) the bond market is more sensitive to bad news than to good announcements. Finally, we evidence an empirical monotonic relationship between the surprises' impact and their corresponding news' publication date and/or their sign. We find that the sign of the surprise matters in case of short-maturity bonds, while the publication date plays a key role for long-maturity bonds-the strongest impact being observed for news published at the beginning or the end of the month. The macroeconomic news that are characterized by such features are mainly activity indicators, explaining their "market mover" key role.

  -axis: macroeconomic announcements' date (day of the month), y-axis : number of zero surprises.

Figure 1 :

 1 Figure 1: Publication date vs. surprises

  Table1summarizes descriptive statistics regarding bond price returns series for China, U.K., and the U.S. For China and U.K., we use a long span of high frequency data for all T-Bonds for which more than 6 years of data are available, and set the data frequency to 5 minutes. The time period spans from January 1, 2007 to March 15, 2013, corresponding to 2148 trading days. The daily time interval covers the 24 hours, each day consisting of 288 intraday 5minutes intervals, giving us a total of about 632,000 observations. For the U.S., we consider a 15-minutes frequency to avoid microstructure noise issues.10 The U.S. sample covers the period from January 1, 2007 to July 11, 2011, which corresponds to 1611 trading days. 11 Each day consists in 96 intraday 15-minutes intervals, amounting to a total of about 154,656 observations.

	Table 1: Summary statistics on bond price returns series
		China	U.K.		U.S.
		CN2Y	UK2Y	UK10Y	US2Y	US10Y
	Number of observations	632136	632735	632370	158262	158236
	Frequency (minutes)	5	5	5	15	15
	Mean	0.000451 1.66E-07 7.13E-06 -0.000411 1.07E-06
	Std. Dev.	0.033872 0.000161 0.004213 0.020274 0.001370
	Max	4.528806 0.063810 2.005850 0.008119 0.295221
	Min	-0.818949 -0.014658 -0.729650 -1.000000 -0.227379
	Skewness	23.88745 124.7908 207.8209 -49.27977 33.66598
	Kurtosis	1229.371 44582.52 94590.31 2429.643 18911.82

CN: China, UK: United Kingdom, US: United States.

Table 2 :

 2 Estimation results: impact of surprises on bond yields, United Kingdom and United States

	US10Y
	US2Y
	UK10Y
	UK2Y
	News\Bonds

Table 8 :

 8 United Kingdom (U.K.) -Macroeconomic news announcements description

	Source		ONS		GfK NOP	ONS	ONS		ONS	ONS	ONS		ONS
	Type of announcement Variable name Release time Reporting convention	Activity Indicators	Industrial Production IP 09:30 Rate / % Change	Consumption and Employment Indicators	GfK Consumer Confidence Survey CCF 00:01 Value /	Retail Sales Less Auto RSLA 09:30 Rate / % Change	ILO Unemployment Rates UP 09:30 Rate / % RATIO	Inflation Indicators	Producer Price Index CPI 09:30 Rate / % Change	Consumer Price Index PPI 09:30 Rate / % Change	CPI Ex Food and Energy CPIC 09:30 Rate / % Change	Foreign Trade Indicators	Visible Trade Balance TB 09:30 Value / Millions	All announcements are monthly. ONS: Office for National Statistics.

Table 9 :

 9 China (CN) -Macroeconomic news announcements description Bank of China; NBSC : National Bureau of Statistics of China.

	Source		NBSC		NBSC	NBSC		POC
	Type of announcements Variable name Release time Reporting convention	Activity Indicators	Industrial Production IP 03:00 -06:30 Rate / % Change	Inflation Indicators	Consumer Price Index CPI 2:30 -04:00 Rate / % Change	Producer Price Index PPI 02:00 -04:00 Rate / % Change	Monetary Policy Indicators	Rate / % Change Money Supply 2 M2 08:00 -10:00	All announcements are monthly. POC: People's

Table 11 :

 11 Japan (JP) -Macroeconomic news announcements description Ministry of Economy Trade & Industry Japan; ESRIJ: Economic and Social Research Institute Japan; MFJ: Ministry of Finance Japan; MIAC: Ministry of Internal Affairs and Communications; BoJ: Bank of Japan.Table 12: Panel U.S. -Descriptive statistics on macroeconomic surprises News CCD CCF CPI CPIC DGO FO IP ISM NFP NHS PCE PHIL PPI PPIC RSLA TB UP

	Source		MET&IJ	MET&IJ	ESRIJ		MFJ	MIAC	MET&IJ		BoJ	MIAC		MIAC
	Type of announcement Variable name Release time Reporting convention	Activity Indicators	Industrial Production IP 23:50 / 00:50 Rate / % Change	Tertiary Industry TI 23:50 / 00:50 Rate / % Change	Machine Orders MO 23:50 / 00:50 Rate / % Change	Consumption and Employment Indicators	23:30 / 00:30 Rate / % Change Jobless Rate UP	23:30 / 00:30 Rate / % Change Household Spending HSPD	23:50 / 00:50 Rate / % Change Retail Trade RT	Inflation Indicators	23:30 / 00:30 Index Point Consumer Price Index CPI	23:50 / 00:50 Rate / % Change Domestic Corporate Goods Price DCGP	Foreign Trade Indicators	23:50 / 00:50 Value / Billions JPY Trade Balance TB	All announcements are monthly. MET&IJ: Release Date

Table 14 :

 14 Panel China -Descriptive statistics on macroeconomic surprises

	News PPI CPI M2 IP	Release Date 11 12 12 15	Negative Surp 31 24 31 30	Positive Sup 25 29 33 27	Zero Surp 20 23 12 19

Table 15 :

 15 Panel Germany -Descriptive statistics on macroeconomic surprises News PMIMF PMISV FO IP CPI ZEW PPI BC RS UP

	24 28 29	31 50 31	44 21 16	1 5 29
	20	35	35	6
	16	38	38	0
	6 8 12	41 42 1	33 32 11	2 2 64
	4	37	35	4
	1	27	38	11
	Release Date	Negative Surp	Positive Sup	Zero Surp

Table 16 :

 16 Panel Japan -Descriptive statistics on macroeconomic surprises News MO DCGP TI TB CPI RT HSPD UP IP

	29 30	32 42	23 29	21 5
	29	38	33	5
	28	28	44	5
	27	36	24	4
	16 23	36 38	30 35	3 16
	12	25	36	10
	Release Date 10	Negative Surp 39	Positive Sup 33	Zero Surp 15

See Ederington and Lee (1993),[START_REF] Balduzzi | Economic News and Bond Prices: Evidence from the U.S. Treasury Market[END_REF],[START_REF] Andersen | Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange[END_REF],[START_REF] Dungey | Empirical Evidence on Jumps in the Term Structure of the US Treasury Market[END_REF] among others.

Especially for important news, such as those related to consumer price index, durable goods orders, GDP, personal spending and retail sales.

See also[START_REF] Dungey | Empirical Evidence on Jumps in the Term Structure of the US Treasury Market[END_REF] who show that U.S. Treasuries tend to co-jump across maturities, with more unique jumps at both ends of the term curve, providing some support for both liquidity and preferred habitat hypotheses.

Also called "consensus" data, i.e. the median of individual forecasts of the announcement i made each month by professional forecasters working mostly in banks, brokerages or forecast agencies.

See Lee and Mykland (2008) for more details.

The period is shorter than for China and U.K., due to a limited access to high frequency data for the U.S.

Results of unit root tests are available upon request to the authors.

China exhibits a different pattern because news are published mid-month.

Computed as the mean between bid and ask prices.

According to[START_REF] Laurencelle | Le tau et le tau-b de Kendall pour la corrélation de variables ordinales simples ou catégorielles[END_REF], it has indeed two advantages over the other tests (such as Spearman, Pearson, Gamma-based tests...): it transcends the metric of measured variables and removes the need for a parametric model, making it a truly non-parametric index, suitable for categorical ordinal variables (see also[START_REF] Agresti | The Effect of Category Choice on Some Ordinal Measures of Association[END_REF] and[START_REF] Khamis | Measures of Association: How to Choose?[END_REF]).

Descriptive statistics for the data used in our analysis are reported in Tables 12 to 16 in Appendix.

Only significant results are reported (the Kendall τ b statistic is not significant for the 10-year maturity U.K. bond, nor for China).


Jean Cartelier

Entrepreneurs and wage-earners: a monetary approach

The purpose of the paper is to o¤er a logical genesis of the di¤erenciation of agents in two classes: capitalist entrepreneurs and wage-earners. The model presented here does not follow the Classical (or Marxian) tradition (where the two opposed classes are the straight consequence of the concentration of the means of production in the hands of a limited fraction of people). It does not follow mainstream economists either (no di¤erence according to general competitive equilibrium or a di¤erence taken as given in labour economics in general).

Models belonging to those traditions fail to reproduce a major stylised fact: wage-earners cannot be distinguished from entrepreneurs when they are in the market for ccommodities but they radically di¤er in the 'market for labour' or in production (wage-earners do not produce for their own account but for that of entrepreneurs who get pro…ts, not wages).

Modern tentatives to deal with the di¤erenciation of agents (Matsuyama for instance) explain it by a progressive di¤erenciation of the level of wealth up to a threshold which makes some agents able to accumulate and others not.

We propose a di¤erent view based on the process of issuance of money. If a fraction of agents have not a direct access to that process they cannot act in the market for their own account. The alternatives they have are limited to autarky or to work for the account of those who have additional alternatives due to their direct access to money (to be independent producers or entrepreneurs hiring wage-earners).

The model makes explicit the necessary and su¢ cient conditions for the existence of an E-equilibrium in which co-exist heterogeneous agents (entrepreneurs and wage-earners) starting from a population homogeneous except for bank rationing. These reasonable conditions are: an e¢ cient monetary system, a su¢ cient gap between productivity of production in mass compared to other types and a possibility to induce wage-earners to work signi…cantly more than they would as free producers.

A non-Marxian notion of exploitation is suggested to conclude.

1

Introduction

The trend of growth since the 18th century in Europe and after in the rest of the world is not mainly due to independent producers (not to slaves either) but to waged workers hired by capitalist entrepreneurs [START_REF] Cartelier | Chômage involontaire d'équilibre et asymétrie entre salariés et non-salariés: la loi de Walras restreinte[END_REF] . Adam Smith was so conscious of that fact that he conceived the process of growth as one of extension of the proportion of waged labour in the total labour expended (he called productive labour the labour exchanged against capital and non productive the labour exchanged against income). Does waged labour imply a qualitative difference between economic agents? Do entrepreneurs and wage-earners belong to di¤erent classes? Economic theory provides various answers to these questions. Schematically, stories told by economists about the di¤erence between capitalist entrepreneurs and wage-earners 2 follow one of these two traditions: English Classical tradition or Neoclassical approach.

Economists following the English Classicial tradition generally do not consider wage-earners proper but the commodities they consume. Real wages are ingredients of the production on the same footing as raw products and machines. The latter are determined by the technique, the former by physiology, custom or class struggle. Market has no role here; it comes after. Capitalist entrepreneurs are the only ones able to take economic decisions (to consume or to accumulate, to hire or not hire wage-earners). Wage-earners do not exist as economic agents, no more than horses or machines. Entrepreneurs and wage-earners belong to absolutely di¤erent classes. Why? Because the former own or have the control over the means of production whereas the latter have not. Equilibrium in Classical models is of von Neuman-Sra¤a type.

Classical view has the merit to stress the dependence of wage-earners and their radical di¤erence with entrepreneurs. However, it is not relevant for our 'open'societies where castes do not exist. Ownership of the means of production should not be presupposed. Ownership in our market economies is the outcome of economic activity; it has to be validated by the market. The fact that only a fraction of people own the means of production has to be explained and should not be considered as given. Moreover, wage-earners are free to choose their consumption goods in the limit of their incomes. For these reasons, Classical tradition is not well-suited for thinking the heterogeneity between entrepreneurs and wage-earners in our modern societies.

Most of modern academic economists adopt an opposite view. Wage-earners and entrepreneurs are described as bargaining wages and employment on a market for labour. Even if they acknowledge some asymmetries, academic econo- [START_REF] Cartelier | Chômage involontaire d'équilibre et asymétrie entre salariés et non-salariés: la loi de Walras restreinte[END_REF] I am grateful to Carlo Benetti, Vincent Bignon, Antoine Rebeyrol, Mariana Rojas Breu and participants to the seminars Philosophie et théorie économique and Echanges for their remarks and critiques. I have a special debt to Régis Breton who has made me understand the lacunae of a …rst version of this paper. I remain responsible for its main thesis and for the remaining errors. [START_REF] Jacques | Primitive Accumulation, Growth and the Genesis of Social Classes[END_REF] Here the term entrepreneurs indi¤erently denotes managers and capital owners. It is true that the separation between property and management entails many important consequences in the real life. But, at the high level of abstraction of the present paper it would not be worth considering them with great details. mists do not think that the asymmetries put into question the basic fact that wage-earners and entrepreneurs have market relations with each other. They are on the same footing and their relations are ruled by equivalence. These asymmetries are not viewed as generating an heterogeneity of the condition of these agents. In general equilibrium theory, capital and labour as 'factors of production'di¤er in the same way as 'corn' and 'silver' di¤er as commodities. Agents endowed with capital are not in a di¤erent position as agents endowed with labour (entrepreneurs exist there only as a coordination principle). In more specialized theories asymmetries are introduced but they do not generate a qualitative di¤erence between entrepreneurs and wage-earners. Neoclassical approach is relevant in that it clearly shows that wage-earners are not cattle or machines and are free to spend wages as they please but does not account for the hierarchy in production: wage-earners do not decide anything in the sphere of production [START_REF] Keynes | The General Theory of Money, Interest and Employment[END_REF] . Therefore, Neoclassical tradition is not in accordance with a basic feature of our economies.

To sum up, the two traditions do not o¤er a relevant view about the wage relationship at its present stage. They do not account for the following major stylised fact: entrepreneurs and wage-earners are in the same qualitative position in the markets for commodities (both maximize utility under a budgetary constraint) but they are in a qualitative opposed position in the 'market for labour' and in production (wage-earners do not decide what, how neither how much to produce). The co-existence of two features of the wage relationship, one of equivalence in the market for commodities the other of subordination in production, is responsible for the symmetric failure of both traditions to give an appropriate view of it. A further question, given that stylized fact, is whether wage-earners and entrepreneurs should be treated as homogeneous agents (differing only quantitatively in their market allocations) or as heterogeneous agents (di¤ering qualitatively in their capacity to intervene in the market). An answer to that question may be found not by presupposing either homogeneity or heterogeneity but by making explicit the process through which an a priori homogeneous population became split into two groups or classes: entrepreneurs and wage-earners. The nature of that process will give the key to the question above.

Matsuyama is one of the few authors to have dealt with that proces of di¤erenciation and to have proposed a solution (see [4]). His paper is an outstanding one. At the heart of it is the evolution of the distribution of wealth. Two conditions must be ful…lled in order to become an entrepreneur: (i) entrepreneur position must yield an income greater than that of wage-earner (rentability condition) (ii) wealth must be such that a certain investment threshold may be reached thanks to some borrowing (indebtedness constraint). At a given instant, an agent's wealth depends on his/her wealth at the preceding instant (interperiodic transfer of wealth). The wage level is determined by the market for labour equilibrium and depends on the proportion of entrepreneurs (demand) and wage-earners (supply). The main result of the model is that two steady-states exist according to the level of the wage. For values less than a critical threshold, there exist two classes, entrepreneurs being the richer. For the critical value, all agents could be entrepreneurs since they ful…l rentability condition and indebtedness constraint. Not all will be actually entrepreneurs but it does not matter for Matsuyama since all have the same wealth whatever the position they have. Jean-François Jacques et Antoine Rebeyrol also propose a logical genesis of classes starting from a Solow model in which a fraction of people experience an evolution leading to a complete destruction of their capital (see [2]). Like for Matsuyama, a basic point is that inequality of wealth is the origin of the division in classes.

The thesis suggested in the present paper is di¤erent. That the richer become entrepreneurs and the poorer wage-earners is not the intuition at the root of the model. Even if such an intuition is sensible and in accordance with common sense, it does not help much in understanding the logic of an economy where production is due to wage-earners working for entrepreneurs. Our intuition would be inverse to Matsuyama's: it is because some individuals become entrepreneurs that they become richer and, symmetrically, because others become wage-earners that they are poorer. From a logical point of view (di¤erent fron an historical one), wealth inequality is a consequence of the di¤erenciation into classes not its cause. In the model below, there would be no sense in maintaining that equality of wealth precludes a division in classes.

Matsuyama's model is suited to the story told by Adam Smith. According to Smith, the di¤erence in the progressive accumulation of wealth (saving is a virtue) generates the division between entrepreneurs and wage-earners. Our model is suited to the story told by Schumpeter, a very di¤erent one. According to Schumpeter it is the ability to bene…t from money creation through bank credit which is the distinctive feature of entrepreneurs (they can …nance innovations thanks to credit): 'l'entrepreneur est dans l'économie nationale le seul débiteur typique' ( [5], p. 148). An exclusive access to new means of payment allows a would-be entrepreneur to modify the allocation of the present means of production (and the property rights), to realize an innovation and eventually pro…ts. Entrepreneur's position is provisional and is not guaranted by any level of wealth. The model presented below, although static, is more Schumpeterian than Smithian in that access to new means of payment is more important than the level of wealth. The purpose is not to analyse the distribution of wealth per se but to understand how an economy with entrepreneurs and wage-earners may come out of an economy where everybody has the same position at the start. It is more the heterogeneity of conditions than di¤erence of wealth which matters here.

The institutional setting of our economy is quite simple. Besides individuals having the same characteristics there is a bank issuing on demand non durable means of payment. Individuals resort to money only when they decide to engage into a specialized production. Three techniques of production are available to individuals corresponding to di¤erent social relations: autarky, specialized independent production and production with wage-earners. Here, the choice of a technique is at the same time a choice of a certain type of social relation of production.

The story told by the model goes in three stages. In the …rst one the bank posts the cost of the issuance of new means of payment and agents decide to go or not to go to the bank. In the second one, the bank decides to satisfy a certain proportion of individuals. Non-rationed individuals have a strategy set larger than that of rationed since they are able to engage into a specialized production. Two modes of existence only are eligible for the latter: autarky or being wage-earners. The former have two additional eligible strategies: becoming independent producers or becoming entrepreneurs (hiring rationed people giving them an indirect access to new means of payment). If rationed individuals choose to produce in autarky non-rationed agents have no choice but to be independent producers If rationed individuals choose to be wage-earners nonrationed agents may become entrepreneurs if that position is preferred to that of independent producer. What the model is about are the conditions under which exists an equilibrium with entrepreneurs and wage-earners (an E-equilibrium).

These reasonable conditions are: an e¢ cient monetary system, a su¢ cient gap between productivity of production in mass compared to other types and a possibility to induce wage-earners to work signi…cantly more than they would as free producers. These conditions being ful…lled, a partial rationing by the bank is a necessary and su¢ cient condition for the existence of a constrained E-equilibrium. A di¤ erenciation in the access to money is ever present in an economy with entrepreneurs and wage-earners; it may be a su¢ cient condition for the existence of an E-equilibrium depending on other parameters, namely the intensity of e¤ ort of wage-earners.

The model is presented in section 2. Section 3 is devoted to an endogeneization of the bank and to a discussion of the role of wealth in the model. A non-Marxian notion of exploitation is suggested to conclude.

The model

A distinctive feature of the model is that money is used at equilibrium (except in autarky). Money is essential (in the sense of Wallace) when production is specialized. The absence of a double coincidence of wants makes barter impraticable. Transactions cannot be realized but thanks to a generally accepted means of exchange called money. Since money is necessary as an intermediary of exchange (and not as store of value) parsimony in arguments commands that money be non-durable. Consequently, agents cannot engage in a specialized production if they do not get new means of payment from the bank. This reminds us that in a monetary economy there are not only purchases and sales; there is also a speci…c operation which cannot be reduced to a purchase or a sale: the issuance of money. In all monetary systems, issuance of money is the outcome of a confrontation between demands of individuals and reactions of a monetary authority. In a metallic system, individuals have to bring their precious metals to the Mint which accepts (or not) to transform them in legal coins. The Mint decides if the coinage is free and or costly and if melting coins is legal or not. The transformation of gold into coins is not a purchase or a sale. In the same way, in a credit sytem individuals ask to the bank to recognize that they have a certain amount of capital (a discounted sum of future reimbursement payments) by lending them that precise amount of money. Banks accept or refuse according to the characteristics of the individuals but also as a consequence of a monetary policy decided by a monetary authority.

Capital plays here the role gold plays in a metallic system. In both cases, money does not preexist to that operation which, consequently, cannot be interpreted as a purchase or a sale. Money disappears either by melting coins or by paying back the money to the bank.

Issuance of money is crucial in the model since the relative capacity of individuals to get new means of payment has important e¤ects. That capacity may be independent of wealth and, in any case, analytically distinct from it. It will be shown that deprivation of access to money for a minimal fraction of individuals may be a su¢ cient condition for the existence of a E-equilibrium; it is in any case a typical feature of such an equilibrium.

Assumptions and data

Let be an economy populated by a continuum of unit mass of identical individuals characterized by their specialization in production and consumption. Individuals are equally distributed between N types i = 1; :::; N such that ln i (q i ) > 0 and ln i (q j6 =i ) = 0 where ln( ) is the fonction of utility (chosen for the sake of simplicity). The N goods are identical except for the 'colour'. Individuals can produce either their consumption good (their 'colour') or, more e¢ ciently, specialize in the production of good i + 1. In the latter case, to overcome the absence of double coincidence of wants, they resort to money. They demand some money to the bank at a cost r. Money is non-durable (it must be paid back after the market) and is used for transactions only. The bank may decide to satisfy the demands of a fraction 1 s only of individuals. A fraction s is rationed.

Techniques of production

Three techniques of production exist but their utilization may be conditional upon an access to money.

All individuals can produce for themselves their consumption good with a technique q i = A(x i ) where x i is the e¤ort measured in terms of utility, q i the quantity of good, a parameter 0 < < 1 and A an index of e¢ ciency. Net utility is ln(q i ) x i = ln A + ln x i x i ; it varies with the e¤ort. Maximization of utility in autarky leads to an optimal e¤ort x aut = .

Autarky maximum utility function is thus:

U aut = ln A + ln (1)
All individuals, non-rationed by the bank, may produce the good in which they are more e¢ cient in production (not their consumption good). Money they get from the bank allows them to buy their consumption good and the sale of their production allows them to pay back the bank. A specialized individual of type i will produce good i + 1 with technique q i+1 = B(x i ) with B > A. Specialized production is more e¢ cient than autarky and than any other (q j6 =i;i+1 = B(x i ) = 0). Bank issues one unit of money for each individual choosing specialization plus r unit for itself (in view of purchasing a quantity of good i + 1 as real income). Let consider symmetrical positions only. Only a fraction of production of good i is consumed by the producer of good i + 1, the bank getting a fraction r 1+r . The independent producer gets a fraction 1 1+r of good i + 1. Sale of that fraction allows him/her to buy a fraction 1 1+r of good i. The net utility of a specialized producer, in a symmetrical position, is:

ln( Bx 1 + r ) x = ln B ln(1 + r) + ln x x
Maximization of net utility leads to an optimal e¤ort x ind = .

Maximum utility function for an independent specialized producer is:

U ind = ln B ln(1 + r) + ln (2)
When a fraction s of individuals of type i are rationed by the bank, non rationed individuals of type i may resort to a technique involving rationed individuals of type i. In such a case, the former are entrepreneurs, the latter wage-earners. Assume that entrepreneurs and wage-earners are of the same type in order to keep the idea of specialization. If = s 1 s is the dimension of an entrepreneur in terms of employment, the technique is q = K( x) , with x (the e¤ort of wage-earners is assumed to be greater than that of individuals working for their own account) and K B où K is an e¢ ciency parameter. If entrepreneurs demand one unit of money per wage-earner (wage-earners are a continuum of mass ), the bank gets a fraction r (1+r) = r 1+r of the production of each entrepreneur. What remains is shared between wage-earners and entrepreneur according to a proportion w (1+r) and (1 w) (1+r) respectively. Each wage-earner gets a fraction: w (1+r) . Wage-earners do not decide anything about production. Their e¤ort x is determined outside the model. The only relevant maximization is that of entrepreneurs. Consequently, w is determined by equality of marginal productivity of wage-earners K x 1 and real wage:

K x 1 = w (1 + r) Kx ! w = (1 + r) with r < r = 1 (3)
Using the value of w given by (3), it is possible to calculate the real income of an entrepreneur and of a wage-earner, that is ( 1 1+r

)K( x) and K [START_REF] Cartelier | Chômage involontaire d'équilibre et asymétrie entre salariés et non-salariés: la loi de Walras restreinte[END_REF] x respectively. Maximum utility functions, if transactions are e¤ectively realized, are thus: for an entrepreneur:

U ent = ln(( 1 1 + r )K x ) = ln( 1 1 + r ) + ln K + ln + ln x (4)
A higher and a lower r make an entrepreneur better o¤ [START_REF] Matsuyama | The Lawrence R. Klein Lecture: Emergent Class Structure[END_REF] .

for a wage-earner, taking the e¤ort x into account:

U w = ln( K (1 ) x ) x = ln + ln K (1 ) ln + ln x x (5)
A lower makes a wage-earner better o¤ [START_REF] Schumpeter | Théorie de l'évolution économique[END_REF] .

Transactions

If all individuals choose autarky no transactions, no problem. When specialized production is chosen, either by independent producers or by entrepreneurs hiring wage-earners, money is used as an exclusive intermediary. Purchases and sales are realized simultaneously (introducing costs of transaction other than r will complicate the story without any advantage). Each producer of type i (either entrepreneur or independent producer) spends the money he/she has got from the bank (one unit or units indirectly via wage-earners) toward a producer of type i 1 and pays interest (r or r) to the bank; this is possible if he/she sells a fraction of his/her production to the bank for r (or r) units of money and what is remaining to individuals of type i + 1. In the case of entrepreneurs and wage-earners, production is partly sold to wage-earners of type i + 1 and partly (say a fraction ) to entrepreneurs of type i + 1.

The schema below describes the transactions in that case [START_REF] Simon | A formal theory of the employment relationship[END_REF] . Dotted lines show how money enters and leaves circulation and full lines show purchases and sales.

As it clearly appears, transactions cannot all be realized but if there is a mutual compatibility between individual actions. Symmetry between di¤erent types (but not between individuals of each type) is the most obvious condition.

Individual stratégies and equilibria

At the end of the game an individual may be in one of these four positions: autarky, independent producer, entrepreneur or wage-earner. Three stages: [START_REF] Matsuyama | The Lawrence R. Klein Lecture: Emergent Class Structure[END_REF] Partial derivatives are: @ @ (ln( 1 1+r

) + ln K + ln + ln x) = > 0 and @ @r (ln( 1 1+r

) + ln K + ln + ln x) = 1 (1+r)(1 ( +r))
0 si 1 1+r which is the case for 0 < w < 1

5 Partial derivative is negative: @ @ (ln + ln K (1 ) ln + ln x x) = 1 ( 1) < 0 6 Through expenditures to entrepreneur i 1 wage-earners of type i get a quantity of good i 1 w 1+r K( x) = K( x) , which implies a price p = 1 Kx . Through expenditures to entrepreneur i 1, entrepreneur i gets a quantiity of good i 1 1 w 1+r K( x) = 1 (1+r) (1+r) K( x) . That quantity times price gives:

1 (1+r) (1+r) = ! = 1 (1+r) (1+r) .
1. the bank posts r, cost if issuance of one unit of money 2. money demanders learn if they are rationed 3. non-rationed individuals chose, given others'choices, their preferred position; rationed individuals chose either autarky or to be wage-earners.

At stage 1, two strategies only are possible: to go or not to go to the bank.

To go or not to ge to the bank

This …rst choice does not make sense unless independent producer or entrepreneur positions are preferred to autarky and wage-earner postions. To keep the story simple and without loss of generality, assume that to go to the bank does not engage individuals. In the case they would not or they could not use money they may pay it back to the bank without incurring cost r. As a consequence, 'to go to the bank'is a weakly dominant strategy and is always chosen by individuals.

To be or not to be rationed by the bank

Stage 2 opens by bank decision about rationing. Individuals learn whether they are or not rationed. In other terms they get (with a probability 1 1+ = 1 s) or they do not get the money they have demanded (with a probability 1+ = s).

Bank decision (considered provisionally as exogenous) splits individuals into two categories. Non-rationed individuals have a strategy set larger than rationed ones. The former can choose between four strategies: autarky, to be wage-earner (labour suppliers), to be independent producer or to be entrepreneur (labour demanders). The latter can choose only between autarky and to be wage-earner.

Autarky yield a net utility independent of the choice of other individuals. Autarky here is an outside option. Other positions yield a net utility which highly depends on the choice of other individuals. We are looking for equilibria positions only, that is situations in which any individual cannot improve each utility if no one changes his/her strategy. In such situations nobody has an interest to deviate.

Equilibria

As the transaction schema above makes it clear, equilibria requires that individuals of di¤erent types behave symmetrically. The production of a specialized producer (either independent or entrepreneur) of type i cannot be sold but if a same fraction of individuals of all types has chosen to be a specialized producer.

Consider …rst the choice : 'independent producer'. There is a continuum of situations such that a fraction (0 = i 8i 1) of individuals of all types are specialized, a fraction 1 being in autarky. These situations are all equilibrium situations. Let call them -equilibria. When = 0, it is a Aequilibrium (A for autarky): nobody chooses to be specialized (a variant is: the bank rations everybody: ! 1). All individuals are in autarky and nobody has an interest to deviate, i. e. to specialize, since he could not sell his/her production. When = 1, it is a I-equilibrium (I for independent producer): nobody is rationed by the bank ( = 0) and nobody prefers to be entrepreneur (U ind > U ent ; U ind > U w ; U ind > U aut ); all individuals are independent producers and the economy is in its true sense a 'market economy'. For positive and …nite values of , a fraction 1 1+ = of individuals of each type is specialized and a fraction 1+ prefer to produce in autarky. In all these situations nobody has an interest to deviate: to leave autarky or specialization generates a loss in utility: in the …rst case the good is not sold and an opportunity to produce his/her own consumption good is lost, in the second the advantage of specialization is lost.

But conditions U ind > U ent ; U ind > U w ; U ind > U aut may not be all ful-…lled. Equilibria other than -equilibira may exist. If U ind < U ent non-rationed individuals prefer to be entrepreneurs rather than independent producers. If, at the same time, rationed individuals prefer to be wage-earners rather than autarky producers (U w > U aut ) and, …nally, if entrepreneurs are better o¤ than wage-earners (U ent U w ) there is a room for E-equilibria, (E for entrepreneurs) that is for situations where entrepreneurs employ wage-earners to produce for their own account.

By contrast with A-and I-equilibria, an economy in E-equilibrium is made of two di¤erent classes of individuals. Entrepreneurs and wage-earners belong to two heterogeneous groups of people; there is a hierarchy between these groups, the strategy set of the latter being more restricted and included in the strategy set of the former. Wage-earners do not take the lead in the market since they are deprived from what is the condition for any initiative in production, money. They have no choice but to work for others in order to get some money. Not working for their own accounts they cannot even choose freely their e¤ort.

Let see the conditions for the existence of a E-equilibrium.

The existence of a E-equilibrium

Three conditions must be simultaneously ful…lled for an E-equilibirum to exist:

U w > U aut makes sure that rationed individuals participate in a entrepreneurial economy; using (1) and ( 5), it may be written as:

ln ln ln(( K A ) 1 1 ) + 1 ln x + x 1 (6)
U ent U ind , makes sure that non-rationed individuals do not become independent producers; using ( 4) and ( 2), it may be written as:

ln ln 1 ln( B K(1 (1 + r)) ) + ln x 1 (7)
U ent U w makes sure that non-rationed individuals not wishing to be independent producers do not prefer to become wage-earners; using (4) and ( 5), it may be written as:

ln ln ln (1 + r) 1 (1 + r) x (8)
.

Conditions ( 6) and ( 7) cannot be simultaneously ful…lled unless > , which requires in turn that:

ln + 1 ln K B + ln B A + 1 ln(1 (1 + r)) + 1 x + ln x x S > 0 (9)
and that . Recall that r is bounded above (r < r = 1 ) and that K is not. For r < r, A; B; x and given, it always exists values for K such that (9) is valid 7 . If bank rationing is su¢ ciently severe, namely if

, a E-equilibrium exists. That a high K is a condition for the existence of a E-equilibrium is not 7 Partial derivative @ @K (S) est positive ( @ @K (S) = 1 K > 0) and @ @r (S) < 0, is bounded since r r.

a surprise but that a su¢ cient deprivation of means of payment for a fraction of individuals may be also a condition is less trivial and, in any case, rarely mentioned. Schema below shows how, for given values of r, an higher value of K increases the set of values of for which an entrepreneurial economy is an equilibrium.

But this is not the end of the story. Condition (8) must be considered as well. It says that entrepreneur's utility has to be at least equal to that of wageearners. It depends only on the e¤ort of wage-earners and on the real wage (recall that w = (1 + r)). Condition (8) has a very important meaning. It leads to de…ne, if holds, two kinds of E-equilibrium:

1. A non-constrained E-equilibrium if < .
Such a E-equilibrium exists with a voluntary rationing. Bank rationing is not binding since some individuals ( ) voluntarily decide not to use the means of payment they get from the bank8 . Non-rationed individuals are indi¤erent between to be an entrepreneur or to be a wage-earner. Nobody has an interest to deviate: becoming a wage-earner, an entrepreneur would loose in utility ( increases) and, on the other hand, a (non-rationed) wage-earner could not become an entrepreneur since he would not …nd wage-earners to employ. In that case, bank rationing is not responsibe for the existence of an economy with heterogeneous groups of individuals, entrepreneurs and wage-earners.

A constrained E-equilibrium if

< . Bank rationing is more severe than that individuals would voluntarily decide ( > ). In that case, entrepreneurs have no interest to deviate, that is to become wageearners (U ent > U w ) and wage-earners have no possibiliy to change their position since they are constrained by the bank (see schema). a a a D

Non participation of wage-earners No incentive to become entrepreneur

Range of values for which an E-equilibrium exists (for r, A and B given)

/ /K ÝaÞ < 0 / /K ÝaÞ > 0
Active bank rationing a A crucial point for the main thesis of the present paper is to establish the condition under which, when (9) holds, only constrained E-equilibria exist and non-constrained E-equilibria do not. The condition is obviously < < . If that condition is satis…ed, entrepreneurs and wage-earners have the same utility but the situation is not an equilibrium: non-rationed individuals have interest to deviate and to become independent producers and, consequently, rationed individuals have no choice but to be in autarky. There does not exist non constrained E-equilibria. If < < holds, only constrained E-equilibria exist.

The e¤ort x wage-earners must supply (not chosen by them) is decisive for condition < to hold. Substituting in condition < the values of and derived from (8) and (7) respectively and de…ning x = with 1, allow to get :

T ln 1 1 ln K B ln (1 + r) 1 ln(1 (1 + r)) > 0 (10)
Here, a high relative e¢ ciency of entrepreneurial production K has a negative in ‡uence. A high K makes less likely condition (10) hold. For K B , and r given, it is the relative intensity of e¤ort of the wage-earners which matters. Partial derivative of T is @ @ (T ) = 1 with < 1 and 1. For low values of ( < 1 ), @ @ (T ) < 0; @ @ (T ) = 0 for = 1 and is positive for > 1 , which is the case considered here. Clearly an increase of is favourable to the existence of a constrained E-equilibrium. For given values of other parameters (techniques, preferences, etc.) and if bank rationing respects condition (9) 9 , a su¢ ciently high intensity of e¤ort of wage-earners (compared to that of an independent producer) ensures the existence of a constrained E-equilibrium.

To sum up, necessary and su¢ cient conditions for the existence of a constrained E-equilibrium are 10 :

8 > < > : r < r = 1 T ln 1 1 ln K B ln (1 + r) 1 ln(1 (1 + r)) > 0 9 > = > ;
(11) These formal conditions may be translated in plain language: (i) a minimal e¢ ciency of the process of issuance of money implying a cost not to high, (ii) a relatively high productivity of wage-earners compared to that of independent producer is responsible for a large range of posible values of , (iii) a rigorous discipline imposed to wage-earners (a high ) makes sure that entrepreneurs have a better position than wage-earners (moreover a low e¢ ciency of production in autarky deprives rationed individuals from the outside option of autarky). 9 Partial derivative: @ @r (T ) is positive ( @ @r (T ) =

Beyond the model

Beyond the conditions for the existence of a constrained E-equilibrum, two questions must be evoked: (i) should bank's behaviour be introduced into the model? (ii) Is a comparison between entrepreneur's and wage-earner's utility legitimate?

3.1 The bank and the closure of the model So far the bank has been treated as exogenous and its decisions have been considered like those of 'nature'.

It is certainly possible to be content with that. The bank would symbolize a more or less favourable environment for an entrepreneurial economy to emerge. A severe rationing would mean a great scarcity of means of payment as so many observed in the past. A high cost r could be interpreted as signalling a primitive and poorly e¢ cient monetary system.

But, economists do not like exogenous variables. They prefer a closed model to an open one. Moreover, they need to check the consistency of the model. The question is: would really a pro…t maximizing bank ration money such that a constrained E-equilibrium exists? Is there not a contradiction between bank's own interest and the values of r and associate to a constrained E-equilibrium?

The point is worth examining since the bank does not get the same amount of goods (or the same utility, which is equivalent if the bank is assumed to be indi¤erent to the "colour" of goods anf its utility function is increasing in goods) in an entrepreneurial economy and in a pure market economy. Assume that the bank desires to get the greater quantity of goods: what are the terms of arbitrage? Let compare the quantity of goods the bank gets in a I-equilibrium, r 1+r B , and in a E-equilibrium1 1+ r 1+r K x . Note that the rate of interest (if < r ) does not play any role.

If x = , the bank will favour an entrepreneurial economy if:

r 1 + r B 1 1 + r 1 + r K ! K B 1 +
In the general case, x = avec > 1, the condition is weaker:

K B 1 + (12)
If K B < 1+ , the bank wishes a market economy of independent producers; it posts a rate of interest r = B A 1 r and = 0. As for the rate of interest bank's advantage is at its best for the higher level of r compatible with a positive demand for new means of payment ( r 1+r increases with r). The condition K B 1+ holds for a certain range of . Whether this range partially overlaps the range for which exists a constrained E-equilibirum depends on the value of the parameters of e¢ ciency of the two techniques of production 11 .

A step further in the endogeneiztion of the bank consists in looking for its optimal behaviour (which is tantamount to assuming that the bank follows the same rationality as individuals, forgetting that it acts as a monetary authority). Assume the bank maximizes the quantity of goods it receives in an entrepreneurial economy, that is 1 1+ r 1+r K x . Bank's behaviour is given by a FOC

@ @ ( 1 1+ r 1+r K x ) = Krx 1 (1+ ) 2 (1+r) ( (1 + ) ) = 0 ! opt = 1
For all > 0 and r < r, the optimal bank rationing is opt = 1 12 .

Is a comparison between entrepreneurs and wage-earner' s utility legitimate?

We have taken for granted that condition (8) plays a central role in the existence of an entrepreneurial economy. That condition, U ent U w , states that at equilibrium entrepreneur's utility cannot be less than wage-earner's utility. That point deserves a little bit of a discussion.

In the model, heterogeneity between individuals concerns the strategy set: non-rationed individuals may choose strategies non-eligible to rationed individuals. The latter have no choice but submit themselves to non-rationed individuals or quit. How is it possible to express that heterogeneity using standard analytical tools?

We are put into a dilemma: to accept a comparison in terms of utility, as it is done in the model, is tantamount to acknowledging an homogeneity between entrepreneur and wage-earner, which is precisely contrary to the model's intuition; to refuse a comparison in terms of utility is equivalent to presuppose that heterogeneity and to renounce to endogeneize it, which is precisely what the model aims at.

Two false solutions must be discarded. The …rst would consist in giving a positive utility to the dimension of the strategy set. As a result entrepreneur's utility would be arbitrarily increased in order to legitimate a comparison in terms of utility. The second false solution would consist in considering that entrepreneur's position has an absolute advantage on wage-earner's position (lexicographic utility). This would be equivalent to presuppose an heterogeneity instead of making it emerge from the model.

There is no solution to our problem. But it is however useful to stress that the comparison between utilities is not symmetrical. It does not make sense for rationed individuals becoming wage-earners since they cannot become entrepreneurs. If an entrepreneur can switch for wage-earner's position, the inverse switch is not available to the wage-earner. Deprived from a direct access to the bank, a wage-earner must accept an inequality between both situations utility. Inequality of utilities (or of wealth) is a consequence of a di¤ erenciation between entreprenurs and wage-earners but not the cause. What matters is less the range of associate to a constrained E-equilibrium. Here, bank's interest is perfectly compatible with the existence of an entreprenurial economy. utility than status. This appears also in the fact that wage-earners do not determine their e¤ort and that the wage level is given by the pro…t maximization of entrepreneur's pro…t.

Conclusion

Some brief remarks to conclude.

1. An economy of independent producers (I-equilibrium) and an entrepreneurial economy (E-equilibrium) are both monetary economies in which relations between individuals are expressed by payments. That fact gives a misleading homogeneity between the two economies or between entrepreneurs and wage-earners. Relations between independent producers or between entrepreneurs are market relations ruled by the principle of equivalence. Relations between entrepreneurs and wage-earners are ruled by another logic, that of monetary submission. Equivalence does not play any role since wage-earners do not sell anything (they are wage-earners precisely because thay cannot produce for the market). Entrepreneurs not wage-earners are responsible for the production (recall that wage-earners do not choose their e¤ort). Consequently the sanction for a failure is not the same: an entrepreneur may go bankrupt, a wage-earner looses his/her employment.

2. Condition (8) compares entrepreneur and wage-earner's utility but one may think that the comparison is biased since there is no e¤ort from the entrepreneur. We have compared ln w K( x) 1+r

x for the wage-earner and ln(1 w) K( x) 1+r for the entrepreneur. An objection may be that an entrepreneur also supplies an e¤ort. Taking this into account would have the merit not to attribute from the start a rent to the entrepreneur. Consider then the entrepreneur's e¤ort and assume that its level is (the same e¤ort as an independent producer). A comparison between entrepreneurs and wage-earners on this new basis makes appear what may be called an exploitation of the latter by the former, in a sense di¤erent from Marx.

Let compare ln w K( x) 1+r for wage-earners, on the one hand, and ln(1

w) K( x)
1+r , for entrepreneurs, on the other. For w = 1 2 , entrepreneurs' position di¤er from wage-eaners' position by x = 1. An equal sharing of production does not generate an equality in position as it should be if wage-earners and entrepreneurs had an homogeneous status. The gap between the two positions in case of equal sharing of production reveals an exploitation due to the di¤erence between the amount (and the nature) of the e¤ort supplied. Here we do not compare paid and unpaid labour as Marx did but a free activity with an e¤ort realized as a consequence of a monetary submission. That exploitation does not depends on the wage but on the status. If a relative high e¢ ciency of the entrepreneurial production is a condition for the existence of a constrained E-equilibrium, another important condition is a high degree of exploitation.

3. At the outset, individuals are all alike and are free to choose their position. The di¤erence in their position vis-à-vis of the bank makes them di¤er in their strategy set. Once they become either entrepreneurs or wageearners they are really di¤erent. Entrepreneurs have all the prerogatives traditionally acknowledged in economic theory: they can maximize their advantage (utility or pro…t) taking into account the two legs of a budgetary constraint (resources and expenses). Wage-earners do not work for themselves. They maximize their advantage (utility) but under a di¤erent constraint: they control only one leg of the constraint not the e¤ort x and not the resource (w is the outcome of a pro…t maximization by entrepreneurs). It is precisely the argument Keynes invokes in General Theory to reject what he called 'the second classical postulate'(see [3], chapter 2). As wage-earners budgetary constraint is not of the same type as that of entrepreneurs, Walras Law (i. e. the sum of budgetary constraints over all individuals) applies in Keynes economics only in a restricted way. 'Restricted Walras Law'does not encompass the 'market for labour'(see [1]).

It is this very fact, and this very fact only, which gives sense to Keynes' main proposition, namely the existence of a general competitive equilibrium with involuntary unemployment.

  numerical example may illustrate what is said in the text. Take A = 3:4161 (ln A = 1:2285), B = 3:7577 (ln B = 1:3238) and K = 6: 685 9 (ln K = 1:9); assume = 0:8; it follows that r = 0:25; let r = 0:05 < r, the value of x such that it is indi¤erent to be entrepreneur or wage-earner is x = 2:0081 . Let x = 2:1. It is easy to derive: w = 0:8(1:05) = 0:84, = 1:1794 and = 6:447. A constrained E-equilibrium exists for all values of such that 1:1794 6:447.

1 2 1 = 4

 114 In our numerical example, a constrained E-equilibrium exists (and is unique) since opt = belongs to the 'good'range of values of .

For instance, Herbert Simon accounts for entrepreneur's authority over wage-earners by a distinction between a sale and an employment contract. But he does not explain why one of the agents B became 'boss' and the other W the 'worker' (see[START_REF] Simon | A formal theory of the employment relationship[END_REF]). He does not say whether the di¤erence between B and W makes them belong or not to a same category of agents either.

If 'to go to the bank' would have not been a weak dominant strategy, they would have chosen 'not to go to the bank'.

[START_REF] Cartelier | Chômage involontaire d'équilibre et asymétrie entre salariés et non-salariés: la loi de Walras restreinte[END_REF] In our numerical example, condition is 1 841:64. This interval encompasses